Random causes with directed effects: the Indo-European language spread and the stochastic loss of lineages

Since the beginning, studies of Indo-European have seen it as a large phenomenon necessarily having a large, usually single cause. Yet apparent pattern can arise from chance causes that need have no great historical order. In a minimalist view, set out here as a theoretical hypothesis, the pattern of Indo-European can simply arise from a kind of social Brownian motion, in which a large pattern invents itself out of countless little perturbations between adjacent language communities

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Integrated Fractional white Noise as an Alternative to Multifractional Brownian Motion

Journal of Applied Probability ◽

10.1017/s0021900200003041 ◽

2007 ◽

Vol 44 (02) ◽

pp. 393-408 ◽

Cited By ~ 1

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.

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Brownian motion with quadratic killing and some implications

Journal of Applied Probability ◽

10.1017/s0021900200116079 ◽

1986 ◽

Vol 23 (04) ◽

pp. 893-903 ◽

Cited By ~ 2

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.

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Brownian Motion, Hardy Spaces and Bounded Mean Oscillation

10.1017/cbo9780511662386 ◽

1977 ◽

Cited By ~ 17

Author(s):

K. E. Petersen

Keyword(s):

Brownian Motion ◽

Hardy Spaces ◽

Bounded Mean Oscillation ◽

Mean Oscillation

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Suicide Attempts During Adolescence: Systematic Hospitalization and Crisis Treatment

Crisis ◽

10.1027//0227-5910.20.1.41 ◽

1999 ◽

Vol 20 (1) ◽

pp. 41-48 ◽

Cited By ~ 11

Author(s):

Jérôme Ottino

Keyword(s):

Attempted Suicide ◽

Suicide Attempts ◽

Psychiatric Treatment ◽

Health Workers ◽

Inpatient Unit ◽

Theoretical Hypothesis ◽

Initial Resistance ◽

Provision Of Care ◽

Suicidal Crisis

This paper deals with an inpatient unit that recently opened in Geneva, specializing in the treatment of patients aged 16-21 years who had attempted suicide or felt the desire to commit suicide. This particular center was established because of the significant weaknesses found in the provision of care to adolescents who had attempted suicide. Despite the growing interest of health workers in this area of study over recent years, the frequency of suicide among the young has not decreased and there are numerous recurrences of the suicide attempts. Further, all efforts to improve the adolescents' compliance with psychiatric treatment have failed to date. The number of drop-outs from treatment is still very high. Thus, the objectives of our inpatient unit are as follows: (1) to overcome initial resistance to treatment and to improve long-term compliance; (2) to decrease the number of recurrent attempts as a consequence of the above, thus increasing life expectancy; (3) to offer the adolescents who have tried (or have contemplated) committing suicide an improved quality of life, after first helping them overcome the suicidal crisis. To achieve these goals, the therapeutic team of the unit proposes short stays during which the work with the adolescents consists of a very intensive psychoanalytic-oriented crisis intervention. Numerous practical aspects of our therapeutic approach in the inpatient unit are related here in detail, always with reference to our theoretical hypothesis.

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