The appearance of numbers enumerating alternating sign matrices in stationary states of certain stochastic processes on matchings is reviewed. New conjectures concerning nest distribution functions are presented as well as a bijection between certain classes of alternating sign matrices and lozenge tilings of hexagons with cut off corners.

humans suffer transient or persistent starvation due to a lack of food intake, either because of fasting, voluntary dieting, or due to the scarcity of available food. at the cellular level it is possible to possess pathological starvation during ischemia and solid tumors. blood provides many nutrients to our cells, and researchers provide these nutrients to cells in culture in the form of enric...

Soliton graphs having an alternating cycle are characterized with the help of a shrinking procedure. This characterization leads to a method testing the existence of an alternating cycle in a soliton graph. The suggested algorithm runs in O(n3) time, where n is the number of vertices in the graph. Key-Words: Combinatorial Problems, Graph Matchings, Alternating cycles, Soliton graphs, 1-extendab...

The state-alternating context-free grammars are introduced, and the language classes obtained from them are compared to the classes of the Chomsky hierarchy as well as to some well-known complexity classes. In particular, the state-alternating context-free grammars are compared to the alternating context-free grammars of Moriya (1989) and to the alternating pushdown automata. Further, various d...

Grossman and HH aggkvist gave a characterisation of two-edge-coloured graphs, which have an alternating cycle (i.e. a cycle in which no two consecutive edges have the same colour). We extend their characterisa-tion to edge-coloured graphs, with any number of colours. That is we show that if there is no alternating cycle in an edge-coloured graph, G, then it contains a vertex z, such that there ...

Given integers $k,l\geq 2$, where either $l$ is odd or $k$ even, let $n(k,l)$ denote the largest integer $n$ such that each element of $A_n$ a product many $l$-cycles. In 2008, M. Herzog, G. Kaplan and A. Lev proved if $k,l$ both are odd, $3\mid l$ $l>3$, then $n(k,l)=\frac{2}{3}kl$. They further conjectured even l$, $n(k,l)=\frac{2}{3}kl+1$. this article, we prove conjecture. We also $n(k,3)=2...

Abstract In 2021, Casares, Colcombet, and Fijalkow introduced the Alternating Cycle Decomposition (ACD) to study properties transformations of Muller automata. We present first practical implementation ACD in two different tools, Owl Spot, adapt it framework Emerson-Lei automata, i.e., $$\omega $$ ω -automata...

The Na(+)/K(+)-pump maintains the physiological K(+) and Na(+) electrochemical gradients across the cell membrane. It operates via an 'alternating-access' mechanism, making iterative transitions between inward-facing (E1) and outward-facing (E2) conformations. Although the general features of the transport cycle are known, the detailed physicochemical factors governing the binding site selectiv...

The value of a postremission treatment in acute myelogenous leukemia (AML), with alternating combinations of non-cross-resistant drugs, has been prospectively assessed. Of 515 evaluable patients, 347 (67.4%) entered into complete remission (CR), following induction treatment with daunorubicin (DNR), vincristine (VCR), and cytosine arabinoside (ara-C). After one consolidation course, 248 patient...