randomized and distributed self configuration of wireless networks two layer markov random fields and near optimality this work studies the near optimality versus the complexity of distributed configuration management for wireless networks we first develop a global probabilistic graphical model for a network configuration which characterizes jointly the statistical spatial dependence of a physical and a logical configuration the global model is a gibbs distribution that results from the internal network properties on node positions wireless channel and interference and the external management constraints on physical connectivity and signal quality a local model is a two layer markov random field i e a random bond model that approximates the global model with the local spatial dependence of neighbors the complexity of the local model is defined through the communication range among nodes which corresponds to the number of neighbors in the two layer markov random field the local model is near optimal when the approximation error to the global model is within a given bound we analyze the tradeoff between approximation error and complexity we then derive sufficient conditions on the near optimality of the local model for a fast decaying wireless channel with power attenuation factor 4 a node only needs to communicate with o 1 neighbors for a local model to be near optimal for a slowly decaying channel with a power attenuation factor 2 4 a node may have to communicate with more than o n 4 4 neighbors to result in a bounded approximation error if the communication range is kept to be o 1 a bounded approximation error can also be achieved by reducing the density of active links to o n 4 4 for 4 the two layer markov random fields enable a class of randomized distributed algorithms such as the stochastic relaxation that allows a node to self configure based on information from neighbors we validate the model the analysis and the randomized distributed algorithms through simulation

spectral shift functions and dirichlet to neumann maps the spectral shift function of a pair of self adjoint operators is expressed via an abstract operator valued titchmarsh weyl m function this general result is applied to different self adjoint realizations of second order elliptic partial differential operators on smooth domains with compact boundaries and schrodinger operators with compactly supported potentials in these applications the spectral shift function is determined in an explicit form with the help of energy parameter dependent dirichlet to neumann maps

least squares quadratic b spline finite element method for the regularised long wave equation abstract an approximate solution consisting of a combination of the quadratic b spline functions is incorporated into the least squares method an application of this method is presented for computing the solution of the regularised long wave rlw equation quadratic b spline solution of the rlw equation leads to tridiagonal matrix system which is solved easily by using the thomas algorithm performance of this scheme is tested by obtaining a solitary wave solution of the equation and by studying the development of the undular bore numerical results of the proposed algorithm is shown to have higher accuracy in terms of l 2 error norm compared studying the migration of the solitary wave a fourier stability analysis of the method is investigated

collocation solution for rlw equation with septic spline a collocation solution using the septic splines as a shape function for the regularized long wave rlw equation is presented here a linear stability analysis shows the scheme to be unconditionally stable test problems which migration and interaction of solitary waves are used to validate our scheme by calculate l 2 norm and l norm and three invariants of motion are evaluates to determine the conservation properties of the algorithm the numerical scheme is compared with other published methods and shown to be accurate and efficient

facets and algorithms for capacitated lot sizing the dynamic economic lot sizing model which lies at the core of numerous production planning applications is one of the most highly studied models in all of operations research and yet capacitated multi item versions of this problem remain computationally elusive we study the polyhedral structure of an integer programming formulation of a single item capacitated version of this problem and use these results to develop solution methods for multi item applications in particular we introduce a set of valid inequalities for the problem and show that they define facets of the underlying integer programming polyhedron computational results on several single and multiple product examples show that these inequalities can be used quite effectively to develop an efficient cutting plane branch and bound procedure moreover our results show that in many instances adding certain of these inequalities a priori to the problem formulation and avoiding the generation of cutting planes can be equally effective

delay guarantees for throughput optimal wireless link scheduling we consider the question of obtaining tight delay guarantees for throughout optimal link scheduling in arbitrary topology wireless ad hoc networks two classes of scheduling policies are considered 1 a maximum queue length weighted independent set scheduling policy and 2 a randomized independent set scheduling policy where the set scheduling probabilities are selected optimally both policies stabilize all queues for any set of feasible packet arrival rates and are therefore throughput optimal for these policies we show that the average packet delay is bounded by a constant that depends on the chromatic number of the interference graph and the arrival slack in the system a metric representing the overall load on the network we prove that this upper bound is asymptotically tight in the sense that there exist classes of topologies where the expected delay attained by any scheduling policy is lower bounded by the same constant we extend our upper bounds to the case of multi hop sessions through simulations we study how our analysis compares with actual delays computed for i i d markovian and trace driven packet arrival processes

scheduling file transfers we consider a problem of scheduling file transfers in a network so as to minimize overall finishing time although the general problem is np complete we identify polynomial time solvable special cases and derive good performance bounds for several natural approximation algorithms assuming the existence of a central controller we also show how these bounds can be maintained in a distributed regime

queue length stability in trees under slowly convergent traffic using sequential maximal scheduling in this paper we consider queue length stability in wireless networks under a general class of arrival processes that only requires that the empirical average converges to the actual average polynomially fast we present a scheduling policy sequential maximal scheduling and use novel proof techniques to show that it attains 2 3 of the maximum stability region in tree graphs under primary interference constraints for all such arrival processes for degree bounded networks the computation time of the policy varies as the the logarithm of the network size our results are a significant improvement over previous results that attain only 1 2 of the maximum throughput region even for graphs that have a simple path topology in similar computation time under stronger i e markovian assumptions on the arrival process

on the evolution of a reflection coefficient under the korteweg de vries flow we are concerned with the korteweg de vries equation on the full line with real nondecaying initial profiles we find the time evolution of a relative reflection coefficient an inverse spectral formalism is also considered for certain mixed problems on the full line

on functional determinants of matrix differential operators with multiple zero modes we generalize the method of computing functional determinants with a single excluded zero eigenvalue developed by mckane and tarlie to differential operators with multiple zero eigenvalues we derive general formulas for such functional determinants of r times r matrix second order differential operators o with 0 n leqslant 2r linearly independent zero modes we separately discuss the cases of the homogeneous dirichlet boundary conditions when the number of zero modes cannot exceed r and the case of twisted boundary conditions including the periodic and anti periodic ones when the number of zero modes is bounded above by 2r in all cases the determinants with excluded zero eigenvalues can be expressed only in terms of the n zero modes and other r n or 2r n depending on the boundary conditions solutions of the homogeneous equation o h 0 in the spirit of gel fand yaglom approach in instanton calculations the contribution of the zero modes is taken into account by introducing the so called collective coordinates we show that there is a remarkable cancellation of a factor involving scalar products of zero modes between the jacobian of the transformation to the collective coordinates and the functional fluctuation determinant with excluded zero eigenvalues this cancellation drastically simplifies instanton calculations when one uses our formulas

sensitivity theorems in integer linear programming we consider integer linear programming problems with a fixed coefficient matrix and varying objective function and right hand side vector among our results we show that for any optimal solution to a linear program max wx ax b the distance to the nearest optimal solution to the corresponding integer program is at most the dimension of the problem multiplied by the largest subdeterminant of the integral matrixa using this we strengthen several integer programming proximity results of blair and jeroslow graver and wolsey we also show that the chvatal rank of a polyhedron x ax b can be bounded above by a function of the matrixa independent of the vectorb a result which as blair observed is equivalent to blair and jeroslow s theorem that each integer programming value function is a gomory function

solitary wave solutions of the grlw equation using septic b spline collocation method in this work solitary wave solutions of the generalized regularized long wave grlw equation are obtained by using septic b spline collocation method with two different linearization techniques to demonstrate the accuracy and efficiency of the numerical scheme three test problems are studied by calculating the error norms l2 and l and the invariants i1 i2 and i3 a linear stability analysis based on the von neumann method of the numerical scheme is also investigated consequently our findings indicate that our numerical scheme is preferable to some recent numerical schemes

the very unusual properties of the resolvent heat kernel and zeta function for the operator d2 dr2 1 4r2 in this paper we analyze the resolvent the heat kernel and the spectral zeta function of the operator d2 dr2 1 4r2 over the finite interval the structural properties of these spectral functions depend strongly on the chosen self adjoint realization of the operator a choice being made necessary because of the singular potential present only for the friedrichs realization standard properties are reproduced for all other realizations highly nonstandard properties are observed in particular for k n we find terms like logt k in the small t asymptotic expansion of the heat kernel furthermore the zeta function has s 0 as a logarithmic branch point

trace formulas for additive and non additive perturbations abstract trace formulas for pairs of self adjoint maximal dissipative and accumulative as well as other types of resolvent comparable operators are obtained in particular the existence of a complex valued spectral shift function for a pair h h of maximal accumulative operators has been proved we investigate also the existence of a real valued spectral shift function moreover we treat in detail the case of additive trace class perturbations assuming that h and h h v are maximal accumulative and v is trace class we prove the existence of a summable complex valued spectral shift function we also obtain trace formulas for pairs h h assuming only that h and h are resolvent comparable in this case the determinant of the characteristic function of h is involved in trace formulas the results rely on the technique of boundary triplets for densely and non densely defined closed symmetric operators the approach allows to express the spectral shift function of a pair of extensions in terms of the abstract weyl function and the boundary operator we improve and generalize certain classical results of m g kre n for pairs of self adjoint and dissipative operators results of a v rybkin for such pairs as well as of v m adamjan b s pavlov and m g kre n for pairs h h with a maximal dissipative operator h

determinants finite difference operators and boundary value problems we relate the determinants of differential and difference operators to the boundary values of solutions of the operators previous proofs of related results have involved considering one parameter families of such operators showing the desired quantities are equal up to a constant and then calculating the constant we take a more direct approach for a fixed operator we prove immediately that the two sides of our formulas are equal by using the following simple observation proposition 1 3 let u su n c write u in block form u left begin array 20 c u 11 u 12 u 21 u 22 end array right where u11and u22are square matrices then det u 11 overline det u 22

on linear characterizations of combinatorial optimization problems we show that there can be no computationally tractable description by linear inequalities of the polyhedron associated with any np complete combinatorial optimization problem unless np co np a very unlikely event we also apply the ellipsoid method for linear programming to show that a combinatorial optimization problem is solvable in polynomial time if and only if it admits a small generator of violated inequalities

scheduling agreement graph vs resource constraints abstract we investigate two scheduling problems the first is scheduling with agreements swa that consists in scheduling a set of jobs non preemptively on identical machines in a minimum time subject to constraints that only some specific jobs can be scheduled concurrently these constraints are represented by an agreement graph we extend the np hardness of swa with three distinct values of processing times to only two values and this definitely closes the complexity status of swa on two machines with two fixed processing times the second problem is the so called resource constrained scheduling we prove that swa is polynomially equivalent to a special case of the resource constrained scheduling and deduce new complexity results of the latter

solitary waves of the regularized long wave equation abstract a finite element solution of the regularised long wave equation based on galerkin s method using cubic splines as element shape functions is set up a linear stability analysis shows the scheme to be unconditionally stable test problems including the migration and interaction of solitary waves are used to validate the method which is found to be accurate and efficient the three invariants of the motion are evaluated to determine the conservation properties of the algorithm the temporal evolution of a maxwellian initial pulse is then studied

odd minimum cut sets and b matchings we show that the determination of a minimum cut set of odd cardinality in a graph with even and odd vertices can be dealt with by a minor modification of the polynomially bounded algorithm of gomory and hu for multi terminal networks we connect this problem to the problem of identifying a matching or blossom constraint that chops off a point which is not contained in the convex hull of matchings or proving that no such inequality exists both the b matching problems without and with upper bounds are considered we discuss how the results of this paper can be used in conjunction with commercial lp packages lo solve b matching problems

on the determinant of one dimensional elliptic boundary value problems we discuss the regularized determinant of elliptic boundary value problems on a line segment our framework is applicable for separated and non separated boundary conditions

higher order spectral shift abstract we construct higher order spectral shift functions extending the perturbation theory results of m g krein m g krein on a trace formula in perturbation theory mat sb 33 1953 597 626 in russian and l s koplienko l s koplienko trace formula for perturbations of nonnuclear type sibirsk mat zh 25 1984 62 71 in russian translation in trace formula for nontrace class perturbations siberian math j 25 1984 735 743 on representations for the remainders of the first and second order taylor type approximations of operator functions the higher order spectral shift functions represent the remainders of higher order taylor type approximations they can be expressed recursively via the lower order in particular krein s and koplienko s ones we also obtain higher order spectral averaging formulas generalizing the birman solomyak spectral averaging formula the results are obtained in the semi finite von neumann algebra setting with the perturbation taken in the hilbert schmidt class of the algebra

application of cubic b splines for numerical solution of the rlw equation cubic b spline functions have been used to develop a collocation method to solve the regularized long wave rlw equation which is used to model solitary waves undular bore development and wave generation performance of the scheme is tested by computing a solitary wave solution of the rlw equation and made comparison with analytical results undular bore development and wave generation is shown to be in good agreement with available results

a collocation method with cubic b splines for solving the mrlw equation the modified regularized long wave mrlw equation is solved numerically by collocation method using cubic b splines finite element a linear stability analysis of the scheme is shown to be marginally stable three invariants of motion are evaluated to determine the conservation properties of the algorithm also the numerical scheme leads to accurate and efficient results moreover interaction of two and three solitary waves are studied through computer simulation and the development of the maxwellian initial condition into solitary waves is also shown

greedy maximal matching performance limits for arbitrary network graphs under the node exclusive interference model greedy maximal matching gmm is an important scheduling scheme for multi hop wireless networks it is computationally simple and has often been numerically shown to achieve throughput that is close to optimal however to date the performance limits of gmm have not been well understood in particular although a lower bound on its performance has been well known this bound has been empirically found to be quite loose in this paper we focus on the well established node exclusive interference model and provide new analytical results that characterize the performance of gmm through a topological notion called the local pooling factor we show that for a given network graph with single hop traffic the efficiency ratio of gmm i e the worst case ratio of the throughput of gmm to that of the optimal is equal to its local pooling factor further we estimate the local pooling factor for arbitrary network graphs under the node exclusive interference model and show that the efficiency ratio of gmm is no smaller than d 2d 1 in a network topology of maximum node degree d using these results we identify specific network topologies for which the efficiency ratio of gmm is strictly less than 1 we also extend the results to the more general scenario with multi hop traffic and show that gmm can achieve similar efficiency ratios when a flow regulator is used at each hop

a krein like formula for singular perturbations of self adjoint operators and applications abstract given a self adjoint operator a d a h h and a continuous linear operator d a x with range h 0 x a banach space we explicitly construct a family a of self adjoint operators such that any a coincides with the original a on the kernel of such a family is obtained by giving a krein like formula where the role of the deficiency spaces is played by the dual pair x x the parameter belongs to the space of symmetric operators from x to x when x c one recovers the h 2 construction of kiselev and simon and so to some extent our results can be regarded as an extension of it to the infinite rank case considering the situation in which h l 2 r n and is the trace restriction operator along some null subset we give various applications to singular perturbations of non necessarily elliptic pseudo differential operators thus unifying and extending previously known results

solving the generalized regularized long wave equation on the basis of a reproducing kernel space on the basis of a reproducing kernel space an iterative algorithm for solving the generalized regularized long wave equation is presented the analytical solution in the reproducing kernel space is shown in a series form and the approximate solution u n is constructed by truncating the series to n terms the convergence of u n to the analytical solution is also proved results obtained by the proposed method imply that it can be considered as a simple and accurate method for solving such evolution equations

arbitrary throughput versus complexity tradeoffs in wireless networks using graph partitioning several policies have recently been proposed for attaining the maximum throughput region or a guaranteed fraction thereof through dynamic link scheduling among these policies the ones that attain the maximum throughput region require a computation time which is linear in the network size and the ones that require constant or logarithmic computation time attain only certain fractions of the maximum throughput region in contrast in this paper we propose policies that can attain any desirable fraction of the maximum throughput region using a computation time that is largely independent of the network size first using a combination of graph partitioning techniques and lyapunov arguments we propose a simple policy for tree topologies under the primary interference model that requires each link to exchange only 1 bit information with its adjacent links and approximates the maximum throughput region using a computation time that depends only on the maximum degree of nodes and the approximation factor then we develop a framework for attaining arbitrary close approximations for the maximum throughput region in arbitrary networks and use this framework to obtain any desired tradeoff between throughput guarantees and computation times for a large class of networks and interference models specifically given any epsiv 0 the maximum throughput region can be approximated in these networks within a factor of 1 epsiv using a computation time that depends only on the maximum node degree and epsiv

regular singular sturm liouville operators and their zeta determinants abstract we consider sturm liouville operators on the line segment 0 1 with general regular singular potentials and separated boundary conditions we establish existence and a formula for the associated zeta determinant in terms of the wronski determinant of a fundamental system of solutions adapted to the boundary conditions this generalizes the earlier work of the first author treating general regular singular potentials but only the dirichlet boundary conditions at the singular end and the recent results by kirsten loya park for general separated boundary conditions but only special regular singular potentials

extension theory and kreĭn type resolvent formulas for nonsmooth boundary value problems for a strongly elliptic second order operator a on a bounded domainr n it has been known for many years how to interpret the general closed l2 realizations of a as representing boundary conditions generally nonlocal when the domain and coe cients are smooth the purpose of the present paper is to extend this representation to nonsmooth domains and coecients including the case of hol der c 3 2 smoothness in such a way that pseudodierential methods are still avail able for resolvent construc tions and ellipticity considerations we show how it can be done for domains with

spectral shift function of higher order this paper resolves affirmatively koplienko s sib mat zh 25 62 71 1984 conjecture on existence of higher order spectral shift measures moreover the paper establishes absolute continuity of these measures and thus existence of the higher order spectral shift functions a spectral shift function of order n is the function n n h v such that operatorname tr biggl f h v sum k 0 n 1 frac 1 k frac d k dt k bigl f h tv bigr bigg t 0 biggr int mathbb r f n t eta n t dt for every sufficiently smooth function f where h is a self adjoint operator defined in a separable hilbert space and v is a self adjoint operator in the n th schatten von neumann ideal sn existence and summability of 1 and 2 were established by krein mat sb 33 597 626 1953 and koplienko sib mat zh 25 62 71 1984 respectively whereas for n 2 the problem was unresolved we show that n h v exists integrable and vert eta n vert l 1 mathbb r leq c n vert v vert s n n for some constant cn depending only on n our results for n rely on estimates for multiple operator integrals obtained in this paper our method also applies to the general semi finite von neumann algebra setting of the perturbation theory

a computational method for the regularized long wave rlw equation a numerical solution of the regularized long wave rlw equation based on collocation method using cubic b spline finite elements is used to simulate the migration and interaction of solitary waves interaction of solitary waves with different amplitudes are shown the three invariants of the motion are evaluated to determine the conservation properties of the system the temporal evaluation of a maxwellian initial pulse is then studied and then we prove that the number of solitons which are generated from maxwellian initial condition are determined

a finite difference scheme for generalized regularized long wave equation in this paper a finite difference method for a cauchy problem of generalized regularized long wave grlw equation was considered an energy conservative finite difference scheme was proposed convergence and stability of the difference solution were proved numerical results demonstrate that the method is efficient and reliable

koplienko spectral shift function on the unit circle the note shows that for every pair of contractions a trace formula of koplienko holds with a summable spectral shift function see theorem 1 below this answers a question by f gesztesy a pushnitski b simon see zh mat fiz anal geom 4 1 63 107 202 2008 open question 11 2

a petrov galerkin method for solving the generalized regularized long wave grlw equation the generalized regularized long wave grlw equation is solved numerically by the petrov galerkin method which uses a linear hat function as the trial function and a quintic b spline function as the test function product approximation has been used in this method a linear stability analysis of the scheme shows it to be conditionally stable test problems including the single soliton and the interaction of solitons are used to validate the suggested method which is found to be accurate and efficient finally the maxwellian initial condition pulse is studied

numerical analysis of generalized regularized long wave equation using the element free kp ritz method abstract a numerical analysis of the generalized regularized long wave grlw equation by application of the element free kp ritz method is performed to approximate the displacement field an element free kernel particle estimation is employed and a system of nonlinear discrete equations is achieved by using the ritz minimization procedure to the energy expressions validation of the present numerical solutions with the exact results has been conducted by numerical examples and evidenced a good agreement

link scheduling in polynomial time two polynomial time algorithms are given for scheduling conversations in a spread spectrum radio network the constraint on conversations is that each station can converse with only one other station at a time the first algorithm is strongly polynomial and finds a schedule of minimum length that allows each pair of neighboring stations to converse directly for a prescribed length of time the second algorithm is designed for the situation in which messages must be relayed multiple hops the algorithm produces in polynomial time a routing vector and compatible link schedule that jointly meet a prespecified end to end demand so that the schedule has the smallest possible length

b spline quasi interpolation based numerical methods for some sobolev type equations in this article we intend to use quadratic and cubic b spline quasi interpolants to develop higher order numerical methods for some sobolev type equations in one space dimension our aim is also to compare the performance of the proposed methods in terms of the accuracy and the rate of convergence we also discuss another approach to the cubic b spline quasi interpolation based method where we achieve fourth order of accuracy in space we theoretically establish the order of accuracy for the three proposed methods and also establish the l 2 stability in the linear case using von neumann analysis as a particular case of the sobolev type equations we take the equal width and the benjamin bona mahony burgers equations and perform several numerical experiments to support our theoretical results

generalized resolvents and the boundary value problems for hermitian operators with gaps a hermitian operator a with gaps j j 1 j m is studied the self adjoint extensions which put exactly kj eigenvalues into each gap j j in particular for kj 0 1 j m the extensions preserving the gaps are described in terms of boundary conditions the generalized resolvents of the extensions with the indicated properties are described also a solvability criterion and description of all the solutions of the hamburger moment problem with supports in r j 1m j j are obtained in terms of the nevanlinna matrix

krein like extensions and the lower boundedness problem for elliptic operators abstract for selfadjoint extensions a of a symmetric densely defined positive operator a min the lower boundedness problem is the question of whether a is lower bounded if and only if an associated operator t in abstract boundary spaces is lower bounded it holds when the friedrichs extension a has compact inverse grubb 1974 also gorbachuk and mikhailets 1976 this applies to elliptic operators a on bounded domains for exterior domains a 1 is not compact and whereas the lower bounds satisfy m t m a the implication of lower boundedness from t to a has only been known when m t m a we now show it for general t the operator a a corresponding to t a i generalizing the krein von neumann extension a 0 appears here its possible lower boundedness for all real a is decisive we study this krein like extension showing for bounded domains that the discrete eigenvalues satisfy n t a a c a t n 2 m o t n 1 e 2 m for t

absolute continuity of spectral shift abstract in this paper we develop the method of double operator integrals to prove trace formulae for functions of contractions dissipative operators unitary operators and self adjoint operators to establish the absolute continuity of spectral shift we use the sz nagy theorem on the absolute continuity of the spectral measure of the minimal unitary dilation of a completely nonunitary contraction we also give a construction of an intermediate contraction for a pair of contractions with trace class difference

numerical solution of the nonlinear klein gordon equation a numerical method is developed to solve the nonlinear one dimensional klein gordon equation by using the cubic b spline collocation method on the uniform mesh points we solve the problem for both dirichlet and neumann boundary conditions the convergence and stability of the method are proved the method is applied on some test examples and the numerical results have been compared with the exact solutions the l 2 l and root mean square errors rms in the solutions show the efficiency of the method computationally

the complexity of path coloring and call scheduling abstract modern high performance communication networks pose a number of challenging problems concerning the efficient allocation of resources to connection requests in all optical networks with wavelength division multiplexing connection requests must be assigned paths and colors wavelengths such that intersecting paths receive different colors and the goal is to minimize the number of colors used this path coloring problem is proved np hard for undirected and bidirected ring networks path coloring in undirected tree networks is shown to be equivalent to edge coloring of multigraphs which implies a polynomial time optimal algorithm for trees of constant degree as well as np hardness and an approximation algorithm with absolute approximation ratio 4 3 and asymptotic approximation ratio 1 1 for trees of arbitrary degree for bidirected trees path coloring is shown to be np hard even in the binary case a polynomial time optimal algorithm is given for path coloring in undirected or bidirected trees with n nodes under the assumption that the number of paths touching every single node of the tree is o log n 1 e call scheduling is the problem of assigning paths and starting times to calls in a network with bandwidth reservation such that the maximum completion time is minimized in the case of unit bandwidth requirements unit edge capacities and unit call durations call scheduling is equivalent to path coloring if either the bandwidth requirements or the call durations can be arbitrary call scheduling is shown np hard for virtually every network topology

a sequential approach for optimal broadcast scheduling in packet radio networks an important problem that arises in the design of packet radio networks is that of scheduling access to the high speed communications channel in such a way as to avoid interference while keeping the frame length to a minimum the broadcast scheduling problem is known to be np hard and to date this problem has been formulated as a nonlinear discrete optimization problem for a given frame length and solved via heuristic approaches by parametrically varying the length of the frame this paper presents a linear integer programming formulation for the composite problem of maximizing channel utilization while minimizing the length of the frame it then introduces a solution approach based on solving two relatively easier though still np complete integer programs in succession computational experiments are conducted on a set of benchmark cases and additional randomly generated problem instances results show that this sequential integer programming approach is very effective solving all the problems optimally within a few seconds these results imply that optimal solutions can be identified in very little time for problems of realistic size and that heuristic approaches will be needed only when problems get much larger than those considered in the literature to date

the np completeness of edge coloring we show that it is np complete to determine the chromatic index of an arbitrary graph the problem remains np complete even for cubic graphs

on achieving local view capacity via maximal independent graph scheduling if we know more we can achieve more this adage also applies to communication networks where more information about the network state translates into higher sum rates in this paper we formalize this increase of sum rate with increased knowledge of the network state the knowledge of network state is measured in terms of the number of hops h of information available to each transmitter and is labeled as h local view to understand how much capacity is lost due to limited information we propose to use the metric of normalized sum capacity which is the h local view sum capacity divided by global view sum capacity for the cases of one and two local view we characterize the normalized sum capacity for many classes of deterministic and gaussian interference networks in many cases a scheduling scheme called maximal independent graph scheduling is shown to achieve normalized sum capacity we also show that its generalization for 1 local view labeled coded set scheduling achieves normalized sum capacity in some cases where its uncoded counterpart fails to do so

the determinant of one dimensional polyharmonic operators of arbitrary order abstract we obtain an explicit expression for the regularised spectral determinant of the polyharmonic operator p n 1 n x 2 n on 0 t with dirichlet boundary conditions and n a positive integer and show that it satisfies the asymptotics log det p n n 2 log n 7 3 2 2 3 2 log t 4 n 2 o n for large n this is a consequence of sharp upper and lower bounds for log det p n valid for all n and which coincide in the terms up to order n these results form the basis to analyse more general operators with nonconstant coefficients and show that the corresponding determinants have a similar asymptotic behaviour

modeling and solving the two facility capacitated network loading problem this paper studies a topical and economically significant capacitated network design problem that arises in the telecommunications industry in this problem given point to point communication demand in a network must be met by installing loading capacitated facilities on the arcs loading a facility incurs an arc specific and facility dependent cost this paper develops modeling and solution approaches for loading facilities to satisfy the given demand at minimum cost we consider two approaches for solving the underlying mixed integer program a lagrangian relaxation strategy and a cutting plane approach that uses three classes of valid inequalities that we identify for the problem we show that a linear programming formulation that includes these inequalities always approximates the value of the mixed integer program at least as well as the lagrangian relaxation bound our computational results on a set of prototypical telecommunication data show that including these inequalities considerably improves the gap between the integer programming formulation and its linear programming relaxation from an average of 25 to an average of 8 these results show that strong cutting planes can be an effective modeling and algorithmic tool for solving problems of the size that arise in the telecommunications industry

an extension of the koplienko neidhardt trace formulae abstract koplienko sibirsk mat zh 25 5 1984 62 found a trace formula for perturbations of self adjoint operators by operators of hilbert schmidt class s 2 a similar formula in the case of unitary operators was obtained by neidhardt math nachr 138 1988 7 in this paper we improve their results and obtain sharp conditions under which the koplienko neidhardt trace formulae hold

on the essential spectrum of a class of singular matrix differential operators ii weyl s limit circles for the hain lust operator whenever quasi regularity conditions are not satisfied on the essential spectrum of a class of singular matrix differential operators ii weyl s limit circles for hain lust operator whenever quasiregularity conditions are not satisfied

spectral functions for regular sturm liouville problems in this paper we provide a detailed analysis of the analytic continuation of the spectral zeta function associated with one dimensional regular sturm liouville problems endowed with self adjoint separated and coupled boundary conditions the spectral zeta function is represented in terms of a complex integral and the analytic continuation in the entire complex plane is achieved by using the well known liouville green or wkb asymptotic expansion of the eigenfunctions associated with the problem the analytically continued expression of the spectral zeta function is then used to compute the functional determinant of the sturm liouville operator and the coefficients of the asymptotic expansion of the associated heat kernel

how to compute the volume in high dimension in some areas of theoretical computer science we feel that randomized algorithms are better and in some others we can prove that they are more efficient than the deterministic ones

functional determinants and geometry in this paper we study the zeta function determinant in the context of elliptic boundary value problems our main technique is to relate the determinant of an operator or a ratio of determinants to the boundary values of the solutions of the operator this has the advantage of restricting attention to the solutions of the operator which do not depend on the boundary conditions and can often be written down explicitly rather than the eigenvalues which are usually difficult to work with in addition the problem is reduced to a calculation over the boundary of the manifold which is a closed manifold of dimension one less than the original manifold this has special significance in the case that the manifold is a finite interval in this case the boundary is a pair of points and the determinant of an ordinary differential operator is expressed in terms of the determinant of a finite matrix

reducing matching to polynomial size linear programming the question of whether the maximum weight matching problem can be reduced to a linear program of polynomial size is studied a partial answer to it is given i e it is shown that the chinese postman problem and optimum matching reduces to a sequence of o m 2 log n minimum mean cycle problems it is shown that this last problem can be formulated as a linear program of polynomial size this gives a polynomial algorithm for matching based on any polynomial method for linear programming a combinatorial algorithm for finding minimum mean cycles in undirected graphs is also given

relative zeta functions relative determinants and scattering theory we use the method of zeta function regularization to regularize the ratio det a det a0 of the determinants of two elliptic self adjoint operators a a0 satisfying certain natural assumptions this is of interest especially if the regularized determinants of the individual operators don t exist as for example in the case of elliptic operators on a noncompact manifold

effective computation of traces determinants and ζ functions for sturm liouville operators abstract the principal aim in this paper is to develop an effective and unified approach to the computation of traces of resolvents and resolvent differences fredholm determinants functions and function regularized determinants associated with linear operators in a hilbert space in particular we detail the connection between fredholm and function regularized determinants concrete applications of our formalism to general i e three coefficient regular sturm liouville operators on bounded intervals with various separated and coupled boundary conditions and schrodinger operators on a half line are provided and further illustrated with an array of examples

functional determinants for general sturm liouville problems simple and analytically tractable expressions for functional determinants are known to exist for many cases of interest we extend the range of situations for which these hold to cover systems of self adjoint operators of the sturm liouville type with arbitrary linear boundary conditions the results hold whether or not the operators have negative eigenvalues the physically important case of functional determinants of operators with a zero mode but where that mode has been extracted is studied in detail for the same range of situations as when no zero mode exists the method of proof uses the properties of generalized zeta functions the general form of the final results is the same for the entire range of problems considered

uniqueness theorems in inverse spectral theory for one dimensional schrodinger operators new unique characterization results for the potential v x in connection with schrodinger operators on r and on the half line 0 are proven in terms of appropriate krein spectral shift functions particular results obtained include a generalization of a well known uniqueness theorem of borg and marchenko for schrodinger operators on the half line with purely discrete spectra to arbitrary spectral types and a new uniqueness result for schrodinger operators with confining potentials on the entire real line

asymptotics of the number of zeros and of the eigenvalues of general weighted sturm liouville problems soit n le nombre de zeros d une solution de l equation de sturm liouville ponderee generale p x y r x q x y 0 sur 0 b ou 0 b p q r 0 b r et 1 p q r l 0 b on donne une demonstration directe de l estimation asymptotique de n

variations on a theme of jost and pais abstract we explore the extent to which a variant of a celebrated formula due to jost and pais which reduces the fredholm perturbation determinant associated with the schrodinger operator on a half line to a simple wronski determinant of appropriate distributional solutions of the underlying schrodinger equation generalizes to higher dimensions in this multi dimensional extension the half line is replaced by an open set r n n n n 2 where has a compact nonempty boundary satisfying certain regularity conditions our variant involves ratios of perturbation determinants corresponding to dirichlet and neumann boundary conditions on and invokes the corresponding dirichlet to neumann map as a result we succeed in reducing a certain ratio of modified fredholm perturbation determinants associated with operators in l 2 d n x n n to modified fredholm determinants associated with operators in l 2 d n 1 n 2 applications involving the birman schwinger principle and eigenvalue counting functions are discussed