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MIX is a 2-MCFL and the word problem in Z2 is captured by the IO and the OI hierarchies

Sylvain Salvati, S. Salvati

Journal of Computer and System Sciences > 2015 > 81 > 7 > 1252-1277

In this work we establish that the language MIX={w∈{a;b;c}⁎||w|a=|w|b=|w|c} and the language O2={w∈{a;a¯;b;b¯}||w|a=|w|a¯∧|w|b=|w|b¯} are 2-MCFLs. As 2-MCFLs form a class of languages that is included in both the IO and OI hierarchies, and as O2 is the group language of a simple presentation of Z2 we exhibit here the first, to our knowledge, non-virtually-free group language (i.e. non-context-free...

article

2D+t track detection via relative persistent homology

Rabih Assaf, Alban Goupil, Abbas Rammal, Valeriu Vrabie, more

International Journal of Imaging Systems and Technology > 31 > 2 > 753 - 762

In this paper, we demonstrate that algebraic topology can be used to perform 2D+t object detection. After the construction of a topological complex for a 2D+t image sequence, we build a nested sequence of cell complexes on which relative persistent homology is computed. The relative homology adds to “absolute” homology the computation of classes related to the first and last frames of the sequence...

article

Professor Andrzej Szczepan Białynicki-Birula (1935–2021)

Jackowski, Stefan, Jackowski, Stefan

Nauka > 2021 > 4

article

Non-backtracking cycles: length spectrum theory and graph mining applications

Leo Torres, Pablo Suárez-Serrato, Tina Eliassi-Rad

Applied Network Science > 2019 > 4 > 1 > 1-35

Graph distance and graph embedding are two fundamental tasks in graph mining. For graph distance, determining the structural dissimilarity between networks is an ill-defined problem, as there is no canonical way to compare two networks. Indeed, many of the existing approaches for network comparison differ in their heuristics, efficiency, interpretability, and theoretical soundness. Thus, having a...

article

On the Contribution of Wu Wen-Tsün to Algebraic Topology

Jean-Paul Brasselet

Journal of Systems Science and Complexity > 2019 > 32 > 1 > 3-36

The aim of this article is to present the contribution of Wu Wen-Tsün to Algebraic Topology and more precisely to the theory of characteristic classes. Several papers provide complete and welldocumented biography and academic career of Wu Wen-Tsün, in particular, Hudecek, 2014; O’Connor and Robertson, 2006; Wen-Tsün Wu’s Academic Career, 2006; Selected works of Wen-Tsun Wu, 2008. The author does not...

article

The Dold–Thom theorem via factorization homology

Lauren Bandklayder

Journal of Homotopy and Related Structures > 2019 > 14 > 2 > 579-593

We give a new proof of the classical Dold–Thom theorem using factorization homology. Our method is direct and conceptual, avoiding the Eilenberg–Steenrod axioms entirely in favor of a more general geometric argument.

article

Persistent homology and Euler integral transforms

Robert Ghrist, Rachel Levanger, Huy Mai

Journal of Applied and Computational Topology > 2018 > 2 > 1-2 > 55-60

The Euler calculus—an integral calculus based on Euler characteristic as a valuation on constructible functions—is shown to be an incisive tool for answering questions about injectivity and invertibility of recent transforms based on persistent homology for shape characterization.

article

Mathematical deep learning for pose and binding affinity prediction and ranking in D3R Grand Challenges

Duc Duy Nguyen, Zixuan Cang, Kedi Wu, Menglun Wang, more

Journal of Computer-Aided Molecular Design > 2019 > 33 > 1 > 71-82

Advanced mathematics, such as multiscale weighted colored subgraph and element specific persistent homology, and machine learning including deep neural networks were integrated to construct mathematical deep learning models for pose and binding affinity prediction and ranking in the last two D3R Grand Challenges in computer-aided drug design and discovery. D3R Grand Challenge 2 focused on the pose...

article

Detecting intermediate protein conformations using algebraic topology

Nurit Haspel, Dong Luo, Eduardo González

BMC Bioinformatics > 2017 > 18 > 15 > 31-39

Background Understanding protein structure and dynamics is essential for understanding their function. This is a challenging task due to the high complexity of the conformational landscapes of proteins and their rugged energy levels. In particular, it is important to detect highly populated regions which could correspond to intermediate structures or local minima. Results We present a hierarchical...

chapter

Self-Stabilising Target Counting in Wireless Sensor Networks Using Euler Integration

Danilo Pianini, Simon Dobson, Mirko Viroli

2017 IEEE 11th International Conference on Self-Adaptive and Self-Organizing Systems (SASO) > 11 - 20

2017 IEEE 11th International Conference on Self-Adaptive and Self-Organizing Systems (SASO)

Target counting is an established challenge for sensor networks: given a set of sensors that can count (but not identify) targets, how many targets are there? The problem is complicated because of the need to disambiguate duplicate observations of the same target by different sensors. A number of approaches have been proposed in the literature, and in this paper we take an existing technique based...

article

Certain generalized higher derived functors associated to quasitoric manifolds

José Luz, David Allen

Journal of Homotopy and Related Structures > 2018 > 13 > 2 > 395-421

In this paper, we show that the higher derived functors of the primitive element functor of $$E_*(M)$$ E∗(M) where M is a quasitoric manifold and E is a complex-orientable homology theory are independent of the torus action, implying they depend on the orbit space. This extends the results of an earlier work by both authors. By applying cosimplicial methods to coalgebras that are free modules over...

article

Fundamental groups of simplicial complexes

E. Wheeler

Journal of Algebra > 2017 > 478 > C > 283-295

We define two different simplicial complexes, the common divisor simplicial complex and the prime divisor simplicial complex, from a set of integers, and explore their similarities. We will define a map between the two simplicial complexes, and use this map to show that for any set of integers, the fundamental groups of the resulting simplicial complexes are isomorphic.

chapter

Two Convergence Problems for Robots on Graphs

Armando Castaneda, Sergio Rajsbaum, Matthieu Roy

2016 Seventh Latin-American Symposium on Dependable Computing (LADC) > 81 - 90

2016 Seventh Latin-American Symposium on Dependable Computing (LADC)

The class of robot convergence tasks has been shown to capture fundamental aspects of fault-tolerant computability. A set of asynchronous robots that may fail by crashing, start from unknown places in some given space, and have to move towards positions close to each other. In this article, we study the case where the space is uni-dimensional, modeled as a graph G. In graph convergence, robots have...

article

On the non-existence of torus actions

José La Luz, David Allen

Topology and its Applications > 2016 > 209 > C > 347-366

In this paper we compute the higher left derived functors of the indecomposable functor, in certain degrees, for a general class of algebras. The techniques do not depend on the existence of a Projective extension sequence—a common method used to make such computations throughout the literature and as a result, we generalize all known computations of these higher derived functors. As a result of these...

article

Directed Homology Theories and Eilenberg-Steenrod Axioms

Jérémy Dubut, Eric Goubault, Jean Goubault-Larrecq

Applied Categorical Structures > 2017 > 25 > 5 > 775-807

In this paper, we define and study a homology theory, that we call “natural homology”, which associates a natural system of abelian groups to every space in a large class of directed spaces and precubical sets. We show that this homology theory enjoys many important properties, as an invariant for directed homotopy. Among its properties, we show that subdivided precubical sets have the same homology...

chapter

Discovery and diagnosis of the organization for the governance of information logistics and transport business systems

Zineb Besri, Azedine Boulmakoul

2016 3rd International Conference on Logistics Operations Management (GOL) > 1 - 7

2016 3rd International Conference on Logistics Operations Management (GOL)

In order that the logistics and transport sector be efficient, it is necessary to reach a certain maturity of its business processes. Hence, the strong recommendation to reduce non-compliance compared to the strategy of the top management, which weigh certain processes and activities (logistic, supply and transport) of companies in this kind of activity sector. The organizations are required to implement...

chapter

Building Topological Spaces for Musical Objects

Louis Bigo, Jean-Louis Giavitto, Antoine Spicher

Lecture Notes in Computer Science > Mathematics and Computation in Music > Long Papers > 13-28

The development of spatial representations of musical objects allows for a reformulation of algorithmic problems arising in musical theory, fosters novel classifications and provides new computational tools. In this paper, we show how a topological representation for n-note chords associated with the degrees of the diatonic scale and for the All-Interval Series (AIS) can be automatically built using...

chapter

Introduction to the special session on Topological Data Analysis, ICASSP 2016

Harish Chintakunta, Michael Robinson, Hamid Krim

2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) > 6410 - 6414

ICASSP 2016 - 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

Topological Data Analysis (TDA) is a topic which has recently seen many applications. The goal of this special session is to highlight the bridge between signal processing, machine learning and techniques in topological data analysis. In this way, we hope to encourage more engineers to start exploring TDA and its applications. This paper briefly introduces the standard techniques used in this area,...

article

Divisible groups in the K-theory completion of SU(n)

Peter L. Gregory

Topology and its Applications > 2015 > 196 > PA > 60-71

Results of Bendersky and Thompson for the E(1)-based E2 -term of S2n+1, and the results of Bendersky and Davis concerning the v1-periodic groups of SU(n) are used to compute the E(1)-based E2-term for SU(n) at odd primes. This computation is performed using the Bendersky Thompson spectral sequence for SU(n). For spaces like SU(n) this spectral sequence converges to homotopy groups of the K-theory...

article

Samuel Gitler and his work

Jesús González, Ernesto Lupercio

Boletín de la Sociedad Matemática Mexicana > 2015 > 21 > 1 > 3-8

In this note, we review the life and mathematics of the distinguished Mexican mathematician Samuel Gitler.

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Search results

MIX is a 2-MCFL and the word problem in Z2 is captured by the IO and the OI hierarchies

2D+t track detection via relative persistent homology

Professor Andrzej Szczepan Białynicki-Birula (1935–2021)

Non-backtracking cycles: length spectrum theory and graph mining applications

On the Contribution of Wu Wen-Tsün to Algebraic Topology

The Dold–Thom theorem via factorization homology

Persistent homology and Euler integral transforms

Mathematical deep learning for pose and binding affinity prediction and ranking in D3R Grand Challenges

Detecting intermediate protein conformations using algebraic topology

Self-Stabilising Target Counting in Wireless Sensor Networks Using Euler Integration

Certain generalized higher derived functors associated to quasitoric manifolds

Fundamental groups of simplicial complexes

Two Convergence Problems for Robots on Graphs

On the non-existence of torus actions

Directed Homology Theories and Eilenberg-Steenrod Axioms

Discovery and diagnosis of the organization for the governance of information logistics and transport business systems

Building Topological Spaces for Musical Objects

Introduction to the special session on Topological Data Analysis, ICASSP 2016

Divisible groups in the K-theory completion of SU(n)

Samuel Gitler and his work

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