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...

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...

K. Rastle and M. Coltheart (1999; see also M. Coltheart & K. Rastle, 1994) reported data demonstrating that the cost of irregularity in reading aloud low-frequency exception words is modulated by the position of the irregularity in the word. They argued that these data implicated a serial process and falsified all models of reading aloud that operate solely in parallel, a conclusion that M. Zor...

BACKGROUND Menstrual irregularity is a common major complaint in women of reproductive age. It is also a known marker for underlying insulin resistance. We investigated the association between menstrual irregularity and metabolic syndrome in the general population of middle-aged women in Korea. METHODS This cross-sectional study used data from the Korea National Health and Nutrition Examinati...

Irregularity is an important aspect of the cardiovascular system dynamics. Numerical indices irregularity, such as largest Lyapunov exponent and correlation dimension estimated from interbeat interval time series, are early markers diseases. However, there no consensus on origin irregularity in system. A common hypothesis suggests importance nonlinear bidirectional coupling between respiratory ...

PURPOSE To report refractive and visual acuity outcomes using wavefront-guided optical path difference custom ablation treatments (OPDCAT; NIDEK Co Ltd) for myopia and myopic astigmatism. METHODS One hundred eyes of 50 patients with preoperative manifest refraction spherical equivalent (MRSE) of 4.62+/-1.30 diopters (D) (range: -1.38 to -7.25 D) with mean astigmatism of -0.57+/-0.37 D (range:...

A new formulation of Randić index is carried out as a minimization of a quadratic form which involves the Laplacian matrix of a graph. Using this formulation it is easy to realize that Randić index is useful in defining a new index of irregularity, which is then formulated here. A new context for the study of irregularity of graphs is advanced as a necessity for studying complex (biological) ne...