Related papers: A geometric characterization of Poisson type distr…
The paper deals with planar segment processes given by a density with respect to the Poisson process. Parametric models involve reference distributions of directions and/or lengths of segments. These distributions generally do not coincide…
We present the geometry and symmetries of radiative transfer theory. Our geometrization exploits recent work in the literature that enables to obtain the Hamiltonian formulation of radiative transfer as the semiclassical limit of a phase…
We present some basic results on a natural Poisson structure on any compact symmetric space. The symplectic leaves of this structure are related to the orbits of the corresponding real semisimple group on the complex flag manifold.
Transmuted geometric distribution with two parameters and is proposed as a new generalization of the geometric distribution by employing the quadratic transmutation techniques of Shaw and Buckley (2007). Its important distributional and…
Real-world signals typically span across multiple dimensions, that is, they naturally reside on multi-way data structures referred to as tensors. In contrast to standard ``flat-view'' multivariate matrix models which are agnostic to data…
We construct a first order local model for Poisson manifolds around a large class of Poisson submanifolds and we give conditions under which this model is a local normal form. The resulting linearization theorem includes as special cases…
An $(n,k)$-Poisson Multinomial Distribution (PMD) is the distribution of the sum of $n$ independent random vectors supported on the set ${\cal B}_k=\{e_1,\ldots,e_k\}$ of standard basis vectors in $\mathbb{R}^k$. We prove a structural…
In wireless networks with random node distribution, the underlying point process model and the channel fading process are usually considered separately. A unified framework is introduced that permits the geometric characterization of fading…
In this paper, we introduce a new approach to generate flexible parametric families of distributions. These models arise on competitive and complementary risks scenario, in which the lifetime associated with a particular risk is not…
Many real-world networks known as attributed networks contain two types of information: topology information and node attributes. It is a challenging task on how to use these two types of information to explore structural regularities. In…
Statistics of the single-particle levels in a deformed Woods-Saxon potential is analyzed in terms of the Poisson and Wigner nearest-neighbor distributions for several deformations and multipolarities of its surface distortions. We found the…
Consider the random quadratic form $T_n=\sum_{1 \leq u < v \leq n} a_{uv} X_u X_v$, where $((a_{uv}))_{1 \leq u, v \leq n}$ is a $\{0, 1\}$-valued symmetric matrix with zeros on the diagonal, and $X_1,$ $X_2, \ldots, X_n$ are i.i.d.…
The properties of the natural modes in a dispersive stratified N-layer medium are investigated. The focus is on the (over)completeness properties of these modes. Also the distribution of the natural frequencies is considered. Both the…
A family of new algebraic Poisson varieties will be constructed, generalising the complex character varieties of Riemann surfaces. Then the well-known (Poisson) mapping class group actions on the character varieties will be generalised.
General framework for Poisson homogeneous spaces of Poisson groups is introduced. Poisson Minkowski spaces are discussed as a particular example.
We prove a number of results, new and old, about the cycle type of a random permutation on S_n. Underlying our analysis is the idea that the number of cycles of size k is roughly Poisson distributed with parameter 1/k. In particular, we…
In this paper we study left invariant CR structures on Lie groups which are compatible with geometric properties as Poisson and kahler properties.
Transport-based metrics and related embeddings (transforms) have recently been used to model signal classes where nonlinear structures or variations are present. In this paper, we study the geodesic properties of time series data with a…
In this short note we give a complete characterization of a certain class of compact corank one Poisson manifolds, those equipped with a closed one-form defining the symplectic foliation and a closed two-form extending the symplectic form…
We classify real Poisson structures on complex toric manifolds of type $(1,1)$ and initiate an investigation of their Poisson cohomology. For smooth toric varieties, such structures are necessarily algebraic and are homogeneous quadratic in…