Imaginary dimensions in physics require an imaginary set of base Planck units and some negative parameter $c_n$ corresponding to the speed of light in vacuum $c$. The second, negative fine-structure constant $\alpha_2^{-1} \approx -140.178$ present in Fresnel coefficients for the normal incidence of electromagnetic radiation on monolayer graphene leads to the imaginary Planck units. Furthermore, it sets $c_n \approx -3.06 \times 10^8~\text{[m/s]}$. It follows that electric charges are the same in real and imaginary dimensions. Neutron stars and white dwarfs, objects emitting perfect black-body radiation, need energy exceeding their mass-energy equivalence ratios. Complex energies are defined in terms of real and imaginary Planck units. Their imaginary parts, inaccessible for direct observation, store the excess of these energies. It follows that black holes are fundamentally uncharged, charged micro neutron stars and white dwarfs with masses lower than $5.7275 \times 10^{-10}~[\text{kg}]$ are unphysical, and the radii of white dwarfs' cores are limited to $R_{\text{WD}} < 6.7933~G M_{\text{WD}}/c^2$. It is conjectured that the maximum atomic number $Z=238$. A black-body object is in the equilibrium of complex energies of masses, charges, and wavelengths if its radius $R_\text{eq} \approx 2.7665~G M_{\text{BBO}}/c^2$, which corrects the value of the photon sphere radius $R_{\text{ps}}=3G M/c^2$, taking into account the value(s) of the fine-structure constant(s), which is otherwise neglected in general relativity.

The identification of an action principle for directing basic system energy exchanges can be used in a general framework for the study of dynamics in systems. The application of such action principles using Lagrangian procedures has become a very powerful methodology for the analysis of complicated problems in modern physics. This form of analytics has recently been considered as the mapping of the system state information in the context of system constraints. The process of translating perceived information into adaptive responses is considered to be the driving action dynamic for the living system. Reconciliation processes that provide for a minimization of the divergence of this information signature from a state of system stability are preferred. Such a state is naturally that of maximal entropy in the context of the operational constraints of the open living system. A mathematical expression incorporating inferential information entropy processing into biologic replicator dynamics describes the mechanics of the perception-action adaptive processes of living systems. From this framework, Kullback’s Principle of Minimum Information Discrimination is identified as the innate axiomatic action principle for guiding the dynamics of biological systems.

In this study, we evaluate the nonlinear dynamics of convection flow using the thermodynamic variational principle, focusing on scenarios where multiple external forces, such as a thermal gradient and rotational field, are applied to a shallow annular pool. We observed that with the increase in the thermal gradient, the flow changed from an axial flow to a rotational oscillatory flow with the wave amplitudes aligned. Further increasing the temperature difference led to a rotational oscillatory flow characterized by alternating wave generation and annihilation. Our analysis of the flow, considering heat fluxes orthogonal to the thermal gradient, allowed us to describe the flow state as a phase at equilibrium. The state transition of the flow was accompanied by a discontinuous jump in the heat flux, which occurred at the intersection of the entropy production curves.

In this paper we discuss whether Einstein’s initial expectations before he developed the theory of general relativity were fulfilled and whether general relativity fully satisfied him in this respect. Einstein employed the equivalence principle as a guiding principle in the development of general relativity. We follow Einstein’s historical reasoning on the equivalence principle by adopting a dynamical approach to relativity and question the theory of general relativity he arrived at in terms of his initial expectations. The key issue here is related to the interpretation of gravitational and inertial “fields” in the equivalence principle. Einstein spoke of the identity of these two notions. This reveals that his intention was to unify gravitation and inertia. In fact, the issue is also related to the extent of generalisation provided by general relativity. Einstein demands a strong generalization in general relativity that requires the equality of all frames, including accelerating frames, in the same way that the relative character of velocity provides in special relativity. However, general relativity does not provide such a strong generalisation as expected from it. Furthermore, in general relativity, the gravitational field is reduced to inertia, but the two are not fully unified. We therefore argue that Einstein’s initial expectations of general relativity were not met and that the theory did not fully satisfy him. Nevertheless, we show that there is a satisfactory way out. On the basis of some heuristic arguments, we demonstrate that if gravitational and non-gravitational interactions are unified into a single elementary interaction at the most fundamental level in nature, then inertia and gravitation are fully unified and the strong generalisation being sought can be obtained. We speculate that Einstein was well aware of this fact and one of his motivations (perhaps the most important one) in his long search for a unified field theory was an attempt to fulfill his initial expectations about general relativity.

The arrest of Pavel Durov, the CEO of Telegram, represents a critical moment in the ongoing discourse surrounding free speech and content moderation. This event exemplifies the tension between upholding individual liberties and addressing the potential societal harms caused by unregulated digital communication. This paper explores the implications of Durov’s arrest and Telegram’s stance on free speech through the lens of John Stuart Mill’s Harm Principle. The Harm Principle, as articulated in Mill’s seminal work On Liberty (1859), provides a valuable theoretical framework for examining the balance between individual freedom and societal protection. This paper argues that the application of the Harm Principle can offer a nuanced perspective on the ethical responsibilities of digital platforms like Telegram in the age of global communication.

We proposed an equation of motion as a constraint condition on the gauge degree of freedom in general relativity theory based on a co-moving framework. This constraint equation transformed the gauge degree freedom of general relativity theory into an natural equation of motion, and provide an explicit theoretical understanding on the Mach's principle and rotating bucket experiment. The galaxy rotation curves is derived directly from general relativity theory under this constraints equation. This work may inspires different understanding on dark matter, dark energy, and the quantization of gravity.

This article develops duality principles applicable to originally non-convex primal variational formulations. More specifically, as a first application, we establish a convex dual approximate variational formulation for a non-linear Kirchhoff-Love plate model. The results are obtained through basic tools of functional analysis, calculus of variations, duality and optimization theory in infinite dimensional spaces. We emphasize such a convex dual approximate formulation obtained may be applied to a large class of similar models in the calculus of variations. Finally, in the last section, we present a duality principle and respective convex dual formulation for a Ginzburg-Landau type equation.

Discovered as an apparent pattern, a universal relation between geometry and information called the holographic principle has yet to be explained. This relation is unfolded in the present paper. As it is demonstrated there, the origin of the holographic principle lies in the fact that a geometry of physical space has only a finite number of points. Furthermore, it is shown that the puzzlement of the holographic principle can be explained by a magnification of grid cells used to discretize geometrical magnitudes such as areas and volumes into sets of points. To wit, when grid cells of the Planck scale are projected from the surface of the observable universe into its interior, they become enlarged. For that reason, the space inside the observable universe is described by the set of points whose cardinality is equal to the number of points that constitute the universe’s surface.

Optimal control is a critical tool for mechanical robotic systems, facilitating precise manipulation of dynamic processes. These processes are described through differential equations governed by a control function, addressing a time-optimal problem with bilinear characteristics. Our study utilizes the classical approach complemented by Pontryagin's Maximum Principle (PMP) to explore this inverse optimal problem. The objective is to develop an exact piecewise control function that effectively manages trajectory control while considering the effects of viscous friction. Our simulations demonstrate that the proposed control law markedly diminishes oscillations induced by boundary conditions. This research not only aims to delineate the reachability set but also strives to determine the minimal time required for the process. The findings include an exact analytical solution for the stated control problem.

Gedanken experiments illustrating exemplifications of the Landauer principle in the free falling Einstein elevator are treated. Double-well simplest information system embedded into the free falling elevator is addressed. Infinitesimal horizontal force applied to the particle m transfers it from position “0” to position “1”, emerging from the free falling double-well system confining mass m. When thermal noise is considered, the potential barrier of kBT should be surmounted for the erasing of one bit of information. Entropic forces arising in the free falling elevator are considered. The maximal change in the entropy of free-joint polymer chain attached to the free falling elevator is estimated as ΔSmax≅kB, and it is remarkably independent of the mass attached to the chain and the parameters of the chain itself. Free falling minimal Szilard engine is treated. The informational re-interpretation of the minimal Szilard process is shaped as follows: the energy kBTln2 necessary for erasing of 1 bit of information is spent for lifting up mass, whatever, is the value of this mass. Appropriate choice of frames enables elimination of gravity in the considered system; however elimination of the thermal noise (dissipation processes) by the same procedure is impossible.

System-of-systems (SoS) evolution is a complex and unpredictable process. Although various principles to facilitate collaborative SoS evolution have been proposed, there is a lack of experimental data validating their effectiveness. To address these issues, we present an Agent-Based Model (ABM) for SoS evolution in the Internet of Vehicles (IoV) , serving as a quantitative analysis tool for SoS research. By integrating multiple complex and rational behaviors of individuals, we aim to simulate real-world scenarios as accurately as possible. To simulate the SoS evolution process, our model employs multiple agents with autonomous interactions and incorporates external environmental variables. Furthermore, we propose three evaluation metrics: evolutionary time, degree of variation, and evolutionary cost, to assess the performance of SoS evolution. Our study demonstrates that enhanced information transparency significantly improves the evolutionary performance of distributed SoS. Conversely, the adoption of uniform standards only brings limited performance enhancement to distributed SoSs. Although our proposed model has limitations, it stands out from other approaches that utilize Agent-Based Modeling to analyze SoS theories. Our model focuses on realistic problem contexts and simulates realistic interaction behaviors. This study enhances the comprehension of SoS evolution processes and provides valuable insights for the formulation of effective evolutionary strategies.

Motivated from Deutsch entropic uncertainty principle and several product uncertainty principles, we derive an uncertainty principle for the product of entropies using functions.

The II law of thermodynamics is most often given in three supposedly equivalent formulations: two Clausius (I and II) and one Kelvin. The most general and indisputable entropy formulation belong to Clausius (II). The earlier Clausius I principle determines the natural direction heat flow between bodies at different temperatures. On the other hand, the Kelvin principle states that it is impossible to completely convert heat into work. The author argues that the Kelvin principle is a weaker statement (or more strictly non-equivalent) than Clausius I principle, and the latter is a weaker statement than Carnot principle, which is equivalent to Clausius II principle. As a result, the Kelvin principle and the Clausius I principle are not exhaustive formulations of the II law of thermodynamics. At the same time, it turns out that the Carnot principle becomes such a formulation. Apart from providing a complete set of proof and disproof, the author, indicates where the methodological errors were made in the alleged proof of the equivalence of the Kelvin principle and both Clausius principles.

Identifying locations of landslide slip surfaces provides critical information for understanding the volume of landslides and the scale of disasters, which is essential for formulating disaster preparedness and mitigation strategies. Based on hydrogeological survey data from 24 deep-seated landslide-prone sites in Taiwan's mountainous regions, this study first developed the hydraulic conductivity potential index (HCPI) using principal component analysis to quantify hydraulic properties of disturbed rock formation with six geological factors. Then, The regression analysis was performed to construct a permeability estimation model for the geological environment of landslides. Finally, the established model was utilized to develop an identification method for potential slip depths in landslide-prone sites. Results indicated a strong relation between HCPI and hydraulic conductivity with a determination coefficient of 0.895. The relation equation confirmed that its generated data concerning the depths of significant changes in hydraulic conductivity could be used to identify potential slip surfaces. Additionally, this study successfully establishes a rule for identifying potential slip zones by summarizing data concerning the generated hydraulic conductivity profiles, stratigraphic lithology, existing inclinometer slip depth records, and groundwater level of landslide sites. This identification method was then applied to predict potential slip depths for ten landslide sites where slip surfaces have not yet occurred. These findings offer a new alternative to having early information on potential sliding depths for timely disaster management and control implementation.

The interaction of matter when separated by a distance is a fundamental question, whether such interactions occur through instantaneous action at a distance or retarded interaction (principle of locality)? While the mainstream consensus favors the principle of locality, instantaneous action at a distance offers certain advantages. Previously, instantaneous action at a distance has been viewed as an appearance or representation from specific gauge choices of electromagnetic potentials (retarded). In this paper, we propose a novel approach that combines Weber’s electrodynamics with the concept of vacuum polarization to explore a new possible connection between the two viewpoints: instantaneous action at a distance and the locality principle. This new approach aligns with the observation of locality in signal/energy propagation while retaining the notion of instantaneous action at a distance.

We consider a constrained optimal control problem and an extension of it, in which the set of strict-sense trajectories is enlarged. Extension is a common procedure in optimal control, used to derive necessary and sufficient optimality conditions for the original problem from the extended one, which usually admits a minimizer and has a more regular structure. However, this procedure fails if the two problems have different infima. It is therefore relevant to identify such situations. Following on from earlier work by Warga but adopting perturbation techniques developed in non-smooth analysis, we investigate the relation between the occurrence of an infimum gap and abnormality of necessary conditions. For a notion of local minimizer based on control distance and an extension including the impulsive one, we prove that (i) a local extended minimizer which is not a local minimizer of the original problem and (ii) a local strict-sense minimizer which is not a local minimizer of the extended problem, both satisfy the extended maximum principle in abnormal form. The main novelty is result (ii), as until now it had only been shown that a strict-sense minimizer which is not an extended minimizer is abnormal for an `averaged version’ of the maximum principle.

Molecular-scale density fluctuations at equilibrium produce cavities in a liquid and can be analyzed to shed light on the statistics of the number of molecules occupying observation volumes of increasing radius. An information theory approach led to the conclusion that these probabilities should follow a Gaussian distribution function. This prediction has been confirmed by computer simulations in different liquid models if the size of the observation volume is not large. The reversible work of cavity creation is exactly linked to the probability of finding zero molecules in a given observation volume. The Gaussian formula for the latter probability is scrutinized to arrive at the enthalpy and entropy changes associated with cavity creation. The reversible work of cavity creation has a purely entropic origin due to the solvent-excluded volume effect produced by the inaccessibility of a given region of the configurational space. The consequent structural reorganization of liquid molecules leads to exactly compensating enthalpy and entropy changes. These results are in line with those obtained in a direct statistical mechanical study by Lee.

Coulomb’s law and Newton’s law of gravitation are formally identical. Is it a mere coincidence? It seems to us that physics has answered yes so far, at least tacitly. We, on the other hand, do not believe in chance. Since the alternative to the fact that the strong similarity is only the result of chance is to believe that it is not, and in this case there must be a reason for this similarity, we have chosen the path of investigating the possibility that the two fields are not distinct, but have a common root that we will try to find. We propose an electrodynamics of electrically neutral bodies based on the hypothesis that the Coulomb constant in the case of attraction between charges of opposite sign is slightly greater than that of the case of repulsion between charges of the same magnitude as the previous ones, but of the same sign. If this difference were to exist, even small to the point of not being directly measurable in the laboratory, it could still produce macroscopic effects detectable in the case of large aggregates of charges, even if globally electrically neutral, as happens in the astronomical field. We deduce the electromagnetism of such a model and show the results obtained applying the theory to some significant cases such the light deflection in a gravitational field, a planet perihelion precession, the power radiated by merging black holes, the behaviour of antimatter in a gravitational field and, when available, we compare the predictions with the experimental data.

In this work, we try to find a way to describe the physical law of micro-world under the frame of a space-time theory. By introducing the scalar fields $\mathcal{D}\left( x\right)$ and $\zeta\left( x\right) $, we rewrite the action of conventional field theory and the Lagrangian describing the motion of the particle, where a modified space-time relation is obtained. To test the correctness of this attempt, we demonstrate the Klein-Gordon equation by the Hamilton-Jacobi method in four dimensional form and present a time delay for the ground state of hydrogen atom.

Let X be a 3-product space. Let A : D(A) ⊆ X → X , B : D(B) ⊆ X → X and C : D(C) ⊆ X → X be possibly unbounded 3-self-adjoint operators. Then for all x ∈ D(ABC) ∩ D(ACB) ∩ D(BAC) ∩ D(BCA) ∩ D(CAB) ∩ D(CBA) with ⟨x, x, x⟩ = 1, we show that (1) ∆x(3, A)∆x(3, B)∆x(3, C) ≥ |⟨(ABC − aBC − bAC − cAB)x, x, x⟩ + 2abc|, where ∆x(3, A) := ∥Ax − ⟨Ax, x, x⟩x∥, a := ⟨Ax, x, x⟩, b := ⟨Bx, x, x⟩, c := ⟨Cx, x, x⟩. We call Inequality (1) as 3-Heisenberg-Robertson-Schrodinger uncertainty principle. Classical HeisenbergRobertson-Schrodinger uncertainty principle (by Schrodinger in 1930) considers two operators whereas Inequality (1) considers three operators.

Four decades of snooker rankings are analyzed in terms of prize money distributions. In particular, it is investigated how much these rankings are dominated by the top players, and also by players from the UK. The main conclusions are: (1) with an increasing amount of available prize money, the rankings are less dominated by the top players, and (2) players from the UK have historically earned a significantly larger share of the available prize money than could be reasonably expected based on the actual percentage of UK players.

A non-relativistic theory of inertia based on Mach's principle is presented as has been envisaged but not achieved by Ernst Mach in 1872. Central feature is a space-dependent, anisotropic, symmetric inert mass tensor. The contribution of a mass element $dm$ to the inertia of a particle $m_0$ experiencing an acceleration from rest is proportional to $\cos^2\alpha$, where $\alpha$ is the angle between the line connecting $m_0$ and $dm$ and the direction of the acceleration. Apsidal precession for planets circling around a central star is not a consequence of this theory, thereby avoiding the prediction of an apsidal precession with wrong sign as is done by Mach-like theories with isotropic inert mass.

A theoretical account of development in mesocortical anatomy is derived from the free energy principle, operating in a neural field with both Hebbian and anti-Hebbian neural plasticity. An elementary structural unit is proposed, in which synaptic connections at mesoscale are arranged in paired patterns with mirror symmetry. Exchanges of synaptic flux in each pattern form coupled spatial eigenmodes, and the line of mirror reflection between the paired patterns operates as a Markov blanket, so that prediction errors in exchanges between the pairs are minimized. The theoretical analysis is then compared to the outcomes from a biological model of cortical neurodevelopment, in which neuron precursors are selected by apoptosis for cell body and synaptic connections maximizing synchrony and also minimizing axonal length. It is shown that this model results in patterns of connection with the anticipated mirror symmetries, at micro-, meso- and inter-arial scales, among lateral connections, and in cortical depth, explaining the spatial organization and functional significance of neuron response preferences, and compatible with features of both columnar and noncolumnar cortex. Multi-way interactions of mirrored representations provide a preliminary anatomically realistic model of cortical information processing.

The present paper discusses an elliptic equation with Steklov boundary conditions and $(p(x),q(x))$-Laplacian. Using mountain pass theorem together with Ekeland's variational principle, we prove, under appropriate conditions on the functions involved, that the problem admits at least two solutions.

The informational re-interpretation of the basic laws of the mechanics exploiting the Landauer principle is suggested. When a physical body is in rest or it moves rectilinearly with the constant speed, zero information is transferred; thus, the informational affinity of the rest state and the rectilinear motion with a constant speed is established. The analysis of the minimal Szilard thermal engine as seen from the non-inertial frame of references is carried out. The Szilard single-particle minimal thermal engine undergoes the isobaric expansion relatively to the accelerated frame of references, enabling the erasure of 1 bit of information. The energy ΔQ spent by the inertial force for the erasure of 1 bit of information is estimated as: ΔQ≅5/3 k_B T ̅, which is larger than the Landauer bound but qualitatively close to it. The informational interpretation of the equivalence principle is proposed: the informational content of the inertial and gravitational masses is the same.

The paper is concerned with the concept of elementary observations (EO). EOs are experimental answers to the question whether a matter-instrument interaction had taken place at the micro-scale of quantum phenomena. Focusing on the specific case of photon detection, we show that during their lifetimes EOs proceed through the four phases of initiation, detection, erasure and reset. Once generated, the observational value of EOs can be measured in units of the Planck quantum of physical action h=4.136×10^(-15) eVs. Once terminated, each unit of entropy of size k_B=8.617×10^(-5) eV⁄K, which had been created in the instrument during the observational phase, needs to be removed from the instrument to ready it for a new round of photon detection. This withdrawal of entropy takes place at an energetic cost of at least two units of the Landauer minimum energy bound of E_La=ln⁡〖(2) k_B T_D 〗 for each unit of entropy of size k_B.

This paper derives measurement and identical principles, then makes the two principles into measurement and identical theorems of quantum mechanics, plus the three theorems derived earlier, we deduce the axiom system of current quantum mechanics, the general quantum theory no axiom presumptions not only solves the crisis to understand in current quantum mechanics, but also obtains new discoveries, e.g., discovers the velocities of quantum collapse and entanglement are instantaneously infinitely large. We deduce the general Schrȍdinger equation of any n particles from two aspects, and the wave function not only has particle properties of the complex square root state vector of the classical probability density of any n particles, but also has the plane wave properties of any n particles. Thus, the current crisis of the dispute about the origin of wave- particle duality of any n microscopic particles is solved. We display the classical locality and quantum non-locality for any n particle system, show entanglement origins, and discover not only any n-particle wave function system has the original, superposition and across entanglements, but also the entanglements are of interactions preserving conservation or correlation, three kinds of entanglements directly give lots of entanglement sources. This paper discovers, one of two pillars of modern physics, quantum mechanics of any n particle system is a generalization ( mechanics ) theory of the complex square root ( of real density function ) of classical statistical mechanics, any n particle system’s quantum mechanics of being just a generalization theory of the complex square root of classical statistical mechanics is both a revolutionary discovery and key new physics, which are influencing people’s philosophical thinking for modern physics, solve all the crisises in current quantum theories, quantum information and so on, and make quantum theory have scientific solid foundations checked, no basic axiom presumption and no all quantum strange incomprehensible properties, because classical statistical mechanics and its complex square root have scientific solid foundations checked. Thus, all current studies on various entanglements and their uses to quantum computer, quantum information and so on must be further updated and classified by the new entanglements. This and our early papers derive quantum physics, solve all crisises of basses of quantum mechanics, e.g., wave-particle duality & the first quantization origins, quantum nonlocality, entanglement origins & classifications, wave collapse and so on.Key words: quantum mechanics, operator, basic presumptions, wave-particle duality, principle of measurement, identical principle, superposition principle of states, entanglement origin, quantum communication, wave collapse, classical statistical mechanics, classical mechanics

Assuming the Multiple Point Principle (MPP) as a new law of Nature, we considered the existence of the two degenerate vacua of the Universe: a) the first Electroweak (EW) vacuum at $v_1\approx 246$ GeV—“true vacuum”, and b) the second Planck scale “false vacuum” at $v_2 \sim 10^{18}$ GeV. In these vacua, we investigated different topological defects. The main aim of the paper is an investigation of the black-hole-hedgehogs configurations as defects of the false vacuum. In the framework of the $f(R)$ gravity, described by the Gravi-Weak unification model, we considered a black-hole solution, which corresponds to a “hedgehog”—global monopole, that has been “swallowed” by the black-hole with mass core $M_{BH}\sim 10^{18}$ GeV and radius $\delta\sim 10^{-21}$ GeV$^{-1}$. Considering the results of the hedgehog lattice theory in the framework of the $SU(2)$ Yang-Mills gauge-invariant theory with hedgehogs in the Wilson loops, we have used the critical value of temperature for the hedgehogs’ confinement phase ($T_c\sim 10^{18}$ GeV). This result gave us the possibility to conclude that the SM shows a new physics (with contributions of the $SU(2)$-triplet Higgs bosons) at the scale $\sim 10$ TeV. This theory predicts the stability of the EW-vacuum and the accuracy of the MPP.

This paper presents Double Database Decomposition Framework, which integrates vertical and horizontal table decompositions to minimize data leakage due to intrusions. Vertical decompositions segregate sensitive attributes, while horizontal ones partition data based on user access patterns. In this way, the framework ensures that users access only the data necessary for their operations, adhering to the principle of least privilege. This double decomposition approach improves the robustness of the original database against impersonation attacks and limits the blast radius of potential intrusions. Furthermore, the framework significantly mitigates the risks associated with data breaches by confining unauthorized access to specific data subsets and restricting the exposure of sensitive information. Performance analysis highlights the trade-offs between robustness and overhead offered by distinct allocation strategies of the output of the decompositions to, among other, physical machines, virtual machines, and containers, to balance security and resource efficiency. We present a case study in a healthcare environment that confirms both the effectiveness of the framework and its applicability in complex systems where data security is paramount. By integrating advanced security measures and optimising data access, the framework results in a scalable and adaptable solution for enhancing database security and performance in various domains.

Machine learning has gained significant recognition within healthcare organizations as a potent technology for medical image analytics. Among various medical image modalities, Contrast-Enhanced CT (CECT) is widely utilized to acquire additional diagnostic information that can help to better visualize and evaluate certain structures or abnormalities in the human body. Accordingly, there is an increasing demand for machine learning systems for disease analytics using CECT. However, developing such systems presents two significant challenges: high technical complexity and high development effort. This paper presents a software platform that can effectively remedy these challenges. This platform embodies a unified software process for CECT-specific disease diagnosis including oncological diseases, cardiovascular diseases, and gastrointestinal diseases. It integrates multiple types of machine learning models into the disease diagnosis process, where the models can diagnose lesions, malignancies, tumors, medical features of tumors, temporal transitions with a contrast agent, and disease progress. The platform has been implemented in Python using Scikit-learn and TensorFlow libraries. To validate its applicability and reusability, a Hepatocellular Carcinoma (HCC) diagnosis system has been implemented.

Similarly to his special theory of relativity, Einstein's special principle of relativity extends beyond the limits currently known to it. Up to now, the principle has not been suspected to have the potential to translate laws. However, the principle holds an inherent capacity to translate physical laws and, in so doing, speeds up our understanding and control of physical reality. Such a translation of laws leads to the faster discovery of other laws, such as the Laws of Electronic Motion, characterizing the motion of electrons around the atomic nucleus, and the Third Law of Biological Resistance, facilitating the successful control of drug resistance in medicine. The ability of the special principle of relativity to translate laws shines forth once the said principle is duly interpreted. This interpretation exposes a parallelism between experimental frames of reference and justifies the applicability of the laws of one frame of reference in other parallel frames of reference. This process opens the door to our faster discovery of the laws governing a multiplicity of frames parallel to a frame we already know the laws of. In practice, the interpretation of Einstein's special principle of relativity speeds up our understanding of the workings of physical reality and strengthens our capacity to subdue matter.

One open question remains regarding the theory of the generalized variational principle, that is, why the stress-strain relation still be derived from the generalized variational principle while the Lagrangian multiplier method is applied in vain? This study shows that the generalized variational principle can only be understood and implemented correctly within the framework of thermodynamics. As long as the functional has one of the combination $A(\epsilon_{ij})-\sigma_{ij}\epsilon_{ij}$ or $B(\sigma_{ij})-\sigma_{ij}\epsilon_{ij}$, its corresponding variational principle will produce the stress-strain relation without the need to introduce extra constraints by the Lagrangian multiplier method. It is proved herein that the Hu-Washizu functional $\Pi_{HW}[u_i,\epsilon_{ij},\sigma_{ij}]$ and Hu-Washizu variational principle comprise a real three-field functional.

This brief note is aimed to dissociate from quantum physics contextuality, where the latter is standardly defined on the basis of families of compatible observables. In quantum physics, contextuality is just an exhibition of incompatibility of observables and, hence, Bohr's principle of complementarity. At the same time we recognize that contextuality can play the important role outside of physics.

Let $(\{f_n\}_{n=1}^\infty, \{\tau_n\}_{n=1}^\infty)$ and $(\{g_n\}_{n=1}^\infty, \{\omega_n\}_{n=1}^\infty)$ be unbounded continuous p-Schauder frames ($0<p<1$) for a disc Banach space $\mathcal{X}$. Then for every $x \in ( \mathcal{D}(\theta_f) \cap\mathcal{D}(\theta_g))\setminus\{0\}$, we show that \begin{align}\label{UB} \|\theta_f x\|_0\|\theta_g x\|_0 \geq \frac{1}{\left(\displaystyle\sup_{n,m \in \mathbb{N} }|f_n(\omega_m)|\right)^p\left(\displaystyle\sup_{n, m \in \mathbb{N}}|g_m(\tau_n)|\right)^p}, \end{align} where \begin{align*} & \theta_f: \mathcal{D}(\theta_f) \ni x \mapsto \theta_fx \coloneqq \{f_n(x)\}_{n=1}^\infty\in \ell^p(\mathbb{N}), \quad \theta_g: \mathcal{D}(\theta_g) \ni x \mapsto \theta_gx \coloneqq \{g_n(x)\}_{n=1}^\infty\in \ell^p(\mathbb{N}). \end{align*} Inequality (1) is unexpectedly different from both bounded uncertainty principle \textit{[arXiv:2308.00312v1]} and unbounded uncertainty principle \textit{[arXiv:2312.00366v1]} for Banach spaces.

Let $(\Omega, \mu)$, $(\Delta, \nu)$ be measure spaces. Let $(\{f_\alpha\}_{\alpha\in \Omega}, \{\tau_\alpha\}_{\alpha\in \Omega})$ and $(\{g_\beta\}_{\beta\in \Delta}, \{\omega_\beta\}_{\beta\in \Delta})$ be unbounded continuous 1-Schauder frames for a Banach space $\mathcal{X}$. Then for every $x \in ( \mathcal{D}(\theta_f) \cap\mathcal{D}(\theta_g))\setminus\{0\}$, we show that \begin{align}\label{UB} \mu(\operatorname{supp}(\theta_f x))\nu(\operatorname{supp}(\theta_g x)) \geq \frac{1}{\left(\displaystyle\sup_{\alpha \in \Omega, \beta \in \Delta}|f_\alpha(\omega_\beta)|\right)\left(\displaystyle\sup_{\alpha \in \Omega , \beta \in \Delta}|g_\beta(\tau_\alpha)|\right)}. \end{align} where \begin{align*} &\theta_f:\mathcal{D}(\theta_f) \ni x \mapsto \theta_fx \in \mathcal{L}^1(\Omega, \mu); \quad \theta_fx: \Omega \ni \alpha \mapsto (\theta_fx) (\alpha):= f_\alpha (x) \in \mathbb{K},\\ &\theta_g: \mathcal{D}(\theta_g) \ni x \mapsto \theta_gx \in \mathcal{L}^1(\Delta, \nu); \quad \theta_gx: \Delta \ni \beta \mapsto (\theta_gx) (\beta):= g_\beta (x) \in \mathbb{K}. \end{align*} We call Inequality (\ref{UB}) as \textbf{Unbounded Donoho-Stark-Elad-Bruckstein-Ricaud-Torr\'{e}sani Uncertainty Principle}. Along with recent \textbf{Functional Continuous Uncertainty Principle} (derived in [arXiv:2308.00312v1 [math.FA], 1 August 2023]), Inequality (\ref{UB}) also improves Ricaud-Torr\'{e}sani uncertainty principle \textit{[IEEE Trans. Inform. Theory, 2013]}. In particular, it improves Elad-Bruckstein uncertainty principle \textit{[IEEE Trans. Inform. Theory, 2002]} and Donoho-Stark uncertainty principle \textit{[SIAM J. Appl. Math., 1989]}.

Entropy is usually understood as the quantitative measure of “chaos” or “disorder”. However, the notions of “chaos” and “disorder” are definitely obscure. This leads to numerous misinterpretations of entropy. We propose to see the disorder as an absence of symmetry and to identify “ordering” with symmetrizing of a physical system; in other words, introducing the elements of symmetry into initially disordered physical system. We demonstrate with the binary system of elementary magnets that introducing elements of symmetry necessarily diminishes its entropy. This is true for 1D and 2D systems of elementary magnets. Imposing symmetry does not influence the Landauer Principle valid for the addressed systems. Imposing the symmetry restrictions onto the system built of particles contained within the chamber divided by the permeable partition also diminishes its entropy.

The Landauer principle supplies the estimation of the minimal mass of a particle which is capable to record/erase information within a thermal bath at the temperature of T. Particles lighter than ${\tilde{m}}_0=\frac{k_{B}Tln2}{c^2}$will not transform the information to the surrounding bodies and are well expected to be undetectable. The relation of the Landauer principle to the problem of “dark matter” is discussed. The maximal informational content of a particle at rest, estimated as $I_{max}=\frac{m_0{c}^2}{k_{B}Tkn2}$ is introduced. The Landauer principle also allows the estimation of minimal energy of the field which is capable to record/erase 1 bit of information in the surrounding at the temperature of T. The relativistic aspects of the Landauer principle and its relation to the relativistic transformation of temperature are addressed.

The mutual information between the state of a neural network and the state of the external world represents the amount of information stored in the neural network that is associated with the external world. In contrast, the surprise of the sensory input indicates the unpredictability of the current input. In other words, this is a measure of inference ability, and an upper bound of the surprise is known as the variational free energy. According to the free-energy principle (FEP), a neural network continuously minimizes the free energy to perceive the external world. For the survival of animals, inference ability is considered to be more important than simply memorized information. In this study, the free energy is shown to represent the gap between the amount of information stored in the neural network and that available for inference. This concept involves both the FEP and the infomax principle, and will be a useful measure for quantifying the amount of information available for inference.

The physical roots, interpretation, controversies and precise meaning of the Landauer Principle are surveyed. Landauer's principle is a physical principle pertaining to the lower theoretical limit of energy consumption of computation. It states that an irreversible change in information stored in a computer, such as merging two computational paths, dissipates a minimum amount of heat kBTln2 per a bit of information to its surrounding. The Landauer Principle is discussed in the context of fundamental physical limiting principles, such as the Abbe diffraction limit, the Margolus-Levitin limit and the Bekenstein limit. Synthesis of the Landauer bound with the Abbe, Margolus-Levitin limit and Bekenstein limits yields the minimal time of computation, which scales as τmin~hkBT. Decrease in a temperature of a thermal bath will decrease the energy consumption of a single computation, but, in parallel, it will slow the computation. The Landauer principle bridges between John Archibald Wheeler “it from bit” paradigm and thermodynamics. Experimental verifications of the Landauer Principle are surveyed. Interrelation between thermodynamic and logical irreversibility is addressed. Generalization of the Landauer principle to the quantum and non-equilibrium systems is addressed. Landauer Principle represents the powerful heuristic principle bridging the physics, information theory and computer engineering.

A new model of gravity is presented here similar to the earlier work of Verlinde on Emergent Gravity but without the use of thermodynamic assumptions. The theory does not use the main assumption of Verlinde on the nature of gravity as an entropic force using the First Law of Thermodynamics. Moreover, it does not use the Equipartition Theorem such that there is no need to define a thermal bath enclosed within a holographic screen. Instead of Equipartition Theorem, the theory uses $E=NE_{p}$, for the total energy of a massive object where $E_{p}$ is the Planck Energy while $N$ is the number of Planck Energy to represent the maximum possible density of information that can reside in matter. The theory uses also the Holographic Principle as the basis for an information-theoretic approach to the nature of gravity. It is shown here that gravity emerges whenever there is an updating of the information within a given volume of space by the presence of matter.

With reference to Planck scale Hubble parameter, super luminal expansion speeds, super luminal rotation speeds, Mach’s principle and Holographic principle, we review the current cosmological observations with eight simple assumptions. By understanding Yuri N. Obukhov and V.A. Korotky proposed cosmic rotational effects of polarization of radiation due to massive bodies, to some extent cosmic rotation can be deep-rooted in an observational approach and the ratio of current angular velocity and Hubble parameter can be estimated. It is possible to show that, at H₀ =70 km/sec/Mpc, current cosmic temperature, age, radius, mass, mass density are 2.721 K, 4.41x10¹⁷ sec, 90 billion light years, 1.14654x10⁵⁴ kg, 0.0482 times the current critical density respectively. Clearly speaking, current universe seems to constitute 267 Hubble spheres. Important point to be noted is that, current rotational kinetic energy is 0.6667 times the current critical energy. Based on the estimated current mass density and current rotational kinetic energy, current cosmic dark matter density can be shown to be 0.2851 times the current critical density. These numerical coincidences cast serious doubt on the on the real existence of currently believed ‘dark energy’. Initial and current expansion speeds are 3x10⁸ m/sec and 3.56x10⁹ m/sec respectively. With increasing cosmic age and increasing cosmic expansion speed, current universe is expanding with a speed of 11.885c. By knowing the time to time future cosmic temperatures, future Hubble parameters and corresponding future cosmic expansion speeds can be estimated and thus future expansion speed can be understood. Starting from ‘speed of light’, our model assumes a continuous increase in expansion speed and attains a current radius of 90 billion light years (without inflationary concepts) and casts a serious doubt on the actuality of currently believed ‘inflation’.

Active inference under the Free Energy Principle has been proposed as an across-scales compatible framework for understanding and modelling behaviour and self-maintenance. Crucially, a collective of active inference agents can, if they maintain a group-level Markov Blanket, constitute a larger group-level active inference agent with a generative model of its own. This potential for computational, scale-free structures speaks to the application of active inference to self-organizing systems across spatiotemporal scales, from cells to human collectives. Due to the difficulty of reconstructing the generative model — that explains the behaviour — of emergent group-level agents, there has been little research on this kind of multi-scale active inference. Here, we propose a data-driven methodology for characterising the relation between the generative model of a group-level agent and the dynamics of its constituent individual agents. We apply methods from computational cognitive modelling and computational psychiatry, applicable for active inference as well as other types of modelling approaches. Using a simple multi-armed bandit task as an example, we employ the new ActiveInference.jl library for Julia to simulate a collective of agents who are equipped with a Markov blanket. We use sampling-based parameter estimation to make inferences about the generative model of the group-level agent and we show that there is a non-trivial relationship between the generative models of individual agents and the group-level agent they constitute, even in this simple setting. Finally, we point to a number of ways in which this methodology might be applied to better understand the relations between nested active inference agents across scales.

We consider that the relationship between entropy in statistical mechanics, which is the Boltzmann principle, and the complex velocity potential in complex fluid dynamics. We define the generalized complex entropy which expanded entropy from real space to complex space. We show that the complex entropy can be expressed by the composition of sources, sinks and laminar flows of the complex velocity potential. Therefore, the complex entropy is considered a special case of the complex fluid dynamics,that is, the complex velocity potential. In other words, we show that the complex entropy is expressed by the complex velocity potential. Moreover, we show that a complex number is expressed by the complex entropy. Thus, we show that the complex velocity potential is expressed by the complex entropy. Namely, we will expand entropy to complex space and see that the complex entropy is expressed by the complex velocity potential. Furthermore, we examine the possibility that it is an expansion of Boltzmann's principle and Planck distribution.

On 17 October 1947, Niels Bohr was made a knight of the Order of the Elephant by the King of Denmark in view of his outstanding achievements and contributions to science. Bohr designed his own coat of arms that featured a pattern of Yin and Yang (Tai Chi symbol) to symbolize the wave-particle complementarity. However, Bohr’s Yin-Yang diagram (YYD) was neither drawn based on the principles of quantum mechanics, nor did it originate from the traditional Taoist YYD. Scientists still have doubts about the legitimacy of using YYD as the icon of the wave-particle complementarity, because the YYD belonging to quantum mechanics itself is unknown so far. This article reports the YYDs existing in quantum mechanics and justifies the role of YYD in the wave-particle duality by showing that any system, whether classical or quantum, has an ideal YYD as long as it satisfies Bohr’s principle of complementarity (BPC). The deviation of a deformed YYD from the ideal YYD indicates the extent to which a real system satisfies BPC. This article constructs the quantum YYD by the complex quantum trajectory of a particle tunneling via a step barrier, which displays the continuous transition between the wave behavior and the particle behavior. It appears that the YYD designed by Bohr in his coat of arms resembles the YYD generated by tunneling motion, not only in appearance but also in the governing equation.

: Solar sails use radiation from the sun to generate thrust without any fuel or propellant. Since this is a form of propulsion that has theoretically infinite use, we would like to test its capability on long-term missions by simulating a spacecraft equipped with solar sails to the Sun-Earth L5 Lagrange point. To control the sail angle, which is the main form of control we have over the sail’s performance, we will devise a form of optimal control based on Pontryagin’s Minimum Principle. Simulating the dynamics in MATLAB SIMULINK, we find that such a control method relies on iterating over initial conditions for the co-states to find the necessary parameters for the trajectory to reach the desired point. Therefore, an autonomous control scheme that uses this form of optimal control will need a way to numerically find said initial conditions in order to find the control angle needed at any point in time, which may be computationally intensive.

We derive an uncertainty principle for Lipschitz maps acting on subsets of Banach spaces. We show that this nonlinear uncertainty principle reduces to the Heisenberg-Robertson-Schrodinger uncertainty principle for linear operators acting on Hilbert spaces.

Let $(\Omega, \mu)$, $(\Delta, \nu)$ be measure spaces. Let $(\{f_\alpha\}_{\alpha\in \Omega}, \{\tau_\alpha\}_{\alpha\in \Omega})$ and $(\{g_\beta\}_{\beta\in \Delta}, \{\omega_\beta\}_{\beta\in \Delta})$ be continuous 1-Schauder frames for a Banach space $\mathcal{X}$. Then for every $x \in \mathcal{X}\setminus\{0\}$, we show that \begin{align*} \mu(\operatorname{supp}(\theta_f x)) \geq \frac{1}{\displaystyle\sup_{\alpha \in \Omega, \beta \in \Delta}|f_\alpha(\omega_\beta)|}, \quad \nu(\operatorname{supp}(\theta_g x))\geq \frac{1}{\displaystyle\sup_{\alpha \in \Omega , \beta \in \Delta}|g_\beta(\tau_\alpha)|}. \end{align*} where \begin{align*} &\theta_f: \mathcal{X} \ni x \mapsto \theta_fx \in \mathcal{L}^1(\Omega, \mu); \quad \theta_fx: \Omega \ni \alpha \mapsto (\theta_fx) (\alpha):= f_\alpha (x) \in \mathbb{K},\\ &\theta_g: \mathcal{X} \ni x \mapsto \theta_gx \in \mathcal{L}^1(\Delta, \nu); \quad \theta_gx: \Delta \ni \beta \mapsto (\theta_gx) (\beta):= g_\beta (x) \in \mathbb{K}. \end{align*} This solves a problem asked by K. M. Krishna in the paper 'Functional Continuous Uncertainty Principle' \textit{[arXiv:2308.00312v1]}.

Let $(\Omega, \mu)$, $(\Delta, \nu)$ be measure spaces. Let $(\{f_\alpha\}_{\alpha\in \Omega}, \{\tau_\alpha\}_{\alpha\in \Omega})$ and $(\{g_\beta\}_{\beta\in \Delta}, \{\omega_\beta\}_{\beta\in \Delta})$ be continuous p-Schauder frames for a Banach space $\mathcal{X}$. Then for every $x \in \mathcal{X}\setminus\{0\}$, we show that \begin{align}\label{CUE} \mu(\operatorname{supp}(\theta_f x))^\frac{1}{p} \nu(\operatorname{supp}(\theta_g x))^\frac{1}{q} \geq \frac{1}{\displaystyle\sup_{\alpha \in \Omega, \beta \in \Delta}|f_\alpha(\omega_\beta)|}, \quad \nu(\operatorname{supp}(\theta_g x))^\frac{1}{p} \mu(\operatorname{supp}(\theta_f x))^\frac{1}{q}\geq \frac{1}{\displaystyle\sup_{\alpha \in \Omega , \beta \in \Delta}|g_\beta(\tau_\alpha)|}. \end{align} where \begin{align*} &\theta_f: \mathcal{X} \ni x \mapsto \theta_fx \in \mathcal{L}^p(\Omega, \mu); \quad \theta_fx: \Omega \ni \alpha \mapsto (\theta_fx) (\alpha):= f_\alpha (x) \in \mathbb{K},\\ &\theta_g: \mathcal{X} \ni x \mapsto \theta_gx \in \mathcal{L}^p(\Delta, \nu); \quad \theta_gx: \Delta \ni \beta \mapsto (\theta_gx) (\beta):= g_\beta (x) \in \mathbb{K} \end{align*} and $q$ is the conjugate index of $p$. We call Inequality (\ref{CUE}) as \textbf{Functional Continuous Uncertainty Principle}. It improves the Functional Donoho-Stark-Elad-Bruckstein-Ricaud-Torr\'{e}sani Uncertainty Principle obtained by M. Krishna in \textit{[arXiv:2304.03324v1, 2023]}. It also answers a question asked by Prof. Philip B. Stark to the author.

This brief work tenets that inflationary genesis can be obtained within the standard model based on only a few general assumptions. These are that the origin began at a singularity of Planck length and that all quantum transitions take place within Planck time units. From these, the subsequent effects from the Pauli Exclusion Principle (PEP) and the uncertainty principle can then give rise to an inflationary origin.

We define life as the amplification of quantum uncertainty up to macroscopic scales. A living being is any amplifier that achieves this goal. We argue that everything we know about life can be explained from this idea. We study a ladder mechanism to estimate the probability that the amplification occurs spontaneously in nature. The amplification mechanism is so sensitive to small variations of its own parameters that it acts as a bifurcation itself, i.e. it implies that the universe is either everywhere dead or alive wherever possible. Since the first option is excluded by the existence of life on earth, we infer that the universe hosts a huge number of inhabited planets (possibly one per star on average). We also investigate models of conscious and unconscious learning processes, as well as the structure of the brain and evolution. Finally, we address the problem of creating artificial life.

In computational neuroscience, spiking neurons are often analyzed as computing devices that register bits of information, with each action potential carrying at most one bit of Shannon entropy. Here, I question this interpretation by using Landauer's principle to estimate an upper limit for the quantity of thermodynamic information that can be dissipated by a single action potential in a typical mammalian neuron. I show that an action potential in a typical mammalian cortical pyramidal cell can carry up to approximately 3.4e11 natural units of thermodynamic information, or about 4.9e11 bits of Shannon entropy. This result suggests that an action potential can process much more information than a single bit of Shannon entropy.

We prove a quasi-pseudometric version of the strong Ekeland principle proved by P. Georgiev and T. Suzuki.

Sphalerite has been recognized as the most important carrier of critical metal of Indium (In) due to that In mainly exists in the sphalerite lattice by isomorphic substitution. There are two significant replacing schemes for In entry into sphalerite, these are, Ag++In3+→2Zn2+ and Cu++In3+→2Zn2+. In order to understand the reaction process and constraints of the two substitution schemes, this paper uses first-principles methods to calculate In and Ag, Cu replacing Zn in sphalerite. According to the substitution schemes of Ag++In3+→2Zn2+ and Cu++In3+→2Zn2+, two doped sphalerite systems of Zn30InAgS32 and Zn30InCuS32 were constructed using 2×2×2 supercell model of sphalerite. Firstly, the pressure is controlled to 30MPa, and the temperature is set from 20-40MPa to simulate the response of the two doped sphalerite systems to temperature; Then, the control temperature was unchanged to 600K, and the pressure was set from 20-40MPa to investigate the pressure control of the two doped sphalerite systems. The lattice parameters, substitution energy, electronic structure, and population analysis of the designed models before and after replacement have been critically compared. The main conclusions can be drawn that it is more stable for In to enter sphalerite via the coupled substitution scheme Cu++In3+→2Zn2+, and the conditions that the two substitution schemes most likely to occur are 650K and 40MPa. This study not only reveals the physical and chemical properties of In-rich sphalerite formed by the two reaction processes of Ag++In3+→2Zn2+ and Cu++In3+→2Zn2+, but also has a certain enlightenment effect on the search for indium in sphalerite, and promotes the application of first principles in mineralization analysis.

Explaining the emergence of behavior and understanding on the basis of neuronal mechanisms is still elusive. One renowned proposal is the Free Energy Principle (FEP), which uses an information-theoretic framework derived from thermodynamic considerations to describe how behavior and understanding would emerge. FEP starts from a whole organism approach, based on mental states and phenomena, mapping them into the neuronal substrate. An alternative approach, the Energy Homeostasis Principle (EHP), initiates a similar explanatory effort, but starting from single neuron phenomena and building up to the whole organism’s behavior and understanding. In this work, we develop the EHP as an alternative but complementary vision to FEP and try to explain how behavior and understanding would emerge from the local requirements of the neurons. Based on EHP and a strict naturalist approach that sees living beings as physical and deterministic systems, we explain scenarios where learning would emerge without the need for volition or goals. Given these starting points, we state several considerations of how we see the nervous system, particularly the role of function, purpose, and the conception of goal-oriented behaviors. We problematize these conceptions, giving an alternative teleology-free framework in which behavior and, ultimately, understanding would still emerge. We reinterpret neural processing explaining basic learning situations up to simple anticipatory behavior. Finally, we end the work with an evolutionary perspective of how this non-goal-oriented behavior appears. We acknowledge that in the current form of our proposal, we are still far from explaining the emergence of understanding. Still, we set the ground for an alternative neuron-based framework to ultimately explain understanding.

Models with age as a variable but actual dynamics invariant under age structure allow use of MaxEnt to predict uniform age structure. Interpretations include a major role for accepting randomness as a causal principle in ecology (in the face of ignorance, in a further interpretative stance).

According to Landauer’s principle, the energy of a particle may be used to record or erase N number of information bits within the thermal bath. The maximum number of information N recorded by the particle in the heat bath is found to be inversely proportional to its temperature T. If at least one bit of information is transferred from the particle to the medium, then the particle might exchange information with the medium. Therefore for at least one bit of information, the limiting mass that can carry or transform information assuming a temperature T= 2.73 K is equal to m = 4.71810-40 kg which is many orders of magnitude smaller that the masse of most of today’s elementary particles. Next, using the corresponding temperature of a graviton relic and assuming at least one bit of information the corresponding graviton mass is calculated and from that, a relation for the number of information N carried by a graviton as a function of the graviton mass mgr is derived. Furthermore, the range of information number contained in a graviton is also calculated for the given range of graviton mass as given by Nieto and Goldhaber, from which we find that the range of the graviton is inversely proportional to the information number N. Finally, treating the gravitons as harmonic oscillators in an enclosure of size R we derive the range of a graviton as a function of the cosmological parameters in the present era

We consider the conjecture of the relationship between the entanglement entropy of spacetime, matter and the action in Einstein's general relativity. Our analysis suggests the possibility of regarding the entanglement entropy of spacetime and matter as the dimensionless action in general relativity by using Planck units. In this case, the action principle originates from the maximization of the entanglement entropy. We also show that the fundamental property of entanglement entropy leads to attractive characteristic of gravitational force for classical particles.

Software testing is an integral yet time-consuming component of software development, and even with capable software testing resources (technology and people), it is still regarded as problematic. Test automation is widely being utilised within the software industry to provide increased testing capacity to ensure high product quality and reliability. In this paper, we are specifically addressing automated testing whereby test cases are manually written. Test automation has its benefits, drawbacks, and impacts on different stages of development. Furthermore, there is often a disconnect between non-technical and technical roles, where non-technical roles (e.g., management) predominantly strive to reduce costs and delivery time whereas technical roles are often driven by quality and completeness. Although it is widely understood that there are challenges with adopting and using automated testing, there is a lack of evidence to understand the different attitudes toward automated testing (AtAT), focusing specifically on why it is not adopted. In this paper, the authors have surveyed practitioners within the software industry from different roles to determine common trends and draw conclusions. A two-stage approach is presented, comprising a comprehensive descriptive analysis and the use of Principle Component Analysis. In total, 81 participants were provided with a series of 22 questions and their responses are compared against job role types and experience levels. In summary, 6 key findings are presented covering expertise, time, cost, tools and techniques, utilisation, organisation, and capacity

Analytical mechanics is the most basic discipline. The basic principles of analytical mechanics should also be applicable to general deformed objects. However, the virtual displacement principle proposed by analytical mechanics is only applicable to particle systems and rigid body systems, but not to general deformed objects. In this paper, the generalized virtual displacement principle of general deformed objects (such as, elastic objects, plastic objects, elasto-platic objects and flexible objects etc ) is derived by the method of analytical mechanics, which is also applicable to particle systems and rigid body systems. First of all, according to the method of analytical mechanics, the external force, internal force, constraint reaction force and elastic recovery force of the deformed object system under the equilibrium state are analyzed, and the concepts of virtual displacement, ideal constraint and virtual work are introduced, and the generalized virtual displacement principle (also called generalized virtual work principle) of deformed objects is proposed; secondly, vector form, coordinate component form and generalized coordinate form of generalized virtual displacement principle of deformed object are given; thirdly, as the application of the principle, the virtual displacement principle of deformed objects in plane polar coordinate system, space cylindrical coordinate system and spherical coordinate system is given; finally, a brief conclusion is drawn. This work unifies the virtual displacement principle of elastic object, plastic, elastoplastic etc deformed object systems and rigid object systems with the basic method of analytical mechanics. It is a basic principle for dealing with the static problems of deformed objects. This work also lays a foundation for the further study of the dynamics of deformed object systems.

Science evolves over a gentle arc spanning centuries, with scientists building upon and extending the hypotheses and discoveries of their forebears when nurturing their own work from ideation to crystallization and finally implementation. However, evidence suggests several limitations of our modern academic pursuits including major inertia and epistemological biases to implement even major advancements. For instance, the transformative uncertainty principles of quantum mechanics are yet to be satisfactorily integrated in modern analyses and publications, even almost a century after Heisenberg received the Nobel prize for these. Another example is ever expanding reliance on mathematics to validate the hypotheses of Physics, and undermine the opinions to the contrary. In addition, modern science limits itself to the era post fifteenth century and hastily rejects premodern achievements despite glaring examples. This reluctance and inertia to capitalize on existing knowledge is a challenge that imperils our intellectual pursuits. A salient facet of science is "the willingness to admit ignorance". Only on this foundational principle can science meaningfully evolve. It is time we take a step back to evaluate widely accepted and foundational premises of modern science and institute structured processes to implement the treasure trove of knowledge amassed by our predecessors. This essay highlights some of the opportunities that can and should be availed capitalizing upon the recent developments of computational and analytical capabilities along with artificial intelligence.

We prove a version of Ekeland Variational Principle (EkVP) in a weighted graph $G$ and its equivalence to Caristi fixed point theorem and to Takahashi minimization principle. The usual completeness and topological notions are replaced with some weaker versions expressed in terms of the graph $G$. The main tool used in the proof is the OSC property for sequences in a graph. Converse results, meaning the completeness of graphs for which one of these principles holds is also considered.

Abstract Background. There is an inherent limit in the accuracy of our measurements, set by nature itself and predicted by Heisenberg's uncertainty principle, which defines the properties of nature in the microcosmos. There is a fundamental limit to the accuracy with which complementary phys-ical quantities of a particle can be predicted from their initial conditions. As classical physics is essentially considered at borderline of quantum mechanics, so the power of uncertainty princi-ple is limited in describing everyday life perceived or managed phenomena. Method. In this study, we apply Heisenberg's uncertainty principle to children under diagnostic uncertainty re-garding appendicitis. We analyze this phenomenon in clinical practice. Results. Medical practice is full of uncertainty. False negative decisions correlate with delays in treatment and adverse outcomes in children with atypical appendicitis. On the other hand, false-positive surgery deci-sions result in negative appendectomies. With improvement of technology, the incidence of complicated appendicitis or negative appendectomies due to diagnostic uncertainty has de-creased but cannot be ignored or eliminated. Conclusion. According to the principle, there is a fundamental limit to the accuracy with which the complementary variables of negative appen-dectomy and complicated appendicitis can be observed or measured simultaneously. What does all this mean for the physician?

The free energy principle states that self-organization occurs through minimization of free energy, which is a measure of potential thermodynamic work. By minimizing free energy, the organism happens to also minimize surprise over its boundary, promoting chances of survival. We discuss the ethical implications of the cognitive goal in detail from an empirical point of view, highlighting the principle of least action as a physical basis of Occam's razor, the universality of the free energy principle, and its explanation of natural selection. We explain that the free energy principle extends to groups of organisms and helps us understand group-scale adaptations and selection in biology. The free energy principle applies to all scales of organization in the organism from single cells to the entire nervous system. When this principle is taken to its logical extremes of modeling groups, populations and ecosystems, we uncover a new, evolutionarily sensible path at explaining puzzling aspects of human motivation and judgement, including ethical decisions. To minimize free energy, populations have to act to maximize gathering of information, while building effective models at mitigating changes to its dynamic structure. The free energy principle thus provides a naturalistic explanation of some of our deepest ethical intuitions, and valuable principles of social behavior. We interpret the cognitive goal that corresponds to the principle as seeking a dynamic, fruitful, yet peaceful activity that sustains the organism. This state of mind is interestingly similar to the Buddhist intuition of mental equanimity; the organism's final goal is to be at peace and harmony with the environment. Another immediately relevant aspect is that assemblies must form to promote symbiotic, synergistic, positive feedback loops, which coincides with the findings of ecologists. Therefore, ethics naturally emerges in self-organizing systems. Assemblies of organisms must ultimately unite in macro-minds to achieve the greatest reduction in free energy, as well as building technological extensions of themselves to improve their capacity to do such, therefore the principle also predicts a post-singularity world-mind composed mostly of artificial intelligence.

The entangled antipodal points on black hole surfaces, recently described by t’Hooft, display an unnoticed relationship with the Borsuk-Ulam theorem. Taking into account this observation and other recent claims, suggesting that quantum entanglement takes place on the antipodal points of a S³ hypersphere, a novel framework can be developed, based on algebraic topological issues: a feature encompassed in an S² unentangled state gives rise, when projected one dimension higher, to two entangled particles. This allows us to achieve a mathematical description of the holographic principle occurring in S². Furthermore, our observations let us to hypothesize that a) quantum entanglement might occur in a four-dimensional spacetime, while disentanglement might be achieved on a motionless, three-dimensional manifold; b) a negative mass might exist on the surface of a black hole.

Einstein was skeptical of part of quantum mechanics, and he believed that Heisenberg’s uncertainty principle did not reflected the full depth of reality. He famously stated, ”God does not play dice with the universe.” However, since quantum mechanics has passed so many experimental tests, most physicists today assume that Einstein was wrong. Nevertheless, we will demonstrate that Heisenberg’s uncertainty principle must be modified to unify gravity with quantum mechanics. This modification leads to the Certainty-Uncertainty principle where the certainty part is strongly linked to gravity. This means Einstein likely was right in his intuition also on this point. The key is to understand that the de Broglie wavelength is not the actual wavelength of matter but merely a derivative of the true matter wavelength, namely the Compton wavelength. Furthermore, one must understand that the gravitational constant, first introduced in 1873, is simply a composite constant needed to rectify the incomplete definition of kilogram mass introduced into Newtonian gravity in 1873.

The physics of Hubble's law, motivated by the anomalous acceleration of Pioneer 10/11, suggests that the Hubble constant corresponds to a gravitational field of the Universe. The Hubble constant inferred from Pioneer 10/11 data is $\sim 69$ km/s/Mpc. The anomalous acceleration of Pioneer 10/11 can be interpreted as an observational evidence for Mach's principle. The redshift is an apparent value. Its intrinsic value has a limit resulting to $v

This paper reports applying Minimax principle and impulsive differential inequality to derive the existence of multiple stationary solutions and the global stability of a positive stationary solution for a delayed feedback Gilpin-Ayala competition model with impulsive disturbance. The conclusion obtained in this paper reduces the conservatism of the algorithm compared with the known literature, for the impulsive disturbance is not limited to impulsive control.

Let $\{\tau_n\}_{n=1}^\infty$ and $\{\omega_m\}_{m=1}^\infty$ be two modular Parseval frames for a Hilbert C*-module $\mathcal{E}$. Then for every $x \in \mathcal{E}\setminus\{0\}$, we show that \begin{align}\label{UE} \|\theta_\tau x \|_0 \|\theta_\omega x \|_0 \geq \frac{1}{\sup_{n, m \in \mathbb{N}} \|\langle \tau_n, \omega_m\rangle \|^2}. \end{align} We call Inequality (\ref{UE}) as \textbf{Noncommutative Donoho-Stark-Elad-Bruckstein-Ricaud-Torr\'{e}sani Uncertainty Principle}. Inequality (\ref{UE}) is the noncommutative analogue of breakthrough Ricaud-Torr\'{e}sani uncertainty principle \textit{[IEEE Trans. Inform. Theory, 2013]}. In particular, Inequality (\ref{UE}) extends Elad-Bruckstein uncertainty principle \textit{[IEEE Trans. Inform. Theory, 2002]} and Donoho-Stark uncertainty principle \textit{[SIAM J. Appl. Math., 1989]}.

Let $\mathcal{X}$ be a Banach space. Let $\{\tau_j\}_{j=1}^n, \{\omega_k\}_{k=1}^m\subseteq \mathcal{X}$ and $\{f_j\}_{j=1}^n$, $\{g_k\}_{k=1}^m\subseteq \mathcal{X}^*$ satisfy $ |f_j(\tau_j)|\geq 1$ for all $ 1\leq j \leq n$, $|g_k(\omega_k)|\geq 1 $ for all $1\leq k \leq m$. If $x \in \mathcal{X}\setminus \{0\}$ is such that $x=\theta_\tau\theta_f x=\theta_\omega\theta_g x$, then we show that \begin{align}\label{FKDB} \|\theta_fx\|_0\|\theta_gx\|_0\geq \frac{\bigg[1-(\|\theta_fx\|_0-1)\max\limits_{1\leq j,r \leq n,j\neq r}|f_j(\tau_r)|\bigg]^+\bigg[1-(\|\theta_g x\|_0-1)\max\limits_{1\leq k,s \leq m,k\neq s}|g_k(\omega_s)|\bigg]^+}{\left(\displaystyle\max_{1\leq j \leq n, 1\leq k \leq m}|f_j(\omega_k)|\right)\left(\displaystyle\max_{1\leq j \leq n, 1\leq k \leq m}|g_k(\tau_j)|\right)}. \end{align} We call Inequality (\ref{FKDB}) as \textbf{Functional Kuppinger-Durisi-B\"{o}lcskei Uncertainty Principle}. Inequality (\ref{FKDB}) improves the uncertainty principle obtained by Kuppinger, Durisi and B\"{o}lcskei \textit{[IEEE Trans. Inform. Theory (2012)]} (which improved the Donoho-Stark-Elad-Bruckstein uncertainty principle \textit{[SIAM J. Appl. Math. (1989), IEEE Trans. Inform. Theory (2002)]}). We also derive functional form of the uncertainity principle obtained by Studer, Kuppinger, Pope and B\"{o}lcskei \textit{[EEE Trans. Inform. Theory, (2012)]}.

Hidden collapse refers to the existence of environmental indicators indicative of future collapse of forests, even though the forest appears intact and not at risk of ecosystem collapse. Professor David Lindenmayer and Dr Chloe Sato (Lindenmayer) first identified hidden collapse in 2018 in Mountain Ash forests of Victoria, Australia. The risk of hidden collapse represents a long term environmental threat and is a potential trigger for application of the precautionary principle (principle). Implicit in hidden collapse are two preconditions for application of the principle; the risk of a serious or irreversible environmental threat, and the existence of scientific uncertainty about the nature of the risk. Despite hidden collapse satisfying these essential preconditions for applying the principle, decision makers did not apply it in respect hidden collapse of Mountain Ash forests in Victoria. This article considers the current status of the principle in regulation and how it can be adjusted to address long term environmental risk. There is growing evidence around the world of serious decline in biodiversity requiring urgent application of precautionary risk management. A better regulatory regime for precautionary management of long term risk is now an urgent priority.

This paper presents one of the approaches to solution of the problem of the repulsion origin in gravity. The approach is based on the property of compactness characteristic for a self-gravitating object in General Relativity. Here we understand compactness as estimation of the upper boundary for mass such an object in a static two--dimensional sphere. Repulsion originates when this boundary is violated. The main hypothesis is formulated in the form of the principle of maximal mass within a two-dimensional static sphere. It is demonstrated that the principle is true for Schwarzschild black holes on absorption of the matter in the process of accretion, both in the classical case and with due regard for quantum-gravitational corrections. The results have been extended to black holes with the Schwarzschild-de Sitter metric in the early Universe. The applicability of the principle suggested is analyzed for the early and for the present Universe.

The Vogel-Fulcher-Tammann equation is exposed as a particular example of the mean field theory. It is generalized by taking into account an arbitrary critical exponent of susceptibility, discriminating between different classes of universality. The Bell-Evans-Polanyi principle is employed to estimate the difference between the activation energies of flows in crystals and glasses, which appears to coincide with the excess Gibbs energy of the glass compared to the crystal.

In this study, we evaluated and compared several major carbon sequestration methods based on the first principles, namely, energy use efficiency and elemental stoichiometry. This study suggested that, at present, wood burial is the only feasible carbon sequestration method because it can be implemented immediately on a large scale, is cost-effective and efficient, has a long sequestration time, has low technical requirements, and has a relatively low impact on agriculture.

The Landauer principle asserts that “the information is physical”. In its strict meaning Landauer's principle states that there is a minimum possible amount of energy required to erase one bit of information, known as the Landauer bound W=kBTln2 where T is the temperature of a thermal reservoir used in the process and kB is Boltzmann’s constant. Modern computers use the binary system in which a number expressed in the base-2 numeral system. We demonstrate that the Landauer principle remains valid for the physical computing device based on the ternary and more generally N-based logic. The energy necessary for erasure of one bit of information (the Landauer bound) W=kBTln2 remains untouched for the computing devices exploiting a many-valued logic.

Through a brief analysis of the basic principle of relativity, it is found that there is a contradiction in principle between general relativity and special relativity in solving the specific problem of the clock moving around the earth, and one of them must be wrong. Through comparative analysis of five physical phenomena and experiments, it is proved that there are serious problems in the space concept of relativity theory and classical physic. At the same time, the different concept of absolute airspace is further expounded and demonstrated, and the related space-time physical phenomena and experiments are perfectly explained by this concept. According to this idea, a new time transformation relation is deduced and its correctness is demonstrated. It is proved that the principle of special relativity and special relativity are wrong, and a series of physical laws and physical explanations generated by special relativity may also be wrong, and a series of amendments or new interpretations need to be made.

Cardiovascular disease is the number one cause of death in the world and Quoting from WHO, around 31% of deaths in the world are caused by cardiovascular diseases and more than 75% of deaths occur in developing countries. The results of patients with cardiovascular disease produce many medical records that can be used for further patient management. This study aims to develop a method of data mining by grouping patients with cardiovascular disease to determine the level of patient complications in the two clusters. The method applied is principal component analysis (PCA) which aims to reduce the dimensions of the large data available and the techniques of data mining in the form of cluster analysis which implements the K-Medoids algorithm. The results of data reduction with PCA resulted in five new components with a cumulative proportion variance of 0.8311. The five new components are implemented for cluster formation using the K-Medoids algorithm which results in the form of two clusters with a silhouette coefficient of 0.35. Combination of techniques of Data reduction by PCA and the application of the K-Medoids clustering algorithm are new ways for grouping data of patients with cardiovascular disease based on the level of patient complications in each cluster of data generated.

The experiments of Project 8 have been excellent, but the expected goals still difficult to achieve. So much so that some of the results at your fingertips were also missing. In view of this, the focus of this article is to clarify several easy confused concepts. Only in this way, we can reasonably explain the experimental data. The main points are as follows: 1. The value c of the light speed in vacuum and a particle with zero static mass, both of which do not exist in the reality. That is to say, the so-called a photon's static mass is equal to zero but has energy, which is a paradox that confuses two different definitional domains. 2. In the reality, photons are high-speed particles generated by electromagnetic radiation. They must have the characteristics of (static) mass, energy and wave, in order to describe the main body to aim at photons from different angles. 3. After any main body comes into being electromagnetic radiation, its static mass will inevitably decrease accordingly. 4. The charge-mass ratio of an electron is a physical constant, which is the ratio of its charge to the amount of matter, and is not affected by relativistic effects and electromagnetic radiation. 5. The uncertainty of moving electrons is caused by random electromagnetic radiations. Finally, it is pointed out that if the cyclotron frequency of a single electron is measured, and at the same time, its de Broglie wavelength or frequency can also be measured, then its static mass can be obtained. Even so, the expected goals are still difficult to achieve, because random electromagnetic radiations are always taking away continually the matter composition of the single electron being measured. However, this was precisely a result of the research obtained by Project 8, and had universality, which should be reflect on.

The electronic, optical, and magnetic properties of Nd-doped ZnO systems were calculated using the DFT/GGA+U method. According to the results, the Nd dopant causes lattice parameter expansion, negative formation energy, and bandgap narrowing, resulting in the formation of an n-type degenerate semiconductor. Overlapping of the generated impurity and Fermi levels results in a significant trap effect that prevents electron-hole recombination. The absorption spectrum demonstrates a redshift in the visible region and improved intensity, leading to enhanced photocatalytic performance. The Nd-doped ZnO system displays ferromagnetic, with FM coupling due to strong spd-f hybridization through magnetic exchange interaction between the Nd-4f state and O-2p, Zn-4s, and Zn-3p states. These findings imply that Nd-doped ZnO may be a promising material for DMS spintronic devices.

Interdisciplinary research consists of many levels and pathways. One research level that has emerged since the early 21st century is called integration science. Specifically, we focus on a research pathway that structurally integrates social sciences with theoretical physics from perspectives of dynamic analysis. Building on nearly 20 years of prior work, this paper proposes a basic theory of integration science, laying the theoretical foundation for its subsequent development. The significance of integration science operates on three levels. First, identifying structural connections between different disciplines helps in our holistic understanding of natural and social phenomena. Second, generally speaking, the current level of conceptualization and modeling in natural sciences, especially physics, is ahead of social sciences. Integration science research can help elevate the level of conceptualization and modeling in social sciences. Third, the structural similarity across different disciplines reflects the shared thinking of scientists from various fields. Integration science is not simply a synthesis of knowledge from different disciplines. The standard of integration science is to enable social sciences and natural sciences to share the same mathematical structures, thereby possessing a unified mathematical language for description. The empirical basis of integration science is discussed, proposing a unified theory of interdisciplinary scientific observation. This includes concepts like the directionality of scientific observation and the orthogonal principle, the concept of observational disturbance and the diagonal law, defining low and high disturbance quadrants, and discussing why different disturbance quadrants follow their respective mathematical paths. The basic theory of integration science is proposed. The application of category theory in integration science is introduced, along with the necessary semantic supplements. The fundamental concepts of integration mathematics are proposed, defining concepts like integration points, lines, plans, and bulks, and discussing their algebraic and functional analysis methods, thereby laying the mathematical foundation for the integration science. The structural force hypothesis is proposed, along with an axiomatic system of structural forces, thereby laying the philosophical foundation for integrative science. Based on prior work, specific cases of integrative points, lines, plans, and bulks are provided.

Chi-squared automatic interaction detector (CHAID) algorithm is considered to be one of the mostly used supervised learning methods as it is adaptable to solving any kind of problem at hand. We have been starkly aware of CHAID maps non-linear relationships quite well, and it can empower predictive models with stability. But we don’t know how high its accuracy is precisely. To find out the perfect scope CHAID algorithm fits into, this paper presents the analysis of the accuracy of the CHAID algorithm. We introduce the causes, applicable conditions and application scope of CHAID algorithm at first, and then highlight the difference of branching principal between the CHAID algorithm and several other common decision tree algorithms, which is our first step towards basic analysis on CHAID algorithm. We next employee an actual branching case to help us understand CHAID algorithm better. Specifically, we use vehicle customer satisfaction data to compare multiple decision tree algorithms, and cite some factors that affecting the accuracy and some corresponding countermeasures which are more conducive to us to obtain accurate results. The results show that CHAID can analyze the data very well, and detect the significantly correlated factors surely. In this paper, we learn the clear information required to understand CHAID algorithm, thereby make better choices when we need to use decision tree algorithms.

The capital allocation framework proposed by [] presents capital allocation principles as solutions to particular optimization problems and provides a general solution of the quadratic allocation problem via a geometric proof. However, the widely used haircut allocation principle is not reconcilable with that optimization setting. In this paper we provide an alternative proof of the quadratic allocation problem based on the Lagrange multipliers method to reach the general solution. We show that the haircut allocation principle can be accommodated to the optimization setting with the quadratic optimization criterion if one of the original conditions is relaxed. Two examples are provided to illustrate the accommodation of this allocation principle.

Due to the lack of theoretical research on the amount of spatio-temporal information in the high-speed photography technologies, obtaining an optimized system with a best amount of spatio-temporal information remains a challenge, resulting in insufficient effective information and observation accuracy for ultrafast events. The paper presents an ultrafast raster imaging (URI) system with a large amount of spatio-temporal information based on the all-optical raster principle in single-shot. Specifically, we derive the optimal equation of spatial resolution and the expression for the maximum amount of spatio-temporal information that can achieve excellent performance for an URI system. It serves as a general guideline for getting a large amount of information design in the URI system. Compared to the existing URI systems, the advanced URI system exhibits an improvement of nearly 1 order of magnitude in the amount of spatio-temporal information, and more than twofold in spatial resolution. It shows a great potential for capturing intricate and non-repetitive ultrafast events on the femtosecond time scale.

In the paper, a fully discrete compact difference scheme with $O(\tau^{2}+h^{4})$ precision is established by considering the numerical approximation of the one-dimensional Allen-Cahn equation. The numerical solutions satisfy discrete maximum principle under reasonable step ratio and time step constraint is proved. And the energy stability for the fully discrete scheme is investigated. An example is finally presented to show the effectiveness of scheme.

In a recent paper, we have shown how gravity and information can be related. The relation is based on the thermodynamic extension of the gravitational system under consideration using the holographic principle. Using this idea, we were able to derive the Gullstrand-Painlevé (GP) metric. In this short paper, we re-derive the GP metric using information. However, we now extend the spacetime to 5D with the fifth dimension being time, that is, the (3+1)D spacetime is now promoted to (3+1+1)D spacetime. We also comment on the possible Braneworld interpretation of this model.

This work tackles the problem of image restoration, a crucial task in many fields of applied sciences, focusing on removing degradation caused by blur and noise during the acquisition process. Drawing inspiration from the multi-penalty approach based on the Uniform Penalty principle introduced in [Bortolotti et al. arXiv.math.NA/2309.14163], we develop here a new image restoration model and an iterative algorithm for its effective solution. The model incorporates pixel-wise regularization terms and establishes a rule for parameters selection, aiming to restore images through the solution of a sequence of constrained optimization problems. To achieve this, we present a modified version of the Newton Projection method, adapted to multi-penalty scenarios, and prove its convergence. Numerical experiments demonstrate the efficacy of the method in eliminating noise and blur while preserving the image edges.

Let $(\{f_j\}_{j=1}^n, \{\tau_j\}_{j=1}^n)$ and $(\{g_k\}_{k=1}^n, \{\omega_k\}_{k=1}^n)$ be two p-orthonormal bases for a finite dimensional Banach space $\mathcal{X}$. If $ x \in \mathcal{X}\setminus\{0\}$ is such that $\theta_fx$ is $\varepsilon$-supported on $M\subseteq \{1,\dots, n\}$ w.r.t. p-norm and $\theta_gx$ is $\delta$-supported on $N\subseteq \{1,\dots, n\}$ w.r.t. p-norm, then we show that \begin{align}\label{ME} &o(M)^\frac{1}{p}o(N)^\frac{1}{q}\geq \frac{1}{\displaystyle \max_{1\leq j,k\leq n}|f_j(\omega_k) |}\max \{1-\varepsilon-\delta, 0\},\\ &o(M)^\frac{1}{q}o(N)^\frac{1}{p}\geq \frac{1}{\displaystyle \max_{1\leq j,k\leq n}|g_k(\tau_j) |}\max \{1-\varepsilon-\delta, 0\},\label{ME2} \end{align} where \begin{align*} \theta_f: \mathcal{X} \ni x \mapsto (f_j(x) )_{j=1}^n \in \ell^p([n]); \quad \theta_g: \mathcal{X} \ni x \mapsto (g_k(x) )_{k=1}^n \in \ell^p([n]) \end{align*} and $q$ is the conjugate index of $p$. We call Inequalities (\ref{ME}) and (\ref{ME2}) as \textbf{Functional Donoho-Stark Approximate Support Uncertainty Principle}. Inequalities (\ref{ME}) and (\ref{ME2}) improve the finite approximate support uncertainty principle obtained by Donoho and Stark \textit{[SIAM J. Appl. Math., 1989]}.

Let $(\{f_j\}_{j=1}^n, \{\tau_j\}_{j=1}^n)$ and $(\{g_k\}_{k=1}^n, \{\omega_k\}_{k=1}^n)$ be two p-orthonormal bases for a finite dimensional Banach space $\mathcal{X}$. Let $M,N\subseteq \{1, \dots, n\}$ be such that \begin{align*} o(M)^\frac{1}{q}o(N)^\frac{1}{p}< \frac{1}{\displaystyle \max_{1\leq j,k\leq n}|g_k(\tau_j) |}, \end{align*} where $q$ is the conjugate index of $p$. Then for all $x \in \mathcal{X}$, we show that \begin{align}\label{FGJU} (1) \quad \quad \quad \quad \|x\|\leq \left(1+\frac{1}{1-o(M)^\frac{1}{q}o(N)^\frac{1}{p}\displaystyle\max_{1\leq j,k\leq n}|g_k(\tau_j)|}\right)\left[\left(\sum_{j\in M^c}|f_j(x)|^p\right)^\frac{1}{p}+\left(\sum_{k\in N^c}|g_k(x) |^p\right)^\frac{1}{p}\right]. \end{align} We call Inequality (1) as \textbf{Functional Ghobber-Jaming Uncertainty Principle}. Inequality (1) improves the uncertainty principle obtained by Ghobber and Jaming \textit{[Linear Algebra Appl., 2011]}.

We demonstrate, in the context of Loop Quantum Gravity, the Quantum Holographic Principle, according to which the area of the boundary surface enclosing a region of space encodes a qubit per Planck unit. To this aim, we introduce fermion fields in the bulk, whose boundary surface is the two-dimensional sphere. The doubling of the fermionic degrees of freedom and the use of the Bogoliubov transformations lead to pairs of spin network’s edges piercing the boundary surface with double punctures, giving rise to pixels of area encoding a qubit. The proof is also valid in the case of a fuzzy sphere.

The classical uncertainty principle inequalities were imposed as a mathematical constraint over the general relativity geodesic equation. In this way, the uncertainty principle was reformulated in terms of the proper space-time length element, Planck length and a geodesic-derived scalar, leading to a geometric expression for the uncertainty principle (GeUP). This re-formulation confirmed the necessity for a minimum length for the space-time line element in the geodesic, dependent on a geodesic-derived scalar which made the expression Lorentz-covariant. In agreement with quantum gravity theories, GeUP required the imposition of a perturbation over the background Minkowski metric unrelated to classical gravity. When applied to the Schwarzschild metric, a geodesic exclusion zone was found around the singularity where uncertainty in space-time diverged to infinity.

The Boltzmann-Gibbs (BG) entropy has been used in a wide variety of problems for more than a century. It is well known that BG entropy is extensive, but for certain systems such as those dictated by long-range interactions, the entropy must be non-extensive. Tsallis entropy possesses non-extensive characteristics, which is parametrized by a variable q (q = 1 being the classic BG limit), but unless q is determined from microscopic dynamics, the model remains but a phenomenological tool. To this date very few examples have emerged in which q can be computed from first principles. This paper shows that the space plasma environment, which is governed by long-range collective electromagnetic interaction, represents a perfect example for which the q parameter can be computed from micro-physics. By taking the electron velocity distribution function measured in the heliospheric environment into account, and considering them to be in quasi equilibrium state with electrostatic turbulence known as the quasi-thermal noise, it is shown that the value corresponding to q = 9/13 = 0.6923 may be deduced. This prediction is verified against observation made by spacecraft, and it is shown to be in excellent agreement.

In our investigation of the time evolution of energy states Einstein’s interpretation from more than a century ago is found to have greater internal consistency than that of non-relativistic quantum mechanics. We choose to align more closely with his methods by abandoning the non-relativistic Hamiltonian method, which has been the standard for nearly a century, in favor of a relativistically correct Lagrangian method. Integral equations of motion for the absorption and emission of radiation are derived that underlie and anticipate the differentially motivated Schrödinger equation. This new interpretation applies to a large volume of experimental evidence of both classical and quantum mechanical origin. Among the examples discussed in support are Planck’s law describing black body radiation, matrix mechanics, the function of the simplest quantum mechanical system an electron cyclotron, chaos theory, and evolutionary biology.

Physical roots, exemplifications and consequences of periodic and aperiodic ordering (represented by Fibonacci series) in biological systems are discussed. The role and physical and biological roots of symmetry and asymmetry appearing in biological patterns is addressed. Generalization of the Curie-Neumann Principle as applied to biological objects is presented, briefly summarized as: “asymmetry is what creates a biological phenomenon”. The “up-bottom approach” and “bottom up” approaches to the explanation of symmetry in organisms are presented in detail. The “up-bottom approach”, implies that the symmetry of the biological structure follows the symmetry of media in which this structure is functioning; the “bottom-up” approach, in turn, adopt that the symmetry of biological structures emerges from the symmetry of molecules constituting the structure. A diversity of mathematical measures applicable for quantification of ordering in biological patterns is introduced. The continuous, Shannon and Voronoi measures of symmetry/ordering and their application to biology objects are addressed. The fine structure of the notion of “ordering” is discussed. Informational/algorithmic roots of ordering inherent for the biological systems are considered. Ordered/symmetrical patterns provide economy of biological information, necessary for algorithmic description of a biological entity. Application of the Landauer principle bridging physics and theory of information to the biological systems is discussed.

In 1911, A. Einstein suggested that gravity affects at the electromagnetic radiation originating from the distant sources, namely, it shifts the spectral lines in the red side of the spectrum and derived the gravitational redshift formula. A modern science claims that Einstein’s formula is mathematically immaculate. We show that this is not true: in fact, this formula is approximate. Using the law of conservation of mechanical energy, we derived two exact formulas оf the gravitational redshift.

When solving the Einstein's equations for an isolated system of masses, V. Fock introduces harmonic reference frame and obtains an unambiguous solution. Further, he concludes that there exists a harmonic reference frame which is determined uniquely apart from a Lorentz transformation if suitable supplementary conditions are imposed. It is known that wave equations keep the same form under Lorentz transformations. Thus, we speculate that Fock's special harmonic reference frames may have provided us a clue to derive the Einstein's equations in some special class of non-inertial reference frames. Following this clue, generalized Einstein's equations in some special non-inertial reference frames are derived based on the theory of vacuum mechanics. If the field is weak and the reference frame is quasi-inertial, these generalized Einstein's equations reduce to Einstein's equations. Thus, this theory may also explain all the experiments which support the theory of general relativity. There exist some differences between this theory and the theory of general relativity.

HIGHLIGHTS This paper is presenting an experiment based on Ehrenfest's paradox where an effect of special relativity was expected but not observed. The validity of special relativity in our macro world will be questioned and an alternative will be offered. Indeed, special relativity has been successful in describing the behaviour of particles (Rossi & Hall, 1941), but since particles obey quantum rules, there is no observation of special relativity in our everyday world. On the contrary, there are at least two paradoxes based on special relativity: the twin paradox (Langevin, 1911) and Ehrenfest's paradox (1909). ABSTRACT After presenting the history of special relativity, the non-simultaneity of special relativity is questioned in our macro world. In addition, some issues between light clocks and the application of Lorentz transformation are presented. All this indicates that special relativity appears to be correct only for particles and would be invalid in our macro world. A new hypothesis is presented based on an adaptation of special relativity; this new hypothesis solves the anomalies and could be a solution to the twin paradox. This new hypothesis has a prediction in disagreement with special relativity. To test that prediction, a new experiment has been carried out and the preliminary results support the new hypothesis. Previously, a lack of special relativistic effects has been observed in the universe (Davis et al., 2004); that second observation is also explained with the new hypothesis.

Physics and neuroscience share overlapping objectives, the major of which is probably the attempt to reduce the observed universe to a set of rules. The approaches are complementary, attempting to find a reduced description of the universe or of the observer, respectively. We propose here that combining the two approaches within an observer-inclusive physical scheme, bears significant advantages. In such a scheme, the same set of rules applies to the universe and its observers, and the two descriptions are entangled. We show here that analyzing special relativity in an observer-inclusive framework can resolve its contradiction with the observed non-locality of physical interactions. The contradiction is resolved by reducing the universe (including the observer) to a dynamic distribution of closed strings (“ceons”) whose vibration waves travel at c. This ceons model is consistent with general relativity, non-locality, the holographic principle and loop quantum gravity; it also eliminates Zeno’s motion paradoxes. Yet, the model entails several new empirical predictions. Finally, the ceons model suggests a fundamental physical implementation of active biological perception. Paraphrasing Torricelli, this paper suggests that we live submerged in a c of light.

Double-spiral galaxies are common in the Universe. It is known that the logarithmic double spiral is a Maximum Entropy geometry and represents spiral galaxies well. It is also known that the virial mass of such a galaxy can be approximately determined from the entropy of its central supermassive black hole. But over time the black hole must accrete mass, and therefore the overall galactic entropy must increase. From the associated entropic Euler-Lagrange equation (forming the basis of the Principle of Least Exertion, and also enabling the application of Nöther’s theorem) we show that the galactic entropy production is a conserved quantity, and we derive an appropriate expression for the relativistic entropic Hamiltonian of an idealised spiral galaxy. We generalise Onsager’s celebrated expression for entropy production and demonstrate that galactic entropy production has two parts, one many orders of magnitude larger than the other, and where the smaller is comparable to the Hawking radiation of the central supermassive black hole. We conclude that galaxies cannot be isolated, since even idealised spiral galaxies have non-zero entropy production.

We consider the quantum thermodynamic origin of the gravitational force of matter by applying the spacetime entanglement entropy and the Unruh effect originating from vacuum quantum fluctuations. By analyzing both the local thermal equilibrium and quasi-static processes of a system, we may get both the magnitude and direction of Newton's gravitational force in our theoretical model. Our work shows the possibility that the elusive Unruh effect has already shown its manifestation through gravitational force.

The fundamental divergence in foundation of modern physics lies in the incompatibility between quantum theory and relativity. This study created a relative continuum, found a mathematical tool for the cosmic continuum; proposed dark particle hypothesis, filled gap on minimum existence quantity particle; discovered new equivalence principle, bridged differences in foundation of physics; and established an ideal model, revealed deep essence of cosmic and material structure. In this model, any cosmic system is a continuum composed of existence continuum relative to the wavelength of bosons energy waves and its dimension continuum. This model provides new perspectives on the fundamental problems of physics and cosmology. Firstly, it elucidated the physical mechanism of bosons in fundamental interactions. Secondly, it reconstructed the understanding of the basic unit of the cosmic and material structure. Thirdly, it updated the inherent concepts about the existence form and existence dimension. Fourthly, it restored the causality truth of wave function collapse in quantum mechanics.

The Equator Principle is the goal of promoting the harmonious development of my country's economy and society. It promotes the green transformation and upgrading of the industrial structure by strictly controlling the flow of commercial bank funds, so as to achieve the goal of environmental protection and the coordinated development of the national economy. This paper uses factor analysis to reduce the dimensions of 10 financial indicators and non-financial indicators that measure the operating performance and development potential of joint-stock commercial banks, and then compares the comprehensive operating performance, liquidity, and safety of Industrial Bank and comparable banks. And the level of profitability, analyze the difference in comprehensive operating performance of joint-stock commercial banks joining the Equator Principles compared with commercial banks that have not joined the Equator Principles. The results of the study found that joining the Equator Principles of joint-stock commercial banks can improve comprehensive operating performance in the short term. In the long run, the development trend of Industrial Bank will be similar to that of comparable banks in the same category. Joining the Equator Principles of Industrial Bank can improve its liquidity and profitability, but it will not in the long run. Conducive to the improvement of the asset quality of joint-stock commercial banks. In this regard, the government, enterprises and financial institutions should work together to help commercial banks achieve an effective balance between operating performance and social responsibility, so as to achieve the goals of "carbon peak" and "carbon neutral".