2,122 research outputs found
Statistical mechanics of temporal association in neural networks with transmission delays
We study the representation of static patterns and temporal sequences in neural networks with signal delays and a stochastic parallel dynamics. For a wide class of delay distributions, the asymptotic network behavior can be described by a generalized Gibbs distribution, generated by a novel Lyapunov functional for the determination dynamics. We extend techniques of equilibrium statistical mechanics so as to deal with time-dependent phenomena, derive analytic results for both retrieval quality and storage capacity, and compare them with numerical simulations
Exciton bimolecular annihilation dynamics in supramolecular nanostructures of conjugated oligomers
We present femtosecond transient absorption measurements on -conjugated
supramolecular assemblies in a high pump fluence regime.
Oligo(\emph{p}-phenylenevinylene) monofunctionalized with
ureido-\emph{s}-triazine (MOPV) self-assembles into chiral stacks in dodecane
solution below 75C at a concentration of M. We
observe exciton bimolecular annihilation in MOPV stacks at high excitation
fluence, indicated by the fluence-dependent decay of B-exciton
spectral signatures, and by the sub-linear fluence dependence of time- and
wavelength-integrated photoluminescence (PL) intensity. These two
characteristics are much less pronounced in MOPV solution where the phase
equilibrium is shifted significantly away from supramolecular assembly,
slightly below the transition temperature. A mesoscopic rate-equation model is
applied to extract the bimolecular annihilation rate constant from the
excitation fluence dependence of transient absorption and PL signals. The
results demonstrate that the bimolecular annihilation rate is very high with a
square-root dependence in time. The exciton annihilation results from a
combination of fast exciton diffusion and resonance energy transfer. The
supramolecular nanostructures studied here have electronic properties that are
intermediate between molecular aggregates and polymeric semiconductors
Why, what, and how? case study on law, risk, and decision making as necessary themes in built environment teaching
The paper considers (and defends) the necessity of including legal studies as a core part of built environment undergraduate and postgraduate curricula. The writer reflects upon his own experience as a lawyer working alongside and advising built environment professionals in complex land remediation and site safety management situations in the United Kingdom and explains how themes of liability, risk, and decision making can be integrated into a practical simulation in order to underpin more traditional lecture-based law teaching. Through reflection upon the writer's experiments with simulation-based teaching, the paper suggests some innovations that may better orientate law teaching to engage these themes and, thereby, enhance the relevance of law studies to the future needs of built environment professionals in practice.</p
Temperature Dependence of Exciton Diffusion in Conjugated Polymers
The temperature dependence of the exciton dynamics in a conjugated polymer is studied using time-resolved spectroscopy. Photoluminescence decays were measured in heterostructured samples containing a sharp polymer-fullerene interface, which acts as an exciton quenching wall. Using a 1D diffusion model, the exciton diffusion length and diffusion coefficient were extracted in the temperature range of 4-293 K. The exciton dynamics reveal two temperature regimes: in the range of 4-150 K, the exciton diffusion length (coefficient) of ~3 nm (~1.5 × 10-4 cm2/s) is nearly temperature independent. Increasing the temperature up to 293 K leads to a gradual growth up to 4.5 nm (~3.2 × 10-4 cm2/s). This demonstrates that exciton diffusion in conjugated polymers is governed by two processes: an initial downhill migration toward lower energy states in the inhomogenously broadened density of states, followed by temperature activated hopping. The latter process is switched off below 150 K.
Phase Diagram for the Winfree Model of Coupled Nonlinear Oscillators
In 1967 Winfree proposed a mean-field model for the spontaneous
synchronization of chorusing crickets, flashing fireflies, circadian pacemaker
cells, or other large populations of biological oscillators. Here we give the
first bifurcation analysis of the model, for a tractable special case. The
system displays rich collective dynamics as a function of the coupling strength
and the spread of natural frequencies. Besides incoherence, frequency locking,
and oscillator death, there exist novel hybrid solutions that combine two or
more of these states. We present the phase diagram and derive several of the
stability boundaries analytically.Comment: 4 pages, 4 figure
Noncommutative Figa-Talamanca-Herz algebras for Schur multipliers
We introduce a noncommutative analogue of the Fig\'a-Talamanca-Herz algebra
on the natural predual of the operator space of
completely bounded Schur multipliers on Schatten space . We determine the
isometric Schur multipliers and prove that the space of bounded
Schur multipliers on Schatten space is the closure in the weak operator
topology of the span of isometric multipliers.Comment: 24 pages; corrected typo
Spatial representation of temporal information through spike timing dependent plasticity
We suggest a mechanism based on spike time dependent plasticity (STDP) of
synapses to store, retrieve and predict temporal sequences. The mechanism is
demonstrated in a model system of simplified integrate-and-fire type neurons
densely connected by STDP synapses. All synapses are modified according to the
so-called normal STDP rule observed in various real biological synapses. After
conditioning through repeated input of a limited number of of temporal
sequences the system is able to complete the temporal sequence upon receiving
the input of a fraction of them. This is an example of effective unsupervised
learning in an biologically realistic system. We investigate the dependence of
learning success on entrainment time, system size and presence of noise.
Possible applications include learning of motor sequences, recognition and
prediction of temporal sensory information in the visual as well as the
auditory system and late processing in the olfactory system of insects.Comment: 13 pages, 14 figures, completely revised and augmented versio
Jacobi structures revisited
Jacobi algebroids, that is graded Lie brackets on the Grassmann algebra
associated with a vector bundle which satisfy a property similar to that of the
Jacobi brackets, are introduced. They turn out to be equivalent to generalized
Lie algebroids in the sense of Iglesias and Marrero and can be viewed also as
odd Jacobi brackets on the supermanifolds associated with the vector bundles.
Jacobi bialgebroids are defined in the same manner. A lifting procedure of
elements of this Grassmann algebra to multivector fields on the total space of
the vector bundle which preserves the corresponding brackets is developed. This
gives the possibility of associating canonically a Lie algebroid with any local
Lie algebra in the sense of Kirillov.Comment: 20 page
Associative memory storing an extensive number of patterns based on a network of oscillators with distributed natural frequencies in the presence of external white noise
We study associative memory based on temporal coding in which successful
retrieval is realized as an entrainment in a network of simple phase
oscillators with distributed natural frequencies under the influence of white
noise. The memory patterns are assumed to be given by uniformly distributed
random numbers on so that the patterns encode the phase differences
of the oscillators. To derive the macroscopic order parameter equations for the
network with an extensive number of stored patterns, we introduce the effective
transfer function by assuming the fixed-point equation of the form of the TAP
equation, which describes the time-averaged output as a function of the
effective time-averaged local field. Properties of the networks associated with
synchronization phenomena for a discrete symmetric natural frequency
distribution with three frequency components are studied based on the order
parameter equations, and are shown to be in good agreement with the results of
numerical simulations. Two types of retrieval states are found to occur with
respect to the degree of synchronization, when the size of the width of the
natural frequency distribution is changed.Comment: published in Phys. Rev.
Noise Stabilization of Self-Organized Memories
We investigate a nonlinear dynamical system which ``remembers'' preselected
values of a system parameter. The deterministic version of the system can
encode many parameter values during a transient period, but in the limit of
long times, almost all of them are forgotten. Here we show that a certain type
of stochastic noise can stabilize multiple memories, enabling many parameter
values to be encoded permanently. We present analytic results that provide
insight both into the memory formation and into the noise-induced memory
stabilization. The relevance of our results to experiments on the
charge-density wave material is discussed.Comment: 29 pages, 6 figures, submitted to Physical Review
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