Synchronization of the minimal models of bursting neurons coupled by delayed chemical or electrical synapses

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.

Computational evaluation of the dynamic minimal model for the root causes of hypoglycemia

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.

Solution of Modified Bergman Minimal Blood Glucose-Insulin Model Using Caputo-Fabrizio Fractional Derivative

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.

The Log Minimal Model Program for Horospherical Varieties Via Moment Polytopes

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.

On the Relative Minimal Model Program for Threefolds in Low Characteristics

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.

A Simple Proof of ACC for Minimal Log Discrepancies for Surfaces

Following Shokurov's idea,we give a simple proof of the ACC conjecture for minimal log discrepancies for surfaces.

Minimal conceptual models for tropical cyclone intensification

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.

Study of new boson W1^± in the Minimal Higgsless Model at the LHC

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.

Hiding neutrinoless double beta decay in the minimal seesaw model with the TM1 orμ-τreflection symmetry

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.

Three-dimensional organ modeling based on deformable surfaces applied to radio-oncology

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.

Implementation of a new network equilibrium model of travel choices

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.

On the Termination of Flips for Log Canonical Generalized Pairs

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.

STOCHASTIC VARIATIONAL INEQUALITY APPROACHES TO THE STOCHASTIC GENERALIZED NASH EQUILIBRIUM WITH SHARED CONSTRAINTS

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.

On the Dirichlet Problem for a Class of Singular Complex Monge–Ampère Equations

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.

On Generalised Abundance,Ⅱ

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.

A New Complementarity Function and Applications in Stochastic Second-Order Cone Complementarity Problems

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.

Markov decision processes associated with two threshold probability criteria

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.