Narrow Results

The experiments at the Large Hadron Collider (LHC) rely upon a complex distributed computing infrastructure (WLCG) consisting of hundreds of individual sites worldwide at universities and national laboratories, providing about half a billion computing job slots and an exabyte of storage interconnected through high speed networks. Wide Area Networking (WAN) is one of the three pillars (together with computational resources and storage) of LHC computing. More than 5 PB/day are transferred between WLCG sites. Monitoring is one of the crucial components of WAN and experiments operations. In the past years all experiments have invested significant effort to improve monitoring and integrate networking information with data management and workload management systems. All WLCG sites are equipped with perfSONAR servers to collect a wide range of network metrics. We will present the latest development to provide the 3D force directed graph visualization for data collected by perfSONAR. The visualization package allows site admins, network engineers, scientists and network researchers to better understand the topology of our Research and Education networks and it provides the ability to identify nonreliable or/and nonoptimal network paths, such as those with routing loops or rapidly changing routes.

Persistent path homology represents an advanced mathematical approach explicitly tailored for directed systems. With its remarkable ability to characterize unbalanced or asymmetrical relationships within data, this method demonstrates great promise in qualitative analysis of the intrinsic topological features present in materials and molecules. In this work, we introduce persistent path homology at the first time for carborane analysis. Intrinsic path topological features are used to predict the stability of closo-carboranes. We qualitatively explain the connection between path topological features and properties on o-C₂B${}_{10}$H${}_{12}$, m-C₂B${}_{10}$H${}_{12}$ and p-C₂B${}_{10}$H${}_{12}$. The correlation coefficients between linear predictions based on persistent path homology and thermodynamic stability are higher than 0.95, and that for chemical stability are about 0.85. While the correlation coefficients based on nonlinear models are increased to 0.99 and 0.95, respectively. These results indicate that persistent path homology shows excellent capabilities in structural and stability analysis of multi-element cluster physics.

We present a laboratory developed in the mathematics activities during the lessons of the research project Mathematical High School at the University of Salerno. We consider a continuous location optimization problem, where an optimal location is found in a continuum on a plane, using a topological approach involving the Voronoi diagram and the Delaunay triangulation to find the equilibrium point.

We investigate the topology of Schwarzschild's black holes through the immersion of this space-time in space of higher dimension. Through the immersions of Kasner and Fronsdal we calculate the extension of the Schwarzschilds black hole.

Watermarking techniques for vector graphics dislocate vertices in order to embed imperceptible, yet detectable, statistical features into the input data. The embedding process may result in a change of the topology of the input data, e.g., by introducing self-intersections, which is undesirable or even disastrous for many applications. In this paper we present a watermarking framework for two-dimensional vector graphics that employs conventional watermarking techniques but still provides the guarantee that the topology of the input data is preserved. The geometric part of this framework computes so-called maximum perturbation regions (MPR) of vertices. We propose two efficient algorithms to compute MPRs based on Voronoi diagrams and constrained triangulations. Furthermore, we present two algorithms to conditionally correct the watermarked data in order to increase the watermark embedding capacity and still guarantee topological correctness. While we focus on the watermarking of input formed by straight-line segments, one of our approaches can also be extended to circular arcs. We conclude the paper by demonstrating and analyzing the applicability of our framework in conjunction with two well-known watermarking techniques.

We study the transition graph of generic Hamiltonian surface flows, whose vertices are the topological equivalence classes of generic Hamiltonian surface flows and whose edges are the generic transitions. Using the transition graph, we can describe time evaluations of generic Hamiltonian surface flows (e.g., fluid phenomena) as walks on the graph. We propose a method for constructing the complete transition graph of all generic Hamiltonian flows. In fact, we construct two complete transition graphs of Hamiltonian surface flows having three and four genus elements. Moreover, we demonstrate that a lower bound on the transition distance between two Hamiltonian surface flows with any number of genus elements can be calculated by solving an integer programming problem using vector representations of Hamiltonian surface flows.

Dramatic advances in the field of complex networks have been witnessed in the past few years. This paper reviews some important results in this direction of rapidly evolving research, with emphasis on the relationship between the dynamics and the topology of complex networks. Basic quantities and typical examples of various complex networks are described; and main network models are introduced, including regular, random, small-world and scale-free models. The robustness of connectivity and the epidemic dynamics in complex networks are also evaluated. To that end, synchronization in various dynamical networks are discussed according to their regular, small-world and scale-free connections.

It is shown that topological changes in space-time are necessary to make General Relativity compatible with the Newtonian limit and to solve the hierarchy of the fundamental interactions. We detail how topology and topological changes appear in General Relativity and how it leaves an observable footprint in space-time. In cosmology we show that such topological observable is the cosmic radiation produced by the acceleration of the universe. The cosmological constant is a very particular case which occurs when the expansion of the universe into the vacuum occurs only in the direction of the cosmic time flow.

In this work we propose a new procedure on how to extract global information of a space-time. We consider a space-time immersed in a higher dimensional space and formulate the equations of Einstein through the Frobenius conditions of immersion. Through an algorithm and implementation into algebraic computing system we calculate normal vectors from the immersion to find the second fundamental form. We make an application for a static space-time with spherical symmetry. We solve Einstein's equations in the vacuum and obtain space-times with different topologies.

Characterizing accurately chaotic behaviors is not a trivial problem and must allow to determine the properties that two given chaotic invariant sets share or not. The underlying problem is the classification of chaotic regimes, and their labeling. Addressing these problems corresponds to the development of a dynamical taxonomy, exhibiting the key properties discriminating the variety of chaotic behaviors discussed in the abundant literature. Starting from the hierarchy of chaos initially proposed by one of us, we systematized the description of chaotic regimes observed in three- and four-dimensional spaces, which cover a large variety of known (and less known) examples of chaos. Starting with the spectrum of Lyapunov exponents as the first taxonomic ranks, we extended the description to higher ranks with some concepts inherited from topology (bounding torus, surface of section, first-return map, …).

By treating extensively the Rössler and the Lorenz attractors, we extended the description of branched manifold — the highest known taxonomic rank for classifying chaotic attractor — by a linking matrix (or linker) to multicomponent attractors (bounded by a torus whose genus $g\ge 3$).

In this paper, we construct a class of quantum systems in a space continuum inspired by results from topological insulator physics. Instead of adding spin–orbit coupling terms suggested by time-reversal invariance as in conventional topological insulators, the terms $L\cdot S$ are determined using supersymmetry as a starting point. This procedure not only restricts the number of possible continuous topological insulators models, but also provides a systematic way to find new continuous topological insulators models. Some explicit quantum mechanical examples are discussed and applications to dark matter physics are also outlined.

Topology, a well-established concept in mathematics, has nowadays become essential to describe condensed matter. At its core are chiral electron states on the bulk, surfaces and edges of the condensed matter systems, in which spin and momentum of the electrons are locked parallel or anti-parallel to each other. Magnetic and non-magnetic Weyl semimetals, for example, exhibit chiral bulk states that have enabled the realization of predictions from high energy and astrophysics involving the chiral quantum number, such as the chiral anomaly, the mixed axial-gravitational anomaly and axions. The potential for connecting chirality as a quantum number to other chiral phenomena across different areas of science, including the asymmetry of matter and antimatter and the homochirality of life, brings topological materials to the fore.

This paper shows that the topological structures of particle orbits generated by a generic class of vector fields on spherical surfaces, called the flow of finite type, are in one-to-one correspondence with discrete structures such as trees/graphs and sequences of letters. The flow of finite type is an extension of structurally stable Hamiltonian vector fields, which appear in many theoretical and numerical investigations of two-dimensional (2D) incompressible fluid flows. Moreover, it contains compressible 2D vector fields such as the Morse–Smale vector fields and the projection of 3D vector fields onto 2D sections. The discrete representation is not only a simple symbolic identifier for the topological structure of complex flows, but it also gives rise to a new methodology of topological data analysis for flows when applied to data brought by measurements, experiments, and numerical simulations of complex flows. As a proof of concept, we provide some applications of the representation theory to 2D compressible vector fields and a 3D vector field arising in an industrial problem.

When hadron-quark continuity is formulated in terms of a topology change at a density higher than twice the nuclear matter density $(n_0)$, the core of massive compact stars can be described in terms of quasiparticles of fractional baryon charges, behaving neither like pure baryons nor like deconfined quarks. Hidden symmetries, both local gauge and pseudo-conformal (or broken scale), emerge and give rise both to the long-standing “effective $g_A^{\ast }\approx 1$” in nuclear Gamow–Teller (GT) transitions at $\lesssim n_0$ and to the pseudo-conformal sound velocity $v_{\mathrm{\text{pcs}}}^2/c^2\approx 1/3$ at $\gtrsim 3n_0$. It is suggested that what has been referred to, since a long time, as “quenched $g_A$” in light nuclei reflects what leads to the dilaton-limit $g_A^{\mathrm{\text{DL}}}=1$ at near the (putative) infrared fixed point of scale invariance. These properties are confronted with the recent observations in GT transitions and in astrophysical observations.

We prove that there is a sequence of purely imaginary parameter values ${\lambda }_n$ converging to $0$ such that the Julia set for $z\mapsto {\lambda }_n(z+1/z)$ is homeomorphic to the Sierpiński carpet fractal; however, for any distinct pair of such parameter values, the dynamics of the map restricted to the Julia set are not conjugate.

QCD axions are at the crossroads of QCD topology and Dark Matter searches. We present here the current status of topological studies on the lattice, and their implication on axion physics. We outline the specific challenges posed by lattice topology, the different proposals for handling them, the observable effects of topology on the QCD spectrum and its interrelation with chiral and axial symmetries. We review the transition to the quark–gluon plasma, the fate of topology at the transition, and the approach to the high temperature limit. We discuss the extrapolations needed to reach the regime of cosmological relevance, and the resulting constraints on the QCD axion.

The non-orientable 4-genus of a knot $K$ in $S^3$ is defined to be the minimum first Betti number of a non-orientable surface $F$ smoothly embedded in $B^4$ so that $K$ bounds $F$. We will survey the tools used to compute the non-orientable 4-genus, and use various techniques to calculate this invariant for non-alternating 11 crossing knots. We will also view obstructions to a knot bounding a Möbius band given by the double branched cover of $S^3$ branched over $K$.

In this paper, we are concerned with the $T$-Graphs, which are graphs defined based on the Topological structure of the given set. Precisely, for a given topology $T$ on a set $X$, a $T$-Graph ‘$G=(V,E)$’ is an undirected simple graph with the vertex set $V$ as $P(X)$ and the edge set $E$ as the set of all unordered pairs of nodes $u,v$ in $V$, denoted by $(u,v)\text{ or }(v,u)$, satisfying either ‘$u\in T$ and $u^{\text{c}}\cap v\in T$’ (or) ‘$v\in T$ and $v^{\text{c}}\cap u\in T$’.

The main purpose of this paper is to study the structure of $T$-Graphs for various topologies $T$ on a set $X$. Our goals in this paper are threefold. First, to show the $L_d(2,1)$ labeling number $\lambda (G,d)$ of any $T$-Graph $G$ exists finitely, if the labeling is $d$ multiple of non-negative integral values. In addition to show this labeling number $\lambda (G,d)$ is not just bounded above but bounded below as well. Second, to measure the bound values in terms of $d$ multiple of the order of the $T$-Graphs and finding a relation between the order of the $T$-Graphs and the maximum degree $\mathrm{\Delta }$ of the $T$-Graphs. Finally, third is to show that in case of $L(2,1)$$T$-graphs on a set with atleast 2 elements, the labeling number is $2(\mathrm{\Delta }+1)$ and is smaller than that of Griggs and Yeh’s conjecture value ${\mathrm{\Delta }}^2$.

This paper introduces the $LM$-fuzzy topology induced by a descending family of $L$-topologies on a given set and derives many of its properties.

Approximation space can be said to play a critical role in the accuracy of the set’s approximations. The idea of “approximation space” was introduced by Pawlak in 1982 as a core to describe information or knowledge induced from the relationships between objects of the universe. The main objective of this paper is to create new types of rough set models through the use of different neighborhoods generated by a binary relation. New approximations are proposed representing an extension of Pawlak’s rough sets and some of their generalizations, where the precision of these approximations is substantially improved. To elucidate the effectiveness of our approaches, we provide some comparisons between the proposed methods and the previous ones. Finally, we give a medical application of lung cancer disease as well as provide an algorithm which is tested on the basis of hypothetical data in order to compare it with current methods.