Advances on the fixed point results via simulation function involving rational terms

In this paper, we propose two new contractions via simulation function that involves rational expression in the setting of partial b-metric space. The obtained results not only extend, but also generalize and unify the existing results in two senses: in the sense of contraction terms and in the sense of the abstract setting. We present an example to indicate the validity of the main theorem.

How do People Choose Between Biased Information Sources? Evidence from a Laboratory Experiment

People in our experiment choose between two information sources with opposing biases in order to inform their guesses about a binary state. By varying the nature of the bias, we vary whether it is optimal to consult information sources biased towards or against prior beliefs. Even in our deliberately-abstract setting, there is strong evidence of confirmation-seeking and to a lesser extent contradiction-seeking heuristics leading people to choose information sources biased towards or against their priors. Analysis of post-experiment survey questions suggests that subjects follow these rules due to fundamental errors in reasoning about the relative informativeness of biased information sources.

Masserstein: robust linear deconvolution by optimal transport

A common theme in many applications of computational mass spectrometry is fitting a linear combination of reference spectra to an experimental one in order to estimate the quantities of different ions, potentially with overlapping isotopic envelopes. In this work, we study this procedure in an abstract setting, in order to develop new approaches applicable to a diverse range of experiments. We introduce an application of a new spectral dissimilarity measure, known in other fields as the Wasserstein or the Earth Mover’s distance, in order to overcome the sensitivity of ordinary linear regression to measurement inaccuracies. Usinga a data set of 200 mass spectra, we demonstrate that our approach is capable of accurate estimation of ion proportions without extensive pre-processing required for state-of-the-art methods. The conclusions are further substantiated using data sets simulated in a way that mimics most of the measurement inaccuracies occurring in real experiments. We have implemented our methods in a Python 3 package, freely available at https://github.com/mciach/masserstein.

Profinite Separation Systems

Separation systems are posets with additional structure that form an abstract setting in which tangle-like clusters in graphs, matroids and other combinatorial structures can be expressed and studied. This paper offers some basic theory about infinite separation systems and how they relate to the finite separation systems they induce. They can be used to prove tangle-type duality theorems for infinite graphs and matroids, which will be done in future work that will build on this paper.

A proof-theoretic study of abstract termination principles

We carry out a proof-theoretic analysis of the wellfoundedness of recursive path orders in an abstract setting. We outline a general termination principle and extract from its wellfoundedness proof subrecursive bounds on the size of derivation trees that can be defined in Gödel’s system T plus bar recursion. We then carry out a complexity analysis of these terms and demonstrate how this can be applied to bound the derivational height of term rewrite systems.

Finding small counterexamples for abstract rewriting properties

Rewriting notions like termination, normal forms and confluence can be described in an abstract way referring to rewriting only as a binary relation. Several theorems on rewriting, like Newman's lemma, can be proved in this abstract setting. For investigating possible generalizations of such theorems, it is fruitful to have counterexamples showing that particular generalizations do not hold. In this paper, we develop a technique to find such counterexamples fully automatically, and we describe our tool Carpa that follows this technique. The basic idea is to fix the number of objects of the abstract rewrite system, and to express the conditions and the negation of the conclusion in a satisfiability (SAT) formula, and then call a current SAT solver. In case the formula turns out to be satisfiable, the resulting satisfying assignment yields a counterexample to the encoded property. We give several examples of finite abstract rewrite systems having remarkable properties that are found in this way fully automatically.

Spectral methods for Langevin dynamics and associated error estimates

We prove the consistency of Galerkin methods to solve Poisson equations where the differential operator under consideration is hypocoercive. We show in particular how the hypocoercive nature of the generator associated with Langevin dynamics can be used at the discrete level to first prove the invertibility of the rigidity matrix, and next provide error bounds on the approximation of the solution of the Poisson equation. We present general convergence results in an abstract setting, as well as explicit convergence rates for a simple example discretized using a tensor basis. Our theoretical findings are illustrated by numerical simulations.