206,620 research outputs found
Stochastic Landau-Lifshitz-Gilbert equations for frustrated magnets under fluctuating currents
We examine a stochastic Landau-Lifshitz-Gilbert equation for a frustrated
ferromagnet with competing first and second order exchange interactions exposed
to deterministic and random spin transfer torques in form of transport noise.
We prove the existence and pathwise uniqueness of weak martingale solutions in
the energy space. The result ensures the persistence of topological patterns,
occurring in such magnetic systems, under the influence of a fluctuating spin
current
Coarse-Grained Modeling of Genetic Circuits as a Function of the Inherent Time Scales
From a coarse-grained perspective the motif of a self-activating species,
activating a second species which acts as its own repressor, is widely found in
biological systems, in particular in genetic systems with inherent oscillatory
behavior. Here we consider a specific realization of this motif as a genetic
circuit, in which genes are described as directly producing proteins, leaving
out the intermediate step of mRNA production. We focus on the effect that
inherent time scales on the underlying fine-grained scale can have on the
bifurcation patterns on a coarser scale in time. Time scales are set by the
binding and unbinding rates of the transcription factors to the promoter
regions of the genes. Depending on the ratio of these rates to the decay times
of the proteins, the appropriate averaging procedure for obtaining a
coarse-grained description changes and leads to sets of deterministic
equations, which differ in their bifurcation structure. In particular the
desired intermediate range of regular limit cycles fades away when the binding
rates of genes are of the same order or less than the decay time of at least
one of the proteins. Our analysis illustrates that the common topology of the
widely found motif alone does not necessarily imply universal features in the
dynamics.Comment: 29 pages, 16 figure
Spatial pattern formation induced by Gaussian white noise
The ability of Gaussian noise to induce ordered states in dynamical systems
is here presented in an overview of the main stochastic mechanisms able to
generate spatial patterns. These mechanisms involve: (i) a deterministic local
dynamics term, accounting for the local rate of variation of the field
variable, (ii) a noise component (additive or multiplicative) accounting for
the unavoidable environmental disturbances, and (iii) a linear spatial coupling
component, which provides spatial coherence and takes into account diffusion
mechanisms. We investigate these dynamics using analytical tools, such as
mean-field theory, linear stability analysis and structure function analysis,
and use numerical simulations to confirm these analytical results.Comment: 11 pages, 8 figure
Patchiness and Demographic Noise in Three Ecological Examples
Understanding the causes and effects of spatial aggregation is one of the
most fundamental problems in ecology. Aggregation is an emergent phenomenon
arising from the interactions between the individuals of the population, able
to sense only -at most- local densities of their cohorts. Thus, taking into
account the individual-level interactions and fluctuations is essential to
reach a correct description of the population. Classic deterministic equations
are suitable to describe some aspects of the population, but leave out features
related to the stochasticity inherent to the discreteness of the individuals.
Stochastic equations for the population do account for these
fluctuation-generated effects by means of demographic noise terms but, owing to
their complexity, they can be difficult (or, at times, impossible) to deal
with. Even when they can be written in a simple form, they are still difficult
to numerically integrate due to the presence of the "square-root" intrinsic
noise. In this paper, we discuss a simple way to add the effect of demographic
stochasticity to three classic, deterministic ecological examples where
aggregation plays an important role. We study the resulting equations using a
recently-introduced integration scheme especially devised to integrate
numerically stochastic equations with demographic noise. Aimed at scrutinizing
the ability of these stochastic examples to show aggregation, we find that the
three systems not only show patchy configurations, but also undergo a phase
transition belonging to the directed percolation universality class.Comment: 20 pages, 5 figures. To appear in J. Stat. Phy
A Novel Predictive-Coding-Inspired Variational RNN Model for Online Prediction and Recognition
This study introduces PV-RNN, a novel variational RNN inspired by the
predictive-coding ideas. The model learns to extract the probabilistic
structures hidden in fluctuating temporal patterns by dynamically changing the
stochasticity of its latent states. Its architecture attempts to address two
major concerns of variational Bayes RNNs: how can latent variables learn
meaningful representations and how can the inference model transfer future
observations to the latent variables. PV-RNN does both by introducing adaptive
vectors mirroring the training data, whose values can then be adapted
differently during evaluation. Moreover, prediction errors during
backpropagation, rather than external inputs during the forward computation,
are used to convey information to the network about the external data. For
testing, we introduce error regression for predicting unseen sequences as
inspired by predictive coding that leverages those mechanisms. The model
introduces a weighting parameter, the meta-prior, to balance the optimization
pressure placed on two terms of a lower bound on the marginal likelihood of the
sequential data. We test the model on two datasets with probabilistic
structures and show that with high values of the meta-prior the network
develops deterministic chaos through which the data's randomness is imitated.
For low values, the model behaves as a random process. The network performs
best on intermediate values, and is able to capture the latent probabilistic
structure with good generalization. Analyzing the meta-prior's impact on the
network allows to precisely study the theoretical value and practical benefits
of incorporating stochastic dynamics in our model. We demonstrate better
prediction performance on a robot imitation task with our model using error
regression compared to a standard variational Bayes model lacking such a
procedure.Comment: The paper is accepted in Neural Computatio
Pattern formation in individual-based systems with time-varying parameters
We study the patterns generated in finite-time sweeps across
symmetry-breaking bifurcations in individual-based models. Similar to the
well-known Kibble-Zurek scenario of defect formation, large-scale patterns are
generated when model parameters are varied slowly, whereas fast sweeps produce
a large number of small domains. The symmetry breaking is triggered by
intrinsic noise, originating from the discrete dynamics at the micro-level.
Based on a linear-noise approximation, we calculate the characteristic length
scale of these patterns. We demonstrate the applicability of this approach in a
simple model of opinion dynamics, a model in evolutionary game theory with a
time-dependent fitness structure, and a model of cell differentiation. Our
theoretical estimates are confirmed in simulations. In further numerical work,
we observe a similar phenomenon when the symmetry-breaking bifurcation is
triggered by population growth.Comment: 16 pages, 9 figures. Published version. Corrected missing appendix
link from previous versio
Stochastic reaction & diffusion on growing domains: understanding the breakdown of robust pattern formation
Many biological patterns, from population densities to animal coat markings, can be thought of as heterogeneous spatiotemporal distributions of mobile agents. Many mathematical models have been proposed to account for the emergence of this complexity, but, in general, they have consisted of deterministic systems of differential equations, which do not take into account the stochastic nature of population interactions. One particular, pertinent criticism of these deterministic systems is that the exhibited patterns can often be highly sensitive to changes in initial conditions, domain geometry, parameter values, etc. Due to this sensitivity, we seek to understand the effects of stochasticity and growth on paradigm biological patterning models. In this paper, we extend spatial Fourier analysis and growing domain mapping techniques to encompass stochastic Turing systems. Through this we find that the stochastic systems are able to realize much richer dynamics than their deterministic counterparts, in that patterns are able to exist outside the standard Turing parameter range. Further, it is seen that the inherent stochasticity in the reactions appears to be more important than the noise generated by growth, when considering which wave modes are excited. Finally, although growth is able to generate robust pattern sequences in the deterministic case, we see that stochastic effects destroy this mechanism for conferring robustness. However, through Fourier analysis we are able to suggest a reason behind this lack of robustness and identify possible mechanisms by which to reclaim it
Bridging the Gap between Probabilistic and Deterministic Models: A Simulation Study on a Variational Bayes Predictive Coding Recurrent Neural Network Model
The current paper proposes a novel variational Bayes predictive coding RNN
model, which can learn to generate fluctuated temporal patterns from exemplars.
The model learns to maximize the lower bound of the weighted sum of the
regularization and reconstruction error terms. We examined how this weighting
can affect development of different types of information processing while
learning fluctuated temporal patterns. Simulation results show that strong
weighting of the reconstruction term causes the development of deterministic
chaos for imitating the randomness observed in target sequences, while strong
weighting of the regularization term causes the development of stochastic
dynamics imitating probabilistic processes observed in targets. Moreover,
results indicate that the most generalized learning emerges between these two
extremes. The paper concludes with implications in terms of the underlying
neuronal mechanisms for autism spectrum disorder and for free action.Comment: This paper is accepted the 24th International Conference On Neural
Information Processing (ICONIP 2017). The previous submission to arXiv is
replaced by this version because there was an error in Equation
Spatiotemporal patterns and predictability of cyberattacks
A relatively unexplored issue in cybersecurity science and engineering is
whether there exist intrinsic patterns of cyberattacks. Conventional wisdom
favors absence of such patterns due to the overwhelming complexity of the
modern cyberspace. Surprisingly, through a detailed analysis of an extensive
data set that records the time-dependent frequencies of attacks over a
relatively wide range of consecutive IP addresses, we successfully uncover
intrinsic spatiotemporal patterns underlying cyberattacks, where the term
"spatio" refers to the IP address space. In particular, we focus on analyzing
{\em macroscopic} properties of the attack traffic flows and identify two main
patterns with distinct spatiotemporal characteristics: deterministic and
stochastic. Strikingly, there are very few sets of major attackers committing
almost all the attacks, since their attack "fingerprints" and target selection
scheme can be unequivocally identified according to the very limited number of
unique spatiotemporal characteristics, each of which only exists on a
consecutive IP region and differs significantly from the others. We utilize a
number of quantitative measures, including the flux-fluctuation law, the Markov
state transition probability matrix, and predictability measures, to
characterize the attack patterns in a comprehensive manner. A general finding
is that the attack patterns possess high degrees of predictability, potentially
paving the way to anticipating and, consequently, mitigating or even preventing
large-scale cyberattacks using macroscopic approaches
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