Pub Date : 2020-04-15DOI: 10.5772/intechopen.90696
M. Tamm
In this chapter, a combinatorial model for cosmology is analyzed. We consider each universe as a path in a graph, and the set of all such paths can be made into a finite probability space. We can then consider the probabilities for different kinds of behavior and under certain circumstances argue that a scenario where the behavior of the entropy is monotonic, either increasing or decreasing, should be much more likely than a scenario where the behavior is symmetric with respect to time. In this way we can attempt to construct a model for a multiverse which is completely time symmetric but where the individual universes tend to be time asymmetric, i.e., have an arrow of time. One of the main points with this approach is that this kind of broken symmetry can be studied in very small models using exact mathematical methods from, e.g., combinatorics. Even if the amount of computations needed increases very rapidly with the size of the model, we can still hope for valuable information about what properties more realistic models should have. Some suggestions for further research are pointed out.
{"title":"Combinatorial Cosmology","authors":"M. Tamm","doi":"10.5772/intechopen.90696","DOIUrl":"https://doi.org/10.5772/intechopen.90696","url":null,"abstract":"In this chapter, a combinatorial model for cosmology is analyzed. We consider each universe as a path in a graph, and the set of all such paths can be made into a finite probability space. We can then consider the probabilities for different kinds of behavior and under certain circumstances argue that a scenario where the behavior of the entropy is monotonic, either increasing or decreasing, should be much more likely than a scenario where the behavior is symmetric with respect to time. In this way we can attempt to construct a model for a multiverse which is completely time symmetric but where the individual universes tend to be time asymmetric, i.e., have an arrow of time. One of the main points with this approach is that this kind of broken symmetry can be studied in very small models using exact mathematical methods from, e.g., combinatorics. Even if the amount of computations needed increases very rapidly with the size of the model, we can still hope for valuable information about what properties more realistic models should have. Some suggestions for further research are pointed out.","PeriodicalId":184595,"journal":{"name":"Probability, Combinatorics and Control","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122578162","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 : 2019-11-27DOI: 10.5772/INTECHOPEN.88894
Gennady Yu. Shmal, V. Nadein, N. Makhutov, P. Truskov, V. Osipov
Offshore platforms should be referred to critically and strategically important objects of a technosphere due to technological and operational challenges, on the one hand, and the danger potential level, on the other hand. Environmental, social and economic losses occurred over several decades of accidents and disasters in unique Great Britain, Norwegian. The Russian and the USA platforms were evaluated in death of dozens of operators, destruction of platforms, environment contamination and hence in multi-bullion losses. All of these indicate insufficiency of currently taken engineering solutions, providing structure strength, operational life and safety. The scientific, design, expert and supervising organizations in Russia and in the world are developing and improving mathematical and physical methods, implementing the probabilistic formulations for accidents and disasters, risk assessment and risks reduction on offshore platforms. The solutions of the following problems are included: extension of the comprehensive computational and experimental strength, operational life and survivability analysis to the cases of nonroutine events, accidental and catastrophic conditions; numerical justification of modelling of critical elements, zones and points with the maximum tension, deformations and damages occurring under impacts of external extreme seismic, ice, wind, low temperature; implementation of comprehensive diagnostic methods for damage states evaluation within nonlinear and probabilistic fracture mechanics; and use of new structural design and technological systems for reduction of negative extreme impacts as well as emergency protection systems. The solution of the specified problems is illustrated by case studies of the Russian specialists for each life cycle stage of the platforms offshore Caspian and Kara Seas and Sea of Okhotsk.
{"title":"Hybrid Modeling of Offshore Platforms’ Stress-Deformed and Limit States Taking into Account Probabilistic Parameters","authors":"Gennady Yu. Shmal, V. Nadein, N. Makhutov, P. Truskov, V. Osipov","doi":"10.5772/INTECHOPEN.88894","DOIUrl":"https://doi.org/10.5772/INTECHOPEN.88894","url":null,"abstract":"Offshore platforms should be referred to critically and strategically important objects of a technosphere due to technological and operational challenges, on the one hand, and the danger potential level, on the other hand. Environmental, social and economic losses occurred over several decades of accidents and disasters in unique Great Britain, Norwegian. The Russian and the USA platforms were evaluated in death of dozens of operators, destruction of platforms, environment contamination and hence in multi-bullion losses. All of these indicate insufficiency of currently taken engineering solutions, providing structure strength, operational life and safety. The scientific, design, expert and supervising organizations in Russia and in the world are developing and improving mathematical and physical methods, implementing the probabilistic formulations for accidents and disasters, risk assessment and risks reduction on offshore platforms. The solutions of the following problems are included: extension of the comprehensive computational and experimental strength, operational life and survivability analysis to the cases of nonroutine events, accidental and catastrophic conditions; numerical justification of modelling of critical elements, zones and points with the maximum tension, deformations and damages occurring under impacts of external extreme seismic, ice, wind, low temperature; implementation of comprehensive diagnostic methods for damage states evaluation within nonlinear and probabilistic fracture mechanics; and use of new structural design and technological systems for reduction of negative extreme impacts as well as emergency protection systems. The solution of the specified problems is illustrated by case studies of the Russian specialists for each life cycle stage of the platforms offshore Caspian and Kara Seas and Sea of Okhotsk.","PeriodicalId":184595,"journal":{"name":"Probability, Combinatorics and Control","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115959627","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 : 2019-11-19DOI: 10.5772/intechopen.88288
Cristina Martínez Ramírez, Alberto Besana
We study and enumerate cyclic codes which include generalised Reed-Solomon codes as function field codes. This geometrical approach allows to construct longer codes and to get more information on the parameters defining the codes. We provide a closed formula in terms of Stirling numbers for the number of irreducible polynomials and we relate it with other formulas existing in the literature. Further, we study quasi-cyclic codes as orbit codes in the Grassmannian parameterizing constant dimension codes. In addition, we review Horn ’ s algorithm and apply it to construct classical codes by their defining ideals.
{"title":"A Geometrical Realisation of Quasi-Cyclic Codes","authors":"Cristina Martínez Ramírez, Alberto Besana","doi":"10.5772/intechopen.88288","DOIUrl":"https://doi.org/10.5772/intechopen.88288","url":null,"abstract":"We study and enumerate cyclic codes which include generalised Reed-Solomon codes as function field codes. This geometrical approach allows to construct longer codes and to get more information on the parameters defining the codes. We provide a closed formula in terms of Stirling numbers for the number of irreducible polynomials and we relate it with other formulas existing in the literature. Further, we study quasi-cyclic codes as orbit codes in the Grassmannian parameterizing constant dimension codes. In addition, we review Horn ’ s algorithm and apply it to construct classical codes by their defining ideals.","PeriodicalId":184595,"journal":{"name":"Probability, Combinatorics and Control","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124955744","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 : 2019-11-14DOI: 10.5772/intechopen.89036
D. Neganov, N. Makhutov
Within the long-term Russian and foreign practice, deterministic methods of basic strength calculations have been developed and are being developed at the design stage of long-distance pipelines. Occurring operational damages, failures, accidents, and catastrophes show there are no direct substantiations for the pre-vention of such emergencies in the framework of existing calculations. In order to respond to these situations, the following are developed: additional precise deterministic, static, and probabilistic calculations with linear and nonlinear criteria of deformation and fracture mechanics, complex diagnostics of the state of the pipeline using in-line pigs, and laboratory, model, bench, and field tests of pipelines with technological and operational defects. The results of systematic scientific research and applied developments are presented.
{"title":"Combined Calculated, Experimental and Determinated and Probable Justifications for Strength of Trunk Crude Oil Pipelines","authors":"D. Neganov, N. Makhutov","doi":"10.5772/intechopen.89036","DOIUrl":"https://doi.org/10.5772/intechopen.89036","url":null,"abstract":"Within the long-term Russian and foreign practice, deterministic methods of basic strength calculations have been developed and are being developed at the design stage of long-distance pipelines. Occurring operational damages, failures, accidents, and catastrophes show there are no direct substantiations for the pre-vention of such emergencies in the framework of existing calculations. In order to respond to these situations, the following are developed: additional precise deterministic, static, and probabilistic calculations with linear and nonlinear criteria of deformation and fracture mechanics, complex diagnostics of the state of the pipeline using in-line pigs, and laboratory, model, bench, and field tests of pipelines with technological and operational defects. The results of systematic scientific research and applied developments are presented.","PeriodicalId":184595,"journal":{"name":"Probability, Combinatorics and Control","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124912468","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 : 2019-10-23DOI: 10.5772/intechopen.88741
Davood Shiri, Sibel Salman
In this chapter, we study new variations of the online k -Canadian Traveler Problem ( k -CTP) in which there is an input graph with a given source node O and a destination node D. For a specified set consisting of k edges, the edge costs are unknown (we call these uncertain edges). Costs of the remaining edges are known and given. The objective is to find an online strategy such that the traveling agent finds a route from O to D with minimum total travel cost. The agent learns the cost of an uncertain edge, when she arrives at one of its end-nodes and decides on her travel path based on the discovered cost. We call this problem the online k -Cana-dian Traveler Problem with uncertain edges. We analyze both the single-agent and the multi-agent versions of the problem. We propose a tight lower bound on the competitive ratio of deterministic online strategies together with an optimal online strategy for the single-agent version. We consider the multi-agent version with two different objectives. We suggest lower bounds on the competitive ratio of deterministic online strategies to these two problems.
{"title":"New Variations of the Online k-Canadian Traveler Problem: Uncertain Costs at Known Locations","authors":"Davood Shiri, Sibel Salman","doi":"10.5772/intechopen.88741","DOIUrl":"https://doi.org/10.5772/intechopen.88741","url":null,"abstract":"In this chapter, we study new variations of the online k -Canadian Traveler Problem ( k -CTP) in which there is an input graph with a given source node O and a destination node D. For a specified set consisting of k edges, the edge costs are unknown (we call these uncertain edges). Costs of the remaining edges are known and given. The objective is to find an online strategy such that the traveling agent finds a route from O to D with minimum total travel cost. The agent learns the cost of an uncertain edge, when she arrives at one of its end-nodes and decides on her travel path based on the discovered cost. We call this problem the online k -Cana-dian Traveler Problem with uncertain edges. We analyze both the single-agent and the multi-agent versions of the problem. We propose a tight lower bound on the competitive ratio of deterministic online strategies together with an optimal online strategy for the single-agent version. We consider the multi-agent version with two different objectives. We suggest lower bounds on the competitive ratio of deterministic online strategies to these two problems.","PeriodicalId":184595,"journal":{"name":"Probability, Combinatorics and Control","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127687135","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 : 2019-10-22DOI: 10.5772/intechopen.89659
V. Korolev, A. Zeifman
This chapter contains a possible explanation of the emergence of heavy-tailed distributions observed in practice instead of the expected normal laws. The bases for this explanation are limit theorems for random sums and statistics constructed from samples with random sizes. As examples of the application of general theorems, conditions are presented for the convergence of the distributions of random sums of independent random vectors with finite covariance matrices to multivariate elliptically contoured stable and Linnik distributions. Also, conditions are presented for the convergence of the distributions of asymptotically normal (in the traditional sense) statistics to multivariate Student distributions. The joint asymptotic behavior of sample quantiles is also considered.
{"title":"From Asymptotic Normality to Heavy-Tailedness via Limit Theorems for Random Sums and Statistics with Random Sample Sizes","authors":"V. Korolev, A. Zeifman","doi":"10.5772/intechopen.89659","DOIUrl":"https://doi.org/10.5772/intechopen.89659","url":null,"abstract":"This chapter contains a possible explanation of the emergence of heavy-tailed distributions observed in practice instead of the expected normal laws. The bases for this explanation are limit theorems for random sums and statistics constructed from samples with random sizes. As examples of the application of general theorems, conditions are presented for the convergence of the distributions of random sums of independent random vectors with finite covariance matrices to multivariate elliptically contoured stable and Linnik distributions. Also, conditions are presented for the convergence of the distributions of asymptotically normal (in the traditional sense) statistics to multivariate Student distributions. The joint asymptotic behavior of sample quantiles is also considered.","PeriodicalId":184595,"journal":{"name":"Probability, Combinatorics and Control","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128416469","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 : 2019-09-28DOI: 10.5772/intechopen.89168
A. Kostogryzov, V. Korolev
As a result of the analysis of dispatcher intelligence centers and aerial, land, underground, underwater, universal, and functionally focused artificial intelligence robotics systems, the problems of rational control, due to be performed under specific conditions of uncertainties, are chosen for probabilistic study. The choice covers the problems of planning the possibilities of functions performance on the base of monitored information about events and conditions and the problem of robot route optimization under limitations on risk of “ failure ” in conditions of uncertainties. These problems are resolved with a use of the proposed probabilistic approach. The proposed methods are based on selected probabilistic models (for “ black box ” and complex systems), which are implemented effectively in wide application areas. The cognitive solving of problems consists in improvements, accumulation, analysis, and use of appearing knowledge. The described analytical solutions are demonstrated by practical examples.
{"title":"Probabilistic Methods for Cognitive Solving of Some Problems in Artificial Intelligence Systems","authors":"A. Kostogryzov, V. Korolev","doi":"10.5772/intechopen.89168","DOIUrl":"https://doi.org/10.5772/intechopen.89168","url":null,"abstract":"As a result of the analysis of dispatcher intelligence centers and aerial, land, underground, underwater, universal, and functionally focused artificial intelligence robotics systems, the problems of rational control, due to be performed under specific conditions of uncertainties, are chosen for probabilistic study. The choice covers the problems of planning the possibilities of functions performance on the base of monitored information about events and conditions and the problem of robot route optimization under limitations on risk of “ failure ” in conditions of uncertainties. These problems are resolved with a use of the proposed probabilistic approach. The proposed methods are based on selected probabilistic models (for “ black box ” and complex systems), which are implemented effectively in wide application areas. The cognitive solving of problems consists in improvements, accumulation, analysis, and use of appearing knowledge. The described analytical solutions are demonstrated by practical examples.","PeriodicalId":184595,"journal":{"name":"Probability, Combinatorics and Control","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132303885","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 : 2019-09-03DOI: 10.5772/intechopen.88699
Franck Adékambi
In this chapter, with renewal argument, we derive higher simple moments of the Discounted Compound Delay Renewal Risk Process (DCDRRP) when introducing dependence between the inter-occurrence time and the subsequent claim size. To illustrate our results, we assume that the inter-occurrence time is following a delay-Poisson process and the claim amounts is following a mixture of Exponential distribution, we then provide numerical results for the first two moments. The dependence structure between the inter-occurrence time and the subsequent claim size is defined by a Farlie-Gumbel-Morgenstern copula. Assuming that the claim distribution has finite moments, we obtain a general formula for all the moments of the DCDRRP process.
{"title":"Moments of the Discounted Aggregate Claims with Delay Inter-Occurrence Distribution and Dependence Introduced by a FGM Copula","authors":"Franck Adékambi","doi":"10.5772/intechopen.88699","DOIUrl":"https://doi.org/10.5772/intechopen.88699","url":null,"abstract":"In this chapter, with renewal argument, we derive higher simple moments of the Discounted Compound Delay Renewal Risk Process (DCDRRP) when introducing dependence between the inter-occurrence time and the subsequent claim size. To illustrate our results, we assume that the inter-occurrence time is following a delay-Poisson process and the claim amounts is following a mixture of Exponential distribution, we then provide numerical results for the first two moments. The dependence structure between the inter-occurrence time and the subsequent claim size is defined by a Farlie-Gumbel-Morgenstern copula. Assuming that the claim distribution has finite moments, we obtain a general formula for all the moments of the DCDRRP process.","PeriodicalId":184595,"journal":{"name":"Probability, Combinatorics and Control","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115114608","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 : 2019-08-31DOI: 10.5772/intechopen.88805
C. R. Lucatero
In this chapter, I will talk about some of the enumerative combinatorics problems that have interested researchers during the last decades. For some of those enumeration problems, it is possible to obtain closed mathematical expressions, and for some other it is possible to obtain an estimation by the use of asymptotic methods. Some of the methods used in both cases will be covered in this chapter as well as some application of graph enumeration in different fields. An overview about the enumeration of trees will be given as an example of combinatorial problem solved in a closed mathematical form. Similarly, the problem of enumeration of regular graphs will be discussed as an example of combinatorial enumeration for which it is hard to obtain a closed mathematical form solution and apply the asymptotic estimation method used frequently in analytic combinatorics for this end. An example of application of the enumerative combinatorics for obtaining a result of applicability criteria of selection nodes in a virus spreading control problem will be given as well.
{"title":"Combinatorial Enumeration of Graphs","authors":"C. R. Lucatero","doi":"10.5772/intechopen.88805","DOIUrl":"https://doi.org/10.5772/intechopen.88805","url":null,"abstract":"In this chapter, I will talk about some of the enumerative combinatorics problems that have interested researchers during the last decades. For some of those enumeration problems, it is possible to obtain closed mathematical expressions, and for some other it is possible to obtain an estimation by the use of asymptotic methods. Some of the methods used in both cases will be covered in this chapter as well as some application of graph enumeration in different fields. An overview about the enumeration of trees will be given as an example of combinatorial problem solved in a closed mathematical form. Similarly, the problem of enumeration of regular graphs will be discussed as an example of combinatorial enumeration for which it is hard to obtain a closed mathematical form solution and apply the asymptotic estimation method used frequently in analytic combinatorics for this end. An example of application of the enumerative combinatorics for obtaining a result of applicability criteria of selection nodes in a virus spreading control problem will be given as well.","PeriodicalId":184595,"journal":{"name":"Probability, Combinatorics and Control","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115584329","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 : 2019-08-25DOI: 10.5772/intechopen.88554
I. Hudson, Susan W. Kim, M. Keatley
A new approach to assess synchronicity developed in this chapter is a novel bivariate extension of the generalised mixture transition distribution (MTDg) model (we coin this B-MTD). The aim of this chapter is to test MTDg an extended MTD with interactions model and its bivariate extension of MTD (B-MTD) to investigate synchrony of flowering of four Eucalypts speciesE. leucoxylon, E. microcarpa, E. polyanthemos and E. tricarpa over a 31 year period. The mixture transition distribution (MTDg) is a method to estimate transition probabilities of high order Markov chains. Our B-MTD approach allows us the derive rules of thumb for synchrony and asynchrony between pairs of species, e.g. flowering of the four species. The latter B-MTD rules are based on transition probabilities between all possible on and off flowering states from previous to current time. We also apply MTDg modelling using lagged flowering states and climate covariates as predictors to model current flowering status (on/off) to assess synchronisation using residuals from the resultant models via our adaptation of Morans classic synchrony statistic. We compare these MTDg (with covariates)-based synchrony measures with our B-MTD results in addition to those from extended Kalman filter (EKF)-based residuals.
{"title":"Mixture Transition Distribution Modelling of Multivariate Time Series of Discrete State Processes: With an Application to Modelling Flowering Synchronisation with Respect to Climate Dynamics","authors":"I. Hudson, Susan W. Kim, M. Keatley","doi":"10.5772/intechopen.88554","DOIUrl":"https://doi.org/10.5772/intechopen.88554","url":null,"abstract":"A new approach to assess synchronicity developed in this chapter is a novel bivariate extension of the generalised mixture transition distribution (MTDg) model (we coin this B-MTD). The aim of this chapter is to test MTDg an extended MTD with interactions model and its bivariate extension of MTD (B-MTD) to investigate synchrony of flowering of four Eucalypts speciesE. leucoxylon, E. microcarpa, E. polyanthemos and E. tricarpa over a 31 year period. The mixture transition distribution (MTDg) is a method to estimate transition probabilities of high order Markov chains. Our B-MTD approach allows us the derive rules of thumb for synchrony and asynchrony between pairs of species, e.g. flowering of the four species. The latter B-MTD rules are based on transition probabilities between all possible on and off flowering states from previous to current time. We also apply MTDg modelling using lagged flowering states and climate covariates as predictors to model current flowering status (on/off) to assess synchronisation using residuals from the resultant models via our adaptation of Morans classic synchrony statistic. We compare these MTDg (with covariates)-based synchrony measures with our B-MTD results in addition to those from extended Kalman filter (EKF)-based residuals.","PeriodicalId":184595,"journal":{"name":"Probability, Combinatorics and Control","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130832892","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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