ORBi<sup>lu</sup> Collection: Mathematics
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First Order Feynman-Kac Formula
http://hdl.handle.net/10993/32296
Title: First Order Feynman-Kac Formula
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<br/>Author, co-author: Li, Xue-Mei; Thompson, James
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<br/>Abstract: We study the parabolic integral kernel associated with the weighted Laplacian and the Feynman-Kac kernels. For manifold with a pole we deduce formulas and estimates for them and for their derivatives, given in terms of a Gaussian term and the semi-classical bridge. Assumptions are on the Riemannian data.Mon, 18 Sep 2017 13:34:32 GMTRecurrence and Transience of Frogs with Drift on Z^d
http://hdl.handle.net/10993/32192
Title: Recurrence and Transience of Frogs with Drift on Z^d
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<br/>Author, co-author: Döbler, Christian; Gantert, Nina; Höfelsauer, Thomas; Popov, Serguei; Weidner, FelizitasTue, 12 Sep 2017 12:08:00 GMTScattering theory without injectivity radius assumptions and spectral stability for the Ricci flow
http://hdl.handle.net/10993/32162
Title: Scattering theory without injectivity radius assumptions and spectral stability for the Ricci flow
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<br/>Author, co-author: Güneysu, Batu; Thalmaier, Anton
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<br/>Abstract: We prove a completely new integral criterion for the existence and completeness of the wave operators W_{\pm}(-\Delta_h,-\Delta_g, I_{g,h}) corresponding to the (unique self-adjoint realizations of) the Laplace-Beltrami operators -\Delta_j, j=g,h, that are induced by two quasi-isometric complete Riemannian metrics g and h on an open manifold M. In particular, this result provides a criterion for the absolutely continuous spectra of -\Delta_g and -\Delta_h to coincide. Our proof relies on estimates that are obtained using a probabilistic Bismut type formula for the gradient of a heat semigroup. Unlike all previous results, our integral criterion only requires some lower control on the Ricci curvatures and some upper control on the heat kernels, but no control at all on the injectivity radii. As a consequence, we obtain a stability result for the absolutely continuous spectrum under a Ricci flow.Fri, 08 Sep 2017 20:31:14 GMTPivotal decomposition schemes inducing clones of operations
http://hdl.handle.net/10993/31952
Title: Pivotal decomposition schemes inducing clones of operations
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<br/>Author, co-author: Couceiro, Miguel; Teheux, Bruno
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<br/>Abstract: We study pivotal decomposition schemes and investigate classes of pivotally decomposable operations.
We provide sufficient conditions on pivotal operations that
guarantee that the corresponding classes of pivotally decomposable operations are clones, and show that under certain assumptions
these conditions are also necessary. In the latter case, the pivotal operation together with the constant operations generate the corresponding clone.Tue, 22 Aug 2017 12:46:34 GMTKoszul-Tate resolutions as cofibrant replacements of algebras over differential operators
http://hdl.handle.net/10993/31947
Title: Koszul-Tate resolutions as cofibrant replacements of algebras over differential operators
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<br/>Author, co-author: Di Brino, Gennaro; Pistalo, Damjan; Poncin, NorbertSat, 19 Aug 2017 09:52:26 GMTOn Koszul-Tate resolutions and Sullivan models
http://hdl.handle.net/10993/31946
Title: On Koszul-Tate resolutions and Sullivan models
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<br/>Author, co-author: Pistalo, Damjan; Poncin, NorbertSat, 19 Aug 2017 09:44:07 GMTEvolution systems of measures and semigroup properties on evolving manifolds
http://hdl.handle.net/10993/31923
Title: Evolution systems of measures and semigroup properties on evolving manifolds
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<br/>Author, co-author: Cheng, Li Juan; Thalmaier, Anton
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<br/>Abstract: An evolving Riemannian manifold (M,g_t)_{t\in I} consists of a smooth d-dimensional manifold M, equipped with a geometric flow g_t of complete Riemannian metrics, parametrized by I=(-\infty,T). Given an additional C^{1,1} family of vector fields (Z_t)_{t\in I} on M. We study the family of operators L_t=\Delta_t +Z_t where \Delta_t denotes the Laplacian with respect to the metric g_t. We first give sufficient conditions, in terms of space-time Lyapunov functions, for non-explosion of the diffusion generated by L_t, and for existence of evolution systems of probability measures associated to it. Coupling methods are used to establish uniqueness of the evolution systems under suitable curvature conditions. Adopting such a unique system of probability measures as reference measures, we characterize supercontractivity, hypercontractivity and ultraboundedness of the corresponding time-inhomogeneous semigroup. To this end, gradient estimates and a family of (super-)logarithmic Sobolev inequalities are established.Wed, 16 Aug 2017 16:45:42 GMTQuantitative C1-estimates by Bismut formulae
http://hdl.handle.net/10993/31856
Title: Quantitative C1-estimates by Bismut formulae
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<br/>Author, co-author: Cheng, Li Juan; Thalmaier, Anton; Thompson, James
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<br/>Abstract: For a C2 function u and an elliptic operator L, we prove a quantitative estimate for the derivative du in terms of local bounds on u and Lu. An integral version of this estimate is then used to derive a condition for the zero-mean value property of Δu. An extension to differential forms is also given. Our approach is probabilistic and could easily be adapted to other settings.Fri, 04 Aug 2017 17:48:49 GMTSub-Laplacian comparison theorems on totally geodesic Riemannian foliations
http://hdl.handle.net/10993/31846
Title: Sub-Laplacian comparison theorems on totally geodesic Riemannian foliations
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<br/>Author, co-author: Baudoin, Fabrice; Grong, Erlend; Kuwada, Kazumasa; Thalmaier, Anton
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<br/>Abstract: We develop a variational theory of geodesics for the canonical variation of the metric of a totally geodesic foliation. As a consequence, we obtain comparison theorems for the horizontal and vertical Laplacians. In the case of Sasakian foliations, we show that sharp horizontal and vertical comparison theorems for the sub-Riemannian distance may be obtained as a limit of horizontal and vertical comparison theorems for the Riemannian distances approximations.Thu, 03 Aug 2017 15:19:18 GMTThe Vanishing of Low-Dimensional Cohomology Groups of the Witt and the Virasoro algebra
http://hdl.handle.net/10993/31809
Title: The Vanishing of Low-Dimensional Cohomology Groups of the Witt and the Virasoro algebra
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<br/>Author, co-author: Ecker, Jill Marie-Anne; Schlichenmaier, Martin
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<br/>Abstract: A proof of the vanishing of the first and the third cohomology groups of the Witt algebra with values in the adjoint module is given. The proofs given in the present article are completely algebraic and independent of any underlying topology. They are a generalization of the ones provided by Schlichenmaier, who proved the vanishing of the second cohomology group using purely algebraic methods. In the case of the third cohomology group though, extra difficulties arise and the involved proofs are distinctly more complicated.Wed, 26 Jul 2017 06:54:15 GMTIntroduction to Berezin-Toeplitz quantization (3 Lectures)
http://hdl.handle.net/10993/31807
Title: Introduction to Berezin-Toeplitz quantization (3 Lectures)
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<br/>Author, co-author: Schlichenmaier, MartinTue, 25 Jul 2017 17:30:13 GMTIntroduction to Berezin-Toeplitz quantization
http://hdl.handle.net/10993/31806
Title: Introduction to Berezin-Toeplitz quantization
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<br/>Author, co-author: Schlichenmaier, MartinTue, 25 Jul 2017 17:27:14 GMTDeformations of pre-symplectic structures and the Koszul L-infty-algebra
http://hdl.handle.net/10993/31775
Title: Deformations of pre-symplectic structures and the Koszul L-infty-algebra
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<br/>Author, co-author: Schätz, Florian; Zambon, Marco
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<br/>Abstract: We study the deformation theory of pre-symplectic structures, i.e. closed two-forms of fixed rank. The main result is a parametrization of nearby deformations of a given pre-symplectic structure in terms of an $L_\infty$-algebra, which we call the Koszul $L_\infty$-algebra. This
$L_\infty$-algebra is a cousin of the Koszul dg Lie algebra associated to a Poisson manifold, and its proper geometric understanding relies on Dirac geometry. In addition, we show that a quotient of the Koszul $L_{\infty}$-algebra is isomorphic to the $L_\infty$-algebra which controls the deformations of the underlying characteristic foliation. Finally, we show that
the infinitesimal deformations of pre-symplectic structures and of foliations are both obstructed.Thu, 20 Jul 2017 14:19:36 GMTEulerian idempotent, pre-Lie logarithm and combinatorics of trees
http://hdl.handle.net/10993/31774
Title: Eulerian idempotent, pre-Lie logarithm and combinatorics of trees
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<br/>Author, co-author: Bandiera, Ruggero; Schätz, Florian
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<br/>Abstract: The aim of this paper is to bring together the three objects in the title. Recall that, given a Lie algebra g, the Eulerian idempotent is a canonical projection from the enveloping algebra U(g) to
g. The Baker-Campbell-Hausdorff product and the Magnus expansion can both be expressed in terms of the Eulerian idempotent, which makes it interesting to establish explicit formulas for the latter. We show how to reduce the computation of the Eulerian idempotent to the computation of a logarithm in a certain pre-Lie algebra of planar, binary, rooted trees. The problem of finding formulas for the pre-Lie logarithm, which is interesting in its own right – being related to operad theory, numerical analysis and renormalization – is addressed using techniques inspired by umbral calculus. As a consequence of our analysis, we find formulas both for the Eulerian idempotent and the pre-Lie logarithm in terms of the combinatorics of trees.Thu, 20 Jul 2017 14:06:53 GMTModal extensions of Ł_n-valued logics, coalgebraically
http://hdl.handle.net/10993/31753
Title: Modal extensions of Ł_n-valued logics, coalgebraically
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<br/>Author, co-author: Kurz, Alexander; Teheux, Bruno; Bílková, MartaTue, 18 Jul 2017 08:31:49 GMTGeneralized qualitative Sugeno integrals
http://hdl.handle.net/10993/31752
Title: Generalized qualitative Sugeno integrals
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<br/>Author, co-author: Dubois, Didier; Prade, Henri; Rico, Agnès; Teheux, Bruno
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<br/>Abstract: Sugeno integrals are aggregation operations involving a criterion weighting scheme based on the use of set functions called capacities or fuzzy measures. In this paper, we define generalized versions of Sugeno integrals on totally ordered bounded chains, by extending the operation that combines the value of the capacity on each subset of criteria and the value of the utility function over elements of the subset. We show that the generalized concept of Sugeno integral splits into two functionals, one based on a general multiple-valued conjunction (we call integral) and one based on a general multiple-valued implication (we call cointegral). These fuzzy conjunction and implication connectives are related via a so-called semiduality property, involving an involutive negation. Sugeno integrals correspond to the case when the fuzzy conjunction is the minimum and the fuzzy implication is Kleene-Dienes implication, in which case integrals and cointegrals coincide. In this paper, we consider a very general class of fuzzy conjunction operations on a finite setting, that reduce to Boolean conjunctions on extreme values of the bounded chain, and are non-decreasing in each place, and the corresponding general class of implications (their semiduals). The merit of these new aggregation operators is to go beyond pure lattice polynomials, thus enhancing the expressive power of qualitative aggregation functions, especially as to the way an importance weight can affect a local rating of an object to be chosen.Tue, 18 Jul 2017 08:22:03 GMTLinear Algebra 2
http://hdl.handle.net/10993/31714
Title: Linear Algebra 2
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<br/>Author, co-author: Wiese, GaborMon, 10 Jul 2017 15:11:59 GMTFourth moment theorems on The Poisson space in any dimension
http://hdl.handle.net/10993/31706
Title: Fourth moment theorems on The Poisson space in any dimension
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<br/>Author, co-author: Döbler, Christian; Vidotto, Anna; Zheng, GuangquMon, 10 Jul 2017 11:12:32 GMTProbability signatures of multistate systems made up of two-state components
http://hdl.handle.net/10993/31679
Title: Probability signatures of multistate systems made up of two-state components
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<br/>Author, co-author: Marichal, Jean-Luc; Mathonet, Pierre; Jorge, Navarro; Paroissin, Christian
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<br/>Abstract: The structure signature of a system made up of $n$ components having continuous and i.i.d. lifetimes was defined in the eighties by Samaniego as the $n$-tuple whose $k$-th coordinate is the probability that the $k$-th component failure causes the system to fail. More recently, a bivariate version of this concept was considered as follows. The joint structure signature of a pair of systems built on a common set of components having continuous and i.i.d. lifetimes is a square matrix of order $n$ whose $(k,l)$-entry is the probability that the $k$-th failure causes the first system to fail and the $l$-th failure causes the second system to fail. This concept was successfully used to derive a signature-based decomposition of the joint reliability of the two systems. In this talk we will show an explicit formula to compute the joint structure signature of two or more systems and extend this formula to the general non-i.i.d. case, assuming only that the distribution of the component lifetimes has no ties. Then we will discuss a condition on this distribution for the joint reliability of the systems to have a signature-based decomposition. Finally we will show how these results can be applied to the investigation of the reliability and signature of multistate systems made up of two-state components.Sat, 08 Jul 2017 12:07:56 GMTAlgèbre linéaire 2
http://hdl.handle.net/10993/31654
Title: Algèbre linéaire 2
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<br/>Author, co-author: Wiese, GaborFri, 07 Jul 2017 20:10:14 GMT