Piecewise linear processes with Poisson‐modulated exponential switching times

We consider the jump telegraph process when switching intensities depend on external shocks also accompanying with jumps. The incomplete financial market model based on this process is studied. The Esscher transform, which changes only unobservable parameters, is considered in detail. The financial market model based on this transform can price switching risks as well as jump risks of the model.     

Entropy in the category of perfect complexes with cohomology of finite length

Local and category-theoretical entropies associated with an endomorphism of finite length (i.e., with zero-dimensional closed fiber) of a commutative Noetherian local ring are compared. Local entropy is shown to be less than or equal to category-theoretical entropy. The two entropies are shown to be equal when the ring is regular, and also for the Frobenius endomorphism of a complete local ring of positive characteristic.Furthermore, given a flat morphism of Cohen–Macaulay local rings endowed with compatible endomorphisms of finite length, it is shown that local entropy is “additive”. Finally, over a ring that is a homomorphic image of a regular local ring, a formula for local entropy in terms of an asymptotic partial Euler characteristic is given.     

Minimizing Uniformly Convex Functions by Cubic Regularization of Newton Method

Journal of Optimization Theory and Applications - In this paper, we study the iteration complexity of cubic regularization of Newton method for solving composite minimization problems with...     

CD47 in the Brain and Neurodegeneration: An Update on the Role in Neuroinflammatory Pathways

CD47 is a receptor belonging to the immunoglobulin (Ig) superfamily and broadly expressed on cell membranes. Through interactions with ligands such as SIRPα, TSP-1, integrins, and SH2-domain bearing protein tyrosine phosphatase substrate-1 (SHPS-1), CD47 regulates numerous functions like cell adhesion, proliferation, apoptosis, migration, homeostasis, and the immune system. In this aspect, previous research has shown that CD47 modulates phagocytosis via macrophages, the transmigration of neutrophils, and the activation of T-cells, dendritic cells, and B-cells. Moreover, several studies have reported the increased expression of the CD47 receptor in a variety of diseases, including acute lymphoblastic leukemia (ALL), chronic myeloid leukemia, non-Hodgkin’s lymphoma (NHL), multiple myeloma (MM), bladder cancer, acute myeloid leukemia (AML), Gaucher disease, Multiple Sclerosis and stroke among others. The ubiquitous expression of the CD47 cell receptor on most resident cells of the CNS has previously been established through different methodologies. However, there is little information concerning its precise functions in the development of different neurodegenerative pathologies in the CNS. Consequently, further research pertaining to the specific functions and roles of CD47 and SIRP is required prior to its exploitation as a druggable approach for the targeting of various neurodegenerative diseases that affect the human population. The present review attempts to summarize the role of both CD47 and SIRP and their therapeutic potential in neurodegenerative disorders.     

Femtosecond laser interactions with dielectric materials: insights of a detailed modeling of electronic excitation and relaxation processes

Electronic excitation–relaxation processes induced by ultra-short laser pulses are studied numerically for dielectric targets. A detailed kinetic approach is used in the calculations accounting for the absence of equilibrium in the electronic subsystem. Such processes as electron–photon–phonon, electron–phonon and electron–electron scatterings are considered in the model. In addition, both laser field ionization ranging from multi-photon to tunneling one, and electron impact (avalanche) ionization processes are included in the model. The calculation results provide electron energy distribution. Based on the time-evolution of the energy distribution function, we estimate the electron thermalization time as a function of laser parameters. The effect of the density of conduction band electrons on this time is examined. By using the average electron energy, a new criterion is proposed based on determined damage threshold in agreement with recent experiments (Sanner et al. in Appl. Phys. Lett. 96:071111, 2010).     

On the Gibbs Properties of Bernoulli Convolutions Related to β-Numeration in Multinacci Bases

We consider infinitely convolved Bernoulli measures (or simply Bernoulli convolutions) related to the -numeration. A matrix decomposition of these measures is obtained in the case when is a PV number. We also determine their Gibbs properties for being a multinacci number, which makes the multifractal analysis of the corresponding Bernoulli convolution possible.     

Isotropy of unitary involutions

We prove the so-called unitary isotropy theorem, a result on isotropy of a unitary involution. The analogous previously known results on isotropy of orthogonal and symplectic involutions as well as on hyperbolicity of orthogonal, symplectic, and unitary involutions are formal consequences of this theorem. A component of the proof is a detailed study of the quasi-split unitary grassmannians.     

A new high order compact off-step discretization for the system of 3D quasi-linear elliptic partial differential equations

We present a new fourth order compact finite difference scheme based on off-step discretization for the solution of the system of 3D quasi-linear elliptic partial differential equations subject to appropriate Dirichlet boundary conditions. We also develop new fourth order methods to obtain the numerical solution of first order normal derivatives of the solution. In all the cases, we use only 19-grid points of a single computational cell to compute the problem. The proposed methods are directly applicable to singular problems and the problems in polar coordinates, without any modification required unlike the previously developed high order schemes of [14] and [30]. We discuss the convergence analysis of the proposed method in details. Many physical problems are solved and comparative results are given to illustrate the usefulness of the proposed methods.