The minimal two-dimensional model of bursting neuronal dynamics is used to study the influence of time-delay on the properties of synchronization of bursting neurons. Generic properties of bursting and dependence of t...The minimal two-dimensional model of bursting neuronal dynamics is used to study the influence of time-delay on the properties of synchronization of bursting neurons. Generic properties of bursting and dependence of the stability of synchronization on the time-lag and the strength of coupling are described, and compared with the two common types of synaptical coupling, i.e., time-delayed chemical and electrical synapses.展开更多
This research is an attempt to validate how glu-cose-insulin dynamic mathematical model facilitate to identify the root causes for hypoglycaemia. The purpose is to determine whether increased insulin sensitivity or in...This research is an attempt to validate how glu-cose-insulin dynamic mathematical model facilitate to identify the root causes for hypoglycaemia. The purpose is to determine whether increased insulin sensitivity or increased insulin secretion causes post- prandial hypoglycemic (PPH) response, by linking experimental patient data with dynamic mathematical model. For this purpose two groups, as hypoglycemic Group 1 and non-hypoglycemic Group 2, each of which consists of 10 people, are formed. The oral glucose tolerance test (OGTT) is carried out for each person in the groups by measuring plasma glucose and insulin concentrations at every 30 minutes for a period of 5 hours. To distinguish the actual cause of hypoglycemia, the glucose minimal dynamic model is used. The model is executed in MATLAB platform using patient data and the results showed that insulin secretion is assumed to be the potential root cause for the hypoglycemia.展开更多
Diabetes is a burning issue in the whole world.It is the imbalance between body glucose and insulin.The study of this imbalance is very much needed from a research point of view.For this reason,Bergman gave an importa...Diabetes is a burning issue in the whole world.It is the imbalance between body glucose and insulin.The study of this imbalance is very much needed from a research point of view.For this reason,Bergman gave an important model named-Bergman minimalmodel.In the present work,using Caputo-Fabrizio(CF)fractional derivative,we generalize Bergman’s minimal blood glucose-insulin model.Further,we modify the old model by including one more component known as diet D(t),which is also essential for the blood glucose model.We solve the modified modelwith the help of Sumudu transformand fixed-point iteration procedures.Also,using the fixed point theorem,we examine the existence and uniqueness of the results along with their numerical and graphical representation.Furthermore,the comparison between the values of parameters obtained by calculating different values of t with experimental data is also studied.Finally,we draw the graphs of G(t),X(t),I(t),andD(t)for different values ofτ.It is also clear from the obtained results and their graphical representation that the obtained results of modified Bergman’s minimal model are better than Bergman’s model.展开更多
In a previous work, we described the Minimal Model Program in the family of Q-Gorenstein projective horospherical varieties, by studying certain continuous changes of moment polytopes of polarized horospherical variet...In a previous work, we described the Minimal Model Program in the family of Q-Gorenstein projective horospherical varieties, by studying certain continuous changes of moment polytopes of polarized horospherical varieties. Here, we summarize the results of the previous work and we explain how to generalize them in order to describe the Log Minimal Model Program for pairs(X, Δ) when X is a projective horospherical variety.展开更多
We show the validity of the relative dlt MMP overℚ-factorial threefolds in all characteristics p>0.As a corollary,we generalise many recent results to low characteristics including:WO-rationality of klt singulariti...We show the validity of the relative dlt MMP overℚ-factorial threefolds in all characteristics p>0.As a corollary,we generalise many recent results to low characteristics including:WO-rationality of klt singularities,inversion of adjunction,and normality of divisorial centres up to a universal homeomorphism.展开更多
We examine a hierarchy of minimal conceptual models for tropical cyclone intensification.These models are framed mostly in terms of axisymmetric balance dynamics.In the first set of models,the heating rate is prescrib...We examine a hierarchy of minimal conceptual models for tropical cyclone intensification.These models are framed mostly in terms of axisymmetric balance dynamics.In the first set of models,the heating rate is prescribed in such a way to mimic a deep overturning circulation with convergence in the lower troposphere and divergence in the upper troposphere,characteristic of a region of deep moist convection.In the second set,the heating rate is related explicitly to the latent heat release of ascending air parcels.The release of latent heat markedly reduces the local static stability of ascending air,raising two possibilities in the balance framework.The first possibility is that the effective static stability and the related discriminant in the Eliassen equation for the overturning circulation in saturated air,although small,remains positive so the Eliassen equation is globally elliptic.The second possibility,the more likely one during vortex intensification,is that the effective static stability in saturated air is negative and the Eliassen equation becomes locally hyperbolic.These models help to understand the differences between the early Ooyama models of 1968 and 1969,the Emanuel,1989 model,and the later Emanuel models of 1995,1997 and 2012.They provide insight also into the popular explanation of the WISHE feedback mechanism for tropical cyclone intensification.Some implications for recent work are discussed.展开更多
The Minimal Higgsless Model predicts the existence of new vector gauge boson W1^±, By the process PP →W1^±qq →W^±Z^0qq, Z^0→ 1^+1^-, W^±→ qq (1=e,μ; q is hadronized to be jets), we study th...The Minimal Higgsless Model predicts the existence of new vector gauge boson W1^±, By the process PP →W1^±qq →W^±Z^0qq, Z^0→ 1^+1^-, W^±→ qq (1=e,μ; q is hadronized to be jets), we study the sensitivity of searching for this possible vector gauge boson in the level of generator events of signal and backgrounds, then give integrated luminosity required to discover 5σ signal as a function of W1^± mass. The generator for the signal PP → W1^±qq →W^±Z^0qq at tree level is developed with the Minimal Higgsless Model and then interfaced with PYTHIA for the patton showers and hadronization. The backgrounds are produced with MadGraph and PYTHIA.展开更多
In Asaka et al(2021 Phys.Rev.D 103,015014),Asaka,Ishida and Tanaka put forward an interesting possibility that the neutrinoless double beta decay can be hidden in the minimal seesaw model with the two right-handed neu...In Asaka et al(2021 Phys.Rev.D 103,015014),Asaka,Ishida and Tanaka put forward an interesting possibility that the neutrinoless double beta decay can be hidden in the minimal seesaw model with the two right-handed neutrinos having a hierarchical mass structure:the lighter one is lighter enough than the typical Fermi-momentum scale of nuclei while the heavier one is sufficiently heavy to decouple from the neutrinoless double beta decay.Then,in the basis where the mass matrices of the charged leptons and right-handed neutrinos are diagonal,for some particular texture of the Dirac neutrino mass matrix M_(D),the neutrinoless double beta decay can be hidden.In this paper,on top of this specified model,we study the interesting scenario that M_(D)further obeys the TM1 symmetry orμ-τreflection symmetry which are well motivated by the experimental results for the neutrino mixing parameters.展开更多
This paper describes a method based on an energy minimizing deformable model applied to the 3D biomechanical modeling of a set of organs considered as regions of interest (ROI) for radiotherapy. The initial model cons...This paper describes a method based on an energy minimizing deformable model applied to the 3D biomechanical modeling of a set of organs considered as regions of interest (ROI) for radiotherapy. The initial model consists of a quadratic surface that is deformed to the exact contour of the ROI by means of the physical properties of a mass-spring system. The exact contour of each ROI is first obtained using a geodesic active contour model. The ROI is then parameterized by the vibration modes resulting from the deformation process. Once each structure has been defined, the method provides a 3D global model including the whole set of ROIs. This model allows one to describe statistically the most significant variations among its structures. Statistical ROI variations among a set of patients or through time can be analyzed. Experimental results are presented using the pelvic zone to simulate anatomical variations among structures and its application in radiotherapy treatment planning.展开更多
This paper develops a new combined network equilibrium model by using more behaviorally sound mathematical forms to represent the four travel choices(i.e., trip frequency,destination, mode, and route) in a conventio...This paper develops a new combined network equilibrium model by using more behaviorally sound mathematical forms to represent the four travel choices(i.e., trip frequency,destination, mode, and route) in a conventional travel demand forecasting process. Trip frequency choice relates to the traveler decision on “making a trip” or “not making a trip”so it is given by a binary logit model. Destination choice is formulated as a parameterized dogit model of which the captivity parameters(expressed as functions of independent variables) allow individual travelers to be captive to specific destinations. Mode choice is given by a two-level nested logit model to avoid IIA restriction. Trip assignment is based on Wardrop's “user-optimized” principle. All model forms describing travel choices are in response to the level of services incurred by the transportation system. Through the introduction of inclusive values, the traveler decisions concerning trip frequency, destination, mode, and route choices are inherently interrelated and jointly determined.To obtain solutions of the new combined model, it was reformulated as an equivalent convex programming problem with linear constraints, a great advantage from the computational aspects. The model was applied empirically to a transportation network in New Jersey. The application results show that the new model is consistently better than the commonly used logit combined model in reproducing the observed trip flows from origin zones, origin to destination(O-D) trip flows, O-D trip flows by mode, and trip flows on the network links.展开更多
We prove the termination of flips for pseudo-effective NQC log canonical generalized pairs of dimension 4.As main ingredients,we verify the termination of flips for 3-dimensional NQC log canonical generalized pairs,an...We prove the termination of flips for pseudo-effective NQC log canonical generalized pairs of dimension 4.As main ingredients,we verify the termination of flips for 3-dimensional NQC log canonical generalized pairs,and show that the termination of flips for pseudo-effective NQC log canonical generalized pairs which admit NQC weak Zariski decompositions follows from the termination of flips in lower dimensions.展开更多
In this paper,we consider the generalized Nash equilibrium with shared constraints in the stochastic environment,and we call it the stochastic generalized Nash equilibrium.The stochastic variational inequalities are e...In this paper,we consider the generalized Nash equilibrium with shared constraints in the stochastic environment,and we call it the stochastic generalized Nash equilibrium.The stochastic variational inequalities are employed to solve this kind of problems,and the expected residual minimization model and the conditional value-at-risk formulations defined by the residual function for the stochastic variational inequalities are discussed.We show the risk for different kinds of solutions for the stochastic generalized Nash equilibrium by the conditional value-at-risk formulations.The properties of the stochastic quadratic generalized Nash equilibrium are shown.The smoothing approximations for the expected residual minimization formulation and the conditional value-at-risk formulation are employed.Moreover,we establish the gradient consistency for the measurable smoothing functions and the integrable functions under some suitable conditions,and we also analyze the properties of the formulations.Numerical results for the applications arising from the electricity market model illustrate that the solutions for the stochastic generalized Nash equilibrium given by the ERM model have good properties,such as robustness,low risk and so on.展开更多
We study the Dirichlet problem of the n-dimensional complex Monge-Ampere equation det(uij) = F/|z|2a, where 0 〈 a 〈 n. This equation comes from La Nave-Tian's continuity approach to the Analytic Minimal Model P...We study the Dirichlet problem of the n-dimensional complex Monge-Ampere equation det(uij) = F/|z|2a, where 0 〈 a 〈 n. This equation comes from La Nave-Tian's continuity approach to the Analytic Minimal Model Program.展开更多
In our previous work,we introduced the Generalised Nonvanishing Conjecture,which generalises several central conjectures in algebraic geometry.In this paper,we derive some remarkable nonvanishing results for pluricano...In our previous work,we introduced the Generalised Nonvanishing Conjecture,which generalises several central conjectures in algebraic geometry.In this paper,we derive some remarkable nonvanishing results for pluricanonical bundles which were not predicted by the Minimal Model Program,by making progress towards the Generalised Nonvanishing Conjecture in every dimension.The main step is to establish that a somewhat stronger version of the Generalised Nonvanishing Conjecture holds almost always in the presence of metrics with generalised algebraic singularities,assuming the Minimal Model Program in lower dimensions.展开更多
This paper considers the so-called expected residual minimization(ERM)formulation for stochastic second-order cone complementarity problems,which is based on a new complementarity function called termwise residual com...This paper considers the so-called expected residual minimization(ERM)formulation for stochastic second-order cone complementarity problems,which is based on a new complementarity function called termwise residual complementarity function associated with second-order cone.We show that the ERM model has bounded level sets under the stochastic weak R0-property.We further derive some error bound results under either the strong monotonicity or some kind of constraint qualifications.Then,we apply the Monte Carlo approximation techniques to solve the ERM model and establish a comprehensive convergence analysis.Furthermore,we report some numerical results on a stochastic second-order cone model for optimal power flow in radial networks.展开更多
This paper deals with Markov decision processes with a target set for nonpositive rewards. Two types of threshold probability criteria are discussed. The first criterion is a probability that a total reward is not gre...This paper deals with Markov decision processes with a target set for nonpositive rewards. Two types of threshold probability criteria are discussed. The first criterion is a probability that a total reward is not greater than a given initial threshold value, and the second is a probability that the total reward is less than it. Our first (resp. second) optimizing problem is to minimize the first (resp. second) threshold probability. These problems suggest that the threshold value is a permissible level of the total reward to reach a goal (the target set), that is, we would reach this set over the level, if possible. For the both problems, we show that 1) the optimal threshold probability is a unique solution to an optimality equation, 2) there exists an optimal deterministic stationary policy, and 3) a value iteration and a policy space iteration are given. In addition, we prove that the first (resp. second) optimal threshold probability is a monotone increasing and right (resp. left) continuous function of the initial threshold value and propose a method to obtain an optimal policy and the optimal threshold probability in the first problem by using them in the second problem.展开更多
基金Project supported by the Serbian Ministry of Science(Grant Nos.171017 and 174010)
文摘The minimal two-dimensional model of bursting neuronal dynamics is used to study the influence of time-delay on the properties of synchronization of bursting neurons. Generic properties of bursting and dependence of the stability of synchronization on the time-lag and the strength of coupling are described, and compared with the two common types of synaptical coupling, i.e., time-delayed chemical and electrical synapses.
文摘This research is an attempt to validate how glu-cose-insulin dynamic mathematical model facilitate to identify the root causes for hypoglycaemia. The purpose is to determine whether increased insulin sensitivity or increased insulin secretion causes post- prandial hypoglycemic (PPH) response, by linking experimental patient data with dynamic mathematical model. For this purpose two groups, as hypoglycemic Group 1 and non-hypoglycemic Group 2, each of which consists of 10 people, are formed. The oral glucose tolerance test (OGTT) is carried out for each person in the groups by measuring plasma glucose and insulin concentrations at every 30 minutes for a period of 5 hours. To distinguish the actual cause of hypoglycemia, the glucose minimal dynamic model is used. The model is executed in MATLAB platform using patient data and the results showed that insulin secretion is assumed to be the potential root cause for the hypoglycemia.
文摘Diabetes is a burning issue in the whole world.It is the imbalance between body glucose and insulin.The study of this imbalance is very much needed from a research point of view.For this reason,Bergman gave an important model named-Bergman minimalmodel.In the present work,using Caputo-Fabrizio(CF)fractional derivative,we generalize Bergman’s minimal blood glucose-insulin model.Further,we modify the old model by including one more component known as diet D(t),which is also essential for the blood glucose model.We solve the modified modelwith the help of Sumudu transformand fixed-point iteration procedures.Also,using the fixed point theorem,we examine the existence and uniqueness of the results along with their numerical and graphical representation.Furthermore,the comparison between the values of parameters obtained by calculating different values of t with experimental data is also studied.Finally,we draw the graphs of G(t),X(t),I(t),andD(t)for different values ofτ.It is also clear from the obtained results and their graphical representation that the obtained results of modified Bergman’s minimal model are better than Bergman’s model.
文摘In a previous work, we described the Minimal Model Program in the family of Q-Gorenstein projective horospherical varieties, by studying certain continuous changes of moment polytopes of polarized horospherical varieties. Here, we summarize the results of the previous work and we explain how to generalize them in order to describe the Log Minimal Model Program for pairs(X, Δ) when X is a projective horospherical variety.
基金supported by NSF research Grants no.DMS-1300750,DMS-1840190,DMS-1801851 and by a grant from the Simons Foundation,Award number 256202supported by the Engineering and Physical Sciences Research Council(EP/L015234/1)during his PhD at Imperial College London+1 种基金the National Science Foundation under Grant no.DMS-1638352 at the Institute for Advanced Study in Princetonthe National Science Foundation under Grant no.DMS-1440140 while the author was in residence at the Mathematical Sciences Research Institute in Berkeley,California,during the Spring 2019 semester.
文摘We show the validity of the relative dlt MMP overℚ-factorial threefolds in all characteristics p>0.As a corollary,we generalise many recent results to low characteristics including:WO-rationality of klt singularities,inversion of adjunction,and normality of divisorial centres up to a universal homeomorphism.
基金the support of NSF grant IAA1656075ONR grant N0001417WX00336the U.S.Naval Postgraduate School。
文摘We examine a hierarchy of minimal conceptual models for tropical cyclone intensification.These models are framed mostly in terms of axisymmetric balance dynamics.In the first set of models,the heating rate is prescribed in such a way to mimic a deep overturning circulation with convergence in the lower troposphere and divergence in the upper troposphere,characteristic of a region of deep moist convection.In the second set,the heating rate is related explicitly to the latent heat release of ascending air parcels.The release of latent heat markedly reduces the local static stability of ascending air,raising two possibilities in the balance framework.The first possibility is that the effective static stability and the related discriminant in the Eliassen equation for the overturning circulation in saturated air,although small,remains positive so the Eliassen equation is globally elliptic.The second possibility,the more likely one during vortex intensification,is that the effective static stability in saturated air is negative and the Eliassen equation becomes locally hyperbolic.These models help to understand the differences between the early Ooyama models of 1968 and 1969,the Emanuel,1989 model,and the later Emanuel models of 1995,1997 and 2012.They provide insight also into the popular explanation of the WISHE feedback mechanism for tropical cyclone intensification.Some implications for recent work are discussed.
基金Supported by NSFC (10435070,10721140381,10099630)China Ministry of Science and Technology (2007CB16101)+1 种基金CAS(KJCX2-N17,1730911111)China Postdoctoral Science Foundation (20090450577)
文摘The Minimal Higgsless Model predicts the existence of new vector gauge boson W1^±, By the process PP →W1^±qq →W^±Z^0qq, Z^0→ 1^+1^-, W^±→ qq (1=e,μ; q is hadronized to be jets), we study the sensitivity of searching for this possible vector gauge boson in the level of generator events of signal and backgrounds, then give integrated luminosity required to discover 5σ signal as a function of W1^± mass. The generator for the signal PP → W1^±qq →W^±Z^0qq at tree level is developed with the Minimal Higgsless Model and then interfaced with PYTHIA for the patton showers and hadronization. The backgrounds are produced with MadGraph and PYTHIA.
基金supported in part by the National Natural Science Foundation of China under Grant Nos.11605081,12142507 and 12147214the Natural Science Foundation of the Liaoning Scientific Committee under grant NO.2022-MS-314。
文摘In Asaka et al(2021 Phys.Rev.D 103,015014),Asaka,Ishida and Tanaka put forward an interesting possibility that the neutrinoless double beta decay can be hidden in the minimal seesaw model with the two right-handed neutrinos having a hierarchical mass structure:the lighter one is lighter enough than the typical Fermi-momentum scale of nuclei while the heavier one is sufficiently heavy to decouple from the neutrinoless double beta decay.Then,in the basis where the mass matrices of the charged leptons and right-handed neutrinos are diagonal,for some particular texture of the Dirac neutrino mass matrix M_(D),the neutrinoless double beta decay can be hidden.In this paper,on top of this specified model,we study the interesting scenario that M_(D)further obeys the TM1 symmetry orμ-τreflection symmetry which are well motivated by the experimental results for the neutrino mixing parameters.
基金Project partially supported by the VI FP and VII FP of the European Commission through MAESTRO and ENVISIONprojects (Nos. IP CE503564 and SP CE241851)Spanish Junta de Comunidades de Castilla–La Mancha (Nos. PBC06-0019 and PI-2006/01.1)
文摘This paper describes a method based on an energy minimizing deformable model applied to the 3D biomechanical modeling of a set of organs considered as regions of interest (ROI) for radiotherapy. The initial model consists of a quadratic surface that is deformed to the exact contour of the ROI by means of the physical properties of a mass-spring system. The exact contour of each ROI is first obtained using a geodesic active contour model. The ROI is then parameterized by the vibration modes resulting from the deformation process. Once each structure has been defined, the method provides a 3D global model including the whole set of ROIs. This model allows one to describe statistically the most significant variations among its structures. Statistical ROI variations among a set of patients or through time can be analyzed. Experimental results are presented using the pelvic zone to simulate anatomical variations among structures and its application in radiotherapy treatment planning.
文摘This paper develops a new combined network equilibrium model by using more behaviorally sound mathematical forms to represent the four travel choices(i.e., trip frequency,destination, mode, and route) in a conventional travel demand forecasting process. Trip frequency choice relates to the traveler decision on “making a trip” or “not making a trip”so it is given by a binary logit model. Destination choice is formulated as a parameterized dogit model of which the captivity parameters(expressed as functions of independent variables) allow individual travelers to be captive to specific destinations. Mode choice is given by a two-level nested logit model to avoid IIA restriction. Trip assignment is based on Wardrop's “user-optimized” principle. All model forms describing travel choices are in response to the level of services incurred by the transportation system. Through the introduction of inclusive values, the traveler decisions concerning trip frequency, destination, mode, and route choices are inherently interrelated and jointly determined.To obtain solutions of the new combined model, it was reformulated as an equivalent convex programming problem with linear constraints, a great advantage from the computational aspects. The model was applied empirically to a transportation network in New Jersey. The application results show that the new model is consistently better than the commonly used logit combined model in reproducing the observed trip flows from origin zones, origin to destination(O-D) trip flows, O-D trip flows by mode, and trip flows on the network links.
基金supported by the China National Postdoctoral Program for Innovative Talents(Grant No.BX2021269)by the China Postdoctoral Science Foundation(Grant No.2021M702925)。
文摘We prove the termination of flips for pseudo-effective NQC log canonical generalized pairs of dimension 4.As main ingredients,we verify the termination of flips for 3-dimensional NQC log canonical generalized pairs,and show that the termination of flips for pseudo-effective NQC log canonical generalized pairs which admit NQC weak Zariski decompositions follows from the termination of flips in lower dimensions.
基金National Natural Science Foundation of China(No.11601541,No.12171027)State Key Laboratory of Scientific and Engineering Computing,Chinese Academy of SciencesYouth Foundation of Minzu University of China(No.2021QNPY98).
文摘In this paper,we consider the generalized Nash equilibrium with shared constraints in the stochastic environment,and we call it the stochastic generalized Nash equilibrium.The stochastic variational inequalities are employed to solve this kind of problems,and the expected residual minimization model and the conditional value-at-risk formulations defined by the residual function for the stochastic variational inequalities are discussed.We show the risk for different kinds of solutions for the stochastic generalized Nash equilibrium by the conditional value-at-risk formulations.The properties of the stochastic quadratic generalized Nash equilibrium are shown.The smoothing approximations for the expected residual minimization formulation and the conditional value-at-risk formulation are employed.Moreover,we establish the gradient consistency for the measurable smoothing functions and the integrable functions under some suitable conditions,and we also analyze the properties of the formulations.Numerical results for the applications arising from the electricity market model illustrate that the solutions for the stochastic generalized Nash equilibrium given by the ERM model have good properties,such as robustness,low risk and so on.
基金supported by NSFC(Grant No.11331001)supported by NSFC(Grant No.11501285)
文摘We study the Dirichlet problem of the n-dimensional complex Monge-Ampere equation det(uij) = F/|z|2a, where 0 〈 a 〈 n. This equation comes from La Nave-Tian's continuity approach to the Analytic Minimal Model Program.
文摘In our previous work,we introduced the Generalised Nonvanishing Conjecture,which generalises several central conjectures in algebraic geometry.In this paper,we derive some remarkable nonvanishing results for pluricanonical bundles which were not predicted by the Minimal Model Program,by making progress towards the Generalised Nonvanishing Conjecture in every dimension.The main step is to establish that a somewhat stronger version of the Generalised Nonvanishing Conjecture holds almost always in the presence of metrics with generalised algebraic singularities,assuming the Minimal Model Program in lower dimensions.
基金This work was supported in part by the National Natural Science Foundation of China(Nos.71831008,11671250,11431004 and 11601458)Humanity and Social Science Foundation of Ministry of Education of China(No.15YJA630034)+2 种基金Shandong Province Natural Science Fund(No.ZR2014AM012)Higher Educational Science and Technology Program of Shandong Province(No.J13LI09)Scientific Research of Young Scholar of Qufu Normal University(No.XKJ201315).
文摘This paper considers the so-called expected residual minimization(ERM)formulation for stochastic second-order cone complementarity problems,which is based on a new complementarity function called termwise residual complementarity function associated with second-order cone.We show that the ERM model has bounded level sets under the stochastic weak R0-property.We further derive some error bound results under either the strong monotonicity or some kind of constraint qualifications.Then,we apply the Monte Carlo approximation techniques to solve the ERM model and establish a comprehensive convergence analysis.Furthermore,we report some numerical results on a stochastic second-order cone model for optimal power flow in radial networks.
文摘This paper deals with Markov decision processes with a target set for nonpositive rewards. Two types of threshold probability criteria are discussed. The first criterion is a probability that a total reward is not greater than a given initial threshold value, and the second is a probability that the total reward is less than it. Our first (resp. second) optimizing problem is to minimize the first (resp. second) threshold probability. These problems suggest that the threshold value is a permissible level of the total reward to reach a goal (the target set), that is, we would reach this set over the level, if possible. For the both problems, we show that 1) the optimal threshold probability is a unique solution to an optimality equation, 2) there exists an optimal deterministic stationary policy, and 3) a value iteration and a policy space iteration are given. In addition, we prove that the first (resp. second) optimal threshold probability is a monotone increasing and right (resp. left) continuous function of the initial threshold value and propose a method to obtain an optimal policy and the optimal threshold probability in the first problem by using them in the second problem.