truncation strategies in matching markets roth and rothblum roth a e u g rothblum 1999 truncation strategies in matching markets in search of advice for participants econometrica67 21 43 showed that for matching markets using the deferred acceptance algorithm a physician with symmetric incomplete information possibly gains only by truncating her true ranking we show that in symmetric information environments this result is identical for all priority mechanisms and all linear programming mechanisms introduced in british entry level medical markets and in public school choice in some american cities

conflict and coincidence of interest in job matching some new results and open questions the game theoretic solution to certain job assignment problems allows the interests of agents on the same side of the market e g firms or workers to be simultaneously maximized this is shown to follow from the lattice structure of the set of stable outcomes however it is shown that in a more general class of problems the optimality results persist but the lattice structures do not thus this paper raises as many questions as it answers

non linear rough heat equations this article is devoted to define and solve an evolution equation of the form dyt yt dt dx t yt wherestands for the laplace operator on a space of the form l p r n and x is a finite dimensional noisy nonlinearity whose typical form is given by xt n i 1 x i fi where each x x 1 x n is a holder function generating a rough path and each fi is a smooth enough function defined on l p r n the generalization of the usual rough path theory allowing to cope with such

hard variants of stable marriage the stable marriage problem and its many variants have been widely studied in the literature gusfield and irving the stable marriage problem structure and algorithms mit press cambridge ma 1989 roth and sotomayor two sided matching a study in game theoretic modeling and analysis econometric society monographs vol 18 cambridge university press cambridge 1990 knuth stable marriage and its relation to other combinatorial problems crm proceedings and lecture notes vol 10 american mathematical society providence ri 1997 partly because of the inherent appeal of the problem partly because of the elegance of the associated structures and algorithms and partly because of important practical applications such as the national resident matching program roth j political economy 92 6 1984 991 and similar large scale matching schemes here we present the first comprehensive study of variants of the problem in which the preference lists of the participants are not necessarily complete and not necessarily totally ordered we show that under surprisingly restrictive assumptions a number of these variants are hard and hard to approximate the key observation is that in contrast to the case where preference lists are complete or strictly ordered or both a given problem instance may admit stable matchings of different sizes in this setting examples of problems that are hard are finding a stable matching of maximum or minimum size determining whether a given pair is stableeven if the indifference takes the form of ties on one side only the ties are at the tails of lists there is at most one tie per list and each tie is of length 2 and finding or approximating both an egalitarian and a minimum regret stable matching however we give a 2 approximation algorithm for the problems of finding a stable matching of maximum or minimum size we also discuss the significant implications of our results for practical matching schemes

on houseswapping the strict core segmentation and linear programming we consider then player houseswapping game of shapley and scarf 1974 with indifferences in preferences allowed it is well known that the strict core of such a game may be empty single valued or multi valued we define a condition on such games called segmentability which means that the set of players can be partitioned into a top trading segmentation it generalizes gale s well known idea of the partition of players into top trading cycles which is used to find the unique strict core allocation in the model with no indifference we prove that a game has a nonempty strict core if and only if it is segmentable we then use this result to devise ano n3 algorithm which takes as input any houseswapping game and returns either a strict core allocation or a report that the strict core is empty finally we are also able to construct a linear inequality system whose feasible region s extreme points precisely correspond to the allocations of the strict core this last result parallels the results of vande vate 1989 and rothblum 1992 for the marriage game of gale and shapley 1962

polyhedral aspects of stable marriage in the setting of the stable matching sm problem it has been observed that some of the man woman pairs cannot be removed although they participate in no stable matching since such a removal would alter the set of solutions these pairs are yet to be identified likewise and despite the sizeable literature some of the fundamental characteristics of the sm polytope e g its dimension its facets etc have not been established in the current work we show that these two seemingly distant open issues are closely related more specifically we identify the pairs with the above mentioned property and present a polynomial algorithm for producing a set of minimal preference lists we utilize this result in the context of two different representations of the sm structure rotation poset graph and algebraic formulation and derive the dimension of the sm polytope to obtain all alternative minimal linear descriptions

statistical estimation of the parameters of a moving source from array data on propose une methode d estimation des parametres d un modele de retard temporel lineaire la methode compare les transformees de fourier a differentes frequences

stable matchings optimal assignments and linear programming vande vate 1989 described the polytope whose extreme points are the stable core matchings in the marriage problem rothblum 1989 simplified and extended this result this paper explores a corresponding linear program its dual and consequences of the fact that the dual solutions have an unusually direct relation to the primal solutions this close relationship allows us to provide simple proofs both of vande vate and rothblum s results and of other important results about the core of marriage markets these proofs help explain the structure shared by the marriage problem without sidepayments and the assignment game with sidepayments the paper further explores fractional matchings which may be interpreted as lotteries over possible matches or as time sharing arrangements we show that those fractional matchings in the stable marriage polytope form a lattice with respect to a partial ordering that involves stochastic dominance thus all expected utility functions corresponding to the same ordinal preferences will agree on the relevant comparisons finally we provide linear programming proofs of slightly stronger versions of known incentive compatibility results

many to one stable matching geometry and fairness baiou and balinski characterized the stable admissions polytope using a system of linear inequalities the structure of feasible solutions to this system of inequalities fractional stable matchings is the focus of this paper the main result associates a geometric structure with each fractional stable matching this insight appears to be interesting in its own right and can be viewed as a generalization of the lattice structure for integral stable matchings to fractional stable matchings in addition to obtaining simple proofs of many known results the geometric structure is used to prove the following two results first it is shown that assigning each agent their median choice among all stable partners results in a stable matching which can be viewed as a fair compromise second sufficient conditions are identified under which stable matchings exist in a problem with externalities in particular in the stable matching problem with couples

diffusions conditionnelles i hypoellipticite partielle this paper is devoted to the proof of certain results on conditional diffusions by using the malliavin calculus of variations it is shown that under minimal conditions on the vectors fields which define a two component diffusion xt zt and their lie brackets a s for any t 0 the conditional law of xt t 0 given b zs s t a c density

matching with indifferences a comparison of algorithms in the context of course allocation abstract we evaluate six one and eight two sided matching mechanisms with preferences based on a collection of 28 field data sets although important properties of matching mechanisms such as strategy proofness or pareto efficiency can be shown by formal proofs the size the average rank and the popularity of matchings ask for an empirical evaluation we introduce different metrics to compare the results the study shows trade offs between various design desiderata which are relevant in the field the results provide guidelines for the selection of matching mechanisms

a two sided discrete concave market with possibly bounded side payments an approach by discrete convex analysis the marriage model due to gale and shapley gale d l s shapley 1962 college admissions and the stability of marriage amer math monthly69 9 15 and the assignment model due to shapley and shubik shapley l s m shubik 1972 the assignment game i the core internat j game theory1 111 130 are standard in the theory of two sided matching markets we give a common generalization of these models by utilizing discrete concave functions and considering possibly bounded side payments we show the existence of a pairwise stable outcome in our model our present model is a further natural extension of the model examined in our previous paper fujishige s a tamura a general two sided matching market with discrete concave utility functions discrete appl math 154 950 970 and the proof of the existence of a pairwise stable outcome is even simpler than the previous one

deconvolution and estimation of transfer function phase and coefficients for nongaussian linear processes nongaussian linear processes are considered it is shown that the phase of the transfer function can be estimated under broad conditions this is not true of gaussian linear processes and in this sense gaussian linear processes are atypical the asymptotic behavior of a phase estimate is determined the phase estimates make use of bispectral estimates these ideas are applied to a problem of deconvolution which is effective even when the transfer function is not minimum phase a number of computational illustrations are given

a note on roth s consensus property of many to one matching roth roth ae 1985 conflict and coincidence of interest in job matching some new results and open questions math oper res 103 379 389 claimed that i if each firm is allowed to select its most preferred subset of employees from those that assigned to it at two different stable matchings then the choices result in a stable matching and ii the set of stable matchings is a lattice under the partial order of the firms common interests here we provide counterexamples that show that these claims are incorrect and we explain the flaws in roth s reasoning

deconvolution of multiple time series the problem of estimating simultaneously two convolved vector time series corrupted by additive noise is considered by regarding one of the series as being stochastic and the other as fixed it is shown that the fixed component can be estimated by maximizing a frequency domain approximation to the likelihood the stochastic series is estimated by using an approximation to the conditional mean evaluated at the current maximum likelihood estimators an example involving a multiple deconvolution of seismic source and receiver functions is given

a test for second order stationarity of a multivariate time series it is well known that the discrete fourier transforms dft of a second order stationary time series between two distinct fourier frequencies are asymptotically uncorrelated in contrast for a large class of second order nonstationary time series including locally stationary time series this property does not hold in this paper these starkly differing properties are used to define a global test for stationarity based on the dft of a vector time series it is shown that the test statistic under the null of stationarity asymptotically has a chi squared distribution whereas under the alternative of local stationarity asymptotically it has a noncentral chi squared distribution further if the time series is gaussian and stationary the test statistic is pivotal however in many econometric applications the assumption of gaussianity can be too strong but under weaker conditions the test statistic involves an unknown variance that is extremely difficult to directly estimate from the data to overcome this issue a scheme to estimate the unknown variance based on the stationary bootstrap is proposed the properties of the stationary bootstrap under both stationarity and nonstationarity are derived these results are used to show consistency of the bootstrap estimator under stationarity and to derive the power of the test under nonstationarity the method is illustrated with some simulations the test is also used to test for stationarity of ftse 100 and dax 30 stock indexes from january 2011 december 2012

a matroid approach to stable matchings with lower quotas in 2010 huang introduced the laminar classified stable matching problem lcsm for short that is motivated by academic hiring this problem is an extension of the well known hospitals residents problem in which a hospital has laminar classes of residents and it sets lower and upper bounds on the number of residents that it can hire in each class against the intuition that variations of the stable matching problem with lower quotas are difficult in general huang proved that lcsm can be solved in polynomial time in this paper we present a matroid based approach to lcsm and we obtain the following results i we solve a generalization of lcsm in which both sides have quotas ii huang raised a question about a polyhedral description of the set of stable assignments in lcsm we give a positive answer for this question by exhibiting a polyhedral description of the set of stable assignments in a generalization of lcsm iii we prove that the set of stable assignments in a generalization of lcsm has a la

random paths to stability in two sided matching empirical studies of two sided matching have so far concentrated on markets in which certain kinds of market failures were addressed by resorting to centralized deterministic matching procedures loosely speaking the results of these studies are that those centralized procedures which achieved stable outcomes resolved the market failures while those markets organized through procedures that yielded unstable outcomes continued to fail 2 so the market failures seem to be associated with instability of the outcomes but many entry level labor markets and other two sided matching situations don t employ centralized matching procedures and yet aren t observed to experience such failures so we can conjecture that at least some of these markets may reach stable outcomes by means of decentralized decision making and decentralized decision making in complex environments presumably introduces some randomness into what matchings are achieved however as far as we are aware no nondeterministic models leading to stable outcomes have yet been studied the present paper demonstrates that starting from an arbitrary matching the process of allowing randomly chosen blocking pairs to match will converge to a stable matching with probability one this resolves an open question raised by knuth 1976 who showed that such a process may cycle furthermore every stable matching can arise

characterization of stable matchings as extreme points of a polytope the purpose of this paper is to extend a modified version of a recent result of vande vate 1989 which characterizes stable matchings as the extreme points of a certain polytope our proofs are simpler and more transparent than those of vande vate

on a cutting plane heuristic for the stable roommates problem and its applications abstract we propose a new cutting plane heuristic for the classical stable roommates problem our approach utilises a new linear programming formulation for the problem and the underlying geometric properties of the fractional solution to construct the violated inequality we test the approach on moderate size problems with encouraging computational performance to further illustrate the versatility of this approach we also show how it can be suitably extended to handle variants of the basic stable roommates model

blockers and antiblockers of stable matchings an implicit linear description of the stable matching polytope is provided in terms of the blocker and antiblocker sets of constraints of the matroid kernel polytope the explicit identification of both these sets is based on a partition of the stable pairs in which each agent participates here we expose the relation of such a partition to rotations we provide a time optimal algorithm for obtaining such a partition and establish some new related results most importantly that this partition is unique

a smoothness priors time varying ar coefficient modeling of nonstationary covariance time series a smoothness priors time varying ar coefficient model approach for the modeling of nonstationary in the covariance time series is shown smoothness priors in the form of a difference equation constraint excited by an independent white noise are imposed on each ar coefficient the unknown white noise variances are hyperparameters of the ar coefficient distribution the critical computation is of the likelihood of the hyperparameters of the bayesian model this computation is facilitated by a state space representation kalman filter implementation the best difference equation order best ar model order best hyperparameter model locally in time is selected using the minimum aic method also an instantaneous spectral density is defined in terms of the instantaneous ar model coefficients and a smoothed estimate of the instantaneous time series variance an earthquake record is analyzed the changing spectral analysis of the original data and of simulations from a time varying ar coefficient model of that data are shown

on the lattice structure of stable allocations in a two sided discrete concave market the stable allocation model is a many to many matching model in which each pair s partnership is represented by a nonnegative integer this paper establishes a link between two different formulations of this model the choice function model studied thoroughly by alkan and gale and the discrete concave m concave value function model introduced by eguchi fujishige and tamura we show that the choice functions induced from m concave value functions are endowed with consistency persistence and size monotonicity this implies by the result of alkan and gale that the stable allocations for m concave value functions form a distributive lattice with several significant properties such as polarity complementarity and uni size property furthermore we point out that these results can be extended for quasi m concave value functions

popular matchings with two sided preference lists and matroid constraints abstract in this paper we consider the popular matching problem with two sided preference lists and matroid constraints which is based on the variants of the popular matching problem proposed by brandl and kavitha and nasre and rawat we prove that there always exists a popular matching in our model and a popular matching can be found in polynomial time furthermore we prove that if every matroid is weakly base orderable then we can find a maximum size popular matching in polynomial time

restricted canonical correlations given two random vectors y 1 and y 2 the first canonical correlation between them is defined as sup correlation y 1 y 2 e rp e rq however in many practical situations e g educational testing problems neural networks some natural restrictions on the coefficients and may arise which should be incorporated in this maximization procedure the maximum correlation subject to such constraints is referred to as the restricted canonical correlation this problem is treated here under the nonnegativity restriction on and the analysis is extended to more general form of inequality constraints and also when the restrictions are present only on some of the coefficients restricted versions of some other related measures are also discussed this includes principal component analysis and different modifications of canonical correlations anomalies with higher order correlation are also described some properties of restricted canonical correlation including its bounds are studied

the college admissions problem with lower and common quotas we study two generalised stable matching problems motivated by the current matching scheme used in the higher education sector in hungary the first problem is an extension of the college admissions problem in which the colleges have lower quotas as well as the normal upper quotas here we show that a stable matching may not exist and we prove that the problem of determining whether one does is np complete in general the second problem is a different extension in which as usual individual colleges have upper quotas but in addition certain bounded subsets of colleges have common quotas smaller than the sum of their individual quotas again we show that a stable matching may not exist and the related decision problem is np complete on the other hand we prove that when the bounded sets form a nested set system a stable matching can be found by generalising in non trivial ways both the applicant oriented and college oriented versions of the classical gale shapley algorithm finally we present an alternative view of this nested case using the concept of choice functions and with the aid of a matroid model we establish some interesting structural results for this case

a test for stationarity for irregularly spaced spatial data summary the analysis of spatial data is based on a set of assumptions which in practice need to be checked a commonly used assumption is that the spatial random field is second order stationary in the paper a test for spatial stationarity for irregularly sampled data is proposed the test is based on a transformation of the data a type of fourier transform where the correlations between the transformed data are close to 0 if the random field is second order stationary however if the random field were second order non stationary this property does not hold using this property a test for second order stationarity is constructed the test statistic is based on measuring the degree of correlation in the transformed data the asymptotic sampling properties of the test statistic are derived under both stationarity and non stationarity of the random field these results motivate a graphical tool which allows a visual representation of the non stationary features the method is illustrated with simulations and a real data example

on a robust version of the integral representation formula of nonlinear filtering the paper is concerned with completing unfinished business on a robust representation formula for the conditional expectation operator of nonlinear filtering such a formula robust in the sense that its dependence on the process of observations is continuous was stated in 2 without proof the main purpose of this paper is to repair this deficiency

searching for structure in curve samples abstract the shape of a regression curve can to a large extent be characterized by the succession of structural features like extrema inflection points and so on when analyzing a sample of regression curves it is often important to know at an early stage of data analysis which structural features are occurring consistently in each curve of the sample such a definition is usually not easy due to substantial interindividual variation both in the x and the y axis and due to the influence of noise a method is proposed for identifying typical features without relying on an a priori specified functional model for the curves the approach is based on the frequencies of occurrence of structural features as for example maxima in the curve sample along the x axis important tools are nonparametric regression and differentiation and kernel density estimation apart from a theoretical foundation the usefulness of the method is documented by application to two interesting biomedical areas growth and develop

beta mapping and beta regression for changes of ordinal rating measurements on likert scales a comparison of the change scores among multiple treatment groups patient reported outcome and observer evaluative studies in clinical trials and post hoc analyses often use instruments that measure responses on ordinal rating or likert scales we propose a flexible distributional approach by modeling the change scores from the baseline to the end of the study using independent beta distributions the two shape parameters of the fitted beta distributions are estimated by matching moments covariates and the interaction terms are included in multivariate beta regression analyses under generalized linear mixed models these methods are illustrated on the treatment satisfaction data in an overactive bladder drug study with four treatment arms monte carlo simulations were conducted to compare the type 1 errors and statistical powers using a beta likelihood ratio test of the proposed method against its fully nonparametric or parametric alternatives

a new approach to stable matching problems it is shown that stable matching problems are the same as problems about stable configurations of x networks consequences include easy proofs of old theorems a new simple algorithm for finding a stable matching an understanding of the difference between stable marriage and stable roommates np completeness of three party stable marriage cc completeness of several stable matching problems and a fast parallel reduction from the stable marriage problem to the assignment problem

kusuoka stroock gradient bounds for the solution of the filtering equation abstract we obtain sharp gradient bounds for perturbed diffusion semigroups in contrast with existing results the perturbation is here random and the bounds obtained are pathwise our approach builds on the classical work of kusuoka and stroock 13 14 16 17 and extends their program developed for the heat semi group to solutions of stochastic partial differential equations the work is motivated by and applied to nonlinear filtering the analysis allows us to derive pathwise gradient bounds for the un normalised conditional distribution of a partially observed signal it uses a pathwise representation of the perturbed semigroup following ocone 22 the estimates we derive have sharp small time asymptotics

stable fractional matchings abstract we study a generalization of the classical stable matching problem that allows for cardinal preferences as opposed to ordinal and fractional matchings as opposed to integral in this cardinal setting stable fractional matchings can have much larger social welfare than stable integral ones our goal is to understand the computational complexity of finding an optimal i e welfare maximizing stable fractional matching we consider both exact and approximate stability notions and provide simple approximation algorithms with weak welfare guarantees our main result is that somewhat surprisingly achieving better approximations is computationally hard to the best of our knowledge these are the first computational complexity results for stable fractional matchings in the cardinal model en route to these results we provide a number of structural observations that could be of independent interest

the revealed preference theory of stable and extremal stable matchings we investigate the testable implications of the theory of stable matchings we provide a characterization of the matchings that are rationalizable as stable matchings when agents preferences are unobserved the characterization is a simple nonparametric test for stability in the tradition of revealed preference tests we also characterize the observed stable matchings when monetary transfers are allowed and the stable matchings that are best for one side of the market extremal stable matchings we find that the theory of extremal stable matchings is observationally equivalent to requiring that there be a unique stable matching or that the matching be consistent with unrestricted monetary transfers

the lattice structure of the set of stable matchings with multiple partners we continue recent work on the matching problem for firms and workers and show that for a suitable ordering the set of stable matchings is a lattice

analysis on wiener spaces i nonlinear maps abstract the author introduces several kinds of capacities and regularity of nonlinear maps on wiener spaces and studies their properties

some statistical methods for random process data from seismology and neurophysiology examples are presented of statistical techniques for the analysis of random process data and of their uses in the substantive fields of seismology and neurophysiology the problems addressed include frequency estimation for decaying cosinusoids signal estimation association measurement causal connection assessment estimation of speed and direction and structural modeling the techniques employed include complex demodulation nonlinear regression probit analysis deconvolution maximum likelihood singular value decomposition fourier analysis and averaging

a maximum likelihood approach to frequency wavenumber analysis this paper is concerned with the likelihood ratio detection and maximum likelihood estimation of plane waves traversing a small array on irregularly placed sensors a new detection statistic is proposed this statistic is related to the high resolution procedure of capon however it has a known null distribution in the case that no signal is present given that a wave is present the asymptotic distribution of the maximum likelihood estimate of the wave parameters is derived the problems of detection and estimation are distinguished they are approached via the fundamental statistical procedures of likelihood ratio testing and maximum likelihood estimation the solutions of both problems are found to be based upon the same quantity the maximum likelihood statistic the development leads to a clarification of the interrelationships and comparative properties of the conventional the least squares the high resolution and the new procedure the approach is via fourier inference

the stable admissions polytope the stable admissions polytope the convex hull of the stable assignments of the university admissions problem is described by a set of linear inequalities it depends on a new characterization of stability and arguments that exploit and extend a graphical approach that has been fruitful in the analysis of the stable marriage problem

strategy proofness makes the difference deferred acceptance with responsive priorities in college admissions and student placements at public schools the admission decision can be thought of as assigning indivisible objects with capacity constraints to a set of students such that each student receives at most one object and monetary compensations are not allowed in these important market design problems the agent proposing deferred acceptance da mechanism with responsive strict priorities performs well and economists have successfully implemented da mechanisms or slight variants thereof we show that almost all real life mechanisms used in such environments including the large classes of priority mechanisms and linear programming mechanisms satisfy a set of simple and intuitive properties once we add strategy proofness to these properties da mechanisms are the only ones surviving in market design problems that are based on weak priorities like school choice generally multiple tie breaking mtb procedures are used and then a mechanism is implemented with the obtained strict priorities by adding stability with respect to the weak priorities we establish the rst normative foundation

the geometry of fractional stable matchings and its applications we study the classical stable marriage and stable roommates problems using a polyhedral approach we propose a new lp formulation for the stable roommates problem which has a feasible solution if and only if the underlying roommates problem has a stable matching furthermore for certain special weight functions on the edges we construct a 2 approximation algorithm for the optimal stable roommates problem our technique exploits features of the geometry of fractional solutions of this formulation for the stable marriage problem we show that a related geometry allows us to express any fractional solution in the stable marriage polytope as a convex combination of stable marriage solutions this also leads to a genuinely simple proof of the integrality of the stable marriage polytope

a generalized polymatroid approach to stable matchings with lower quotas classified stable matching proposed by huang describes a matching model between academic institutes and applicants in which each institute has upper and lower quotas on classes i e subsets of applicants huang showed that the problem to decide whether there exists a stable matching or not is np hard in general on the other hand he showed that the problem is solvable if classes form a laminar family for this case fleiner and kamiyama gave a concise interpretation in terms of matroids and showed the lattice structure of stable matchings in this paper we introduce stable matchings on generalized matroids extending the model of fleiner and kamiyama we design a polynomial time algorithm which finds a stable matching or reports the nonexistence we also show that the set of stable matchings if nonempty forms a lattice with several significant properties furthermore we extend this structural result to the polyhedral framework which we call stable allocations on generalized polymatroids

stable matching with incomplete information we formulate a notion of stable outcomes in matching problems with one sided asymmetric information the key conceptual problem is to formulate a notion of a blocking pair that takes account of the inferences that the uninformed agent might make from the hypothesis that the current allocation is stable we show that the set of stable outcomes is nonempty in incomplete information environments and is a superset of the set of complete information stable outcomes we then provide sucient conditions for incomplete information stable matchings to be ecient lastly we dene a notion of price sustainable allocations and show that the set of incomplete information stable matchings is a subset of the set of such allocations

the economics of matching stability and incentives this paper considers some game theoretic aspects of matching problems and procedures of the sort which involve matching the members of one group of agents with one or more members of a second disjoint group of agents ail of whom have preferences over the possible resulting matches the main focus of this paper is on determining the extent to which matching procedures can be designed which give agents the incentive to honestly reveal their preferences and which produce stable matches two principal results are demonstrated the first is that no matching procedure exists which always yields a stable outcome and gives players the incentive to reveal their true preferences even though procedures exist which accomplish either of these goals separately the second result is that matching procedures do exist however which always yield a stable outcome and which always give all the agents in one of the two disjoint sets of agents the incentive to reveal their true preferences

a fixed point approach to stable matchings and some applications we describe a fixed point based approach to the theory of bipartite stable matchings by this we provide a common framework that links together seemingly distant results like the stable marriage theorem of gale and shapley the mendelsohn dulmage theorem the kundu lawler theorem tarski s fixed point theorem the cantor bernstein theorem pym s linking theorem or the monochromatic path theorem of sands et al in this framework we formulate a matroid generalization of the stable marriage theorem and study the lattice structure of generalized stable matchings based on the theory of lattice polyhedra and blocking polyhedra we extend results of vande vate and rothblum on the bipartite stable matching polytope

on firing rate estimation for dependent interspike intervals if interspike intervals are dependent the instantaneous firing rate does not catch important features of spike trains in this case the conditional instantaneous rate plays the role of the instantaneous firing rate for the case of samples of independent interspike intervals if the conditional distribution of the interspikes intervals isis is unknown it becomes difficult to evaluate the conditional firing rate we propose a nonparametric estimator for the conditional instantaneous firing rate for markov stationary and ergodic isis an algorithm to check the reliability of the proposed estimator is introduced and its consistency properties are proved the method is applied to data obtained from a stochastic two compartment model and to in vitro experimental data

testing for self excitation in jumps this paper extends the notion of self excitation in jumps to a rich class of continuous time semimartingale models proposes statistical tests to detect its presence in a discretely observed sample path at high frequency and derives the tests asymptotic properties our statistical setting is semiparametric except for necessary parametric assumptions on the jump size measure the other components of the semimartingale model are left essentially unrestricted we analyze the finite sample performance of our tests in monte carlo simulations