scholarly journals Stationary distributions of systems with discreteness-induced transitions

2020 ◽  
Vol 17 (168) ◽  
pp. 20200243
Author(s):  
Enrico Bibbona ◽  
Jinsu Kim ◽  
Carsten Wiuf
Keyword(s):  
Theoretical Analysis ◽  
Stationary Distribution ◽  
Critical Value ◽  
Reaction Networks ◽  
Geometric Ergodicity ◽  
Positive Recurrence ◽  
The Family ◽  
Analytic Expression ◽  
Parameter Values ◽  
Stationary Behaviour

We provide a theoretical analysis of some autocatalytic reaction networks exhibiting the phenomenon of discreteness-induced transitions. The family of networks that we address includes the celebrated Togashi and Kaneko model. We prove positive recurrence, finiteness of all moments and geometric ergodicity of the models in the family. For some parameter values, we find the analytic expression for the stationary distribution and discuss the effect of volume scaling on the stationary behaviour of the chain. We find the exact critical value of the volume for which discreteness-induced transitions disappear.

Theoretical Analysis of Time-to-Peak Responses in Biological Reaction Networks

2010 ◽  
Vol 73 (5) ◽  
pp. 978-1003 ◽  
Author(s):  
Fabian J. Theis ◽  
Sebastian Bohl ◽  
Ursula Klingmüller
Keyword(s):  
Theoretical Analysis ◽  
Reaction Networks ◽  
Time To Peak ◽  
Biological Reaction

scholarly journals Families of toric chemical reaction networks

2020 ◽  
Vol 58 (9) ◽  
pp. 2061-2093
Author(s):  
Michael F. Adamer ◽  
Martin Helmer
Keyword(s):  
Chemical Reaction ◽  
Chemical Reaction Networks ◽  
Steady States ◽  
Reaction Networks ◽  
Core Network ◽  
Entire Family ◽  
Data Set ◽  
The Family ◽  
Positive Steady States ◽  
State Behaviour

Abstract We study families of chemical reaction networks whose positive steady states are toric, and therefore can be parameterized by monomials. Families are constructed algorithmically from a core network; we show that if a family member is multistationary, then so are all subsequent networks in the family. Further, we address the questions of model selection and experimental design for families by investigating the algebraic dependencies of the chemical concentrations using matroids. Given a family with toric steady states and a constant number of conservation relations, we construct a matroid that encodes important information regarding the steady state behaviour of the entire family. Among other things, this gives necessary conditions for the distinguishability of families of reaction networks with respect to a data set of measured chemical concentrations. We illustrate our results using multi-site phosphorylation networks.

Hausdorff Dimension of Sets of Escaping Points and Escaping Parameters for Elliptic Functions

2015 ◽  
Vol 59 (3) ◽  
pp. 671-690
Author(s):  
Piotr Gałązka ◽  
Janina Kotus
Keyword(s):  
Hausdorff Dimension ◽  
Elliptic Function ◽  
Meromorphic Functions ◽  
Elliptic Functions ◽  
Critical Value ◽  
Parameter Plane ◽  
Dynamical Plane ◽  
The Family ◽  
Maximal Multiplicity ◽  
Additional Assumptions

AbstractLetbe a non-constant elliptic function. We prove that the Hausdorff dimension of the escaping set offequals 2q/(q+1), whereqis the maximal multiplicity of poles off. We also consider theescaping parametersin the familyfβ=βf, i.e. the parametersβfor which the orbit of one critical value offβescapes to infinity. Under additional assumptions onfwe prove that the Hausdorff dimension of the set of escaping parametersεin the familyfβis greater than or equal to the Hausdorff dimension of the escaping set in the dynamical space. This demonstrates an analogy between the dynamical plane and the parameter plane in the class of transcendental meromorphic functions.

Analysis and Design of Operational Amplifier Stability Using Routh-Hurwitz Stability Criterion

2019 ◽  
Vol 888 ◽  
pp. 1-10
Author(s):  
Jian Long Wang ◽  
Gopal Adhikari ◽  
Haruo Kobayashi ◽  
Nobukazu Tsukiji ◽  
Mayu Hirano ◽  
...  
Keyword(s):  
Theoretical Analysis ◽  
Stability Condition ◽  
Stability Criterion ◽  
Operational Amplifier ◽  
Amplifier Circuit ◽  
Analysis And Design ◽  
Hurwitz Stability ◽  
Parameter Values

This paper proposes to use Routh-Hurwitz stability criterion for analysis and design of the operational amplifier stability; this can lead to explicit stability condition derivation for operational amplifier circuit parameters, and this is very effective to understand which parameter values should be increased or decreased for the operational amplifier stability. The proposed method has been verified by three amplifiers with theoretical analysis and SPICE simulations for three operational amplifier examples.

scholarly journals Computing the Parameter Values for the Emergence of Homochirality in Complex Networks

Life ◽  
2019 ◽  
Vol 9 (3) ◽  
pp. 74
Author(s):  
Andrés Montoya ◽  
Elkin Cruz ◽  
Jesús Ágreda
Keyword(s):  
Symmetry Breaking ◽  
Heuristic Algorithm ◽  
Mirror Symmetry ◽  
Steady States ◽  
Chemical Mechanism ◽  
Reaction Networks ◽  
Nonlinear Character ◽  
Algorithmic Problems ◽  
Algorithmic Analysis ◽  
Parameter Values

The goal of our research is the development of algorithmic tools for the analysis of chemical reaction networks proposed as models of biological homochirality. We focus on two algorithmic problems: detecting whether or not a chemical mechanism admits mirror symmetry-breaking; and, given one of those networks as input, sampling the set of racemic steady states that can produce mirror symmetry-breaking. Algorithmic solutions to those two problems will allow us to compute the parameter values for the emergence of homochirality. We found a mathematical criterion for the occurrence of mirror symmetry-breaking. This criterion allows us to compute semialgebraic definitions of the sets of racemic steady states that produce homochirality. Although those semialgebraic definitions can be processed algorithmically, the algorithmic analysis of them becomes unfeasible in most cases, given the nonlinear character of those definitions. We use Clarke’s system of convex coordinates to linearize, as much as possible, those semialgebraic definitions. As a result of this work, we get an efficient algorithm that solves both algorithmic problems for networks containing only one enantiomeric pair and a heuristic algorithm that can be used in the general case, with two or more enantiomeric pairs.

Planar and Perpendicular Conductivity of Doping Modulated Amorphous Silicon Multilayers

1986 ◽  
Vol 70 ◽  
Author(s):  
H. Steemers ◽  
I. Chen ◽  
J. Mort ◽  
F. Jansen ◽  
M. Morgan ◽  
...  
Keyword(s):  
Theoretical Analysis ◽  
Space Charge ◽  
Amorphous Silicon ◽  
Layer Thickness ◽  
Critical Value ◽  
Dark Conductivity ◽  
Charge Doping ◽  
Phosphorus Doped

ABSTRACTThe conductivity of a-Si:H multilayers consisting of alternating boron and phosphorus doped layers has been studied as a function of sub-layer thickness. The planar and perpendicular dark conductivity is compared with theoretical analysis of space-charge doping in these structures and this effect is found to dominate the transport as the sub-layer thickness is reduced below a critical value

scholarly journals Stationary solution to the fluid queue fed by an M/M/1 queue

2002 ◽  
Vol 39 (2) ◽  
pp. 359-369 ◽  
Author(s):  
N. Barbot ◽  
B. Sericola
Keyword(s):  
Stationary Solution ◽  
Stationary Distribution ◽  
Generating Functions ◽  
The State ◽  
Finite Capacity ◽  
Fluid Queue ◽  
Analytic Expression ◽  
Joint Stationary Distribution

We consider an infinite-capacity buffer receiving fluid at a rate depending on the state of an M/M/1 queue. We obtain a new analytic expression for the joint stationary distribution of the buffer level and the state of the M/M/1 queue. This expression is obtained by the use of generating functions which are explicitly inverted. The case of a finite capacity fluid queue is also considered.

The Calibration of Gravity, Entropy, and Related Models of Spatial Interaction

1972 ◽  
Vol 4 (2) ◽  
pp. 205-233 ◽  
Author(s):  
M Batty ◽  
S Mackie
Keyword(s):  
Maximum Likelihood ◽  
Spatial Interaction ◽  
Interaction Models ◽  
Spatial Interaction Models ◽  
Calibration Methods ◽  
The Family ◽  
Newton Raphson ◽  
Best Parameter ◽  
Parameter Values ◽  
Raphson Method

This paper presents a methodology for deriving best statistics for the calibration of spatial interaction models, and several procedures for finding best parameter values are described. The family of spatial interaction models due to Wilson is first outlined, and then some existing calibration methods are briefly reviewed. A procedure for deriving best statistics based on the principle of maximum-likelihood is then developed from the work of Hyman and Evans, and the methodology is illustrated using the example of a retail gravity model. Five methods for solving the maximum-likelihood equations are outlined: procedures based on a simple first-order iterative process, the Newton—Raphson method for several variables, multivariate Fibonacci search, search using the Simplex method, and search based on quadratic convergence, are all tested and compared. It appears that the Newton—Raphson method is the most efficient, and this is further tested in the calibration of disaggregated residential location models.

scholarly journals "Large" strange attractors in the unfolding of a heteroclinic attractor

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Alexandre Rodrigues
Keyword(s):  
Strange Attractor ◽  
Invariant Manifolds ◽  
Strange Attractors ◽  
Positive Lebesgue Measure ◽  
Dimensional Sphere ◽  
3 Dimensional ◽  
Srb Measures ◽  
The Family ◽  
Parameter Values ◽  
Heteroclinic Network

<p style='text-indent:20px;'>We present a mechanism for the emergence of strange attractors in a one-parameter family of differential equations defined on a 3-dimensional sphere. When the parameter is zero, its flow exhibits an attracting heteroclinic network (Bykov network) made by two 1-dimensional connections and one 2-dimensional separatrix between two saddles-foci with different Morse indices. After slightly increasing the parameter, while keeping the 1-dimensional connections unaltered, we concentrate our study in the case where the 2-dimensional invariant manifolds of the equilibria do not intersect. We will show that, for a set of parameters close enough to zero with positive Lebesgue measure, the dynamics exhibits strange attractors winding around the "ghost'' of a torus and supporting Sinai-Ruelle-Bowen (SRB) measures. We also prove the existence of a sequence of parameter values for which the family exhibits a superstable sink and describe the transition from a Bykov network to a strange attractor.</p>

scholarly journals EMOTIONAL WELFARE AS A DETERMINING FACTOR IN THE DEVELOPMENT OF THE MOTIVATIONAL AND SEMANTIC SPHERE WITH DIABETES SUGAR PATIENTS

2021 ◽  
Vol 3 (47) ◽  
Author(s):  
I. Volzhentseva
Keyword(s):  
Theoretical Analysis ◽  
Value Orientations ◽  
Educational Institutions ◽  
The Family ◽  
The World ◽  
Patients With Diabetes ◽  
Determining Factor

The article provides a theoretical analysis of the problem of emotional welfare / disadvantage. It is emphasized that emotional welfare is a determining factor in the development of the motivational and semantic sphere of patients with diabetes sugar, which ensures an active attitude to the world, needs, goals, motivational attitudes, meaning-life, and value orientations. The importance of emotional welfare in the family and educational institutions as a determining factor in the development of the personality of a child with diabetes sugar is emphasized. A number of reasons that violate emotional welfare are presented, and components that can contribute to creating an atmosphere of emotional welfare of a child with diabetes are highlighted.Key words: patients, diabetes sugar, emotional welfare, emotional disadvantage, motivational and semantic sphere.

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