Stochastic self-assembly of incommensurate clusters

We examine the classic problem of homogeneous nucleation and growth by deriving and analyzing a fully discrete stochastic master equation. Upon comparison with results obtained from the corresponding mean-field Becker-D\"{o}ring equations we find striking differences between the two corresponding equilibrium mean cluster concentrations. These discrepancies depend primarily on the divisibility of the total available mass by the maximum allowed cluster size, and the remainder. When such mass incommensurability arises, a single remainder particle can "emulsify" or "disperse" the system by significantly broadening the mean cluster size distribution. This finite-sized broadening effect is periodic in the total mass of the system and can arise even when the system size is asymptotically large, provided the ratio of the total mass to the maximum cluster size is finite. For such finite ratios we show that homogeneous nucleation in the limit of large, closed systems is not accurately described by classical mean-field mass-action approaches.Comment: 5 pages, 4 figures, 1 tabl

Mean First Passage Time in Periodic Attractors

The properties of the mean first passage time in a system characterized by multiple periodic attractors are studied. Using a transformation from a high dimensional space to 1D, the problem is reduced to a stochastic process along the path from the fixed point attractor to a saddle point located between two neighboring attractors. It is found that the time to switch between attractors depends on the effective size of the attractors, $\tau$, the noise, $\epsilon$, and the potential difference between the attractor and an adjacent saddle point as: $~T = {c \over \tau} \exp({\tau \over \epsilon} \Delta {\cal{U}})~$; the ratio between the sizes of the two attractors affects $\Delta {\cal{U}}$. The result is obtained analytically for small $\tau$ and confirmed by numerical simulations. Possible implications that may arise from the model and results are discussed.Comment: 14 pages, 3 figures, submitted to journal of physics

Language dysfunction in schizophrenia: Assessing neural tracking to characterize the underlying disorder(s)?

Deficits in language production and comprehension are characteristic of schizophrenia. To date, it remains unclear whether these deficits arise from dysfunctional linguistic knowledge, or dysfunctional predictions derived from the linguistic context. Alternatively, the deficits could be a result of dysfunctional neural tracking of auditory information resulting in decreased auditory information fidelity and even distorted information. Here, we discuss possible ways for clinical neuroscientists to employ neural tracking methodology to independently characterize deficiencies on the auditory–sensory and abstract linguistic levels. This might lead to a mechanistic understanding of the deficits underlying language related disorder(s) in schizophrenia. We propose to combine naturalistic stimulation, measures of speech–brain synchronization, and computational modeling of abstract linguistic knowledge and predictions. These independent but likely interacting assessments may be exploited for an objective and differential diagnosis of schizophrenia, as well as a better understanding of the disorder on the functional level—illustrating the potential of neural tracking methodology as translational tool in a range of psychotic populations

The triple-mode pulsating variable V823 Cas

Based on extended multicolour CCD photometry of the triple-mode radial pulsator V823 Cas we studied the properties of the coupling frequencies invoked by nonlinear processes. Our results support that a resonance connection as suggested by Antonello & Aikawa (1998) affects the mode coupling behaviour. The P1/P0 period ratio of V823 Cas has an "out of range" value if compared with the period ratios of the known double mode pulsators, while the P2/P1 period ratio is normal. The periods and period ratios cannot be consistently interpret without conflict with pulsation and/or evolution models. We attempt to interpret this failure by the suggestion that at present, the periods of V823 Cas are in a transient, resonance affected state, thus do not reflect the true parameters of the object. The anomalous period change behaviour of the fundamental and second overtone modes supports this idea. We have also raised the possibility that a f0 + f2 = 2f1 resonance may act in triple mode pulsators.Comment: 10 pages, 7 figures, 5 tables. Accepted for publication in Astronomy and Astrophysic

Time-Dependent Density Functional Theory for Driven Lattice Gas Systems with Interactions

We present a new method to describe the kinetics of driven lattice gases with particle-particle interactions beyond hard-core exclusions. The method is based on the time-dependent density functional theory for lattice systems and allows one to set up closed evolution equations for mean site occupation numbers in a systematic manner. Application of the method to a totally asymmetric site exclusion process with nearest-neighbor interactions yields predictions for the current-density relation in the bulk, the phase diagram of non-equilibrium steady states and the time evolution of density profiles that are in good agreement with results from kinetic Monte Carlo simulations.Comment: 11 pages, 3 figure

Oscillatory Bursting as a Mechanism for Temporal Coupling and Information Coding

© Copyright © 2020 Tal, Neymotin, Bickel, Lakatos and Schroeder. Even the simplest cognitive processes involve interactions between cortical regions. To study these processes, we usually rely on averaging across several repetitions of a task or across long segments of data to reach a statistically valid conclusion. Neuronal oscillations reflect synchronized excitability fluctuations in ensembles of neurons and can be observed in electrophysiological recordings in the presence or absence of an external stimulus. Oscillatory brain activity has been viewed as sustained increase in power at specific frequency bands. However, this perspective has been challenged in recent years by the notion that oscillations may occur as transient burst-like events that occur in individual trials and may only appear as sustained activity when multiple trials are averaged together. In this review, we examine the idea that oscillatory activity can manifest as a transient burst as well as a sustained increase in power. We discuss the technical challenges involved in the detection and characterization of transient events at the single trial level, the mechanisms that might generate them and the features that can be extracted from these events to study single-trial dynamics of neuronal ensemble activity