We study a process of pattern formation for generic model species anchored to the nodes network where local reactions take place, and that experience non-reciprocal long-range interactions, encoded by directed links. By assuming system exhibit stable homogeneous equilibrium whenever only interactions are considered, we prove such can turn unstable once suitable allowed for. Stated differently p...

In recent years, active periodic structures with in-time modulated parameters have drawn ever-increasing attention due to their peculiar (and sometimes exotic) wave propagation properties. Although many experimental works shown the efficacy of time-modulation strategies, benchmarks proposed until now been mostly proof-of-concept demonstrators, little feasibility solution for practical purposes....

Community initiatives are started in a variety of ways including tackling tenacious community issues and addressing persistent disparities across residents. An urban/rural, county-wide initiative the southeastern United States, gathered cross-sector group to create culture literacy. Armed with an “all children our children” attitude, stakeholders transformed thoughts into programs (...

We obtain the limiting behavior of the sum of reciprocal powers of a random sample. In particular, the mean sample reciprocal tends to a Cauchy distribution centered on the principal value (PV) of the mean population reciprocal. AMS 2000 subject classification: Primary 60E07; Secondary 60F05.

In this contribution, we first investigate sharp bounds for the reciprocal sum-degree distance of graphs with a given matching number. The corresponding extremal graphs are characterized completely. Then we explore the k-decomposition for the reciprocal sum-degree distance. Finally,we establish formulas for the reciprocal sum-degree distance of join and the Cartesian product of graphs.

In this paper we address the problem of identifying reciprocal relationships in English. In particular we introduce an algorithm that semi-automatically discovers patterns encoding reciprocity based on a set of simple but effective pronoun templates. Using a set of most frequently occurring patterns, we extract pairs of reciprocal pattern instances by searching the web. Then we apply two unsupe...