We classify functions $$f:(a,b)\rightarrow \mathbb {R}$$ which satisfy the inequality $$\begin{aligned} {\text {tr}}f(A)+f(C)\ge {tr}}f(B)+f(D) \end{aligned}$$ when $$A\le B\le C$$ are self-adjoint matrices, $$D= A+C-B$$ , so-called trace minmax functions. (Here B$$ if $$B-A$$ is positive semidefinite, and f evaluated via functional calculus.) A function only its derivative analytically continu...

recordings of ambient noise or microtremors are increasingly used to find valuable information on soil in one dimension at a given site. ambient vibrations, which are assumed to be mainly composed of surface waves, can be used to determine the surface wave dispersion curve in order to retrieve shear wave velocity profile. in this regard, microtremors are usually recorded simultaneously in an ar...

Hierarchical clustering constructs a hierarchy of clusters by either repeatedly merging two smaller clusters into a larger one or splitting a larger cluster into smaller ones. The crucial step is how to best select the next cluster(s) to split or merge. Here we provide a comprehensive analysis of selection methods and propose several new methods. We perform extensive clustering experiments to t...

We consider a special packing-covering pair of problems. The packing problem is a natural generalization of finding a (weighted) maximum independent set in an interval graph, the covering problem generalizes the problem of finding a (weighted) minimum clique cover in an interval graph. The problem pair involves weights and capacities; we consider the case of unit weights and the case of unit ca...

In a recent paper [10], an algorithmic approach was presented for the robust (minmax regret) absolute deviation location problem on networks with vertex weights which are linear functions of an uncertain or dynamically changing parameter. In this paper, we present algorithmic and analytical improvements that significantly reduce the computational complexity bounds for the algorithm.

In this paper the minmax (regret) versions of some basic polynomially solvable deterministic network problems are discussed. It is shown that if the number of scenarios is unbounded, then the problems under consideration are not approximable within logK for any ǫ > 0 unless NP ⊆ DTIME(n log ), where K is the number of scenarios.

We establish an existence result for a class of quasilinear elliptic boundary value problems with jumping nonlinearities using variational arguments. First we calculate certain homotopy groups of sublevel sets of the asymptotic part of the variational functional. Then we use these groups to show that the full functional admits a linking geometry and hence a minmax critical point.

The perfect monitoring assumption is replaced by a signalling structure that models, for each player, the information about the opponent’s previous action. The value of a stochastic game may not exist any more. For the class of absorbing games, we are able to show the existence of the maxmin and the minmax. The value does not exist if they are different.

In this paper we survey variational characterizations of eigenvalues of nonlinear eigenproblems, i.e. generalizations of Rayleigh’s principle, the minmax characterization of Poincaré, and the maxmin characterization of Courant, Fischer and Weyl to eigenvalue problems containing the eigenparameter nonlinearly. In this note we consider the nonlinear eigenvalue problem

A sequence is called perfect if its autocorrelation function is a delta function. In this paper, we give a new definition of autocorrelation function: generalized even and odd periodic autocorrelation, and generalized even and odd periodic cyclically conjugated autocorrelation. In particular, we study a special case of autocorrelation function called cyclically conjugated autocorrelation functi...