nils-herrmann/clean_scirepeval huggingface dataset:
VC Dimension of an Integrate-and-Fire Neuron Model

We compute the VC dimension of a leaky integrate-and-fire neuron model. The VC dimension quantifies the ability of a function class to partition an input pattern space, and can be considered a measure of computational capacity. In this case, the function class is the class of integrate-and-fire models generated by varying the integration time constant T and the threshold , the input space they partition is the space of continuous-time signals, and the binary partition is specified by whether or not the model reaches threshold at some specified time. We show that the VC dimension diverges only logarithmically with the input signal bandwidth N. We also extend this approach to arbitrary passive dendritic trees. The main contributions of this work are (1) it offers a novel treatment of computational capacity of this class of dynamic system; and (2) it provides a framework for analyzing the computational capabilities of the dynamic systems defined by networks of spiking neurons.
Garbage collection with pointers to individuals cells

In the heap model in which garbage collectors usually operate, the heap is an array of cells. Each cell contains 
either a non-pointer, to be ignored, or a pointer to a block of cells somewhere in the heap, called an object. The 
objects do not overlap. In addition, there are a bunch of cells not in the heap, called the root set. It is possible to 
determine from a cell whether it contains a pointer or not, and it is possible to determine from a pointer how long 
the object pointed to is.
A Context-Sensitive Generalization of ICA

Source separation arises in a surprising number of signal processing applications, from speech 
recognition to EEG analysis. In the square linear blind source separation problem without time delays, 
one must find an unmixing matrix which can detangle the result of mixing n unknown independent sources 
through an unknown n x n mixing matrix. The recently introduced ICA blind source separation algorithm 
(Baram and Roth 1994; Bell and Sejnowski 1995) is a powerful and surprisingly simple technique for solving 
this problem. ICA is all the more remarkable for performing so well despite making absolutely no use of the 
temporal structure of its input! This paper presents a new algorithm, contextual ICA, which derives from a 
maximum likelihood density estimation formulation of the problem. cICA can incorporate arbitrarily complex 
adaptive history-sensitive source models, and thereby make use of the temporal structure of its input. 
This allows it to separate in a number of situations where standard ICA cannot, including sources with low 
kurtosis, colored gaussian sources, and sources which have gaussian histograms. Since ICA is a special case 
of cICA, the MLE derivation provides as a corollary a rigorous derivation of classic ICA.
Doing the Twist: Diagonal Meshes Are Isomorphic to Twisted Toroidal Meshes

We show that a k/spl times/n diagonal mesh is isomorphic to a (n+k)/2/spl times/(n+k)/2-(n-k)/2/spl times/(n-k)/2 twisted toroidal mesh, i.e., a network similar to a standard (n+k)/2/spl times/(n+k)/2 toroidal mesh, but with opposite handed twists of (n-k)/2 in the two directions, which results in a loss of ((n-k)/2)/sup 2/ nodes.
Gradient calculations for dynamic recurrent neural networks: a survey

Surveys learning algorithms for recurrent neural networks with hidden units and puts the various techniques into a common framework. The authors discuss fixed point learning algorithms, namely recurrent backpropagation and deterministic Boltzmann machines, and nonfixed point algorithms, namely backpropagation through time, Elman's history cutoff, and Jordan's output feedback architecture. Forward propagation, an on-line technique that uses adjoint equations, and variations thereof, are also discussed. In many cases, the unified presentation leads to generalizations of various sorts. The author discusses advantages and disadvantages of temporally continuous neural networks in contrast to clocked ones continues with some "tricks of the trade" for training, using, and simulating continuous time and recurrent neural networks. The author presents some simulations, and at the end, addresses issues of computational complexity and learning speed.
Time-Skew Hebb Rule in a Nonisopotential Neuron

In an isopotential neuron with rapid response, it has been shown that the receptive fields formed by Hebbian synaptic modulation depend on the principal eigenspace of Q(0), the input autocorrelation matrix, where Qij() = i() j(t T) and i(t) is the input to synapse i at time t (Oja 1982). We relax the assumption of isopotentiality, introduce a time-skewed Hebb rule, and find that the dynamics of synaptic evolution are determined by the principal eigenspace of . This matrix is defined by , where Kij() is the neuron's voltage response to a unit current injection at synapse j as measured seconds later at synapse i, and i() is the time course of the opportunity for modulation of synapse i following the arrival of a presynaptic action potential.
Relating egomotion and image evolution

By considering the dynamics of the apparent motion of a stationary object relative to a 
moving observer, we construct a partial differential equation that relates the changes 
in an image to the motion of the observer. These come in two varieties: a first order 
system that describes the coevolution of the egocentric radial distances to objects 
and the visual scene, and a second order system that does not involve any distances 
or other geometry. The later equation leads, via the calculus of variations, to a novel 
technique for recovering egomotion from image sequences, a so-called visual yaw 
detector, which is tested on real data. For expository purposes the derivation is 
carried out in two dimensions, but the approach extends immediately to three.
Independent Component Analysis

Given a set of M signal mixtures (x 1 ;x 2 ;:::;x M ) (e.g. microphone out- puts), each of which is a dierent mixture of a set of M statistically independent source signals (s 1 ;s 2 ;:::;s M ) (e.g. voices), independent component analysis (ICA) recovers the source signals (voices) from the signal mixtures. ICA is based on the assumptions that source signals are statistically independent and that they have non-Gaussian dis- tributions. Dierent physical processes usually generate statistically independent and non-Gaussian signals, so that, in the process of extracting such signals from a set of signal mixtures, ICA eectively recovers the underlying physical causes for a given set of measured signal mixtures.
Methods for Blind Source Separation

Independent component analysis (ICA) is becoming an increasingly important tool for analyzing large data sets. In essence, ICA separates an observed set of signal mixtures into a set of statistically independent component signals, or source signals. In so doing, this powerful method can extract the relatively small amount of useful information typically found in large data sets. The applications for ICA range from speech processing, brain imaging, and electrical brain signals to telecommunications and stock predictions.In Independent Component Analysis, Jim Stone presents the essentials of ICA and related techniques (projection pursuit and complexity pursuit) in a tutorial style, using intuitive examples described in simple geometric terms. The treatment fills the need for a basic primer on ICA that can be used by readers of varying levels of mathematical sophistication, including engineers, cognitive scientists, and neuroscientists who need to know the essentials of this evolving method.An overview establishes the strategy implicit in ICA in terms of its essentially physical underpinnings and describes how ICA is based on the key observations that different physical processes generate outputs that are statistically independent of each other. The book then describes what Stone calls "the mathematical nuts and bolts" of how ICA works. Presenting only essential mathematical proofs, Stone guides the reader through an exploration of the fundamental characteristics of ICA.Topics covered include the geometry of mixing and unmixing; methods for blind source separation; and applications of ICA, including voice mixtures, EEG, fMRI, and fetal heart monitoring. The appendixes provide a vector matrix tutorial, plus basic demonstration computer code that allows the reader to see how each mathematical method described in the text translates into working Matlab computer code.
Independent Component Analysis: A Tutorial Introduction

Independent component analysis (ICA) is becoming an increasingly important tool for analyzing large data sets. In essence, ICA separates an observed set of signal mixtures into a set of statistically independent component signals, or source signals. In so doing, this powerful method can extract the relatively small amount of useful information typically found in large data sets. The applications for ICA range from speech processing, brain imaging, and electrical brain signals to telecommunications and stock predictions. In Independent Component Analysis, Jim Stone presents the essentials of ICA and related techniques (projection pursuit and complexity pursuit) in a tutorial style, using intuitive examples described in simple geometric terms. The treatment fills the need for a basic primer on ICA that can be used by readers of varying levels of mathematical sophistication, including engineers, cognitive scientists, and neuroscientists who need to know the essentials of this evolving method. An overview establishes the strategy implicit in ICA in terms of its essentially physical underpinnings and describes how ICA is based on the key observations that different physical processes generate outputs that are statistically independent of each other. The book then describes what Stone calls "the mathematical nuts and bolts" of how ICA works. Presenting only essential mathematical proofs, Stone guides the reader through an exploration of the fundamental characteristics of ICA. Topics covered include the geometry of mixing and unmixing; methods for blind source separation; and applications of ICA, including voice mixtures, EEG, fMRI, and fetal heart monitoring. The appendixes provide a vector matrix tutorial, plus basic demonstration computer code that allows the reader to see how each mathematical method described in the text translates into working Matlab computer code.
Projection Pursuit Gradient Ascent

Independent component analysis (ICA) is becoming an increasingly important tool for analyzing large data sets. In essence, ICA separates an observed set of signal mixtures into a set of statistically independent component signals, or source signals. In so doing, this powerful method can extract the relatively small amount of useful information typically found in large data sets. The applications for ICA range from speech processing, brain imaging, and electrical brain signals to telecommunications and stock predictions.In Independent Component Analysis, Jim Stone presents the essentials of ICA and related techniques (projection pursuit and complexity pursuit) in a tutorial style, using intuitive examples described in simple geometric terms. The treatment fills the need for a basic primer on ICA that can be used by readers of varying levels of mathematical sophistication, including engineers, cognitive scientists, and neuroscientists who need to know the essentials of this evolving method.An overview establishes the strategy implicit in ICA in terms of its essentially physical underpinnings and describes how ICA is based on the key observations that different physical processes generate outputs that are statistically independent of each other. The book then describes what Stone calls "the mathematical nuts and bolts" of how ICA works. Presenting only essential mathematical proofs, Stone guides the reader through an exploration of the fundamental characteristics of ICA.Topics covered include the geometry of mixing and unmixing; methods for blind source separation; and applications of ICA, including voice mixtures, EEG, fMRI, and fetal heart monitoring. The appendixes provide a vector matrix tutorial, plus basic demonstration computer code that allows the reader to see how each mathematical method described in the text translates into working Matlab computer code.
Recurrent cerebellar architecture solves the motor-error problem

Current views of cerebellar function have been heavily influenced by the models of Marr and Albus, who suggested that the climbing fibre input to the cerebellum acts as a teaching signal for motor learning. It is commonly assumed that this teaching signal must be motor error (the difference between actual and correct motor command), but this approach requires complex neural structures to estimate unobservable motor error from its observed sensory consequences. We have proposed elsewhere a recurrent decorrelation control architecture in which Marr–Albus models learn without requiring motor error. Here, we prove convergence for this architecture and demonstrate important advantages for the modular control of systems with multiple degrees of freedom. These results are illustrated by modelling adaptive plant compensation for the three–dimensional vestibular ocular reflex. This provides a functional role for recurrent cerebellar connectivity, which may be a generic anatomical feature of projections between regions of cerebral and cerebellar cortex.
Projection Pursuit: Stepwise Separation of Sources

Independent component analysis (ICA) is becoming an increasingly important tool for analyzing large data sets. In essence, ICA separates an observed set of signal mixtures into a set of statistically independent component signals, or source signals. In so doing, this powerful method can extract the relatively small amount of useful information typically found in large data sets. The applications for ICA range from speech processing, brain imaging, and electrical brain signals to telecommunications and stock predictions.In Independent Component Analysis, Jim Stone presents the essentials of ICA and related techniques (projection pursuit and complexity pursuit) in a tutorial style, using intuitive examples described in simple geometric terms. The treatment fills the need for a basic primer on ICA that can be used by readers of varying levels of mathematical sophistication, including engineers, cognitive scientists, and neuroscientists who need to know the essentials of this evolving method.An overview establishes the strategy implicit in ICA in terms of its essentially physical underpinnings and describes how ICA is based on the key observations that different physical processes generate outputs that are statistically independent of each other. The book then describes what Stone calls "the mathematical nuts and bolts" of how ICA works. Presenting only essential mathematical proofs, Stone guides the reader through an exploration of the fundamental characteristics of ICA.Topics covered include the geometry of mixing and unmixing; methods for blind source separation; and applications of ICA, including voice mixtures, EEG, fMRI, and fetal heart monitoring. The appendixes provide a vector matrix tutorial, plus basic demonstration computer code that allows the reader to see how each mathematical method described in the text translates into working Matlab computer code.
Independent Component Analysis and Blind Source Separation

Independent component analysis (ICA) is becoming an increasingly important tool for analyzing large data sets. In essence, ICA separates an observed set of signal mixtures into a set of statistically independent component signals, or source signals. In so doing, this powerful method can extract the relatively small amount of useful information typically found in large data sets. The applications for ICA range from speech processing, brain imaging, and electrical brain signals to telecommunications and stock predictions.In Independent Component Analysis, Jim Stone presents the essentials of ICA and related techniques (projection pursuit and complexity pursuit) in a tutorial style, using intuitive examples described in simple geometric terms. The treatment fills the need for a basic primer on ICA that can be used by readers of varying levels of mathematical sophistication, including engineers, cognitive scientists, and neuroscientists who need to know the essentials of this evolving method.An overview establishes the strategy implicit in ICA in terms of its essentially physical underpinnings and describes how ICA is based on the key observations that different physical processes generate outputs that are statistically independent of each other. The book then describes what Stone calls "the mathematical nuts and bolts" of how ICA works. Presenting only essential mathematical proofs, Stone guides the reader through an exploration of the fundamental characteristics of ICA.Topics covered include the geometry of mixing and unmixing; methods for blind source separation; and applications of ICA, including voice mixtures, EEG, fMRI, and fetal heart monitoring. The appendixes provide a vector matrix tutorial, plus basic demonstration computer code that allows the reader to see how each mathematical method described in the text translates into working Matlab computer code.
Complexity Pursuit Gradient Ascent

Independent component analysis (ICA) is becoming an increasingly important tool for analyzing large data sets. In essence, ICA separates an observed set of signal mixtures into a set of statistically independent component signals, or source signals. In so doing, this powerful method can extract the relatively small amount of useful information typically found in large data sets. The applications for ICA range from speech processing, brain imaging, and electrical brain signals to telecommunications and stock predictions.In Independent Component Analysis, Jim Stone presents the essentials of ICA and related techniques (projection pursuit and complexity pursuit) in a tutorial style, using intuitive examples described in simple geometric terms. The treatment fills the need for a basic primer on ICA that can be used by readers of varying levels of mathematical sophistication, including engineers, cognitive scientists, and neuroscientists who need to know the essentials of this evolving method.An overview establishes the strategy implicit in ICA in terms of its essentially physical underpinnings and describes how ICA is based on the key observations that different physical processes generate outputs that are statistically independent of each other. The book then describes what Stone calls "the mathematical nuts and bolts" of how ICA works. Presenting only essential mathematical proofs, Stone guides the reader through an exploration of the fundamental characteristics of ICA.Topics covered include the geometry of mixing and unmixing; methods for blind source separation; and applications of ICA, including voice mixtures, EEG, fMRI, and fetal heart monitoring. The appendixes provide a vector matrix tutorial, plus basic demonstration computer code that allows the reader to see how each mathematical method described in the text translates into working Matlab computer code.
Decorrelation control by the cerebellum achieves oculomotor plant compensation in simulated vestibulo-ocular reflex

We introduce decorrelation control as a candidate algorithm for the cerebellar microcircuit and demonstrate its utility for oculomotor plant compensation in a linear model of the vestibulo–ocular reflex (VOR). Using an adaptive–filter representation of cerebellar cortex and an anti–Hebbian learning rule, the algorithm learnt to compensate for the oculomotor plant by minimizing correlations between a predictor variable (eye–movement command) and a target variable (retinal slip), without requiring a motor–error signal. Because it also provides an estimate of the unpredicted component of the target variable, decorrelation control can simplify both motor coordination and sensory acquisition. It thus unifies motor and sensory cerebellar functions.
Spatiotemporal Independent Component Analysis of Event-Related fMRI Data Using Skewed Probability Density Functions

We introduce two independent component analysis (ICA) methods, spatiotemporal ICA (stICA) and skew-ICA, and demonstrate the utility of these methods in analyzing synthetic and event-related fMRI data. First, stICA simultaneously maximizes statistical independence over both time and space. This contrasts with conventional ICA methods, which maximize independence either over time only or over space only; these methods often yield physically improbable solutions. Second, skew-ICA is based on the assumption that images have skewed probability density functions (pdfs), an assumption consistent with spatially localized regions of activity. In contrast, conventional ICA is based on the physiologically unrealistic assumption that images have symmetric pdfs. We combine stICA and skew-ICA, to form skew-stICA, and use it to analyze synthetic data and data from an event-related, left-right visual hemifield fMRI experiment. Results obtained with skew-stICA are superior to those of principal component analysis, spatial ICA (sICA), temporal ICA, stICA, and skew-sICA. We argue that skew-stICA works because it is based on physically realistic assumptions and that the potential of ICA can only be realized if such prior knowledge is incorporated into ICA methods.
Blind Source Separation Using Temporal Predictability

A measure of temporal predictability is defined and used to separate linear mixtures of signals. Given any set of statistically independent source signals, it is conjectured here that a linear mixture of those signals has the following property: the temporal predictability of any signal mixture is less than (or equal to) that of any of its component source signals. It is shown that this property can be used to recover source signals from a set of linear mixtures of those signals by finding an un-mixing matrix that maximizes a measure of temporal predictability for each recovered signal. This matrix is obtained as the solution to a generalized eigenvalue problem; such problems have scaling characteristics of O (N3), where N is the number of signal mixtures. In contrast to independent component analysis, the temporal predictability method requires minimal assumptions regarding the probability density functions of source signals. It is demonstrated that the method can separate signal mixtures in which each mixture is a linear combination of source signals with supergaussian, sub-gaussian, and gaussian probability density functions and on mixtures of voices and music.
When is now? Perception of simultaneity

We address the following question: Is there a difference (D) between the amount of time for auditory and visual stimuli to be perceived? On each of 1000 trials, observers were presented with a light–sound pair, separated by a stimulus onset asynchrony (SOA) between–250 ms (sound first) and 250 ms. Observers indicated if the light–sound pair came on simultaneously by pressing one of two (yes or no) keys. The SOA most likely to yield affirmative responses was defined as the point of subjective simultaneity (PSS). PSS values were between–21 ms (i.e. sound 21ms before light) and 150 ms. Evidence is presented that each PSS is observer specific. In a second experiment, each observer was tested using two observerstimulus distances. The resultant PSS values are highly correlated (r = 0.954, p = 0.003) suggesting that each observer's PSS is stable. PSS values were significantly affected by observer–stimulus distance, suggesting that observers do not take account of changes in distance on the resultant difference in arrival times of light and sound. The difference RTd in simple reaction time to single visual and auditory stimuli was also estimated; no evidence that RTd is observer specific or stable was found. The implications of these findings for the perception of multisensory stimuli are discussed.