A hypergraph is k-irregular if there is no set of k vertices all of which have the same degree. We asymptotically determine the probability that a random uniform hypergraph is k-irregular.

Let G = (V,E), V = {1,2, . . . ,n}, be a simple graph without isolated vertices, with vertex degree sequence d1 ≥ d2 ≥ ·· · ≥ dn > 0, di = d(i). A graph G is regular if and only if d1 = d2 = · · · = dn. A graph invariant I(G) is measure of irregularity of graph G with the property I(G) = 0 if and only ifG is regular, and I(G)> 0 otherwise. In this paper we introduce some new irregularity measures.

In aortic stenosis, systemic arterial peak systolic pressure may remain relatively steady in the face of marked, arrhythmia-induced, variations in left ventricular peak systolic pressure. A possible basis for this phenomenon is presented. It is suggested that beat-tobeat variations in the systolic pressure gradient across the aortic valve region may not always reflect variations in stroke volume.

It is an elementary exercise to show that any non-trivial simple graph has two vertices with the same degree. This is not the case for digraphs and multigraphs. We consider generating irregular digraphs from arbitrary digraphs by adding multiple arcs. To this end, we define an irregular labeling of a digraph D to be an arc labeling of the digraph such that the ordered pairs of the sums of the i...

Introduction. The purpose of this report is to draw attention to some nontrivial connections between the ("continuous") theory of irregularities of distribution and discrete mathematics. The object of the theory of irregularities of distribution is to measure the uniformity (or nonuniformity) of sequences and point sets. For instance: how uniformly can an arbitrary set of N points in the unit c...

’n Steekproef van 47 Blanke Suid-Afrikaners is bestudeer met die oog op hulle ervaringe van en houding teenoor nieortodokse genesers. Die uitslag van die beperkte ondersoek beklemtoon die uiters mitiese aard van wat deurgaan vir wat algemeen bekend is oor alternatiewe praktisyns. Verskeie bedenksels word ondersoek en daar word tot die slotsom gekom dat Blanke Suid-Afrikaners gewoonlik deeglik b...

High firing irregularity is a hallmark of cortical neurons in vivo, and modeling studies suggest a balance of excitation and inhibition is necessary to explain this high irregularity. Such a balance must be generated, at least partly, from local interconnected networks of excitatory and inhibitory neurons, but the details of the local network structure are largely unknown. The dynamics of the n...

The total irregularity of a simple undirected graphG is defined as irrt(G) = 1 2 ∑ u,v∈V (G) |dG(u)− dG(v)|, where dG(u) denotes the degree of a vertex u ∈ V (G). Obviously, irrt(G) = 0 if and only if G is regular. Here, we characterize the non-regular graphs with minimal total irregularity and thereby resolve the recent conjecture by Zhu, You and Yang [18] about the lower bound on the minimal ...

The Internet of Things (IoT) refers to a large cyber-physical system centered around the Internet that connects not just computer systems but a plethora of systems, devices, and objects, collectively referred to as ”Things”. It encompasses technologies for identification and tracking, sensing and actuation, both wired and wireless communications, and also, intelligence and cognition. Wireless c...