mazur tate elements of nonordinary modular forms we establish formulae for the iwasawa invariants of mazur tate elements of cuspidal eigenforms generalizing known results in weight 2 our first theorem deals with forms of medium weight and our second deals with forms of small slope we give examples illustrating the strange behavior which can occur in the high weight high slope case

constrained linear quadratic regulation the paper is a contribution to the theory of the infinite horizon linear quadratic regulator lqr problem subject to inequality constraints on the inputs and states extending an approach first proposed by sznaier and damborg 1987 a solution algorithm is presented which requires solving a finite number of finite dimensional positive definite quadratic programs the constrained lqr outlined does not feature the undesirable mismatch between open loop and closed loop nominal system trajectories which is present in the other popular forms of model predictive control mpc that can be implemented with a finite quadratic programming algorithm the constrained lqr is shown to be both optimal and stabilizing the solution algorithm is guaranteed to terminate in finite time with a computational cost that has a reasonable upper bound compared to the minimal cost for computing the optimal solution inherent to the approach is the removal of a tuning parameter the control horizon which is present in other mpc approaches and for which no reliable tuning guidelines are available two examples are presented that compare constrained lqr and two other popular forms of mpc the examples demonstrate that constrained lqr achieves significantly better performance than the other forms of mpc on some plants and the computational cost is not prohibitive for online implementation

an alternative use of the riccati recursion for efficient optimization in optimization routines used for on line model predictive control mpc linear systems of equations are solved in each iteration this is true both for active set as solvers as well as for interior point ip solvers and for linear mpc as well as for nonlinear mpc and hybrid mpc the main computational effort is spent while solving these linear systems of equations and hence it is of great interest to solve them efficiently in high performance solvers for mpc this is performed using riccati recursions or generic sparsity exploiting algorithms to be able to get this performance gain the problem has to be formulated in a sparse way which introduces more variables the alternative is to use a smaller formulation where the objective function hessian is dense in this work it is shown that it is possible to exploit the structure also when using the dense formulation more specifically it is shown that it is possible to efficiently compute a standard cholesky factorization for the dense formulation this results in a computational complexity that grows quadratically in the prediction horizon length instead of cubically as for the generic cholesky factorization

on universal elliptic curves over igusa curves the purpose of this note is to introduce the arithmetic study of the universal elliptic curve over igusa curves specifically its hasse weill function is computed in terms of modular forms and is shown to have interesting zeros explicit examples are presented for which the birch and swinnerton dyer conjecture is verified

branch and price column generation for solving huge integer programs we discuss formulations of integer programs with a huge number of variables and their solution by column generation methods i e implicit pricing of nonbasic variables to generate new columns or to prove lp optimality at a node of the branch and bound tree we present classes of models for which this approach decomposes the problem provides tighter lp relaxations and eliminates symmetry we then discuss computational issues and implementation of column generation branch and bound algorithms including special branching rules and efficient ways to solve the lp relaxation we also discuss the relationship with lagrangian duality

certification of modular galois representations we show how the output of the algorithm to compute modular galois representations described in our previous article can be certified we have used this process to compute certified tables of such galois representations obtained thanks to an improved version of this algorithm including representations modulo primes up to 31 and representations attached to a newform with non rational but of course algebraic coefficients which had never been done before these computations take place in the jacobian of modular curves of genus up to 26 the resulting data are available on the author s webpage

multi step length gradient iterative algorithm for equation error type models abstract this letter develops a multi step length gradient iterative algorithm for equation error type eet models the algorithm analysis is based upon the gradient search principle by applying the gram schmidt procedure the eet model can be turned into an orthogonal model in which each parameter in the parameter vector is independent of the other parameters then a multi step length gradient iterative algorithm is proposed for the orthogonal model and can estimate the parameters in one iteration finally based on the estimated parameters the parameter estimates of the eet model can be computed different from the traditional gradient iterative algorithm which has slower convergence rates and is sensitive to the initial values of the unknown variables the method in this letter has quicker convergence rates and is robust to the initial values of the unknown variables the simulation studies demonstrate the feasibility and effectiveness of the proposed algorithm

variation of iwasawa invariants in hida families let gq gl2 k be an absolutely irreducible modular galois representation over a finite field k of characteristic p assume further that is p ordinary and p distinguished in the sense that the restriction of to a decomposition group at p is reducible and non scalar the hida family h of is the set of all p ordinary p stabilized newforms f with mod p galois representation isomorphic to if is unramified at p then one must also fix an unramified line in and require that the ordinary line of f reduces to this fixed line these newforms are a dense set of points in a certain p adic analytic space of overconvergent eigenforms consisting of an intersecting system of branches i e irreducible components t a indexed by the minimal primes a of a certain hecke algebra to each modular form f h one may associate the iwasawa invariants an f an f alg f and alg f the analytic resp algebraic invariants are the number of zeroes of the p adic l function resp of the characteristic power series of the dual of the selmer group of f while the invariants are the exponents of the powers of p dividing the same objects in this paper we prove the following results on the behavior of these iwasawa invariants as f varies over h

on constrained infinite time linear quadratic optimal control abstract this work presents a solution to the infinite time linear quadratic optimal control itlqoc problem with state and control constraints it is shown that a single finite dimensional convex program of known size can yield this solution properties of the resulting value function with respect to initial conditions are also established and are shoen to be useful in determining the aforementioned problem size an example illustrating the method is finally presented

on serre s conjecture for mod l galois representations over totally real fields in 1987 serre conjectured that any mod two dimensional irre ducible odd representation of the absolute galois group of the rationals came from a modular form in a precise way we present a generalisation of this conjecture to 2 dimensional representations of the absolute galois group of a totally real eld where is unramied the hard work is in formulating an analogue of the weight part of serre s conjecture serre furthermore asked whether his conjecture could be rephrased in terms of a mod langlands philosophy using ideas of emerton and vign eras we formulate a mod local global principle for the group d where d is a quaternion algebra over a totally real eld split above and at 0 or 1 innite places and show how it implies the conjecture

a dual ascent procedure for large scale uncapacitated network design the fixed charge network design problem arises in a variety of problem contexts including transportation communication and production scheduling we develop a family of dual ascent algorithms for this problem this approach generalizes known ascent procedures for solving shortest path plant location steiner network and directed spanning tree problems our computational results for several classes of test problems with up to 500 integer and 1 98 million continuous variables and constraints show that the dual ascent procedure and an associated drop add heuristic generate solutions that in almost all cases are guaranteed to be within 1 to 4 of optimality moreover the procedure requires no more than 150 seconds on an ibm 3083 computer the test problems correspond to dense and sparse networks including some models that arise in freight transport

serre s modularity conjecture ii we provide proofs of theorems 4 1 and 5 1 of khare and wintenberger invent math doi 10 1007 s00222 009 0205 7 2009

weights of galois representations associated to hilbert modular forms let f be a totally real field p 3 a rational prime unramified in f and p a place of f over p let gal f f gl2 fp be a two dimensional mod p galois representation which is assumed to be modular of some weight and whose restriction to a decomposition subgroup at p is irreducible we specify a set of weights determined by the restriction of to inertia at p which contains all the modular weights for this proves part of a conjecture of diamond buzzard and jarvis which provides an analogue of serre s epsilon conjecture for hilbert modular forms mod p

on icosahedral artin representations ii we prove that some new infinite families of odd two dimensional icosahedral representations of the absolute galois group of inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i are modular and hence satsify the artin conjecture we also give an account of work of ramakrishna on lifting mod l galois representations to characteristic zero

exact holomorphic differentials on a quotient of the ree curve abstract we produce several families of exact holomorphic differentials on a quotient x of the ree curve in characteristic 3 defined by x y q y x q 0 x q x f q where q 0 3 s s 1 and q 3 q 0 2 we conjecture that they span the whole space of exact holomorphic differentials and prove this in the cases s 1 and s 2 by calculating the kernel of the cartier operator

applications of splitting algorithm to decomposition in convex programming and variational inequalities recently han and lou proposed a highly parallelizable decomposition algorithm for minimizing a strongly convex cost over the intersection of closed convex sets it is shown that their algorithm is in fact a special case of a splitting algorithm analyzed by gabay for finding a zero of the sum of two maximal monotone operators gabay s convergence analysis for the splitting algorithm is sharpened and new applications of this algorithm to variational inequalities convex programming and the solution of linear complementarily problems are proposed for convex programs with a certain separable structure a multiplier method that is closely related to the alternating direction method of multipliers of gabay mercier and of glowinski marrocco but which uses both ordinary and augmented lagrangians is obtained

conjecture de type de serre et formes compagnons pour gsp4 we present a serre type conjecture on the modularity of four dimensional symplectic mod p galois representations we assume that the galois representation is irreducible and odd in the symplectic sense the modularity condition is formulated using the etale and the algebraic de rham cohomology of siegel modular varieties of level prime to p we concentrate on the case when the galois representation is ordinary at p and we give a corresponding list of serre weights when the representation is moreover tamely ramified at p we conjecture that all weights of this list are modular otherwise we describe a subset of weights on the list that should be modular we propose a construction of de rham cohomology classes using the dual bgg complex which should realise some of these weights partiellement soutenu par la nsf grant dms 0902044 et accord dms 0635607 partiellement soutenu par le projet blanc anr 10 blan 0114

torsion points on modular curves let n 23 be a prime number in this paper we prove a conjecture of coleman kaskel and ribet about the valued points of the modular curve x 0 n which map to torsion points on j 0 n via the cuspidal embedding we give some generalizations to other modular curves and to noncuspidal embeddings of x 0 n into j 0 n

a capacity improvement lower bound for fixed charge network design problems network design problems concern flows over networks in which a fixed charge must be incurred before an arc becomes available for use the uncapacitated multicommodity network design problem is modeled with aggregate and disaggregate forcing constraints forcing constraints ensure logical relationships between the fixed charge related and the flow related decision variables a new lower bound for this problem referred to as the capacity improvement ci bound is presented and an efficient implementation scheme using shortest path and linearized knapsack programs is described a key feature of the ci lower bound is that it is based on the lp relaxation of the aggregate version of the problem a numerical example illustrates that the ci lower bound can converge to the optimal objective function value of the ip formulation

coefficients of half integral weight modular forms modulo lj suppose that l 5 is prime that j 0 is an integer and that f z is a half integral weight modular form with integral fourier coefficients we give some general conditions under which the coefficients of f are well distributed modulo lj as a consequence we settle many cases of a classical conjecture of newman by proving for each prime power lj with l 5 that the ordinary partition function p n takes each value modulo lj infinitely often

metric selection in fast dual forward backward splitting the performance of fast forward backward splitting or equivalently fast proximal gradient methods depends on the conditioning of the optimization problem data this conditioning is related to a metric that is defined by the space on which the optimization problem is stated selecting a space on which the optimization data is better conditioned improves the performance of the algorithm in this paper we propose several methods with different computational complexity to find a space on which the algorithm performs well we evaluate the proposed metric selection procedures by comparing the performance to the case when the euclidean space is used for the most ill conditioned problem we consider the computational complexity is improved by two to three orders of magnitude we also report comparable to superior performance compared to state of the art optimization software

an analogue of serre s conjecture for galois representations and hecke eigenclasses in the mod p cohomology of gl n ℤ

computation of the constrained infinite time linear quadratic regulator this paper presents an efficient algorithm for computing the solution to the constrained infinite time linear quadratic regulator clqr problem for discrete time systems the algorithm combines multi parametric quadratic programming with reachability analysis to obtain the optimal piecewise affine pwa feedback law the algorithm reduces the time necessary to compute the pwa solution for the clqr when compared to other approaches it also determines the minimal finite horizon email protected s such that the constrained finite horizon lqr problem equals the clqr problem for a compact set of states s the on line computational effort for the implementation of the clqr can be significantly reduced as well either by evaluating the pwa solution or by solving the finite dimensional quadratic program associated with the clqr for a horizon of email protected s

l functions of universal elliptic curves over igusa curves this paper is concerned with computing the l functions of the title in terms of modular forms because one can produce zeros of these l functions they seem to provide interesting test cases for various conjectures relating l functions to cycles in the first three sections we state the theorem review some consequences and give a brief sketch of the proof this proof is based on recent results of katz and mazur so in sections 4 through 6 we establish notation by reviewing the relevant parts of their work in sections 7 and 8 we prove an eichler shimura style result on a hecke operator the proof proper occupies sections 9 through 12 the paper 11 provides an introduction to the universal curves over igusa curves

solving mixed integer programming problems using automatic reformulation in this paper we describe computational experience in solving mixed 0 1 programming problems using strong valid inequalities as cutting planes in particular we report on the solution to optimality of 18 medium to large size problems including production planning problems with setup costs and capacity constraints multilevel distribution planning problems drainage and heating system design problems and electricity generator scheduling problems the solution approach uses the theory of strong valid inequalities that we developed in a series of earlier papers here we report specifically on the implementation of an experimental system mpsarx which consists of the sciconic mathematical programming system and an automatic reformulation executor arx that use this theory and on the results obtained with this system

solutions to arithmetic differential equations in algebraically closed fields abstract arithmetic differential equations or geometry exploits analogies between derivations and p derivations arising from lifts of frobenius to study problems in arithmetic geometry along the way two main classes such functions describable as series arose prominently namely characters of abelian schemes and isogeny covariant modular forms however the theory of these functions is not as straightforward in ramified settings overconvergence was introduced in 13 to account for these issues which essentially imposes growth conditions extensions of these series to a fixed level of ramification necessary as such extensions have non trivial fractional coefficients in this article we introduce a rescaling process which identifies a class of functions we call totally overconvergent which extend all the way to the algebraic closure of ring of integers of the maximally unramified extension of q p applications built on these functions allow one to remove boundedness assumptions on ramification the bulk of the article is devoted to establishing that most functions arising in practice namely those in the applications described in 5 7 8 are totally overconvergent which essentially extends results in 13 to unbounded ramification

solving the infinite horizon constrained lqr problem using accelerated dual proximal methods this work presents an algorithmic scheme for solving the infinite time constrained linear quadratic regulation problem we employ an accelerated version of a popular proximal gradient scheme commonly known as the forward backward splitting fbs and prove its convergence to the optimal solution in our infinite dimensional setting each iteration of the algorithm requires only finite memory is computationally cheap and makes no use of terminal invariant sets hence the algorithm can be applied to systems of very large dimensions the acceleration brings in optimal convergence rates o 1 k 2 for function values and o 1 k for primal iterates and renders the proposed method a practical alternative to model predictive control schemes for setpoint tracking in addition for the case when the true system is subject to disturbances or modelling errors we propose an efficient warm starting procedure which significantly reduces the number of iterations when the algorithm is applied in closed loop numerical examples demonstrate the approach

railroad blocking a network design application in this study we formulate the railroad blocking problems as a network design problem with maximum degree and flow constraints on the nodes and propose a heuristic lagrangian relaxation approach to solve the problem the newapproach decomposes the complicated mixed integer programming problem into two simple subproblems so that the storage requirement and computational effort are greatly reduced a set of inequalities are added to one subproblem to tighten the lower bounds and facilitate generating feasible solutions subgradient optimization is used to solve the lagrangian dual an advanced dual feasible solution is generated to speed up the convergence of the subgradient method the model is tested on blocking problems from a major railroad and the results show that the blocking plans generated have the potential to reduce the railroad s operating costs by millions of dollars annually

modularity lifting beyond the taylor wiles method we prove new modularity lifting theorems for p adic galois representations in situations where the methods of wiles and taylor wiles do not apply previous generalizations of these methods have been restricted to situations where the automorphic forms in question contribute to a single degree of cohomology in practice this imposes several restrictions one must be in a shimura variety setting and the automorphic forms must be of regular weight at infinity in this paper we essentially show how to remove these restrictions our most general result is a modularity lifting theorem which on the automorphic side applies to automorphic forms on the group mathrm gl n over a general number field it is contingent on a conjecture which in particular predicts the existence of galois representations associated to torsion classes in the cohomology of the associated locally symmetric space we show that if this conjecture holds then our main theorem implies the following if e is an elliptic curve over an arbitrary number field then e is potentially automorphic and satisfies the sato tate conjecture in addition we also prove some unconditional results for example in the setting of mathrm gl 2 over mathbf q we identify certain minimal global deformation rings with the hecke algebras acting on spaces of p adic katz modular forms of weight 1 such algebras may well contain p torsion moreover we also completely solve the problem for p odd of determining the multiplicity of an irreducible modular representation overline rho in the jacobian j 1 n where n is the minimal level such that overline rho arises in weight two

a lagrangian heuristic based branch and bound approach for the capacitated network design problem the capacitated network design problem is a multicommodity minimal cost network flow problem with fixed charges on the arcs and is well known to be np hard the problem type is very common in the context of transportation networks telecommunication networks etc in this paper we propose an efficient method for this problem based on a lagrangian heuristic within a branch and bound framework the lagrangian heuristic uses a lagrangian relaxation to obtain easily solved subproblems and solves the lagrangian dual by subgradient optimization it also includes techniques for finding primal feasible solutions the lagrangian heuristic is then embedded into a branch and bound scheme that yields further primal improvements special penalty tests and cutting criteria are developed the branch and bound scheme can either be an exact method that guarantees the optimal solution of the problem or be a quicker heuristic the method has been tested on networks of various structures and sizes computational comparisons between this method and a state of the art mixed integer code are presented the method is found to be capable of generating good feasible solutions to large scale problems within reasonable time and data storage limits

the geometry of hida families i λ adic de rham cohomology we construct the lambda adic de rham analogue of hida s ordinary lambda adic etale cohomology and of ohta s lambda adic hodge cohomology and by exploiting the geometry of integral models of modular curves over the cyclotomic extension of mathbf q p we give a purely geometric proof of the expected finiteness control and lambda adic duality theorems following ohta we then prove that our lambda adic module of differentials is canonically isomorphic to the space of ordinary lambda adic cuspforms in the sequel cais compos math to appear to this paper we construct the crystalline counterpart to hida s ordinary lambda adic etale cohomology and employ integral p adic hodge theory to prove lambda adic comparison isomorphisms between all of these cohomologies as applications of our work in this paper and cais compos math to appear we will be able to provide a cohomological construction of the family of varphi gamma modules attached to hida s ordinary lambda adic etale cohomology by dee j algebra 235 2 636 664 2001 as well as a new and purely geometric proof of hida s finiteness and control theorems we are also able to prove refinements of the main theorems in mazur and wiles compos math 59 2 231 264 1986 and ohta j reine angew math 463 49 98 1995

on modular representations of bar q q arising from modular forms where g is the galois group gai i q and f is a finite field of characteristic i 3 suppose that p is modular of level n i e that it arises from a weight 2 newform of level dividing n and trivial nebentypus character then p is an odd representation the matrix p c where c is a complex conjugation in g has eigenvalues 1 1 since 1 and 1 are distinct in f p is absolutely irreducible and has a model over every subfield of f containing the set trace p we assume that f has been chosen so that it is generated by this set assume that p is a prime which exactly divides n we write p i n and restrict p to a decomposition group of g for the prime p view the restriction as a representation p p of gal t p qp we say that p is finite at p 34 or 35 w if there is a finite flat f vector space scheme h over zp for which the action of gal t p qp on the f vector space h 1 p gives pp i f p 9 is finite at p if and only if pp is unramified it is clear that p is finite at p whenever p is already modular of level n p in w of 34 cf 35 serre conjectured the converse i e that if p is finite then p is modular of level n p soon thereafter mazur 1 20 proved this conjecture in the case

weakly holomorphic modular forms of half integral weight with nonvanishing constant terms modulo l let l be a prime and j 0 be an integer suppose that f z n a n q n is a weakly holomorphic modular form of weight 1 2 and that a 0 0 mod l we prove that if the coefficients of f z are not well distributed modulo l j then 0 or 1 mod l 1 2 this implies that under the additional restriction 0 0 mod l the following conjecture of balog darmon and ono is true if the coefficients of a modular form of weight 1 2 are almost but not all divisible by l then either 0 mod l 1 2 or 1 mod l 1 2 we also prove that if 0 and 1 mod l 1 2 then there does not exist an integer 0 l such that ln 0 mod l for every nonnegative integer n as an application we study congruences for the values of the overpartition function

ring theoretic properties of certain hecke algebras the purpose of this article is to provide a key ingredient of w2 by establishing that certain minimal hecke algebras considered there are complete intersections as is recorded in w2 a method going back to mazur m allows one to show that these algebras are gorenstein but for the complete intersection property a new approach is required the methods of this paper are related to those of chapter 3 of w2 the methods of section 3 of this paper are based on a previous approach of one of us a w we would like to thank henri darmon fred diamond and gerd faltings for carefully reading the first version of this article gerd faltings has also suggested a simplification of our argument as well as of the argument of chapter 3 of w2 and we would like to thank him for allowing us to reproduce these in the appendix to this paper r t would like to thank a w for his invitation to collaborate and for sharing his many insights into the questions considered r t would also like to thank princeton university universite de paris 7 and harvard university for their hospitality during this collaboration a w was supported by an nsf grant

on a conjecture of conrad diamond and taylor we prove a conjecture of conrad diamond and taylor on the size of certain deformation rings parametrizing potentially barsotti tate ga lois representations to achieve this we extend results of breuil and m ezard classifying galois lattices in semistable representations in terms of strongly divisible modules to the potentially crystalline case in hodge tate weights 0 1 we then use these strongly divisible modules to compute the desired deformation rings as a corollary we obtain new results on the modularity of potentially barsotti tate representations

models and algorithms for network reduction abstract we study models and algorithms for a network reduction nr problem that entails constructing a reduced network in place of an existing large network so that the shortest path lengths between specified node pairs in this network are equal to or only slightly longer than the corresponding shortest path lengths in the original network solving this problem can be very useful both to accelerate shortest path calculations in many practical contexts and to reduce the size of optimization models that contain embedded shortest path problems this work was motivated by a real problem of scheduling and routing resources to perform spatially dispersed jobs but also has other applications we consider two variants of the nr problem a min size nr problem that minimizes the number of arcs in the reduced network while ensuring that the shortest path lengths in this network are close to the original lengths and a min length nr problem that minimizes a weighted sum of shortest path lengths over all the specified node pairs while limiting the number of arcs in the reduced network we model both problems as integer programs with multi commodity flows and propose optimization based heuristic algorithms to solve them these methods include preprocessing a shortest path based procedure with local improvement and a dual ascent algorithm we report on the successful applications to reduce the network for practical infrastructure project planning and to condense a transportation network for distribution planning we also compare these solutions with those obtained using algorithms for minimum length trees

supersingular elliptic curves theta series and weight two modular forms this paper deals with two subjects and their interaction the first is the problem of spanning spaces of modular forms by theta series the second is the commutative algebraic properties of hecke modules arising in the arithmetic theory of modular forms let p be a prime and let b denote the quaternion algebra over q that is ramified at p and and at no other places if l is a left ideal in a maximal order of b then l is a rank four z module equipped in a natural way with a positive definite quadratic form 6 1 we shall say that l is a rank four quadratic space and remark that the isomorphism class of l as a quadratic space depends only on the left ideal class of l in its maximal order eichler 5 proved that the theta series of l is a weight two modular form on 0 p and that as l ranges over a collection of left ideal class representatives of all left ideals in all maximal orders of b these theta series span the vector space of weight two modular forms on 0 p over q in this paper we strengthen this result as follows if l is as above then the q expansion of its theta series l has constant term equal to one and all other coefficients equal to even integers suppose that f is a modular form whose qexpansion coefficients are even integers except perhaps for its constant term which we require merely to be an integer it follows from eichler s theorem that f may be written as a linear combination of l with l ranging over a collection of left ideals of maximal orders of b with rational coefficients we show that in fact these coefficients can be taken to be integers let t denote the z algebra of hecke operators acting on the space of weight two modular forms on 0 p the proof that we give of our result hinges on analyzing the structure of a certain t module x we can say what x is it is the free zmodule of divisors supported on the set of singular points of the reducible nodal curve x0 p in characteristic p the key properties of x which imply the above result on theta series are that the natural map t endt x is an isomorphism and that furthermore x is locally free of rank one in a zariski neighbourhood of the eisenstein ideal of t we remark that it is comparatively easy to prove the analogous statements after tensoring with q for they then follow from the fact that x is a faithful t module indeed combining this with the semi simplicity of the q algebra t z q one deduces that x z q is a free t z q module of rank one and in particular that the map t z q endt zq x z q is an isomorphism