Homogeneous Branching Processes with Non-Homogeneous Immigration

2021 ◽  
Vol 36 (2) ◽  
pp. 165-183
Author(s):  
Ibrahim Rahimov
Keyword(s):  
Asymptotic Behavior ◽  
Branching Process ◽  
Branching Processes ◽  
Limited Effect ◽  
Immigration Rate ◽  
Current State ◽  
State Of Research ◽  
New Phenomena ◽  
Changes Over Time ◽  
Over Time

Abstract The stationary immigration has a limited effect over the asymptotic behavior of the underlying branching process. It affects mostly the limiting distribution and the life-period of the process. In contrast, if the immigration rate changes over time, then the asymptotic behavior of the process is significantly different and a variety of new phenomena are observed. In this review we discuss branching processes with time non-homogeneous immigration. Our goal is to help researchers interested in the topic to familiarize themselves with the current state of research.

Technical Report: Monitoring and Communicating Changes in Disturbance Regimes (Version 1.0)

2021 ◽  
Author(s):  
Emma Tait ◽  
◽  
Pia Ruisi-Besares ◽  
Matthias Sirch ◽  
Alyx Belisle ◽  
...  
Keyword(s):  
Cold Water ◽  
Forest Health ◽  
Web Portal ◽  
Ecosystem Monitoring ◽  
Disturbance Regimes ◽  
Current State ◽  
Technical Report ◽  
Changes Over Time ◽  
High Winds ◽  
Over Time

Shifts in disturbance patterns across the Northeast are of increasing concern as the climate continues to change. In particular, changes in patterns of frequency, severity and extent of disturbance event may have detrimental cascading impacts on forest ecosystems and human communities. To explore how changing disturbance regimes might impact future forest health and management it is necessary to understand the historical trends and impacts of disturbance in the region. Although individual types of disturbance have already been analyzed, there is a need for a consolidated overview of the current state of disturbance in northeastern forests. To address this need, the Forest Ecosystem Monitoring Cooperative (FEMC) developed the FEMC: Tracking Shifts in Disturbance Regimes web portal for users to explore changes over time of key disturbance drivers, identify important disturbance responses, and discover where monitoring is happening for both drivers and responses. In collaboration with our advisory committee, we identified key disturbance drivers—flood, high winds, fire, drought, pests—and responses—macroinvertebrates, cold-water fisheries, invasive plants—that are of particular concern in the region. For each of the drivers we identified a suitable regional dataset and analyzed changes over time in frequency, severity, and extent. We also created a structured framework to catalogue programs across the region that are monitoring for these disturbance drivers and responses. Version 1.0 of the FEMC: Tracking Shifts in Disturbance Regimes (https://uvm.edu/femc/disturbance) web portal, first released in October 2021, contains 272 data programs, 11 drivers and three responses. Through the web portal users can browse programs by state, driver type or response type, and explore where monitoring is happening across the region. Driver-specific analyses allow users to quickly see the trends in severity, frequency and extent of selected disturbances and compare the impacts in selected states to regional data. We hope that this collection of programs and the analysis of trends provide researchers and land managers with an easy way to understand the current state of disturbance in northeastern forests that enables them to analyze and plan for future impacts.

scholarly journals Modeling Y-Linked Pedigrees through Branching Processes

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 256
Author(s):  
Miguel González ◽  
Cristina Gutiérrez ◽  
Rodrigo Martínez
Keyword(s):  
Hearing Loss ◽  
Asymptotic Behavior ◽  
Gibbs Sampler ◽  
Mutant Allele ◽  
Branching Process ◽  
Branching Processes ◽  
Dominant Allele ◽  
Linked Gene ◽  
Different Types ◽  
The Mean

A multidimensional two-sex branching process is introduced to model the evolution of a pedigree originating from the mutation of an allele of a Y-linked gene in a monogamous population. The study of the extinction of the mutant allele and the analysis of the dominant allele in the pedigree is addressed on the basis of the classical theory of multi-type branching processes. The asymptotic behavior of the number of couples of different types in the pedigree is also derived. Finally, using the estimates of the mean growth rates of the allele and its mutation provided by a Gibbs sampler, a real Y-linked pedigree associated with hearing loss is analyzed, concluding that this mutation will persist in the population although without dominating the pedigree.

scholarly journals Asymptotic behavior of projections of supercritical multi-type continuous-state and continuous-time branching processes with immigration

2021 ◽  
Vol 53 (4) ◽  
pp. 1023-1060
Author(s):  
Mátyás Barczy ◽  
Sandra Palau ◽  
Gyula Pap
Keyword(s):  
Asymptotic Behavior ◽  
Continuous Time ◽  
Branching Process ◽  
Branching Processes ◽  
Order Moment ◽  
Moment Condition ◽  
First Order ◽  
Continuous State ◽  
Branching Process With Immigration ◽  
Continuous Time Branching Processes

AbstractUnder a fourth-order moment condition on the branching and a second-order moment condition on the immigration mechanisms, we show that an appropriately scaled projection of a supercritical and irreducible continuous-state and continuous-time branching process with immigration on certain left non-Perron eigenvectors of the branching mean matrix is asymptotically mixed normal. With an appropriate random scaling, under some conditional probability measure, we prove asymptotic normality as well. In the case of a non-trivial process, under a first-order moment condition on the immigration mechanism, we also prove the convergence of the relative frequencies of distinct types of individuals on a suitable event; for instance, if the immigration mechanism does not vanish, then this convergence holds almost surely.

scholarly journals Conditional limit theorems for branching processes

1991 ◽  
Vol 4 (4) ◽  
pp. 263-292 ◽  
Author(s):  
Lajos Takács
Keyword(s):  
Asymptotic Behavior ◽  
Limit Theorems ◽  
Branching Process ◽  
Branching Processes ◽  
Random Variables ◽  
Random Variable ◽  
Conditional Limit Theorems ◽  
Total Progeny ◽  
Number Of Individuals ◽  
Conditional Limit

Let [ξ(m),m=0,1,2,…] be a branching process in which each individual reproduces independently of the others and has probability pj(j=0,1,2,…) of giving rise to j descendants in the following generation. The random variable ξ(m) is the number of individuals in the mth generation. It is assumed that P{ξ(0)=1}=1. Denote by ρ the total progeny, μ, the time of extinction, and τ, the total number of ancestors of all the individuals in the process. This paper deals with the distributions of the random variables ξ(m), μ and τ under the condition that ρ=n and determines the asymptotic behavior of these distributions in the case where n→∞ and m→∞ in such a way that m/n tends to a finite positive limit.

The SS in heavy metal lyrics

2020 ◽  
Vol 6 (3) ◽  
pp. 359-374 ◽  
Author(s):  
Henning Pieper
Keyword(s):  
Heavy Metal ◽  
Time Span ◽  
Historical Background ◽  
Accurate Analysis ◽  
Current State ◽  
State Of Research ◽  
Over Time

The article seeks to examine why heavy metal bands used history and imagery associated with the ‘Schutzstaffel’ (SS). This includes the reasons for the focus on this particular organization as well as the intentions behind it: are compositions about historical facts or rather fictitious topics, that is, are they an accurate analysis, a provocation or just entertainment? The article takes a closer look at the historical background and the content of the songs; it also questions the awareness of the criminal character of the SS displayed by the musicians. The time span covered by the songs in question reaches from the mid-1980s to the early 2000s. Thus, it can be asked if the attitude of musicians changed over time and if they included the current state of research in their lyrics.

Decomposable branching processes with two types of particles

2018 ◽  
Vol 28 (2) ◽  
pp. 119-130 ◽  
Author(s):  
Vladimir A. Vatutin ◽  
Elena E. Dyakonova
Keyword(s):  
Asymptotic Behavior ◽  
Discrete Time ◽  
Conditional Distribution ◽  
Limit Theorems ◽  
Branching Process ◽  
Branching Processes ◽  
Random Variable ◽  
Infinite Variance ◽  
Tail Distribution

Abstract A two-type critical decomposable branching process with discrete time is considered in which particles of the first type may produce at the death moment offspring of both types while particles of the second type may produce at the death moment offspring of their own type only. Assuming that the offspring distributions of particles of both types may have infinite variance, the asymptotic behavior of the tail distribution of the random variable Ξ2, the total number of the second type particles ever born in the process is found. Limit theorems are proved describing (as N → ∞) the conditional distribution of the amount of the first type particles in different generations given that either Ξ2 = N or Ξ2 > N.

scholarly journals Gluten-Free Diet in Celiac Disease—Forever and for All?

Nutrients ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 1796 ◽  
Author(s):  
Alice Itzlinger ◽  
Federica Branchi ◽  
Luca Elli ◽  
Michael Schumann
Keyword(s):  
Celiac Disease ◽  
Gluten Free Diet ◽  
Gluten Free ◽  
Research Groups ◽  
Current State ◽  
Appropriate Treatment ◽  
State Of Research ◽  
Definition Of ◽  
Patient Subgroups ◽  
Over Time

The gluten-free diet is the only effective treatment available for celiac disease. However, it is difficult to adhere to and a closer look on the diet’s implementation and indications reveals several ambiguities: Not only is there controversy on the threshold of gluten that can be tolerated in the frame of a strict gluten-free diet, but it is also unclear whether the gluten-free diet is an appropriate treatment in patient subgroups with asymptomatic or potential celiac disease. Reports from a number of research groups suggest that a certain proportion of patients may effectively develop tolerance to gluten and thus become suitable for gluten reintroduction over time. In this review, we set out to create an overview about the current state of research as regards the definition of a strict gluten-free diet in terms of the gluten thresholds considered tolerable and the indication for a gluten-free diet in the absence of histological abnormalities or symptoms. Furthermore, we discuss the concept that a gluten-free diet must be followed for life by all patients.

Large deviation rates for Markov branching processes

2020 ◽  
Vol 18 (03) ◽  
pp. 447-468 ◽  
Author(s):  
Junping Li ◽  
Lan Cheng ◽  
Anthony G. Pakes ◽  
Anyue Chen ◽  
Liuyan Li
Keyword(s):  
Asymptotic Behavior ◽  
Branching Process ◽  
Large Deviation ◽  
Branching Processes ◽  
Markov Branching Process

Large deviation rates are determined for quantities associated with a Markov branching process [Formula: see text] having offspring mean [Formula: see text] and split rate [Formula: see text]. The principal quantities examined are [Formula: see text] and [Formula: see text], where [Formula: see text] is the almost sure limit of an appropriately normed version of [Formula: see text]. Modifications and conditional versions are examined. Some of this requires determination of the asymptotic behavior of harmonic moments [Formula: see text].

Some Contributions to the Theory of Near-Critical Bisexual Branching Processes

2007 ◽  
Vol 44 (02) ◽  
pp. 492-505
Author(s):  
M. Molina ◽  
M. Mota ◽  
A. Ramos
Keyword(s):  
Branching Process ◽  
Branching Processes ◽  
Sufficient Conditions ◽  
Positive Probability ◽  
Limit Laws ◽  
Bisexual Branching Processes ◽  
Probabilistic Evolution

We investigate the probabilistic evolution of a near-critical bisexual branching process with mating depending on the number of couples in the population. We determine sufficient conditions which guarantee either the almost sure extinction of such a process or its survival with positive probability. We also establish some limiting results concerning the sequences of couples, females, and males, suitably normalized. In particular, gamma, normal, and degenerate distributions are proved to be limit laws. The results also hold for bisexual Bienaymé–Galton–Watson processes, and can be adapted to other classes of near-critical bisexual branching processes.

Comparison of two devices for measuring exercise transcutaneous oxygen pressures in patients with claudication

VASA ◽  
2015 ◽  
Vol 44 (5) ◽  
pp. 355-362 ◽  
Author(s):  
Marie Urban ◽  
Alban Fouasson-Chailloux ◽  
Isabelle Signolet ◽  
Christophe Colas Ribas ◽  
Mathieu Feuilloy ◽  
...  
Keyword(s):  
Oxygen Pressure ◽  
Optical Sensors ◽  
Chemical Sensors ◽  
Transcutaneous Oxygen ◽  
Starting Values ◽  
Two Systems ◽  
Transcutaneous Oxygen Pressure ◽  
New Sensors ◽  
Changes Over Time ◽  
Over Time

Abstract. Summary: Background: We aimed at estimating the agreement between the Medicap® (photo-optical) and Radiometer® (electro-chemical) sensors during exercise transcutaneous oxygen pressure (tcpO2) tests. Our hypothesis was that although absolute starting values (tcpO2rest: mean over 2 minutes) might be different, tcpO2-changes over time and the minimal value of the decrease from rest of oxygen pressure (DROPmin) results at exercise shall be concordant between the two systems. Patients and methods: Forty seven patients with arterial claudication (65 + / - 7 years) performed a treadmill test with 5 probes each of the electro-chemical and photo-optical devices simultaneously, one of each system on the chest, on each buttock and on each calf. Results: Seventeen Medicap® probes disconnected during the tests. tcpO2rest and DROPmin values were higher with Medicap® than with Radiometer®, by 13.7 + / - 17.1 mm Hg and 3.4 + / - 11.7 mm Hg, respectively. Despite the differences in absolute starting values, changes over time were similar between the two systems. The concordance between the two systems was approximately 70 % for classification of test results from DROPmin. Conclusions: Photo-optical sensors are promising alternatives to electro-chemical sensors for exercise oximetry, provided that miniaturisation and weight reduction of the new sensors are possible.

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