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

global strong solution with bv derivatives to singular solid on solid model with exponential nonlinearity abstract in this work we consider the one dimensional very singular fourth order equation for solid on solid model in attachment detachment limit regime with exponential nonlinearity h t 1 h e e h 1 h e h h where total energy e h is the total variation of h using a logarithmic correction for total energy e h ln h d x and gradient flow structure with a suitable defined functional we prove the one dimensional evolution variational inequality solution preserves a positive gradient h x which has upper and lower bounds but in bv space we also obtain the global strong solution to the solid on solid model which allows an asymmetric singularity h x x to happen

a new approach to the pareto stable matching problem in two sided matching markets the concept of stability proposed by gale and shapley is one of the most important solution concepts in this paper we consider a problem related to stability of a matching in a two sided matching market with indifferences it is known that stability does not guarantee pareto efficiency in a two sided matching market with indifferences however erdil and ergin proved that there always exists a stable and pareto efficient matching in a many to one matching market with indifferences and gave a polynomial time algorithm for finding it later on chen proved that there always exists a stable and pareto efficient matching in a many to many matching market with indifferences and gave a polynomial time algorithm for finding it in this paper we propose a new approach to the problem of finding a stable and pareto efficient matching in a many to many matching market with indifferences our algorithm is an alternative proof of the existence of a stable and pareto efficient matching

a differential complex for poisson manifolds construction du complexe canonique d une variete de poisson homologie canonique des varietes symplectiques application a l homologie de hochschild des algebres non commutatives

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

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

poisson homology in degree 0 for some rings of symplectic invariants abstract let g be a finite dimensional semi simple lie algebra h a cartan subalgebra of g and w its weyl group the group w acts diagonally on v h h as well as on c v the purpose of this article is to study the poisson homology of the algebra of invariants c v w endowed with the standard symplectic bracket to begin with we give general results about the poisson homology space in degree 0 denoted by hp 0 c v w in the case where g is of type b n c n or d n results which support alev s conjecture then we are focusing the interest on the particular cases of ranks 2 and 3 by computing the poisson homology space in degree 0 in the cases where g is of type b 2 so 5 d 2 so 4 then b 3 so 7 and d 3 a 3 so 6 sl 4 in order to do this we make use of a functional equation introduced by y berest p etingof and v ginzburg we recover by a different method the result established by j alev and l foissy according to which the dimension of hp 0 c v w equals 2 for b 2 then we calculate the dimension of this space and we show that it is equal to 1 for d 2 we also calculate it for the rank 3 cases we show that it is equal to 3 for b 3 c 3 and 1 for d 3 a 3

a boundary value problem for the poisson equation with multi scale oscillating boundary the paper is concerned with the homogenization problem for the poisson equation in a domain a part of whose boundary is rapidly oscillating according to several scales such a problem arises in the processing of devices with very small features such as semiconductors we construct homogenized boundary layers and use them to establish effective approximation to the solution

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

poisson co homology of polynomial poisson algebras in dimension four sklyanin s case abstract in this paper we compute the poisson co homology of a polynomial poisson structure given by two casimir polynomial functions which define a complete intersection with an isolated singularity

a new approach to the continuum modeling of epitaxial growth slope selection coarsening and the role of the uphill current abstract we develop a new approach to the macroscopic modeling of epitaxial growth focusing on the slope selection and coarsening observed in spiral mode growth our model distinguishes between the surface height and the surface adatom density these quantities evolve by a coupled pair of partial differential equations a hamilton jacobi equation for the height coupled to a nonlinear diffusion equation for the adatom density the influence of the ehrlich schwoebel barrier is included through an uphill current in the equation for adatom density our model predicts slope selection and coarsening thus it offers a possible mechanism for these effects the model predicts in particular that the coarsening rate depends mainly on the strength of the ehrlich schwoebel barrier

twisted poincare duality between poisson homology and poisson cohomology abstract a version of the twisted poincare duality is proved between the poisson homology and cohomology of a polynomial poisson algebra with values in an arbitrary poisson module the duality is achieved by twisting the poisson module structure in a canonical way which is constructed from the modular derivation in the case that the poisson structure is unimodular the twisted poincare duality reduces to the poincare duality in usual sense the main result generalizes the work of launois and richard 8 for the quadratic poisson structures and zhu 25 for the linear poisson structures

continuum theory of epitaxial crystal growth i we present various continuum limits to describe epitaxial thin film growth we consider a hierarchy of models which can take into account the diffusion of terrace adatoms attachment and detachment of edge adatoms vapor phase diffusion and the effect of multiple species the starting point is the burton cabrera frank type step flow model we have obtained partial differential equations in the form of a coupled system of diffusion equation for the adatom density and a hamilton jacobi equation for the film height function this is supplemented with appropriate boundary conditions at the continuum level to describe the growth at the peaks and valleys on the film the results here can be used in a macroscopic description of thin film growth

local matching dynamics in social networks we study stable marriage and roommates problems under locality constraints each player is a vertex in a social network and strives to be matched to other players the value of a match is specified by an edge weight players explore possible matches only based on their current neighborhood we study convergence of natural better response dynamics that converge to locally stable matchings matchings that allow no incentive to deviate with respect to their imposed information structure in the social network if we have global information and control to steer the convergence process then quick convergence is possible and for every starting state we can construct in polynomial time a sequence of polynomially many better response moves to a locally stable matching in contrast for a large class of oblivious dynamics including random and concurrent better response the convergence time turns out to be exponential in such distributed settings a small amount of random memory can ensure polynomial convergence time even for many to many matchings and more general notions of neighborhood here the type of memory is crucial as for several variants of cache memory we provide exponential lower bounds on convergence times

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

gerstenhaber algebras and bv algebras in poisson geometry the purpose of this paper is to establish an explicit correspondence between various geometric structures on a vector bundle with some well known algebraic structures such as gerstenhaber algebras and bv algebras some applications are discussed in particular we find an explicit connection between the koszul brylinski operator and the modular class of a poisson manifold as a consequence we prove that poisson homology is isomorphic to poisson cohomology for unimodular poisson structures

the boundary value problem in domains with very rapidly oscillating boundary abstract we study the asymptotic behavior of the solution to boundary value problem for the second order elliptic equation in the bounded domain e rnwith a very rapidly oscillating locally periodic boundary we assume that the fourier boundary condition involving a small positive parameter e is posed on the oscillating part of the boundary and that the n 1 dimensional volume of this part goes to infinity as e 0 under proper normalization conditions that homogenized problem is found and the estimates of the residual are obtained also we construct an additional term of the asymptotics to improve the estimates of the residual it is shown that the limiting problem can involve dirichlet fourier or neumann boundary conditions depending on the structure of the coefficient of the original problem

from crystal steps to continuum laws behavior near large facets in one dimension abstract the passage from discrete schemes for surface line defects steps to nonlinear macroscopic laws for crystals is studied via formal asymptotics in one space dimension our goal is to illustrate by explicit computations the emergence from step motion laws of continuum scale power series expansions for the slope near the edges of large flat surface regions facets we consider surface diffusion kinetics via the burton cabrera and frank bcf model by which adsorbed atoms diffuse on terraces and attach detach at steps nearest neighbor step interactions are included the setting is a monotone train of n steps separating two semi infinite facets at fixed heights we show how boundary conditions for the continuum slope and flux and expansions in the height variable near facets may emerge from the algebraic structure of discrete schemes as n our technique relies on the use of self similar discrete slopes conversion of discrete schemes to sum equations and their reduction to nonlinear integral equations for the continuum scale slope approximate solutions to the continuum equations near facet edges are constructed formally by direct iterations for elastic dipole and multipole step interactions the continuum slope is found in agreement with a previous hypothesis of local equilibrium

the local structure of poisson manifolds varietes de poisson et applications decomposition structures de poisson lineaires approximation lineaire systemes hamiltoniens le probleme de linearisation groupes de fonction realisations et applications impulsion paires duales et groupes de jauge existence des realisations unicite des realisations les problemes des 3 corps restreints et autres exemples

solutions for the stable roommates problem with payments the stable roommates problem with payments has as input a graph g v e with an edge weighting w e r 0 and the problem is to find a stable solution by pinpointing a relationship to the accessibility of the coalition structure core of matching games we give a constructive proof for showing that every yes instance of the stable roommates problem with payments allows a path of linear length that starts in an arbitrary unstable solution and that ends in a stable solution this generalizes a result of chen fujishige and yang 2011 4 for bipartite instances to general instances we also show that the problems blocking pairs and blocking value which are to find a solution with a minimum number of blocking pairs or a minimum total blocking value respectively are np hard finally we prove that the variant of the first problem in which the number of blocking pairs must be minimized with respect to some fixed matching is np hard whereas this variant of the second problem is polynomial time solvable

poisson cohomology of the affine plane abstract we compute the poisson cohomology of homogeneous poisson structures on the plane the singular locus of such a poisson structure consists of a family of lines passing through o and we show how the dimensions of the first and second cohomology groups are related to the weight of o as a singular point of

the evolution of a crystal surface analysis of a one dimensional step train connecting two facets in the adl regime abstract we study the evolution of a monotone step train separating two facets of a crystal surface the model is one dimensional and we consider only the attachment detachment limited regime starting with the well known odes for the velocities of the steps we consider the system of odes giving the evolution of the discrete slopes it is the l 2 steepest descent of a certain functional using this structure we prove that the solution exists for all time and is asymptotically self similar we also discuss the continuum limit of the discrete self similar solution characterizing it variationally identifying its regularity and discussing its qualitative behavior our approach suggests a pde for the slope as a function of height and time in the continuum setting however existence uniqueness and asymptotic self similarity remain open for the continuum version of the problem

generalized double affine hecke algebras of rank 1 and quantized del pezzo surfaces abstract let d be a simply laced dynkin diagram of rank r whose affinization has the shape of a star i e d 4 e 6 e 7 e 8 to such a diagram one can attach a group g whose generators correspond to the legs of the affinization have orders equal to the leg lengths plus 1 and the product of the generators is 1 the group g is then a 2 dimensional crystallographic group g z l z 2 where l is 2 3 4 and 6 respectively in this paper we define a flat deformation h t q of the group algebra c g of this group by replacing the relations saying that the generators have prescribed orders by their deformations saying that the generators satisfy monic polynomial equations of these orders with arbitrary roots which are deformation parameters the algebra h t q for d 4 is the cherednik algebra of type c c 1 which was studied by noumi sahi and stokman and controls askey wilson polynomials we prove that h t q is the universal deformation of the twisted group algebra of g and that this deformation is compatible with certain filtrations on c g we also show that if q is a root of unity then for generic t the algebra h t q is an azumaya algebra and its center is the function algebra on an affine del pezzo surface for generic q the spherical subalgebra e h t q e provides a quantization of such surfaces we also discuss connections of h t q with preprojective algebras and painleve vi

homologies of cubic artin schelter regular algebras abstract the hochschild homology of cubic artin schelter regular algebras of type a with generic coefficients is computed we follow the method used by van den bergh k theory 8 1994 213 230 in the quadratic case and consider these algebras as deformations of a polynomial algebra with remarkable poisson brackets a new morphism of resolutions is introduced the de rham cohomology cyclic and periodic cyclic homologies and the hochschild cohomology are also computed

uniqueness of multiplicative determinants on elliptic pseudodifferential operators we describe all multiplicative determinants on the pathwise connected component of identity in the group of invertible classical pseudodifferential operators on a closed manifold that are continuous along continuous paths and the restriction to zero order operators of which is of class c1 this boils down to a description of all traces on zero order classical pseudodifferential operators which turn out to be linear combinations of the wodzicki residue w and leading symbol traces introduced in pr1 both of which are continuous consequently multiplicative determinants are parametrized by the residue determinant w87 sc and a new leading symbol determinant both of which are expressed in terms of a homogeneous component of the symbol of the logarithm of the operator

poisson co homology and isolated singularities abstract to each polynomial f x y z is associated a poisson structure on f 3 a surface and a poisson structure on this surface when is weight homogeneous with an isolated singularity we determine the poisson cohomology and homology of the two poisson varieties obtained

examples of non kahler hamiltonian circle manifolds with the strong lefschetz property abstract in this paper we construct six dimensional compact non kahler hamiltonian circle manifolds which satisfy the strong lefschetz property themselves but nevertheless have a non lefschetz symplectic quotient this provides the first known counterexamples to the question whether the strong lefschetz property descends to the symplectic quotient we also give examples of hamiltonian strong lefschetz circle manifolds which have a non lefschetz fixed point submanifold in addition we establish a sufficient and necessary condition for a finitely presentable group to be the fundamental group of a strong lefschetz manifold we then use it to show the existence of lefschetz four manifolds with non lefschetz finite covering spaces

symplectic reflection algebras calogero moser space and deformed harish chandra homomorphism to any finite group sp v of automorphisms of a symplectic vector space v we associate a new multi parameter deformation h of the algebra v smash product of with the polynomial algebra on v the parameter runs over points of r where r number of conjugacy classes of symplectic reflections in the algebra h called a symplectic reflection algebra is related to the coordinate ring of a poisson deformation of the quotient singularity v this leads to a symplectic analogue of mckay correspondence which is most complete in case of wreath products if is the weyl group of a root system in a vector space and v then the algebras h are certain rational degenerations of the double affine hecke algebra introduced earlier by cherednik

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

on one class of exact poisson structures we discuss some properties of a natural class of poisson structures on euclidean spaces and abstract manifolds in particular it is proved that such structures are always exact and may be reconstructed from their casimir functions it is shown that in low dimensions they give the whole class of exact poisson structures the dimension of poisson homology of these structures is computed in terms of the milnor number of their casimir functions we also analyze some concrete examples of such structures in low dimensions and show that their centers are generated by casimir functions

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 microscopic time scale approximation to the behavior of the local slope on the faceted surface under a nonuniformity in supersaturation abstract the morphological stability of a growing faceted crystal is discussed we argue that the interplay between nonuniformity in supersaturation on a growing facet and anisotropy of surface kinetics derived from the lateral motion of steps leads to a faceted instability qualitatively speaking as long as the nonuniformity in supersaturation on the facet is not too large it can be compensated for by a variation of step density along the facet and the faceted crystal can grow in a stable manner the problem can be modeled as a hamilton jacobi equation for height of the crystal surface the notion of a maximal stable region of a growing facet is introduced for microscopic time scale approximation of the original hamilton jacobi equation it is shown that the maximal stable region keeps its shape determined by profile of the surface supersaturation with constant growth rate by studying large time behavior of solution of macroscopic time scale approximation a quantitative criterion for the facet stability is given

hard lefschetz theorem for sasakian manifolds we prove that on a compact sasakian manifold m g of dimension 2n 1 for any 0 p n the wedge product with d defines an isomorphism between the spaces of harmonic forms n p m and n p 1 m therefore it induces an isomorphism between the de rham cohomology spaces h m and h m such isomorphism is proven to be independent of the choice of a compatible sasakian metric on a given contact manifold as a consequence an obstruction for a contact manifold to admit sasakian structures is found

the surface statistics of a granular aggregate the problem of the surface fluctuations in a settled granular material is posed a simple model is given which describes the process by which a particle settles and comes to rest on the existing surface of the packing and from this a set of langevin equations for the fourier modes of the surface are derived these equations imply that the fourier amplitudes behave like the velocities of a set of independent brownian particles we show that this results in logarithmically divergent surface fluctuations if the flux of particles onto the surface is random the divergence being removed by a more accurate description of the settling material for example by having the granules fall through a sieve