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

complexity and multiple complexes in this chapter we introduce the notion of the complexity of a module and explore some related ideas complexity was first defined by jon alperin in the late 1970 s and it helped to motivate much of the development of the homological properties of modules in fact the complexity of a finitely generated kg module m is a rather crude invariant in that it only measures the polynomial rate of growth of a minimal projective resolution of the module the original theorem of alperin and evens which extended quillen s dimension theorem to modules was proved only in terms of complexity later it was extended to support varieties as well the theorem computes the complexity of a kg module m as the maximum of the complexities of the restrictions of m to the elementary abelian subgroups of the group g

optimal annealing schedules for a modified tsallis statistics in this paper for a number of example systems optimal schedules for simulated annealing with a modified tsallis statistics for various parameters q are analyzed it turns out that in general depending on the objective function minimizing the mean energy or maximizing the ground state probability different schedules have to be chosen furthermore the optimal objective function value reached with the optimal schedule shows a monotonic dependency on q where better values are reached for smaller q thus in stochastic optimization the limit case q corresponding to threshold accepting should be chosen in order to get the best possible optimization results with as little effort as possible

the varieties and the cohomology ring of a module let g be a finite group and let k be a field of characteristic p 0 recently several studies have focused on the homological invariants of finitely generated kg modules in l alperin proposed the study of the complexity of a module the complexity is related to the degree of the polynomial rate of growth of the terms in a projective resolution of the module see definition 2 4 in 2 alperin and evens proved that the complexity of a kg module m is equal to the maximum of the complexities of the restrictions of m to elementary abelian p subgroups of g one of the roots of the alperin evens theorem is quillen s dimension theorem see 21 or 22 which with some difficulty can be interpreted as saying the same thing for the special case of the trivial kg module alperin and evens 3 and avrunin 4 have further studied the annihilator in ext k k of the cohomology of m and have produced theorems of a similar nature these are related to the work in 9 on the structure of the cohomology ring ext m m the purpose of this paper is to investigate the relationship between these homological invariants and the structure of the module we concentrate on the case in which g is an elementary abelian p group however using such results as those mentioned above we can apply the present work to more general groups even as the earlier results indicate that much of the structure and cohomology of a module is revealed in the restrictions to elementary abelian p subgroups we show here that in the case of an elementary abelian group much of this information can be found by looking at the restrictions to cyclic p subgroups of the group of units of kg some of the results in this paper were announced in s let g xl xn be an elementary abelian group of order p suppose that k is algebraically closed to any finitely generated kg module m we

optimal power assignment for minimizing the average total transmission power in hybrid arq rayleigh fading links we address the fundamental problem of identifying the optimal power assignment sequence for hybrid automatic repeat request h arq communications over quasi static rayleigh fading channels for any targeted h arq link outage probability we find the sequence of power values that minimizes the average total expended transmission power we first derive a set of equations that describe the optimal transmission power assignment and enable its exact recursive calculation to reduce calculation complexity we also develop an approximation to the optimal power sequence that is close to the numerically calculated exact result the newly founded power allocation solution reveals that conventional equal power h arq assignment is far from optimal for example for targeted outage probability of 10 3 with a maximum of two transmissions the average total transmission power with the optimal assignment is 9 db lower than the equal power protocol the difference in average total power cost grows further when the number of allowable retransmissions increases for example 11 db gain with a cap of 5 transmissions or the targeted outage probability decreases 27 db gain with outage probability 10 5 and transmissions capped at 5 interestingly the optimal transmission power assignment sequence is neither increasing nor decreasing its form depends on given total power budget and targeted outage performance levels extensive numerical and simulation results are presented to illustrate the theoretical development

renyi entropies and fisher informations as measures of nonextensivity in a tsallis setting abstract we study nonextensive statistical scenarios a la tsallis with reference to fisher s information and renyi s entropy a new way of evaluating tsallis generalized expectation values is examined within such a context and is shown to lead to a much better cramer rao bound than the customary procedure a connection between the information measures of fisher s and renyi s is found we show that fisher s measure for translation families remains additive even in a non extensive tsallis setting

enhancing synchronizability of diffusively coupled dynamical networks a survey in this paper we review the literature on enhancing synchronizability of diffusively coupled dynamical networks with identical nodes the last decade has witnessed intensive investigations on the collective behavior over complex networks and synchronization of dynamical systems is the most common form of collective behavior for many applications it is desired that the synchronizability the ability of networks in synchronizing activity of their individual dynamical units is enhanced there are a number of methods for improving the synchronization properties of dynamical networks through structural perturbation in this paper we survey such methods including adding removing nodes and or edges rewiring the links and graph weighting these methods often try to enhance the synchronizability through minimizing the eigenratio of the laplacian matrix of the connection graph a synchronizability measure based on the master stability function formalism we also assess the performance of the methods by numerical simulations on a number of real world networks as well as those generated through models such as preferential attachment watts strogatz and erdos renyi

on support varieties and tensor products for finite dimensional algebras abstract it has been asked whether there is a version of the tensor product property for support varieties over finite dimensional algebras defined in terms of hochschild cohomology we show that in general no such version can exist in particular we show that for certain quantum complete intersections there are modules and bimodules for which the variety of the tensor product is not even contained in the variety of the one sided module

annihilators of cohomology modules let g be a finite group k a field of characteristic p 0 and u a kgmodule recently alperin and evens l proved that the complexity of u a numerical invariant defined in terms of the minimal projective resolution of u is determined by the restrictions of u to elementary abelian p subgroups this result has also been obtained by carlson 2 as a consequence of a theorem concerning the dimension of the sum of the nonprojective components of such a restriction in this paper we focus on annihilators of modules for the cohomology ring h g k and show how to obtain the alperin evens theorem and some of its corollaries from a decomposition theorem for certain ideals

representation theoretic support spaces for finite group schemes we introduce the space p g of abelian p points of a finite group scheme over an algebraically closed field of characteristic p 0 we construct a homeomorphism g p g proj g from p g to the projectivization of the cohomology variety for any finite group g for an elementary abelian p group respectively an infinitesimal group scheme p g can be identified with the projectivization of the variety of cyclic shifted subgroups resp variety of 1 parameter subgroups for a finite dimensional g module m g restricts to a homeomorphism p g m proj g m thereby giving a representation theoretic interpretation of the cohomological support variety

optimization of non linear gravity models through generalized simulated annealing abstract in this paper we apply the generalized simulated annealing gsa approach to the inversion of gravity data for 2 d and 3 d density distributions we consider a modeling process where the input is the vector of model parameters m that can be density contrast mass or some coordinates and the output is described by the transformation h m d where d is the vector of data parameters we generally have access in practical problems if the vector d describes the observed actual output of the system the problem is to choose or estimate the parameters m est in order to minimize in some sense in our case in the least squares sense the difference between the observed vector d and the prescribed output of the system h m est the tests with synthetic data show the promising application of gsa in gravity inversion the results obtained suggest us that the gsa approach enables to find quickest optimization machines than the two conventional approaches boltzmann and cauchy machines

the stochastic traveling salesman problem finite size scaling and the cavity prediction we study the random link traveling salesman problem where lengths lij between city i and city j are taken to be independent identically distributed random variables we discuss a theoretical approach the cavity method that has been proposed for finding the optimum tour length over this random ensemble given the assumption of replica symmetry using finite size scaling and a renormalized model we test the cavity predictions against the results of simulations and find excellent agreement over a range of distributions we thus provide numerical evidence that the replica symmetric solution to this problem is the correct one finally we note a surprising result concerning the distribution of k th nearest neighbor links in optimal tours and invite a theoretical understanding of this phenomenon

polynomial expansion of diffusion and drift coefficients for classical and quantum statistics abstract we study by means of a kinetic approach recently proposed phys rev e 49 5103 1994 both classical and quantum statistics stationary solutions of a non linear fokker planck equation the non linear term in this equation has origin in a generalized exclusion inclusion principle which takes into account the quantum effects due to the bosonic fermionic or intermediate behaviour of the particles if the drift and diffusion coefficients are polynomials in the velocity variable of degree 2m 1 and 2n respectively only one well defined statistics can be derived for any particular pair of values m n in the case of classical particles in addition to the macroscopic fokker planck equation we derive the associated microscopic langevin equation and demonstrate that the pairs 0 0 1 0 and 0 1 correspond respectively to maxwell boltzmann druyvenstein and tsallis statistical distributions we study also the distribution related to the pair 1 1 which is the simplest generalization of the tsallis 1 one finally the above statistics are extended to the quantum case of particles obeying the exclusion inclusion principle

representations of elementary abelian p groups and bundles on grassmannians abstract we initiate the study of representations of elementary abelian p groups via restrictions to truncated polynomial subalgebras of the group algebra generated by r nilpotent elements k t 1 t r t 1 p t r p we introduce new geometric invariants based on the behavior of modules upon restrictions to such subalgebras we also introduce modules of constant radical and socle type generalizing modules of constant jordan type and provide several general constructions of modules with these properties we show that modules of constant radical and socle type lead to families of algebraic vector bundles on grassmannians and illustrate our theory with numerous examples

the varieties for some specht modules abstract j carlson introduced the cohomological and rank variety for a module over a finite group algebra we give a general form for the largest component of the variety for the specht module for the partition p p of p 2 restricted to a maximal elementary abelian p subgroup of rank p we determine the varieties of a large class of specht modules corresponding to p regular partitions to any partition of np of not more than p parts with empty p core we associate a unique partition of np where the rank variety of the restricted specht module s e n to a maximal elementary abelian p subgroup e n of rank n is v e n k if and only if v e n s v e n k in some cases where is a 2 part partition we show that the rank variety v e n s is v e n k in particular the complexity of the specht module s is n

on the average rate performance of hybrid arq in quasi static fading channels the problem of efficient communication over a scalar quasi static fading channel is considered the single layer transmission slt and multi layer transmission mlt schemes do not require any knowledge of the channel state information csi at the transmitter but their performance is also limited it is shown that using hybrid arq harq can significantly improve the average rate performance provided that the rate assignment between different arq rounds is carefully chosen the average rate performance of several harq schemes is optimized and compared in addition optimal power allocation among retransmissions is derived and shown to further increase the average rate this power allocation gain is remarkable at low signal to noise ratio snr but becomes negligible at high snr comparison of two different types of limited feedback sequential feedback arq and one shot feedback quantized csi is made from several perspectives although the optimization problem is formed with respect to the average rate simulation results give a comprehensive comparison under different metrics including average rate outage probability and the combination of both substantial performance improvement is observed with even one arq retransmission in all simulations more importantly this gain appears to be robust with respect to the fading distributions

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

support varieties for infinitesimal group schemes the representation theory of a connected smooth affine group scheme over a field k of characteristic p 0 is faithfully captured by that of its family of frobenius kernels such frobenius kernels are examples of infinitesimal group schemes affine group schemes g whose coordinate hopf algebra k g is a finite dimensional local k algebra this paper presents a study of the cohomology algebra h g k of an arbitrary infinitesimal group scheme over k we provide a geometric determination of the cohomological support variety cgl spec h g k analogous to that given by d quillen for the cohomology of finite groups q we further study finite dimensional rational g modules m for arbitrary infinitesimal group schemes g over k in a manner initiated by j alperin and l evens a e and j carlson ci for finite groups we consider the variety igim c igi of the ideal im ker hev g k ext m m and provide a geometric description of this variety which is analogous to that given by g avrunin and l scott for finite dimensional modules for finite groups a s this paper is a continuation of our recent work establishing the finite generation of h g k f s and investigating the infinitesimal 1 parameter subgroups of g s f b earlier work of e friedlander and b parshall fp1 fp2 fp3 fp4 and j jantzen ji concerning the cohomology of restricted lie algebras are forerunners of the results presented here finite dimensional restricted lie algebras are in 1 1 correspondence with infinitesimal group schemes of height 1 our main theorems theorems 5 2 and 6 7 below when restricted to infinitesimal group schemes of height 1 significantly strengthen previously known cohomological information for restricted lie algebras an interesting aspect of our work is the extent to which infinitesimal 1 parameter subgroups v g a r g for infinitesimal group schemes g of height r play the role of elementary abelian p subgroups and their generalizations shifted subgroups for finite groups indeed much of our effort is dedicated to proving that cohomology classes are detected modulo nilpotence by such 1 parameter subgroups this is first done in 2 for unipotent infinitesimal group schemes using an induction argument made possible by a structure theorem presented in 1 this structure theorem is the analogue in our context of a theorem of j p serre characterizing elementary abelian p groups s

quillen stratification for modules let g be a finite group and k a fixed algebraically closed field of characteristic p o if p is odd let h be the subring of h g k consisting of elements of even degree following 20 221 we take h h g k if p 2 though one could just as well use the subring of elements of even degree for all p h is a finitely generated commutative k algebra 13 and we let v denote its associated affine variety max h if m is any finitely generated kg module then the cohomology variety v m of m may be defined as the support in v of the h module h g m if g is a p group and in general as the largest support of h g l m where l is any kg module 4 91 a module l with each irreducible kc module as a direct summand will serve d quillen 20 221 proved a number of beautiful results relating k to the varieties v associated with the various elementary abelian p subgroups e of g culminating in his stratification theorem 20 221 this theorem gives a piecewise description of v almost explicitly in terms of the subgroups e and their normalizers in g a well known corollary is that dim v max dim v where e

the variety of an indecomposable module is connected let g be a finite group and let k be an algebraically closed field of characteristic p 0 the connections between the modular representation theory of finite groups and cohomology theory is currently a topic of great interest in particular cohomology theory has been used to attach to each finitely generated kgmodule m a homogeneous affine variety v m if we let 17 m be the corresponding projective variety then our main result is the following

stratification and π cosupport finite groups we introduce the notion of pi cosupport as a new tool for the stable module category of a finite group scheme in the case of a finite group we use this to give a new proof of the classification of tensor ideal localising subcategories in a sequel to this paper we carry out the corresponding classification for finite group schemes

multifractality levinthal paradox and energy hypersurface instituto de fi sica universidad federal da bahia campus de ondina 40210 340 salvador bahia brazil received 21 june 2000 published 10 january 2001 multifractal properties in the potential energy hypersurface of polypeptides and proteins are investigated characteristic multifractal behavior for different molecular systems is obtained from the f a spectra theanalysis shows that the dimension of the phase space of the problem in uences the accessibility to differentparts of the potential energy hypersurface also we show that it is necessary to take into account the h bondformation between amino acids in the conformational folding search the present ndings indicate that thef a function describes some structural properties of a protein the behavior of the f a spectra gives analternative explanation about the levinthal paradox furthermore the anomalous temperature dependence ofthe raman spin lattice relaxation rates can be related to the perturbations in the secondary structures doi 10 1103 physreve 63 020901 pacs number s 87 14 cc 05 45 df 87 15 aa 05 10 ln

spectral duality for block cohomology abstract throughout this paper k denotes an algebraically closed field of characteristic p 0 g denotes a finite group b denotes a p block of g corresponding to the indecomposable algebra summand kb of kg d denotes a defect group of b it is unique up to conjugacy in g p denotes the p rank of d that is the maximum of the ranks of its elementary abelian p subgroups and s t denote kb modules a graded polynomial subalgebra r of h g k is specified by taking p algebraically independent canonical homogeneous elements which are certain chern classes to be its generators a spectral sequence is constructed with ext r ext kb s t r as its e2 term and with ext kb t s with a displaced grading as its abutment the latter is thus naturally filtered a brief account of the relevant algebraic topology commutative algebra and homological algebra is given

weil restriction and support varieties this paper extends the comparison results for cohomological support varieties for chevalley groups of the form g fp established by j carlson z lin and d nakano to chevalley groups of the form g fpd other topics considered are complexity and non maximal support varieties for modules techniques developed by j pevtsova and the author together with the use of weil restriction functors are employed

optimization with extremal dynamics for the traveling salesman problem abstract by mapping the optimization problems to physical systems the paper presents a general purpose stochastic optimization method with extremal dynamics it is built up with the traveling salesman problem tsp being a typical np complete problem as self organized critical processes of extremal dynamics the optimization dynamics successively updates the states of those cities with high energy consequently a near optimal solution can be quickly obtained through the optimization processes combining the two phases of greedy searching and fluctuated explorations ergodic walk near the phase transition the computational results demonstrate that the proposed optimization method may provide much better performance than other optimization techniques developed from statistical physics such as simulated annealing sa since the proposed fundamental solution is based on the principles and micromechanisms of computational systems it can provide systematic viewpoints and effective computational methods on a wide spectrum of combinatorial and physical optimization problems

optimal power allocation for hybrid arq with chase combining in i i d rayleigh fading channels we consider the optimization of chase combining cc based hybrid automatic repeat request harq schemes with a limit on the maximum number of retransmissions we formulate two optimization problems i minimizing the packet drop probability pdp under a total average transmit power constraint and ii minimizing the average transmit power under a fixed pdp constraint towards solving these equivalent optimization problems we provide a closed form expression for the outage probability of a cc harq scheme we then show that solving the optimization problems using an exact expression of the outage probability becomes complex with an increase in the maximum number of retransmissions we propose an alternative approach in which we approximate the optimization problems by using an approximate outage probability expression and formulate the two optimization problems as two equivalent geometric programming problems gpps which can be solved efficiently even for a large limit on the maximum number of retransmissions the results show that the optimal power allocation solution provides significant gains over the equal power allocation solution for pdp values below 10 3 the optimal solution provided by the gpp approach has a performance close to that of the solution provided by solving the optimization problem exactly using nonlinear optimization techniques

a simple approach to time inhomogeneous dynamics and applications to fast simulated annealing we study time inhomogeneous stochastic dynamical systems with vanishing noise conditions implying strong ergodicity are proposed the asymptotic probability distribution is characterized and we estimate the speed of relaxation applying these results to simulated annealing enables us to introduce systems that converge faster than a classical annealing dynamics determined by a gibbs factor

on the q 1 2 non extensive maximum entropy distribution abstract a detailed mathematical analysis on the q 1 2 non extensive maximum entropy distribution of tsallis is undertaken the analysis is based upon the splitting of such a distribution into two orthogonal components one of the components corresponds to the minimum norm solution of the problem posed by the fulfillment of the a priori conditions on the given expectation values the remaining component takes care of the normalization constraint and is the projection of a constant onto the null space of the expectation values transformation

the avrunin and scott theorem and a truncated polynomial algebra we prove an analogue of a theorem of avrunin and scott for truncated polynomial algebras m k x 1 x m x 2 i over an algebraically closed field of arbitrary characteristic the avrunin and scott theorem relates the support variety for a finite dimensional ke module to its rank variety where char k p and e is an elementary abelian p group the analogue of the avrunin and scott theorem relates the support variety for a finite dimensional m module using hochschild cohomology to its rank variety developed in k erdmann m holloway rank varieties and projectivity for a class of local algebras math z 247 2004 441 460 using clifford algebras along the way to proving our main result we provide a new proof of the avrunin and scott theorem for elementary abelian p group algebras which we are then able to generalise to the setting of m algebras

graded analogues of one parameter subgroups and applications to the cohomology of glm n r abstract we introduce a family m r f of infinitesimal supergroup schemes which we call multiparameter supergroups that generalize the infinitesimal frobenius kernels g a r of the additive group scheme g a then following the approach of suslin friedlander and bendel we use functor cohomology to define characteristic extension classes for the general linear supergroup g l m n and we calculate how these classes restrict along homomorphisms m r f g l m n finally we apply our calculations to describe up to a finite surjective morphism the spectrum of the cohomology ring of the r th frobenius kernel g l m n r of the general linear supergroup g l m n

varieties in finite transformation groups the equivariant cohomology ring of a g space x defines a homogeneous affine variety quillen q and w y hsiang hs have determined the relation between such varieties and the family of isotropy subgroups as well as their fixed point sets when dim x oo in modular representation theory j carlson cj introduced cohomological support varieties and rank varieties the latter depending on the group algebra and explored their relationship we define rank and support varieties for g spaces and g chain complexes and apply them to cohomological problems in transformation groups as a corollary a useful criterion for zg projectivity of the reduced total homology of certain g spaces is obtained which improves the projectivity criteria of rim r chouinard ch and dade d

defect theory for maximal ideals and simple functors keywords green functor source green correspondence maximal ideal finite group fixed point algebra defect theory for g algebras defect group restriction transfer conjugation defect pair functorial ideal simple g functors reference ctg article 1991 002doi 10 1016 0021 8693 91 90168 8 record created on 2008 12 16 modified on 2017 05 12

generic and maximal jordan types for a finite group scheme g over a field k of characteristic p 0 we associate new invariants to a finite dimensional kg module m namely for each generic point of the projectivized cohomological variety text proj mathop h bullet g k we exhibit a generic jordan type of m in the very special case in which g e is an elementary abelian p group our construction specializes to the non trivial observation that the jordan type obtained by restricting m via a generic cyclic shifted subgroup does not depend upon a choice of generators for e furthermore we construct the non maximal support variety g m a closed subset of text proj mathop h bullet g k which is proper even when the dimension of m is not divisible by p

support varieties for the steenrod algebra in recent years the spectrum of the cohomology ring has been a fundamental object of interest in the study of modular group cohomology quillen q1 2 proved that this variety can be expressed as a disjoint union of locally closed varieties involving elementary abelian subgroups avrunin and scott as later generalized quillen s result for varieties associated to modules defined by carlson c1 for restricted lie algebra cohomology no such stratification theorem exists friedlander and parshall fp1 2 have shown that the cohomological varieties in this context can be realized as subvarieties of the given lie algebra when viewed as an affine space fix a prime p and let a be the mod p steenrod algebra the cohomology of a exta fp fp is an object of much interest in algebraic topology one way to study the cohomology ring is to approximate a by finite dimensional sub hopf algebras and then try to compute their cohomology rings by a theorem of wilkerson w the cohomology of any of these finite dimensional hopf algebras is a finitely generated commutative fp algebra hence one can get a great deal of information as in the case of groups and lie algebras by studying the spectrum of this ring one of the goals of this paper will be to show how the aforementioned results for finite groups and restricted lie algebras can be used to study the cohomological varieties for finite dimensional subhopf algebras of the steenrod algebra given a finite dimensional sub hopf algebra b of a let b fp be the spectrum of extb fp fp for a finite dimensional b module m the

traveling salesman problem and tsallis statistics a generalization of the stochastic method of simulated annealing algorithm based on tsallis statistics is proposed this algorithm is considerably faster than the traditional ones in solving the traveling salesman problem acceptable solutions are found in fewer steps and higher temperatures than both the classical and the fast simulated annealings recent developments in solving np complete problems can be incorporated and improve the performance even more

blocks and support varieties we describe the block decomposition of thick subcategories of the stable category of kg modules where g is a finite group and k is a field of characteristic p dividing the order of g of particular interest are the thick subcategories determined by single lines in the support variety among other things we demonstrate a strong connection with linckelmann s theory of block cohomology

the avrunin scott theorem for quantum complete intersections abstract we prove the avrunin scott theorem for quantum complete intersections relating the rank variety of a module to its support variety

complexes and vanishing of cohomology for group schemes abstract completely reducible homology complexes were originally introduced in the context of finite groups and used to study the question of vanishing of cohomology in this paper we study these complexes and the vanishing of cohomology for arbitrary finite dimensional cocommutative hopf algebras applications are later provided for infinitesimal group schemes of reductive and solvable algebraic groups

nilpotence for modules over the mod 2 steenrod algebra ii we imitate much of the work of hopkins and smith in 7 in the context of modules over the mod 2 steenrod algebra a our main result is an analog of the periodicity theorem of 7 implying for example the existence of infinitely many non nilpotent elements in ext a f2 f2

method to solve the travelling salesman problem using the inverse of diffusion process abstract the travelling salesman problem in which the best route between cities to be visited is chosen from a large number of possible routes is reconsidered using the time reversal of physical dynamics e g an inverse of the diffusion process information mediators assigned to every city diffuse as time passes eventually merging into a single peak when the time reversal of the dynamics is performed the single peak splits into two peaks each of which splits into two peaks eventually resulting in peaks at all the cities the hierarchy of the above bifurcations tells us how the distribution of the cities looks as the level of focus changes this scheme is applied to a travelling salesman problem involving 532 us cities the result of which is a 17 longer path than the optimal path

on module varieties and quotient groups let g be a finite group and k be an algebraically closed field of characteristic p 0 all modules considered here are assumed to be finitely generated let e k 1 p ext k k then e k is a finitely generated commutative k algebra and so it has an associated afline variety v k max eg k which is the set of maximal ideals of e k endowed with the zariski topology let m be a kg module and j m be the annihilator in e k of ext fc m m x to extijm m following carlson 4 we define the variety v m of m as the subvariety of v k associated to jg m which is equal to the support of m in z let h be a subgroup of g then the affine map h g v k v k is induced by the restriction map resg h ef k e k in their paper 1 avrunin and scott showed that i has the property vc m v m see theorem 3 1 in 1 i the main purpose of this paper is to give a similar result as the above for the inflation map let h be a normal subgroup of g and m be a k g h module then we can define the affine map agqgih v k p vgih k induced by the inflation map inf e k e k and under the above notation we shall prove the following

tsallis like information measures and the analysis of complex signals abstract a tsallis like information measure that elaborates upon those of the tsallis type is shown to be a rather powerful tool for the analysis of complex non stationary signals as exemplified by the henon map and eegs the ensuing results could be of importance concerning the automatic detection of epileptic spikes

convergence of simulated annealing using the generalized transition probability we prove weak ergodicity of the inhomogeneous markov process generated by the generalized transition probability of tsallis and stariolo under power law decay of the temperature we thus have a mathematical foundation to conjecture convergence of simulated annealing processes with the generalized transition probability to the minimum of the cost function an explicitly solvable example in one dimension is analyzed in which the generalized transition probability leads to a fast convergence of the cost function to the optimal value we also investigate how far our arguments depend upon the specific form of the generalized transition probability proposed by tsallis and stariolo it is shown that a few requirements on analyticity of the transition probability are sufficient to assure fast convergence in the case of the solvable model in one dimension

optimized annealing of traveling salesman problem from the nth nearest neighbor distribution abstract we report a new statistical general property in traveling salesman problem that the n th nearest neighbor distribution of optimal tours verifies with very high accuracy an exponential decay as a function of the order of neighbor n defining the energy function as deviation from this exponential decay which is different to the tour length d in normal annealing processes we propose a distinct highly optimized annealing scheme which is performed in space and d space by turns the simulation results of some standard traveling salesman problems in tsplib95 are presented it is shown that our annealing recipe is superior to the canonical simulated annealing

generalization of shannon s theorem for tsallis entropy by using the assumptions that the entropy must i be a continuous function of the probabilities pi pi 0 1 i only ii be a monotonic increasing function of the number of states w in the case of equiprobability iii satisfy the pseudoadditivity relation sq a b k sq a k sq b k 1 q sq a sq b k2 a and b being two independent systems q r and k a positive constant and iv satisfy the relation sq pi sq pl pm pl qsq pi pl pm qsq pi pm where pl pm 1 pl i 1wlpi and pm i wl 1wpi we prove along shannon s lines that the unique function that satisfies all these properties is the generalized tsallis entropy sq k 1 i 1wpiq q 1

quillen stratification for hochschild cohomology of blocks we decompose the maximal ideal spectrum of the hochschild cohomology ring of a block of a finite group into a disjoint union of subvarieties corresponding to elementary abelian p subgroups of a defect group these subvarieties are described in terms of group cohomological varieties and the alperin broue correspondence on blocks our description leads in particular to a homeomorphism between the hochschild variety of the principal block and the group cohomological variety the proofs require a result of stephen f siegel given in the appendix which states that nilpotency in hochschild cohomology is detected on elementary abelian p subgroups

maximum entropy approach to stretched exponential probability distributions we introduce a nonextensive entropy functionals whose optimization under simple constraints mean values of some standard quantities yields stretched exponential probability distributions which occur in many complex systems the new entropy functional is characterized by a parameter the stretching exponent such that for d 1 the standard logarithmic entropy is recovered we study its mathematical properties showing that the basic requirements for a well behaved entropy functional are verified i e s possesses the usual properties of positivity equiprobability concavity and irreversibility and verifies khinchin axioms except the one related to additivity since s is nonextensive the entropys is shown to be superadditive for 1

study on probability distributions for evolution in modified extremal optimization abstract it is widely believed that the power law is a proper probability distribution being effectively applied for evolution in eo extremal optimization a general purpose stochastic local search approach inspired by self organized criticality and its applications in some np hard problems e g graph partitioning graph coloring spin glass etc in this study we discover that the exponential distributions or hybrid ones e g power laws with exponential cutoff being popularly used in the research of network sciences may replace the original power laws in a modified eo method called self organized algorithm soa and provide better performances than other statistical physics oriented methods such as simulated annealing eo and soa etc from the experimental results on random euclidean traveling salesman problems tsp and non uniform instances from the perspective of optimization our results appear to demonstrate that the power law is not the only proper probability distribution for evolution in eo similar methods at least for tsp the exponential and hybrid distributions may be other choices

multistage extremal optimization for hard travelling salesman problem abstract the adjustable parameters of probability distributions adopted by extremal optimization eo and its modified versions play a critical role in controlling their performances unlike the traditional static probability distribution based strategy this paper presents a novel method called multistage eo to explore the configuration space of hard travelling salesman problem tsp by using different values of the parameters in different stages this method is to optimize with multi start techniques starting from random states in the first stage in all later stages it always selects the best configuration obtained from the last stage as the initial one for optimization in the current stage the superior performance of the proposed method is proved by the experimental tests with the well known hard tsp instances

support varieties for modules over chevalley groups and classical lie algebras let g be a connected reductive algebraic group over an algebraically closed field of characteristic p 0 g 1 be the first frobenius kernel and g f p be the corresponding finite chevalley group let m be a rational g module in this paper we relate the support variety of m over the first frobenius kernel with the support variety of m over the group algebra kg f p this provides an answer to a question of parshall applications of our new techniques are presented which allow us to extend results of alperin mason and janiszczak jantzen and to calculate the dimensions of support varieties for finite chevalley groups

pi supports for modules for finite group schemes we introduce the space g of equivalence classes of points of a finite group scheme g and associate a subspace g m to any g module m our results extend to arbitrary finite group schemes g over arbitrary fields k of positive characteristic and to arbitrarily large g modules the basic results about cohomological support varieties and their interpretation in terms of representation theory in particular we prove that the projectivity of any possibly infinite dimensional g module can be detected by its restriction along points of g unlike the cohomological support variety of a g module m the invariant m 7 g m satisfies good properties for all modules thereby enabling us to determine the thick tensor ideal subcategories of the stable module category of finite dimensional g modules finally using the stable module category of g we provide g with the structure of a ringed space which we show to be isomorphic to the scheme projh g k

modular representation theory of lie algebras on etudie les representations non necessairement restreintes de l algebre universelle enveloppante u 7b g pour une algebre de lie restreinte 7b g

permutation complexes and modular representation theory hc g o iti has two basic functors a rg 2 di rh and a rh 2 rg given by restriction and induction which play an essential role in representation theory an important and elementary class of rg representations is permutation modules which are direct sums of modules indz r obtained by induction from the trivial rh module r for various hs g in another extreme one has rg modules which arise by induction from rh projective modules leading to the concept of relative projectivity and green s theory of vertices and sources cr gr the value of these subcategories of modules in representation theory and related areas is well known in a different direction influenced by algebraic geometry and topology one considers not only module categories but various categories of chain complexes of modules and their cohomologies this culminates in the more recent approaches to representation theory through the theory of derived categories see sc cps and their many references

maximum likelihood estimators for generalized cauchy processes maximum likelihood estimator mle for a generalized cauchy process gcp is studied with the aid of the method of information geometry in statistics our gcp is described by the langevin equation with multiplicative and additive noises the exact expressions of mles are given for the two cases that the two types of noises are uncorrelated and mutually correlated it is shown that the mles for these two gcps are free from divergence even in the parameter region wherein the ordinary moments diverge the mle relations can be regarded as a generalized fluctuation dissipation theorem for the present langevin equation availability of them and of some other higher order statistics is demonstrated theoretically and numerically

the role of constraints within generalized nonextensive statistics the gibbs jaynes path for introducing statistical mechanics is based on the adoption of a specific entropic form sand of physically appropriate constraints for instance for the usual canonical ensemble one adopts i ii ipi 1 and iii ei eigenvalues of the hamiltonian u1 internal energy equilibrium consists in optimizing s1 with regard to pi in the presence of constraints ii and iii within the recently introduced nonextensive statistics i is generalized into sq k 1 ipiq q 1 q 1 reproduces s1 ii is maintained and iii is generalized in a manner which might involve piq in the present effort we analyze the consequences of some special choices for iii and their formal and practical implications for the various physical systems that have been studied in the literature to illustrate some mathematically relevant points we calculate the specific heat respectively associated with a nondegenerate two level system as well as with the classical and quantum harmonic oscillators

a quillen stratification theorem for modules let g be a finite group and k a fixed algebraically closed field of characteristic p 0 if p is odd let hg be the subring of g k consisting of elements of even degree take hg g k if p 2 hg is a finitely generated commutative fc algebra and we let vg denote its associated affine variety max hg if m is any finitely generated fcg module the cohomology variety vg m of m may be defined as the support in vg of the hg module h g m if g is a pgroup and in general as the largest support of g l m where l is any kgmodule a module l with each irreducible fcg module as a direct summand will do 3 d quillen 9 10 proved a number of beautiful results relating vg to the varieties ve associated with the elementary abelian p subgroups e of gf culminating in his stratification theorem this theorem gives a piecewise description of vg in terms of the subgroups e and their normalizers in g some of quillen s results have been extended to the variety vg m associated with a fcg module m 1 4 5 6 7 8 and the work of alperin and evens 2 and avrunin 3 showed that there was at least a surjection iie ve m vg m however the stratification theorem for vg m remained elusive since one still needed to know that a point in vg m in the image of a given ve was in fact in the image of ve m we announce here a proof of the stratification theorem for vg m 9 as well as a proof of a conjecture of j carlson regarding ve m for e an elementary abelian p subgroup we are also able to generalize several of quillen s other results to the module case for h vg be the transfer map induced by restriction on the cohomology rings for an elementary abelian p subgroup e let v ewf e te f f and let km v n p 0othen p k ew tgev o vg m we have the following stratification theorem