Narrow Results

The evacuation of human crowds consisting of several groups in complex venues is studied, in this paper, by the kinetic theory of active particles. We consider a complex venue that consists of several chambers which are separated by interior walls and doors, for which the geometrical effects may come from the walls both on the boundary and inside the domain, the exits, and the doors connecting the chambers. The geometrical properties are incorporated in the geometrical preferred direction, which is specified such that an individual can avoid the wall and approach the exit through the evacuation vector. The notion of group is corresponding to the concept of functional subsystem in the mathematical theory of active particles. In the present framework of several groups, the rules of interactions can be specified for both the interactions among the same group and the interactions between different groups. Furthermore, the motility is assigned for each group, which serves as the average activity of a group. Some interesting features and phenomena are shown in the numerical tests of the evacuation of a crowd with one, two or three groups.

Uniform spanning trees on finite graphs and their analogues on infinite graphs are a well-studied area. On a Cayley graph of a group, we show that they are related to the first ℓ²-Betti number of the group. Our main aim, however, is to present the basic elements of a higher-dimensional analogue on finite and infinite CW-complexes, which relate to the higher ℓ²-Betti numbers. One consequence is a uniform isoperimetric inequality extending work of Lyons, Pichot, and Vassout. We also present an enumeration similar to recent work of Duval, Klivans and Martin.

Strongly Lensed systems, and in particular gravitational arcs, are useful tools for a variety of astrophysical applications. Finding arcs in wide-field surveys such as the Dark Energy Survey (DES) requires automated algorithms to select arc candidates due to the large amount of data. In this contribution we present a new arcfinding method that uses the Mediatrix filamentation method coupled to a neural network to select arc candidates. We carry out a systematic comparison between this method and three other arcfinders available in the literature — Lenzen et al. (2004), Horesh et al. (2005), and More et al. (2012) — on a sample of arc simulated with the PaintArcs method.

We present modeling strategies that describe the motion and interaction of groups of pedestrians in obscured spaces. We start off with an approach based on balance equations in terms of measures and then we exploit the descriptive power of a probabilistic cellular automaton model.

Based on a variation of the simple symmetric random walk on the square lattice, we test the interplay between population size and an interpersonal attraction parameter for the evacuation of confined and darkened spaces. We argue that information overload and coordination costs associated with information processing in small groups are two key processes that influence the evacuation rate. Our results show that substantial computational resources are necessary to compensate for incomplete information — the more individuals in (information processing) groups the higher the exit rate for low population size. For simple social systems, it is likely that the individual representations are not redundant and large group sizes ensure that this non-redundant information is actually available to a substantial number of individuals. For complex social systems, information redundancy makes information evaluation and transfer inefficient and, as such, group size becomes a drawback rather than a benefit. The effect of group sizes on outgoing fluxes, evacuation times and wall effects is carefully studied with a Monte Carlo framework accounting also for the presence of an internal obstacle.

In 2019, Öztürk et al. [Gamma semigroups on weak nearness approximation spaces, Journal of the International Mathematical Virtual Institute9 (2019) 53–72] defined the first algebraic structure on weak nearness approximation spaces which is the gamma semigroup. After this study, the view on the nearness of algebraic structures has completely changed. This view was first expressed in a previous study in 2021 [M. A. Öztürk, Nearness $d$-algebras, Journal of Algebraic Hyperstructures and Logical Algebras2 (2021) 73–84]. Our aim is to give the concept of modulo in the nearness group $G$ as in the nearness group $(Z,+)$, where $Z$ is the set of integers. Afterward, based on the concept of modulo in the nearness group $G$, the nearness cosets of the nearness group $G$ are constructed and its basic properties are examined. Lastly, it is seen that Lagrange theorem is not valid for the nearness subgroups as compared to the usual subgroups.

Let M be a closed connected manifold and let D be an elliptic operator on M. Let G be a discrete countable group and let be a principal G-bundle. Connes and Moscovici showed that this data defines an analytic index ind_ℓ¹(G)(D) ∈ K₀(ℓ¹(G)). If B is a unital tracial C*-algebra, we give a formula for the trace of the image of ind_ℓ¹(G)(D) in K₀(B) under the map induced by a quasi-representation of G in B. As an application, we reprove and generalize a formula of Exel and Loring to surface groups.