This article is concerned with a general scheme on how to obtain constructive proofs for combinatorial theorems that have topological proofs so far. To this end the combinatorial concept of Tucker-property of a finite group G is introduced and its relation to the topological Borsuk-Ulam-property is discussed. Applications of the Tucker-property in combinatorics are demonstrated.

Several new observations which lead to new correctness proofs of two known algorithms (Hu-Tucker and Garsia-Wachs) for construction of optimal alphabetic trees are presented. A generalized version of the Garsia-Wachs algorithm is given. Proof of this generalized version works in a structured and illustrative way and clariies the usually poorly-understood behavior of both the Hu-Tucker and Garsi...

Tucker decomposition is a standard method for processing multi-way (tensor) measurements and finds many applications in machine learning data mining, among other fields. When tensor arrive streaming fashion or are too to jointly decompose, incremental analysis preferred. In addition, dynamic adaptation of bases desired when the nominal subspaces change. At same time, it has been documented that...

A tribute for Tucker Childs

Signal recogni t ion particle (SRP) is a r ibonucleoprotein consist ing of six distinct polypept ides and one molecule of smal l cytoplasmic 7SL-RNA. The particle was previously shown to funct ion in protein translocat ion across and protein integrat ion into the endoplasmic ret iculum membrane. fract ions. The part i t ioning of SRP is shown to be dependent on the ionic condi t ions of the fra...

Sequential optimality conditions provide adequate theoretical tools to justify stopping criteria for nonlinear programming solvers. Here, nonsmooth approximate gradient projection and complementary approximate Karush-Kuhn-Tucker conditions are presented. These sequential optimality conditions are satisfied by local minimizers of optimization problems independently of the fulfillment of constrai...

The concept of generalized order statistics (GOSs) was introduced as a unified approach to a variety of models of ordered random variables. The purpose of this paper is to investigate condi- tions on the underlying distribution functions and the parameters on which GOSs are based, to establish Shaked-Shanthikumar multivari- ate dispersive ordering of GOSs from one sample and Khaledi-Kochar mu...