BACKGROUND Spike trains are series of interspike intervals in a specific order that can be charac... more BACKGROUND Spike trains are series of interspike intervals in a specific order that can be characterized by their probability distributions and order in time which refer to the concepts of rate and spike timing features. Periodic structure in the spike train can be reflected in oscillatory activities. Thus, there is a direct link between oscillator activities and the spike train. The proposed methods are to investigate the dependency of emerging oscillatory activities to the rate and the spike timing features. METHOD First, the circular statistics methods were compared to Fast Fourier Transform for best estimation of spectra. Second, two statistical tests were introduced to help make decisions regarding the dependency of spectrum, or individual frequencies, onto rate and spike timing. Third, the methodology is applied to in-vivo recordings of basal ganglia neurons in mouse, primate, and human. Finally, this novel framework is shown to allow the investigation of subsets of spikes contributing to individual oscillators. RESULTS Use of circular statistical methods, in comparison to FFT, minimizes spectral leakage. Using virtual spike trains, the Rate versus Timing Dependency Spectrum Test (or RTDs-Test) permits identifying spectral spike trains solely dependent on the rate feature from those that are also dependent on the spike timing feature. Similarly, the Rate versus Timing Dependency Frequency Test (or RTDf-Test), allows to identify individual oscillators with partial dependency on spike timing. Dependency on spike timing was found for all in-vivo recordings but only in few frequencies. The mapping in frequency and time of dependencies showed a dynamical process that may be organizing the basal ganglia function. CONCLUSIONS The methodology may improve our understanding of the emergence of oscillatory activities and, possibly, the relation between oscillatory activities and circuitry functions.
We apply computational-mathematical models to elucidate the brain's pattern recognition from ... more We apply computational-mathematical models to elucidate the brain's pattern recognition from music in tasks such as classification of music pieces according to style and historical period, such as Baroque, Classical and Romantic periods. We propose deep learning as the computational intelligence medium of choice to implement the model. The feasibility study reported below explores a special case to design an algorithm that could distinguish different styles of music, especially the Baroque music and the romantic music. The input is a piece of music, and the output will be the style of the music.
Individuals with autism spectrum disorder struggle with motor difficulties throughout the life sp... more Individuals with autism spectrum disorder struggle with motor difficulties throughout the life span, and these motor difficulties may affect independent living skills and quality of life. Yet, we know little about how whole-body movement may distinguish individuals with autism spectrum disorder from individuals with typical development. In this study, kinematic and postural sway data were collected during multiple sessions of videogame play in 39 youth with autism spectrum disorder and 23 age-matched youth with typical development (ages 7–17 years). The youth on the autism spectrum exhibited more variability and more entropy in their movements. Machine learning analysis of the youths’ motor patterns distinguished between the autism spectrum and typically developing groups with high aggregate accuracy (up to 89%), with no single region of the body seeming to drive group differences. Moreover, the machine learning results corresponded to individual differences in performance on standa...
TABLA DE CONTENIDO RESUMEN The purpose of this paper is to prove the following characterization o... more TABLA DE CONTENIDO RESUMEN The purpose of this paper is to prove the following characterization of the invertible elements of the Green ring of a p-elementary Abelian group. Let G =3D (Z/p)m, and let k be an algebraically closed field of characteristic p. Suppose M is a finitely ...
In our study, the primary goal was to gain insights into cognition by measuring spatial memorabil... more In our study, the primary goal was to gain insights into cognition by measuring spatial memorability for two different types of approaches to geometry in interior design (biomorphic design and non–biomorphic rectilinear design). To better understand the processes behind the memorability differences, we also looked at how spatial memorability interacted with visual attention and spatial pleasantness. After extensive pre–testing, two standardized photographic stimulus sets were created and used during the experiment, controlling for variables such as novelty, complexity, pleasantness, and the number and density of interior architectural elements. Each stimulus set contained equal numbers of photographs with biomorphic elements and photographs with non–biomorphic elements. Subjects ( N = 68 students, mean age = 25.4 years) viewed the first stimulus set, then were given a “distractor” task. Next, subjects viewed the second stimulus set, and for each photograph indicated whether the imag...
ABSTRACT Architecture brings together diverse elements to enhance the observer's measure ... more ABSTRACT Architecture brings together diverse elements to enhance the observer's measure of esthetics and the convenience of functionality. Architects often conceptualize synthesis of design elements to invoke the observer's sense of harmony and positive affect. How does an observer's brain respond to harmony of design in interior spaces? One implicit consideration by architects is the role of guided visual attention by observers while navigating indoors. Prior visual experience of natural scenes provides the perceptual basis for Gestalt of design elements. In contrast, Gestalt of organization in design varies according to the architect's decision. We outline a quantitative theory to measure the success in utilizing the observer's psychological factors to achieve the desired positive affect. We outline a unified framework for perception of geometry and motion in interior spaces, which integrates affective and cognitive aspects of human vision in the context of anthropocentric interior design. The affective criteria are derived from contemporary theories of interior design. Our contribution is to demonstrate that the neural computations in an observer's eye movement could be used to elucidate harmony in perception of form, space and motion, thus a measure of goodness of interior design. Through mathematical modeling, we argue the plausibility of the relevant hypotheses.
Understanding the structure of relationships between objects in a given database is one of the mo... more Understanding the structure of relationships between objects in a given database is one of the most important problems in the field of data mining. The structure can be defined for a set of single objects (clustering) or a set of groups of objects (network mapping). We propose a method for discovering relationships between individuals (single or groups) that is based on what we call the empirical topology, a system-theoretic measure of functional proximity. To illustrate the suitability and efficiency of the method, we apply it to an astronomical data base.
Differential gene expression analysis in treatment of Parkinson's disease using the moduli s... more Differential gene expression analysis in treatment of Parkinson's disease using the moduli space of triangles
2017 International Conference on Computational Science and Computational Intelligence (CSCI), 2017
While persistent homology is a basic but useful tool for describing the topological features of s... more While persistent homology is a basic but useful tool for describing the topological features of spaces, it has rarely been applied to describe the chaotic attractor whose shape could be very intriguing and complex. Especially for high-dimensional chaotic attractors, on one hand it reveals the evolution and stability of dynamical systems yet on the other hand, since it is a natural restriction for human researchers that they are unable to see more than three dimensionalities, methods for categorizing high dimensional attractors are lacking. Therefore, in this article we propose the method of applying persistent homology calculation to high-dimensional chaotic attractors and give several representative examples from different genres of chaotic systems for whose topological structure being displayed.
Motivation: The process of assigning a finite set of tags or labels to a collection of observatio... more Motivation: The process of assigning a finite set of tags or labels to a collection of observations, subject to side conditions, is notable for its computational complexity. This labeling paradigm has theoretical and practical significance to a wide range of applications. For example, macromolecular structure determination by nuclear magnetic resonance (NMR) spectroscopy, a key method in the field of structural biology, relies on assigning or correlating observable spectral features to particular atoms known to be present from the sequence of the biomolecule. In the early stages of determining the threedimensional NMR structure of a protein, it is necessary to associate the observed data with atom labels, residue labels (type and position in the sequence), secondary structure labels, and other discrete attributes. In addition to the high cardinality of the set of possible labels, the characteristics of the underlying data, which often are noisy and incomplete and contain false posit...
The ubiquitous role of the cyber-infrastructures, such as the WWW, provides myriad opportunities ... more The ubiquitous role of the cyber-infrastructures, such as the WWW, provides myriad opportunities for machine learning and its broad spectrum of application domains taking advantage of digital communication. Pattern classification and feature extraction are among the first applications of machine learning that have received extensive attention. The most remarkable achievements have addressed data sets of moderate-to-large size. The 'data deluge' in the last decade or two has posed new challenges for AI researchers to design new, effective and accurate algorithms for similar tasks using ultra-massive data sets and complex (natural or synthetic) dynamical systems. We propose a novel principled approach to feature extraction in hybrid architectures comprised of humans and machines in networked communication, who collaborate to solve a pre-assigned pattern recognition (feature extraction) task. There are two practical considerations addressed below: (1) Human experts, such as pla...
BACKGROUND Spike trains are series of interspike intervals in a specific order that can be charac... more BACKGROUND Spike trains are series of interspike intervals in a specific order that can be characterized by their probability distributions and order in time which refer to the concepts of rate and spike timing features. Periodic structure in the spike train can be reflected in oscillatory activities. Thus, there is a direct link between oscillator activities and the spike train. The proposed methods are to investigate the dependency of emerging oscillatory activities to the rate and the spike timing features. METHOD First, the circular statistics methods were compared to Fast Fourier Transform for best estimation of spectra. Second, two statistical tests were introduced to help make decisions regarding the dependency of spectrum, or individual frequencies, onto rate and spike timing. Third, the methodology is applied to in-vivo recordings of basal ganglia neurons in mouse, primate, and human. Finally, this novel framework is shown to allow the investigation of subsets of spikes contributing to individual oscillators. RESULTS Use of circular statistical methods, in comparison to FFT, minimizes spectral leakage. Using virtual spike trains, the Rate versus Timing Dependency Spectrum Test (or RTDs-Test) permits identifying spectral spike trains solely dependent on the rate feature from those that are also dependent on the spike timing feature. Similarly, the Rate versus Timing Dependency Frequency Test (or RTDf-Test), allows to identify individual oscillators with partial dependency on spike timing. Dependency on spike timing was found for all in-vivo recordings but only in few frequencies. The mapping in frequency and time of dependencies showed a dynamical process that may be organizing the basal ganglia function. CONCLUSIONS The methodology may improve our understanding of the emergence of oscillatory activities and, possibly, the relation between oscillatory activities and circuitry functions.
We apply computational-mathematical models to elucidate the brain's pattern recognition from ... more We apply computational-mathematical models to elucidate the brain's pattern recognition from music in tasks such as classification of music pieces according to style and historical period, such as Baroque, Classical and Romantic periods. We propose deep learning as the computational intelligence medium of choice to implement the model. The feasibility study reported below explores a special case to design an algorithm that could distinguish different styles of music, especially the Baroque music and the romantic music. The input is a piece of music, and the output will be the style of the music.
Individuals with autism spectrum disorder struggle with motor difficulties throughout the life sp... more Individuals with autism spectrum disorder struggle with motor difficulties throughout the life span, and these motor difficulties may affect independent living skills and quality of life. Yet, we know little about how whole-body movement may distinguish individuals with autism spectrum disorder from individuals with typical development. In this study, kinematic and postural sway data were collected during multiple sessions of videogame play in 39 youth with autism spectrum disorder and 23 age-matched youth with typical development (ages 7–17 years). The youth on the autism spectrum exhibited more variability and more entropy in their movements. Machine learning analysis of the youths’ motor patterns distinguished between the autism spectrum and typically developing groups with high aggregate accuracy (up to 89%), with no single region of the body seeming to drive group differences. Moreover, the machine learning results corresponded to individual differences in performance on standa...
TABLA DE CONTENIDO RESUMEN The purpose of this paper is to prove the following characterization o... more TABLA DE CONTENIDO RESUMEN The purpose of this paper is to prove the following characterization of the invertible elements of the Green ring of a p-elementary Abelian group. Let G =3D (Z/p)m, and let k be an algebraically closed field of characteristic p. Suppose M is a finitely ...
In our study, the primary goal was to gain insights into cognition by measuring spatial memorabil... more In our study, the primary goal was to gain insights into cognition by measuring spatial memorability for two different types of approaches to geometry in interior design (biomorphic design and non–biomorphic rectilinear design). To better understand the processes behind the memorability differences, we also looked at how spatial memorability interacted with visual attention and spatial pleasantness. After extensive pre–testing, two standardized photographic stimulus sets were created and used during the experiment, controlling for variables such as novelty, complexity, pleasantness, and the number and density of interior architectural elements. Each stimulus set contained equal numbers of photographs with biomorphic elements and photographs with non–biomorphic elements. Subjects ( N = 68 students, mean age = 25.4 years) viewed the first stimulus set, then were given a “distractor” task. Next, subjects viewed the second stimulus set, and for each photograph indicated whether the imag...
ABSTRACT Architecture brings together diverse elements to enhance the observer's measure ... more ABSTRACT Architecture brings together diverse elements to enhance the observer's measure of esthetics and the convenience of functionality. Architects often conceptualize synthesis of design elements to invoke the observer's sense of harmony and positive affect. How does an observer's brain respond to harmony of design in interior spaces? One implicit consideration by architects is the role of guided visual attention by observers while navigating indoors. Prior visual experience of natural scenes provides the perceptual basis for Gestalt of design elements. In contrast, Gestalt of organization in design varies according to the architect's decision. We outline a quantitative theory to measure the success in utilizing the observer's psychological factors to achieve the desired positive affect. We outline a unified framework for perception of geometry and motion in interior spaces, which integrates affective and cognitive aspects of human vision in the context of anthropocentric interior design. The affective criteria are derived from contemporary theories of interior design. Our contribution is to demonstrate that the neural computations in an observer's eye movement could be used to elucidate harmony in perception of form, space and motion, thus a measure of goodness of interior design. Through mathematical modeling, we argue the plausibility of the relevant hypotheses.
Understanding the structure of relationships between objects in a given database is one of the mo... more Understanding the structure of relationships between objects in a given database is one of the most important problems in the field of data mining. The structure can be defined for a set of single objects (clustering) or a set of groups of objects (network mapping). We propose a method for discovering relationships between individuals (single or groups) that is based on what we call the empirical topology, a system-theoretic measure of functional proximity. To illustrate the suitability and efficiency of the method, we apply it to an astronomical data base.
Differential gene expression analysis in treatment of Parkinson's disease using the moduli s... more Differential gene expression analysis in treatment of Parkinson's disease using the moduli space of triangles
2017 International Conference on Computational Science and Computational Intelligence (CSCI), 2017
While persistent homology is a basic but useful tool for describing the topological features of s... more While persistent homology is a basic but useful tool for describing the topological features of spaces, it has rarely been applied to describe the chaotic attractor whose shape could be very intriguing and complex. Especially for high-dimensional chaotic attractors, on one hand it reveals the evolution and stability of dynamical systems yet on the other hand, since it is a natural restriction for human researchers that they are unable to see more than three dimensionalities, methods for categorizing high dimensional attractors are lacking. Therefore, in this article we propose the method of applying persistent homology calculation to high-dimensional chaotic attractors and give several representative examples from different genres of chaotic systems for whose topological structure being displayed.
Motivation: The process of assigning a finite set of tags or labels to a collection of observatio... more Motivation: The process of assigning a finite set of tags or labels to a collection of observations, subject to side conditions, is notable for its computational complexity. This labeling paradigm has theoretical and practical significance to a wide range of applications. For example, macromolecular structure determination by nuclear magnetic resonance (NMR) spectroscopy, a key method in the field of structural biology, relies on assigning or correlating observable spectral features to particular atoms known to be present from the sequence of the biomolecule. In the early stages of determining the threedimensional NMR structure of a protein, it is necessary to associate the observed data with atom labels, residue labels (type and position in the sequence), secondary structure labels, and other discrete attributes. In addition to the high cardinality of the set of possible labels, the characteristics of the underlying data, which often are noisy and incomplete and contain false posit...
The ubiquitous role of the cyber-infrastructures, such as the WWW, provides myriad opportunities ... more The ubiquitous role of the cyber-infrastructures, such as the WWW, provides myriad opportunities for machine learning and its broad spectrum of application domains taking advantage of digital communication. Pattern classification and feature extraction are among the first applications of machine learning that have received extensive attention. The most remarkable achievements have addressed data sets of moderate-to-large size. The 'data deluge' in the last decade or two has posed new challenges for AI researchers to design new, effective and accurate algorithms for similar tasks using ultra-massive data sets and complex (natural or synthetic) dynamical systems. We propose a novel principled approach to feature extraction in hybrid architectures comprised of humans and machines in networked communication, who collaborate to solve a pre-assigned pattern recognition (feature extraction) task. There are two practical considerations addressed below: (1) Human experts, such as pla...
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