Related papers: Non-commutative Combinatorial Inverse Systems
We discuss some basic issues that arise when one attempts to model quantum mechanical systems on a computer, and we describe the mathematical structure of the resulting discretized cannonical commutation relations.
We extend some classical constructions in commutative algebra to the setting of modules over orders in (non-commutative) semisimple algebras. Our theory incorporates, inter alia, `reduced' versions of the notions of higher Fitting…
Our objective is to estimate the unknown compositional input from its output response through an unknown system after estimating the inverse of the original system with a training set. The proposed methods using artificial neural networks…
In this article, we propose a novel Bayesian multiple testing formulation for model and variable selection in inverse setups, judiciously embedding the idea of inverse reference distributions proposed by Bhattacharya (2013) in a mixture…
Incorporating nonlinearity into quantum machine learning is essential for learning a complicated input-output mapping. We here propose quantum algorithms for nonlinear regression, where nonlinearity is introduced with feature maps when…
We investigate a quantum nonrelativistic system describing the interaction of two particles with spin 1/2 and spin 0, respectively. We assume that the Hamiltonian is rotationally invariant and parity conserving and identify all such systems…
Combinatorial transgressions are secondary invariants of a space admitting triangulations. They arise from subdivisions and are analogous to transgressive forms such as those arising in Chern-Weil theory. Unlike combinatorial characteristic…
Some fundamental aspects related with the construction of Robertson-Schr\"odinger like uncertainty principle inequalities are reported in order to provide an overall description of quantumness, separability and nonlocality of quantum…
After surveying classical results, we introduce a generalized notion of inference system to support structural recursion on non-well-founded data types. Besides axioms and inference rules with the usual meaning, a generalized inference…
Converse negative imaginary theorems for linear time-invariant systems are derived. In particular, we provide necessary and sufficient conditions for a feedback system to be robustly stable against various types of negative imaginary (NI)…
We analyze some features of alternative Hermitian and quasi-Hermitian quantum descriptions of simple and bipartite compound systems. We show that alternative descriptions of two interacting subsystems are possible if and only if the metric…
A combinatorial characterization of measurable filters on a countable set is found. We apply it to the problem of measurability of the intersection of nonmeasurable filters.
Seemingly unrelated linear regression models are introduced in which the distribution of the errors is a finite mixture of Gaussian components. Identifiability conditions are provided. The score vector and the Hessian matrix are derived.…
Interpretation of the nonclassical total probability formula arising in some quantum experiments is provided based on stochastic models described by means of a sequence of random vectors changing in the measurement procedures.
Let X be a subshift satisfy non-uniform structure. In this paper, we give quantitative estimate of the recurrence sets. These results can be applied to a large class of symbolic systems, including beta-shifts, S-gap shifts and their…
In this paper we present methods for the synthesis of polynomial invariants for probabilistic transition systems. Our approach is based on martingale theory. We construct invariants in the form of polynomials over program variables, which…
In this paper, we discuss the non-collapsibility concept and propose a new approach based on Dirichlet process mixtures to estimate the conditional effect of covariates in non-collapsible models. Using synthetic data, we evaluate the…
We revisit the problem of computing (robust) controlled invariant sets for discrete-time linear systems. Departing from previous approaches, we consider implicit, rather than explicit, representations for controlled invariant sets.…
In the context of the variational bi-complex, we re-explain that irreducible gauge systems define a particular example of a Lie algebroid. This is used to review some recent and not so recent results on gauge, global and asymptotic…
Understanding invertibility in restricted mis\`ere play has been challenging; in particular, the possibility of non-conjugate inverses posed difficulties. Advances have been made in a few specific universes, but a general theorem was…