on the minimal free resolution of n 1 general forms o roig abstract let r k x1 xn and let i be the ideal of n 1 generically chosen forms of degrees d1 dn 1 we give the precise graded betti numbers of r i in the following cases n 3 n 4 and p5 1 di is even n 4 p 5 1 di is odd and d2 d3 d4 d1 d5 4 n is even and all generators have the same degree a which is even pn 1 i 1 di i n is even and d2 dn d1 dn 1 n p n 1 i 1 di i n is odd n 6 is even d2 dn d1 dn 1 n and d1 dn i dn 1 i n 0 we give very good bounds on the graded betti numbers in many other cases we also extend a result of m boij by giving the graded betti numbers for a generic compressed gorenstein algebra i e one for which the hilbert function is maximal given n and the socle degree when n is even and the socle degree is large a recurring theme is to examine when and why the minimal free resolution may be forced to have redundant summands we conjecture that if the forms all have the same degree then there are no redundant summands and we present some evidence for this conjecture

cayley bacharach schemes and their canonical modules a set of s points in p d is called a cayley bacharach scheme cb scheme if every subset of s 1 points has the same hilbert function we investigate the consequences of this weak uniformity the main result characterizes cb schemes in terms of the structure of the canonical module of their projective coordinate ring from this we get that the hilbert function of a cb scheme x has to satisfy growth conditions which are only slightly weaker than the ones given by harris and eisenbud for points with the uniform position property we also characterize cb schemes in terms of the conductor of the projective coordinate ring in its integral closure and in terms of the forms of minimal degree passing through a linked set of points

linear free resolutions and minimal multiplicity let s k x x be a polynomial ring over a field and let a4 a m be a finitely generated graded module in the most interesting case a4 is an ideal of s for a given natural number p there is a great interest in the question can m be generated by homogeneous elements of degree p no simple answer say in terms of the local cohomology of m is known but somewhat surprisingly the stronger question can the jth syzygy of m be generated by elements of degree qp j for all j 0 l n does admit a simple response the following is neither new nor difficult to prove though it seems not well known

a fixed point iteration approach for multibody dynamics with contact and small friction acceleration force setups for multi rigid body dynamics are known to be inconsistent for some configurations and sufficiently large friction coefficients a painleve paradox this difficulty is circumvented by time stepping methods using impulse velocity approaches which solve complementarity problems with possibly nonconvex solution sets we show that very simple configurations involving two bodies may have a nonconvex solution set for any nonzero value of the friction coefficient we construct two fixed point iteration algorithms that solve convex subproblems and that are guaranteed for sufficiently small friction coefficients to retrieve at a linear convergence rate the unique velocity solution of the nonconvex linear complementarity problem whenever the frictionless configuration can be disassembled in addition we show that one step of one of the iterative algorithms provides an excellent approximation to the velocity solution of the original possibly nonconvex problem if for all contacts we have that either the friction coefficient is small or the slip velocity is small

learning by distances a model of learning by distances is presented in this model a concept is a point in a metric space at each step of the learning process the student guesses a hypothesis and receives from the teacher an approximation of its distance to the target a notion of a distance measuring the proximity of a hypothesis to the correct answer is common to many models of learnability by focusing on this fundamental aspect we discover some general and simple tools for the analysis of learnability tasks as a corollary we present new learning algorithms for valiant s pac scenario with any given distribution these algorithms can learn any pac learnable class and in some cases settle for significantly less information than the usual labeled examples insight gained by the new model is applied to show that every class of subsets c that has a finite vc dimension is pac learnable with respect to any fixed distribution previously known results of this nature were subject to complicated measurability constraints

differential variational inequalities this paper introduces and studies the class of differential variational inequalities dvis in a finite dimensional euclidean space the dvi provides a powerful modeling paradigm for many applied problems in which dynamics inequalities and discontinuities are present examples of such problems include constrained time dependent physical systems with unilateral constraints differential nash games and hybrid engineering systems with variable structures the dvi unifies several mathematical problem classes that include ordinary differential equations odes with smooth and discontinuous right hand sides differential algebraic equations daes dynamic complementarity systems and evolutionary variational inequalities conditions are presented under which the dvi can be converted either locally or globally to an equivalent ode with a lipschitz continuous right hand function for dvis that cannot be so converted we consider their numerical resolution via an euler time stepping procedure which involves the solution of a sequence of finite dimensional variational inequalities borrowing results from differential inclusions dis with upper semicontinuous closed and convex valued multifunctions we establish the convergence of such a procedure for solving initial value dvis we also present a class of dvis for which the theory of dis is not directly applicable and yet similar convergence can be established finally we extend the method to a boundary value dvi and provide conditions for the convergence of the method the results in this paper pertain exclusively to systems with index not exceeding two and which have absolutely continuous solutions

minimal resolution of relatively compressed level algebras a relatively compressed algebra with given socle degrees is an artinian quotient a of a given graded algebra r c whose hilbert function is maximal among such quotients with the given socle degrees for us c is usually a general complete intersection and we usually require that a be level the precise value of the hilbert function of a relatively compressed algebra is open and we show that finding this value is equivalent to the froberg conjecture we then turn to the minimal free resolution of a level algebra relatively compressed with respect to a general complete intersection when the algebra is gorenstein of even socle degree we give the precise graded betti numbers when it is of odd socle degree we give good bounds on the graded betti numbers we also relate this case to the minimal resolution conjecture of musta for points on a projective variety finding the graded betti numbers is essentially equivalent to determining to what extent there can be redundant summands i e ghost terms in the minimal free resolution i e when copies of the same r t can occur in two consecutive free modules this is easy to arrange using koszul syzygies we show that it can also occur in more surprising situations that are not koszul using the equivalence to the froberg conjecture we show that in a polynomial ring where that conjecture holds e g in three variables the possible non koszul ghost terms are extremely limited finally we use the connection to the froberg conjecture as well as the calculation of the minimal free resolution for relatively compressed gorenstein algebras to find the minimal free resolution of general artinian almost complete intersections in many new cases this greatly extends previous work of the first two authors

compressed algebras artin algebras having given socle degrees and maximal length j emsalem and the author showed in 18 that a general polynomialf of degree j in the ring sp k yl yr has jr rl 1 linearly independent partial derivates of order i for i 0 1 t j 2 here we generalize the proof to show that the various partial derivates of s polynomials of specified degrees are as independent as possible given the room available using this result we construct and describe the varieties g e and z e parametrizing the graded and nongraded compressed algebra quotients a r i of the power series ring r k xl sxr having given socle type e these algebras are artin algebras having maximal length dimk a possible given the embedding degree r and given the socle type sequence e els s es where ei is the number of generators of the dual module a of a having degree i the variety z e is locally closed irreducible and is a bundle over g e fibred by affine spaces an whose dimension is known we consider the compressed algebras a new class of interesting algebras and a source of examples many of them are nonsmoothable have no deformation to k k for dimension reasons for some choices of the sequence e d buchsbaum d eisenbud and the author have shown that the graded compressed algebras of socle type e have almost linear minimal resolutions over r with ranks and degrees determined by e other examples have given type e dimk socle a and are defined by an ideal i with certain given numbers of generators in r

nonsmooth contact dynamics for the large scale simulation of granular material for the large scale simulation of granular material the nonsmooth contact dynamics method nscd is examined first the equations of motion of nonsmooth mechanical systems are introduced and classified as a differential variational inequality dvi that has a structure similar to differential algebraic equations daes using a galerkin projection in time we derive nonsmooth extensions of the shake and rattle schemes a matrix free interior point method ipm is used for the complementarity problems that need to be solved in each time step we demonstrate that in this way the nscd approach yields highly accurate results and is competitive compared to the discrete element method dem

curves of maximum genus in range a and stick figures in this paper we show the existence of smooth connected space curves not contained in a surface of degree less than m with genus maximal with respect to the degree in half of the so called range a the main tool is a technique of deformation of stick figures due to g floystad

a comparison of numerical methods for solving multibody dynamics problems with frictional contact modeled via differential variational inequalities abstract we investigate two classes of solvers used to determine the time evolution of large systems of rigid bodies that mutually interact through contact with friction the contact is modeled through a complementarity condition the friction is posed as a variational problem the system dynamics is described by a set of differential algebraic equations coupled with differential variational inequalities dvi upon discretization in time the complementarity conditions enforced at the velocity level are relaxed to obtain a cone complementarity problem ccp the solution of the ccp which becomes the simulation bottleneck is found by minimizing an equivalent quadratic optimization problem with conic constraints herein we investigate two classes of solvers for this constrained optimization problem the projected gauss jacobi pgj projected gauss seidel pgs and accelerated projected gradient descent apgd methods are exponents of the first class of solvers they are first order using only cost function value and gradient information the second class of solvers is represented by a symmetric cone interior point scip method and a primal dual interior point pdip method these second order methods rely on a newton step to identify the descent direction and a line search to compute the step size all five methods draw on parallel computing on graphics processing unit gpu cards the newton step employs a sparse parallel gpu solver two types of numerical experiments filling and drafting are carried out to evaluate the performance of the five solution strategies in terms of convergence rate accuracy and computational cost for consistency all numerical experiments were performed in the same open source code modified to host the five methods of interest

k configurations in p3all have extremal resolutions abstract we prove that allk configurations of points in p 3have the extremal resolution for a cohen macaulay scheme with the hilbert function

liaison classes of modules abstract we propose a concept of module liaison that extends gorenstein liaison of ideals and provides an equivalence relation among unmixed modules over a commutative gorenstein ring analyzing the resulting equivalence classes we show that several results known for gorenstein liaison are still true in the more general case of module liaison in particular we construct two maps from the set of even liaison classes of modules of fixed codimension into stable equivalence classes of certain reflexive modules as a consequence we show that the intermediate cohomology modules and properties like being perfect cohen macaulay buchsbaum or surjective buchsbaum are preserved in even module liaison classes furthermore we prove that the module liaison class of a complete intersection of codimension one consists of precisely all perfect modules of codimension one

on the first infinitesimal neighborhood of a linear configuration of points in p2 abstract we consider the following open questions fix a hilbert function h that occurs for a reduced zero dimensional subscheme of p 2 among all subschemes x with hilbert function h what are the possible hilbert functions and graded betti numbers for the first infinitesimal neighborhood z of x i e the double point scheme supported on x is there a minimum h min and maximum h max such function the numerical information encoded in h translates to a type vector which allows us to find unions of points on lines called linear configurations with hilbert function h we give necessary and sufficient conditions for the hilbert function and graded betti numbers of the first infinitesimal neighborhoods of all such linear configurations to be the same even for those h for which the hilbert functions or graded betti numbers of the resulting double point schemes are not uniquely determined we give one depending only on h that does occur we prove the existence of h max in general and discuss h min our methods include liaison techniques

a gauss seidel like algorithm to solve frictional contact problems abstract the purpose of this work is to present some mathematical and numerical results concerning an implicit method devoted to frictional contact problems it has been implemented in a dynamical deep drawing simulation software simem3 renault where unilateral contact and dry friction is assumed between the metal sheet and the tools the method may be viewed as a nonlinear block gauss seidel algorithm a convergence theorem is proved using nonsmooth analysis theory several numerical results are presented to illustrate the behaviour of this algorithm

reduced arithmetically gorenstein schemes and simplicial polytopes with maximal betti numbers abstract an si sequence is a finite sequence of positive integers which is symmetric unimodal and satisfies a certain growth condition these are known to correspond precisely to the possible hilbert functions of graded artinian gorenstein algebras with the weak lefschetz property a property shared by a nonempty open set of the family of all graded artinian gorenstein algebras having a fixed hilbert function that is an si sequence starting with an arbitrary si sequence we construct a reduced arithmetically gorenstein configuration g of linear varieties of arbitrary dimension whose artinian reduction has the given si sequence as hilbert function and has the weak lefschetz property furthermore we show that g has maximal graded betti numbers among all arithmetically gorenstein subschemes of projective space whose artinian reduction has the weak lefschetz property and the given hilbert function as an application we show that over a field of characteristic zero every set of simplicial polytopes with fixed h vector contains a polytope with maximal graded betti numbers

reformulations of measure differential inclusions and their closed graph property abstract new formulations are given for measure differential inclusions dx dt k t r n where x is a function of bounded variation and k is a set valued map with closed convex values and has closed graph measure differential inclusions were first named by j j moreau for studying rigid body with impacts shocks and coulomb friction and assumed that k t is always a cone the new formulations are used to show that the graph of the solution operator is closed under point wise convergence of the solutions x and weak convergence of the differential measures dx provided that the minimum norm points of k t are bounded and the asymptotic cones k t are always pointed

a general lower bound on the number of examples needed for learning abstract we prove a lower bound of 1 ln 1 vcdim c on the number of random examples required for distribution free learning of a concept class c where vcdim c is the vapnik chervonenkis dimension and and are the accuracy and confidence parameters this improves the previous best lower bound of 1 ln 1 vcdim c and comes close to the known general upper bound of o 1 ln 1 vcdim c ln 1 for consistent algorithms we show that for many interesting concept classes including k cnf and k dnf our bound is actually tight to within a constant factor

learnability and the vapnik chervonenkis dimension valiant s learnability model is extended to learning classes of concepts defined by regions in euclidean space e n the methods in this paper lead to a unified treatment of some of valiant s results along with previous results on distribution free convergence of certain pattern recognition algorithms it is shown that the essential condition for distribution free learnability is finiteness of the vapnik chervonenkis dimension a simple combinatorial parameter of the class of concepts to be learned using this parameter the complexity and closure properties of learnable classes are analyzed and the necessary and sufficient conditions are provided for feasible learnability

non zenoness of a class of differential quasi variational inequalities the zeno phenomenon of a switched dynamical system refers to the infinite number of mode switches in finite time the absence of this phenomenon is crucial to the numerical simulation of such a system by time stepping methods and to the understanding of the behavior of the system trajectory extending a previous result for a strongly regular differential variational inequality this paper establishes that a certain class of non strongly regular differential variational inequalities is devoid of the zeno phenomenon the proof involves many supplemental results that are of independent interest specialized to a frictional contact problem with local compliance and polygonal friction laws this non zenoness result is of fundamental significance and the first of its kind

optimization based simulation of nonsmooth rigid multibody dynamics we present a time stepping method to simulate rigid multibody dynamics with inelastic collision contact and friction the method progresses with fixed time step without backtracking for collision and solves at every step a strictly convex quadratic program we prove that a solution sequence of the method converges to the solution of a measure differential inclusion we present numerical results for a few examples and we illustrate the difference between the results from our scheme and previous linear complementarity based time stepping schemes

quaternion based rigid body rotation integration algorithms for use in particle methods the resolution of translational motion in discrete element method and molecular dynamics applications is a straightforward task however resolving rotational motion is less obvious many applications update rotation using an explicit integration involving products of matrices which has well known drawbacks although rigid body rotation has received attention in large angle rotation applications relatively little attention has been dedicated to the unique requirements of particle methods using explicit time stepping algorithms this paper reviews existing explicit algorithms and shows the benefits of using a quaternion based re parameterization of both the central difference algorithm and the approach of munjiza et al int j numer meth engng 2003 56 36 55 the improvement not only provides guaranteed orthonormality of the resulting rotation but also allows the assumption of small angle rotation to be relaxed and the use of a more accurate taylor expansion instead the current and quaternion based algorithms are compared for accuracy and computational efficiency copyright 2007 john wiley sons ltd

an iterative construction of gorenstein ideals in this paper we present a method to inductively construct gorenstein ideals of any codimension c we start from a gorenstein ideal i of codimension c contained in a complete intersection ideal j of the same codimension and we prove that under suitable hypotheses there exists a new gorenstein ideal contained in the residual ideal i j we compare some numerical data of the starting and the resulting gorenstein ideals of the construction we compare also the buchsbaum eisenbud matrices of the two ideals in the codimension three case furthermore we show that this construction is independent from the other known geometrical constructions of gorenstein ideals providing examples

generic initial ideals and squeezed spheres in 1988 kalai constructed a large class of simplicial spheres called squeezed spheres and in 1991 presented a conjecture about generic initial ideals of stanley reisner ideals of squeezed spheres in the present paper this conjecture will be proved in order to prove kalai s conjecture based on the fact that every squeezed d 1 sphere is the boundary of a certain d ball called a squeezed d ball generic initial ideals of stanley reisner ideals of squeezed balls will be determined in addition generic initial ideals of exterior face ideals of squeezed balls are determined on the other hand we study the squeezing operation which assigns to each gorenstein complex g having the weak lefschetz property a squeezed sphere sq g and show that this operation increases graded betti numbers

convergence of a class of semi implicit time stepping schemes for nonsmooth rigid multibody dynamics in this work we present a framework for the convergence analysis in a measure differential inclusion sense of a class of time stepping schemes for multibody dynamics with contacts joints and friction this class of methods solves one linear complementarity problem per step and contains the semi implicit euler method as well as trapezoidal like methods for which second order convergence was recently proved under certain conditions by using the concept of a reduced friction cone the analysis includes for the first time a convergence result for the case that includes joints an unexpected intermediary result is that we are able to define a discrete velocity function of bounded variation although the natural discrete velocity function produced by our algorithm may have unbounded variation

maximal families of gorenstein algebras the purpose of this paper is to study maximal irreducible families of gorenstein quotients of a polynomial ring r let gradalg h r be the scheme parametrizing graded quotients of r with hilbert function h we prove there is a close relationship between the irreducible components of gradalg h r whose general member is a gorenstein codimension c 1 quotient and the irreducible components of gradalg h r whose general member b is a codimension c cohen macaulay algebra of hilbert function h related to h if the castelnuovo mumford regularity of the gorenstein quotient is large compared to the castelnuovo mumford regularity of b this relationship actually determines a well defined injective mapping from such cohen macaulay components of gradalg h r to gorenstein components of gradalg h r in which generically smooth components correspond moreover the dimension of the gorenstein components is computed in terms of the dimension of the corresponding cohen macaulay component and a sum of two invariants of b using linkage by a complete intersection we show how to compute these invariants linkage also turns out to be quite effective in verifying the assumptions which appear in a generalization of the main theorem

a matrix free cone complementarity approach for solving large scale nonsmooth rigid body dynamics this paper proposes an iterative method that can simulate mechanical systems featuring a large number of contacts and joints between rigid bodies the numerical method behaves as a contractive mapping that converges to the solution of a cone complementarity problem by means of iterated fixed point steps with separable projections onto convex manifolds since computational speed and robustness are important issues when dealing with a large number of frictional contacts we have performed special algorithmic optimizations in order to translate the numerical scheme into a matrix free algorithm with o n space complexity and easy implementation a modified version that can run on parallel computers is discussed a multithreaded version of the method has been used to simulate systems with more than a million contacts with friction

noether lefschetz space curves and mathematical instantons there are three areas of study of geometric entities living in the three dimensional projective space over the complex numbers which have proved to be strictly connected the classification of space curves surfaces and vector bundles despite all the production in these areas several key unsolved problems still challenge us after the work of many classical and modern authors see h1 h2 for a bibliography the problem of classifying space curves has been divided into two main parts 1 the so called halphen problem find all the triples of integers n g s such that there exists a smooth irreducible curve c ip 3 of degree n and genus g lying on a surface of degree s but not on any surface of lower degree 2 study the properties of the hilbert scheme hn g of smooth irreducible curves in ip namely its irreducible components dimension singular points let g n s be the maximum genus of a curve of degree n not contained in a surface of degree less than s then part 1 above falls in turn into three ranges for n and s

betti numbers of chordal graphs and f vectors of simplicial complexes abstract let g be a chordal graph and i g its edge ideal let i g 0 1 p denote the betti sequence of i g where i stands for the ith total betti number of i g and where p is the projective dimension of i g it will be shown that there exists a simplicial complex of dimension p whose f vector f f 0 f 1 f p coincides with i g

inverse systems of zero dimensional schemes in p n abstract the authors construct the global macaulay inverse system l z for a zero dimensional subscheme z of projective n space p n over an algebraically closed field k from the local inverse systems of the irreducible components of z they show that when z is locally gorenstein a generic element f of degree d apolar to z determines z if d is larger than an invariant z as a consequence of this globalization they show that a natural upper bound for the hilbert function of gorenstein artin quotients of the coordinate ring of z is achieved for large socle degree they also show the uniqueness of generalized additive decompositions of a homogeneous form into powers of linear forms under suitable hypotheses the main tools are elementary but delicate they involve a careful study of how to homogenize a local inverse system and of the behavior of the homogenization under a change of coordinates

using krylov subspace and spectral methods for solving complementarity problems in many body contact dynamics simulation summary many body dynamics problems are expected to handle millions of unknowns when for instance investigating the three dimensional flow of granular material unfortunately the size of the problems tractable by existing numerical solution techniques is severely limited on convergence grounds this is typically the case when the equations of motion embed a differential variational inequality problem that captures contact and possibly frictional interactions between rigid and or flexible bodies as the size of the physical system increases the speed and or the quality of the numerical solution decreases this paper describes three methods the gradient projected minimum residual method the preconditioned spectral projected gradient with fallback method and the modified proportioning with reduced gradient projection method that demonstrate better scalability than the projected jacobi and gauss seidel methods commonly used to solve contact problems that draw on a differential variational inequality based modeling approach copyright 2013 john wiley sons ltd

the weak and strong lefschetz properties for artinian k algebras abstract let a i 0ai be a standard graded artinian k algebra where chark 0 then a has the weak lefschetz property if there is an element l of degree 1 such that the multiplication l a i a i 1 has maximal rank for every i and a has the strong lefschetz property if l d a i a i d has maximal rank for every i and d the main results obtained in this paper are the following 1 every height three complete intersection has the weak lefschetz property our method surprisingly uses rank two vector bundles on p 2 and the grauert mulich theorem 2 we give a complete characterization including a concrete construction of the hilbert functions that can occur for k algebras with the weak or strong lefschetz property and the characterization is the same one 3 we give a sharp bound on the graded betti numbers achieved by our construction of artinian k algebras with the weak or strong lefschetz property and fixed hilbert function this bound is again the same for both properties some hilbert functions in fact force the algebra to have the maximal betti numbers 4 every artinian ideal in k x y possesses the strong lefschetz property this is false in higher codimension

combinatorial interpretations of some boij soderberg decompositions boij soderberg theory shows that the betti table of a graded module can be written as a linear combination of pure diagrams with integer coefficients using ferrers hypergraphs and simplicial polytopes we provide interpretations of these coefficients for ideals with a d linear resolution their quotient rings and for gorenstein rings whose resolution has essentially at most two linear strands we also establish a structural result on the decomposition in the case of quasi gorenstein modules

extremal point sets and gorenstein ideals the hilbert function of a homogeneous ideal in r k x0 xn k a field is a much studied object this is not surprising since the hilbert function encodes important algebraic combinatorial and geometric information about the ideal the fact that recent computer algebra developments have made the hilbert function computable has not only sustained interest in them but sparked interest in many new questions about them in this paper we will concentrate on the hilbert functions which are the hilbert functions of points in p from 11 we know that this is the same as studying 0 dimensional differentiable o sequences equivalently the hilbert functions of graded artinian quotients of k x1 xn in our earlier paper 9 we began a discussion of n type vectors and showed that they were in 1 1 correspondence with hilbert functions of doi 10 1006 aima 1998 1889 available online at http www idealibrary com on

on the existence of certain families of curves introduction 25 w 1 generalities on families of curves in ip 28 w the map 0 d 33 w 3 the number of moduli of a family 40 w 4 plane curves existence of families with the expected number of moduli 43 w 5 smoothing certain reducible curves in ip r r 3 47 w 6 curves in ip r 3 existence of families with the expected number of moduli 52 w curves in ip3 a more general existence theorem 55

convergence of a time stepping scheme for rigid body dynamics and resolution of painleve s problem this paper gives convergence theory for a new implicit time stepping scheme for general rigid body dynamics with coulomb friction and purely inelastic collisions and shocks an important consequence of this work is the proof of existence of solutions of rigid body problems which include the famous counterexamples of painleve the mathematical basis for this work is the formulation of the rigid body problem in terms of measure differential inclusions of moreau and monteiro marques the implicit time stepping method is based on complementarity problems and is essentially a particular case of the algorithm described in anitescu potra 2 which in turn is based on the formulation in stewart trinkle 47

learning regular sets from queries and counterexamples the problem of identifying an unknown regular set from examples of its members and nonmembers is addressed it is assumed that the regular set is presented by a minimamy adequate teacher which can answer membership queries about the set and can also test a conjecture and indicate whether it is equal to the unknown set and provide a counterexample if not a counterexample is a string in the symmetric difference of the correct set and the conjectured set a learning algorithm l is described that correctly learns any regular set from any minimally adequate teacher in time polynomial in the number of states of the minimum dfa for the set and the maximum length of any counterexample provided by the teacher it is shown that in a stochastic setting the ability of the teacher to test conjectures may be replaced by a random sampling oracle ex a polynomial time learning algorithm is shown for a particular problem of context free language identification

an inexact interior point method for the large scale simulation of granular material abstract non smooth contact dynamics provides an increasingly popular simulation framework for granular material in contrast to classical discrete element methods this approach is stable for arbitrary time steps and produces visually acceptable results in very short computing time yet when it comes to the prediction of draft forces non smooth contact dynamics is typically not accurate enough we therefore propose to combine the method class with an interior point algorithm for higher accuracy our specific algorithm is based on the so called jordan algebras and exploits the relation to symmetric cones in order to tackle the conical constraints that are intrinsic to frictional contact problems in every interior point iteration a linear system has to be solved we analyze how the interior point method behaves when it is combined with krylov subspace solvers and incomplete factorizations we show that efficient preconditioners and efficient linear solvers are essential for the method to be applicable to large scale problems using cg as a linear solver and incomplete lu factorizations we substantially improve the accuracy in comparison to the projected gaus jacobi solver

convergence of time stepping method for initial and boundary value frictional compliant contact problems beginning with a proof of the existence of a discrete time trajectory this paper establishes the convergence of a time stepping method for solving continuous time boundary value problems for dynamic systems with frictional contacts characterized by local compliance in the normal and tangential directions our investigation complements the analysis of the initial value rigid body model with one frictional contact encountering inelastic impacts by stewart arch ration mech anal 145 1998 pp 215 260 and the recent analysis by anitescu optimization based simulation for nonsmooth rigid multibody dynamics argonne national laboratory argonne il 2004 using the framework of measure differential inclusions in contrast to the measure theoretic approach of these authors we follow a differential variational approach and address a broader class of problems with multiple elastic or inelastic impacts applicable to both initial and affine boundary value problems our main convergence result pertains to the case where the compliance in the normal direction is decoupled from the compliance in the tangential directions and where the friction coefficients are sufficiently small

time stepping for three dimensional rigid body dynamics traditional methods for simulating rigid body dynamics involves determining the current contact arrangement e g each contact is either a rolling or sliding contact the development of this approach is most clearly seen in the work of haug et al mech machine theory 21 1986 401 425 and pfeiffer and glocker multibody dynamics with unilateral contacts wiley 1996 however there has been a controversy about the status of rigid body dynamics as a theory due to simple problems in the area which do not appear to have solutions the most famous if not the earliest is due to paul painleve c r acad sci paris 121 1895 112 115 recently a number of time stepping methods have been developed to overcome these difficulties these time stepping methods use integrals of the forces over time steps rather than the actual forces this allows impulsive forces without the need for a separate formulation or special procedures to cover this case the newest of these methods are developed in terms of complementarity problems the complementarity problems that define the time stepping procedure are solvable unlike previous methods for simulating rigid body dynamics with friction proof of the existence of solutions to the continuous problem can be shown in the sense of measure differential inclusions in terms of these methods in this paper a number of these variants will be discussed and their essential properties proven

global and finite termination of a two phase augmented lagrangian filter method for general quadratic programs we present a two phase algorithm for solving large scale quadratic programs qps in the first phase gradient projection iterations approximately minimize a bound constrained augmented lagrangian function and provide an estimate of the optimal active set in the second phase an equality constrained qp defined by the current active set is approximately minimized in order to generate a second order search direction a filter determines the required accuracy of the subproblem solutions and provides an acceptance criterion for the search directions the resulting algorithm is globally and finitely convergent the algorithm is suitable for large scale problems with many degrees of freedom and provides an alternative to interior point methods when iterative methods must be used to solve the underlying linear systems numerical experiments on a subset of the cuter qp test problems demonstrate the effectiveness of the approach