ORBi<sup>lu</sup> Collection: Mathematics
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Canonical quantization for compact quantizable Kaehler manifolds
http://hdl.handle.net/10993/39501
Title: Canonical quantization for compact quantizable Kaehler manifolds
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<br/>Author, co-author: Schlichenmaier, MartinThu, 16 May 2019 12:44:48 GMTRank n swapping algebra for PGLn Fock--Goncharov X moduli space
http://hdl.handle.net/10993/39495
Title: Rank n swapping algebra for PGLn Fock--Goncharov X moduli space
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<br/>Author, co-author: Sun, Zhe
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<br/>Abstract: The rank n swapping algebra is a Poisson algebra defined on the set of ordered pairs of points of the circle using linking numbers, whose geometric model is given by a certain subspace of (K^n×K^{n∗})^r/GL(n,K). For any ideal triangulation of D_k---a disk with k points on its boundary, using determinants, we find an injective Poisson algebra homomorphism from the fraction algebra generated by the Fock--Goncharov coordinates for X_{PGL_n,D_k} to the rank n swapping multifraction algebra for r=k⋅(n−1) with respect to the (Atiyah--Bott--)Goldman Poisson bracket and the swapping bracket. This is the building block of the general surface case. Two such injective Poisson algebra homomorphisms related to two ideal triangulations T and T′ are compatible with each other under the flips.Wed, 15 May 2019 09:12:07 GMTMcShane identities for Higher Teichmüller theory and the Goncharov-Shen potential
http://hdl.handle.net/10993/39494
Title: McShane identities for Higher Teichmüller theory and the Goncharov-Shen potential
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<br/>Author, co-author: Sun, Zhe; Huang, Yi
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<br/>Abstract: In [GS15], Goncharov and Shen introduce a family of mapping class group invariant regular functions on their A-moduli space to explicitly formulate a particular homological mirror symmetry conjecture. Using these regular functions, we obtain McShane identities general rank positive surface group representations with loxodromic boundary monodromy and (non-strict) McShane-type inequalities for general rank positive representations with unipotent boundary monodromy. Our identities are expressed in terms of projective invariants, and we study these invariants: we establish boundedness and Fuchsian rigidity results for triple ratios. Moreover, we obtain McShane identities for finite-area cusped convex real projective surfaces by generalizing the Birman--Series geodesic scarcity theorem. We apply our identities to derive the simple spectral discreteness of unipotent bordered positive representations, collar lemmas, and generalizations of the Thurston metric.Wed, 15 May 2019 08:45:14 GMTRank n swapping algebra for Grassmannian
http://hdl.handle.net/10993/39493
Title: Rank n swapping algebra for Grassmannian
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<br/>Author, co-author: Sun, Zhe
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<br/>Abstract: The rank n swapping algebra is the Poisson algebra defined on the ordered pairs of points on a circle using the linking numbers, where a subspace of (K^n×K^{n∗})^r/GL(n,K) is its geometric mode. In this paper, we find an injective Poisson homomorphism from the Poisson algebra on Grassmannian G(n,r) arising from boundary measurement map to the rank n swapping fraction algebra.Wed, 15 May 2019 08:25:47 GMTSingle-peakedness in aggregation function theory
http://hdl.handle.net/10993/39492
Title: Single-peakedness in aggregation function theory
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<br/>Author, co-author: Devillet, Jimmy; Couceiro, Miguel; Marichal, Jean-Luc
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<br/>Abstract: Due to their great importance in data fusion, aggregation functions have been extensively investigated for a few decades. Among these functions, fuzzy connectives (such as uninorms) play an important role in fuzzy logic.
We establish a remarkable connection between a family of associative aggregation functions, which includes the class of idempotent uninorms, and the concepts of single-peakedness and single-plateaudness, introduced in social choice theory by D. Black. Finally, we enumerate those orders when the underlying set is finite.Tue, 14 May 2019 15:03:21 GMTDisplacement based polytopal elements a strain smoothing and scaled boundary approach
http://hdl.handle.net/10993/39442
Title: Displacement based polytopal elements a strain smoothing and scaled boundary approach
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<br/>Author, co-author: Bordas, Stéphane; Natarajan, SundararajanFri, 03 May 2019 08:08:06 GMTVolumes of quasifuchsian manifolds
http://hdl.handle.net/10993/39407
Title: Volumes of quasifuchsian manifolds
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<br/>Author, co-author: Schlenker, Jean-Marc
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<br/>Abstract: Quasifuchsian hyperbolic manifolds, or more generally convex co-compact hyperbolic manifolds, have infinite volume, but they have a well-defined ``renormalized'' volume. We outline some relations between this renormalized volume and the volume, or more precisely the ``dual volume'', of the convex core. On one hand, there are striking similarities between them, for instance in their variational formulas. On the other, object related to them tend to be within bounded distance. Those analogies and proximities lead to several questions. Both the renormalized volume and the dual volume can be used for instance to bound the volume of the convex core in terms of the Weil-Petersson distance between the conformal metrics at infinity.Sun, 28 Apr 2019 15:45:56 GMTHyperideal polyhedra in the 3-dimensional anti-de Sitter space
http://hdl.handle.net/10993/39402
Title: Hyperideal polyhedra in the 3-dimensional anti-de Sitter space
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<br/>Author, co-author: Chen, Qiyu; Schlenker, Jean-Marc
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<br/>Abstract: We study hyperideal polyhedra in the 3-dimensional anti-de Sitter space AdS3, which are defined as the intersection of the projective model of AdS3 with a convex polyhedron in RP3 whose vertices are all outside of AdS3 and whose edges all meet AdS3. We show that hyperideal polyhedra in AdS3 are uniquely determined by their combinatorics and dihedral angles, as well as by the induced metric on their boundary together with an additional combinatorial data, and describe the possible dihedral angles and the possible induced metrics on the boundary.Sat, 27 Apr 2019 06:35:12 GMTVerification of the Quillen conjecture in the rank 2 imaginary quadratic case
http://hdl.handle.net/10993/39373
Title: Verification of the Quillen conjecture in the rank 2 imaginary quadratic case
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<br/>Author, co-author: Rahm, Alexander; Bui, Anh Tuan
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<br/>Abstract: 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.Sun, 21 Apr 2019 10:01:37 GMTAll quasitrivial n-ary semigroups are reducible to semigroups
http://hdl.handle.net/10993/39337
Title: All quasitrivial n-ary semigroups are reducible to semigroups
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<br/>Author, co-author: Couceiro, Miguel; Devillet, Jimmy
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<br/>Abstract: We show that every quasitrivial n-ary semigroup is reducible to
a binary semigroup, and we provide necessary and sufficient conditions for
such a reduction to be unique. These results are then refined in the case of
symmetric n-ary semigroups. We also explicitly determine the sizes of these
classes when the semigroups are defined on finite sets. As a byproduct of these
enumerations, we obtain several new integer sequences.Thu, 11 Apr 2019 22:02:30 GMTOn indefinite sums weighted by periodic sequences
http://hdl.handle.net/10993/39332
Title: On indefinite sums weighted by periodic sequences
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<br/>Author, co-author: Marichal, Jean-Luc
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<br/>Abstract: For any integer $q\geq 2$ we provide a formula to express indefinite sums of a sequence $(f(n))_{n\geq 0}$ weighted by $q$-periodic sequences in terms of indefinite sums of sequences $(f(qn+p))_{n\geq 0}$, where $p\in\{0,\ldots,q-1\}$. When explicit expressions for the latter sums are available, this formula immediately provides explicit expressions for the former sums. We also illustrate this formula through some examples.Thu, 11 Apr 2019 07:25:06 GMTExplicit Kummer Theory for the rational numbers
http://hdl.handle.net/10993/39282
Title: Explicit Kummer Theory for the rational numbers
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<br/>Author, co-author: Perucca, Antonella; Sgobba, Pietro; Tronto, SebastianoThu, 04 Apr 2019 14:47:08 GMTN point Virasoro algebras are multi-point Krichever Novikov type algebras
http://hdl.handle.net/10993/39274
Title: N point Virasoro algebras are multi-point Krichever Novikov type algebras
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<br/>Author, co-author: Schlichenmaier, MartinWed, 03 Apr 2019 18:47:45 GMTOn quasitrivial semigroups
http://hdl.handle.net/10993/39222
Title: On quasitrivial semigroups
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<br/>Author, co-author: Devillet, JimmyThu, 28 Mar 2019 17:43:09 GMTLinear system identification from ensemble snapshot observations
http://hdl.handle.net/10993/39109
Title: Linear system identification from ensemble snapshot observations
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<br/>Author, co-author: Aalto, Atte; Goncalves, Jorge
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<br/>Abstract: Developments in transcriptomics techniques have caused a large demand in tailored computational methods for modelling gene expression dynamics from experimental data. Recently, so-called single-cell experiments have revolutionised genetic studies. These experiments yield gene expression data
in single cell resolution for a large number of cells at a time. However, the cells are destroyed in the measurement process, and so the data consist of snapshots of an ensemble evolving over time, instead of time series. The problem studied in this article is how such data can be used in modelling gene regulatory dynamics. Two different paradigms are studied for linear system identification. The first is based on tracking the evolution of the distribution of cells over time. The second is based on the so-called pseudotime concept, identifying a common trajectory through the state space, along which cells propagate with different rates. Therefore, at any given time, the population contains cells in different stages of the trajectory. Resulting methods are compared in numerical experiments.Thu, 21 Mar 2019 10:01:09 GMTConformal actions of higher-rank lattices on pseudo-Riemannian manifolds
http://hdl.handle.net/10993/39064
Title: Conformal actions of higher-rank lattices on pseudo-Riemannian manifolds
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<br/>Author, co-author: Pecastaing, Vincent
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<br/>Abstract: We investigate conformal actions of cocompact lattices in higher-rank simple Lie groups on compact pseudo-Riemannian manifolds. Our main result gives a general bound on the real-rank of the lattice, which was already known for the action of the full Lie group ([33]). When the real-rank is maximal, we prove that the manifold is conformally flat. This indicates that a global conclusion similar to that of [1] and [17] in the case of a Lie group action might be obtained. We also give better estimates for actions of cocompact lattices in exceptional groups. Our work is strongly inspired by the recent breakthrough of Brown, Fisher and Hurtado on Zimmer’s conjecture [7].Sat, 16 Mar 2019 14:59:04 GMTOn two theorems about local automorphisms of geometric structures
http://hdl.handle.net/10993/39063
Title: On two theorems about local automorphisms of geometric structures
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<br/>Author, co-author: Pecastaing, Vincent
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<br/>Abstract: This article investigates a few questions about orbits of local automorphisms in manifolds endowed with rigid geometric structures. We give suf- ficient conditions for local homogeneity in a broad class of such structures, namely Cartan geometries, extending a classical result of Singer about locally homogeneous Riemannian manifolds. We also revisit a strong result of Gromov which describes the structure of the orbits of local automorphisms of manifolds endowed with A- rigid structures, and give a statement and a simpler proof of this result in the setting of Cartan geometries.Sat, 16 Mar 2019 14:54:24 GMTThe Latent Topic Block Model for the Co-Clustering of Textual Interaction Data
http://hdl.handle.net/10993/39017
Title: The Latent Topic Block Model for the Co-Clustering of Textual Interaction Data
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<br/>Author, co-author: Berge, Laurent; Bouveyron, Charles; Corneli, Marco; Latouche, PierreTue, 12 Mar 2019 16:13:31 GMTHet kunstgalerijprobleem
http://hdl.handle.net/10993/39007
Title: Het kunstgalerijprobleem
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<br/>Author, co-author: Perucca, Antonella
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<br/>Commentary: Translated into Dutch and edited by Luc Van den Broeck.Mon, 11 Mar 2019 13:16:54 GMTEstimating Matching Affinity Matrix under Low-Rank Constraints
http://hdl.handle.net/10993/39006
Title: Estimating Matching Affinity Matrix under Low-Rank Constraints
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<br/>Author, co-author: Dupuy, Arnaud; Galichon, Alfred; Sun, Yifei
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<br/>Abstract: In this paper, we address the problem of estimating transport surplus (a.k.a. matching affinity) in high dimensional optimal transport problems. Classical optimal transport theory specifies the matching affinity and determines the optimal joint distribution. In contrast, we study the inverse problem of estimating matching affinity based on the observation of the joint distribution, using an entropic regularization of the problem. To accommodate high dimensionality of the data, we propose a novel method that incorporates a nuclear norm regularization which effectively enforces a rank constraint on the affinity matrix. The low-rank matrix estimated in this way reveals the main factors which are relevant for matching.Mon, 11 Mar 2019 10:48:00 GMT