Pub Date : 2016-10-17DOI: 10.1007/978-3-319-65142-2_10
C. Skiadas, C. Skiadas
{"title":"The Health Status of a Population: Health State and Survival Curves and HALE Estimates","authors":"C. Skiadas, C. Skiadas","doi":"10.1007/978-3-319-65142-2_10","DOIUrl":"https://doi.org/10.1007/978-3-319-65142-2_10","url":null,"abstract":"","PeriodicalId":119149,"journal":{"name":"arXiv: Quantitative Methods","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133725015","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-10-11DOI: 10.1371/CURRENTS.MD.6AF74D0CEC0834554DAC78F0045CFDED
A. Cameron, Matthew T Houston, Juan B. Gutiérrez
Muscular dystrophy (MD) describes generalized progressive muscular weakness due to the wasting of muscle fibers. The progression of the disease is affected by known immunological and mechanical factors, and possibly other unknown mechanisms. These dynamics have begun to be elucidated in the last two decades. This article reviews mathematical models of MD that characterize molecular and cellular components implicated in MD progression. A biological background for these processes is also presented. Molecular effectors that contribute to MD include mitochondrial bioenergetics and genetic factors; both drive cellular metabolism, communication and signaling. These molecular events leave cells vulnerable to mechanical stress which can activate an immunological cascade that weakens cells and surrounding tissues. This review article lays the foundation for a systems biology approach to study MD progression.
{"title":"A Review of Mathematical Models for Muscular Dystrophy: A Systems Biology Approach","authors":"A. Cameron, Matthew T Houston, Juan B. Gutiérrez","doi":"10.1371/CURRENTS.MD.6AF74D0CEC0834554DAC78F0045CFDED","DOIUrl":"https://doi.org/10.1371/CURRENTS.MD.6AF74D0CEC0834554DAC78F0045CFDED","url":null,"abstract":"Muscular dystrophy (MD) describes generalized progressive muscular weakness due to the wasting of muscle fibers. The progression of the disease is affected by known immunological and mechanical factors, and possibly other unknown mechanisms. These dynamics have begun to be elucidated in the last two decades. This article reviews mathematical models of MD that characterize molecular and cellular components implicated in MD progression. A biological background for these processes is also presented. Molecular effectors that contribute to MD include mitochondrial bioenergetics and genetic factors; both drive cellular metabolism, communication and signaling. These molecular events leave cells vulnerable to mechanical stress which can activate an immunological cascade that weakens cells and surrounding tissues. This review article lays the foundation for a systems biology approach to study MD progression.","PeriodicalId":119149,"journal":{"name":"arXiv: Quantitative Methods","volume":"402 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133075036","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Reconstructing who infected whom is a central challenge in analysing epidemiological data. Recently, advances in sequencing technology have led to increasing interest in Bayesian approaches to inferring who infected whom using genetic data from pathogens. The logic behind such approaches is that isolates that are nearly genetically identical are more likely to have been recently transmitted than those that are very different. A number of methods have been developed to perform this inference. However, testing their convergence, examining posterior sets of transmission trees and comparing methods' performance are challenged by the fact that the object of inference - the transmission tree - is a complicated discrete structure. We introduce a metric on transmission trees to quantify distances between them. The metric can accommodate trees with unsampled individuals, and highlights differences in the source case and in the number of infections per infector. We illustrate its performance on simple simulated scenarios and on posterior transmission trees from a TB outbreak. We find that the metric reveals where the posterior is sensitive to the priors, and where collections of trees are composed of distinct clusters. We use the metric to define median trees summarising these clusters. Quantitative tools to compare transmission trees to each other will be required for assessing MCMC convergence, exploring posterior trees and benchmarking diverse methods as this field continues to mature.
{"title":"Estimating transmission from genetic and epidemiological data: a metric to compare transmission trees","authors":"M. Kendall, D. Ayabina, C. Colijn","doi":"10.1214/17-STS637","DOIUrl":"https://doi.org/10.1214/17-STS637","url":null,"abstract":"Reconstructing who infected whom is a central challenge in analysing epidemiological data. Recently, advances in sequencing technology have led to increasing interest in Bayesian approaches to inferring who infected whom using genetic data from pathogens. The logic behind such approaches is that isolates that are nearly genetically identical are more likely to have been recently transmitted than those that are very different. A number of methods have been developed to perform this inference. However, testing their convergence, examining posterior sets of transmission trees and comparing methods' performance are challenged by the fact that the object of inference - the transmission tree - is a complicated discrete structure. We introduce a metric on transmission trees to quantify distances between them. The metric can accommodate trees with unsampled individuals, and highlights differences in the source case and in the number of infections per infector. We illustrate its performance on simple simulated scenarios and on posterior transmission trees from a TB outbreak. We find that the metric reveals where the posterior is sensitive to the priors, and where collections of trees are composed of distinct clusters. We use the metric to define median trees summarising these clusters. Quantitative tools to compare transmission trees to each other will be required for assessing MCMC convergence, exploring posterior trees and benchmarking diverse methods as this field continues to mature.","PeriodicalId":119149,"journal":{"name":"arXiv: Quantitative Methods","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133883712","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-09-21DOI: 10.1103/PHYSREVAPPLIED.6.034012
G. Costantini, Z. Budrikis, A. Taloni, Alexander K. Buell, S. Zapperi, C. Porta
Autocatalytic fibril nucleation has recently been proposed to be a determining factor for the spread of neurodegenerative diseases, but the same process could also be exploited to amplify minute quantities of protein aggregates in a diagnostic context. Recent advances in microfluidic technology allow analysis of protein aggregation in micron-scale samples potentially enabling such diagnostic approaches, but the theoretical foundations for the analysis and interpretation of such data are so far lacking. Here we study computationally the onset of protein aggregation in small volumes and show that the process is ruled by intrinsic fluctuations whose volume dependent distribution we also estimate theoretically. Based on these results, we develop a strategy to quantify in silico the statistical errors associated with the detection of aggregate containing samples. Our work opens a new perspective on the forecasting of protein aggregation in asymptomatic subjects.
{"title":"Fluctuations in protein aggregation: Design of preclinical screening for early diagnosis of neurodegenerative disease","authors":"G. Costantini, Z. Budrikis, A. Taloni, Alexander K. Buell, S. Zapperi, C. Porta","doi":"10.1103/PHYSREVAPPLIED.6.034012","DOIUrl":"https://doi.org/10.1103/PHYSREVAPPLIED.6.034012","url":null,"abstract":"Autocatalytic fibril nucleation has recently been proposed to be a determining factor for the spread of neurodegenerative diseases, but the same process could also be exploited to amplify minute quantities of protein aggregates in a diagnostic context. Recent advances in microfluidic technology allow analysis of protein aggregation in micron-scale samples potentially enabling such diagnostic approaches, but the theoretical foundations for the analysis and interpretation of such data are so far lacking. Here we study computationally the onset of protein aggregation in small volumes and show that the process is ruled by intrinsic fluctuations whose volume dependent distribution we also estimate theoretically. Based on these results, we develop a strategy to quantify in silico the statistical errors associated with the detection of aggregate containing samples. Our work opens a new perspective on the forecasting of protein aggregation in asymptomatic subjects.","PeriodicalId":119149,"journal":{"name":"arXiv: Quantitative Methods","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123712166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-08-11DOI: 10.13140/RG.2.2.29167.02720
S. Hagler
The biomechanics of the human body allow humans a range of possible ways of executing movements to attain specific goals. Nevertheless, humans exhibit significant patterns in how they execute movements. We propose that the observed patterns of human movement arise because subjects select those ways to execute movements that are, in a rigorous sense, optimal. In this project, we show how this proposition can guide the development of computational models of movement selection and thereby account for human movement patterns. We proceed by first developing a movement utility formalism that operationalizes the concept of a best or optimal way of executing a movement using a utility function so that the problem of movement selection becomes the problem of finding the movement that maximizes the utility function. Since the movement utility formalism includes a contribution of the metabolic energy of the movement (maximum utility movements try to minimize metabolic energy), we also develop a metabolic energy formalism that we can use to construct estimators of the metabolic energies of particular movements. We then show how we can construct an estimator for the metabolic energies of normal walking gaits and we use that estimator to construct a movement utility model of the selection of normal walking gaits and show that the relationship between avg. walking speed and avg. step length predicted by this model agrees with observation. We conclude by proposing a physical mechanism that a subject might use to estimate the metabolic energy of a movement in practice.
{"title":"Patterns of Selection of Human Movements I: Movement Utility, Metabolic Energy, and Normal Walking Gaits","authors":"S. Hagler","doi":"10.13140/RG.2.2.29167.02720","DOIUrl":"https://doi.org/10.13140/RG.2.2.29167.02720","url":null,"abstract":"The biomechanics of the human body allow humans a range of possible ways of executing movements to attain specific goals. Nevertheless, humans exhibit significant patterns in how they execute movements. We propose that the observed patterns of human movement arise because subjects select those ways to execute movements that are, in a rigorous sense, optimal. In this project, we show how this proposition can guide the development of computational models of movement selection and thereby account for human movement patterns. We proceed by first developing a movement utility formalism that operationalizes the concept of a best or optimal way of executing a movement using a utility function so that the problem of movement selection becomes the problem of finding the movement that maximizes the utility function. Since the movement utility formalism includes a contribution of the metabolic energy of the movement (maximum utility movements try to minimize metabolic energy), we also develop a metabolic energy formalism that we can use to construct estimators of the metabolic energies of particular movements. We then show how we can construct an estimator for the metabolic energies of normal walking gaits and we use that estimator to construct a movement utility model of the selection of normal walking gaits and show that the relationship between avg. walking speed and avg. step length predicted by this model agrees with observation. We conclude by proposing a physical mechanism that a subject might use to estimate the metabolic energy of a movement in practice.","PeriodicalId":119149,"journal":{"name":"arXiv: Quantitative Methods","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125186167","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Biochemical reaction networks are often modelled using discrete-state, continuous-time Markov chains. System statistics of these Markov chains usually cannot be calculated analytically and therefore estimates must be generated via simulation techniques. There is a well documented class of simulation techniques known as exact stochastic simulation algorithms, an example of which is Gillespie's direct method. These algorithms often come with high computational costs, therefore approximate stochastic simulation algorithms such as the tau-leap method are used. However, in order to minimise the bias in the estimates generated using them, a relatively small value of tau is needed, rendering the computational costs comparable to Gillespie's direct method. The multi-level Monte Carlo method (Anderson and Higham, Multiscale Model. Simul. 10:146-179, 2012) provides a reduction in computational costs whilst minimising or even eliminating the bias in the estimates of system statistics. This is achieved by first crudely approximating required statistics with many sample paths of low accuracy. Then correction terms are added until a required level of accuracy is reached. Recent literature has primarily focussed on implementing the multi-level method efficiently to estimate a single system statistic. However, it is clearly also of interest to be able to approximate entire probability distributions of species counts. We present two novel methods that combine known techniques for distribution reconstruction with the multi-level method. We demonstrate the potential of our methods using a number of examples.
{"title":"Multi-level methods and approximating distribution functions","authors":"D. Wilson, R. Baker","doi":"10.1063/1.4960118","DOIUrl":"https://doi.org/10.1063/1.4960118","url":null,"abstract":"Biochemical reaction networks are often modelled using discrete-state, continuous-time Markov chains. System statistics of these Markov chains usually cannot be calculated analytically and therefore estimates must be generated via simulation techniques. There is a well documented class of simulation techniques known as exact stochastic simulation algorithms, an example of which is Gillespie's direct method. These algorithms often come with high computational costs, therefore approximate stochastic simulation algorithms such as the tau-leap method are used. However, in order to minimise the bias in the estimates generated using them, a relatively small value of tau is needed, rendering the computational costs comparable to Gillespie's direct method. \u0000The multi-level Monte Carlo method (Anderson and Higham, Multiscale Model. Simul. 10:146-179, 2012) provides a reduction in computational costs whilst minimising or even eliminating the bias in the estimates of system statistics. This is achieved by first crudely approximating required statistics with many sample paths of low accuracy. Then correction terms are added until a required level of accuracy is reached. Recent literature has primarily focussed on implementing the multi-level method efficiently to estimate a single system statistic. However, it is clearly also of interest to be able to approximate entire probability distributions of species counts. We present two novel methods that combine known techniques for distribution reconstruction with the multi-level method. We demonstrate the potential of our methods using a number of examples.","PeriodicalId":119149,"journal":{"name":"arXiv: Quantitative Methods","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123590231","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Over the past few decades, magnetoreception has been discovered in several species of teleost and elasmobranch fishes by employing varied experimental methods including conditioning experiments, observations of alignment with external fields, and experiments with magnetic deterrents. Biogenic magnetite has been confirmed to be an important receptor mechanism in some species, but there is ongoing debate regarding whether other mechanisms are at work. This paper presents evidence for magnetoreception in three additional species, red drum (Sciaenops ocellatus), black drum (Pogonias cromis), and sea catfish (Ariopsis felis), by employing experiments to test whether fish respond differently to bait on a magnetic hook than on a control. In red drum, the control hook outcaught the magnetic hook by 32 - 18 for chi-squared = 3.92 and a P-value of 0.048. Black drum showed a significant attraction for the magnetic hook, which prevailed over the control hook by 11 - 3 for chi-squared = 4.57 and a P-value of 0.033. Gafftopsail catfish (Bagre marinus) showed no preference with a 31 - 35 split between magnetic hook and control for chi-squared = 0.242 and a P-value of 0.623. In a sample of 100 sea catfish in an analogous experiment using smaller hooks, the control hook was preferred 62-38 for chi-squared = 5.76 and a P-value of < 0.001. Such a simple method for identifying magnetoreceptive species may quickly expand the number of known magnetoreceptive species and allow for easier access to magnetoreceptive species and thus facilitate testing of magnetoreceptive hypotheses.
{"title":"Evidence for Magnetoreception in Red Drum (Sciaenops ocellatus), Black Drum (Pogonias cromis), and Sea Catfish (Ariopsis felis)","authors":"Joshua M. Courtney, M. Courtney","doi":"10.5296/AST.V4I1.8711","DOIUrl":"https://doi.org/10.5296/AST.V4I1.8711","url":null,"abstract":"Over the past few decades, magnetoreception has been discovered in several species of teleost and elasmobranch fishes by employing varied experimental methods including conditioning experiments, observations of alignment with external fields, and experiments with magnetic deterrents. Biogenic magnetite has been confirmed to be an important receptor mechanism in some species, but there is ongoing debate regarding whether other mechanisms are at work. This paper presents evidence for magnetoreception in three additional species, red drum (Sciaenops ocellatus), black drum (Pogonias cromis), and sea catfish (Ariopsis felis), by employing experiments to test whether fish respond differently to bait on a magnetic hook than on a control. In red drum, the control hook outcaught the magnetic hook by 32 - 18 for chi-squared = 3.92 and a P-value of 0.048. Black drum showed a significant attraction for the magnetic hook, which prevailed over the control hook by 11 - 3 for chi-squared = 4.57 and a P-value of 0.033. Gafftopsail catfish (Bagre marinus) showed no preference with a 31 - 35 split between magnetic hook and control for chi-squared = 0.242 and a P-value of 0.623. In a sample of 100 sea catfish in an analogous experiment using smaller hooks, the control hook was preferred 62-38 for chi-squared = 5.76 and a P-value of < 0.001. Such a simple method for identifying magnetoreceptive species may quickly expand the number of known magnetoreceptive species and allow for easier access to magnetoreceptive species and thus facilitate testing of magnetoreceptive hypotheses.","PeriodicalId":119149,"journal":{"name":"arXiv: Quantitative Methods","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124648418","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-09-30DOI: 10.1007/978-3-319-45833-5_2
Alexander Andreychenko, L. Bortolussi, R. Grima, Philipp Thomas, V. Wolf
{"title":"Distribution Approximations for the Chemical Master Equation: Comparison of the Method of Moments and the System Size Expansion","authors":"Alexander Andreychenko, L. Bortolussi, R. Grima, Philipp Thomas, V. Wolf","doi":"10.1007/978-3-319-45833-5_2","DOIUrl":"https://doi.org/10.1007/978-3-319-45833-5_2","url":null,"abstract":"","PeriodicalId":119149,"journal":{"name":"arXiv: Quantitative Methods","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132380860","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-09-22DOI: 10.13140/RG.2.2.13192.62723
S. Hagler
While the use of technology to provide accurate and objective measurements of human movement performance is presently an area of great interest, efforts to quantify the performance of movement are hampered by the lack of a principled model that describes how a subject goes about making a movement. We put forward a principled mathematical formalism that describes human movements using an optimal control model in which the subject controls the jerk of the movement. We construct the formalism by assuming that the movement a subject chooses to make is better than the alternatives. We quantify the relative quality of movements mathematically by specifying a cost functional that assigns a numerical value to every possible movement; the subject makes the movement that minimizes the cost functional. We develop the mathematical structure of movements that minimize a cost functional, and observe that this development parallels the development of analytical mechanics from the Principle of Least Action. We derive a constant of the motion for human movements that plays a role that is analogous to the role that the energy plays in classical mechanics. We apply the formalism to the description of two movements: (1) rapid, targeted movements of a computer mouse, and (2) finger-tapping, and show that the constant of the motion that we have derived provides a useful value with which we can characterize the performance of the movements. In the case of rapid, targeted movements of a computer mouse, we show how the model of human movement that we have developed can be made to agree with Fitts' law, and we show how Fitts' law is related to the constant of the motion that we have derived. We finally show that solutions exist within the model of human movements that exhibit an oscillatory character reminiscent of tremor.
{"title":"On the Principled Description of Human Movements","authors":"S. Hagler","doi":"10.13140/RG.2.2.13192.62723","DOIUrl":"https://doi.org/10.13140/RG.2.2.13192.62723","url":null,"abstract":"While the use of technology to provide accurate and objective measurements of human movement performance is presently an area of great interest, efforts to quantify the performance of movement are hampered by the lack of a principled model that describes how a subject goes about making a movement. We put forward a principled mathematical formalism that describes human movements using an optimal control model in which the subject controls the jerk of the movement. We construct the formalism by assuming that the movement a subject chooses to make is better than the alternatives. We quantify the relative quality of movements mathematically by specifying a cost functional that assigns a numerical value to every possible movement; the subject makes the movement that minimizes the cost functional. We develop the mathematical structure of movements that minimize a cost functional, and observe that this development parallels the development of analytical mechanics from the Principle of Least Action. We derive a constant of the motion for human movements that plays a role that is analogous to the role that the energy plays in classical mechanics. We apply the formalism to the description of two movements: (1) rapid, targeted movements of a computer mouse, and (2) finger-tapping, and show that the constant of the motion that we have derived provides a useful value with which we can characterize the performance of the movements. In the case of rapid, targeted movements of a computer mouse, we show how the model of human movement that we have developed can be made to agree with Fitts' law, and we show how Fitts' law is related to the constant of the motion that we have derived. We finally show that solutions exist within the model of human movements that exhibit an oscillatory character reminiscent of tremor.","PeriodicalId":119149,"journal":{"name":"arXiv: Quantitative Methods","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115416629","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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