Machine learning techniques are successfully used in many fields, image processing and computer vision among others. Reconstruction software in super-resolution microscopy, on the other hand, are still very user dependent, leading to an error prone processing of the acquired frames; image processing techniques, when exploited, are often very basic. This though now, machine learning has proven h...

We study the fine geometric structure of bifurcation currents in the parameter space of cubic polynomials viewed as dynamical systems. In particular we prove that these currents have some laminar structure in a large region of parameter space, reflecting the possibility of quasiconformal deformations. On the other hand, there is a natural bifurcation measure, supported on the closure of rigid p...

Dijkgraaf and Vafa have conjectured the correspondences between topological string theories, N = 1 gauge theories and matrix models. By the use of this conjecture, we calculate the quantum deformations of Calabi-Yau threefolds with ADE singularities from ADE multi-matrix models. We obtain the effective superpotentials of the dual quiver gauge theories in terms of the geometric engineering for t...

A special class of solutions to the generalised WDVV equations related to a finite set of covectors is investigated. Some geometric conditions on such a set which guarantee that the corresponding function satisfies WDVV equations are found (∨-conditions). These conditions are satisfied for all root systems and their special deformations discovered in the theory of the Calogero-Moser systems by ...

We show that infinitesimal automorphisms and infinitesimal deformations of parabolic geometries can be nicely described in terms of the twisted de–Rham sequence associated to a certain linear connection on the adjoint tractor bundle. For regular normal geometries, this description can be related to the underlying geometric structure using the machinery of BGG sequences. In the locally flat case...

An analytic construction of compact Calabi-Yau manifolds with del Pezzo singularities is found. We present complete intersection CY manifolds for all del Pezzo singularities and study the complex deformations of these singularities. An example of the quintic CY manifold with del Pezzo 6 singularity and some number of conifold singularities is studied in details. The possibilities for the ’geome...

We continue our study of quantum Riemann surfaces initiated in 1, 2, 3]. We construct a one parameter family of deformations of compact Riemann surfaces of genus g 2. Our construction does not require any discretness condition on the value of Planck's constant. It coincides with the construction of 2] in the case when Planck's constant assumes the discrete set of values dictated by geometric qu...

We couple three-dimensional Chern-Simons gauge theory with BF theory and study deformations of the theory by means of the antifield BRST formalism. We analyze all possible consistent interaction terms for the action under physical requirements and find a new topological field theory in three dimension with new nontrivial terms and a nontrivial gauge symmetry. We consider a geometric interpretat...

We analyze, numerically by the finite element method, three-dimensional electromechanical deformations of a thick laminated plate with layers made of aluminum, a viscoelastic material and a piezoceramic (PZT). Two arrangements of layers are considered. In one case a central PZT layer is surrounded on both sides by viscoelastic layers and aluminum layers are on the outside surfaces. The PZT is p...

Geometric variations of local systems are families Hodge structure; they typically correspond to fibrations Kähler manifolds for which each fibre itself is fibred by codimension one manifolds. In this article, we introduce the formalism geometric and then specialize theory study elliptic surfaces. We interpret a construction twisted surface used Besser—Livné in terms middle convolution functor,...