Tootfinder

internet_top_pop: Internet topology (PoP level) (1969-2012)
Assorted snapshots of internet graph at the Point of Presence (PoP) level (which lies between the IP and AS levels), collected from around the world and at various times. The earliest snapshots are for ARPANET (1969-1972), with a few more from pre-2000. Most are from 2006 onward. Metadata include link type or speed, longitudes, and latitudes of nodes, URL, and date of record.
This network has 16 nodes and 15 edges.

Multijet event shape variables for Mueller Navelet jet topologies
C. Baldenegro, G. Chachamis, M. Kampshoff, M. Klasen, G. J. Milhano, C. Royon, A. Sabio Vera
https://arxiv.org/abs/2406.10681

Multijet event shape variables for Mueller Navelet jet topologies
This paper presents a new set of multijet event shape variables introduced to further understand the Mueller-Navelet jet topology. This topology consists of having at least one pair of jets with a very large rapidity separation between them, treating additional jet activity inclusively. This multijet topology is expected to shed light on the radiation pattern that is expected in the high-energy limit of the strong interaction. The paper relies on a Monte Carlo event generator analysis. One set …

This https://arxiv.org/abs/2304.00814 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Strong large deviation principles for pair empirical measures of random walks in the Mukherjee-Varadhan topology
In this paper we introduce a topology under which the pair empirical measure of a large class of random walks satisfies a strong Large Deviation principle. The definition of the topology is inspired by the recent article by Mukherjee and Varadhan [16]. This topology is natural for translation-invariant problems such as the downward deviations of the volume of a Wiener sausage or simple random walk, known as the Swiss cheese model [18]. We also adapt our result to some rescaled random walks and …

Observations of Fan-Spine Topology by Solar Orbiter/EUI: Rotational Motions and Indications of Alfv\'en Waves
E. Petrova, T. Van Doorsselaere, D. Berghmans, S. Parenti, G. Valori, J. Plowman
https://arxiv.org/abs/2404.10577

Observations of Fan-Spine Topology by Solar Orbiter/EUI: Rotational Motions and Indications of Alfvén Waves
Torsional Alfvén waves do not produce any intensity variation and are, therefore, challenging to observe with imaging instruments. Previously, Alfvén wave observations were reported throughout all the layers of the solar atmosphere using spectral imaging. We present an observation of a torsional Alfvén wave detected in an inverted y-shape structure observed with the HRIEUV telescope of the EUI instrument onboard Solar Orbiter in its 174 Å channel. The feature consists of two footpoints conn…

This https://arxiv.org/abs/2403.20245 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A topology on the poset of quiver mutation classes
To better understand mutation-invariant and hereditary properties of quivers (and more generally skew-symmetrizable matrices), we have constructed a topology on the set of all mutation classes of quivers which we call the mutation class topology. This topology is the Alexandrov topology induced by the poset structure on the set of mutation classes of quivers from the partial order of quiver embedding. The closed sets of our topology -- equivalently, the lower sets of the poset -- are in bijecti…

Multi-scale Topology Optimization using Neural Networks
Hongrui Chen, Xingchen Liu, Levent Burak Kara
https://arxiv.org/abs/2404.08708 https://

Multi-scale Topology Optimization using Neural Networks
A long-standing challenge is designing multi-scale structures with good connectivity between cells while optimizing each cell to reach close to the theoretical performance limit. We propose a new method for direct multi-scale topology optimization using neural networks. Our approach focuses on inverse homogenization that seamlessly maintains compatibility across neighboring microstructure cells. Our approach consists of a topology neural network that optimizes the microstructure shape and distr…

This https://arxiv.org/abs/2007.07879 has been replaced.
link: https://scholar.google.com/scholar?q=a

Preservation Theorems Through the Lens of Topology
In this paper, we introduce a family of topological spaces that captures the existence of preservation theorems. The structure of those spaces allows us to study the relativisation of preservation theorems under suitable definitions of surjective morphisms, subclasses, sums, products, topological closures, and projective limits. Throughout the paper, we also integrate already known results into this new framework and show how it captures th essence of their proofs.

Multijet event shape variables for Mueller Navelet jet topologies
C. Baldenegro, G. Chachamis, M. Kampshoff, M. Klasen, G. J. Milhano, C. Royon, A. Sabio Vera
https://arxiv.org/abs/2406.10681

Multijet event shape variables for Mueller Navelet jet topologies
This paper presents a new set of multijet event shape variables introduced to further understand the Mueller-Navelet jet topology. This topology consists of having at least one pair of jets with a very large rapidity separation between them, treating additional jet activity inclusively. This multijet topology is expected to shed light on the radiation pattern that is expected in the high-energy limit of the strong interaction. The paper relies on a Monte Carlo event generator analysis. One set …

topology: Internet AS graph (2004)
An integrated snapshot of the structure of the Internet at the level of Autonomous Systems (ASs), reconstructed from multiple sources, including the RouteViews and RIPE BGP trace collectors, route servers, looking glasses, and the Internet Routing Registry databases. This snapshot was created around October 2004.
This network has 34761 nodes and 171403 edges.
Tags: Technological, Communication, Unweighted, Multigraph, Timestamps

This https://arxiv.org/abs/2302.03057 has been replaced.
initial toot: https://mastoxiv.page/@a…

Topological Non-Hermitian skin effect
This article reviews recent developments in the non-Hermitian skin effect (NHSE), particularly on its rich interplay with topology. The review starts off with a pedagogical introduction on the modified bulk-boundary correspondence, the synergy and hybridization of NHSE and band topology in higher dimensions, as well as, the associated topology on the complex energy plane such as spectral winding topology and spectral graph topology. Following which, emerging topics are introduced such as non-He…

Visceral theories without assumptions
Will Johnson
https://arxiv.org/abs/2404.11453 https://arxiv.org/pdf/2404.11453

Visceral theories without assumptions
Let $T$ be a theory with a definable topology. $T$ is t-minimal in the sense of Mathews if every definable set in one variable has finite boundary. If $T$ is t-minimal, we show that there is a good dimension theory for definable sets, satisfying properties similar to dp-rank in dp-minimal theories, with one key exception: the dimension of $\operatorname{dom}(f)$ can be less than the dimension of $\operatorname{im}(f)$ for a definable function $f$. Using the dimension theory, we show that any de…

This https://arxiv.org/abs/2309.10110 has been replaced.
initial toot: https://mastoxiv.page/@a…

Topological modes and spectral flows in inhomogeneous PT-symmetric continuous media
In classical Hermitian continuous media, the spectral-flow index of topological modes is linked to the bulk topology via index theorem. However, the interface between two bulks is usually non-Hermitian due to the inhomogeneities of system parameters. We show that the connection between topological modes and bulk topology still exists despite the non-Hermiticity at the interface if the system is endowed with PT symmetry. The theoretical framework developed is applied to the Hall magnetohydrodyna…

This https://arxiv.org/abs/2401.17484 has been replaced.
link: https://scholar.google.com/scholar?q=a

Pixel to Elevation: Learning to Predict Elevation Maps at Long Range using Images for Autonomous Offroad Navigation
Understanding terrain topology at long-range is crucial for the success of off-road robotic missions, especially when navigating at high-speeds. LiDAR sensors, which are currently heavily relied upon for geometric mapping, provide sparse measurements when mapping at greater distances. To address this challenge, we present a novel learning-based approach capable of predicting terrain elevation maps at long-range using only onboard egocentric images in real-time. Our proposed method is comprised …

Topology optimization of blazed gratings under conical incidence
Simon Ans (Laboratoire d'Astrophysique de Marseille, Institut Fresnel), Fr\'ed\'eric Zamkotsian (Laboratoire d'Astrophysique de Marseille), Guillaume Dem\'esy (Institut Fresnel)
https://arxiv.org/abs/2403.10174

Topology optimization of blazed gratings under conical incidence
A topology optimization method is presented and applied to a blazed diffraction grating in reflection under conical incidence. This type of gratings is meant to disperse the incident light on one particular diffraction order and this property is fundamental in spectroscopy. Conventionally, a blazed metallic grating is made of a sawtooth profile designed to work with the +/-1st diffraction order in reflection. In this paper, we question this intuitive triangular pattern and look for optimal opto…

Tuneable band topology and optical conductivity in altermagnets
Peng Rao, Alexander Mook, Johannes Knolle
https://arxiv.org/abs/2403.10509 https://<…

Tuneable band topology and optical conductivity in altermagnets
We study two-dimensional $d$-wave altermagnetic metals taking into account the presence of substrate-induced Rashba spin-orbit coupling. We consider the altermagnet bandstructure using a 2D band Hamiltonian near the $Γ$ point under external magnetic field. It is shown that time-reversal-symmetry breaking due to altermagnetism, together with Rashba coupling and external magnetic field, can result in non-trivial band topology. The topological phases can be tuned by magnetic field strength and di…

[2024-06-17 Mon (UTC), 1 new article found for math.AT Algebraic Topology]

Thermodynamic topology of Phantom AdS Black Holes in Massive Gravity
Hao Chen, Meng-Yao Zhang, Hassan Hassanabadi, Zheng-Wen Long
https://arxiv.org/abs/2404.08243

Thermodynamic topology of Phantom AdS Black Holes in Massive Gravity
In this work, we explore the thermodynamic topology of phantom AdS black holes in the context of massive gravity. To this end, we evaluate these black holes in two distinct ensembles: the canonical and grand canonical ensembles (GCE). We begin by examining the topological charge linked to the critical point and confirming the existence of a conventional critical point $(CP_{1})$ in the canonical ensemble (CE), this critical point has a topological charge of $-1$ and acts as a point of phase ann…

[2024-06-17 Mon (UTC), 5 new articles found for math.GT Geometric Topology]

On the genericity of singularities in spacetimes with weakly trapped submanifolds
Victor Luis Espinoza, Ivan Pontual Costa e Silva
https://arxiv.org/abs/2406.09651

On the genericity of singularities in spacetimes with weakly trapped submanifolds
We investigate suitable, physically motivated conditions on spacetimes containing certain submanifolds - the so-called {weakly trapped submanifolds} - that ensure, in a set of neighboring metrics with respect to a convenient topology, that the phenomenon of nonspacelike geodesic incompleteness (i.e., the existence of singularities) is generic in a precise technical sense. We obtain two sets of results. First, we use strong Whitney topologies on spaces of Lorentzian metrics on a manifold $M$, in…

Diagram Control and Model Order for Sugiyama Layouts
S\"oren Domr\"os, Reinhard von Hanxleden
https://arxiv.org/abs/2406.11393 https://

Diagram Control and Model Order for Sugiyama Layouts
Graphical WYSIWYG editors programming languages are popular since they allow to control the diagram layout to express intention via secondary notation such as proximity and topology. However, such editors typically require users to do manual layout. Conversely, automatic layout of diagrams typically fails to capture intention because graphs are usually considered to not contain any order. Model order can combine the desire for control of secondary notation with automatic layout, without additio…

Optimization policy for file replica placement in fog domains
Carlos Guerrero, Isaac Lera, Carlos Juiz
https://arxiv.org/abs/2406.09824 https://

Optimization policy for file replica placement in fog domains
Fog computing architectures distribute computational and storage resources along the continuum from the cloud to things. Therefore, the execution of services or the storage of files can be closer to the users. The main objectives of fog computing domains are to reduce the user latency and the network usage. Availability is also an issue in fog architectures because the topology of the network does not guarantee redundant links between devices. Consequently, the definition of placement polices i…

[2024-03-18 Mon (UTC), 1 new article found for math.GN General Topology]

This https://arxiv.org/abs/2307.06553 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

Coordinated Path Following of UAVs over Time-Varying Digraphs Connected in an Integral Sense
This paper presents a new connectivity condition on the information flow between UAVs to achieve coordinated path following. The information flow is directional, so that the underlying communication network topology is represented by a time-varying digraph. We assume that this digraph is connected in an integral sense. This is a much more general assumption than the one currently used in the literature. Under this assumption, it is shown that a decentralized coordination controller ensures expo…

This https://arxiv.org/abs/2306.13757 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A topology on E-theory
For separable $C^*$-algebras $A$ and $B$, we define a topology on the set $[[A, B]]$ consisting of homotopy classes of asymptotic morphisms from $A$ to $B$. This gives an enrichment of the Connes--Higson asymptotic category over topological spaces. We show that the Hausdorffization of this category is equivalent to the shape category of Dadarlat. As an application, we obtain a topology on the $E$-theory group $E(A, B)$ with properties analogous to those of the topology on $KK(A, B)$. The Hausdo…

Hidden zero modes and topology of multiband non-Hermitian systems
K. Monkman, J. Sirker
https://arxiv.org/abs/2405.09728 https://arxi…

Global topological synchronization of weighted simplicial complexes
Runyue Wang, Riccardo Muolo, Timoteo Carletti, Ginestra Bianconi
https://arxiv.org/abs/2404.11337

Global topological synchronization of weighted simplicial complexes
Higher-order networks are able to capture the many-body interactions present in complex systems and to unveil new fundamental phenomena revealing the rich interplay between topology, geometry, and dynamics. Simplicial complexes are higher-order networks that encode higher-order topology and dynamics of complex systems. Specifically, simplicial complexes can sustain topological signals, i.e., dynamical variables not only defined on nodes of the network but also on their edges, triangles, and so …

topology: Internet AS graph (2004)
An integrated snapshot of the structure of the Internet at the level of Autonomous Systems (ASs), reconstructed from multiple sources, including the RouteViews and RIPE BGP trace collectors, route servers, looking glasses, and the Internet Routing Registry databases. This snapshot was created around October 2004.
This network has 34761 nodes and 171403 edges.
Tags: Technological, Communication, Unweighted, Multigraph, Timestamps

This https://arxiv.org/abs/2309.06340 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Non-Hausdorff germinal groupoids for actions of countable groups
We study conditions under which the germinal groupoid associated to a minimal equicontinuous action of a countable group on a Cantor set has non-Hausdorff topology. We develop a new criterion, which serves as an obstruction for the étale topology on the groupoid to be non-Hausdorff. We use this and other criteria to study the topology of germinal groupoids for a few classes of actions. In particular, we give examples of families of contracting and non-contracting self-similar groups, which are…

Some of you think this is probably vaporware by now, but there actually has been a 2D/3D mesh package since 2016, which for various reasons has been dormant for the past few years, since I never got around refactoring & publishing it properly, mostly because some of the features are very low level and in need of a more TS/JS-friendly API (though I made several attempts on that front since).
The mesh implementation combines my favorite modeling, topology & traversal features of …

Generic, modular, extensible API bridge and infrastructure for hybrid JS & WebAssembly projects

This https://arxiv.org/abs/2310.16886 has been replaced.
initial toot: https://mastoxiv.page/@a…

Photo-induced electronic and spin topological phase transitions in monolayer bismuth
Ultrathin bismuth exhibits rich physics including strong spin-orbit coupling, ferroelectricity, nontrivial topology, and light-induced structural dynamics. We use \textit{ab initio} calculations to show that light can induce structural transitions to four transient phases in bismuth monolayers. These light-induced phases exhibit nontrivial topological character, which we illustrate using the recently introduced concept of spin bands and spin-resolved Wilson loops. Specifically, we find that the…

This https://arxiv.org/abs/2209.06319 has been replaced.
link: https://scholar.google.com/scholar?q=a

Structural, point-free, non-Hausdorff topological realization of Borel groupoid actions
We extend the Becker--Kechris topological realization and change-of-topology theorems for Polish group actions in several directions. For Polish group actions, we prove a single result that implies the original Becker--Kechris theorems, as well as Sami's and Hjorth's sharpenings adapted levelwise to the Borel hierarchy; automatic continuity of Borel actions via homeomorphisms; and the equivalence of "potentially open" versus "orbitwise open" Borel sets. We also characterize "potentially open" $…

This https://arxiv.org/abs/2111.12670 has been replaced.
link: https://scholar.google.com/scholar?q=a

A representation theorem for end spaces of infinite graphs
End-structures of infinite graphs sit at the interface between graph theory, group theory and topology. They arise as the boundary of an infinite graph in a standard sense generalising the theory of the Freudenthal boundary developed by Freudenthal and Hopf in the 1940's for infinite~groups. A long-standing quest in infinite graph theory with a rich body of literature seeks to represent or capture the end-structures of infinite graphs. Halin, Diestel and Carmesin raised open questions that fo…

Heute.

[2024-05-17 Fri (UTC), 4 new articles found for math.GT Geometric Topology]

This https://arxiv.org/abs/2310.01968 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCE_…

PyHexTop: a compact Python code for topology optimization using hexagonal elements
Python serves as an open-source and cost-effective alternative to the MATLAB programming language. This paper introduces a concise topology optimization Python code, named ``\texttt{PyHexTop}," primarily intended for educational purposes. Code employs hexagonal elements to parameterize design domains as such elements provide checkerboard-free optimized design naturally. \texttt{PyHexTop} is developed based on the ``\texttt{HoneyTop90}" MATLAB code~\cite{kumar2023honeytop90} and uses the \texttt…

[2024-05-17 Fri (UTC), 5 new articles found for math.AT Algebraic Topology]

Evolving Self-Assembling Neural Networks: From Spontaneous Activity to Experience-Dependent Learning
Erwan Plantec, Joachin W. Pedersen, Milton L. Montero, Eleni Nisioti, Sebastian Risi
https://arxiv.org/abs/2406.09787

Evolving Self-Assembling Neural Networks: From Spontaneous Activity to Experience-Dependent Learning
Biological neural networks are characterized by their high degree of plasticity, a core property that enables the remarkable adaptability of natural organisms. Importantly, this ability affects both the synaptic strength and the topology of the nervous systems. Artificial neural networks, on the other hand, have been mainly designed as static, fully connected structures that can be notoriously brittle in the face of changing environments and novel inputs. Building on previous works on Neural De…

Fixed points of generalized contractions on O-metric spaces
Hallowed O. Olaoluwa, Aminat O. Ige, Johnson O. Olaleru
https://arxiv.org/abs/2403.09655 https:…

Fixed points of generalized contractions on O-metric spaces
The class of O-metric spaces generalize several existing metric-types in literature including metric spaces, b-metric spaces, and ultra metric spaces. In this paper, we discuss the properties of the topology induced by an O-metric and establish in the setting, fixed point theorems of contractions and generalized contractions. The proofs of the theorems rely heavily on polygon O-inequalities which are a natural generalization of the triangle inequality, and the construction of which leads to the…

This https://arxiv.org/abs/2404.01422 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On Strong Bounds for Trotter and Zeno Product Formulas with Bosonic Applications
The Trotter product formula and the quantum Zeno effect are both indispensable tools for constructing time-evolutions using experimentally feasible building blocks. In this work, we discuss assumptions under which quantitative bounds can be proven in the strong operator topology on Banach spaces and provide natural bosonic examples. Specially, we assume the existence of a continuously embedded Banach space, which relatively bounds the involved generators and creates an invariant subspace of the…

Magnetic Evolution of an Active Region Producing Successive Flares and Confined Eruptions
Marcelo L\'opez Fuentes, Mariano Poisson, Cristina H. Mandrini
https://arxiv.org/abs/2404.10517

Magnetic Evolution of an Active Region Producing Successive Flares and Confined Eruptions
We analyze the magnetic evolution of solar active region (AR) NOAA 11476 that, between 9 and 10 May 2012, produced a series of surge-type eruptions accompanied by GOES X-ray class M flares. Using force-free models of the AR coronal structure and observations in several wavelengths, in previous works we studied the detailed evolution of those eruptions, relating them to the characteristic magnetic topology of the AR and reconstructing the involved reconnection scheme. We found that the eruptions…

Simple $k$-crashing Plan with a Good Approximation Ratio
Ruixi Luo, Kai Jin, Zelin Ye
https://arxiv.org/abs/2404.10514 https://arxiv.…

Simple $k$-crashing Plan with a Good Approximation Ratio
In project management, a project is typically described as an activity-on-edge network (AOE network), where each activity / job is represented as an edge of some network $N$ (which is a DAG). Some jobs must be finished before others can be started, as described by the topology structure of $N$. It is known that job $j_i$ in normal speed would require $b_i$ days to be finished after it is started. Given the network $N$ with the associated edge lengths $b_1,\ldots,b_m$, the duration of the projec…

Homology and homotopy for arbitrary categories
Suddhasattwa Das
https://arxiv.org/abs/2404.03735 https://arxiv.org/pdf/2404.03735

Homology and homotopy for arbitrary categories
One of the prime motivation for topology was Homotopy theory, which captures the general idea of a continuous transformation between two entities, which may be spaces or maps. In later decades, an algebraic formulation of topology was discovered with the development of Homology theory. Some of the deepest results in topology are about the connections between Homotopy and Homology. These results are proved using intricate constructions. This paper takes an axiomatic approach that provides a comm…

Facilitating Feature and Topology Lightweighting: An Ethereum Transaction Graph Compression Method for Malicious Account Detection
Xuanze Chen, Chenkai Hu, Shengbo Gong, Chengxiang Jin, Jiajun Zhou, Shanqing Yu, Qi Xuan
https://arxiv.org/abs/2405.08278

[2024-05-17 Fri (UTC), 1 new article found for math.GN General Topology]

Modular data of non-semisimple modular categories
Liang Chang, Quinn T. Kolt, Zhenghan Wang, Qing Zhang
https://arxiv.org/abs/2404.09314 https://

Modular data of non-semisimple modular categories
We investigate non-semisimple modular categories with an eye towards a structure theory, low-rank classification, and applications to low dimensional topology and topological physics. We aim to extend the well-understood theory of semisimple modular categories to the non-semisimple case by using representations of factorizable ribbon Hopf algebras as a case study. We focus on the Cohen-Westreich modular data, which is obtained from the Lyubashenko-Majid modular representation restricted to the …

Totally bounded sets in the absolute weak topology
Halimeh Ardakani, Jin Xi Chen
https://arxiv.org/abs/2406.09013 https://arxiv.org/p…

Totally bounded sets in the absolute weak topology
In this paper, almost Dunford-Pettis operators with ranges in $c_0$ are used to identify totally bounded sets in the absolute weak topology. That is, a bounded subset $A$ of a Banach lattice $E$ is $|σ|(E,E^\prime)$-totally bounded if and only if $T(A)\subset c_0$ is relatively compact for every almost Dunford-Pettis operator $T:E\to{c_0}$. As an application, we show that for two Banach lattices $E$ and $F$ every positive operator from $E$ to $F$ dominated by a PL-compact operator is…

This https://arxiv.org/abs/2111.12670 has been replaced.
link: https://scholar.google.com/scholar?q=a

A representation theorem for end spaces of infinite graphs
End-structures of infinite graphs sit at the interface between graph theory, group theory and topology. They arise as the boundary of an infinite graph in a standard sense generalising the theory of the Freudenthal boundary developed by Freudenthal and Hopf in the 1940's for infinite~groups. A long-standing quest in infinite graph theory with a rich body of literature seeks to represent or capture the end-structures of infinite graphs. Halin, Diestel and Carmesin raised open questions that fo…

Large-scale geometry and topology of gas fields: the effects of AGN and stellar feedback
Carlo Schimd, Katarina Kraljic, Romeel Dav\'e, Christophe Pichon
https://arxiv.org/abs/2406.04430

Large-scale geometry and topology of gas fields: the effects of AGN and stellar feedback
Stellar and AGN feedback primarily affect the formation and evolution of galaxies and the circumgalactic medium, leaving some imprint on larger scales. Based on the SIMBA hydrodynamical simulation suite, and using the full set of Minkowski functionals (MFs), this study systematically analyses the time evolution of the global geometry and topology of the gas temperature, pressure, density (total, HI and H$_2$), and metallicity fields between redshift $z=5$ and $z=0$. MFs show that small-scale as…

[2024-03-18 Mon (UTC), 6 new articles found for math.GT Geometric Topology]

Non-Hermitian Topology in Hermitian Topological Matter
Shu Hamanaka, Tsuneya Yoshida, Kohei Kawabata
https://arxiv.org/abs/2405.10015 https://

[2024-03-18 Mon (UTC), no new articles found for math.AT Algebraic Topology]

Variational analysis of unbounded and discontinuous generalized eigenvalue functions with application to topology optimization
Akatsuki Nishioka, Yoshihiro Kanno
https://arxiv.org/abs/2405.04805

Variational analysis of unbounded and discontinuous generalized eigenvalue functions with application to topology optimization
The maximum (or minimum) generalized eigenvalue of symmetric positive semidefinite matrices that depend on optimization variables often appears as objective or constraint functions in structural topology optimization when we consider robustness, vibration, and buckling. It can be an unbounded or discontinuous function where matrices become singular (where a topological change of the structural design occurs). Based on variational analysis, we redefine the maximum (and minimum) generalized eigen…

Topology of shallow-water waves on the rotating sphere
Nicolas Perez, Armand Leclerc, Guillaume Laibe, Pierre Delplace
https://arxiv.org/abs/2404.07655 htt…

Topology of shallow-water waves on the rotating sphere
Topological properties of the spectrum of shallow-water waves on a rotating spherical body are established. Particular attention is paid to its spectral flow, i.e. the modes whose frequencies transit between the Rossby and inertia-gravity wavebands as the zonal wave number is varied. Organising the modes according to the number of zeros of their meridional velocity, we conclude that the net number of modes transiting between the shallow-water wavebands on the sphere is null, in contrast with th…

[2024-04-18 Thu (UTC), no new articles found for math.GN General Topology]

[2024-03-18 Mon (UTC), 6 new articles found for math.GT Geometric Topology]

[2024-03-18 Mon (UTC), no new articles found for math.AT Algebraic Topology]

A Gray-Box Stability Analysis Mechanism for Power Electronic Converters
Rui Kong, Subham Sahoo, Yubo Song, Frede Blaabjerg
https://arxiv.org/abs/2404.09801

A Gray-Box Stability Analysis Mechanism for Power Electronic Converters
This paper proposes a gray-box stability analysis mechanism based on data-driven dynamic mode decomposition (DMD) for commercial grid-tied power electronics converters with limited information on its control parameters and topology. By fusing the underlying physical constraints of the state equations into data snapshots, the system dynamic state matrix and input matrix are simultaneously approximated to identify the dominant system dynamic modes and eigenvalues using the DMD with control (DMDc)…

internet_top_pop: Internet topology (PoP level) (1969-2012)
Assorted snapshots of internet graph at the Point of Presence (PoP) level (which lies between the IP and AS levels), collected from around the world and at various times. The earliest snapshots are for ARPANET (1969-1972), with a few more from pre-2000. Most are from 2006 onward. Metadata include link type or speed, longitudes, and latitudes of nodes, URL, and date of record.
This network has 21 nodes and 31 edges.

[2024-04-17 Wed (UTC), no new articles found for math.GN General Topology]

On the Bures metric, C*-norm, and the quantum metric
Konrad Aguilar, Karina Behera, Tron Omland, Nicole Wu
https://arxiv.org/abs/2406.07219 https://…

On the Bures metric, C*-norm, and the quantum metric
We prove that the topology on the density space with respect to a unital C*-algebra and a faithful induced by the C*-norm is finer than the Bures metric topology. We also provide an example when this containment is strict. Next, we provide a metric on the density space induced by a quantum metric in the sense of Rieffel and prove that the induced topology is the same as the topology induced by the Bures metric and C*-norm when the C*-algebra is assumed to be finite dimensional. Finally, we prov…

On homotopy properties of solutions of some differential inclusions in the $W^{1,p}$-topology
Erasmo Caponio, Antonio Masiello, Stefan Suhr
https://arxiv.org/abs/2404.07614

On homotopy properties of solutions of some differential inclusions in the $W^{1,p}$-topology
We consider a differential inclusion on a manifold, defined by a field of open half-spaces whose boundary in each tangent space is the kernel of a one-form. We make the assumption that the corank one distribution associated to the kernel is completely nonholonomic. We identify a subset of solutions of the differential inclusion, satisfying two endpoints and periodic boundary conditions, which are homotopically equivalent in the $W^{1,p}$-topology, for any $p\in [1,+\infty)$, to the based loop s…

Modular data of non-semisimple modular categories
Liang Chang, Quinn T. Kolt, Zhenghan Wang, Qing Zhang
https://arxiv.org/abs/2404.09314 https://

Modular data of non-semisimple modular categories
We investigate non-semisimple modular categories with an eye towards a structure theory, low-rank classification, and applications to low dimensional topology and topological physics. We aim to extend the well-understood theory of semisimple modular categories to the non-semisimple case by using representations of factorizable ribbon Hopf algebras as a case study. We focus on the Cohen-Westreich modular data, which is obtained from the Lyubashenko-Majid modular representation restricted to the …

This https://arxiv.org/abs/2403.04147 has been replaced.
initial toot: https://mastoxiv.page/@a…

Dual Symmetry Classification of Non-Hermitian Systems and $\mathbb{Z}_2$ Point-Gap Topology of a Non-Unitary Quantum Walk
Non-Hermitian systems exhibit richer topological properties compared to their Hermitian counterparts. It is well known that non-Hermitian systems have been classified based on either the symmetry relations for non-Hermitian Hamiltonians or the symmetry relations for non-unitary time-evolution operators in the context of Floquet topological phases. In this work, we propose that non-Hermitian systems can always be classified in two ways; a non-Hermitian system can be classified using the symmetry…

This https://arxiv.org/abs/2012.15431 has been replaced.
link: https://scholar.google.com/scholar?q=a

Exact categories of topological vector spaces with linear topology
We explain why the naive definition of a natural exact category structure on complete, separated topological vector spaces with linear topology fails. In particular, contrary to arXiv:0711.2527, the category of such topological vector spaces is not quasi-abelian. We present a corrected definition of exact category structure which works OK. Then we explain that the corrected definition still has a shortcoming in that a natural tensor product functor is not exact in it, and discuss ways to refine…

Classification of Cellular Fake Surfaces
Lucas Fagan, Yang Qiu, Zhenghan Wang
https://arxiv.org/abs/2406.09439 https://arxiv.org/pdf/…

Classification of Cellular Fake Surfaces
Generic polyhedra are interesting mathematical objects to study in their own right. In this paper, we initialize a systematic study of two-dimensional generic polyhedra with an eye towards applications to low-dimensional topology, especially the Andrews-Curtis and Zeeman conjectures. After recalling the basic notions of generic polyhedra and fake surfaces, we derive some interesting properties of fake surfaces. Our main result is a complete classification of acyclic cellular fake surfaces up to…

[2024-06-17 Mon (UTC), no new articles found for math.GN General Topology]

This https://arxiv.org/abs/2311.11658 has been replaced.
initial toot: https://mastoxiv.page/@…

Nonequilibrium protection and spatial localization of noise-induced fluctuations: quasi-one-dimensional driven lattice gas with partially penetrable obstacle
We consider a nonequilibrium transition that leads to the formation of nonlinear steady-state structures due to the gas flow scattering on a partially penetrable obstacle. The resulting nonequilibrium steady state (NESS) corresponds to a two-domain gas structure attained at certain critical parameters. We use a simple mean-field model of the driven lattice gas with ring topology to demonstrate that this transition is accompanied by the emergence of local invariants related to a complex composed…

topology: Internet AS graph (2004)
An integrated snapshot of the structure of the Internet at the level of Autonomous Systems (ASs), reconstructed from multiple sources, including the RouteViews and RIPE BGP trace collectors, route servers, looking glasses, and the Internet Routing Registry databases. This snapshot was created around October 2004.
This network has 34761 nodes and 171403 edges.
Tags: Technological, Communication, Unweighted, Multigraph, Timestamps

Variational analysis of unbounded and discontinuous generalized eigenvalue functions with application to topology optimization
Akatsuki Nishioka, Yoshihiro Kanno
https://arxiv.org/abs/2405.04805

Variational analysis of unbounded and discontinuous generalized eigenvalue functions with application to topology optimization
The maximum (or minimum) generalized eigenvalue of symmetric positive semidefinite matrices that depend on optimization variables often appears as objective or constraint functions in structural topology optimization when we consider robustness, vibration, and buckling. It can be an unbounded or discontinuous function where matrices become singular (where a topological change of the structural design occurs). Based on variational analysis, we redefine the maximum (and minimum) generalized eigen…

This https://arxiv.org/abs/2308.15555 has been replaced.
initial toot: https://mastoxiv.page/@a…

Three-dimensional $\mathcal{P}\mathcal{T}$-symmetric topological phases with Pontryagin index
We report on a certain class of three-dimensional topological insulators and semimetals protected by spinless $\mathcal{P}\mathcal{T}$ symmetry, hosting an integer-valued bulk invariant. We show using homotopy arguments that these phases host multi-gap topology, providing a realization of a single $\mathbb{Z}$ invariant in three spatial dimensions that is distinct from the Hopf index. We identify this invariant with the Pontryagin index, which describes BPST instantons in particle physics conte…

On cardinal invariants related to Rosenthal families and large-scale topology
Arturo Mart\'inez-Celis, Tomasz \.Zuchowski
https://arxiv.org/abs/2404.06639

On cardinal invariants related to Rosenthal families and large-scale topology
Given a function $f \in ω^ω$, a set $A \in [ω]^ω$ is free for $f$ if $f[A] \cap A$ is finite. For a class of functions $Γ\subseteq ω^ω$, we define $\mathfrak{ros}_Γ$ as the smallest size of a family $\mathcal{A}\subseteq [ω]^ω$ such that for every $f\inΓ$ there is a set $A \in \mathcal{A}$ which is free for $f$, and $Δ_Γ$ as the smallest size of a family $\mathcal{F}\subseteqΓ$ such that for every $A\in[ω]^ω$ there is $f\in\mathcal{F}$ such that $A$ is not free for $f$. We compa…

topology: Internet AS graph (2004)
An integrated snapshot of the structure of the Internet at the level of Autonomous Systems (ASs), reconstructed from multiple sources, including the RouteViews and RIPE BGP trace collectors, route servers, looking glasses, and the Internet Routing Registry databases. This snapshot was created around October 2004.
This network has 34761 nodes and 171403 edges.
Tags: Technological, Communication, Unweighted, Multigraph, Timestamps

Polynomial-time derivation of optimal k-tree topology from Markov networks
Fereshteh R. Dastjerdi, Liming Cai
https://arxiv.org/abs/2404.05991 https://

Polynomial-time derivation of optimal k-tree topology from Markov networks
Characterization of joint probability distribution for large networks of random variables remains a challenging task in data science. Probabilistic graph approximation with simple topologies has practically been resorted to; typically the tree topology makes joint probability computation much simpler and can be effective for statistical inference on insufficient data. However, to characterize network components where multiple variables cooperate closely to influence others, model topologies bey…

Eigenvalue Preferential Attachment Networks A Dandelion Structure
Vadood Adami, Zahra Ebadi, Morteza Nattagh-Najafi
https://arxiv.org/abs/2404.09238 https:…

Eigenvalue Preferential Attachment Networks A Dandelion Structure
In this paper we introduce a new type of preferential attachment network, the growth of which is based on the eigenvalue centrality. In this network, the agents attach most probably to the nodes with larger eigenvalue centrality which represents that the agent has stronger connections. A new network is presented, namely a dandelion network, which shares some properties of star-like structure and also a hierarchical network. We show that this network, having hub-and-spoke topology is not general…

[2024-05-16 Thu (UTC), 1 new article found for math.AT Algebraic Topology]

Signature of non-trivial band topology in Shubnikov--de Haas oscillations
Denis R. Candido, Sigurdur I. Erlingsson, Jo\~ao Vitor I. Costa, J. Carlos Egues
https://arxiv.org/abs/2406.08977

Signature of non-trivial band topology in Shubnikov--de Haas oscillations
We investigate the Shubnikov-de Haas (SdH) magneto-oscillations in the resistivity of two-dimensional topological insulators (TIs). Within the Bernevig-Hughes-Zhang (BHZ) model for TIs in the presence of a quantizing magnetic field, we obtain analytical expressions for the SdH oscillations by combining a semiclassical approach for the resistivity and a trace formula for the density of states. We show that when the non-trivial topology is produced by inverted bands with ''Mexican-hat'' shape, Sd…

[2024-05-16 Thu (UTC), 2 new articles found for math.GT Geometric Topology]

Compact subspaces of the space of separately continuous functions with the cross-uniform topology
Oleksandr Maslyuchenko, Vadym Myronyk, Roman Ivasiuk
https://arxiv.org/abs/2406.05705

Compact subspaces of the space of separately continuous functions with the cross-uniform topology
We consider two natural topologies on the space $S(X\times Y,Z)$ of all separately continuous functions defined on the product of two topological spaces $X$ and $Y$ and ranged into a topological or metric space $X$. These topologies are the cross-open topology and the cross-uniform topology. We show that these topologies coincides if $X$ and $Y$ are pseudocompacts and $Z$ is a metric space. We prove that a compact space $K$ embeds into $S(X\times Y,Z)$ for infinite compacts $X$, $Y$ and a metri…

[2024-04-16 Tue (UTC), 6 new articles found for math.GT Geometric Topology]

Intersection Multiplicity in Loop Spaces and the String Topology Coproduct
Philippe Kupper, Maximilian Stegemeyer
https://arxiv.org/abs/2404.03460 https://…

Intersection Multiplicity in Loop Spaces and the String Topology Coproduct
The string topology coproduct is often perceived as a counterpart in string topology to the Chas-Sullivan product. However, in certain aspects the string topology coproduct is much harder to understand than the Chas-Sullivan product. In particular the coproduct is not homotopy-invariant and it seems much harder to compute. In this article we give an overview over the string topology coproduct and use the notion of intersection multiplicity of homology classes in loop spaces to show that the str…

topology: Internet AS graph (2004)
An integrated snapshot of the structure of the Internet at the level of Autonomous Systems (ASs), reconstructed from multiple sources, including the RouteViews and RIPE BGP trace collectors, route servers, looking glasses, and the Internet Routing Registry databases. This snapshot was created around October 2004.
This network has 34761 nodes and 171403 edges.
Tags: Technological, Communication, Unweighted, Multigraph, Timestamps

[2024-05-16 Thu (UTC), 2 new articles found for math.GN General Topology]

Intersection Multiplicity in Loop Spaces and the String Topology Coproduct
Philippe Kupper, Maximilian Stegemeyer
https://arxiv.org/abs/2404.03460 https://…

Intersection Multiplicity in Loop Spaces and the String Topology Coproduct
The string topology coproduct is often perceived as a counterpart in string topology to the Chas-Sullivan product. However, in certain aspects the string topology coproduct is much harder to understand than the Chas-Sullivan product. In particular the coproduct is not homotopy-invariant and it seems much harder to compute. In this article we give an overview over the string topology coproduct and use the notion of intersection multiplicity of homology classes in loop spaces to show that the str…

This https://arxiv.org/abs/2307.06447 has been replaced.
initial toot: https://mastoxiv.page/@a…

Interacting Local Topological Markers: A one-particle density matrix approach for characterizing the topology of interacting and disordered states
While topology is a property of a quantum state itself, most existing methods for characterizing the topology of interacting phases of matter require direct knowledge of the underlying Hamiltonian. We offer an alternative by utilizing the one-particle density matrix formalism to extend the concept of the Chern, chiral, and Chern-Simons markers to include interactions. The one-particle density matrix of a free-fermion state is a projector onto the occupied bands, defining a Brillouin zone bundle…

[2024-04-16 Tue (UTC), no new articles found for math.GN General Topology]

The Macias topology on integral domains
Jhixon Mac\'ias
https://arxiv.org/abs/2406.04623 https://arxiv.org/pdf/2406.04623<…

The Macias topology on integral domains
In this manuscript, a recent topology on the positive integers, generated by the collection of relatively prime positive integers, is generalized over integral domains. Some of its topological properties are studied. Properties of this topology on infinite principal ideal domains that are not fields are also explored, and a new topological proof of the infinitude of prime elements is obtained (assuming the set of units is finite), different from those presented in the style of H. Furstenberg. F…

On Hasse norm principle for 3-manifolds in arithmetic topology
Hirotaka Tashiro
https://arxiv.org/abs/2404.06464 https://arxiv.org/pd…

On Hasse norm principle for 3-manifolds in arithmetic topology
Following the analogies between knots and primes, 3-manifolds and number rings in arithmetic topology, we show a topological analogue of the Hasse norm principle for finite cyclic coverings of 3-manifolds, which was originally stated for finite cyclic extensions of number fields.

Tunable moir\'e materials for probing Berry physics and topology
Pratap Chandra Adak, Subhajit Sinha, Amit Agarwal, Mandar M. Deshmukh
https://arxiv.org/abs/2405.08959

[2024-05-15 Wed (UTC), 1 new article found for math.AT Algebraic Topology]

gnutella: Gnutella p2p networks (2002)
A sequence of 9 snapshots of the Gnutella peer-to-peer file sharing network from 5-31 August 2002. Nodes are hosts in the Gnutella network topology and edges are connections between them.
This network has 62586 nodes and 147892 edges.
Tags: Technological, Peer-to-peer, Unweighted
https://…

This https://arxiv.org/abs/2403.07846 has been replaced.
initial toot: https://mastoxiv.page/@a…

Antiferromagnetic magnons on a Möbius strip: topology-induced symmetry breaking
A Möbius strip comprising of two antiferromagnetically coupled spin chains showcase exotic magnon excitations with non-trivial physical behavior, which is solely attributed to the real-space boundary condition even in the absence of local curvature effects. Counterintuitively, magnons on a Möbius strip feature linear polarization of the Néel vector devoid of chirality even when the spin Hamiltonian preserves local rotational symmetry around the anisotropic easy axis. These linearly-polarized…

[2024-05-15 Wed (UTC), 2 new articles found for math.GT Geometric Topology]

This https://arxiv.org/abs/2406.04623 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The Macias topology on integral domains
In this manuscript, a recent topology on the positive integers, generated by the collection of relatively prime positive integers, is generalized over integral domains. Some of its topological properties are studied. Properties of this topology on infinite principal ideal domains that are not fields are also explored, and a new topological proof of the infinitude of prime elements is obtained (assuming the set of units is finite), different from those presented in the style of H. Furstenberg. F…

gnutella: Gnutella p2p networks (2002)
A sequence of 9 snapshots of the Gnutella peer-to-peer file sharing network from 5-31 August 2002. Nodes are hosts in the Gnutella network topology and edges are connections between them.
This network has 36682 nodes and 88328 edges.
Tags: Technological, Peer-to-peer, Unweighted
https://

[2024-04-15 Mon (UTC), 3 new articles found for math.GT Geometric Topology]

topology: Internet AS graph (2004)
An integrated snapshot of the structure of the Internet at the level of Autonomous Systems (ASs), reconstructed from multiple sources, including the RouteViews and RIPE BGP trace collectors, route servers, looking glasses, and the Internet Routing Registry databases. This snapshot was created around October 2004.
This network has 34761 nodes and 171403 edges.
Tags: Technological, Communication, Unweighted, Multigraph, Timestamps

[2024-06-14 Fri (UTC), 8 new articles found for math.GT Geometric Topology]

[2024-05-15 Wed (UTC), no new articles found for math.GN General Topology]

gnutella: Gnutella p2p networks (2002)
A sequence of 9 snapshots of the Gnutella peer-to-peer file sharing network from 5-31 August 2002. Nodes are hosts in the Gnutella network topology and edges are connections between them.
This network has 26518 nodes and 65369 edges.
Tags: Technological, Peer-to-peer, Unweighted
https://

Realizing pairs of multicurves as cylinders on translation surfaces
Juliet Aygun, Janet Barkdoll, Aaron Calderon, Jenavie Lorman, Theodore Sandstrom
https://arxiv.org/abs/2404.08096

Realizing pairs of multicurves as cylinders on translation surfaces
Any pair of intersecting cylinders on a translation surface is "coherent," in that the geometric and algebraic intersection numbers of their core curves are equal (up to sign). In this paper, we investigate when a pair of multicurves can be simultaneously realized as the core curves of cylinders on some translation surface. Our main tools are surface topology and the "flat grafting" deformation introduced by Ser-Wei Fu.