Related papers: Methods of generating soft topologies and soft sep…

We use numerical simulations to understand how random deviations from the ideal spherical shape affect the ability of hard particles to form fcc crystalline structures. Using a system of hard spheres as a reference, we determine the…

Starting from filters over the set of indices, we introduce structures in a product of sets where the coordinate sets have the given structures.

We introduce a framework for constructing fractal trees via analytic generator fields, replacing discrete affine transformations and symbolic rewriting rules by the integration of smooth vector fields in an internal state space. In this…

Topological invariants have proved useful for analyzing emergent function as they characterize a property of the entire system, and are insensitive to local details, disorder, and noise. They support boundary states, which reduce the system…

Soft theorems can be recast as Ward identities of asymptotic symmetries. We review such relation for the leading and subleading soft graviton theorems in arbitrary even dimensions. While soft theorems are trivially generalized to dimensions…

We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. In this second part we introduce the fundamental concepts of topological spaces, convergence, and continuity, as…

We identify two orthogonal sources of structural entropy in rattler-free granular systems - affine, involving structural changes that only deform the contact network, and topological, corresponding to different topologies of the contact…

Solids deform and fluids flow, but soft glassy materials, such as emulsions, foams, suspensions, and pastes, exhibit an intricate mix of solid and liquid-like behavior. While much progress has been made to understand their elastic (small…

Products between phase-type distributed random variables and any independent, positive and continuous random variable are studied. Their asymptotic properties are established, and an expectation-maximization algorithm for their effective…

A pattern of interaction that arises again and again in programming is a "handshake", in which two agents exchange data. The exchange is thought of as provision of a service. Each interaction is initiated by a specific agent--the client or…

We present a unified framework to systematically embed complex knotted and linked structures, beyond the torus family, into diverse topological phases, including Hopf insulators, classical spin liquids, topological semimetals, and…

In many combinatorial problems one may need to model the diversity or similarity of assignments in a solution. For example, one may wish to maximise or minimise the number of distinct values in a solution. To formulate problems of this…

We consider various notions of completeness in symplectic topology and ask two related questions. Does a complete open symplectic manifold remain complete after excising a subset? Can two sets be made arbitrarily far apart by adjusting the…

We construct a `nice' subcomplex of the Outer Space for a free product in order to give a geometric proof that the pure symmetric outer automorphisms of a given splitting of a free product are generated by factor outer automorphisms and…

We consider a metapopulation version of the Schelling model of segregation over several complex networks and lattice. We show that the segregation process is topology independent and hence it is intrinsic to the individual tolerance. The…

Developable surfaces are commonly observed in various applications such as architecture, product design, manufacturing, mechanical materials, and data physicalization as well as in the development of tangible interaction and deformable…

We investigate some properties of topological groups related to disconnectedness or Archimedeanness. We prove or disprove the preservation of those under operations as subgroups, quotients, products, etc. Characterizations of…

While topology given by a linear order has been extensively studied, this cannot be said about the case when the order is given only locally. The aim of this paper is to fill this gap. We consider relation between local orderability and…

One approach to monitoring a dynamic system relies on decomposition of the system into weakly interacting subsystems. An earlier paper introduced a notion of weak interaction called separability, and showed that it leads to exact…

This paper considers networks where relationships between nodes are represented by directed dissimilarities. The goal is to study methods for the determination of hierarchical clusters, i.e., a family of nested partitions indexed by a…