scholarly journals Potential survival of some, but not all, diversification methods

2021 ◽  
Author(s):  
Brian O'Meara ◽  
Jeremy M. Beaulieu
Keyword(s):  
Brownian Motion ◽  
Heterogeneous Models ◽  
Coin Flipping ◽  
Over Time

Models have long been used for understanding changing diversification patterns over time. The rediscovery that models with very different rates through time can fit a phylogeny equally well has led to great concern about the use of these models. We share and add to these concerns: even with time heterogeneous models without these issues, the distribution of the data means that estimates will be very uncertain. However, we argue that congruence issues such as this also occur in models as basic as Brownian motion and coin flipping. Taxon-heterogeneous models such as many SSE models appear not to have this particular issue.

scholarly journals Investing and Stopping

2014 ◽  
Vol 51 (4) ◽  
pp. 898-909
Author(s):  
Moritz Duembgen ◽  
L. C. G. Rogers
Keyword(s):  
Brownian Motion ◽  
Random Walk ◽  
Optimal Stopping ◽  
Numerical Scheme ◽  
Optimization Problem ◽  
Hedge Fund ◽  
Optimal Stopping Problem ◽  
Over Time

In this paper we solve the hedge fund manager's optimization problem in a model that allows for investors to enter and leave the fund over time depending on its performance. The manager's payoff at the end of the year will then depend not just on the terminal value of the fund level, but also on the lowest and the highest value reached over that time. We establish equivalence to an optimal stopping problem for Brownian motion; by approximating this problem with the corresponding optimal stopping problem for a random walk we are led to a simple and efficient numerical scheme to find the solution, which we then illustrate with some examples.

Investing and Stopping

2014 ◽  
Vol 51 (04) ◽  
pp. 898-909
Author(s):  
Moritz Duembgen ◽  
L. C. G. Rogers
Keyword(s):  
Brownian Motion ◽  
Random Walk ◽  
Optimal Stopping ◽  
Numerical Scheme ◽  
Optimization Problem ◽  
Hedge Fund ◽  
Optimal Stopping Problem ◽  
Over Time

In this paper we solve the hedge fund manager's optimization problem in a model that allows for investors to enter and leave the fund over time depending on its performance. The manager's payoff at the end of the year will then depend not just on the terminal value of the fund level, but also on the lowest and the highest value reached over that time. We establish equivalence to an optimal stopping problem for Brownian motion; by approximating this problem with the corresponding optimal stopping problem for a random walk we are led to a simple and efficient numerical scheme to find the solution, which we then illustrate with some examples.

scholarly journals On the Integral of the Fractional Brownian Motion and Some Pseudo-Fractional Gaussian Processes

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 991 ◽  
Author(s):  
Mario Abundo ◽  
Enrica Pirozzi
Keyword(s):  
Brownian Motion ◽  
Markov Process ◽  
Gaussian Process ◽  
Fractional Brownian Motion ◽  
Gaussian Processes ◽  
Statistical Parameters ◽  
Uhlenbeck Process ◽  
Ornstein Uhlenbeck Process ◽  
Over Time

We investigate the main statistical parameters of the integral over time of the fractional Brownian motion and of a kind of pseudo-fractional Gaussian process, obtained as a classical Gauss–Markov process from Doob representation by replacing Brownian motion with fractional Brownian motion. Possible applications in the context of neuronal models are highlighted. A fractional Ornstein–Uhlenbeck process is considered and relations with the integral of the pseudo-fractional Gaussian process are provided.

scholarly journals Estudo de padrões de clusters surgidos em uma dinâmica de perseguição e fuga

2019 ◽  
Vol 42 ◽  
pp. e48
Author(s):  
Pedro Henrique Fernandes Lobo ◽  
Suzielli Martins Mendonça ◽  
Matheus Jatkoske Lazo ◽  
Everaldo Arashiro
Keyword(s):  
Brownian Motion ◽  
Random Walk ◽  
Stochastic Model ◽  
Virtual Network ◽  
Main Interest ◽  
Number Of Clusters ◽  
Agent Based ◽  
Over Time

An agent-based stochastic model was developed with the objective of studying the movement and formation of clusters in systems composed of prey and predators. A discrete virtual network was created, where two types of agents can move in, one of them moving like prey and it is programmed to move away from the second type, which behaves like a predator. In this model, as the main interest was to study the patterns formed by the dynamics of persecution, the proportions of these agents are kept fixed in each simulation. The rules of movement are based on an asymmetric random walk, which causes the two types of agents, with their respective behaviors, to perform a Brownian motion when far apart. However, the dynamics of persecution begin to get more intense as these two approaches. To analyze the conditions in which the clusters emerge, the concentrations of the two types of agents were varied and a parameter σ, which acts as a mediator, amplifying or attenuating the "forces" of attraction/repulsion between the individuals. The simulations revealed patterns of randomly positioned agents in the network, as well as the counting of the average number of clusters over time.

Integrated Fractional white Noise as an Alternative to Multifractional Brownian Motion

2007 ◽  
Vol 44 (02) ◽  
pp. 393-408 ◽  
Author(s):  
Allan Sly
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
White Noise ◽  
Gaussian Process ◽  
Discrete Data ◽  
Hölder Exponent ◽  
Scaling Properties ◽  
Multifractional Brownian Motion ◽  
Local Properties

Multifractional Brownian motion is a Gaussian process which has changing scaling properties generated by varying the local Hölder exponent. We show that multifractional Brownian motion is very sensitive to changes in the selected Hölder exponent and has extreme changes in magnitude. We suggest an alternative stochastic process, called integrated fractional white noise, which retains the important local properties but avoids the undesirable oscillations in magnitude. We also show how the Hölder exponent can be estimated locally from discrete data in this model.

Brownian motion with quadratic killing and some implications

1986 ◽  
Vol 23 (04) ◽  
pp. 893-903 ◽  
Author(s):  
Michael L. Wenocur
Keyword(s):  
Brownian Motion ◽  
Weibull Distribution ◽  
Special Function ◽  
Function Theory ◽  
Killing Rate

Brownian motion subject to a quadratic killing rate and its connection with the Weibull distribution is analyzed. The distribution obtained for the process killing time significantly generalizes the Weibull. The derivation involves the use of the Karhunen–Loève expansion for Brownian motion, special function theory, and the calculus of residues.

Social transmission bias and the cultural evolution of folk-economic beliefs

2018 ◽  
Vol 41 ◽  
Author(s):  
David Hirshleifer ◽  
Siew Hong Teoh
Keyword(s):  
Cultural Evolution ◽  
Social Transmission ◽  
Cognitive Approach ◽  
Economic Problems ◽  
Economic Attitudes ◽  
The Social ◽  
Economic Beliefs ◽  
Over Time

AbstractEvolved dispositions influence, but do not determine, how people think about economic problems. The evolutionary cognitive approach offers important insights but underweights the social transmission of ideas as a level of explanation. The need for asocialexplanation for the evolution of economic attitudes is evidenced, for example, by immense variations in folk-economic beliefs over time and across individuals.

Articulatory Generalization in Two Word-Medial, Ambisyllabic Contexts

1988 ◽  
Vol 19 (3) ◽  
pp. 251-258 ◽  
Author(s):  
Virginia I. Wolfe ◽  
Suzanne D. Blocker ◽  
Norma J. Prater
Keyword(s):  
Common View ◽  
Perceptual Salience ◽  
The Common ◽  
Unitary Concept ◽  
Over Time

Articulatory generalization of velar cognates /k/, /g/ in two phonologically disordered children was studied over time as a function of sequential word-morpheme position training. Although patterns of contextual acquisition differed, correct responses to the word-medial, inflected context (e.g., "picking," "hugging") occurred earlier and exceeded those to the word-medial, noninflected context (e.g., "bacon," "wagon"). This finding indicates that the common view of the word-medial position as a unitary concept is an oversimplification. Possible explanations for superior generalization to the word-medial, inflected position are discussed in terms of coarticulation, perceptual salience, and the representational integrity of the word.

Treatment Fidelity Procedures for an Aphasia Intervention Within a Randomized Controlled Trial: Design, Feasibility, and Results

2020 ◽  
Vol 29 (1S) ◽  
pp. 412-424
Author(s):  
Elissa L. Conlon ◽  
Emily J. Braun ◽  
Edna M. Babbitt ◽  
Leora R. Cherney
Keyword(s):  
Randomized Controlled Trial ◽  
Controlled Trial ◽  
Treatment Protocol ◽  
Treatment Fidelity ◽  
Protocol Adherence ◽  
Study Condition ◽  
Randomized Controlled ◽  
Aphasia Therapy ◽  
Percent Accuracy ◽  
Over Time

Purpose This study reports on the treatment fidelity procedures implemented during a 5-year randomized controlled trial comparing intensive and distributed comprehensive aphasia therapy. Specifically, the results of 1 treatment, verb network strengthening treatment (VNeST), are examined. Method Eight participants were recruited for each of 7 consecutive cohorts for a total of 56 participants. Participants completed 60 hr of aphasia therapy, including 15 hr of VNeST. Two experienced speech-language pathologists delivered the treatment. To promote treatment fidelity, the study team developed a detailed manual of procedures and fidelity checklists, completed role plays to standardize treatment administration, and video-recorded all treatment sessions for review. To assess protocol adherence during treatment delivery, trained research assistants not involved in the treatment reviewed video recordings of a subset of randomly selected VNeST treatment sessions and completed the fidelity checklists. This process was completed for 32 participants representing 2 early cohorts and 2 later cohorts, which allowed for measurement of protocol adherence over time. Percent accuracy of protocol adherence was calculated across clinicians, cohorts, and study condition (intensive vs. distributed therapy). Results The fidelity procedures were sufficient to promote and verify a high level of adherence to the treatment protocol across clinicians, cohorts, and study condition. Conclusion Treatment fidelity strategies and monitoring are feasible when incorporated into the study design. Treatment fidelity monitoring should be completed at regular intervals during the course of a study to ensure that high levels of protocol adherence are maintained over time and across conditions.

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