A5050249107- Topological and Geometric Data Analysis
- Computational Geometry and Mesh Generation
- Advanced Graph Theory Research
- Data Management and Algorithms
- Complexity and Algorithms in Graphs
- Limits and Structures in Graph Theory
- Advanced Combinatorial Mathematics
- Mathematical Dynamics and Fractals
- Cryptographic Implementations and Security
- Graph theory and applications
- Natural Language Processing Techniques
- semigroups and automata theory
- Human Mobility and Location-Based Analysis
- Pickering emulsions and particle stabilization
- Historical Geography and Cartography
- Network Packet Processing and Optimization
- Educational Tools and Methods
- Computer Graphics and Visualization Techniques
- Advanced Graph Neural Networks
- Advanced Topology and Set Theory
- Scientific Computing and Data Management
- Computational Physics and Python Applications
- Advanced Malware Detection Techniques
- Remote Sensing and LiDAR Applications
- Online and Blended Learning
Institute of Science and Technology Austria
2016-2023
KES International
2022
IDEMS International Community Interest Company
2022
Google (United States)
2021
Karlsruhe Institute of Technology
2012-2013
Given a finite set A⊂Rd, let Covr,k denote the of all points within distance r to at least k A. Allowing and vary, we obtain 2-parameter family spaces that grow larger when increases or decreases, called multicover bifiltration. Motivated by problem computing homology this bifiltration, introduce two closely related combinatorial bifiltrations, one polyhedral other simplicial, which are both topologically equivalent bifiltration far smaller than Čech-based model considered in prior work...
We present a simple algorithm for computing higher-order Delaunay mosaics that works in Euclidean spaces of any finite dimensions. The selects the vertices order-
Given a locally finite X subseteq R^d and radius r >= 0, the k-fold cover of consists all points in that have k or more within distance r. We consider two filtrations - one scale obtained by fixing increasing r, other depth decreasing we compute persistence diagrams both. While standard methods suffice for filtration scale, need novel geometric topological concepts depth. In particular, introduce rhomboid tiling R^{d+1} whose horizontal integer slices are order-k Delaunay mosaics X,...
Given a locally finite X⊆Rd and radius r≥0 , the k-fold cover of X r consists all points in Rd that have k or more within distance r. We consider two filtrations-one scale obtained by fixing increasing r, other depth decreasing k-and we compute persistence diagrams both. While standard methods suffice for filtration scale, need novel geometric topological concepts depth. In particular, introduce rhomboid tiling Rd+1 whose horizontal integer slices are order-k Delaunay mosaics X, construct...
We show attacks on five data-independent memory-hard functions (iMHF) that were submitted to the password hashing competition (PHC). Informally, an MHF is a function which cannot be evaluated dedicated hardware, like ASICs, at significantly lower hardware and/or energy cost than evaluating single instance standard single-core architecture. Data-independent means memory access pattern of independent input; this makes iMHFs harder construct data-dependent ones, but latter can attacked by...
Two common representations of close packings identical spheres consisting hexagonal layers, called Barlow stackings, appear abundantly in minerals and metals. These motifs, however, occupy an portion space bear first-order topological signatures as measured by persistent homology. Here we present a novel method based on k-fold covers that unambiguously distinguishes between these patterns. Moreover, our approach provides evidence the FCC motif is more stable two context evolving experimental...
Even though Delaunay originally introduced his famous triangulations in the case of infinite point sets with translational periodicity, a software that computes such general is not yet available, to best our knowledge. Combining and generalizing previous work, we present practical algorithm for computing triangulations. The has been implemented experiments show its performance as good one CGAL package, which restricted cubic periodicity.
We present LiveTraVeL (Live Transit Vehicle Labeling), a real-time system to label stream of noisy observations transit vehicle trajectories with the routes they are serving (e.g., northbound bus #5). In order scale efficiently large networks, our first retrieves small set candidate from geometrically indexed data structure, then applies fine-grained scoring step choose best match. Given that remains unavailable for majority world's agencies, these inferences can help feed map system's...
Abstract—Systems for Teaching and Assessment using Computer Algebra Kernel (STACK) is a computer-aided assessment plug-in the Moodle learning management system that provides sophisticated tools student in mathematics related disciplines, with emphasis on formative assessment. In last four years, IDEMS international has supported School of Mathematics at Maseno to integrate STACK use it teaching, learning, undergraduate students nine courses. One courses was “Introduction Complex Analysis'',...
Given a finite set A ⊂ ℝ^d, let Cov_{r,k} denote the of all points within distance r to at least k A. Allowing and vary, we obtain 2-parameter family spaces that grow larger when increases or decreases, called multicover bifiltration. Motivated by problem computing homology this bifiltration, introduce two closely related combinatorial bifiltrations, one polyhedral other simplicial, which are both topologically equivalent bifiltration far smaller than Cech-based model considered in prior...
We present a simple algorithm for computing higher-order Delaunay mosaics that works in Euclidean spaces of any finite dimensions. The selects the vertices order-$k$ mosaic from incrementally constructed lower-order and uses an weighted first-order as black-box to construct its vertices. Beyond this black-box, only combinatorial operations, thus facilitating easy implementation. extend compute $α$-shapes provide open-source implementations. experimental results properties random point sets.
Abstract Given a locally finite set $$X \subseteq {{\mathbb {R}}}^d$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>X</mml:mi> <mml:mo>⊆</mml:mo> <mml:msup> <mml:mi>R</mml:mi> </mml:mrow> <mml:mi>d</mml:mi> </mml:msup> </mml:math> and an integer $$k \ge 0$$ <mml:mi>k</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>0</mml:mn> , we consider the function $${\mathbf{w}_{k}^{}} :{\mathrm{Del}_{k}{({X})}} \rightarrow {R}}}$$ <mml:msubsup> <mml:mi>w</mml:mi> <mml:mrow />...
Cesar Ilharco, Afsaneh Shirazi, Arjun Gopalan, Arsha Nagrani, Blaz Bratanic, Chris Bregler, Christina Funk, Felipe Ferreira, Gabriel Barcik, Georg Osang, Jannis Bulian, Jared Frank, Lucas Smaira, Qin Cao, Ricardo Marino, Roma Patel, Thomas Leung, Vaiva Imbrasaite. Proceedings of the 59th Annual Meeting Association for Computational Linguistics and 11th International Joint Conference on Natural Language Processing: Tutorial Abstracts. 2021.
Given a finite set $A\subset\mathbb{R}^d$, let Cov$_{r,k}$ denote the of all points within distance $r$ to at least $k$ $A$. Allowing and vary, we obtain 2-parameter family spaces that grow larger when increases or decreases, called \emph{multicover bifiltration}. Motivated by problem computing homology this bifiltration, introduce two closely related combinatorial bifiltrations, one polyhedral other simplicial, which are both topologically equivalent multicover bifiltration far smaller than...
Motivated by the problem in [6], which studies relative efficiency of propositional proof systems, 2-edge colorings complete bipartite graphs are investigated. It is shown that if edges $G=K_{n,n}$ colored with black and white such number differs from at most 1, then there least $n(1-1/\sqrt{2})$ vertex-disjoint forks centers same partite set $G$. Here, a fork graph formed two adjacent different colors. The bound sharp. Moreover, an algorithm running time $O(n^2 \log n \sqrt{n α(n^2,n) n})$...