IA Scholar Query: An Approximate Algorithm for the Minimal Vertex Nested Polygon Problem.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgThu, 29 Sep 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440Minimum Link Fencing
https://scholar.archive.org/work/pcqqifrxdbdgxnpgublv6gdfxu
We study a variant of the geometric multicut problem, where we are given a set 𝒫 of colored and pairwise interior-disjoint polygons in the plane. The objective is to compute a set of simple closed polygon boundaries (fences) that separate the polygons in such a way that any two polygons that are enclosed by the same fence have the same color, and the total number of links of all fences is minimized. We call this the minimum link fencing (MLF) problem and consider the natural case of bounded minimum link fencing (BMLF), where 𝒫 contains a polygon Q that is unbounded in all directions and can be seen as an outer polygon. We show that BMLF is NP-hard in general and that it is XP-time solvable when each fence contains at most two polygons and the number of segments per fence is the parameter. Finally, we present an O(n log n)-time algorithm for the case that the convex hull of 𝒫∖{Q} does not intersect Q.Sujoy Bhore, Fabian Klute, Maarten Löffler, Martin Nöllenburg, Soeren Terziadis, Anaïs Villedieuwork_pcqqifrxdbdgxnpgublv6gdfxuThu, 29 Sep 2022 00:00:00 GMTNumerical shape optimization of the Canham-Helfrich-Evans bending energy
https://scholar.archive.org/work/zhrxohiazzec3nlhwpzz2jq3x4
In this paper we propose a novel numerical scheme for the Canham-Helfrich-Evans bending energy based on a three-field lifting procedure of the distributional shape operator to an auxiliary mean curvature field. Together with its energetic conjugate scalar stress field as Lagrange multiplier the resulting fourth order problem is circumvented and reduced to a mixed saddle point problem involving only second order differential operators. Further, we derive its analytical first variation (also called first shape derivative), which is valid for arbitrary polynomial order, and discuss how the arising shape derivatives can be computed automatically in the finite element software NGSolve. We finish the paper with several numerical simulations showing the pertinence of the proposed scheme and method.Michael Neunteufel, Joachim Schöberl, Kevin Sturmwork_zhrxohiazzec3nlhwpzz2jq3x4Wed, 28 Sep 2022 00:00:00 GMTNearest neighbour clutter removal for estimating features in point process on linear networks
https://scholar.archive.org/work/biuqbllg7fefbiei6tvi6e7ux4
We consider the problem of features detection in the presence of clutter in point processes on a linear network. For the purely spatial case, previous studies addressed the issue of nearest-neighbour clutter removal. We extend this classification methodology to a more complex geometric context, where the classical properties of a point process change and data visualization is not intuitive. As a result, the method is suitable for a feature with clutter as two superimposed Poisson processes on the same linear network, without assumptions about the feature shapes. We present simulations and examples of road traffic accidents that resulted in injuries or deaths in two cities of Colombia to illustrate the method.Juan F. Diaz-Sepulveda, Nicoletta D'Angelo, Giada Adelfio, Jonatan A. Gonzalez, Francisco J. Rodriguez-Corteswork_biuqbllg7fefbiei6tvi6e7ux4Wed, 28 Sep 2022 00:00:00 GMTFinding Weakly Simple Closed Quasigeodesics on Polyhedral Spheres
https://scholar.archive.org/work/augiga4morejzdz7nk2k64dbau
A closed quasigeodesic on a convex polyhedron is a closed curve that is locally straight outside of the vertices, where it forms an angle at most π on both sides. While the existence of a simple closed quasigeodesic on a convex polyhedron has been proved by Pogorelov in 1949, finding a polynomial-time algorithm to compute such a simple closed quasigeodesic has been repeatedly posed as an open problem. Our first contribution is to propose an extended definition of quasigeodesics in the intrinsic setting of (not necessarily convex) polyhedral spheres, and to prove the existence of a weakly simple closed quasigeodesic in such a setting. Our proof does not proceed via an approximation by smooth surfaces, but relies on an adapation of the disk flow of Hass and Scott to the context of polyhedral surfaces. Our second result is to leverage this existence theorem to provide a finite algorithm to compute a weakly simple closed quasigeodesic on a polyhedral sphere. On a convex polyhedron, our algorithm computes a simple closed quasigeodesic, solving an open problem of Demaine, Hersterberg and Ku.Jean Chartier, Arnaud de Mesmaywork_augiga4morejzdz7nk2k64dbauWed, 28 Sep 2022 00:00:00 GMTMathematical foundations of adaptive isogeometric analysis
https://scholar.archive.org/work/vzzhahrg55fklhu3mw4vhk3xuq
This paper reviews the state of the art and discusses recent developments in the field of adaptive isogeometric analysis, with special focus on the mathematical theory. This includes an overview of available spline technologies for the local resolution of possible singularities as well as the state-of-the-art formulation of convergence and quasi-optimality of adaptive algorithms for both the finite element method (FEM) and the boundary element method (BEM) in the frame of isogeometric analysis (IGA).Annalisa Buffa, Gregor Gantner, Carlotta Giannelli, Dirk Praetorius, Rafael Vázquezwork_vzzhahrg55fklhu3mw4vhk3xuqWed, 21 Sep 2022 00:00:00 GMTCombinatorial geometry of neural codes, neural data analysis, and neural networks
https://scholar.archive.org/work/4hudx3fjozfltjck6hl5tww4pm
This dissertation explores applications of discrete geometry in mathematical neuroscience. We begin with convex neural codes, which model the activity of hippocampal place cells and other neurons with convex receptive fields. In Chapter 4, we introduce order-forcing, a tool for constraining convex realizations of codes, and use it to construct new examples of non-convex codes with no local obstructions. In Chapter 5, we relate oriented matroids to convex neural codes, showing that a code has a realization with convex polytopes iff it is the image of a representable oriented matroid under a neural code morphism. We also show that determining whether a code is convex is at least as difficult as determining whether an oriented matroid is representable, implying that the problem of determining whether a code is convex is NP-hard. Next, we turn to the problem of the underlying rank of a matrix. This problem is motivated by the problem of determining the dimensionality of (neural) data which has been corrupted by an unknown monotone transformation. In Chapter 6, we introduce two tools for computing underlying rank, the minimal nodes and the Radon rank. We apply these to analyze calcium imaging data from a larval zebrafish. In Chapter 7, we explore the underlying rank in more detail, establish connections to oriented matroid theory, and show that computing underlying rank is also NP-hard. Finally, we study the dynamics of threshold-linear networks (TLNs), a simple model of the activity of neural circuits. In Chapter 9, we describe the nullcline arrangement of a threshold linear network, and show that a subset of its chambers are an attracting set. In Chapter 10, we focus on combinatorial threshold linear networks (CTLNs), which are TLNs defined from a directed graph. We prove that if the graph of a CTLN is a directed acyclic graph, then all trajectories of the CTLN approach a fixed point.Caitlin Lienkaemperwork_4hudx3fjozfltjck6hl5tww4pmThu, 15 Sep 2022 00:00:00 GMTAdvancing a Wavelet-Based Spatial Audio Format
https://scholar.archive.org/work/rblob452snhhzkbsc3ewrmqtky
This work further develops the theory of Spherical Wavelet Format (SWF), a spatial audio format inspired by Ambisonics that makes use of Spherical Wavelets as a basis to decompose the soundfield. In particular, we have specified a version of SWF that implements a method to build an arbitrary wavelet representation on an arbitrary triangular mesh. We make use of a modified lifting scheme to optimize the interpolating scaling functions for optimal playback reproduction, and we have demonstrated its functionality and competitiveness with state-of-the-art spatial audio algorithms on a 7.1.4 layout. The resulting SWF specification is available for use and further research in an open source python library. The python library is flexible enough to support any layout, and includes presets for the original Octahedral mesh from the first publication of SWF, as well as the 7.0.4-based SWF format used for objective and subjective evaluation in this report, and a Spherical Wavelet Format that naturally interpolates between standard surround sound formats (11.1.8,9.1.6,7.1.4,etc.). The library is intended to be used with the trivial decoding from the coarsest level of mesh, but can also be decoded using other strategies from less coarse representations.Samuel Narváez, Daniel Arteaga, Davide Scainiwork_rblob452snhhzkbsc3ewrmqtkyThu, 15 Sep 2022 00:00:00 GMTRecognizing weighted and seeded disk graphs
https://scholar.archive.org/work/a5w5be7buzanvk4debowcptl2y
Disk intersection representations realize graphs by mapping vertices bijectively to disks in the plane such that two disks intersect each other if and only if the corresponding vertices are adjacent in the graph. If intersections are restricted to touching points of the boundaries, we call them disk contact representations. Deciding whether a vertex-weighted planar graph can be realized such that the disks' radii coincide with the vertex weights is known to be NP-hard for both contact and intersection representations. In this work, we reduce the gap between hardness and tractability by analyzing the problem for special graph classes. We show that in the contact scenario it remains NP-hard for outerplanar graphs with unit weights and for stars with arbitrary weights, strengthening the previous hardness results. On the positive side, we present constructive linear-time recognition algorithms for caterpillars with unit weights and for embedded stars with arbitrary weights. We also consider a version of the problem in which the disks of a representation are supposed to cover preassigned points, called seeds. We show that both for contact and intersection representations this problem is NP-hard for unit weights even if the given graph is a path. If the disks' radii are not prescribed, the problem remains NP-hard for trees in the contact scenario.Boris Klemz, Martin Nöllenburg, Roman Prutkinwork_a5w5be7buzanvk4debowcptl2yWed, 14 Sep 2022 00:00:00 GMTQuantiles, Ranks and Signs in Metric Spaces
https://scholar.archive.org/work/sdmq3frztvdlhabku34bnr34am
Non-Euclidean data is currently prevalent in many fields, necessitating the development of novel concepts such as distribution functions, quantiles, rankings, and signs for these data in order to conduct nonparametric statistical inference. This study provides new thoughts on quantiles, both locally and globally, in metric spaces. This is realized by expanding upon metric distribution function proposed by Wang et al. (2021). Rank and sign are defined at both the local and global levels as a natural consequence of the center-outward ordering of metric spaces brought about by the local and global quantiles. The theoretical properties are established, such as the root-n consistency and uniform consistency of the local and global empirical quantiles and the distribution-freeness of ranks and signs. The empirical metric median, which is defined here as the 0th empirical global metric quantile, is proven to be resistant to contaminations by means of both theoretical and numerical approaches. Quantiles have been shown valuable through extensive simulations in a number of metric spaces. Moreover, we introduce a family of fast rank-based independence tests for a generic metric space. Monte Carlo experiments show good finite-sample performance of the test. Quantiles are demonstrated in a real-world setting by analysing hippocampal data.Hang Liu, Xueqin Wang, Jin Zhuwork_sdmq3frztvdlhabku34bnr34amFri, 09 Sep 2022 00:00:00 GMTThe Cut-Cell Method for the Prediction of 2D/3D Flows in Complex Geometries and the Adjoint-Based Shape Optimization
https://scholar.archive.org/work/vlcycl6zxzbsxmj7jm3aljzsfa
This dissertation thesis develops integrated, robust, and reliable Computational Fluid Dynamics (CFD) methods and software for the analysis and shape optimization in real-world applications in fluid mechanics and aerodynamics. To this end, the cut-cell method, which removes mesh generation barriers from the flow analysis and design process is adopted. The computational domain is firstly covered with a Cartesian mesh and then parts occupied by the solid bodies are discarded, giving rise to the cut-cell mesh. The benefits of this method are profound in fluid problems with moving solid bodies which are allowed to move upon the stationary background mesh, avoiding the use of mesh deformation tools. Moreover, contrary to body-conforming approaches, the changes in shape during an optimization loop do not affect the surrounding mesh, preventing mesh generation failure and the premature breakdown of the optimization loop. Therefore, this dissertation thesis exploits these beneficial features and develops a cut-cell-based flow solver and shape optimization tool for compressible and incompressible flow problems.Konstantinos Samouchos, National Technological University Of Athenswork_vlcycl6zxzbsxmj7jm3aljzsfaThu, 08 Sep 2022 00:00:00 GMTUniversality for two-dimensional critical cellular automata
https://scholar.archive.org/work/ro3wmpmdwzbdljos6um67mdami
We study the class of monotone, two-state, deterministic cellular automata, in which sites are activated (or 'infected') by certain configurations of nearby infected sites. These models have close connections to statistical physics, and several specific examples have been extensively studied in recent years by both mathematicians and physicists. This general setting was first studied only recently, however, by Bollobás, Smith and Uzzell, who showed that the family of all such 'bootstrap percolation' models on ℤ^2 can be naturally partitioned into three classes, which they termed subcritical, critical and supercritical. In this paper we determine the order of the threshold for percolation (complete occupation) for every critical bootstrap percolation model in two dimensions. This 'universality' theorem includes as special cases results of Aizenman and Lebowitz, Gravner and Griffeath, Mountford, and van Enter and Hulshof, significantly strengthens bounds of Bollobás, Smith and Uzzell, and complements recent work of Balister, Bollobás, Przykucki and Smith on subcritical models.Béla Bollobás, Hugo Duminil-Copin, Robert Morris, Paul Smithwork_ro3wmpmdwzbdljos6um67mdamiThu, 08 Sep 2022 00:00:00 GMTSemi-Automatic Residential Floor Plan Detection
https://scholar.archive.org/work/tzphfyqh65bufcbyqqfo23ggaa
Architectural floor plans are tangible cultural history artifacts, valuable for documenting how people live, work, and recreate, both in the present and going back hundreds or even thousands of years. Today, floor plans are created using digital technologies, but prior to the 1990s, the majority were drafted by hand. For archives, the storage, conservation, and handling of hand-drawn floor plans, which are often oversized and fragile, can be challenging. The digitization of floor plans, therefore, can reduce the possibility of damage while providing greater accessibility. However, even with digitization, researchers and archives continue to encounter barriers utilizing and cataloging these collections. Manually processing, collecting, and analyzing information contained in floor plans is time-consuming and prone to human error, particularly when working with large floor plan corpora. A tool to facilitate the broader use of archival floor plans is needed. Here we propose the Building Database and Analytics System (BuDAS), a tool for the detection, storage, and analysis of floor plan information to assist scholars' research on collections and support metadata capture. In this paper, we explore the challenges of detecting floor plan information and provide an overview of BuDAS, which we developed to address these problems. In addition, we test BuDAS's room detection system on two groups of floor plans sourced from archives, representing different levels of detection difficulty. The limitations and future implications of BuDAS and floor plan detection will also be discussed.Elise King, Katie Pierce Meyer, King-Ip (David) Linwork_tzphfyqh65bufcbyqqfo23ggaaWed, 07 Sep 2022 00:00:00 GMTAvian Wing Joints Provide Longitudinal Flight Stability and Control
https://scholar.archive.org/work/3h225wlzgzdvrp57fffzbfjwui
Uncrewed aerial vehicle (UAV) design has advanced substantially over the past century; however, there are still scenarios where birds outperform UAVs. Birds regularly maneuver through cluttered environments or adapt to sudden changes in flight conditions, tasks that challenge even the most advanced UAVs. Thus, there remains a gap in our general knowledge of flight maneuverability and adaptability that can be filled by improving our understanding of how birds achieve these desirable flight characteristics. Although maneuverability is difficult to quantify, one approach is to leverage an expected trade-off between stability and maneuverability, wherein a stable flyer must generate larger moments to maneuver than an unstable flyer. Bird's stability, and adaptability, has previously been associated with their ability to morph their wing shape in flight. Birds morph their wings by actuating their musculoskeletal system, including the shoulder, elbow and wrist joints. Thus, to take an important step towards deciphering avian flight stability and adaptability, I investigated how the manipulating avian wing joints affect longitudinal stability and control characteristics. First, I used an open-source low fidelity model to calculate the lift and pitching moment of a gull wing and body across the full range of flexion and extension of the elbow and wrist. To validate the model, I measured the forces and moments on nine 3D printed equivalent wing-body models mounted in a wind tunnel. With the validated numerical results, I identified that extending the wing using different combinations of elbow and wrist angles would provide a method for adaptive control of loads and static stability. However, I also found that gulls were unable to trim for the tested shoulder angle. Next, I developed an open-source, mechanics-based method (AvInertia) to calculate the inertial characteristics of 22 bird species across the full range of flexion and extension of the elbow and wrist. This method allowed a detailed investigation of how manipula [...]Christina Harvey, University, Mywork_3h225wlzgzdvrp57fffzbfjwuiTue, 06 Sep 2022 00:00:00 GMTSelf-Assembly and Real-Space Modeling in Binary Hard-Particle and Quasicrystalline Systems
https://scholar.archive.org/work/6imzahus3bfjxjvmnx3ucpcpiy
In this thesis, I will show a fundamentally new way to understand and construct quasicrystal tilings based on a new formulation of the quasi-unit cell called layering. There are many methods for generating quasitilings including Ammann/pentagrid methods, cut-and-project higher-dimensional projections, deflation/inflation substitutions, and various approaches using matching rules and non-local forced moves. The only other method which has a real-space quasi-unit cell comes from covering theory. However, covering approaches, much like matching-rule approaches, do not provide a recipe for error-free construction of the quasitiling and lack a description of the phason flips—a new type of local particle movement only observed in quasicrystals. In this thesis, I will showcase that layering does provide a way to construct perfect quasitiling from a quasi-unit cell and naturally gives rise to a real-space description of the phason mode of particle movement. This new method was applied to the three Penrose pentagonal tilings, the Ammann-Beenker octagonal tiling, the Tübingen triangle decagonal tiling, the Niizeki-Gähler dodecagonal tiling, and finally the Ammann-Kramer-Neri icosahedral tiling. In addition, simulations were performed using a patchy hard-particle set of Penrose rhombuses as a demonstration of the power of the analysis method. The last chapter of this thesis reports the formation of a binary crystal of hard polyhedra due solely to entropic forces. Although the alternating arrangement of octahedra and tetrahedra is a known space-tessellation from Maurolyctus in 1529 (Lagarias, 2015), it had not previously been observed in self-assembly simulations. Both known one-component phases—the dodecagonal quasicrystal of tetrahedra and the densest-packing of octahedra in the Minkowski lattice—are found to coexist with the binary phase. Apart from an alternative, monoclinic packing of octahedra, no additional crystalline phases were observed.Andrew Cadotte, University, Mywork_6imzahus3bfjxjvmnx3ucpcpiyTue, 06 Sep 2022 00:00:00 GMTMorphing Rectangular Duals
https://scholar.archive.org/work/pgklnyxapnffnaf3heoljra3pu
A rectangular dual of a plane graph G is a contact representations of G by interior-disjoint axis-aligned rectangles such that (i) no four rectangles share a point and (ii) the union of all rectangles is a rectangle. A rectangular dual gives rise to a regular edge labeling (REL), which captures the orientations of the rectangle contacts. We study the problem of morphing between two rectangular duals of the same plane graph. If we require that, at any time throughout the morph, there is a rectangular dual, then a morph exists only if the two rectangular duals realize the same REL. Therefore, we allow intermediate contact representations of non-rectangular polygons of constant complexity. Given an n-vertex plane graph, we show how to compute in O(n^3) time a piecewise linear morph that consists of O(n^2) linear morphing steps.Steven Chaplick, Philipp Kindermann, Jonathan Klawitter, Ignaz Rutter, Alexander Wolffwork_pgklnyxapnffnaf3heoljra3puWed, 31 Aug 2022 00:00:00 GMTOptimal geometric multigrid preconditioners for HDG-P0 schemes for the reaction-diffusion equation and the generalized Stokes equations
https://scholar.archive.org/work/pl2kel4lhrektaw22r7byxuyuu
We present the lowest-order hybridizable discontinuous Galerkin schemes with numerical integration, denoted as HDG-P0, for the reaction-diffusion equation and the generalized Stokes equations in two- and three-dimensions. Here by lowest order, we mean that the (hybrid) finite element space for the global HDG facet degrees of freedom (DOFs) is the space of piecewise constants on the mesh skeleton. We give the optimal a priori error analysis of the proposed HDG-P0 schemes, which hasn't appeared in the literature yet for HDG discretizations as far as numerical integration is concerned. Moreover, we propose optimal geometric multigrid preconditioners for the statically condensed HDG-P0 linear systems. In both cases, we first establish the equivalence of the statically condensed HDG system with a (slightly modified) nonconforming Crouzeix-Raviart (CR) discretization, where the global (piecewise-constant) HDG finite element space on the mesh skeleton has a natural one-to-one correspondence to the nonconforming CR (piecewise-linear) finite element space that live on the whole mesh. This equivalence then allows us to use the well-established nonconforming geometry multigrid theory to precondition the condensed HDG system. Numerical results in two- and three-dimensions are presented to verify our theoretical findings.Guosheng Fu, Wenzheng Kuangwork_pl2kel4lhrektaw22r7byxuyuuTue, 30 Aug 2022 00:00:00 GMTDagstuhl Reports, Volume 12, Issue 2, February 2022, Complete Issue
https://scholar.archive.org/work/scntyrlsivecdcac4psbic4qzy
Dagstuhl Reports, Volume 12, Issue 2, February 2022, Complete Issuework_scntyrlsivecdcac4psbic4qzyTue, 23 Aug 2022 00:00:00 GMTError estimation and adaptivity for stochastic collocation finite elements Part I: single-level approximation
https://scholar.archive.org/work/w2zrynqhinhydnppwnd7l5pwfq
A general adaptive refinement strategy for solving linear elliptic partial differential equation with random data is proposed and analysed herein. The adaptive strategy extends the a posteriori error estimation framework introduced by Guignard and Nobile in 2018 (SIAM J. Numer. Anal., 56, 3121--3143) to cover problems with a nonaffine parametric coefficient dependence. A suboptimal, but nonetheless reliable and convenient implementation of the strategy involves approximation of the decoupled PDE problems with a common finite element approximation space. Computational results obtained using such a single-level strategy are presented in this paper (part I). Results obtained using a potentially more efficient multilevel approximation strategy, where meshes are individually tailored, will be discussed in part II of this work. The codes used to generate the numerical results are available on GitHubAlex Bespalov, David Silvester, Feng Xuwork_w2zrynqhinhydnppwnd7l5pwfqMon, 22 Aug 2022 00:00:00 GMTLIPIcs, Volume 240, COSIT 2022, Complete Volume
https://scholar.archive.org/work/7m7bfxazsra63myunecp6u6qgm
LIPIcs, Volume 240, COSIT 2022, Complete VolumeToru Ishikawa, Sara Irina Fabrikant, Stephan Winterwork_7m7bfxazsra63myunecp6u6qgmMon, 22 Aug 2022 00:00:00 GMTIdentifying diffuse spatial structures in high-energy photon lists
https://scholar.archive.org/work/x7drflovjnfxfd3n2kxqmujmdy
Data from high-energy observations are usually obtained as lists of photon events. A common analysis task for such data is to identify whether diffuse emission exists, and to estimate its surface brightness, even in the presence of point sources that may be superposed. We have developed a novel non-parametric event list segmentation algorithm to divide up the field of view into distinct emission components. We use photon location data directly, without binning them into an image. We first construct a graph from the Voronoi tessellation of the observed photon locations and then grow segments using a new adaptation of seeded region growing, that we call Seeded Region Growing on Graph, after which the overall method is named SRGonG. Starting with a set of seed locations, this results in an over-segmented dataset, which SRGonG then coalesces using a greedy algorithm where adjacent segments are merged to minimize a model comparison statistic; we use the Bayesian Information Criterion. Using SRGonG we are able to identify point-like and diffuse extended sources in the data with equal facility. We validate SRGonG using simulations, demonstrating that it is capable of discerning irregularly shaped low surface-brightness emission structures as well as point-like sources with strengths comparable to that seen in typical X-ray data. We demonstrate SRGonG's use on the Chandra data of the Antennae galaxies, and show that it segments the complex structures appropriately.Minjie Fan, Jue Wang, Vinay L. Kashyap, Thomas C. M. Lee, David A. van Dyk, Andreas Zezaswork_x7drflovjnfxfd3n2kxqmujmdyMon, 15 Aug 2022 00:00:00 GMT