Bogen, K T
2007-01-30
As reflected in the 2005 USEPA Guidelines for Cancer Risk Assessment, some chemical carcinogens may have a site-specific mode of action (MOA) that is dual, involving mutation in addition to cell-killing induced hyperplasia. Although genotoxicity may contribute to increased risk at all doses, the Guidelines imply that for dual MOA (DMOA) carcinogens, judgment be used to compare and assess results obtained using separate ''linear'' (genotoxic) vs. ''nonlinear'' (nongenotoxic) approaches to low-level risk extrapolation. However, the Guidelines allow the latter approach to be used only when evidence is sufficient to parameterize a biologically based model that reliably extrapolates risk to low levels of concern. The Guidelines thus effectively prevent MOA uncertainty from being characterized and addressed when data are insufficient to parameterize such a model, but otherwise clearly support a DMOA. A bounding factor approach--similar to that used in reference dose procedures for classic toxicity endpoints--can address MOA uncertainty in a way that avoids explicit modeling of low-dose risk as a function of administered or internal dose. Even when a ''nonlinear'' toxicokinetic model cannot be fully validated, implications of DMOA uncertainty on low-dose risk may be bounded with reasonable confidence when target tumor types happen to be extremely rare. This concept was illustrated for the rodent carcinogen naphthalene. Bioassay data, supplemental toxicokinetic data, and related physiologically based pharmacokinetic and 2-stage stochastic carcinogenesis modeling results all clearly indicate that naphthalene is a DMOA carcinogen. Plausibility bounds on rat-tumor-type specific DMOA-related uncertainty were obtained using a 2-stage model adapted to reflect the empirical link between genotoxic and cytotoxic effects of the most potent identified genotoxic naphthalene metabolites, 1,2- and 1,4-naphthoquinone. Resulting bounds each provided the basis for a corresponding
Bogen, K T
2007-05-11
A relatively simple, quantitative approach is proposed to address a specific, important gap in the appr approach recommended by the USEPA Guidelines for Cancer Risk Assessment to oach address uncertainty in carcinogenic mode of action of certain chemicals when risk is extrapolated from bioassay data. These Guidelines recognize that some chemical carcinogens may have a site-specific mode of action (MOA) that is dual, involving mutation in addition to cell-killing induced hyperplasia. Although genotoxicity may contribute to increased risk at all doses, the Guidelines imply that for dual MOA (DMOA) carcinogens, judgment be used to compare and assess results obtained using separate 'linear' (genotoxic) vs. 'nonlinear' (nongenotoxic) approaches to low low-level risk extrapolation. However, the Guidelines allow the latter approach to be used only when evidence is sufficient t to parameterize a biologically based model that reliably o extrapolates risk to low levels of concern. The Guidelines thus effectively prevent MOA uncertainty from being characterized and addressed when data are insufficient to parameterize such a model, but otherwise clearly support a DMOA. A bounding factor approach - similar to that used in reference dose procedures for classic toxicity endpoints - can address MOA uncertainty in a way that avoids explicit modeling of low low-dose risk as a function of administere administered or internal dose. Even when a 'nonlinear' toxicokinetic model cannot be fully validated, implications of DMOA uncertainty on low low-dose risk may be bounded with reasonable confidence when target tumor types happen to be extremely rare. This concept was i illustrated llustrated for a likely DMOA rodent carcinogen naphthalene, specifically to the issue of risk extrapolation from bioassay data on naphthalene naphthalene-induced nasal tumors in rats. Bioassay data, supplemental toxicokinetic data, and related physiologically based p pharmacokinetic and 2 harmacokinetic 2-stage
Stochastic elimination of cancer cells.
Michor, Franziska; Nowak, Martin A; Frank, Steven A; Iwasa, Yoh
2003-01-01
Tissues of multicellular organisms consist of stem cells and differentiated cells. Stem cells divide to produce new stem cells or differentiated cells. Differentiated cells divide to produce new differentiated cells. We show that such a tissue design can reduce the rate of fixation of mutations that increase the net proliferation rate of cells. It has, however, no consequence for the rate of fixation of neutral mutations. We calculate the optimum relative abundance of stem cells that minimizes the rate of generating cancer cells. There is a critical fraction of stem cell divisions that is required for a stochastic elimination ('wash out') of cancer cells. PMID:14561289
A stochastic model for immunotherapy of cancer
Baar, Martina; Coquille, Loren; Mayer, Hannah; Hölzel, Michael; Rogava, Meri; Tüting, Thomas; Bovier, Anton
2016-01-01
We propose an extension of a standard stochastic individual-based model in population dynamics which broadens the range of biological applications. Our primary motivation is modelling of immunotherapy of malignant tumours. In this context the different actors, T-cells, cytokines or cancer cells, are modelled as single particles (individuals) in the stochastic system. The main expansions of the model are distinguishing cancer cells by phenotype and genotype, including environment-dependent phenotypic plasticity that does not affect the genotype, taking into account the effects of therapy and introducing a competition term which lowers the reproduction rate of an individual in addition to the usual term that increases its death rate. We illustrate the new setup by using it to model various phenomena arising in immunotherapy. Our aim is twofold: on the one hand, we show that the interplay of genetic mutations and phenotypic switches on different timescales as well as the occurrence of metastability phenomena raise new mathematical challenges. On the other hand, we argue why understanding purely stochastic events (which cannot be obtained with deterministic models) may help to understand the resistance of tumours to therapeutic approaches and may have non-trivial consequences on tumour treatment protocols. This is supported through numerical simulations. PMID:27063839
Stochastic Gompertzian model for breast cancer growth process
NASA Astrophysics Data System (ADS)
Mazlan, Mazma Syahidatul Ayuni Binti; Rosli, Norhayati
2017-05-01
In this paper, a stochastic Gompertzian model is developed to describe the growth process of a breast cancer by incorporating the noisy behavior into a deterministic Gompertzian model. The prediction quality of the stochastic Gompertzian model is measured by comparing the simulated result with the clinical data of breast cancer growth. The kinetic parameters of the model are estimated via maximum likelihood procedure. 4-stage stochastic Runge-Kutta (SRK4) is used to simulate the sample path of the model. Low values of mean-square error (MSE) of stochastic model indicate good fits. It is shown that the stochastic Gompertzian model is adequate in explaining the breast cancer growth process compared to the deterministic model counterpart.
Gompertzian stochastic model with delay effect to cervical cancer growth
NASA Astrophysics Data System (ADS)
Mazlan, Mazma Syahidatul Ayuni binti; Rosli, Norhayati binti; Bahar, Arifah
2015-02-01
In this paper, a Gompertzian stochastic model with time delay is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of cervical cancer growth. Low values of Mean-Square Error (MSE) of Gompertzian stochastic model with delay effect indicate good fits.
Gompertzian stochastic model with delay effect to cervical cancer growth
Mazlan, Mazma Syahidatul Ayuni binti; Rosli, Norhayati binti; Bahar, Arifah
2015-02-03
In this paper, a Gompertzian stochastic model with time delay is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of cervical cancer growth. Low values of Mean-Square Error (MSE) of Gompertzian stochastic model with delay effect indicate good fits.
Hwang, Ji Young; Kim, Da Hee; Bae, Hyo Sook; Kim, Mi-La; Jung, Yong Wook; Yun, Bo Seong; Seong, Seok Ju; Shin, Eunah; Kim, Mi Kyoung
2017-05-01
The aim of this study was to evaluate the oncologic and pregnancy outcomes of combined oral medroxyprogesterone acetate (MPA)/levonorgestrel-intrauterine system (LNG-IUS) treatment in young women with grade 2-differentiated stage IA endometrial adenocarcinoma who wish to preserve fertility. We retrospectively reviewed the medical records of patients with grade 2 stage IA endometrial adenocarcinoma who had received fertility-sparing treatment at CHA Gangnam Medical Center between 2011 and 2015. All of the patients were treated with combined oral MPA (500 mg/d)/LNG-IUS, and follow-up dilatation and curettage were performed every 3 months. A total of 5 patients were included in the study. The mean age was 30.4 ± 5.3 years (range, 25-39 years). After a mean treatment duration of 11.0 ± 6.2 months (range, 6-18 months), complete response (CR) was shown in 3 of the 5 patients, with partial response (PR) in the other 2 patients. One case of recurrence was reported 14 months after achieving CR. This patient was treated again with combined oral MPA/LNG-IUS and achieved CR by 6 months. The average follow-up period was 44.4 ± 26.2 months (range, 12-71 months). There were no cases of progressive disease. No treatment-related complications arose. Combined oral MPA/LNG-IUS treatment is considered to be a reasonably effective fertility-sparing treatment of grade 2 stage IA endometrial cancer. Although our results are encouraging, it is preliminary and should be considered with experienced oncologists in well-defined protocol and with close follow-up.
Epigenetic stochasticity, nuclear structure and cancer: the implications for medicine.
Feinberg, A P
2014-07-01
The aim of this review is to summarize an evolution of thinking about the epigenetic basis of human cancer, from the earliest studies of altered DNA methylation in cancer to the modern comprehensive epigenomic era. Converging data from epigenetic studies of primary cancers and from experimental studies of chromatin in development and epithelial-mesenchymal transition suggest a role for epigenetic stochasticity as a driving force of cancer, with Darwinian selection of tumour cells at the expense of the host. This increased epigenetic stochasticity appears to be mediated by large-scale changes in DNA methylation and chromatin in domains associated with the nuclear lamina. The implications for diagnosis include the potential to identify stochastically disrupted progenitor cells years before cancer develops, and to target drugs to epigenetic drivers of gene expression instability rather than to mean effects per se. © 2014 The Association for the Publication of the Journal of Internal Medicine.
Epigenetic stochasticity, nuclear structure and cancer: the implications for medicine
Feinberg, Andrew P.
2014-01-01
The aim of this review is to summarize an evolution of thinking about the epigenetic basis of human cancer, from the earliest studies of altered DNA methylation in cancer to the modern comprehensive epigenomic era. Converging data from epigenetic studies of primary cancers and from experimental studies of chromatin in development and epithelial–mesenchymal transition suggest a role for epigenetic stochasticity as a driving force of cancer, with Darwinian selection of tumour cells at the expense of the host. This increased epigenetic stochasticity appears to be mediated by large-scale changes in DNA methylation and chromatin in domains associated with the nuclear lamina. The implications for diagnosis include the potential to identify stochastically disrupted progenitor cells years before cancer develops, and to target drugs to epigenetic drivers of gene expression instability rather than to mean effects per se. PMID:24635672
Cancer growth dynamics: stochastic models and noise induced effects
NASA Astrophysics Data System (ADS)
Spagnolo, B.; Fiasconaro, A.; Pizzolato, N.; Valenti, D.; Adorno, D. Persano; Caldara, P.; Ochab-Marcinek, A.; Gudowska-Nowak, E.
2009-04-01
In the framework of the Michaelis-Menten (MM) reaction kinetics, we analyze the cancer growth dynamics in the presence of the immune response. We found the coexistence of noise enhanced stability (NES) and resonant activation (RA) phenomena which act in an opposite way with respect to the extinction of the tumor. The role of the stochastic resonance (SR) in the case of weak cancer therapy has been analyzed. The evolutionary dynamics of a system of cancerous cells in a model of chronic myeloid leukemia (CML) is investigated by a Monte Carlo approach. We analyzed the effects of a targeted therapy on the evolutionary dynamics of normal, first-mutant and cancerous cell populations. We show how the patient response to the therapy changes when an high value of the mutation rate from healthy to cancerous cells is present. Our results are in agreement with clinical observations.
Second Cancers After Fractionated Radiotherapy: Stochastic Population Dynamics Effects
NASA Technical Reports Server (NTRS)
Sachs, Rainer K.; Shuryak, Igor; Brenner, David; Fakir, Hatim; Hahnfeldt, Philip
2007-01-01
When ionizing radiation is used in cancer therapy it can induce second cancers in nearby organs. Mainly due to longer patient survival times, these second cancers have become of increasing concern. Estimating the risk of solid second cancers involves modeling: because of long latency times, available data is usually for older, obsolescent treatment regimens. Moreover, modeling second cancers gives unique insights into human carcinogenesis, since the therapy involves administering well characterized doses of a well studied carcinogen, followed by long-term monitoring. In addition to putative radiation initiation that produces pre-malignant cells, inactivation (i.e. cell killing), and subsequent cell repopulation by proliferation can be important at the doses relevant to second cancer situations. A recent initiation/inactivation/proliferation (IIP) model characterized quantitatively the observed occurrence of second breast and lung cancers, using a deterministic cell population dynamics approach. To analyze ifradiation-initiated pre-malignant clones become extinct before full repopulation can occur, we here give a stochastic version of this I I model. Combining Monte Carlo simulations with standard solutions for time-inhomogeneous birth-death equations, we show that repeated cycles of inactivation and repopulation, as occur during fractionated radiation therapy, can lead to distributions of pre-malignant cells per patient with variance >> mean, even when pre-malignant clones are Poisson-distributed. Thus fewer patients would be affected, but with a higher probability, than a deterministic model, tracking average pre-malignant cell numbers, would predict. Our results are applied to data on breast cancers after radiotherapy for Hodgkin disease. The stochastic IIP analysis, unlike the deterministic one, indicates: a) initiated, pre-malignant cells can have a growth advantage during repopulation, not just during the longer tumor latency period that follows; b) weekend
Second Cancers After Fractionated Radiotherapy: Stochastic Population Dynamics Effects
NASA Technical Reports Server (NTRS)
Sachs, Rainer K.; Shuryak, Igor; Brenner, David; Fakir, Hatim; Hahnfeldt, Philip
2007-01-01
When ionizing radiation is used in cancer therapy it can induce second cancers in nearby organs. Mainly due to longer patient survival times, these second cancers have become of increasing concern. Estimating the risk of solid second cancers involves modeling: because of long latency times, available data is usually for older, obsolescent treatment regimens. Moreover, modeling second cancers gives unique insights into human carcinogenesis, since the therapy involves administering well characterized doses of a well studied carcinogen, followed by long-term monitoring. In addition to putative radiation initiation that produces pre-malignant cells, inactivation (i.e. cell killing), and subsequent cell repopulation by proliferation can be important at the doses relevant to second cancer situations. A recent initiation/inactivation/proliferation (IIP) model characterized quantitatively the observed occurrence of second breast and lung cancers, using a deterministic cell population dynamics approach. To analyze ifradiation-initiated pre-malignant clones become extinct before full repopulation can occur, we here give a stochastic version of this I I model. Combining Monte Carlo simulations with standard solutions for time-inhomogeneous birth-death equations, we show that repeated cycles of inactivation and repopulation, as occur during fractionated radiation therapy, can lead to distributions of pre-malignant cells per patient with variance >> mean, even when pre-malignant clones are Poisson-distributed. Thus fewer patients would be affected, but with a higher probability, than a deterministic model, tracking average pre-malignant cell numbers, would predict. Our results are applied to data on breast cancers after radiotherapy for Hodgkin disease. The stochastic IIP analysis, unlike the deterministic one, indicates: a) initiated, pre-malignant cells can have a growth advantage during repopulation, not just during the longer tumor latency period that follows; b) weekend
Detecting breast cancer using microwave imaging and stochastic optimization.
Jeremic, Aleksandar; Khoshrowshahli, Elham
2015-01-01
Breast cancer detection is one of the most important problems in health care as it is second most frequent cancer according to WHO. Breast cancer is among cancers which are most probably curable, only if it is diagnosed at early stages. To this purpose it has been recently proposed that microwave imaging could be used as a cheaper and safer alternative to the commonly used combination of mammography. From a physical standpoint breast cancer can be modelled as a scatterer with a significantly (tenfold) larger conductivity than a healthy tissue. In our previous work we proposed a maximum likelihood based method for detection of cancer which estimates the unknown parameters by minimizing the residual error vector assuming that the error can be modelled as a multivariate (multiple antennas) random variable. In this paper we utilize stochastic optimization technique and evaluate its applicability to the detection of cancer using numerical models. Although these models have significant limitations they are potentially useful as they provide insight in required levels of noise in order to achieve desirable detection rates.
Kerns, Sarah L.; Stock, Richard; Stone, Nelson; Buckstein, Michael; Shao, Yongzhao; Campbell, Christopher; Rath, Lynda; De Ruysscher, Dirk; Lammering, Guido; Hixson, Rosetta; Cesaretti, Jamie; Terk, Mitchell; Ostrer, Harry; Rosenstein, Barry S.
2013-01-01
Purpose: To identify single nucleotide polymorphisms (SNPs) associated with development of erectile dysfunction (ED) among prostate cancer patients treated with radiation therapy. Methods and Materials: A 2-stage genome-wide association study was performed. Patients were split randomly into a stage I discovery cohort (132 cases, 103 controls) and a stage II replication cohort (128 cases, 102 controls). The discovery cohort was genotyped using Affymetrix 6.0 genome-wide arrays. The 940 top ranking SNPs selected from the discovery cohort were genotyped in the replication cohort using Illumina iSelect custom SNP arrays. Results: Twelve SNPs identified in the discovery cohort and validated in the replication cohort were associated with development of ED following radiation therapy (Fisher combined P values 2.1 Multiplication-Sign 10{sup -5} to 6.2 Multiplication-Sign 10{sup -4}). Notably, these 12 SNPs lie in or near genes involved in erectile function or other normal cellular functions (adhesion and signaling) rather than DNA damage repair. In a multivariable model including nongenetic risk factors, the odds ratios for these SNPs ranged from 1.6 to 5.6 in the pooled cohort. There was a striking relationship between the cumulative number of SNP risk alleles an individual possessed and ED status (Sommers' D P value = 1.7 Multiplication-Sign 10{sup -29}). A 1-allele increase in cumulative SNP score increased the odds for developing ED by a factor of 2.2 (P value = 2.1 Multiplication-Sign 10{sup -19}). The cumulative SNP score model had a sensitivity of 84% and specificity of 75% for prediction of developing ED at the radiation therapy planning stage. Conclusions: This genome-wide association study identified a set of SNPs that are associated with development of ED following radiation therapy. These candidate genetic predictors warrant more definitive validation in an independent cohort.
Kerns, Sarah L; Stone, Nelson N; Stock, Richard G; Rath, Lynda; Ostrer, Harry; Rosenstein, Barry S
2013-07-01
We identified single nucleotide polymorphisms associated with change in the AUA Symptom Score after radiotherapy for prostate cancer. A total of 723 patients treated with brachytherapy with or without external beam radiation therapy were assessed at baseline and annually after radiotherapy using the AUA Symptom Score. A 2-stage genome-wide association study was performed with the primary end point of change in AUA Symptom Score from baseline at each of 4 followup periods. Single nucleotide polymorphism associations were assessed using multivariable linear regression adjusting for pre-radiotherapy AUA Symptom Score severity category and clinical variables. Fisher's trend method was used to calculate combined p values from the discovery and replication cohorts. A region on chromosome 9p21.2 containing 8 single nucleotide polymorphisms showed the strongest association with change in AUA Symptom Score (combined p values 8.8×10(-6) to 6.5×10(-7) at 2 to 3 years after radiotherapy). These single nucleotide polymorphisms form a haplotype block that encompasses the inflammation signaling gene IFNK. These single nucleotide polymorphisms were independently associated with change in AUA Symptom Score after adjusting for clinical predictors including smoking history, hypertension, α-blocker use and pre-radiotherapy AUA Symptom Score. An additional 24 single nucleotide polymorphisms showed moderate significance for association with change in AUA Symptom Score. Several of these single nucleotide polymorphisms were more strongly associated with change in specific AUA Symptom Score items, including rs13035033 in the MYO3B gene, which was associated with straining (beta coefficient 0.9, 95% CI 0.6-1.2, p = 5.0×10(-9)). If validated, these single nucleotide polymorphisms could provide insight into the biology underlying urinary symptoms following radiotherapy and could lead to development of an assay to identify patients at risk for experiencing these effects. Copyright © 2013
NASA Astrophysics Data System (ADS)
Syahidatul Ayuni Mazlan, Mazma; Rosli, Norhayati; Jauhari Arief Ichwan, Solachuddin; Suhaity Azmi, Nina
2017-09-01
A stochastic model is introduced to describe the growth of cancer affected by anti-cancer therapeutics of Chondroitin Sulfate (CS). The parameters values of the stochastic model are estimated via maximum likelihood function. The numerical method of Euler-Maruyama will be employed to solve the model numerically. The efficiency of the stochastic model is measured by comparing the simulated result with the experimental data.
Doubly stochastic (pseudo)gene expression in the regulation of cancer
NASA Astrophysics Data System (ADS)
Petrosyan, K. G.; Hu, Chin-Kun
2017-08-01
We extend a model of the regulation of cancer by gene and pseudogene messenger RNAs to take into account cell-to-cell variability. This introduces an additional randomness to the intensity of the intracellular noise. The intracellular stochasticity is modelled via an additive white noise source and the intercellular stochasticity, or randomness, is modelled via a steady-state Γ -distribution for the intracellular noise intensity. The doubly stochastic process is treated numerically and displays a difference compared with the single stochastic (pseudo)gene expression process, which is the randomness-induced shift of the onset of even-odd oscillations in the number of molecules. Similarities to experimental outcomes in the related literature are pointed out.
Wang, Weikang; Quan, Yi; Fu, Qibin; Liu, Yu; Liang, Ying; Wu, Jingwen; Yang, Gen; Luo, Chunxiong; Ouyang, Qi; Wang, Yugang
2014-01-01
Tumors are often heterogeneous in which tumor cells of different phenotypes have distinct properties. For scientific and clinical interests, it is of fundamental importance to understand their properties and the dynamic variations among different phenotypes, specifically under radio- and/or chemo-therapy. Currently there are two controversial models describing tumor heterogeneity, the cancer stem cell (CSC) model and the stochastic model. To clarify the controversy, we measured probabilities of different division types and transitions of cells via in situ immunofluorescence. Based on the experiment data, we constructed a model that combines the CSC with the stochastic concepts, showing the existence of both distinctive CSC subpopulations and the stochastic transitions from NSCCs to CSCs. The results showed that the dynamic variations between CSCs and non-stem cancer cells (NSCCs) can be simulated with the model. Further studies also showed that the model can be used to describe the dynamics of the two subpopulations after radiation treatment. More importantly, analysis demonstrated that the experimental detectable equilibrium CSC proportion can be achieved only when the stochastic transitions from NSCCs to CSCs occur, indicating that tumor heterogeneity may exist in a model coordinating with both the CSC and the stochastic concepts. The mathematic model based on experimental parameters may contribute to a better understanding of the tumor heterogeneity, and provide references on the dynamics of CSC subpopulation during radiotherapy. PMID:24416258
Stochastic Effects in Computational Biology of Space Radiation Cancer Risk
NASA Technical Reports Server (NTRS)
Cucinotta, Francis A.; Pluth, Janis; Harper, Jane; O'Neill, Peter
2007-01-01
Estimating risk from space radiation poses important questions on the radiobiology of protons and heavy ions. We are considering systems biology models to study radiation induced repair foci (RIRF) at low doses, in which less than one-track on average transverses the cell, and the subsequent DNA damage processing and signal transduction events. Computational approaches for describing protein regulatory networks coupled to DNA and oxidative damage sites include systems of differential equations, stochastic equations, and Monte-Carlo simulations. We review recent developments in the mathematical description of protein regulatory networks and possible approaches to radiation effects simulation. These include robustness, which states that regulatory networks maintain their functions against external and internal perturbations due to compensating properties of redundancy and molecular feedback controls, and modularity, which leads to general theorems for considering molecules that interact through a regulatory mechanism without exchange of matter leading to a block diagonal reduction of the connecting pathways. Identifying rate-limiting steps, robustness, and modularity in pathways perturbed by radiation damage are shown to be valid techniques for reducing large molecular systems to realistic computer simulations. Other techniques studied are the use of steady-state analysis, and the introduction of composite molecules or rate-constants to represent small collections of reactants. Applications of these techniques to describe spatial and temporal distributions of RIRF and cell populations following low dose irradiation are described.
Stochastic Effects in Computational Biology of Space Radiation Cancer Risk
NASA Technical Reports Server (NTRS)
Cucinotta, Francis A.; Pluth, Janis; Harper, Jane; O'Neill, Peter
2007-01-01
Estimating risk from space radiation poses important questions on the radiobiology of protons and heavy ions. We are considering systems biology models to study radiation induced repair foci (RIRF) at low doses, in which less than one-track on average transverses the cell, and the subsequent DNA damage processing and signal transduction events. Computational approaches for describing protein regulatory networks coupled to DNA and oxidative damage sites include systems of differential equations, stochastic equations, and Monte-Carlo simulations. We review recent developments in the mathematical description of protein regulatory networks and possible approaches to radiation effects simulation. These include robustness, which states that regulatory networks maintain their functions against external and internal perturbations due to compensating properties of redundancy and molecular feedback controls, and modularity, which leads to general theorems for considering molecules that interact through a regulatory mechanism without exchange of matter leading to a block diagonal reduction of the connecting pathways. Identifying rate-limiting steps, robustness, and modularity in pathways perturbed by radiation damage are shown to be valid techniques for reducing large molecular systems to realistic computer simulations. Other techniques studied are the use of steady-state analysis, and the introduction of composite molecules or rate-constants to represent small collections of reactants. Applications of these techniques to describe spatial and temporal distributions of RIRF and cell populations following low dose irradiation are described.
Moderate stem-cell telomere shortening rate postpones cancer onset in a stochastic model
NASA Astrophysics Data System (ADS)
Holbek, Simon; Bendtsen, Kristian Moss; Juul, Jeppe
2013-10-01
Mammalian cells are restricted from proliferating indefinitely. Telomeres at the end of each chromosome are shortened at cell division and when they reach a critical length, the cell will enter permanent cell cycle arrest—a state known as senescence. This mechanism is thought to be tumor suppressing, as it helps prevent precancerous cells from dividing uncontrollably. Stem cells express the enzyme telomerase, which elongates the telomeres, thereby postponing senescence. However, unlike germ cells and most types of cancer cells, stem cells only express telomerase at levels insufficient to fully maintain the length of their telomeres, leading to a slow decline in proliferation potential. It is not yet fully understood how this decline influences the risk of cancer and the longevity of the organism. We here develop a stochastic model to explore the role of telomere dynamics in relation to both senescence and cancer. The model describes the accumulation of cancerous mutations in a multicellular organism and creates a coherent theoretical framework for interpreting the results of several recent experiments on telomerase regulation. We demonstrate that the longest average cancer-free lifespan before cancer onset is obtained when stem cells start with relatively long telomeres that are shortened at a steady rate at cell division. Furthermore, the risk of cancer early in life can be reduced by having a short initial telomere length. Finally, our model suggests that evolution will favor a shorter than optimal average cancer-free lifespan in order to postpone cancer onset until late in life.
Moderate stem-cell telomere shortening rate postpones cancer onset in a stochastic model.
Holbek, Simon; Bendtsen, Kristian Moss; Juul, Jeppe
2013-10-01
Mammalian cells are restricted from proliferating indefinitely. Telomeres at the end of each chromosome are shortened at cell division and when they reach a critical length, the cell will enter permanent cell cycle arrest-a state known as senescence. This mechanism is thought to be tumor suppressing, as it helps prevent precancerous cells from dividing uncontrollably. Stem cells express the enzyme telomerase, which elongates the telomeres, thereby postponing senescence. However, unlike germ cells and most types of cancer cells, stem cells only express telomerase at levels insufficient to fully maintain the length of their telomeres, leading to a slow decline in proliferation potential. It is not yet fully understood how this decline influences the risk of cancer and the longevity of the organism. We here develop a stochastic model to explore the role of telomere dynamics in relation to both senescence and cancer. The model describes the accumulation of cancerous mutations in a multicellular organism and creates a coherent theoretical framework for interpreting the results of several recent experiments on telomerase regulation. We demonstrate that the longest average cancer-free lifespan before cancer onset is obtained when stem cells start with relatively long telomeres that are shortened at a steady rate at cell division. Furthermore, the risk of cancer early in life can be reduced by having a short initial telomere length. Finally, our model suggests that evolution will favor a shorter than optimal average cancer-free lifespan in order to postpone cancer onset until late in life.
Low-Let-Induced Radioprotective Mechanisms Within a Stochastic Two-Stage Cancer Model
Schöllnberger, H.; Stewart, R.D.; Mitchel, R.E.J.
2005-01-01
A stochastic two-stage cancer model with clonal expansion was used to investigate the potential impact on human lung cancer incidence of some aspects of the hormesis mechanisms suggested by Feinendegen (Health Phys. 52 663–669, 1987). The model was applied to low doses of low-LET radiation delivered at low dose rates. Non-linear responses arise in the model because radiologically induced adaptations in radical scavenging and DNA repair may reduce the biological consequences of DNA damage formed by endogenous processes and ionizing radiation. Sensitivity studies were conducted to identify critical model inputs and to help define the changes in cellular defense mechanisms necessary to produce a lifetime probability for lung cancer that deviates from a linear no-threshold (LNT) type of response. Our studies suggest that lung cancer risk predictions may be very sensitive to the induction of DNA damage by endogenous processes. For doses comparable to background radiation levels, endogenous DNA damage may account for as much as 50 to 80% of the predicted lung cancers. For an additional lifetime dose of 1 Gy from low-LET radiation, endogenous processes may still account for as much as 20% of the predicted cancers (Fig. 2). When both repair and scavengers are considered as inducible, radiation must enhance DNA repair and radical scavenging in excess of 30 to 40% of the baseline values to produce lifetime probabilities for lung cancer outside the range expected for endogenous processes and background radiation. PMID:18648628
A unified model of the hierarchical and stochastic theories of gastric cancer
Song, Yanjing; Wang, Yao; Tong, Chuan; Xi, Hongqing; Zhao, Xudong; Wang, Yi; Chen, Lin
2017-01-01
Gastric cancer (GC) is a life-threatening disease worldwide. Despite remarkable advances in treatments for GC, it is still fatal to many patients due to cancer progression, recurrence and metastasis. Regarding the development of novel therapeutic techniques, many studies have focused on the biological mechanisms that initiate tumours and cause treatment resistance. Tumours have traditionally been considered to result from somatic mutations, either via clonal evolution or through a stochastic model. However, emerging evidence has characterised tumours using a hierarchical organisational structure, with cancer stem cells (CSCs) at the apex. Both stochastic and hierarchical models are reasonable systems that have been hypothesised to describe tumour heterogeneity. Although each model alone inadequately explains tumour diversity, the two models can be integrated to provide a more comprehensive explanation. In this review, we discuss existing evidence supporting a unified model of gastric CSCs, including the regulatory mechanisms of this unified model in addition to the current status of stemness-related targeted therapy in GC patients. PMID:28301871
A unified model of the hierarchical and stochastic theories of gastric cancer.
Song, Yanjing; Wang, Yao; Tong, Chuan; Xi, Hongqing; Zhao, Xudong; Wang, Yi; Chen, Lin
2017-04-11
Gastric cancer (GC) is a life-threatening disease worldwide. Despite remarkable advances in treatments for GC, it is still fatal to many patients due to cancer progression, recurrence and metastasis. Regarding the development of novel therapeutic techniques, many studies have focused on the biological mechanisms that initiate tumours and cause treatment resistance. Tumours have traditionally been considered to result from somatic mutations, either via clonal evolution or through a stochastic model. However, emerging evidence has characterised tumours using a hierarchical organisational structure, with cancer stem cells (CSCs) at the apex. Both stochastic and hierarchical models are reasonable systems that have been hypothesised to describe tumour heterogeneity. Although each model alone inadequately explains tumour diversity, the two models can be integrated to provide a more comprehensive explanation. In this review, we discuss existing evidence supporting a unified model of gastric CSCs, including the regulatory mechanisms of this unified model in addition to the current status of stemness-related targeted therapy in GC patients.
Little, Mark P; Vineis, Paolo; Li, Guangquan
2008-09-21
A generalization of the two-mutation stochastic carcinogenesis model of Moolgavkar, Venzon and Knudson and certain models constructed by Little [Little, M.P. (1995). Are two mutations sufficient to cause cancer? Some generalizations of the two-mutation model of carcinogenesis of Moolgavkar, Venzon, and Knudson, and of the multistage model of Armitage and Doll. Biometrics 51, 1278-1291] and Little and Wright [Little, M.P., Wright, E.G. (2003). A stochastic carcinogenesis model incorporating genomic instability fitted to colon cancer data. Math. Biosci. 183, 111-134] is developed; the model incorporates multiple types of progressive genomic instability and an arbitrary number of mutational stages. The model is fitted to US Caucasian colon cancer incidence data. On the basis of the comparison of fits to the population-based data, there is little evidence to support the hypothesis that the model with more than one type of genomic instability fits better than models with a single type of genomic instability. Given the good fit of the model to this large dataset, it is unlikely that further information on presence of genomic instability or of types of genomic instability can be extracted from age-incidence data by extensions of this model.
Warren, Patrick B
2009-09-01
A recently proposed model for skin cell proliferation [E. Clayton, Nature (London) 446, 185 (2007)] is extended to incorporate mitotic autoregulation, and hence homeostasis as a fixed point of the dynamics. Unlimited cell proliferation in such a model can be viewed as a model for carcinogenesis. One way in which this can arise is homeostatic metastability, in which the cell populations escape from the homeostatic basin of attraction by a large but rare stochastic fluctuation. Such an event can be viewed as the final step in a multistage model of carcinogenesis. Homeostatic metastability offers a possible explanation for the peculiar epidemiology of lung cancer in ex-smokers.
NASA Astrophysics Data System (ADS)
Warren, Patrick B.
2009-09-01
A recently proposed model for skin cell proliferation [E. Clayton , Nature (London) 446, 185 (2007)] is extended to incorporate mitotic autoregulation, and hence homeostasis as a fixed point of the dynamics. Unlimited cell proliferation in such a model can be viewed as a model for carcinogenesis. One way in which this can arise is homeostatic metastability, in which the cell populations escape from the homeostatic basin of attraction by a large but rare stochastic fluctuation. Such an event can be viewed as the final step in a multistage model of carcinogenesis. Homeostatic metastability offers a possible explanation for the peculiar epidemiology of lung cancer in ex-smokers.
NASA Astrophysics Data System (ADS)
Zamani Dahaj, Seyed Alireza; Kumar, Niraj; Sundaram, Bala; Celli, Jonathan; Kulkarni, Rahul
The phenotypic heterogeneity of cancer cells is critical to their survival under stress. A significant contribution to heterogeneity of cancer calls derives from the epithelial-mesenchymal transition (EMT), a conserved cellular program that is crucial for embryonic development. Several studies have investigated the role of EMT in growth of early stage tumors into invasive malignancies. Also, EMT has been closely associated with the acquisition of chemoresistance properties in cancer cells. Motivated by these studies, we analyze multi-phenotype stochastic models of the evolution of cancers cell populations under stress. We derive analytical results for time-dependent probability distributions that provide insights into the competing rates underlying phenotypic switching (e.g. during EMT) and the corresponding survival of cancer cells. Experimentally, we evaluate these model-based predictions by imaging human pancreatic cancer cell lines grown with and without cytotoxic agents and measure growth kinetics, survival, morphological changes and (terminal evaluation of) biomarkers with associated epithelial and mesenchymal phenotypes. The results derived suggest approaches for distinguishing between adaptation and selection scenarios for survival in the presence of external stresses.
Figueredo, Grazziela P; Siebers, Peer-Olaf; Owen, Markus R; Reps, Jenna; Aickelin, Uwe
2014-01-01
There is great potential to be explored regarding the use of agent-based modelling and simulation as an alternative paradigm to investigate early-stage cancer interactions with the immune system. It does not suffer from some limitations of ordinary differential equation models, such as the lack of stochasticity, representation of individual behaviours rather than aggregates and individual memory. In this paper we investigate the potential contribution of agent-based modelling and simulation when contrasted with stochastic versions of ODE models using early-stage cancer examples. We seek answers to the following questions: (1) Does this new stochastic formulation produce similar results to the agent-based version? (2) Can these methods be used interchangeably? (3) Do agent-based models outcomes reveal any benefit when compared to the Gillespie results? To answer these research questions we investigate three well-established mathematical models describing interactions between tumour cells and immune elements. These case studies were re-conceptualised under an agent-based perspective and also converted to the Gillespie algorithm formulation. Our interest in this work, therefore, is to establish a methodological discussion regarding the usability of different simulation approaches, rather than provide further biological insights into the investigated case studies. Our results show that it is possible to obtain equivalent models that implement the same mechanisms; however, the incapacity of the Gillespie algorithm to retain individual memory of past events affects the similarity of some results. Furthermore, the emergent behaviour of ABMS produces extra patters of behaviour in the system, which was not obtained by the Gillespie algorithm.
A stochastic carcinogenesis model incorporating genomic instability fitted to colon cancer data.
Little, M P; Wright, E G
2003-06-01
A generalization of the two-mutation stochastic carcinogenesis model of Moolgavkar, Venzon and Knudson and certain models constructed by Little is developed; the model incorporates progressive genomic instability and an arbitrary number of mutational stages. This model is shown to have the property that, at least in the case when the parameters of the model are eventually constant, the excess relative and absolute cancer rates following changes in any of the parameters will eventually tend to zero. It is also shown that when the parameters governing the processes of cell division, death, or additional mutation (whether of the normal sort or that resulting in genomic destabilization) at the penultimate stage are subject to perturbations, there are relatively large fluctuations in the hazard function for the model, which start almost as soon as the parameters are changed. The model is fitted to US Caucasian colon cancer incidence data. A model with five stages and two levels of genomic destabilization fits the data well. Comparison with patterns of excess risk in the Japanese atomic bomb survivor colon cancer incidence data indicate that radiation might act on early mutation rates in the model; a major role for radiation in initiating genomic destabilization is less likely.
Stochasticity in physiologically based kinetics models: implications for cancer risk assessment.
Péry, Alexandre Roger Raymond; Bois, Frederic Yves
2009-08-01
In case of low-dose exposure to a substance, its concentration in cells is likely to be stochastic. Assessing the consequences of this stochasticity in toxicological risk assessment requires the coupling of macroscopic dynamics models describing whole-body kinetics with microscopic tools designed to simulate stochasticity. In this article, we propose an approach to approximate stochastic cell concentration of butadiene in the cells of diverse organs. We adapted the dynamics equations of a physiologically based pharmacokinetic (PBPK) model and used a stochastic simulator for the system of equations that we derived. We then coupled kinetics simulations with a deterministic hockey stick model of carcinogenicity. Stochasticity induced substantial modifications relative to dose-response curve, compared with the deterministic situation. In particular, there was nonlinearity in the response and the stochastic apparent threshold was lower than the deterministic one. The approach that we developed could easily be extended to other biological studies to assess the influence of stochasticity at macroscopic scale for compound dynamics at the cell level.
Hermann, Philipp; Mrkvička, Tomáš; Mattfeldt, Torsten; Minárová, Mária; Helisová, Kateřina; Nicolis, Orietta; Wartner, Fabian; Stehlík, Milan
2015-08-15
Fractals are models of natural processes with many applications in medicine. The recent studies in medicine show that fractals can be applied for cancer detection and the description of pathological architecture of tumors. This fact is not surprising, as due to the irregular structure, cancerous cells can be interpreted as fractals. Inspired by Sierpinski carpet, we introduce a flexible parametric model of random carpets. Randomization is introduced by usage of binomial random variables. We provide an algorithm for estimation of parameters of the model and illustrate theoretical and practical issues in generation of Sierpinski gaskets and Hausdorff measure calculations. Stochastic geometry models can also serve as models for binary cancer images. Recently, a Boolean model was applied on the 200 images of mammary cancer tissue and 200 images of mastopathic tissue. Here, we describe the Quermass-interaction process, which can handle much more variations in the cancer data, and we apply it to the images. It was found out that mastopathic tissue deviates significantly stronger from Quermass-interaction process, which describes interactions among particles, than mammary cancer tissue does. The Quermass-interaction process serves as a model describing the tissue, which structure is broken to a certain level. However, random fractal model fits well for mastopathic tissue. We provide a novel discrimination method between mastopathic and mammary cancer tissue on the basis of complex wavelet-based self-similarity measure with classification rates more than 80%. Such similarity measure relates to Hurst exponent and fractional Brownian motions. The R package FractalParameterEstimation is developed and introduced in the paper.
Analysis of retinoblastoma age incidence data using a fully stochastic cancer model.
Little, Mark P; Kleinerman, Ruth A; Stiller, Charles A; Li, Guangquan; Kroll, Mary E; Murphy, Michael F G
2012-02-01
Retinoblastoma (RB) is an important ocular malignancy of childhood. It has been commonly accepted for some time that knockout of the two alleles of the RB1 gene is the principal molecular target associated with the occurrence of RB. In this article, we examine the validity of the two-hit theory for RB by comparing the fit of a stochastic model with two or more mutational stages. Unlike many such models, our model assumes a fully stochastic stem cell compartment, which is crucial to its behavior. Models are fitted to a population-based dataset comprising 1,553 cases of RB for the period 1962-2000 in Great Britain (England, Scotland and Wales). The population incidence of RB is best described by a fully stochastic model with two stages, although models with a deterministic stem cell compartment yield equivalent fit; models with three or more stages fit much less well. The results strongly suggest that knockout of the two alleles of the RB1 gene is necessary and may be largely sufficient for the development of RB, in support of Knudson's two-hit hypothesis.
Stochastic tunneling and metastable states during the somatic evolution of cancer.
Ashcroft, Peter; Michor, Franziska; Galla, Tobias
2015-04-01
Tumors initiate when a population of proliferating cells accumulates a certain number and type of genetic and/or epigenetic alterations. The population dynamics of such sequential acquisition of (epi)genetic alterations has been the topic of much investigation. The phenomenon of stochastic tunneling, where an intermediate mutant in a sequence does not reach fixation in a population before generating a double mutant, has been studied using a variety of computational and mathematical methods. However, the field still lacks a comprehensive analytical description since theoretical predictions of fixation times are available only for cases in which the second mutant is advantageous. Here, we study stochastic tunneling in a Moran model. Analyzing the deterministic dynamics of large populations we systematically identify the parameter regimes captured by existing approaches. Our analysis also reveals fitness landscapes and mutation rates for which finite populations are found in long-lived metastable states. These are landscapes in which the final mutant is not the most advantageous in the sequence, and resulting metastable states are a consequence of a mutation-selection balance. The escape from these states is driven by intrinsic noise, and their location affects the probability of tunneling. Existing methods no longer apply. In these regimes it is the escape from the metastable states that is the key bottleneck; fixation is no longer limited by the emergence of a successful mutant lineage. We used the so-called Wentzel-Kramers-Brillouin method to compute fixation times in these parameter regimes, successfully validated by stochastic simulations. Our work fills a gap left by previous approaches and provides a more comprehensive description of the acquisition of multiple mutations in populations of somatic cells. Copyright © 2015 by the Genetics Society of America.
Producing a functional eukaryotic messenger RNA (mRNA) requires the coordinated activity of several large protein complexes to initiate transcription, elongate nascent transcripts, splice together exons, and cleave and polyadenylate the 3’ end. Kinetic competition between these various processes has been proposed to regulate mRNA maturation, but this model could lead to multiple, randomly determined, or stochastic, pathways or outcomes. Regulatory checkpoints have been suggested as a means of ensuring quality control. However, current methods have been unable to tease apart the contributions of these processes at a single gene or on a time scale that could provide mechanistic insight. To begin to investigate the kinetic relationship between transcription and splicing, Daniel Larson, Ph.D., of CCR’s Laboratory of Receptor Biology and Gene Expression, and his colleagues employed a single-molecule RNA imaging approach to monitor production and processing of a human β-globin reporter gene in living cells.
A stochastic model for tumor geometry evolution during radiation therapy in cervical cancer
Liu, Yifang; Lee, Chi-Guhn; Chan, Timothy C. Y.; Cho, Young-Bin; Islam, Mohammad K.
2014-02-15
Purpose: To develop mathematical models to predict the evolution of tumor geometry in cervical cancer undergoing radiation therapy. Methods: The authors develop two mathematical models to estimate tumor geometry change: a Markov model and an isomorphic shrinkage model. The Markov model describes tumor evolution by investigating the change in state (either tumor or nontumor) of voxels on the tumor surface. It assumes that the evolution follows a Markov process. Transition probabilities are obtained using maximum likelihood estimation and depend on the states of neighboring voxels. The isomorphic shrinkage model describes tumor shrinkage or growth in terms of layers of voxels on the tumor surface, instead of modeling individual voxels. The two proposed models were applied to data from 29 cervical cancer patients treated at Princess Margaret Cancer Centre and then compared to a constant volume approach. Model performance was measured using sensitivity and specificity. Results: The Markov model outperformed both the isomorphic shrinkage and constant volume models in terms of the trade-off between sensitivity (target coverage) and specificity (normal tissue sparing). Generally, the Markov model achieved a few percentage points in improvement in either sensitivity or specificity compared to the other models. The isomorphic shrinkage model was comparable to the Markov approach under certain parameter settings. Convex tumor shapes were easier to predict. Conclusions: By modeling tumor geometry change at the voxel level using a probabilistic model, improvements in target coverage and normal tissue sparing are possible. Our Markov model is flexible and has tunable parameters to adjust model performance to meet a range of criteria. Such a model may support the development of an adaptive paradigm for radiation therapy of cervical cancer.
Solan, Eilon; Vieille, Nicolas
2015-01-01
In 1953, Lloyd Shapley contributed his paper “Stochastic games” to PNAS. In this paper, he defined the model of stochastic games, which were the first general dynamic model of a game to be defined, and proved that it admits a stationary equilibrium. In this Perspective, we summarize the historical context and the impact of Shapley’s contribution. PMID:26556883
2–stage stochastic Runge–Kutta for stochastic delay differential equations
Rosli, Norhayati; Jusoh Awang, Rahimah; Bahar, Arifah; Yeak, S. H.
2015-05-15
This paper proposes a newly developed one-step derivative-free method, that is 2-stage stochastic Runge-Kutta (SRK2) to approximate the solution of stochastic delay differential equations (SDDEs) with a constant time lag, r > 0. General formulation of stochastic Runge-Kutta for SDDEs is introduced and Stratonovich Taylor series expansion for numerical solution of SRK2 is presented. Local truncation error of SRK2 is measured by comparing the Stratonovich Taylor expansion of the exact solution with the computed solution. Numerical experiment is performed to assure the validity of the method in simulating the strong solution of SDDEs.
NASA Astrophysics Data System (ADS)
Eichhorn, Ralf; Aurell, Erik
2014-04-01
'Stochastic thermodynamics as a conceptual framework combines the stochastic energetics approach introduced a decade ago by Sekimoto [1] with the idea that entropy can consistently be assigned to a single fluctuating trajectory [2]'. This quote, taken from Udo Seifert's [3] 2008 review, nicely summarizes the basic ideas behind stochastic thermodynamics: for small systems, driven by external forces and in contact with a heat bath at a well-defined temperature, stochastic energetics [4] defines the exchanged work and heat along a single fluctuating trajectory and connects them to changes in the internal (system) energy by an energy balance analogous to the first law of thermodynamics. Additionally, providing a consistent definition of trajectory-wise entropy production gives rise to second-law-like relations and forms the basis for a 'stochastic thermodynamics' along individual fluctuating trajectories. In order to construct meaningful concepts of work, heat and entropy production for single trajectories, their definitions are based on the stochastic equations of motion modeling the physical system of interest. Because of this, they are valid even for systems that are prevented from equilibrating with the thermal environment by external driving forces (or other sources of non-equilibrium). In that way, the central notions of equilibrium thermodynamics, such as heat, work and entropy, are consistently extended to the non-equilibrium realm. In the (non-equilibrium) ensemble, the trajectory-wise quantities acquire distributions. General statements derived within stochastic thermodynamics typically refer to properties of these distributions, and are valid in the non-equilibrium regime even beyond the linear response. The extension of statistical mechanics and of exact thermodynamic statements to the non-equilibrium realm has been discussed from the early days of statistical mechanics more than 100 years ago. This debate culminated in the development of linear response
The National Center for Environmental Assessment (NCEA) has conducted and supported research addressing uncertainties in 2-stage clonal growth models for cancer as applied to formaldehyde. In this report, we summarized publications resulting from this research effort, discussed t...
The National Center for Environmental Assessment (NCEA) has conducted and supported research addressing uncertainties in 2-stage clonal growth models for cancer as applied to formaldehyde. In this report, we summarized publications resulting from this research effort, discussed t...
Kossenko, M M; Hoffman, D A; Thomas, T L
2000-07-01
The Mayak Industrial Association, located in the South Ural Mountains, began operation in 1948 and was the first Russian site for the production and separation of plutonium. During the early days of operation, technological failures resulted in the release of large amounts of radioactive waste into the Techa River. Residents who lived in villages on the banks of the Techa and Iset Rivers were exposed to varying levels of radioactivity. The objective of this study is to assess stochastic (carcinogenic) effects in populations exposed to offsite releases of radioactive materials from the Mayak nuclear facility in Russia. Subjects of the present study are those individuals who lived during the period January 1950 through December 1960 in any of the exposed villages along the Techa River in Chelyabinsk Oblast. Death certificates and cancer incidence data have been routinely collected in the past from a five-rayon catchment area of Chelyabinsk Oblast. The registry of exposed residents along the Techa River assembled and maintained by the Urals Research Center for Radiation Medicine for the past 40 y is the basis for identifying study subjects for this project. Specific study objectives are to evaluate the incidence of cancer among current and former residents of Chelyabinsk Oblast who are in the exposed Techa River cohort; integrate results from the dose-reconstruction study to estimate doses for risk assessment; and develop a structure for maintaining continued follow-up of the cohort for cancer incidence. In the earlier part of our collaborative effort, the focus has been to enhance the cancer morbidity registry by updating it with cancer cases diagnosed through 1997, to conduct a series of validation procedures to ensure completeness and accuracy of the registry, and to reduce the numbers of subjects lost to follow-up. A feasibility study to determine cancer morbidity in migrants from the catchment area has been proposed. Our preliminary analyses of cancer morbidity
NASA Astrophysics Data System (ADS)
Ross, D. K.; Moreau, William
1995-08-01
We investigate stochastic gravity as a potentially fruitful avenue for studying quantum effects in gravity. Following the approach of stochastic electrodynamics ( sed), as a representation of the quantum gravity vacuum we construct a classical state of isotropic random gravitational radiation, expressed as a spin-2 field,h µυ (x), composed of plane waves of random phase on a flat spacetime manifold. Requiring Lorentz invariance leads to the result that the spectral composition function of the gravitational radiation,h(ω), must be proportional to 1/ω 2. The proportionality constant is determined by the Planck condition that the energy density consist ofħω/2 per normal mode, and this condition sets the amplitude scale of the random gravitational radiation at the order of the Planck length, giving a spectral composition functionh(ω) =√16πc 2Lp/ω2. As an application of stochastic gravity, we investigate the Davies-Unruh effect. We calculate the two-point correlation function (R iojo(Oτ-δτ/2)R kolo(O,τ+δτ/2)) of the measureable geodesic deviation tensor field,R iojo, for two situations: (i) at a point detector uniformly accelerating through the random gravitational radiation, and (ii) at an inertial detector in a heat bath of the random radiation at a finite temperature. We find that the two correlation functions agree to first order inaδτ/c provided that the temperature and acceleration satisfy the relationkT=ħa/2πc.
Oroji, Amin; Omar, Mohd; Yarahmadian, Shantia
2016-10-21
In this paper, a new mathematical model is proposed for studying the population dynamics of breast cancer cells treated by radiotherapy by using a system of stochastic differential equations. The novelty of the model is essentially in capturing the concept of the cell cycle in the modeling to be able to evaluate the tumor lifespan. According to the cell cycle, each cell belongs to one of three subpopulations G, S, or M, representing gap, synthesis and mitosis subpopulations. Cells in the M subpopulation are highly radio-sensitive, whereas cells in the S subpopulation are highly radio-resistant. Therefore, in the process of radiotherapy, cell death rates of different subpopulations are not equal. In addition, since flow cytometry is unable to detect apoptotic cells accurately, the small changes in cell death rate in each subpopulation during treatment are considered. Subsequently, the proposed model is calibrated using experimental data from previous experiments involving the MCF-7 breast cancer cell line. Consequently, the proposed model is able to predict tumor lifespan based on the number of initial carcinoma cells. The results show the effectiveness of the radiation under the condition of stability, which describes the decreasing trend of the tumor cells population.
Blaskiewicz, M.
2011-01-01
Stochastic Cooling was invented by Simon van der Meer and was demonstrated at the CERN ISR and ICE (Initial Cooling Experiment). Operational systems were developed at Fermilab and CERN. A complete theory of cooling of unbunched beams was developed, and was applied at CERN and Fermilab. Several new and existing rings employ coasting beam cooling. Bunched beam cooling was demonstrated in ICE and has been observed in several rings designed for coasting beam cooling. High energy bunched beams have proven more difficult. Signal suppression was achieved in the Tevatron, though operational cooling was not pursued at Fermilab. Longitudinal cooling was achieved in the RHIC collider. More recently a vertical cooling system in RHIC cooled both transverse dimensions via betatron coupling.
The 2-stage liver transplant: 3 clinical scenarios.
Gedik, Ender; Bıçakçıoğlu, Murat; Otan, Emrah; İlksen Toprak, Hüseyin; Işık, Burak; Aydın, Cemalettin; Kayaalp, Cüneyt; Yılmaz, Sezai
2015-04-01
The main goal of 2-stage liver transplant is to provide time to obtain a new liver source. We describe our experience of 3 patients with 3 different clinical conditions. A 57-year-old man was retransplanted successfully with this technique due to hepatic artery thrombosis. However, a 38-year-old woman with fulminant toxic hepatitis and a 5-year-old-boy with abdominal trauma had poor outcome. This technique could serve as a rescue therapy for liver transplant patients who have toxic liver syndrome or abdominal trauma. These patients required intensive support during long anhepatic states. The transplant team should decide early whether to use this technique before irreversible conditions develop.
Rood, A S; McGavran, P D; Aanenson, J W; Till, J E
2001-08-01
Carbon tetrachloride is a degreasing agent that was used at the Rocky Flats Plant (RFP) in Colorado to clean product components and equipment. The chemical is considered a volatile organic compound and a probable human carcinogen. During the time the plant operated (1953-1989), most of the carbon tetrachloride was released to the atmosphere through building exhaust ducts. A smaller amount was released to the air via evaporation from open-air burn pits and ground-surface discharge points. Airborne releases from the plant were conservatively estimated to be equivalent to the amount of carbon tetrachloride consumed annually by the plant, which was estimated to be between 3.6 and 180 Mg per year. This assumption was supported by calculations that showed that most of the carbon tetrachloride discharged to the ground surface would subsequently be released to the atmosphere. Atmospheric transport of carbon tetrachloride from the plant to the surrounding community was estimated using a Gaussian Puff dispersion model (RATCHET). Time-integrated concentrations were estimated for nine hypothetical but realistic exposure scenarios that considered variation in lifestyle, location, age, and gender. Uncertainty distributions were developed for cancer slope factors and atmospheric dispersion factors. These uncertainties were propagated through to the final risk estimate using Monte Carlo techniques. The geometric mean risk estimates varied from 5.2 x 10(-6) for a hypothetical rancher or laborer working near the RFP to 3.4 x 10(-9) for an infant scenario. The distribution of incremental lifetime cancer incidence risk for the hypothetical rancher was between 1.3 x 10(-6) (5% value) and 2.1 x 10(-5) (95% value). These estimates are similar to or exceed estimated cancer risks posed by releases of radionuclides from the site.
Brennan,J.M.; Blaskiewicz, M. M.; Severino, F.
2009-05-04
After the success of longitudinal stochastic cooling of bunched heavy ion beam in RHIC, transverse stochastic cooling in the vertical plane of Yellow ring was installed and is being commissioned with proton beam. This report presents the status of the effort and gives an estimate, based on simulation, of the RHIC luminosity with stochastic cooling in all planes.
Stochastic differential equations
Sobczyk, K. )
1990-01-01
This book provides a unified treatment of both regular (or random) and Ito stochastic differential equations. It focuses on solution methods, including some developed only recently. Applications are discussed, in particular an insight is given into both the mathematical structure, and the most efficient solution methods (analytical as well as numerical). Starting from basic notions and results of the theory of stochastic processes and stochastic calculus (including Ito's stochastic integral), many principal mathematical problems and results related to stochastic differential equations are expounded here for the first time. Applications treated include those relating to road vehicles, earthquake excitations and offshore structures.
Stochastic symmetries of Wick type stochastic ordinary differential equations
NASA Astrophysics Data System (ADS)
Ünal, Gazanfer
2015-04-01
We consider Wick type stochastic ordinary differential equations with Gaussian white noise. We define the stochastic symmetry transformations and Lie equations in Kondratiev space (S)-1N. We derive the determining system of Wick type stochastic partial differential equations with Gaussian white noise. Stochastic symmetries for stochastic Bernoulli, Riccati and general stochastic linear equation in (S)-1N are obtained. A stochastic version of canonical variables is also introduced.
Lenormand, Thomas; Roze, Denis; Rousset, François
2009-03-01
The debate over the role of stochasticity is central in evolutionary biology, often summarised by whether or not evolution is predictable or repeatable. Here we distinguish three types of stochasticity: stochasticity of mutation and variation, of individual life histories and of environmental change. We then explain when stochasticity matters in evolution, distinguishing four broad situations: stochasticity contributes to maladaptation or limits adaptation; it drives evolution on flat fitness landscapes (evolutionary freedom); it might promote jumps from one fitness peak to another (evolutionary revolutions); and it might shape the selection pressures themselves. We show that stochasticity, by directly steering evolution, has become an essential ingredient of evolutionary theory beyond the classical Wright-Fisher or neutralist-selectionist debates.
Stochastic longshore current dynamics
NASA Astrophysics Data System (ADS)
Restrepo, Juan M.; Venkataramani, Shankar
2016-12-01
We develop a stochastic parametrization, based on a 'simple' deterministic model for the dynamics of steady longshore currents, that produces ensembles that are statistically consistent with field observations of these currents. Unlike deterministic models, stochastic parameterization incorporates randomness and hence can only match the observations in a statistical sense. Unlike statistical emulators, in which the model is tuned to the statistical structure of the observation, stochastic parametrization are not directly tuned to match the statistics of the observations. Rather, stochastic parameterization combines deterministic, i.e physics based models with stochastic models for the "missing physics" to create hybrid models, that are stochastic, but yet can be used for making predictions, especially in the context of data assimilation. We introduce a novel measure of the utility of stochastic models of complex processes, that we call consistency of sensitivity. A model with poor consistency of sensitivity requires a great deal of tuning of parameters and has a very narrow range of realistic parameters leading to outcomes consistent with a reasonable spectrum of physical outcomes. We apply this metric to our stochastic parametrization and show that, the loss of certainty inherent in model due to its stochastic nature is offset by the model's resulting consistency of sensitivity. In particular, the stochastic model still retains the forward sensitivity of the deterministic model and hence respects important structural/physical constraints, yet has a broader range of parameters capable of producing outcomes consistent with the field data used in evaluating the model. This leads to an expanded range of model applicability. We show, in the context of data assimilation, the stochastic parametrization of longshore currents achieves good results in capturing the statistics of observation that were not used in tuning the model.
A Stochastic Employment Problem
ERIC Educational Resources Information Center
Wu, Teng
2013-01-01
The Stochastic Employment Problem(SEP) is a variation of the Stochastic Assignment Problem which analyzes the scenario that one assigns balls into boxes. Balls arrive sequentially with each one having a binary vector X = (X[subscript 1], X[subscript 2],...,X[subscript n]) attached, with the interpretation being that if X[subscript i] = 1 the ball…
Research in Stochastic Processes
1988-10-10
26 L. Gorostiza ................................................. 25 G. Hardy...Technical Report No. 219, Dec. 1987. Sequential Anat., 7. 1988, 111-126 25 DONALD DAWSON and LUIS G. GOROSTIZA The work of Professors Dawson and Gorostiza ... Gorostiza , Generalized solutions of a class of nuclear space valued stochastic evolution equations. University of North Carolina Center for Stochastic
Stochastic Convection Parameterizations
NASA Technical Reports Server (NTRS)
Teixeira, Joao; Reynolds, Carolyn; Suselj, Kay; Matheou, Georgios
2012-01-01
computational fluid dynamics, radiation, clouds, turbulence, convection, gravity waves, surface interaction, radiation interaction, cloud and aerosol microphysics, complexity (vegetation, biogeochemistry, radiation versus turbulence/convection stochastic approach, non-linearities, Monte Carlo, high resolutions, large-Eddy Simulations, cloud structure, plumes, saturation in tropics, forecasting, parameterizations, stochastic, radiation-clod interaction, hurricane forecasts
A Stochastic Employment Problem
ERIC Educational Resources Information Center
Wu, Teng
2013-01-01
The Stochastic Employment Problem(SEP) is a variation of the Stochastic Assignment Problem which analyzes the scenario that one assigns balls into boxes. Balls arrive sequentially with each one having a binary vector X = (X[subscript 1], X[subscript 2],...,X[subscript n]) attached, with the interpretation being that if X[subscript i] = 1 the ball…
Evolution with Stochastic Fitness and Stochastic Migration
Rice, Sean H.; Papadopoulos, Anthony
2009-01-01
Background Migration between local populations plays an important role in evolution - influencing local adaptation, speciation, extinction, and the maintenance of genetic variation. Like other evolutionary mechanisms, migration is a stochastic process, involving both random and deterministic elements. Many models of evolution have incorporated migration, but these have all been based on simplifying assumptions, such as low migration rate, weak selection, or large population size. We thus have no truly general and exact mathematical description of evolution that incorporates migration. Methodology/Principal Findings We derive an exact equation for directional evolution, essentially a stochastic Price equation with migration, that encompasses all processes, both deterministic and stochastic, contributing to directional change in an open population. Using this result, we show that increasing the variance in migration rates reduces the impact of migration relative to selection. This means that models that treat migration as a single parameter tend to be biassed - overestimating the relative impact of immigration. We further show that selection and migration interact in complex ways, one result being that a strategy for which fitness is negatively correlated with migration rates (high fitness when migration is low) will tend to increase in frequency, even if it has lower mean fitness than do other strategies. Finally, we derive an equation for the effective migration rate, which allows some of the complex stochastic processes that we identify to be incorporated into models with a single migration parameter. Conclusions/Significance As has previously been shown with selection, the role of migration in evolution is determined by the entire distributions of immigration and emigration rates, not just by the mean values. The interactions of stochastic migration with stochastic selection produce evolutionary processes that are invisible to deterministic evolutionary theory
Evolution with stochastic fitness and stochastic migration.
Rice, Sean H; Papadopoulos, Anthony
2009-10-09
Migration between local populations plays an important role in evolution - influencing local adaptation, speciation, extinction, and the maintenance of genetic variation. Like other evolutionary mechanisms, migration is a stochastic process, involving both random and deterministic elements. Many models of evolution have incorporated migration, but these have all been based on simplifying assumptions, such as low migration rate, weak selection, or large population size. We thus have no truly general and exact mathematical description of evolution that incorporates migration. We derive an exact equation for directional evolution, essentially a stochastic Price equation with migration, that encompasses all processes, both deterministic and stochastic, contributing to directional change in an open population. Using this result, we show that increasing the variance in migration rates reduces the impact of migration relative to selection. This means that models that treat migration as a single parameter tend to be biassed - overestimating the relative impact of immigration. We further show that selection and migration interact in complex ways, one result being that a strategy for which fitness is negatively correlated with migration rates (high fitness when migration is low) will tend to increase in frequency, even if it has lower mean fitness than do other strategies. Finally, we derive an equation for the effective migration rate, which allows some of the complex stochastic processes that we identify to be incorporated into models with a single migration parameter. As has previously been shown with selection, the role of migration in evolution is determined by the entire distributions of immigration and emigration rates, not just by the mean values. The interactions of stochastic migration with stochastic selection produce evolutionary processes that are invisible to deterministic evolutionary theory.
Stochastic Pseudo-Boolean Optimization
2011-07-31
analysis of two-stage stochastic minimum s-t cut problems; (iv) exact solution algorithm for a class of stochastic bilevel knapsack problems; (v) exact...57 5 Bilevel Knapsack Problems with Stochastic Right-Hand Sides 58 6 Two-Stage Stochastic Assignment Problems 59 6.1 Introduction...programming formulations and related computational complexity issues. • Section 5 considers a specific stochastic extension of the bilevel knapsack
Spring, William Joseph
2009-04-13
We consider quantum analogues of n-parameter stochastic processes, associated integrals and martingale properties extending classical results obtained in [1, 2, 3], and quantum results in [4, 5, 6, 7, 8, 9, 10].
Research in Stochastic Processes.
1985-09-01
appear. G. Kallianpur, Finitely additive approach to nonlinear filtering, Proc. Bernoulli Soc. Conf. on Stochastic Processes, T. Hida , ed., Springer, to...Nov. 85, in Proc. Bernoulli Soc. Conf. on Stochastic Processes, T. Hida , ed., Springer, to appear. i. Preparation T. Hsing, Extreme value theory for...1507 Carroll, R.J., Spiegelman, C.H., Lan, K.K.G., Bailey , K.T. and Abbott, R.D., Errors in-variables for binary regression models, Aug.82. 1508
Hirakawa, Akihiro; Miyamoto, Kei; Masuda, Takahiro; Fukuta, Shoji; Hosoe, Hideo; Iinuma, Nobuki; Iwai, Chizuo; Nishimoto, Hirofumi; Shimizu, Katsuji
2010-04-01
A prospective study on the clinical outcomes in patients with tuberculous spondylitis treated by a 2-stage operation (posterior and anterior) using posterior spinal instrumentation. To evaluate the clinical outcomes of the 2-stage surgical treatment (first stage: placement of posterior instrumentation and second stage: anterior debridement and bone grafting) for tuberculous spondylitis. There have been few reports describing the effects of 2-stage surgical treatment for tuberculous spondylitis. Ten patients (5 men and 5 women) with tuberculous spondylitis were treated by 2-stage operations. Age at the initial operation was 64.6+/-14.8 years (average+/-SD) (range: 47 to 83 y). The clinical outcomes were evaluated before and after the surgery in terms of hematologic examination, pain level, and neurologic status. Bone fusion and changes in sagittal alignment were examined radiographically. All patients showed suppression of infection, bony fusion, relief of pain, and recovery of neurologic function. No significant changes were observed in kyphosis angle at the final follow-up. There were no incidences of severe complications or recurrence. Our results showed that posterior and anterior 2-stage surgical treatment for tuberculous spondylitis is a viable surgical option for cases in which conservative treatment has failed. However, the changes in sagittal alignment showed that this strategy provides limited kyphosis correction.
Losick, Richard; Desplan, Claude
2008-01-01
Summary Fundamental to living cells is the capacity to differentiate into subtypes with specialized attributes. Understanding the way cells acquire their fates is a major challenge in developmental biology. How cells adopt a particular fate is usually thought of as being deterministic, and in the large majority of cases it is. That is, cells acquire their fate by virtue of their lineage or their proximity to an inductive signal from another cell. In some cases, however, and in organisms ranging from bacteria to humans, cells choose one or another pathway of differentiation stochastically without apparent regard to environment or history. Stochasticity has important mechanistic requirements as we discuss. We will also speculate on why stochasticity is advantageous, and even critical in some circumstances, to the individual, the colony, or the species. PMID:18388284
Stochastic cooling at Fermilab
Marriner, J.
1986-08-01
The topics discussed are the stochastic cooling systems in use at Fermilab and some of the techniques that have been employed to meet the particular requirements of the anti-proton source. Stochastic cooling at Fermilab became of paramount importance about 5 years ago when the anti-proton source group at Fermilab abandoned the electron cooling ring in favor of a high flux anti-proton source which relied solely on stochastic cooling to achieve the phase space densities necessary for colliding proton and anti-proton beams. The Fermilab systems have constituted a substantial advance in the techniques of cooling including: large pickup arrays operating at microwave frequencies, extensive use of cryogenic techniques to reduce thermal noise, super-conducting notch filters, and the development of tools for controlling and for accurately phasing the system.
STOCHASTIC COOLING FOR BUNCHED BEAMS.
BLASKIEWICZ, M.
2005-05-16
Problems associated with bunched beam stochastic cooling are reviewed. A longitudinal stochastic cooling system for RHIC is under construction and has been partially commissioned. The state of the system and future plans are discussed.
Stochastic demographic forecasting.
Lee, R D
1992-11-01
"This paper describes a particular approach to stochastic population forecasting, which is implemented for the U.S.A. through 2065. Statistical time series methods are combined with demographic models to produce plausible long run forecasts of vital rates, with probability distributions. The resulting mortality forecasts imply gains in future life expectancy that are roughly twice as large as those forecast by the Office of the Social Security Actuary.... Resulting stochastic forecasts of the elderly population, elderly dependency ratios, and payroll tax rates for health, education and pensions are presented."
Stochastic modeling of rainfall
Guttorp, P.
1996-12-31
We review several approaches in the literature for stochastic modeling of rainfall, and discuss some of their advantages and disadvantages. While stochastic precipitation models have been around at least since the 1850`s, the last two decades have seen an increased development of models based (more or less) on the physical processes involved in precipitation. There are interesting questions of scale and measurement that pertain to these modeling efforts. Recent modeling efforts aim at including meteorological variables, and may be useful for regional down-scaling of general circulation models.
Markov stochasticity coordinates
NASA Astrophysics Data System (ADS)
Eliazar, Iddo
2017-01-01
Markov dynamics constitute one of the most fundamental models of random motion between the states of a system of interest. Markov dynamics have diverse applications in many fields of science and engineering, and are particularly applicable in the context of random motion in networks. In this paper we present a two-dimensional gauging method of the randomness of Markov dynamics. The method-termed Markov Stochasticity Coordinates-is established, discussed, and exemplified. Also, the method is tweaked to quantify the stochasticity of the first-passage-times of Markov dynamics, and the socioeconomic equality and mobility in human societies.
Analysis of bilinear stochastic systems
NASA Technical Reports Server (NTRS)
Willsky, A. S.; Martin, D. N.; Marcus, S. I.
1975-01-01
Analysis of stochastic dynamical systems that involve multiplicative (bilinear) noise processes. After defining the systems of interest, consideration is given to the evolution of the moments of such systems, the question of stochastic stability, and estimation for bilinear stochastic systems. Both exact and approximate methods of analysis are introduced, and, in particular, the uses of Lie-theoretic concepts and harmonic analysis are discussed.
Research in Stochastic Processes.
1982-10-31
locally convex spaces is studied. We obtain a general form of convergent p-cylindrical martingales in barrelled spaces. Using the locally convex space...topology of certain Orlicz and Lorentz spaces. References 1. Z. Suchanecki and A. Weron, Decomposability of p-cylindrical martingales, Center for Stochastic
Stochastic Local Distinguishability
NASA Astrophysics Data System (ADS)
Bandyopadhyay, Somshubhro; Roy, Anirban; Walgate, Jonathan
2007-03-01
We pose the question, ``when is globally available information is also locally available?'', formally as the problem of local state discrimination, and show that the deep qualitative link between local distinguishability and entanglement lies at the level of stochastic rather than deterministic local protocols. We restrict our attention to sets of mutually orthogonal pure quantum states. We define a set of states |ψi> as beingstochastically locally distinguishable if and only if there is a LOCC protocol whereby the parties can conclusively identify a member of the set with some nonzero probability. If a set is stochastically locally distinguishable, then the complete global information is potentially locally available. If not, the physical information encoded by the system can never be completely locally exposed. Our results are proved true for all orthogonal quantum states regardless of their dimensionality or multipartiality. First, we prove that entanglement is a necessary property of any system whose total global information can never be locally accessed. Second, entangled states that form part of an orthogonal basis can never be locally singled out. Completely entangled bases are, always stochastically locally indistinguishable. Third, we prove that any set of three orthogonal states, is stochastically locally distinguishable.
ERIC Educational Resources Information Center
Wolff, Hans
This paper deals with a stochastic process for the approximation of the root of a regression equation. This process was first suggested by Robbins and Monro. The main result here is a necessary and sufficient condition on the iteration coefficients for convergence of the process (convergence with probability one and convergence in the quadratic…
Research in Stochastic Processes
1988-08-31
25 L. de Haan ................................................... 26 L. Gorostiza ...DAISON and LUIS C. COROSTIZA The work of Professors Dawson and Gorostiza is concerned with obtaining a Langevin equation for the fluctuation limit of a...its uniqueness established. Reference 1. D.A. Dawson and L.G. Gorostiza , Generalized solutions of a class of nuclear space valued stochastic
Stochastic decentralized systems
NASA Astrophysics Data System (ADS)
Barfoot, Timothy David
Fundamental aspects of decentralized systems are considered from a control perspective. The stochastic framework afforded by Markov systems is presented as a formal setting in which to study decentralized systems. A stochastic algebra is introduced which allows Markov systems to be considered in matrix format but also strikes an important connection to the classic linear system originally studied by Kalman [1960]. The process of decentralization is shown to impose constraints on observability and controllability of a system. However, it is argued that communicating decentralized controllers can implement any control law possible with a centralized controller. Communication is shown to serve a dual role, both enabling sensor data to be shared and actions to be coordinated. The viabilities of these two types of communication are tested on a real network of mobile robots where they are found to be successful at a variety of tasks. Action coordination is reframed as a decentralized decision making process whereupon stochastic cellular automata (SCA) are introduced as a model. Through studies of SCA it is found that coordination in a group of arbitrarily and sparsely connected agents is possible using simple rules. The resulting stochastic mechanism may be immediately used as a practical decentralized decision making tool (it is tested on a group of mobile robots) but, it furthermore provides insight into the general features of self-organizing systems.
Controlled Stochastic Dynamical Systems
2007-04-18
the existence of value functions of two-player zero-sum stochastic differential games Indiana Univ. Math. Journal, 38 (1989), pp 293-314. [6] George ...control problems, Adv. Appl. Prob., 15, (1983) pp 225-254. [10] Karatzas, I. Ocone, D., Wang, H. and Zervos , M., Finite fuel singular control with
Tollestrup, A.V.; Dugan, G
1983-12-01
Major headings in this review include: proton sources; antiproton production; antiproton sources and Liouville, the role of the Debuncher; transverse stochastic cooling, time domain; the accumulator; frequency domain; pickups and kickers; Fokker-Planck equation; calculation of constants in the Fokker-Planck equation; and beam feedback. (GHT)
Uçkay, Ilker; von Dach, Elodie; Perez, Cédric; Agostinho, Americo; Garnerin, Philippe; Lipsky, Benjamin A; Hoffmeyer, Pierre; Pittet, Didier
2017-07-01
To assess the optimal surgical approach and costs for patients hospitalized with septic bursitis. From May 1, 2011, through December 24, 2014, hospitalized patients with septic bursitis at University of Geneva Hospitals were randomized (1:1) to receive 1- vs 2-stage bursectomy. All the patients received postsurgical oral antibiotic drug therapy for 7 days. Of 164 enrolled patients, 130 had bursitis of the elbow and 34 of the patella. The surgical approach used was 1-stage in 79 patients and 2-stage in 85. Overall, there were 22 treatment failures: 8 of 79 patients (10%) in the 1-stage arm and 14 of 85 (16%) in the 2-stage arm (Pearson χ(2) test; P=.23). Recurrent infection was caused by the same pathogen in 7 patients (4%) and by a different pathogen in 5 (3%). Outcomes were better in the 1- vs 2-stage arm for wound dehiscence for elbow bursitis (1 of 66 vs 9 of 64; Fisher exact test P=.03), median length of hospital stay (4.5 vs 6.0 days), nurses' workload (605 vs 1055 points), and total costs (Sw₣6881 vs Sw₣11,178; all P<.01). For adults with moderate to severe septic bursitis requiring hospital admission, bursectomy with primary closure, together with antibiotic drug therapy for 7 days, was safe, effective, and resource saving. Using a 2-stage approach may be associated with a higher rate of wound dehiscence for olecranon bursitis than the 1-stage approach. Clinicaltrials.gov Identifier: NCT01406652. Copyright © 2017 Mayo Foundation for Medical Education and Research. Published by Elsevier Inc. All rights reserved.
The Effects of a 2-Stage Injection Technique on Inferior Alveolar Nerve Block Injection Pain
Nusstein, John; Steinkruger, Geoffrey; Reader, Al; Beck, Mike; Weaver, Joel
2006-01-01
The purpose of this prospective, randomized, single-blinded, crossover study was to compare the pain of a traditional 1-stage inferior alveolar nerve (IAN) block injection to a 2-stage IAN block technique. Using a crossover design, 51 subjects randomly received, in a single-blinded manner, either the traditional IAN block or the 2-stage IAN block in 2 appointments spaced at least 1 week apart. For the 2-stage injection, the needle was inserted submucosally and 0.4 mL of 2% lidocaine with epinephrine was slowly given over 1 minute. After 5 minutes, the needle was reinserted and advanced to the target site (needle placement), and 1.8 mL of 2% lidocaine with epinephrine was deposited. For the traditional IAN block, following needle penetration, the needle was advanced while depositing 0.4 mL of 2% lidocaine with epinephrine (needle placement) and then 1.8 mL of 2% lidocaine with epinephrine was deposited at the target site. A Heft-Parker visual analogue scale was used to measure the pain of needle insertion, needle placement, and anesthetic solution deposition. There were no significant differences, as analyzed by Wilcoxon matched-pairs signed-ranks test, between needle insertion and solution deposition for the 2 techniques in men or women. However, there was significantly less pain with the 2-stage injection for needle placement in women. In conclusion, the 2-stage injection significantly reduced the pain of needle placement for women when compared to the traditional IAN technique. PMID:17177591
Stochastic computing with biomolecular automata.
Adar, Rivka; Benenson, Yaakov; Linshiz, Gregory; Rosner, Amit; Tishby, Naftali; Shapiro, Ehud
2004-07-06
Stochastic computing has a broad range of applications, yet electronic computers realize its basic step, stochastic choice between alternative computation paths, in a cumbersome way. Biomolecular computers use a different computational paradigm and hence afford novel designs. We constructed a stochastic molecular automaton in which stochastic choice is realized by means of competition between alternative biochemical pathways, and choice probabilities are programmed by the relative molar concentrations of the software molecules coding for the alternatives. Programmable and autonomous stochastic molecular automata have been shown to perform direct analysis of disease-related molecular indicators in vitro and may have the potential to provide in situ medical diagnosis and cure.
Impact of 2-staged stereotactic radiosurgery for treatment of brain metastases ≥ 2 cm.
Angelov, Lilyana; Mohammadi, Alireza M; Bennett, Elizabeth E; Abbassy, Mahmoud; Elson, Paul; Chao, Samuel T; Montgomery, Joshua S; Habboub, Ghaith; Vogelbaum, Michael A; Suh, John H; Murphy, Erin S; Ahluwalia, Manmeet S; Nagel, Sean J; Barnett, Gene H
2017-09-22
OBJECTIVE Stereotactic radiosurgery (SRS) is the primary modality for treating brain metastases. However, effective radiosurgical control of brain metastases ≥ 2 cm in maximum diameter remains challenging and is associated with suboptimal local control (LC) rates of 37%-62% and an increased risk of treatment-related toxicity. To enhance LC while limiting adverse effects (AEs) of radiation in these patients, a dose-dense treatment regimen using 2-staged SRS (2-SSRS) was used. The objective of this study was to evaluate the efficacy and toxicity of this treatment strategy. METHODS Fifty-four patients (with 63 brain metastases ≥ 2 cm) treated with 2-SSRS were evaluated as part of an institutional review board-approved retrospective review. Volumetric measurements at first-stage stereotactic radiosurgery (first SSRS) and second-stage SRS (second SSRS) treatments and on follow-up imaging studies were determined. In addition to patient demographic data and tumor characteristics, the study evaluated 3 primary outcomes: 1) response at first follow-up MRI, 2) time to local progression (TTP), and 3) overall survival (OS) with 2-SSRS. Response was analyzed using methods for binary data, TTP was analyzed using competing-risks methods to account for patients who died without disease progression, and OS was analyzed using conventional time-to-event methods. When needed, analyses accounted for multiple lesions in the same patient. RESULTS Among 54 patients, 46 (85%) had 1 brain metastasis treated with 2-SSRS, 7 patients (13%) had 2 brain metastases concurrently treated with 2-SSRS, and 1 patient underwent 2-SSRS for 3 concurrent brain metastases ≥ 2 cm. The median age was 63 years (range 23-83 years), 23 patients (43%) had non-small cell lung cancer, and 14 patients (26%) had radioresistant tumors (renal or melanoma). The median doses at first and second SSRS were 15 Gy (range 12-18 Gy) and 15 Gy (range 12-15 Gy), respectively. The median duration between stages was 34 days
Stochastic ice stream dynamics
Bertagni, Matteo Bernard; Ridolfi, Luca
2016-01-01
Ice streams are narrow corridors of fast-flowing ice that constitute the arterial drainage network of ice sheets. Therefore, changes in ice stream flow are key to understanding paleoclimate, sea level changes, and rapid disintegration of ice sheets during deglaciation. The dynamics of ice flow are tightly coupled to the climate system through atmospheric temperature and snow recharge, which are known exhibit stochastic variability. Here we focus on the interplay between stochastic climate forcing and ice stream temporal dynamics. Our work demonstrates that realistic climate fluctuations are able to (i) induce the coexistence of dynamic behaviors that would be incompatible in a purely deterministic system and (ii) drive ice stream flow away from the regime expected in a steady climate. We conclude that environmental noise appears to be crucial to interpreting the past behavior of ice sheets, as well as to predicting their future evolution. PMID:27457960
BLASKIEWICZ,M.BRENNAN,J.M.CAMERON,P.WEI,J.
2003-05-12
Emittance growth due to Intra-Beam Scattering significantly reduces the heavy ion luminosity lifetime in RHIC. Stochastic cooling of the stored beam could improve things considerably by counteracting IBS and preventing particles from escaping the rf bucket [1]. High frequency bunched-beam stochastic cooling is especially challenging but observations of Schottky signals in the 4-8 GHz band indicate that conditions are favorable in RHIC [2]. We report here on measurements of the longitudinal beam transfer function carried out with a pickup kicker pair on loan from FNAL TEVATRON. Results imply that for ions a coasting beam description is applicable and we outline some general features of a viable momentum cooling system for RHIC.
Stochastic ice stream dynamics.
Mantelli, Elisa; Bertagni, Matteo Bernard; Ridolfi, Luca
2016-08-09
Ice streams are narrow corridors of fast-flowing ice that constitute the arterial drainage network of ice sheets. Therefore, changes in ice stream flow are key to understanding paleoclimate, sea level changes, and rapid disintegration of ice sheets during deglaciation. The dynamics of ice flow are tightly coupled to the climate system through atmospheric temperature and snow recharge, which are known exhibit stochastic variability. Here we focus on the interplay between stochastic climate forcing and ice stream temporal dynamics. Our work demonstrates that realistic climate fluctuations are able to (i) induce the coexistence of dynamic behaviors that would be incompatible in a purely deterministic system and (ii) drive ice stream flow away from the regime expected in a steady climate. We conclude that environmental noise appears to be crucial to interpreting the past behavior of ice sheets, as well as to predicting their future evolution.
Stochastic ice stream dynamics
NASA Astrophysics Data System (ADS)
Mantelli, Elisa; Bertagni, Matteo Bernard; Ridolfi, Luca
2016-08-01
Ice streams are narrow corridors of fast-flowing ice that constitute the arterial drainage network of ice sheets. Therefore, changes in ice stream flow are key to understanding paleoclimate, sea level changes, and rapid disintegration of ice sheets during deglaciation. The dynamics of ice flow are tightly coupled to the climate system through atmospheric temperature and snow recharge, which are known exhibit stochastic variability. Here we focus on the interplay between stochastic climate forcing and ice stream temporal dynamics. Our work demonstrates that realistic climate fluctuations are able to (i) induce the coexistence of dynamic behaviors that would be incompatible in a purely deterministic system and (ii) drive ice stream flow away from the regime expected in a steady climate. We conclude that environmental noise appears to be crucial to interpreting the past behavior of ice sheets, as well as to predicting their future evolution.
Stochastic response surface methodology: A study in the human health area
Oliveira, Teresa A. Oliveira, Amílcar; Leal, Conceição
2015-03-10
In this paper we review Stochastic Response Surface Methodology as a tool for modeling uncertainty in the context of Risk Analysis. An application in the survival analysis in the breast cancer context is implemented with R software.
Holmes-Cerfon, Miranda
2016-11-01
We study a model of rolling particles subject to stochastic fluctuations, which may be relevant in systems of nano- or microscale particles where rolling is an approximation for strong static friction. We consider the simplest possible nontrivial system: a linear polymer of three disks constrained to remain in contact and immersed in an equilibrium heat bath so the internal angle of the polymer changes due to stochastic fluctuations. We compare two cases: one where the disks can slide relative to each other and the other where they are constrained to roll, like gears. Starting from the Langevin equations with arbitrary linear velocity constraints, we use formal homogenization theory to derive the overdamped equations that describe the process in configuration space only. The resulting dynamics have the formal structure of a Brownian motion on a Riemannian or sub-Riemannian manifold, depending on if the velocity constraints are holonomic or nonholonomic. We use this to compute the trimer's equilibrium distribution with and without the rolling constraints. Surprisingly, the two distributions are different. We suggest two possible interpretations of this result: either (i) dry friction (or other dissipative, nonequilibrium forces) changes basic thermodynamic quantities like the free energy of a system, a statement that could be tested experimentally, or (ii) as a lesson in modeling rolling or friction more generally as a velocity constraint when stochastic fluctuations are present. In the latter case, we speculate there could be a "roughness" entropy whose inclusion as an effective force could compensate the constraint and preserve classical Boltzmann statistics. Regardless of the interpretation, our calculation shows the word "rolling" must be used with care when stochastic fluctuations are present.
Stochastic Thermodynamics of Learning
NASA Astrophysics Data System (ADS)
Goldt, Sebastian; Seifert, Udo
2017-01-01
Virtually every organism gathers information about its noisy environment and builds models from those data, mostly using neural networks. Here, we use stochastic thermodynamics to analyze the learning of a classification rule by a neural network. We show that the information acquired by the network is bounded by the thermodynamic cost of learning and introduce a learning efficiency η ≤1 . We discuss the conditions for optimal learning and analyze Hebbian learning in the thermodynamic limit.
Dorogovtsev, Andrei A
2010-06-29
For sets in a Hilbert space the concept of quadratic entropy is introduced. It is shown that this entropy is finite for the range of a stochastic flow of Brownian particles on R. This implies, in particular, the fact that the total time of the free travel in the Arratia flow of all particles that started from a bounded interval is finite. Bibliography: 10 titles.
Methodology for Stochastic Modeling.
1985-01-01
AD-AISS 851 METHODOLOGY FOR STOCHASTIC MODELING(U) ARMY MATERIEL 11 SYSTEMS ANALYSIS ACTIYITY ABERDEEN PROVING GROUND MD H E COHEN JAN 95 RNSAA-TR-41...FORM T REPORT NUMBER 2. GOVT ACCESSION NO. 3. RECIPIENT’$ CATALOG NUMBER 4. TITLE (and Subtitle) S. TYPE OF REPORT & PERIOD COVERED Methodology for...autoregression models, moving average models, ARMA, adaptive modeling, covariance methods , singular value decom- position, order determination rational
NASA Astrophysics Data System (ADS)
Holmes-Cerfon, Miranda
2016-11-01
We study a model of rolling particles subject to stochastic fluctuations, which may be relevant in systems of nano- or microscale particles where rolling is an approximation for strong static friction. We consider the simplest possible nontrivial system: a linear polymer of three disks constrained to remain in contact and immersed in an equilibrium heat bath so the internal angle of the polymer changes due to stochastic fluctuations. We compare two cases: one where the disks can slide relative to each other and the other where they are constrained to roll, like gears. Starting from the Langevin equations with arbitrary linear velocity constraints, we use formal homogenization theory to derive the overdamped equations that describe the process in configuration space only. The resulting dynamics have the formal structure of a Brownian motion on a Riemannian or sub-Riemannian manifold, depending on if the velocity constraints are holonomic or nonholonomic. We use this to compute the trimer's equilibrium distribution with and without the rolling constraints. Surprisingly, the two distributions are different. We suggest two possible interpretations of this result: either (i) dry friction (or other dissipative, nonequilibrium forces) changes basic thermodynamic quantities like the free energy of a system, a statement that could be tested experimentally, or (ii) as a lesson in modeling rolling or friction more generally as a velocity constraint when stochastic fluctuations are present. In the latter case, we speculate there could be a "roughness" entropy whose inclusion as an effective force could compensate the constraint and preserve classical Boltzmann statistics. Regardless of the interpretation, our calculation shows the word "rolling" must be used with care when stochastic fluctuations are present.
Stochastic Quantization of Instantons
NASA Astrophysics Data System (ADS)
Grandati, Y.; Bérard, A.; Grangé, P.
1996-03-01
The method of Parisi and Wu to quantize classical fields is applied to instanton solutionsϕIof euclidian non-linear theory in one dimension. The solutionϕεof the corresponding Langevin equation is built through a singular perturbative expansion inε=ℏ1/2in the frame of the center of mass of the instanton, where the differenceϕε-ϕIcarries only fluctuations of the instanton form. The relevance of the method is shown for the stochasticK dVequation with uniform noise in space: the exact solution usually obtained by the inverse scattering method is retrieved easily by the singular expansion. A general diagrammatic representation of the solution is then established which makes a thorough use of regrouping properties of stochastic diagrams derived in scalar field theory. Averaging over the noise and in the limit of infinite stochastic time, we obtain explicit expressions for the first two orders inεof the perturbed instanton and of its Green function. Specializing to the Sine-Gordon andϕ4models, the first anharmonic correction is obtained analytically. The calculation is carried to second order for theϕ4model, showing good convergence.
A retrodictive stochastic simulation algorithm
Vaughan, T.G. Drummond, P.D.; Drummond, A.J.
2010-05-20
In this paper we describe a simple method for inferring the initial states of systems evolving stochastically according to master equations, given knowledge of the final states. This is achieved through the use of a retrodictive stochastic simulation algorithm which complements the usual predictive stochastic simulation approach. We demonstrate the utility of this new algorithm by applying it to example problems, including the derivation of likely ancestral states of a gene sequence given a Markovian model of genetic mutation.
Portfolio Optimization with Stochastic Dividends and Stochastic Volatility
ERIC Educational Resources Information Center
Varga, Katherine Yvonne
2015-01-01
We consider an optimal investment-consumption portfolio optimization model in which an investor receives stochastic dividends. As a first problem, we allow the drift of stock price to be a bounded function. Next, we consider a stochastic volatility model. In each problem, we use the dynamic programming method to derive the Hamilton-Jacobi-Bellman…
Portfolio Optimization with Stochastic Dividends and Stochastic Volatility
ERIC Educational Resources Information Center
Varga, Katherine Yvonne
2015-01-01
We consider an optimal investment-consumption portfolio optimization model in which an investor receives stochastic dividends. As a first problem, we allow the drift of stock price to be a bounded function. Next, we consider a stochastic volatility model. In each problem, we use the dynamic programming method to derive the Hamilton-Jacobi-Bellman…
2-stage revision of 120 deep infected hip and knee prostheses using gentamicin-PMMA beads.
Janssen, Daniël M C; Geurts, Jan A P; Jütten, Liesbeth M C; Walenkamp, Geert H I M
2016-08-01
Background and purpose - A 2-stage revision is the most common treatment for late deep prosthesis-related infections and in all cases of septic loosening. However, there is no consensus about the optimal interval between the 2 stages. Patients and methods - We retrospectively studied 120 deep infections of total hip (n = 95) and knee (n = 25) prostheses that had occurred over a period of 25 years. The mean follow-up time was 5 (2-20) years. All infections had been treated with extraction, 1 or more debridements with systemic antibiotics, and implantation of gentamicin-PMMA beads. There had been different time intervals between extraction and reimplantation: median 14 (11-47) days for short-term treatment with uninterrupted hospital stay, and 7 (3-22) months for long-term treatment with temporary discharge. We analyzed the outcome regarding resolution of the infection and clinical results. Results - 88% (105/120) of the infections healed, with no difference in healing rate between short- and long-term treatment. 82 prostheses were reimplanted. In the most recent decade, we treated patients more often with a long-term treatment but reduced the length of time between the extraction and the reimplantation. More reimplantations were performed in long-term treatments than in short-term treatments, despite more having difficult-to-treat infections with worse soft-tissue condition. Interpretation - Patient, wound, and infection considerations resulted in an individualized treatment with different intervals between stages. The 2-stage revision treatment in combination with local gentamicin-PMMA beads gave good results even with difficult prosthesis infections and gentamicin-resistant bacteria.
2-stage repair in infancy for severe hypospadias with chordee: long-term results after puberty.
Lam, Po N; Greenfield, Saul P; Williot, Pierre
2005-10-01
Urinary and sexual functions were assessed in post-pubescent boys who had undergone 2-stage hypospadias repair in infancy for severe hypospadias with chordee. A total of 44 boys who had undergone 2-stage hypospadias repair from 1985 to 1993 and who were at least 13 years old were contacted. Of the 44 boys 27 (61%) with an average age of 15.4 years (range 13 to 21) responded. Meatal locations were midshaft in 14 cases, penoscrotal in 9 and perineal in 4. Four boys had bifid scrotum and 5 had intersex disorders. Intramuscular testosterone was administered preoperatively to 15 (56%) boys. A Nesbit procedure was performed in 18 boys (67%). Average patient age at stage 2 repair was 2.3 years. Mean followup was 12.7 years (range 10.7 to 17.2). Additional surgery was performed for diverticuli in 5 cases, fistula in 3 and minor strictures in 4. Of the 27 patients 25 presented for examination and 2 responded to questionnaire only. All patients had normal meatal position, normal glanular anatomy, a well-defined coronal sulcus, normal cylindrical shafts without extra skin and well-defined penoscrotal junctions. Ten boys (40%) had minor spraying of stream, all stood to void and 10 (40%) milked the urethra after voiding. None had chordee. Twenty patients were able to ejaculate and 9 (42.9%) had to milk the ejaculate. Two patients (7.7%) had minor pain with erection. All subjects were satisfied with urinary, erectile and ejaculatory functions, and 23 (92%) were pleased with appearance. The 2-stage approach for severe hypospadias results in excellent function, cosmesis and patient satisfaction after puberty, with no chordee. Minor voiding and ejaculatory problems are to be expected. Late complications are rare. The use of extragenital skin to either primarily repair or salvage a "cripple" has not been necessary.
Stochastic ontogenetic growth model
NASA Astrophysics Data System (ADS)
West, B. J.; West, D.
2012-02-01
An ontogenetic growth model (OGM) for a thermodynamically closed system is generalized to satisfy both the first and second law of thermodynamics. The hypothesized stochastic ontogenetic growth model (SOGM) is shown to entail the interspecies allometry relation by explicitly averaging the basal metabolic rate and the total body mass over the steady-state probability density for the total body mass (TBM). This is the first derivation of the interspecies metabolic allometric relation from a dynamical model and the asymptotic steady-state distribution of the TBM is fit to data and shown to be inverse power law.
Stochastic processes in cosmology
NASA Astrophysics Data System (ADS)
Cáceres, Manuel O.; Diaz, Mario C.; Pullin, Jorge A.
1987-08-01
The behavior of a radiation filled de Sitter universe in which the equation of state is perturbed by a stochastic term is studied. The corresponding two-dimensional Fokker-Planck equation is solved. The finiteness of the cosmological constant appears to be a necessary condition for the stability of the model which undergoes an exponentially expanding state. Present address: Facultad de Matemática Astronomía y Física, Universidad Nacional de Córdoba, Laprida 854, 5000 Códoba, Argentina.
Stochastic Coupled Cluster Theory
NASA Astrophysics Data System (ADS)
Thom, Alex J. W.
2010-12-01
We describe a stochastic coupled cluster theory which represents excitation amplitudes as discrete excitors in the space of excitation amplitudes. Reexpressing the coupled cluster (CC) equations as the dynamics of excitors in this space, we show that a simple set of rules suffices to evolve a distribution of excitors to sample the CC solution and correctly evaluate the CC energy. These rules are not truncation specific and this method can calculate CC solutions to an arbitrary level of truncation. We present results of calculation on the neon atom, and nitrogen and water molecules showing the ability to recover both truncated and full CC results.
Stochastic thermodynamics of resetting
NASA Astrophysics Data System (ADS)
Fuchs, Jaco; Goldt, Sebastian; Seifert, Udo
2016-03-01
Stochastic dynamics with random resetting leads to a non-equilibrium steady state. Here, we consider the thermodynamics of resetting by deriving the first and second law for resetting processes far from equilibrium. We identify the contributions to the entropy production of the system which arise due to resetting and show that they correspond to the rate with which information is either erased or created. Using Landauer's principle, we derive a bound on the amount of work that is required to maintain a resetting process. We discuss different regimes of resetting, including a Maxwell demon scenario where heat is extracted from a bath at constant temperature.
NASA Astrophysics Data System (ADS)
Hairer, Martin
2006-03-01
We consider a class of parabolic stochastic PDEs driven by white noise in time, and we are interested in showing ergodicity for some cases where the noise is degenerate, i.e., acts only on part of the equation. In some cases where the standard Strong Feller / Irreducibility argument fails, one can nevertheless implement a coupling construction that ensures uniqueness of the invariant measure. We focus on the example of the complex Ginzburg-Landau equation driven by real space-time white noise.
Dimensional accuracy of 2-stage putty-wash impressions: influence of impression trays and viscosity.
Balkenhol, Markus; Ferger, Paul; Wöstmann, Bernd
2007-01-01
The aim of this in vitro study was to evaluate the influence of the impression tray and viscosity of the wash material on the dimensional accuracy of impressions taken using a 2-stage putty-wash technique. Identically shaped metal stock trays (MeTs) and disposable plastic stock trays (DiTs) were used for taking impressions (n = 10) of a mandibular cast (4 abutments) with 2 different impression materials. Dies were poured and the relative diameter deviation was calculated after measurement. Zero viscosity of the materials was determined. Dimensional accuracy was significantly affected when DiTs were used. Lower-viscosity wash materials led to more precise impressions.
An evaluation of a Simon 2-Stage phase II clinical trial design incorporating toxicity monitoring.
Ray, H E; Rai, S N
2011-05-01
Phase II clinical trials are usually designed to measure efficacy but patient safety is also a very important aspect. Previous authors suggested a methodology that allows one to monitor the cumulative number of toxic events after each patient is treated, which is also known as continuous toxicity monitoring. In this work we describe how to combine the continuous toxicity monitoring methodology with the Simon 2-Stage design for response. Then we investigate through simulation the combined procedure's type I and type II error rates under various combinations of design parameters. We include the underlying relationship between toxicity and response in our examination of the error rates.
Schilstra, Maria J; Martin, Stephen R
2009-01-01
Stochastic simulations may be used to describe changes with time of a reaction system in a way that explicitly accounts for the fact that molecules show a significant degree of randomness in their dynamic behavior. The stochastic approach is almost invariably used when small numbers of molecules or molecular assemblies are involved because this randomness leads to significant deviations from the predictions of the conventional deterministic (or continuous) approach to the simulation of biochemical kinetics. Advances in computational methods over the three decades that have elapsed since the publication of Daniel Gillespie's seminal paper in 1977 (J. Phys. Chem. 81, 2340-2361) have allowed researchers to produce highly sophisticated models of complex biological systems. However, these models are frequently highly specific for the particular application and their description often involves mathematical treatments inaccessible to the nonspecialist. For anyone completely new to the field to apply such techniques in their own work might seem at first sight to be a rather intimidating prospect. However, the fundamental principles underlying the approach are in essence rather simple, and the aim of this article is to provide an entry point to the field for a newcomer. It focuses mainly on these general principles, both kinetic and computational, which tend to be not particularly well covered in specialist literature, and shows that interesting information may even be obtained using very simple operations in a conventional spreadsheet.
Stochastic power flow modeling
Not Available
1980-06-01
The stochastic nature of customer demand and equipment failure on large interconnected electric power networks has produced a keen interest in the accurate modeling and analysis of the effects of probabilistic behavior on steady state power system operation. The principle avenue of approach has been to obtain a solution to the steady state network flow equations which adhere both to Kirchhoff's Laws and probabilistic laws, using either combinatorial or functional approximation techniques. Clearly the need of the present is to develop sound techniques for producing meaningful data to serve as input. This research has addressed this end and serves to bridge the gap between electric demand modeling, equipment failure analysis, etc., and the area of algorithm development. Therefore, the scope of this work lies squarely on developing an efficient means of producing sensible input information in the form of probability distributions for the many types of solution algorithms that have been developed. Two major areas of development are described in detail: a decomposition of stochastic processes which gives hope of stationarity, ergodicity, and perhaps even normality; and a powerful surrogate probability approach using proportions of time which allows the calculation of joint events from one dimensional probability spaces.
Aerodynamic characteristics of the National Launch System (NLS) 1 1/2 stage launch vehicle
NASA Technical Reports Server (NTRS)
Springer, A. M.; Pokora, D. C.
1994-01-01
The National Aeronautics and Space Administration (NASA) is studying ways of assuring more reliable and cost effective means to space. One launch system studied was the NLS which included the l l/2 stage vehicle. This document encompasses the aerodynamic characteristics of the 1 l/2 stage vehicle. To support the detailed configuration definition two wind tunnel tests were conducted in the NASA Marshall Space Flight Center's 14x14-Inch Trisonic Wind Tunnel during 1992. The tests were a static stability and a pressure test, each utilizing 0.004 scale models. The static stability test resulted in the forces and moments acting on the vehicle. The aerodynamics for the reference configuration with and without feedlines and an evaluation of three proposed engine shroud configurations were also determined. The pressure test resulted in pressure distributions over the reference vehicle with and without feedlines including the reference engine shrouds. These pressure distributions were integrated and balanced to the static stability coefficients resulting in distributed aerodynamic loads on the vehicle. The wind tunnel tests covered a Mach range of 0.60 to 4.96. These ascent flight aerodynamic characteristics provide the basis for trajectory and performance analysis, loads determination, and guidance and control evaluation.
Lenzenweger, M F; Loranger, A W; Korfine, L; Neff, C
1997-04-01
There is no epidemiology of personality disorders (PDs) comparable with that currently available for most other mental disorders. One reason for this is that an Axis II diagnosis usually requires considerable clinical sophistication and it is expensive to deploy clinicians rather than trained laypersons to examine large community samples. This study explores the feasibility of using a 2-stage method in which only subjects who were screened as positive for PD would be interviewed by clinicians. University students were screened with a self-administered Axis II inventory and subsequently interviewed by clinicians with the use of the International Personality Disorder Examination. The screen detected all individuals who subsequently received a definite diagnosis on the interview, and a specificity rate of detection was 61%. The point-prevalence estimate for diagnosable PD in this nonclinical population was 11.01% (95% confidence interval, 7.57%-14.52%). If these results can be replicated in a more representative community sample, this 2-stage method might substantially reduce the number of persons who needed to be interviewed in a major epidemiological study of PDs, with little or no loss in diagnostic accuracy, while presumably lowering the cost of such an investigation.
Variance decomposition in stochastic simulators
Le Maître, O. P.; Knio, O. M.; Moraes, A.
2015-06-28
This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.
Richard V. Field, Jr.; Emery, John M.; Grigoriu, Mircea Dan
2015-05-19
The stochastic collocation (SC) and stochastic Galerkin (SG) methods are two well-established and successful approaches for solving general stochastic problems. A recently developed method based on stochastic reduced order models (SROMs) can also be used. Herein we provide a comparison of the three methods for some numerical examples; our evaluation only holds for the examples considered in the paper. The purpose of the comparisons is not to criticize the SC or SG methods, which have proven very useful for a broad range of applications, nor is it to provide overall ratings of these methods as compared to the SROM method.more » Furthermore, our objectives are to present the SROM method as an alternative approach to solving stochastic problems and provide information on the computational effort required by the implementation of each method, while simultaneously assessing their performance for a collection of specific problems.« less
Richard V. Field, Jr.; Emery, John M.; Grigoriu, Mircea Dan
2015-05-19
The stochastic collocation (SC) and stochastic Galerkin (SG) methods are two well-established and successful approaches for solving general stochastic problems. A recently developed method based on stochastic reduced order models (SROMs) can also be used. Herein we provide a comparison of the three methods for some numerical examples; our evaluation only holds for the examples considered in the paper. The purpose of the comparisons is not to criticize the SC or SG methods, which have proven very useful for a broad range of applications, nor is it to provide overall ratings of these methods as compared to the SROM method. Furthermore, our objectives are to present the SROM method as an alternative approach to solving stochastic problems and provide information on the computational effort required by the implementation of each method, while simultaneously assessing their performance for a collection of specific problems.
Stochastic simulation of transport phenomena
Wedgewood, L.E.; Geurts, K.R.
1995-10-01
In this paper, four examples are given to demonstrate how stochastic simulations can be used as a method to obtain numerical solutions to transport problems. The problems considered are two-dimensional heat conduction, mass diffusion with reaction, the start-up of Poiseuille flow, and Couette flow of a suspension of Hookean dumbbells. The first three examples are standard problems with well-known analytic solutions which can be used to verify the results of the stochastic simulation. The fourth example combines a Brownian dynamics simulation for Hookean dumbbells, a crude model of a dilute polymer suspension, and a stochastic simulation for the suspending, Newtonian fluid. These examples illustrate appropriate methods for handling source/sink terms and initial and boundary conditions. The stochastic simulation results compare well with the analytic solutions and other numerical solutions. The goal of this paper is to demonstrate the wide applicability of stochastic simulation as a numerical method for transport problems.
Stochastic and delayed stochastic models of gene expression and regulation.
Ribeiro, Andre S
2010-01-01
Gene expression and gene regulatory networks dynamics are stochastic. The noise in the temporal amounts of proteins and RNA molecules in cells arises from the stochasticity of transcription initiation and elongation (e.g., due to RNA polymerase pausing), translation, and post-transcriptional regulation mechanisms, such as reversible phosphorylation and splicing. This is further enhanced by the fact that most RNA molecules and proteins exist in cells in very small amounts. Recently, the time needed for transcription and translation to be completed once initiated were shown to affect the stochasticity in gene networks. This observation stressed the need of either introducing explicit delays in models of transcription and translation or to model processes such as elongation at the single nucleotide level. Here we review stochastic and delayed stochastic models of gene expression and gene regulatory networks. We first present stochastic non-delayed and delayed models of transcription, followed by models at the single nucleotide level. Next, we present models of gene regulatory networks, describe the dynamics of specific stochastic gene networks and available simulators to implement these models. Copyright 2009 Elsevier Inc. All rights reserved.
Boelter, Fred W; Xia, Yulin; Dell, Linda
2015-05-01
Sanding joint compounds is a dusty activity and exposures are not well characterized. Until the mid 1970s, asbestos-containing joint compounds were used by some people such that sanding could emit dust and asbestos fibers. We estimated the distribution of 8-h TWA concentrations and cumulative exposures to respirable dusts and chrysotile asbestos fibers for four worker groups: (1) drywall specialists, (2) generalists, (3) tradespersons who are bystanders to drywall finishing, and (4) do-it-yourselfers (DIYers). Data collected through a survey of experienced contractors, direct field observations, and literature were used to develop prototypical exposure scenarios for each worker group. To these exposure scenarios, we applied a previously developed semi-empirical mathematical model that predicts area as well as personal breathing zone respirable dust concentrations. An empirical factor was used to estimate chrysotile fiber concentrations from respirable dust concentrations. On a task basis, we found mean 8-h TWA concentrations of respirable dust and chrysotile fibers are numerically highest for specialists, followed by generalists, DIYers, and bystander tradespersons; these concentrations are estimated to be in excess of the respective current but not historical Threshold Limit Values. Due to differences in frequency of activities, annual cumulative exposures are highest for specialists, followed by generalists, bystander tradespersons, and DIYers. Cumulative exposure estimates for chrysotile fibers from drywall finishing are expected to result in few, if any, mesothelioma or excess lung cancer deaths according to recently published risk assessments. Given the dustiness of drywall finishing, we recommend diligence in the use of readily available source controls.
Stochastic models of gene expression and post-transcriptional regulation
NASA Astrophysics Data System (ADS)
Pendar, Hodjat; Kulkarni, Rahul; Jia, Tao
2011-10-01
The intrinsic stochasticity of gene expression can give rise to phenotypic heterogeneity in a population of genetically identical cells. Correspondingly, there is considerable interest in understanding how different molecular mechanisms impact the 'noise' in gene expression. Of particular interest are post-transcriptional regulatory mechanisms involving genes called small RNAs, which control important processes such as development and cancer. We propose and analyze general stochastic models of gene expression and derive exact analytical expressions quantifying the noise in protein distributions [1]. Focusing on specific regulatory mechanisms, we analyze a general model for post-transcriptional regulation of stochastic gene expression [2]. The results obtained provide new insights into the role of post-transcriptional regulation in controlling the noise in gene expression. [4pt] [1] T. Jia and R. V. Kulkarni, Phys. Rev. Lett.,106, 058102 (2011) [0pt] [2] T. Jia and R. V. Kulkarni, Phys. Rev. Lett., 105, 018101 (2010)
Threshold for extinction and survival in stochastic tumor immune system
NASA Astrophysics Data System (ADS)
Li, Dongxi; Cheng, Fangjuan
2017-10-01
This paper mainly investigates the stochastic character of tumor growth and extinction in the presence of immune response of a host organism. Firstly, the mathematical model describing the interaction and competition between the tumor cells and immune system is established based on the Michaelis-Menten enzyme kinetics. Then, the threshold conditions for extinction, weak persistence and stochastic persistence of tumor cells are derived by the rigorous theoretical proofs. Finally, stochastic simulation are taken to substantiate and illustrate the conclusion we have derived. The modeling results will be beneficial to understand to concept of immunoediting, and develop the cancer immunotherapy. Besides, our simple theoretical model can help to obtain new insight into the complexity of tumor growth.
Fast approximate stochastic tractography.
Iglesias, Juan Eugenio; Thompson, Paul M; Liu, Cheng-Yi; Tu, Zhuowen
2012-01-01
Many different probabilistic tractography methods have been proposed in the literature to overcome the limitations of classical deterministic tractography: (i) lack of quantitative connectivity information; and (ii) robustness to noise, partial volume effects and selection of seed region. However, these methods rely on Monte Carlo sampling techniques that are computationally very demanding. This study presents an approximate stochastic tractography algorithm (FAST) that can be used interactively, as opposed to having to wait several minutes to obtain the output after marking a seed region. In FAST, tractography is formulated as a Markov chain that relies on a transition tensor. The tensor is designed to mimic the features of a well-known probabilistic tractography method based on a random walk model and Monte-Carlo sampling, but can also accommodate other propagation rules. Compared to the baseline algorithm, our method circumvents the sampling process and provides a deterministic solution at the expense of partially sacrificing sub-voxel accuracy. Therefore, the method is strictly speaking not stochastic, but provides a probabilistic output in the spirit of stochastic tractography methods. FAST was compared with the random walk model using real data from 10 patients in two different ways: 1. the probability maps produced by the two methods on five well-known fiber tracts were directly compared using metrics from the image registration literature; and 2. the connectivity measurements between different regions of the brain given by the two methods were compared using the correlation coefficient ρ. The results show that the connectivity measures provided by the two algorithms are well-correlated (ρ = 0.83), and so are the probability maps (normalized cross correlation 0.818 ± 0.081). The maps are also qualitatively (i.e., visually) very similar. The proposed method achieves a 60x speed-up (7 s vs. 7 min) over the Monte Carlo sampling scheme, therefore
Stochastization in gravitating systems
NASA Astrophysics Data System (ADS)
Ovod, D. V.; Ossipkov, L. P.
2013-10-01
We discuss the effective stochastization time τ_e for gravitating systems in terms of the Krylov and Gurzadyan-Savvidi paradigm. The truncated Holtsmark distribution for a random force proposed by Rastorguev and Sementsov implies {τ_e/τ_c ∝ N0.20}, where τ_c is the crossing time. We find in the case of the Petrovskaya distribution for a random force {τ_e/τ_c ∝ Nk}, where {k=0.27}-0.31, depending on the oblateness and rotation of the system, and {τ_e/τ_c ∝ N1/3/(ln N)1/2} when N≫ 1. The latter result agrees with those of Genkin (1969) and Gurzadyan & Kocharyan (2009) (k=1/3). Dedicated to Igor L'vovich Genkin (1931-2011)
Bunched beam stochastic cooling
Wei, Jie.
1992-01-01
The scaling laws for bunched-beam stochastic cooling has been derived in terms of the optimum cooling rate and the mixing condition. In the case that particles occupy the entire sinusoidal rf bucket, the optimum cooling rate of the bunched beam is shown to be similar to that predicted from the coasting-beam theory using a beam of the same average density and mixing factor. However, in the case that particles occupy only the center of the bucket, the optimum rate decrease in proportion to the ratio of the bunch area to the bucket area. The cooling efficiency can be significantly improved if the synchrotron side-band spectrum is effectively broadened, e.g. by the transverse tune spread or by using a double rf system.
Bunched beam stochastic cooling
Wei, Jie
1992-09-01
The scaling laws for bunched-beam stochastic cooling has been derived in terms of the optimum cooling rate and the mixing condition. In the case that particles occupy the entire sinusoidal rf bucket, the optimum cooling rate of the bunched beam is shown to be similar to that predicted from the coasting-beam theory using a beam of the same average density and mixing factor. However, in the case that particles occupy only the center of the bucket, the optimum rate decrease in proportion to the ratio of the bunch area to the bucket area. The cooling efficiency can be significantly improved if the synchrotron side-band spectrum is effectively broadened, e.g. by the transverse tune spread or by using a double rf system.
Pulse shape distortion in a 2-stage all-fiber Er-doped amplifier
NASA Astrophysics Data System (ADS)
Michalska, M.; Mamajek, M.
2013-07-01
The issue of temporal pulse distortion occurring during amplification process in a 2-stage, fiber amplifier, operating in the eye-safe spectral region, is discussed. The amplifier was built in a Master Oscillator Power Amplifier (MOPA) configuration and seeded by a distributed feedback (DFB) laser providing nanosecond pulses at a repetition rate of 20 kHz. It operated at a wavelength of 1549.13 nm and generated over 200 mW of output power with a slope efficiency of up to 28%. The comparison between the calculated and measured results on saturation-induced pulse shape deformation, for ~300-ns pulses, is presented. The analyzed pulse shapes embraced rectangle, Gaussian, triangle and "M" letter.
Choi, Mihye; Kulber, David A.; Downey, Susan; Duda, Gloria; Kind, Gabriel M.; Jewell, Mark L.; Murphy, Diane K.; Lehfeldt, Max R.; Fine, Neil
2017-01-01
Background: Soft-tissue support devices are used during breast reconstruction. This study investigated long-term clinical data following SERI Surgical Scaffold (SERI) implantation, a bioresorbable, silk-derived scaffold for soft-tissue support. Methods: This was a prospective, multicenter study in 103 subjects who received SERI during stage 1 of 2-stage breast reconstruction with subpectoral tissue expander placement (Natrelle Style 133V; Allergan plc, Dublin, Ireland) followed by subpectoral breast implant placement. Investigator satisfaction (11-point scale: 0, very dissatisfied and 10, very satisfied) at 6 months was the primary endpoint. Ease of use, satisfaction, scaffold palpability/visibility, breast anatomy measurements via 3D images, SERI integration, histology, and safety were also assessed through 2 years after stage 1 surgery. Results: Analyses were performed on the per-protocol population (103 subjects; 161 breasts) with no protocol deviations that could affect outcomes. Ease of use and subject and investigator satisfaction with SERI were high throughout 2 years. Breast anatomy measurements with 3D images demonstrated long-term soft-tissue stability of the lower breast mound. Key complication rates per breast were tissue/skin necrosis and wrinkling/rippling (8.1% each) and seroma, wound dehiscence, and breast redness (5.0% each). Over 2 years, 4 breasts in 4 subjects underwent reoperation with explantation of any device; 2 breasts required SERI explantation. SERI was retained in 98.8% of breasts (159/161) at 2 years. Conclusions: SERI was associated with high and consistent levels of investigator and subject satisfaction and demonstrated soft-tissue stability in the lower breast through 2 years. SERI provides a safe, long-term benefit for soft-tissue support in 2-stage breast reconstruction. PMID:28607855
Karp, Nolan; Choi, Mihye; Kulber, David A; Downey, Susan; Duda, Gloria; Kind, Gabriel M; Jewell, Mark L; Murphy, Diane K; Lehfeldt, Max R; Fine, Neil
2017-05-01
Soft-tissue support devices are used during breast reconstruction. This study investigated long-term clinical data following SERI Surgical Scaffold (SERI) implantation, a bioresorbable, silk-derived scaffold for soft-tissue support. This was a prospective, multicenter study in 103 subjects who received SERI during stage 1 of 2-stage breast reconstruction with subpectoral tissue expander placement (Natrelle Style 133V; Allergan plc, Dublin, Ireland) followed by subpectoral breast implant placement. Investigator satisfaction (11-point scale: 0, very dissatisfied and 10, very satisfied) at 6 months was the primary endpoint. Ease of use, satisfaction, scaffold palpability/visibility, breast anatomy measurements via 3D images, SERI integration, histology, and safety were also assessed through 2 years after stage 1 surgery. Analyses were performed on the per-protocol population (103 subjects; 161 breasts) with no protocol deviations that could affect outcomes. Ease of use and subject and investigator satisfaction with SERI were high throughout 2 years. Breast anatomy measurements with 3D images demonstrated long-term soft-tissue stability of the lower breast mound. Key complication rates per breast were tissue/skin necrosis and wrinkling/rippling (8.1% each) and seroma, wound dehiscence, and breast redness (5.0% each). Over 2 years, 4 breasts in 4 subjects underwent reoperation with explantation of any device; 2 breasts required SERI explantation. SERI was retained in 98.8% of breasts (159/161) at 2 years. SERI was associated with high and consistent levels of investigator and subject satisfaction and demonstrated soft-tissue stability in the lower breast through 2 years. SERI provides a safe, long-term benefit for soft-tissue support in 2-stage breast reconstruction.
Stochastic reinforcement benefits skill acquisition.
Dayan, Eran; Averbeck, Bruno B; Richmond, Barry J; Cohen, Leonardo G
2014-02-14
Learning complex skills is driven by reinforcement, which facilitates both online within-session gains and retention of the acquired skills. Yet, in ecologically relevant situations, skills are often acquired when mapping between actions and rewarding outcomes is unknown to the learning agent, resulting in reinforcement schedules of a stochastic nature. Here we trained subjects on a visuomotor learning task, comparing reinforcement schedules with higher, lower, or no stochasticity. Training under higher levels of stochastic reinforcement benefited skill acquisition, enhancing both online gains and long-term retention. These findings indicate that the enhancing effects of reinforcement on skill acquisition depend on reinforcement schedules.
Stochastic Physicochemical Dynamics
NASA Astrophysics Data System (ADS)
Tsekov, R.
2001-02-01
Thermodynamic Relaxation in Quantum Systems: A new approach to quantum Markov processes is developed and the corresponding Fokker-Planck equation is derived. The latter is examined to reproduce known results from classical and quantum physics. It was also applied to the phase-space description of a mechanical system thus leading to a new treatment of this problem different from the Wigner presentation. The equilibrium probability density obtained in the mixed coordinate-momentum space is a reasonable extension of the Gibbs canonical distribution. The validity of the Einstein fluctuation-dissipation relation is discussed in respect to the type of relaxation in an isothermal system. The first model, presuming isothermic fluctuations, leads to the Einstein formula. The second model supposes adiabatic fluctuations and yields another relation between the diffusion coefficient and mobility of a Brownian particle. A new approach to relaxations in quantum systems is also proposed that demonstrates applicability only of the adiabatic model for description of the quantum Brownian dynamics. Stochastic Dynamics of Gas Molecules: A stochastic Langevin equation is derived, describing the thermal motion of a molecule immersed in a rested fluid of identical molecules. The fluctuation-dissipation theorem is proved and a number of correlation characteristics of the molecular Brownian motion are obtained. A short review of the classical theory of Brownian motion is presented. A new method is proposed for derivation of the Fokker-Planck equations, describing the probability density evolution, from stochastic differential equations. It is also proven via the central limit theorem that the white noise is only Gaussian. The applicability of stochastic differential equations to thermodynamics is considered and a new form, different from the classical Ito and Stratonovich forms, is introduced. It is shown that the new presentation is more appropriate for the description of thermodynamic
Nonlinear Stochastic PDEs: Analysis and Approximations
2016-05-23
3.4.1 Nonlinear Stochastic PDEs: Analysis and Approximations We compare Wiener chaos and stochastic collocation methods for linear advection-reaction...ADDRESS (ES) U.S. Army Research Office P.O. Box 12211 Research Triangle Park, NC 27709-2211 nonlinear stochastic PDEs (SPDEs), nonlocal SPDEs, Navier...3.4.1 Nonlinear Stochastic PDEs: Analysis and Approximations Report Title We compare Wiener chaos and stochastic collocation methods for linear
Rubinstein, Larry; Litwin, Samuel; Yothers, Greg
2012-01-01
Background Most phase II clinical trials utilize a single primary endpoint to determine the promise of a regimen for future study. However, many disorders manifest themselves in complex ways. For example, migraine headaches can cause pain, auras, photophobia, and emesis. Investigators may believe a drug is effective at reducing migraine pain and the severity of emesis during an attack. Nevertheless, they could still be interested in proceeding with development of the drug if it is effective against only one of these symptoms. Such a study would be a candidate for a clinical trial with co-primary endpoints. Purpose The purpose of the article is to provide a method for designing a 2-stage clinical trial with dichotomous co-primary endpoints of efficacy that has the ability to detect activity on either response measure with high probability when the drug is active on one or both measures, while at the same time rejecting the drug with high probability when there is little activity on both dimensions. The design enables early closure for futility and is flexible with regard to attained accrual. Methods The design is proposed in the context of cancer clinical trials where tumor response is used to assess a drug's ability to kill tumor cells and progression-free survival (PFS) status after a certain period is used to evaluate the drug's ability to stabilize tumor growth. Both endpoints are assumed to be distributed as binomial random variables, and uninteresting probabilities of success are determined from historical controls. Given the necessity of accrual flexibility, exhaustive searching algorithms to find optimum designs do not seem feasible at this time. Instead, critical values are determined for realized sample sizes using specific procedures. Then accrual windows are found to achieve a design's desired level of significance, probability of early termination (PET), and power. Results The design is illustrated with a clinical trial that examined bevacizumab in
Statistical validation of stochastic models
Hunter, N.F.; Barney, P.; Paez, T.L.; Ferregut, C.; Perez, L.
1996-12-31
It is common practice in structural dynamics to develop mathematical models for system behavior, and the authors are now capable of developing stochastic models, i.e., models whose parameters are random variables. Such models have random characteristics that are meant to simulate the randomness in characteristics of experimentally observed systems. This paper suggests a formal statistical procedure for the validation of mathematical models of stochastic systems when data taken during operation of the stochastic system are available. The statistical characteristics of the experimental system are obtained using the bootstrap, a technique for the statistical analysis of non-Gaussian data. The authors propose a procedure to determine whether or not a mathematical model is an acceptable model of a stochastic system with regard to user-specified measures of system behavior. A numerical example is presented to demonstrate the application of the technique.
Adaptive and Optimal Control of Stochastic Dynamical Systems
2015-09-14
control and stochastic differential games . Stochastic linear-quadratic, continuous time, stochastic control problems are solved for systems with noise...control problems for systems with arbitrary correlated n 15. SUBJECT TERMS Adaptive control, optimal control, stochastic differential games 16. SECURITY...explicit results have been obtained for problems of stochastic control and stochastic differential games . Stochastic linear- quadratic, continuous time
Network Analysis with Stochastic Grammars
2015-09-17
a variety of ways on a lower level. For a grammar , each phase is essentially a Task and a network attack is, at the highest level, a five Task...NETIVORK ANALYSIS \\\\’ITH STOCHASTIC GRAMMARS DISSERTATION Alan C. Lin, Maj , USAF AFIT-ENG-DS-15-S-014 DEPARTMENT OF THE AIR FORCE AIR...subject to copyright protection in the United States. AFIT-ENG-DS-15-S-014 NETWORK ANALYSIS WITH STOCHASTIC GRAMMARS DISSERTATION Presented
Stochastic roots of growth phenomena
NASA Astrophysics Data System (ADS)
De Lauro, E.; De Martino, S.; De Siena, S.; Giorno, V.
2014-05-01
We show that the Gompertz equation describes the evolution in time of the median of a geometric stochastic process. Therefore, we induce that the process itself generates the growth. This result allows us further to exploit a stochastic variational principle to take account of self-regulation of growth through feedback of relative density variations. The conceptually well defined framework so introduced shows its usefulness by suggesting a form of control of growth by exploiting external actions.
Some Topics in Stochastic Control
2010-10-14
Flows of Diffeomorphisms , (viii)Feller and Stability Properties of the Nonlinear Filter, (ix) Particle filter methods for Atmospheric and Oceanic data... Diffeomorphisms , Bernoulli, 16 (2010), no. 1, 91- -113. 5. A. Budhiraja, P. Dupuis and V. Maroulas. Variational Representations for Continuous Time...treat a setting with state dependent rates. 16 C.III. Large Deviations for Stochastic Flows of Diffeomorphisms [11]. Stochastic flows of diffeomorphisms
Stochastic Models of Polymer Systems
2016-01-01
Distribution Unlimited Final Report: Stochastic Models of Polymer Systems The views, opinions and/or findings contained in this report are those of the...peer-reviewed journals: Number of Papers published in non peer-reviewed journals: Final Report: Stochastic Models of Polymer Systems Report Title...field limit of a dynamical model for polymer systems, Science China Mathematics, (11 2012): 0. doi: TOTAL: 1 Number of Non Peer-Reviewed Conference
Stochastic superparameterization in quasigeostrophic turbulence
Grooms, Ian; Majda, Andrew J.
2014-08-15
In this article we expand and develop the authors' recent proposed methodology for efficient stochastic superparameterization algorithms for geophysical turbulence. Geophysical turbulence is characterized by significant intermittent cascades of energy from the unresolved to the resolved scales resulting in complex patterns of waves, jets, and vortices. Conventional superparameterization simulates large scale dynamics on a coarse grid in a physical domain, and couples these dynamics to high-resolution simulations on periodic domains embedded in the coarse grid. Stochastic superparameterization replaces the nonlinear, deterministic eddy equations on periodic embedded domains by quasilinear stochastic approximations on formally infinite embedded domains. The result is a seamless algorithm which never uses a small scale grid and is far cheaper than conventional SP, but with significant success in difficult test problems. Various design choices in the algorithm are investigated in detail here, including decoupling the timescale of evolution on the embedded domains from the length of the time step used on the coarse grid, and sensitivity to certain assumed properties of the eddies (e.g. the shape of the assumed eddy energy spectrum). We present four closures based on stochastic superparameterization which elucidate the properties of the underlying framework: a ‘null hypothesis’ stochastic closure that uncouples the eddies from the mean, a stochastic closure with nonlinearly coupled eddies and mean, a nonlinear deterministic closure, and a stochastic closure based on energy conservation. The different algorithms are compared and contrasted on a stringent test suite for quasigeostrophic turbulence involving two-layer dynamics on a β-plane forced by an imposed background shear. The success of the algorithms developed here suggests that they may be fruitfully applied to more realistic situations. They are expected to be particularly useful in providing accurate and
Phenomenology of stochastic exponential growth
NASA Astrophysics Data System (ADS)
Pirjol, Dan; Jafarpour, Farshid; Iyer-Biswas, Srividya
2017-06-01
Stochastic exponential growth is observed in a variety of contexts, including molecular autocatalysis, nuclear fission, population growth, inflation of the universe, viral social media posts, and financial markets. Yet literature on modeling the phenomenology of these stochastic dynamics has predominantly focused on one model, geometric Brownian motion (GBM), which can be described as the solution of a Langevin equation with linear drift and linear multiplicative noise. Using recent experimental results on stochastic exponential growth of individual bacterial cell sizes, we motivate the need for a more general class of phenomenological models of stochastic exponential growth, which are consistent with the observation that the mean-rescaled distributions are approximately stationary at long times. We show that this behavior is not consistent with GBM, instead it is consistent with power-law multiplicative noise with positive fractional powers. Therefore, we consider this general class of phenomenological models for stochastic exponential growth, provide analytical solutions, and identify the important dimensionless combination of model parameters, which determines the shape of the mean-rescaled distribution. We also provide a prescription for robustly inferring model parameters from experimentally observed stochastic growth trajectories.
Brennan J. M.; Blaskiewicz, M.; Mernick, K.
2012-05-20
The full 6-dimensional [x,x'; y,y'; z,z'] stochastic cooling system for RHIC was completed and operational for the FY12 Uranium-Uranium collider run. Cooling enhances the integrated luminosity of the Uranium collisions by a factor of 5, primarily by reducing the transverse emittances but also by cooling in the longitudinal plane to preserve the bunch length. The components have been deployed incrementally over the past several runs, beginning with longitudinal cooling, then cooling in the vertical planes but multiplexed between the Yellow and Blue rings, next cooling both rings simultaneously in vertical (the horizontal plane was cooled by betatron coupling), and now simultaneous horizontal cooling has been commissioned. The system operated between 5 and 9 GHz and with 3 x 10{sup 8} Uranium ions per bunch and produces a cooling half-time of approximately 20 minutes. The ultimate emittance is determined by the balance between cooling and emittance growth from Intra-Beam Scattering. Specific details of the apparatus and mathematical techniques for calculating its performance have been published elsewhere. Here we report on: the method of operation, results with beam, and comparison of results to simulations.
NASA Astrophysics Data System (ADS)
McDonnell, Mark D.; Amblard, Pierre-Olivier; Stocks, Nigel G.
2009-01-01
We introduce and define the concept of a stochastic pooling network (SPN), as a model for sensor systems where redundancy and two forms of 'noise'—lossy compression and randomness—interact in surprising ways. Our approach to analysing SPNs is information theoretic. We define an SPN as a network with multiple nodes that each produce noisy and compressed measurements of the same information. An SPN must combine all these measurements into a single further compressed network output, in a way dictated solely by naturally occurring physical properties—i.e. pooling—and yet cause no (or negligible) reduction in mutual information. This means that SPNs exhibit redundancy reduction as an emergent property of pooling. The SPN concept is applicable to examples in biological neural coding, nanoelectronics, distributed sensor networks, digital beamforming arrays, image processing, multiaccess communication networks and social networks. In most cases the randomness is assumed to be unavoidably present rather than deliberately introduced. We illustrate the central properties of SPNs for several case studies, where pooling occurs by summation, including nodes that are noisy scalar quantizers, and nodes with conditionally Poisson statistics. Other emergent properties of SPNs and some unsolved problems are also briefly discussed.
Stochastic processes in gravitropism.
Meroz, Yasmine; Bastien, Renaud
2014-01-01
In this short review we focus on the role of noise in gravitropism of plants - the reorientation of plants according to the direction of gravity. We briefly introduce the conventional picture of static gravisensing in cells specialized in sensing. This model hinges on the sedimentation of statoliths (high in density and mass relative to other organelles) to the lowest part of the sensing cell. We then present experimental observations that cannot currently be understood within this framework. Lastly we introduce some current alternative models and directions that attempt to incorporate and interpret these experimental observations, including: (i) dynamic sensing, where gravisensing is suggested to be enhanced by stochastic events due to thermal and mechanical noise. These events both effectively lower the threshold of response, and lead to small-distance sedimentation, allowing amplification, and integration of the signal. (ii) The role of the cytoskeleton in signal-to-noise modulation and (iii) in signal transduction. In closing, we discuss directions that seem to either not have been explored, or that are still poorly understood.
NASA Technical Reports Server (NTRS)
Whitney, W. J.; Behning, F. P.; Moffitt, T. P.; Hotz, G. M.
1980-01-01
The stage group performance of a 4 1/2 stage turbine with an average stage loading factor of 4.66 and high specific work output was determined in cold air at design equivalent speed. The four stage turbine configuration produced design equivalent work output with an efficiency of 0.856; a barely discernible difference from the 0.855 obtained for the complete 4 1/2 stage turbine in a previous investigation. The turbine was designed and the procedure embodied the following design features: (1) controlled vortex flow, (2) tailored radial work distribution, and (3) control of the location of the boundary-layer transition point on the airfoil suction surface. The efficiency forecast for the 4 1/2 stage turbine was 0.886, and the value predicted using a reference method was 0.862. The stage group performance results were used to determine the individual stage efficiencies for the condition at which design 4 1/2 stage work output was obtained. The efficiencies of stages one and four were about 0.020 lower than the predicted value, that of stage two was 0.014 lower, and that of stage three was about equal to the predicted value. Thus all the stages operated reasonably close to their expected performance levels, and the overall (4 1/2 stage) performance was not degraded by any particularly inefficient component.
Unsteady Aero Computation of a 1 1/2 Stage Large Scale Rotating Turbine
NASA Technical Reports Server (NTRS)
To, Wai-Ming
2012-01-01
This report is the documentation of the work performed for the Subsonic Rotary Wing Project under the NASA s Fundamental Aeronautics Program. It was funded through Task Number NNC10E420T under GESS-2 Contract NNC06BA07B in the period of 10/1/2010 to 8/31/2011. The objective of the task is to provide support for the development of variable speed power turbine technology through application of computational fluid dynamics analyses. This includes work elements in mesh generation, multistage URANS simulations, and post-processing of the simulation results for comparison with the experimental data. The unsteady CFD calculations were performed with the TURBO code running in multistage single passage (phase lag) mode. Meshes for the blade rows were generated with the NASA developed TCGRID code. The CFD performance is assessed and improvements are recommended for future research in this area. For that, the United Technologies Research Center's 1 1/2 stage Large Scale Rotating Turbine was selected to be the candidate engine configuration for this computational effort because of the completeness and availability of the data.
A 2-Stage Surgical and Endovascular Treatment of Rare Multiple Aneurysms of Pancreatic Arteries.
Aryal, Bibek; Komokata, Teruo; Ueno, Takayuki; Yamamoto, Bunsei; Senokuchi, Terutoshi; Yasuda, Hiroshi; Kaieda, Mamoru; Imoto, Yutaka
2017-04-01
Aneurysms of pancreatic arteries (PAs) are often found incidentally during evaluation of other abdominal pathology. Aneurysms involving multiple PAs are rarely reported in the literature. In case reports of PA aneurysm, inferior pancreaticoduodenal artery is the usual site of aneurysm occurrence. PA aneurysms can be treated surgically by aneurysm exclusion, excision, and by endovascular techniques. However, no clear consensus exists regarding treatment modality, leaving the surgeon to determine the most appropriate approach bearing in mind their experience, anatomical location of the aneurysm, involved artery, and urgency of the procedure. We report a rare PA aneurysm involving dorsal pancreatic artery (DPA) and anterior inferior pancreaticoduodenal artery (AIPDA) associated with celiac stenosis that was incidentally diagnosed in a patient with hepatic hemangioma. In addition, we reviewed data from the literature on patients with diffuse or multiple PA aneurysms and discuss the treatment modality in these rare variants. Both surgical and endovascular procedures are equally advocated in treatment of multiple PA aneurysms. In our report, we demonstrate a 2-stage surgical and endovascular treatment modality; DPA aneurysm that was not suitable for endovascular treatment was surgically resected and an iliohepatic bypass was made between left common iliac artery and AIPDA to ensure good hepatic perfusion. One month after the first procedure, AIPDA aneurysm was treated with endovascular embolization. Two-stage surgical and endovascular procedure may represent a useful strategy to treat aneurysms involving multiple PAs. Copyright © 2016 Elsevier Inc. All rights reserved.
Segmentation of stochastic images with a stochastic random walker method.
Pätz, Torben; Preusser, Tobias
2012-05-01
We present an extension of the random walker segmentation to images with uncertain gray values. Such gray-value uncertainty may result from noise or other imaging artifacts or more general from measurement errors in the image acquisition process. The purpose is to quantify the influence of the gray-value uncertainty onto the result when using random walker segmentation. In random walker segmentation, a weighted graph is built from the image, where the edge weights depend on the image gradient between the pixels. For given seed regions, the probability is evaluated for a random walk on this graph starting at a pixel to end in one of the seed regions. Here, we extend this method to images with uncertain gray values. To this end, we consider the pixel values to be random variables (RVs), thus introducing the notion of stochastic images. We end up with stochastic weights for the graph in random walker segmentation and a stochastic partial differential equation (PDE) that has to be solved. We discretize the RVs and the stochastic PDE by the method of generalized polynomial chaos, combining the recent developments in numerical methods for the discretization of stochastic PDEs and an interactive segmentation algorithm. The resulting algorithm allows for the detection of regions where the segmentation result is highly influenced by the uncertain pixel values. Thus, it gives a reliability estimate for the resulting segmentation, and it furthermore allows determining the probability density function of the segmented object volume.
Stacking with stochastic cooling
NASA Astrophysics Data System (ADS)
Caspers, Fritz; Möhl, Dieter
2004-10-01
Accumulation of large stacks of antiprotons or ions with the aid of stochastic cooling is more delicate than cooling a constant intensity beam. Basically the difficulty stems from the fact that the optimized gain and the cooling rate are inversely proportional to the number of particles 'seen' by the cooling system. Therefore, to maintain fast stacking, the newly injected batch has to be strongly 'protected' from the Schottky noise of the stack. Vice versa the stack has to be efficiently 'shielded' against the high gain cooling system for the injected beam. In the antiproton accumulators with stacking ratios up to 105 the problem is solved by radial separation of the injection and the stack orbits in a region of large dispersion. An array of several tapered cooling systems with a matched gain profile provides a continuous particle flux towards the high-density stack core. Shielding of the different systems from each other is obtained both through the spatial separation and via the revolution frequencies (filters). In the 'old AA', where the antiproton collection and stacking was done in one single ring, the injected beam was further shielded during cooling by means of a movable shutter. The complexity of these systems is very high. For more modest stacking ratios, one might use azimuthal rather than radial separation of stack and injected beam. Schematically half of the circumference would be used to accept and cool new beam and the remainder to house the stack. Fast gating is then required between the high gain cooling of the injected beam and the low gain stack cooling. RF-gymnastics are used to merge the pre-cooled batch with the stack, to re-create free space for the next injection, and to capture the new batch. This scheme is less demanding for the storage ring lattice, but at the expense of some reduction in stacking rate. The talk reviews the 'radial' separation schemes and also gives some considerations to the 'azimuthal' schemes.
A Stochastic Collocation Algorithm for Uncertainty Analysis
NASA Technical Reports Server (NTRS)
Mathelin, Lionel; Hussaini, M. Yousuff; Zang, Thomas A. (Technical Monitor)
2003-01-01
This report describes a stochastic collocation method to adequately handle a physically intrinsic uncertainty in the variables of a numerical simulation. For instance, while the standard Galerkin approach to Polynomial Chaos requires multi-dimensional summations over the stochastic basis functions, the stochastic collocation method enables to collapse those summations to a one-dimensional summation only. This report furnishes the essential algorithmic details of the new stochastic collocation method and provides as a numerical example the solution of the Riemann problem with the stochastic collocation method used for the discretization of the stochastic parameters.
Stochastic models: theory and simulation.
Field, Richard V., Jr.
2008-03-01
Many problems in applied science and engineering involve physical phenomena that behave randomly in time and/or space. Examples are diverse and include turbulent flow over an aircraft wing, Earth climatology, material microstructure, and the financial markets. Mathematical models for these random phenomena are referred to as stochastic processes and/or random fields, and Monte Carlo simulation is the only general-purpose tool for solving problems of this type. The use of Monte Carlo simulation requires methods and algorithms to generate samples of the appropriate stochastic model; these samples then become inputs and/or boundary conditions to established deterministic simulation codes. While numerous algorithms and tools currently exist to generate samples of simple random variables and vectors, no cohesive simulation tool yet exists for generating samples of stochastic processes and/or random fields. There are two objectives of this report. First, we provide some theoretical background on stochastic processes and random fields that can be used to model phenomena that are random in space and/or time. Second, we provide simple algorithms that can be used to generate independent samples of general stochastic models. The theory and simulation of random variables and vectors is also reviewed for completeness.
Enhanced algorithms for stochastic programming
Krishna, A.S.
1993-09-01
In this dissertation, we present some of the recent advances made in solving two-stage stochastic linear programming problems of large size and complexity. Decomposition and sampling are two fundamental components of techniques to solve stochastic optimization problems. We describe improvements to the current techniques in both these areas. We studied different ways of using importance sampling techniques in the context of Stochastic programming, by varying the choice of approximation functions used in this method. We have concluded that approximating the recourse function by a computationally inexpensive piecewise-linear function is highly efficient. This reduced the problem from finding the mean of a computationally expensive functions to finding that of a computationally inexpensive function. Then we implemented various variance reduction techniques to estimate the mean of a piecewise-linear function. This method achieved similar variance reductions in orders of magnitude less time than, when we directly applied variance-reduction techniques directly on the given problem. In solving a stochastic linear program, the expected value problem is usually solved before a stochastic solution and also to speed-up the algorithm by making use of the information obtained from the solution of the expected value problem. We have devised a new decomposition scheme to improve the convergence of this algorithm.
Stochastic simulation in systems biology.
Székely, Tamás; Burrage, Kevin
2014-11-01
Natural systems are, almost by definition, heterogeneous: this can be either a boon or an obstacle to be overcome, depending on the situation. Traditionally, when constructing mathematical models of these systems, heterogeneity has typically been ignored, despite its critical role. However, in recent years, stochastic computational methods have become commonplace in science. They are able to appropriately account for heterogeneity; indeed, they are based around the premise that systems inherently contain at least one source of heterogeneity (namely, intrinsic heterogeneity). In this mini-review, we give a brief introduction to theoretical modelling and simulation in systems biology and discuss the three different sources of heterogeneity in natural systems. Our main topic is an overview of stochastic simulation methods in systems biology. There are many different types of stochastic methods. We focus on one group that has become especially popular in systems biology, biochemistry, chemistry and physics. These discrete-state stochastic methods do not follow individuals over time; rather they track only total populations. They also assume that the volume of interest is spatially homogeneous. We give an overview of these methods, with a discussion of the advantages and disadvantages of each, and suggest when each is more appropriate to use. We also include references to software implementations of them, so that beginners can quickly start using stochastic methods for practical problems of interest.
Stochastic simulation in systems biology
Székely, Tamás; Burrage, Kevin
2014-01-01
Natural systems are, almost by definition, heterogeneous: this can be either a boon or an obstacle to be overcome, depending on the situation. Traditionally, when constructing mathematical models of these systems, heterogeneity has typically been ignored, despite its critical role. However, in recent years, stochastic computational methods have become commonplace in science. They are able to appropriately account for heterogeneity; indeed, they are based around the premise that systems inherently contain at least one source of heterogeneity (namely, intrinsic heterogeneity). In this mini-review, we give a brief introduction to theoretical modelling and simulation in systems biology and discuss the three different sources of heterogeneity in natural systems. Our main topic is an overview of stochastic simulation methods in systems biology. There are many different types of stochastic methods. We focus on one group that has become especially popular in systems biology, biochemistry, chemistry and physics. These discrete-state stochastic methods do not follow individuals over time; rather they track only total populations. They also assume that the volume of interest is spatially homogeneous. We give an overview of these methods, with a discussion of the advantages and disadvantages of each, and suggest when each is more appropriate to use. We also include references to software implementations of them, so that beginners can quickly start using stochastic methods for practical problems of interest. PMID:25505503
Stochastic determination of matrix determinants.
Dorn, Sebastian; Ensslin, Torsten A
2015-07-01
Matrix determinants play an important role in data analysis, in particular when Gaussian processes are involved. Due to currently exploding data volumes, linear operations-matrices-acting on the data are often not accessible directly but are only represented indirectly in form of a computer routine. Such a routine implements the transformation a data vector undergoes under matrix multiplication. While efficient probing routines to estimate a matrix's diagonal or trace, based solely on such computationally affordable matrix-vector multiplications, are well known and frequently used in signal inference, there is no stochastic estimate for its determinant. We introduce a probing method for the logarithm of a determinant of a linear operator. Our method rests upon a reformulation of the log-determinant by an integral representation and the transformation of the involved terms into stochastic expressions. This stochastic determinant determination enables large-size applications in Bayesian inference, in particular evidence calculations, model comparison, and posterior determination.
Intrinsic optimization using stochastic nanomagnets
NASA Astrophysics Data System (ADS)
Sutton, Brian; Camsari, Kerem Yunus; Behin-Aein, Behtash; Datta, Supriyo
2017-03-01
This paper draws attention to a hardware system which can be engineered so that its intrinsic physics is described by the generalized Ising model and can encode the solution to many important NP-hard problems as its ground state. The basic constituents are stochastic nanomagnets which switch randomly between the ±1 Ising states and can be monitored continuously with standard electronics. Their mutual interactions can be short or long range, and their strengths can be reconfigured as needed to solve specific problems and to anneal the system at room temperature. The natural laws of statistical mechanics guide the network of stochastic nanomagnets at GHz speeds through the collective states with an emphasis on the low energy states that represent optimal solutions. As proof-of-concept, we present simulation results for standard NP-complete examples including a 16-city traveling salesman problem using experimentally benchmarked models for spin-transfer torque driven stochastic nanomagnets.
Nonlinear optimization for stochastic simulations.
Johnson, Michael M.; Yoshimura, Ann S.; Hough, Patricia Diane; Ammerlahn, Heidi R.
2003-12-01
This report describes research targeting development of stochastic optimization algorithms and their application to mission-critical optimization problems in which uncertainty arises. The first section of this report covers the enhancement of the Trust Region Parallel Direct Search (TRPDS) algorithm to address stochastic responses and the incorporation of the algorithm into the OPT++ optimization library. The second section describes the Weapons of Mass Destruction Decision Analysis Center (WMD-DAC) suite of systems analysis tools and motivates the use of stochastic optimization techniques in such non-deterministic simulations. The third section details a batch programming interface designed to facilitate criteria-based or algorithm-driven execution of system-of-system simulations. The fourth section outlines the use of the enhanced OPT++ library and batch execution mechanism to perform systems analysis and technology trade-off studies in the WMD detection and response problem domain.
Intrinsic optimization using stochastic nanomagnets
Sutton, Brian; Camsari, Kerem Yunus; Behin-Aein, Behtash; Datta, Supriyo
2017-01-01
This paper draws attention to a hardware system which can be engineered so that its intrinsic physics is described by the generalized Ising model and can encode the solution to many important NP-hard problems as its ground state. The basic constituents are stochastic nanomagnets which switch randomly between the ±1 Ising states and can be monitored continuously with standard electronics. Their mutual interactions can be short or long range, and their strengths can be reconfigured as needed to solve specific problems and to anneal the system at room temperature. The natural laws of statistical mechanics guide the network of stochastic nanomagnets at GHz speeds through the collective states with an emphasis on the low energy states that represent optimal solutions. As proof-of-concept, we present simulation results for standard NP-complete examples including a 16-city traveling salesman problem using experimentally benchmarked models for spin-transfer torque driven stochastic nanomagnets. PMID:28295053
Stochastic excitation of stellar oscillations
NASA Astrophysics Data System (ADS)
Samadi, Reza
2001-05-01
Since more than about thirty years, solar oscillations are thought to be excited stochastically by the turbulent motions in the solar convective zone. It is currently believed that oscillations of stars lower than 2 solar masses - which possess an upper convective zone - are excited stochastically by turbulent convection in their outer layers. Providing that accurate measurements of the oscillation amplitudes and damping rates are available it is possible to evaluate the power injected into the modes and thus - by comparison with the observations - to constrain current theories. A recent theoretical work (Samadi & Goupil, 2001; Samadi et al., 2001) supplements and reinforces the theory of stochastic excitation of star vibrations. This process was generalized to a global description of the turbulent state of their convective zone. The comparison between observation and theory, thus generalized, will allow to better know the turbulent spectrum of stars, and this in particular thanks to the COROT mission.
Principal axes for stochastic dynamics
NASA Astrophysics Data System (ADS)
Vasconcelos, V. V.; Raischel, F.; Haase, M.; Peinke, J.; Wächter, M.; Lind, P. G.; Kleinhans, D.
2011-09-01
We introduce a general procedure for directly ascertaining how many independent stochastic sources exist in a complex system modeled through a set of coupled Langevin equations of arbitrary dimension. The procedure is based on the computation of the eigenvalues and the corresponding eigenvectors of local diffusion matrices. We demonstrate our algorithm by applying it to two examples of systems showing Hopf bifurcation. We argue that computing the eigenvectors associated to the eigenvalues of the diffusion matrix at local mesh points in the phase space enables one to define vector fields of stochastic eigendirections. In particular, the eigenvector associated to the lowest eigenvalue defines the path of minimum stochastic forcing in phase space, and a transform to a new coordinate system aligned with the eigenvectors can increase the predictability of the system.
NASA Technical Reports Server (NTRS)
Lacksonen, Thomas A.
1994-01-01
Small space flight project design at NASA Langley Research Center goes through a multi-phase process from preliminary analysis to flight operations. The process insures that each system achieves its technical objectives with demonstrated quality and within planned budgets and schedules. A key technical component of early phases is decision analysis, which is a structure procedure for determining the best of a number of feasible concepts based upon project objectives. Feasible system concepts are generated by the designers and analyzed for schedule, cost, risk, and technical measures. Each performance measure value is normalized between the best and worst values and a weighted average score of all measures is calculated for each concept. The concept(s) with the highest scores are retained, while others are eliminated from further analysis. This project automated and enhanced the decision analysis process. Automation of the decision analysis process was done by creating a user-friendly, menu-driven, spreadsheet macro based decision analysis software program. The program contains data entry dialog boxes, automated data and output report generation, and automated output chart generation. The enhancements to the decision analysis process permit stochastic data entry and analysis. Rather than enter single measure values, the designers enter the range and most likely value for each measure and concept. The data can be entered at the system or subsystem level. System level data can be calculated as either sum, maximum, or product functions of the subsystem data. For each concept, the probability distributions are approximated for each measure and the total score for each concept as either constant, triangular, normal, or log-normal distributions. Based on these distributions, formulas are derived for the probability that the concept meets any given constraint, the probability that the concept meets all constraints, and the probability that the concept is within a given
Partial ASL extensions for stochastic programming.
Gay, David
2010-03-31
partially completed extensions for stochastic programming to the AMPL/solver interface library (ASL).modeling and experimenting with stochastic recourse problems. This software is not primarily for military applications
Comments on optical stochastic cooling
K.Y. Ng, S.Y. Lee and Y.K. Zhang
2002-10-08
An important necessary condition for transverse phase space damping in the optical stochastic cooling with transit-time method is derived. The longitudinal and transverse damping dynamics for the optical stochastic cooling is studied. The authors also obtain an optimal laser focusing condition for laser-beam interaction in the correction undulator. The amplification factor and the output peak power of the laser amplifier are found to differ substantially from earlier publications. The required power is large for hadron colliders at very high energy.
Stochastic Kinetics of Nascent RNA
NASA Astrophysics Data System (ADS)
Xu, Heng; Skinner, Samuel O.; Sokac, Anna Marie; Golding, Ido
2016-09-01
The stochastic kinetics of transcription is typically inferred from the distribution of RNA numbers in individual cells. However, cellular RNA reflects additional processes downstream of transcription, hampering this analysis. In contrast, nascent (actively transcribed) RNA closely reflects the kinetics of transcription. We present a theoretical model for the stochastic kinetics of nascent RNA, which we solve to obtain the probability distribution of nascent RNA per gene. The model allows us to evaluate the kinetic parameters of transcription from single-cell measurements of nascent RNA. The model also predicts surprising discontinuities in the distribution of nascent RNA, a feature which we verify experimentally.
Stochastic Optimization of Complex Systems
Birge, John R.
2014-03-20
This project focused on methodologies for the solution of stochastic optimization problems based on relaxation and penalty methods, Monte Carlo simulation, parallel processing, and inverse optimization. The main results of the project were the development of a convergent method for the solution of models that include expectation constraints as in equilibrium models, improvement of Monte Carlo convergence through the use of a new method of sample batch optimization, the development of new parallel processing methods for stochastic unit commitment models, and the development of improved methods in combination with parallel processing for incorporating automatic differentiation methods into optimization.
Bar shapes and orbital stochasticity
Athanassoula, E. )
1990-06-01
Several independent lines of evidence suggest that the isophotes or isodensities of bars in barred galaxies are not really elliptical in shape but more rectangular. The effect this might have on the orbits in two different types of bar potentials is studied, and it is found that in both cases the percentage of stochastic orbits is much larger when the shapes are more rectangularlike or, equivalently, when the m = 4 components are more important. This can be understood with the help of the Chirikov criterion, which can predict the limit for the onset of global stochasticity. 9 refs.
QB1 - Stochastic Gene Regulation
Munsky, Brian
2012-07-23
Summaries of this presentation are: (1) Stochastic fluctuations or 'noise' is present in the cell - Random motion and competition between reactants, Low copy, quantization of reactants, Upstream processes; (2) Fluctuations may be very important - Cell-to-cell variability, Cell fate decisions (switches), Signal amplification or damping, stochastic resonances; and (3) Some tools are available to mode these - Kinetic Monte Carlo simulations (SSA and variants), Moment approximation methods, Finite State Projection. We will see how modeling these reactions can tell us more about the underlying processes of gene regulation.
SPINDLE: A 2-Stage Nuclear-Powered Cryobot for Ocean World Exploration
NASA Astrophysics Data System (ADS)
Stone, W.; Hogan, B.; Siegel, V. L.; Howe, T.; Howe, S.; Harman, J.; Richmond, K.; Flesher, C.; Clark, E.; Lelievre, S.; Moor, J.; Rothhammer, B.
2016-12-01
SPINDLE (Sub-glacial Polar Ice Navigation, Descent, and Lake Exploration) is a 2-stage autonomous vehicle system consisting of a robotic ice-penetrating carrier vehicle (cryobot) and a marsupial, hovering autonomous underwater vehicle (HAUV). The cryobot will descend through an ice body into a sub-ice aqueous environment and deploy the HAUV to conduct long range reconnaissance, life search, and sample collection. The HAUV will return to, and auto-dock with, the cryobot at the conclusion of the mission for subsequent data uplink and sample return to the surface. The SPINDLE cryobot has been currently designed for a 1.5 kilometer penetration through a terrestrial ice sheet and the HAUV has been designed for persistent exploration and science presence in for deployments up to a kilometer radius from the cryobot. Importantly, the cryobot is bi-directional and vertically controllable both in an ice sheet as well as following breakthrough into a subglacial water cavity / ocean. The vehicle has been designed for long-duration persistent science in subglacial cavities and to allow for subsequent return-to-surface at a much later date or subsequent season. Engineering designs for the current SPINDLE cryobot will be presented in addition to current designs for autonomous rendezvous, docking, and storing of the HAUV system into the cryobot for subsequent recovery of the entire system to the surface. Taken to completion in a three-phase program, SPINDLE will deliver an integrated and field-tested system that will be directly transferable into a Flagship-class mission to either the hypothesized shallow lakes of Europa, the sub-surface ocean of Ganymede, or the geyser/plume sources on both Europa and Enceladus. We present the results of several parallel laboratory investigations into advanced power transmission systems (laser, high voltage) as well as onboard systems that enable the SPINDLE vehicle to access any subglacial lake on earth while using non-nuclear surrogate, surface
The Hamiltonian Mechanics of Stochastic Acceleration
Burby, J. W.
2013-07-17
We show how to nd the physical Langevin equation describing the trajectories of particles un- dergoing collisionless stochastic acceleration. These stochastic di erential equations retain not only one-, but two-particle statistics, and inherit the Hamiltonian nature of the underlying microscopic equations. This opens the door to using stochastic variational integrators to perform simulations of stochastic interactions such as Fermi acceleration. We illustrate the theory by applying it to two example problems.
NASA Astrophysics Data System (ADS)
Michta, Mariusz
2017-02-01
In the paper we study properties of solutions to stochastic differential inclusions and set-valued stochastic differential equations with respect to semimartingale integrators. We present new connections between their solutions. In particular, we show that attainable sets of solutions to stochastic inclusions are subsets of values of multivalued solutions of certain set-valued stochastic equations. We also show that every solution to stochastic inclusion is a continuous selection of a multivalued solution of an associated set-valued stochastic equation. The results obtained in the paper generalize results dealing with this topic known both in deterministic and stochastic cases.
EDITORIAL: Stochasticity in fusion plasmas Stochasticity in fusion plasmas
NASA Astrophysics Data System (ADS)
Unterberg, Bernhard
2010-03-01
Structure formation and transport in stochastic plasmas is a topic of growing importance in many fields of plasma physics from astrophysics to fusion research. In particular, the possibility to control transport in the boundary of confined fusion plasmas by resonant magnetic perturbations has been investigated extensively during recent years. A major research achievement was finding that the intense transient particle and heat fluxes associated with edge localized modes (here type-I ELMs) in magnetically confined fusion plasmas can be mitigated or even suppressed by resonant magnetic perturbation fields. This observation opened up a possible scheme to avoid too large erosion and material damage by such transients in future fusion devices such as ITER. However, it is widely recognized that a more basic understanding is needed to extrapolate the results obtained in present experiments to future fusion devices. The 4th workshop on Stochasticity in Fusion Plasmas was held in Jülich, Germany, from 2 to 4 March 2009. This series of workshops aims at gathering fusion experts from various plasma configurations such as tokamaks, stellarators and reversed field pinches to exchange knowledge on structure formation and transport in stochastic fusion plasmas. The workshops have attracted colleagues from both experiment and theory and stimulated fruitful discussions about the basics of stochastic fusion plasmas. Important papers from the first three workshops in 2003, 2005 and 2007 have been published in previous special issues of Nuclear Fusion (stacks.iop.org/NF/44/i=6, stacks.iop.org/NF/46/i=4 and stacks.iop.org/NF/48/i=2). This special issue comprises contributions presented at the 4th SFP workshop, dealing with the main subjects such as formation of stochastic magnetic layers, energy and particle transport in stochastic magnetic fields, plasma response to external, non-axis-symmetric perturbations and last but not least application of resonant magnetic perturbations for
Variational principles for stochastic soliton dynamics
Holm, Darryl D.; Tyranowski, Tomasz M.
2016-01-01
We develop a variational method of deriving stochastic partial differential equations whose solutions follow the flow of a stochastic vector field. As an example in one spatial dimension, we numerically simulate singular solutions (peakons) of the stochastically perturbed Camassa–Holm (CH) equation derived using this method. These numerical simulations show that peakon soliton solutions of the stochastically perturbed CH equation persist and provide an interesting laboratory for investigating the sensitivity and accuracy of adding stochasticity to finite dimensional solutions of stochastic partial differential equations. In particular, some choices of stochastic perturbations of the peakon dynamics by Wiener noise (canonical Hamiltonian stochastic deformations, CH-SD) allow peakons to interpenetrate and exchange order on the real line in overtaking collisions, although this behaviour does not occur for other choices of stochastic perturbations which preserve the Euler–Poincaré structure of the CH equation (parametric stochastic deformations, P-SD), and it also does not occur for peakon solutions of the unperturbed deterministic CH equation. The discussion raises issues about the science of stochastic deformations of finite-dimensional approximations of evolutionary partial differential equation and the sensitivity of the resulting solutions to the choices made in stochastic modelling. PMID:27118922
Variational principles for stochastic soliton dynamics.
Holm, Darryl D; Tyranowski, Tomasz M
2016-03-01
We develop a variational method of deriving stochastic partial differential equations whose solutions follow the flow of a stochastic vector field. As an example in one spatial dimension, we numerically simulate singular solutions (peakons) of the stochastically perturbed Camassa-Holm (CH) equation derived using this method. These numerical simulations show that peakon soliton solutions of the stochastically perturbed CH equation persist and provide an interesting laboratory for investigating the sensitivity and accuracy of adding stochasticity to finite dimensional solutions of stochastic partial differential equations. In particular, some choices of stochastic perturbations of the peakon dynamics by Wiener noise (canonical Hamiltonian stochastic deformations, CH-SD) allow peakons to interpenetrate and exchange order on the real line in overtaking collisions, although this behaviour does not occur for other choices of stochastic perturbations which preserve the Euler-Poincaré structure of the CH equation (parametric stochastic deformations, P-SD), and it also does not occur for peakon solutions of the unperturbed deterministic CH equation. The discussion raises issues about the science of stochastic deformations of finite-dimensional approximations of evolutionary partial differential equation and the sensitivity of the resulting solutions to the choices made in stochastic modelling.
Forward Stochastic Nonlinear Adaptive Control Method
NASA Technical Reports Server (NTRS)
Bayard, David S.
1990-01-01
New method of computation for optimal stochastic nonlinear and adaptive control undergoing development. Solves systematically stochastic dynamic programming equations forward in time, using nested-stochastic-approximation technique. Main advantage, simplicity of programming and reduced complexity with clear performance/computation trade-offs.
Stochastically forced zonal flows
NASA Astrophysics Data System (ADS)
Srinivasan, Kaushik
an approximate equation for the vorticity correlation function that is then solved perturbatively. The Reynolds stress of the pertubative solution can then be expressed as a function of the mean-flow and its y-derivatives. In particular, it is shown that as long as the forcing breaks mirror-symmetry, the Reynolds stress has a wave-like term, as a result of which the mean-flow is governed by a dispersive wave equation. In a separate study, Reynolds stress induced by an anisotropically forced unbounded Couette flow with uniform shear gamma, on a beta-plane, is calculated in conjunction with the eddy diffusivity of a co-evolving passive tracer. The flow is damped by linear drag on a time scale mu--1. The stochastic forcing is controlled by a parameter alpha, that characterizes whether eddies are elongated along the zonal direction (alpha < 0), the meridional direction (alpha > 0) or are isotropic (alpha = 0). The Reynolds stress varies linearly with alpha and non-linearly and non-monotonically with gamma; but the Reynolds stress is independent of beta. For positive values of alpha, the Reynolds stress displays an "anti-frictional" effect (energy is transferred from the eddies to the mean flow) and a frictional effect for negative values of alpha. With gamma = beta =0, the meridional tracer eddy diffusivity is v'2/(2mu), where v' is the meridional eddy velocity. In general, beta and gamma suppress the diffusivity below v'2/(2mu).
Universality in Stochastic Exponential Growth
NASA Astrophysics Data System (ADS)
Iyer-Biswas, Srividya; Crooks, Gavin E.; Scherer, Norbert F.; Dinner, Aaron R.
2014-07-01
Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. The model makes minimal assumptions, and we describe how more complex reaction networks can reduce to such a cycle. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth.
Stochastic-field cavitation model
Dumond, J.; Magagnato, F.; Class, A.
2013-07-15
Nonlinear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally, the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian “particles” or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and, in particular, to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. First, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.
Universality in stochastic exponential growth.
Iyer-Biswas, Srividya; Crooks, Gavin E; Scherer, Norbert F; Dinner, Aaron R
2014-07-11
Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. The model makes minimal assumptions, and we describe how more complex reaction networks can reduce to such a cycle. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth.
STOCHASTIC POINT PROCESSES: LIMIT THEOREMS.
A stochastic point process in R(n) is a triple (M,B,P) where M is the class of all countable sets in R(n) having no limit points, B is the smallest...converge to a mixture of Poisson processes. These results are established via a generalization of a classical limit theorem for Bernoulli trials. (Author)
Birch regeneration: a stochastic model
William B. Leak
1968-01-01
The regeneration of a clearcutting with paper or yellow birch is expressed as an elementary stochastic (probabalistic) model that is computationally similar to an absorbing Markov chain. In the general case, the model contains 29 states beginning with the development of a flower (ament) and terminating with the abortion of a flower or seed, or the development of an...
Stochastic cooling: recent theoretical directions
Bisognano, J.
1983-03-01
A kinetic-equation derivation of the stochastic-cooling Fokker-Planck equation of correlation is introduced to describe both the Schottky spectrum and signal suppression. Generalizations to nonlinear gain and coupling between degrees of freedom are presented. Analysis of bunch beam cooling is included.
Stochastic resonance on a circle
Wiesenfeld, K. ); Pierson, D.; Pantazelou, E.; Dames, C.; Moss, F. )
1994-04-04
We describe a new realization of stochastic resonance, applicable to a broad class of systems, based on an underlying excitable dynamics with deterministic reinjection. A simple but general theory of such single-trigger'' systems is compared with analog simulations of the Fitzhugh-Nagumo model, as well as experimental data obtained from stimulated sensory neurons in the crayfish.
Brownian motors and stochastic resonance.
Mateos, José L; Alatriste, Fernando R
2011-12-01
We study the transport properties for a walker on a ratchet potential. The walker consists of two particles coupled by a bistable potential that allow the interchange of the order of the particles while moving through a one-dimensional asymmetric periodic ratchet potential. We consider the stochastic dynamics of the walker on a ratchet with an external periodic forcing, in the overdamped case. The coupling of the two particles corresponds to a single effective particle, describing the internal degree of freedom, in a bistable potential. This double-well potential is subjected to both a periodic forcing and noise and therefore is able to provide a realization of the phenomenon of stochastic resonance. The main result is that there is an optimal amount of noise where the amplitude of the periodic response of the system is maximum, a signal of stochastic resonance, and that precisely for this optimal noise, the average velocity of the walker is maximal, implying a strong link between stochastic resonance and the ratchet effect.
Algorithmic advances in stochastic programming
Morton, D.P.
1993-07-01
Practical planning problems with deterministic forecasts of inherently uncertain parameters often yield unsatisfactory solutions. Stochastic programming formulations allow uncertain parameters to be modeled as random variables with known distributions, but the size of the resulting mathematical programs can be formidable. Decomposition-based algorithms take advantage of special structure and provide an attractive approach to such problems. We consider two classes of decomposition-based stochastic programming algorithms. The first type of algorithm addresses problems with a ``manageable`` number of scenarios. The second class incorporates Monte Carlo sampling within a decomposition algorithm. We develop and empirically study an enhanced Benders decomposition algorithm for solving multistage stochastic linear programs within a prespecified tolerance. The enhancements include warm start basis selection, preliminary cut generation, the multicut procedure, and decision tree traversing strategies. Computational results are presented for a collection of ``real-world`` multistage stochastic hydroelectric scheduling problems. Recently, there has been an increased focus on decomposition-based algorithms that use sampling within the optimization framework. These approaches hold much promise for solving stochastic programs with many scenarios. A critical component of such algorithms is a stopping criterion to ensure the quality of the solution. With this as motivation, we develop a stopping rule theory for algorithms in which bounds on the optimal objective function value are estimated by sampling. Rules are provided for selecting sample sizes and terminating the algorithm under which asymptotic validity of confidence interval statements for the quality of the proposed solution can be verified. Issues associated with the application of this theory to two sampling-based algorithms are considered, and preliminary empirical coverage results are presented.
NASA Astrophysics Data System (ADS)
Zhang, Ming
2015-10-01
A theory of 2-stage acceleration of Galactic cosmic rays in supernova remnants is proposed. The first stage is accomplished by the supernova shock front, where a power-law spectrum is established up to a certain cutoff energy. It is followed by stochastic acceleration with compressible waves/turbulence in the downstream medium. With a broad \\propto {k}-2 spectrum for the compressible plasma fluctuations, the rate of stochastic acceleration is constant over a wide range of particle momentum. In this case, the stochastic acceleration process extends the power-law spectrum cutoff energy of Galactic cosmic rays to the knee without changing the spectral slope. This situation happens as long as the rate of stochastic acceleration is faster than 1/5 of the adiabatic cooling rate. A steeper spectrum of compressible plasma fluctuations that concentrate their power in long wavelengths will accelerate cosmic rays to the knee with a small bump before its cutoff in the comic-ray energy spectrum. This theory does not require a strong amplification of the magnetic field in the upstream interstellar medium in order to accelerate cosmic rays to the knee energy.
NASA Technical Reports Server (NTRS)
Whitney, W. J.
1977-01-01
The stage work distribution among the three stages was very close to the design value. The specific work output-mass flow characteristics of the three stages were closely matched. The efficiency of the 3 1/2 stage turbine at design specific work output and design speed was within 0.008 of the estimated value, and this agreement was felt to demonstrate the adequacy of the prediction method in the high stage loading factor regime.
Lian, Zixuan; Qiao, Longshan; Zhu, Guanghong; Deng, Yun; Qian, Bingjun; Yue, Jin; Zhao, Yanyun
2014-03-01
The effects of use of sodium dodecyl sulfate (SDS) pretreatment and 2-stage curing on the microbial, physicochemical, and microstructural qualities of salted duck eggs were studied. After pretreatment in 0.5% (w/v) SDS solution at room conditions for 15 min, no discolorations were observed and no microorganisms were detected on the egg shells. In the 2-stage curing process, 25% (w/v) and 30% (w/v) saline solutions were evaluated in the 1st step (Stage I, approximately 18 d), whereas 4% (w/v) saline solution was applied in the 2nd step (Stage II, approximately 15 d). Along with increased curing time, water content decreased and NaCl content increased in the egg yolks from approximately 0.40% to 0.86%, whereas the water content of egg albumen remained at approximately 85% during the 2-stage curing. More importantly, the NaCl content of albumen maintained at approximately 4.0% at Stage II curing. Yolk index as a sign of maturity for salted duck eggs reached 1 at the end of Stage I (18 d) and retained the same value during Stage II curing regardless of the NaCl concentration in the Stage I saline solution. Oil exudation in egg yolks increased as the time of curing increased. As seen from scanning electron microscopy, oil was released from yolk granules. This study indicated that SDS pretreatment is effective to reduce microbial load on the shells of fresh duck eggs and the 2-stage curing can improve physicochemical qualities of the salted duck eggs and shortened curing time to about 7 to 17 d as compared to the traditional 1-step curing method. Spoiled saline solution and uneven distribution of salt are the 2 major problems in producing salted duck eggs. Sodium dodecyl sulfate (SDS) pretreatment and 2-stage curing process have shown effective to solve these problems, respectively. The SDS pretreatment was able to remove microorganisms and soil from the surface of fresh egg shells, thus preventing the spoilage of the saline solution. The 2-stage curing process
Stochastic resonance in nanomechanical systems
NASA Astrophysics Data System (ADS)
Badzey, Robert L.
The phenomenon of stochastic resonance is a counter-intuitive one: adding noise to a noisy nonlinear system under the influence of a modulation results in coherent behavior. The signature of the effect is a resonance in the signal-to-noise ratio of the response over a certain range of noise power; this behavior is absent if either the modulation or the noise are absent. Stochastic resonance has attracted considerable interest over the past several decades, having been seen in a great number of physical and biological systems. Here, observation of stochastic resonance is reported for nanomechanical systems consisting of a doubly-clamped beam resonators fabricated from single-crystal silicon. Such oscillators have been found to display nonlinear and bistable behavior under the influence of large driving forces. This bistability is exploited to produce a controllable nanomechanical switch, a device that may be used as the basis for a new generation of computational memory elements. These oscillators possess large intrinsic resonance frequencies (MHz range or higher) due to their small size and relatively high stiffness; thus they have the potential to rival the current state-of-the-art of electronic and magnetic storage technologies. This small size also allows them to be packed in densities which meet or exceed the superparamagnetic limit for magnetic storage media of 100 GB/in2. Two different doubly-clamped beams were cooled to low temperatures (300 mK--4 K), and excited with a magnetomotive technique. They were driven into the nonlinear response regime, and then modulated to induce switching between their bistable states. When the modulation was reduced, the switching died out. Application of noise, either with an external broadband source or via an increase in temperature, resulted in a distinct resonance in the signal-to-noise ratio. Aside from establishing the phenomenon of stochastic resonance in yet another physical system, the observation of this effect has
... Healthcare ManagementFamily HealthProcedures & DevicesHealthcare ManagementRelated TopicsCancer: Medical VocabularyRead Article >>Cancer: Medical Vocabulary Learn the definitions of various terms ...
Cancer begins in your cells, which are the building blocks of your body. Normally, your body forms ... be benign or malignant. Benign tumors aren't cancer while malignant ones are. Cells from malignant tumors ...
Stochastic dynamics of cholera epidemics
NASA Astrophysics Data System (ADS)
Azaele, Sandro; Maritan, Amos; Bertuzzo, Enrico; Rodriguez-Iturbe, Ignacio; Rinaldo, Andrea
2010-05-01
We describe the predictions of an analytically tractable stochastic model for cholera epidemics following a single initial outbreak. The exact model relies on a set of assumptions that may restrict the generality of the approach and yet provides a realm of powerful tools and results. Without resorting to the depletion of susceptible individuals, as usually assumed in deterministic susceptible-infected-recovered models, we show that a simple stochastic equation for the number of ill individuals provides a mechanism for the decay of the epidemics occurring on the typical time scale of seasonality. The model is shown to provide a reasonably accurate description of the empirical data of the 2000/2001 cholera epidemic which took place in the Kwa Zulu-Natal Province, South Africa, with possibly notable epidemiological implications.
Stochastic thermodynamics with information reservoirs
NASA Astrophysics Data System (ADS)
Barato, Andre C.; Seifert, Udo
2014-10-01
We generalize stochastic thermodynamics to include information reservoirs. Such information reservoirs, which can be modeled as a sequence of bits, modify the second law. For example, work extraction from a system in contact with a single heat bath becomes possible if the system also interacts with an information reservoir. We obtain an inequality, and the corresponding fluctuation theorem, generalizing the standard entropy production of stochastic thermodynamics. From this inequality we can derive an information processing entropy production, which gives the second law in the presence of information reservoirs. We also develop a systematic linear response theory for information processing machines. For a unicyclic machine powered by an information reservoir, the efficiency at maximum power can deviate from the standard value of 1 /2 . For the case where energy is consumed to erase the tape, the efficiency at maximum erasure rate is found to be 1 /2 .
Wavelet entropy of stochastic processes
NASA Astrophysics Data System (ADS)
Zunino, L.; Pérez, D. G.; Garavaglia, M.; Rosso, O. A.
2007-06-01
We compare two different definitions for the wavelet entropy associated to stochastic processes. The first one, the normalized total wavelet entropy (NTWS) family [S. Blanco, A. Figliola, R.Q. Quiroga, O.A. Rosso, E. Serrano, Time-frequency analysis of electroencephalogram series, III. Wavelet packets and information cost function, Phys. Rev. E 57 (1998) 932-940; O.A. Rosso, S. Blanco, J. Yordanova, V. Kolev, A. Figliola, M. Schürmann, E. Başar, Wavelet entropy: a new tool for analysis of short duration brain electrical signals, J. Neurosci. Method 105 (2001) 65-75] and a second introduced by Tavares and Lucena [Physica A 357(1) (2005) 71-78]. In order to understand their advantages and disadvantages, exact results obtained for fractional Gaussian noise ( -1<α< 1) and fractional Brownian motion ( 1<α< 3) are assessed. We find out that the NTWS family performs better as a characterization method for these stochastic processes.
Stochastic dynamics of cholera epidemics.
Azaele, Sandro; Maritan, Amos; Bertuzzo, Enrico; Rodriguez-Iturbe, Ignacio; Rinaldo, Andrea
2010-05-01
We describe the predictions of an analytically tractable stochastic model for cholera epidemics following a single initial outbreak. The exact model relies on a set of assumptions that may restrict the generality of the approach and yet provides a realm of powerful tools and results. Without resorting to the depletion of susceptible individuals, as usually assumed in deterministic susceptible-infected-recovered models, we show that a simple stochastic equation for the number of ill individuals provides a mechanism for the decay of the epidemics occurring on the typical time scale of seasonality. The model is shown to provide a reasonably accurate description of the empirical data of the 2000/2001 cholera epidemic which took place in the Kwa Zulu-Natal Province, South Africa, with possibly notable epidemiological implications.
Stochastic kinetic mean field model
NASA Astrophysics Data System (ADS)
Erdélyi, Zoltán; Pasichnyy, Mykola; Bezpalchuk, Volodymyr; Tomán, János J.; Gajdics, Bence; Gusak, Andriy M.
2016-07-01
This paper introduces a new model for calculating the change in time of three-dimensional atomic configurations. The model is based on the kinetic mean field (KMF) approach, however we have transformed that model into a stochastic approach by introducing dynamic Langevin noise. The result is a stochastic kinetic mean field model (SKMF) which produces results similar to the lattice kinetic Monte Carlo (KMC). SKMF is, however, far more cost-effective and easier to implement the algorithm (open source program code is provided on http://skmf.eu website). We will show that the result of one SKMF run may correspond to the average of several KMC runs. The number of KMC runs is inversely proportional to the amplitude square of the noise in SKMF. This makes SKMF an ideal tool also for statistical purposes.
Stochastic phase segregation on surfaces.
Gera, Prerna; Salac, David
2017-08-01
Phase separation and coarsening is a phenomenon commonly seen in binary physical and chemical systems that occur in nature. Often, thermal fluctuations, modelled as stochastic noise, are present in the system and the phase segregation process occurs on a surface. In this work, the segregation process is modelled via the Cahn-Hilliard-Cook model, which is a fourth-order parabolic stochastic system. Coarsening is analysed on two sample surfaces: a unit sphere and a dumbbell. On both surfaces, a statistical analysis of the growth rate is performed, and the influence of noise level and mobility is also investigated. For the spherical interface, it is also shown that a lognormal distribution fits the growth rate well.
Stochastic cooling technology at Fermilab
NASA Astrophysics Data System (ADS)
Pasquinelli, Ralph J.
2004-10-01
The first antiproton cooling systems were installed and commissioned at Fermilab in 1984-1985. In the interim period, there have been several major upgrades, system improvements, and complete reincarnation of cooling systems. This paper will present some of the technology that was pioneered at Fermilab to implement stochastic cooling systems in both the Antiproton Source and Recycler accelerators. Current performance data will also be presented.
Stochastic resonance across bifurcation cascades
NASA Astrophysics Data System (ADS)
Nicolis, C.; Nicolis, G.
2017-03-01
The classical setting of stochastic resonance is extended to account for parameter variations leading to transitions between a unique stable state, bistability, and multistability regimes, across singularities of various kinds. Analytic expressions for the amplitude and the phase of the response in terms of key parameters are obtained. The conditions for optimal responses are derived in terms of the bifurcation parameter, the driving frequency, and the noise strength.
Optimality Functions in Stochastic Programming
2009-12-02
nonconvex. Non - convex stochastic optimization problems arise in such diverse applications as estimation of mixed logit models [2], engineering design...first- order necessary optimality conditions ; see for example Propositions 3.3.1 and 3.3.5 in [7] or Theorem 2.2.4 in [25]. If the evaluation of f j...procedures for validation analysis of a candidate point x ∈ IRn. Since P may be nonconvex, we focus on first-order necessary optimality conditions as
Cosmological stochastic Higgs field stabilization
NASA Astrophysics Data System (ADS)
Gong, Jinn-Ouk; Kitajima, Naoya
2017-09-01
We show that the stochastic evolution of an interacting system of the Higgs field and a spectator scalar field naturally gives rise to an enhanced probability of settling down at the electroweak vacuum at the end of inflation. Subsequent destabilization due to parametric resonance between the Higgs field and the spectator field can be avoided in a wide parameter range. We further argue that the spectator field can play the role of dark matter.
Stochastic background of atmospheric cascades
Wilk, G. ); Wlodarczyk, Z. )
1993-06-15
Fluctuations in the atmospheric cascades developing during the propagation of very high energy cosmic rays through the atmosphere are investigated using stochastic branching model of pure birth process with immigration. In particular, we show that the multiplicity distributions of secondaries emerging from gamma families are much narrower than those resulting from hadronic families. We argue that the strong intermittent like behaviour found recently in atmospheric families results from the fluctuations in the cascades themselves and are insensitive to the details of elementary interactions.
Stochastic Fluctuations in Gene Regulation
2005-04-01
AFRL-IF- RS -TR-2005-126 Final Technical Report April 2005 STOCHASTIC FLUCTUATIONS IN GENE REGULATION Boston University...be releasable to the general public, including foreign nations. AFRL-IF- RS -TR-2005-126 has been reviewed and is approved for publication...AGENCY REPORT NUMBER AFRL-IF- RS -TR-2005-126 11. SUPPLEMENTARY NOTES AFRL Project Engineer: Peter J. Costianes/IFED/(315) 330-4030
Stochastic Modeling Of Biochemical Reactions
2006-11-01
chemical reactions. Often for these reactions, the dynamics of the first M-order statistical moments of the species populations do not form a closed...results a stochastic model for gene expression is investigated. We show that in gene expression mechanisms , in which a protein inhibits its own...chemical reactions [7, 8, 4, 9, 10]. Since one is often interested in only the first and second order statistical moments for the number of molecules of
Acetabular spacers in 2-stage hip revision: is it worth it? A single-centre retrospective study.
Burastero, Giorgio; Basso, Marco; Carrega, Giuliana; Cavagnaro, Luca; Chiarlone, Francesco; Salomone, Carlo; Papa, Gabriele; Felli, Lamberto
2017-03-31
The aim of this work is to evaluate an acetabular antibiotic loaded bone cement spacer in 2-stage revision surgery as a potential approach able to reduce complications during the inter-stage period (i.e. dislocation, acetabular wear), as well as simplify 2-stage hip revision surgery and improve hip biomechanics. We performed a retrospective comparative study and evaluated clinical, radiological and surgical data of 71 patients affected by periprosthetic hip infection who were treated with 2-stage exchange. 31 patients were treated using an acetabular spacer in addition to the femoral (group A) while 40 underwent a standard revision surgery (femoral spacer only, group B). Mean time of surgery for the first stage was 148 ± 59 minutes and 142 ± 45 minutes for group A and B respectively; we noted a statistically significant reduction (26 min, p = 0.015) in the same parameter for the second stage (83 ± 35 minutes for group A and 109 ± 36 minutes for group B). We observed the following interstage complications: 5 femoral spacer dislocations (1 for group A and 4 for group B); 1 spacer fracture (group B), 1 spacer fracture (group A), 2 periprosthetic fractures (group B) and 2 patients with acetabular spacer instability (group B). Additionally, we observed a significant improvement in leg length restoration for group A (p = 0.03). Our data show that the acetabular spacer technique is able to reduce the interstage complication rate and allow improved hip biomechanics restoration.
Mechanical Autonomous Stochastic Heat Engine.
Serra-Garcia, Marc; Foehr, André; Molerón, Miguel; Lydon, Joseph; Chong, Christopher; Daraio, Chiara
2016-07-01
Stochastic heat engines are devices that generate work from random thermal motion using a small number of highly fluctuating degrees of freedom. Proposals for such devices have existed for more than a century and include the Maxwell demon and the Feynman ratchet. Only recently have they been demonstrated experimentally, using, e.g., thermal cycles implemented in optical traps. However, recent experimental demonstrations of classical stochastic heat engines are nonautonomous, since they require an external control system that prescribes a heating and cooling cycle and consume more energy than they produce. We present a heat engine consisting of three coupled mechanical resonators (two ribbons and a cantilever) subject to a stochastic drive. The engine uses geometric nonlinearities in the resonating ribbons to autonomously convert a random excitation into a low-entropy, nonpassive oscillation of the cantilever. The engine presents the anomalous heat transport property of negative thermal conductivity, consisting in the ability to passively transfer energy from a cold reservoir to a hot reservoir.
Turbulence, Spontaneous Stochasticity and Climate
NASA Astrophysics Data System (ADS)
Eyink, Gregory
Turbulence is well-recognized as important in the physics of climate. Turbulent mixing plays a crucial role in the global ocean circulation. Turbulence also provides a natural source of variability, which bedevils our ability to predict climate. I shall review here a recently discovered turbulence phenomenon, called ``spontaneous stochasticity'', which makes classical dynamical systems as intrinsically random as quantum mechanics. Turbulent dissipation and mixing of scalars (passive or active) is now understood to require Lagrangian spontaneous stochasticity, which can be expressed by an exact ``fluctuation-dissipation relation'' for scalar turbulence (joint work with Theo Drivas). Path-integral methods such as developed for quantum mechanics become necessary to the description. There can also be Eulerian spontaneous stochasticity of the flow fields themselves, which is intimately related to the work of Kraichnan and Leith on unpredictability of turbulent flows. This leads to problems similar to those encountered in quantum field theory. To quantify uncertainty in forecasts (or hindcasts), we can borrow from quantum field-theory the concept of ``effective actions'', which characterize climate averages by a variational principle and variances by functional derivatives. I discuss some work with Tom Haine (JHU) and Santha Akella (NASA-Goddard) to make this a practical predictive tool. More ambitious application of the effective action is possible using Rayleigh-Ritz schemes.
Stochastic processes, slaves and supersymmetry
NASA Astrophysics Data System (ADS)
Drummond, I. T.; Horgan, R. R.
2012-03-01
We extend the work of Tănase-Nicola and Kurchan on the structure of diffusion processes and the associated supersymmetry algebra by examining the responses of a simple statistical system to external disturbances of various kinds. We consider both the stochastic differential equations (SDEs) for the process and the associated diffusion equation. The influence of the disturbances can be understood by augmenting the original SDE with an equation for slave variables. The evolution of the slave variables describes the behaviour of line elements carried along in the stochastic flow. These line elements, together with the associated surface and volume elements constructed from them, provide the basis of the supersymmetry properties of the theory. For ease of visualization, and in order to emphasize a helpful electromagnetic analogy, we work in three dimensions. The results are all generalizable to higher dimensions and can be specialized to one and two dimensions. The electromagnetic analogy is a useful starting point for calculating asymptotic results at low temperature that can be compared with direct numerical evaluations. We also examine the problems that arise in a direct numerical simulation of the stochastic equation together with the slave equations. We pay special attention to the dependence of the slave variable statistics on temperature. We identify in specific models the critical temperature below which the slave variable distribution ceases to have a variance and consider the effect on estimates of susceptibilities.
Multiple fields in stochastic inflation
Assadullahi, Hooshyar; Firouzjahi, Hassan; Noorbala, Mahdiyar; Vennin, Vincent; Wands, David
2016-06-24
Stochastic effects in multi-field inflationary scenarios are investigated. A hierarchy of diffusion equations is derived, the solutions of which yield moments of the numbers of inflationary e-folds. Solving the resulting partial differential equations in multi-dimensional field space is more challenging than the single-field case. A few tractable examples are discussed, which show that the number of fields is, in general, a critical parameter. When more than two fields are present for instance, the probability to explore arbitrarily large-field regions of the potential, otherwise inaccessible to single-field dynamics, becomes non-zero. In some configurations, this gives rise to an infinite mean number of e-folds, regardless of the initial conditions. Another difference with respect to single-field scenarios is that multi-field stochastic effects can be large even at sub-Planckian energy. This opens interesting new possibilities for probing quantum effects in inflationary dynamics, since the moments of the numbers of e-folds can be used to calculate the distribution of primordial density perturbations in the stochastic-δN formalism.
Stochastic modeling of carbon oxidation
Chen, W.Y,; Kulkarni, A.; Milum, J.L.; Fan, L.T.
1999-12-01
Recent studies of carbon oxidation by scanning tunneling microscopy indicate that measured rates of carbon oxidation can be affected by randomly distributed defects in the carbon structure, which vary in size. Nevertheless, the impact of this observation on the analysis or modeling of the oxidation rate has not been critically assessed. This work focuses on the stochastic analysis of the dynamics of carbon clusters' conversions during the oxidation of a carbon sheet. According to the classic model of Nagle and Strickland-Constable (NSC), two classes of carbon clusters are involved in three types of reactions: gasification of basal-carbon clusters, gasification of edge-carbon clusters, and conversion of the edge-carbon clusters to the basal-carbon clusters due to the thermal annealing. To accommodate the dilution of basal clusters, however, the NSC model is modified for the later stage of oxidation in this work. Master equations governing the numbers of three classes of carbon clusters, basal, edge and gasified, are formulated from stochastic population balance. The stochastic pathways of three different classes of carbon during oxidation, that is, their means and the fluctuations around these means, have been numerically simulated independently by the algorithm derived from the master equations, as well as by an event-driven Monte Carlo algorithm. Both algorithms have given rise to identical results.
Stochastic analysis of dimerization systems.
Barzel, Baruch; Biham, Ofer
2009-09-01
The process of dimerization, in which two monomers bind to each other and form a dimer, is common in nature. This process can be modeled using rate equations, from which the average copy numbers of the reacting monomers and of the product dimers can then be obtained. However, the rate equations apply only when these copy numbers are large. In the limit of small copy numbers the system becomes dominated by fluctuations, which are not accounted for by the rate equations. In this limit one must use stochastic methods such as direct integration of the master equation or Monte Carlo simulations. These methods are computationally intensive and rarely succumb to analytical solutions. Here we use the recently introduced moment equations which provide a highly simplified stochastic treatment of the dimerization process. Using this approach, we obtain an analytical solution for the copy numbers and reaction rates both under steady-state conditions and in the time-dependent case. We analyze three different dimerization processes: dimerization without dissociation, dimerization with dissociation, and heterodimer formation. To validate the results we compare them with the results obtained from the master equation in the stochastic limit and with those obtained from the rate equations in the deterministic limit. Potential applications of the results in different physical contexts are discussed.
Mechanical Autonomous Stochastic Heat Engine
NASA Astrophysics Data System (ADS)
Serra-Garcia, Marc; Foehr, André; Molerón, Miguel; Lydon, Joseph; Chong, Christopher; Daraio, Chiara
2016-07-01
Stochastic heat engines are devices that generate work from random thermal motion using a small number of highly fluctuating degrees of freedom. Proposals for such devices have existed for more than a century and include the Maxwell demon and the Feynman ratchet. Only recently have they been demonstrated experimentally, using, e.g., thermal cycles implemented in optical traps. However, recent experimental demonstrations of classical stochastic heat engines are nonautonomous, since they require an external control system that prescribes a heating and cooling cycle and consume more energy than they produce. We present a heat engine consisting of three coupled mechanical resonators (two ribbons and a cantilever) subject to a stochastic drive. The engine uses geometric nonlinearities in the resonating ribbons to autonomously convert a random excitation into a low-entropy, nonpassive oscillation of the cantilever. The engine presents the anomalous heat transport property of negative thermal conductivity, consisting in the ability to passively transfer energy from a cold reservoir to a hot reservoir.
Rand, Jacob H; Wu, Xiao-Xuan; Wolgast, Lucia R; Lei, Victor; Conway, Edward M
2017-08-01
The antiphospholipid syndrome (APS) is marked by autoantibodies that recognize anionic phospholipids in a cofactor-dependent manner. A role for complement has been implicated in the pathophysiology, however, elevations of complement activation markers have not been consistently demonstrated in clinical studies. We therefore designed a proof-of-principle study to determine whether complement activation might be detectable in APS by first exposing plasmas to phospholipid vesicles. We examined complement activation markers in patients with APS, non-APS thrombosis, systemic lupus erythematosus, cancer, patients with antiphospholipid antibodies without thrombosis (APL) and healthy controls. Direct measurements of plasma C5a and sC5b-9 levels were compared to levels that were generated in normal serum by phospholipid vesicles that had been pre-incubated with the same plasmas. We then determined the effects of the C5 inhibitor, eculizumab, examined the complement pathways involved, and determined whether the effects could be reproduced with purified IgGs and β2-glycoprotein I (β2GPI). Plasma levels of C5a and sC5b-9 were higher, but not significantly increased in APS patients compared to healthy controls. In contrast, phospholipid vesicles pre-incubated with APS plasmas generated significantly higher levels than healthy controls and the other groups, except for APL patients. Complement activation was abrogated by addition of eculizumab. The results with substrate sera indicated that the alternative and classical/lectin pathways were involved. The results were reproducible with purified IgGs and β2GPI. This proof-of-principle study confirms a role for complement in APS and opens the possibility of monitoring complement activation by including phospholipid vesicles in assay systems. Copyright © 2017 Elsevier Ltd. All rights reserved.
AESS: Accelerated Exact Stochastic Simulation
NASA Astrophysics Data System (ADS)
Jenkins, David D.; Peterson, Gregory D.
2011-12-01
The Stochastic Simulation Algorithm (SSA) developed by Gillespie provides a powerful mechanism for exploring the behavior of chemical systems with small species populations or with important noise contributions. Gene circuit simulations for systems biology commonly employ the SSA method, as do ecological applications. This algorithm tends to be computationally expensive, so researchers seek an efficient implementation of SSA. In this program package, the Accelerated Exact Stochastic Simulation Algorithm (AESS) contains optimized implementations of Gillespie's SSA that improve the performance of individual simulation runs or ensembles of simulations used for sweeping parameters or to provide statistically significant results. Program summaryProgram title: AESS Catalogue identifier: AEJW_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJW_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: University of Tennessee copyright agreement No. of lines in distributed program, including test data, etc.: 10 861 No. of bytes in distributed program, including test data, etc.: 394 631 Distribution format: tar.gz Programming language: C for processors, CUDA for NVIDIA GPUs Computer: Developed and tested on various x86 computers and NVIDIA C1060 Tesla and GTX 480 Fermi GPUs. The system targets x86 workstations, optionally with multicore processors or NVIDIA GPUs as accelerators. Operating system: Tested under Ubuntu Linux OS and CentOS 5.5 Linux OS Classification: 3, 16.12 Nature of problem: Simulation of chemical systems, particularly with low species populations, can be accurately performed using Gillespie's method of stochastic simulation. Numerous variations on the original stochastic simulation algorithm have been developed, including approaches that produce results with statistics that exactly match the chemical master equation (CME) as well as other approaches that approximate the CME. Solution
Long time behaviour of a stochastic nanoparticle
NASA Astrophysics Data System (ADS)
Étoré, Pierre; Labbé, Stéphane; Lelong, Jérôme
2014-09-01
In this article, we are interested in the behaviour of a single ferromagnetic mono-domain particle submitted to an external field with a stochastic perturbation. This model is the first step toward the mathematical understanding of thermal effects on a ferromagnet. In a first part, we present the stochastic model and prove that the associated stochastic differential equation is well defined. The second part is dedicated to the study of the long time behaviour of the magnetic moment and in the third part we prove that the stochastic perturbation induces a non-reversibility phenomenon. Last, we illustrate these results through numerical simulations of our stochastic model. The main results presented in this article are on the one hand the rate of convergence of the magnetization toward the unique stable equilibrium of the deterministic model and on the other hand a sharp estimate of the hysteresis phenomenon induced by the stochastic perturbation (remember that with no perturbation, the magnetic moment remains constant).
Network motif identification in stochastic networks
NASA Astrophysics Data System (ADS)
Jiang, Rui; Tu, Zhidong; Chen, Ting; Sun, Fengzhu
2006-06-01
Network motifs have been identified in a wide range of networks across many scientific disciplines and are suggested to be the basic building blocks of most complex networks. Nonetheless, many networks come with intrinsic and/or experimental uncertainties and should be treated as stochastic networks. The building blocks in these networks thus may also have stochastic properties. In this article, we study stochastic network motifs derived from families of mutually similar but not necessarily identical patterns of interconnections. We establish a finite mixture model for stochastic networks and develop an expectation-maximization algorithm for identifying stochastic network motifs. We apply this approach to the transcriptional regulatory networks of Escherichia coli and Saccharomyces cerevisiae, as well as the protein-protein interaction networks of seven species, and identify several stochastic network motifs that are consistent with current biological knowledge. expectation-maximization algorithm | mixture model | transcriptional regulatory network | protein-protein interaction network
Extended local equilibrium approach to stochastic thermodynamics
NASA Astrophysics Data System (ADS)
De Decker, Y.; Garcia Cantú Ros, A.; Nicolis, G.
2015-07-01
A new approach to stochastic thermodynamics is developed, in which the local equilibrium hypothesis is extended to incorporate the effect of fluctuations. A fluctuating entropy in the form of a random functional of the fluctuating state variables is introduced, whose balance equation allows to identify the stochastic entropy flux and stochastic entropy production. The statistical properties of these quantities are analyzed and illustrated on representative examples.
Stochastic Evolution Equations Driven by Fractional Noises
2016-11-28
Stochastic Evolution Equations Driven by Fractional Noises We have introduced a modification of the classical Euler numerical scheme for stochastic...of Papers published in peer-reviewed journals: Final Report: Stochastic Evolution Equations Driven by Fractional Noises Report Title We have introduced...case the evolution form of the equation will involve a Stratonovich integral (or path-wise Young integral). The product can also be interpreted as a
Stochastic Vorticity and Associated Filtering Theory
Amirdjanova, A.; Kallianpur, G.
2002-12-19
The focus of this work is on a two-dimensional stochastic vorticity equation for an incompressible homogeneous viscous fluid. We consider a signed measure-valued stochastic partial differential equation for a vorticity process based on the Skorohod-Ito evolution of a system of N randomly moving point vortices. A nonlinear filtering problem associated with the evolution of the vorticity is considered and a corresponding Fujisaki-Kallianpur-Kunita stochastic differential equation for the optimal filter is derived.
Applications of stochastic optimization, Task 4
1994-12-01
This report illustrates the power of the new stochastic optimization and stochastic programming capabilities developed around the ASPEN simulator in solving various types of design and analysis problems for advanced energy systems. A case study is presented for the Lurgi air-blown dry ash gasifier IGCC system. In addition the stochastic optimization capability can also be used for off-line quality control. The methodology is presented in the context of a simple gas turbine combustor flowsheet.
Stochastic Linear Quadratic Optimal Control Problems
Chen, S.; Yong, J.
2001-07-01
This paper is concerned with the stochastic linear quadratic optimal control problem (LQ problem, for short) for which the coefficients are allowed to be random and the cost functional is allowed to have a negative weight on the square of the control variable. Some intrinsic relations among the LQ problem, the stochastic maximum principle, and the (linear) forward-backward stochastic differential equations are established. Some results involving Riccati equation are discussed as well.
Paul, Subhadip; Roy, Prasun Kumar
2016-09-01
The efficacy of radiation therapy, a primary modality of cancer treatment, depends in general upon the total radiation dose administered to the tumour during the course of therapy. Nevertheless, the delivered radiation also irradiates normal tissues and dose escalation procedure often increases the elimination of normal tissue as well. In this article, we have developed theoretical frameworks under the premise of linear-quadratic-linear (LQL) model using stochastic differential equation and Jensen's inequality for exploring the possibility of attending to the two therapeutic performance objectives in contraposition-increasing the elimination of prostate tumour cells and enhancing the relative sparing of normal tissue in fractionated radiation therapy, within a prescribed limit of total radiation dose. Our study predicts that stochastic temporal modulation in radiation dose-rate appreciably enhances prostate tumour cell elimination, without needing dose escalation in radiation therapy. However, constant higher dose-rate can also enhance the elimination of tumour cells. In this context, we have shown that the sparing of normal tissue with stochastic dose-rate is considerably more than the sparing of normal tissue with the equivalent constant higher dose-rate. Further, by contrasting the stochastic dose-rate effects under LQL and linear-quadratic (LQ) models, we have also shown that the LQ model over-estimates stochastic dose-rate effect in tumour and under-estimates the stochastic dose-rate effect in normal tissue. Our study indicates the possibility of utilizing stochastic modulation of radiation dose-rate for designing enhanced radiation therapy protocol for cancer.
Continuous Variable Teleportation Within Stochastic Electrodynamics
NASA Astrophysics Data System (ADS)
Carmichael, H. J.; Nha, Hyunchul
2004-12-01
Stochastic electrodynamics provides a local realistic interpretation of the continuous variable teleportation of coherent light. Time-domain simulations illustrate broadband features of the teleportation process.
de la Peña-López, Roberto; Remolina-Bonilla, Yuly Andrea
2016-09-01
Cancer is a group of diseases which represents a significant public health problem in Mexico and worldwide. In Mexico neoplasms are the second leading cause of death. An increased morbidity and mortality are expected in the next decades. Several preventable risk factors for cancer development have been identified, the most relevant including tobacco use, which accounts for 30% of the cancer cases; and obesity, associated to another 30%. These factors, in turn, are related to sedentarism, alcohol abuse and imbalanced diets. Some agents are well knokn to cause cancer such as ionizing radiation, viruses such as the papilloma virus (HPV) and hepatitis virus (B and C), and more recently environmental pollution exposure and red meat consumption have been pointed out as carcinogens by the International Agency for Research in Cancer (IARC). The scientific evidence currently available is insufficient to consider milk either as a risk factor or protective factor against different types of cancer.
Martin, George M.
2011-01-01
All phenotypes result from interactions between Nature, Nurture and Chance. The constitutional genome is clearly the dominant factor in explaining the striking differences in the pace and patterns of ageing among species. We are now in a position to reveal salient features underlying these differential modulations, which are likely to be dominated by regulatory domains. By contrast, I shall argue that stochastic events are the major players underlying the surprisingly large intra-specific variations in lifespan and healthspan. I shall review well established as well as more speculative categories of chance events – somatic mutations, protein synthesis error catastrophe and variegations of gene expression (epigenetic drift), with special emphasis upon the latter. I shall argue that stochastic drifts in variegated gene expression are the major contributors to intra-specific differences in the pace and patterns of ageing within members of the same species. They may be responsible for the quasi-stochastic distributions of major types of geriatric pathologies, including the “big three” of Alzheimer's disease, atherosclerosis and, via the induction of hyperplasis, cancer. They may be responsible for altered stoichiometries of heteromultimeric mitochondrial complexes, potentially leading to such disorders as sarcopenia, nonischemic cardiomyopathy and Parkinson's disease. PMID:21963385
Arciero, Cletus A; Yang, Jing; Peng, Limin; Ward, Kevin C; O'Regan, Ruth; Sahin, Aysegul A; Li, Xiaoxian
2017-08-30
Racial disparity of breast cancer in each subtype and substage is not clear. We reviewed 156,938 patients with breast cancer from 2010 to 2012 from the National Cancer Institute Surveillance, Epidemiology, and End Results database. Breast cancer was subtyped by hormone receptor (HR) and human epidermal growth factor 2 (HER2) status as HR+/HER2-, HR+/HER2+, HR-/HER2+, and HR-/HER2-. African American (AA) patients had worse overall survival (OS) and breast cancer cause-specific survival (BCSS) in HR+/HER2- stages III and IV breast cancer and HR-/HER2+ stage IV cancer; they had worse OS but not BCSS in HR+ /HER2- stage II cancer and HR-/HER2- stage II cancer. AA patients with breast cancer had worse survival in certain subtype and stage, especially in ER+ breast cancer.
Molecular Motors and Stochastic Models
NASA Astrophysics Data System (ADS)
Lipowsky, Reinhard
The behavior of single molecular motors such as kinesin or myosin V, which move on linear filaments, involves a nontrivial coupling between the biochemical motor cycle and the stochastic movement. This coupling can be studied in the framework of nonuniform ratchet models which are characterized by spatially localized transition rates between the different internal states of the motor. These models can be classified according to their functional relationships between the motor velocity and the concentration of the fuel molecules. The simplest such relationship applies to two subclasses of models for dimeric kinesin and agrees with experimental observations on this molecular motor.
Bifurcation and Optimal Stochastic Control.
1982-03-01
as soon as luX InW w’(0) n L nis boundeI. To sir.iplity the notations, we denote by u = 1 . Without loss of n generality we may assume that c l...Stochastic Control. F O R M I II I • Il I i ,iii i, DD I JAP7 1473 EDITION OF I NOV S IS OSOLE’TE UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE i(,en bot. EntereJ) DAT FILMEI DIC
Constrained Stochastic Extended Redundancy Analysis.
DeSarbo, Wayne S; Hwang, Heungsun; Stadler Blank, Ashley; Kappe, Eelco
2015-06-01
We devise a new statistical methodology called constrained stochastic extended redundancy analysis (CSERA) to examine the comparative impact of various conceptual factors, or drivers, as well as the specific predictor variables that contribute to each driver on designated dependent variable(s). The technical details of the proposed methodology, the maximum likelihood estimation algorithm, and model selection heuristics are discussed. A sports marketing consumer psychology application is provided in a Major League Baseball (MLB) context where the effects of six conceptual drivers of game attendance and their defining predictor variables are estimated. Results compare favorably to those obtained using traditional extended redundancy analysis (ERA).
Stochastic Model of Microtubule Dynamics
NASA Astrophysics Data System (ADS)
Hryniv, Ostap; Martínez Esteban, Antonio
2017-10-01
We introduce a continuous time stochastic process on strings made of two types of particle, whose dynamics mimics that of microtubules in a living cell. The long term behaviour of the system is described in terms of the velocity v of the string end. We show that v is an analytic function of its parameters and study its monotonicity properties. We give a complete characterisation of the phase diagram of the model and derive several criteria of the growth (v>0) and the shrinking (v<0) regimes of the dynamics.
Resolution for Stochastic Boolean Satisfiability
NASA Astrophysics Data System (ADS)
Teige, Tino; Fränzle, Martin
The stochastic Boolean satisfiability (SSAT) problem was introduced by Papadimitriou in 1985 by adding a probabilistic model of uncertainty to propositional satisfiability through randomized quantification. SSAT has many applications, e.g., in probabilistic planning and, more recently by integrating arithmetic, in probabilistic model checking. In this paper, we first present a new result on the computational complexity of SSAT: SSAT remains PSPACE-complete even for its restriction to 2CNF. Second, we propose a sound and complete resolution calculus for SSAT complementing the classical backtracking search algorithms.
Stochastic thermodynamics of information processing
NASA Astrophysics Data System (ADS)
Cardoso Barato, Andre
2015-03-01
We consider two recent advancements on theoretical aspects of thermodynamics of information processing. First we show that the theory of stochastic thermodynamics can be generalized to include information reservoirs. These reservoirs can be seen as a sequence of bits which has its Shannon entropy changed due to the interaction with the system. Second we discuss bipartite systems, which provide a convenient description of Maxwell's demon. Analyzing a special class of bipartite systems we show that they can be used to study cellular information processing, allowing for the definition of an entropic rate that quantifies how much a cell learns about a fluctuating external environment and that is bounded by the thermodynamic entropy production.
Stochastic Models of Human Errors
NASA Technical Reports Server (NTRS)
Elshamy, Maged; Elliott, Dawn M. (Technical Monitor)
2002-01-01
Humans play an important role in the overall reliability of engineering systems. More often accidents and systems failure are traced to human errors. Therefore, in order to have meaningful system risk analysis, the reliability of the human element must be taken into consideration. Describing the human error process by mathematical models is a key to analyzing contributing factors. Therefore, the objective of this research effort is to establish stochastic models substantiated by sound theoretic foundation to address the occurrence of human errors in the processing of the space shuttle.
Hamilton's principle in stochastic mechanics
NASA Astrophysics Data System (ADS)
Pavon, Michele
1995-12-01
In this paper we establish three variational principles that provide new foundations for Nelson's stochastic mechanics in the case of nonrelativistic particles without spin. The resulting variational picture is much richer and of a different nature with respect to the one previously considered in the literature. We first develop two stochastic variational principles whose Hamilton-Jacobi-like equations are precisely the two coupled partial differential equations that are obtained from the Schrödinger equation (Madelung equations). The two problems are zero-sum, noncooperative, stochastic differential games that are familiar in the control theory literature. They are solved here by means of a new, absolutely elementary method based on Lagrange functionals. For both games the saddle-point equilibrium solution is given by the Nelson's process and the optimal controls for the two competing players are precisely Nelson's current velocity v and osmotic velocity u, respectively. The first variational principle includes as special cases both the Guerra-Morato variational principle [Phys. Rev. D 27, 1774 (1983)] and Schrödinger original variational derivation of the time-independent equation. It also reduces to the classical least action principle when the intensity of the underlying noise tends to zero. It appears as a saddle-point action principle. In the second variational principle the action is simply the difference between the initial and final configurational entropy. It is therefore a saddle-point entropy production principle. From the variational principles it follows, in particular, that both v(x,t) and u(x,t) are gradients of appropriate principal functions. In the variational principles, the role of the background noise has the intuitive meaning of attempting to contrast the more classical mechanical features of the system by trying to maximize the action in the first principle and by trying to increase the entropy in the second. Combining the two variational
Stochastic solution to quantum dynamics
NASA Technical Reports Server (NTRS)
John, Sarah; Wilson, John W.
1994-01-01
The quantum Liouville equation in the Wigner representation is solved numerically by using Monte Carlo methods. For incremental time steps, the propagation is implemented as a classical evolution in phase space modified by a quantum correction. The correction, which is a momentum jump function, is simulated in the quasi-classical approximation via a stochastic process. The technique, which is developed and validated in two- and three- dimensional momentum space, extends an earlier one-dimensional work. Also, by developing a new algorithm, the application to bound state motion in an anharmonic quartic potential shows better agreement with exact solutions in two-dimensional phase space.
Stochastic Gain in Population Dynamics
NASA Astrophysics Data System (ADS)
Traulsen, Arne; Röhl, Torsten; Schuster, Heinz Georg
2004-07-01
We introduce an extension of the usual replicator dynamics to adaptive learning rates. We show that a population with a dynamic learning rate can gain an increased average payoff in transient phases and can also exploit external noise, leading the system away from the Nash equilibrium, in a resonancelike fashion. The payoff versus noise curve resembles the signal to noise ratio curve in stochastic resonance. Seen in this broad context, we introduce another mechanism that exploits fluctuations in order to improve properties of the system. Such a mechanism could be of particular interest in economic systems.
Optimal Control for Stochastic Delay Evolution Equations
Meng, Qingxin; Shen, Yang
2016-08-15
In this paper, we investigate a class of infinite-dimensional optimal control problems, where the state equation is given by a stochastic delay evolution equation with random coefficients, and the corresponding adjoint equation is given by an anticipated backward stochastic evolution equation. We first prove the continuous dependence theorems for stochastic delay evolution equations and anticipated backward stochastic evolution equations, and show the existence and uniqueness of solutions to anticipated backward stochastic evolution equations. Then we establish necessary and sufficient conditions for optimality of the control problem in the form of Pontryagin’s maximum principles. To illustrate the theoretical results, we apply stochastic maximum principles to study two examples, an infinite-dimensional linear-quadratic control problem with delay and an optimal control of a Dirichlet problem for a stochastic partial differential equation with delay. Further applications of the two examples to a Cauchy problem for a controlled linear stochastic partial differential equation and an optimal harvesting problem are also considered.
Variational principles for stochastic fluid dynamics
Holm, Darryl D.
2015-01-01
This paper derives stochastic partial differential equations (SPDEs) for fluid dynamics from a stochastic variational principle (SVP). The paper proceeds by taking variations in the SVP to derive stochastic Stratonovich fluid equations; writing their Itô representation; and then investigating the properties of these stochastic fluid models in comparison with each other, and with the corresponding deterministic fluid models. The circulation properties of the stochastic Stratonovich fluid equations are found to closely mimic those of the deterministic ideal fluid models. As with deterministic ideal flows, motion along the stochastic Stratonovich paths also preserves the helicity of the vortex field lines in incompressible stochastic flows. However, these Stratonovich properties are not apparent in the equivalent Itô representation, because they are disguised by the quadratic covariation drift term arising in the Stratonovich to Itô transformation. This term is a geometric generalization of the quadratic covariation drift term already found for scalar densities in Stratonovich's famous 1966 paper. The paper also derives motion equations for two examples of stochastic geophysical fluid dynamics; namely, the Euler–Boussinesq and quasi-geostropic approximations. PMID:27547083
Variational principles for stochastic fluid dynamics.
Holm, Darryl D
2015-04-08
This paper derives stochastic partial differential equations (SPDEs) for fluid dynamics from a stochastic variational principle (SVP). The paper proceeds by taking variations in the SVP to derive stochastic Stratonovich fluid equations; writing their Itô representation; and then investigating the properties of these stochastic fluid models in comparison with each other, and with the corresponding deterministic fluid models. The circulation properties of the stochastic Stratonovich fluid equations are found to closely mimic those of the deterministic ideal fluid models. As with deterministic ideal flows, motion along the stochastic Stratonovich paths also preserves the helicity of the vortex field lines in incompressible stochastic flows. However, these Stratonovich properties are not apparent in the equivalent Itô representation, because they are disguised by the quadratic covariation drift term arising in the Stratonovich to Itô transformation. This term is a geometric generalization of the quadratic covariation drift term already found for scalar densities in Stratonovich's famous 1966 paper. The paper also derives motion equations for two examples of stochastic geophysical fluid dynamics; namely, the Euler-Boussinesq and quasi-geostropic approximations.
Stochastic and Coherence Resonance in Hippocampal Neurons
2007-11-02
decreases the signal to noise ratio of subthreshold synaptic inputs. Keywords - Hippocampus , neurons, stochastic resonance I. INTRODUCTION... subthreshold signals in the hippocampus ,” J. Neurophysiology , in press. [3] J. Collins C.C. Chow and T.T. Imboff, “Stochastic resonance without...nonlinear systems whereby the introduction of noise enhances the detection of subthreshold signals. Both computer simulations and experimental
From Complex to Simple: Interdisciplinary Stochastic Models
ERIC Educational Resources Information Center
Mazilu, D. A.; Zamora, G.; Mazilu, I.
2012-01-01
We present two simple, one-dimensional, stochastic models that lead to a qualitative understanding of very complex systems from biology, nanoscience and social sciences. The first model explains the complicated dynamics of microtubules, stochastic cellular highways. Using the theory of random walks in one dimension, we find analytical expressions…
From Complex to Simple: Interdisciplinary Stochastic Models
ERIC Educational Resources Information Center
Mazilu, D. A.; Zamora, G.; Mazilu, I.
2012-01-01
We present two simple, one-dimensional, stochastic models that lead to a qualitative understanding of very complex systems from biology, nanoscience and social sciences. The first model explains the complicated dynamics of microtubules, stochastic cellular highways. Using the theory of random walks in one dimension, we find analytical expressions…
Stochastic Modeling of Laminar-Turbulent Transition
NASA Technical Reports Server (NTRS)
Rubinstein, Robert; Choudhari, Meelan
2002-01-01
Stochastic versions of stability equations are developed in order to develop integrated models of transition and turbulence and to understand the effects of uncertain initial conditions on disturbance growth. Stochastic forms of the resonant triad equations, a high Reynolds number asymptotic theory, and the parabolized stability equations are developed.
Research of Stochastic Robustness: Results and conclusions
NASA Technical Reports Server (NTRS)
Marrison, Chris
1995-01-01
With stochastic robustness we are creating tools to design robust compensators for practical systems. During this year, the stochastic robustness research achieved the following results: refined the search tools needed for synthesis; successfully designed robust compensators for the American Controls Conference benchmark problem; and successfully designed robust compensators for a nonlinear hypersonic aircraft model with uncertainties in 28 parameters.
Stochastic Methods for Aircraft Design
NASA Technical Reports Server (NTRS)
Pelz, Richard B.; Ogot, Madara
1998-01-01
The global stochastic optimization method, simulated annealing (SA), was adapted and applied to various problems in aircraft design. The research was aimed at overcoming the problem of finding an optimal design in a space with multiple minima and roughness ubiquitous to numerically generated nonlinear objective functions. SA was modified to reduce the number of objective function evaluations for an optimal design, historically the main criticism of stochastic methods. SA was applied to many CFD/MDO problems including: low sonic-boom bodies, minimum drag on supersonic fore-bodies, minimum drag on supersonic aeroelastic fore-bodies, minimum drag on HSCT aeroelastic wings, FLOPS preliminary design code, another preliminary aircraft design study with vortex lattice aerodynamics, HSR complete aircraft aerodynamics. In every case, SA provided a simple, robust and reliable optimization method which found optimal designs in order 100 objective function evaluations. Perhaps most importantly, from this academic/industrial project, technology has been successfully transferred; this method is the method of choice for optimization problems at Northrop Grumman.
Extinction of metastable stochastic populations
NASA Astrophysics Data System (ADS)
Assaf, Michael; Meerson, Baruch
2010-02-01
We investigate the phenomenon of extinction of a long-lived self-regulating stochastic population, caused by intrinsic (demographic) noise. Extinction typically occurs via one of two scenarios depending on whether the absorbing state n=0 is a repelling (scenario A) or attracting (scenario B) point of the deterministic rate equation. In scenario A the metastable stochastic population resides in the vicinity of an attracting fixed point next to the repelling point n=0 . In scenario B there is an intermediate repelling point n=n1 between the attracting point n=0 and another attracting point n=n2 in the vicinity of which the metastable population resides. The crux of the theory is a dissipative variant of WKB (Wentzel-Kramers-Brillouin) approximation which assumes that the typical population size in the metastable state is large. Starting from the master equation, we calculate the quasistationary probability distribution of the population sizes and the (exponentially long) mean time to extinction for each of the two scenarios. When necessary, the WKB approximation is complemented (i) by a recursive solution of the quasistationary master equation at small n and (ii) by the van Kampen system-size expansion, valid near the fixed points of the deterministic rate equation. The theory yields both entropic barriers to extinction and pre-exponential factors, and holds for a general set of multistep processes when detailed balance is broken. The results simplify considerably for single-step processes and near the characteristic bifurcations of scenarios A and B.
RHIC stochastic cooling motion control
Gassner, D.; DeSanto, L.; Olsen, R.H.; Fu, W.; Brennan, J.M.; Liaw, CJ; Bellavia, S.; Brodowski, J.
2011-03-28
Relativistic Heavy Ion Collider (RHIC) beams are subject to Intra-Beam Scattering (IBS) that causes an emittance growth in all three-phase space planes. The only way to increase integrated luminosity is to counteract IBS with cooling during RHIC stores. A stochastic cooling system for this purpose has been developed, it includes moveable pick-ups and kickers in the collider that require precise motion control mechanics, drives and controllers. Since these moving parts can limit the beam path aperture, accuracy and reliability is important. Servo, stepper, and DC motors are used to provide actuation solutions for position control. The choice of motion stage, drive motor type, and controls are based on needs defined by the variety of mechanical specifications, the unique performance requirements, and the special needs required for remote operations in an accelerator environment. In this report we will describe the remote motion control related beam line hardware, position transducers, rack electronics, and software developed for the RHIC stochastic cooling pick-ups and kickers.
Birdsell, S.A.; Willms, R.S.; Wilhelm, R.C.
1996-12-31
A 2-stage cold (non-tritium) PMR system was tested with the ITER mix in61 days of continuous operation. No decrease in performance was observed over the duration of the test. Decontamination factor (DF) was found to increase with decreasing inlet rate. Decontamination factors in excess of 1.4 {times} 10{sup 5} were obtained, but the exact value of the highest DF could not be determined because of analysis limitations. Results of the 61-day test were used to design a 2-stage PMR system for use in tritium testing. The PMR system was scaled up by a factor of 6 and built into a glovebox in the Tritium Systems Test Assembly (TSTA) of the Los Alamos National Laboratory. This system is approximately 1/5th of the expected full ITER scale. The ITER mix was injected into the PMR system for 31 hours, during which 4.5 g of tritium were processed. The 1st stage had DF = 200 and the 2nd stage had DF = 2.9 {times} 10{sup 6}. The overall DF = 5.8 {times} 10{sup 8}, which is greater than ITER requirements.
NASA Technical Reports Server (NTRS)
Springer, A.
1994-01-01
An experimental investigation of plume-induced flow separation on the National Launch System (NLS) 1 1/2-stage launch vehicle was done. This investigation resulted from concerns raised about the flow separation that was encountered on the Saturn 5. A large similarity exists between configurations and nominal trajectories. The study involved the use of solid plume simulators to simulate the base pressure encountered by the vehicle due to engine exhaust plumes at predetermined critical Mach numbers based on Saturn 5 flight plume effects. The solid plume was varied in location, resulting in a parametric study of base pressure effects on flow separation. In addition to the parametric study of arbitrary plume locations, the base pressure resulting from the nominal trajectory was tested. This analysis was accomplished through two wind tunnel tests run at NASA Marshall Space Flight Center's 14 x 14-inch Trisonic Wind Tunnel during 1992. The two tests were a static stability and a pressure test each using a 0.004-scale NLS 1 1/2-stage model. This study verified that flow separation is present at Mach 2.74 and 3.48 for predicted flight base pressures at nominal or higher levels. The flow separation at the predicted base pressure is only minor and should not be of great concern. It is not of the magnitude of the flow separation that was experienced on the Saturn 5. If the base pressure exceeds these nominal conditions, the flow separation can drastically increase, and is of concern.
Yeo, Ingwon; Cha, Hoon-Suk; Yoon, Young Cheol; Park, Youn-Soo; Lim, Seung-Jae
2016-01-01
Abstract Introduction: Synovitis, acne, pustulosis, hyperostosis, and osteitis (SAPHO) syndrome is an increasingly recognized entity. The hip joint is known as a less frequently affected site in SAPHO syndrome, and there has been limited reports about hip joint diseases caused by SAPHO syndrome, and as such adequate treatment for this disease spectrum is still not fully elucidated. Case: We describe the case of a 52-year-old man admitted for SAPHO syndrome who went on to be diagnosed with advanced secondary hip arthritis associated with disabling right hip pain. The diagnosis of SAPHO syndrome was delayed; the patient was given a clinical diagnosis of osteomyelitis and treated with prolonged courses of antibiotics and open surgical debridement at previous tertiary health facility. The patient underwent 2-stage joint replacement surgery in our hospital. At 1 year after the surgery, he is well, with minimal right hip pain and the prosthesis is functioning well. Conclusion: This case shows the safety and effectiveness of the 2-stage joint replacement in treating destructive hip disease caused by SAPHO syndrome mimicking infectious arthritis. PMID:27399138
Stochastic ion acceleration by beating electrostatic waves.
Jorns, B; Choueiri, E Y
2013-01-01
A study is presented of the stochasticity in the orbit of a single, magnetized ion produced by the particle's interaction with two beating electrostatic waves whose frequencies differ by the ion cyclotron frequency. A second-order Lie transform perturbation theory is employed in conjunction with a numerical analysis of the maximum Lyapunov exponent to determine the velocity conditions under which stochasticity occurs in this dynamical system. Upper and lower bounds in ion velocity are found for stochastic orbits with the lower bound approximately equal to the phase velocity of the slower wave. A threshold condition for the onset of stochasticity that is linear with respect to the wave amplitudes is also derived. It is shown that the onset of stochasticity occurs for beating electrostatic waves at lower total wave energy densities than for the case of a single electrostatic wave or two nonbeating electrostatic waves.
Image-based histologic grade estimation using stochastic geometry analysis
NASA Astrophysics Data System (ADS)
Petushi, Sokol; Zhang, Jasper; Milutinovic, Aladin; Breen, David E.; Garcia, Fernando U.
2011-03-01
Background: Low reproducibility of histologic grading of breast carcinoma due to its subjectivity has traditionally diminished the prognostic value of histologic breast cancer grading. The objective of this study is to assess the effectiveness and reproducibility of grading breast carcinomas with automated computer-based image processing that utilizes stochastic geometry shape analysis. Methods: We used histology images stained with Hematoxylin & Eosin (H&E) from invasive mammary carcinoma, no special type cases as a source domain and study environment. We developed a customized hybrid semi-automated segmentation algorithm to cluster the raw image data and reduce the image domain complexity to a binary representation with the foreground representing regions of high density of malignant cells. A second algorithm was developed to apply stochastic geometry and texture analysis measurements to the segmented images and to produce shape distributions, transforming the original color images into a histogram representation that captures their distinguishing properties between various histological grades. Results: Computational results were compared against known histological grades assigned by the pathologist. The Earth Mover's Distance (EMD) similarity metric and the K-Nearest Neighbors (KNN) classification algorithm provided correlations between the high-dimensional set of shape distributions and a priori known histological grades. Conclusion: Computational pattern analysis of histology shows promise as an effective software tool in breast cancer histological grading.
Stochastic sensing through covalent interactions
Bayley, Hagan; Shin, Seong-Ho; Luchian, Tudor; Cheley, Stephen
2013-03-26
A system and method for stochastic sensing in which the analyte covalently bonds to the sensor element or an adaptor element. If such bonding is irreversible, the bond may be broken by a chemical reagent. The sensor element may be a protein, such as the engineered P.sub.SH type or .alpha.HL protein pore. The analyte may be any reactive analyte, including chemical weapons, environmental toxins and pharmaceuticals. The analyte covalently bonds to the sensor element to produce a detectable signal. Possible signals include change in electrical current, change in force, and change in fluorescence. Detection of the signal allows identification of the analyte and determination of its concentration in a sample solution. Multiple analytes present in the same solution may be detected.
Robust stochastic mine production scheduling
NASA Astrophysics Data System (ADS)
Kumral, Mustafa
2010-06-01
The production scheduling of open pit mines aims to determine the extraction sequence of blocks such that the net present value (NPV) of a mining project is maximized under capacity and access constraints. This sequencing has significant effect on the profitability of the mining venture. However, given that the values of coefficients in the optimization procedure are obtained in a medium of sparse data and unknown future events, implementations based on deterministic models may lead to destructive consequences to the company. In this article, a robust stochastic optimization (RSO) approach is used to deal with mine production scheduling in a manner such that the solution is insensitive to changes in input data. The approach seeks a trade off between optimality and feasibility. The model is demonstrated on a case study. The findings showed that the approach can be used in mine production scheduling problems efficiently.
Heuristic-biased stochastic sampling
Bresina, J.L.
1996-12-31
This paper presents a search technique for scheduling problems, called Heuristic-Biased Stochastic Sampling (HBSS). The underlying assumption behind the HBSS approach is that strictly adhering to a search heuristic often does not yield the best solution and, therefore, exploration off the heuristic path can prove fruitful. Within the HBSS approach, the balance between heuristic adherence and exploration can be controlled according to the confidence one has in the heuristic. By varying this balance, encoded as a bias function, the HBSS approach encompasses a family of search algorithms of which greedy search and completely random search are extreme members. We present empirical results from an application of HBSS to the realworld problem of observation scheduling. These results show that with the proper bias function, it can be easy to outperform greedy search.
Stochastic hyperfine interactions modeling library
NASA Astrophysics Data System (ADS)
Zacate, Matthew O.; Evenson, William E.
2011-04-01
The stochastic hyperfine interactions modeling library (SHIML) provides a set of routines to assist in the development and application of stochastic models of hyperfine interactions. The library provides routines written in the C programming language that (1) read a text description of a model for fluctuating hyperfine fields, (2) set up the Blume matrix, upon which the evolution operator of the system depends, and (3) find the eigenvalues and eigenvectors of the Blume matrix so that theoretical spectra of experimental techniques that measure hyperfine interactions can be calculated. The optimized vector and matrix operations of the BLAS and LAPACK libraries are utilized; however, there was a need to develop supplementary code to find an orthonormal set of (left and right) eigenvectors of complex, non-Hermitian matrices. In addition, example code is provided to illustrate the use of SHIML to generate perturbed angular correlation spectra for the special case of polycrystalline samples when anisotropy terms of higher order than A can be neglected. Program summaryProgram title: SHIML Catalogue identifier: AEIF_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIF_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU GPL 3 No. of lines in distributed program, including test data, etc.: 8224 No. of bytes in distributed program, including test data, etc.: 312 348 Distribution format: tar.gz Programming language: C Computer: Any Operating system: LINUX, OS X RAM: Varies Classification: 7.4 External routines: TAPP [1], BLAS [2], a C-interface to BLAS [3], and LAPACK [4] Nature of problem: In condensed matter systems, hyperfine methods such as nuclear magnetic resonance (NMR), Mössbauer effect (ME), muon spin rotation (μSR), and perturbed angular correlation spectroscopy (PAC) measure electronic and magnetic structure within Angstroms of nuclear probes through the hyperfine interaction. When
Thermodynamics of stochastic Turing machines.
Strasberg, Philipp; Cerrillo, Javier; Schaller, Gernot; Brandes, Tobias
2015-10-01
In analogy to Brownian computers we explicitly show how to construct stochastic models which mimic the behavior of a general-purpose computer (a Turing machine). Our models are discrete state systems obeying a Markovian master equation, which are logically reversible and have a well-defined and consistent thermodynamic interpretation. The resulting master equation, which describes a simple one-step process on an enormously large state space, allows us to thoroughly investigate the thermodynamics of computation for this situation. Especially in the stationary regime we can well approximate the master equation by a simple Fokker-Planck equation in one dimension. We then show that the entropy production rate at steady state can be made arbitrarily small, but the total (integrated) entropy production is finite and grows logarithmically with the number of computational steps.
Stochastic evolution of staying together.
Ghang, Whan; Nowak, Martin A
2014-11-07
Staying together means that replicating units do not separate after reproduction, but remain attached to each other or in close proximity. Staying together is a driving force for evolution of complexity, including the evolution of multi-cellularity and eusociality. We analyze the fixation probability of a mutant that has the ability to stay together. We assume that the size of the complex affects the reproductive rate of its units and the probability of staying together. We examine the combined effect of natural selection and random drift on the emergence of staying together in a finite sized population. The number of states in the underlying stochastic process is an exponential function of population size. We develop a framework for any intensity of selection and give closed form solutions for special cases. We derive general results for the limit of weak selection. Copyright © 2014 Elsevier Ltd. All rights reserved.
Stochastic thermodynamics for active matter
NASA Astrophysics Data System (ADS)
Speck, Thomas
2016-05-01
The theoretical understanding of active matter, which is driven out of equilibrium by directed motion, is still fragmental and model oriented. Stochastic thermodynamics, on the other hand, is a comprehensive theoretical framework for driven systems that allows to define fluctuating work and heat. We apply these definitions to active matter, assuming that dissipation can be modelled by effective non-conservative forces. We show that, through the work, conjugate extensive and intensive observables can be defined even in non-equilibrium steady states lacking a free energy. As an illustration, we derive the expressions for the pressure and interfacial tension of active Brownian particles. The latter becomes negative despite the observed stable phase separation. We discuss this apparent contradiction, highlighting the role of fluctuations, and we offer a tentative explanation.
Stochastic resonance in attention control
NASA Astrophysics Data System (ADS)
Kitajo, K.; Yamanaka, K.; Ward, L. M.; Yamamoto, Y.
2006-12-01
We investigated the beneficial role of noise in a human higher brain function, namely visual attention control. We asked subjects to detect a weak gray-level target inside a marker box either in the left or the right visual field. Signal detection performance was optimized by presenting a low level of randomly flickering gray-level noise between and outside the two possible target locations. Further, we found that an increase in eye movement (saccade) rate helped to compensate for the usual deterioration in detection performance at higher noise levels. To our knowledge, this is the first experimental evidence that noise can optimize a higher brain function which involves distinct brain regions above the level of primary sensory systems -- switching behavior between multi-stable attention states -- via the mechanism of stochastic resonance.
Multiscale Stochastic Simulation and Modeling
James Glimm; Xiaolin Li
2006-01-10
Acceleration driven instabilities of fluid mixing layers include the classical cases of Rayleigh-Taylor instability, driven by a steady acceleration and Richtmyer-Meshkov instability, driven by an impulsive acceleration. Our program starts with high resolution methods of numerical simulation of two (or more) distinct fluids, continues with analytic analysis of these solutions, and the derivation of averaged equations. A striking achievement has been the systematic agreement we obtained between simulation and experiment by using a high resolution numerical method and improved physical modeling, with surface tension. Our study is accompanies by analysis using stochastic modeling and averaged equations for the multiphase problem. We have quantified the error and uncertainty using statistical modeling methods.
Multiple Stochastic Point Processes in Gene Expression
NASA Astrophysics Data System (ADS)
Murugan, Rajamanickam
2008-04-01
We generalize the idea of multiple-stochasticity in chemical reaction systems to gene expression. Using Chemical Langevin Equation approach we investigate how this multiple-stochasticity can influence the overall molecular number fluctuations. We show that the main sources of this multiple-stochasticity in gene expression could be the randomness in transcription and translation initiation times which in turn originates from the underlying bio-macromolecular recognition processes such as the site-specific DNA-protein interactions and therefore can be internally regulated by the supra-molecular structural factors such as the condensation/super-coiling of DNA. Our theory predicts that (1) in case of gene expression system, the variances ( φ) introduced by the randomness in transcription and translation initiation-times approximately scales with the degree of condensation ( s) of DNA or mRNA as φ ∝ s -6. From the theoretical analysis of the Fano factor as well as coefficient of variation associated with the protein number fluctuations we predict that (2) unlike the singly-stochastic case where the Fano factor has been shown to be a monotonous function of translation rate, in case of multiple-stochastic gene expression the Fano factor is a turn over function with a definite minimum. This in turn suggests that the multiple-stochastic processes can also be well tuned to behave like a singly-stochastic point processes by adjusting the rate parameters.
Incorporating landscape stochasticity into population viability analysis.
Chisholm, Ryan A; Wintle, Brendan A
2007-03-01
The importance of incorporating landscape dynamics into population viability analysis (PVA) has previously been acknowledged, but the need to repeat the landscape generation process to encapsulate landscape stochasticity in model outputs has largely been overlooked. Reasons for this are that (1) there is presently no means for quantifying the relative effects of landscape stochasticity and population stochasticity on model outputs, and therefore no means for determining how to allocate simulation time optimally between the two; and (2) the process of generating multiple landscapes to incorporate landscape stochasticity is tedious and user-intensive with current PVA software. Here we demonstrate that landscape stochasticity can be an important source of variance in model outputs. We solve the technical problems with incorporating landscape stochasticity by deriving a formula that gives the optimal ratio of population simulations to landscape simulations for a given model, and by providing a computer program that incorporates the formula and automates multiple landscape generation in a dynamic landscape metapopulation (DLMP) model. Using a case study of a bird population, we produce estimates of DLMP model output parameters that are up to four times more precise than those estimated from a single landscape in the same amount of total simulation time. We use the DLMP modeling software RAMAS Landscape to run the landscape and metapopulation models, though our method is general and could be applied to any PVA platform. The results of this study should motivate DLMP modelers to consider landscape stochasticity in their analyses.
Stochastic string models with continuous semimartingales
NASA Astrophysics Data System (ADS)
Bueno-Guerrero, Alberto; Moreno, Manuel; Navas, Javier F.
2015-09-01
This paper reformulates the stochastic string model of Santa-Clara and Sornette using stochastic calculus with continuous semimartingales. We present some new results, such as: (a) the dynamics of the short-term interest rate, (b) the PDE that must be satisfied by the bond price, and (c) an analytic expression for the price of a European bond call option. Additionally, we clarify some important features of the stochastic string model and show its relevance to price derivatives and the equivalence with an infinite dimensional HJM model to price European options.
A multilevel stochastic collocation method for SPDEs
Gunzburger, Max; Jantsch, Peter; Teckentrup, Aretha; Webster, Clayton
2015-03-10
We present a multilevel stochastic collocation method that, as do multilevel Monte Carlo methods, uses a hierarchy of spatial approximations to reduce the overall computational complexity when solving partial differential equations with random inputs. For approximation in parameter space, a hierarchy of multi-dimensional interpolants of increasing fidelity are used. Rigorous convergence and computational cost estimates for the new multilevel stochastic collocation method are derived and used to demonstrate its advantages compared to standard single-level stochastic collocation approximations as well as multilevel Monte Carlo methods.
Permanence of Stochastic Lotka-Volterra Systems
NASA Astrophysics Data System (ADS)
Liu, Meng; Fan, Meng
2017-04-01
This paper proposes a new definition of permanence for stochastic population models, which overcomes some limitations and deficiency of the existing ones. Then, we explore the permanence of two-dimensional stochastic Lotka-Volterra systems in a general setting, which models several different interactions between two species such as cooperation, competition, and predation. Sharp sufficient criteria are established with the help of the Lyapunov direct method and some new techniques. This study reveals that the stochastic noises play an essential role in the permanence and characterize the systems being permanent or not.
Stochastic system identification in structural dynamics
Safak, Erdal
1988-01-01
Recently, new identification methods have been developed by using the concept of optimal-recursive filtering and stochastic approximation. These methods, known as stochastic identification, are based on the statistical properties of the signal and noise, and do not require the assumptions of current methods. The criterion for stochastic system identification is that the difference between the recorded output and the output from the identified system (i.e., the residual of the identification) should be equal to white noise. In this paper, first a brief review of the theory is given. Then, an application of the method is presented by using ambient vibration data from a nine-story building.
Connecting deterministic and stochastic metapopulation models.
Barbour, A D; McVinish, R; Pollett, P K
2015-12-01
In this paper, we study the relationship between certain stochastic and deterministic versions of Hanski's incidence function model and the spatially realistic Levins model. We show that the stochastic version can be well approximated in a certain sense by the deterministic version when the number of habitat patches is large, provided that the presence or absence of individuals in a given patch is influenced by a large number of other patches. Explicit bounds on the deviation between the stochastic and deterministic models are given.
A stochastic subgrid model for sheared turbulence
NASA Astrophysics Data System (ADS)
Bertoglio, J. P.
A new subgrid model for homogeneous turbulence is proposed. The model is used in a method of Large Eddy Simulation coupled with an E.D.Q.N.M. prediction of the statistical properties of the small scales. The model is stochastic in order to allow a 'disaveraging' of the informations provided by the E.D.Q.N.M. closure. It is based on stochastic amplitude equations for two-point closures. It allows backflow of energy from the small scales, introduces stochasticity into L.E.S., and is well adapted to nonisotropic fields. A few results are presented here.
Large Deviations for Stochastic Flows of Diffeomorphisms
2007-01-01
be the unique solution of the ordinary differential equation ∂ηs,t(x) ∂t .= b ( ηs,t(x), t ) , ηs,s(x) = x, 0 ≤ s ≤ t ≤ 1. (5.2) Then it follows that...solving finite dimensional Itô stochastic differential equations . More precisely, suppose b, fi, i = 1, . . . ,m are functions from Rd × [0, T ] to Rd...s, T ]. This stochastic process is called the solution of Itô’s stochastic differential equation based on the Brownian motion F . From [15, Theorem
Stochastic Satbility and Performance Robustness of Linear Multivariable Systems
NASA Technical Reports Server (NTRS)
Ryan, Laurie E.; Stengel, Robert F.
1990-01-01
Stochastic robustness, a simple technique used to estimate the robustness of linear, time invariant systems, is applied to a single-link robot arm control system. Concepts behind stochastic stability robustness are extended to systems with estimators and to stochastic performance robustness. Stochastic performance robustness measures based on classical design specifications are introduced, and the relationship between stochastic robustness measures and control system design parameters are discussed. The application of stochastic performance robustness, and the relationship between performance objectives and design parameters are demonstrated by means of example. The results prove stochastic robustness to be a good overall robustness analysis method that can relate robustness characteristics to control system design parameters.
Stochastic pump effect and geometric phases in dissipative and stochastic systems
Sinitsyn, Nikolai
2008-01-01
The success of Berry phases in quantum mechanics stimulated the study of similar phenomena in other areas of physics, including the theory of living cell locomotion and motion of patterns in nonlinear media. More recently, geometric phases have been applied to systems operating in a strongly stochastic environment, such as molecular motors. We discuss such geometric effects in purely classical dissipative stochastic systems and their role in the theory of the stochastic pump effect (SPE).
Liu, Meng; Wang, Ke; Wu, Qiong
2011-09-01
Stochastic competitive models with pollution and without pollution are proposed and studied. For the first system with pollution, sufficient criteria for extinction, nonpersistence in the mean, weak persistence in the mean, strong persistence in the mean, and stochastic permanence are established. The threshold between weak persistence in the mean and extinction for each population is obtained. It is found that stochastic disturbance is favorable for the survival of one species and is unfavorable for the survival of the other species. For the second system with pollution, sufficient conditions for extinction and weak persistence are obtained. For the model without pollution, a partial stochastic competitive exclusion principle is derived.
NASA Astrophysics Data System (ADS)
Hertfelder, C.; Kümmerer, B.
2001-03-01
The mathematical model describing a light beam prepared in an arbitrary quantum optical state is a quasifree quantum stochastic process on the C* algebra of the canonical commutatation relations. For such quantum stochastic processes the concept of stochastic states is introduced. Stochastic quantum states have a classical analog in the following sense: If the light beam is prepared in a stochastic state, one can construct a generalized classical stochastic process, such that the distributions of the quantum observables and the classical random variables coincide. A sufficient algebraic condition for the stochasticity of a quantum state is formulated. The introduced formalism generalizes the Wigner representation from a single field mode to a continuum of modes. For the special case of a single field mode the stochasticity condition provides a new criterion for the positivity of the Wigner function related to the given state. As an example the quantized eletromagnetic field in empty space at temperature T=0 is discussed. It turns out that the corresponding classical stochastic process is not a white noise but a colored noise with a linearly increasing spectrum.
Bootstrap performance profiles in stochastic algorithms assessment
Costa, Lino; Espírito Santo, Isabel A.C.P.; Oliveira, Pedro
2015-03-10
Optimization with stochastic algorithms has become a relevant research field. Due to its stochastic nature, its assessment is not straightforward and involves integrating accuracy and precision. Performance profiles for the mean do not show the trade-off between accuracy and precision, and parametric stochastic profiles require strong distributional assumptions and are limited to the mean performance for a large number of runs. In this work, bootstrap performance profiles are used to compare stochastic algorithms for different statistics. This technique allows the estimation of the sampling distribution of almost any statistic even with small samples. Multiple comparison profiles are presented for more than two algorithms. The advantages and drawbacks of each assessment methodology are discussed.
Stochastic structure formation in random media
NASA Astrophysics Data System (ADS)
Klyatskin, V. I.
2016-01-01
Stochastic structure formation in random media is considered using examples of elementary dynamical systems related to the two-dimensional geophysical fluid dynamics (Gaussian random fields) and to stochastically excited dynamical systems described by partial differential equations (lognormal random fields). In the latter case, spatial structures (clusters) may form with a probability of one in almost every system realization due to rare events happening with vanishing probability. Problems involving stochastic parametric excitation occur in fluid dynamics, magnetohydrodynamics, plasma physics, astrophysics, and radiophysics. A more complicated stochastic problem dealing with anomalous structures on the sea surface (rogue waves) is also considered, where the random Gaussian generation of sea surface roughness is accompanied by parametric excitation.
Stochasticity in plant cellular growth and patterning.
Meyer, Heather M; Roeder, Adrienne H K
2014-01-01
Plants, along with other multicellular organisms, have evolved specialized regulatory mechanisms to achieve proper tissue growth and morphogenesis. During development, growing tissues generate specialized cell types and complex patterns necessary for establishing the function of the organ. Tissue growth is a tightly regulated process that yields highly reproducible outcomes. Nevertheless, the underlying cellular and molecular behaviors are often stochastic. Thus, how does stochasticity, together with strict genetic regulation, give rise to reproducible tissue development? This review draws examples from plants as well as other systems to explore stochasticity in plant cell division, growth, and patterning. We conclude that stochasticity is often needed to create small differences between identical cells, which are amplified and stabilized by genetic and mechanical feedback loops to begin cell differentiation. These first few differentiating cells initiate traditional patterning mechanisms to ensure regular development.
Stochasticity in plant cellular growth and patterning
Meyer, Heather M.; Roeder, Adrienne H. K.
2014-01-01
Plants, along with other multicellular organisms, have evolved specialized regulatory mechanisms to achieve proper tissue growth and morphogenesis. During development, growing tissues generate specialized cell types and complex patterns necessary for establishing the function of the organ. Tissue growth is a tightly regulated process that yields highly reproducible outcomes. Nevertheless, the underlying cellular and molecular behaviors are often stochastic. Thus, how does stochasticity, together with strict genetic regulation, give rise to reproducible tissue development? This review draws examples from plants as well as other systems to explore stochasticity in plant cell division, growth, and patterning. We conclude that stochasticity is often needed to create small differences between identical cells, which are amplified and stabilized by genetic and mechanical feedback loops to begin cell differentiation. These first few differentiating cells initiate traditional patterning mechanisms to ensure regular development. PMID:25250034
Communication: Embedded fragment stochastic density functional theory
Neuhauser, Daniel; Baer, Roi; Rabani, Eran
2014-07-28
We develop a method in which the electronic densities of small fragments determined by Kohn-Sham density functional theory (DFT) are embedded using stochastic DFT to form the exact density of the full system. The new method preserves the scaling and the simplicity of the stochastic DFT but cures the slow convergence that occurs when weakly coupled subsystems are treated. It overcomes the spurious charge fluctuations that impair the applications of the original stochastic DFT approach. We demonstrate the new approach on a fullerene dimer and on clusters of water molecules and show that the density of states and the total energy can be accurately described with a relatively small number of stochastic orbitals.
K-Minimax Stochastic Programming Problems
NASA Astrophysics Data System (ADS)
Nedeva, C.
2007-10-01
The purpose of this paper is a discussion of a numerical procedure based on the simplex method for stochastic optimization problems with partially known distribution functions. The convergence of this procedure is proved by the condition on dual problems.
Stochasticity and determinism in models of hematopoiesis.
Kimmel, Marek
2014-01-01
This chapter represents a novel view of modeling in hematopoiesis, synthesizing both deterministic and stochastic approaches. Whereas the stochastic models work in situations where chance dominates, for example when the number of cells is small, or under random mutations, the deterministic models are more important for large-scale, normal hematopoiesis. New types of models are on the horizon. These models attempt to account for distributed environments such as hematopoietic niches and their impact on dynamics. Mixed effects of such structures and chance events are largely unknown and constitute both a challenge and promise for modeling. Our discussion is presented under the separate headings of deterministic and stochastic modeling; however, the connections between both are frequently mentioned. Four case studies are included to elucidate important examples. We also include a primer of deterministic and stochastic dynamics for the reader's use.
Evolutionary stability concepts in a stochastic environment
NASA Astrophysics Data System (ADS)
Zheng, Xiu-Deng; Li, Cong; Lessard, Sabin; Tao, Yi
2017-09-01
Over the past 30 years, evolutionary game theory and the concept of an evolutionarily stable strategy have been not only extensively developed and successfully applied to explain the evolution of animal behaviors, but also widely used in economics and social sciences. Nonetheless, the stochastic dynamical properties of evolutionary games in randomly fluctuating environments are still unclear. In this study, we investigate conditions for stochastic local stability of fixation states and constant interior equilibria in a two-phenotype model with random payoffs following pairwise interactions. Based on this model, we develop the concepts of stochastic evolutionary stability (SES) and stochastic convergence stability (SCS). We show that the condition for a pure strategy to be SES and SCS is more stringent than in a constant environment, while the condition for a constant mixed strategy to be SES is less stringent than the condition to be SCS, which is less stringent than the condition in a constant environment.
Extending stochastic network calculus to loss analysis.
Luo, Chao; Yu, Li; Zheng, Jun
2013-01-01
Loss is an important parameter of Quality of Service (QoS). Though stochastic network calculus is a very useful tool for performance evaluation of computer networks, existing studies on stochastic service guarantees mainly focused on the delay and backlog. Some efforts have been made to analyse loss by deterministic network calculus, but there are few results to extend stochastic network calculus for loss analysis. In this paper, we introduce a new parameter named loss factor into stochastic network calculus and then derive the loss bound through the existing arrival curve and service curve via this parameter. We then prove that our result is suitable for the networks with multiple input flows. Simulations show the impact of buffer size, arrival traffic, and service on the loss factor.
Stochastic differential equation model to Prendiville processes
NASA Astrophysics Data System (ADS)
Granita, Bahar, Arifah
2015-10-01
The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution.
Stochastic resonance during a polymer translocation process
NASA Astrophysics Data System (ADS)
Mondal, Debasish; Muthukumar, Murugappan
We study the translocation of a flexible polymer in a confined geometry subjected to a time-periodic external drive to explore stochastic resonance. We describe the equilibrium translocation process in terms of a Fokker-Planck description and use a discrete two-state model to describe the effect of the external driving force on the translocation dynamics. We observe that no stochastic resonance is possible if the associated free-energy barrier is purely entropic in nature. The polymer chain experiences a stochastic resonance effect only in presence of an energy threshold in terms of polymer-pore interaction. Once stochastic resonance is feasible, the chain entropy controls the optimal synchronization conditions significantly.
Stochastic differential equation model to Prendiville processes
Granita; Bahar, Arifah
2015-10-22
The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution.
Stochastic description of quantum Brownian dynamics
NASA Astrophysics Data System (ADS)
Yan, Yun-An; Shao, Jiushu
2016-08-01
Classical Brownian motion has well been investigated since the pioneering work of Einstein, which inspired mathematicians to lay the theoretical foundation of stochastic processes. A stochastic formulation for quantum dynamics of dissipative systems described by the system-plus-bath model has been developed and found many applications in chemical dynamics, spectroscopy, quantum transport, and other fields. This article provides a tutorial review of the stochastic formulation for quantum dissipative dynamics. The key idea is to decouple the interaction between the system and the bath by virtue of the Hubbard-Stratonovich transformation or Itô calculus so that the system and the bath are not directly entangled during evolution, rather they are correlated due to the complex white noises introduced. The influence of the bath on the system is thereby defined by an induced stochastic field, which leads to the stochastic Liouville equation for the system. The exact reduced density matrix can be calculated as the stochastic average in the presence of bath-induced fields. In general, the plain implementation of the stochastic formulation is only useful for short-time dynamics, but not efficient for long-time dynamics as the statistical errors go very fast. For linear and other specific systems, the stochastic Liouville equation is a good starting point to derive the master equation. For general systems with decomposable bath-induced processes, the hierarchical approach in the form of a set of deterministic equations of motion is derived based on the stochastic formulation and provides an effective means for simulating the dissipative dynamics. A combination of the stochastic simulation and the hierarchical approach is suggested to solve the zero-temperature dynamics of the spin-boson model. This scheme correctly describes the coherent-incoherent transition (Toulouse limit) at moderate dissipation and predicts a rate dynamics in the overdamped regime. Challenging problems
Desynchronization of stochastically synchronized chemical oscillators
Snari, Razan; Tinsley, Mark R. E-mail: kshowalt@wvu.edu; Faramarzi, Sadegh; Showalter, Kenneth E-mail: kshowalt@wvu.edu; Wilson, Dan; Moehlis, Jeff; Netoff, Theoden Ivan
2015-12-15
Experimental and theoretical studies are presented on the design of perturbations that enhance desynchronization in populations of oscillators that are synchronized by periodic entrainment. A phase reduction approach is used to determine optimal perturbation timing based upon experimentally measured phase response curves. The effectiveness of the perturbation waveforms is tested experimentally in populations of periodically and stochastically synchronized chemical oscillators. The relevance of the approach to therapeutic methods for disrupting phase coherence in groups of stochastically synchronized neuronal oscillators is discussed.
Stochastic Semidefinite Programming: Applications and Algorithms
2012-03-03
doi: 2011/09/07 13:38:21 13 TOTAL: 1 Number of Papers published in non peer-reviewed journals: Baha M. Alzalg and K. A. Ariyawansa, Stochastic...symmetric programming over integers. International Conference on Scientific Computing, Las Vegas, Nevada, July 18--21, 2011. Baha M. Alzalg. On recent...Proceeding publications (other than abstracts): PaperReceived Baha M. Alzalg, K. A. Ariyawansa. Stochastic mixed integer second-order cone programming
Stochastic differential games with inside information
NASA Astrophysics Data System (ADS)
Draouil, Olfa; Øksendal, Bernt
2016-08-01
We study stochastic differential games of jump diffusions, where the players have access to inside information. Our approach is based on anticipative stochastic calculus, white noise, Hida-Malliavin calculus, forward integrals and the Donsker delta functional. We obtain a characterization of Nash equilibria of such games in terms of the corresponding Hamiltonians. This is used to study applications to insider games in finance, specifically optimal insider consumption and optimal insider portfolio under model uncertainty.
Optimal factory scheduling using stochastic dominance A
Wurman, P.R.
1996-12-31
Generating optimal production schedules for manufacturing facilities an area of great theoretical and practical importance. During the last decade, an effort has been made to reconcile the techniques developed by the AI and OR communities. The work described here aims to continue in this vein by showing how a class of well-defined stochastic scheduling problems can be mapped into a general search procedure. This approach improves upon other methods by handling the general case of multidimensional stochastic costs.
Complexity and synchronization in stochastic chaotic systems
NASA Astrophysics Data System (ADS)
Dang, Thai Son; Palit, Sanjay Kumar; Mukherjee, Sayan; Hoang, Thang Manh; Banerjee, Santo
2016-02-01
We investigate the complexity of a hyperchaotic dynamical system perturbed by noise and various nonlinear speech and music signals. The complexity is measured by the weighted recurrence entropy of the hyperchaotic and stochastic systems. The synchronization phenomenon between two stochastic systems with complex coupling is also investigated. These criteria are tested on chaotic and perturbed systems by mean conditional recurrence and normalized synchronization error. Numerical results including surface plots, normalized synchronization errors, complexity variations etc show the effectiveness of the proposed analysis.
Stochastic Simulations of Cellular Biological Processes
2007-06-01
model kinetics of a system of chemical reactions is to use a stochastic 2. Stochastic Simulation Algorithm approach in terms of the Chemical Master...number of processors and running time) for interactive disk spae ad, herfor, my ceat meory simulations. Therefore, in addition to running in an...management problems for simulations involving a large inteative mode, foNScan as o run in ’n number of long runs or for large reaction networks. interactive
Stochastic synchronization in finite size spiking networks.
Doiron, Brent; Rinzel, John; Reyes, Alex
2006-09-01
We study a stochastic synchronization of spiking activity in feedforward networks of integrate-and-fire model neurons. A stochastic mean field analysis shows that synchronization occurs only when the network size is sufficiently small. This gives evidence that the dynamics, and hence processing, of finite size populations can be drastically different from that observed in the infinite size limit. Our results agree with experimentally observed synchrony in cortical networks, and further strengthen the link between synchrony and propagation in cortical systems.
Some stochastic aspects of intergranular creep cavitation
Fariborz, S.J.; Farris, J.P.; Harlow, D.G.; Delph, T.J.
1987-10-01
We present some results obtained from a simplified stochastic model of intergranular creep cavitation. The probabilistic features of the model arise from the inclusion of random cavity placement on the grain boundary and time-discrete stochastic cavity nucleation. Among the predictions of the model are Weibull-distributed creep rupture failure times and a Weibull distribution of cavity radii. Both of these predictions have qualitative experimental support. 18 refs., 7 figs.
Sequential decision analysis for nonstationary stochastic processes
NASA Technical Reports Server (NTRS)
Schaefer, B.
1974-01-01
A formulation of the problem of making decisions concerning the state of nonstationary stochastic processes is given. An optimal decision rule, for the case in which the stochastic process is independent of the decisions made, is derived. It is shown that this rule is a generalization of the Bayesian likelihood ratio test; and an analog to Wald's sequential likelihood ratio test is given, in which the optimal thresholds may vary with time.
Stochastic resonance mechanism in aerosol index dynamics.
De Martino, S; Falanga, M; Mona, L
2002-09-16
We consider satellite time series concerning the atmospheric aerosol content. We prove that these time series are well described by a stochastic dynamical model. The principal peak in the power spectrum of these signals can be explained by stochastic resonance, linking variable external factors, such as Sun-Earth radiation budget and local insolation, to fluctuations on smaller spatial and temporal scale due to internal weather and antrophic components.
Stochastic resonance during a polymer translocation process
NASA Astrophysics Data System (ADS)
Mondal, Debasish; Muthukumar, M.
2016-04-01
We have studied the occurrence of stochastic resonance when a flexible polymer chain undergoes a single-file translocation through a nano-pore separating two spherical cavities, under a time-periodic external driving force. The translocation of the chain is controlled by a free energy barrier determined by chain length, pore length, pore-polymer interaction, and confinement inside the donor and receiver cavities. The external driving force is characterized by a frequency and amplitude. By combining the Fokker-Planck formalism for polymer translocation and a two-state model for stochastic resonance, we have derived analytical formulas for criteria for emergence of stochastic resonance during polymer translocation. We show that no stochastic resonance is possible if the free energy barrier for polymer translocation is purely entropic in nature. The polymer chain exhibits stochastic resonance only in the presence of an energy threshold in terms of polymer-pore interactions. Once stochastic resonance is feasible, the chain entropy controls the optimal synchronization conditions significantly.
Stochastic flux freezing and magnetic dynamo
Eyink, Gregory L.
2011-05-15
Magnetic flux conservation in turbulent plasmas at high magnetic Reynolds numbers is argued neither to hold in the conventional sense nor to be entirely broken, but instead to be valid in a statistical sense associated to the ''spontaneous stochasticity'' of Lagrangian particle trajectories. The latter phenomenon is due to the explosive separation of particles undergoing turbulent Richardson diffusion, which leads to a breakdown of Laplacian determinism for classical dynamics. Empirical evidence is presented for spontaneous stochasticity, including numerical results. A Lagrangian path-integral approach is then exploited to establish stochastic flux freezing for resistive hydromagnetic equations and to argue, based on the properties of Richardson diffusion, that flux conservation must remain stochastic at infinite magnetic Reynolds number. An important application of these results is the kinematic, fluctuation dynamo in nonhelical, incompressible turbulence at magnetic Prandtl number (Pr{sub m}) equal to unity. Numerical results on the Lagrangian dynamo mechanisms by a stochastic particle method demonstrate a strong similarity between the Pr{sub m}=1 and 0 dynamos. Stochasticity of field-line motion is an essential ingredient of both. Finally, some consequences for nonlinear magnetohydrodynamic turbulence, dynamo, and reconnection are briefly considered.
Automated Flight Routing Using Stochastic Dynamic Programming
NASA Technical Reports Server (NTRS)
Ng, Hok K.; Morando, Alex; Grabbe, Shon
2010-01-01
Airspace capacity reduction due to convective weather impedes air traffic flows and causes traffic congestion. This study presents an algorithm that reroutes flights in the presence of winds, enroute convective weather, and congested airspace based on stochastic dynamic programming. A stochastic disturbance model incorporates into the reroute design process the capacity uncertainty. A trajectory-based airspace demand model is employed for calculating current and future airspace demand. The optimal routes minimize the total expected traveling time, weather incursion, and induced congestion costs. They are compared to weather-avoidance routes calculated using deterministic dynamic programming. The stochastic reroutes have smaller deviation probability than the deterministic counterpart when both reroutes have similar total flight distance. The stochastic rerouting algorithm takes into account all convective weather fields with all severity levels while the deterministic algorithm only accounts for convective weather systems exceeding a specified level of severity. When the stochastic reroutes are compared to the actual flight routes, they have similar total flight time, and both have about 1% of travel time crossing congested enroute sectors on average. The actual flight routes induce slightly less traffic congestion than the stochastic reroutes but intercept more severe convective weather.
Stochastic resonance during a polymer translocation process.
Mondal, Debasish; Muthukumar, M
2016-04-14
We have studied the occurrence of stochastic resonance when a flexible polymer chain undergoes a single-file translocation through a nano-pore separating two spherical cavities, under a time-periodic external driving force. The translocation of the chain is controlled by a free energy barrier determined by chain length, pore length, pore-polymer interaction, and confinement inside the donor and receiver cavities. The external driving force is characterized by a frequency and amplitude. By combining the Fokker-Planck formalism for polymer translocation and a two-state model for stochastic resonance, we have derived analytical formulas for criteria for emergence of stochastic resonance during polymer translocation. We show that no stochastic resonance is possible if the free energy barrier for polymer translocation is purely entropic in nature. The polymer chain exhibits stochastic resonance only in the presence of an energy threshold in terms of polymer-pore interactions. Once stochastic resonance is feasible, the chain entropy controls the optimal synchronization conditions significantly.
Stochastic learning via optimizing the variational inequalities.
Tao, Qing; Gao, Qian-Kun; Chu, De-Jun; Wu, Gao-Wei
2014-10-01
A wide variety of learning problems can be posed in the framework of convex optimization. Many efficient algorithms have been developed based on solving the induced optimization problems. However, there exists a gap between the theoretically unbeatable convergence rate and the practically efficient learning speed. In this paper, we use the variational inequality (VI) convergence to describe the learning speed. To this end, we avoid the hard concept of regret in online learning and directly discuss the stochastic learning algorithms. We first cast the regularized learning problem as a VI. Then, we present a stochastic version of alternating direction method of multipliers (ADMMs) to solve the induced VI. We define a new VI-criterion to measure the convergence of stochastic algorithms. While the rate of convergence for any iterative algorithms to solve nonsmooth convex optimization problems cannot be better than O(1/√t), the proposed stochastic ADMM (SADMM) is proved to have an O(1/t) VI-convergence rate for the l1-regularized hinge loss problems without strong convexity and smoothness. The derived VI-convergence results also support the viewpoint that the standard online analysis is too loose to analyze the stochastic setting properly. The experiments demonstrate that SADMM has almost the same performance as the state-of-the-art stochastic learning algorithms but its O(1/t) VI-convergence rate is capable of tightly characterizing the real learning speed.
Modular and Stochastic Approaches to Molecular Pathway Models of ATM, TGF beta, and WNT Signaling
NASA Technical Reports Server (NTRS)
Cucinotta, Francis A.; O'Neill, Peter; Ponomarev, Artem; Carra, Claudio; Whalen, Mary; Pluth, Janice M.
2009-01-01
Deterministic pathway models that describe the biochemical interactions of a group of related proteins, their complexes, activation through kinase, etc. are often the basis for many systems biology models. Low dose radiation effects present a unique set of challenges to these models including the importance of stochastic effects due to the nature of radiation tracks and small number of molecules activated, and the search for infrequent events that contribute to cancer risks. We have been studying models of the ATM, TGF -Smad and WNT signaling pathways with the goal of applying pathway models to the investigation of low dose radiation cancer risks. Modeling challenges include introduction of stochastic models of radiation tracks, their relationships to more than one substrate species that perturb pathways, and the identification of a representative set of enzymes that act on the dominant substrates. Because several pathways are activated concurrently by radiation the development of modular pathway approach is of interest.
Modular and Stochastic Approaches to Molecular Pathway Models of ATM, TGF beta, and WNT Signaling
NASA Technical Reports Server (NTRS)
Cucinotta, Francis A.; O'Neill, Peter; Ponomarev, Artem; Carra, Claudio; Whalen, Mary; Pluth, Janice M.
2009-01-01
Deterministic pathway models that describe the biochemical interactions of a group of related proteins, their complexes, activation through kinase, etc. are often the basis for many systems biology models. Low dose radiation effects present a unique set of challenges to these models including the importance of stochastic effects due to the nature of radiation tracks and small number of molecules activated, and the search for infrequent events that contribute to cancer risks. We have been studying models of the ATM, TGF -Smad and WNT signaling pathways with the goal of applying pathway models to the investigation of low dose radiation cancer risks. Modeling challenges include introduction of stochastic models of radiation tracks, their relationships to more than one substrate species that perturb pathways, and the identification of a representative set of enzymes that act on the dominant substrates. Because several pathways are activated concurrently by radiation the development of modular pathway approach is of interest.
Stochastic phase-change neurons.
Tuma, Tomas; Pantazi, Angeliki; Le Gallo, Manuel; Sebastian, Abu; Eleftheriou, Evangelos
2016-08-01
Artificial neuromorphic systems based on populations of spiking neurons are an indispensable tool in understanding the human brain and in constructing neuromimetic computational systems. To reach areal and power efficiencies comparable to those seen in biological systems, electroionics-based and phase-change-based memristive devices have been explored as nanoscale counterparts of synapses. However, progress on scalable realizations of neurons has so far been limited. Here, we show that chalcogenide-based phase-change materials can be used to create an artificial neuron in which the membrane potential is represented by the phase configuration of the nanoscale phase-change device. By exploiting the physics of reversible amorphous-to-crystal phase transitions, we show that the temporal integration of postsynaptic potentials can be achieved on a nanosecond timescale. Moreover, we show that this is inherently stochastic because of the melt-quench-induced reconfiguration of the atomic structure occurring when the neuron is reset. We demonstrate the use of these phase-change neurons, and their populations, in the detection of temporal correlations in parallel data streams and in sub-Nyquist representation of high-bandwidth signals.
Multidimensional stochastic approximation Monte Carlo
NASA Astrophysics Data System (ADS)
Zablotskiy, Sergey V.; Ivanov, Victor A.; Paul, Wolfgang
2016-06-01
Stochastic Approximation Monte Carlo (SAMC) has been established as a mathematically founded powerful flat-histogram Monte Carlo method, used to determine the density of states, g (E ) , of a model system. We show here how it can be generalized for the determination of multidimensional probability distributions (or equivalently densities of states) of macroscopic or mesoscopic variables defined on the space of microstates of a statistical mechanical system. This establishes this method as a systematic way for coarse graining a model system, or, in other words, for performing a renormalization group step on a model. We discuss the formulation of the Kadanoff block spin transformation and the coarse-graining procedure for polymer models in this language. We also apply it to a standard case in the literature of two-dimensional densities of states, where two competing energetic effects are present g (E1,E2) . We show when and why care has to be exercised when obtaining the microcanonical density of states g (E1+E2) from g (E1,E2) .
Stochastic phase-change neurons
NASA Astrophysics Data System (ADS)
Tuma, Tomas; Pantazi, Angeliki; Le Gallo, Manuel; Sebastian, Abu; Eleftheriou, Evangelos
2016-08-01
Artificial neuromorphic systems based on populations of spiking neurons are an indispensable tool in understanding the human brain and in constructing neuromimetic computational systems. To reach areal and power efficiencies comparable to those seen in biological systems, electroionics-based and phase-change-based memristive devices have been explored as nanoscale counterparts of synapses. However, progress on scalable realizations of neurons has so far been limited. Here, we show that chalcogenide-based phase-change materials can be used to create an artificial neuron in which the membrane potential is represented by the phase configuration of the nanoscale phase-change device. By exploiting the physics of reversible amorphous-to-crystal phase transitions, we show that the temporal integration of postsynaptic potentials can be achieved on a nanosecond timescale. Moreover, we show that this is inherently stochastic because of the melt-quench-induced reconfiguration of the atomic structure occurring when the neuron is reset. We demonstrate the use of these phase-change neurons, and their populations, in the detection of temporal correlations in parallel data streams and in sub-Nyquist representation of high-bandwidth signals.
Simulations of stochastic biological phenomena.
Hayot, Fernand
2011-09-20
This Teaching Resource provides lecture notes, slides, and a student assignment for a two-part lecture that introduces stochastic modeling of biological systems. The first lecture uses biological examples to present the concept of cell-to-cell variability and makes the connection between the variability of single-cell measurements and concepts from statistical mechanics and probability theory. This section makes the point that for low copy number of a species, the usual differential equation formalism is no longer applicable and needs to be replaced by a probabilistic approach based on the so-called Master Equation. As an example, a simple model of gene transcription is discussed in detail, the different contributions to the relevant Master Equation are highlighted, and the equation itself is derived. The second lecture describes how, for more complex and biologically interesting applications, direct solution of the Master Equation becomes difficult. Gillespie's algorithm, which is used in most cases of biological interest, is then introduced as a practical alternative. The lecture delves into the crux of Gillespie's algorithm, which entails the drawing of two random numbers at each time step. It establishes the corresponding formalism, details the connection between chemical rate constants and Gillespie rates, and culminates in a description and explanation of a core MATLAB program for the transcriptional model considered in the first lecture. This core program, written for a single cell, is expanded by the students in the homework assignment to consider both transcription and translation.
Stochastic Mechanisms in Gene Expression
NASA Astrophysics Data System (ADS)
McAdams, Harley H.; Arkin, Adam
1997-02-01
In cellular regulatory networks, genetic activity is controlled by molecular signals that determine when and how often a given gene is transcribed. In genetically controlled pathways, the protein product encoded by one gene often regulates expression of other genes. The time delay, after activation of the first promoter, to reach an effective level to control the next promoter depends on the rate of protein accumulation. We have analyzed the chemical reactions controlling transcript initiation and translation termination in a single such ``genetically coupled'' link as a precursor to modeling networks constructed from many such links. Simulation of the processes of gene expression shows that proteins are produced from an activated promoter in short bursts of variable numbers of proteins that occur at random time intervals. As a result, there can be large differences in the time between successive events in regulatory cascades across a cell population. In addition, the random pattern of expression of competitive effectors can produce probabilistic outcomes in switching mechanisms that select between alternative regulatory paths. The result can be a partitioning of the cell population into different phenotypes as the cells follow different paths. There are numerous unexplained examples of phenotypic variations in isogenic populations of both prokaryotic and eukaryotic cells that may be the result of these stochastic gene expression mechanisms.
Stochastic modelling of animal movement
Smouse, Peter E.; Focardi, Stefano; Moorcroft, Paul R.; Kie, John G.; Forester, James D.; Morales, Juan M.
2010-01-01
Modern animal movement modelling derives from two traditions. Lagrangian models, based on random walk behaviour, are useful for multi-step trajectories of single animals. Continuous Eulerian models describe expected behaviour, averaged over stochastic realizations, and are usefully applied to ensembles of individuals. We illustrate three modern research arenas. (i) Models of home-range formation describe the process of an animal ‘settling down’, accomplished by including one or more focal points that attract the animal's movements. (ii) Memory-based models are used to predict how accumulated experience translates into biased movement choices, employing reinforced random walk behaviour, with previous visitation increasing or decreasing the probability of repetition. (iii) Lévy movement involves a step-length distribution that is over-dispersed, relative to standard probability distributions, and adaptive in exploring new environments or searching for rare targets. Each of these modelling arenas implies more detail in the movement pattern than general models of movement can accommodate, but realistic empiric evaluation of their predictions requires dense locational data, both in time and space, only available with modern GPS telemetry. PMID:20566497
Stochastic models of intracellular transport
NASA Astrophysics Data System (ADS)
Bressloff, Paul C.; Newby, Jay M.
2013-01-01
The interior of a living cell is a crowded, heterogenuous, fluctuating environment. Hence, a major challenge in modeling intracellular transport is to analyze stochastic processes within complex environments. Broadly speaking, there are two basic mechanisms for intracellular transport: passive diffusion and motor-driven active transport. Diffusive transport can be formulated in terms of the motion of an overdamped Brownian particle. On the other hand, active transport requires chemical energy, usually in the form of adenosine triphosphate hydrolysis, and can be direction specific, allowing biomolecules to be transported long distances; this is particularly important in neurons due to their complex geometry. In this review a wide range of analytical methods and models of intracellular transport is presented. In the case of diffusive transport, narrow escape problems, diffusion to a small target, confined and single-file diffusion, homogenization theory, and fractional diffusion are considered. In the case of active transport, Brownian ratchets, random walk models, exclusion processes, random intermittent search processes, quasi-steady-state reduction methods, and mean-field approximations are considered. Applications include receptor trafficking, axonal transport, membrane diffusion, nuclear transport, protein-DNA interactions, virus trafficking, and the self-organization of subcellular structures.
[Stochastic radiation transfer]. Final report
Byrne, N.
1992-12-31
The original proposal was to produce a new cloud parameterization based upon an innovative stochastic radiative transfer techniques, in which the parameters will be validated by ARM data. The authors intended to construct a subgrid model for use in GCMs that would account for the effects of unresolved clouds on radiation flow, and they pointed out that scattering could be accommodated in this approach. They were to use ARM site data on cloud morphology and cloud/radiative energy balance in developing the new model. The data was to be supplemented by satellite data since they knew the projected rich set of ARM data would not be available immediately. The new technique was to be first checked out by incorporation into the Scripps single-column model, and after a period of refinement and proving itself was to be incorporated in a version of the CCM code. Among the minor goals was the use of these studies to provide guidance to ARM program managers and experimenters and to engender intercommunity scientific collaboration between private industry, the DOE/ARM and academia.
Lower hybrid wavepacket stochasticity revisited
Fuchs, V.; Krlín, L.; Pánek, R.; Preinhaelter, J.; Seidl, J.; Urban, J.
2014-02-12
Analysis is presented in support of the explanation in Ref. [1] for the observation of relativistic electrons during Lower Hybrid (LH) operation in EC pre-heated plasma at the WEGA stellarator [1,2]. LH power from the WEGA TE11 circular waveguide, 9 cm diameter, un-phased, 2.45 GHz antenna, is radiated into a B≅0.5 T, Ðœ„n{sub e}≅5×10{sup 17} 1/m{sup 3} plasma at T{sub e}≅10 eV bulk temperature with an EC generated 50 keV component [1]. The fast electrons cycle around flux or drift surfaces with few collisions, sufficient for randomizing phases but insufficient for slowing fast electrons down, and thus repeatedly interact with the rf field close to the antenna mouth, gaining energy in the process. Our antenna calculations reveal a standing electric field pattern at the antenna mouth, with which we formulate the electron dynamics via a relativistic Hamiltonian. A simple approximation of the equations of motion leads to a relativistic generalization of the area-preserving Fermi-Ulam (F-U) map [3], allowing phase-space global stochasticity analysis. At typical WEGA plasma and antenna conditions, the F-U map predicts an LH driven current of about 230 A, at about 225 W of dissipated power, in good agreement with the measurements and analysis reported in [1].
Stochastic Optical Reconstruction Microscopy (STORM).
Xu, Jianquan; Ma, Hongqiang; Liu, Yang
2017-07-05
Super-resolution (SR) fluorescence microscopy, a class of optical microscopy techniques at a spatial resolution below the diffraction limit, has revolutionized the way we study biology, as recognized by the Nobel Prize in Chemistry in 2014. Stochastic optical reconstruction microscopy (STORM), a widely used SR technique, is based on the principle of single molecule localization. STORM routinely achieves a spatial resolution of 20 to 30 nm, a ten-fold improvement compared to conventional optical microscopy. Among all SR techniques, STORM offers a high spatial resolution with simple optical instrumentation and standard organic fluorescent dyes, but it is also prone to image artifacts and degraded image resolution due to improper sample preparation or imaging conditions. It requires careful optimization of all three aspects-sample preparation, image acquisition, and image reconstruction-to ensure a high-quality STORM image, which will be extensively discussed in this unit. © 2017 by John Wiley & Sons, Inc. Copyright © 2017 John Wiley & Sons, Inc.
Kurkewicz, Richard; Shinogle, Heather; Kimmig, Julien; MacGabhann, Breandán Anraoi
2017-01-01
The morphology and affinities of newly discovered disc-shaped, soft-bodied fossils from the early Cambrian (Series 2: Stage 4, Dyeran) Carrara Formation are discussed. These specimens show some similarity to the Ordovician Discophyllum Hall, 1847; traditionally this taxon had been treated as a fossil porpitid. However, recently it has instead been referred to as another clade, the eldonids, which includes the enigmatic Eldonia Walcott, 1911 that was originally described from the Cambrian Burgess Shale. The status of various Proterozoic and Phanerozoic taxa previously referred to porpitids and eldonids is also briefly considered. To help ascertain that the specimens were not dubio- or pseudofossils, elemental mapping using energy dispersive X-ray spectroscopy (EDS) was conducted. This, in conjunction with the morphology of the specimens, indicated that the fossils were not hematite, iron sulfide, pyrolusite, or other abiologic mineral precipitates. Instead, their status as biologic structures and thus actual fossils is supported. Enrichment in the element carbon, and also possibly to some extent the elements magnesium and iron, seems to be playing some role in the preservation process. PMID:28603667
Albuquerque, M G E; Concas, S; Bengtsson, S; Reis, M A M
2010-09-01
Polyhydroxyalkanoates (PHAs) are promising biodegradable polymers. The use of mixed microbial cultures (MMC) and low cost feedstocks have a positive impact on the cost-effectiveness of the process. It has typically been carried out in Sequencing Batch Reactors (SBR). In this study, a 2-stage CSTR system (under Feast and Famine conditions) was used to effectively select for PHA-storing organisms using fermented molasses as feedstock. The effect of influent substrate concentration (60-120 Cmmol VFA/L) and HRT ratio between the reactors (0.2-0.5h/h) on the system's selection efficiency was assessed. It was shown that Feast reactor residual substrate concentration impacted on the selective pressure for PHA storage (due to substrate-dependent kinetic limitation). Moreover, a residual substrate concentration coming from the Feast to the Famine reactor did not jeopardize the physiological adaptation required for enhanced PHA storage. The culture reached a maximum PHA content of 61%. This success opens new perspectives to the use of wastewater treatment infrastructure for PHA production, thus valorizing either excess sludge or wastewaters.
Wagstaff, Marcus James Dermot; Rooke, Michael; Caplash, Yugesh
2016-01-01
Objectives: To share our experience of an extensive calvarial reconstruction in a severely burn-injured, elderly patient in a 2-stage procedure utilizing a novel biodegradable temporizing matrix (NovoSorb BTM), followed by autograft. Materials and Methods: A 66-year-old patient with 75% full-thickness burns, including 7% total body surface area head and neck, with calvarial exposure of approximately 350 cm2, complicated by acute renal failure and smoke inhalation injury. Exposed calvarium was burred down to diploe and biodegradable temporizing matrix was applied. Over the next 29 days, the biodegradable temporizing matrix integrated by vascular and tissue ingrowth from the diploe. Delamination and grafting occurred, however, at 43 days postimplantation of biodegradable temporizing matrix due to skin graft donor-site constraints. Results: Graft take was complete, yielding a robust and aesthetically pleasing early result (26 days post–graft application). Conclusions: Biodegradable temporizing matrix offers an additional resource for reconstructive surgeons faced with fragile patients and complex wounds. PMID:27222681
Kahnberg, Karl-Erik; Vannas-Löfqvist, Lena
2008-01-01
The aim of this study was to report the long-term results of a 2-stage sinus lift procedure with autologous bone graft and Astra Tech Tioblast ST implants (Astra Tech, Mölndal, Sweden). Sinus lift procedures were carried out in 36 patients, 25 unilateral and 11 bilateral. Bone grafts were obtained from the iliac crest, mandibular angle, or chin region. Healing time for bone grafts varied between 4 and 5 months. Implants were allowed to heal for 6 months. The patients were followed in a standardized clinical and radiographic method for up to 5 years. Patients with partial dentition in the maxilla and limited bone volume below the sinus cavity (6 to 7 mm) were consecutively included in the study. Smoking was a contraindication to inclusion in the study unless patients who smoked quit smoking for at least 6 months prior to surgery. All patients have been successfully restored with fixed complete dentures. There was no implant loss. Radiographic examination showed minor changes in bone graft height (1 to 1.5 mm) over 5 years and moderate bone remodeling (1 to 2 mm over 5 years). Signs of sinus infection appeared in 8 patients. In 4 patients, partial loss of bone graft material occurred. Two-stage sinus lift procedure with autologous bone graft material in combination with Astra Tech Tioblast ST implants has a predictable outcome. The method is reliable and useful for patients with severe resorption of the posterior maxilla.
Time series modeling with pruned multi-layer perceptron and 2-stage damped least-squares method
NASA Astrophysics Data System (ADS)
Voyant, Cyril; Tamas, Wani; Paoli, Christophe; Balu, Aurélia; Muselli, Marc; Nivet, Marie-Laure; Notton, Gilles
2014-03-01
A Multi-Layer Perceptron (MLP) defines a family of artificial neural networks often used in TS modeling and forecasting. Because of its "black box" aspect, many researchers refuse to use it. Moreover, the optimization (often based on the exhaustive approach where "all" configurations are tested) and learning phases of this artificial intelligence tool (often based on the Levenberg-Marquardt algorithm; LMA) are weaknesses of this approach (exhaustively and local minima). These two tasks must be repeated depending on the knowledge of each new problem studied, making the process, long, laborious and not systematically robust. In this paper a pruning process is proposed. This method allows, during the training phase, to carry out an inputs selecting method activating (or not) inter-nodes connections in order to verify if forecasting is improved. We propose to use iteratively the popular damped least-squares method to activate inputs and neurons. A first pass is applied to 10% of the learning sample to determine weights significantly different from 0 and delete other. Then a classical batch process based on LMA is used with the new MLP. The validation is done using 25 measured meteorological TS and cross-comparing the prediction results of the classical LMA and the 2-stage LMA.
Lieberman, Bruce S; Kurkewicz, Richard; Shinogle, Heather; Kimmig, Julien; MacGabhann, Breandán Anraoi
2017-01-01
The morphology and affinities of newly discovered disc-shaped, soft-bodied fossils from the early Cambrian (Series 2: Stage 4, Dyeran) Carrara Formation are discussed. These specimens show some similarity to the Ordovician Discophyllum Hall, 1847; traditionally this taxon had been treated as a fossil porpitid. However, recently it has instead been referred to as another clade, the eldonids, which includes the enigmatic Eldonia Walcott, 1911 that was originally described from the Cambrian Burgess Shale. The status of various Proterozoic and Phanerozoic taxa previously referred to porpitids and eldonids is also briefly considered. To help ascertain that the specimens were not dubio- or pseudofossils, elemental mapping using energy dispersive X-ray spectroscopy (EDS) was conducted. This, in conjunction with the morphology of the specimens, indicated that the fossils were not hematite, iron sulfide, pyrolusite, or other abiologic mineral precipitates. Instead, their status as biologic structures and thus actual fossils is supported. Enrichment in the element carbon, and also possibly to some extent the elements magnesium and iron, seems to be playing some role in the preservation process.
Felice, Pietro; Pistilli, Roberto; Piattelli, Maurizio; Soardi, Elisa; Pellegrino, Gerardo; Corvino, Valeria; Esposito, Marco
2013-01-01
To compare the efficacy of 1-stage versus 2-stage lateral maxillary sinus lift procedures. Sixty partially edentulous patients requiring 1 to 3 implants and having 1 to 3 mm of residual bone height and at least 5 mm of bone width below the maxillary sinus, as measured on CT scans, were randomised into two equal groups to receive either a 1-stage lateral window sinus lift with simultaneous implant placement or a 2-stage procedure with implant placement delayed by 4 months using a bone substitute in 3 different centres. Implants were submerged for 4 months and loaded with reinforced provisional prostheses, which were replaced, after 4 months, by definitive prostheses. Outcome measures were augmentation procedure failures, prosthesis failures, implant failures, complications and marginal peri-implant bone loss assessed by a blinded outcome assessor. Patients were followed up to 4 months after loading. Only data of implants placed in 1 to 3 mm of bone height were reported. Two patients dropped out from the 1-stage group and none from the 2-stage group. No sinus lift procedure failed in the 1-stage group but 1 failed in the 2-stage group, the difference was not statistically significant (P = 1.00). Two prostheses failed or could not be placed in the planned time in the 1-stage group and 1 in the 2-stage group, the difference was not statistically significant (P = 0.51). Three implants failed in 3 patients of the 1-stage group versus 1 implant in the 2-stage group, the difference was not statistically significant (P = 0.28). Two complications occurred in the 1-stage group and 1 in the 2-stage group, the difference was not statistically significant (P = 0.61). There were no statistically significant differences in bone loss between groups at loading (0.05 mm). Sites treated in 1 stage lost an average of 0.56 mm (SD: 0.36; 95% CI: -0.70 to -0.42; P < 0.001) of peri-implant bone and 2-stage sites approximately 0.61 mm (SD: 0.34; 95% CI: -0.74 to -0.48; P < 0.001). No
Felice, Pietro; Pistilli, Roberto; Piattelli, Maurizio; Soardi, Elisa; Barausse, Carlo; Esposito, Marco
2014-01-01
To compare the efficacy of 1-stage versus 2-stage lateral maxillary sinus lift procedures. Sixty partially edentulous patients requiring 1 to 3 implants and having 1 to 3 mm of residual bone height and at least 5 mm bone width below the maxillary sinus, as measured on CT scans were selected. They were randomised according to a parallel group study design into two equal arms to receive either a 1-stage lateral window sinus lift with simultaneous implant placement or a 2-stage procedure with implant placement delayed by 4 months, using a bone substitute in three different centres. Implants were submerged for 4 months, loaded with reinforced provisional prostheses, which were replaced, after 4 months, by definitive prostheses. Outcome measures, assessed by masked assessors, were: augmentation procedure failures; prosthesis failures and implant failures; complications; and marginal peri-implant bone level changes. Patients were followed up to 1 year after loading. Only data of implants placed in 1 to 3 mm of bone height were reported. Two patients dropped out from the 1-stage group and none from the 2-stage group. No sinus lift procedure failed in the 1-stage group but one failed in the 2-stage group, the difference being not statistically significant (P = 1.00). Two prostheses failed or could not be placed in the planned time in the 1-stage group and one in the 2-stage group, the difference being not statistically significant (P = 0.51). Three implants failed in three patients of the 1-stage group, versus one implant in the 2-stage group, the difference being not statistically significant (P = 0.28). Two complications occurred in the 1-stage group and one in the 2-stage group, the difference being not statistically significant (P = 0.61). One year after loading, 1-stage treated patients lost an average of -1.01 mm (SD: 0.56) of peri-implant bone and 2-stage sites about -0.93 mm (SD: 0.40). There were no statistically significant differences in bone level change
Pointwise nonparametric maximum likelihood estimator of stochastically ordered survivor functions.
Park, Yongseok; Taylor, Jeremy M G; Kalbfleisch, John D
2012-06-01
In this paper, we consider estimation of survivor functions from groups of observations with right-censored data when the groups are subject to a stochastic ordering constraint. Many methods and algorithms have been proposed to estimate distribution functions under such restrictions, but none have completely satisfactory properties when the observations are censored. We propose a pointwise constrained nonparametric maximum likelihood estimator, which is defined at each time t by the estimates of the survivor functions subject to constraints applied at time t only. We also propose an efficient method to obtain the estimator. The estimator of each constrained survivor function is shown to be nonincreasing in t, and its consistency and asymptotic distribution are established. A simulation study suggests better small and large sample properties than for alternative estimators. An example using prostate cancer data illustrates the method.
Pointwise nonparametric maximum likelihood estimator of stochastically ordered survivor functions
Park, Yongseok; Taylor, Jeremy M. G.; Kalbfleisch, John D.
2012-01-01
In this paper, we consider estimation of survivor functions from groups of observations with right-censored data when the groups are subject to a stochastic ordering constraint. Many methods and algorithms have been proposed to estimate distribution functions under such restrictions, but none have completely satisfactory properties when the observations are censored. We propose a pointwise constrained nonparametric maximum likelihood estimator, which is defined at each time t by the estimates of the survivor functions subject to constraints applied at time t only. We also propose an efficient method to obtain the estimator. The estimator of each constrained survivor function is shown to be nonincreasing in t, and its consistency and asymptotic distribution are established. A simulation study suggests better small and large sample properties than for alternative estimators. An example using prostate cancer data illustrates the method. PMID:23843661
Trace distance in stochastic dephasing with initial correlation
Ban, Masashi; Kitajima, Sachiko; Shibata, Fumiaki
2011-10-15
The time evolution of the trace distance between quantum states of a qubit which is placed under the influence of stochastic dephasing is investigated within the framework of the stochastic Liouville equation. When stochastic dephasing is subject to the homogeneous Gauss-Markov process, the trace distance is exactly calculated in the presence of the initial correlation between the qubit and the stochastic process, where the stochastic process is inevitably a nonstationary process. It is found that even the initial correlation with the classical environment can make the trace distance greater than the initial value if stochastic dephasing causes the slow modulation of the qubit.
Stochastic Microlensing: Mathematical Theory and Applications
NASA Astrophysics Data System (ADS)
Teguia, Alberto Mokak
Stochastic microlensing is a central tool in probing dark matter on galactic scales. From first principles, we initiate the development of a mathematical theory of stochastic microlensing. We first construct a natural probability space for stochastic microlensing and characterize the general behaviour of the random time delay functions' random critical sets. Next we study stochastic microlensing in two distinct random microlensing scenarios: The uniform stars' distribution with constant mass spectrum and the spatial stars' distribution with general mass spectrum. For each scenario, we determine exact and asymptotic (in the large number of point masses limit) stochastic properties of the random time delay functions and associated random lensing maps and random shear tensors, including their moments and asymptotic density functions. We use these results to study certain random observables, such as random fixed lensed images, random bending angles, and random magnifications. These results are relevant to the theory of random fields and provide a platform for further generalizations as well as analytical limits for checking astrophysical studies of stochastic microlensing. Continuing our development of a mathematical theory of stochastic microlensing, we study the stochastic version of the Image Counting Problem, first considered in the non-random setting by Einstein and generalized by Petters. In particular, we employ the Kac-Rice formula and Morse theory to deduce general formulas for the expected total number of images and the expected number of saddle images for a general random lensing scenario. We further generalize these results by considering random sources defined on a countable compact covering of the light source plane. This is done to introduce the notion of global expected number of positive parity images due to a general lensing map. Applying the result to the uniform stars' distribution random microlensing scenario, we calculate the asymptotic global
A 2-stage phase II design with direct assignment option in stage II for initial marker validation.
An, Ming-Wen; Mandrekar, Sumithra J; Sargent, Daniel J
2012-08-15
Biomarkers are critical to targeted therapies, as they may identify patients more likely to benefit from a treatment. Several prospective designs for biomarker-directed therapy have been previously proposed, differing primarily in the study population, randomization scheme, or both. Recognizing the need for randomization, yet acknowledging the possibility of promising but inconclusive results after a stage I cohort of randomized patients, we propose a 2-stage phase II design on marker-positive patients that allows for direct assignment in a stage II cohort. In stage I, marker-positive patients are equally randomized to receive experimental treatment or control. Stage II has the option to adopt "direct assignment" whereby all patients receive experimental treatment. Through simulation, we studied the power and type I error rate of our design compared with a balanced randomized two-stage design, and conducted sensitivity analyses to study the effect of timing of stage I analysis, population shift effects, and unbalanced randomization. Our proposed design has minimal loss in power (<1.8%) and increased type I error rate (<2.1%) compared with a balanced randomized design. The maximum increase in type I error rate in the presence of a population shift was between 3.1% and 5%, and the loss in power across possible timings of stage I analysis was less than 1.2%. Our proposed design has desirable statistical properties with potential appeal in practice. The direct assignment option, if adopted, provides for an "extended confirmation phase" as an alternative to stopping the trial early for evidence of efficacy in stage I.
NASA Astrophysics Data System (ADS)
Jia, Wei; Liu, Huoxing
2014-06-01
The pressing demand for future advanced gas turbine requires to identify the losses in a turbine and to understand the physical mechanisms producing them. In low pressure turbines with shrouded blades, a large portion of these losses is generated by tip shroud leakage flow and associated interaction. For this reason, shroud leakage losses are generally grouped into the losses of leakage flow itself and the losses caused by the interaction between leakage flow and mainstream. In order to evaluate the influence of shroud leakage flow and related losses on turbine performance, computational investigations for a 2-stage low pressure turbine is presented and discussed in this paper. Three dimensional steady multistage calculations using mixing plane approach were performed including detailed tip shroud geometry. Results showed that turbines with shrouded blades have an obvious advantage over unshrouded ones in terms of aerodynamic performance. A loss mechanism breakdown analysis demonstrated that the leakage loss is the main contributor in the first stage while mixing loss dominates in the second stage. Due to the blade-to-blade pressure gradient, both inlet and exit cavity present non-uniform leakage injection and extraction. The flow in the exit cavity is filled with cavity vortex, leakage jet attached to the cavity wall and recirculation zone induced by main flow ingestion. Furthermore, radial gap and exit cavity size of tip shroud have a major effect on the yaw angle near the tip region in the main flow. Therefore, a full calculation of shroud leakage flow is necessary in turbine performance analysis and the shroud geometric features need to be considered during turbine design process.
Stochastic Indicators for Waste Site Characterization
NASA Astrophysics Data System (ADS)
Christakos, George; Hristopulos, Dionissios T.
1996-08-01
Site characterization is an important prerequisite of risk assessment and remediation strategies. Evaluation of the health effects of groundwater and soil contamination depends on the adequate analysis of spatial heterogeneity, exceedance levels, and uncertainties. In this work we formulate and calculate stochastic indicators that provide a rigorous characterization of exposure levels in sites with heterogeneous contaminant distributions and offer valuable information for a cost-effective cleanup analysis. These site indicators are general and can be used for different types and distributions of groundwater and soil contaminants. Important properties of the stochastic indicators are examined which can evaluate the potential for contamination at large scales, and improve understanding of threatened and damaged ecosystems. Analytically tractable formulas are derived that allow the practical estimation of site indicators on the basis of experimental data. Scale and modeling effects on contaminant level analysis are examined in terms of the stochastic indicators. Site cleanup costs depend directly on inferred characteristics of the stochastic indicators, which thus can play an important role in waste site management. Applications are discussed that offer insight regarding certain aspects of stochastic site characterization. Analytical methods of site characterization are compared to numerical simulations. It is shown that the latter can provide a practical alternative to the former, but they could lead to inaccurate results if they are not interpreted carefully.
On methods for studying stochastic disease dynamics
Keeling, M.J; Ross, J.V
2007-01-01
Models that deal with the individual level of populations have shown the importance of stochasticity in ecology, epidemiology and evolution. An increasingly common approach to studying these models is through stochastic (event-driven) simulation. One striking disadvantage of this approach is the need for a large number of replicates to determine the range of expected behaviour. Here, for a class of stochastic models called Markov processes, we present results that overcome this difficulty and provide valuable insights, but which have been largely ignored by applied researchers. For these models, the so-called Kolmogorov forward equation (also called the ensemble or master equation) allows one to simultaneously consider the probability of each possible state occurring. Irrespective of the complexities and nonlinearities of population dynamics, this equation is linear and has a natural matrix formulation that provides many analytical insights into the behaviour of stochastic populations and allows rapid evaluation of process dynamics. Here, using epidemiological models as a template, these ensemble equations are explored and results are compared with traditional stochastic simulations. In addition, we describe further advantages of the matrix formulation of dynamics, providing simple exact methods for evaluating expected eradication (extinction) times of diseases, for comparing expected total costs of possible control programmes and for estimation of disease parameters. PMID:17638650
On methods for studying stochastic disease dynamics.
Keeling, M J; Ross, J V
2008-02-06
Models that deal with the individual level of populations have shown the importance of stochasticity in ecology, epidemiology and evolution. An increasingly common approach to studying these models is through stochastic (event-driven) simulation. One striking disadvantage of this approach is the need for a large number of replicates to determine the range of expected behaviour. Here, for a class of stochastic models called Markov processes, we present results that overcome this difficulty and provide valuable insights, but which have been largely ignored by applied researchers. For these models, the so-called Kolmogorov forward equation (also called the ensemble or master equation) allows one to simultaneously consider the probability of each possible state occurring. Irrespective of the complexities and nonlinearities of population dynamics, this equation is linear and has a natural matrix formulation that provides many analytical insights into the behaviour of stochastic populations and allows rapid evaluation of process dynamics. Here, using epidemiological models as a template, these ensemble equations are explored and results are compared with traditional stochastic simulations. In addition, we describe further advantages of the matrix formulation of dynamics, providing simple exact methods for evaluating expected eradication (extinction) times of diseases, for comparing expected total costs of possible control programmes and for estimation of disease parameters.
Robustness analysis of stochastic biochemical systems.
Ceska, Milan; Safránek, David; Dražan, Sven; Brim, Luboš
2014-01-01
We propose a new framework for rigorous robustness analysis of stochastic biochemical systems that is based on probabilistic model checking techniques. We adapt the general definition of robustness introduced by Kitano to the class of stochastic systems modelled as continuous time Markov Chains in order to extensively analyse and compare robustness of biological models with uncertain parameters. The framework utilises novel computational methods that enable to effectively evaluate the robustness of models with respect to quantitative temporal properties and parameters such as reaction rate constants and initial conditions. We have applied the framework to gene regulation as an example of a central biological mechanism where intrinsic and extrinsic stochasticity plays crucial role due to low numbers of DNA and RNA molecules. Using our methods we have obtained a comprehensive and precise analysis of stochastic dynamics under parameter uncertainty. Furthermore, we apply our framework to compare several variants of two-component signalling networks from the perspective of robustness with respect to intrinsic noise caused by low populations of signalling components. We have successfully extended previous studies performed on deterministic models (ODE) and showed that stochasticity may significantly affect obtained predictions. Our case studies demonstrate that the framework can provide deeper insight into the role of key parameters in maintaining the system functionality and thus it significantly contributes to formal methods in computational systems biology.
Plasma Equilibria With Stochastic Magnetic Fields
NASA Astrophysics Data System (ADS)
Krommes, J. A.; Reiman, A. H.
2009-05-01
Plasma equilibria that include regions of stochastic magnetic fields are of interest in a variety of applications, including tokamaks with ergodic limiters and high-pressure stellarators. Such equilibria are examined theoretically, and a numerical algorithm for their construction is described.^2,3 % The balance between stochastic diffusion of magnetic lines and small effects^2 omitted from the simplest MHD description can support pressure and current profiles that need not be flattened in stochastic regions. The diffusion can be described analytically by renormalizing stochastic Langevin equations for pressure and parallel current j, with particular attention being paid to the satisfaction of the periodicity constraints in toroidal configurations with sheared magnetic fields. The equilibrium field configuration can then be constructed by coupling the prediction for j to Amp'ere's law, which is solved numerically. A. Reiman et al., Pressure-induced breaking of equilibrium flux surfaces in the W7AS stellarator, Nucl. Fusion 47, 572--8 (2007). J. A. Krommes and A. H. Reiman, Plasma equilibrium in a magnetic field with stochastic regions, submitted to Phys. Plasmas. J. A. Krommes, Fundamental statistical theories of plasma turbulence in magnetic fields, Phys. Reports 360, 1--351.
Robustness Analysis of Stochastic Biochemical Systems
Česka, Milan; Šafránek, David; Dražan, Sven; Brim, Luboš
2014-01-01
We propose a new framework for rigorous robustness analysis of stochastic biochemical systems that is based on probabilistic model checking techniques. We adapt the general definition of robustness introduced by Kitano to the class of stochastic systems modelled as continuous time Markov Chains in order to extensively analyse and compare robustness of biological models with uncertain parameters. The framework utilises novel computational methods that enable to effectively evaluate the robustness of models with respect to quantitative temporal properties and parameters such as reaction rate constants and initial conditions. We have applied the framework to gene regulation as an example of a central biological mechanism where intrinsic and extrinsic stochasticity plays crucial role due to low numbers of DNA and RNA molecules. Using our methods we have obtained a comprehensive and precise analysis of stochastic dynamics under parameter uncertainty. Furthermore, we apply our framework to compare several variants of two-component signalling networks from the perspective of robustness with respect to intrinsic noise caused by low populations of signalling components. We have successfully extended previous studies performed on deterministic models (ODE) and showed that stochasticity may significantly affect obtained predictions. Our case studies demonstrate that the framework can provide deeper insight into the role of key parameters in maintaining the system functionality and thus it significantly contributes to formal methods in computational systems biology. PMID:24751941
Stochastic approach to equilibrium and nonequilibrium thermodynamics.
Tomé, Tânia; de Oliveira, Mário J
2015-04-01
We develop the stochastic approach to thermodynamics based on stochastic dynamics, which can be discrete (master equation) and continuous (Fokker-Planck equation), and on two assumptions concerning entropy. The first is the definition of entropy itself and the second the definition of entropy production rate, which is non-negative and vanishes in thermodynamic equilibrium. Based on these assumptions, we study interacting systems with many degrees of freedom in equilibrium or out of thermodynamic equilibrium and how the macroscopic laws are derived from the stochastic dynamics. These studies include the quasiequilibrium processes; the convexity of the equilibrium surface; the monotonic time behavior of thermodynamic potentials, including entropy; the bilinear form of the entropy production rate; the Onsager coefficients and reciprocal relations; and the nonequilibrium steady states of chemical reactions.
Stochastic resonance in geomagnetic polarity reversals.
Consolini, Giuseppe; De Michelis, Paola
2003-02-07
Among noise-induced cooperative phenomena a peculiar relevance is played by stochastic resonance. In this paper we offer evidence that geomagnetic polarity reversals may be due to a stochastic resonance process. In detail, analyzing the distribution function P(tau) of polarity residence times (chrons), we found the evidence of a stochastic synchronization process, i.e., a series of peaks in the P(tau) at T(n) approximately (2n+1)T(Omega)/2 with n=0,1,...,j and T(omega) approximately 0.1 Myr. This result is discussed in connection with both the typical time scale of Earth's orbit eccentricity variation and the recent results on the typical time scale of climatic long-term variation.
Structural factoring approach for analyzing stochastic networks
NASA Technical Reports Server (NTRS)
Hayhurst, Kelly J.; Shier, Douglas R.
1991-01-01
The problem of finding the distribution of the shortest path length through a stochastic network is investigated. A general algorithm for determining the exact distribution of the shortest path length is developed based on the concept of conditional factoring, in which a directed, stochastic network is decomposed into an equivalent set of smaller, generally less complex subnetworks. Several network constructs are identified and exploited to reduce significantly the computational effort required to solve a network problem relative to complete enumeration. This algorithm can be applied to two important classes of stochastic path problems: determining the critical path distribution for acyclic networks and the exact two-terminal reliability for probabilistic networks. Computational experience with the algorithm was encouraging and allowed the exact solution of networks that have been previously analyzed only by approximation techniques.
Computational stochastic model of ions implantation
Zmievskaya, Galina I. Bondareva, Anna L.; Levchenko, Tatiana V.; Maino, Giuseppe
2015-03-10
Implantation flux ions into crystal leads to phase transition /PT/ 1-st kind. Damaging lattice is associated with processes clustering vacancies and gaseous bubbles as well their brownian motion. System of stochastic differential equations /SDEs/ Ito for evolution stochastic dynamical variables corresponds to the superposition Wiener processes. The kinetic equations in partial derivatives /KE/, Kolmogorov-Feller and Einstein-Smolukhovskii, were formulated for nucleation into lattice of weakly soluble gases. According theory, coefficients of stochastic and kinetic equations uniquely related. Radiation stimulated phase transition are characterized by kinetic distribution functions /DFs/ of implanted clusters versus their sizes and depth of gas penetration into lattice. Macroscopic parameters of kinetics such as the porosity and stress calculated in thin layers metal/dielectric due to Xe{sup ++} irradiation are attracted as example. Predictions of porosity, important for validation accumulation stresses in surfaces, can be applied at restoring of objects the cultural heritage.
The effective stochastization time in stellar systems
NASA Astrophysics Data System (ADS)
Ovod, D. V.; Ossipkov, L. P.
2014-10-01
Stochastization in stellar systems is analyzed in the framework of the paradigm of Krylov and Gurzadyan-Savvidi. The use of a Holtsmark distribution for the random forces with a Rastorguev-Sementsov cutoff confirms that τ e / τ c ∝ N 1/5, where τ c is the crossing time, τ e is the effective stochastization time, and N is the number of stars. More oblate systems evolve more rapidly, and rotation slows stochastization. The need for a cutoff does not arise if a Petrovskaya distribution is adopted for the random forces (although applying a cutoff does not change the results). In this case, τ e / τ c varies with N approximately as N 0.3. It is found theoretically that τ e / τ c ∝ N 1/3/(ln N)1/2 for large N. Thus, the evolutionary scale found is close to that proposed earlier by Genkin.
Functional integral approach for multiplicative stochastic processes.
Arenas, Zochil González; Barci, Daniel G
2010-05-01
We present a functional formalism to derive a generating functional for correlation functions of a multiplicative stochastic process represented by a Langevin equation. We deduce a path integral over a set of fermionic and bosonic variables without performing any time discretization. The usual prescriptions to define the Wiener integral appear in our formalism in the definition of Green's functions in the Grassman sector of the theory. We also study nonperturbative constraints imposed by Becchi, Rouet and Stora symmetry (BRS) and supersymmetry on correlation functions. We show that the specific prescription to define the stochastic process is wholly contained in tadpole diagrams. Therefore, in a supersymmetric theory, the stochastic process is uniquely defined since tadpole contributions cancels at all order of perturbation theory.
Maximal stochastic transport in the Lorenz equations
NASA Astrophysics Data System (ADS)
Agarwal, Sahil; Wettlaufer, John
2015-11-01
We calculate the stochastic upper bounds for the Lorenz equations using an extension of the background method. In analogy with Rayleigh-Benard convection the upper bounds are for heat transport versus Rayleigh number. As might be expected the stochastic upper bounds are larger than the deterministic counterpart of Souza and Doering (2015), but their variation with noise amplitude exhibits surprising behavior. Below the transition to chaotic dynamics the upper bounds increase monotonically with noise amplitude. However, in the chaotic regime this monotonicity is lost; at a particular Rayleigh number the bound may increase or decrease with noise amplitude. The origin of this behavior is the coupling between the noise and unstable periodic orbits. This is confirmed by examining the close returns plots of the full solutions to the stochastic equations. Finally, we note that these solutions demonstrate that the effect of noise is equivalent to the effect of chaos.
Solving stochastic inflation for arbitrary potentials
Martin, Jerome; Musso, Marcello
2006-02-15
A perturbative method for solving the Langevin equation of inflationary cosmology in the presence of backreaction is presented. In the Gaussian approximation, the method permits an explicit calculation of the probability distribution of the inflaton field for an arbitrary potential, with or without the volume effects taken into account. The perturbative method is then applied to various concrete models, namely, large field, small field, hybrid, and running mass inflation. New results on the stochastic behavior of the inflaton field in those models are obtained. In particular, it is confirmed that the stochastic effects can be important in new inflation while it is demonstrated they are negligible in (vacuum dominated) hybrid inflation. The case of stochastic running mass inflation is discussed in some details and it is argued that quantum effects blur the distinction between the four classical versions of this model. It is also shown that the self-reproducing regime is likely to be important in this case.
Stochastic Differential Equation of Earthquakes Series
NASA Astrophysics Data System (ADS)
Mariani, Maria C.; Tweneboah, Osei K.; Gonzalez-Huizar, Hector; Serpa, Laura
2016-07-01
This work is devoted to modeling earthquake time series. We propose a stochastic differential equation based on the superposition of independent Ornstein-Uhlenbeck processes driven by a Γ (α, β ) process. Superposition of independent Γ (α, β ) Ornstein-Uhlenbeck processes offer analytic flexibility and provides a class of continuous time processes capable of exhibiting long memory behavior. The stochastic differential equation is applied to the study of earthquakes by fitting the superposed Γ (α, β ) Ornstein-Uhlenbeck model to earthquake sequences in South America containing very large events (Mw ≥ 8). We obtained very good fit of the observed magnitudes of the earthquakes with the stochastic differential equations, which supports the use of this methodology for the study of earthquakes sequence.
Control of stochastic multistable systems: Experimental demonstration
NASA Astrophysics Data System (ADS)
Goswami, B. K.; Euzzor, S.; Al Naimee, K.; Geltrude, A.; Meucci, R.; Arecchi, F. T.
2009-07-01
Stochastic disturbances and spikes (sudden sharp fluctuations of any system parameter), commonly observed among natural and laboratory-scale systems, can perturb the multistable dynamics significantly and become a serious impediment when the device is designed for a certain dynamical behavior. We experimentally demonstrate that suitable periodic modulation of any system parameter may efficiently control such stochastic multistability related problems. The control mechanism is verified individually with two standard models (namely, an analog circuit of Lorenz equations and a cavity-loss modulated CO2 laser), against three externally introduced disturbing signals, (namely, white Gaussian noise, pink noise, and train of spikes). Indeed, with both the systems, it has been observed that the modulation is capable to significantly control untoward jumps to coexisting attractors that otherwise would have occurred due to either of the disturbances. These results establish the robustness and wide applicability of this control mechanism in resolving stochastic multistability related problems.
Fokker-Planck response of stochastic satellites
NASA Technical Reports Server (NTRS)
Huang, T. C.; Das, A.
1982-01-01
The present investigation is concerned with the effects of stochastic geometry and random environmental torques on the pointing accuracy of spinning and three-axis stabilized satellites. The study of pointing accuracies requires a knowledge of the rates of error growth over and above any criteria for the asymptotic stability of the satellites. For this reason the investigation is oriented toward the determination of the statistical properties of the responses of the satellites. The geometries of the satellites are considered stochastic so as to have a phenomenological model of the motions of the flexible structural elements of the satellites. A widely used method of solving stochastic equations is the Fokker-Planck approach where the equations are assumed to define a Markoff process and the transition probability densities of the responses are computed directly as a function of time. The Fokker-Planck formulation is used to analyze the response vector of a rigid satellite.
Modelling metapopulations with stochastic membrane systems.
Besozzi, Daniela; Cazzaniga, Paolo; Pescini, Dario; Mauri, Giancarlo
2008-03-01
Metapopulations, or multi-patch systems, are models describing the interactions and the behavior of populations living in fragmented habitats. Dispersal, persistence and extinction are some of the characteristics of interest in ecological studies of metapopulations. In this paper, we propose a novel method to analyze metapopulations, which is based on a discrete and stochastic modelling framework in the area of Membrane Computing. New structural features of membrane systems, necessary to appropriately describe a multi-patch system, are introduced, such as the reduction of the maximal parallel consumption of objects, the spatial arrangement of membranes and the stochastic creation of objects. The role of the additional features, their meaning for a metapopulation model and the emergence of relevant behaviors are then investigated by means of stochastic simulations. Conclusive remarks and ideas for future research are finally presented.
Vaccine enhanced extinction in stochastic epidemic models
NASA Astrophysics Data System (ADS)
Billings, Lora; Mier-Y-Teran, Luis; Schwartz, Ira
2012-02-01
We address the problem of developing new and improved stochastic control methods that enhance extinction in disease models. In finite populations, extinction occurs when fluctuations owing to random transitions act as an effective force that drives one or more components or species to vanish. Using large deviation theory, we identify the location of the optimal path to extinction in epidemic models with stochastic vaccine controls. These models not only capture internal noise from random transitions, but also external fluctuations, such as stochastic vaccination scheduling. We quantify the effectiveness of the randomly applied vaccine over all possible distributions by using the location of the optimal path, and we identify the most efficient control algorithms. We also discuss how mean extinction times scale with epidemiological and social parameters.
Regeneration of stochastic processes: an inverse method
NASA Astrophysics Data System (ADS)
Ghasemi, F.; Peinke, J.; Sahimi, M.; Rahimi Tabar, M. R.
2005-10-01
We propose a novel inverse method that utilizes a set of data to construct a simple equation that governs the stochastic process for which the data have been measured, hence enabling us to reconstruct the stochastic process. As an example, we analyze the stochasticity in the beat-to-beat fluctuations in the heart rates of healthy subjects as well as those with congestive heart failure. The inverse method provides a novel technique for distinguishing the two classes of subjects in terms of a drift and a diffusion coefficients which behave completely differently for the two classes of subjects, hence potentially providing a novel diagnostic tool for distinguishing healthy subjects from those with congestive heart failure, even at the early stages of the disease development.
Topology optimization under stochastic stiffness
NASA Astrophysics Data System (ADS)
Asadpoure, Alireza
Topology optimization is a systematic computational tool for optimizing the layout of materials within a domain for engineering design problems. It allows variation of structural boundaries and connectivities. This freedom in the design space often enables discovery of new, high performance designs. However, solutions obtained by performing the optimization in a deterministic setting may be impractical or suboptimal when considering real-world engineering conditions with inherent variabilities including (for example) variabilities in fabrication processes and operating conditions. The aim of this work is to provide a computational methodology for topology optimization in the presence of uncertainties associated with structural stiffness, such as uncertain material properties and/or structural geometry. Existing methods for topology optimization under deterministic conditions are first reviewed. Modifications are then proposed to improve the numerical performance of the so-called Heaviside Projection Method (HPM) in continuum domains. Next, two approaches, perturbation and Polynomial Chaos Expansion (PCE), are proposed to account for uncertainties in the optimization procedure. These approaches are intrusive, allowing tight and efficient coupling of the uncertainty quantification with the optimization sensitivity analysis. The work herein develops a robust topology optimization framework aimed at reducing the sensitivity of optimized solutions to uncertainties. The perturbation-based approach combines deterministic topology optimization with a perturbation method for the quantification of uncertainties. The use of perturbation transforms the problem of topology optimization under uncertainty to an augmented deterministic topology optimization problem. The PCE approach combines the spectral stochastic approach for the representation and propagation of uncertainties with an existing deterministic topology optimization technique. The resulting compact representations
EDITORIAL: Stochasticity in fusion plasmas
NASA Astrophysics Data System (ADS)
Finken, K. H.
2006-04-01
In recent years the importance of externally imposed resonant magnetic fields on plasma has become more and more recognized. These fields will cause ergodization at well defined plasma layers and can induce large size islands at rational q-surfaces. A hope for future large scale tokamak devices is the development of a reliable method for mitigating the large ELMs of type 1 ELMy-H-modes by modifying the edge transport. Other topics of interest for fusion reactors are the option of distributing the heat to a large area and optimizing methods for heat and particle exhaust, or the understanding of the transport around tearing mode instabilities. The cluster of papers in this issue of Nuclear Fusion is a successor to the 2004 special issue (Nuclear Fusion 44 S1-122 ) intended to raise interest in the subject. The contents of this present issue are based on presentations at the Second Workshop on Stochasticity in Fusion Plasmas (SFP) held in Juelich, Germany, 15-17 March 2005. The SFP workshops have been stimulated by the installation of the Dynamic Ergodic Divertor (DED) in the TEXTOR tokamak. It has attracted colleagues working on various plasma configurations such as tokamaks, stellarators or reversed field pinches. The workshop was originally devoted to phenomena on the plasma edge but it has been broadened to transport questions over the whole plasma cross-section. It is a meeting place for experimental and theoretical working groups. The next workshop is planned for February/March 2007 in Juelich, Germany. For details see http://www.fz-juelich.de/sfp/. The content of the workshop is summarized in the following conference summary (K.H. Finken 2006 Nuclear Fusion 46 S107-112). At the workshop experimental results on the plasma transport resulting from ergodization in various devices were presented. Highlights were the results from DIII-D on the mitigation of ELMs (see also T.E. Evans et al 2005 Nuclear Fusion 45 595 ). Theoretical work was focused around the topics
Stochastic P-bifurcation and stochastic resonance in a noisy bistable fractional-order system
NASA Astrophysics Data System (ADS)
Yang, J. H.; Sanjuán, Miguel A. F.; Liu, H. G.; Litak, G.; Li, X.
2016-12-01
We investigate the stochastic response of a noisy bistable fractional-order system when the fractional-order lies in the interval (0, 2]. We focus mainly on the stochastic P-bifurcation and the phenomenon of the stochastic resonance. We compare the generalized Euler algorithm and the predictor-corrector approach which are commonly used for numerical calculations of fractional-order nonlinear equations. Based on the predictor-corrector approach, the stochastic P-bifurcation and the stochastic resonance are investigated. Both the fractional-order value and the noise intensity can induce an stochastic P-bifurcation. The fractional-order may lead the stationary probability density function to turn from a single-peak mode to a double-peak mode. However, the noise intensity may transform the stationary probability density function from a double-peak mode to a single-peak mode. The stochastic resonance is investigated thoroughly, according to the linear and the nonlinear response theory. In the linear response theory, the optimal stochastic resonance may occur when the value of the fractional-order is larger than one. In previous works, the fractional-order is usually limited to the interval (0, 1]. Moreover, the stochastic resonance at the subharmonic frequency and the superharmonic frequency are investigated respectively, by using the nonlinear response theory. When it occurs at the subharmonic frequency, the resonance may be strong and cannot be ignored. When it occurs at the superharmonic frequency, the resonance is weak. We believe that the results in this paper might be useful for the signal processing of nonlinear systems.
Minimum uncertainty and squeezing in diffusion processes and stochastic quantization
NASA Technical Reports Server (NTRS)
Demartino, S.; Desiena, S.; Illuminati, Fabrizo; Vitiello, Giuseppe
1994-01-01
We show that uncertainty relations, as well as minimum uncertainty coherent and squeezed states, are structural properties for diffusion processes. Through Nelson stochastic quantization we derive the stochastic image of the quantum mechanical coherent and squeezed states.
Use it or average it: stochasticity in plant development.
Roeder, Adrienne Hk
2017-08-21
A process that is stochastic has a probabilistic or randomly determined outcome. At the molecular level, all processes are stochastic; but development is highly reproducible, suggesting that plants and other multicellular organisms have evolved mechanisms to ensure robustness (achieving correct development despite stochastic and environmental perturbations). Mechanisms of robustness can be discovered through isolating mutants with increased variability in phenotype; such mutations do not necessarily change the average phenotype. Surprisingly, some developmental robustness mechanisms actually exploit stochasticity as a useful source of variation. For example, gene expression is stochastic and can be utilized to create subtle differences between identical cells that can initiate the patterning of specialized cell types. Stochasticity can also be used to promote robustness through spatiotemporal averaging-stochasticity can be averaged out across space and over time. Thus, organisms often harness stochasticity to ensure robust development. Copyright © 2017 Elsevier Ltd. All rights reserved.
On strongly GA-convex functions and stochastic processes
NASA Astrophysics Data System (ADS)
Bekar, Nurgül Okur; Akdemir, Hande Günay; Işcan, Imdat
2014-08-01
In this study, we introduce strongly GA-convex functions and stochastic processes. We provide related well-known Kuhn type results and Hermite-Hadamard type inequality for strongly GA-convex functions and stochastic processes.
Propagation of ultra-short solitons in stochastic Maxwell's equations
Kurt, Levent; Schäfer, Tobias
2014-01-15
We study the propagation of ultra-short short solitons in a cubic nonlinear medium modeled by nonlinear Maxwell's equations with stochastic variations of media. We consider three cases: variations of (a) the dispersion, (b) the phase velocity, (c) the nonlinear coefficient. Using a modified multi-scale expansion for stochastic systems, we derive new stochastic generalizations of the short pulse equation that approximate the solutions of stochastic nonlinear Maxwell's equations. Numerical simulations show that soliton solutions of the short pulse equation propagate stably in stochastic nonlinear Maxwell's equations and that the generalized stochastic short pulse equations approximate the solutions to the stochastic Maxwell's equations over the distances under consideration. This holds for both a pathwise comparison of the stochastic equations as well as for a comparison of the resulting probability densities.
On strongly GA-convex functions and stochastic processes
Bekar, Nurgül Okur; Akdemir, Hande Günay; İşcan, İmdat
2014-08-20
In this study, we introduce strongly GA-convex functions and stochastic processes. We provide related well-known Kuhn type results and Hermite-Hadamard type inequality for strongly GA-convex functions and stochastic processes.
A Note on the Stochastic Nature of Feynman Quantum Paths
NASA Astrophysics Data System (ADS)
Botelho, Luiz C. L.
2016-11-01
We propose a Fresnel stochastic white noise framework to analyze the stochastic nature of the Feynman paths entering on the Feynman Path Integral expression for the Feynman Propagator of a particle quantum mechanically moving under a time-independent potential.
Absolute Value Boundedness, Operator Decomposition, and Stochastic Media and Equations
NASA Technical Reports Server (NTRS)
Adomian, G.; Miao, C. C.
1973-01-01
The research accomplished during this period is reported. Published abstracts and technical reports are listed. Articles presented include: boundedness of absolute values of generalized Fourier coefficients, propagation in stochastic media, and stationary conditions for stochastic differential equations.
Master-equation approach to stochastic neurodynamics
NASA Astrophysics Data System (ADS)
Ohira, Toru; Cowan, Jack D.
1993-09-01
A master-equation approach to the stochastic neurodynamics proposed by Cowan [in Advances in Neural Information Processing Systems 3, edited by R. P. Lippman, J. E. Moody, and D. S. Touretzky (Morgan Kaufmann, San Mateo, 1991), p. 62] is investigated in this paper. We deal with a model neural network that is composed of two-state neurons obeying elementary stochastic transition rates. We show that such an approach yields concise expressions for multipoint moments and an equation of motion. We apply the formalism to a (1+1)-dimensional system. Exact and approximate expressions for various statistical parameters are obtained and compared with Monte Carlo simulations.
Canonical Bose gas simulations with stochastic gauges.
Drummond, P D; Deuar, P; Kheruntsyan, K V
2004-01-30
A technique to simulate the grand canonical ensembles of interacting Bose gases is presented. Results are generated for many temperatures by averaging over energy-weighted stochastic paths, each corresponding to a solution of coupled Gross-Pitaevskii equations with phase noise. The stochastic gauge method used relies on an off-diagonal coherent-state expansion, thus taking into account all quantum correlations. As an example, the second-order spatial correlation function and momentum distribution for an interacting 1D Bose gas are calculated.
Stochastic stability and instability of model ecosystems
NASA Technical Reports Server (NTRS)
Ladde, G. S.; Siljak, D. D.
1975-01-01
In this work, we initiate a stability study of multispecies communities in stochastic environment by using Ito's differential equations as community models. By applying the direct method of Liapunov, we obtain sufficient conditions for stability and instability in the mean of the equilibrium populations. The conditions are expressed in terms of the dominant diagonal property of community matrices, which is a suitable mechanism for resolving the central problem of 'complexity vs stability' in model ecosystems. As a by-product of this analysis we exhibit important structural properties of the stochastic density-dependent models, and establish tolerance of community stability to a broad class of nonlinear time-varying perturbations.
Stochastic mirage phenomenon in a random medium.
McDaniel, Austin; Mahalov, Alex
2017-05-15
In the framework of geometric optics, we consider the problem of characterizing the ray trajectory in a random medium with a mean refractive index gradient. Such a gradient results in the mirage phenomenon where an object's observed location is displaced from its actual location. We derive formulas for the mean ray path in both the situation of isotropic stochastic fluctuations and an important anisotropic case. For the isotropic model, the mean squared displacement is also given by a simple formula. Our results could be useful for applications involving the propagation of electromagnetic waves through the atmosphere, where larger-scale mean gradients and smaller-scale stochastic fluctuations are both present.
Stochastic 2-D Navier-Stokes Equation
Menaldi, J.L. Sritharan, S.S.
2002-10-01
In this paper we prove the existence and uniqueness of strong solutions for the stochastic Navier-Stokes equation in bounded and unbounded domains. These solutions are stochastic analogs of the classical Lions-Prodi solutions to the deterministic Navier-Stokes equation. Local monotonicity of the nonlinearity is exploited to obtain the solutions in a given probability space and this significantly improves the earlier techniques for obtaining strong solutions, which depended on pathwise solutions to the Navier-Stokes martingale problem where the probability space is also obtained as a part of the solution.
Stochasticity from external magnetic field measurements
Castle, G.G.; Wootton, A.J. . Fusion Research Center)
1994-08-01
To determine whether or not magnetic field lines inside a tokamak plasma are stochastic the authors need the Fourier coefficients of any perturbing radial field inside the plasma. Usually what is measured with magnetic pick-up coils is the root mean square poloidal field outside the plasma. Although no unique transformation is available, they present a model which allows an interpretation of the measured (external) root mean square field in terms of the internal Fourier harmonics. The results are applied to particular TEXT discharges, and suggest a link between magnetic stochasticity and in increasing (more positive) radial electric field, as measured with a heavy ion beam probe.
Scattering theory of stochastic electromagnetic light waves.
Wang, Tao; Zhao, Daomu
2010-07-15
We generalize scattering theory to stochastic electromagnetic light waves. It is shown that when a stochastic electromagnetic light wave is scattered from a medium, the properties of the scattered field can be characterized by a 3 x 3 cross-spectral density matrix. An example of scattering of a spatially coherent electromagnetic light wave from a deterministic medium is discussed. Some interesting phenomena emerge, including the changes of the spectral degree of coherence and of the spectral degree of polarization of the scattered field.
Stochastic optimization algorithms for barrier dividend strategies
NASA Astrophysics Data System (ADS)
Yin, G.; Song, Q. S.; Yang, H.
2009-01-01
This work focuses on finding optimal barrier policy for an insurance risk model when the dividends are paid to the share holders according to a barrier strategy. A new approach based on stochastic optimization methods is developed. Compared with the existing results in the literature, more general surplus processes are considered. Precise models of the surplus need not be known; only noise-corrupted observations of the dividends are used. Using barrier-type strategies, a class of stochastic optimization algorithms are developed. Convergence of the algorithm is analyzed; rate of convergence is also provided. Numerical results are reported to demonstrate the performance of the algorithm.
On orthogonality preserving quadratic stochastic operators
Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd
2015-05-15
A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too.
Existence Theory for Stochastic Power Law Fluids
NASA Astrophysics Data System (ADS)
Breit, Dominic
2015-06-01
We consider the equations of motion for an incompressible non-Newtonian fluid in a bounded Lipschitz domain during the time interval (0, T) together with a stochastic perturbation driven by a Brownian motion W. The balance of momentum reads as where v is the velocity, the pressure and f an external volume force. We assume the common power law model and show the existence of martingale weak solution provided . Our approach is based on the -truncation and a harmonic pressure decomposition which are adapted to the stochastic setting.
Stochastic model for supersymmetric particle branching process
NASA Astrophysics Data System (ADS)
Zhang, Yuanyuan; Chan, Aik Hui; Oh, Choo Hiap
2017-01-01
We develop a stochastic branching model to describe the jet evolution of supersymmetric (SUSY) particles. This model is a modified two-phase branching process, or more precisely, a two-phase simple birth process plus Poisson process. Both pure SUSY partons initiated jets and SUSY plus ordinary partons initiated jets scenarios are considered. The stochastic branching equations are established and the Multiplicity Distributions (MDs) are derived for these two scenarios. We also fit the distribution of the general case (SUSY plus ordinary partons initiated jets) with experimental data. The fitting shows the SUSY particles have not participated in branching at current collision energy yet.
Stochastic Large Eddy Simulation of Geostrophic Turbulence
NASA Astrophysics Data System (ADS)
Nadiga, B.; Livescu, D.; McKay, C. Q.
2005-05-01
Results are presented of (fine-scale) eddy-resolving simulations of different instances of turbulent quasi-geostrophic ocean circulation. A stochastic model for the effects of neglected subgrid degrees-of-freedom in coarse-scale simulations is proposed and the results compared to the fine simulations results as well as with existing models. As a precursor to the introduction of the models, we also study various aspects of the nonlinear rectification of stochastic forcing in quasi-geostrophic models of ocean circulation.
Methods for Scaling to Doubly Stochastic Form,
1981-06-26
BIRKHOFF, G.: Tres observaciones sobre le algebra lineal , Rev. univ. nec. Tucuman, ser A, . 147-151, [1948] BRUALDI, R.A., S.V. PARTER, and H. SCHNEIDER...scaling square, nonnegative matrices to dou- bly stochastic form are described. A generalized version of the convergence theorem in SINKI-ORN and KNOPP... matrices D and E for a given square nonnegative matrix, A, such that DAE is doubly stochastic--or determine that such :.p h" du:es 7’. -,.xist. A
Stochastic processes in muon ionization cooling
NASA Astrophysics Data System (ADS)
Errede, D.; Makino, K.; Berz, M.; Johnstone, C. J.; Van Ginneken, A.
2004-02-01
A muon ionization cooling channel consists of three major components: the magnet optics, an acceleration cavity, and an energy absorber. The absorber of liquid hydrogen contained by thin aluminum windows is the only component which introduces stochastic processes into the otherwise deterministic acceleration system. The scattering dynamics of the transverse coordinates is described by Gaussian distributions. The asymmetric energy loss function is represented by the Vavilov distribution characterized by the minimum number of collisions necessary for a particle undergoing loss of the energy distribution average resulting from the Bethe-Bloch formula. Examples of the interplay between stochastic processes and deterministic beam dynamics are given.
Operation of Distributed Generation Under Stochastic Prices
Siddiqui, Afzal S.; Marnay, Chris
2005-11-30
We model the operating decisions of a commercial enterprisethatneeds to satisfy its periodic electricity demand with either on-sitedistributed generation (DG) or purchases from the wholesale market. Whilethe former option involves electricity generation at relatively high andpossibly stochastic costs from a set of capacity-constrained DGtechnologies, the latter implies unlimited open-market transactions atstochastic prices. A stochastic dynamic programme (SDP) is used to solvethe resulting optimisation problem. By solving the SDP with and withoutthe availability of DG units, the implied option values of the DG unitsare obtained.
Fermilab recycler stochastic cooling commissioning and performance
D. Broemmelsiek; Ralph Pasquinelli
2003-06-04
The Fermilab Recycler is a fixed 8 GeV kinetic energy storage ring located in the Fermilab Main Injector tunnel near the ceiling. The Recycler has two roles in Run II. First, to store antiprotons from the Fermilab Antiproton Accumulator so that the antiproton production rate is no longer compromised by large numbers of antiprotons stored in the Accumulator. Second, to receive antiprotons from the Fermilab Tevatron at the end of luminosity periods. To perform each of these roles, stochastic cooling in the Recycler is needed to preserve and cool antiprotons in preparation for transfer to the Tevatron. The commissioning and performance of the Recycler stochastic cooling systems will be reviewed.
An exact accelerated stochastic simulation algorithm.
Mjolsness, Eric; Orendorff, David; Chatelain, Philippe; Koumoutsakos, Petros
2009-04-14
An exact method for stochastic simulation of chemical reaction networks, which accelerates the stochastic simulation algorithm (SSA), is proposed. The present "ER-leap" algorithm is derived from analytic upper and lower bounds on the multireaction probabilities sampled by SSA, together with rejection sampling and an adaptive multiplicity for reactions. The algorithm is tested on a number of well-quantified reaction networks and is found experimentally to be very accurate on test problems including a chaotic reaction network. At the same time ER-leap offers a substantial speedup over SSA with a simulation time proportional to the 23 power of the number of reaction events in a Galton-Watson process.
Statistical mechanics of stochastic growth phenomena
NASA Astrophysics Data System (ADS)
Alekseev, Oleg; Mineev-Weinstein, Mark
2017-07-01
We develop statistical mechanics for stochastic growth processes and apply it to Laplacian growth by using its remarkable connection with a random matrix theory. The Laplacian growth equation is obtained from the variation principle and describes adiabatic (quasistatic) thermodynamic processes in the two-dimensional Dyson gas. By using Einstein's theory of thermodynamic fluctuations we consider transitional probabilities between thermodynamic states, which are in a one-to-one correspondence with simply connected domains occupied by gas. Transitions between these domains are described by the stochastic Laplacian growth equation, while the transitional probabilities coincide with a free-particle propagator on an infinite-dimensional complex manifold with a Kähler metric.
Three-dimensional stochastic vortex flows
NASA Astrophysics Data System (ADS)
Esposito, R.; Pulvirenti, M.
1989-08-01
It is well known that the dynamics of point vortices approximate, under suitable limits, the two-dimensional Euler flow for an ideal fluid. To find particle models for three-dimensional flows is a more intricate problem. A stochastic version of the algorithm introduced by Beale amd Maida (1982) for simulating the behavior of a three-dimensional Euler flow is introduced here, and convergence to the Navier-Stokes (NS) flow in R exp 3 is shown. The result is based on a stochastic Lagrangian picture of the NS equations.
Microscopic origins of stochastic crack growth
NASA Astrophysics Data System (ADS)
Pardee, W. J.; Morris, W. L.; Cox, B. N.
Physical arguments are made to obtain a mathematical model of the stochastic growth of surface fatigue cracks in a ductile metal alloy. The model is a set of coupled partial differential equations for the expected statistical density of cracks per unit area. The differential equations describe the smooth, deterministic local evolution of crack states, with the stochastic effects of abrupt local changes of material in the crack path appearing as transitions between distinct subspaces of single crack state space. Results are related to observables such as statistical distributions of crack growth rate and of time for at least one crack to reach macroscopic length.
Cao Yang . E-mail: ycao@cs.ucsb.edu; Gillespie, Dan . E-mail: GillespieDT@mailaps.org; Petzold, Linda . E-mail: petzold@engineering.ucsb.edu
2005-07-01
In this paper, we introduce a multiscale stochastic simulation algorithm (MSSA) which makes use of Gillespie's stochastic simulation algorithm (SSA) together with a new stochastic formulation of the partial equilibrium assumption (PEA). This method is much more efficient than SSA alone. It works even with a very small population of fast species. Implementation details are discussed, and an application to the modeling of the heat shock response of E. Coli is presented which demonstrates the excellent efficiency and accuracy obtained with the new method.
Stochastic model of the residual acceleration environment in microgravity
NASA Technical Reports Server (NTRS)
Vinals, Jorge
1994-01-01
We describe a theoretical investigation of the effects that stochastic residual accelerations (g-jitter) onboard spacecraft can have on experiments conducted in a microgravity environment. We first introduce a stochastic model of the residual acceleration field, and develop a numerical algorithm to solve the equations governing fluid flow that allow for a stochastic body force. We next summarize our studies of two generic situations: stochastic parametric resonance and the onset of convective flow induced by a fluctuating acceleration field.
Stochastic population growth in spatially heterogeneous environments
Evans, Steven N.; Ralph, Peter L.; Sen, Arnab
2016-01-01
Classical ecological theory predicts that environmental stochasticity increases extinction risk by reducing the average per-capita growth rate of populations. For sedentary populations in a spatially homogeneous yet temporally variable environment, a simple model of population growth is a stochastic differential equation dZt = μZtdt + σ ZtdWt, t ≥ 0, where the conditional law of Zt+Δt − Zt given Zt = z has mean and variance approximately zμΔt and z2σ2Δt when the time increment Δt is small. The long-term stochastic growth rate limt→∞ t−1 log Zt for such a population equals μ−σ22. Most populations, however, experience spatial as well as temporal variability. To understand the interactive effects of environmental stochasticity, spatial heterogeneity, and dispersal on population growth, we study an analogous model Xt=(Xt1,…,Xtn), t ≥ 0, for the population abundances in n patches: the conditional law of Xt+Δt given Xt = x is such that the conditional mean of Xt+Δti−Xti is approximately [xiμi +∑j (xj Dji − xi Dij)]Δt where μi is the per capita growth rate in the ith patch and Dij is the dispersal rate from the ith patch to the jth patch, and the conditional covariance of Xt+Δti−Xti and Xt+Δtj−Xtj is approximately xixjσijΔt for some covariance matrix Σ = (σij). We show for such a spatially extended population that if St=Xt1+⋯+Xtn denotes the total population abundance, then Yt = Xt /St, the vector of patch proportions, converges in law to a random vector Y∞ as t → ∞, and the stochastic growth rate limt→∞ t−1 log St equals the space-time average per-capita growth rate ∑iμi𝔼[Y∞j] experienced by the population minus half of the space-time average temporal variation 𝔼[∑i,jσijY∞iY∞j] experienced by the population. Using this characterization of the stochastic growth rate, we derive an explicit expression for the stochastic growth rate for populations living in two patches, determine which
Stochastic population growth in spatially heterogeneous environments.
Evans, Steven N; Ralph, Peter L; Schreiber, Sebastian J; Sen, Arnab
2013-02-01
Classical ecological theory predicts that environmental stochasticity increases extinction risk by reducing the average per-capita growth rate of populations. For sedentary populations in a spatially homogeneous yet temporally variable environment, a simple model of population growth is a stochastic differential equation dZ(t) = μZ(t)dt + σZ(t)dW(t), t ≥ 0, where the conditional law of Z(t+Δt)-Z(t) given Z(t) = z has mean and variance approximately z μΔt and z²σ²Δt when the time increment Δt is small. The long-term stochastic growth rate lim(t→∞) t⁻¹ log Z(t) for such a population equals μ − σ²/2 . Most populations, however, experience spatial as well as temporal variability. To understand the interactive effects of environmental stochasticity, spatial heterogeneity, and dispersal on population growth, we study an analogous model X(t) = (X¹(t) , . . . , X(n)(t)), t ≥ 0, for the population abundances in n patches: the conditional law of X(t+Δt) given X(t) = x is such that the conditional mean of X(i)(t+Δt) − X(i)(t) is approximately [x(i)μ(i) + Σ(j) (x(j) D(ji) − x(i) D(i j) )]Δt where μ(i) is the per capita growth rate in the ith patch and D(ij) is the dispersal rate from the ith patch to the jth patch, and the conditional covariance of X(i)(t+Δt)− X(i)(t) and X(j)(t+Δt) − X(j)(t) is approximately x(i)x(j)σ(ij)Δt for some covariance matrix Σ = (σ(ij)). We show for such a spatially extended population that if S(t) = X¹(t)+· · ·+ X(n)(t) denotes the total population abundance, then Y(t) = X(t)/S(t), the vector of patch proportions, converges in law to a random vector Y(∞) as t → ∞, and the stochastic growth rate lim(t→∞) t⁻¹ log S(t) equals the space-time average per-capita growth rate Σ(i)μ(i)E[Y(i)(∞)] experienced by the population minus half of the space-time average temporal variation E[Σ(i,j) σ(i j)Y(i)(∞) Y(j)(∞)] experienced by the population. Using this characterization of the
Teaching Tip: When a Matrix and Its Inverse Are Stochastic
ERIC Educational Resources Information Center
Ding, J.; Rhee, N. H.
2013-01-01
A stochastic matrix is a square matrix with nonnegative entries and row sums 1. The simplest example is a permutation matrix, whose rows permute the rows of an identity matrix. A permutation matrix and its inverse are both stochastic. We prove the converse, that is, if a matrix and its inverse are both stochastic, then it is a permutation matrix.
Influence of stochastic perturbation on prey-predator systems.
Rudnicki, Ryszard; Pichór, Katarzyna
2007-03-01
We analyse the influence of various stochastic perturbations on prey-predator systems. The prey-predator model is described by stochastic versions of a deterministic Lotka-Volterra system. We study long-time behaviour of both trajectories and distributions of the solutions. We indicate the differences between the deterministic and stochastic models.
Teaching Tip: When a Matrix and Its Inverse Are Stochastic
ERIC Educational Resources Information Center
Ding, J.; Rhee, N. H.
2013-01-01
A stochastic matrix is a square matrix with nonnegative entries and row sums 1. The simplest example is a permutation matrix, whose rows permute the rows of an identity matrix. A permutation matrix and its inverse are both stochastic. We prove the converse, that is, if a matrix and its inverse are both stochastic, then it is a permutation matrix.
Analysis of bilinear stochastic systems. [involving multiplicative noise processes
NASA Technical Reports Server (NTRS)
Willsky, A. S.; Marcus, S. I.; Martin, D. N.
1974-01-01
Analysis of stochastic dynamical systems that involve multiplicative (bilinear) noise processes is considered. After defining the systems of interest, the evolution of the moments of such systems, the question of stochastic stability, and estimation for bilinear stochastic systems are discussed. Both exact and approximate methods of analysis are introduced, and, in particular, the uses of Lie-theoretic concepts and harmonic analysis are discussed.
Stochastic functionals and fluctuation theorem for multikangaroo processes.
Van den Broeck, C; Toral, R
2014-06-01
We introduce multikangaroo Markov processes and provide a general procedure for evaluating a certain type of stochastic functional. We calculate analytically the large deviation properties. We apply our results to zero-crossing statistics and to stochastic thermodynamics, including the derivation of the fluctuation theorem and the large deviation properties for the stochastic entropy production in a typical solid state device.
Low-Dose Radiation and Genotoxic Chemicals Can Protect Against Stochastic Biological Effects
Scott, Bobby R.; Walker, Dale M.; Walker, Vernon E.
2004-01-01
A protective apoptosis-mediated (PAM) process that is turned on in mammalian cells by low-dose photon (X and γ) radiation and appears to also be turned on by the genotoxic chemical ethylene oxide is discussed. Because of the PAM process, exposure to low-dose photon radiation (and possibly also some genotoxic chemicals) can lead to a reduction in the risk of stochastic effects such as problematic mutations, neoplastic transformation (an early step in cancer occurrence), and cancer. These findings indicate a need to revise the current low-dose risk assessment paradigm for which risk of cancer is presumed to increase linearly with dose (without a threshold) after exposure to any amount of a genotoxic agent such as ionizing radiation. These findings support a view seldom mentioned in the past, that cancer risk can actually decrease, rather than increase, after exposure to low doses of photon radiation and possibly some other genotoxic agents. The PAM process (a form of natural protection) may contribute substantially to cancer prevention in humans and other mammals. However, new research is needed to improve our understanding of the process. The new research could unlock novel strategies for optimizing cancer prevention and novel protocols for low-dose therapy for cancer. With low-dose cancer therapy, normal tissue could be spared from severe damage while possibly eliminating the cancer. PMID:19330143
Cardaliaguet, P.; Rainer, C.
2013-08-01
We introduce a new notion of pathwise strategies for stochastic differential games. This allows us to give a correct meaning to some statement asserted in Cardaliaguet and Rainer (Appl. Math. Optim. 59: 1-36, 2009)
Stochastic light-cone CTMRG: a new DMRG approach to stochastic models
NASA Astrophysics Data System (ADS)
Kemper, A.; Gendiar, A.; Nishino, T.; Schadschneider, A.; Zittartz, J.
2003-01-01
We develop a new variant of the recently introduced stochastic transfer matrix DMRG which we call stochastic light-cone corner-transfer-matrix DMRG (LCTMRG). It is a numerical method to compute dynamic properties of one-dimensional stochastic processes. As suggested by its name, the LCTMRG is a modification of the corner-transfer-matrix DMRG, adjusted by an additional causality argument. As an example, two reaction-diffusion models, the diffusion-annihilation process and the branch-fusion process are studied and compared with exact data and Monte Carlo simulations to estimate the capability and accuracy of the new method. The number of possible Trotter steps of more than 105 shows a considerable improvement on the old stochastic TMRG algorithm.
Stochastic Differential Games with Asymmetric Information
Cardaliaguet, Pierre Rainer, Catherine
2009-02-15
We investigate a two-player zero-sum stochastic differential game in which the players have an asymmetric information on the random payoff. We prove that the game has a value and characterize this value in terms of dual viscosity solutions of some second order Hamilton-Jacobi equation.
Random Walk Analysis in Antagonistic Stochastic Games
2010-07-01
Journal of Mathematical Analysis and Applications , 353...and Applications, an Honorary Volume of Cambridge Scientific Publishers, Journal of Mathematical Analysis and Applications , Mathematical and Computer...J.H. and Ke, H-J., Multilayers in a Modulated Stochastic Game, Journal of Mathematical Analysis and Applications , 353 (2009), 553-565. [8
Adaptive Control of Nonlinear and Stochastic Systems
1991-01-14
Hernmndez-Lerma and S.I. Marcus, Nonparametric adaptive control of dis- crete time partially observable stochastic systems, Journal of Mathematical Analysis and Applications 137... Journal of Mathematical Analysis and Applications 137 (1989), 485-514. [19] A. Arapostathis and S.I. Marcus, Analysis of an identification algorithm
White Noise Path Integrals in Stochastic Neurodynamics
NASA Astrophysics Data System (ADS)
Carpio-Bernido, M. Victoria; Bernido, Christopher C.
2008-06-01
The white noise path integral approach is used in stochastic modeling of neural activity, where the primary dynamical variables are the relative membrane potentials, while information on transmembrane ionic currents is contained in the drift coefficient. The white noise path integral allows a natural framework and can be evaluated explicitly to yield a closed form for the conditional probability density.
Minimum Entropy Rate Simplification of Stochastic Processes.
Henter, Gustav Eje; Kleijn, W Bastiaan
2016-02-23
This document contains supplemental material for the IEEE Transactions on Pattern Analysis and Machine Intelligence article "Minimum Entropy Rate Simplification of Stochastic Processes." The supplement is divided into three appen- dices: the first on MERS for Gaussian processes, and the remaining two on, respectively, the theory and the experimental results of MERS for Markov chains.
Stochastic Prognostics for Rolling Element Bearings
NASA Astrophysics Data System (ADS)
Li, Y.; Kurfess, T. R.; Liang, S. Y.
2000-09-01
The capability to accurately predict the remaining life of a rolling element bearing is prerequisite to the optimal maintenance of rotating machinery performance in terms of cost and productivity. Due to the probabilistic nature of bearing integrity and operation condition, reliable estimation of a bearing's remaining life presents a challenging aspect in the area of maintenance optimisation and catastrophic failure avoidance. Previous study has developed an adaptive prognostic methodology to estimate the rate of bearing defect growth based on a deterministic defect-propagation model. However, deterministic models are inadequate in addressing the stochastic nature of defect-propagation. In this paper, a stochastic defect-propagation model is established by instituting a lognormal random variable in a deterministic defect-propagation rate model. The resulting stochastic model is calibrated on-line by a recursive least-squares (RLS) approach without the requirement of a priori knowledge on bearing characteristics. An augmented stochastic differential equation vector is developed with the consideration of model uncertainties, parameter estimation errors, and diagnostic model inaccuracies. It involves two ordinary differential equations for the first and second moments of its random variables. Solving the two equations gives the mean path of defect propagation and its dispersion at any instance. This approach is suitable for on-line monitoring, remaining life prediction, and decision making for optimal maintenance scheduling. The methodology has been verified by numerical simulations and the experimental testing of bearing fatigue life.
A Note on Boolean Stochastic Processes
NASA Astrophysics Data System (ADS)
Fidaleo, Francesco
2015-03-01
For the quantum stochastic processes generated by the Boolean commutation relations, we prove the following version of De Finetti Theorem: each of such Boolean processes is exchangeable if and only if it is independent and identically distributed with respect to the tail algebra.
Stochastic genetic networks with solvable structures
Lipan, Ovidiu
2014-12-10
We describe a set of basic stochastic biocircuits for which the Master Equation is completely solvable. Beside linear circuits, which are known to be solvable, we show that tree-like circuits with polynomial transition functions are also completely solvable. We associate a simple but unambiguous graphical representation to such circuits. The graphical representation shows the signal propagation through these simple circuits.
Maximal stochastic transport in the Lorenz equations
NASA Astrophysics Data System (ADS)
Agarwal, Sahil; Wettlaufer, J. S.
2016-01-01
We calculate the stochastic upper bounds for the Lorenz equations using an extension of the background method. In analogy with Rayleigh-Bénard convection the upper bounds are for heat transport versus Rayleigh number. As might be expected, the stochastic upper bounds are larger than the deterministic counterpart of Souza and Doering [1], but their variation with noise amplitude exhibits interesting behavior. Below the transition to chaotic dynamics the upper bounds increase monotonically with noise amplitude. However, in the chaotic regime this monotonicity depends on the number of realizations in the ensemble; at a particular Rayleigh number the bound may increase or decrease with noise amplitude. The origin of this behavior is the coupling between the noise and unstable periodic orbits, the degree of which depends on the degree to which the ensemble represents the ergodic set. This is confirmed by examining the close returns plots of the full solutions to the stochastic equations and the numerical convergence of the noise correlations. The numerical convergence of both the ensemble and time averages of the noise correlations is sufficiently slow that it is the limiting aspect of the realization of these bounds. Finally, we note that the full solutions of the stochastic equations demonstrate that the effect of noise is equivalent to the effect of chaos.
Stochastic models for convective momentum transport.
Majda, Andrew J; Stechmann, Samuel N
2008-11-18
The improved parameterization of unresolved features of tropical convection is a central challenge in current computer models for long-range ensemble forecasting of weather and short-term climate change. Observations, theory, and detailed smaller-scale numerical simulations suggest that convective momentum transport (CMT) from the unresolved scales to the resolved scales is one of the major deficiencies in contemporary computer models. Here, a combination of mathematical and physical reasoning is utilized to build simple stochastic models that capture the significant intermittent upscale transports of CMT on the large scales due to organized unresolved convection from squall lines. Properties of the stochastic model for CMT are developed below in a test column model environment for the large-scale variables. The effects of CMT from the stochastic model on a large-scale convectively coupled wave in an idealized setting are presented below as a nontrivial test problem. Here, the upscale transports from stochastic effects are significant and even generate a large-scale mean flow which can interact with the convectively coupled wave.
Stochastic game dynamics under demographic fluctuations
Huang, Weini; Hauert, Christoph; Traulsen, Arne
2015-01-01
Frequency-dependent selection and demographic fluctuations play important roles in evolutionary and ecological processes. Under frequency-dependent selection, the average fitness of the population may increase or decrease based on interactions between individuals within the population. This should be reflected in fluctuations of the population size even in constant environments. Here, we propose a stochastic model that naturally combines these two evolutionary ingredients by assuming frequency-dependent competition between different types in an individual-based model. In contrast to previous game theoretic models, the carrying capacity of the population, and thus the population size, is determined by pairwise competition of individuals mediated by evolutionary games and demographic stochasticity. In the limit of infinite population size, the averaged stochastic dynamics is captured by deterministic competitive Lotka–Volterra equations. In small populations, demographic stochasticity may instead lead to the extinction of the entire population. Because the population size is driven by fitness in evolutionary games, a population of cooperators is less prone to go extinct than a population of defectors, whereas in the usual systems of fixed size the population would thrive regardless of its average payoff. PMID:26150518
Vector Lyapunov Functions for Stochastic Interconnected Systems
NASA Technical Reports Server (NTRS)
Boussalis, D.
1985-01-01
Theoretical paper presents set of sufficient conditions for asymptotic and exponential stability with probability 1 for class of stochastic interconnected systems. Theory applicable to complicated, large-scale mechanical or electrical systems, and, for several design problems, it reduces computational difficulty by relating stability criteria to fundamental structural features of system.
Stochastic models for turbulent reacting flows
Kerstein, A.
1993-12-01
The goal of this program is to develop and apply stochastic models of various processes occurring within turbulent reacting flows in order to identify the fundamental mechanisms governing these flows, to support experimental studies of these flows, and to further the development of comprehensive turbulent reacting flow models.
Stochastic Cooling with Schottky Band Overlap
NASA Astrophysics Data System (ADS)
Lebedev, Valeri
2006-03-01
Optimal use of stochastic cooling is essential to maximize the antiproton stacking rate for Tevatron Run II. Good understanding and characterization of the cooling is important for the optimization. The paper is devoted to derivation of the Fokker-Plank equations justified in the case of near or full Schottky base overlap for both longitudinal and transverse coolings.
Stochastic beamforming for cochlear implant coding
NASA Astrophysics Data System (ADS)
Morse, Robert P.; Holmes, Stephen D.; Shulgin, Boris; Nikitin, Alexander; Stocks, Nigel G.
2007-06-01
Cochlear implants are prosthetic devices used to provide hearing to people who would otherwise be profoundly deaf. The deliberate addition of noise to the electrode signals could increase the amount of information transmitted, but standard cochlear implants do not replicate the noise characteristic of normal hearing because if noise is added in an uncontrolled manner with a limited number of electrodes then it will almost certainly lead to worse performance. Only if partially independent stochastic activity can be achieved in each nerve fibre can mechanisms like suprathreshold stochastic resonance be effective. We are investigating the use of stochastic beamforming to achieve greater independence. The strategy involves presenting each electrode with a linear combination of independent Gaussian noise sources. Because the cochlea is filled with conductive salt solutions, the noise currents from the electrodes interact and the effective stimulus for each nerve fibre will therefore be a different weighted sum of the noise sources. To some extent therefore, the effective stimulus for a nerve fibre will be independent of the effective stimulus of neighbouring fibres. For a particular patient, the electrode position and the amount of current spread are fixed. The objective is therefore to find the linear combination of noise sources that leads to the greatest independence between nerve discharges. In this theoretical study we show that it is possible to get one independent point of excitation (one null) for each electrode and that stochastic beamforming can greatly decrease the correlation between the noise exciting different regions of the cochlea.
Aspects of stochastic modeling for structural firesafety.
Gross, D
1983-05-01
A brief review is presented of methods for stochastic modeling of fires of sufficient severity to threaten the structural safety of buildings. Information is provided on the rate of fire occurrences according to the floor area at risk for the major occupancy types.
Stochastic Cooling with Schottky Band Overlap
Lebedev, Valeri; /Fermilab
2005-12-01
Optimal use of stochastic cooling is essential to maximize the antiproton stacking rate for Tevatron Run II. Good understanding and characterization of the cooling is important for the optimization. The paper is devoted to derivation of the Fokker-Planck equations justified in the case of near or full Schottky base overlap for both longitudinal and transverse coolings.
Stochastic Simulation Tool for Aerospace Structural Analysis
NASA Technical Reports Server (NTRS)
Knight, Norman F.; Moore, David F.
2006-01-01
Stochastic simulation refers to incorporating the effects of design tolerances and uncertainties into the design analysis model and then determining their influence on the design. A high-level evaluation of one such stochastic simulation tool, the MSC.Robust Design tool by MSC.Software Corporation, has been conducted. This stochastic simulation tool provides structural analysts with a tool to interrogate their structural design based on their mathematical description of the design problem using finite element analysis methods. This tool leverages the analyst's prior investment in finite element model development of a particular design. The original finite element model is treated as the baseline structural analysis model for the stochastic simulations that are to be performed. A Monte Carlo approach is used by MSC.Robust Design to determine the effects of scatter in design input variables on response output parameters. The tool was not designed to provide a probabilistic assessment, but to assist engineers in understanding cause and effect. It is driven by a graphical-user interface and retains the engineer-in-the-loop strategy for design evaluation and improvement. The application problem for the evaluation is chosen to be a two-dimensional shell finite element model of a Space Shuttle wing leading-edge panel under re-entry aerodynamic loading. MSC.Robust Design adds value to the analysis effort by rapidly being able to identify design input variables whose variability causes the most influence in response output parameters.
Stochastic Cooling with Schottky Band Overlap
Lebedev, Valeri
2006-03-20
Optimal use of stochastic cooling is essential to maximize the antiproton stacking rate for Tevatron Run II. Good understanding and characterization of the cooling is important for the optimization. The paper is devoted to derivation of the Fokker-Plank equations justified in the case of near or full Schottky base overlap for both longitudinal and transverse coolings.
Stochastic processes, estimation theory and image enhancement
NASA Technical Reports Server (NTRS)
Assefi, T.
1978-01-01
An introductory account of stochastic processes, estimation theory, and image enhancement is presented. The book is primarily intended for first-year graduate students and practicing engineers and scientists whose work requires an acquaintance with the theory. Fundamental concepts of probability were reviewed that are required to support the main topics. The appendices discuss the remaining mathematical background.
Stochastic dominance and medical decision making.
Leshno, Moshe; Levy, Haim
2004-08-01
Stochastic Dominance (SD) criteria are decision making tools which allow us to choose among various strategies with only partial information on the decision makers' preferences. The notion of Stochastic Dominance has been extensively employed and developed in the area of economics, finance, agriculture, statistics, marketing and operation research since the late 1960s. For example, it may tell us which of two medical treatments with uncertain outcomes is preferred in the absence of full information on the patients' preferences. This paper presents a short review of the SD paradigm and demonstrates how the SD criteria may be employed in medical decision making, using the case of small abdominal aortic aneurysms as an illustration. Thus, for instance by assuming risk aversion one can employ second-degree stochastic dominance to divide the set of all possible treatments into the efficient set, from which the decision makers should always choose, and the inefficient (inferior) set. By employing Prospect Stochastic Dominance (PSD) a similar division can be conducted corresponding to all S-shaped utility functions.
The Stochastic Nonlinear Damped Wave Equation
Barbu, V. Da Prato, G.
2002-12-19
We prove the existence of an invariant measure for the transition semigroup associated with a nonlinear damped stochastic wave equation in R{sup n} of the Klein-Gordon type. The uniqueness of the invariant measure and the structure of the corresponding Kolmogorov operator are also studied.
Statistical Inference and Stochastic Simulation for Microrheology
2013-12-18
inference and stochastic simulation to analyze time series data from passive microrheology experiments of biofluids, especially mucus . During the time...analyze time series data from passive microrheology experiments of biofluids, especially mucus . During the time of the grant, progress was made on both
Elliptic Equations of Higher Stochastic Order
2009-01-01
stochastic spaces, such as Hida or Kondratiev spaces [11, 12], or even larger exponential spaces [16]. The traditional approach [17, 20, 21, etc.] has to...2, 384–408. [7] T. Hida , H-H. Kuo, J. Potthoff, and L. Sreit, White noise, Kluwer Academic Publishers, Boston, 1993. [8] H. Holden, B. Øksendal, J
Stochastic nonhomogeneous incompressible Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Cutland, Nigel J.; Enright, Brendan
We construct solutions for 2- and 3-D stochastic nonhomogeneous incompressible Navier-Stokes equations with general multiplicative noise. These equations model the velocity of a mixture of incompressible fluids of varying density, influenced by random external forces that involve feedback; that is, multiplicative noise. Weak solutions for the corresponding deterministic equations were first found by Kazhikhov [A.V. Kazhikhov, Solvability of the initial and boundary-value problem for the equations of motion of an inhomogeneous viscous incompressible fluid, Soviet Phys. Dokl. 19 (6) (1974) 331-332; English translation of the paper in: Dokl. Akad. Nauk SSSR 216 (6) (1974) 1240-1243]. A stochastic version with additive noise was solved by Yashima [H.F. Yashima, Equations de Navier-Stokes stochastiques non homogènes et applications, Thesis, Scuola Normale Superiore, Pisa, 1992]. The methods here extend the Loeb space techniques used to obtain the first general solutions of the stochastic Navier-Stokes equations with multiplicative noise in the homogeneous case [M. Capiński, N.J. Cutland, Stochastic Navier-Stokes equations, Applicandae Math. 25 (1991) 59-85]. The solutions display more regularity in the 2D case. The methods also give a simpler proof of the basic existence result of Kazhikhov.
Comparing Several Robust Tests of Stochastic Equality.
ERIC Educational Resources Information Center
Vargha, Andras; Delaney, Harold D.
In this paper, six statistical tests of stochastic equality are compared with respect to Type I error and power through a Monte Carlo simulation. In the simulation, the skewness and kurtosis levels and the extent of variance heterogeneity of the two parent distributions were varied across a wide range. The sample sizes applied were either small or…
Stochastic Resonance in Protein Folding Dynamics.
Davtyan, Aram; Platkov, Max; Gruebele, Martin; Papoian, Garegin A
2016-05-04
Although protein folding reactions are usually studied under static external conditions, it is likely that proteins fold in a locally fluctuating cellular environment in vivo. To mimic such behavior in in vitro experiments, the local temperature of the solvent can be modulated either harmonically or using correlated noise. In this study, coarse-grained molecular simulations are used to investigate these possibilities, and it is found that both periodic and correlated random fluctuations of the environment can indeed accelerate folding kinetics if the characteristic frequencies of the applied fluctuations are commensurate with the internal timescale of the folding reaction; this is consistent with the phenomenon of stochastic resonance observed in many other condensed-matter processes. To test this theoretical prediction, the folding dynamics of phosphoglycerate kinase under harmonic temperature fluctuations are experimentally probed using Förster resonance energy transfer fluorescence measurements. To analyze these experiments, a combination of theoretical approaches is developed, including stochastic simulations of folding kinetics and an analytical mean-field kinetic theory. The experimental observations are consistent with the theoretical predictions of stochastic resonance in phosphoglycerate kinase folding. When combined with an alternative experiment on the protein VlsE using a power spectrum analysis, elaborated in Dave et al., ChemPhysChem 2016, 10.1002/cphc.201501041, the overall data overwhelmingly point to the experimental confirmation of stochastic resonance in protein folding dynamics.
Investigation of the stochastic properties of wind
NASA Astrophysics Data System (ADS)
Dimitriadis, Panayiotis; Koutsoyiannis, Demetris; Papanicolaou, Panos
2016-04-01
Understanding atmospheric motion in the form of wind is essential to many fields in hydroclimatics. The wind is considered one of the most important processes in hydrometeorology since, along with temperature, it generates and drives climate dynamics. Currently, the interest has increased due to its involvement to renewable energy resources through wind power production and forecasting. However, there seems to be a puzzle about which stochastic model best describes the wind process. In this analysis, we attempt to explain the reason around this confusion regarding the stochastic properties of the wind process using statistical as well as hydrometeorological reasoning, starting from the microscale of turbulence and extending the analysis to the macroscale of climatic processes. Particularly, some models seem to exhibit good agreement with data mostly due to instrumental errors. Moreover, we show that extending the theory of turbulence to the atmospheric motion can reveal stochastic properties that are not only accompanied with physical interference but also exhibit excellent agreement with wind measurements. Finally, we apply the theoretical analysis to multiple stations around the globe and we derive conclusions on the variation of stochastic parameters of wind regarding dominant climatic conditions.
Stochastic motif extraction using hidden Markov model
Fujiwara, Yukiko; Asogawa, Minoru; Konagaya, Akihiko
1994-12-31
In this paper, we study the application of an HMM (hidden Markov model) to the problem of representing protein sequences by a stochastic motif. A stochastic protein motif represents the small segments of protein sequences that have a certain function or structure. The stochastic motif, represented by an HMM, has conditional probabilities to deal with the stochastic nature of the motif. This HMM directive reflects the characteristics of the motif, such as a protein periodical structure or grouping. In order to obtain the optimal HMM, we developed the {open_quotes}iterative duplication method{close_quotes} for HMM topology learning. It starts from a small fully-connected network and iterates the network generation and parameter optimization until it achieves sufficient discrimination accuracy. Using this method, we obtained an HMM for a leucine zipper motif. Compared to the accuracy of a symbolic pattern representation with accuracy of 14.8 percent, an HMM achieved 79.3 percent in prediction. Additionally, the method can obtain an HMM for various types of zinc finger motifs, and it might separate the mixed data. We demonstrated that this approach is applicable to the validation of the protein databases; a constructed HMM b as indicated that one protein sequence annotated as {open_quotes}lencine-zipper like sequence{close_quotes} in the database is quite different from other leucine-zipper sequences in terms of likelihood, and we found this discrimination is plausible.
On doubly stochastic rarefaction of renewal processes
NASA Astrophysics Data System (ADS)
Korolev, V. Yu.; Korchagin, A. Yu.; Zeifman, A. I.
2017-07-01
In the paper, the concepts of π-mixed geometric and π-mixed binomial distributions are introduced within the setting of Bernoulli trials with a random probability of success. A generalization of the Rényi theorem concerning the asymptotic behavior of rarefied renewal processes is proved for doubly stochastic rarefaction resulting in that the limit process is mixed Poisson.
Stochastic Processes and the Guttman Simplex
ERIC Educational Resources Information Center
Groen, Guy J.
1971-01-01
The problem of whether a precise connection exists between the stochastic processes considered in mathematical learning theory and the Guttman simplex is investigated. The approach used is to derive a set of conditions which a probabilistic model must satisfy in order to generate inter-trial correlations with the perfect simplex property.…
An Epistemological View on Fundamental Stochastic Ideas
ERIC Educational Resources Information Center
Heitele, Dietger
1975-01-01
Arguing that the teaching of stochastic processes should reflect the experience and reality of the student, the author urges concentration on fundamental ideas. The development of intuition should be encouraged, and to this end continuity in teaching and a spiralled curriculum are important. (SD)
Optimal Maintenance for Stochastically Degrading Staellite Constellations
2005-03-01
to the case of a finite number of series components in which one component is not monitored and all others are monitored. Vergin and Scriabin [43...nance models for stochastically deteriorating single-unit systems. Naval Research Logistics, 36, 419-446. BIB-3 43. Vergin, R. C., and M. Scriabin (1977
Modeling animal movements using stochastic differential equations
Haiganoush K. Preisler; Alan A. Ager; Bruce K. Johnson; John G. Kie
2004-01-01
We describe the use of bivariate stochastic differential equations (SDE) for modeling movements of 216 radiocollared female Rocky Mountain elk at the Starkey Experimental Forest and Range in northeastern Oregon. Spatially and temporally explicit vector fields were estimated using approximating difference equations and nonparametric regression techniques. Estimated...
Perspective: Stochastic algorithms for chemical kinetics
Gillespie, Daniel T.; Hellander, Andreas; Petzold, Linda R.
2013-01-01
We outline our perspective on stochastic chemical kinetics, paying particular attention to numerical simulation algorithms. We first focus on dilute, well-mixed systems, whose description using ordinary differential equations has served as the basis for traditional chemical kinetics for the past 150 years. For such systems, we review the physical and mathematical rationale for a discrete-stochastic approach, and for the approximations that need to be made in order to regain the traditional continuous-deterministic description. We next take note of some of the more promising strategies for dealing stochastically with stiff systems, rare events, and sensitivity analysis. Finally, we review some recent efforts to adapt and extend the discrete-stochastic approach to systems that are not well-mixed. In that currently developing area, we focus mainly on the strategy of subdividing the system into well-mixed subvolumes, and then simulating diffusional transfers of reactant molecules between adjacent subvolumes together with chemical reactions inside the subvolumes. PMID:23656106
STOCHASTIC INTEGRATION FOR TEMPERED FRACTIONAL BROWNIAN MOTION.
Meerschaert, Mark M; Sabzikar, Farzad
2014-07-01
Tempered fractional Brownian motion is obtained when the power law kernel in the moving average representation of a fractional Brownian motion is multiplied by an exponential tempering factor. This paper develops the theory of stochastic integrals for tempered fractional Brownian motion. Along the way, we develop some basic results on tempered fractional calculus.
Stochastic resonance in Gaussian quantum channels
NASA Astrophysics Data System (ADS)
Lupo, Cosmo; Mancini, Stefano; Wilde, Mark M.
2013-02-01
We determine conditions for the presence of stochastic resonance in a lossy bosonic channel with a nonlinear, threshold decoding. The stochastic resonance effect occurs if and only if the detection threshold is outside of a ‘forbidden interval’. We show that it takes place in different settings: when transmitting classical messages through a lossy bosonic channel, when transmitting over an entanglement-assisted lossy bosonic channel and when discriminating channels with different loss parameters. Moreover, we consider a setting in which stochastic resonance occurs in the transmission of a qubit over a lossy bosonic channel with a particular encoding and decoding. In all cases, we assume the addition of Gaussian noise to the signal and show that it does not matter who, between sender and receiver, introduces such a noise. Remarkably, different results are obtained when considering a setting for private communication. In this case, the symmetry between sender and receiver is broken and the ‘forbidden interval’ may vanish, leading to the occurrence of stochastic resonance effects for any value of the detection threshold.
Multidimensional stochastic approximation using locally contractive functions
NASA Technical Reports Server (NTRS)
Lawton, W. M.
1975-01-01
A Robbins-Monro type multidimensional stochastic approximation algorithm which converges in mean square and with probability one to the fixed point of a locally contractive regression function is developed. The algorithm is applied to obtain maximum likelihood estimates of the parameters for a mixture of multivariate normal distributions.
Stochastic properties of the plant circadian clock.
Guerriero, Maria Luisa; Pokhilko, Alexandra; Fernández, Aurora Piñas; Halliday, Karen J; Millar, Andrew J; Hillston, Jane
2012-04-07
Circadian clocks are gene regulatory networks whose role is to help the organisms to cope with variations in environmental conditions such as the day/night cycle. In this work, we explored the effects of molecular noise in single cells on the behaviour of the circadian clock in the plant model species Arabidopsis thaliana. The computational modelling language Bio-PEPA enabled us to give a stochastic interpretation of an existing deterministic model of the clock, and to easily compare the results obtained via stochastic simulation and via numerical solution of the deterministic model. First, the introduction of stochasticity in the model allowed us to estimate the unknown size of the system. Moreover, stochasticity improved the description of the available experimental data in several light conditions: noise-induced fluctuations yield a faster entrainment of the plant clock under certain photoperiods and are able to explain the experimentally observed dampening of the oscillations in plants under constant light conditions. The model predicts that the desynchronization between noisy oscillations in single cells contributes to the observed damped oscillations at the level of the cell population. Analysis of the phase, period and amplitude distributions under various light conditions demonstrated robust entrainment of the plant clock to light/dark cycles which closely matched the available experimental data.
Doubly perturbed neutral stochastic functional equations
NASA Astrophysics Data System (ADS)
Hu, Lanying; Ren, Yong
2009-09-01
In this paper, we prove the existence and uniqueness of the solution to a class of doubly perturbed neutral stochastic functional equations (DPNSFEs in short) under some non-Lipschitz conditions. The solution is constructed by successive approximation. Furthermore, we give the continuous dependence of the solution on the initial value by means of the corollary of Bihari inequality.
Stochastic thermodynamics for linear kinetic equations
NASA Astrophysics Data System (ADS)
Van den Broeck, C.; Toral, R.
2015-07-01
Stochastic thermodynamics is formulated for variables that are odd under time reversal. The invariance under spatial rotation of the collision rates due to the isotropy of the heat bath is shown to be a crucial ingredient. An alternative detailed fluctuation theorem is derived, expressed solely in terms of forward statistics. It is illustrated for a linear kinetic equation with kangaroo rates.
Fingering in Stochastic Growth Models
Aristotelous, Andreas C.; Durrett, Richard
2015-01-01
Motivated by the widespread use of hybrid-discrete cellular automata in modeling cancer, two simple growth models are studied on the two dimensional lattice that incorporate a nutrient, assumed to be oxygen. In the first model the oxygen concentration u(x, t) is computed based on the geometry of the growing blob, while in the second one u(x, t) satisfies a reaction-diffusion equation. A threshold θ value exists such that cells give birth at rate β(u(x, t) − θ)+ and die at rate δ(θ − u(x, t)+. In the first model, a phase transition was found between growth as a solid blob and “fingering” at a threshold θc = 0.5, while in the second case fingering always occurs, i.e., θc = 0. PMID:26430353
2014-01-01
Background Biochemical systems with relatively low numbers of components must be simulated stochastically in order to capture their inherent noise. Although there has recently been considerable work on discrete stochastic solvers, there is still a need for numerical methods that are both fast and accurate. The Bulirsch-Stoer method is an established method for solving ordinary differential equations that possesses both of these qualities. Results In this paper, we present the Stochastic Bulirsch-Stoer method, a new numerical method for simulating discrete chemical reaction systems, inspired by its deterministic counterpart. It is able to achieve an excellent efficiency due to the fact that it is based on an approach with high deterministic order, allowing for larger stepsizes and leading to fast simulations. We compare it to the Euler τ-leap, as well as two more recent τ-leap methods, on a number of example problems, and find that as well as being very accurate, our method is the most robust, in terms of efficiency, of all the methods considered in this paper. The problems it is most suited for are those with increased populations that would be too slow to simulate using Gillespie’s stochastic simulation algorithm. For such problems, it is likely to achieve higher weak order in the moments. Conclusions The Stochastic Bulirsch-Stoer method is a novel stochastic solver that can be used for fast and accurate simulations. Crucially, compared to other similar methods, it better retains its high accuracy when the timesteps are increased. Thus the Stochastic Bulirsch-Stoer method is both computationally efficient and robust. These are key properties for any stochastic numerical method, as they must typically run many thousands of simulations. PMID:24939084
A Stochastic Maximum Principle for a Stochastic Differential Game of a Mean-Field Type
Hosking, John Joseph Absalom
2012-12-15
We construct a stochastic maximum principle (SMP) which provides necessary conditions for the existence of Nash equilibria in a certain form of N-agent stochastic differential game (SDG) of a mean-field type. The information structure considered for the SDG is of a possible asymmetric and partial type. To prove our SMP we take an approach based on spike-variations and adjoint representation techniques, analogous to that of S. Peng (SIAM J. Control Optim. 28(4):966-979, 1990) in the optimal stochastic control context. In our proof we apply adjoint representation procedures at three points. The first-order adjoint processes are defined as solutions to certain mean-field backward stochastic differential equations, and second-order adjoint processes of a first type are defined as solutions to certain backward stochastic differential equations. Second-order adjoint processes of a second type are defined as solutions of certain backward stochastic equations of a type that we introduce in this paper, and which we term conditional mean-field backward stochastic differential equations. From the resulting representations, we show that the terms relating to these second-order adjoint processes of the second type are of an order such that they do not appear in our final SMP equations. A comparable situation exists in an article by R. Buckdahn, B. Djehiche, and J. Li (Appl. Math. Optim. 64(2):197-216, 2011) that constructs a SMP for a mean-field type optimal stochastic control problem; however, the approach we take of using these second-order adjoint processes of a second type to deal with the type of terms that we refer to as the second form of quadratic-type terms represents an alternative to a development, to our setting, of the approach used in their article for their analogous type of term.
2015-08-13
which have now been accepted for publication. Topics covered in this research include theory of large deviations, stochastic differential games ...Existence and uniqueness of solutions to such reflected stochastic differential equations (SDE) follows from the classical theory and well...Knoxville, Knoxville, TN March 21-23, 2014. • Infinity Laplacian and Stochastic Differential Games . Quasilinear PDEs and Game Theory , December 2-4
Stochastic variation in Cardamine hirsuta petal number.
Monniaux, Marie; Pieper, Bjorn; Hay, Angela
2016-04-01
Floral development is remarkably robust in terms of the identity and number of floral organs in each whorl, whereas vegetative development can be quite plastic. This canalization of flower development prevents the phenotypic expression of cryptic genetic variation, even in fluctuating environments. A cruciform perianth with four petals is a hallmark of the Brassicaceae family, typified in the model species Arabidopsis thaliana However, variable petal loss is found in Cardamine hirsuta, a genetically tractable relative of A. thaliana Cardamine hirsuta petal number varies in response to stochastic, genetic and environmental perturbations, which makes it an interesting model to study mechanisms of decanalization and the expression of cryptic variation. Multitrait quantitative trait locus (QTL) analysis in recombinant inbred lines (RILs) was used to identify whether the stochastic variation found in C. hirsuta petal number had a genetic basis. Stochastic variation (standard error of the average petal number) was found to be a heritable phenotype, and four QTL that influenced this trait were identified. The sensitivity to detect these QTL effects was increased by accounting for the effect of ageing on petal number variation. All QTL had significant effects on both average petal number and its standard error, indicating that these two traits share a common genetic basis. However, for some QTL, a degree of independence was found between the age of the flowers where allelic effects were significant for each trait. Stochastic variation in C. hirsuta petal number has a genetic basis, and common QTL influence both average petal number and its standard error. Allelic variation at these QTL can, therefore, modify petal number in an age-specific manner via effects on the phenotypic mean and stochastic variation. These results are discussed in the context of trait evolution via a loss of robustness. © The Author 2015. Published by Oxford University Press on behalf of the Annals
Stochastic flux analysis of chemical reaction networks.
Kahramanoğulları, Ozan; Lynch, James F
2013-12-07
Chemical reaction networks provide an abstraction scheme for a broad range of models in biology and ecology. The two common means for simulating these networks are the deterministic and the stochastic approaches. The traditional deterministic approach, based on differential equations, enjoys a rich set of analysis techniques, including a treatment of reaction fluxes. However, the discrete stochastic simulations, which provide advantages in some cases, lack a quantitative treatment of network fluxes. We describe a method for flux analysis of chemical reaction networks, where flux is given by the flow of species between reactions in stochastic simulations of the network. Extending discrete event simulation algorithms, our method constructs several data structures, and thereby reveals a variety of statistics about resource creation and consumption during the simulation. We use these structures to quantify the causal interdependence and relative importance of the reactions at arbitrary time intervals with respect to the network fluxes. This allows us to construct reduced networks that have the same flux-behavior, and compare these networks, also with respect to their time series. We demonstrate our approach on an extended example based on a published ODE model of the same network, that is, Rho GTP-binding proteins, and on other models from biology and ecology. We provide a fully stochastic treatment of flux analysis. As in deterministic analysis, our method delivers the network behavior in terms of species transformations. Moreover, our stochastic analysis can be applied, not only at steady state, but at arbitrary time intervals, and used to identify the flow of specific species between specific reactions. Our cases study of Rho GTP-binding proteins reveals the role played by the cyclic reverse fluxes in tuning the behavior of this network.
Stochastic variation in Cardamine hirsuta petal number
Monniaux, Marie; Pieper, Bjorn; Hay, Angela
2016-01-01
Background and Aims Floral development is remarkably robust in terms of the identity and number of floral organs in each whorl, whereas vegetative development can be quite plastic. This canalization of flower development prevents the phenotypic expression of cryptic genetic variation, even in fluctuating environments. A cruciform perianth with four petals is a hallmark of the Brassicaceae family, typified in the model species Arabidopsis thaliana. However, variable petal loss is found in Cardamine hirsuta, a genetically tractable relative of A. thaliana. Cardamine hirsuta petal number varies in response to stochastic, genetic and environmental perturbations, which makes it an interesting model to study mechanisms of decanalization and the expression of cryptic variation. Methods Multitrait quantitative trait locus (QTL) analysis in recombinant inbred lines (RILs) was used to identify whether the stochastic variation found in C. hirsuta petal number had a genetic basis. Key Results Stochastic variation (standard error of the average petal number) was found to be a heritable phenotype, and four QTL that influenced this trait were identified. The sensitivity to detect these QTL effects was increased by accounting for the effect of ageing on petal number variation. All QTL had significant effects on both average petal number and its standard error, indicating that these two traits share a common genetic basis. However, for some QTL, a degree of independence was found between the age of the flowers where allelic effects were significant for each trait. Conclusions Stochastic variation in C. hirsuta petal number has a genetic basis, and common QTL influence both average petal number and its standard error. Allelic variation at these QTL can, therefore, modify petal number in an age-specific manner via effects on the phenotypic mean and stochastic variation. These results are discussed in the context of trait evolution via a loss of robustness. PMID:26346720
Stochastic flux analysis of chemical reaction networks
2013-01-01
Background Chemical reaction networks provide an abstraction scheme for a broad range of models in biology and ecology. The two common means for simulating these networks are the deterministic and the stochastic approaches. The traditional deterministic approach, based on differential equations, enjoys a rich set of analysis techniques, including a treatment of reaction fluxes. However, the discrete stochastic simulations, which provide advantages in some cases, lack a quantitative treatment of network fluxes. Results We describe a method for flux analysis of chemical reaction networks, where flux is given by the flow of species between reactions in stochastic simulations of the network. Extending discrete event simulation algorithms, our method constructs several data structures, and thereby reveals a variety of statistics about resource creation and consumption during the simulation. We use these structures to quantify the causal interdependence and relative importance of the reactions at arbitrary time intervals with respect to the network fluxes. This allows us to construct reduced networks that have the same flux-behavior, and compare these networks, also with respect to their time series. We demonstrate our approach on an extended example based on a published ODE model of the same network, that is, Rho GTP-binding proteins, and on other models from biology and ecology. Conclusions We provide a fully stochastic treatment of flux analysis. As in deterministic analysis, our method delivers the network behavior in terms of species transformations. Moreover, our stochastic analysis can be applied, not only at steady state, but at arbitrary time intervals, and used to identify the flow of specific species between specific reactions. Our cases study of Rho GTP-binding proteins reveals the role played by the cyclic reverse fluxes in tuning the behavior of this network. PMID:24314153
Stochastic partial differential equations in turbulence related problems
NASA Technical Reports Server (NTRS)
Chow, P.-L.
1978-01-01
The theory of stochastic partial differential equations (PDEs) and problems relating to turbulence are discussed by employing the theories of Brownian motion and diffusion in infinite dimensions, functional differential equations, and functional integration. Relevant results in probablistic analysis, especially Gaussian measures in function spaces and the theory of stochastic PDEs of Ito type, are taken into account. Linear stochastic PDEs are analyzed through linearized Navier-Stokes equations with a random forcing. Stochastic equations for waves in random media as well as model equations in turbulent transport theory are considered. Markovian models in fully developed turbulence are discussed from a stochastic equation viewpoint.
Stochastic triangulation for prostate positioning during radiotherapy using short CBCT arcs.
Hoegele, Wolfgang; Loeschel, Rainer; Dobler, Barbara; Koelbl, Oliver; Beard, Clair; Zygmanski, Piotr
2013-02-01
Fast and reliable tumor localization is an important part of today's radiotherapy utilizing new delivery techniques. This proof-of-principle study demonstrates the use of a method called herein 'stochastic triangulation' for this purpose. Stochastic triangulation uses very short imaging arcs and a few projections. A stochastic Maximum A Posteriori (MAP) estimator is proposed based on an uncertainty-driven model of the acquisition geometry and inter-/intra-fractional deformable anatomy. The application of this method was designed to use the available linac-mounted cone-beam computed tomography (CBCT) and/or electronic portal imaging devices (EPID) for the patient setup based on short imaging arcs. For the proof-of-principle clinical demonstration, the MAP estimator was applied to 5 CBCT scans of a prostate cancer patient with 2 implanted gold markers. Estimation was performed for several (18) very short imaging arcs of 5° with 10 projections resulting in 90 estimations. Short-arc stochastic triangulation led to residual radial errors compared to manual inspection with a mean value of 1.4mm and a standard deviation of 0.9 mm (median 1.2mm, maximum 3.8mm) averaged over imaging directions all around the patient. Furthermore, abrupt intra-fractional motion of up to 10mm resulted in radial errors with a mean value of 1.8mm and a standard deviation of 1.1mm (median 1.5mm, maximum 5.6mm). Slow periodic intra-fractional motions in the range of 12 mm resulted in radial errors with a mean value of 1.8mm and a standard deviation of 1.1mm (median 1.6mm, maximum 4.7 mm). Based on this study, the proposed stochastic method is fast, robust and can be used for inter- as well as intra-fractional target localization using current CBCT units. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.
Distinguishing between stochasticity and determinism: Examples from cell cycle duration variability.
Pearl Mizrahi, Sivan; Sandler, Oded; Lande-Diner, Laura; Balaban, Nathalie Q; Simon, Itamar
2016-01-01
We describe a recent approach for distinguishing between stochastic and deterministic sources of variability, focusing on the mammalian cell cycle. Variability between cells is often attributed to stochastic noise, although it may be generated by deterministic components. Interestingly, lineage information can be used to distinguish between variability and determinism. Analysis of correlations within a lineage of the mammalian cell cycle duration revealed its deterministic nature. Here, we discuss the sources of such variability and the possibility that the underlying deterministic process is due to the circadian clock. Finally, we discuss the "kicked cell cycle" model and its implication on the study of the cell cycle in healthy and cancerous tissues. © 2015 WILEY Periodicals, Inc.
Joint analysis of stochastic processes with application to smoking patterns and insomnia.
Luo, Sheng
2013-12-20
This article proposes a joint modeling framework for longitudinal insomnia measurements and a stochastic smoking cessation process in the presence of a latent permanent quitting state (i.e., 'cure'). We use a generalized linear mixed-effects model and a stochastic mixed-effects model for the longitudinal measurements of insomnia symptom and for the smoking cessation process, respectively. We link these two models together via the latent random effects. We develop a Bayesian framework and Markov Chain Monte Carlo algorithm to obtain the parameter estimates. We formulate and compute the likelihood functions involving time-dependent covariates. We explore the within-subject correlation between insomnia and smoking processes. We apply the proposed methodology to simulation studies and the motivating dataset, that is, the Alpha-Tocopherol, Beta-Carotene Lung Cancer Prevention study, a large longitudinal cohort study of smokers from Finland. Copyright © 2013 John Wiley & Sons, Ltd.
Extinction risk depends strongly on factors contributing to stochasticity.
Melbourne, Brett A; Hastings, Alan
2008-07-03
Extinction risk in natural populations depends on stochastic factors that affect individuals, and is estimated by incorporating such factors into stochastic models. Stochasticity can be divided into four categories, which include the probabilistic nature of birth and death at the level of individuals (demographic stochasticity), variation in population-level birth and death rates among times or locations (environmental stochasticity), the sex of individuals and variation in vital rates among individuals within a population (demographic heterogeneity). Mechanistic stochastic models that include all of these factors have not previously been developed to examine their combined effects on extinction risk. Here we derive a family of stochastic Ricker models using different combinations of all these stochastic factors, and show that extinction risk depends strongly on the combination of factors that contribute to stochasticity. Furthermore, we show that only with the full stochastic model can the relative importance of environmental and demographic variability, and therefore extinction risk, be correctly determined. Using the full model, we find that demographic sources of stochasticity are the prominent cause of variability in a laboratory population of Tribolium castaneum (red flour beetle), whereas using only the standard simpler models would lead to the erroneous conclusion that environmental variability dominates. Our results demonstrate that current estimates of extinction risk for natural populations could be greatly underestimated because variability has been mistakenly attributed to the environment rather than the demographic factors described here that entail much higher extinction risk for the same variability level.
Quantum stochastic calculus associated with quadratic quantum noises
Ji, Un Cig; Sinha, Kalyan B.
2016-02-15
We first study a class of fundamental quantum stochastic processes induced by the generators of a six dimensional non-solvable Lie †-algebra consisting of all linear combinations of the generalized Gross Laplacian and its adjoint, annihilation operator, creation operator, conservation, and time, and then we study the quantum stochastic integrals associated with the class of fundamental quantum stochastic processes, and the quantum Itô formula is revisited. The existence and uniqueness of solution of a quantum stochastic differential equation is proved. The unitarity conditions of solutions of quantum stochastic differential equations associated with the fundamental processes are examined. The quantum stochastic calculus extends the Hudson-Parthasarathy quantum stochastic calculus.
Quantum stochastic calculus associated with quadratic quantum noises
NASA Astrophysics Data System (ADS)
Ji, Un Cig; Sinha, Kalyan B.
2016-02-01
We first study a class of fundamental quantum stochastic processes induced by the generators of a six dimensional non-solvable Lie †-algebra consisting of all linear combinations of the generalized Gross Laplacian and its adjoint, annihilation operator, creation operator, conservation, and time, and then we study the quantum stochastic integrals associated with the class of fundamental quantum stochastic processes, and the quantum Itô formula is revisited. The existence and uniqueness of solution of a quantum stochastic differential equation is proved. The unitarity conditions of solutions of quantum stochastic differential equations associated with the fundamental processes are examined. The quantum stochastic calculus extends the Hudson-Parthasarathy quantum stochastic calculus.
Stochastic simulations of a synthetic bacteria-yeast ecosystem
2012-01-01
Background The field of synthetic biology has greatly evolved and numerous functions can now be implemented by artificially engineered cells carrying the appropriate genetic information. However, in order for the cells to robustly perform complex or multiple tasks, co-operation between them may be necessary. Therefore, various synthetic biological systems whose functionality requires cell-cell communication are being designed. These systems, microbial consortia, are composed of engineered cells and exhibit a wide range of behaviors. These include yeast cells whose growth is dependent on one another, or bacteria that kill or rescue each other, synchronize, behave as predator-prey ecosystems or invade cancer cells. Results In this paper, we study a synthetic ecosystem comprising of bacteria and yeast that communicate with and benefit from each other using small diffusible molecules. We explore the behavior of this heterogeneous microbial consortium, composed of Saccharomyces cerevisiae and Escherichia coli cells, using stochastic modeling. The stochastic model captures the relevant intra-cellular and inter-cellular interactions taking place in and between the eukaryotic and prokaryotic cells. Integration of well-characterized molecular regulatory elements into these two microbes allows for communication through quorum sensing. A gene controlling growth in yeast is induced by bacteria via chemical signals and vice versa. Interesting dynamics that are common in natural ecosystems, such as obligatory and facultative mutualism, extinction, commensalism and predator-prey like dynamics are observed. We investigate and report on the conditions under which the two species can successfully communicate and rescue each other. Conclusions This study explores the various behaviors exhibited by the cohabitation of engineered yeast and bacterial cells. The way that the model is built allows for studying the dynamics of any system consisting of two species communicating with one
Stochastic simulations of a synthetic bacteria-yeast ecosystem.
Biliouris, Konstantinos; Babson, David; Schmidt-Dannert, Claudia; Kaznessis, Yiannis N
2012-06-06
The field of synthetic biology has greatly evolved and numerous functions can now be implemented by artificially engineered cells carrying the appropriate genetic information. However, in order for the cells to robustly perform complex or multiple tasks, co-operation between them may be necessary. Therefore, various synthetic biological systems whose functionality requires cell-cell communication are being designed. These systems, microbial consortia, are composed of engineered cells and exhibit a wide range of behaviors. These include yeast cells whose growth is dependent on one another, or bacteria that kill or rescue each other, synchronize, behave as predator-prey ecosystems or invade cancer cells. In this paper, we study a synthetic ecosystem comprising of bacteria and yeast that communicate with and benefit from each other using small diffusible molecules. We explore the behavior of this heterogeneous microbial consortium, composed of Saccharomyces cerevisiae and Escherichia coli cells, using stochastic modeling. The stochastic model captures the relevant intra-cellular and inter-cellular interactions taking place in and between the eukaryotic and prokaryotic cells. Integration of well-characterized molecular regulatory elements into these two microbes allows for communication through quorum sensing. A gene controlling growth in yeast is induced by bacteria via chemical signals and vice versa. Interesting dynamics that are common in natural ecosystems, such as obligatory and facultative mutualism, extinction, commensalism and predator-prey like dynamics are observed. We investigate and report on the conditions under which the two species can successfully communicate and rescue each other. This study explores the various behaviors exhibited by the cohabitation of engineered yeast and bacterial cells. The way that the model is built allows for studying the dynamics of any system consisting of two species communicating with one another via chemical signals
Zhang, Qichun; Zhou, Jinglin; Wang, Hong; Chai, Tianyou
2016-01-01
In this paper, stochastic coupling attenuation is investigated for a class of multi-variable bilinear stochastic systems and a novel output feedback m-block backstepping controller with linear estimator is designed, where gradient descent optimization is used to tune the design parameters of the controller. It has been shown that the trajectories of the closed-loop stochastic systems are bounded in probability sense and the stochastic coupling of the system outputs can be effectively attenuated by the proposed control algorithm. Moreover, the stability of the stochastic systems is analyzed and the effectiveness of the proposed method has been demonstrated using a simulated example.
Stochastic Models for Precipitable Water in Convection
NASA Astrophysics Data System (ADS)
Leung, Kimberly
Atmospheric precipitable water vapor (PWV) is the amount of water vapor in the atmosphere within a vertical column of unit cross-sectional area and is a critically important parameter of precipitation processes. However, accurate high-frequency and long-term observations of PWV in the sky were impossible until the availability of modern instruments such as radar. The United States Department of Energy (DOE)'s Atmospheric Radiation Measurement (ARM) Program facility made the first systematic and high-resolution observations of PWV at Darwin, Australia since 2002. At a resolution of 20 seconds, this time series allowed us to examine the volatility of PWV, including fractal behavior with dimension equal to 1.9, higher than the Brownian motion dimension of 1.5. Such strong fractal behavior calls for stochastic differential equation modeling in an attempt to address some of the difficulties of convective parameterization in various kinds of climate models, ranging from general circulation models (GCM) to weather research forecasting (WRF) models. This important observed data at high resolution can capture the fractal behavior of PWV and enables stochastic exploration into the next generation of climate models which considers scales from micrometers to thousands of kilometers. As a first step, this thesis explores a simple stochastic differential equation model of water mass balance for PWV and assesses accuracy, robustness, and sensitivity of the stochastic model. A 1000-day simulation allows for the determination of the best-fitting 25-day period as compared to data from the TWP-ICE field campaign conducted out of Darwin, Australia in early 2006. The observed data and this portion of the simulation had a correlation coefficient of 0.6513 and followed similar statistics and low-resolution temporal trends. Building on the point model foundation, a similar algorithm was applied to the National Center for Atmospheric Research (NCAR)'s existing single-column model as a test
NASA Technical Reports Server (NTRS)
Sadunas, J. A.; French, E. P.; Sexton, H.
1973-01-01
A 1/25 scale model S-2 stage base region thermal environment test is presented. Analytical results are included which reflect the effect of engine operating conditions, model scale, turbo-pump exhaust gas injection on base region thermal environment. Comparisons are made between full scale flight data, model test data, and analytical results. The report is prepared in two volumes. The description of analytical predictions and comparisons with flight data are presented. Tabulation of the test data is provided.
Stochastic resonance in a tristable optomechanical system
NASA Astrophysics Data System (ADS)
Fan, Bixuan; Xie, Min
2017-02-01
In this work we theoretically investigate the stochastic resonance (SR) effect in an optomechanical membrane system subject to two weak signals (one optical field and one mechanical force). The quadratic optomechanical coupling allows us to find a region with tristability where the noise-activated stochastic switching among three stable states occurs and SR phenomena are observed at the cooperation of input signals and noise. We show that the mechanical force and the optical field respectively serve as an additive signal and a multiplicative signal to the membrane position, and they induce completely different SR behaviors. Moreover, when two signals coexist the SR effect can be enhanced, and the beating effect appears in the SR synchronization process with unsynchronized signals.
From stochastic resonance to brain waves
NASA Astrophysics Data System (ADS)
Balázsi, G.; Kish, L. B.
2000-01-01
Biological neurons are good examples of a threshold device - this is why neural systems are in the focus when looking for realization of Stochastic Resonance (SR) and spatio-temporal stochastic resonance (STSR) phenomena. In this Letter a simple integrate-and fire model is used to demonstrate the possibility of STSR in a chain of neurons. The theoretical and computational models so far suggest that SR and STSR could occur in neural systems. However, how significant is the role played by these phenomena and what implications might they have on neurobiology is still a question. Because the direct biological proof of SR and STSR seems to be a tough issue one might look at indirect ways to decide whether the internal noise plays any constructive role in the nervous system. A loop of neurons is shown to have interesting features (frequency selection) which might supply a clue for answering the previous question.
Aquifer Structure Identification Using Stochastic Inversion
Harp, Dylan R; Dai, Zhenxue; Wolfsberg, Andrew V; Vrugt, Jasper A
2008-01-01
This study presents a stochastic inverse method for aquifer structure identification using sparse geophysical and hydraulic response data. The method is based on updating structure parameters from a transition probability model to iteratively modify the aquifer structure and parameter zonation. The method is extended to the adaptive parameterization of facies hydraulic parameters by including these parameters as optimization variables. The stochastic nature of the statistical structure parameters leads to nonconvex objective functions. A multi-method genetically adaptive evolutionary approach (AMALGAM-SO) was selected to perform the inversion given its search capabilities. Results are obtained as a probabilistic assessment of facies distribution based on indicator cokriging simulation of the optimized structural parameters. The method is illustrated by estimating the structure and facies hydraulic parameters of a synthetic example with a transient hydraulic response.
Stochastic Gene Expression in a Single Cell
NASA Astrophysics Data System (ADS)
Elowitz, Michael B.; Levine, Arnold J.; Siggia, Eric D.; Swain, Peter S.
2002-08-01
Clonal populations of cells exhibit substantial phenotypic variation. Such heterogeneity can be essential for many biological processes and is conjectured to arise from stochasticity, or noise, in gene expression. We constructed strains of Escherichia coli that enable detection of noise and discrimination between the two mechanisms by which it is generated. Both stochasticity inherent in the biochemical process of gene expression (intrinsic noise) and fluctuations in other cellular components (extrinsic noise) contribute substantially to overall variation. Transcription rate, regulatory dynamics, and genetic factors control the amplitude of noise. These results establish a quantitative foundation for modeling noise in genetic networks and reveal how low intracellular copy numbers of molecules can fundamentally limit the precision of gene regulation.
Entropy production of doubly stochastic quantum channels
Müller-Hermes, Alexander; Stilck França, Daniel Wolf, Michael M.
2016-02-15
We study the entropy increase of quantum systems evolving under primitive, doubly stochastic Markovian noise and thus converging to the maximally mixed state. This entropy increase can be quantified by a logarithmic-Sobolev constant of the Liouvillian generating the noise. We prove a universal lower bound on this constant that stays invariant under taking tensor-powers. Our methods involve a new comparison method to relate logarithmic-Sobolev constants of different Liouvillians and a technique to compute logarithmic-Sobolev inequalities of Liouvillians with eigenvectors forming a projective representation of a finite abelian group. Our bounds improve upon similar results established before and as an application we prove an upper bound on continuous-time quantum capacities. In the last part of this work we study entropy production estimates of discrete-time doubly stochastic quantum channels by extending the framework of discrete-time logarithmic-Sobolev inequalities to the quantum case.
Stochasticity effects in quantum radiation reaction.
Neitz, N; Di Piazza, A
2013-08-02
When an ultrarelativistic electron beam collides with a sufficiently intense laser pulse, radiation-reaction effects can strongly alter the beam dynamics. In the realm of classical electrodynamics, radiation reaction has a beneficial effect on the electron beam as it tends to reduce its energy spread. Here we show that when quantum effects become important, radiation reaction induces the opposite effect; i.e., the energy distribution of the electron beam spreads out after interacting with the laser pulse. We identify the physical origin of this opposite tendency in the intrinsic stochasticity of photon emission, which becomes substantial in the quantum regime. Our numerical simulations indicate that the predicted effects of the stochasticity can be measured already with presently available lasers and electron accelerators.
Dynamic range of hypercubic stochastic excitable media
NASA Astrophysics Data System (ADS)
Assis, Vladimir R. V.; Copelli, Mauro
2008-01-01
We study the response properties of d -dimensional hypercubic excitable networks to a stochastic stimulus. Each site, modeled either by a three-state stochastic susceptible-infected-recovered-susceptible system or by the probabilistic Greenberg-Hastings cellular automaton, is continuously and independently stimulated by an external Poisson rate h . The response function (mean density of active sites ρ versus h ) is obtained via simulations (for d=1,2,3,4 ) and mean-field approximations at the single-site and pair levels (∀d) . In any dimension, the dynamic range and sensitivity of the response function are maximized precisely at the nonequilibrium phase transition to self-sustained activity, in agreement with a reasoning recently proposed. Moreover, the maximum dynamic range attained at a given dimension d is a decreasing function of d .
Stochastic simulations of genetic switch systems.
Loinger, Adiel; Lipshtat, Azi; Balaban, Nathalie Q; Biham, Ofer
2007-02-01
Genetic switch systems with mutual repression of two transcription factors are studied using deterministic methods (rate equations) and stochastic methods (the master equation and Monte Carlo simulations). These systems exhibit bistability, namely two stable states such that spontaneous transitions between them are rare. Induced transitions may take place as a result of an external stimulus. We study several variants of the genetic switch and examine the effects of cooperative binding, exclusive binding, protein-protein interactions, and degradation of bound repressors. We identify the range of parameters in which bistability takes place, enabling the system to function as a switch. Numerous studies have concluded that cooperative binding is a necessary condition for the emergence of bistability in these systems. We show that a suitable combination of network structure and stochastic effects gives rise to bistability even without cooperative binding. The average time between spontaneous transitions is evaluated as a function of the biological parameters.
Stochasticity of comet P/Slaughter-Burnham
NASA Technical Reports Server (NTRS)
Benest, Daniel; Gonczi, R.
1992-01-01
Three comets are now known to be at or near the 1/1 resonance with Jupiter: P/Slaughter-Burnham, P/Boethin and the newly discovered P/Ge-Wang. Although details of the individual orbits differ, the three comets have very similar dynamical behavior: their orbits show many transitions between the different types of resonant motion (satellite libration, anti-satellite libration, and circulating motion). The stochastic character of such cometary orbits, mainly due to encounters with Jupiter is investigated using Lyapunov Characteristic Indicators. For each comet of the group, we study the influences on the stochasticity of initial eccentricity, inclination, longitude of node, and l-l(sub J) (mean longitude of comet minus mean longitude of Jupiter). We present here our first results for P/Slaughter-Burnham.
Stochastic Precipitation Downscaling with Orographic Corrections
NASA Astrophysics Data System (ADS)
Brussolo, Elisa; von Hardenberg, Jost; Rebora, Nicola; Provenzale, Antonello
2010-05-01
Few existing stochastic precipitation downscaling methods take into account orography, even if orographic precipitation plays an important role in determining precipitation intensities at small scales, particularly in Alpine areas. In this work we present a modification of the RainFARM stochastic downscaling method (Rebora et al. 2006) in order to take into account orographic effects. The model is calibrated using an orographic signature obtained from a database of 450 pluviometric timeseries in North-Western Italy from 2004 to 2008. An out-of-sample verification is performed on data from 2009. We discuss the limitations and the applicability of this approach to downscaling of climate scenarios. References: N. Rebora, L. Ferraris, J. von Hardenberg, A. Provenzale, 2006: RainFARM: Rainfall Downscaling by a Filtered Autoregressive Model. J. Hydrometeorology, 7, 724-738.
Stochastic magnetization dynamics in single domain particles
NASA Astrophysics Data System (ADS)
Giordano, Stefano; Dusch, Yannick; Tiercelin, Nicolas; Pernod, Philippe; Preobrazhensky, Vladimir
2013-06-01
Magnetic particles are largely utilized in several applications ranging from magnetorheological fluids to bioscience and from nanothechnology to memories or logic devices. The behavior of each single particle at finite temperature (under thermal stochastic fluctuations) plays a central role in determining the response of the whole physical system taken into consideration. Here, the magnetization evolution is studied through the Landau-Lifshitz-Gilbert formalism and the non-equilibrium statistical mechanics is introduced with the Langevin and Fokker-Planck methodologies. As result of the combination of such techniques we analyse the stochastic magnetization dynamics and we numerically determine the convergence time, measuring the velocity of attainment of thermodynamic equilibrium, as function of the system temperature.
Stochastic cooling of a high energy collider
Blaskiewicz, M.; Brennan, J.M.; Lee, R.C.; Mernick, K.
2011-09-04
Gold beams in RHIC revolve more than a billion times over the course of a data acquisition session or store. During operations with these heavy ions the event rates in the detectors decay as the beams diffuse. A primary cause for this beam diffusion is small angle Coloumb scattering of the particles within the bunches. This intra-beam scattering (IBS) is particularly problematic at high energy because the negative mass effect removes the possibility of even approximate thermal equilibrium. Stochastic cooling can combat IBS. A theory of bunched beam cooling was developed in the early eighties and stochastic cooling systems for the SPS and the Tevatron were explored. Cooling for heavy ions in RHIC was also considered.
Stochastic robustness of linear control systems
NASA Technical Reports Server (NTRS)
Stengel, Robert F.; Ryan, Laura E.
1990-01-01
A simple numerical procedure for estimating the stochastic robustness of a linear, time-invariant system is described. Monte Carlo evaluation of the system's eigenvalues allows the probability of instability and the related stochastic root locus to be estimated. This definition of robustness is an alternative to existing deterministic definitions that address both structured and unstructured parameter variations directly. This analysis approach treats not only Gaussian parameter uncertainties but non-Gaussian cases, including uncertain-but-bounded variations. Trivial extensions of the procedure admit alternate discriminants to be considered. Thus, the probabilities that stipulated degrees of instability will be exceeded or that closed-loop roots will leave desirable regions also can be estimated. Results are particularly amenable to graphical presentation.
Double inverse stochastic resonance with dynamic synapses
NASA Astrophysics Data System (ADS)
Uzuntarla, Muhammet; Torres, Joaquin J.; So, Paul; Ozer, Mahmut; Barreto, Ernest
2017-01-01
We investigate the behavior of a model neuron that receives a biophysically realistic noisy postsynaptic current based on uncorrelated spiking activity from a large number of afferents. We show that, with static synapses, such noise can give rise to inverse stochastic resonance (ISR) as a function of the presynaptic firing rate. We compare this to the case with dynamic synapses that feature short-term synaptic plasticity and show that the interval of presynaptic firing rate over which ISR exists can be extended or diminished. We consider both short-term depression and facilitation. Interestingly, we find that a double inverse stochastic resonance (DISR), with two distinct wells centered at different presynaptic firing rates, can appear.
A stochastic model of eye lens growth.
Šikić, Hrvoje; Shi, Yanrong; Lubura, Snježana; Bassnett, Steven
2015-07-07
The size and shape of the ocular lens must be controlled with precision if light is to be focused sharply on the retina. The lifelong growth of the lens depends on the production of cells in the anterior epithelium. At the lens equator, epithelial cells differentiate into fiber cells, which are added to the surface of the existing fiber cell mass, increasing its volume and area. We developed a stochastic model relating the rates of cell proliferation and death in various regions of the lens epithelium to deposition of fiber cells and radial lens growth. Epithelial population dynamics were modeled as a branching process with emigration and immigration between proliferative zones. Numerical simulations were in agreement with empirical measurements and demonstrated that, operating within the strict confines of lens geometry, a stochastic growth engine can produce the smooth and precise growth necessary for lens function. Copyright © 2015 Elsevier Ltd. All rights reserved.
Differential form representation of stochastic electromagnetic fields
NASA Astrophysics Data System (ADS)
Haider, Michael; Russer, Johannes A.
2017-09-01
In this work, we revisit the theory of stochastic electromagnetic fields using exterior differential forms. We present a short overview as well as a brief introduction to the application of differential forms in electromagnetic theory. Within the framework of exterior calculus we derive equations for the second order moments, describing stochastic electromagnetic fields. Since the resulting objects are continuous quantities in space, a discretization scheme based on the Method of Moments (MoM) is introduced for numerical treatment. The MoM is applied in such a way, that the notation of exterior calculus is maintained while we still arrive at the same set of algebraic equations as obtained for the case of formulating the theory using the traditional notation of vector calculus. We conclude with an analytic calculation of the radiated electric field of two Hertzian dipole, excited by uncorrelated random currents.
The stochastic Gross Pitaevskii equation: II
NASA Astrophysics Data System (ADS)
Gardiner, C. W.; Davis, M. J.
2003-12-01
We provide a derivation of a more accurate version of the stochastic Gross-Pitaevskii equation, as introduced by Gardiner et al (2002 J. Phys. B: At. Mol. Opt. Phys. 35 1555). This derivation does not rely on the concept of local energy and momentum conservation and is based on a quasiclassical Wigner function representation of a 'high temperature' master equation for a Bose gas, which includes only modes below an energy cut-off ER that are sufficiently highly occupied (the condensate band). The modes above this cut-off (the non-condensate band) are treated as being essentially thermalized. The interaction between these two bands, known as growth and scattering processes, provides noise and damping terms in the equation of motion for the condensate band, which we call the stochastic Gross-Pitaevskii equation. This approach is distinguished by the control of the approximations made in its derivation and by the feasibility of its numerical implementation.
Conditional reversibility in nonequilibrium stochastic systems
NASA Astrophysics Data System (ADS)
Bonança, Marcus V. S.; Jarzynski, Christopher
2016-02-01
For discrete-state stochastic systems obeying Markovian dynamics, we establish the counterpart of the conditional reversibility theorem obtained by Gallavotti for deterministic systems [Ann. de l'Institut Henri Poincaré (A) 70, 429 (1999)]. Our result states that stochastic trajectories conditioned on opposite values of entropy production are related by time reversal, in the long-time limit. In other words, the probability of observing a particular sequence of events, given a long trajectory with a specified entropy production rate σ , is the same as the probability of observing the time-reversed sequence of events, given a trajectory conditioned on the opposite entropy production, -σ , where both trajectories are sampled from the same underlying Markov process. To obtain our result, we use an equivalence between conditioned ("microcanonical") and biased ("canonical") ensembles of nonequilibrium trajectories. We provide an example to illustrate our findings.
Estimating optimal partitions for stochastic complex systems
NASA Astrophysics Data System (ADS)
Hirata, Yoshito; Aihara, Kazuyuki
2013-06-01
Partitions provide simple symbolic representations for complex systems. For a deterministic system, a generating partition establishes one-to-one correspondence between an orbit and the infinite symbolic sequence generated by the partition. For a stochastic system, however, a generating partition does not exist. In this paper, we propose a method to obtain a partition that best specifies the locations of points for a time series generated from a stochastic system by using the corresponding symbolic sequence under a constraint of an information rate. When the length of the substrings is limited with a finite length, the method coincides with that for estimating a generating partition from a time series generated from a deterministic system. The two real datasets analyzed in Kennel and Buhl, Phys. Rev. Lett. 91, 084102 (2003), are reanalyzed with the proposed method to understand their underlying dynamics intuitively.
Conditional reversibility in nonequilibrium stochastic systems.
Bonança, Marcus V S; Jarzynski, Christopher
2016-02-01
For discrete-state stochastic systems obeying Markovian dynamics, we establish the counterpart of the conditional reversibility theorem obtained by Gallavotti for deterministic systems [Ann. de l'Institut Henri Poincaré (A) 70, 429 (1999)]. Our result states that stochastic trajectories conditioned on opposite values of entropy production are related by time reversal, in the long-time limit. In other words, the probability of observing a particular sequence of events, given a long trajectory with a specified entropy production rate σ, is the same as the probability of observing the time-reversed sequence of events, given a trajectory conditioned on the opposite entropy production, -σ, where both trajectories are sampled from the same underlying Markov process. To obtain our result, we use an equivalence between conditioned ("microcanonical") and biased ("canonical") ensembles of nonequilibrium trajectories. We provide an example to illustrate our findings.
Intelligent controllers as hierarchical stochastic automata.
Lima, P U; Saridis, G N
1999-01-01
This paper introduces a design methodology for intelligent controllers, based on a hierarchical linguistic model of command translation by tasks-primitive tasks-primitive actions, and on a two-stage hierarchical learning stochastic automaton that models the translation interfaces of a three-level hierarchical intelligent controller. The methodology relies on the designer's a priori knowledge on how to implement by primitive actions the different primitive tasks which define the intelligent controller. A cost function applicable to any primitive task is introduced and used to learn on-line the optimal choices from the corresponding predesigned sets of primitive actions. The same concept applies to the optimal tasks for each command, whose choice is based on conflict sets of stochastic grammar productions. Optional designs can be compared using this performance measure. A particular design evolves towards the command translation (by tasks-primitive tasks-primitive actions) that minimizes the cost function.
COSMIC DUST AGGREGATION WITH STOCHASTIC CHARGING
Matthews, Lorin S.; Hyde, Truell W.; Shotorban, Babak
2013-10-20
The coagulation of cosmic dust grains is a fundamental process which takes place in astrophysical environments, such as presolar nebulae and circumstellar and protoplanetary disks. Cosmic dust grains can become charged through interaction with their plasma environment or other processes, and the resultant electrostatic force between dust grains can strongly affect their coagulation rate. Since ions and electrons are collected on the surface of the dust grain at random time intervals, the electrical charge of a dust grain experiences stochastic fluctuations. In this study, a set of stochastic differential equations is developed to model these fluctuations over the surface of an irregularly shaped aggregate. Then, employing the data produced, the influence of the charge fluctuations on the coagulation process and the physical characteristics of the aggregates formed is examined. It is shown that dust with small charges (due to the small size of the dust grains or a tenuous plasma environment) is affected most strongly.
Entropy production of doubly stochastic quantum channels
NASA Astrophysics Data System (ADS)
Müller-Hermes, Alexander; Stilck França, Daniel; Wolf, Michael M.
2016-02-01
We study the entropy increase of quantum systems evolving under primitive, doubly stochastic Markovian noise and thus converging to the maximally mixed state. This entropy increase can be quantified by a logarithmic-Sobolev constant of the Liouvillian generating the noise. We prove a universal lower bound on this constant that stays invariant under taking tensor-powers. Our methods involve a new comparison method to relate logarithmic-Sobolev constants of different Liouvillians and a technique to compute logarithmic-Sobolev inequalities of Liouvillians with eigenvectors forming a projective representation of a finite abelian group. Our bounds improve upon similar results established before and as an application we prove an upper bound on continuous-time quantum capacities. In the last part of this work we study entropy production estimates of discrete-time doubly stochastic quantum channels by extending the framework of discrete-time logarithmic-Sobolev inequalities to the quantum case.
A Stochastic Model of Eye Lens Growth
Šikić, Hrvoje; Shi, Yanrong; Lubura, Snježana; Bassnett, Steven
2015-01-01
The size and shape of the ocular lens must be controlled with precision if light is to be focused sharply on the retina. The lifelong growth of the lens depends on the production of cells in the anterior epithelium. At the lens equator, epithelial cells differentiate into fiber cells, which are added to the surface of the existing fiber cell mass, increasing its volume and area. We developed a stochastic model relating the rates of cell proliferation and death in various regions of the lens epithelium to deposition of fiber cells and lens growth. Epithelial population dynamics were modeled as a branching process with emigration and immigration between various proliferative zones. Numerical simulations were in agreement with empirical measurements and demonstrated that, operating within the strict confines of lens geometry, a stochastic growth engine can produce the smooth and precise growth necessary for lens function. PMID:25816743
Stochastic Chaos in a Turbulent Swirling Flow
NASA Astrophysics Data System (ADS)
Faranda, D.; Sato, Y.; Saint-Michel, B.; Wiertel, C.; Padilla, V.; Dubrulle, B.; Daviaud, F.
2017-07-01
We report the experimental evidence of the existence of a random attractor in a fully developed turbulent swirling flow. By defining a global observable which tracks the asymmetry in the flux of angular momentum imparted to the flow, we can first reconstruct the associated turbulent attractor and then follow its route towards chaos. We further show that the experimental attractor can be modeled by stochastic Duffing equations, that match the quantitative properties of the experimental flow, namely, the number of quasistationary states and transition rates among them, the effective dimensions, and the continuity of the first Lyapunov exponents. Such properties can be recovered neither using deterministic models nor using stochastic differential equations based on effective potentials obtained by inverting the probability distributions of the experimental global observables. Our findings open the way to low-dimensional modeling of systems featuring a large number of degrees of freedom and multiple quasistationary states.
An exact accelerated stochastic simulation algorithm
NASA Astrophysics Data System (ADS)
Mjolsness, Eric; Orendorff, David; Chatelain, Philippe; Koumoutsakos, Petros
2009-04-01
An exact method for stochastic simulation of chemical reaction networks, which accelerates the stochastic simulation algorithm (SSA), is proposed. The present "ER-leap" algorithm is derived from analytic upper and lower bounds on the multireaction probabilities sampled by SSA, together with rejection sampling and an adaptive multiplicity for reactions. The algorithm is tested on a number of well-quantified reaction networks and is found experimentally to be very accurate on test problems including a chaotic reaction network. At the same time ER-leap offers a substantial speedup over SSA with a simulation time proportional to the 2/3 power of the number of reaction events in a Galton-Watson process.
An exact accelerated stochastic simulation algorithm
Mjolsness, Eric; Orendorff, David; Chatelain, Philippe; Koumoutsakos, Petros
2009-01-01
An exact method for stochastic simulation of chemical reaction networks, which accelerates the stochastic simulation algorithm (SSA), is proposed. The present “ER-leap” algorithm is derived from analytic upper and lower bounds on the multireaction probabilities sampled by SSA, together with rejection sampling and an adaptive multiplicity for reactions. The algorithm is tested on a number of well-quantified reaction networks and is found experimentally to be very accurate on test problems including a chaotic reaction network. At the same time ER-leap offers a substantial speedup over SSA with a simulation time proportional to the 2∕3 power of the number of reaction events in a Galton–Watson process. PMID:19368432
Stochastic model for protein flexibility analysis.
Xia, Kelin; Wei, Guo-Wei
2013-12-01
Protein flexibility is an intrinsic property and plays a fundamental role in protein functions. Computational analysis of protein flexibility is crucial to protein function prediction, macromolecular flexible docking, and rational drug design. Most current approaches for protein flexibility analysis are based on Hamiltonian mechanics. We introduce a stochastic model to study protein flexibility. The essential idea is to analyze the free induction decay of a perturbed protein structural probability, which satisfies the master equation. The transition probability matrix is constructed by using probability density estimators including monotonically decreasing radial basis functions. We show that the proposed stochastic model gives rise to some of the best predictions of Debye-Waller factors or B factors for three sets of protein data introduced in the literature.
Characterizing phonon dynamics using stochastic sampling
Kunal, K.; Aluru, N. R.
2016-03-21
Predicting phonon relaxation time from molecular dynamics (MD) requires a long simulation time to compute the mode energy auto-correlation function. Here, we present an alternative approach to infer the phonon life-time from an approximate form of the energy auto-correlation function. The method requires as an input a set of sampled equilibrium configurations. A stochastic sampling method is used to generate the equilibrium configurations. We consider a truncated Taylor series expansion of the phonon energy auto-correlation function. The different terms in the truncated correlation function are obtained using the stochastic sampling approach. The expansion terms, thus, obtained are in good agreement with the corresponding values obtained using MD. We then use the approximate function to compute the phonon relaxation time. The relaxation time computed using this method is compared with that obtained from the exact correlation function. The two values are in agreement with each other.
Noise-free logical stochastic resonance.
Gupta, Animesh; Sohane, Aman; Kohar, Vivek; Murali, K; Sinha, Sudeshna
2011-11-01
The phenomena of logical stochastic resonance (LSR) was demonstrated recently [Phys. Rev. Lett. 102, 104101 (2009)]: namely, when a bistable system is driven by two inputs it consistently yields a response mirroring a logic function of the two inputs in an optimal window of moderate noise. Here we examine the intriguing possibility of obtaining dynamical behavior equivalent to LSR in a noise-free bistable system, subjected only to periodic forcing, such as sinusoidal driving or rectangular pulse trains. We find that such a system, despite having no stochastic influence, also yields phenomena analogous to LSR, in an appropriate window of frequency and amplitude of the periodic forcing. The results are corroborated by circuit experiments.
Stochastic dynamic models and Chebyshev splines
Fan, Ruzong; Zhu, Bin; Wang, Yuedong
2015-01-01
In this article, we establish a connection between a stochastic dynamic model (SDM) driven by a linear stochastic differential equation (SDE) and a Chebyshev spline, which enables researchers to borrow strength across fields both theoretically and numerically. We construct a differential operator for the penalty function and develop a reproducing kernel Hilbert space (RKHS) induced by the SDM and the Chebyshev spline. The general form of the linear SDE allows us to extend the well-known connection between an integrated Brownian motion and a polynomial spline to a connection between more complex diffusion processes and Chebyshev splines. One interesting special case is connection between an integrated Ornstein–Uhlenbeck process and an exponential spline. We use two real data sets to illustrate the integrated Ornstein–Uhlenbeck process model and exponential spline model and show their estimates are almost identical. PMID:26045632
Relative dispersion in 2D stochastic flows
NASA Astrophysics Data System (ADS)
Piterbarg, L. I.
We investigate the relative dispersion for two types of stochastic flows—Brownian flow (Kraichnan model) and a flow with memory (inertial particles). In the first case well-known asymptotics are rigorously derived for a self-similar spectrum of the velocity field by using a half-century-old Feller's theorem. Exact limits of the asymptotics and exact values for dimensionless constants are obtained. The second part of the paper addresses a relatively new object: the first-order Markov stochastic flow modelling inertial particle motion. Both local and non-local dynamics are investigated. In the first case an exact exponential asymptotic is obtained for the relative dispersion. In turn, two regimes are considered in the case of non-smooth forcing: weak and strong turbulence. For weak turbulence the obtained asymptotic of relative dispersion is similar to that of the Brownian flow. As for strong turbulence, an upper bound is obtained for the scaling of relative dispersion.
Stochasticity in the yeast mating pathway
NASA Astrophysics Data System (ADS)
Wang, Hong-Li; Fu, Zheng-Ping; Xu, Xin-Hang; Ouyang, Qi
2009-05-01
We report stochastic simulations of the yeast mating signal transduction pathway. The effects of intrinsic and external noise, the influence of cell-to-cell difference in the pathway capacity, and noise propagation in the pathway have been examined. The stochastic temporal behaviour of the pathway is found to be robust to the influence of inherent fluctuations, and intrinsic noise propagates in the pathway in a uniform pattern when the yeasts are treated with pheromones of different stimulus strengths and of varied fluctuations. In agreement with recent experimental findings, extrinsic noise is found to play a more prominent role than intrinsic noise in the variability of proteins. The occurrence frequency for the reactions in the pathway are also examined and a more compact network is obtained by dropping most of the reactions of least occurrence.
Modeling the evolution space of breakage fusion bridge cycles with a stochastic folding process.
Greenman, C D; Cooke, S L; Marshall, J; Stratton, M R; Campbell, P J
2016-01-01
Breakage-fusion-bridge cycles in cancer arise when a broken segment of DNA is duplicated and an end from each copy joined together. This structure then 'unfolds' into a new piece of palindromic DNA. This is one mechanism responsible for the localised amplicons observed in cancer genome data. Here we study the evolution space of breakage-fusion-bridge structures in detail. We firstly consider discrete representations of this space with 2-d trees to demonstrate that there are [Formula: see text] qualitatively distinct evolutions involving [Formula: see text] breakage-fusion-bridge cycles. Secondly we consider the stochastic nature of the process to show these evolutions are not equally likely, and also describe how amplicons become localized. Finally we highlight these methods by inferring the evolution of breakage-fusion-bridge cycles with data from primary tissue cancer samples.
Stochastic histories of refractory interstellar dust
NASA Technical Reports Server (NTRS)
Liffman, Kurt; Clayton, Donald D.
1988-01-01
Histories of refractory interstellar dust particles (IDPs) are calculated. The profile of a particle population is assembled from a large number of stochastic, or Monte Carlo, histories of single particles; the probabilities for each of the events that may befall a given particle are specified, and the particle's history is unfolded by a sequence of random numbers. The assumptions that are made and the techniques of the calculation are described together with the results obtained. Several technical demonstrations are presented.
STOCHASTIC COOLING STUDIES IN RHIC, II.
BLASKIEWICZ,M.BRENNAN,J.M.WEI,J.
2004-07-05
Intra-beam scattering (IBS) is unavoidable for highly charged heavy ions and causes emittance growth during the store for collision physics. A longitudinal bunched beam stochastic cooling system will confine the bunch within the RF bucket increasing the useful luminosity. We describe a series of measurements in RHIC that have been used to verify our understanding of the relevant physics and the cooling system architecture that is being prototyped.
Stochastic histories of refractory interstellar dust
NASA Technical Reports Server (NTRS)
Liffman, Kurt; Clayton, Donald D.
1988-01-01
Histories of refractory interstellar dust particles (IDPs) are calculated. The profile of a particle population is assembled from a large number of stochastic, or Monte Carlo, histories of single particles; the probabilities for each of the events that may befall a given particle are specified, and the particle's history is unfolded by a sequence of random numbers. The assumptions that are made and the techniques of the calculation are described together with the results obtained. Several technical demonstrations are presented.
Lie algebras of classical and stochastic electrodynamics
NASA Astrophysics Data System (ADS)
Neto, J. J. Soares; Vianna, J. D. M.
1994-03-01
The Lie algebras associated with infinitesimal symmetry transformations of third-order differential equations of interest to classical electrodynamics and stochastic electrodynamics have been obtained. The structure constants for a general case are presented and the Lie algebra for each particular application is easily achieved. By the method used here it is not necessary to know the explicit expressions of the infinitesimal generators in order to determine the structure constants of the Lie algebra.
The Foundations of Linear Stochastic Electrodynamics
NASA Astrophysics Data System (ADS)
Peña, L. De La; Cetto, A. M.
2006-03-01
An analysis is briefly presented of the possible causes of the failure of stochastic electrodynamics (SED) when applied to systems with nonlinear forces, on the basis that the main principles of the theory are correct. In light of this analysis, an alternative approach to the theory is discussed, whose postulates allow to establish contact with quantum mechanics in a natural way. The ensuing theory, linear SED, confirms the essential role of the vacuum particle interaction as the source of quantum phenomena.
Modeling heart rate variability by stochastic feedback
NASA Technical Reports Server (NTRS)
Amaral, L. A.; Goldberger, A. L.; Stanley, H. E.
1999-01-01
We consider the question of how the cardiac rhythm spontaneously self-regulates and propose a new mechanism as a possible answer. We model the neuroautonomic regulation of the heart rate as a stochastic feedback system and find that the model successfully accounts for key characteristics of cardiac variability, including the 1/f power spectrum, the functional form and scaling of the distribution of variations of the interbeat intervals, and the correlations in the Fourier phases which indicate nonlinear dynamics.
Stochastic approximation boosting for incomplete data problems.
Sexton, Joseph; Laake, Petter
2009-12-01
Boosting is a powerful approach to fitting regression models. This article describes a boosting algorithm for likelihood-based estimation with incomplete data. The algorithm combines boosting with a variant of stochastic approximation that uses Markov chain Monte Carlo to deal with the missing data. Applications to fitting generalized linear and additive models with missing covariates are given. The method is applied to the Pima Indians Diabetes Data where over half of the cases contain missing values.
Moment Closure for the Stochastic Logistic Model
2006-01-16
for Collaborative Biotech- nologies through grant DAAD19-03-D-0004 from the U.S. Army Research Office and by the National Science Foundation under Grant...No. CCR-0311084. 2 abhi@engineering.ucsb.edu, hespanha@ece.ucsb.edu Preprint submitted to Elsevier Science 16 January 2006 Report Documentation Page...Comput. Science . Springer-Verlag, Berlin, pp. 387–401. Hespanha, J. P., Singh, A., 2005. Stochastic models for chemically reacting systems using
Stochastic Games with Average Payoff Criterion
Ghosh, M. K.; Bagchi, A.
1998-11-15
We study two-person stochastic games on a Polish state and compact action spaces and with average payoff criterion under a certain ergodicity condition. For the zero-sum game we establish the existence of a value and stationary optimal strategies for both players. For the nonzero-sum case the existence of Nash equilibrium in stationary strategies is established under certain separability conditions.
Stochastic electromagnetic radiation of complex sources.
Naus, H W L
2007-08-01
The emission of electromagnetic radiation by localized complex electric charge and current distributions is studied. A statistical formalism in terms of general dynamical multipole fields is developed. The appearing coefficients are treated as stochastic variables. Hereby as much as possible a priori physical knowledge is exploited. First results of simulated statistical electromagnetic fields as a function of position are presented. Sampling this field at one point approximates its resulting probability density.
Modeling heart rate variability by stochastic feedback
NASA Technical Reports Server (NTRS)
Amaral, L. A.; Goldberger, A. L.; Stanley, H. E.
1999-01-01
We consider the question of how the cardiac rhythm spontaneously self-regulates and propose a new mechanism as a possible answer. We model the neuroautonomic regulation of the heart rate as a stochastic feedback system and find that the model successfully accounts for key characteristics of cardiac variability, including the 1/f power spectrum, the functional form and scaling of the distribution of variations of the interbeat intervals, and the correlations in the Fourier phases which indicate nonlinear dynamics.
Stochastic Nonlinear Dynamics of Floating Structures
1994-08-03
examples of colored noise filters exist in the literature. Billah and Shinozuka [4] use the following Tr/(t) = -y(t) + F(t), (8) where rc is the...several sources such as Billah and Shinozuka [6]. Because the Fokker-Planck equation requires that the governing equations be cast as a series of first...Nonlinear Stochastic Dynamics Engineering systems, pages 87- 100, New York, 1987. IUTAM, Springer-Verlag. [6] K.Y.R. Billah and M. Shinozuka
Stochastic behavior of nanoscale dielectric wall buckling.
Friedman, Lawrence H; Levin, Igor; Cook, Robert F
2016-03-01
The random buckling patterns of nanoscale dielectric walls are analyzed using a nonlinear multi-scale stochastic method that combines experimental measurements with simulations. The dielectric walls, approximately 200 nm tall and 20 nm wide, consist of compliant, low dielectric constant (low-k) fins capped with stiff, compressively stressed TiN lines that provide the driving force for buckling. The deflections of the buckled lines exhibit sinusoidal pseudoperiodicity with amplitude fluctuation and phase decorrelation arising from stochastic variations in wall geometry, properties, and stress state at length scales shorter than the characteristic deflection wavelength of about 1000 nm. The buckling patterns are analyzed and modeled at two length scales: a longer scale (up to 5000 nm) that treats randomness as a longer-scale measurable quantity, and a shorter-scale (down to 20 nm) that treats buckling as a deterministic phenomenon. Statistical simulation is used to join the two length scales. Through this approach, the buckling model is validated and material properties and stress states are inferred. In particular, the stress state of TiN lines in three different systems is determined, along with the elastic moduli of low-k fins and the amplitudes of the small-scale random fluctuations in wall properties-all in the as-processed state. The important case of stochastic effects giving rise to buckling in a deterministically sub-critical buckling state is demonstrated. The nonlinear multiscale stochastic analysis provides guidance for design of low-k structures with acceptable buckling behavior and serves as a template for how randomness that is common to nanoscale phenomena might be measured and analyzed in other contexts.
Stochastic differential equations and turbulent dispersion
NASA Technical Reports Server (NTRS)
Durbin, P. A.
1983-01-01
Aspects of the theory of continuous stochastic processes that seem to contribute to an understanding of turbulent dispersion are introduced and the theory and philosophy of modelling turbulent transport is emphasized. Examples of eddy diffusion examined include shear dispersion, the surface layer, and channel flow. Modeling dispersion with finite-time scale is considered including the Langevin model for homogeneous turbulence, dispersion in nonhomogeneous turbulence, and the asymptotic behavior of the Langevin model for nonhomogeneous turbulence.
Optimization Testbed Cometboards Extended into Stochastic Domain
NASA Technical Reports Server (NTRS)
Patnaik, Surya N.; Pai, Shantaram S.; Coroneos, Rula M.; Patnaik, Surya N.
2010-01-01
COMparative Evaluation Testbed of Optimization and Analysis Routines for the Design of Structures (CometBoards) is a multidisciplinary design optimization software. It was originally developed for deterministic calculation. It has now been extended into the stochastic domain for structural design problems. For deterministic problems, CometBoards is introduced through its subproblem solution strategy as well as the approximation concept in optimization. In the stochastic domain, a design is formulated as a function of the risk or reliability. Optimum solution including the weight of a structure, is also obtained as a function of reliability. Weight versus reliability traced out an inverted-S-shaped graph. The center of the graph corresponded to 50 percent probability of success, or one failure in two samples. A heavy design with weight approaching infinity could be produced for a near-zero rate of failure that corresponded to unity for reliability. Weight can be reduced to a small value for the most failure-prone design with a compromised reliability approaching zero. The stochastic design optimization (SDO) capability for an industrial problem was obtained by combining three codes: MSC/Nastran code was the deterministic analysis tool, fast probabilistic integrator, or the FPI module of the NESSUS software, was the probabilistic calculator, and CometBoards became the optimizer. The SDO capability requires a finite element structural model, a material model, a load model, and a design model. The stochastic optimization concept is illustrated considering an academic example and a real-life airframe component made of metallic and composite materials.
Planning with Continuous Resources in Stochastic Domains
NASA Technical Reports Server (NTRS)
Mausam, Mausau; Benazera, Emmanuel; Brafman, Roneu; Hansen, Eric
2005-01-01
We consider the problem of optimal planning in stochastic domains with metric resource constraints. Our goal is to generate a policy whose expected sum of rewards is maximized for a given initial state. We consider a general formulation motivated by our application domain--planetary exploration--in which the choice of an action at each step may depend on the current resource levels. We adapt the forward search algorithm AO* to handle our continuous state space efficiently.
Stochastic behavior of nanoscale dielectric wall buckling
Friedman, Lawrence H.; Levin, Igor; Cook, Robert F.
2016-01-01
The random buckling patterns of nanoscale dielectric walls are analyzed using a nonlinear multi-scale stochastic method that combines experimental measurements with simulations. The dielectric walls, approximately 200 nm tall and 20 nm wide, consist of compliant, low dielectric constant (low-k) fins capped with stiff, compressively stressed TiN lines that provide the driving force for buckling. The deflections of the buckled lines exhibit sinusoidal pseudoperiodicity with amplitude fluctuation and phase decorrelation arising from stochastic variations in wall geometry, properties, and stress state at length scales shorter than the characteristic deflection wavelength of about 1000 nm. The buckling patterns are analyzed and modeled at two length scales: a longer scale (up to 5000 nm) that treats randomness as a longer-scale measurable quantity, and a shorter-scale (down to 20 nm) that treats buckling as a deterministic phenomenon. Statistical simulation is used to join the two length scales. Through this approach, the buckling model is validated and material properties and stress states are inferred. In particular, the stress state of TiN lines in three different systems is determined, along with the elastic moduli of low-k fins and the amplitudes of the small-scale random fluctuations in wall properties—all in the as-processed state. The important case of stochastic effects giving rise to buckling in a deterministically sub-critical buckling state is demonstrated. The nonlinear multiscale stochastic analysis provides guidance for design of low-k structures with acceptable buckling behavior and serves as a template for how randomness that is common to nanoscale phenomena might be measured and analyzed in other contexts. PMID:27330220
Stochastic behavior of nanoscale dielectric wall buckling
Friedman, Lawrence H.; Levin, Igor; Cook, Robert F.
2016-03-21
The random buckling patterns of nanoscale dielectric walls are analyzed using a nonlinear multi-scale stochastic method that combines experimental measurements with simulations. The dielectric walls, approximately 200 nm tall and 20 nm wide, consist of compliant, low dielectric constant (low-k) fins capped with stiff, compressively stressed TiN lines that provide the driving force for buckling. The deflections of the buckled lines exhibit sinusoidal pseudoperiodicity with amplitude fluctuation and phase decorrelation arising from stochastic variations in wall geometry, properties, and stress state at length scales shorter than the characteristic deflection wavelength of about 1000 nm. The buckling patterns are analyzed and modeled at two length scales: a longer scale (up to 5000 nm) that treats randomness as a longer-scale measurable quantity, and a shorter-scale (down to 20 nm) that treats buckling as a deterministic phenomenon. Statistical simulation is used to join the two length scales. Through this approach, the buckling model is validated and material properties and stress states are inferred. In particular, the stress state of TiN lines in three different systems is determined, along with the elastic moduli of low-k fins and the amplitudes of the small-scale random fluctuations in wall properties—all in the as-processed state. The important case of stochastic effects giving rise to buckling in a deterministically sub-critical buckling state is demonstrated. The nonlinear multiscale stochastic analysis provides guidance for design of low-k structures with acceptable buckling behavior and serves as a template for how randomness that is common to nanoscale phenomena might be measured and analyzed in other contexts.
On a class of nonstationary stochastic processes
NASA Technical Reports Server (NTRS)
Miamee, A. G.; Hardin, Jay C.
1989-01-01
A new class of nonstationary stochastic processes is introduced and some of the essential properties of its members are investigated. This class is richer than the class of stationary processes and has the potential of modeling some nonstationary time series. The relation between these newly defined processes with other important classes of nonstationary processes is investigated. Several examples of linearly correlated processes which are not stationary, periodically correlated, or harmonizable are given.
Stochastic Stability of Pollicott-Ruelle Resonances
NASA Astrophysics Data System (ADS)
Drouot, Alexis
2017-08-01
Kinetic Brownian motion on the cosphere bundle of a Riemannian manifold M is a stochastic process that models the geodesic equation perturbed by a random white force of size {ɛ} . When M is compact and negatively curved, we show that the L 2-spectrum of the infinitesimal generator of this process converges to the Pollicott-Ruelle resonances of M as {ɛ} goes to 0.
Modeling stochastic noise in gene regulatory systems.
Meister, Arwen; Du, Chao; Li, Ye Henry; Wong, Wing Hung
2014-03-01
The Master equation is considered the gold standard for modeling the stochastic mechanisms of gene regulation in molecular detail, but it is too complex to solve exactly in most cases, so approximation and simulation methods are essential. However, there is still a lack of consensus about the best way to carry these out. To help clarify the situation, we review Master equation models of gene regulation, theoretical approximations based on an expansion method due to N.G. van Kampen and R. Kubo, and simulation algorithms due to D.T. Gillespie and P. Langevin. Expansion of the Master equation shows that for systems with a single stable steady-state, the stochastic model reduces to a deterministic model in a first-order approximation. Additional theory, also due to van Kampen, describes the asymptotic behavior of multistable systems. To support and illustrate the theory and provide further insight into the complex behavior of multistable systems, we perform a detailed simulation study comparing the various approximation and simulation methods applied to synthetic gene regulatory systems with various qualitative characteristics. The simulation studies show that for large stochastic systems with a single steady-state, deterministic models are quite accurate, since the probability distribution of the solution has a single peak tracking the deterministic trajectory whose variance is inversely proportional to the system size. In multistable stochastic systems, large fluctuations can cause individual trajectories to escape from the domain of attraction of one steady-state and be attracted to another, so the system eventually reaches a multimodal probability distribution in which all stable steady-states are represented proportional to their relative stability. However, since the escape time scales exponentially with system size, this process can take a very long time in large systems.