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

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

55.48%

#Quantitative Biology - Neurons and Cognition#Condensed Matter - Statistical Mechanics#Quantitative Biology - Quantitative Methods

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

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## Statistics of spikes trains, synaptic plasticity and Gibbs distributions

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 22/10/2008
Português

Relevância na Pesquisa

55.37%

#Nonlinear Sciences - Adaptation and Self-Organizing Systems#Condensed Matter - Statistical Mechanics#Mathematical Physics#Nonlinear Sciences - Chaotic Dynamics#Quantitative Biology - Neurons and Cognition

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

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## On the VC-dimension of neural networks with binary weights

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)

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## Stochastic Neural Networks with the Weighted Hebb Rule

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

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## Memcomputing with membrane memcapacitive systems

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

45.41%

#Computer Science - Emerging Technologies#Condensed Matter - Mesoscale and Nanoscale Physics#Computer Science - Neural and Evolutionary Computing

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.

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## Nonlinear brain dynamics and many-body field dynamics

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

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## Simple universal models capture all spin physics

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)

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

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 03/07/2003
Português

Relevância na Pesquisa

55.41%

#Condensed Matter#Computer Science - Neural and Evolutionary Computing#Physics - Data Analysis, Statistics and Probability

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)

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

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

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## A topological approach to neural complexity

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 04/11/2004
Português

Relevância na Pesquisa

45.43%

#Nonlinear Sciences - Adaptation and Self-Organizing Systems#Condensed Matter - Statistical Mechanics#Quantitative Biology - Neurons and Cognition

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

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## Teaching Memory Circuit Elements via Experiment-Based Learning

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 22/12/2011
Português

Relevância na Pesquisa

45.41%

#Physics - Instrumentation and Detectors#Condensed Matter - Mesoscale and Nanoscale Physics#Computer Science - Emerging Technologies

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...

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## Statistical mechanics of complex networks

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

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## Efficient Behavior of Small-World Networks

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

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

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...

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

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

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

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.

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

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)

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## Towards a feasible implementation of quantum neural networks using quantum dots

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

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

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...

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## Chiral boundary conditions for Quantum Hall systems

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)

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