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The ``evolving constants'' method of defining the quantum dynamics of time-reparametrization-invariant theories is investigated for a particular implementation of parametrized non-relativistic quantum mechanics (PNRQM). The wide range of…
We extend the standard reinforcement learning framework to random time horizons. While the classical setting typically assumes finite and deterministic or infinite runtimes of trajectories, we argue that multiple real-world applications…
We develop an abstract look at linear optical networks from the viewpoint of combinatorics and permanents. In particular we show that calculation of matrix elements of unitarily transformed photonic multi-mode states is intimately linked to…
The inferential model (IM) framework provides valid prior-free probabilistic inference by focusing on predicting unobserved auxiliary variables. But, efficient IM-based inference can be challenging when the auxiliary variable is of higher…
Non-negative matrix factorization (NMF) is a fundamental non-convex optimization problem with numerous applications in Machine Learning (music analysis, document clustering, speech-source separation etc). Despite having received extensive…
For a given set of intervals on the real line, we consider the problem of ordering the intervals with the goal of minimizing an objective function that depends on the exposed interval pieces (that is, the pieces that are not covered by…
The rapid advancement of models based on artificial intelligence demands innovative monitoring techniques which can operate in real time with low computational costs. In machine learning, especially if we consider artificial neural networks…
It is known that any symmetric matrix $M$ with entries in $\R[x]$ and which is positive semi-definite for any substitution of $x\in\R$, has a Smith normal form whose diagonal coefficients are constant sign polynomials in $\R[x]$. We…
We introduce a parallel machine scheduling problem in which the processing times of jobs are not given in advance but are determined by a system of linear constraints. The objective is to minimize the makespan, i.e., the maximum job…
The electromagnetic nucleon form-factors data are studied with artificial feed forward neural networks. As a result the unbiased model-independent form-factor parametrizations are evaluated together with uncertainties. The Bayesian approach…
In this paper we study the complexity of the problems: given a loop, described by linear constraints over a finite set of variables, is there a linear or lexicographical-linear ranking function for this loop? While existence of such…
We develop a criterion to certify whether causal effects are identifiable in linear structural equation models with latent variables. Linear structural equation models correspond to directed graphs whose nodes represent the random variables…
Physical reasoning requires forward prediction: the ability to forecast what will happen next given some initial world state. We study the performance of state-of-the-art forward-prediction models in the complex physical-reasoning tasks of…
Nonnegative matrix factorization (NMF) has become a very popular technique in machine learning because it automatically extracts meaningful features through a sparse and part-based representation. However, NMF has the drawback of being…
Unambiguous automata are nondeterministic automata in which every word has at most one accepting run. In this paper we give a polynomial-time algorithm for model checking discrete-time Markov chains against \omega-regular specifications…
As recommender systems become increasingly complex, transparency is essential to increase user trust, accountability, and regulatory compliance. Neuro-symbolic approaches that integrate symbolic reasoning with sub-symbolic learning offer a…
Here, we give an algorithm for deciding if the nonnegative rank of a matrix $M$ of dimension $m \times n$ is at most $r$ which runs in time $(nm)^{O(r^2)}$. This is the first exact algorithm that runs in time singly-exponential in $r$. This…
Pairwise Markov Random Fields (MRFs) or undirected graphical models are parsimonious representations of joint probability distributions. Variables correspond to nodes of a graph, with edges between nodes corresponding to conditional…
The computational complexity of the isomorphism problem for regular trees, regular linear orders, and regular words is analyzed. A tree is regular if it is isomorphic to the prefix order on a regular language. In case regular languages are…
A polynomial-time algorithm for computing the permanent in any field of characteristic 3 is presented in this article. The principal objects utilized for that purpose are the Cauchy and Vandermonde matrices, the discriminant function and…