Related papers: Computational Mechanics of Input-Output Processes:…
A computer code or simulator is a mathematical representation of a physical system, for example a set of differential equations. Running the code with given values of the vector of inputs, x, leads to an output y(x) or several such outputs.…
After collecting data from observations or experiments, the next step is to build an appropriate mathematical or stochastic model to describe the data so that further studies can be done with the help of the models. In this article, the…
Statistical mechanics is a powerful framework for analyzing optimization yielding analytical results for matching, optimal transport, and other combinatorial problems. However, these methods typically target the zero-temperature limit,…
Data-Driven Computational Mechanics is a novel computing paradigm that enables the transition from standard data-starved approaches to modern data-rich approaches. At this early stage of development, one can distinguish two mainstream…
Quantum information-processing techniques enable work extraction from a system's inherently quantum features, in addition to the classical free energy it contains. Meanwhile, the science of computational mechanics affords tools for the…
In computational physics, machine learning has now emerged as a powerful complementary tool to explore efficiently candidate designs in engineering studies. Outputs in such supervised problems are signals defined on meshes, and a natural…
A prediction makes a claim about a system's future given knowledge of its past. A retrodiction makes a claim about its past given knowledge of its future. The bidirectional machine is an ambidextrous hidden Markov chain that does both…
We need much better understanding of information processing and computation as its primary form. Future progress of new computational devices capable of dealing with problems of big data, internet of things, semantic web, cognitive robotics…
The main goal of this paper is to give a rigorous mathematical description of systems for processing quantum information. To do it authors consider abstract state machines as models of classical computational systems. This class of machines…
In this work we design a specific simulation tool for quantum channels which is based on the use of a control system. This allows us to simulate an average quantum channel which is expressed in terms of an ensemble of channels, even when…
The $\epsilon$-machine is a stochastic process' optimal model -- maximally predictive and minimal in size. It often happens that to optimally predict even simply-defined processes, probabilistic models -- including the $\epsilon$-machine --…
Stochastic computing (SC) is an emerging computing technique that promises high density, low power, and error tolerant solutions. In SC, values are encoded as unary bitstreams and SC arithmetic circuits operate on one or more bitstreams. In…
We discuss how the ideal formalism of Computational Mechanics can be adapted to apply to a non-infinite series of corrupted and correlated data, that is typical of most observed natural time series. Specifically, a simple filter that…
Uncovering the structure of socioeconomic systems and timely estimation of socioeconomic status are significant for economic development. The understanding of socioeconomic processes provides foundations to quantify global economic…
The structural cohesion model is a powerful theoretical conception of cohesion in social groups, but its diffusion in empirical literature has been hampered by operationalization and computational problems. In this paper we start from the…
Stochastic processes have found numerous applications in science, as they are broadly used to model a variety of natural phenomena. Due to their intrinsic randomness and uncertainty, they are, however, difficult to characterize. Here, we…
In the study of stochastic systems, the committor function describes the probability that a system starting from an initial configuration $x$ will reach a set $B$ before a set $A$. This paper introduces an efficient and interpretable…
Simulation methods are among the most ubiquitous methodological tools in statistical science. In particular, statisticians often is simulation to explore properties of statistical functionals in models for which developed statistical theory…
This brief article gives an overview of quantum mechanics as a {\em quantum probability theory}. It begins with a review of the basic operator-algebraic elements that connect probability theory with quantum probability theory. Then quantum…
In this paper, we analyze Gaussian processes using statistical mechanics. Although the input is originally multidimensional, we simplify our model by considering the input as one-dimensional for statistical mechanical analysis. Furthermore,…