Related papers: Most-Intersection of Countable Sets
In noninteracting limit, the density of states of a many body system can be expressed as the convolution of single body density of states of its subunits. Here we use the formulation to derive the ensemble averaged many body density of…
The control of traffic signals is fundamental and critical to alleviate traffic congestion in urban areas. However, it is challenging since traffic dynamics are complicated in real-world scenarios. Because of the high complexity of the…
We develop a general mathematical framework to study mixtures of different physical systems brought together on a discrete interface. Adapting work by M\u{a}ntoiu et al., we use an operator algebraic framework such that the bulk systems at…
A critical task in systems biology is the identification of genes that interact to control cellular processes by transcriptional activation of a set of target genes. Many methods have been developed to use statistical correlations in…
TThe problem is to identify a probability associated with a set of natural numbers, given an infinite data sequence of elements from the set. If the given sequence is drawn i.i.d. and the probability mass function involved (the target)…
Probabilistic reasoning systems combine different probabilistic rules and probabilistic facts to arrive at the desired probability values of consequences. In this paper we describe the MESA-algorithm (Maximum Entropy by Simulated Annealing)…
Many complex systems in nature and society can be described in terms of networks capturing the intricate web of connections among the units they are made of. A key question is how to interpret the global organization of such networks as the…
Motivated by an ongoing project on computer aided derivation of asymptotic models governed by partial differential equations, we introduce a class of term transformations that consists of traversal strategies and insertion of contexts. We…
The maximum entropy ansatz, as it is often invoked in the context of time-series analysis, suggests the selection of a power spectrum which is consistent with autocorrelation data and corresponds to a random process least predictable from…
The development of complex component software systems can be made more manageable by first creating an abstract model and then incrementally adding details. Model transformation is an approach to add such details in a controlled way. In…
Optimization problems, generalized equations, and the multitude of other variational problems invariably lead to the analysis of sets and set-valued mappings as well as their approximations. We review the central concept of set-convergence…
This paper shows how the study of colored compositions of integers reveals some unexpected and original connection with the Invert operator. The Invert operator becomes an important tool to solve the problem of directly counting the number…
A coreset is a subset of the training set, using which a machine learning algorithm obtains performances similar to what it would deliver if trained over the whole original data. Coreset discovery is an active and open line of research as…
The structure of naming systems in natural languages hinges on a trade-off between high informativeness and low complexity. Prior work capitalizes on information theory to formalize these notions; however, these studies generally rely on…
Coherent superposition and entanglement are two fundamental aspects of non-classicality. Here we provide a quantitative connection between the two on the level of operations by showing that the dynamical coherence of an operation upper…
Multivariate information theory provides a general and principled framework for understanding how the components of a complex system are connected. Existing analyses are coarse in nature -- built up from characterizations of discrete…
The principle of maximum entropy provides a useful method for inferring statistical mechanics models from observations in correlated systems, and is widely used in a variety of fields where accurate data are available. While the assumptions…
Random forests are among the most famous algorithms for solving classification problems, in particular for large-scale data sets. Considering a set of labeled points and several decision trees, the method takes the majority vote to classify…
We show that the decidability of the first-order theory of the language that combines Boolean algebras of sets of uninterpreted elements with Presburger arithmetic operations. We thereby disprove a recent conjecture that this theory is…
We initiate and study the theory of ``real decomposable maps" between real operator systems. Formally, this is new even in the complex case, which hitherto has restricted itself to the case where the systems are complex C*-algebras. We…