There has been in the past ten to fifteen years a surge of activity concerning the cohomology of semi-direct product groups of the form $\mathbb{Z}^{n}\rtimes$G with G finite. A problem first stated by Adem-Ge-Pan-Petrosyan ...
We consider the behavior of zeros of random polynomials of the from
\begin{equation*}
P_{n,m}(z) := \eta_0\varphi_m^{(m)}(z) + \eta_1 \varphi_{m+1}^{(m)}(z) + \cdots + \eta_n \varphi_{n+m}^{(m)}(z)
\end{equation*}
...
Neural synchrony in the brain at rest is usually variable and intermittent, thus intervals of predominantly synchronized activity are interrupted by intervals of desynchronized activity. Prior studies suggested that this ...
We describe a reproduction procedure which, given a solution of the gl(m|n) Gaudin Bethe ansatz equation associated to a tensor product of polynomial modules, produces a family P of other solutions called the population.
To ...
We study the Gaudin model associated to Lie algebras of classical types.
First, we derive explicit formulas for solutions of the Bethe ansatz equations of the Gaudin model associated to the tensor product of one arbitrary ...
We consider actions of the current Lie algebras $\gl_{n}[t]$ and $\gl_{k}[t]$ on the space $\mathfrak{P}_{kn}$ of polynomials in $kn$ anticommuting variables. The actions depend on parameters $\bar{z}=(z_{1},\dots ,z_{k})$ ...
We consider orthogonal polynomials P_n satisfying orthogonality relations where the measure of orthogonality is, in general, a complex-valued Borel measure supported on subsets of the complex plane. In our consideration ...
Associated to any finite simple graph $\Gamma$ is the
{\em chromatic polynomial} $\P_\Gamma(q)$ whose complex zeros are called the {\em
chromatic zeros} of $\Gamma$. A hierarchical lattice is a sequence of finite
simple ...
We introduce the quantum toroidal superalgebra E(m|n) associated with the Lie superalgebra gl(m|n) and initiate its study. For each choice of parity "s" of gl(m|n), a corresponding quantum toroidal superalgebra E(s) is ...
In the present work, we consider a class of Finsler metrics using the warped product notion introduced by B. Chen, Z. Shen and L. Zhao (2018), with another “warping”, one that is consistent with the form of metrics modeling ...
For massive data analysis, the computational bottlenecks exist in two ways. Firstly, the data could be too large that it is not easy to store and read. Secondly, the computation time could be too long. To tackle these ...
A significant hurdle for analyzing big data is the lack of effective technology and statistical inference methods. A popular approach for analyzing data with large sample is subsampling. Many subsampling probabilities have ...
In this work we use and develop Riemann-Hilbert techniques to study the asymptotic behavior of structured determinants. In chapter one we will review the main underlying
definitions and ideas which will be extensively ...
Given a parametrized family of Iterated Function System (IFS) we give sufficient conditions for a parameter on the boundary of the connectedness locus, M, to be accessible from the complement of M.
Moreover, we provide a ...
We derive the diﬀerential identities for isomonodromic tau functions, describing their
monodromy dependence. For Painlev´e equations we obtain them from the relation of tau
function to classical action which is a consequence ...
There are two computational bottlenecks for Big Data analysis: (1) the data is too large
for a desktop to store, and (2) the computing task takes too long waiting time to finish.
While the Divide-and-Conquer approach ...
Much is known about periodic orbits in dynamical systems of
continuous interval maps. Of note is the theorem of Sharkovsky.
In 1964 he proved that, for a continuous map $f$ on $\mathbb{R}$,
the existence ...
Thermoregulation system in mammal keeps their body temperature in a vital and yet narrow range of temperature by adjusting two main activities, heat generation, and heat loss. Also, these activities get triggered by other ...
The interplay between biomechanics and blood perfusion in the optic nerve head (ONH) has a critical role in ocular pathologies, especially glaucomatous optic neuropathy. Elucidating the complex interactions of ONH perfusion ...
Glaucoma is a multi-factorial ocular disease associated with death of retinal ganglion cells and irreversible vision loss. Many risk factors contribute to glaucomatous damage, including elevated intraocular pressure (IOP), ...