Subjects -> MATHEMATICS (Total: 1013 journals)     - APPLIED MATHEMATICS (92 journals)    - GEOMETRY AND TOPOLOGY (23 journals)    - MATHEMATICS (714 journals)    - MATHEMATICS (GENERAL) (45 journals)    - NUMERICAL ANALYSIS (26 journals)    - PROBABILITIES AND MATH STATISTICS (113 journals) APPLIED MATHEMATICS (92 journals)
 Showing 1 - 82 of 82 Journals sorted alphabetically Advances in Applied Mathematics       (Followers: 15) Advances in Applied Mathematics and Mechanics       (Followers: 6) Advances in Applied Mechanics       (Followers: 15) AKCE International Journal of Graphs and Combinatorics American Journal of Applied Mathematics and Statistics       (Followers: 11) American Journal of Applied Sciences       (Followers: 22) American Journal of Modeling and Optimization       (Followers: 3) Annals of Actuarial Science       (Followers: 2) Applied Mathematical Modelling       (Followers: 22) Applied Mathematics and Computation       (Followers: 31) Applied Mathematics and Mechanics       (Followers: 4) Applied Mathematics and Nonlinear Sciences Applied Mathematics and Physics       (Followers: 2) Biometrical Letters British Actuarial Journal       (Followers: 2) Bulletin of Mathematical Sciences and Applications Communication in Biomathematical Sciences       (Followers: 2) Communications in Applied and Industrial Mathematics       (Followers: 1) Communications on Applied Mathematics and Computation       (Followers: 1) Differential Geometry and its Applications       (Followers: 4) Discrete and Continuous Models and Applied Computational Science Discrete Applied Mathematics       (Followers: 10) Doğuş Üniversitesi Dergisi e-Journal of Analysis and Applied Mathematics Engineering Mathematics Letters       (Followers: 1) European Actuarial Journal Foundations and Trends® in Optimization       (Followers: 3) Frontiers in Applied Mathematics and Statistics       (Followers: 1) Fundamental Journal of Mathematics and Applications International Journal of Advances in Applied Mathematics and Modeling       (Followers: 1) International Journal of Applied Mathematics and Statistics       (Followers: 3) International Journal of Computer Mathematics : Computer Systems Theory International Journal of Data Mining, Modelling and Management       (Followers: 10) International Journal of Engineering Mathematics       (Followers: 7) International Journal of Fuzzy Systems International Journal of Swarm Intelligence       (Followers: 2) International Journal of Theoretical and Mathematical Physics       (Followers: 13) International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems       (Followers: 3) Journal of Advanced Mathematics and Applications       (Followers: 1) Journal of Advances in Mathematics and Computer Science Journal of Applied & Computational Mathematics Journal of Applied Intelligent System Journal of Applied Mathematics & Bioinformatics       (Followers: 6) Journal of Applied Mathematics and Physics       (Followers: 9) Journal of Computational Geometry       (Followers: 3) Journal of Innovative Applied Mathematics and Computational Sciences       (Followers: 6) Journal of Mathematical Sciences and Applications       (Followers: 2) Journal of Mathematics and Music: Mathematical and Computational Approaches to Music Theory, Analysis, Composition and Performance       (Followers: 12) Journal of Mathematics and Statistics Studies Journal of Physical Mathematics       (Followers: 2) Journal of Symbolic Logic       (Followers: 2) Letters in Biomathematics       (Followers: 1) Mathematical and Computational Applications       (Followers: 3) Mathematical Models and Computer Simulations       (Followers: 3) Mathematics and Computers in Simulation       (Followers: 3) Modeling Earth Systems and Environment       (Followers: 1) Moscow University Computational Mathematics and Cybernetics Multiscale Modeling and Simulation       (Followers: 2) Pacific Journal of Mathematics for Industry Partial Differential Equations in Applied Mathematics       (Followers: 1) Ratio Mathematica Results in Applied Mathematics       (Followers: 1) Scandinavian Actuarial Journal       (Followers: 2) SIAM Journal on Applied Dynamical Systems       (Followers: 3) SIAM Journal on Applied Mathematics       (Followers: 11) SIAM Journal on Computing       (Followers: 11) SIAM Journal on Control and Optimization       (Followers: 18) SIAM Journal on Discrete Mathematics       (Followers: 8) SIAM Journal on Financial Mathematics       (Followers: 3) SIAM Journal on Imaging Sciences       (Followers: 7) SIAM Journal on Mathematical Analysis       (Followers: 4) SIAM Journal on Matrix Analysis and Applications       (Followers: 3) SIAM Journal on Numerical Analysis       (Followers: 7) SIAM Journal on Optimization       (Followers: 12) SIAM Journal on Scientific Computing       (Followers: 16) SIAM Review       (Followers: 9) SIAM/ASA Journal on Uncertainty Quantification       (Followers: 2) Swarm Intelligence       (Followers: 3) Theory of Probability and its Applications       (Followers: 2) Uniform Distribution Theory Universal Journal of Applied Mathematics       (Followers: 2) Universal Journal of Computational Mathematics       (Followers: 3)
Similar Journals
 Journal of Computational GeometryNumber of Followers: 3     Open Access journal ISSN (Print) 1920-180X Published by Carleton University  [3 journals]
• Weight balancing on boundaries

• Authors: Luis Barba, Otfried Cheong, Michael Dobkins, Rudolf Fleischer, Akitoshi Kawamura, Matias Korman, Yoshio Okamoto, János Pach, Yuan Tang, Takeshi Tokuyama, Sander Verdonschot
Pages: 1–12 - 1–12
Abstract: Given a polygonal region containing a target point (which we assume is the origin), it is not hard to see that there are two points on the perimeter that are antipodal, that is, whose midpoint is the origin. We prove three generalizations of this fact. (1) For any polygon (or any compact planar set) containing the origin, it is possible to place a given set of weights on the boundary so that their barycenter (center of mass) coincides with the origin, provided that the largest weight does not exceed the sum of the other weights. (2) On the boundary of any 3-dimensional compact set containing the origin, there exist three points that form an equilateral triangle centered at the origin. (3) For any $d$-dimensional bounded convex polyhedron containing the origin, there exists a pair of antipodal points consisting of a point on a $\lfloor d/2 \rfloor$-face and a point on a $\lceil d/2\rceil$-face.
PubDate: 2022-04-20
DOI: 10.20382/jocg.v13i1a1
Issue No: Vol. 13, No. 1 (2022)

• A combinatorial bound for beacon-based routing in orthogonal polygons

• Authors: Thomas Shermer
Pages: 13–5 - 13–5
Abstract: Beacon attraction is a movement system whereby a robot (modeled as a point in 2D) moves in a free space so as to always locally inimize its Euclidean distance to an activated beacon (which is also a point). This results in the robot moving directly towards the beacon when it can, and otherwise sliding along the edge of an obstacle. When a robot can reach the activated beacon by this method, we say that the beacon attracts the robot. A beacon routing from $p$ to $q$ is a sequence $b_1,b_2 ,\ldots,b_k$ of beacons such that activating the beacons in order will attract a robot from $p$ to $b_1$ to $b_2$ \ldots to $b_k$ to $q$ , where $q$ is considered to be a beacon. A routing set of beacons is a set $B$ of beacons such that any two points $p, q$ in the free space have a beacon routing with the intermediate beacons $b_1,b_2,\ldots,b_k$ all chosen from $B$ . Here we address the question of "how large must such a $B$ be'" in singly-connected orthogonal polygons, and show that the answer is "sometimes as large as $\left\lfloor\frac{n−4}{3}\right\rfloor$, but never larger."
PubDate: 2022-04-20
DOI: 10.20382.jocg.v13i1a2
Issue No: Vol. 13, No. 1 (2022)

• Improved polytope volume calculations based on Hamiltonian Monte Carlo
with boundary reflections and sweet arithmetics

• Authors: Frederic Cazals, Augustin Chevallier, Sylvain Pion
Pages: 52–8 - 52–8
Abstract: Computing the volume of a high dimensional polytope is a fundamental problem in geometry, also connected to the calculation of densities of states in statistical physics, and a central building block of such algorithms is the method used to sample a target probability distribution. This paper studies Hamiltonian Monte Carlo (HMC) with reflections on the boundary ofdomain, providing an enhanced alternative to Hit-and-run (HAR) to sample a target distribution restricted to the polytope. We make three contributions. First, we provide a convergence bound, paving the way to more precise mixing time analysis. Second, we present a robust implementation based on multi-precision arithmetic, a mandatory ingredient to guarantee exact predicates and robust constructions. We however allow controlled failures to happen, introducing the Sweeten Exact Geometric Computing (SEGC) paradigm. Third, we use our HMC random walk to perform H-polytope volume calculations, using it as an alternative to HAR within the volume algorithm by
Cousins and Vempala. The systematic tests conducted up to dimension n = 100 on the cube, the isotropic and the standard simplex show that HMC significantly outperforms HAR both in terms of accuracy and running time. Additional tests show that calculations may be handled up to dimension n = 500. These tests also establish that multiprecision is mandatory to avoid exits from the polytope.
PubDate: 2022-04-20
DOI: 10.20382.jocg.v13i1a3
Issue No: Vol. 13, No. 1 (2022)

• FPT-Algorithms for computing Gromov-Hausdorff and interleaving distances
between trees

• Authors: Elena Farahbakhsh Touli, Yusu Wang
Pages: 89–1 - 89–1
Abstract: The Gromov-Hausdorff distance is a natural way to measure the distortion between two metric spaces. However, there has been only limited algorithmic development to compute or approximate this distance. We focus on computing the Gromov-Hausdorff distance between two metric trees. Roughly speaking, a metric tree is a metric space that can be realized by the shortest path metric on a tree. Any finite tree with positive edge weight can be viewed as a metric tree where the weight is treated as edge length and the metric is the induced shortest path metric in the tree. Previously, Agarwal et al. showed that even for trees with unit edge length, it is NP-hard to approximate the Gromov-Hausdorff distance between them within a factor of $3$. In this paper, we present a fixed-parameter tractable (FPT) algorithm that can approximatethe Gromov-Hausdorff distance between two general metric trees within a multiplicative factor of $14$. Interestingly, the development of our algorithm is made possible by a connection betweenthe Gromov-Hausdorff distance for metric trees and the interleaving distance for the so-called merge trees. The merge trees arise in practice naturally as a simple yet meaningful topological summary (it is a variant of the Reeb graphs and contour trees), and are of independent interest. It turns out that an exact or approximation algorithm for the interleaving distance leads to an approximation algorithm for the Gromov-Hausdorff distance. One of the key contributions of our work is that we redefine the interleaving distance in a way that makes it easier to develop dynamic programming approaches to compute it. We then present a fixed-parameter tractable algorithm to compute the interleaving distance between two merge trees exactly, which ultimately leads to an FPT-algorithm to approximate the Gromov-Hausdorff distance between two metric trees. This exact FPT-algorithm to compute the interleaving distance between merge trees is of interest itself, as it is known that it is NP-hard to approximate it within a factor of $3$, and previously the best known algorithm has an approximation factor of $O(\sqrt{n})$ even for trees with unit edge length.
PubDate: 2022-04-20
DOI: 10.20382.jocg.v13i1a4
Issue No: Vol. 13, No. 1 (2022)

• Delaunay triangulations of generalized Bolza surfaces

• Authors: Matthijs Ebbens, Iordan Iordanov, Monique Teillaud, Gert Vegter
Pages: 125– - 125–
Abstract: The Bolza surface can be seen as the quotient of the hyperbolic plane, represented by the Poincar\'e disk model, under the action of the group generated by the hyperbolic isometries identifying opposite sides of a regular octagon centered at the origin. We consider generalized Bolza surfaces $\mathbb{M}_g$, where the octagon is replaced by a regular $4g$-gon, leading to a genus $g$ surface. We propose an extension of Bowyer's algorithm to these surfaces. In particular, we compute the value of the systole of $\mathbb{M}_g$. We also propose algorithms computing small sets of points on $\mathbb{M}_g$ that are used to initialize Bowyer's algorithm.
PubDate: 2022-04-21
DOI: 10.20382.jocg.v13i1a5
Issue No: Vol. 13, No. 1 (2022)

• Sometimes reliable spanners of almost linear size

• Authors: Kevin Buchin, Sariel Har-Peled, Dániel Oláh
Pages: 178– - 178–
PubDate: 2022-04-21
DOI: 10.20382/jocg.v13i1a6
Issue No: Vol. 13, No. 1 (2022)

• A Geometric Approach to Inelastic Collapse

• Authors: Yufei Zheng, Kritkorn Karntikoon, Bernard Chazelle
Pages: 197– - 197–
Abstract: We show in this note how to interpret logarithmic spiral tilings as one-dimensional particle systems undergoing inelastic collapse. By deforming the spirals appropriately, we can simulate collisions among particles with distinct or varying coefficients of restitution. Our geometric constructions provide a strikingly simple illustration of a widely studied phenomenon in the physics of dissipative gases: the collapse of inelastic particles.
PubDate: 2022-04-25
DOI: 10.20382/jocg.v13i1a7
Issue No: Vol. 13, No. 1 (2022)

• A near-linear time approximation scheme for geometric transportation with

• Authors: Kyle Fox, Jiashuai Lu
Pages: 204– - 204–
Abstract: $\newcommand{\R}{\mathbb{R}}\DeclareMathOperator{\poly}{poly}\DeclareMathOperator{\polylog}{polylog}$The geometric transportation problem takes as input a set of points $$P$$ in $$d$$-dimensional Euclidean space and a supply function $$\mu : P \to \R$$.
The goal is to find a transportation map, a non-negative assignment $$\tau : P \times P \to \R_{\geq 0}$$ to pairs of points, so the total assignment leaving each point is equal to its supply, i.e., $$\sum_{r \in P} \tau(q, r) - \sum_{p \in P} \tau(p, q) = \mu(q)$$ for all points $$q \in P$$. The goal is to minimize the weighted sum of Euclidean distances for the pairs, $$\sum_{(p, q) \in P \times P} \tau(p, q) \cdot q - p _2$$. We describe the first algorithm for this problem that returns, with high probability, a $$(1 + \epsilon)$$-approximation to the optimal transportation map in $$O(n \poly(1 / \epsilon) \polylog{n})$$ time. In contrast to the previous best algorithms for this problem, our near-linear running time bound is independent of the spread of $$P$$ and the magnitude of its real-valued supplies.
PubDate: 2022-06-06
DOI: 10.20382/jocg.v13i1a8
Issue No: Vol. 13, No. 1 (2022)

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