scholarly journals A Markov chain identity and monotonicity of the diffusion constants for a random walk in a heterogeneous environment

1990 ◽  
Vol 108 (1) ◽  
pp. 111-126 ◽  
Author(s):  
J. B. T. M. Roerdink
Keyword(s):  
Random Walk ◽  
Transition Probabilities ◽  
Monotonicity Property ◽  
Square Lattice ◽  
Electric Networks ◽  
Monotonic Functions ◽  
Diffusion Constants ◽  
A Cell ◽  
Finite Markov Chains ◽  
The Individual

AbstractWe consider a 2-dimensional square lattice which is partitioned into a periodic array of rectangular cells, on which a nearest neighbour random walk with symmetric increments is defined whose transition probabilities only depend on the relative position within a cell. On the basis of a determinantal identity proved in this paper, we obtain a result for finite Markov chains which shows that the diffusion constants for the random walk are monotonic functions of the individual transition probabilities. We point out the similarity of this monotonicity property to Rayleigh's Monotonicity Law for electric networks or, equivalently, reversible random walks.

Nonspecific Chronic Back Pain: Sixth Edition Approaches

2019 ◽  
Vol 24 (5) ◽  
pp. 14-15
Author(s):  
Jay Blaisdell ◽  
James B. Talmage
Keyword(s):  
Back Pain ◽  
Chronic Back Pain ◽  
Intervertebral Disk ◽  
Key Factors ◽  
Sixth Edition ◽  
Whole Person ◽  
Class 1 ◽  
A Cell ◽  
Intervertebral Disk Herniation ◽  
The Individual

Abstract Ratings for “non-specific chronic, or chronic reoccurring, back pain” are based on the diagnosis-based impairment method whereby an impairment class, usually representing a range of impairment values within a cell of a grid, is selected by diagnosis and “specific criteria” (key factors). Within the impairment class, the default impairment value then can be modified using non-key factors or “grade modifiers” such as functional history, physical examination, and clinical studies using the net adjustment formula. The diagnosis of “nonspecific chronic, or chronic reoccurring, back pain” can be rated in class 0 and 1; the former has a default value of 0%, and the latter has a default value of 2% before any modifications. The key concept here is that the physician believes that the patient is experiencing pain, yet there are no related objective findings, most notably radiculopathy as distinguished from “nonverifiable radicular complaints.” If the individual is found not to have radiculopathy and the medical record shows that the patient has never had clinically verifiable radiculopathy, then the diagnosis of “intervertebral disk herniation and/or AOMSI [alteration of motion segment integrity] cannot be used.” If the patient is asymptomatic at maximum medical improvement, then impairment Class 0 should be chosen, not Class 1; a final whole person impairment rating of 1% indicates incorrect use of the methodology.

scholarly journals Order and stochasticity in the folding of individual Drosophila genomes

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Sergey V. Ulianov ◽  
Vlada V. Zakharova ◽  
Aleksandra A. Galitsyna ◽  
Pavel I. Kos ◽  
Kirill E. Polovnikov ◽  
...  
Keyword(s):  
Random Walk ◽  
High Resolution ◽  
3D Genome ◽  
Topologically Associating Domains ◽  
Chromatin Folding ◽  
A Cell ◽  
Single Nucleus ◽  
High Level ◽  
Cell To Cell Variability

AbstractMammalian and Drosophila genomes are partitioned into topologically associating domains (TADs). Although this partitioning has been reported to be functionally relevant, it is unclear whether TADs represent true physical units located at the same genomic positions in each cell nucleus or emerge as an average of numerous alternative chromatin folding patterns in a cell population. Here, we use a single-nucleus Hi-C technique to construct high-resolution Hi-C maps in individual Drosophila genomes. These maps demonstrate chromatin compartmentalization at the megabase scale and partitioning of the genome into non-hierarchical TADs at the scale of 100 kb, which closely resembles the TAD profile in the bulk in situ Hi-C data. Over 40% of TAD boundaries are conserved between individual nuclei and possess a high level of active epigenetic marks. Polymer simulations demonstrate that chromatin folding is best described by the random walk model within TADs and is most suitably approximated by a crumpled globule build of Gaussian blobs at longer distances. We observe prominent cell-to-cell variability in the long-range contacts between either active genome loci or between Polycomb-bound regions, suggesting an important contribution of stochastic processes to the formation of the Drosophila 3D genome.

Perturbation theory and finite Markov chains

1968 ◽  
Vol 5 (2) ◽  
pp. 401-413 ◽  
Author(s):  
Paul J. Schweitzer
Keyword(s):  
Perturbation Theory ◽  
Markov Chain ◽  
Markov Chains ◽  
Stationary Distribution ◽  
Fundamental Matrix ◽  
Transition Probabilities ◽  
Semi Group ◽  
Partial Derivatives ◽  
Finite Markov Chains ◽  
Derivatives Of

A perturbation formalism is presented which shows how the stationary distribution and fundamental matrix of a Markov chain containing a single irreducible set of states change as the transition probabilities vary. Expressions are given for the partial derivatives of the stationary distribution and fundamental matrix with respect to the transition probabilities. Semi-group properties of the generators of transformations from one Markov chain to another are investigated. It is shown that a perturbation formalism exists in the multiple subchain case if and only if the change in the transition probabilities does not alter the number of, or intermix the various subchains. The formalism is presented when this condition is satisfied.

scholarly journals Photosensitization to ultraviolet irradiation and selective killing of cells following uptake of pyrene-containing fatty acid

1986 ◽  
Vol 85 (1) ◽  
pp. 149-159
Author(s):  
E. Fibach ◽  
O. Morand ◽  
S. Gatt
Keyword(s):  
Fatty Acid ◽  
Ultraviolet Irradiation ◽  
Plasma Membranes ◽  
Incubation Temperature ◽  
Serum Proteins ◽  
Neutral Lipids ◽  
Cell Types ◽  
Dodecanoic Acid ◽  
A Cell ◽  
The Individual

Cells were incubated with 12-(1-pyrene)-dodecanoic acid (P12), a long-chain fatty acid to which a pyrene ring has been attached covalently. This acid was transported across the plasma membranes of cells and subsequently incorporated into their neutral lipids and phospholipids. Irradiation of these pyrene-containing cells for short periods (0.5-4 min) with ultraviolet light at 366 nm resulted in eventual cell death. Similar irradiation had no effect on cells that had not been exposed to P12. The time of the period of irradiation necessary for inducing the toxic process was related to the quantity of P12 incorporated, the latter being a function of the respective metabolic activity of the individual cell type. The degree of incorporation of P12 into a cell, and consequently its acquired sensitivity to killing by ultraviolet irradiation at 366 nm, was affected by the incubation temperature and addition of non-fluorescent fatty acid, albumin or other serum proteins. Different degrees of incorporation of P12 into various cell types were used for selective killing and elimination of cell populations by irradiation at 366 nm. The combined procedure of preincubation with P12 followed by ultraviolet irradiation thus permitted selection of cell types with a greater resistance to this procedure.

scholarly journals Effects of aspiration-induced adaptation and migration on the evolution of cooperation

2014 ◽  
Vol 25 (07) ◽  
pp. 1450025 ◽  
Author(s):  
Yu Peng ◽  
Xu-Wen Wang ◽  
Qian Lu ◽  
Qing-Ke Zeng ◽  
Bing-Hong Wang
Keyword(s):  
Data Envelopment Analysis ◽  
Prospect Theory ◽  
Evolution Of Cooperation ◽  
Square Lattice ◽  
Data Envelopment ◽  
Aspiration Level ◽  
Aspiration Levels ◽  
Emergence Of Cooperation ◽  
And Migration ◽  
The Individual

In the light of the prospect theory (PT), we study the prisoner's dilemma game (PDG) on square lattice by integrating the deterministic and Data envelopment analysis (DEA) efficient rule into adaptive rules: the individual will change evolutionary rule and migrate if its payoff is lower than their aspiration levels. Whether the individual choose to change the evolutionary rule and migrate is determined by the relation between its payoff and aspiration level. The results show that the cooperation frequency can hold unchange with the increasing of temptation to defect. The individual chooses to adopt DEA efficient rule and to migrate that can induce the emergence of cooperation as the payoff is lower than its aspiration.

scholarly journals A rapid method for determining diffusion constants in solution

1948 ◽  
Vol 192 (1030) ◽  
pp. 382-402 ◽  
Keyword(s):  
Monochromatic Light ◽  
Diffusion Constant ◽  
Initial Boundary ◽  
Optic Axis ◽  
Theory And Practice ◽  
Dilute Solution ◽  
Sharp Boundary ◽  
Diffusion Constants ◽  
A Cell ◽  
Molecular Substances

A method has been rediscovered, and developed in theory and practice, for optical observation of the earliest stages of diffusion across an initially sharp boundary between a dilute solution and a solvent. It enables the diffusion constant of a monodisperse solute to be measured about fifty times as quickly as by other methods, at lower concentration and possibly with greater accuracy; it should therefore be particularly valuable for the study of high molecular substances. The method is based on the interference pattern which is formed when monochromatic light from a horizontal slit is focused after passing through a cell where diffusion is occurring. The pattern, a set of horizontal bands, contracts towards the optic axis as diffusion proceeds, at a rate from which the diffusion constant can be calculated. By counting the bands in the pattern the refractive increment of the solute can be determined. The sharp initial boundary is obtained by flowing the solution and solvent out through a common narrow horizontal slit. The construction, calibration, and use of the apparatus are described.

scholarly journals Free to move or trapped in your group: Mathematical modeling of information overload and coordination in crowded populations

2018 ◽  
Vol 28 (09) ◽  
pp. 1831-1856 ◽  
Author(s):  
Alessandro Ciallella ◽  
Emilio N. M. Cirillo ◽  
Petru L. Curşeu ◽  
Adrian Muntean
Keyword(s):  
Information Processing ◽  
Population Size ◽  
Information Overload ◽  
Interpersonal Attraction ◽  
Social Systems ◽  
Square Lattice ◽  
Coordination Costs ◽  
The Individual ◽  
Computational Resources ◽  
Number Of Individuals

We present modeling strategies that describe the motion and interaction of groups of pedestrians in obscured spaces. We start off with an approach based on balance equations in terms of measures and then we exploit the descriptive power of a probabilistic cellular automaton model.Based on a variation of the simple symmetric random walk on the square lattice, we test the interplay between population size and an interpersonal attraction parameter for the evacuation of confined and darkened spaces. We argue that information overload and coordination costs associated with information processing in small groups are two key processes that influence the evacuation rate. Our results show that substantial computational resources are necessary to compensate for incomplete information — the more individuals in (information processing) groups the higher the exit rate for low population size. For simple social systems, it is likely that the individual representations are not redundant and large group sizes ensure that this non-redundant information is actually available to a substantial number of individuals. For complex social systems, information redundancy makes information evaluation and transfer inefficient and, as such, group size becomes a drawback rather than a benefit. The effect of group sizes on outgoing fluxes, evacuation times and wall effects is carefully studied with a Monte Carlo framework accounting also for the presence of an internal obstacle.

On Sieved Orthogonal Polynomials II: Random Walk Polynomials

1986 ◽  
Vol 38 (2) ◽  
pp. 397-415 ◽  
Author(s):  
Jairo Charris ◽  
Mourad E. H. Ismail
Keyword(s):  
Random Walk ◽  
Markov Process ◽  
Orthogonal Polynomials ◽  
Transition Probabilities ◽  
Death Process ◽  
Birth And Death Process ◽  
Stationary Markov Process ◽  
Image Position

A birth and death process is a stationary Markov process whose states are the nonnegative integers and the transition probabilities(1.1)satisfy(1.2)as t → 0. Here we assume βn > 0, δn + 1 > 0, n = 0, 1, …, but δ0 ≦ 0. Karlin and McGregor [10], [11], [12], showed that each birth and death process gives rise to two sets of orthogonal polynomials. The first is the set of birth and death process polynomials {Qn(x)} generated by

The ultrastructure of Methanothrix concilii, a mesophilic aceticlastic methanogen

1986 ◽  
Vol 32 (9) ◽  
pp. 703-710 ◽  
Author(s):  
Terry J. Beveridge ◽  
Girish B. Patel ◽  
Bob J. Harris ◽  
G. Dennis Sprott
Keyword(s):  
Cell Wall ◽  
Plasma Membrane ◽  
Circular Plates ◽  
A Cell ◽  
Granular Matrix ◽  
A Chain ◽  
The Individual

Methanothrix concilii strain GP6 consists of a chain of rod-shaped cells, ca. 2.5 μm in length and 0.8 μm in width, which are encased in a tubular proteinaceous sheath. The sheath is composed of annular hoops, ca. 8.0 nm wide and 9.0 nm thick, which are stacked together to form the tube. The ends of the sheath, and therefore the cell filament, are blocked by single, multilayered, 13.5 nm thick, circular plates, designated as "spacer plugs," which contain a series of concentric rings; these also separate the individual cells within each filament. Each cell is therefore bounded by a tubular section of sheath and two spacer plugs. Completely encapsulating each cell, and lying between the sheath and cell, is an amorphous granular matrix. Overlying the plasma membrane and surrounding each protoplast is a thin veil of material which resembles a cell wall, but which is unable to maintain the rod shape when cells are extruded from the sheath.

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