on the lower central quotients of the free groups of finite rank of a certain variety abstract let f n be a free group of rank n and k f n the k th term of the lower central series of f n for l 1 we denote by f n q l the quotient group of f n by a normal subgroup 2 3 f n l 2 2 f n in this paper we show that each of the graded quotients of the lower central series of the group f n q l for any l 1 is a free abelian group and give a basis of it by using a generalized chen s integration in free groups

shallow deep and very deep cuts in the analytic center cutting plane method in this paper we show that the cut does not need to go through the query point it can be deep or shallow the primal framework leads to a simple analysis of the potential variation which shows that the inequality needed for convergence of the algorithm is in fact attained at the first iterate of the feasibility step

a potential reduction algorithm allowing column generation using the dantzig wolfe decomposition technique a potential reduction algorithm allowing column generation for the linear feasibility lf problem is developed the point of departure is a simple containing polytope and its analytic center in each iteration an inequality violated at the current center is selected used to cut the polytope and then used to find the new center for the shrunken polytope the potential value associated with the containing polytope is reduced by a constant at each step and the algorithm is terminated in a polynomial time that depends only on the number and data length of the inequalities generated in the iterative process

simplex and interior point specialized algorithms for solving nonoriented multicommodity flow problems multicommodity network flow models arise in a wide variety of contexts typical among which is the dimensioning of telecommunication networks in this paper we present various approaches based on specialization of the simplex algorithm and interior point methods to solve nonoriented multicommodity flowproblems algorithms are tested with data from the france telecom paris district transmission network first we focus on a specialization for the node arc formulation of the problem a primal simplex and dual affine scaling algorithms exploiting the particular structure of the constraint matrix are presented and compared numerical results are provided for problems up to about 800 000 constraints and 6 000 000 variables however much more powerful approaches based on specialized decomposition methods can be implemented for solving the problem a dantzig wolfe decomposition method is designed and compared with a specialized implementation of the analytic center cutting plane method accpm partitioning techniques are used to exploit the structure of the master programs involved in those methods

a primal dual decomposition algorithm for multistage stochastic convex programming this paper presents a new and high performance solution method for multistage stochastic convex programming stochastic programming is a quantitative tool developed in the field of optimization to cope with the problem of decision making under uncertainty among others stochastic programming has found many applications in finance such as asset liability and bond portfolio management however many stochastic programming applications still remain computationally intractable because of their overwhelming dimensionality in this paper we propose a new decomposition algorithm for multistage stochastic programming with a convex objective and stochastic recourse matrices based on the path following interior point method combined with the homogeneous self dual embedding technique our preliminary numerical experiments show that this approach is very promising in many ways for solving generic multistage stochastic programming including its superiority in terms of numerical efficiency as well as the flexibility in testing and analyzing the model

a log barrier method with benders decomposition for solving two stage stochastic linear programs an algorithm incorporating the logarithmic barrier into the benders decomposition technique is proposed for solving two stage stochastic programs basic properties concerning the existence and uniqueness of the solution and the underlying path are studied when applied to problems with a finite number of scenarios the algorithm is shown to converge globally and to run in polynomial time

residual p properties of mapping class groups and surface groups let m p be the mapping class group of a punctured oriented surface e p where p may be empty and let t p p be the kernel of the action of m p on h 1 p f p we prove that t p p is residually p in particular this shows that m p is virtually residually p for a group g we denote by ip g the kernel of the natural action of out g on h 1 g f p in order to achieve our theorem we prove that under certain conditions g is conjugacy p separable and has property a the group ip g is residually p the fact that free groups and surface groups have property a is due to grossman the fact that free groups are conjugacy p separable is due to lyndon and schupp the fact that surface groups are conjugacy p separable is from a technical point of view the main result of the paper

a cutting plane algorithm for convex programming that uses analytic centers anoracle for a convex sets n accepts as input any pointz in n and ifz s then it returns yes while ifz s then it returns no along with a separating hyperplane we give a new algorithm that finds a feasible point ins in cases where an oracle is available our algorithm uses the analytic center of a polytope as test point and successively modifies the polytope with the separating hyperplanes returned by the oracle the key to establishing convergence is that hyperplanes judged to be unimportant are pruned from the polytope if a ball of radius 2 l is contained ins ands is contained in a cube of side 2l 1 then we can show our algorithm converges after o nl2 iterations and performs a total of o n4l3 tnl2 arithmetic operations wheret is the number of arithmetic operations required for a call to the oracle the bound is independent of the number of hyperplanes generated in the algorithm an important application in which an oracle is available is minimizing a convex function overs

speed accuracy response models scoring rules based on response time and accuracy starting from an explicit scoring rule for time limit tasks incorporating both response time and accuracy and a definite trade off between speed and accuracy a response model is derived since the scoring rule is interpreted as a sufficient statistic the model belongs to the exponential family the various marginal and conditional distributions for response accuracy and response time are derived and it is shown how the model parameters can be estimated the model for response accuracy is found to be the two parameter logistic model it is found that the time limit determines the item discrimination and this effect is illustrated with the amsterdam chess test ii

on the implementation of interior point decomposition algorithms for two stage stochastic conic programs in this paper we develop a practical primal interior decomposition algorithm for two stage stochastic programming problems the framework of this algorithm is similar to the framework in s mehrotra and m g ozevin decomposition based interior point methods for two stage stochastic convex quadratic programs with recourse to appear in oper res s mehrotra and m g ozevin siam j optim 18 2007 pp 206 222 and g zhao math program 90 2001 pp 507 536 however their algorithm is altered in a simple yet fundamental way to achieve practical performance in particular this new algorithm weighs the log barrier terms in the second stage problems differently from the theoretical algorithms analyzed in s mehrotra and m g ozevin oper res to appear s mehrotra and m g ozevin siam j optim 18 2007 pp 206 222 and g zhao math program 90 2001 pp 507 536 we give a method for generating a suitable starting point a method for selecting a good starting barrier parameter a heuristic for first stage step length calculation without performing line searches and a method for adaptive addition of new scenarios over the course of the algorithm the decomposition algorithm is implemented to solve two stage stochastic conic programs with recourse whose underlying cones are cartesian products of linear second order and semidefinite cones the performance of primal decomposition method is studied on a set of randomly generated test problems as well as a two stage stochastic programming extension of the markowitz portfolio selection model the computational results show that an efficient and stable implementation of the primal decomposition method is possible these results also show that in problems with a large number of scenarios the adaptive addition of scenarios can yield computational savings of up to 80

generalized johnson homomorphisms for extended n series abstract the johnson filtration of the mapping class group of a compact oriented surface is the descending series consisting of the kernels of the actions on the nilpotent quotients of the fundamental group of the surface each term of the johnson filtration admits a johnson homomorphism whose kernel is the next term in the filtration in this paper we consider a general situation where a group acts on a group with a filtration called an extended n series we develop a theory of johnson homomorphisms in this general setting including many known variants of the original johnson homomorphisms as well as several new variants

the cokernel of the johnson homomorphisms of the automorphism group of a free metabelian group in this paper we determine the cokernel of the k th johnson homomorphisms of the automorphism group of a free metabelian group for k 2 and n 4 as a corollary we obtain a lower bound on the rank of the graded quotient of the johnson filtration of the automorphism group of a free group furthermore by using the second johnson homomorphism we determine the image of the cup product map in the rational second cohomology group of the ia automorphism group of a free metabelian group and show that it is isomorphic to that of the ia automorphism group of a free group which is already determined by pettet finally by considering the kernel of the magnus representations of the automorphism group of a free group and a free metabelian group we show that there are non trivial rational second cohomology classes of the ia automorphism group of a free metabelian group which are not in the image of the cup product map

a nonlinear analytic center cutting plane method for a class of convex programming problems a cutting plane algorithm for minimizing a convex function subject to constraints defined by a separation oracle is presented the algorithm is based on approximate analytic centers the nonlinearity of the objective function is taken into account yet the feasible region is approximated by a containing polytope this containing polytope is regularly updated by adding a new cut through a test point each test point is an approximate analytic center of the intersection of a containing polytope and a level set of the nonlinear objective function we establish the complexity of the algorithm our complexity estimate is given in terms of the problem dimension the desired accuracy of an approximate solution and other parameters that depend on the geometry of a specific instance of the problem

two interpretations of the discrimination parameter in this paper we propose two interpretations for the discrimination parameter in the two parameter logistic model 2plm the interpretations are based on the relation between the 2plm and two stochastic models in the first interpretation the 2plm is linked to a diffusion model so that the probability of absorption equals the 2plm the discrimination parameter is the distance between the two absorbing boundaries and therefore the amount of information that has to be collected before a response to an item can be given for the second interpretation the 2plm is connected to a specific type of race model in the race model the discrimination parameter is inversely related to the dependency of the information used in the decision process extended versions of both models with person to person variability in the difficulty parameter are considered when fitted to a data set it is shown that a generalization of the race model that allows for dependency between choices and response times rts is the best fitting model

complexity estimates of some cutting plane methods based on the analytic barrier in this paper we establish the efficiency estimates for two cutting plane methods based on the analytic barrier we prove that the rate of convergence of the second method is optimal uniformly in the number of variables we present a modification of the second method in this modified version each test point satisfies an approximate centering condition we also use the standard strategy for updating approximate hessians of the logarithmic barrier function we prove that the rate of convergence of the modified scheme remains optimal and demonstrate that the number of newton steps in the auxiliary minimization processes is bounded by an absolute constant we also show that the approximate hessian strategy significantly improves the total arithmetical complexity of the method

solving combinatorial optimization problems using karmakar s algorithm we describe a cutting plane algorithm for solving combinatorial optimization problems the primal projective standard form variant of karmarkar s algorithm for linear programming is applied to the duals of a sequence of linear programming relaxations of the combinatorial optimization problem

a scaling technique for finding the weighted analytical center of a polytope let a bounded full dimensional polytope be defined by the systemax b wherea is anm n matrix letai denote theith row of the matrixa and define theweighted analytic center of the polytope to be the point that minimizes the strictly convex barrier function i 1mwi ln aitx bi the proper selection of weightswi can make any desired point in the interior of the polytope become the weighted analytic center as a result the weighted analytic center has applications in both linear and general convex programming for simplicity we assume that the weights are positive integers if some of thewi s are much larger than others then newton s method for minimizing the resulting barrier function is very unstable and can be very slow previous methods for finding the weighted analytic center relied upon a rather direct application of newton s method potentially resulting in very slow global convergence we present a method for finding the weighted analytic center that is based on the scaling technique of edmonds and karp and is an enhancement of newton s method the scaling algorithm runs in o sqrt m log w iterations wherem is the number of constraints defining the polytope andw is the largest weight given on any constraint each iteration involves taking a step in the newton direction and its complexity is dominated by the time needed to solve a system of linear equations

a cutting plane method from analytic centers for stochastic programming the stochastic linear programming problem with recourse has a dual block angular structure it can thus be handled by benders decomposition or by kelley s method of cutting planes equivalently the dual problem has a primal block angular structure and can be handled by dantzig wolfe decomposition the two approaches are in fact identical by duality here we shall investigate the use of the method of cutting planes from analytic centers applied to similar formulations the only significant difference form the aforementioned methods is that new cutting planes or columns by duality will be generated not from the optimum of the linear programming relaxation but from the analytic center of the set of localization

on vaidya s volumetric cutting plane method for convex programming we describe a simplified and strengthened version of vaidya s volumetric cutting plane method for finding a point in a convex set x1d49e rn at each step the algorithm has a system of linear inequality constraints which defines a polyhedron x1d4ab x1d49e and an interior point x x1d4ab the algorithm then either drops one constraint or calls an oracle to check if x x1d49e and if not obtain a new constraint that separates x from x1d49e following the addition or deletion of a constraint the algorithm takes a small number of newton steps for the volumetric barrier v progress of the algorithm is measured in terms of changes in v the algorithm is terminated when either it is discovered that x x1d49e or v becomes large enough to demonstrate that the volume of x1d49e must be below some prescribed amount the complexity of the algorithm compares favorably with that of the ellipsoid method especially in terms of the number of calls to the separation oracle compared to vaidya s original analysis we decrease the total number

a generalized speed accuracy response model for dichotomous items we propose a generalization of the speed accuracy response model sarm introduced by maris and van der maas psychometrika 77 615 633 2012 in these models the scores that result from a scoring rule that incorporates both the speed and accuracy of item responses are modeled our generalization is similar to that of the one parameter logistic or rasch model to the two parameter logistic or birnbaum model in item response theory an expectation maximization em algorithm for estimating model parameters and standard errors was developed furthermore methods to assess model fit are provided in the form of generalized residuals for item score functions and saddlepoint approximations to the density of the sum score the presented methods were evaluated in a small simulation study the results of which indicated good parameter recovery and reasonable type i error rates for the residuals finally the methods were applied to two real data sets it was found that the two parameter sarm showed improved fit compared to the one parameter sarm in both data sets

complexity analysis of the analytic center cutting plane method that uses multiple cuts we analyze the complexity of the analytic center cutting plane or column generation algorithm for solving general convex problems defined by a separation oracle the oracle is called at the analytic center of a polytope which contains a solution set and is given by the intersection of the linear inequalities previously generated from the oracle if the center is not in the solution set separating hyperplanes will be placed through the center to shrink the containing polytope while the complexity result has been recently established for the algorithm when one cutting plane is placed in each iteration the result remains open when multiple cuts are added moreover adding multiple cuts actually is a key to practical effectiveness in solving many problems and it presents theoretical difficulties in analyzing cutting plane methods in this paper we show that the analytic center cutting plane algorithm with multiple cuts added in each iteration still is a fully polynomial approximation algorithm

mapping class group action versus galois action on profinite fundamental groups let x be an algebraic curve of genus g n punctured defined over a number field k then the profinite or the pro l completion of the topological fundamental group of x admits two actions the action of the profinite completion of the mapping class group of the orientable surface of topological type g n and the action of the absolute galois group of k this paper compares these two in the profinite case it is shown that the intersection of the images of these two actions is trivial if x is affine and its fundamental group is nonabelian on the contrary in the pro l case there are many curves such that the image of the galois action contains the image of the mapping class group action it is proved that the set of points corresponding to such curves is dense in the moduli space of g n curves

decomposition and nondifferentiable optimization with the projective algorithm this paper deals with an application of a variant of karmarkar s projective algorithm for linear programming to the solution of a generic nondifferentiable minimization problem this problem is closely related to the dantzig wolfe decomposition technique used in large scale convex programming the proposed method is based on a column generation technique defining a sequence of primal linear programming maximization problems associated with each problem one defines a weighted potential function which is minimized using a variant of the projective algorithm when a point close to the minimum of the potential function is reached a corresponding point in the dual space is constructed which is close to the analytic center of a polytope containing the solution set of the nondifferentiable optimization problem an admissible cut of the polytope corresponding to a new supporting hyperplane of the epigraph of the function to minimize is then generated at this approximate analytic center in the primal space this new cut translates into a new column for the associated linear programming problem the algorithm has performed well on a set of convex nondifferentiable programming problems

formulating two stage stochastic programs for interior point methods this paper describes an approach for modeling two stage stochastic programs that yields a form suitable for interior point algorithms a staircase constraint structure is created by replacing first stage variables with sparse split variables in conjunction with side constraints dense columns are thereby eliminated the resulting model is larger than traditional stochastic programs but computational savings are substantial over a tenfold improvement for the problems tested a series of experiments with stochastic networks drawn from financial planning demonstrates the attained efficiencies comparisons with minos and the dual block angular stochastic programming model are provided as benchmarks the split variable approach is applicable to general two stage stochastic programs and other dual block angular models

on the fourth johnson homomorphism of the automorphism group of a free group abstract in this paper we consider the johnson homomorphism of the automorphism group of a free group with respect to the lower central series of the ia automorphism group of a free group in particular we determine the rational cokernel of the fourth johnson homomorphism and show that there appears a new obstruction for the surjectivity of the johnson homomorphism furthermore we characterize this obstruction using trace maps

equivalence relations for homology cylinders and the core of the casson invariant let r be a compact oriented surface of genus g with one boundary component homology cylinders over r form a monoid ic into which the torelli group i of r embeds by the mapping cylinder construction two homology cylinders m and m are said to be y k equivalent if m is obtained from m by twisting an arbitrary surface s in m with a homeomorphim belonging to the k th term of the lower central series of the torelli group of s the j k equivalence relation on ic is defined in a similar way using the k th term of the johnson filtration in this paper we characterize the y 3 equivalence with three classical invariants 1 the action on the third nilpotent quotient of the fundamental group of r 2 the quadratic part of the relative alexander polynomial and 3 a by product of the casson invariant similarly we show that the j 3 equivalence is classified by 1 and 2 we also prove that the core of the casson invariant originally defined by morita on the second term of the johnson filtration of i has a unique extension to the corresponding submonoid of ic that is preserved by y 3 equivalence and the mapping class group action

inexact cuts in benders decomposition benders decomposition is a well known technique for solving large linear programs with a special structure in particular it is a popular technique for solving multistage stochastic linear programming problems early termination in the subproblems generated during benders decomposition assuming dual feasibility produces valid cuts that are inexact in the sense that they are not as constraining as cuts derived from an exact solution we describe an inexact cut algorithm prove its convergence under easily verifiable assumptions and discuss a corresponding dantzig wolfe decomposition algorithm the paper is concluded with some computational results from applying the algorithm to a class of stochastic programming problems that arise in hydroelectric scheduling

a primal dual decomposition based interior point approach to two stage stochastic linear programming decision making under uncertainty is a challenge faced by many decision makers stochastic programming is a major tool developed to deal with optimization with uncertainties which has found applications in e g finance such as asset liability and bond portfolio management computationally however many models in stochastic programming remain unsolvable because of overwhelming dimensionality for a model to be well solvable its special structure must be explored most of the solution methods are based on decomposing the data in this paper we propose a new decomposition approach for two stage stochastic programming based on a direct application of the path following method combined with the homogeneous self dual technique numerical experiments show that our decomposition algorithm is very efficient for solving stochastic programs in particular we apply our decomposition method to a two period portfolio selection problem using options on a stock index in this model the investor can invest in a money market account a stock index and european options on this index with different maturities we experiment with our model with market prices of options on the s p500

weight decompositions on etale fundamental groups let x 0 be a smooth or proper variety defined over a finite field k and let x be the base extension of x 0 to the algebraic closure bar k the geometric etale fundamental group pi 1 x bar x of x is a normal subgroup of the weil group so conjugation gives it a weil action for l not dividing the characteristic of k we consider the pro bbb q l algebraic completion of pi 1 x bar x as a nonabelian weil representation lafforgue s theorem and deligne s weil ii theorems imply that this affine group scheme is mixed in the sense that its structure sheaf is a mixed weil representation when x is smooth weight restrictions apply affecting the possibilities for the structure of this group this gives new examples of groups which cannot arise as etale fundamental groups of smooth varieties

an analytic center based column generation algorithm for convex quadratic feasibility problems we consider the analytic center based column generation algorithm for the problem of finding a feasible point in a set defined by a finite number of convex quadratic inequalities at each iteration the algorithm computes an approximate analytic center of the set defined by the intersection of quadratic inequalities generated in the previous iterations if this approximate analytic center is a solution then the algorithm terminates otherwise a quadratic inequality violated at the current center is selected and a new quadratic cut defined by a convex quadratic inequality is placed near the approximate center as the number of cuts increases the set defined by their intersection shrinks and the algorithm eventually finds a solution to the problem previously similar analytic center based column generation algorithms were studied first for the linear feasibility problem and later for the general convex feasibility problem our method differs from these early methods in that we use quadratic cuts in the computation instead of linear cuts moreover our method has a polynomial worst case complexity of o n ln frac 1 varepsilon on the total number of cuts to be used where n is the number of convex quadratic polynomial inequalities in the problem and varepsilon is the radius of the largest ball contained in the feasible set in contrast the early column generation methods using linear cuts can only solve the convex quadratic feasibility problem in pseudopolynomial time

characterizing the manifest probability distributions of three latent trait models for accuracy and response time in this paper we study the statistical relations between three latent trait models for accuracies and response times the hierarchical model hm of van der linden psychometrika 72 3 287 308 2007 the signed residual time model sm proposed by maris and van der maas psychometrika 77 4 615 633 2012 and the drift diffusion model dm as proposed by tuerlinckx and de boeck psychometrika 70 4 629 650 2005 one important distinction between these models is that the hm and the dm either assume or imply that accuracies and response times are independent given the latent trait variables while the sm does not in this paper we investigate the impact of this conditional independence property or a lack thereof on the manifest probability distribution for accuracies and response times we will find that the manifest distributions of the latent trait models share several important features such as the dependency between accuracy and response time but we also find important differences such as in what function of response time is being modeled our method for characterizing the manifest probability distributions is related to the dutch identity holland in psychometrika 55 6 5 18 1990

canonical extensions of the johnson homomorphisms to the torelli groupoid abstract we prove that every trivalent marked bordered fatgraph comes equipped with a canonical generalized magnus expansion in the sense of kawazumi this magnus expansion is used to give canonical extensions of the higher johnson homomorphisms m for m 1 to the torelli groupoid and we provide a recursive combinatorial formula for tensor representatives of these extensions in particular we give an explicit 1 cocycle in the dual fatgraph complex which extends 2 and thus answer affirmatively a question of morita and penner to illustrate our techniques for calculating higher johnson homomorphisms in general we give explicit examples calculating m for m 3

the structure of the torelli group i a finite set of generators for j this is the first of three papers concerning the so called torelli group let m mg be a compact orientable surface of genus g having n boundary components and let 9 xg be its mapping class group that is the group of orientation preserving diffeomorphisms of m which are 1 on the boundary am modulo isotopies which fix 3m pointwise this group is also known to the complex analysts as the teichmuller group or modular group if n 0 or 1 let further 4 jg be the subgroup of d1 which acts trivially on h1 m z the topologists have no traditional name for a but the analysts tell me it was known classically and is called the torelli group several interesting problems and conjectures exist concerning f the principal one can be found in kirby s problem list k and asks if gg is finitely generated in this first paper we shall answer the question affirmatively for both gg 0 and fgg when g 3 and shall give a fairly simple set of generators two other conjectures were made by the author the first involves the subgroup j of f which is generated by twists on nulhomologous simple closed curves ji produces a surjective homomorphism t fgg 1 a3h1 m z which kills c and it is conjectured there that in fact 5y ker t the proof of this is the content of the second paper in the third paper we use the results of the second to compute the abelianization f f explicitly thereby verifying another conjecture in ji the first reasonably simple but infinite set of generators for fg0 was produced by powell in p his generators consist of two types a twists on bounding simple closed curves b opposite twists on a bounding pair of disjoint homologous simple closed curves each of which are nonbounding using his result the author showed in j2 that the maps of the second type which we call bp maps for bounding pair are actually sufficient to generate both kg 0 and fg 1 for g 3 and in fact that we need only those whose two curves bound a genus one subsurface of m note that for g 2 all bp maps are trivial and hence the result fails in this case in the finite set of generators produced in this paper only

specialized fast algorithms for iqc feasibility and optimization problems the conventional way to treat integral quadratic constraint iqc problems is to transform them into semi definite programs sdps sdps can then be solved using interior point methods which have been proven efficient this approach however is not always the most efficient since it introduces additional decision variables to the sdp and the additional decision variables sometimes largely increase the complexity of the problem in this paper we demonstrate how to solve iqc problems by other alternatives more specifically we consider two cutting plane algorithms we will show that in certain cases these cutting plane algorithms can solve iqc problems much faster than the conventional approach numerical examples as well as some explanations from the point of view of computational complexity are provided to support our point

a reduction of the target of the johnson homomorphisms of the automorphism group of a free group let f n be a free group of rank n and f n n the quotient group of f n by a subgroup n 3 n 3 n 2 n 2 n 2 where n k denotes the k th subgroup of the lower central series of the free group f n in this paper we determine the group structure of the graded quotients of the lower central series of the group f n n by using a generalized chen s integration in free groups then we apply it to the study of the johnson homomorphisms of the automorphism group of f n in particular under taking a reduction of the target of the johnson homomorphism induced from a quotient map f n f n n we see that there appear only two irreducible components the morita obstruction s k h q and the schur weyl module of type h k 2 12 q in the cokernel of the rational johnson homomorphism k q k id q for k 5 and n k 2

solving nonlinear multicommodity flow problems by the analytic center cutting plane method the paper deals with nonlinear multicommodity flow problems with convex costs a decomposition method is proposed to solve them the approach applies a potential reduction algorithm to solve the master problem approximately and a column generation technique to define a sequence of primal linear programming problems each subproblem consists of finding a minimum cost flow between an origin and a destination node in an uncapacited network it is thus formulated as a shortest path problem and solved with dijkstra s d heap algorithm an implementation is described that takes full advantage of the supersparsity of the network in the linear algebra operations computational results show the efficiency of this approach on well known nondifferentiable problems and also large scale randomly generated problems up to 1000 arcs and 5000 commodities

vanishing resonance and representations of lie algebras we explore a relationship between the classical representation theory of a complex semisimple lie algebra g and the resonance varieties r v k v attached to irreducible g modules v and submodules k v v in the process we give a precise roots and weights criterion insuring the vanishing of these varieties or equivalently the finiteness of certain modules w v k over the symmetric algebra on v in the case when g sl2 c our approach sheds new light on the modules studied by weyman and eisenbud in the context of green s conjecture on free resolutions of canonical curves in the case when g sln c or sp2g c our approach yields a unified proof of two vanishing results for the resonance varieties of the outer torelli groups of surface groups results which arose in recent work by dimca hain and the authors on homological finiteness in the johnson filtration of mapping class groups and automorphism groups of free groups

decomposition based interior point methods for two stage stochastic convex quadratic programs with recourse zhao showed that the log barrier associated with the recourse function of two stage stochastic linear programs behaves as a strongly self concordant barrier and forms a self concordant family on the first stage solutions in this paper we show that the recourse function is also strongly self concordant and forms a self concordant family for the two stage stochastic convex quadratic programs with recourse this allows us to develop bender s decomposition based linearly convergent interior point algorithms an analysis of such an algorithm is given in this paper

a hierarchical framework for modeling speed and accuracy on test items current modeling of response times on test items has been strongly influenced by the paradigm of experimental reaction time research in psychology for instance some of the models have a parameter structure that was chosen to represent a speed accuracy tradeoff while others equate speed directly with response time also several response time models seem to be unclear as to the level of parametrization they represent a hierarchical framework for modeling speed and accuracy on test items is presented as an alternative to these models the framework allows a plug and play approach with alternative choices of models for the response and response time distributions as well as the distributions of their parameters bayesian treatment of the framework with markov chain monte carlo mcmc computation facilitates the approach use of the framework is illustrated for the choice of a normal ogive response model a lognormal model for the response times and multivariate normal models for their parameters with gibbs sampling from the joint posterior distribution

a polynomial method of approximate centers for linear programming we present a path following algorithm for the linear programming problem with a surprisingly simple and elegant proof of its polynomial behaviour this is done both for the problem in standard form and for its dual problem we also discuss some implementation strategies

multiple cuts in the analytic center cutting plane method we analyze the multiple cut generation scheme in the analytic center cutting plane method we propose an optimal primal and dual updating direction when the cuts are central the direction is optimal in the sense that it maximizes the product of the new dual slacks and of the new primal variables within the trust regions defined by dikin s primal and dual ellipsoids the new primal and dual directions use the variance covariance matrix of the normals to the new cuts in the metric given by dikin s ellipsoid we prove that the recovery of a new analytic center from the optimal restoration direction can be done in o plog p 1 damped newton steps where p is the number of new cuts added by the oracle which may vary with the iteration the results and the proofs are independent of the specific scaling matrix primal dual or primal dual that is used in the computations the computation of the optimal direction uses newton s method applied to a self concordant function of p variables the convergence result of ye math programming 78 1997 pp 85 104 holds here also the algorithm stops after o frac bar p 2n 2 varepsilon 2 cutting planes have been generated where bar p is the maximum number of cuts generated at any given iteration

large step path following methods for linear programming part i barrier function method the algorithm proposed in this paper is the classical logarithmic barrier function method with newton raphson steps for the internal minimization of the penalized function polynomial behavior is obtained by stopping each internal cycle when the iterates approach the central trajectory each master iteration updates the penalty parameter by a constant factor and the overall complexity bound depends on this factor o nl newton iterations for an arbitrary constant and o sqrt n l iterations for a constant dependent on sqrt n

finite type 3 manifold invariants and the structure of the torelli group i using the recently developed theory of finite type invariants of integral homology 3 spheres we study the structure of the torelli group of a closed surface explicitly we construct a natural cocycles of the torelli group with coefficients in a space of trivalent graphs and cohomology classes of the abelianized torelli group b group homomorphisms that detect rationally the nontriviality of the lower central series of the torelli group our results are motivated by the appearance of trivalent graphs in topology and in representation theory and the dual role played by the casson invariant in the theory of finite type invariants of integral homology 3 spheres and in morita s study mo2 mo3 of the structure of the torelli group our results generalize those of s morita mo2 mo3 and complement the recent calculation due to r hain ha2 of the i adic completion of the rational group ring of the torelli group we also give analogous results for two other subgroups of the mapping class group

structure of symplectic invariant lie subalgebras of symplectic derivation lie algebras abstract we study the structure of the symplectic invariant part h g 1 sp of the lie algebra h g 1 consisting of symplectic derivations of the free lie algebra generated by the rational homology group of a closed oriented surface g of genus g first we describe the orthogonal direct sum decomposition of this space which is induced by the canonical metric on it and compute it explicitly up to degree 20 in this framework we give a general constraint which is imposed on the sp invariant component of the bracket of two elements in h g 1 second we clarify the relations among h g 1 and the other two related lie algebras h g and h g which correspond to the cases of a closed surface g with and without base point g in particular based on a theorem of labute we formulate a method of determining these differences and describe them explicitly up to degree 20 third by giving a general method of constructing elements of h g 1 sp we reveal a considerable difference between two particular submodules of it one is the sp invariant part of a certain ideal j g 1 and the other is that of the johnson image finally we combine these results to determine the structure of h g 1 completely up to degree 6 including the unstable cases where the genus 1 case has an independent meaning in particular we see a glimpse of the galois obstructions explicitly from our point of view

on the andreadakis johnson filtration of the automorphism group of a free group abstract families of non trivial cohomology classes are given for the discrete groups belonging to the johnson filtration of the automorphism group of a free group generated by n letters the methods are 1 to analyze analogous classes for filtrations of a subgroup of the pure symmetric automorphism group of a free group and 2 to analyze features of these classes which are preserved by the johnson homomorphism with values in the lie algebra of derivations of a free lie algebra one consequence is that the ranks of the cohomology groups in any fixed degree i for 1 i n 2 for the johnson filtrations of ia n increase without bound the actual classes constructed are fragile in the sense that they vanish after passage to successive filtrations furthermore these classes are all naturally in the image of the johnson homomorphism on the level of cohomology the methods are similar to those occurring within the theory of arrangements the authors congratulate corrado de concini on the occasion of his 60 th birthday one of the authors would like to thank corrado for a wonderful time arising from a discussion about cohomology of groups with friends in the basement of il palazzone

a mixture cure rate model for responses and response times in time limit tests many large scale standardized tests are intended to measure skills related to ability rather than the rate at which examinees can work time limits imposed on these tests make it difficult to distinguish between the effect of low proficiency and the effect of lack of time this paper proposes a mixture cure rate model approach to address this issue maximum likelihood estimation is proposed for parameter and variance estimation for three cases when examinee parameters are to be estimated given precalibrated item parameters when item parameters are to be calibrated given known examinee parameters and when item parameters are to be estimated without assuming known examinee parameters large sample properties are established for the cases under suitable regularity conditions simulation studies suggest that the proposed approach is appropriate for inferences concerning model parameters in addition not distinguishing between the effect of low proficiency and the effect of lack of time is shown to have considerable consequences for parameter estimation a real data example is presented to demonstrate the new model choice of survival models for the latent power times is also discussed

exploiting special structure in a primal dual path following algorithm a primal dual path following algorithm that applies directly to a linear program of the form min ctx ax b hx u x 0 x n is presented this algorithm explicitly handles upper bounds generalized upper bounds variable upper bounds and block diagonal structure we also show how the structure of time staged problems and network flow problems can be exploited especially on a parallel computer finally using our algorithm we obtain a complexity bound of o sqrt n ds2 log nk fortransportation problems withs origins d destinations s

large step path following methods for linear programming part ii potential reduction method the algorithm proposed in this paper is the affine polynomial potential reduction method with new procedures for updating the lower bounds for an optimal solution of the linear programming problem a method is developed for updating the lower bounds by large steps with strict control over the duality gaps associated with each iterate two algorithms are obtained by this approach the first one has complexity o nl iterations and a very simple updating procedure the second one updates the lower bounds at points very near the central trajectory and achieves a complexity of o sqrt n l iterations

rational points of universal curves in positive characteristics rational points of universal curves in positive characteristics by tatsunari watanabe department of mathematics duke university

on the computation of weighted analytic centers and dual ellipsoids with the projective algorithm the primal projective algorithm for linear programs with unknown optimal objective function value is extended to the case where one uses a weighted karmarkar potential function this potential is defined with respect to a strict lower bound to the optimum the minimization of this potential when the lower bound is kept fixed yields a primal and a dual feasible solution the dual solution is the weighted analytic center of a certain dual polytope finally one exhibits a pair of homothetic dual ellipsoids that extends results obtained by sonnevend todd ye freund and anstreicher

computing block angular karmarkar projections with applications to stochastic programming we present a variant of karmarkar s algorithm for block angular structured linear programs such as stochastic linear programs by computing the projection efficiently we give a worst case bound on the order of the running time that can be an order of magnitude better than that of karmarkar s standard algorithm further implications for approximations and very large scale problems are given

homogeneous analytic center cutting plane methods for convex problems and variational inequalities in this paper we consider a new analytic center cutting plane method in an extended space we prove the efficiency estimates for the general scheme and show that these results can be used in the analysis of a feasibility problem the variational inequality problem and the problem of constrained minimization our analysis is valid even for problems whose solution belongs to the boundary of the domain

a multicut algorithm for two stage stochastic linear programs outer linearization methods such as van slyke and wets s l shaped method for stochastic linear programs generally apply a single cut on the nonlinear objective at each major iteration the structure of stochastic programs allows for several cuts to be placed at once this paper describes a multicut algorithm to carry out this procedure it presents experimental and theoretical justification for reductions in major iterations

integral homology 3 spheres and the johnson filtration the mapping class group of an oriented surface g 1 of genus g with one boundary component has a natural decreasing filtration mg 1 mg i 3 me i d m g 1 3 where m g 1 k is the kernel of the action of m g 1 on the k th nilpotent quotient of 1 g 1 using a tree lie algebra approximating the graded lie algebra k m g 1 k m g 1 k 1 we prove that any integral homology sphere of dimension 3 has for some g a heegaard decomposition of the form m hg lg h g where g 1 3 and lg is such that h g lg h g s 3 this proves a conjecture due to s morita and shows that the core of the casson invariant is indeed the casson invariant

complexity of some cutting plane methods that use analytic centers we consider cutting plane methods for minimizing a convex possibly nondifferentiable function subject to box constraints at each iteration accumulated subgradient cuts define a polytope that localizes the minimum the objective and its subgradient are evaluated at the analytic center of this polytope to produce one or two cuts that improve the localizing set we give complexity estimates for several variants of such methods our analysis is based on the works of goffin luo and ye

on the graded quotients of the rings of fricke characters of free groups abstract for a free group f n on n generators we consider the aut f n invariant ideal j generated by tr x 2 for all x f n in the ring x q f n of fricke characters of f n this ideal defines a descending filtration j j 2 j 3 of x q f n for each k 1 we introduce the normal subgroup e n k consisting of all automorphisms of f n which act on j j k 1 trivially these normal subgroups define a central filtration of aut f n this is a fricke character analogue of the andreadakis johnson filtration a n k of aut f n the main purpose of the paper is to show that e n 1 coincides with inn f n a n 2 where inn f n is the inner automorphism group of the free group f n and that a n 2 k e n k for any k 1

fi modules and stability for representations of symmetric groups in this paper we introduce and develop the theory of fi modules we apply this theory to obtain new theorems about the cohomology of the configuration space of n distinct ordered points on an arbitrary connected oriented manifold the diagonal coinvariant algebra on r sets of n variables the cohomology and tautological ring of the moduli space of n pointed curves the space of polynomials on rank varieties of n n matrices the subalgebra of the cohomology of the genus n torelli group generated by h1 and more the symmetric group sn acts on each of these vector spaces in most cases almost nothing is known about the characters of these representations or even their dimensions we prove that in each fixed degree the character is given for n large enough by a polynomial in the cycle counting functions that is independent of n in particular the dimension is eventually a polynomial in n in this framework representation stability in the sense of church farb for a sequence of sn representations is converted to a finite generation property for a single fi module

representation theory and homological stability abstract we introduce the idea of representation stability and several variations for a sequence of representations v n of groups g n a central application of the new viewpoint we introduce here is the importation of representation theory into the study of homological stability this makes it possible to extend classical theorems of homological stability to a much broader variety of examples representation stability also provides a framework in which to find and to predict patterns from classical representation theory littlewood richardson and murnaghan rules stability of schur functors to cohomology of groups pure braid torelli and congruence groups to lie algebras and their homology to the equivariant cohomology of flag and schubert varieties to combinatorics the n 1 n 1 conjecture the majority of this paper is devoted to exposing this phenomenon through examples in doing this we obtain applications theorems and conjectures beyond the discovery of new phenomena the viewpoint of representation stability can be useful in solving problems outside the theory in addition to the applications given in this paper it is applied by church ellenberg farb in preparation 20 to counting problems in number theory and finite group theory representation stability is also used by church 2012 19 to give broad generalizations and new proofs of classical homological stability theorems for configuration spaces on oriented manifolds

p johnson homomorphisms and pro p groups abstract we propose an approach to study non abelian iwasawa theory using the idea of johnson homomorphisms in low dimensional topology we introduce arithmetic analogues of johnson homomorphisms maps called the p johnson homomorphisms maps associated to the zassenhaus filtration of a pro p galois group over a z p extension of a number field we give their cohomological interpretation in terms of massey products in galois cohomology