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The main objective of this article is to develop a matrix pencil approach for the study of the controllability and reachability of a class of linear singular discrete time systems. The description equation of a practical system may be…

The tree-loop duality relation is used as a starting point to derive the constraints of causality and unitarity. Specifically, the Bogoliubov causality condition is ab initio derived at the individual graph level. It leads to a…

In this paper we present the initial development of a general theory for mapping inference in predicate logic to computation over Tensor Product Representations (TPRs; Smolensky (1990), Smolensky & Legendre (2006)). After an initial brief…

The Kripke semantics of various logics arises via categorical dualities between a category of relational frames and their maps, and a category of algebras and logical homomorphisms. When the relational frames are considered as computational…

Several recent works have developed a new, probabilistic interpretation for numerical algorithms solving linear systems in which the solution is inferred in a Bayesian framework, either directly or by inferring the unknown action of the…

The discussion on causality in human history dates back to ancient Greece, yet to this day, there is still no consensus. Fundamentally, this stems from the nature of human cognition, as understanding causality requires abstract tools to…

In this paper, we provide the first practical algorithms with provable guarantees for the problem of inferring the topics assigned to each document in an LDA topic model. This is the primary inference problem for many applications of topic…

This paper discusses system consequence, a central idea in the project to lift the theory of information flow to the abstract level of universal logic and the theory of institutions. The theory of information flow is a theory of distributed…

A fundamental aspect of relational data, such as from a social network, is the possibility of dependence among the relations. In particular, the relations between members of one pair of nodes may have an effect on the relations between…

Classical Ramsey theory has successfully extended to relational structures, yielding a wealth of results that have profoundly influenced other areas of mathematics. Interestingly, the same development has not occurred in the case of dual…

Kontsevich's work on Airy matrix integrals has led to explicit results for the intersection numbers of the moduli space of curves. In this article we show that a duality between k-point functions on $N\times N$ matrices and N-point…

We study the problem of combining the outcomes of several different classifiers in a way that provides a coherent inference that satisfies some constraints. In particular, we develop two general approaches for an important…

Linear regressions with endogeneity are widely used to estimate causal effects. This paper studies a framework that involves two common practical issues: endogeneity of the regressors and heteroskedasticity that depends on endogenous…

We pose causal inference as the problem of learning to classify probability distributions. In particular, we assume access to a collection $\{(S_i,l_i)\}_{i=1}^n$, where each $S_i$ is a sample drawn from the probability distribution of $X_i…

We introduce a sequent calculus with a simple restriction of Lambek's product rules that precisely captures the classical Tamari order, i.e., the partial order on fully-bracketed words (equivalently, binary trees) induced by a…

New approach to systems of polynomial recursions is developed based on the Carleman linearization procedure. The article is divided into two main sections: firstly, we focus on the case of uni-variable depth-one polynomial recurrences.…

In Early Transcendentals (The American Mathematical Monthly, Vol. 104, No 7) Steven Weintraub presents a rigorous justifcation of the "early transcendental" calculus textbook approach to the exponential and logarithmic functions. However,…

In past few decades, tensor algebra also known as multi-linear algebra has been developed and customized as a tool to be used for various engineering applications. In particular, with the help of a special form of tensor contracted product,…

In this paper I conceptualise a novel approach for capturing coincidences between events that have not necessarily an observed causal relationship. Building on the Transcendental Information Cascades approach I outline a tensor theory of…

We propose a method that infers whether linear relations between two high-dimensional variables X and Y are due to a causal influence from X to Y or from Y to X. The earlier proposed so-called Trace Method is extended to the regime where…