Página 1 dos resultados de 29 itens digitais encontrados em 0.095 segundos

Zipf's law and criticality in multivariate data without fine-tuning

Schwab, David J.; Nemenman, Ilya; Mehta, Pankaj
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
55.48%
The joint probability distribution of many degrees of freedom in biological systems, such as firing patterns in neural networks or antibody sequence composition in zebrafish, often follow Zipf's law, where a power law is observed on a rank-frequency plot. This behavior has recently been shown to imply that these systems reside near to a unique critical point where the extensive parts of the entropy and energy are exactly equal. Here we show analytically, and via numerical simulations, that Zipf-like probability distributions arise naturally if there is an unobserved variable (or variables) that affects the system, e. g. for neural networks an input stimulus that causes individual neurons in the network to fire at time-varying rates. In statistics and machine learning, these models are called latent-variable or mixture models. Our model shows that no fine-tuning is required, i.e. Zipf's law arises generically without tuning parameters to a point, and gives insight into the ubiquity of Zipf's law in a wide range of systems.; Comment: 5 pages, 3 figures

Statistics of spikes trains, synaptic plasticity and Gibbs distributions

Cessac, B.; Rostro, H.; Vasquez, J. C.; Viéville, T.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 22/10/2008 Português
Relevância na Pesquisa
55.37%
We introduce a mathematical framework where the statistics of spikes trains, produced by neural networks evolving under synaptic plasticity, can be analysed.; Comment: 6 pages, 1 figure, proceeding of the NeuroComp 2008 conference

On the VC-dimension of neural networks with binary weights

Mertens, S.; Engel, A.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 29/08/1996 Português
Relevância na Pesquisa
55.43%
We investigate the VC-dimension of the perceptron and simple two-layer networks like the committee- and the parity-machine with weights restricted to values $\pm1$. For binary inputs, the VC-dimension is determined by atypical pattern sets, i.e. it cannot be found by replica analysis or numerical Monte Carlo sampling. For small systems, exhaustive enumerations yield exact results. For systems that are too large for enumerations, number theoretic arguments give lower bounds for the VC-dimension. For the Ising perceptron, the VC-dimension is probably larger than $N/2$.; Comment: 12 pages, LaTeX2e, 7 figures (eps)

Stochastic Neural Networks with the Weighted Hebb Rule

Marzban, Caren; Viswanathan, Raju
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 04/08/1993 Português
Relevância na Pesquisa
65.45%
Neural networks with synaptic weights constructed according to the weighted Hebb rule, a variant of the familiar Hebb rule, are studied in the presence of noise(finite temperature), when the number of stored patterns is finite and in the limit that the number of neurons $N\rightarrow \infty$. The fact that different patterns enter the synaptic rule with different weights changes the configuration of the free energy surface. For a general choice of weights not all of the patterns are stored as {\sl global} minima of the free energy function. However, as for the case of the usual Hebb rule, there exists a temperature range in which only the stored patterns are minima of the free energy. In particular, in the presence of a single extra pattern stored with an appropriate weight in the synaptic rule, the temperature at which the spurious minima of the free energy are eliminated is significantly lower than for a similar network without this extra pattern. The convergence time of the network, together with the overlaps of the equilibria of the network with the stored patterns, can thereby be improved considerably.; Comment: 14 pages, OKHEP 93-004

Memcomputing with membrane memcapacitive systems

Pershin, Yuriy V.; Traversa, Fabio L.; Di Ventra, Massimiliano
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
45.41%
We show theoretically that networks of membrane memcapacitive systems -- capacitors with memory made out of membrane materials -- can be used to perform a complete set of logic gates in a massively parallel way by simply changing the external input amplitudes, but not the topology of the network. This polymorphism is an important characteristic of memcomputing (computing with memories) that closely reproduces one of the main features of the brain. A practical realization of these membrane memcapacitive systems, using, e.g., graphene or other 2D materials, would be a step forward towards a solid-state realization of memcomputing with passive devices.

Nonlinear brain dynamics and many-body field dynamics

Freeman, Walter J.; Vitiello, Giuseppe
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 09/07/2005 Português
Relevância na Pesquisa
45.41%
We report measurements of the brain activity of subjects engaged in behavioral exchanges with their environments. We observe brain states which are characterized by coordinated oscillation of populations of neurons that are changing rapidly with the evolution of the meaningful relationship between the subject and its environment, established and maintained by active perception. Sequential spatial patterns of neural activity with high information content found in sensory cortices of trained animals between onsets of conditioned stimuli and conditioned responses resemble cinematographic frames. They are not readily amenable to description either with classical integrodifferential equations or with the matrix algebras of neural networks. Their modeling is provided by field theory from condensed matter physics.; Comment: 8 pages, Invited talk presented at Fr\"ohlich Centenary International Symposium "Coherence and Electromagnetic Fields in Biological Systems", July 1-4, 2005, Prague, Czech Republic

Simple universal models capture all spin physics

Cuevas, Gemma De las; Cubitt, Toby S.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 23/06/2014 Português
Relevância na Pesquisa
65.43%
Spin models are used in virtually every study of complex systems---be it condensed matter physics [1-4], neural networks [5] or economics [6,7]---as they exhibit very rich macroscopic behaviour despite their microscopic simplicity. It has long been known that by coarse-graining the system, the low energy physics of the models can be classified into different universality classes [8]. Here we establish a counterpart to this phenomenon: by "fine-graining" the system, we prove that all the physics of every classical spin model is exactly reproduced in the low energy sector of certain `universal models'. This means that (i) the low energy spectrum of the universal model is identical to the entire spectrum of the original model, (ii) the corresponding spin configurations are exactly reproduced, and (iii) the partition function is approximated to any desired precision. We prove necessary and sufficient conditions for a spin model to be universal, which show that complexity in the ground state alone is sufficient to reproduce full energy spectra. We use this to show that one of the simplest and most widely studied models, the 2D Ising model with fields, is universal.; Comment: 4 pages with 2 figures (main text) + 4 pages with 3 figures (supplementary info)

Generation of Explicit Knowledge from Empirical Data through Pruning of Trainable Neural Networks

Gorban, A. N.; Mirkes, Eu. M.; Tsaregorodtsev, V. G.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 03/07/2003 Português
Relevância na Pesquisa
55.41%
This paper presents a generalized technology of extraction of explicit knowledge from data. The main ideas are 1) maximal reduction of network complexity (not only removal of neurons or synapses, but removal all the unnecessary elements and signals and reduction of the complexity of elements), 2) using of adjustable and flexible pruning process (the pruning sequence shouldn't be predetermined - the user should have a possibility to prune network on his own way in order to achieve a desired network structure for the purpose of extraction of rules of desired type and form), and 3) extraction of rules not in predetermined but any desired form. Some considerations and notes about network architecture and training process and applicability of currently developed pruning techniques and rule extraction algorithms are discussed. This technology, being developed by us for more than 10 years, allowed us to create dozens of knowledge-based expert systems. In this paper we present a generalized three-step technology of extraction of explicit knowledge from empirical data.; Comment: 9 pages, The talk was given at the IJCNN '99 (Washington DC, July 1999)

Effects of Static and Dynamic Disorder on the Performance of Neural Automata

Torres, J. J.; Marro, J.; Garrido, P. L.; Cortes, J. M.; Ramos, F.; Munoz, M. A.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 09/12/2003 Português
Relevância na Pesquisa
45.41%
We report on both analytical and numerical results concerning stochastic Hopfield--like neural automata exhibiting the following (biologically inspired) features: (1) Neurons and synapses evolve in time as in contact with respective baths at different temperatures. (2) The connectivity between neurons may be tuned from full connection to high random dilution or to the case of networks with the small--world property and/or scale-free architecture. (3) There is synaptic kinetics simulating repeated scanning of the stored patterns. Though these features may apparently result in additional disorder, the model exhibits, for a wide range of parameter values, an extraordinary computational performance, and some of the qualitative behaviors observed in natural systems. In particular, we illustrate here very efficient and robust associative memory, and jumping between pattern attractors.; Comment: 7 pages. 3 figures

A topological approach to neural complexity

De Lucia, M.; Bottaccio, M.; Montuori, M.; Pietronero, L.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 04/11/2004 Português
Relevância na Pesquisa
45.43%
Considerable efforts in modern statistical physics is devoted to the study of networked systems. One of the most important example of them is the brain, which creates and continuously develops complex networks of correlated dynamics. An important quantity which captures fundamental aspects of brain network organization is the neural complexity C(X)introduced by Tononi et al. This work addresses the dependence of this measure on the topological features of a network in the case of gaussian stationary process. Both anlytical and numerical results show that the degree of complexity has a clear and simple meaning from a topological point of view. Moreover the analytical result offers a straightforward algorithm to compute the complexity than the standard one.; Comment: 6 pages, 4 figures

Teaching Memory Circuit Elements via Experiment-Based Learning

Pershin, Y. V.; Di Ventra, M.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 22/12/2011 Português
Relevância na Pesquisa
45.41%
The class of memory circuit elements which comprises memristive, memcapacitive, and meminductive systems, is gaining considerable attention in a broad range of disciplines. This is due to the enormous flexibility these elements provide in solving diverse problems in analog/neuromorphic and digital/quantum computation; the possibility to use them in an integrated computing-memory paradigm, massively-parallel solution of different optimization problems, learning, neural networks, etc. The time is therefore ripe to introduce these elements to the next generation of physicists and engineers with appropriate teaching tools that can be easily implemented in undergraduate teaching laboratories. In this paper, we suggest the use of easy-to-build emulators to provide a hands-on experience for the students to learn the fundamental properties and realize several applications of these memelements. We provide explicit examples of problems that could be tackled with these emulators that range in difficulty from the demonstration of the basic properties of memristive, memcapacitive, and meminductive systems to logic/computation and cross-bar memory. The emulators can be built from off-the-shelf components, with a total cost of a few tens of dollars...

Statistical mechanics of complex networks

Waclaw, B.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 27/04/2007 Português
Relevância na Pesquisa
55.45%
The science of complex networks is a new interdisciplinary branch of science which has arisen recently on the interface of physics, biology, social and computer sciences, and others. Its main goal is to discover general laws governing the creation and growth as well as processes taking place on networks, like e.g. the Internet, transportation or neural networks. It turned out that most real-world networks cannot be simply reduced to a compound of some individual components. Fortunately, the statistical mechanics, being one of pillars of modern physics, provides us with a very powerful set of tools and methods for describing and understanding these systems. In this thesis, we would like to present a consistent approach to complex networks based on statistical mechanics, with the central role played by the concept of statistical ensemble of networks. We show how to construct such a theory and present some practical problems where it can be applied. Among them, we pay attention to the problem of finite-size corrections and the dynamics of a simple model of mass transport on networks.; Comment: 78 pages, based on PhD thesis, see the Preface for more comments

Efficient Behavior of Small-World Networks

Latora, Vito; Marchiori, Massimo
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
55.46%
We introduce the concept of efficiency of a network, measuring how efficiently it exchanges information. By using this simple measure small-world networks are seen as systems that are both globally and locally efficient. This allows to give a clear physical meaning to the concept of small-world, and also to perform a precise quantitative a nalysis of both weighted and unweighted networks. We study neural networks and man-made communication and transportation systems and we show that the underlying general principle of their construction is in fact a small-world principle of high efficiency.; Comment: 1 figure, 2 tables. Revised version. Accepted for publication in Phys. Rev. Lett

Nonoptimal Component Placement, but Short Processing Paths, due to Long-Distance Projections in Neural Systems

Kaiser, Marcus; Hilgetag, Claus C.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 21/07/2006 Português
Relevância na Pesquisa
55.58%
It has been suggested that neural systems across several scales of organization show optimal component placement, in which any spatial rearrangement of the components would lead to an increase of total wiring. Using extensive connectivity datasets for diverse neural networks combined with spatial coordinates for network nodes, we applied an optimization algorithm to the network layouts, in order to search for wire-saving component rearrangements. We found that optimized component rearrangements could substantially reduce total wiring length in all tested neural networks. Specifically, total wiring among 95 primate (Macaque) cortical areas could be decreased by 32%, and wiring of neuronal networks in the nematode Caenorhabditis elegans could be reduced by 48% on the global level, and by 49% for neurons within frontal ganglia. Wiring length reductions were possible due to the existence of long-distance projections in neural networks. We explored the role of these projections by comparing the original networks with minimally rewired networks of the same size, which possessed only the shortest possible connections. In the minimally rewired networks, the number of processing steps along the shortest paths between components was significantly increased compared to the original networks. Additional benchmark comparisons also indicated that neural networks are more similar to network layouts that minimize the length of processing paths...

A matrix product algorithm for stochastic dynamics on locally tree-like graphs

Barthel, Thomas; De Bacco, Caterina; Franz, Silvio
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 13/08/2015 Português
Relevância na Pesquisa
45.43%
We describe and demonstrate an algorithm for the efficient simulation of generic stochastic dynamics of classical degrees of freedom defined on the vertices of a locally tree-like graph. Networks with cycles are treated in the framework of the cavity method. Such models correspond for example to spin-glass systems, Boolean networks, neural networks, or other technological, biological, and social networks. Building upon ideas from quantum many-body theory, the algorithm is based on a matrix product approximation of the so-called edge messages -- conditional probabilities of vertex variable trajectories. The matrix product edge messages (MPEM) are constructed recursively. Computation costs and precision can be tuned by controlling the matrix dimensions of the MPEM in truncations. In contrast to Monte Carlo simulations, the approach has a better error scaling and works for both, single instances as well as the thermodynamic limit. As we demonstrate at the example of Glauber dynamics, due to the absence of cancellation effects, observables with small expectation values can be evaluated reliably, allowing for the study of decay processes and temporal correlations.; Comment: 5 pages, 3 figures

Artificial Synaptic Arrays Intercoupled by Nanogranular Proton Conductors for Building Neuromorphic Systems

Wan, Changjin; Wu, Guodong; Guo, Liqiang; Zhu, Liqiang; Wan, Qing
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 10/01/2013 Português
Relevância na Pesquisa
55.48%
The highly parallel process in the neuron networks is mediated through a mass of synaptic interconnections. Mimicking single synapse behaviors and highly paralleled neural networks has become more and more fascinating and important. Here, oxide-based artificial synaptic arrays are fabricated on P-doped nanogranular SiO2-based proton conducting films at room temperature. Synaptic plasticity is demonstrated on individual artificial synapse. Most importantly, without any intentional hard-wired connection, such synaptic arrays are intercoupled due to the electric-field induced lateral proton modulation. The natural interconnection is weakly correlative with distance, and is important for neural networks. At last, paralleled summation is also mimicked, which provides a novel approach for building future brain-like computational systems.

Transition from regular to complex behaviour in a discrete deterministic asymmetric neural network model

Crisanti, A.; falcioni, M; Vulpiani, A.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 16/04/1993 Português
Relevância na Pesquisa
55.41%
We study the long time behaviour of the transient before the collapse on the periodic attractors of a discrete deterministic asymmetric neural networks model. The system has a finite number of possible states so it is not possible to use the term chaos in the usual sense of sensitive dependence on the initial condition. Nevertheless, at varying the asymmetry parameter, $k$, one observes a transition from ordered motion (i.e. short transients and short periods on the attractors) to a ``complex'' temporal behaviour. This transition takes place for the same value $k_{\rm c}$ at which one has a change for the mean transient length from a power law in the size of the system ($N$) to an exponential law in $N$. The ``complex'' behaviour during the transient shows strong analogies with the chaotic behaviour: decay of temporal correlations, positive Shannon entropy, non-constant Renyi entropies of different orders. Moreover the transition is very similar to that one for the intermittent transition in chaotic systems: scaling law for the Shannon entropy and strong fluctuations of the ``effective Shannon entropy'' along the transient, for $k > k_{\rm c}$.; Comment: 18 pages + 6 figures, TeX dialect: Plain TeX + IOP macros (included)

Towards a feasible implementation of quantum neural networks using quantum dots

Altaisky, M. V.; Zolnikova, N. N.; Kaputkina, N. E.; Krylov, V. A.; Lozovik, Yu. E.; Dattani, N. S.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
65.5%
We propose an implementation of quantum neural networks using an array of quantum dots with dipole-dipole interactions. We demonstrate that this implementation is both feasible and versatile by studying it within the framework of GaAs based quantum dot qubits coupled to a reservoir of acoustic phonons; a system whose decoherence properties have been experimentally and theoretically characterized with meticulous detail, and is considered one of the most accurately understood open quantum systems. Using numerically exact Feynman integral calculations, we have found that the quantum coherence in our neural networks survive for over a hundred ps even at liquid nitrogen temperatures (77 K), which is three orders of magnitude higher than current implementations which are based on SQUID-based systems operating at temperatures in the mK range. Furthermore, the previous quantum dot based proposals required control via manipulating the phonon bath, which is extremely difficult in real experiments. An advantage of our implementation is that it can be easily controlled, since dipole-dipole interaction strengths can be changed via the spacing between the dots and by applying external fields.; Comment: revtex, 4 pages, 2 eps figures

Emergence and Frustration of Magnetic Order with Variable-Range Interactions in a Trapped Ion Quantum Simulator

Islam, R.; Senko, C.; Campbell, W. C.; Korenblit, S.; Smith, J.; Lee, A.; Edwards, E. E.; Wang, C. -C. J.; Freericks, J. K.; Monroe, C.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 29/09/2012 Português
Relevância na Pesquisa
65.42%
Frustration, or the competition between interacting components of a network, is often responsible for the complexity of many body systems, from social and neural networks to protein folding and magnetism. In quantum magnetic systems, frustration arises naturally from competing spin-spin interactions given by the geometry of the spin lattice or by the presence of long-range antiferromagnetic couplings. Frustrated magnetism is a hallmark of poorly understood systems such as quantum spin liquids, spin glasses and spin ices, whose ground states are massively degenerate and can carry high degrees of quantum entanglement. The controlled study of frustrated magnetism in materials is hampered by short dynamical time scales and the presence of impurities, while numerical modeling is generally intractable when dealing with dynamics beyond N~30 particles. Alternatively, a quantum simulator can be exploited to directly engineer prescribed frustrated interactions between controlled quantum systems, and several small-scale experiments have moved in this direction. In this article, we perform a quantum simulation of a long-range antiferromagnetic quantum Ising model with a transverse field, on a crystal of up to N = 16 trapped Yb+ atoms. We directly control the amount of frustration by continuously tuning the range of interaction and directly measure spin correlation functions and their dynamics through spatially-resolved spin detection. We find a pronounced dependence of the magnetic order on the amount of frustration...

Chiral boundary conditions for Quantum Hall systems

Akkermans, E.; Narevich, R.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 29/09/1997 Português
Relevância na Pesquisa
65.37%
A quantum mesoscopic billiard can be viewed as a bounded electronic system due to some external confining potential. Since, in general, we do not have access to the exact expression of this potential, it is usually replaced by a set of boundary conditions. We discuss, in addition to the standard Dirichlet choice, the other possibilities of boundary conditions which might correspond to more complicated physical situations including the effects of many body interactions or of a strong magnetic field. The latter case is examined more in details using a new kind of chiral boundary conditions for which it is shown that in the Quantum Hall regime, bulk and edge characteristics can be described in a unified way.; Comment: 16 pages, LaTeX, 2 figures, to be published in the Proceedings of the Minerva workshop on Mesoscopics, Fractals and Neural Networks, Phil. Mag. (1997)