Stochastic Linkage Research Articles

An evolution-based high-fidelity method of epistasis measurement: Theory and application to influenza.

Linkage effects in a multi-locus population strongly influence its evolution. The models based on the traveling wave approach enable us to predict the average speed of evolution and the statistics of phylogeny. However, predicting statistically the evolution of specific sites and pairs of sites in the multi-locus context remains a mathematical challenge. In particular, the effects of epistasis, the interaction of gene regions contributing to phenotype, is difficult to predict theoretically and detect experimentally in sequence data. A large number of false-positive interactions arises from stochastic linkage effects and indirect interactions, which mask true epistatic interactions. Here we develop a proof-of-principle method to filter out false-positive interactions. We start by demonstrating that the averaging of haplotype frequencies over multiple independent populations is necessary but not sufficient for epistatic detection, because it still leaves high numbers of false-positive interactions. To compensate for the residual stochastic noise, we develop a three-way haplotype method isolating true interactions. The fidelity of the method is confirmed analytically and on simulated genetic sequences evolved with a known epistatic network. The method is then applied to a large sequence database of neurominidase protein of influenza A H1N1 obtained from various geographic locations to infer the epistatic network responsible for the difference between the pre-pandemic virus and the pandemic strain of 2009. These results present a simple and reliable technique to measure epistatic interactions of any sign from sequence data.

Erratum to: Risk of cancer incidence before the age of 15years after exposure to ionising radiation from computed tomography: results from a German cohort study.

The aim of this cohort study was to assess the risk of developing cancer, specifically leukaemia, tumours of the central nervous system and lymphoma, before the age of 15 years in children previously exposed to computed tomography (CT) in Germany. Data for children with at least one CT between 1980 and 2010 were abstracted from 20 hospitals. Cancer cases occurring between 1980 and 2010 were identified by stochastic linkage with the German Childhood Cancer Registry (GCCR). For all cases and a sample of non-cases, radiology reports were reviewed to assess the underlying medical conditions at time of the CT. Cases were only included if diagnosis occurred at least 2 years after the first CT and no signs of cancer were recorded in the radiology reports. Standardised incidence ratios (SIR) using incidence rates from the general population were estimated. The cohort included information on 71,073 CT examinations in 44,584 children contributing 161,407 person-years at risk with 46 cases initially identified through linkage with the GCCR. Seven cases had to be excluded due to signs possibly suggestive of cancer at the time of first CT. Overall, more cancer cases were observed (O) than expected (E), but this was mainly driven by unexpected and possibly biased results for lymphomas. For leukaemia, the SIR (SIR = O/E) was 1.72 (95 % CI 0.89–3.01, O = 12), and for CNS tumours, the SIR was 1.35 (95 % CI 0.54–2.78, O = 7). Despite careful examination of the medical information, confounding by indication or reverse causation cannot be ruled out completely and may explain parts of the excess. Furthermore, the CT exposure may have been underestimated as only data from the participating clinics were available. This should be taken into account when interpreting risk estimates.

Risk of cancer incidence before the age of 15years after exposure to ionising radiation from computed tomography: results from a German cohort study.

The aim of this cohort study was to assess the risk of developing cancer, specifically leukaemia, tumours of the central nervous system and lymphoma, before the age of 15years in children previously exposed to computed tomography (CT) in Germany. Data for children with at least one CT between 1980 and 2010 were abstracted from 20 hospitals. Cancer cases occurring between 1980 and 2010 were identified by stochastic linkage with the German Childhood Cancer Registry (GCCR). For all cases and a sample of non-cases, radiology reports were reviewed to assess the underlying medical conditions at time of the CT. Cases were only included if diagnosis occurred at least 2years after the first CT and no signs of cancer were recorded in the radiology reports. Standardised incidence ratios (SIR) using incidence rates from the general population were estimated. The cohort included information on 71,073 CT examinations in 44,584 children contributing 161,407 person-years at risk with 46 cases initially identified through linkage with the GCCR. Seven cases had to be excluded due to signs possibly suggestive of cancer at the time of first CT. Overall, more cancer cases were observed (O) than expected (E), but this was mainly driven by unexpected and possibly biased results for lymphomas. For leukaemia, the SIR (SIR=O/E) was 1.72 (95% CI 0.89-3.01, O=12), and for CNS tumours, the SIR was 1.35 (95% CI 0.54-2.78, O=7). Despite careful examination of the medical information, confounding by indication or reverse causation cannot be ruled out completely and may explain parts of the excess. Furthermore, the CT exposure may have been underestimated as only data from the participating clinics were available. This should be taken into account when interpreting risk estimates.

Stochastic linkage model of a compliant bistable micromechanism for mechanical error analysis

Microelectromechanical systems (MEMS) that have micromechanisms as actuators involve inaccuracy problems due to joint clearances and link length tolerances. Since compliant bistable micromechanisms have a wide range of applications in MEMS devices, analysis of the mechanical error of these mechanisms is very important. For compliant mechanisms, it is important to consider the effects of cross-sectional shape and material stiffness variations. In this paper, a compliant bistable micromechanism called Young is modeled by a clearance vector concept. Then a stochastic method is used to determine the errors of potential energy, required moment and coupler point position of mechanism. The range of variations of critical moment of the micromechanism to move from one stable point to the other and the displacement of the second stable point of the mechanism are determined. The Monte Carlo simulation shows that the stochastic method yields accurate results. The clearance vector model is easier and more general to use for micromechanisms than previous works.

Stochastic Linkage Modeling for Mechanical Error Analysis of Planar Mechanisms*

ABSTRACT This paper addresses stochastic linkage modeling for mechanical error analysis of planar mechanisms. Considering the effects of joint angle variations, the effective link length model is generalized. The generalized model produces more accurate predictions of mechanical errors than the effective link length model. However, the generalization requires more complicated mechanical error analysis. This paper proposes a stochastic model to intuitively consider the effects of tolerances and clearances, based on the clearance vector concept. Stochastic models are applied to typical mechanisms and their results are compared with those of Monte Carlo simulations. The comparison shows that the proposed stochastic model is effective for mechanical error analysis. The clearance vector model yields more accurate results and is easier to use than the generalized effective link length model.

Effect of climate change on regional precipitation in Lake Balaton watershed

A methodology is developed and applied to the area of Lake Balaton and its drainage basin, a region of Western Hungary, to estimate the space-time distribution of daily precipitation under climate change. Lake Balaton is the largest lake in Central and Western Europe; it has a central location in the country and its drainage basin covers about the 20% of Hungary (together with the Sio Canal). The methodology is based on an analysis of the semi-Markovian properties of atmospheric macrocirculation pattern types (MCP), and a stochastic linkage between daily (here 700 hPa) MCP types and daily precipitation events. Historical data and General Circulation Model (GCM) output of daily MCP corresponding to 1 · CO2 and 2 · CO2 scenarios are considered in this study. Time series of both local and areal precipitation corresponding for both scenarios are simulated and their statistical properties are compared. For the temperate continental climate of Western Hungary a slightly variable spatial response to climate change is obtained. Under 2 · CO2 conditions most of the local and the areal average precipitation suggests, a somewhat dryer precipitation regime in Western Hungary. The sensitivity of the results to the GCM utilized should be considered.

Estimation of Local and Areal Drought Reflecting Climate Change

A methodology is developed and applied to eastern Nebraska to estimate the statistical properties of a meteorological drought index under climate change. The approach is based on the analysis of atmospheric circulation patterns (CP), followed by a stochastic linkage between daily CP types and daily local hydrometeorological quantities used to calculate the drought index. The methodology is illustrated with a common rainfall deficit-based drought index, the Bhalme-Mooley Drought Index (BMDI). Historical data and General Circulation Model (GCM) output of daily CP corresponding to the present (1xCO2) and doubled atmospheric CO2 (2xCO2) concentration are taken as inputs. Time series of both local and areal BMDI are simulated and their statistics are calculated. Under the dry continental climate of eastern Nebraska a highly variable spatial response to climate change has been obtained. Most of the local and the areal average drought indices reflect a somewhat wetter and a more variable climate under the 2xCO2 conditions. The results may be sensitive to the GCM used. The methodology can be used elsewhere to estimate statistically the impact of global climate change on local/regional drought.

Local temperature estimation under climate change

A methodology to estimate the space-time distribution of daily mean temperature under climate change is developed and applied to a central Nebraska case study. The approach is based on the analysis of the Markov properties of atmospheric circulation pattern (CP) types, and a stochastic linkage between daily (here 500hPa) CP types and daily mean temperatures. Historical data and general circulation model (GCM) output of daily CP corresponding to 1 × CO2 and 2 × CO2 scenarios are considered. The relationship between spatially averaged geopotential height of the 500 hPa surface — within each CP type — and daily mean temperature is described by a nonparametric regression technique. Time series of daily mean temperatures corresponding to each of these cases are simulated and their statistical properties are compared. Under the climate of central Nebraska, the space-time response of daily mean temperature to global climate change is variable. In general, a warmer climate appears to cause about 5°C increase in the winter months, a smaller increase in other months with no change in July and August. The sensitivity of the results to the GCM utilized should be considered.

Space-time precipitation reflecting climate change

Abstract A methodology has been developed and applied to an eastern Nebraska, USA, case study to estimate the space-time distribution of daily precipitation under climate change. The approach is based on the analysis both of the type and of the Markov properties of atmospheric circulation patterns (CPs), and a stochastic linkage between daily (here 500 hPa) CP types and daily precipitation events. Historical data and General Circulation Model (GCM) output of daily CPs corresponding to 1 × CO2 and 2 × CO2 are considered. Time series of both local and regional precipitation corresponding to each of those cases were simulated and their statistical properties were compared. Under the dry continental climate of eastern Nebraska, a highly variable spatial response to climate change was obtained. Most of the local and the regional average precipitation values reflect, under 2 × CO2, a somewhat wetter and a more variable precipitation regime in eastern Nebraska. The sensitivity of the results to the GCM utilized ...

Stochastic linkage: Effect of random fluctuations on a two-state process

When the two-state process A⇄B is asymmetrically perturbed by random fluctuations, a unidirectional shift of the equilibrium between the two states is observed. Random fluctuations destabilize the state that is populated nondeterministically by the fluctuating rate. This effect of random fluctuations on the preexisting equilibrium between the two states is analogous to the allosteric regulation of conformational transitions in biological macromolecules induced by ligand binding to one of the two states. The unidirectional effect of random fluctuations of the two-state process A⇄B can be interpreted as a stochastic linkage that couples noise to conformational transitions.

Optimal Stochastic Design of Four-Bar Mechanisms for Tolerance and Clearance

A formulation of optimal stochastic design of mechanisms considering tolerances on the link lengths and clearances in the joints is presented. The mechanical error is analyzed for the 3σ band of confidence level through a new stochastic model of a four-bar linkage. A multiobjective optimization problem with two objective functions, mechanical error and manufacturing cost, is considered by a weighting method. Tolerance widths and nominal clearance sizes are taken as design variables. The conflicting nature between the two objectives is represented in the form of tradeoff curves. A concept of loop closure error is also introduced and applied to optimum design of the nominal linkage system and the stochastic linkage system. Numerical results are given for a four-bar function generator and a four-bar path generator.