scholarly journals Perron–Frobenius theory for kernels and Crump–Mode–Jagers processes with macro-individuals

2020 ◽  
Vol 57 (3) ◽  
pp. 720-733
Author(s):  
Serik Sagitov
Keyword(s):  
Single Type ◽  
Probabilistic Interpretation ◽  
Major Focus ◽  
Stochastic Kernel ◽  
Positive Recurrent ◽  
Special Case

AbstractPerron–Frobenius theory developed for irreducible non-negative kernels deals with so-called R-positive recurrent kernels. If the kernel M is R-positive recurrent, then the main result determines the limit of the scaled kernel iterations $R^nM^n$ as $n\to\infty$ . In Nummelin (1984) this important result is proven using a regeneration method whose major focus is on M having an atom. In the special case when $M=P$ is a stochastic kernel with an atom, the regeneration method has an elegant explanation in terms of an associated split chain. In this paper we give a new probabilistic interpretation of the general regeneration method in terms of multi-type Galton–Watson processes producing clusters of particles. Treating clusters as macro-individuals, we arrive at a single-type Crump–Mode–Jagers process with a naturally embedded renewal structure.

scholarly journals Counting Nondecreasing Integer Sequences that Lie Below a Barrier

10.37236/149 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
Robin Pemantle ◽  
Herbert S. Wilf
Keyword(s):  
Explicit Formula ◽  
Generating Function ◽  
Binomial Coefficients ◽  
Probabilistic Interpretation ◽  
Integer Sequences ◽  
Bivariate Generating Function ◽  
Linear Recursion ◽  
Special Case

Given a barrier $0 \leq b_0 \leq b_1 \leq \cdots$, let $f(n)$ be the number of nondecreasing integer sequences $0 \leq a_0 \leq a_1 \leq \cdots \leq a_n$ for which $a_j \leq b_j$ for all $0 \leq j \leq n$. Known formulæ for $f(n)$ include an $n \times n$ determinant whose entries are binomial coefficients (Kreweras, 1965) and, in the special case of $b_j = rj+s$, a short explicit formula (Proctor, 1988, p.320). A relatively easy bivariate recursion, decomposing all sequences according to $n$ and $a_n$, leads to a bivariate generating function, then a univariate generating function, then a linear recursion for $\{ f(n) \}$. Moreover, the coefficients of the bivariate generating function have a probabilistic interpretation, leading to an analytic inequality which is an identity for certain values of its argument.

On the weak convergence of sequences of circuit processes: a probabilistic approach

1992 ◽  
Vol 29 (02) ◽  
pp. 374-383 ◽  
Author(s):  
Sophia Kalpazidou
Keyword(s):  
Markov Chain ◽  
Weak Convergence ◽  
Asymptotic Behaviour ◽  
Markov Processes ◽  
Probabilistic Approach ◽  
Probabilistic Interpretation ◽  
Sample Paths ◽  
Convergence Of Sequences ◽  
Recurrent Markov Chain ◽  
Positive Recurrent

The asymptotic behaviour of sequences of Markov processes whose finite distributions depend upon the sample paths ω of a positive recurrent Markov chain ξ is studied. The existence of such sequences depends upon the existence of a unique class of directed weighted circuits having a probabilistic interpretation in terms of the directed circuits occurring along the sample paths of ξ. An application to multiple Markov chains is given.

On the weak convergence of sequences of circuit processes: a probabilistic approach

1992 ◽  
Vol 29 (2) ◽  
pp. 374-383 ◽  
Author(s):  
Sophia Kalpazidou
Keyword(s):  
Markov Chain ◽  
Weak Convergence ◽  
Asymptotic Behaviour ◽  
Markov Processes ◽  
Probabilistic Approach ◽  
Probabilistic Interpretation ◽  
Sample Paths ◽  
Convergence Of Sequences ◽  
Recurrent Markov Chain ◽  
Positive Recurrent

The asymptotic behaviour of sequences of Markov processes whose finite distributions depend upon the sample paths ω of a positive recurrent Markov chain ξ is studied. The existence of such sequences depends upon the existence of a unique class of directed weighted circuits having a probabilistic interpretation in terms of the directed circuits occurring along the sample paths of ξ. An application to multiple Markov chains is given.

Hope, exploration, and equilibrated action schemes

2019 ◽  
Vol 42 ◽  
Author(s):  
Davood G. Gozli ◽  
Ci Jun Gao
Keyword(s):  
Single Type ◽  
Reward Seeking ◽  
Stable Scheme

AbstractThe concepts want, hope, and exploration cannot be organized in relation to a single type of motive (e.g., motive for food). They require, in addition, the motive for acquiring and maintaining a stable scheme that enables reward-directed activity. Facing unpredictability, the animal has to seek not only reward, but also a new equilibrated state within which reward seeking is possible.

Extreme self-sacrifice beyond fusion: Moral expansiveness and the special case of allyship

2018 ◽  
Vol 41 ◽  
Author(s):  
Daniel Crimston ◽  
Matthew J. Hornsey
Keyword(s):  
General Theory ◽  
Biological Markers ◽  
Natural Environment ◽  
Relevant Dimension ◽  
Special Case

AbstractAs a general theory of extreme self-sacrifice, Whitehouse's article misses one relevant dimension: people's willingness to fight and die in support of entities not bound by biological markers or ancestral kinship (allyship). We discuss research on moral expansiveness, which highlights individuals’ capacity to self-sacrifice for targets that lie outside traditional in-group markers, including racial out-groups, animals, and the natural environment.

Determination of the phase structure of polymerblends by electron microscopy

1978 ◽  
Vol 36 (1) ◽  
pp. 492-493
Author(s):  
Dr. G. Kaemof
Keyword(s):  
Screw Extruder ◽  
Electron Microscopic ◽  
Thin Sections ◽  
Single Screw Extruder ◽  
Transmission Electron ◽  
The Matrix ◽  
Twin Screw ◽  
Special Case ◽  
Microscopic Investigations

A mixture of polycarbonate (PC) and styrene-acrylonitrile-copolymer (SAN) represents a very good example for the efficiency of electron microscopic investigations concerning the determination of optimum production procedures for high grade product properties.The following parameters have been varied:components of charge (PC : SAN 50 : 50, 60 : 40, 70 : 30), kind of compounding machine (single screw extruder, twin screw extruder, discontinuous kneader), mass-temperature (lowest and highest possible temperature).The transmission electron microscopic investigations (TEM) were carried out on ultra thin sections, the PC-phase of which was selectively etched by triethylamine.The phase transition (matrix to disperse phase) does not occur - as might be expected - at a PC to SAN ratio of 50 : 50, but at a ratio of 65 : 35. Our results show that the matrix is preferably formed by the components with the lower melting viscosity (in this special case SAN), even at concentrations of less than 50 %.

Fluorescent potentiometric dyes for membrane-potential imaging

1994 ◽  
Vol 52 ◽  
pp. 166-167
Author(s):  
Leslie M. Loew
Keyword(s):  
Membrane Potential ◽  
Single Cells ◽  
Quantitative Imaging ◽  
Optical Recording ◽  
Biological Processes ◽  
Major Focus ◽  
The Past ◽  
Excitable Systems ◽  
Major Application ◽  
The Impact

A major application of potentiometric dyes has been the multisite optical recording of electrical activity in excitable systems. After being championed by L.B. Cohen and his colleagues for the past 20 years, the impact of this technology is rapidly being felt and is spreading to an increasing number of neuroscience laboratories. A second class of experiments involves using dyes to image membrane potential distributions in single cells by digital imaging microscopy - a major focus of this lab. These studies usually do not require the temporal resolution of multisite optical recording, being primarily focussed on slow cell biological processes, and therefore can achieve much higher spatial resolution. We have developed 2 methods for quantitative imaging of membrane potential. One method uses dual wavelength imaging of membrane-staining dyes and the other uses quantitative 3D imaging of a fluorescent lipophilic cation; the dyes used in each case were synthesized for this purpose in this laboratory.

Test Validation Without Measurement

2016 ◽  
Vol 32 (3) ◽  
pp. 204-214 ◽  
Author(s):  
Emilie Lacot ◽  
Mohammad H. Afzali ◽  
Stéphane Vautier
Keyword(s):  
Test Data ◽  
Test Scores ◽  
Scientific Explanation ◽  
Test Validation ◽  
Clinical Tests ◽  
Ethical Perspective ◽  
Power Of Test ◽  
Memory Accuracy ◽  
Social Uses ◽  
Special Case

Abstract. Test validation based on usual statistical analyses is paradoxical, as, from a falsificationist perspective, they do not test that test data are ordinal measurements, and, from the ethical perspective, they do not justify the use of test scores. This paper (i) proposes some basic definitions, where measurement is a special case of scientific explanation; starting from the examples of memory accuracy and suicidality as scored by two widely used clinical tests/questionnaires. Moreover, it shows (ii) how to elicit the logic of the observable test events underlying the test scores, and (iii) how the measurability of the target theoretical quantities – memory accuracy and suicidality – can and should be tested at the respondent scale as opposed to the scale of aggregates of respondents. (iv) Criterion-related validity is revisited to stress that invoking the explanative power of test data should draw attention on counterexamples instead of statistical summarization. (v) Finally, it is argued that the justification of the use of test scores in specific settings should be part of the test validation task, because, as tests specialists, psychologists are responsible for proposing their tests for social uses.

Challenges of Fear Conditioning Research in the Age of RDoC

2017 ◽  
Vol 225 (3) ◽  
pp. 189-199 ◽  
Author(s):  
Tina B. Lonsdorf ◽  
Jan Richter
Keyword(s):  
Fear Conditioning ◽  
Clinical Diagnosis ◽  
Research Domain Criteria ◽  
Major Focus ◽  
The Future ◽  
Definition Of ◽  
Methodological Considerations ◽  
Research Domain

Abstract. As the criticism of the definition of the phenotype (i.e., clinical diagnosis) represents the major focus of the Research Domain Criteria (RDoC) initiative, it is somewhat surprising that discussions have not yet focused more on specific conceptual and procedural considerations of the suggested RDoC constructs, sub-constructs, and associated paradigms. We argue that we need more precise thinking as well as a conceptual and methodological discussion of RDoC domains and constructs, their interrelationships as well as their experimental operationalization and nomenclature. The present work is intended to start such a debate using fear conditioning as an example. Thereby, we aim to provide thought-provoking impulses on the role of fear conditioning in the age of RDoC as well as conceptual and methodological considerations and suggestions to guide RDoC-based fear conditioning research in the future.

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