554 research outputs found
RRS "Discovery" Cruise 43, 7 October - 25 November 1971: 'GLORIA' in Peake and Freen Deeps, and on the Azores-Gibraltar Rise
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
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
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
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
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
Relaxation and Metastability in the RandomWalkSAT search procedure
An analysis of the average properties of a local search resolution procedure
for the satisfaction of random Boolean constraints is presented. Depending on
the ratio alpha of constraints per variable, resolution takes a time T_res
growing linearly (T_res \sim tau(alpha) N, alpha < alpha_d) or exponentially
(T_res \sim exp(N zeta(alpha)), alpha > alpha_d) with the size N of the
instance. The relaxation time tau(alpha) in the linear phase is calculated
through a systematic expansion scheme based on a quantum formulation of the
evolution operator. For alpha > alpha_d, the system is trapped in some
metastable state, and resolution occurs from escape from this state through
crossing of a large barrier. An annealed calculation of the height zeta(alpha)
of this barrier is proposed. The polynomial/exponentiel cross-over alpha_d is
not related to the onset of clustering among solutions.Comment: 23 pages, 11 figures. A mistake in sec. IV.B has been correcte
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