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Journal articles on the topic 'Parametrized graphs'

Author: Grafiati

Published: 4 April 2023

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1

Faran, Rachel, and Orna Kupferman. "A Parametrized Analysis of Algorithms on Hierarchical Graphs." International Journal of Foundations of Computer Science 30, no. 06n07 (2019): 979–1003. http://dx.doi.org/10.1142/s0129054119400252.

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Hierarchical graphs are used in order to describe systems with a sequential composition of sub-systems. A hierarchical graph consists of a vector of subgraphs. Vertices in a subgraph may “call” other subgraphs. The reuse of subgraphs, possibly in a nested way, causes hierarchical graphs to be exponentially more succinct than equivalent flat graphs. Early research on hierarchical graphs and the computational price of their succinctness suggests that there is no strong correlation between the complexity of problems when applied to flat graphs and their complexity in the hierarchical setting. Tha

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ELLIS-MONAGHAN, JOANNA A., and LORENZO TRALDI. "Parametrized Tutte Polynomials of Graphs and Matroids." Combinatorics, Probability and Computing 15, no. 06 (2006): 835. http://dx.doi.org/10.1017/s0963548306007656.

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Asaeda, Marta, and Uffe Haagerup. "Fusion rules on a parametrized series of graphs." Pacific Journal of Mathematics 253, no. 2 (2011): 257–88. http://dx.doi.org/10.2140/pjm.2011.253.257.

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Sadeghian, Ali, Mohammadreza Armandpour, Anthony Colas, and Daisy Zhe Wang. "ChronoR: Rotation Based Temporal Knowledge Graph Embedding." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 7 (2021): 6471–79. http://dx.doi.org/10.1609/aaai.v35i7.16802.

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Despite the importance and abundance of temporal knowledge graphs, most of the current research has been focused on reasoning on static graphs. In this paper, we study the challenging problem of inference over temporal knowledge graphs. In particular, the task of temporal link prediction. In general, this is a difficult task due to data non-stationarity, data heterogeneity, and its complex temporal dependencies. We propose Chronological Rotation embedding (ChronoR), a novel model for learning representations for entities, relations, and time. Learning dense representations is frequently used a

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Keros, Alexandros D., Vidit Nanda, and Kartic Subr. "Dist2Cycle: A Simplicial Neural Network for Homology Localization." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 7 (2022): 7133–42. http://dx.doi.org/10.1609/aaai.v36i7.20673.

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Simplicial complexes can be viewed as high dimensional generalizations of graphs that explicitly encode multi-way ordered relations between vertices at different resolutions, all at once. This concept is central towards detection of higher dimensional topological features of data, features to which graphs, encoding only pairwise relationships, remain oblivious. While attempts have been made to extend Graph Neural Networks (GNNs) to a simplicial complex setting, the methods do not inherently exploit, or reason about, the underlying topological structure of the network. We propose a graph convol

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LEFLOCH, PHILIPPE G. "GRAPH SOLUTIONS OF NONLINEAR HYPERBOLIC SYSTEMS." Journal of Hyperbolic Differential Equations 01, no. 04 (2004): 643–89. http://dx.doi.org/10.1142/s0219891604000287.

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For nonlinear hyperbolic systems of partial differential equations in one-space dimension (in either conservative or non-conservative form) we introduce a geometric framework in which solutions are sought as (continuous) parametrized graphs(t,s) ↦ (X,U)(t,s) satisfying ∂sX ≥ 0, rather than (discontinuous) functions (t,x) ↦ u(t,x). On one hand, we generalize an idea by Dal Maso, LeFloch, and Murat who used a family of traveling wave profiles to define non-conservative products, and we define the notion of graph solution subordinate to a family of Riemann graphs. The latter naturally encodes the

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Hussein, Amru. "Sign-indefinite second-order differential operators on finite metric graphs." Reviews in Mathematical Physics 26, no. 04 (2014): 1430003. http://dx.doi.org/10.1142/s0129055x14300039.

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The question of self-adjoint realizations of sign-indefinite second-order differential operators is discussed in terms of a model problem. Operators of the type [Formula: see text] are generalized to finite, not necessarily compact, metric graphs. All self-adjoint realizations are parametrized using methods from extension theory. The spectral and scattering theories of the self-adjoint realizations are studied in detail.

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Aristoff, David, and Lingjiong Zhu. "On the phase transition curve in a directed exponential random graph model." Advances in Applied Probability 50, no. 01 (2018): 272–301. http://dx.doi.org/10.1017/apr.2018.13.

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Abstract We consider a family of directed exponential random graph models parametrized by edges and outward stars. Much of the important statistical content of such models is given by the normalization constant of the models, and, in particular, an appropriately scaled limit of the normalization, which is called the free energy. We derive precise asymptotics for the normalization constant for finite graphs. We use this to derive a formula for the free energy. The limit is analytic everywhere except along a curve corresponding to a first-order phase transition. We examine unusual behavior of th

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Stefanou, Anastasios. "Tree decomposition of Reeb graphs, parametrized complexity, and applications to phylogenetics." Journal of Applied and Computational Topology 4, no. 2 (2020): 281–308. http://dx.doi.org/10.1007/s41468-020-00051-1.

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Galvez, Carmen, and Félix Moya-Anegón. "The unification of institutional addresses applying parametrized finite-state graphs (P-FSG)." Scientometrics 69, no. 2 (2006): 323–45. http://dx.doi.org/10.1007/s11192-006-0156-3.

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NASTOS, JAMES, and YONG GAO. "BOUNDED SEARCH TREE ALGORITHMS FOR PARAMETRIZED COGRAPH DELETION: EFFICIENT BRANCHING RULES BY EXPLOITING STRUCTURES OF SPECIAL GRAPH CLASSES." Discrete Mathematics, Algorithms and Applications 04, no. 01 (2012): 1250008. http://dx.doi.org/10.1142/s1793830912500085.

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Many fixed-parameter tractable algorithms using a bounded search tree have been repeatedly improved, often by describing a larger number of branching rules involving an increasingly complex case analysis. We introduce a novel and general search strategy that branches on the forbidden subgraphs of a graph class relaxation. By using the class of P4-sparse graphs as the relaxed graph class, we obtain efficient bounded search tree algorithms for several parametrized deletion problems. We give the first non-trivial bounded search tree algorithms for the cograph edge-deletion problem and the trivial

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Blum, Johannes, Stefan Funke, and Sabine Storandt. "Sublinear search spaces for shortest path planning in grid and road networks." Journal of Combinatorial Optimization 42, no. 2 (2021): 231–57. http://dx.doi.org/10.1007/s10878-021-00777-3.

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AbstractShortest path planning is a fundamental building block in many applications. Hence developing efficient methods for computing shortest paths in, e.g., road or grid networks is an important challenge. The most successful techniques for fast query answering rely on preprocessing. However, for many of these techniques it is not fully understood why they perform so remarkably well, and theoretical justification for the empirical results is missing. An attempt to explain the excellent practical performance of preprocessing based techniques on road networks (as transit nodes, hub labels, or

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DEPRETTERE, ED F., PETER HELD, and PAUL WIELAGE. "MODEL AND METHODS FOR REGULAR ARRAY DESIGN." International Journal of High Speed Electronics and Systems 04, no. 02 (1993): 133–201. http://dx.doi.org/10.1142/s012915649300008x.

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We present a unified framework for the transformation of algorithms to architectures in the domains of high speed signal and algebraic processing. The framework starts from algorithmic specifications in a language suited for numerical analysis (such as Matlab), transforms the high level description into hierarchical and structured data flow dependence graphs, allows the designer to manipulate the graphs, to merge them, abstract them, regularize them, cluster and partition them etc… until the description of an architecture which can represent the hardware in a precise manner is obtained. A gene

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SITHARAM, MEERA, YONG ZHOU, and JÖRG PETERS. "RECONCILING CONFLICTING COMBINATORIAL PREPROCESSORS FOR GEOMETRIC CONSTRAINT SYSTEMS." International Journal of Computational Geometry & Applications 20, no. 06 (2010): 631–51. http://dx.doi.org/10.1142/s0218195910003463.

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Polynomial equation systems arising from real applications often have associated combinatorial information, expressible as graphs and underlying matroids. To simplify the system and improve its numerical robustness before attempting to solve it with numeric-algebraic techniques, solvers can employ graph algorithms to extract substructures satisfying or optimizing various combinatorial properties. When there are underlying matroids, these algorithms can be greedy and efficient. In practice, correct and effective merging of the outputs of different graph algorithms to simultaneously satisfy thei

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Zhang, Kewei, Antonio Orlando, and Elaine Crooks. "Compensated convexity and Hausdorff stable geometric singularity extractions." Mathematical Models and Methods in Applied Sciences 25, no. 04 (2015): 747–801. http://dx.doi.org/10.1142/s0218202515500189.

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We develop and apply the theory of lower and upper compensated convex transforms introduced in [K. Zhang, Compensated convexity and its applications, Ann. Inst. H. Poincaré Anal. Non Linéaire 25 (2008) 743–771] to define multiscale, parametrized, geometric singularity extraction transforms of ridges, valleys and edges of function graphs and sets in ℝn. These transforms can be interpreted as "tight" opening and closing operators, respectively, with quadratic structuring functions. We show that these geometric morphological operators are invariant with respect to translation, and stable under cu

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EIDENBENZ, S., A. Å. HANSSON, V. RAMASWAMY, and C. M. REIDYS. "ON A NEW CLASS OF LOAD BALANCING NETWORK PROTOCOLS." Advances in Complex Systems 10, no. 03 (2007): 359–77. http://dx.doi.org/10.1142/s0219525907001148.

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In this paper we study a new class of generic, parametrized, locally load-sensing (LLS) network-routing protocols over simple graphs, Y. These protocols are Y-"local" in the sense that they transmit packets only between Y-adjacent vertices and LLS since they base their "routing decisions" dynamically on queue-sizes of their neighbors and their relative distance to the destination. In the system each vertex has specific data-queues indexed by its respective Y-neighbors. The state of a vertex then consists of the collection of queue-sizes. The data-transmission protocols are formally specified i

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Montenegro, Marcelo, and Sebastián Lorca. "Height estimates for graph parametrized surfaces." Bulletin des Sciences Mathématiques 136, no. 8 (2012): 848–56. http://dx.doi.org/10.1016/j.bulsci.2012.07.002.

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18

de Oliveira Guimarães, José. "Parametrized methods." ACM SIGPLAN Notices 28, no. 11 (1993): 28–32. http://dx.doi.org/10.1145/165564.165572.

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McCarthy, P. J., M. Crampin, and W. Stephenson. "Graphs in the plane invariant under an area preserving linear map and general continuous solutions of certain quadratic functional equations." Mathematical Proceedings of the Cambridge Philosophical Society 97, no. 2 (1985): 261–78. http://dx.doi.org/10.1017/s0305004100062812.

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AbstractThe requirement that the graph of a function be invariant under a linear map is equivalent to a functional equation of f. For area preserving maps M(det (M) = 1), the functional equation is equivalent to an (easily solved) linear one, or to a quadratic one of the formfor all Here 2C = Trace (M). It is shown that (Q) admits continuous solutions ⇔ M has real eigenvalues ⇔ (Q) has linear solutions f(x) = λx ⇔ |C| ≥ 1. For |c| = 1 or C < – 1, (Q) only admits a few simple solutions. For C > 1, (Q) admits a rich supply of continuous solutions. These are parametrised by an arbitrary fun

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Szocinski, Timothy, Duc Duy Nguyen, and Guo-Wei Wei. "AweGNN: Auto-parametrized weighted element-specific graph neural networks for molecules." Computers in Biology and Medicine 134 (July 2021): 104460. http://dx.doi.org/10.1016/j.compbiomed.2021.104460.

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Jenei, Márk, and James A. Elliott. "Substitution effect in the graph model of polymerisation parametrised by atomistic simulations." Computational Materials Science 208 (June 2022): 111315. http://dx.doi.org/10.1016/j.commatsci.2022.111315.

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22

Farin, Gerald. "Rational quadratic circles are parametrized by chord length." Computer Aided Geometric Design 23, no. 9 (2006): 722–24. http://dx.doi.org/10.1016/j.cagd.2006.08.002.

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23

Jeong, Moon-Hwan, and Hyeong-Seok Ko. "Draft-space warping: grading of clothes based on parametrized draft." Computer Animation and Virtual Worlds 24, no. 3-4 (2013): 377–86. http://dx.doi.org/10.1002/cav.1503.

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Wang, F. C., P. K. Wright, B. A. Barsky, and D. C. H. Yang. "Approximately Arc-Length Parametrized C3 Quintic Interpolatory Splines." Journal of Mechanical Design 121, no. 3 (1999): 430–39. http://dx.doi.org/10.1115/1.2829479.

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A quasi-global interpolation method that fits a quintic spline curve to a set of designated data points is described in this paper. The resultant curve has several important features. First, the curve is smooth with C3 continuity and has no unwanted oscillations. Second, the generated quintic spline is “optimally” parametrized; that is, the curve is parametrized very closely to its arc length. In addition, with the interpolation method, straight line segments can be preserved to generate a quintic spline of hybrid curve segments. The properties of C3 continuity and the “near arc length” parame

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BELL, MARK C., VALENTINA DISARLO, and ROBERT TANG. "Cubical geometry in the polygonalisation complex." Mathematical Proceedings of the Cambridge Philosophical Society 167, no. 01 (2018): 1–22. http://dx.doi.org/10.1017/s0305004118000130.

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AbstractWe introduce the polygonalisation complex of a surface, a cube complex whose vertices correspond to polygonalisations. This is a geometric model for the mapping class group and it is motivated by works of Harer, Mosher and Penner. Using properties of the flip graph, we show that the midcubes in the polygonalisation complex can be extended to a family of embedded and separating hyperplanes, parametrised by the arcs in the surface.We study the crossing graph of these hyperplanes and prove that it is quasi-isometric to the arc complex. We use the crossing graph to prove that, generically,

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Barber, David. "Identifying graph clusters using variational inference and links to covariance parametrization." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 367, no. 1906 (2009): 4407–26. http://dx.doi.org/10.1098/rsta.2009.0117.

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Finding clusters of well-connected nodes in a graph is a problem common to many domains, including social networks, the Internet and bioinformatics. From a computational viewpoint, finding these clusters or graph communities is a difficult problem. We use a clique matrix decomposition based on a statistical description that encourages clusters to be well connected and few in number. The formal intractability of inferring the clusters is addressed using a variational approximation inspired by mean-field theories in statistical mechanics. Clique matrices also play a natural role in parametrizing

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Narváez, David E. "A QSAT Benchmark Based on Vertex-Folkman Problems (Student Abstract)." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 10 (2020): 13881–82. http://dx.doi.org/10.1609/aaai.v34i10.7213.

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The purpose of this paper is to draw attention to a particular family of quantified Boolean formulas (QBFs) stemming from encodings of some vertex Folkman problems in extremal graph theory. We argue that this family of formulas is interesting for QSAT research because it is both conceptually simple and parametrized in a way that allows for a fine-grained diversity in the level of difficulty of its instances. Additionally, when coupled with symmetry breaking, the formulas in this family exhibit backbones (unique satisfying assignments) at the top-level existential variables. This benchmark is t

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BIELECKI, WLODZIMIERZ, TOMASZ KLIMEK, MAREK PALKOWSKI, and ANNA BELETSKA. "AN ITERATIVE ALGORITHM OF COMPUTING THE TRANSITIVE CLOSURE OF A UNION OF PARAMETRIZED AFFINE INTEGER TUPLE RELATIONS." Discrete Mathematics, Algorithms and Applications 04, no. 01 (2012): 1250011. http://dx.doi.org/10.1142/s1793830912500115.

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A novel iterative algorithm of calculating the exact transitive closure of a parametrized graph being represented by a union of simple affine integer tuple relations is presented. When it is not possible to calculate exact transitive closure, the algorithm produces its upper bound. To calculate the transitive closure of the union of all simple relations, the algorithm recognizes the class of each simple relations, calculates its exact transitive closure, forms the union of calculated transitive closures, and applies this union in an iterative procedure. Results of experiments aimed at the comp

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BOWLIN, GARRY, and MATTHEW G. BRIN. "COLORING PLANAR GRAPHS VIA COLORED PATHS IN THE ASSOCIAHEDRA." International Journal of Algebra and Computation 23, no. 06 (2013): 1337–418. http://dx.doi.org/10.1142/s0218196713500276.

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Hassler Whitney's theorem of 1931 reduces the task of finding proper, vertex 4-colorings of triangulations of the 2-sphere to finding such colorings for the class ℌ of triangulations of the 2-sphere that have a Hamiltonian circuit. This has been used by Whitney and others from 1936 to the present to find equivalent reformulations of the 4 Color Theorem (4CT). Recently there has been activity to try to use some of these reformulations to find a shorter proof of the 4CT. Every triangulation in ℌ has a dual graph that is a union of two binary trees with the same number of leaves. Elements of a gr

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Rakowska, J., R. T. Haftka, and L. T. Watson. "An active set algorithm for tracing parametrized optima." Structural Optimization 3, no. 1 (1991): 29–44. http://dx.doi.org/10.1007/bf01743487.

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WATANABE, Y., and K. FUKUMIZU. "New Graph Polynomials from the Bethe Approximation of the Ising Partition Function." Combinatorics, Probability and Computing 20, no. 2 (2010): 299–320. http://dx.doi.org/10.1017/s0963548310000258.

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We introduce two graph polynomials and discuss their properties. One is a polynomial of two variables whose investigation is motivated by the performance analysis of the Bethe approximation of the Ising partition function. The other is a polynomial of one variable that is obtained by the specialization of the first one. It is shown that these polynomials satisfy deletion–contraction relations and are new examples of the V-function, which was introduced by Tutte (Proc. Cambridge Philos. Soc.43, 1947, p. 26). For these polynomials, we discuss the interpretations of special values and then obtain

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van Emmerik, Maarten J. G. M. "Creation and modification of parametrized solid models by graphical interaction." Computers & Graphics 13, no. 1 (1989): 71–76. http://dx.doi.org/10.1016/0097-8493(89)90041-1.

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FISH, JOEL W. "ESTIMATES FOR J-CURVES AS SUBMANIFOLDS." International Journal of Mathematics 22, no. 10 (2011): 1375–431. http://dx.doi.org/10.1142/s0129167x11007306.

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In this paper, we develop some basic analytic tools to study compactness properties of J-curves (i.e. pseudoholomorphic curves) when regarded as submanifolds. Incorporating techniques from the theory of minimal surfaces, we derive an inhomogeneous mean curvature equation for such curves by establishing an extrinsic monotonicity principle for nonnegative functions f satisfying Δf ≥ -c2f, we show that curves locally parametrized as a graph over a coordinate tangent plane have all derivatives a priori bounded in terms of curvature and ambient geometry, and we thus establish ϵ-regularity for the s

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GRAFFI, SANDRO, and LORENZO ZANELLI. "GEOMETRIC APPROACH TO THE HAMILTON–JACOBI EQUATION AND GLOBAL PARAMETRICES FOR THE SCHRÖDINGER PROPAGATOR." Reviews in Mathematical Physics 23, no. 09 (2011): 969–1008. http://dx.doi.org/10.1142/s0129055x11004497.

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We construct a family of global Fourier Integral Operators, defined for arbitrary large times, representing a global parametrix for the Schrödinger propagator when the potential is quadratic at infinity. This construction is based on the geometric approach to the corresponding Hamilton–Jacobi equation and thus sidesteps the problem of the caustics generated by the classical flow. Moreover, a detailed study of the real phase function allows us to recover a WKB semiclassical approximation which necessarily involves the multivaluedness of the graph of the Hamiltonian flow past the caustics.

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Albert, Michael, and Vincent Vatter. "An Elementary Proof of Bevan's Theorem on the Growth of Grid Classes of Permutations." Proceedings of the Edinburgh Mathematical Society 62, no. 4 (2019): 975–84. http://dx.doi.org/10.1017/s0013091519000026.

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AbstractBevan established that the growth rate of a monotone grid class of permutations is equal to the square of the spectral radius of a related bipartite graph. We give an elementary and self-contained proof of a generalization of this result using only Stirling's formula, the method of Lagrange multipliers, and the singular value decomposition of matrices. Our proof relies on showing that the maximum over the space of n × n matrices with non-negative entries summing to one of a certain function of those entries, parametrized by the entries of another matrix Γ of non-negative real numbers,

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Zhuang, Chungang, Zhenhua Xiong, and Han Ding. "Temperature-constrained topology optimization of nonlinear heat conduction problems." Journal of Computational Design and Engineering 8, no. 4 (2021): 1059–81. http://dx.doi.org/10.1093/jcde/qwab032.

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Abstract This paper presents topology optimization of nonlinear heat conduction problems with multiple domains and multiple constraints, including regional temperature and material volume for reducing temperature. Maximum approximation temperatures in the constraint regions are accurately and dynamically calculated, though temperature and temperature-dependent thermal conductivity change with the update of material distribution. A temperature measure with constant error to approximate regional maximum temperature is adaptive to different temperature ranges. A strategy of hole nucleation genera

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Savický, Petr, and Petr Kučera. "Generating Models of a Matched Formula With a Polynomial Delay." Journal of Artificial Intelligence Research 56 (June 29, 2016): 379–402. http://dx.doi.org/10.1613/jair.4989.

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A matched formula is a CNF formula whose incidence graph admits a matching which matches a distinct variable to every clause. Such a formula is always satisfiable. Matched formulas are used, for example, in the area of parametrized complexity. We prove that the problem of counting the number of the models (satisfying assignments) of a matched formula is #P-complete. On the other hand, we define a class of formulas generalizing the matched formulas and prove that for a formula in this class one can choose in polynomial time a variable suitable for splitting the tree for the search of the models

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Pitler, Emily. "A Crossing-Sensitive Third-Order Factorization for Dependency Parsing." Transactions of the Association for Computational Linguistics 2 (December 2014): 41–54. http://dx.doi.org/10.1162/tacl_a_00164.

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Parsers that parametrize over wider scopes are generally more accurate than edge-factored models. For graph-based non-projective parsers, wider factorizations have so far implied large increases in the computational complexity of the parsing problem. This paper introduces a “crossing-sensitive” generalization of a third-order factorization that trades off complexity in the model structure (i.e., scoring with features over multiple edges) with complexity in the output structure (i.e., producing crossing edges). Under this model, the optimal 1-Endpoint-Crossing tree can be found in O( n4) time,

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Pérez-Díaz, Sonia, та Li-Yong Shen. "Inversion, degree, reparametrization and implicitization of improperly parametrized planar curves using μ-basis". Computer Aided Geometric Design 84 (січень 2021): 101957. http://dx.doi.org/10.1016/j.cagd.2021.101957.

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Prasad, J., and A. R. Diaz. "Synthesis of Bistable Periodic Structures Using Topology Optimization and a Genetic Algorithm." Journal of Mechanical Design 128, no. 6 (2005): 1298–306. http://dx.doi.org/10.1115/1.2338576.

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A formulation for the automatic synthesis of two-dimensional bistable, compliant periodic structures is presented, based on standard methods for topology optimization. The design space is parametrized using nonlinear beam elements and a ground structure approach. A performance criterion is suggested, based on characteristics of the load-deformation curve of the compliant structure. A genetic algorithm is used to find candidate solutions. A numerical implementation of this methodology is discussed and illustrated using simple examples.

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Kosina, H., and C. Troger. "SPIN – A Schrödinger-Poisson Solver Including Nonparabolic Bands." VLSI Design 8, no. 1-4 (1998): 489–93. http://dx.doi.org/10.1155/1998/39231.

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Nonparabolicity effects in two-dimensional electron systems are quantitatively analyzed. A formalism has been developed which allows to incorporate a nonparabolic bulk dispersion relation into the Schrödinger equation. As a consequence of nonparabolicity the wave functions depend on the in-plane momentum. Each subband is parametrized by its energy, effective mass and a subband nonparabolicity coefficient. The formalism is implemented in a one-dimensional Schrödinger-Poisson solver which is applicable both to silicon inversion layers and heterostructures.

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Mühlherr, Bernhard, and Richard M. Weiss. "Tits Triangles." Canadian Mathematical Bulletin 62, no. 3 (2018): 583–601. http://dx.doi.org/10.4153/s0008439518000140.

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AbstractA Tits polygon is a bipartite graph in which the neighborhood of every vertex is endowed with an “opposition relation” satisfying certain properties. Moufang polygons are precisely the Tits polygons in which these opposition relations are all trivial. There is a standard construction that produces a Tits polygon whose opposition relations are not all trivial from an arbitrary pair $(\unicode[STIX]{x1D6E5},T)$, where $\unicode[STIX]{x1D6E5}$ is a building of type $\unicode[STIX]{x1D6F1}$, $\unicode[STIX]{x1D6F1}$ is a spherical, irreducible Coxeter diagram of rank at least $3$, and $T$

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CAPPELLO, PETER, and ÖMER EĞECIOĞLU. "PROCESSOR LOWER BOUND FORMULAS FOR ARRAY COMPUTATIONS AND PARAMETRIC DIOPHANTINE SYSTEMS." International Journal of Foundations of Computer Science 09, no. 04 (1998): 351–75. http://dx.doi.org/10.1142/s0129054198000295.

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Using a directed acyclic graph (dag) model of algorithms, we solve a problem related to precedence-constrained multiprocessor schedules for array computations: Given a sequence of dags and linear schedules parametrized by n, compute a lower bound on the number of processors required by the schedule as a function of n. In our formulation, the number of tasks that are scheduled for execution during any fixed time step is the number of non-negative integer solutions dn to a set of parametric linear Diophantine equations. We present an algorithm based on generating functions for constructing a for

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Shah, Nirav Vasant, Michele Girfoglio, Peregrina Quintela, et al. "Finite element based Model Order Reduction for parametrized one-way coupled steady state linear thermo-mechanical problems." Finite Elements in Analysis and Design 212 (December 2022): 103837. http://dx.doi.org/10.1016/j.finel.2022.103837.

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Izumi, Masaki, Scott Morrison, and David Penneys. "Quotients of A2 * T2." Canadian Journal of Mathematics 68, no. 5 (2016): 999–1022. http://dx.doi.org/10.4153/cjm-2015-017-4.

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AbstractWe study unitary quotients of the free product unitary pivotal category A2 * T2. We show that such quotients are parametrized by an integer n ≥ 1 and an 2n–th root of unity ω. We show that for n = 1, 2, 3, there is exactly one quotient and ω = 1. For 4 ≤ n ≤ 10, we show that there are no such quotients. Our methods also apply to quotients of T2 * T2, where we have a similar result.The essence of our method is a consistency check on jellyfish relations. While we only treat the specific cases of A2 × T2 and T2 . T2, we anticipate that our technique can be extended to a general method for

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Fayolle, Pierre-Alain, Alexander Pasko, Benjamin Schmitt, and Nikolay Mirenkov. "Constructive Heterogeneous Object Modeling Using Signed Approximate Real Distance Functions." Journal of Computing and Information Science in Engineering 6, no. 3 (2005): 221–29. http://dx.doi.org/10.1115/1.2218366.

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We introduce a smooth approximation of the min∕max operations, called signed approximate real distance function (SARDF), for maintaining an approximate signed distance function in constructive shape modeling. We apply constructive distance-based shape modeling to design objects with heterogeneous material distribution in the constructive hypervolume model framework. The introduced distance approximation helps intuitively model material distributions parametrized by distances to so-called material features. The smoothness of the material functions, provided here by the smoothness of the definin

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BARLET, D., and M. KADDAR. "INCIDENCE DIVISOR." International Journal of Mathematics 14, no. 04 (2003): 339–59. http://dx.doi.org/10.1142/s0129167x03001867.

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Let Z be a complex manifold of dimension n+1 and (Xs)s∈S be an analytic family of n-cycles (not necessarily compact) parametrized by a reduced analytic complex space S. Denote by X the graph of this family and p1 (resp. p2) the canonical projection of S × Z on S (resp. on Z). The construction of Barlet-Magnusson assigns to each n+1-codimensionnal subspace in Z which is assumed to be a local complete intersection and to satisfy: C1[Formula: see text] is proper and finite on its image which is nowhere dense in S, an effective Cartier divisor ΣY in S. Nice functorial properties of this correspond

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Giacomini, Matteo, Luca Borchini, Ruben Sevilla, and Antonio Huerta. "Separated response surfaces for flows in parametrised domains: Comparison of a priori and a posteriori PGD algorithms." Finite Elements in Analysis and Design 196 (November 2021): 103530. http://dx.doi.org/10.1016/j.finel.2021.103530.

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Badescu, Mircea, and Constantinos Mavroidis. "Workspace Optimization of 3-Legged UPU and UPS Parallel Platforms With Joint Constraints." Journal of Mechanical Design 126, no. 2 (2004): 291–300. http://dx.doi.org/10.1115/1.1667922.

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In this paper the workspace optimization of 3-legged translational UPU and orientational UPS parallel platforms under joint constraints is performed. The workspace of both platforms is parametrized using several design parameters that span a large range of values. In this paper both the unconstrained and the constrained workspaces (i.e., workspace with joint limits) are used. For the workspace of each design configuration three performance indices are calculated using a Monte Carlo method: a) the workspace volume; b) the average of the inverse of the condition number and c) a Global Condition

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Yang, D. C. H., and Fu-Chung Wang. "A Quintic Spline Interpolator for Motion Command Generation of Computer-Controlled Machines." Journal of Mechanical Design 116, no. 1 (1994): 226–31. http://dx.doi.org/10.1115/1.2919351.

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This paper presents a new method of motion command generation for computer controlled multi-axis machines. The method is based on a quintic spline interpolator (QSI) which generates motion commands to trace a set of desired discrete position data via a composite quintic spline (CQS). This CQS is nearly arc length parametrized and has second order continuous at the data points. Consequently, the generated motion trajectories are continuous in both velocity and acceleration throughout the motion. A quick motion command generation scheme is also developed. Compared to the existing linear interpol

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