The complexity of any optimisation problem depends critically on the form of the objective function. Valued constraint satisfaction problems are discrete optimisation problems where the function to be minimised is given as a sum of cost functions defined on specified subsets of variables. These cost functions are chosen from some fixed set of available cost functions, known as a valued constrai...

The H-Coloring problem can be expressed as a particular case of the Constraint Satisfaction Problem (CSP) whose computational complexity has been intensively studied under various approaches in the last several years. We show that the dichotomy theorem proved by P.Hell and J.Nešetřil [12] for the complexity of the H-Coloring problem for undirected graphs can be obtained using general methods fo...

A valued constraint satisfaction problem (VCSP) instance (V,Π, w) is a set of variables V with a set of constraints Π weighted by w. Given a VCSP instance, we are interested in a re-weighted sub-instance (V,Π′ ⊂ Π, w′) such that preserves the value of the given instance (under every assignment to the variables) within factor 1± . A well-studied special case is cut sparsification in graphs, whic...

Motivated by problems of anomaly detection, this paper implements the Neyman-Pearson paradigm to deal with asymmetric errors in binary classification with a convex loss. Given a finite collection of classifiers, we combine them and obtain a new classifier that satisfies simultaneously the two following properties with high probability: (i), its probability of type I error is below a pre-specifi...

This paper proposes a chance-constrained multi-objective goal programming model for supplier selection problem with uncertain factors. Considering uncertain factors of demand, capacity and lead time and several objectives, the proposed approach provides chance constraints leading to a order allocation decision-making result. The decision keeps the confidence and risk of constraints to a certain...

We consider a two player bimatrix game where the entries of the payoff matrices are random variables. We formulate this problem as a chance-constrained game by considering that the payoff of each player is defined using a chance constraint. We consider the case where the entries of the payoff matrices are independent normal/Cauchy random variables. We show a one-to-one correspondence between a ...

Loss of selective constraint on a gene may be expected following changes in the environment or life history that render its function unnecessary. The long-term persistence of protein-coding genes after the loss of known functional necessity can occur by chance or because of selective maintenance of an unknown gene function. The selective maintenance of an alternative gene function is not demons...

In his ‘Objective Bayesian calibration and the problem of non-convex evidence’, Gregory Wheeler criticises the principle I invoke in Williamson (2010) for calibrating degrees of belief with chances. Bayesian epistemologists commonly appeal to some sort of Calibration norm that says that degrees of belief should be calibrated to known chances. Typically they invoke a principle variously known as...