90 research outputs found
On the Integer-antimagic Spectra of Non-Hamiltonian Graphs
Let be a nontrivial abelian group. A connected simple graph is -\textbf{antimagic} if there exists an edge labeling such that the induced vertex labeling , defined by , is a one-to-one map. In this paper, we analyze the group-antimagic property for Cartesian products, hexagonal nets and theta graphs
Group-antimagic Labelings of Multi-cyclic Graphs
Let be a non-trivial abelian group. A connected simple graph is -\textbf{antimagic} if there exists an edge labeling such that the induced vertex labeling , defined by , is a one-to-one map. The \textit{integer-antimagic spectrum} of a graph is the set IAM. In this paper, we analyze the integer-antimagic spectra for various classes of multi-cyclic graphs
Zero-sum magic graphs and their null sets
For any element h of the Natural numbers, a graph G=(V,E), with vertex set V and edge set E, is said to be h-magic if there exists a labeling of the edge set E, using the integer group mod h such that the induced vertex labeling, the sum of all edges incident to a vertex, is a constant map. When this constant is 0 we call G a zero-sum h-magic graph. The null set of G is the set of all natural numbers h for which G admits a zero-sum h-magic labeling. A graph G is said to be uniformly null if every magic labeling of G induces zero sum. In this thesis we will identify the null sets of certain classes of Planar Graphs
Dehn filling of the "magic" 3-manifold
We classify all the non-hyperbolic Dehn fillings of the complement of the
chain-link with 3 components, conjectured to be the smallest hyperbolic
3-manifold with 3 cusps. We deduce the classification of all non-hyperbolic
Dehn fillings of infinitely many 1-cusped and 2-cusped hyperbolic manifolds,
including most of those with smallest known volume. Among other consequences of
this classification, we mention the following:
- for every integer n we can prove that there are infinitely many hyperbolic
knots in the 3-sphere having exceptional surgeries n, n+1, n+2, n+3, with n+1,
n+2 giving small Seifert manifolds and n, n+3 giving toroidal manifolds;
- we exhibit a 2-cusped hyperbolic manifold that contains a pair of
inequivalent knots having homeomorphic complements;
- we exhibit a chiral 3-manifold containing a pair of inequivalent hyperbolic
knots with orientation-preservingly homeomorphic complements;
- we give explicit lower bounds for the maximal distance between small
Seifert fillings and any other kind of exceptional filling.Comment: 56 pages, 10 figures, 16 tables. Some consequences of the
classification adde
Enhancing Mesh Deformation Realism: Dynamic Mesostructure Detailing and Procedural Microstructure Synthesis
Propomos uma solução para gerar dados de mapas de relevo dinâmicos para simular deformações em superfÃcies macias, com foco na pele humana. A solução incorpora a simulação de rugas ao nÃvel mesoestrutural e utiliza texturas procedurais para adicionar detalhes de microestrutura estáticos. Oferece flexibilidade além da pele humana, permitindo a geração de padrões que imitam deformações em outros materiais macios, como couro, durante a animação.
As soluções existentes para simular rugas e pistas de deformação frequentemente dependem de hardware especializado, que é dispendioso e de difÃcil acesso. Além disso, depender exclusivamente de dados capturados limita a direção artÃstica e dificulta a adaptação a mudanças. Em contraste, a solução proposta permite a sÃntese dinâmica de texturas que se adaptam à s deformações subjacentes da malha de forma fisicamente plausÃvel.
Vários métodos foram explorados para sintetizar rugas diretamente na geometria, mas sofrem de limitações como auto-interseções e maiores requisitos de armazenamento. A intervenção manual de artistas na criação de mapas de rugas e mapas de tensão permite controle, mas pode ser limitada em deformações complexas ou onde maior realismo seja necessário.
O nosso trabalho destaca o potencial dos métodos procedimentais para aprimorar a geração de padrões de deformação dinâmica, incluindo rugas, com maior controle criativo e sem depender de dados capturados. A incorporação de padrões procedimentais estáticos melhora o realismo, e a abordagem pode ser estendida além da pele para outros materiais macios.We propose a solution for generating dynamic heightmap data to simulate deformations for soft surfaces, with a focus on human skin. The solution incorporates mesostructure-level wrinkles and utilizes procedural textures to add static microstructure details. It offers flexibility beyond human skin, enabling the generation of patterns mimicking deformations in other soft materials, such as leater, during animation.
Existing solutions for simulating wrinkles and deformation cues often rely on specialized hardware, which is costly and not easily accessible. Moreover, relying solely on captured data limits artistic direction and hinders adaptability to changes. In contrast, our proposed solution provides dynamic texture synthesis that adapts to underlying mesh deformations.
Various methods have been explored to synthesize wrinkles directly to the geometry, but they suffer from limitations such as self-intersections and increased storage requirements. Manual intervention by artists using wrinkle maps and tension maps provides control but may be limited to the physics-based simulations.
Our research presents the potential of procedural methods to enhance the generation of dynamic deformation patterns, including wrinkles, with greater creative control and without reliance on captured data. Incorporating static procedural patterns improves realism, and the approach can be extended to other soft-materials beyond skin
Around the circular law
These expository notes are centered around the circular law theorem, which
states that the empirical spectral distribution of a nxn random matrix with
i.i.d. entries of variance 1/n tends to the uniform law on the unit disc of the
complex plane as the dimension tends to infinity. This phenomenon is the
non-Hermitian counterpart of the semi circular limit for Wigner random
Hermitian matrices, and the quarter circular limit for Marchenko-Pastur random
covariance matrices. We present a proof in a Gaussian case, due to Silverstein,
based on a formula by Ginibre, and a proof of the universal case by revisiting
the approach of Tao and Vu, based on the Hermitization of Girko, the
logarithmic potential, and the control of the small singular values. Beyond the
finite variance model, we also consider the case where the entries have heavy
tails, by using the objective method of Aldous and Steele borrowed from
randomized combinatorial optimization. The limiting law is then no longer the
circular law and is related to the Poisson weighted infinite tree. We provide a
weak control of the smallest singular value under weak assumptions, using
asymptotic geometric analysis tools. We also develop a quaternionic
Cauchy-Stieltjes transform borrowed from the Physics literature.Comment: Added: one reference and few comment
Some recent advances for limit theorems
We present some recent developments for limit theorems in probability theory, illustrating the variety of this field of activity. The recent results we discuss range from Stein’s method, as well as for infinitely divisible distributions as applications of this method in stochastic geometry, to asymptotics for some discrete models. They deal with rates of convergence, functional convergences for correlated random walks and shape theorems for growth models
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