scholarly journals Support theorem for jump process of canonical type

2001 ◽  
Vol 77 (6) ◽  
pp. 79-83 ◽  
Author(s):  
Yashushi Ishikawa
Keyword(s):  
Jump Process ◽  
Support Theorem ◽  
Canonical Type

scholarly journals Asymptotic support theorem for planar isotropic Brownian flows

2013 ◽  
Vol 41 (2) ◽  
pp. 699-721
Author(s):  
Moritz Biskamp
Keyword(s):  
Support Theorem

scholarly journals Approximation and Support Theorem for a Wave Equation in Two Space Dimensions

Bernoulli ◽  
2000 ◽  
Vol 6 (5) ◽  
pp. 887 ◽  
Author(s):  
Annie Millet ◽  
Marta Sanz-Solé ◽  
Marta Sanz-Sole
Keyword(s):  
Wave Equation ◽  
Support Theorem ◽  
Two Space Dimensions

A non-canonical type 2 immune response coordinates tuberculous granuloma formation and epithelialization

Cell ◽  
2021 ◽  
Author(s):  
Mark R. Cronan ◽  
Erika J. Hughes ◽  
W. Jared Brewer ◽  
Gopinath Viswanathan ◽  
Emily G. Hunt ◽  
...  
Keyword(s):  
Immune Response ◽  
Granuloma Formation ◽  
Type 2 Immune Response ◽  
Tuberculous Granuloma ◽  
Canonical Type

scholarly journals Smooth density and its short time estimate for jump process determined by SDE

2018 ◽  
Vol 128 (9) ◽  
pp. 3181-3219 ◽  
Author(s):  
Yasushi Ishikawa ◽  
Hiroshi Kunita ◽  
Masaaki Tsuchiya
Keyword(s):  
Jump Process ◽  
Time Estimate ◽  
Short Time ◽  
Smooth Density

scholarly journals Multivariate fractional phase–type distributions

2020 ◽  
Vol 23 (5) ◽  
pp. 1431-1451 ◽  
Author(s):  
Hansjörg Albrecher ◽  
Martin Bladt ◽  
Mogens Bladt
Keyword(s):  
Tail Dependence ◽  
Jump Process ◽  
Multivariate Distributions ◽  
New Class ◽  
Natural Time ◽  
Special Cases ◽  
Phase Type ◽  
Phase Type Distributions ◽  
Markovian Jump Process ◽  
Heavy Tailed

Abstract We extend the Kulkarni class of multivariate phase–type distributions in a natural time–fractional way to construct a new class of multivariate distributions with heavy-tailed Mittag-Leffler(ML)-distributed marginals. The approach relies on assigning rewards to a non–Markovian jump process with ML sojourn times. This new class complements an earlier multivariate ML construction [2] and in contrast to the former also allows for tail dependence. We derive properties and characterizations of this class, and work out some special cases that lead to explicit density representations.

scholarly journals Sub-Diffusive Dynamics Lead to Depleted Particle Densities Near Cellular Borders

2018 ◽  
Author(s):  
William R. Holmes
Keyword(s):  
Particle Density ◽  
Specific Model ◽  
Transport Processes ◽  
Generalized Langevin Equation ◽  
Diffusive Motion ◽  
Protein Activation ◽  
Cellular Environment ◽  
Anomalous Particle ◽  
Canonical Type ◽  
Different Characteristics

AbstractIt has long been known that the complex cellular environment leads to anomalous motion of intracellular particles. At a gross level, this is characterized by mean squared displacements that deviate from the standard linear profile. Statistical analysis of particle trajectories has helped further elucidate how different characteristics of the cellular environment can introduce different types of anomalousness. A significant majority of this literature has however focused on characterizing the properties of trajectories that do not interact with cell borders (e.g. cell membrane or nucleus). Numerous biological processes ranging from protein activation to exocytosis however require particles to be near a membrane. This study investigates the consequences of a canonical type of sub-diffusive motion, Fractional Brownian Motion (FBM), and its physical analogue Generalized Langevin Equation (GLE) Dynamics, on the spatial localization of particles near reflecting boundaries. Results show that this type of sub-diffusive motion leads to the formation of significant zones of depleted particle density near boundaries, and that this effect is independent of the specific model details encoding those dynamics. Rather these depletion layers are a natural and robust consequence of the anti-correlated nature of motion increments that is at the core of FBM / GLE dynamics. If such depletion zones are present, it would be of profound importance given the wide array of signaling and transport processes that occur near membranes. If not, that would suggest our understanding of this type of anomalous motion may be flawed. Either way, this result points to the need to further investigate the consequences of anomalous particle motions near cell borders from both theoretical and experimental perspectives.

scholarly journals Extraction of accurate cytoskeletal actin velocity distributions from noisy measurements

2020 ◽  
Author(s):  
Cayla M. Miller ◽  
Elgin Korkmazhan ◽  
Alexander R. Dunn
Keyword(s):  
Single Molecule ◽  
Actin Filaments ◽  
Dynamical Behavior ◽  
Jump Process ◽  
Pairwise Distance ◽  
Actin Dynamics ◽  
Cell Cortex ◽  
Superresolution Microscopy ◽  
Distance Distributions ◽  
Primary Fibroblasts

Dynamic remodeling of the actin cytoskeleton allows cells to migrate, change shape, and exert mechanical forces on their surroundings. How the complex dynamical behavior of the cytoskeleton arises from the interactions of its molecular components remains incompletely understood. Tracking the movement of individual actin filaments in living cells can in principle provide a powerful means of addressing this question. However, single-molecule fluorescence imaging measurements that could provide this information are limited by low signal-to-noise ratios, with the result that the localization errors for individual fluorophore fiducials attached to filamentous (F)-actin are comparable to the distances traveled by actin filaments between measurements. In this study we tracked the movement F-actin labeled with single-molecule densities of the fluorogenic label SiR-actin in primary fibroblasts and endothelial cells. We then used a Bayesian statistical approach to estimate true, underlying actin filament velocity distributions from the tracks of individual actin-associated fluorophores along with quantified localization uncertainties. This analysis approach is broadly applicable to inferring statistical pairwise distance distributions arising from noisy point localization measurements such as occur in superresolution microscopy. We found that F-actin velocity distributions were better described by a statistical jump process, in which filaments exist in mechanical equilibria punctuated by abrupt, jump-like movements, than by models incorporating combinations of diffusive motion and drift. A model with exponentially distributed time- and length-scales for filament jumps recapitulated F-actin velocity distributions measured for the cell cortex, integrin-based adhesions, and actin stress fibers, indicating that a common physical model can potentially describe F-actin dynamics in a variety of cellular contexts.

scholarly journals Crucial Players for Inter-Organelle Communication: PI5P4Ks and Their Lipid Product PI-4,5-P2 Come to the Surface

2022 ◽  
Vol 9 ◽  
Author(s):  
Archna Ravi ◽  
Lavinia Palamiuc ◽  
Brooke M. Emerling
Keyword(s):  
Stress Response ◽  
Human Diseases ◽  
Type Ii ◽  
Metabolic Homeostasis ◽  
Cellular Homeostasis ◽  
Evolutionarily Conserved ◽  
Lipid Product ◽  
Canonical Type ◽  
Organelle Communication ◽  
A Minor

While organelles are individual compartments with specialized functions, it is becoming clear that organellar communication is essential for maintaining cellular homeostasis. This cooperation is carried out by various interactions taking place on the membranes of organelles. The membranes themselves contain a multitude of proteins and lipids that mediate these connections and one such class of molecules facilitating these relations are the phospholipids. There are several phospholipids, but the focus of this perspective is on a minor group called the phosphoinositides and specifically, phosphatidylinositol 4,5-bisphosphate (PI-4,5-P2). This phosphoinositide, on intracellular membranes, is largely generated by the non-canonical Type II PIPKs, namely, Phosphotidylinositol-5-phosphate-4-kinases (PI5P4Ks). These evolutionarily conserved enzymes are emerging as key stress response players in cells. Further, PI5P4Ks have been shown to modulate pathways by regulating organelle crosstalk, revealing roles in preserving metabolic homeostasis. Here we will attempt to summarize the functions of the PI5P4Ks and their product PI-4,5-P2 in facilitating inter-organelle communication and how they impact cellular health as well as their relevance to human diseases.

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