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Lauricella hypergeometric functions, unipotent fundamental groups of the punctured Riemann sphere, and their motivic coactionsJul 15 2019We prove a recent conjecture arising in the context of scattering amplitudes for a `motivic' Galois group action on Gauss' ${}_2F_1$ hypergeometric function. More generally, we show on the one hand how the coefficients in a Laurent expansion of a Lauricella ... More

Creating and Flattening Cusp Singularities by Deformations of Bi-conformal EnergyJul 15 2019Mappingsofbi-conformalenergyformthewidestclass of homeomorphisms that one can hope to build a viable extension of Geometric Function Theory with connections to mathematical models of Nonlinear Elasticity. Such mappings are exactly the ones with finite ... More

Integration by parts formula for non-pluripolar productJul 15 2019In this paper, we prove the integration by parts formula for the non-pluripolar product on a compact K\"ahler manifold. Our result generalizes the special case of potentials with small unbounded loci proved in [BEGZ10].

Remarks on Gross' technique for obtaining a conformal Skorohod embedding of planar Brownian motionJul 15 2019In a recent work by Gross, it was proved that, given a distribution $\mu$ with zero mean and finite second moment, we can find a simply connected domain $\Omega$ such that if $Z_{t}$ is a standard planar BM, then $\mathcal{R}e(Z_{\tau_{\Omega}})$ has ... More

Weyl symbols and boundedness of Toeplitz operatorsJul 13 2019We study Toeplitz operators on the Bargmann space, with Toeplitz symbols that are exponentials of inhomogeneous quadratic polynomials. It is shown that the boundedness of such operators is implied by the boundedness of the corresponding Weyl symbols.

The royal road to automatic noncommutative real analyticity, monotonicity, and convexityJul 12 2019It was shown classically that matrix monotone and matrix convex functions must be real analytic by L\"owner and Kraus respectively. Recently, various analogues have been found in several noncommuting variables. We develop a general framework for lifting ... More

A variational approach to the Hermitian-Einstein metrics and the Quot-scheme limit of Fubini-Study metricsJul 12 2019This is a sequel of our paper [arXiv:1809.08425] on the Quot-scheme limit and variational properties of Donaldson's functional, which established its coercivity for slope stable holomorphic vector bundles over smooth projective varieties. Assuming that ... More

The structure of Schmidt subspaces of Hankel operators: a short proofJul 12 2019We give a short proof of the main result of our previous paper [2]: every Schmidt subspace of a Hankel operator is the image of a model space by an isometric multiplier. This class of subspaces is closely related to nearly $S^*$-invariant subspaces, and ... More

Holomorphic distributions and connectivity by integral curves of distributionsJul 12 2019It is known that the classical Frobenius theorem on conditions of integrability for distributions of planes can be extended to the case of complex holomorphic distributions. We show that an alternative criterion for integrability, namely, non-connectivity, ... More

Wild boundary behaviour of holomorphic functions in domains of $\mathbb{C}^N$Jul 11 2019Given a domain of holomorphy $D$ in $\mathbb{C}^N$, $N\geq 2$, we show that the set of holomorphic functions in $D$ whose cluster sets along any finite length paths to the boundary of $D$ is maximal, is residual, densely lineable and spaceable in the ... More

Commutant lifting and Nevanlinna-Pick interpolation in several variablesJul 11 2019This paper concerns a commutant lifting theorem and a Nevanlinna-Pick type interpolation result in the setting of multipliers from vector-valued Drury-Arveson space to a large class of vector-valued reproducing kernel Hilbert spaces over the unit ball ... More

Single Image Super-Resolution via CNN Architectures and TV-TV MinimizationJul 11 2019Super-resolution (SR) is a technique that allows increasing the resolution of a given image. Having applications in many areas, from medical imaging to consumer electronics, several SR methods have been proposed. Currently, the best performing methods ... More

Bernstein--Sato Varieties, $\mathscr{D}_{X}[S]F^{S}$, the Map $\nabla_{A}$, and Cohomology Support LociJul 11 2019Given a complex germ $f$ near the point $\mathfrak{x}$ of the complex manifold $X$, equipped with a factorization $f = f_{1} \cdots f_{r}$, we consider the $\mathscr{D}_{X,\mathfrak{x}}[s_{1}, \dots, s_{r}]$-module generated by $ F^{S} := f_{1}^{s_{1}} ... More

Further remarks on rigidity of Hénon mapsJul 11 2019For a H\'{e}non map $H$ in $\mathbb{C}^2$, we characterize the polynomial automorphisms of $\mathbb{C}^2$ which keep any fixed level set of the Green function of $H$ completely invariant. The interior of any non-zero sublevel set of the Green function ... More

An equilibrium problem on the sphere with two equal chargesJul 10 2019We study the equilibrium measure on the two dimensional sphere in the presence of an external field generated by two equal point charges. The support of the equilibrium measure is known as the droplet. Brauchart et al. showed that the complement of the ... More

Constructing a quasiregular analogue of $z \exp(z)$ in dimension 3Jul 10 2019We construct a quasiregular analogue of the function $z\exp(z)$ in dimension 3, which gives the first explicit example of a quasiregular mapping of transcendental type that has exactly one zero. We then modify the construction to create a family of such ... More

A Projectional Ansatz to ReconstructionJul 10 2019Recently the field of inverse problems has seen a growing usage of mathematically only partially understood learned and non-learned priors. Based on first principles we develop a projectional approach to inverse problems which addresses the incorporation ... More

Radii of starlikeness and convexity of $q-$Mittag--Leffler functionsJul 10 2019In this paper we deal with the radii of starlikeness and convexity of the $q-$Mittag--Leffler function for three different kinds of normalization by making use of their Hadamard factorization in such a way that the resulting functions are analytic in ... More

A note on the boundary behaviour of the squeezing function and Fridman invariantJul 10 2019Let $\Omega$ be a domain in $\mathbb C^n$. Suppose that $\partial\Omega$ is smooth pseudoconvex of D'Angelo finite type near a boundary point $\xi_0\in \partial\Omega$ and the Levi form has corank at most $1$ at $\xi_0$. Our goal is to show that if the ... More

Noncommutative Schur-type products and their Schoenberg theoremJul 10 2019Schoenberg showed that a function $f:(-1,1)\rightarrow \mathbb{R}$ such that $C=[c_{ij}]_{i,j}$ positive semi-definite implies that $f(C)=[f(c_{ij})]_{i,j}$ is also positive semi-definite must be analytic and have Taylor series coefficients nonnegative ... More

An affine model of a Riemann surface associated to a Schwarz-Christoffel mappingJul 09 2019In this paper we construct an affine model of a Riemann surface with a flat Riemannian metric associated to a Schwarz-Christoffel mapping of the upper half plane onto a rational triangle. We explain the relation between the geodesics on this Riemann surface ... More

Global Optimality Guarantees for Nonconvex Unsupervised Video SegmentationJul 09 2019In this paper, we consider the problem of unsupervised video object segmentation via background subtraction. Specifically, we pose the nonsemantic extraction of a video's moving objects as a nonconvex optimization problem via a sum of sparse and low-rank ... More

Wandering domains arising from Lavaurs maps with Siegel disksJul 09 2019The classification of Fatou components for rational functions was concluded with Sullivan's proof of the No Wandering Domains Theorem in 1985. In 2016 it was shown, in joint work of the first and last author with Buff, Dujardin and Raissy, that wandering ... More

On a $q-$analog of a singularly perturbed problem of irregular type with two complex time variablesJul 09 2019Analytic solutions and their formal asymptotic expansions for a family of the singularly perturbed $q-$difference-differential equations in the complex domain are constructed. They stand for a $q-$analog of the singularly perturbed partial differential ... More

On the Exact Recovery Conditions of 3D Human Motion from 2D Landmark Motion with Sparse Articulated MotionJul 09 2019In this paper, we address the problem of exact recovery condition in retrieving 3D human motion from 2D landmark motion. We use a skeletal kinematic model to represent the 3D human motion as a vector of angular articulation motion. We address this problem ... More

Classification of generalized Kähler-Ricci solitons on complex surfacesJul 08 2019Using toric geometry we give an explicit construction of the compact steady solitons for pluriclosed flow first constructed in arXiv:1802.00170. This construction also reveals that these solitons are generalized K\"ahler in two distinct ways, with vanishing ... More

On Competing Definitions for the Diederich-Fornæss IndexJul 08 2019Let $\Omega\subset\mathbb{C}^n$ be a bounded pseudoconvex domain. We define the Diederich-Forn{\ae}ss index with respect to a family of functions to be the supremum over the set of all exponents $0<\eta<1$ such that there exists a function $\rho_\eta$ ... More

Gluing Theorems for Subharmonic FunctionsJul 07 2019Jul 12 2019In our articles of recent years, the technique of gluing two subharmonic functions turned out to be very useful in studying the distribution of the roots or masses of holomorphic or subharmonic functions, respectively. Here we develop and improve this ... More

Gluing Theorems for Subharmonic FunctionsJul 07 2019In our articles of recent years, the technique of gluing two subharmonic functions turned out to be very useful in studying the distribution of the roots or masses of holomorphic or subharmonic functions, respectively. Here we develop and improve this ... More

Regularizing linear inverse problems with convolutional neural networksJul 06 2019Deep convolutional neural networks trained on large datsets have emerged as an intriguing alternative for compressing images and solving inverse problems such as denoising and compressive sensing. However, it has only recently been realized that even ... More

Bilevel Integrative Optimization for Ill-posed Inverse ProblemsJul 06 2019Classical optimization techniques often formulate the feasibility of the problems as set, equality or inequality constraints. However, explicitly designing these constraints is indeed challenging for complex real-world applications and too strict constraints ... More

Nikishin systems on star-like sets: Ratio asymptotic formulae for the associated multiple orthogonal polynomialsJul 05 2019In this paper we continue the investigations initiated in \cite{LopLopstar} on ratio asymptotics of multiple orthogonal polynomials and functions of the second kind associated with Nikishin systems on star-like sets. We describe in detail the limiting ... More

Construction of labyrinths in pseudoconvex domainsJul 05 2019We build in a given pseudoconvex (Runge) domain $D$ of $\mathbb{C}^N$ a $\mathcal O(D)$ convex set $\Gamma$, every connected component of which is a holomorphically contractible (convex) compact set, enjoying the property that any continuous path $\gamma:[0,1)\rightarrow ... More

On the continuous extension of Kobayashi isometriesJul 04 2019We provide a sufficient condition for the continuous extension of isometries for the Kobayashi distance between bounded convex domains in complex Euclidean spaces having boundaries that are only slightly more regular than $\mathcal{C}^1$. This is a generalization ... More

Asymptotic expantion of covariant symbol on the complex unit sphereJul 03 2019Jul 08 2019Starting from a complete family (not defined by the reproducing kernel) for the unit sphere $\mathbf S^n$ in the complex $n$-space $\mathbb C^n$, we obtain an asymptotic expansion for the associated Berezin transform. The proof involves the computation ... More

Asymptotic expantion of covariant symbol on the complex unit sphereJul 03 2019Starting from a complete family (not defined by the reproducing kernel) for the unit sphere $\mathbf S^n$ in the complex $n$-space $\mathbb C^n$, we obtain an asymptotic expansion for the associated Berezin transform. The proof involves the computation ... More

Quaternionic Analysis, Representation Theory and Physics IIJul 02 2019We develop further quaternionic analysis introducing left and right doubly regular functions. We derive Cauchy-Fueter type formulas for these doubly regular functions that can be regarded as another counterpart of Cauchy's integral formula for the second ... More

Constructive description of analytic Besov spaces in strictly pseudoconvex domainsJul 02 2019We use the method of pseudoanalytic continuation to obtain a characterization of spaces of holomorphic functions with boundary values in Besov spaces in terms of polynomial approximations.

On a mixed Monge-Ampère operator for quasiplurisubharmonic functions with analytic singularitiesJul 02 2019We consider mixed Monge-Amp\`ere products of quasiplurisubharmonic functions with analytic singularities, and show that such products may be regularized as explicit one parameter limits of mixed Monge-Amp\`ere products of smooth functions, generalizing ... More

Applications of Zalcman's lemma in $C^n$Jul 01 2019The aim of this paper is to give some applications of Zalcman's Rescalling Lemma.

On the degeneracy of integral points and entire curves in the complement of nef effective divisorsJul 01 2019As a consequence of our recently established generalized Schmidt's subspace theorem for closed subschemes in general position, we prove a degeneracy theorem for integral points on the complement of a union of nef effective divisors. A novel aspect of ... More

Complex structures and slice-regular functions on real associative algebrasJul 01 2019In this paper, we study the (complex) geometry of the set $S$ of the square roots of $-1$ in a real associative algebra $A$, showing that $S$ carries a natural complex structure, given by an embedding into the Grassmannian of $\mathbb{C}\otimes A$. With ... More

The CR Ahlfors derivative and a new invariant for spherically equivalent CR mapsJul 01 2019We study a CR analogue of the Ahlfors derivative for conformal immersions of Stowe [23] that generalizes the CR Schwarzian derivative studied earlier by the second-named author [21]. This notion possesses several important properties similar to those ... More

Entire functions polynomially bounded in several variablesJul 01 2019In this paper we show that if an entire function $f(z_1,z_2)$ of two (or more) complex variables verifies $\norm{f(z_1,z_2)}\leq K(\norm{P(z_1,z_2)})$, where $P(z_1,z_2)$ is a polynomial that is not a power in $\CC[[z_1,z_2]]$, and $K$ is any positive-valued ... More

A Boundedness Criterion for Singular Integral Operators of convolution type on the Fock SpaceJul 01 2019We show that for an entire function $\varphi$ belonging to the Fock space ${\mathscr F}^2(\mathbb{C}^n)$ on the complex Euclidean space $\mathbb{C}^n$, that the integral operator \begin{eqnarray*} S_{\varphi}F(z)= \frac{1}{\pi^n}\int_{\mathbb{C}^n} F(w) ... More

A Boundedness Criterion for Singular Integral Operators of convolution type on the Fock SpaceJul 01 2019Jul 12 2019We show that for an entire function $\varphi$ belonging to the Fock space ${\mathscr F}^2(\mathbb{C}^n)$ on the complex Euclidean space $\mathbb{C}^n$, that the integral operator \begin{eqnarray*} S_{\varphi}F(z)= \frac{1}{\pi^n}\int_{\mathbb{C}^n} F(w) ... More

Weighted Sobolev $L^{p}$ estimates for homotopy operators on strictly pseudoconvex domains with $C^{2}$ boundaryJun 29 2019We derive estimates in a weighted Sobolev space $W^{k,p}_{\mu}(D)$ for a homotopy operator on a bounded strictly pseudoconvex domain $D$ of $C^2$ boundary in ${\C}^n$. As a result, we show that given any $2n < p < \infty$, $k > 1$, $q \geq 1$, and a $\dbar$-closed ... More

Polynomial approximation avoiding values in countable setsJun 29 2019We generalize a version of Lavrent\'ev's theorem which says that a function that is continuous on a compact set K with connected complement and without interior points can be uniformly approximated as closely as desired by a polynomial without zeros on ... More

Some properties of $h$-extendible domains in $\mathbb C^{n+1}$Jun 29 2019Jul 06 2019The purpose of this article is twofold. The first aim is to characterize $h$-extendibility of smoothly bounded pseudoconvex domains in $\mathbb C^{n+1}$ by their noncompact automorphism groups. Our second goal is to show that if the squeezing function ... More

Some properties of $H$-extendible domains in $\mathbb C^{n+1}$Jun 29 2019The purpose of this article is twofold. The first aim is to characterize $h$-extendibility of smoothly bounded pseudoconvex domains in $\mathbb C^{n+1}$ by their noncompact automorphism groups. Our second goal is to show that if the squeezing function ... More

On uniqueness of two meromorphic functions sharing a small functionJun 28 2019In this paper, we have investigated the uniqueness problems of entire and meromorphic functions concerning differential polynomials sharing a small function. Our results radically extended and improved the results of Bhoosnurmath-Pujari and Harina - Anand ... More

Bounded point derivations and functions of bounded mean oscillationJun 27 2019Let $X$ be a subset of the complex plane and let $A_0(X)$ denote the space of VMO functions that are analytic on $X$. $A_0(X)$ is said to admit a bounded point derivation of order $t$ at a point $x_0 \in \partial X$ if there exists a constant $C$ such ... More

Regularity of the Schramm-Loewner field and refined Garsia-Rodemich-Rumsey estimatesJun 27 2019Schramm-Loewner evolution (SLE$_\kappa$) is classically studied via Loewner evolution with half-plane capacity parametrization, driven by $\sqrt{\kappa}$ times Brownian motion. This yields a (half-plane) valued random field $\gamma = \gamma (t, \kappa; ... More

Hermitian curvature flow on locally homogeneous complex surfacesJun 27 2019We study the Hermitian curvature flow of locally homogeneous non-K\"ahler metrics on compact complex surfaces. In particular, we characterize the long-time behaviour of the solutions to the flow. Finally, we compute the Gromov-Hausdorff limit of immortal ... More

Classification of homogeneous strictly pseudoconvex hypersurfaces in $\mathbb C^3$Jun 26 2019Locally homogeneous strictly pseudoconvex hypersurfaces in $\mathbb C^2$ were classified by E.\,Cartan in 1932. In this work, we complete the classification of locally homogeneous strictly pseudoconvex hypersurfaces in $\mathbb C^3$.

Subharmonicity of direct images and applicationsJun 26 2019In this article we establish new positivity properties for direct images of twisted pluricanonical bundle of an algebraic fiber space. As a corollary we obtain an algebraicity criteria for holomorphic foliations which partly confirms a conjecture of Pereira-Touzet. ... More

Singularities of rational inner functions in higher dimensionsJun 26 2019We study the boundary behavior of rational inner functions (RIFs) in dimensions three and higher from both analytic and geometric viewpoints. On the analytic side, we use the critical integrability of the derivative of a rational inner function of several ... More

Improved Hölder regularity for strongly elliptic PDEsJun 26 2019We establish surprising improved Schauder regularity properties for solutions to the Leray-Lions divergence type equation in the plane. The results are achieved by studying the nonlinear Beltrami equation and making use of special new relations between ... More

Parabolic complex Monge-Ampere equations on compact Kahler manifoldsJun 24 2019We study the long-time existence and convergence of general parabolic complex Monge-Ampere type equations whose second order operator is not necessarily convex or concave in the Hessian matrix of the unknown solution.

Bergman kenel and oscillation theory of plurisubharmonic functionsJun 24 2019ased on Harnack's inequality and convex analysis we show that each plurisubharmonic function has bounded upper oscillation with respect to polydiscs of finite type but not for arbitrary polydiscs. As an application we obtain an approximation formula for ... More

Kähler-Einstein metrics on symmetric general arrangement varietiesJun 24 2019Jul 03 2019We calculate Chow quotients of some families of symmetric \(T\)-varieties. In complexity two we obtain new examples of K\"ahler-Einstein metrics by bounding the symmetric alpha invariant of their orbifold quotients. As an additional application we determine ... More

Kähler-Einstein metrics on symmetric general arrangement varietiesJun 24 2019Jun 29 2019We calculate Chow quotients of some families of symmetric \(T\)-varieties. In complexity two we obtain new examples of K\"ahler-Einstein metrics by bounding the symmetric alpha invariant of their orbifold quotients. As an additional application we determine ... More

Kähler-Einstein metrics on symmetric general arrangement varietiesJun 24 2019We calculate Chow quotients of some families of symmetric \(T\)-varieties. In complexity two we obtain new examples of K\"ahler-Einstein metrics by bounding the symmetric alpha invariant of their orbifold quotients. As an additional application we determine ... More

The complex Monge-Ampère equation with a gradient termJun 24 2019We consider the complex Monge-Amp\`ere equation with an additional linear gradient term inside the determinant. We prove existence and uniqueness of solutions to this equation on compact Hermitian manifolds.

Real-analytic coordinates for smooth strictly pseudoconvex CR-structuresJun 24 2019For a smooth strictly pseudoconvex hypersurface in a complex manifold, we give a necessary and sufficient condition for being CR-diffeomorphic to a real-analytic CR manifold. Our condition amounts to a holomorphic extension property for the canonically ... More

On Lisbon integralsJun 24 2019We introduce a family of integral transforms, the Lisbon Integrals, which naturally arise in the study of the affine space of unitary polynomials P s (z) where s $\in$ C k and z $\in$ C, s i identified to the i-th symmetric function of the roots of P ... More

On Lisbon integralsJun 24 2019Jun 26 2019We introduce a family of integral transforms, the Lisbon Integrals, which naturally arise in the study of the affine space of unitary polynomials P s (z) where s $\in$ C k and z $\in$ C, s i identified to the i-th symmetric function of the roots of P ... More

Relative regular Riemann-Hilbert correspondenceJun 24 2019In previous works by the last named authors, the notion of regularity for a relative holonomic $\mathcal D$-module has been introduced, as well as that of relative constructible complex, and it has been proved that, if the parameter space has dimension ... More

On the genesis of BBP formulasJun 23 2019We present a general procedure to generate infinitely many BBP and BBP-like formulas for the simplest transcendental numbers. This provides some insight and a better understanding into their nature. In particular, we can derive the main known BBP formulas ... More

Morse-type integrals on non-Kähler manifoldsJun 23 2019We pose a conjecture about Morse-type integrals in nef (1,1) classes on compact Hermitian manifolds, and we show that it holds for semipositive classes, or when the manifold admits certain special Hermitian metrics.

The solution of the Brannan conjectureJun 22 2019We make the final step to give a proof for the Brannan's conjecture. The basic tool of the study is a Mac-Laurin development and an adequately estimation of an integral.

Multichannel scattering theory for Toeplitz operators with piecewise continuous symbolsJun 22 2019Self-adjoint Toeplitz operators have purely absolutely continuous spectrum. For Toeplitz operators $T$ with piecewise continuous symbols, we suggest a further spectral classification determined by propagation properties of the operator $T$, that is, by ... More

On overconvergent subsequencs of closed to rows classical Pade' approximantsJun 21 2019Let $f$ be a power series with positive radius of convergence. In the present paper, we study the phenomenon of overconvergence of sequences of classical Pade' approximants pi{n,m_n} associated with f, where m(n)<=m(n+1)<=m(n) and m(n) = o(n/\log n), ... More

Learning the Sampling Pattern for MRIJun 20 2019The discovery of the theory of compressed sensing brought the realisation that many inverse problems can be solved even when measurements are "incomplete". This is particularly interesting in magnetic resonance imaging (MRI), where long acquisition times ... More

Sharp deviation inequalities for the 2D Coulomb gas and Quantum hall states, IJun 20 2019We establish sharp deviation inequalities for the linear statistics of the 2D Coulomb gas. These imply sub-Gaussian inequalities, where the variance is given by the Dirichlet norm. The proofs use complex geometry and potential theory on Riemann surfaces ... More

Transcendental versions in C n of the Nagata conjectureJun 20 2019The Nagata Conjecture is one of the most intriguing open problems in the area of curves in the plane. It is easily stated. Namely, it predicts that the smallest degree d of a plane curve passing through r $\ge$ 10 general points in the projective plane ... More

An application of generalized Bessel functions on subclasses of uniformly spirallike functionsJun 19 2019The main object of this paper is to find necessary and sufficient conditions for generalized Bessel functions of first kind $zu_{p}(z)$ to be in the classes $\mathcal{SP}_{p}(\alpha ,\beta )$ and $\mathcal{UCSP}(\alpha ,\beta )$ of uniformly spirallike ... More

Boundary Schwarz lemma for solutions to non-homogeneous biharmonic equationsJun 19 2019In this paper, we establish a boundary Schwarz lemma for solutions to non-homogeneous biharmonic equations.

Model-based Deep MR Imaging: the roadmap of generalizing compressed sensing model using deep learningJun 19 2019Jun 20 2019Accelerating magnetic resonance imaging (MRI) has been an ongoing research topic since its invention in the 1970s. Among a variety of acceleration techniques, compressed sensing (CS) has become an important strategy during the past decades. Although CS-based ... More

Model-based Deep MR Imaging: the roadmap of generalizing compressed sensing model using deep learningJun 19 2019Accelerating magnetic resonance imaging (MRI) has been an ongoing research topic since its invention in the 1970s. Among a variety of acceleration techniques, compressed sensing (CS) has become an important strategy during the past decades. Although CS-based ... More

Model-based Deep MR Imaging: the roadmap of generalizing compressed sensing model using deep learningJun 19 2019Jun 23 2019Accelerating magnetic resonance imaging (MRI) has been an ongoing research topic since its invention in the 1970s. Among a variety of acceleration techniques, compressed sensing (CS) has become an important strategy during the past decades. Although CS-based ... More

XNAS: Neural Architecture Search with Expert AdviceJun 19 2019This paper introduces a novel optimization method for differential neural architecture search, based on the theory of prediction with expert advice. Its optimization criterion is well fitted for an architecture-selection, i.e., it minimizes the regret ... More

Bergman projections induced by doubling weights on the unit ball of CnJun 19 2019The boundedness of $P_\omega:L^\infty(\mathbb{B})\to \mathcal{B}(\mathbb{B})$ and $P_\omega(P_\omega^+):L^p(\mathbb{B},\upsilon dV)\to L^p(\mathbb{B},\upsilon dV)$ on the unit ball of $\mathbb{C}^n$ with $p>1$ and $\omega,\upsilon\in \mathcal{D}$ are ... More

Positivity of direct images of the relative canonical bundlesJun 19 2019Given a fibration $f$ between two projective manifolds $X$ and $Y$, we prove that $f_{\ast}(K_{X/Y}\otimes L)$ is nef, where $(L,h)$ is a pseudo-effective line bundle with mild singularity.

Uniform null controllability of a fourth-order parabolic equation with a transport termJun 18 2019In this paper we prove a uniform controllability result for a fourth order parabolic partial differential equation which includes a transport term, when the coefficients of higher order terms vanish. We prove the null controllability of the system with ... More

Holomorphic one-forms without zeros on threefoldsJun 18 2019We show that a smooth complex projective threefold admits a holomorphic one-form without zeros if and only if the underlying real 6-manifold fibres smoothly over the circle, and we give a complete classification of all threefolds with that property. Our ... More

Zeros of holomorphic one-forms and topology of Kähler manifoldsJun 18 2019A conjecture of Kotschick predicts that a compact K\"ahler manifold $X$ fibres smoothly over the circle if and only if it admits a holomorphic one-form without zeros. In this paper we develop an approach to this conjecture and verify it in dimension two. ... More

Characterizing isolated singularities of conformal hyperbolic metricsJun 18 2019Jul 01 2019We find the explicit local models of isolated singularities of conformal hyperbolic metrics by Complex Analysis, which is interesting in its own and could potentially be extended to high-dimensional case.

A Kollár-type vanishing theoremJun 18 2019Jun 19 2019Let $f:X\rightarrow Y$ be a smooth fibration between two complex manifolds $X$ and $Y$, and let $L$ be a pseudo-effective line bundle on $X$. We obtain a sufficient condition for $R^{q}f_{\ast}(K_{X/Y}\otimes L)$ to be reflexive and hence derive a Koll\'{a}r-type ... More

Optimal transport on completely integrable toric manifoldsJun 17 2019We show that existence and uniqueness of solutions to transported Monge-Ampere problem on complex compact toric manifold follows easily from the real theory of optimal transportation.

Siegel disks of the tangent familyJun 17 2019We study Siegel disks in the dynamics of functions from the tangent family. In particular, we prove that a forward invariant Siegel disk is unbounded if and only if it contains at least one asymptotic value on the boundary. Our argument is elementary ... More

Back-Projection based Fidelity Term for Ill-Posed Linear Inverse ProblemsJun 16 2019Ill-posed linear inverse problems appear in many image processing applications, such as deblurring, super-resolution and compressed sensing. Many restoration strategies involve minimizing a cost function, which is composed of fidelity and prior terms, ... More

Computing Theta Functions with JuliaJun 15 2019We present a new package Theta.jl for computing with the Riemann theta function. It is implemented in Julia and offers accurate numerical evaluation of theta functions with characteristics and their derivatives of arbitrary order. Our package is optimized ... More

Signatures in Shape Analysis: an Efficient Approach to Motion IdentificationJun 14 2019Signatures provide a succinct description of certain features of paths in a reparametrization invariant way. We propose a method for classifying shapes based on signatures, and compare it to current approaches based on the SRV transform and dynamic programming. ... More

Bounded sets of sheaves on Kähler manifolds, IIJun 13 2019We extend previous results on boundedness of sets of coherent sheaves on a compact K\"ahler manifold to the relative and not necessarily smooth case. This enlarged context allows us to prove properness properties of the relative Douady space as well as ... More

Time warping invariants of multidimensional time seriesJun 13 2019In data science, one is often confronted with a time series representing measurements of some quantity of interest. Usually, in a first step, features of the time series need to be extracted. These are numerical quantities that aim to succinctly describe ... More

Fibred algebraic surfaces and commutators in the Symplectic groupJun 13 2019We describe the minimal number of critical points and the minimal number $s$ of singular fibres for a non isotrivial fibration of a surface $S$ over a curve $B$ of genus $1$, constructing a fibration with $s=1$ and irreducible singular fibre with $4$ ... More

Growth estimates for meromorphic solutions of higher order algebraic differential equationsJun 13 2019We establish pointwise growth estimates for the spherical derivative of solutions of the first order algebraic differential equations. A generalization of this result to higher order equations is also given. We discuss the related question of when for ... More

Geometric quantization on CR manifoldsJun 13 2019Let $X$ be a compact connected orientable CR manifold of dimension greater than five with the action of a connected compact Lie group $G$. Assuming that the Levi form of $X$ is positive definite near the inverse image $Y$ of $0$ by the momentum map and ... More

Geometric quantization on CR manifoldsJun 13 2019Jun 17 2019Let $X$ be a compact connected orientable CR manifold of dimension greater than five with the action of a connected compact Lie group $G$. Assuming that the Levi form of $X$ is positive definite near the inverse image $Y$ of $0$ by the momentum map and ... More