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).     

Polarization modulation of light in an optical waveguide under lateral compression

It is shown that a lateral pressure applied to a circular single-mode optical waveguide changes the phase difference between two orthogonally polarized modes and thereby modulates the polarization state of light (elastooptic effect). The efficiency of polarization modulation is characterized by a strain-to-phase difference conversion factor as applied to polarization modes of the fiber. An expression relating the phase difference between the modes and the displacement of squeezing plates is obtained and checked in real experiments and numerically. The efficiency of conversion of lateral pressure to phase difference between the polarization modes is shown to be fairly high, on the order of 10⁴ rad/(μm m).