475 research outputs found
Order-Parameter Flow in the SK Spin-Glass II: Inclusion of Microscopic Memory Effects
We develop further a recent dynamical replica theory to describe the dynamics
of the Sherrington-Kirkpatrick spin-glass in terms of closed evolution
equations for macroscopic order parameters. We show how microscopic memory
effects can be included in the formalism through the introduction of a dynamic
order parameter function: the joint spin-field distribution. The resulting
formalism describes very accurately the relaxation phenomena observed in
numerical simulations, including the typical overall slowing down of the flow
that was missed by the previous simple two-parameter theory. The advanced
dynamical replica theory is either exact or a very good approximation.Comment: same as original, but this one is TeXabl
Finite Size Effects in Separable Recurrent Neural Networks
We perform a systematic analytical study of finite size effects in separable
recurrent neural network models with sequential dynamics, away from saturation.
We find two types of finite size effects: thermal fluctuations, and
disorder-induced `frozen' corrections to the mean-field laws. The finite size
effects are described by equations that correspond to a time-dependent
Ornstein-Uhlenbeck process. We show how the theory can be used to understand
and quantify various finite size phenomena in recurrent neural networks, with
and without detailed balance.Comment: 24 pages LaTex, with 4 postscript figures include
Dynamical Replica Theory for Disordered Spin Systems
We present a new method to solve the dynamics of disordered spin systems on
finite time-scales. It involves a closed driven diffusion equation for the
joint spin-field distribution, with time-dependent coefficients described by a
dynamical replica theory which, in the case of detailed balance, incorporates
equilibrium replica theory as a stationary state. The theory is exact in
various limits. We apply our theory to both the symmetric- and the
non-symmetric Sherrington-Kirkpatrick spin-glass, and show that it describes
the (numerical) experiments very well.Comment: 7 pages RevTex, 4 figures, for PR
Dynamical replica theoretic analysis of CDMA detection dynamics
We investigate the detection dynamics of the Gibbs sampler for code-division
multiple access (CDMA) multiuser detection. Our approach is based upon
dynamical replica theory which allows an analytic approximation to the
dynamics. We use this tool to investigate the basins of attraction when phase
coexistence occurs and examine its efficacy via comparison with Monte Carlo
simulations.Comment: 18 pages, 2 figure
Symmetric sequence processing in a recurrent neural network model with a synchronous dynamics
The synchronous dynamics and the stationary states of a recurrent attractor
neural network model with competing synapses between symmetric sequence
processing and Hebbian pattern reconstruction is studied in this work allowing
for the presence of a self-interaction for each unit. Phase diagrams of
stationary states are obtained exhibiting phases of retrieval, symmetric and
period-two cyclic states as well as correlated and frozen-in states, in the
absence of noise. The frozen-in states are destabilised by synaptic noise and
well separated regions of correlated and cyclic states are obtained. Excitatory
or inhibitory self-interactions yield enlarged phases of fixed-point or cyclic
behaviour.Comment: Accepted for publication in Journal of Physics A: Mathematical and
Theoretica
Poly(triazolyl methacrylate) glycopolymers as potential targeted unimolecular nanocarriers
© The Royal Society of Chemistry 2019.Synthetic glycopolymers are increasingly investigated as multivalent ligands for a range of biological and biomedical applications. This study indicates that glycopolymers with a fine-tuned balance between hydrophilic sugar pendant units and relatively hydrophobic polymer backbones can act as single-chain targeted nanocarriers for low molecular weight hydrophobic molecules. Non-covalent complexes formed from poly(triazolyl methacrylate) glycopolymers and low molecular weight hydrophobic guest molecules were characterised through a range of analytical techniques-DLS, SLS, TDA, fluorescence spectroscopy, surface tension analysis-and molecular dynamics (MD) modelling simulations provided further information on the macromolecular characteristics of these single chain complexes. Finally, we show that these nanocarriers can be utilised to deliver a hydrophobic guest molecule, Nile red, to both soluble and surface-immobilised concanavalin A (Con A) and peanut agglutinin (PNA) model lectins with high specificity, showing the potential of non-covalent complexation with specific glycopolymers in targeted guest-molecule delivery.Peer reviewedFinal Published versio
Chaos in neural networks with a nonmonotonic transfer function
Time evolution of diluted neural networks with a nonmonotonic transfer
function is analitically described by flow equations for macroscopic variables.
The macroscopic dynamics shows a rich variety of behaviours: fixed-point,
periodicity and chaos. We examine in detail the structure of the strange
attractor and in particular we study the main features of the stable and
unstable manifolds, the hyperbolicity of the attractor and the existence of
homoclinic intersections. We also discuss the problem of the robustness of the
chaos and we prove that in the present model chaotic behaviour is fragile
(chaotic regions are densely intercalated with periodicity windows), according
to a recently discussed conjecture. Finally we perform an analysis of the
microscopic behaviour and in particular we examine the occurrence of damage
spreading by studying the time evolution of two almost identical initial
configurations. We show that for any choice of the parameters the two initial
states remain microscopically distinct.Comment: 12 pages, 11 figures. Accepted for publication in Physical Review E.
Originally submitted to the neuro-sys archive which was never publicly
announced (was 9905001
Approximation schemes for the dynamics of diluted spin models: the Ising ferromagnet on a Bethe lattice
We discuss analytical approximation schemes for the dynamics of diluted spin
models. The original dynamics of the complete set of degrees of freedom is
replaced by a hierarchy of equations including an increasing number of global
observables, which can be closed approximately at different levels of the
hierarchy. We illustrate this method on the simple example of the Ising
ferromagnet on a Bethe lattice, investigating the first three possible
closures, which are all exact in the long time limit, and which yield more and
more accurate predictions for the finite-time behavior. We also investigate the
critical region around the phase transition, and the behavior of two-time
correlation functions. We finally underline the close relationship between this
approach and the dynamical replica theory under the assumption of replica
symmetry.Comment: 21 pages, 5 figure
Rapid nano-gram scale screening method of micro-arrays to evaluate drug-polymer blends using high-throughput printing technology
A miniaturized, high-throughput assay was optimized to screen polymer-drug solid dispersions using a 2-D Ink-jet printer. By simply printing nanoliter amounts of polymer and drug solutions onto an inert surface, drug:polymer micro-dots of tunable composition were produced in an easily-addressable micro-array format. The amount of material printed for each dried spot ranged from 25 ng to 650 ng. These arrays were used to assess the stability of drug:polymer dispersions with respect to recrystallization, using polarized light microscopy. One array with a panel of 6 drugs formulated at different ratios with Poly (vinylpyrrolidone-vinyl acetate) copolymer (PVPVA) was developed to estimate a possible bulk (gram-scale) approximation threshold from the final printed nano amount of formulation. Another array was printed at a fixed final amount of material to establish a literature comparison of one drug formulated with different commercial polymers for validation. This new approach may offer significant efficiency in pharmaceutical formulation screening, with each experiment in the nano-micro-array format requiring from 3 up to 6 orders of magnitude lower amounts of sample than conventional screening methods
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