Related papers: Set Regularities and Feasibility Problems
We prove a general quantitative theorem on the asymptotic behavior of stochastic quasi-Fej\'er monotone sequences in a broad metric context. Concretely, our result explicitly constructs a rate of convergence for such process, both in mean…
We present a concept of uniform encodability of theories and develop tools related to this concept. As an application we obtain general undecidability results which are uniform for large families of structures. In the way, we define…
Methods for the reduction of the complexity of computational problems are presented, as well as their connections to renormalization, scaling, and irreversible statistical mechanics. Several statistically stationary cases are analyzed; for…
Control synthesis under constraints is at the forefront of research on autonomous systems, in part due to its broad application from low-level control to high-level planning, where computing control inputs is typically cast as a constrained…
Regularization and Bayesian methods for system identification have been repopularized in the recent years, and proved to be competitive w.r.t. classical parametric approaches. In this paper we shall make an attempt to illustrate how the use…
This paper presents a regularized Newton method (RNM) with generalized regularization terms for unconstrained convex optimization problems. The generalized regularization includes quadratic, cubic, and elastic net regularizations as special…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
We define notions of regularity and (Barr-)exactness for 2-categories. In fact, we define three notions of regularity and exactness, each based on one of the three canonical ways of factorising a functor in Cat: as (surjective on objects,…
The convergence of the algorithm for solving convex feasibility problem is studied by the method of sequential averaged and relaxed projections. Some results of H. H. Bauschke and J. M. Borwein are generalized by introducing new methods.…
Computing reachability probabilities is a fundamental problem in the analysis of probabilistic programs. This paper aims at a comprehensive and comparative account on various martingale-based methods for over- and under-approximating…
In some particular cases we give criteria for morphic sequences to be almost periodic (=uniformly recurrent). Namely, we deal with fixed points of non-erasing morphisms and with automatic sequences. In both cases a polynomial-time algorithm…
Synchronisation and pattern formation have been intensely addressed for systems evolving on static networks. Extending the study to include the inherent ability of the network to adjust over time proved cumbersome and led to conclusions…
We study supervised learning problems using clustering constraints to impose structure on either features or samples, seeking to help both prediction and interpretation. The problem of clustering features arises naturally in text…
We discuss issues that arise in the regularisation of supersymmetric theories. (To appear in the book `Perspectives on Supersymmetry', World Scientific, Editor G. Kane.)
This is a report of a joint work with E. J\"arvenp\"a\"a, M. J\"arvenp\"a\"a, T. Rajala, S. Rogovin, and V. Suomala. In [3], we characterized uniformly porous sets in $s$-regular metric spaces in terms of regular sets by verifying that a…
The convex feasibility problem (CFP) is to find a feasible point in the intersection of finitely many convex and closed sets. If the intersection is empty then the CFP is inconsistent and a feasible point does not exist. However,…
The theory of the functional sequences and series is presented; uniformly convergent, convergent in the sense of a mean square and weakly convergent sequences and series are considered. Sequential approach to constructing generalized…
Modern applications require methods that are computationally feasible on large datasets but also preserve statistical efficiency. Frequently, these two concerns are seen as contradictory: approximation methods that enable computation are…
We propose algorithms and software for computing projections onto the intersection of multiple convex and non-convex constraint sets. The software package, called SetIntersectionProjection, is intended for the regularization of inverse…
We present a new characteristic of a regular ideal language called reset complexity. We find some bounds on the reset complexity in terms of the state complexity of a given language. We also compare the reset complexity and the state…