Search Results (17)

The axiomatic structure of the $\kappa$-statistcal theory is proven. In addition to the first three standard Khinchin–Shannon axioms of continuity, maximality, and expansibility, two further axioms are identified, namely the self-duality axiom and the scaling axiom. It is shown that both the $\kappa$-entropy and its special limiting case, the classical Boltzmann–Gibbs–Shannon entropy, follow unambiguously from the above new set of five axioms. It has been emphasized that the statistical theory that can be built from $\kappa$-entropy has a validity that goes beyond physics and can be used to treat physical, natural, or artificial complex systems. The physical origin of the self-duality and scaling axioms has been investigated and traced back to the first principles of relativistic physics, i.e., the Galileo relativity principle and the Einstein principle of the constancy of the speed of light. It has been shown that the $\kappa$-formalism, which emerges from the $\kappa$-entropy, can treat both simple (few-body) and complex (statistical) systems in a unified way. Relativistic statistical mechanics based on $\kappa$-entropy is shown that preserves the main features of classical statistical mechanics (kinetic theory, molecular chaos hypothesis, maximum entropy principle, thermodynamic stability, H-theorem, and Lesche stability). The answers that the $\kappa$-statistical theory gives to the more-than-a-century-old open problems of relativistic physics, such as how thermodynamic quantities like temperature and entropy vary with the speed of the reference frame, have been emphasized. Full article

This research focuses on combating the increasing problem of antimicrobial resistance, especially in Escherichia coli (E. coli), by assessing the efficacy of aminoglycosides. The study specifically addresses the challenge of developing new therapeutic approaches by integrating experimental data with mathematical modeling to better understand the action of aminoglycosides. It involves testing various antibiotics like streptomycin (SMN), kanamycin (KMN), gentamicin (GMN), tobramycin (TMN), and amikacin (AKN) against the O157:H7 strain of E. coli. The study employs a pharmacodynamics (PD) model to analyze how different antibiotic concentrations affect bacterial growth, utilizing minimum inhibitory concentration (MIC) to gauge the effective bactericidal levels of the antibiotics. The study’s approach involved transforming bacterial growth rates, as obtained from time–kill curve data, into logarithmic values. A model was then developed to correlate these log-transformed values with their respective responses. To generate additional data points, each value was systematically increased by an increment of 0.1. To simulate real-world variability and randomness in the data, a Gaussian scatter model, characterized by parameters like κ and EC₅₀, was employed. The mathematical modeling was pivotal in uncovering the bactericidal properties of these antibiotics, indicating different PD MIC (zMIC) values for each (SMN: 1.22; KMN: 0.89; GMN: 0.21; TMN: 0.32; AKN: 0.13), which aligned with MIC values obtained through microdilution methods. This innovative blend of experimental and mathematical approaches in the study marks a significant advancement in formulating strategies to combat the growing threat of antimicrobial-resistant E. coli, offering a novel pathway to understand and tackle antimicrobial resistance more effectively. Full article

The disease status, progression, and treatment effect of essential tremor (ET) patients are currently assessed with clinical scores, such as the Fahn–Tolosa–Marin Clinical Rating Scale for Tremor (FTM). The use of objective and rater-independent monitoring of tremors may improve clinical care for patients with ET. Therefore, the focus of this study is to develop an objective accelerometry-based method to quantify ET, based on FTM criteria. Thirteen patients with ET and thirteen matched healthy participants underwent FTM tests to rate tremor severity, paired with tri-axial accelerometric measurements at the index fingers. Analogue FTM assessments were performed by four independent raters based on video recordings. Quantitative measures were derived from the accelerometric data, e.g., the area under the curve of power in the 4–8 Hz frequency band (AUCP) and maximal tremor amplitude. As such, accelerometric tremor scores were computed, using thresholds based on healthy measurements and FTM criteria. Agreement between accelerometric and clinical FTM scores was analyzed with Cohen’s kappa coefficient. It was assessed whether there was a relationship between mean FTM scores and the natural logarithm (ln) of the accelerometric outcome measures using linear regression. The agreement between accelerometric and FTM scores was substantial for resting and intention tremor tests (≥72.7%). However, the agreement between accelerometric postural tremor data and clinical FTM ratings (κ = 0.459) was low, although their logarithmic (ln) relationship was substantial (R² ≥ 0.724). Accelerometric test–retest reliability was good to excellent (ICC ≥ 0.753). This pilot study shows that tremors can be quantified with accelerometry, using healthy thresholds and FTM criteria. The test–retest reliability of the accelerometric tremor scoring algorithm indicates that our low-cost accelerometry-based approach is a promising one. The proposed easy-to-use technology could diminish the rater dependency of FTM scores and enable physicians to monitor ET patients more objectively in clinical, intraoperative, and home settings. Full article

In the first part of this investigation, we considered the parameter differentiation of the Whittaker function ${\mathrm{M}}_{\kappa ,\mu }\left(x\right)$. In this second part, first derivatives with respect to the parameters of the Whittaker function ${\mathrm{W}}_{\kappa ,\mu }\left(x\right)$ are calculated. Using the confluent hypergeometric function, these derivatives can be expressed as infinite sums of quotients of the digamma and gamma functions. Furthermore, it is possible to obtain these parameter derivatives in terms of infinite integrals, with integrands containing elementary functions (products of algebraic, exponential, and logarithmic functions), from the integral representation of ${\mathrm{W}}_{\kappa ,\mu }\left(x\right)$. These infinite sums and integrals can be expressed in closed form for particular values of the parameters. Finally, an integral representation of the integral Whittaker function ${\mathrm{wi}}_{\kappa ,\mu }\left(x\right)$ and its derivative with respect to $\kappa$, as well as some reduction formulas for the integral Whittaker functions ${\mathrm{Wi}}_{\kappa ,\mu }\left(x\right)$ and ${\mathrm{wi}}_{\kappa ,\mu }\left(x\right)$, are calculated. Full article

In this paper, first derivatives of the Whittaker function ${\mathrm{M}}_{\kappa ,\mu }\left(x\right)$ are calculated with respect to the parameters. Using the confluent hypergeometric function, these derivarives can be expressed as infinite sums of quotients of the digamma and gamma functions. Moreover, from the integral representation of ${\mathrm{M}}_{\kappa ,\mu }\left(x\right)$ it is possible to obtain these parameter derivatives in terms of finite and infinite integrals with integrands containing elementary functions (products of algebraic, exponential, and logarithmic functions). These infinite sums and integrals can be expressed in closed form for particular values of the parameters. For this purpose, we have obtained the parameter derivative of the incomplete gamma function in closed form. As an application, reduction formulas for parameter derivatives of the confluent hypergeometric function are derived, along with finite and infinite integrals containing products of algebraic, exponential, logarithmic, and Bessel functions. Finally, reduction formulas for the Whittaker functions ${\mathrm{M}}_{\kappa ,\mu }\left(x\right)$ and integral Whittaker functions ${\mathrm{Mi}}_{\kappa ,\mu }\left(x\right)$ and ${\mathrm{mi}}_{\kappa ,\mu }\left(x\right)$ are calculated. Full article

The Calogero–Leyvraz Lagrangian framework, associated with the dynamics of a charged particle moving in a plane under the combined influence of a magnetic field as well as a frictional force, proposed by Calogero and Leyvraz, has some special features. It is endowed with a Shannon “entropic” type kinetic energy term. In this paper, we carry out the constructions of the 2D Lotka–Volterra replicator equations and the $N=2$ Relativistic Toda lattice systems using this class of Lagrangians. We take advantage of the special structure of the kinetic term and deform the kinetic energy term of the Calogero–Leyvraz Lagrangians using the $\kappa$-deformed logarithm as proposed by Kaniadakis and Tsallis. This method yields the new construction of the $\kappa$-deformed Lotka–Volterra replicator and relativistic Toda lattice equations. Full article

Due to the urgent need of innovation in the antimalarial therapeutic arsenal, a series of thirty-seven ring-substituted N-arylcinnamanilides prepared by microwave-assisted synthesis were subjected to primary screening against the chloroquine-sensitive strain of P. falciparum 3D7/MRA-102. The lipophilicity of all compounds was experimentally determined as the logarithm of the capacity factor k, and these data were subsequently used in the discussion of structure-activity relationships. Among the screened compounds, fourteen derivatives exhibited IC₅₀ from 0.58 to 31 µM, whereas (2E)-N-(4-bromo-2-chlorophenyl)-3-phenylprop-2-enamide (24) was the most effective agent (IC₅₀ = 0.58 µM). In addition, (2E)-N-[2,6-dibromo-4-(trifluoromethyl)- phenyl]-3-phenylprop-2-enamide (36), (2E)-N-[4-nitro-3-(trifluoromethyl)phenyl]-3-phenylprop- 2-enamide (18), (2E)-N-(2-bromo-5-fluorophenyl)-3-phenylprop-2-enamide (23), and (2E)-3-phenyl-N-(3,4,5-trichlorophenyl)prop-2-enamide (33) demonstrated efficacy in the IC₅₀ range from 2.0 to 4.3 µM, comparable to the clinically used standard chloroquine. The results of a cell viability screening performed using THP1-Blue™ NF-κB cells showed that none of these highly active compounds displayed any significant cytotoxic effect up to 20 μM, which makes them promising Plasmodium selective substances for further investigations. Full article

This work is mainly interested in ensuring users’ privacy in asymmetric computing, such as cloud computing. In particular, because lots of user data are expressed in non-integer data types, privacy-enhanced applications built on fully homomorphic encryption (FHE) must support real-valued comparisons due to the ubiquity of real numbers in real-world applications. However, as FHE schemes operate in specific domains, such as that of congruent integers, most FHE-based solutions focus only on homomorphic comparisons of integers. Attempts to overcome this barrier can be grouped into two classes. Given point numbers in the form of approximate real numbers, one class of solution uses a special-purpose encoding to represent the point numbers, whereas the other class constructs a dedicated FHE scheme to encrypt point numbers directly. The solutions in the former class may provide depth-efficient arithmetic (i.e., logarithmic depth in the size of the data), but not depth-efficient comparisons between FHE-encrypted point numbers. The second class may avoid this problem, but it requires the precision of point numbers to be determined before the FHE setup is run. Thus, the precision of the data cannot be controlled once the setup is complete. Furthermore, because the precision accuracy is closely related to the sizes of the encryption parameters, increasing the precision of point numbers results in increasing the sizes of the FHE parameters, which increases the sizes of the public keys and ciphertexts, incurring more expensive computation and storage. Unfortunately, this problem also occurs in many of the proposals that fall into the first class. In this work, we are interested in depth-efficient comparison over FHE-encrypted point numbers. In particular, we focus on enabling the precision of point numbers to be manipulated after the system parameters of the underlying FHE scheme are determined, and even after the point numbers are encrypted. To this end, we encode point numbers in continued fraction (CF) form. Therefore, our work lies in the first class of solutions, except that our CF-based approach allows depth-efficient homomorphic comparisons (more precisely, the complexity of the comparison is $O(\log \kappa +\log n)$ for a number of partial quotients n and their bit length $\kappa$ , which is normally small) while allowing users to determine the precision of the encrypted point numbers when running their applications. We develop several useful applications (e.g., sorting) that leverage our CF-based homomorphic comparisons. Full article

Using Fracture Seismic methods to map fluid-conducting fracture zones makes it important to understand fracture connectivity over distances greater 10–20 m in the Earth’s upper crust. The principles required for this understanding are developed here from the observations that (1) the spatial variations in crustal porosity are commonly associated with spatial variations in the magnitude of the natural logarithm of crustal permeability, and (2) many parameters, including permeability have a scale-invariant power law distribution in the crust. The first observation means that crustal permeability has a lognormal distribution that can be described as $\kappa \approx {\kappa }_0\exp \left(\alpha \left(\phi -{\phi }_0\right)\right)$ , where α is the ratio of the standard deviation of ln permeability from its mean to the standard deviation of porosity from its mean. The scale invariance of permeability indicates that αϕ_ο = 3 to 4 and that the natural log of permeability has a 1/k pink noise spatial distribution. Combined, these conclusions mean that channelized flow in the upper crust is expected as the distance traversed by flow increases. Locating the most permeable channels using Seismic Fracture methods, while filling in the less permeable parts of the modeled volume with the correct pink noise spatial distribution of permeability, will produce much more realistic models of subsurface flow. Full article

The purpose of the present paper is to provide further insights on the definition of the parameters of the log-law in open-channel flows with rough mobile granular beds. Emphasis is placed in the study of flows over cohesionless granular beds composed of monosized spherical particles in simple lattice arrangements. Potentially influencing factors such as grain size distribution, grain shape and density or cohesion are not addressed in this study. This allows for a preliminary discussion of the amount of complexity needed to obtain the log-law features observed in more realistic open-channel flows. Data collection included instantaneous streamwise and bed-normal flow velocities, acquired with a two-dimensional and two-component (2D2C) Particle Image Velocimetry (PIV) system. The issue of the non uniqueness of the definition of the parameters of the log-law is addressed by testing several hypotheses. In what concerns the von Kármán parameter, $\kappa$ , it is considered as flow-independent or flow-dependent (a fitting parameter). As for the geometric roughness scale, $k_s$ , it results from a best fit procedure or is computed from a roughness function. In the latter case, the parameter B is imposed as $8.5$ or is calculated from the best fit estimate. The analysis of the results reveals that a flow dependent von Kármán parameter, lower than the constant $\kappa$ = $0.40$ , should be preferred. Forcing $\kappa$ = $0.40$ leads to non-physical values of $k_s$ and would imply extending the inner layer up about 50% of the flow depth which is physically difficult to explain. Considering a flow dependent von Kármán parameter allows for coherent explanations for the values of the remaining parameters (the geometric roughness scale $k_s$ , the displacement height $\Delta$ , the roughness height $z_0$ ). In particular, for the same transport rate, the roughness height obtained in a natural sediment bed is much greater than in the case of bed made of monosized glass spheres, underlining the influence of the bed surface complexity (texture and self-organized bed forms, in the water-worked cases) on the definition of the log-law parameters. Full article

The aim of this study was to evaluate levels of osteocalcin (OC), osteoprotegerin (OPG) and total soluble receptor activator of nuclear factor-κB ligand (RANKL), and bone mineral density (BMD) in patients on long-term acenocoumarol (AC) treatment. The cross-sectional study was carried out in 42 patients treated long-term with AC and 28 control subjects. Serum concentrations of OC, OPG, and sRANKL were measured using enzyme linked immunosorbent assay (ELISA) kits, and BMD at the femoral neck and lumbar spine were assessed by dual energy X-ray absorptiometry. A significantly decreased concentration of OC was found in AC users compared to control subjects (4.94 ± 2.22 vs. 10.68 ± 4.5; p < 0.001). Levels of OPG, sRANKL logarithm (log), sRANKL/OPG log ratio, and BMD were comparable between. In female AC users, positive correlations between OC and RANKL log, and between OC and RANKL/OPG log ratio (p = 0.017; p = 0.005, respectively), and a negative correlation between OC and OPG (p = 0.027) were found. Long-term AC anticoagulation significantly decreases OC concentration, but does not affect other bone metabolism markers or BMD. Our results also suggest the possibility that long-term treatment with AC may alleviate bone resorption in postmenopausal women. Full article

Probiotic-derived polyphosphates have attracted interest as potential therapeutic agents to improve intestinal health. The current study discovered the intracellular accumulation of polyphosphates in a marine cyanobacterium Synechococcus sp. PCC 7002 as nano-sized granules. The maximum accumulation of polyphosphates in Synechococcus sp. PCC 7002 was found at the late logarithmic growth phase when the medium contained 0.74 mM of KH₂PO₄, 11.76 mM of NaNO₃, and 30.42 mM of Na₂SO₄. Biogenic polyphosphate nanoparticles (BPNPs) were obtained intact from the algae cells by hot water extraction, and were purified to remove the organic impurities by Sephadex G-100 gel filtration. By using 100 kDa ultrafiltration, BPNPs were fractionated into the larger and smaller populations with diameters ranging between 30–70 nm and 10–30 nm, respectively. 4′,6-diamidino-2-phenylindole fluorescence and orthophosphate production revealed that a minor portion of BPNPs (about 14–18%) were degraded during simulated gastrointestinal digestion. In vitro studies using lipopolysaccharide-activated RAW264.7 cells showed that BPNPs inhibited cyclooxygenase-2, inducible nitric oxide (NO) synthase expression, and the production of proinflammatory mediators, including NO, tumor necrosis factor-α, interleukin-6, and interleukin-1β through suppressing the Toll-like receptor 4/NF-κB signaling pathway. Overall, there is promise in the use of the marine cyanobacterium Synechococcus sp. PCC 7002 to produce BPNPs, an anti-inflammatory postbiotic. Full article

The study of diet quality in a population provides information for the development of programs to improve nutritional status through better directed actions. The aim of this study was to assess the reproducibility and relative validity of a Mexican Diet Quality Index (ICDMx) for the assessment of the habitual diet of adults. The ICDMx was designed to assess the characteristics of a healthy diet using a validated semi-quantitative food frequency questionnaire (FFQ-Mx). Reproducibility was determined by comparing 2 ICDMx based on FFQs (one-year interval). Relative validity was assessed by comparing the ICDMx (2nd FFQ) with that estimated based on the intake averages from dietary records (nine days). The questionnaires were answered by 97 adults (mean age in years = 27.5, SD = 12.6). Pearson (r) and intraclass correlations (ICC) were calculated; Bland-Altman plots, Cohen’s κ coefficients and blood lipid determinations complemented the analysis. Additional analysis compared ICDMx scores with nutrients derived from dietary records, using a Pearson correlation. These nutrient intakes were transformed logarithmically to improve normality (log10) and adjusted according to energy, prior to analyses. The ICDMx obtained ICC reproducibility values ranged from 0.33 to 0.87 (23/24 items with significant correlations; mean = 0.63), while relative validity ranged from 0.26 to 0.79 (mean = 0.45). Bland-Altman plots showed a high level of agreement between methods. ICDMx scores were inversely correlated (p < 0.05) with total blood cholesterol (r = −0.33) and triglycerides (r = −0.22). ICDMx (as calculated from FFQs and DRs) obtained positive correlations with fiber, magnesium, potassium, retinol, thiamin, riboflavin, pyridoxine, and folate. The ICDMx obtained acceptable levels of reproducibility and relative validity in this population. It can be useful for population nutritional surveillance and to assess the changes resulting from the implementation of nutritional interventions. Full article

We explore the information geometric structures among the thermodynamic potentials in the κ-thermostatistics, which is a generalized thermostatistics based on the κ-deformed entropy. We show that there exists two different kinds of dualistic Hessian structures: one is associated with the κ-escort expectations and the other with the standard expectations. The associated κ-generalized metrics are derived and related to the κ-generalized fluctuation-response relations among the thermodynamic potentials in the κ-thermostatistics. Full article