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On certain finiteness questions in the arithmetic of Galois representations Wiese, Gabor Presentation (2017, June 07) Let p be a fixed prime number. It has been known for a long time that there are only finitely many Galois extensions K/Q with Galois group a finite irreducible subgroup of GL_2(F_p^bar) that are imaginary ... [more ▼] Let p be a fixed prime number. It has been known for a long time that there are only finitely many Galois extensions K/Q with Galois group a finite irreducible subgroup of GL_2(F_p^bar) that are imaginary and unramified outside p. In contrast, there are infinitely many such with Galois group inside GL_2(Z_p^bar), even if one restricts to ones coming from modular forms (this restriction is believed to be local at p). It is tempting to ask what happens "in between" F_p^bar and Z_p^bar, i.e. whether there is still finiteness modulo fixed prime powers. In the talk, I will motivate and explain a conjecture made with Ian Kiming and Nadim Rustom stating that the set of such Galois extensions `modulo p^m' (a proper definition will be given in the talk) coming from modular forms is finite. I will present partial results and a relation of the finiteness conjecture to a strong question by Kevin Buzzard. The talk is based on joint work with Ian Kiming and Nadim Rustom. [less ▲] Detailed reference viewed: 36 (3 UL)On certain finiteness questions in the arithmetic of modular forms ; ; Wiese, Gabor in Journal of the London Mathematical Society (2016), 94(2), 479-502 We investigate certain finiteness questions that arise naturally when studying approximations modulo prime powers of p-adic Galois representations coming from modular forms. We link these finiteness ... [more ▼] We investigate certain finiteness questions that arise naturally when studying approximations modulo prime powers of p-adic Galois representations coming from modular forms. We link these finiteness statements with a question by K. Buzzard concerning p-adic coefficient fields of Hecke eigenforms. Specifically, we conjecture that, for fixed N, m, and prime p with p not dividing N, there is only a finite number of reductions modulo p^m of normalized eigenforms on \Gamma_1(N). We consider various variants of our basic finiteness conjecture, prove a weak version of it, and give some numerical evidence. [less ▲] Detailed reference viewed: 106 (7 UL)On characterizing the relationship between route choice behavior and optimal traffic control solution space Rinaldi, Marco ; ; Viti, Francesco in Transportation Research Procedia (2017), 23 Explicitly including the dynamics of users' route choice behaviour in optimal traffic control applications has been of interest for researchers in the last five decades. This has been recognized as a very ... [more ▼] Explicitly including the dynamics of users' route choice behaviour in optimal traffic control applications has been of interest for researchers in the last five decades. This has been recognized as a very challenging problem, due to the added layer of complexity and the considerable non-convexity of the resulting problem, even when dealing with simple static assignment and analytical link cost functions. In this work we establish a direct behavioural connection between the different shapes and structures emerging in the solution space of such problems and the underlying route choice behaviour. We specifically investigate how changes in the active equilibrium route set exert direct influence on the solution space's structure and behaviour. Based on this result, we then formulate and validate a constrained version of the original problem, yielding desirable properties in terms of solution space regularity. © 2017 The Authors. [less ▲] Detailed reference viewed: 65 (2 UL)On characterizing the relationship between route choice behaviuor and optimal traffic control solution space Rinaldi, Marco ; ; Viti, Francesco in Transportation Research. Part B : Methodological (2017) Explicitly including the dynamics of users' route choice behaviour in optimal traffic control applications has been of interest for researchers in the last five decades. This has been recognized as a very ... [more ▼] Explicitly including the dynamics of users' route choice behaviour in optimal traffic control applications has been of interest for researchers in the last five decades. This has been recognized as a very challenging problem, due to the added layer of complexity and the considerable non-convexity of the resulting problem, even when dealing with simple static assignment and analytical link cost functions. In this work we establish a direct behavioural connection between the different shapes and structures emerging in the solution space of such problems and the underlying route choice behaviour. We specifically investigate how changes in the active equilibrium route set exert direct influence on the solution space's structure and behaviour. Based on this result, we then formulate and validate a constrained version of the original problem, yielding desirable properties in terms of solution space regularity. © 2017. [less ▲] Detailed reference viewed: 63 (3 UL)On Choquet and Sugeno integrals as aggregation functions Marichal, Jean-Luc in Grabisch, Michel; Murofushi, Toshiaki; Sugeno, Michio (Eds.) Fuzzy Measures and Integrals - Theory and Applications (2000) This paper presents a synthesis on the essential mathematical properties of Choquet and Sugeno integrals viewed as aggregation functions. Some axiomatic characterizations are presented. Subfamilies of the ... [more ▼] This paper presents a synthesis on the essential mathematical properties of Choquet and Sugeno integrals viewed as aggregation functions. Some axiomatic characterizations are presented. Subfamilies of the class of those integrals are also investigated. [less ▲] Detailed reference viewed: 71 (3 UL)On clustering in multiple criteria decision aid: Theory and applications Olteanu, Alexandru Doctoral thesis (2013) Detailed reference viewed: 59 (3 UL)On Clustering the Criteria in an Outranking Based Decision Aid Approach Bisdorff, Raymond in Communications in Computer and Information Science (2008), 14 Detailed reference viewed: 52 (1 UL)On combining state space reductions with global fairness assumptions ; ; Pang, Jun et al in Proc. 17th International Symposium on Formal Methods (2011) Detailed reference viewed: 70 (2 UL)On comonotonically modular functions ; Marichal, Jean-Luc in Mesiar, Radko; Pap, Endre; Klement, Erich Peter (Eds.) 34th Linz Seminar on Fuzzy Set Theory (LINZ 2013) - Non-Classical Measures and Integrals (2013) Detailed reference viewed: 22 (2 UL)On comparison meaningfulness of aggregation functions Marichal, Jean-Luc ; Mathonet, Pierre in Journal of Mathematical Psychology (2001), 45(2), 213-223 This paper will give a description of all continuous functions which are comparison meaningful in the sense of measurement theory. Detailed reference viewed: 76 (0 UL)On complex analytic 1|3-dimensional supermanifolds associated with CP^1 Vishnyakova, Elizaveta in Proceedings of the XXXII Workshop on Geometric Methods in Physics (2014) Detailed reference viewed: 32 (1 UL)On Composability and Security of Game-based Password-Authenticated Key Exchange Skrobot, Marjan Doctoral thesis (2017) The main purpose of Password-Authenticated Key Exchange (PAKE) is to allow secure authenticated communication over insecure networks between two or more parties who only share a low-entropy password. It ... [more ▼] The main purpose of Password-Authenticated Key Exchange (PAKE) is to allow secure authenticated communication over insecure networks between two or more parties who only share a low-entropy password. It is common practice that the secret key derived from a PAKE execution is used to authenticate and encrypt some data payload using symmetric key protocols. Unfortunately, most PAKEs of practical interest, including three protocols considered in this thesis, are studied using so-called game-based models, which -- unlike simulation models -- do not guarantee secure composition per se. However, Brzuska et al. (CCS 2011) have shown that a middle ground is possible in the case of authenticated key exchange that relies on Public-Key Infrastructure (PKI): the game-based models do provide secure composition guarantees when the class of higher-level applications is restricted to symmetric-key protocols. The question that we pose in this thesis is whether or not a similar result can be exhibited for PAKE. Our work answers this question positively. More specifically, we show that PAKE protocols secure according to the game-based Real-or-Random (RoR) definition of Abdalla et al. (PKC 2005) allow for automatic, secure composition with arbitrary, higher-level symmetric key protocols. Since there is evidence that most PAKEs secure in the Find-then-Guess (FtG) model of Bellare et al. (EUROCRYPT 2000) are in fact secure according to the RoR definition, we can conclude that nearly all provably secure PAKEs enjoy a certain degree of composition, one that at least covers the case of implementing secure channels. Although many different protocols that accomplish PAKE have been proposed over last two decades, only a few newcomers managed to find their way to real world applications - albeit lacking an intense and prolonged public scrutiny. As a step in the direction of providing one, this dissertation considers the security and efficiency of two relatively recently proposed PAKE protocols - Dragonfly and J-PAKE. In particular, we prove the security of a very close variant of Dragonfly employing the standard FtG model which incorporates forward secrecy. Thus, our work confirms that Dragonfly's main flows are sound. Furthermore, we contribute to the discussion by proposing and examining (in the RoR model of security) two variants of J-PAKE - which we call RO-J-PAKE and CRS-J-PAKE - that each makes the use of two less zero-knowledge proofs than the original protocol, at the cost of an additional security assumption. Our work reveals that CRS-J-PAKE has an edge in terms of efficiency over J-PAKE for both standard group choices: subgroups of finite fields and elliptic curves. The same is true for RO-J-PAKE, but only when instantiated with elliptic curves. [less ▲] Detailed reference viewed: 300 (37 UL)On compositions of clones of Boolean functions Couceiro, Miguel ; ; Lehtonen, Erkko in Simos, T.; Maroulis, G. (Eds.) International Conference of Computational Methods in Sciences and Engineering 2004 (ICCMSE 2004) (2004) We present some compositions of clones of Boolean functions that imply factorizations of ?, the clone of all Boolean functions, into minimal clones. These can be interpreted as representation theorems ... [more ▼] We present some compositions of clones of Boolean functions that imply factorizations of ?, the clone of all Boolean functions, into minimal clones. These can be interpreted as representation theorems, providing representations of Boolean functions analogous to the disjunctive normal form, the conjunctive normal form, and the Zhegalkin polynomial representations. [less ▲] Detailed reference viewed: 42 (0 UL)On confident outrankings with multiple criteria of uncertain significance Bisdorff, Raymond Scientific Conference (2014, November 11) Detailed reference viewed: 20 (0 UL)On conjectures of Sato-Tate and Bruinier-Kohnen Arias De Reyna Dominguez, Sara ; ; Wiese, Gabor in Ramanujan Journal, The (2015), 36(3), 455-481 This article covers three topics. (1) It establishes links between the density of certain subsets of the set of primes and related subsets of the set of natural numbers. (2) It extends previous results on ... [more ▼] This article covers three topics. (1) It establishes links between the density of certain subsets of the set of primes and related subsets of the set of natural numbers. (2) It extends previous results on a conjecture of Bruinier and Kohnen in three ways: the CM-case is included; under the assumption of the same error term as in previous work one obtains the result in terms of natural density instead of Dedekind-Dirichlet density; the latter type of density can already be achieved by an error term like in the prime number theorem. (3) It also provides a complete proof of Sato-Tate equidistribution for CM modular forms with an error term similar to that in the prime number theorem. [less ▲] Detailed reference viewed: 143 (11 UL)On conservative and associative operations on finite chains Devillet, Jimmy ; ; Marichal, Jean-Luc Scientific Conference (2017, June 16) See attached file Detailed reference viewed: 77 (24 UL)On continuity of measurable group representations and homomorphisms Kuznetsova, Julia in Studia Mathematica (2012), 210(3), 197-208 Let G be a locally compact group, and let U be its unitary representation on a Hilbert space H. Endow the space L(H) of bounded linear operators on H with the weak operator topology. We prove that if U is ... [more ▼] Let G be a locally compact group, and let U be its unitary representation on a Hilbert space H. Endow the space L(H) of bounded linear operators on H with the weak operator topology. We prove that if U is a measurable map from G to L(H) then it is continuous. This result was known before for separable H. We also prove that the following statement is consistent with ZFC: every measurable homomorphism from a locally compact group into any topological group is continuous. [less ▲] Detailed reference viewed: 55 (0 UL)On Crystallization and Percolation Schilling, Tanja Scientific Conference (2015, August) Detailed reference viewed: 34 (0 UL)On Deception-Based Protection Against Cryptographic Ransomware Genç, Ziya Alper ; Lenzini, Gabriele ; in 16th Conference on Detection of Intrusions and Malware & Vulnerability Assessment (2019, June 19) In order to detect malicious file system activity, some commercial and academic anti-ransomware solutions implement deception-based techniques, specifically by placing decoy files among user files. While ... [more ▼] In order to detect malicious file system activity, some commercial and academic anti-ransomware solutions implement deception-based techniques, specifically by placing decoy files among user files. While this approach raises the bar against current ransomware, as any access to a decoy file is a sign of malicious activity, the robustness of decoy strategies has not been formally analyzed and fully tested. In this paper, we analyze existing decoy strategies and discuss how they are effective in countering current ransomware by defining a set of metrics to measure their robustness. To demonstrate how ransomware can identify existing deception-based detection strategies, we have implemented a proof-of-concept anti-decoy ransomware that successfully bypasses decoys by using a decision engine with few rules. Finally, we discuss existing issues in decoy-based strategies and propose practical solutions to mitigate them. [less ▲] Detailed reference viewed: 33 (1 UL)On definition and inference of nonlinear Boolean dynamic networks Yue, Zuogong ; Thunberg, Johan ; et al in On definition and inference of nonlinear Boolean dynamic networks (2017, December) Network reconstruction has become particularly important in systems biology, and is now expected to deliver information on causality. Systems in nature are inherently nonlinear. However, for nonlinear ... [more ▼] Network reconstruction has become particularly important in systems biology, and is now expected to deliver information on causality. Systems in nature are inherently nonlinear. However, for nonlinear dynamical systems with hidden states, how to give a useful definition of dynamic networks is still an open question. This paper presents a useful definition of Boolean dynamic networks for a large class of nonlinear systems. Moreover, a robust inference method is provided. The well-known Millar-10 model in systems biology is used as a numerical example, which provides the ground truth of causal networks for key mRNAs involved in eukaryotic circadian clocks. In addition, as second contribution of this paper, we suggest definitions of linear network identifiability, which helps to unify the available work on network identifiability. [less ▲] Detailed reference viewed: 111 (5 UL) |
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