quasistationary trajectories of the mean field xy hamiltonian model a topological perspective we employ a topological approach to investigate the nature of quasistationary states of the mean field xy hamiltonian model we focus on the quasistationary states reached when the system is initially prepared in a fully magnetized configuration by means of numerical simulations and analytical considerations we show that along the quasistationary trajectories the system evolves in a manifold of critical points of the potential energy function although these critical points are maxima the large number of directions with marginal stability may be responsible for the slow relaxation dynamics and the trapping of the system in such trajectories

the commutation theorem for tensor products over von neumann algebras abstract a general commutation theorem is proved for tensor products of von neumann algebras over common von neumann subalgebras roughly speaking if the non common parts of two von neumann algebras m 1 and m 2 on the same hilbert space are appropriately separated by commuting type i von neumann algebras n 1 and n 2 then the commutant of the von neumann algebra generated by m 1 and m 2 is generated by the relative commutants m 1 n 1 and m 2 n 2 as well as by the intersection of the commutants of all concerned von neumann algebras this theorem extends both tomita s classical commutation theorem and a splitting result in tensor products proved recently in the factor case by l ge and r v kadison applications are given to a decomposition criterion in ordinary tensor products and to a partial solution of a conjecture of s popa concerning the maximal injectivity of tensor products of maximal injective von neumann subalgebras

cross validation in survival analysis the predictive value of a statistical model is conceptually different from the explained variation in this paper we construct a measure of the predictive value of the cox proportional hazards model computed from the leave one out regression coefficients these coefficients can also be used to calculate a shrinkage factor which can be applied to improve the predictions and that can be used in r2 type measures of the proportion of explained variation our methods are illustrated by a study of chemotherapy for advanced ovarian cancer

explained variation for logistic regression different measures of the proportion of variation in a dependent variable explained by covariates are reported by different standard programs for logistic regression we review twelve measures that have been suggested or might be useful to measure explained variation in logistic regression models the definitions and properties of these measures are discussed and their performance is compared in an empirical study two of the measures squared pearson correlation between the binary outcome and the predictor and the proportional reduction of squared pearson residuals by the use of covariates give almost identical results agree very well with the multiple r2 of the general linear model have an intuitively clear interpretation and perform satisfactorily in our study for all measures the explained variation for the given sample and also the one expected in future samples can be obtained easily for small samples an adjustment analogous to radj2 in the general linear model is suggested we discuss some aspects of application and recommend the routine use of a suitable measure of explained variation for logistic models

sample size considerations and predictive performance of multinomial logistic prediction models multinomial logistic regression mlr has been advocated for developing clinical prediction models that distinguish between three or more unordered outcomes we present a full factorial simulation study to examine the predictive performance of mlr models in relation to the relative size of outcome categories number of predictors and the number of events per variable it is shown that mlr estimated by maximum likelihood yields overfitted prediction models in small to medium sized data in most cases the calibration and overall predictive performance of the multinomial prediction model is improved by using penalized mlr our simulation study also highlights the importance of events per variable in the multinomial context as well as the total sample size as expected our study demonstrates the need for optimism correction of the predictive performance measures when developing the multinomial logistic prediction model we recommend the use of penalized mlr when prediction models are developed in small data sets or in medium sized data sets with a small total sample size ie when the sizes of the outcome categories are balanced finally we present a case study in which we illustrate the development and validation of penalized and unpenalized multinomial prediction models for predicting malignancy of ovarian cancer

explained variation in survival analysis several measures of explained variation have been suggested for the cox proportional hazards regression model we have categorized these measures into three classes which correspond to three different definitions of multiple r2 of the general linear model in an empirical study we compared the performance of these measures and classified them by their adherence to a set of criteria which we think should be met by a measure of explained variation for survival data we suggest that currently there is no uniformly superior measure particularly as the concepts of either uncensored or censored populations may lead to different choices for uncensored populations a measure by kent and o quigley and the squared rank correlation between survival time and the predictor from a cox regression model appear recommendable choices for the latter censored survival times are terminated using a very recent data augmentation algorithm for multiple imputation under proportional hazards with censored populations schemper s measure v2 could be considered we give an introductory example discuss aspects of application and stress the desirability of routinely evaluating explained variation in studies of survival

a logistic prediction model for individual allowable noise levels annoyance to noise is probably a good measure of the potential for complaint and community action each individual s degree of annoyance to noise cannot be accurately predicted from conventional laboratory studies and social surveys therefore a logistic prediction model for individual allowable noise levels has been developed in a previous paper k furihata et al acta acust acust 93 73 83 2007 an annoyance scale using the most frequently used annoyance ratings related to noise for community noise assessment in japan was constructed the dose response relationships were obtained by actually listening to sounds in a field situation 1474 subjects carried out at 14 metropolitan cities in japan the logistic prediction model was developed using the logistic regression parameters estimated from each cumulative percentage curve of seven annoyance scale scores based on all data n 2940 to verify the hypothesis individual relationships between annoyance and laeq 5min for 24 normal hearing subje

minimum sample size for developing a multivariable prediction model part ii binary and time to event outcomes when designing a study to develop a new prediction model with binary or time to event outcomes researchers should ensure their sample size is adequate in terms of the number of participants n and outcome events e relative to the number of predictor parameters p considered for inclusion we propose that the minimum values of n and e and subsequently the minimum number of events per predictor parameter epp should be calculated to meet the following three criteria i small optimism in predictor effect estimates as defined by a global shrinkage factor of 0 9 ii small absolute difference of 0 05 in the model s apparent and adjusted nagelkerke s r2 and iii precise estimation of the overall risk in the population criteria i and ii aim to reduce overfitting conditional on a chosen p and require prespecification of the model s anticipated cox snell r2 which we show can be obtained from previous studies the values of n and e that meet all three criteria provides the minimum sample size required for model development upon application of our approach a new diagnostic model for chagas disease requires an epp of at least 4 8 and a new prognostic model for recurrent venous thromboembolism requires an epp of at least 23 this reinforces why rules of thumb eg 10 epp should be avoided researchers might additionally ensure the sample size gives precise estimates of key predictor effects this is especially important when key categorical predictors have few events in some categories as this may substantially increase the numbers required

computational topology for configuration spaces of hard disks we explore the topology of configuration spaces of hard disks experimentally and show that several changes in the topology can already be observed with a small number of particles the results illustrate a theorem of baryshnikov bubenik and kahle 2 that critical points correspond to configurations of disks with balanced mechanical stresses and suggest conjectures about the asymptotic topology as the number of disks tends to infinity

dynamics and geometric properties of the k trigonometric model we analyse the dynamics and the geometric properties of the potential energy surfaces pes of the k trigonometric model ktm defined by a fully connected k body interaction this model has no thermodynamic transition for k 1 a second order one for k 2 and a first order one for k 2 in this paper we i show that the single particle dynamics can be traced back to an effective dynamical system with only one degree of freedom ii compute the diffusion constant analytically iii determine analytically several properties of the self correlation functions apart from the relaxation times which we calculate numerically iv relate the collective correlation functions to those of the effective degree of freedom using an exact dyson like equation v using two analytical methods calculate the saddles of the pes that are visited by the system evolving at fixed temperature on the one hand we minimize v 2 as usually done in the numerical study of supercooled liquids and on the other hand we compute the saddles with minimum distance in configuration space from initial equilibrium configurations we find the same result from the two calculations and we speculate that the coincidence might go beyond the specific model investigated here

a note on a general definition of the coefficient of determination summary a generalization of the coefficient of determination r2 to general regression models is discussed a modification of an earlier definition to allow for discrete models is proposed

thermodynamic limits of dynamic cooling we study dynamic cooling where an externally driven two level system is cooled via reservoir a quantum system with initial canonical equilibrium state we obtain explicitly the minimal possible temperature t min 0 reachable for the two level system the minimization goes over all unitary dynamic processes operating on the system and reservoir and over the reservoir energy spectrum the minimal work needed to reach t min grows as 1 t min this work cost can be significantly reduced though if one is satisfied by temperatures slightly above t min our results on t min 0 prove unattainability of the absolute zero temperature without ambiguities that surround its derivation from the entropic version of the third law we also study cooling via a reservoir consisting of n 1 identical spins here we show that t min 1 n and find the maximal cooling compatible with the minimal work determined by the free energy finally we discuss cooling by reservoir with an initially microcanonic state and show that although a purely microcanonic state can yield the zero temperature the unattainability is recovered when taking into account imperfections in preparing the microcanonic state

energy landscape properties studied using symbolic sequences abstract we investigate a classical lattice system with n particles the potential energy v of the scalar displacements is chosen as a 4 on site potential plus interactions its stationary points are solutions of a coupled set of nonlinear equations starting with aubry s anti continuum limit it is easy to establish a one to one correspondence between the stationary points of v and symbolic sequences 1 n with n 0 we prove that this correspondence remains valid for interactions with a coupling constant below a critical value c and that it allows the use of a thermodynamic formalism to calculate statistical properties of the so called energy landscape of v this offers an explanation for why topological quantities of v may become singular like in phase transitions in particular we find that the saddle index distribution is maximum at a saddle index n s max 1 3 for all c furthermore there exists an interval v v max in which the saddle index n s as a function of the average energy v is analytical in v and it vanishes at v above the ground state energy v gs whereas the average saddle index n s as a function of the energy v is highly nontrivial it can exhibit a singularity at a critical energy v c and it vanishes at v gs only close to v gs n s v exhibits power law behavior which even holds for noninteracting particles

energy landscape analysis of the two dimensional nearest neighbor φ4 model the stationary points of the potential energy function of the a 4 model on a two dimensional square lattice with nearest neighbor interactions are studied by means of two numerical methods a numerical homotopy continuation method and a globally convergent newton raphson method we analyze the properties of the stationary points in particular with respect to a number of quantities that have been conjectured to display signatures of the thermodynamic phase transition of the model although no such signatures are found for the nearest neighbor a 4 model our study illustrates the strengths and weaknesses of the numerical methods employed

relationship between phase transitions and topological changes in one dimensional models we address the question of the quantitative relationship between thermodynamic phase transitions and topological changes in the potential energy manifold analyzing two classes of one dimensional models the burkhardt solid on solid model and the peyrard bishop model for dna thermal denaturation both in the confining and nonconfining version these models apparently do not fit m kastner phys rev lett 93 150601 2004 in the general idea that the phase transition is signaled by a topological discontinuity we show that in both models the phase transition energy v c is actually noncoincident with and always higher than the energy v ensuremath theta at which a topological change appears however applying a procedure already successfully employed in other cases as the mean field ensuremath phi 4 model i e introducing a map mathcal m v ensuremath rightarrow v s from levels of the energy hypersurface v to the level of the stationary points visited at temperature t we find that mathcal m v c v ensuremath theta this result enhances the relevance of the underlying stationary points in determining the thermodynamics of a system and extends the validity of the topological approach to the study of phase transition to the elusive one dimensional systems considered here

large deviation techniques applied to systems with long range interactions we discuss a method to solve models with long range interactions in the microcanonical and canonical ensemble the method closely follows the one introduced by r s ellis physica d 133 106 1999 which uses large deviation techniques we show how it can be adapted to obtain the solution of a large class of simple models which can show ensemble inequivalence the model hamiltonian can have both discrete ising potts and continuous hmf free electron laser state variables this latter extension gives access to the comparison with dynamics and to the study of non equilibrium effects we treat both infinite range and slowly decreasing interactions and in particular we present the solution of the ising model in one dimension with 0 1

partial equivalence of statistical ensembles and kinetic energy abstract the phenomenon of partial equivalence of statistical ensembles is illustrated by discussing two examples the mean field xy and the mean field spherical model the configurational parts of these systems exhibit partial equivalence of the microcanonical and the canonical ensemble furthermore the configurational microcanonical entropy is a smooth function whereas a nonanalytic point of the configurational free energy indicates the presence of a phase transition in the canonical ensemble in the presence of a standard kinetic energy contribution partial equivalence is removed and a nonanalyticity arises also microcanonically hence in contrast to the common belief kinetic energy even though a quadratic form in the momenta has a nontrivial effect on the thermodynamic behaviour as a by product we present the microcanonical solution of the mean field spherical model with kinetic energy for finite and infinite system sizes

exploring the energy landscape of xy models we investigate the energy landscape of two and three dimensional xy models with nearest neighbor interactions by analytically constructing several classes of stationary points of the hamiltonian these classes are analyzed in particular with respect to possible signatures of the thermodynamic phase transitions of the models we find that even after explicitly breaking the global o 2 symmetry of the xy spins an exponentially large class of stationary points are singular and occur in continuous one parameter families this property may complicate the use of theoretical tools developed for the investigation of phase transitions based on stationary points of the energy landscape and we discuss strategies to avoid these difficulties

variable screening via quantile partial correlation abstractin quantile linear regression with ultrahigh dimensional data we propose an algorithm for screening all candidate variables and subsequently selecting relevant predictors specifically we first employ quantile partial correlation for screening and then we apply the extended bayesian information criterion ebic for best subset selection our proposed method can successfully select predictors when the variables are highly correlated and it can also identify variables that make a contribution to the conditional quantiles but are marginally uncorrelated or weakly correlated with the response theoretical results show that the proposed algorithm can yield the sure screening set by controlling the false selection rate model selection consistency can be achieved theoretically in practice we proposed using ebic for best subset selection so that the resulting model is screening consistent simulation studies demonstrate that the proposed algorithm performs well and an empirical example is present

amplification of completely bounded operators and tomiyama s slice maps abstract let m n be a pair of von neumann algebras or of dual operator spaces with at least one of them having property s and let be an arbitrary completely bounded mapping on m we present an explicit construction of an amplification of to a completely bounded mapping on m n our approach is based on the concept of slice maps as introduced by tomiyama and makes use of the description of the predual of m n given by effros and ruan in terms of the operator space projective tensor product cf effros and ruan internat j math 1 2 1990 163 j operator theory 27 1992 179 we further discuss several properties of an amplification in connection with the investigations made in may et al arch math basel 53 3 1989 283 where the special case m b h and n b k has been considered for hilbert spaces h and k we will then mainly focus on various applications such as a remarkable purely algebraic characterization of w continuity using amplifications as well as a generalization of the so called ge kadison lemma in connection with the uniqueness problem of amplifications finally our study will enable us to show that the essential assertion of the main result in may et al 1989 concerning completely bounded bimodule homomorphisms actually relies on a basic property of tomiyama s slice maps

phase transitions and topology changes in configuration space the relation between thermodynamic phase transitions in classical systems and topological changes in their configuration space is discussed for two physical models and contains the first exact analytic computation of a topologic invariant the euler characteristic of certain submanifolds in the configuration space of two physical models the models are the mean field xy model and the one dimensional xy model with nearest neighbor interactions the former model undergoes a second order phase transition at a finite critical temperature while the latter has no phase transitions the computation of this topologic invariant is performed within the framework of morse theory in both models topology changes in configuration space are present as the potential energy is varied however in the mean field model there is a particularly strong topology change corresponding to a big jump in the euler characteristic connected with the phase transition which is absent in the one dimensional model with no phase transition the comparison between the two models has two major consequences i it lends new and strong support to a recently proposed topological approach to the study of phase transitions ii it allows us to conjecture which particular topology changes could entail a phase transition in general we also discuss a simplified illustrative model of the topology changes connected to phase transitions using of two dimensional surfaces and a possible direct connection between topological invariants and thermodynamic quantities

a robust alternative to the schemper henderson estimator of prediction error in clinical applications the prediction error of survival models has to be taken into consideration to assess the practical suitability of conclusions drawn from these models different approaches to evaluate the predictive performance of survival models have been suggested in the literature in this article we analyze the properties of the estimator of prediction error developed by schemper and henderson 2000 biometrics 56 249 255 which quantifies the absolute distance between predicted and observed survival functions we provide a formal proof that the estimator proposed by schemper and henderson is not robust against misspecification of the survival model that is the estimator will only be meaningful if the model family used for deriving predictions has been specified correctly to remedy this problem we construct a new estimator of the absolute distance between predicted and observed survival functions we show that this modified schemper henderson estimator is robust against model misspecification allowing its practical application to a wide class of survival models the properties of the schemper henderson estimator and its new modification are illustrated by means of a simulation study and the analysis of two clinical data sets

adaptive model selection and assessment for exponential family distributions in many scientific and engineering problems selecting the optimal model from a large pool of candidate models is important particularly in data mining in the literature model assessment in the context of nonnormal distributions has not yet received a lot of attention indeed many existing model selection criteria such as the bayes information criterion and cp may not be suitable for a situation in which the conditional mean and variance of the response are dependent such as in generalized linear model regression in this article we propose a new adaptive model selection criterion and construct an approximately unbiased kullback leibler loss estimator for model assessment in the context of exponential family distributions this permits comparing any arbitrary complex modeling procedures our proposal uses a concept called generalized degrees of freedom that generalizes the concept originally proposed for the normal distribution the proposed procedure is implemented for the binomial and poisson distr

exact result on topology and phase transitions at any finite n we study analytically the topology of a family of submanifolds of the configuration space of the mean field xy model computing also a topological invariant the euler characteristic we prove that a particular topological change of these submanifolds is connected to the phase transition of this system and exists also at finite n the present result is the first analytic proof that a phase transition has a topological origin and provides a key to a possible better understanding of the origin of phase transitions at their deepest level as well as to a possible definition of phase transitions at finiten

a measure of explained variation for event history data there is no shortage of proposed measures of prognostic value of survival models in the statistical literature they come under different names including explained variation correlation explained randomness and information gain but their goal is common to define something analogous to the coefficient of determination r 2 in linear regression none however have been uniformly accepted none have been extended to general event history data including recurrent events and many cannot incorporate time varying effects or covariates we present here a measure specifically tailored for use with general dynamic event history regression models the measure is applicable and interpretable in discrete or continuous time with tied data or otherwise with time varying time fixed or dynamic covariates with time varying or time constant effects with single or multiple event times with parametric or semiparametric models and under general independent censoring observation for single event survival data with neither censoring nor time dependency it reduces to the concordance index we give expressions for its population value and the variance of the estimator and explore its use in simulations and applications a web link to r software is provided

a comparison of estimators to evaluate the discriminatory power of time to event models discrimination measures for continuous time to event outcomes have become an important tool in medical decision making the idea behind discrimination measures is to evaluate the performance of a prediction model by measuring its ability to distinguish between observations having an event and those having no event researchers proposed a variety of approaches to estimate discrimination measures from a set of right censored data these approaches rely on different regularity assumptions that are needed to ensure consistency of the respective estimators typical examples of regularity assumptions include the proportional hazards assumption in cox regression and the random censoring assumption because regularity assumptions are often violated in practice conducting a sensitivity analysis of the estimators is of considerable interest the aim of the paper is to analyze and to compare the most popular estimators of discrimination measures for event time outcomes on the basis of the results of an extensive simulation study and the analysis of molecular data we investigate the behavior of the estimators in situations where the underlying regularity assumptions do not hold we show that violations of the regularity assumptions may induce a nonignorable bias and may therefore result in biased medical decision making

interpolation by type i factors and the flip automorphism abstract given two von neumann algebras a b we study the relation between the existence of an interpolating type i factor f namely a f b the implementability of the flip automorphism of a a by a unitary in b b and the statistical independence of a and b a and b generate a w tensor product as an application in q f t we derive in a natural way a structure theorem of buchholz for the von neumann algebras of local observables associated to free fields

on the mean field spherical model exact solutions are obtained for the mean field spherical model with or without an external magnetic field for any finite or infinite number n of degrees of freedom both in the microcanonical and in the canonical ensemble the canonical result allows for an exact discussion of the loci of the fisher zeros of the canonical partition function the microcanonical entropy is found to be nonanalytic for arbitrary finite n the mean field spherical model of finite size n is shown to be equivalent to a mixed isovector isotensor model on a lattice of two sites partial equivalence of statistical ensembles is observed for the mean field spherical model in the thermodynamic limit a discussion of the topology of certain state space submanifolds yields insights into the relation of these topological quantities to the thermodynamic behavior of the system in the presence of ensemble nonequivalence

numerical extension of cft amplitude universality to three dimensional systems conformal eld theory cft predicts universal relations between scaling amplitudes and scaling dimensions for two dimensional systems on innite length cylinders which hold true even independent of the model under consideration we discuss dierent possible generalizations of such laws to three dimensional geometries using a cluster update monte carlo algorithm we investigate the nite size scaling fss of the correlation lengths of several representatives of the class of three dimensional classical o n spin models we nd that choosing appropriate boundary conditions the two dimensional situation can be restored c 2000 elsevier science b v all rights reserved

on maximal injective subalgebras of tensor products of von neumann algebras abstract let m i be a von neumann algebra and b i be a maximal injective von neumann subalgebra of m i i 1 2 if m 1 has separable predual and the center of b 1 is atomic e g b 1 is a factor then b 1 b 2 is a maximal injective von neumann subalgebra of m 1 m 2 this partly answers a question of popa

a comparison of regression trees logistic regression generalized additive models and multivariate adaptive regression splines for predicting ami mortality clinicians and health service researchers are frequently interested in predicting patient specific probabilities of adverse events e g death disease recurrence post operative complications hospital readmission there is an increasing interest in the use of classification and regression trees cart for predicting outcomes in clinical studies we compared the predictive accuracy of logistic regression with that of regression trees for predicting mortality after hospitalization with an acute myocardial infarction ami we also examined the predictive ability of two other types of data driven models generalized additive models gams and multivariate adaptive regression splines mars we used data on 9484 patients admitted to hospital with an ami in ontario we used repeated split sample validation the data were randomly divided into derivation and validation samples predictive models were estimated using the derivation sample and the predictive accuracy of the resultant model was assessed using the area under the receiver operating characteristic roc curve in the validation sample this process was repeated 1000 times the initial data set was randomly divided into derivation and validation samples 1000 times and the predictive accuracy of each method was assessed each time the mean roc curve area for the regression tree models in the 1000 derivation samples was 0 762 while the mean roc curve area of a simple logistic regression model was 0 845 the mean roc curve areas for the other methods ranged from a low of 0 831 to a high of 0 851 our study shows that regression trees do not perform as well as logistic regression for predicting mortality following ami however the logistic regression model had performance comparable to that of more flexible data driven models such as gams and mars

role of saddles in mean field dynamics above the glass transition recent numerical developments in the study of glassy systems have shown that it is possible to give a purely geometric interpretation of the dynamic glass transition by considering the properties of unstable saddle points of the energy here we further develop this approach in the context of a mean field model by analytically studying the properties of the closest saddle point to an equilibrium configuration of the system we prove that when the glass transition is approached the energy of the closest saddle goes to the threshold energy defined as the energy level below which the degree of instability of the typical stationary points vanishes moreover we show that the distance between a typical equilibrium configuration and the closest saddle is always very small and that surprisingly it is almost independent of the temperature

spectral properties of tensor products of channels abstract we investigate spectral properties of the tensor products of two completely positive and trace preserving linear maps also known as quantum channels acting on matrix algebras this leads to an important question of when an arbitrary subalgebra can split into the tensor product of two subalgebras we show that for two unital quantum channels the multiplicative domain of their tensor product splits into the tensor product of the individual multiplicative domains consequently we fully describe the fixed points and peripheral eigen operators of the tensor product of channels through a structure theorem of maximal unital proper subalgebras mupsa of a matrix algebra we provide a non trivial upper bound of the recently introduced multiplicative index of a unital channel this bound gives a criteria on when a channel cannot be factored into a product of two different channels we construct examples of channels which cannot be realized as a tensor product of two channels in any way with these techniques and results we found some applications in quantum information theory

the predual of w tensor products over w subalgebras separable case let m n r be w algebras with r unitally embedded in both m and n by using reduction theory we describe the predual m rn of the w tensor product m rn over the common w subalgebra r in the separable predual case we also analyze the case when r is a direct sum of full matrix algebras without any separability assumption in the last situation the predual m rn is described by the center z rm n r of the r r bimodule rm n r the last one being isomorphic to the predual of m n it is also shown that such a reduction free result cannot be extended to the remaining cases

statistical modeling and analysis for robust synthesis of nanostructures we systematically investigate the best process conditions that ensure synthesis of different types of one dimensional cadmium selenide nanostructures with high yield and reproducibility through a designed experiment and rigorous statistical analysis of experimental data models linking the probabilities of obtaining specific morphologies to the process variables are developed a new iterative algorithm for fitting a multinomial generalized linear model is proposed and used the optimum process conditions which maximize the preceding probabilities and make the synthesis process robust i e less sensitive to variations in process variables around set values are derived from the fitted models using monte carlo simulations cadmium selenide has been found to exhibit one dimensional morphologies of nanowires nanobelts and nanosaws often with the three morphologies being intimately intermingled within the as deposited material a slight change in growth condition can result in a totally different morpho

prediction accuracy measures for a nonlinear model and for right censored time to event data this article develops a pair of new prediction summary measures for a nonlinear prediction function with right censored time to event data the first measure defined as the proportion of explained

the mean field φ 4 model entropy analyticity and configuration space topology a large deviation technique is applied to the mean field model phi4 providing an exact expression for the configurational entropy s v m as a function of the potential energy v and the magnetization m although a continuous phase transition occurs at some critical energy vc the entropy is found to be a real analytic function in both arguments and it is only the maximization over m which gives rise to a nonanalyticity in s v supm s v m this mechanism of nonanalyticity generation by maximization over one variable of a real analytic entropy function is restricted to systems with long range interactions and has for continuous phase transitions the generic occurrence of classical critical exponents as an immediate consequence furthermore this mechanism can provide an explanation why contradictory to the so called topological hypothesis the phase transition in the mean field model need not be accompanied by a topology change in the family of constant energy submanifolds

estimation of local microcanonical averages in two lattice mean field models using coupling techniques we consider an application of probabilistic coupling techniques which provides explicit estimates for comparison of local expectation values between label permutation invariant states for instance between certain microcanonical canonical and grand canonical ensemble expectations a particular goal is to obtain good bounds for how such errors will decay with increasing system size as explicit examples we focus on two well studied mean field models the discrete model of a paramagnet and the mean field spherical model of a continuum field both of which are related to the curie weiss model the proof is based on a construction of suitable probabilistic couplings between the relevant states using wasserstein fluctuation distance to control the difference between the expectations in the thermodynamic limit

saddle index properties singular topology and its relation to thermodynamic singularities for a ϕ 4 mean field model we investigate the potential energy surface of a ensuremath phi 4 model with infinite range interactions all stationary points can be uniquely characterized by three real numbers ensuremath alpha ensuremath alpha 0 ensuremath alpha ensuremath with ensuremath alpha ensuremath alpha 0 ensuremath alpha ensuremath 1 provided that the interaction strength ensuremath mu is smaller than a critical value the saddle index n s is equal to ensuremath alpha 0 and its distribution function has a maximum at n s mathrm max 1 3 the density p e of stationary points with energy per particle e as well as the euler characteristic ensuremath chi e are singular at a critical energy e c ensuremath mu if the external field h is zero however e c ensuremath mu ensuremath ne ensuremath upsilon c ensuremath mu where ensuremath upsilon c ensuremath mu is the mean potential energy per particle at the thermodynamic phase transition point t c this proves that previous claims that the topological and thermodynamic transition points coincide is not valid in general both types of singularities disappear for h ensuremath ne 0 the average saddle index overline n s as function of e decreases monotonically with e and vanishes at the ground state energy only in contrast the saddle index n s as function of the average energy overline e n s is given by n s overline e 1 4 overline e for h 0 that vanishes at overline e ensuremath 1 4g ensuremath upsilon 0 the ground state energy

topology and phase transitions from an exactly solvable model to a relation between topology and thermodynamics the elsewhere surmized topological origin of phase transitions is given here important evidence through the analytic study of an exactly solvable model for which both topology of submanifolds of configuration space and thermodynamics are worked out the model is a mean field one with a k body interaction it undergoes a second order phase transition for k 2 and a first order one for kg2 this opens a perspective for the understanding of the deep origin of first and second order phase transitions respectively in particular a remarkable theoretical result consists of a mathematical characterization of first order transitions moreover we show that a reduced configuration space can be defined in terms of collective variables such that the correspondence between phase transitions and topology changes becomes one to one for this model finally an unusual relationship is worked out between the microscopic description of a classical n body system and its macroscopic thermodynamic behavior this consists of a functional dependence of thermodynamic entropy upon the morse indexes of the critical points saddles of the constant energy hypersurfaces of the microscopic 2n dimensional phase space thus phase space and configuration space topology is directly related to thermodynamics

explained variation in a fully specified model for data grouped survival data an additive hazards model may be used to quantify the effect of genetic and environmental predictors on flowering of sugar beet plants recorded as data grouped time to event data estimated predictor effects have an intuitive interpretation rooted in the underlying time dynamics of the flowering process however agricultural experiments are often designed using several plots containing a large number of plants that are subsequently being monitored in this article we consider an additive hazards model with an additional plot structure induced by latent shared frailty variables this approach enables us to derive a method to assess the quality of predictors in terms of how much plot variation they explain we apply the method to a large data set exploring flowering of sugar beet and conclude that the genetic predictor biotype which has a strong effect also explains a substantial amount of the plot variation the method is also applied to a data set from medical research concerning days to virus positivity of serum samples in aids patients

topological hypothesis on phase transitions the simplest case we critically analyze the possibility of finding signatures of a phase transition by looking exclusively at static quantities of statistical systems like e g the topology of potential energy submanifolds pes s this topological hypothesis has been successfully tested in a few statistical models but up to now there has been no rigorous proof of its general validity we make a new test of it analyzing the probably simplest example of a nontrivial system undergoing a continuous phase transition the completely connected version of the spherical model going through the topological properties of its pes it is shown that as expected the phase transition is correlated with a change in their topology nevertheless this change as reflected in the behavior of a particular topological invariant the euler characteristic is small at variance with the strong singularity observed in other systems furthermore it is shown that in the presence of an external field when the phase transition is destroyed a similar topology change in the submanifolds is still observed at the maximum value of the potential energy manifold a level which nevertheless is thermodynamically inaccessible this suggests that static properties of the pes s are not enough in order to decide whether a phase transition will take place some input from dynamics seems necessary