memetic algorithm based on improved inver over operator and lin kernighan local search for the euclidean traveling salesman problem in this study an improved inver over operator is proposed to solve the euclidean traveling salesman problem tsp problem the improved inver over operator is tested on 14 different tsp examples selected from tsplib the application of the improved inver over operator gives much more effective results regarding to the best and average error values than the basic inver over operator then an effective memetic algorithm based on improved inver over operator and lin kernighan local search is implemented to speed up the convergence capability of the presented algorithm a restart technique is employed we evaluate the proposed algorithm based on standard tsp test problems and show that the proposed algorithm performs better than other memetic algorithm in terms of solution quality and computational effort

rational curves and rational singularities we study rational curves on algebraic varieties especially on normal affine varieties endowed with a action for varieties with an isolated singularity covered by a family of rational curves with a general member not passing through the singular point we show that this singularity is rational in particular this provides an explanation of classical results due to h a schwartz and g h halphen on polynomial solutions of the generalized fermat equation

perfect powers expressible as sums of two cubes abstract let n 3 this paper is concerned with the equation a 3 b 3 c n which we attack using a combination of the modular approach via frey curves and galois representations with obstructions to the solutions that are of brauer manin type we shall show that there are no solutions in coprime non zero integers a b c for a set of prime exponents n having dirichlet density 28 219 44 928 0 628 and for a set of exponents n having natural density 1

modular elliptic curves and fermat s last theorem when andrew john wiles was 10 years old he read eric temple bell s the last problem and was so impressed by it that he decided that he would be the first person to prove fermat s last theorem this theorem states that there are no nonzero integers a b c n with n 2 such that an bn cn the object of this paper is to prove that all semistable elliptic curves over the set of rational numbers are modular fermat s last theorem follows as a corollary by virtue of previous work by frey serre and ribet

polynomial parametrization for the solutions of diophantine equations and arithmetic groups a polynomial parametrization for the group of integer two by two matrices with determinant one is given solving an old open problem of skolem and beurkers it follows that for many diophantine equations the integer solutions and the primitive solutions admit polynomial parametrizations

a new hybrid heuristic approach for solving large traveling salesman problem this paper presents a new metaheuristic approach called acomac algorithm for solving the traveling salesman problem tsp we introduce multiple ant clans concept from parallel genetic algorithm to search solution space utilizing various islands to avoid local minima and thus can yield global minimum for solving the traveling salesman problem moreover we present two approaches named the multiple nearest neighbor nn and the dual nearest neighbor dnn to acomac to enhance large tsps to validate the proposed methods numerous simulations were conducted to compare acomac and dorigo s acs with and without the addition of the multiple nearest neighbor nn method or the dual nearest neighbor dnn approach using a range of tsp benchmark problems according to the results of the simulation adding the nn or dnn approach to acomac or acs as initial solutions also significantly enhances the performance of acomac and acs in solving the traveling salesman problem meanwhile using acomac dnn with tsp can yield better solutions than the other stated approaches additionally acomac or acomac nn utilizing five ant clans with a total of 20 ants is verified to yield better solutions furthermore acomac with a local weighting w set to 0 6 can yield better solutions in terms of length

k out of n systems reliability and availability analyses are recognized as essential for guiding decision makers in the implementation of actions addressed to improve the technical and economical performance of complex systems for industrial systems with reparable components the most interesting parameter used to drive maintenance is the stationary availability in this regard the present paper proposes an exact formula for computing the system stationary availability of a k out of n system such a formula is proved to be in agreement with the fundamental theorem of markov chains then a multi objective mathematical model is formulated for choosing the optimal system configuration design the pareto front is developed using the lexicographic goal programming lgp method and the topsis method is successively implemented to choose the k out of n configuration that represents the best compromise between the considered objective functions a numerical example is provided stationary availability formula proposed for k out of n systems validation of the proposed formula by markov chains design of a k out of n system selection of pareto solution by means of topsis multi criteria method

on the modularity of elliptic curves over q wild 3 adic exercises in this paper building on work of wiles wi and of wiles and one of us r t tw we will prove the following two theorems see 2 2 theorem a if e q is an elliptic curve then e is modular theorem b if gal q q gl2 f5 is an irreducible continuous representation with cyclotomic determinant then is modular we will first remind the reader of the content of these results and then briefly outline the method of proof if n is a positive integer then we let 1 n denote the subgroup of sl2 z consisting of matrices that modulo n are of the form 1 0 1

torsion points on curves and p adic abelian integrals theorem a let f c j be an albanese morphism defined over a number field k of a s mooth curve of genus g into its jacobian suppose j has potential complex multiplication let s denote the set of primes p of k satisfying i p does not divide 2 or 3 ii k q is unramified at p iii c has good ordinary reduction over k then the set t of torsion points of a defined over an algebraic closure of k which lie on the image of c is defined over an extension of k unramified above s moreover to pg

galois representations attached to q curves and the generalized fermat equation a 4 b 2 c p we prove that the equation a 4 b 2 c p has no solutions in coprime positive integers when p 211 the main step is to show that for all sufficiently large primes p every q curve over an imaginary quadratic field k with a prime of potentially multiplicative reduction greater than 6 has a surjective mod p galois representation the bound on p depends on k and the degree of the isogeny between e and its galois conjugate but is independent of the choice of e the proof of this theorem combines geometric arguments due to mazur momose darmon and merel with an analytic estimate of the average special values of certain l functions

new approach using ant colony optimization with ant set partition for fuzzy control design applied to the ball and beam system in this paper we describe the design of a fuzzy logic controller for the ball and beam system using a modified ant colony optimization aco method for optimizing the type of membership functions the parameters of the membership functions and the fuzzy rules this is achieved by applying a systematic and hierarchical optimization approach modifying the conventional aco algorithm using an ant set partition strategy the simulation results show that the proposed algorithm achieves better results than the classical aco algorithm for the design of the fuzzy controller

a novel bio inspired approach based on the behavior of mosquitoes this paper proposes a new nature inspired algorithm na mosquito host seeking algorithm mhsa the inspiration for which comes from the host seeking behavior of mosquitoes applying the algorithm to the traveling salesman problem tsp every city pair is treated as an artificial mosquito and the tsp solving process is transformed into the host seeking behavior of a swarm of artificial mosquitoes we study the evolution of swarms the artificial mosquitoes microcosmic actions and macroscopic swarm intelligence and present efficient solutions to tsp using mhsa the proposed mhsa is fundamentally different from the other popular nas in its motivation principle the optimization mechanism its elements and their states and the biological model the mathematical model and theoretical foundation on which it is based we show that 1 mhsa can converge 2 its parameter setting does not depend on algorithm learning or prior knowledge and 3 mhsa can describe complex behaviors and dynamics the properties of mhsa including correctness convergence and stability are discussed in details simulation results attest to the effectiveness and suitability of mhsa

bias reduced and separation proof conditional logistic regression with small or sparse data sets conditional logistic regression is used for the analysis of binary outcomes when subjects are stratified into several subsets e g matched pairs or blocks log odds ratio estimates are usually found by maximizing the conditional likelihood this approach eliminates all strata specific parameters by conditioning on the number of events within each stratum however in the analyses of both an animal experiment and a lung cancer case control study conditional maximum likelihood cml resulted in infinite odds ratio estimates and monotone likelihood estimation can be improved by using cytel inc s well known logxact software which provides a median unbiased estimate and exact or mid p confidence intervals here we suggest and outline point and interval estimation based on maximization of a penalized conditional likelihood in the spirit of firth s biometrika 1993 80 27 38 bias correction method cfl we present comparative analyses of both studies demonstrating some advantages of cfl over competitors we report on a small sample simulation study where cfl log odds ratio estimates were almost unbiased whereas logxact estimates showed some bias and cml estimates exhibited serious bias confidence intervals and tests based on the penalized conditional likelihood had close to nominal coverage rates and yielded highest power among all methods compared respectively therefore we propose cfl as an attractive solution to the stratified analysis of binary data irrespective of the occurrence of monotone likelihood a sas program implementing cfl is available at http www muw ac at msi biometrie programs

path planning on a cuboid using genetic algorithms the traveling salesman problem tsp is one of the most extensively studied problems in the fields of combinatorial optimization and global search heuristics a variety of heuristic algorithms are available for solving euclidean tsp and planar tsps however optimization on a cuboid has potential applications for areas like path planning on the faces of buildings rooms furniture books and products or simulating the behaviors of insects in this paper we address a variant of the tsp in which all points cities and paths solution are on the faces of a cuboid we develop an effective hybrid method based on genetic algorithms and 2 opt to adapt the euclidean tsp to the surface of a cuboid the method was tested on some benchmark problems from tsplib with satisfactory results a web based interactive visualization tool has also been developed using java 3d and optimization results for different point densities on the cuboid are presented

hybrid evolutionary fuzzy learning scheme in the applications of traveling salesman problems abstract this study develops a hybrid evolutionary fuzzy learning algorithm that automatically determines the near optimal traveling path in large scale traveling salesman problems lstsps identifying solutions for lstsps is one of the most complicated topics in the field of global combinatorial optimization problems the proposed hybrid evolutionary fuzzy learning scheme combines the advantages of the adaptive fuzzy c means fcm simple max min merging concept simulated annealing sa learning algorithm and an efficient table transform based particle swarm optimization tpso this study uses the proposed method to deal with the large size tsp routing system the evolutionary tpso learning algorithm is applied to optimize the traveling table which in turn extracts the appropriate traveling table sequence codes for approaching the shorter traveling path the sa local optimal learning algorithm works after the tpso learning scheme using three operators to acquire the optimal traveling solution inversion translation and switching the other considerable notation is to divide the large scale cities into suitable subgroup cities to improve the efficiency of training machine the popular fcm algorithm is a valid unsupervised clustering method that identifies the relational grades of a given traveling city dataset separating them into popular categories based on the critical issue in maximal city number to break the city nodes of the traveling loop and reconnect suitable nodes again with the minimal distance searching procedure the proposed simple but powerful max min merging algorithm to rebuild the new traveling path various sizes of tsp testing instances reveal that the developed hybrid evolutionary fuzzy learning algorithm achieves better results than other learning methods in both the quality of routing and computing time

bias reduction of maximum likelihood estimates summary it is shown how in regular parametric problems the first order term is removed from the asymptotic bias of maximum likelihood estimates by a suitable modification of the score function in exponential families with canonical parameterization the effect is to penalize the likelihood by the jeffreys invariant prior in binomial logistic models poisson log linear models and certain other generalized linear models the jeffreys prior penalty function can be imposed in standard regression software using a scheme of iterative adjustments to the data

on the modularity of ℚ curves a q curve is an elliptic curve over a number field k which is geometrically isogenous to each of its galois conjugates ribet 16 asked whether every q curve is modular and showed that a positive answer would follow from serre s conjecture on mod p galois representations we answer ribet s question in the affirmative subject to certain local conditions at 3 msc classification 11g18 14g35 14h52

comment on bias reduction in conditional logistic regression by j x sun s sinha s wang and t maiti statistics in medicine 2010 doi 10 1002 sim 4105

a proof of convergence for ant algorithms a proof of convergence for ant algorithms is developed ant algorithms were modeled as branching random processes the branching random walk and branching wiener process to derive rates of birth and death of ant paths substitution is then carried out in birth death processes which proves that a stable distribution is surely reached this indicates that ant algorithms converge with probability one this analogy models ant algorithms complexity parameters such as the number of cycles the degrees of freedom of problem and the number of ants

an introduction to stochastic modeling stochastic modeling probability review the major discrete distributions rtant continuous distributions some elementary exercises useful functions integrals and sums conditional probability and conditional expectation the discrete case the dice game craps random sums conditioning on a continuous random variable markov chains introduction definitions transition probability matrices of a markov chain some markov chain models first step analysis some special markov chains functionals of random walks and success runs another look at first step analysis the long run behavior of markov chains regular transition probability matrices examples the classification of states the basic limit theorem of markov chains reducible markov chains sequential decisions and markov chains poisson processes the poisson distribution and the poisson processes the law of rare events distributions associated with the poisson process the uniform distribution and poisson processes spatial poisson processes compound and marked poisson processes continuous time markov chains pure birth processes ptire death processes birth and death processes the limiting behavior of birth and death processes birth and death processes with absorbing states finite state continuous time markov chains set valued processes renewal phenomena definition of a renewal process and related concepts some examples of renewal processes the poisson process viewed as a renewal process the asymptotic 3ehavior as renewal process

on relations between jacobians of certain modular curves abstract we confirm a conjecture of l merel h darmon and l merel j reine angew math 490 1997 81 100 describing a certain relation between the jacobians of various quotients of x p in terms of specific correspondences the method of proof involves reducing this conjecture to a question about certain z gl 2 f p module homomorphisms which is in turn answered by exhibiting some peculiar relations in a double coset algebra

visualising sha 2 in abelian surfaces given an elliptic curve e 1 over a number field k and an element s in its 2 selmer group we give two different ways to construct infinitely many abelian surfaces a such that the homogeneous space representing s occurs as a fibre of a over another elliptic curve e 2 we show that by comparing the 2 selmer groups of e 1 e 2 and a we can obtain information about iii e 1 k 2 and we give examples where we use this to obtain a sharp bound on the mordell weil rank of an elliptic curve as a tool we give a precise description of the m selmer group of an abelian surface a that is m isogenous to a product of elliptic curves e 1 x e 2 one of the constructions can be applied iteratively to obtain information about iii e 1 k 2 n we give an example where we use this iterated application to exhibit an element of order 4 in iii e 1 q

fermat type equations of signature 13 13 p via hilbert cuspforms in this paper we prove that for p 13649 equations of the form x 13 y 13 cz p have no non trivial primitive solutions a b c such that 13 not mid c for an infinite family of values for c our method consists on relating a solution a b c to the previous equation to a solution a b c 1 of another diophantine equation with coefficients in mathbb q sqrt 13 then we attach to a b c 1 a frey curve e a b defined over mathbb q sqrt 13 that is not a mathbb q curve we prove a modularity result of independent interest for certain elliptic curves over totally real abelian number fields satisfying some local conditions at 3 this theorem in particular implies modularity of e a b this enables us to use level lowering results and apply the modular approach via hilbert cuspforms over mathbb q sqrt 13 to prove the non existence of a b c 1 and consequently of a b c

a solution to the problem of monotone likelihood in cox regression the phenomenon of monotone likelihood is observed in the fitting process of a cox model if the likelihood converges to a finite value while at least one parameter estimate diverges to infinity monotone likelihood primarily occurs in small samples with substantial censoring of survival times and several highly predictive covariates previous options to deal with monotone likelihood have been unsatisfactory the solution we suggest is an adaptation of a procedure by firth 1993 biometrika 80 27 38 originally developed to reduce the bias of maximum likelihood estimates this procedure produces finite parameter estimates by means of penalized maximum likelihood estimation corresponding wald type tests and confidence intervals are available but it is shown that penalized likelihood ratio tests and profile penalized likelihood confidence intervals are often preferable an empirical study of the suggested procedures confirms satisfactory performance of both estimation and inference the advantage of the procedure over previous options of analysis is finally exemplified in the analysis of a breast cancer study

empirical evidence for the birch and swinnerton dyer conjectures for modular jacobians of genus 2 curves this paper provides empirical evidence for the birch and swinnerton dyer conjectures for modular jacobians of genus 2 curves the second of these conjectures relates six quantities associated to a jacobian over the rational numbers one of these six quantities is the size of the shafarevich tate group unable to compute that we computed the five other quantities and solved for the last one in all 32 cases the result is very close to an integer that is a power of 2 in addition this power of 2 agrees with the size of the 2 torsion of the shafarevich tate group which we could compute

computing twists of hyperelliptic curves abstract we give an efficient algorithm to compute equations of twists of hyperelliptic curves c of arbitrary genus over any perfect field k of characteristic different from 2 starting with a cocycle in h 1 gal k k aut c we also discuss some interesting examples

how to do a p descent on an elliptic curve in this paper we describe an algorithm that reduces the computation of the full p selmer group of an elliptic curve e over a number field to standard number field computations such as determining the p torsion of the s class group and a basis of the s units modulo pth powers for a suitable set s of primes in particular we give a result reducing this set s of bad primes to a very small set which in many cases only contains the primes above p as of today this provides a feasible algorithm for performing a full 3 descent on an elliptic curve over q but the range of our algorithm will certainly be enlarged by future improvements in computational algebraic number theory when the galois module structure of e p is favorable simplifications are possible and p descents for larger p are accessible even today to demonstrate how the method works several worked examples are included

two cover descent on hyperelliptic curves we describe an algorithm that determines a set of unramified covers of a given hyperelliptic curve with the property that any rational point will lift to one of the covers in particular if the algorithm returns an empty set then the hyperelliptic curve has no rational points this provides a relatively efficiently tested criterion for solvability of hyperelliptic curves we also discuss applications of this algorithm to curves of genus 1 and to curves with rational points

reliability evaluation and optimal design in heterogeneous multi state series parallel systems this paper addresses the heterogeneous redundancy allocation problem in multi state series parallel reliability structures with the objective to minimize the total cost of system design satisfying the given reliability constraint and the consumer load demand the demand distribution is presented as a piecewise cumulative load curve and each subsystem is allowed to consist of parallel redundant components of not more than three types the system uses binary capacitated components chosen from a list of available products to provide redundancy so as to increase system performance and reliability the components are characterized by their feeding capacity reliability and cost a system that consists of elements with different reliability and productivity parameters has the capacity strongly dependent upon the selection of constituent components a binomial probability based method to compute exact system reliability index is suggested to analyze the problem and suggest an optimal near optimal system structure an ant colony optimization algorithm has been presented the solution approach consists of a series of simple steps as used in early ant colony optimization algorithms dealing with other optimization problems and offers straightforward analysis four multi state system design problems have been solved for illustration two problems are taken from the literature and solved to compare the algorithm with the other existing methods the other two problems are based upon randomly generated data the results show that the method can be appealing to many researchers with regard to the time efficiency and yet without compromising over the solution quality

improved time censored reliability test plans for k out of n gamma systems abstract relevant prior knowledge supported by historical data and expert judgments is common in many manufacturing processes the classical viewpoint to the determination of acceptance sampling plans for k out of n gamma systems is generalized to those situations in which the available previous information is appreciable a beta distribution with a reduced parameter space is adopted to describe the stochastic behavior of the fraction of defective systems an integer nonlinear programming problem is stated to find the inspection scheme that minimizes the required number of components to test and keeps the average producer and consumer risks below specified thresholds first lower and upper bounds as well as an approximate solution are derived then an efficient step by step procedure which finds the best acceptance sampling plan in a finite number of iterations is provided the inclusion of prior information into the decision process provides substantial savings in the sample size required for demonstrating system reliability and also more accurate assessments of the actual producer and consumer risks a system of five water pumps for cooling a reactor is analyzed for illustrative and comparative purposes

explicit moduli spaces for congruences of elliptic curves we determine explicit birational models over mathbb q for the modular surfaces parametrising pairs of n congruent elliptic curves in all cases where this surface is an elliptic surface in each case we also determine the rank of the mordell weil lattice and the geometric picard number

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

recipes to fermat type equations of the form x r y r cz p we describe a strategy to attack infinitely many fermat type equations of signature r r p where r ge 7 is a fixed prime and p is a prime allowed to vary indeed to a solution a b c of x r y r cz p we will attach several frey curves e e a b defined over totally real subfields of mathbb q zeta r we prove modularity of all the frey curves and the exsitence of a constant constant m r depending only on r such that for all p m r the representations bar rho e p are absolutely irreducible along the way we also prove modularity of certain elliptic curves that are semistable at all v mid 3 finally we illustrate our methods by proving arithmetic statements about equations of signature 7 7 p among which we emphasize that using a multi frey technique we show there is some constant m such that if p m then the equation x 7 y 7 3z p has no non trivial primitive solutions

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

sieving for rational points on hyperelliptic curves we give a new and efficient method of sieving for rational points on hyperelliptic curves this method is often successful in proving that a given hyperelliptic curve suspected to have no rational points does in fact have no rational points we have often found this to be the case even when our curve has points over all localizations qp we illustrate the practicality of the method with some examples of hyperelliptic curves of genus 1