相关论文: Geometry of iteration stable tessellations: Connec…
Persistent homology is a tool that can be employed to summarize the shape of data by quantifying homological features. When the data is an object in $\mathbb{R}^d$, the (augmented) persistent homology transform ((A)PHT) is a family of…
A new class of planar tessellations, named T-tessellations, was introduced in ([10]). A model was proposed to be considered as a completely random T-tessellation model (CRTT) and its Gibbsian variants were discussed. A general simulation…
Emerging technologies are revealing the spiking activity in ever larger neural ensembles. Frequently, this spiking is far from independent, with correlations in the spike times of different cells. Understanding how such correlations impact…
We show that a purely algebraic structure, a two-dimensional scattering diagram, describes a large part of the wall-crossing behavior of moduli spaces of Bridgeland semistable objects in the derived category of coherent sheaves on…
Generalized complex geometry was classically formulated by the language of differential geometry. In this paper, we reformulated a generalized complex manifold as a holomorphic symplectic differentiable formal stack in a homotopical sense.…
We have introduce a new vision of stochastic processes through the geometry induced by the dilation. The dilation matrices of a given processes are obtained by a composition of rotations matrices, contain the measure information in a…
This paper is the sequel to [PTVV] (IHES Vol. 117, 2013). We develop a general and flexible context for differential calculus in derived geometry, including the de Rham algebra and polyvector fields. We then introduce the formalism of…
Discrete particle simulations are used to study the shear rheology of dense, stabilized, frictional particulate suspensions in a viscous liquid, toward development of a constitutive model for steady shear flows at arbitrary stress. These…
In the series of models with interacting particles in stochastic geometry, a new contribution presents the facet process which is defined in arbitrary Euclidean dimension. In 2D, 3D specially it is a process of interacting segments, flat…
Discrete stability extends the classical notion of stability to random elements in discrete spaces by defining a scaling operation in a randomised way: an integer is transformed into the corresponding binomial distribution. Similarly…
A discrete Gelfand-Tsetlin pattern is a configuration of particles in Z^2. The particles are arranged in a finite number of consecutive rows, numbered from the bottom. There is one particle on the first row, two particles on the second row,…
Popular network models such as the mixed membership and standard stochastic block model are known to exhibit distinct geometric structure when embedded into $\mathbb{R}^{d}$ using spectral methods. The resulting point cloud concentrates…
Stack triangulations appear as natural objects when defining an increasing family of triangulations by successive additions of vertices. We consider two different probability distributions for such objects. We represent, or "draw" these…
We prove tail triviality of determinantal point processes $ \mu $ on continuous spaces. Tail triviality had been proved for such processes only on discrete spaces, and hence we have generalized the result to continuous spaces. To do this,…
Stochastic partition models tailor a product space into a number of rectangular regions such that the data within each region exhibit certain types of homogeneity. Due to constraints of partition strategy, existing models may cause…
The pentagram map is a projectively natural iteration defined on polygons, and also on objects we call twisted polygons (a twisted polygon is a map from Z into the projective plane that is periodic modulo a projective transformation). We…
This note reports the results of an undergraduate research project from the year 2013-14, concerning the convergence of iterated Steiner symmetrizations in the plane. The directions of symmetrization are chosen according to the Van der…
Symplectic and Poisson geometry emerged as a tool to understand the mathematical structure behind classical mechanics. However, due to its huge development over the past century, it has become an independent field of research in…
We introduce a geometric analysis of turbulent mixing in density-stratified flows based on the alignment of the density gradient in two orthogonal bases that are locally constructed from the velocity gradient tensor. The first basis…
The treatment of complex geometries in Computational Fluid Dynamics applications is a challenging endeavor, which immersed boundary and cut-cell techniques can significantly simplify by alleviating the meshing process required by…