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Algorithms and dynamics over networks often involve randomization, and randomization may result in oscillating dynamics which fail to converge in a deterministic sense. In this paper, we observe this undesired feature in three applications,…
We describe an embarrassingly parallel, anytime Monte Carlo method for likelihood-free models. The algorithm starts with the view that the stochasticity of the pseudo-samples generated by the simulator can be controlled externally by a…
We develop parallel algorithms for simulating zeroth-order (aka gradient-free) Metropolis Markov chains based on the Picard map. For Random Walk Metropolis Markov chains targeting log-concave distributions $\pi$ on $\mathbb{R}^d$, our…
The paper deals with the developing of the methodological backgrounds for the modeling and simulation of complex dynamical objects. Such backgrounds allow us to perform coordinate transformation and formulate the algorithm of its usage for…
We consider a disordered system obtained by coupling two mixed even-spin models together. The chaos problem is concerned with the behavior of the coupled system when the external parameters in the two models, such as, temperature, disorder,…
The study of chaos has long relied on computationally intensive methods to quantify unpredictability and design control strategies. Recent advances in machine learning, from convolutional neural networks to transformer architectures,…
Computation of a signal's estimated covariance matrix is an important building block in signal processing, e.g., for spectral estimation. Each matrix element is a sum of products of elements in the input matrix taken over a sliding window.…
Cloud computing refers to maximizing efficiency by sharing computational and storage resources, while data-parallel systems exploit the resources available in the cloud to perform parallel transformations over large amounts of data. In the…
This work redefines the framework of chaos in dynamical systems by extending Devaney's definition to multiple mappings, emphasizing the pivotal role of nonlinearity. We propose a novel theorem demonstrating how nonlinear dynamics within a…
In this chapter we show that chordal structure can be used to devise efficient optimization methods for many common model predictive control problems. The chordal structure is used both for computing search directions efficiently as well as…
The post-Moore era casts a shadow of uncertainty on many aspects of computer system design. Managing that uncertainty requires new algorithmic tools to make quantitative assessments. While prior uncertainty quantification methods, such as…
Multifractal systems usually have singularity spectra defined on bounded sets of H\"older exponents. As a consequence, their associated multifractal scaling exponents are expected to depend linearly upon statistical moment orders at high…
Many real-life problems of practical importance -- spanning a wide range of applications from chip design to bioinformatics -- represent constraint satisfaction problems, where classical solvers have to rely on heuristic approximations due…
The paper discusses the main ideas of the chaos theory and presents mainly the importance of the nonlinearities in the mathematical models. Chaos and order are apparently two opposite terms. The fact that in chaos can be found a certain…
In dynamic Monte Carlo simulations, using for example the Metropolis dynamic, it is often required to simulate for long times and to simulate large systems. We present an overview of advanced algorithms to simulate for larger times and to…
In the field of robust geometric computation it is often necessary to make exact decisions based on inexact floating-point arithmetic. One common approach is to store the computation history in an arithmetic expression dag and to…
Efficient and faithful parallel simulation of large asynchronous systems is a challenging computational problem. It requires using the concept of local simulated times and a synchronization scheme. We study the scalability of massively…
In this paper we show that chordal structure can be used to devise efficient optimization methods for robust model predictive control problems. The chordal structure is used both for computing search directions efficiently as well as for…
Methods based on polynomial chaos expansion allow to approximate the behavior of systems with uncertain parameters by deterministic dynamics. These methods are used in a wide range of applications, spanning from simulation of uncertain…
We present a perception model of ambiguous patterns based on the chaotic neural network and investigate the characteristics through computer simulations. The results induced by the chaotic activity are similar to those of psychophysical…