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Kummer theory for finite fields and p-adic fields Perissinotto, Flavio ; Perucca, Antonella E-print/Working paper (n.d.) Let K be a finite field or a finite extension of Qp for some prime number p. If G is a finitely generated subgroup of K*, then we can consider the degree of the cyclotomic-Kummer extension K(\zeta_N ... [more ▼] Let K be a finite field or a finite extension of Qp for some prime number p. If G is a finitely generated subgroup of K*, then we can consider the degree of the cyclotomic-Kummer extension K(\zeta_N, \sqrt[n]{G})/K, where n divides N. If K is a finite field, then we give a closed formula for the degree, while if K is a p-adic field, then we describe a strategy to compute the degree. [less ▲] Detailed reference viewed: 84 (4 UL)Bayesian inference for the stochastic identification of elastoplastic material parameters: Introduction, misconceptions and insights Rappel, Hussein ; Beex, Lars ; Hale, Jack et al E-print/Working paper (n.d.) We discuss Bayesian inference (BI) for the probabilistic identification of material parameters. This contribution aims to shed light on the use of BI for the identification of elastoplastic material ... [more ▼] We discuss Bayesian inference (BI) for the probabilistic identification of material parameters. This contribution aims to shed light on the use of BI for the identification of elastoplastic material parameters. For this purpose a single spring is considered, for which the stress-strain curves are artificially created. Besides offering a didactic introduction to BI, this paper proposes an approach to incorporate statistical errors both in the measured stresses, and in the measured strains. It is assumed that the uncertainty is only due to measurement errors and the material is homogeneous. Furthermore, a number of possible misconceptions on BI are highlighted based on the purely elastic case. [less ▲] Detailed reference viewed: 381 (106 UL)Beware proportions Perucca, Antonella ; Ronk, Pit Ferdy E-print/Working paper (n.d.) Detailed reference viewed: 41 (8 UL)The first-digit law Perucca, Antonella E-print/Working paper (n.d.) Detailed reference viewed: 75 (0 UL)Galois groups of Kummer extensions of number fields Advocaat, Bryan ; Chan, Chi Wa ; Pajaziti, Antigona et al E-print/Working paper (n.d.) Detailed reference viewed: 54 (2 UL)Four Riddles with Four Brothers Perucca, Antonella E-print/Working paper (n.d.) Detailed reference viewed: 59 (1 UL)Controlling the Error on Target Motion through Real-time Mesh Adaptation: Applications to Deep Brain Stimulation Bui, Huu Phuoc ; Tomar, Satyendra ; et al E-print/Working paper (n.d.) We present an error-controlled mesh refinement procedure for needle insertion simulation and apply it to the simulation of electrode implantation for deep brain stimulation, including brain shift. Our ... [more ▼] We present an error-controlled mesh refinement procedure for needle insertion simulation and apply it to the simulation of electrode implantation for deep brain stimulation, including brain shift. Our approach enables to control the error in the computation of the displacement and stress fields around the needle tip and needle shaft by suitably refining the mesh, whilst maintaining a coarser mesh in other parts of the domain. We demonstrate through academic and practical examples that our approach increases the accuracy of the displacement and stress fields around the needle without increasing the computational expense. This enables real-time simulations. The proposed methodology has direct implications to increase the accuracy and control the computational expense of the simulation of percutaneous procedures such as biopsy, brachytherapy, regional anesthesia, or cryotherapy and can be essential to the development of robotic guidance. [less ▲] Detailed reference viewed: 635 (34 UL)Linear smoothed polygonal and polyhedral finite elements ; ; Bordas, Stéphane et al E-print/Working paper (n.d.) It was observed in [1, 2] that the strain smoothing technique over higher order elements and arbitrary polytopes yields less accurate solutions than other techniques such as the conventional polygonal ... [more ▼] It was observed in [1, 2] that the strain smoothing technique over higher order elements and arbitrary polytopes yields less accurate solutions than other techniques such as the conventional polygonal finite element method. In this work, we propose a linear strain smoothing scheme that improves the accuracy of linear and quadratic approximations over convex polytopes. The main idea is to subdivide the polytope into simplicial subcells and use a linear smoothing function in each subcell to compute the strain. This new strain is then used in the computation of the stiffness matrix. The convergence properties and accuracy of the proposed scheme are discussed by solving few benchmark problems. Numerical results show that the proposed linear strain smoothing scheme makes the approximation based on polytopes to deliver improved accuracy and pass the patch test to machine precision. [less ▲] Detailed reference viewed: 471 (10 UL)A new one point quadrature rule over arbitrary star convex polygon/polyhedron ; ; et al E-print/Working paper (n.d.) The Linear Smoothing (LS) scheme \cite{francisa.ortiz-bernardin2017} ameliorates linear and quadratic approximations over convex polytopes by employing a three-point integration scheme. In this work, we ... [more ▼] The Linear Smoothing (LS) scheme \cite{francisa.ortiz-bernardin2017} ameliorates linear and quadratic approximations over convex polytopes by employing a three-point integration scheme. In this work, we propose a linearly consistent one point integration scheme which possesses the properties of the LS scheme with three integration points but requires one third of the integration computational time. The essence of the proposed technique is to approximate the strain by the smoothed nodal derivatives that are determined by the discrete form of the divergence theorem. This is done by the Taylor's expansion of the weak form which facilitates the evaluation of the smoothed nodal derivatives acting as stabilization terms. The smoothed nodal derivatives are evaluated only at the centroid of each integration cell. These integration cells are the simplex subcells (triangle/tetrahedron in two and three dimensions) obtained by subdividing the polytope. The salient feature of the proposed technique is that it requires only $n$ integrations for an $n-$ sided polytope as opposed to $3n$ in~\cite{francisa.ortiz-bernardin2017} and $13n$ integration points in the conventional approach. The convergence properties, the accuracy, and the efficacy of the LS with one point integration scheme are discussed by solving few benchmark problems in elastostatics. [less ▲] Detailed reference viewed: 72 (3 UL)The distribution of the multiplicative index of algebraic numbers over residue classes ; Perucca, Antonella ; Sgobba, Pietro E-print/Working paper (n.d.) Detailed reference viewed: 44 (1 UL)Verification of the Quillen conjecture in the rank 2 imaginary quadratic case Rahm, Alexander ; E-print/Working paper (n.d.) We confirm a conjecture of Quillen in the case of the mod 2 cohomology of arithmetic groups SL_2(A[1/2]), where A is an imaginary quadratic ring of integers. To make explicit the free module structure on ... [more ▼] We confirm a conjecture of Quillen in the case of the mod 2 cohomology of arithmetic groups SL_2(A[1/2]), where A is an imaginary quadratic ring of integers. To make explicit the free module structure on the cohomology ring conjectured by Quillen, we compute the mod 2 cohomology of SL_2(Z[sqrt(−2)][1/2]) via the amalgamated decomposition of the latter group. [less ▲] Detailed reference viewed: 78 (1 UL)Three-dimensional arithmetic billiards Perucca, Antonella ; Perissinotto, Flavio ; E-print/Working paper (n.d.) Detailed reference viewed: 151 (5 UL)Modelling challenges & simulation results comparison study for inactive elements activation approach in numerical simulation of Selective Laser Melting Additive Manufacturing process Mashhood, Muhammad ; Peters, Bernhard ; et al E-print/Working paper (n.d.) Detailed reference viewed: 45 (12 UL)The Hardest Logic Puzzle Ever Perucca, Antonella E-print/Working paper (n.d.) Detailed reference viewed: 62 (1 UL)Weakening the tight coupling between geometry and simulation in isogeometric analysis: from sub- and super- geometric analysis to Geometry Independent Field approximaTion (GIFT) ; ; Tomar, Satyendra et al E-print/Working paper (n.d.) This paper presents an approach to generalize the concept of isogeometric analysis (IGA) by allowing different spaces for parameterization of the computational domain and for approximation of the solution ... [more ▼] This paper presents an approach to generalize the concept of isogeometric analysis (IGA) by allowing different spaces for parameterization of the computational domain and for approximation of the solution field. The method inherits the main advantage of isogeometric analysis, i.e. preserves the original, exact CAD geometry (for example, given by NURBS), but allows pairing it with an approximation space which is more suitable/flexible for analysis, for example, T-splines, LR-splines, (truncated) hierarchical B-splines, and PHT-splines. This generalization offers the advantage of adaptive local refinement without the need to re-parameterize the domain, and therefore without weakening the link with the CAD model. We demonstrate the use of the method with different choices of the geometry and field splines, and show that, despite the failure of the standard patch test, the optimum convergence rate is achieved for non-nested spaces. [less ▲] Detailed reference viewed: 286 (14 UL)Divisibility conditions on the order of the reductions of algebraic numbers Sgobba, Pietro E-print/Working paper (n.d.) Let K be a number field, and let G be a finitely generated subgroup of K*. Without relying on (GRH) we prove an asymptotic formula for the number of primes \p of K such that the order of (G mod \p) is ... [more ▼] Let K be a number field, and let G be a finitely generated subgroup of K*. Without relying on (GRH) we prove an asymptotic formula for the number of primes \p of K such that the order of (G mod \p) is divisible by a fixed integer. We also provide a rational expression for the natural density of this set. Furthermore, we study the primes \p for which the order is k-free, and those for which the order has a prescribed \ell-adic valuation for finitely many primes \ell. An additional condition on the Frobenius conjugacy class of \p may be considered. In order to establish these results, we prove an unconditional version of the Chebotarev density theorem for Kummer extensions of number fields. [less ▲] Detailed reference viewed: 112 (13 UL)Deniable Public-Key Authenticated Quantum Key Exchange van Wier, Jeroen ; Atashpendar, Arash ; Roenne, Peter E-print/Working paper (n.d.) In this work, we explore the notion of deniability in public-key authenticated quantum key exchange (QKE), which allows two parties to establish a shared secret key without leaving any evidence that would ... [more ▼] In this work, we explore the notion of deniability in public-key authenticated quantum key exchange (QKE), which allows two parties to establish a shared secret key without leaving any evidence that would bind a session to either party. The deniability property is expressed in terms of being able to simulate the transcripts of a protocol. The ability to deny a message or an action has applications ranging from secure messaging to secure e-voting and whistle-blowing. While quite well-established in classical cryptography, it remains largely unexplored in the quantum setting. Here, we first present a natural extension of classical definitions in the simulation paradigm to the setting of quantum computation and formalize the requirements for a deniable QKE scheme. We then prove that the BB84 variant of QKE, when authenticated using a strong designated verifier signature scheme, satisfies deniability and, finally, propose a concrete instantiation. [less ▲] Detailed reference viewed: 48 (11 UL)Prime divisors of the l-Genocchi numbers and the ubiquity of Ramanujan-style congruences of level l ; Sgobba, Pietro E-print/Working paper (n.d.) Let \ell be any fixed prime number. We define the \ell-Genocchi numbers by G_n:=\ell(1-\ell^n)B_n, with B_n the n-th Bernoulli number. They are integers. We introduce and study a variant of Kummer's ... [more ▼] Let \ell be any fixed prime number. We define the \ell-Genocchi numbers by G_n:=\ell(1-\ell^n)B_n, with B_n the n-th Bernoulli number. They are integers. We introduce and study a variant of Kummer's notion of regularity of primes. We say that an odd prime p is \ell-Genocchi irregular if it divides at least one of the \ell-Genocchi numbers G_2,G_4,..., G_{p-3}, and \ell-regular otherwise. With the help of techniques used in the study of Artin's primitive root conjecture, we give asymptotic estimates for the number of \ell-Genocchi irregular primes in a prescribed arithmetic progression in case \ell is odd. The case \ell=2 was already dealt with by Hu, Kim, Moree and Sha (2019). Using similar methods we study the prime factors of (1-\ell^n)B_{2n}/2n and (1+\ell^n)B_{2n}/2n. This allows us to estimate the number of primes p\leq x for which there exist modulo p Ramanujan-style congruences between the Fourier coefficients of an Eisenstein series and some cusp form of prime level \ell. [less ▲] Detailed reference viewed: 57 (3 UL) |
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