Stochastic Accumulation Research Articles

Dynamic stochastic accumulation model with application to pension savings management

We propose a dynamic stochastic accumulation model for determining optimal decision between stock and bond investments during accumulation of pension savings. Stock prices are assumed to be driven by the geometric Brownian motion. Interest rates are modeled by means of the Cox-Ingersoll-Ross model. The optimal decision as a solution to the corresponding dynamic stochastic program is a function of the duration of saving, the level of savings and the short rate. Qualitative and quantitative properties of the optimal solution are analyzed. The model is tested on the funded pillar of the Slovak pension system. The results are calculated for various risk preferences of a saver.

Quantitative measurement of aging using image texture entropy

A key element in understanding the aging of Caenorhabditis elegans is objective quantification of the morphological differences between younger and older animals. Here we propose to use the image texture entropy as an objective measurement that reflects the structural deterioration of the C. elegans muscle tissues during aging. The texture entropy and directionality of the muscle microscopy images were measured using 50 animals on Days 0, 2, 4, 6, 8, 10 and 12 of adulthood. Results show that the entropy of the C. elegans pharynx tissues increases as the animal ages, but a sharper increase was measured between Days 2 and 4, and between Days 8 and 10. These results are in agreement with gene expression findings, and support the contention that the process of C. elegans aging has several distinct stages. This can indicate that C. elegans aging is driven by developmental pathways, rather than stochastic accumulation of damage. The image data are freely available on the Internet at http://ome.grc.nia.nih.gov/iicbu2008/celegans, and the Haralick and Tamura texture analysis source code can be downloaded at http://ome.grc.nia.nih.gov/wnd-charm.

The Role of Consumption and Listed Alternative Investments on the Lifetime-Ruin Probability of U.S. Households

In light of the current subprime and financial crises, retirement planning has gained in importance. Many U.S. households have had to reevaluate their assets and their retirement plans (if they even had plans). Most U.S. households, however, find it difficult to assess their retirements and the attendant risks properly. Households that have noticed a need for action often fail to fully evaluate the effectiveness of any potential actions. In this article we propose to solve the problem for different U.S. households: middle class, upper-middle class and upper class by estimating the risk to be alive when the financial portfolio falls short (life-time ruin probability). We further consider a reduction in consumption as well as portfolio diversification in listed alternative investments and its effect on the reduction of life-time ruin risk. The complex model we employ accounts for the stochastic total wealth accumulation including income, consumption, housing, debt, and saving dynamics (after inflation, tax, and transaction costs). We find that the life-time ruin probability for all considered households is unacceptably high: For the middle class even 75%, and still 54% for the upper class. But, the risk of portfolio ruin can be substantially reduced if the household is willing to decrease living expenses by 30% and diversifies in a na?ve diversified portfolio of listed alternative investments by 30%, even if we account for the financial crisis. Finally we find that the middle class households must reassess their living expenses in the short run since it can only reduce lifetime ruin risk to 25% even if it takes all suggested action. In comparison the middle class and upper-middle class can reduce its lifetime-ruin risk to a reasonable 14% and 12.6%, which can be further decreased with a professional financial planning of the liquid (financial) assets.

An Xpb Mouse Model for Combined Xeroderma Pigmentosum and Cockayne Syndrome Reveals Progeroid Features upon Further Attenuation of DNA Repair

Patients carrying mutations in the XPB helicase subunit of the basal transcription and nucleotide excision repair (NER) factor TFIIH display the combined cancer and developmental-progeroid disorder xeroderma pigmentosum/Cockayne syndrome (XPCS). Due to the dual transcription repair role of XPB and the absence of animal models, the underlying molecular mechanisms of XPB(XPCS) are largely uncharacterized. Here we show that severe alterations in Xpb cause embryonic lethality and that knock-in mice closely mimicking an XPCS patient-derived XPB mutation recapitulate the UV sensitivity typical for XP but fail to show overt CS features unless the DNA repair capacity is further challenged by crossings to the NER-deficient Xpa background. Interestingly, the Xpb(XPCS) Xpa double mutants display a remarkable interanimal variance, which points to stochastic DNA damage accumulation as an important determinant of clinical diversity in NER syndromes. Furthermore, mice carrying the Xpb(XPCS) mutation together with a point mutation in the second TFIIH helicase Xpd are healthy at birth but display neonatal lethality, indicating that transcription efficiency is sufficient to permit embryonal development even when both TFIIH helicases are crippled. The double-mutant cells exhibit sensitivity to oxidative stress, suggesting a role for endogenous DNA damage in the onset of XPB-associated CS.

Efficient Methods for Time-Dependent Fatigue Reliability Analysis

Two efficient methods for time-dependent fatigue reliability analysis are proposed in this paper based on a random process representation of material fatigue properties and a nonlinear damage accumulation rule. The first method is developed by matching the first two central moments of the accumulated damage to a well-known probability distribution, thus facilitating a direct analytical solution of the time-dependent fatigue reliability. The second method uses the first-order reliability method to calculate the reliability index based on a time-dependent limit state function. These two methods represent different tradeoffs between accuracy and computational efficiency. The proposed methods include the covariance structure of the stochastic damage accumulation process under variable amplitude loading. A wide range of fatigue data available in the literature is used to validate the proposed methods, covering several different types of metallic and composite materials under different variable amplitude loading.

Principles and practice of hormetic treatment of aging and age-related diseases

Aging is characterized by stochastic accumulation of molecular damage, progressive failure of maintenance and repair, and consequent onset of age-related diseases. Applying hormesis in aging research and therapy is based on the principle of stimulation of maintenance and repair pathways by repeated exposure to mild stress. Studies on the beneficial biological effects of repeated mild heat shock on human cells in culture, and other studies on the anti-aging and life-prolonging effects of proxidants, hypergravity, irradiation and ethanol on cells and organisms suggest that hormesis as an antiaging and gerontomodulatory approach has a promising future. Its clinical applications include prevention and treatment of diabetes, cataract, osteoporosis, dementia and some cancers.

Quantifying the threat of extinction from Muller's ratchet in the diploid Amazon molly (Poecilia formosa).

BackgroundThe Amazon molly (Poecilia formosa) is a small unisexual fish that has been suspected of being threatened by extinction from the stochastic accumulation of slightly deleterious mutations that is caused by Muller's ratchet in non-recombining populations. However, no detailed quantification of the extent of this threat is available.ResultsHere we quantify genomic decay in this fish by using a simple model of Muller's ratchet with the most realistic parameter combinations available employing the evolution@home global computing system. We also describe simple extensions of the standard model of Muller's ratchet that allow us to deal with selfing diploids, triploids and mitotic recombination. We show that Muller's ratchet creates a threat of extinction for the Amazon molly for many biologically realistic parameter combinations. In most cases, extinction is expected to occur within a time frame that is less than previous estimates of the age of the species, leading to a genomic decay paradox.ConclusionHow then does the Amazon molly survive? Several biological processes could individually or in combination solve this genomic decay paradox, including paternal leakage of undamaged DNA from sexual sister species, compensatory mutations and many others. More research is needed to quantify the contribution of these potential solutions towards the survival of the Amazon molly and other (ancient) asexual species.

BDNF Instructs the Kinase LKB1 To Grow an Axon

Determining which neurite of a differentiating neuron is to become the axon is a crucial step in neuronal morphogenesis. Two groups (Barnes et al., 2007; Shelly et al., 2007) now report that axon specification in vivo is mediated by extracellular signals acting through the serine/threonine kinase LKB1.

LKB1/STRAD Promotes Axon Initiation During Neuronal Polarization

Axon/dendrite differentiation is a critical step in neuronal development. In cultured hippocampal neurons, the accumulation of LKB1 and STRAD, two interacting proteins critical for establishing epithelial polarity, in an undifferentiated neurite correlates with its subsequent axon differentiation. Downregulation of either LKB1 or STRAD by siRNAs prevented axon differentiation, and overexpression of these proteins led to multiple axon formation. Furthermore, interaction of STRAD with LKB1 promoted LKB1 phosphorylation at a PKA site S431 and elevated the LKB1 level, and overexpressing LKB1 with a serine-to-alanine mutation at S431 (LKB1(S431A)) prevented axon differentiation. In developing cortical neurons in vivo, downregulation of LKB1 or overexpression of LKB1(S431A) also abolished axon formation. Finally, local exposure of the undifferentiated neurite to brain-derived neurotrophic factor or dibutyryl-cAMP promoted axon differentiation in a manner that depended on PKA-dependent LKB1 phosphorylation. Thus local LKB1/STRAD accumulation and PKA-dependent LKB1 phosphorylation represents an early signal for axon initiation.

A Population Coding Account for Systematic Variation in Saccadic Dead Time

During movement programming, there is a point in time at which the movement system is committed to executing an action with certain parameters even though new information may render this action obsolete. For saccades programmed to a visual target this period is termed the dead time. Using a double-step paradigm, we examined potential variability in the dead time with variations in overall saccade latency and spatiotemporal configuration of two sequential targets. In experiment 1, we varied overall saccade latency by manipulating the presence or absence of a central fixation point. Despite a large and robust gap effect, decreasing the saccade latency in this way did not alter the dead time. In experiment 2, we varied the separation between the two targets. The dead time increased with separation up to a point and then leveled off. A stochastic accumulator model of the oculomotor decision mechanism accounts comprehensively for our findings. The model predicts a gap effect through changes in baseline activity without producing variations in the dead time. Variations in dead time with separation between the two target locations are a natural consequence of the population coding assumption in the model.

Stochastic fatigue damage modeling under variable amplitude loading

A general methodology for stochastic fatigue life prediction under variable amplitude loading is proposed in this paper. The methodology combines a nonlinear fatigue damage accumulation rule and a stochastic S–N curve representation technique to achieve this objective. The nonlinear damage accumulation rule proposed in this paper improves the deficiencies inherent in the linear damage accumulation rule and still maintains its simplicity in the application. The covariance structure of the stochastic damage accumulation process under variable amplitude loading is included into the methodology by a new stochastic S–N curve approach. A wide range of fatigue data available in the literature is used to validate the proposed methodology, which covers different type of metallic materials under constant and variable amplitude loadings. The prediction results are also compared with existing fatigue models.

Void lattice formation as a nonequilibrium phase transition

The evolution of a void ensemble in the presence of one-dimensionally migrating self-interstitials is considered, consistently taking into account the nucleation of voids via the stochastic accumulation of vacancies. Including the stochastic fluctuations of the fluxes of mobile defects caused by the random nature of diffusion jumps and cascade initiation, the evolution of the void ensemble is treated using the Fokker-Planck equation approach. A system instability signaling a nonequilibrium phase transition is found to occur when the mean free path of the one-dimensionally moving self-interstitials becomes comparable with the average distance between the voids at a sufficiently high void-number density. Due to the exponential dependence of the void nucleation probability on the net vacancy flux, the nucleation of voids is much more favored at the void lattice positions. Simultaneously, voids initially nucleated at positions where neighboring voids are nonaligned will also shrink away. These two processes leave the aligned voids to form a regular lattice. The shrinkage of nonaligned voids is not a usual thermodynamic effect, but is a kinetic effect caused entirely by the stochastic fluctuations in point-defect fluxes received by the voids. It is shown that the shrinkage of the nonaligned voids, and thus the formation of the void lattice, occurs only if the effective fraction of one-dimensional interstitials is small, less than about 1%. The formation of the void lattice in this way can be accomplished at a void swelling of below 1%, in agreement with experimental observation. The dominance of void nucleation at void-lattice positions practically nullifies the effect of void coalescence induced by the one-dimensional self-interstitial transport.

Effect of one-dimensional diffusion on void nucleation

Nucleation of voids via the stochastic accumulation of vacancies is considered when one-dimensionally migrating self-interstitials are present. A system instability signaling a non-equilibrium phase transition is found to occur when the mean free path of the one-dimensionally moving self-interstitials becomes comparable with the average distance between the voids at a sufficiently high void-number density. At this point, due to the exponential dependence of void nucleation probability on the net vacancy flux, the nucleation of voids is much more favored at the void lattice positions. At the same time, voids initially nucleated at positions where neighboring voids are non-aligned will shrink away. The shrinkage of non-aligned voids is caused entirely by the stochastic fluctuations in point-defect fluxes received by the voids. These two processes leave the aligned voids to form a regular lattice. The formation of the void lattice in this way can be accomplished at a void swelling of below 1%, in agreement with experimental observation.

Redox Modulation of Heat Shock Protein Expression by Acetylcarnitine in Aging Brain: Relationship to Antioxidant Status and Mitochondrial Function

There is significant evidence to show that aging is characterized by a stochastic accumulation of molecular damage and by a progressive failure of maintenance and repair processes. Protective mechanisms exist in the brain which are controlled by vitagenes and include members of the heat shock system, heme oxygenase-I, and Hsp70 as critical determinants of brain stress tolerance. Given the broad cytoprotective properties of the heat shock response, molecules inducing this defense mechanism appear to be possible candidates for novel cytoprotective strategies. Acetyl-L-carnitine is proposed as a therapeutic agent for several neurodegenerative disorders, and the present study reports that treatment for 4 months of senescent rats with acetyl-L-carnitine induces heme oxygenase-1 as well as Hsp70 and SOD-2. This effect was associated with upregulation of GSH levels, prevention of age-related changes in mitochondrial respiratory chain complex expression, and decrease in protein carbonyls and HNE formation. We hypothesize that maintenance or recovery of the activity of vitagenes may delay the aging process and decrease the risk of age-related diseases. Particularly, modulation of endogenous cellular defense mechanisms via acetyl-L-carnitine may represent an innovative approach to therapeutic intervention in diseases causing tissue damage, such as neurodegeneration.

P3-30 Altération du traitement phonologique et lexico-sémantique dans l’évolution de la maladie d’Alzheimer : une étude de cas multiples

Flexible language use requires coordinated functioning of two systems: conceptual representations and control. The interaction between the two systems can be observed when people are asked to match a word to a picture. Participants are slower and less accurate for related word-picture pairs (word: banana, picture: apple) relative to unrelated pairs (word: banjo, picture: apple). The mechanism underlying interference however is still unclear. We analyzed word-picture matching (WPM) performance of patients with stroke-induced lesions to the left-temporal (N = 5) or left-frontal cortex (N = 5) and matched controls (N = 12) using the drift diffusion model (DDM). In DDM, the process of making a decision is described as the stochastic accumulation of evidence towards a response. The parameters of the DDM model that characterize this process are decision threshold, drift rate, starting point and non-decision time, each of which bears cognitive interpretability. We compared the estimated model parameters from controls and patients to investigate the mechanisms of WPM interference. WPM performance in controls was explained by the amount of information needed to make a decision (decision threshold): a higher threshold was associated with related word-picture pairs relative to unrelated ones. No difference was found in the quality of the evidence (drift rate). This suggests an executive rather than semantic mechanism underlying WPM interference. Both patients with temporal and frontal lesions exhibited both increased drift rate and decision threshold for unrelated pairs relative to related ones. Left-frontal and temporal damage affected the computations required by WPM similarly, resulting in systematic deficits across lexical-semantic memory and executive functions. These results support a diverse but interactive role of lexical-semantic memory and semantic control mechanisms.

Stackelberg leadership in a dynamic duopoly with stochastic capital accumulation

I propose a dynamic duopoly model where firms enter simultaneously but compete hierarchically a la Stackelberg at each instant over time. They accumulate capacity through costly investment, with capital accumulation dynamics being affected by an additive shock the mean and variance of which are known. The main findings are the following. First, the Stackelberg game is uncontrollable by the leader; hence, it is time consistent. Second, the leader invests more than the follower; as a result, in the steady state, the leader’s capacity and profits are larger than the follower’s. Therefore, the present analysis does not confirm Gibrat’s Law, since the individual growth rate is determined by the timing of moves.

Hormetic Modulation of Aging and Longevity by Mild Heat Stress

Aging is characterized by a stochastic accumulation of molecular damage, progressive failure of maintenance and repair, and consequent onset of age-related diseases. Applying hormesis in aging research and therapy is based on the principle of stimulation of maintenance and repair pathways by repeated exposure to mild stress. In a series of experimental studies we have shown that repetitive mild heat stress has anti-aging hormetic effects on growth and various other cellular and biochemical characteristics of human skin fibroblasts undergoing aging in vitro. These effects include the maintenance of stress protein profiles, reduction in the accumulation of oxidatively and glycoxidatively damaged proteins, stimulation of the proteasomal activities for the degradation of abnormal proteins, improved cellular resistance to ethanol, hydrogen peroxide and ultraviolet-B rays, and enhanced levels of various antioxidant enzymes. Anti-aging hormetic effects of mild heat shock appear to be facilitated by reducing protein damage and protein aggregation by activating internal antioxidant, repair and degradation processes.

Statistical Mechanics: Undamaged ⇐-radiation-⇒ Damaged Atomic Lattice Density Evolution and Stochastic Deformation Functional

AbstractThe deformation kinematics for radiation damage response of bulk materials is presently semi-empirical and phenomenological based on a continuum mechanics supposition: there exists a function space of continuous functions to describe material displacement, strain, strain-rate metrics by using the mathematics of differential calculus. Existing data being assembled from tests on nano-length-scale(NLS) samples provide objective evidence that the continuum mechanics supposition is not an adequate generic mathematical description for radiation damage response in surface-dominated material structures at NLS. An alternative approach will be described that uses concepts and methods from classical statistical mechanics and describe deformation kinematics as a stochastic accumulation of discrete damage events at atomic lattice nano-length-scales. Although radiation damage deformation at a lattice length-scale in solids is mechanistically different from velocity scattering developed by Boltzmann for a kinetic theory of gases, the two problem areas are technically similar and in some simply cases there are useful mathematical analogs. The technical similarities and mathematical analogs will be used to define probability density functions (number per unit volume functions) for undamaged and damaged “size and size change” lattice species (similarity to a probability density function for atomic velocities in gas theory). In general, equations for undamaged and damaged lattice density function evolution are Boltzmann-type equations, which can be approximated and solved for simple cases of radiation induced material damage. Using a path integral approach and the two probability density functions, a stochastic functional will be derived for the relative deformation between any two arbitrary spatial points in a radiation damaged material. Given the relative deformation as an explicit functional of the undamaged and damaged lattice density functions, the kinematics metrics of relative velocity, strain, strain rate, etc., will also be functionals. In the case of radiation damage and annealing, the two lattice density functions are analog expressions to those commonly used to model “birth and death” population evolution.

A Ballistic Model of Choice Response Time.

Almost all models of response time (RT) use a stochastic accumulation process. To account for the benchmark RT phenomena, researchers have found it necessary to include between-trial variability in the starting point and/or the rate of accumulation, both in linear (R. Ratcliff & J. N. Rouder, 1998) and nonlinear (M. Usher & J. L. McClelland, 2001) models. The authors show that a ballistic (deterministic within-trial) model using a simplified version of M. Usher and J. L. McClelland's (2001) nonlinear accumulation process with between-trial variability in accumulation rate and starting point is capable of accounting for the benchmark behavioral phenomena. The authors successfully fit their model to R. Ratcliff and J. N. Rouder's (1998) data, which exhibit many of the benchmark phenomena.

Fast cooling of antiproton and radioactive ion beams in future storage rings at GSI

Key issues of the new accelerator facility proposed for GSI are production, fast cooling, and accumulation of intense secondary beams, antiprotons and rare isotopes (RI). Single primary bunches of 2×1013 protons at 29GeV and 1×1012 U28+-ions at 1GeV/u shall be delivered from the new, fast-ramped 100Tm-synchrotron SIS100. A large acceptance, reversible polarity collector ring is foreseen for fast RF debunching followed by fast stochastic pre-cooling in all phase planes. The envisaged total pre-cooling times are 4–5s for antiprotons at 3GeV and 0.5–1s for fully stripped RI at 740MeV/u. A separate accumulator ring RESR is provided for stochastic accumulation of antiprotons. The RI beams are transferred to a new experimental storage Ring NESR, where electron cooling (EC) is applied simultaneously to internal target and electron–ion collision experiments. For experiments with antiprotons, a special 50Tm storage ring HESR shall be equipped with internal target and EC up to 15GeV, optionally also with stochastic beam halo cooling. A maximum luminosity of 2×1032cm−2s−1 and an energy resolution of about 100keV at lower luminosity are main objectives of the HESR concept. Basic issues for the design of the storage ring complex are discussed.