In this paper, flow models of networks without congestion control are considered. Users generate data transfers according to some Poisson processes and transmit corresponding packet at a fixed rate equal to their access rate until the entire document is received at the destination; some erasure codes are used to make the transmission robust to packet losses. We study the stability of the stocha...

Stochastic models sometimes behave qualitatively differently from their deterministic analogues. We explore the implications of this in ecosystems that shift suddenly from one state to another. This phenomenon is usually studied through deterministic models with multiple stable equilibria under a single set of conditions, with stability defined through linear stability analysis. However, in sto...

The problem of the asymptotic stability independent of delays for a class of linear systems including multiple delays is addressed. Both cases where the delays are allowed to vary independently of each other, and where they are restricted to a one-dimensional subspace of the delay-parameter space are considered. It the latter case it turns out that the resulting dependency between the delays (r...

Central counterparties’ (CCPs) role is to take over the counterparty risk during trading. To fulfill its role, a CCP needs operate multi-level guarantee system that can absorb losses of clearing members’ defaults. Our main question how size changes and cross-guarantee undertaking between members markets if merges systems different markets. This essential from financial stability perspective sin...

We speculate on whether a certain p-adic stability phenomenon, observed by David Robbins empirically for Dodgson condensation, appears in other nonlinear recurrence relations that “unexpectedly” produce integer or nearly-integer sequences. We exhibit an example (number friezes) where this phenomenon provably occurs. This note may be viewed as an addendum to Robbins’s note [5] in this volume. It...

Vascular acrosyndromes constitute a common reason for physician visits. They are associated with connective tissue disease; for example, 90% of patients with scleroderma experience Raynaud's phenomenon. The rheumatologist must strive to establish the diagnosis, to identify a potential underlying cause, and to prescribe effective treatment when the symptoms are incapacitating. Raynaud's phenomen...

Raynauds phenomena (RP) is a commonly encountered clinical manifestation which may be primary or secondary to underlying disease. There is imbalance between vasoconstricting and vasodilating factors. Physical examination, nailfold capillaroscopy and immunological tests can differentiate primary from secondary RP. Treatment involves prevention of RP so that permanent ischemic damage i.e. gangren...

In general weak domination number γw(G) can be made to increase or decrease by the removal of vertices from a graph G. In this paper. Our main objective is the study of this phenomenon. Further, the stability of the weak domination number of a graph G is investigated. Mathematics Subject Classification: 05c69, 05C70