Progressive Screening: Long-Term Contracting with a Privately Known Stochastic Process

2012 ◽  
Vol 80 (1) ◽  
pp. 1-34 ◽  
Author(s):  
R. Boleslavsky ◽  
M. Said
Keyword(s):  
Stochastic Process

Out-of-equilibrium random walks

2020 ◽  
Vol 52 (3) ◽  
pp. 772-797
Author(s):  
Leonardo A. Videla
Keyword(s):  
Stochastic Process ◽  
Random Walks ◽  
Complete Graphs ◽  
Knowledge Process ◽  
Random Walker ◽  
Underlying Graph ◽  
Graph Sequence

AbstractWe study the long-term behaviour of a random walker embedded in a growing sequence of graphs. We define a (generally non-Markovian) real-valued stochastic process, called the knowledge process, that represents the ratio between the number of vertices already visited by the walker and the current size of the graph. We mainly focus on the case where the underlying graph sequence is the growing sequence of complete graphs.

A Formal Specification of the Memorization Process

2011 ◽  
pp. 157-170
Author(s):  
Natalia López ◽  
Manuel Núñez ◽  
Fernando L. Pelayo
Keyword(s):  
Stochastic Process ◽  
Probability Distribution ◽  
Formal Specification ◽  
Cognitive Model ◽  
Distribution Functions ◽  
Cognitive Systems ◽  
Buffer Memory ◽  
Stochastic Time ◽  
Stochastic Process Algebra

In this chapter we present the formal language, stochastic process algebra (STOPA), to specify cognitive systems. In addition to the usual characteristics of these formalisms, this language features the possibility of including stochastic time. This kind of time is useful to represent systems where the delays are not controlled by fixed amounts of time, but are given by probability distribution functions. In order to illustrate the usefulness of our formalism, we will formally represent a cognitive model of the memory. Following contemporary theories of memory classification (see Squire et al., 1993; Solso, 1999) we consider sensory buffer, short-term, and long-term memories. Moreover, borrowing from Y. Wang and Y. Wang (2006), we also consider the so-called action buffer memory.

Habitat and harvest scheduling using Bayesian statistical concepts

1996 ◽  
Vol 26 (8) ◽  
pp. 1375-1383 ◽  
Author(s):  
Paul C. Van Deusen
Keyword(s):  
Stochastic Process ◽  
Infinite Number ◽  
Spatial Distributions ◽  
Harvest Scheduling ◽  
Spatial Constraints ◽  
Model Based ◽  
Land Holdings ◽  
Term Management

A procedure is derived to generate long-term management schedules of habitat and harvest on large land holdings. The method utilizes spatial distributions that are derived using Bayesian statistical concepts. Model-based methods are proposed for incorporating spatial constraints and stochastically creating habitat. Thus, the Bayesian scheduler treats the schedule as a stochastic process rather than a deterministic one and generates virtually an infinite number of potential schedules that share common distributional characteristics. These schedules can then be examined and chosen according to economic or other criteria.

scholarly journals An accurate genetic clock

2015 ◽  
Author(s):  
David H Hamilton
Keyword(s):  
Stochastic Process ◽  
Kin Selection ◽  
Common Ancestor ◽  
Mutation Rates ◽  
Recent Common Ancestor ◽  
Molecular Clocks ◽  
Most Recent Common Ancestor ◽  
Wide Range ◽  
Short And Long Term

Molecular clocks give ``Time to most recent common ancestor'' TMRCA} of genetic trees. By Watson-Galton most lineages terminate, with a few overrepresented singular lineages generated by W. Hamilton's ``kin selection''. Applying current methods to this non-uniform branching produces greatly exaggerated TMRCA. We introduce an inhomogenous stochastic process which detects singular lineages by asymmetries, whose reduction gives true TMRCA. This implies a new method for computing mutation rates. Despite low rates similar to mitosis data, reduction implies younger TMRCA, with smaller errors. We establish accuracy by a comparison across a wide range of time, indeed this is only clock giving consistent results for both short and long term times. In particular we show that the dominant European y-haplotypes R1a1a & R1b1a2, expand from c3700BC, not reaching Anatolia before c3300BC. While this contradicts current clocks which date R1b1a2 to either the Neolithic Near East$ or Paleo-Europe, our dates support recent genetic analysis of ancient skeletons by Reich.

Learning in Neural Networks with Material Synapses

1994 ◽  
Vol 6 (5) ◽  
pp. 957-982 ◽  
Author(s):  
Daniel J. Amit ◽  
Stefano Fusi
Keyword(s):  
Stochastic Process ◽  
Associative Memory ◽  
Electronic Device ◽  
Transition Probabilities ◽  
Variable Number ◽  
Stable States ◽  
Neural Activities ◽  
Stochastic Learning ◽  
Long Time

We discuss the long term maintenance of acquired memory in synaptic connections of a perpetually learning electronic device. This is affected by ascribing each synapse a finite number of stable states in which it can maintain for indefinitely long periods. Learning uncorrelated stimuli is expressed as a stochastic process produced by the neural activities on the synapses. In several interesting cases the stochastic process can be analyzed in detail, leading to a clarification of the performance of the network, as an associative memory, during the process of uninterrupted learning. The stochastic nature of the process and the existence of an asymptotic distribution for the synaptic values in the network imply generically that the memory is a palimpsest but capacity is as low as log N for a network of N neurons. The only way we find for avoiding this tight constraint is to allow the parameters governing the learning process (the coding level of the stimuli; the transition probabilities for potentiation and depression and the number of stable synaptic levels) to depend on the number of neurons. It is shown that a network with synapses that have two stable states can dynamically learn with optimal storage efficiency, be a palimpsest, and maintain its (associative) memory for an indefinitely long time provided the coding level is low and depression is equilibrated against potentiation. We suggest that an option so easily implementable in material devices would not have been overlooked by biology. Finally we discuss the stochastic learning on synapses with variable number of stable synaptic states.

Modelling respiration pulses at rewetting as a stochastic process

2020 ◽  
Author(s):  
Stefano Manzoni ◽  
Arjun Chakrawal ◽  
Thomas Fischer ◽  
Amilcare Porporato ◽  
Giulia Vico
Keyword(s):  
Stochastic Process ◽  
Soil Moisture ◽  
Microbial Respiration ◽  
Climatic Changes ◽  
Statistical Properties ◽  
Relative Contribution ◽  
Rainfall Frequency ◽  
Rain Events ◽  
Rainfall Statistics

<p>Respiration pulses at rewetting are prominent features of soil responses to soil moisture fluctuations. These pulses are much larger compared to respiration rates under constant soil moisture, pointing to variations in water availability as drivers of the enhanced CO<sub>2</sub> production. Moreover, the respiration pulses tend to be larger when soil moisture before rewetting is lower. Thus, both the pre-rainfall soil moisture and the variation in soil moisture control the size of the respiration pulse. While these patterns are known from empirical studies, models have struggled to capture the relations between rainfall statistical properties (frequency of occurrence and rain event depths) and the occurrence and size of respiration pulses, framing the scope of this contribution. Specifically, we ask – how are the statistical properties of respiration pulses related to rainfall statistics?</p><p>Because rainfall can be regarded as a stochastic process generating variations in soil moisture, also respiration pulses at rewetting can be modelled through a probabilistic model. Here we develop such a model based on the premises that rainfall can be described as a marked Poisson process, and that respiration pulses increase with increasing variations of soil moisture (i.e., larger pulses after larger rain events) and decreasing pre-rain soil moisture (i.e., larger pulses after a long dry period). This model provides analytical relations between the statistical properties of soil respiration (e.g., long-term mean and standard deviation) and those of rainfall, allowing to study in a probabilistic framework how respiration varies along existing climatic gradients or in response to climatic changes that affect rainfall statistics.</p><p>Results show that the long-term mean CO<sub>2</sub> production during respiration pulses increases with increasing frequency and depth of rainfall events. However, the relative contribution of respiration pulses to the total microbial respiration decreases with rainfall frequency and depth. Similarly, also the variability of the size of respiration pulses, as measured by their standard deviation, decreases with increasing rainfall frequency and depth. As a consequence, climatic changes exacerbating rainfall intermittency – longer dry periods and more intense rain events – are predicted to increase both the relative contribution of respiration pulses to total microbial respiration and the variability of the pulse sizes.</p>

scholarly journals Dynamic structure of locomotor behavior in walking fruit flies

eLife ◽  
2017 ◽  
Vol 6 ◽  
Author(s):  
Alexander Y Katsov ◽  
Limor Freifeld ◽  
Mark Horowitz ◽  
Seppe Kuehn ◽  
Thomas R Clandinin
Keyword(s):  
Stochastic Process ◽  
Open Problem ◽  
Complex Dynamics ◽  
Dynamic Structure ◽  
Locomotor Behavior ◽  
Finite Memory ◽  
The Brain ◽  
Behavioral Constraint ◽  
Behavior Sequences

The function of the brain is unlikely to be understood without an accurate description of its output, yet the nature of movement elements and their organization remains an open problem. Here, movement elements are identified from dynamics of walking in flies, using unbiased criteria. On one time scale, dynamics of walking are consistent over hundreds of milliseconds, allowing elementary features to be defined. Over longer periods, walking is well described by a stochastic process composed of these elementary features, and a generative model of this process reproduces individual behavior sequences accurately over seconds or longer. Within elementary features, velocities diverge, suggesting that dynamical stability of movement elements is a weak behavioral constraint. Rather, long-term instability can be limited by the finite memory between these elementary features. This structure suggests how complex dynamics may arise in biological systems from elements whose combination need not be tuned for dynamic stability.

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.

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