consistency of the disaggregation process in hierarchical planning this paper deals with the planning process of a manufacturing system in which the aggregation of products sharing similar characteristics leads to a hierarchical structure it gives special attention to the consistency of decisions in a two level structure and presents necessary and sufficient conditions for consistency of a disaggregation procedure using a subset of these conditions improves upon the disaggregation procedure proposed by bitran and hax bitran g r a c hax 1981 disaggregation and resource allocation using convex knapsack problems with bounded variables mgmt sci 27 431 441

higher genus surface operad detects infinite loop spaces abstract the operad studied in conformal field theory and introduced ten years ago by g segal s is built out of moduli spaces of riemann surfaces we show here that this operad which at first sight is a double loop space operad is indeed an infinite loop space operad this leads to a new proof of the fact that the classifying space of the stable mapping class group mathbb z times b gamma infty is an infinite loop space after plus construction t2 this new approach has various advantages in particular the infinite loop space structure is more explicid

separable convex optimization problems with linear ascending constraints separable convex optimization problems with linear ascending inequality and equality constraints are addressed in this paper an algorithm that explicitly characterizes the optimum point in a finite number of steps is described the optimum value is shown to be monotone with respect to a partial order on the constraint parameters moreover the optimum value is convex with respect to these parameters this work generalizes the existing algorithms of morton von randow and ringwald math programming 32 1985 pp 238 241 and viswanath and anantharam ieee trans inform theory 48 2002 pp 1295 1318 to a wider class of separable convex objective functions computational experiments that compare the proposed algorithm with a standard convex optimization tool are also provided

apparatus and method for extracting pitch information from speech signal an apparatus and method for extracting pitch information from a speech signal the apparatus includes a pilot pitch detector for extracting predicted pitch information from a frame of an input speech signal a pitch candidate value selector for selecting one or more pitch candidate values from the predicted pitch information according to a predetermined condition a harmonic noise region decomposer for decomposing a harmonic noise region using each of the selected pitch candidate values a harmonic noise energy ratio calculator for calculating an energy ratio of each of the decomposed harmonic regions to each of the decomposed noise regions and a pitch information selector for selecting a pitch candidate value of a harmonic noise region in which the maximum value among the calculated harmonic noise energy ratio exists as a pitch value of the input frame of the speech signal

algorithms for separable nonlinear resource allocation problems we consider a simple resource allocation problem with a single resource constraint the objective function is composed of separable convex performance functions one for each activity likewise the constraint has separable convex resource usage functions one for each activity the objective is to minimize the sum of the performance functions subject to satisfying the resource constraint and nonnegativity constraints this problem extends the well studied problem in which the resource constraint is linear we present several algorithms to solve the problem these algorithms extend approaches developed for the linearly constrained problem they can readily solve large problems and find the optimal solution in a number of iterations that does not exceed the number of variables we provide several examples for illustration purposes present computational results and highlight the similarities and differences among the algorithms

a unified method for a class of convex separable nonlinear knapsack problems abstract in this paper a unified algorithm is proposed for solving a class of convex separable nonlinear knapsack problems which are characterized by positive marginal cost pmc and increasing marginal loss cost ratio imlcr by taking advantage of these two characteristics the proposed algorithm is applicable to the problem with equality or inequality constraints in contrast to the methods based on karush kuhn tucker kkt conditions our approach has linear computation complexity numerical results are reported to demonstrate the efficacy of the proposed algorithm for different problems

probabilistic solutions for a class of deterministic optimal allocation problems abstract we revisit the general problem of minimizing a separable convex function with both a budget constraint and a set of box constraints this optimization problem arises naturally in many resource allocation problems in engineering economics finance and insurance existing literature tackles this problem by using the traditional kuhn tucker theory which leads to either iterative schemes or yields explicit solutions only under some special classes of convex functions owe to the presence of box constraints this paper presents a novel approach of solving this constrained minimization problem by using the theory of comonotonicity the key step is to apply an integral representation result to express each convex function as the stop loss transform of some suitable random variable by using this approach we can derive and characterize not only the explicit solution but also obtain its geometric meaning and some other qualitative properties

on equitable resource allocation problems a lexicographic minimax approach in this expository paper we review a variety of resource allocation problems in which it is desirable to allocate limited resources equitably among competing activities applications for such problems are found in diverse areas including distribution planning production planning and scheduling and emergency services location each activity is associated with a performance function representing for example the weighted shortfall of the selected activity level from a specified target a resource allocation solution is called equitable if no performance function value can be improved without either violating a constraint or degrading an already equal or worse off i e larger performance function value that is associated with a different activity a lexicographic minimax solution determines this equitable solution that is it determines the lexicographically smallest vector whose elements the performance function values are sorted in nonincreasing order the problems reviewed include large scale allocation problems with multiple knapsack resource constraints multiperiod allocation problems for storable resources and problems with substitutable resources the solution of large scale problems necessitates the design of efficient algorithms that take advantage of special mathematical structures indeed efficient algorithms for many models will be described we expect that this paper will help practitioners to formulate and solve diverse resource allocation problems and motivate researchers to explore new models and algorithmic approaches

algorithms for the continuous nonlinear resource allocation problem new implementations and numerical studies patriksson 2008 provided a then up to date survey on the continuous separable differentiable and convex resource allocation problem with a single resource constraint since the publication of that paper the interest in the problem has grown several new applications have arisen where the problem at hand constitutes a subproblem and several new algorithms have been developed for its efficient solution this paper therefore serves three purposes first it provides an up to date extension of the survey of the literature of the field complementing the survey in patriksson 2008 with more then 20 books and articles second it contributes improvements of some of these algorithms in particular with an improvement of the pegging that is variable fixing process in the relaxation algorithm and an improved means to evaluate subsolutions third it numerically evaluates several relaxation primal and breakpoint dual algorithms incorporating a variety of pegging strategies as well as a quasi newton method our conclusion is that our modification of the relaxation algorithm performs the best at least for problem sizes up to 30 million variables the practical time complexity for the breakpoint and relaxation algorithms is linear

solution techniques for some allocation problems this paper presents methods for solving allocation problems that can be stated as convex knapsack problems with generalized upper bounds such bounds may express upper limits on the total amount allocated to each of several subsets of activities in addition our model arises as a subproblem in more complex mathematical programs we therefore emphasize efficient procedures to recover optimality when minor changes in the parameters occur from one problem instance to the next these considerations lead us to propose novel data structures for such problems also we introduce an approximation method to solve certain equations which arise during the procedures

vanishing of the batalin vilkovisky algebra structure for tcfts the purpose of this short note is to show that for topological conformal field theories in dimension two or closed string field theories the batalin vilkovisky algebra structure on the homology of the brst complex g z is trivial after a certain element of ghost number 0 is inverted the important point here is that we do not restrict our considerations to the tree level but incorporate the action of moduli spaces for higher genera

nonconvex piecewise linear knapsack problems this paper considers the minimization version of a class of nonconvex knapsack problems with piecewise linear cost structure the items to be included in the knapsack have a divisible quantity and a cost function an item can be included partially in the given quantity range and the cost is a nonconvex piecewise linear function of quantity given a demand the optimization problem is to choose an optimal quantity for each item such that the demand is satisfied and the total cost is minimized this problem and its close variants are encountered in manufacturing planning supply chain design volume discount procurement auctions and many other contemporary applications two separate mixed integer linear programming formulations of this problem are proposed and are compared with existing formulations motivated by different scenarios in which the problem is useful the following algorithms are developed 1 a fast polynomial time near optimal heuristic using convex envelopes 2 exact pseudo polynomial time dynamic programming algorithms 3 a 2 approximation algorithm and 4 a fully polynomial time approximation scheme a comprehensive test suite is developed to generate representative problem instances with different characteristics extensive computational experiments show that the proposed formulations and algorithms are faster than the existing techniques

inverse optimization for linearly constrained convex separable programming problems abstract in this paper we study inverse optimization for linearly constrained convex separable programming problems that have wide applications in industrial and managerial areas for a given feasible point of a convex separable program the inverse optimization is to determine whether the feasible point can be made optimal by adjusting the parameter values in the problem and when the answer is positive find the parameter values that have the smallest adjustments a sufficient and necessary condition is given for a feasible point to be able to become optimal by adjusting parameter values inverse optimization formulations are presented with l 1 and l 2 norms these inverse optimization problems are either linear programming when l 1 norm is used in the formulation or convex quadratic separable programming when l 2 norm is used

lower bounds and heuristics for supply chain stock allocation assume that m periods with stochastic demand remain until the next replenishment arrives at a central warehouse how should the available inventory be allocated among n retailers this paper presents a new policy and a new lower bound for the expected cost of this problem the lower bound becomes tight as n the infinite horizon problem then decomposes into n independent m period problems with optimal retailer ship up to levels that decrease over the m periods and the warehouse is optimally replenished by an order up to level that renders zero local warehouse safety stock at the end of each replenishment cycle based on the lower bound solution we suggest a heuristic for finite n in a numerical study it outperforms the heuristic by jackson jackson p l 1988 stock allocation in a two echelon distribution system or what to do until your ship comes in management sci 34 7 880 895 and the new lower bound improves on clark and scarf s clark a j h scarf 1960 optimal policies for a multi echelon inventory problem management sci 6 4 475 490 bound when n is not too small moreover the warehouse zero safety stock heuristic is comparable to clark and scarf s warehouse policy for lead times that are not too long the suggested approach is quite general and may be applied to other logistical problems in the present application it retains some of the risk pooling benefits of holding central warehouse stock

a class of nonlinear nonseparable continuous knapsack and multiple choice knapsack problems this paper considers a general class of continuous nonlinear and nonseparable knapsack problems special cases of which arise in numerous operations and financial contexts we develop important properties of optimal solutions for this problem class based on the properties of a closely related class of linear programs using these properties we provide a solution method that runs in polynomial time in the number of decision variables while also depending on the time required to solve a particular one dimensional optimization problem thus for the many applications in which this one dimensional function is reasonably well behaved e g unimodal the resulting algorithm runs in polynomial time we next develop a related solution approach to a class of continuous nonlinear and nonseparable multiple choice knapsack problems this algorithm runs in polynomial time in both the number of variables and the number of variants per item while again dependent on the complexity of the same one dimensional optimization problem as for the knapsack problem computational testing demonstrates the power of the proposed algorithms over a commercial global optimization software package

on the imbalance of inventories in multi echelon systems a central depot periodically orders or produces new stock and withdraws inventory in order to allocate it among several demand points each experiencing random demands over a finite planning horizon this system gives rise to a dynamic program with a state space of very large dimension we determine a near optimal allocation policy and construct a tractable approximate dynamic program to help determine good orders and withdrawals this is done by exploring the effects of a measure of the imbalance of inventories at the demand points numerical results are included

pitch extraction method and device utilizing autocorrelation of a plurality of frequency bands a pitch extraction method and apparatus whereby the pitch of a speech signal having various characteristics can be extracted accurately the frame based input speech signal band limited by an hpf 12 and an lpf 16 is sent to autocorrelation computing units 13 17 where autocorrelation data is found the pitch lag is computed and normalized in the pitch intensity pitch lag computing units 14 18 the pitch reliability of the input speech signals limited by the hpf 12 and the lpf 16 is computed in elevation parameter calculation units a selection unit 20 selects one of the parameters obtained from the input speech signal limited by the hpf 12 and the lpf 16 using the pitch lag and the evaluation parameter

infinite loop spaces from operads with homological stability abstract motivated by the operad built from moduli spaces of riemann surfaces we consider a general class of operads in the category of spaces that satisfy certain homological stability conditions we prove that such operads are infinite loop space operads in the sense that the group completions of their algebras are infinite loop spaces the recent strong homological stability results of galatius and randal williams for moduli spaces of even dimensional manifolds can be used to construct examples of operads with homological stability as a consequence diffeomorphism groups and mapping class groups are shown to give rise to infinite loop spaces furthermore the map to k theory defined by the action of the diffeomorphisms on the middle dimensional homology is shown to be a map of infinite loop spaces

aggregation and disaggregation techniques and methodology in optimization a fundamental issue in the use of optimization models is the tradeoff between the level of detail and the ease of using and solving the model aggregation and disaggregation techniques have proven to be valuable tools for manipulating data and determining the appropriate policies to employ for this tradeoff furthermore aggregation and disaggregation techniques offer promise for solving large scale optimization models supply a set of promising methodologies for studying the underlying structure of both univariate and multivariate data sets and provide a set of tools for manipulating data for different levels of decision makers in this paper we develop a general framework for aggregation and disaggregation methodology survey previous work regarding aggregation and disaggregation techniques for optimization problems illuminate the appropriate role of aggregation and disaggregation methodology for optimization applications and propose future research directions

method and apparatus for estimating pitch of signal a pitch estimating method and apparatus in which mixture gaussian distributions based on candidate pitches having high period estimating values are generated a mixture gaussian distribution having a high likelihood is selected and dynamic programming is executed so that the pitch of the speech signal can be accurately estimated the pitch estimating method comprises computing a normalized autocorrelation function of a windowed signal obtained by multiplying a frame of a speech signal by a window signal and determining candidate pitches from a peak value of the normalized autocorrelation function of the windowed signal interpolating a period of the determined candidate pitches and a period estimating value representing a length of the period generating gaussian distributions for the candidate pitches for each frame for which the interpolated period estimating value is greater than a first threshold value mixing the gaussian distributions which are located at a distance less than a second threshold value to generate mixture gaussian distributions and selecting at least one of the mixture gaussian distributions that a likelihood exceeding a third threshold value and executing dynamic programming for the frames to estimate the pitch of each frame based on the candidate pitches of each of the frames and the selected mixture gaussian distributions

the nonlinear knapsack problem algorithms and applications abstract we present a survey of algorithms and applications for the nonlinear knapsack problem or the nonlinear resource allocation problem in its most general form the nonlinear knapsack problem will be defined as a nonlinear optimization problem with just one constraint bounds on the variables and in some cases a set of specially structured constraints such as generalized upper bounds gubs this problem is encountered either directly or as a subproblem in a variety of applications including production planning financial modeling stratified sampling and capacity planning in manufacturing health care and computer networks by taking advantage of the special structure of the problem efficient solution methods can be developed problem classes addressed here include continuous and integer problems convex and nonconvex problems separable and nonseparable problems and problems with additional specially structured constraints

breakpoint searching algorithms for the continuous quadratic knapsack problem we give several linear time algorithms for the continuous quadratic knapsack problem in addition we report cycling and wrong convergence examples in a number of existing algorithms and give encouraging computational results for large scale problems

disaggregation and resource allocation using convex knapsack problems with bounded variables the allocation of a specific amount of a given resource among competitive alternatives can often be modelled as a knapsack problem this model formulation is extremely efficient because it allows convex cost representation with bounded variables to be solved without great computational efforts practical applications of this problem abound in the fields of operations management finance manpower planning marketing etc in particular knapsack problems emerge in hierarchical planning systems when a first level of decisions need to be further allocated among specific activities which have been previously treated in an aggregate way in this paper we provide a recursive procedure to solve such problems the method differs from classical optimization algorithms of convex programming in that it determines at each iteration the optimal value of at least one variable applications and computational results are presented

a graphical category for higher modular operads abstract we present a homotopy theory for a weak version of modular operads whose compositions and contractions are only defined up to homotopy this homotopy theory takes the form of a quillen model structure on the collection of simplicial presheaves for a certain category of undirected graphs this new category of undirected graphs denoted u plays a similar role for modular operads that the dendroidal category plays for operads we carefully study properties of u including the existence of certain factorization systems related structures such as cyclic operads and stable modular operads can be similarly treated using categories derived from u

the stable mapping class group of simply connected 4 manifolds we consider mapping class groups m 0diff m fix m of smooth compact simply connected oriented 4 manifolds m bounded by a collection of 3 spheres we show that if m contains cp 2 or cp 2 as a connected summand then all dehn twists around 3 spheres are trivial and furthermore m is independent of the number of boundary components by repackaging classical results in surgery and handlebody theory from wall kreck and quinn we show that the natural homomor phism from the mapping class group to the group of automorphisms of the intersection form becomes an isomorphism after stabilization with respect to connected sum with cp 2 cp 2 we next consider the 3 1 dimensional cobordism 2 category c of 3 spheres 4 manifolds as above and enriched with isotopy classes of diffeomorphisms as 2 morphisms we identify the homotopy type of the classifying space of this cat egory as the hermitian algebraic k theory of the integers we also comment on versions of these results for simply connected spin 4 manifolds finally we observe that a related 4 manifold operad detects infinite loop spaces

local minima for indefinite quadratic knapsack problems we consider the complexity of finding a local minimum for the nonconvex quadratic knapsack problem global minimization for this example of quadratic programming is np hard more and vavasis have investigated the complexity of local minimization for the strictly concave case of qkp here we extend their algorithm to the general indefinite case our main result is an algorithm that computes a local minimum in o n logn 2 steps our approach involves eliminating all but one of the convex variables through parametrization yielding a nondifferentiable problem we use a technique from computational geometry to address the nondifferentiable problem