The category of combinatorial systems is a model category for ”scaling up” algorithms. This involves networks of algorithms, herein called schedules, acting on very wide range of inputs types that are outputs from other algorithms. This patching algorithms over networks gives rise to the subcategory of combinatorial modules which are an algebraic analogy for the creation of manifolds from Eucli...

We present a solution to the inverse scattering problem for differential Laplace operators on metric noncompact graphs. We prove that for almost all boundary conditions (i) the scattering matrix uniquely determines the graph and its metric structure, (ii) the boundary conditions are determined uniquely up to trivial gauge transformations. The main ingredient of our approach is a combinatorial F...

In a semigroup, the combinatorial definitions of syndetic, piecewise syndetic, and IP are equivalent to their algebraic characterizations in terms of βS. We introduce the analogous definitions and characterizations of syndetic, piecewise syndetic, and IP for an adequate partial semigroup and show that equivalence between the combinatorial definition and algebraic characterization is lost once w...

We consider the problem of characterizing the stability of eeectivity functions (EFF), via a combinatorial correspondance between game theoretic and well-known combinatorial concepts. To every EFF we assign a pair of hypergraphs, representing clique covers of two associated graphs, and obtain some necessary and some suucient conditions for the stability of EFFs in terms of graph-properties. The...

Vendor selection decisions are complicated by the fact that various conflicting multi-objective factors must be considered in the decision making process. The problem of vendor selection becomes still more compli-cated with the inclusion of incremental discount pricing schedule. Such hard combinatorial problems when solved using meta heuristics produce near optimal solutions. This paper propose...

In recent years, combinatorial methods have attracted a great deal of attention. Among them, sono-combining techniques have shown a significant potential as an economic technology applicable and environment-friendly technology for wastewater treatment. In this study, Sono Electrochemical SE, Sono Photo Electrochemical SPE and Sono Photo Electro Catalytic SPEC techniques were investigated for de...

In this article we present several developed and improved combinatorial techniques to optimize processing conditions and material properties of organic thin films. The combinatorial approach allows investigations of multi-variable dependencies and is the perfect tool to investigate organic thin films regarding their high performance purposes. In this context we develop and establish the reliabl...

Spinal cord injury (SCI) is one of the devastating conditions leading to functional and neurological deficits following road traffic accidents. To date, there is no definite treatment for repairing damaged spinal cord tissue. In this regard, cell therapy opens a new window in front of scientists by using different cells such as mesenchymal stem cells, olfactory ensheathing cells, Schwann cells,...