The unprecedented prowess of measurement techniques provides a detailed, multi‐scale look into the depths of living systems. Understanding these avalanches of high‐dimensional data—by distilling underlying principles and mechanisms—necessitates dimensional reduction. We propose that living systems achieve exquisite dimensional reduction, originating from their capacity to learn, through evolution and phenotypic plasticity, the relevant aspects of a non‐random, smooth physical reality. We explain how geometric insights by mathematicians allow one to identify these genuine hallmarks of life and (...) distinguish them from universal properties of generic data sets. We illustrate these principles in a concrete example of protein evolution, suggesting a simple general recipe that can be applied to understand other biological systems. (shrink)

A dimensional reduction algorithm is applied to an intelligent classification model with the purpose of improving the efficiency and accuracy. The proposed classification model, used to distinguish the operating mode: Hard- and Soft-Switching, is presented and an analysis of the synchronized rectified step-down converter is done. With the aim of improving the accuracy and reducing the computational cost of the model, three different methods for dimensional reduction are applied to the input dataset of the model: self-organizing (...) maps, principal component analysis and correlation matrix. The obtained results show how the number of variable is highly reduced and the performance of the classification model is boosted: the results manifest an improve in the accuracy and efficiency of the classification. (shrink)

Several studies showed evidence supporting the possibility of hand trajectory decoding from low-frequency electroencephalography. However, the decoding in the source space via source localization is scarcely investigated. In this study, we tried to tackle the problem of collinearity due to the higher number of signals in the source space by two folds: first, we selected signals in predefined regions of interest ; second, we applied dimensionality reduction techniques to each ROI. The dimensionality reduction techniques were computing the mean, (...) principal component analysis, and locality preserving projections. We also investigated the effect of decoding between utilizing a template head model and a subject-specific head model during the source localization. The results indicated that applying source-space decoding with PCA yielded slightly higher correlations and signal-to-noise ratios than the sensor-space approach. We also observed slightly higher correlations and SNRs when applying the subject-specific head model than the template head model. However, the statistical tests revealed no significant differences between the source-space and sensor-space approaches and no significant differences between subject-specific and template head models. The decoder with Mean and PCA utilizes information mainly from precuneus and cuneus to decode the velocity kinematics similarly in the subject-specific and template head models. (shrink)

Due to the introduction of memristors, the memristor-based nonlinear oscillator circuits readily present the state initial-dependent multistability, i.e., coexisting multiple attractors. The dimensionality reduction modeling for a memristive circuit is carried out to realize accurate prediction, quantitative analysis, and physical control of its multistability, which has become one of the hottest research topics in the field of information science. Based on these considerations, this paper briefly reviews the specific multistability phenomenon generating from the memristive circuit in the voltage-current domain (...) and expounds the multistability control strategy. Then, this paper introduces the accurate flux-charge constitutive relation of memristors. Afterwards, the dimensionality reduction modeling method of the memristive circuits, i.e., the incremental flux-charge analysis method, is emphatically introduced, whose core idea is to implement the explicit expressions of the initial conditions in the flux-charge model and to discuss the feasibility and effectiveness of the multistability reconstitution of the memristive circuits using their flux-charge models. Furthermore, the incremental integral transformation method for modeling of the memristive system is reviewed by following the idea of the incremental flux-charge analysis method. The theory and application promotion of the dimensionality reduction modeling and multistability reconstitution are proceeded, and the application prospect is prospected by taking the synchronization application of the memristor-coupled system as an example. (shrink)

SC, CA, QA and QEA denote the classes of Pinter's substitution algebras, Tarski's cylindric algebras, Halmos' quasi-polyadic algebras and quasi-polyadic equality algebras, respectively. Let ω ≤ α < β and let K ∈ {SC,CA,QA,QEA}. We show that the class of α -dimensional neat reducts of algebras in Kβ is not elementary. This solves a problem in [3]. Also our result generalizes results proved in [2] and [3].

Dimensional analysis can offer us explanations by allowing us to answer What-if–things-had-been-different? questions rather than in virtue of, say, unifying diverse phenomena, important as that is. Additionally, it is argued that dimensional analysis is a form of modelling as it involves several of the aspects crucial in modelling, such as misrepresenting aspects of a target system. By highlighting the continuities dimensional analysis has with forms of modelling we are able to describe more precisely what makes dimensional (...) analysis explanatory and understand otherwise puzzling aspects of dimensional reasoning, such as introducing fictitious dimensions and excluding dimensionally relevant information to characterise some systems. Finally, thinking of dimensional arguments as a form of modelling allows an explication of the role abstraction and multiple realisability; not as compatibility with other possible worlds but as compatibility with different fictional descriptions of our own world. (shrink)

Modal logics, originally conceived in philosophy, have recently found many applications in computer science, artificial intelligence, the foundations of mathematics, linguistics and other disciplines. Celebrated for their good computational behaviour, modal logics are used as effective formalisms for talking about time, space, knowledge, beliefs, actions, obligations, provability, etc. However, the nice computational properties can drastically change if we combine some of these formalisms into a many-dimensional system, say, to reason about knowledge bases developing in time or moving objects. To (...) study the computational behaviour of many-dimensional modal logics is the main aim of this book. On the one hand, it is concerned with providing a solid mathematical foundation for this discipline, while on the other hand, it shows that many seemingly different applied many-dimensional systems (e.g., multi-agent systems, description logics with epistemic, temporal and dynamic operators, spatio-temporal logics, etc.) fit in perfectly with this theoretical framework, and so their computational behaviour can be analyzed using the developed machinery. We start with concrete examples of applied one- and many-dimensional modal logics such as temporal, epistemic, dynamic, description, spatial logics, and various combinations of these. Then we develop a mathematical theory for handling a spectrum of 'abstract' combinations of modal logics - fusions and products of modal logics, fragments of first-order modal and temporal logics - focusing on three major problems: decidability, axiomatizability, and computational complexity. Besides the standard methods of modal logic, the technical toolkit includes the method of quasimodels, mosaics, tilings, reductions to monadic second-order logic, algebraic logic techniques. Finally, we apply the developed machinery and obtained results to three case studies from the field of knowledge representation and reasoning: temporal epistemic logics for reasoning about multi-agent systems, modalized description logics for dynamic ontologies, and spatio-temporal logics. The genre of the book can be defined as a research monograph. It brings the reader to the front line of current research in the field by showing both recent achievements and directions of future investigations (in particular, multiple open problems). On the other hand, well-known results from modal and first-order logic are formulated without proofs and supplied with references to accessible sources. The intended audience of this book is logicians as well as those researchers who use logic in computer science and artificial intelligence. More specific application areas are, e.g., knowledge representation and reasoning, in particular, terminological, temporal and spatial reasoning, or reasoning about agents. And we also believe that researchers from certain other disciplines, say, temporal and spatial databases or geographical information systems, will benefit from this book as well. Key Features: Integrated approach to modern modal and temporal logics and their applications in artificial intelligence and computer science Written by internationally leading researchers in the field of pure and applied logic Combines mathematical theory of modal logic and applications in artificial intelligence and computer science Numerous open problems for further research Well illustrated with pictures and tables. (shrink)

Learning to recognize visual objects from examples requires the ability to find meaningful patterns in spaces of very high dimensionality. We present a method for dimensionality reduction which effectively biases the learning system by combining multiple constraints via the use of class labels. The use of extensive class labels steers the resulting lowdimensional representation to become invariant to those directions of variation in the input space that are irrelevant to classification; this is done merely by making class labels independent (...) of these directions. We also show that prior knowledge of the proper dimensionality of the target representation can be imposed by training a multi-layer bottleneck network. Computational experiments involving non-trivial categorization of parameterized fractal images and of human faces indicate that the low-dimensional representation extracted by our method leads to improved generalization in the learned tasks and is likely to preserve the topology of the original space. (shrink)

The reduction from Einstein's to Newton's gravitation theories (and intermediate steps) is used to exemplify reduction in physical theories. Both dimensionless and dimensional reduction are presented, and the advantages and disadvantages of each are pointed out. It is concluded that neither a completely reductionist nor a completely antireductionist view can be maintained. Only the mathematical structure is strictly reducible. The interpretation (the model, the central concepts) of the superseded theory T′ can at best only partially be (...) derived directly from the superseding theory T; it is severely constrained by the mathematical structure, and it can involve qualitatively different central terms that cannot be logically related between T and T′. (shrink)

In recent years, simultaneous localization and mapping based on stochastic state-transition / observation models and Bayesian estimation technique has been the mainstream of the mobile robot mapping research. In contrast to this trend, we present an alternative formulation of the map building problem from the viewpoint of non-linear dimensionality reduction or manifold learning. In this framework, the robot map building is interpreted as a problem of reconstructing the coordinates of objects so that proximities between them in the space of (...) robot's observation history as faithfully as possible. Based on this insight, we generalize the covisibility-based mapping method which was established in previous studies into the map building based on dimensionality reduction of historical visibility data. We applied latest non-linear dimensionality reduction techniques to this framework, and compared them with classical techniques such as PCA and MDS in experimental studies. (shrink)

High-dimensional data analysis has become the most challenging task nowadays. Dimensionality reduction plays an important role here. It focuses on data features, which have proved their impact on accuracy, execution time, and space requirement. In this study, a dimensionality reduction method is proposed based on the convolution of input features. The experiments are carried out on minimal preprocessed nine benchmark datasets. Results show that the proposed method gives an average 38% feature reduction in the original dimensions. (...) The algorithm accuracy is tested using the decision tree, support vector machine, and K-nearest neighbor classifiers and evaluated with the existing principal component analysis algorithm. The average increase in accuracy is 8.06 for DT, 5.80 for SVM, and 18.80 for the KNN algorithm. The most significant characteristic feature of the proposed model is that it reduces attributes, leading to less computation time without loss in classifier accuracy. (shrink)

Text document classification and clustering is an important learning task which fits to both data mining and machine learning areas. The learning task throws several challenges when it is required to process high dimensional text documents. Word distribution in text documents plays a very key role in learning process. Research related to high dimensional text document classification and clustering is usually limited to application of traditional distance functions and most of the research contributions in the existing literature did (...) not consider the word distribution in documents. In this research, we propose a novel similarity function for feature pattern clustering and high dimensional text classification. The similarity function proposed is used to carry supervised learning based dimensionality reduction. The important feature of this work is that the word distribution before and after dimensionality reduction is the same. Experiment results prove the proposed approach achieves dimensionality reduction, retains the word distribution and obtained better classification accuracies compared to other measures. (shrink)

This paper expounds the modern theory of symplectic reduction in finite-dimensional Hamiltonian mechanics. This theory generalizes the well-known connection between continuous symmetries and conserved quantities, i.e. Noether's theorem. It also illustrates one of mechanics' grand themes: exploiting a symmetry so as to reduce the number of variables needed to treat a problem. The exposition emphasises how the theory provides insights about the rotation group and the rigid body. The theory's device of quotienting a state space also casts light (...) on philosophical issues about whether two apparently distinct but utterly indiscernible possibilities should be ruled to be one and the same. These issues are illustrated using ``relationist'' mechanics. (shrink)

Since early 2020, the Covid-19 pandemic has affected our world in multiple ways. What we know and how we know it has shifted on a global scale. How we move throughout the world has been restricted and locked down. How we see one another has changed the cultural narrative in numerous countries throughout the world. As we seek to rid ourselves of the novel coronavirus infecting our everyday, three significant paradigm shifts have mutated our realities and imaginaries in which we (...) dwell. With millions dead or sickened by the evolving Covid-19 virus, we are a different world now than we were. As guest editors for this Special Issue, Visible Mutations of the Information Imaginary: Knowledge, Movement, and Cultural Discourse in the Wake of Covid-19, we pay tribute to the millions affected by these changes by offering this collection of scholarship as a critical path forward. We examine three primary areas in which life, law, and legality have mutated with results that demand our immediate attention. The first section of contributing articles, Knowledge, engages with the dissemination of knowledge and information as either fact or fiction in lexicons and media outlets throughout the world. The second section, Movement, focuses on aspects of motion and its restriction in terms of bodies, legislation, access, and the threat of viral contamination across borders and within communities. The third section, Cultural Discourse, considers the visibility of viral spread ranging from masks that cover the face to the separation of bodies through social distancing to the politicization of religion and vaccination. What once were normative cultural positionalities of space and politics have been volatized by institutionalized risk reduction and the confrontation of the unknown in the tenuous unforeseeable realm we now globally inhabit: L'idée se fait jour qu’il s’agit au moins autant d’une syndémie que d’une pandémie. Alors que la pandémie est une épidémie qui touche une partie importante de la population mondiale, une syndémie caractérise un entrelacement de maladie, de facteurs biologiques et environnementaux qui, par leur synergie, aggravent les conséquences de ces maladies sur la population. Ost F. We hope that this Special Issue helps to contribute as a vital source of critical engagement with the effects of the new pandemic lexicon and re-emerging, yet irrevocably mutated public and private spaces and relationships to each another. (shrink)

SC , CA , QA and QEA stand for the classes of Pinter's substitution algebras, Tarski's cylindric algebras, Halmos' quasipolyadic algebras, and quasipolyadic equality algebras of dimension , respectively. Generalizing a result of Németi on cylindric algebras, we show that for K {SC, CA, QA, QEA} and ordinals , the class Nr K of -dimensional neat reducts of -dimensional K algebras, though closed under taking homomorphic images and products, is not closed under forming subalgebras (i.e. is not a (...) variety) if and only if > 1.From this it easily follows that for 1 , the operation of forming -neat reducts of algebras in K does not commute with forming subalgebras, a notion to be made precise. (shrink)

Starting from the notions of q-entailment and p-entailment, a two-dimensional notion of entailment is developed with respect to certain generalized q-matrices referred to as B-matrices. After showing that every purely monotonic singleconclusion consequence relation is characterized by a class of B-matrices with respect to q-entailment as well as with respect to p-entailment, it is observed that, as a result, every such consequence relation has an inferentially four-valued characterization. Next, the canonical form of B-entailment, a two-dimensional multiple-conclusion notion of (...) entailment based on B-matrices, is introduced, providing a uniform framework for studying several different notions of entailment based on designation, antidesignation, and their complements. Moreover, the two-dimensional concept of a B-consequence relation is defined, and an abstract characterization of such relations by classes of B-matrices is obtained. Finally, a contribution to the study of inferential many-valuedness is made by generalizing Suszko’s Thesis and the corresponding reduction to show that any B-consequence relation is, in general, inferentially four-valued. (shrink)

We investigate the theory of finite observables, i.e., resolutions of the finite-dimensional identity by means of positive operators, that have a physical interpretation in terms of measurement schemes. We focus on extremal and rank-one observables and consider various constructions that reduce observables to simpler ones. However, these constructions do not suffice to generate all finite extremal observables, as we show by means of counter-examples.

SC, CA, QA and QEA denote the class of Pinter’s substitution algebras, Tarski’s cylindric algebras, Halmos’ quasi-polyadic and quasi-polyadic equality algebras, respectively. Let . and . We show that the class of n dimensional neat reducts of algebras in K m is not elementary. This solves a problem in [2]. Also our result generalizes results proved in [1] and [2].

Talk of ‘robustness’ remains vague, despite the fact that it is clearly an important parameter in evaluating models in general and game-theoretic results in particular. Here we want to make it a bit less vague by offering a graphic measure for a particular kind of robustness— ‘matrix robustness’— using a three dimensional display of the universe of 2 x 2 game theory. In a display of this form, familiar games such as the Prisoner’s Dilemma, Stag Hunt, Chicken and Deadlock (...) appear as volumes, making comparison easy regarding the extent of different game-theoretic effects. We illustrate such a comparison in robustness between the triumph of Tit for Tat in a spatialized environment (Grim 1995, Grim, Mar, and St. Denis 1998) and a spatialized modeling of the Contact Hypothesis regarding prejudice reduction (Grim, et. al 2005a, 2005b). The geometrical representation of relative robustness also offers a possibility for links between geometrical theorems and results regarding robustness in game theory. (shrink)

As a result of the complexity inherent in some natural systems, mathematical models employed in ecology are often governed by a large number of variables. For instance, in the study of population dynamics we often find multiregional models for structured populations in which individuals are classified regarding their age and their spatial location. Dealing with such structured populations leads to high dimensional models. Moreover, in many instances the dynamics of the system is controlled by processes whose time scales are (...) very different from each other. For example, in multiregional models migration is often a fast process in comparison to the growth of the population.Approximate reduction techniques take advantage of the presence of different time scales in a system to introduce approximations that allow one to transform the original system into a simpler low dimensional system. In this way, the dynamics of the original system can be approximated in terms of that of the reduced system. This work deals with the study of that approximation. In particular, we work with a non-autonomous discrete time model previously presented in the literature and obtain different bounds for the error we incur when we describe the dynamics of the original system in terms of the reduced one. (shrink)

This article presents a general conception of aesthetic experience built on an analysis of the relationship between the narrative and the ambient dimensions of the aesthetic value of a natural environment, the forest. First of all, the two dimensions are presented with respect to the possibilities and problems raised by distinguishing between them. Next, the possibilities of their relationship are analysed and it is argued that they are strongly complementary. This complementarity becomes the core of the proposed conception of aesthetic (...) experience, which can explain the difference between the aesthetic and the non-aesthetic, and can also provide an answer to the question of the non-reductive differentiation between the aesthetic experience of nature and the experience of a work of art. The conclusion of the article is mainly concerned to eliminate one of the problems localized in presenting the ambient dimension (the ambience paradox), by means of Ricoeur’s conception of the relationship between time and narrative. (shrink)

We study the complexity of the classification problem of conjugacy on dynamical systems on some compact metrizable spaces. Especially we prove that the conjugacy equivalence relation of interval dynamical systems is Borel bireducible to isomorphism equivalence relation of countable graphs. This solves a special case of Hjorth’s conjecture which states that every orbit equivalence relation induced by a continuous action of the group of all homeomorphisms of the closed unit interval is classifiable by countable structures. We also prove that conjugacy (...) equivalence relation of Hilbert cube homeomorphisms is Borel bireducible to the universal orbit equivalence relation. (shrink)

Arguments, claims, and discussions about the “level of description” of a theory are ubiquitous in cognitive science. Such talk is typically expressed more precisely in terms of the granularity of the theory, or in terms of Marr’s three levels. I argue that these ways of understanding levels of description are insufficient to capture the range of different types of theoretical commitments that one can have in cognitive science. When we understand these commitments as points in a multi-dimensional space, we (...) find that we must also reconsider our understanding of intertheoretic relations. In particular, we should understand cognitive theories as constraining one another, rather than reducing to one another. (shrink)

Accurate and rapid defect identification based on pulsed eddy current testing plays an important role in the structural integrity and health monitoring of in-service equipment in the renewable energy system. However, in conventional data-driven defect identification methods, the signal feature extraction is time consuming and requires expert experience. To avoid the difficulty of manual feature extraction and overcome the shortcomings of the classic deep convolutional network, such as large memory and high computational cost, an intelligent defect recognition pipeline based on (...) the general Warblet transform method and optimized two-dimensional DCNN is proposed. The GWT method is used to convert the one-dimensional PECT signal to a 2D grayscale image used as the input of 2D DCNN. A compound method is proposed to optimize the baseline VGG16, a well-known DCNN, from four aspects including reducing the input size, adding batch normalization layer after every convolutional layer and fully connection layer, simplifying the FCs, and removing unimportant filters in Convs so as to reduce memory and computational costs while improving accuracy. Through a pulsed eddy current testing experiment considering interference factors including liftoff and noise, the following conclusion can be obtained. The time-frequency representation obtained by the GWT method not only has excellent ability in terms of the transient component analysis but also is less affected by the reduction of image size; the proposed optimized DCNN can accurately identify defect types without manual feature extraction. And compared to the baseline VGG16, the accuracy obtained by the optimized DCNN is improved by 7%, to about 99.58%, and the memory and computational cost are reduced by 98%. Moreover, compared with other well-known DCNNs, such as GoogLeNet, Inception V3, ResNet50, and AlexNet, the optimized network has significant advantages in terms of accuracy and computational cost, too. (shrink)

An extension of the Hurwitz transformation to a canonical transformation between phase spaces allows conversion of the five-dimensional Kepler problem into that of a constrained harmonic oscillator problem in eight dimensions. Thus a new regularization of the Kepler problem is established. Then, following Dirac, we quantize the extended phase space, imposing constraint conditions as superselection rules. In that way the interchangeability of the reduction and the quantization procedures is proved.

Schoenflies point groups are presented in terms of spatial partitions and Laue classes based on abstract groups. A much simpler system using only a minimal set of generators for three dimensional groups is then presented in the same form. This simplified treatment allows group operations of a given Laue class to be correlated to a greatly simplified Mulliken-style notation for irreducible representations of that class. Transformation matrix representations of point groups in the simplified style can then be manipulated according (...) to their position in the class or to their sub-groups in very clear procedures. Simple rules can replace the large numbers of tables necessary in the Schoenflies approach. Some applications of the method are described. (shrink)

Following research initiated by Tarski, Craig and Nemeti, and futher pursued by Sain and others, we show that for certain subsets G of $^\omega \omega $ , atomic countable G poiyadic algebras are completely representable. G polyadic algebras are obtained by restricting the similarity type and axiomatization of ω-dimensional polyadic algebras to finite quantifiers and substitutions in G. This contrasts the cases of cylindric and relation algebras.

We first note that Gentzen's proof-reduction for his consistency proof of PA can be directly interpreted as moves of Kirby-Paris' Hydra Game, which implies a direct independence proof of the game . Buchholz's Hydra Game for labeled hydras is known to be much stronger than PA. However, we show that the one-dimensional version of Buchholz's Game can be exactly identified to Kirby-Paris' Game , by a simple and natural interpretation . Jervell proposed another type of a combinatorial game, (...) by abstracting Gentzen's proof-reductions and showed that his game is independent of PA. We show that this Jervell's game is actually much stronger than PA, by showing that the critical ordinal of Jervell's game is φω = ϵ0) in the Veblen hierarchy of ordinals. (shrink)

The past two decades have seen an explosion in the methods and directions of neuroscience research. Along with many others, complexity research has rapidly gained traction as both an independent research field and a valuable subdiscipline in computational neuroscience. In the past decade alone, several studies have suggested that psychiatric disorders affect the spatiotemporal complexity of both global and region-specific brain activity (Liu et al., 2013;Adhikari et al., 2017;Li et al., 2018). However, many of these studies have not accounted for (...) the distributed nature of cognition in either the global or regional complexity estimates, which may lead to erroneous interpretations of both global and region-specific entropy estimates. To alleviate this concern, we propose a novel method for estimating complexity. This method relies upon projecting dynamic functional connectivity into a low-dimensional space which captures the distributed nature of brain activity. Dimension-specific entropy may be estimated within this space, which in turn allows for a rapid estimate of global signal complexity. Testing this method on a recently acquired obsessive-compulsive disorder dataset reveals substantial increases in the complexity of both global and dimension-specific activity versus healthy controls, suggesting that obsessive-compulsive patients may experience increased disorder in cognition. To probe the potential causes of this alteration, we estimate subject-level effective connectivityviaa Hopf oscillator-based model dynamic model, the results of which suggest that obsessive-compulsive patients may experience abnormally high connectivity across a broad network in the cortex. These findings are broadly in line with results from previous studies, suggesting that this method is both robust and sensitive to group-level complexity alterations. (shrink)

We propose a novel type of low distortion radial embedding which focuses on one specific entity and its closest neighbors. Our embedding preserves near-exact distances to the focus entity and aims to minimize distortion between the other entities. We present an interactive exploration tool SolarView which places the focus entity at the center of a "solar system" and embeds its neighbors guided by concentric circles. SolarView provides an implementation of our novel embedding and several state-of-the-art dimensionality reduction and embedding (...) techniques, which we adapted to our setting in various ways. We experimentally evaluated our embedding and compared it to these state-of-the-art techniques. The results show that our embedding competes with these techniques and achieves low distortion in practice. Our method performs particularly well when the visualization, and hence the embedding, adheres to the solar system design principle of our application. Nonetheless - as with all dimensionality reduction techniques - the distortion may be high. We leverage interaction techniques to give clear visual cues that allow users to accurately judge distortion. We illustrate the use of SolarView by exploring the high-dimensional metric space of bibliographic entity similarities. (shrink)

Although there is a substantial philosophical literature on dynamical systems theory in the cognitive sciences, the same is not the case for neuroscience. This paper attempts to motivate increased discussion via a set of overlapping issues. The first aim is primarily historical and is to demonstrate that dynamical systems theory is currently experiencing a renaissance in neuroscience. Although dynamical concepts and methods are becoming increasingly popular in contemporary neuroscience, the general approach should not be viewed as something entirely new to (...) neuroscience. Instead, it is more appropriate to view the current developments as making central again approaches that facilitated some of neuroscience’s most significant early achievements, namely, the Hodgkin–Huxley and FitzHugh–Nagumo models. The second aim is primarily critical and defends a version of the “dynamical hypothesis” in neuroscience. Whereas the original version centered on defending a noncomputational and nonrepresentational account of cognition, the version I have in mind is broader and includes both cognition and the neural systems that realize it as well. In view of that, I discuss research on motor control as a paradigmatic example demonstrating that the concepts and methods of dynamical systems theory are increasingly and successfully being applied to neural systems in contemporary neuroscience. More significantly, such applications are motivating a stronger metaphysical claim, that is, understanding neural systems as being dynamical systems, which includes not requiring appeal to representations to explain or understand those phenomena. Taken together, the historical claim and the critical claim demonstrate that the dynamical hypothesis is undergoing a renaissance in contemporary neuroscience. (shrink)

Ataxia is a kind of external characteristics when the human body has poor coordination and balance disorder, it often indicates diseases in certain parts of the body. Many internal factors may causing ataxia; currently, observed external characteristics, combined with Doctor’s personal clinical experience play main roles in diagnosing ataxia. In this situation, different kinds of diseases may be confused, leading to the delay in treatment and recovery. Modern high precision medical instruments would provide better accuracy but the economic cost is (...) a non-negligible factor. In this paper, novel non-contact sensing technique is used to detect and distinguish sensory ataxia and cerebellar ataxia. Firstly, Romberg’s test and gait analysis data are collected by the microwave sensing platform; then, after some preprocessing, some machine learning approaches have been applied to train the models. For Romberg’s test, time domain features are considered, the accuracy of all the three algorithms are higher than 96%; for gait detection, Principal Component Analysis is used for dimensionality reduction, and the accuracies of Back Propagation neural Network, Support Vector Machine, and Random Forest are 97.8, 98.9, and 91.1%, respectively. (shrink)

According to one productive and influential approach to cognition, categorization, object recognition, and higher level cognitive processes operate on a set of fixed features, which are the output of lower level perceptual processes. In many situations, however, it is the higher level cognitive process being executed that influences the lower level features that are created. Rather than viewing the repertoire of features as being fixed by low-level processes, we present a theory in which people create features to subserve the representation (...) and categorization of objects. Two types of category learning should be distinguished. Fixed space category learning occurs when new categorizations are representable with the available feature set. Flexible space category learning occurs when new categorizations cannot be represented with the features available. Whether fixed or flexible, learning depends on the featural contrasts and similarities between the new category to be represented and the individual's existing concepts. Fixed feature approaches face one of two problems with tasks that call for new features: If the fixed features are fairly high level and directly useful for categorization, then they will not be flexible enough to represent all objects that might be relevant for a new task. If the fixed features are small, subsymbolic fragments (such as pixels), then regularities at the level of the functional features required to accomplish categorizations will not be captured by these primitives. We present evidence of flexible perceptual changes arising from category learning and theoretical arguments for the importance of this flexibility. We describe conditions that promote feature creation and argue against interpreting them in terms of fixed features. Finally, we discuss the implications of functional features for object categorization, conceptual development, chunking, constructive induction, and formal models of dimensionality reduction. Key Words: concept learning; conceptual development; features; perceptual learning; stimulus encoding. (shrink)

This paper presents an approach of unsupervised learning of clusters from a citation database, and applies it to a large corpus of articles in philosophy to give an account of the structure of the discipline. Following a list of journals from the PhilPapers-archive, 68,152 records were downloaded from the Reuters Web of Science-Database. Their citation data was processed using dimensionality reduction and clustering. The resulting clusters were identified, and the results are graphically represented. They suggest that the division of (...) analytic and Continental philosophy in the considered timespan is overstated; that analytical, in contrast to Continental philosophy does not form a coherent group in recent philosophy; and that metaphors about the disciplinary structure should focus on the coherence and interconnectedness of a multitude of smaller and larger subfields. (shrink)

Journal of the History of Biology provides a fifty-year long record for examining the evolution of the history of biology as a scholarly discipline. In this paper, we present a new dataset and preliminary quantitative analysis of the thematic content of JHB from the perspectives of geography, organisms, and thematic fields. The geographic diversity of authors whose work appears in JHB has increased steadily since 1968, but the geographic coverage of the content of JHB articles remains strongly lopsided toward the (...) United States, United Kingdom, and western Europe and has diversified much less dramatically over time. The taxonomic diversity of organisms discussed in JHB increased steadily between 1968 and the late 1990s but declined in later years, mirroring broader patterns of diversification previously reported in the biomedical research literature. Finally, we used a combination of topic modeling and nonlinear dimensionality reduction techniques to develop a model of multi-article fields within JHB. We found evidence for directional changes in the representation of fields on multiple scales. The diversity of JHB with regard to the representation of thematic fields has increased overall, with most of that diversification occurring in recent years. Drawing on the dataset generated in the course of this analysis, as well as web services in the emerging digital history and philosophy of science ecosystem, we have developed an interactive web platform for exploring the content of JHB, and we provide a brief overview of the platform in this article. As a whole, the data and analyses presented here provide a starting-place for further critical reflection on the evolution of the history of biology over the past half-century. (shrink)

On the surface, bi- and multilingualism would seem to be an ideal context for exploring questions of typological proximity. The obvious intuition is that the more closely related two languages are, the easier it should be to implement the two languages in one mind. This is the starting point adopted here, but we immediately run into the difficulty that the overwhelming majority of cognitive, computational, and linguistic research on bi- and multilingualism exhibits a monolingual bias (i.e., where monolingual grammars are (...) used as the standard of comparison for outputs from bilingual grammars). The primary questions so far have focused on how bilinguals balance and switch between their two languages, but our perspective on typology leads us to consider the nature of bi- and multi-lingual systems as a whole. Following an initial proposal from Hsin ( 2014 ), we conjecture that bilingual grammars are neither isolated, nor (completely) conjoined with one another in the bilingual mind, but rather exist as integrated source grammars that are further mitigated by a common, combined grammar (Cook, 2016 ; Goldrick et al., 2016a, b ; Putnam and Klosinski, 2017 ). Here we conceive such a combined grammar in a parallel, distributed, and gradient architecture implemented in a shared vector-space model that employs compression through routinization and dimensionality reduction. We discuss the emergence of such representations and their function in the minds of bilinguals. This architecture aims to be consistent with empirical results on bilingual cognition and memory representations in computational cognitive architectures. (shrink)

The Cartan equations defining simple spinors (renamed “pure” by C. Chevalley) are interpreted as equations of motion in compact momentum spaces, in a constructive approach in which at each step the dimensions of spinor space are doubled while those of momentum space increased by two. The construction is possible only in the frame of the geometry of simple or pure spinors, which imposes contraint equations on spinors with more than four components, and then momentum spaces result compact, isomorphic to invariant-mass-spheres (...) imbedded in each other, since the signatures result steadily Lorentzian; starting from dimension four (Minkowski) up to dimension ten with Clifford algebra ℂℓ(1, 9), where the construction naturally ends. The equations of motion met in the construction are most of those traditionally postulated ad hoc: from Weyl equations for neutrinos (and Maxwell's) to Majorana ones, to those for the electroweak model and for the nucleons interacting with the pseudoscalar pion, up to those for the 3 baryon-lepton families, steadily progressing from the description of lower energy phenomena to that of higher ones. The 3 division algebras: complex numbers, quaternions and octonions appear to be strictly correlated with Clifford algebras and then with this spinor-geometrical approach, from which they appear to gradually emerge in the construction, where they play a basic role for the physical interpretation: at the third step complex numbers generate U(1), possible origin of the electric charge and of the existence of charged—neutral fermion pairs, explaining also easily the opposite charges of proton-electron. Another U(1) appears to generate the strong charge at the fourth step. Quaternions generate the signature of space-time at the first step, the SU(2) internal symmetry of isospin and, in the gauge term, the SU(2) L one, of the electroweak model at the third step; they are also at the origin of 3 families; in number equal to that of quaternion imaginary units. At the fifth and last step octonions generate the SU(3) internal symmetry of flavour, with SU(2) isospin subgroup and, in the gauge term, the one of color, correlated with SU(2) L of the electroweak model. These 3 division algebras seem then to be at the origin of charges, families and of the groups of the Standard model. In this approach there seems to be no need of higher dimensional (>4) space-time, here generated by the four Poincaré translations, and dimensional reduction from ℂℓ(1,9) to ℂℓ(1,3) is equivalent to decoupling of the equations of motion. This spinor-geometrical approach is compatible with that based on strings, since these may be expressed bilinearly (as integrals) in terms of Majorana–Weyl simple or pure spinors which are admitted by ℂℓ(1, 9) = R(32). (shrink)

Cognitive theories based on a fixed feature set suffer from frame and symbol grounding problems. Flexible features and other empirically acquired constraints (e.g., analog-to-analog mappings) provide a framework for letting extrinsic relations influence symbol manipulation. By offering a biologically plausible basis for feature learning, nonorthogonal multiresolution analysis and dimensionality reduction, informed by functional constraints, may contribute to a solution to the symbol grounding problem.

The swarm intelligence algorithm simulates the behavior of animal populations in nature and is a new type of intelligent solution that is different from traditional artificial intelligence. Feature selection is a very common data dimensionality reduction method, which requires us to select the feature subset with the best evaluation criteria from the original feature set. Feature selection, as an effective data processing method, has become a hot research topic in the fields of machine learning, pattern recognition, and data mining (...) and has received extensive attention and attention. In order to verify the improvement effect of the feature selection algorithm based on the swarm intelligence algorithm on the data, this paper conducts experiments on six classes in the city’s first middle school with similar conditions. First, count the current situation of the students in the class, then divide them into classes, use different algorithms to teach them, and count the changes of the students after a period of teaching. The experiment found that the performance of students under the feature selection algorithm is about 30% higher than other teaching methods, and the awareness of cooperation between students reaches 0.8. It solves the contradiction between popularization and improvement and solves the problems of polarization and transformation of underachievers. The individuality of the algorithm has been fully utilized and developed. The test results show that the improved algorithm has faster convergence speed and higher solution accuracy, and the feature selection algorithm based on swarm intelligence algorithm can effectively improve the efficiency of the algorithm. (shrink)

In recent years, with the rapid development of computer storage capabilities and network transmission capabilities, users can easily share their own video and image information on social networking sites, and the amount of multimedia data on the network is rapidly increasing. With the continuous increase of the amount of data in the network, the establishment of effective automated data management methods and search methods has become an increasingly urgent need. This paper proposes a retrieval method of human motion data based (...) on motion capture in index space. By extracting key frames from the original motion to perform horizontal dimensionality reduction and defining features based on Laban motion analysis, the motion segment is subjected to vertical feature dimensionality reduction. After extracting features from the input motion segment, motion matching is performed on the index space. This paper designs the optimization method of the phased dynamic time deformation algorithm in time efficiency and analyzes the optimization method of the phased dynamic time deformation algorithm in time complexity. Considering the time efficiency redundancy, this paper optimizes the time complexity of the phased dynamic time deformation method. This improves the time efficiency of the staged dynamic time warping algorithm, making it suitable for larger-scale human motion data problems. Experiments show that the method in this paper has the advantage of speed, is more in line with the semantics of human motion, and can meet the retrieval requirements of human motion databases. (shrink)

General relativity cannot be formulated as a perturbatively renormalizable quantum field theory. An argument relying on the validity of the Bekenstein–Hawking entropy formula aims at dismissing gravity as non-renormalizable per se, against hopes that d-dimensional GR could turn out to have a non-perturbatively renormalizable d–dimensional quantum field theoretic formulation. In this note we discuss various forms of highly problematic semi-classical extrapolations assumed by both sides of the debate concerning what we call The Entropy Argument, and show that a (...) large class of dimensional reduction scenarios leads to the blow-up of Bekenstein–Hawking entropy. (shrink)

The analysis of the operation of tourism companies will provide valid information for the design of policies to reactivate the tourism industry, which has been strongly affected during the pandemic generated by COVID-19. The objective of this paper is to use soft computing techniques to analyse tourism companies in Ecuador. First of all, dimensionality reduction methods are applied: principal component analysis, isometric feature mapping and locally linear embedding, on data of tourism enterprises in Ecuador for the year 2015. In (...) addition, to verify the trend of operational variables, the data of tourism companies in Ecuador in 2019 and 2020 are analysed with dimensionality reduction methods that improve the interpretation by minimizing the loss of information. The data sets are analysed with k-means, k-medoids and Hierarchical Clustering, generating groups according to similar characteristics. The optimal number of clusters is determined with the following: Elbow Method, Silhouette Coefficient, Davies-Bouldin Index and Dunn Index. In addition, an analysis of the operation of tourism companies in the year 2020 concerning previous years is included. The study allows exploring Soft Computing techniques to identify important information for the definition of strategies that contribute to an effective reactivation of the tourist industry of Ecuador. (shrink)

We present a novel method, called graph sparse nonnegative matrix factorization, for dimensionality reduction. The affinity graph and sparse constraint are further taken into consideration in nonnegative matrix factorization and it is shown that the proposed matrix factorization method can respect the intrinsic graph structure and provide the sparse representation. Different from some existing traditional methods, the inertial neural network was developed, which can be used to optimize our proposed matrix factorization problem. By adopting one parameter in the neural (...) network, the global optimal solution can be searched. Finally, simulations on numerical examples and clustering in real-world data illustrate the effectiveness and performance of the proposed method. (shrink)

Applying machine learning algorithms to automatically infer relationships between concepts from large-scale collections of documents presents a unique opportunity to investigate at scale how human semantic knowledge is organized, how people use it to make fundamental judgments (“How similar are cats and bears?”), and how these judgments depend on the features that describe concepts (e.g., size, furriness). However, efforts to date have exhibited a substantial discrepancy between algorithm predictions and human empirical judgments. Here, we introduce a novel approach to generating (...) embeddings for this purpose motivated by the idea that semantic context plays a critical role in human judgment. We leverage this idea by constraining the topic or domain from which documents used for generating embeddings are drawn (e.g., referring to the natural world vs. transportation apparatus). Specifically, we trained state-of-the-art machine learning algorithms using contextually-constrained text corpora (domain-specific subsets of Wikipedia articles, 50+ million words each) and showed that this procedure greatly improved predictions of empirical similarity judgments and feature ratings of contextually relevant concepts. Furthermore, we describe a novel, computationally tractable method for improving predictions of contextually-unconstrained embedding models based on dimensionality reduction of their internal representation to a small number of contextually relevant semantic features. By improving the correspondence between predictions derived automatically by machine learning methods using vast amounts of data and more limited, but direct empirical measurements of human judgments, our approach may help leverage the availability of online corpora to better understand the structure of human semantic representations and how people make judgments based on those. (shrink)