linear programming system identification the general nonnegative parameters case abstract by linear programming system identification we mean the problem of estimating the objective function coefficient vector and the technological coefficient matrix a for a linear programming system that best explains a set of input output vectors input vectors are regarded as available resources output vectors are compared to imputed optimal ones by a decisional efficiency measure and a likelihood function is constructed in an earlier paper we obtained results for a simplified version of the problem in this paper we propose a genetic algorithm approach for the general case in which and a are of arbitrary finite dimensions and have nonnegative components a method based on householder transformations and monte carlo integration is used as an alternative to combinatorial algorithms for the extreme points and volumes of certain required convex polyhedral sets the method exhibits excellent face validity for a published test data set in data envelopment analysis

orbit invariants and an application to the baby monster abstract we prove that the minimal base size for the permutation action of the sporadic simple baby monster group b on the cosets of its 7th and 8th maximal subgroup in decreasing order of size is 3 and 2 respectively motivated by the large sizes of these permutation actions we develop new computational methods to prove that an orbit is regular and to show that two orbits are disjoint

on the durfee size of kronecker products of characters of the symmetric group and its double covers abstract we investigate kronecker products of characters for s n and spin products for the double covers s n we give bounds on the durfee size of these products and provide information on the existence of special constituents also all products of durfee size at most 2 are explicitly described

elements of specified order in simple algebraic groups in this paper we let g be a simple algebraic group and r be a natural number and consider the codimension in g of the variety of elements g g satisfying g r 1 we shall obtain a lower bound for this codimension which is independent of characteristic and show that it is attained if g is of adjoint type

representations of the symmetric group are reducible over simply transitive subgroups if the characteristic of f is zero this problem has been solved by saxl 16 an important feature of saxl s result is that a groupg as in the problem above is either 2 transitive or fixes a point i e is contained in some n 1 the caseg n 1 can then be settled using the branching rule and induction on the other hand an explicit list of k transitive groups for k 2 is available which can be used to complete the proof in characteristic zero see 16 for more details from now on we assume that p 0 in this case the problem is important for determining maximal subgroups of finite classical groups 1 13 however the situation is nowmore complicated for example to determine the pairs g d as above withg an one needs the mullineux conjecture 7 2 ifg is intransitive then up to a conjugation it is contained in a standard young subgroup of the form n k k the irreducible restrictions from n to n 1 have been described in 14 see also 11 6 in 11 it is also

monte carlo study of random walks on a 2d gasket fractal in an external field using monte carlo simulation random walks on a two dimensional sierpinski gasket in the presence of an external field were studied it was observed that the random walk motion of a particle displayed a crossover from anomalous diffusion to drift for a non zero bias field and the crossover time tcr was a decreasing function of the external bias field the associated dynamic exponents obtained in a computer simulation agree with the predictions of stinchcombe s scaling treatment 1985

irreducible restrictions of representations of symmetric and alternating groups in small characteristics abstract building on reduction theorems and dimension bounds for symmetric groups obtained in our earlier work we classify the irreducible restrictions of representations of the symmetric and alternating groups to proper subgroups such a classification is known when the characteristic of the ground field is greater than 3 but the small characteristics cases require a substantially more delicate analysis and new ideas our results fit into the aschbacher scott program on maximal subgroups of finite classical groups

resistance and related scaling properties of self avoiding random walks three scaling exponents for random and self avoiding chains are studied by direct renormalisation these describe the end to end resistance of a conducting chain the arc length of the shortest path traceable between the chain ends and the arc length of chain in no loop the scaling behaviours of these quantities are identical to first order in epsilon 4 d d is the space dimension for a long self avoiding chain the authors predict that each one one is proportional to the chain length

random walk on self avoiding walk in external bias diffusion drift and trapping the effect of external bias on random walks rws on self avoiding walks on square lattices in the presence of bridges is studied by monte carlo simulation the qualitative as well as quantitative features of the latter problem are compared and contrasted with those of rws on percolation clusters in the presence of external bias

subgroups of maximal rank in finite exceptional groups of lie type the purpose of this paper is to investigate a large and natural class of maximal subgroups of the finite exceptional groups of lie type which we call subgroups of maximal rank these subgroups play a prominent role both in the classification of local maximal subgroups in 9 theorem 1 and in the reduction theorem for subgroups in 28 theorem 2 in 9 it is shown that any local maximal subgroup of a finite exceptional group of lie type is either a subgroup of maximal rank or one of a small list of exceptions and in 28 using this result it is proved that any maximal subgroup is either of maximal rank or almost simple or in a known list to describe these subgroups we require the following notation let g be a simple adjoint algebraic group over an algebraically closed field k of characteristic p 0 and let o be an endomorphism of g such that l ga is a finite exceptional simple group of lie type over fq where q p let a be a group such that f x l the group aut l is generated by ga together with field and graph automorphisms see 5 38 all of which extend to morphisms of the abstract group g commuting with o thus there is a subgroup x of caut c a such that x x o and so x acts on the set of a stable subsets of g for a a stable subset y we write nx y for the stabilizer in x of y if d is a a stable closed connected reductive subgroup of g containing a maximal torus t of g and m nx d we call m a subgroup of maximal rank in x in this paper we determine the structure and conjugacy classes of those subgroups of maximal rank which are maximal in x

intersections of matrix algebras and permutation representations of psl n q abstract if g is a group h a subgroup of g and a transitive g set we ask under what conditions one can guarantee that h has a regular orbit of size h on here we prove that if psl n q g pgl n q and h is cyclic then h has a regular orbit in every non trivial g set with few exceptions this result is obtained via a mixture of group theoretical and ring theoretical methods let r be the ring of all n n matrices over the finite field f and let z be the subring of scalar matrices we show that if a and m are proper subrings of r containing z and if a is commutative and semisimple then there exists an element x sl n f such that xax 1 m z or n 2 f

high temperature series for scalar field lattice models generation and analysis an implementation of the free embedding scheme for high temperature series generation on the body centered cubic family of lattices in arbitrary dimensiond is described series to order 21 in inverse temperature are tabulated for several scalar field models both for the magnetic susceptibility and for the second moment of the spin correlation function the critical behavior of a family of 3 dimensional double gaussian models which interpolate continuously between the spin 1 2 ising model and the gaussian model is analyzed in detail away from the gaussian model limit using confluent inhomogeneous secondorder differential approximants with our best estimate of the correction to scaling exponent 0 52 0 03 the leading exponents for the susceptibility and correlation length for this family are consistent with universality and are given by 1 237 0 002 and 0 630 0 0015 respectively and 2 0 0359 0 0007

base sizes of primitive groups bounds with explicit constants abstract we show that the minimal base size b g of a finite primitive permutation group g of degree n is at most 2 log g log n 24 this bound is asymptotically best possible since there exists a sequence of primitive permutation groups g of degrees n such that b g 2 log g log n 2 and b g is unbounded as a corollary we show that a primitive permutation group of degree n that does not contain the alternating group alt n has a base of size at most max n 25

a maximum decisional efficiency estimation principle this paper proposes a systematic approach to certain parameter estimation problems relevant to applied optimization models a context specific measure of decision maker performance called decisional efficiency is defined as a function of the unknown parameter vector the values of this measure are considered to be distributed according to a performance density then a principle of maximum decisional efficiency mde is proposed and its relationship to the maximum likelihood principle of statistics is discussed the principle is first illustrated on a problem of group ideal point estimation next estimation of the ratio of ordering and holding costs in inventories managed by the eoq model is considered the results in both these examples are intuitively appealing suggesting face validity of the principle a more detailed illustration is developed for the problem of deriving a consensus scoring model for credit applicants which combines the data of more than one loan officer

fuchsian groups finite simple groups and representation varieties let be a fuchsian group of genus at least 2 at least 3 if is non oriented we study the spaces of homomorphisms from to finite simple groups g and derive a number of applications concerning random generation and representation varieties precise asymptotic estimates for hom g are given implying in particular that as the rank of g tends to infinity this is of the form g 1 o 1 where is the measure of we then prove that a randomly chosen homomorphism from to g is surjective with probability tending to 1 as g combining our results with lang weil estimates from algebraic geometry we obtain the dimensions of the representation varieties text hom gamma bar g where bar g is gl n k or a simple algebraic group over k an algebraically closed field of arbitrary characteristic a key ingredient of our approach is character theory involving the study of the zeta function g s 1 s where the sum is over all irreducible complex characters of g

order disorder displacive crossover in a structural phase transition model the authors write the partition function of the double gaussian model which is representative of the lambda phi 4 class hamiltonians with unbounded doubly degenerate local potentials exactly as the product of the partition function of a gaussian model and the partition function of a spin 1 2 ising model on the basis of this result they are able to determine the nature and location of the critical points of this model it also follows that the block spin renormalisation group flows in the entire high temperature region converge to a gaussian model fixed point

representations of the symmetric group which are irreducible over subgroups let f be an algebraically closed field of characteristic p and n be the symmetric group on n letters in this paper we classify all pairs g d where d is an irreducible f n module of dimension greater than 1 and g is a proper subgroup of n such that the restriction d g is irreducible provided p 3

irreducible restrictions of representations of symmetric groups in small characteristics reduction theorems we study irreducible restrictions of modules over symmetric groups to subgroups we get reduction results which substantially restrict the classes of subgroups and modules for which this is possible such results are known when the characteristic of the ground field is greater than 3 but the small characteristics cases require a substantially more delicate analysis and new ideas this work fits into the aschbacher scott program on maximal subgroups of finite classical groups

genetic search over probability spaces abstract this paper proposes two new crossover operators for searching over discrete probability spaces the design of the operators is considered in the light of recent theoretical insights into genetic search provided by forma analysis a non trivial test problem in enforcing coherency of probability estimates in cross impact analysis highlights the utility of the designed operators the presented operators will be useful for a variety of probability fitting and optimization applications

kronecker products characters partitions and the tensor square conjectures abstract we study the remarkable saxl conjecture which states that tensor squares of certain irreducible representations of the symmetric groups s n contain all irreducibles as their constituents our main result is that for sufficiently large n they contain representations corresponding to young diagrams of hooks two row and diagrams obtained from hooks and two rows by adding a finite number of squares for that we develop a new sufficient condition for the positivity of kronecker coefficients in terms of characters and apply this tool using combinatorics of rim hook tableaux in combination with known results on unimodality of certain partition functions we also present connections and speculations on random characters of s n

gaussian smearing of spin weight functions in models of phase transitions by smearing with a gaussian distribution a family of single spin weight functions is constructed which interpolates between an arbitrary single spin distribution and a pure gaussian the observation of baker and bishop 1982 concerning the factorisability of the partition function of the double gaussian model remains valid for all gaussian smeared models the effects of smearing gaussian and spherical weight functions are studied in further detail

bases of primitive linear groups abstract we correct and improve a result in 3 giving the structure of finite primitive linear groups of unbounded base size this confirms a well known conjecture of pyber on base sizes of primitive permutation groups in the case of affine groups whose associated linear group is primitive

arithmetic results on orbits of linear groups the first four authors acknowledge the support of an arc discovery grant the first author acknowledges the support of an australian research fellowship the third author acknowledges the support of a federation fellowship the fifth author acknowledges the support of the nsf grants dms 0901241 and dms 1201374

field induced drift and trapping in percolation networks the authors study the effects of a bias producing external field on a random walk on the infinite cluster in the percolation problem there are two competing physical effects drift and trapping which result in a drift velocity nu which rises and then falls as the field increases they study these effects on a one dimensional lattice with random length branches and on the diluted bethe lattice they calculate nu in the first model with a maximum allowed length for each branch in the limit that this cutoff length becomes infinite they find that the velocity vanishes identically above a finite critical value of the field for the bethe lattice they derive an upper bound on the critical field which varies as p pc 1 2 as the percolation concentration pc is approached in the one dimensional model they also investigate the anomalous regime in which the velocity vanishes they discuss the distribution of steady state times required to traverse n sites and find that it can be described in terms of a stable distribution of index x with superimposed oscillations the index x of the stable distribution is given by l xi where xi is a characteristic branch length and l is a bias induced length which describes the exponential buildup of the steady state density of particles towards the end of a branch

maximal overgroups of singer elements in classical groups abstract in this paper we use the results of a recent paper by guralnick penttila praeger and saxl proc london math soc 78 1999 167 214 to calculate an explicit list of the maximal overgroups of the singer elements in the finite special linear general unitary special unitary symplectic and minus type orthogonal groups

representations of the general linear groups which are irreducible over subgroups we classify all triples g v h such that sl n q leq g leq gl n q v is a representation of g of dimension greater than one over an algebraically closed field bbb f of characteristic prime to q and h is a proper subgroup of g such that the restriction v downarrow h is irreducible this problem is a natural part of the aschbacher scott program on maximal subgroups in finite classical groups

simple groups probabilistic methods and a conjecture of kantor and lubotzky abstract we prove that a randomly chosen involution and a randomly chosen additional element of a finite simple groupggenerategwith probability 1 as g this confirms a conjecture of kantor and lubotzky applications and related results are derived for example we show that except for the suzuki groups and finitely many possible other exceptions all finite simple groups can be generated by two elements one of which has order 3 we also obtain sharp estimates on the probabilityp g of generating a finite simple group of exceptional lie typegby two randomly chosen elements this complements analogous estimates of babai and kantor for alternating and classical groups denoting bym g the minimal index of a proper subgroup of a finite simple groupg we conclude in particular thatm g 1 p g is bounded between two positive absolute constants

base sizes for simple groups and a conjecture of cameron let g be a permutation group on a finite set a base for g is a subset b with pointwise stabilizer in g that is trivial we write b g for the smallest size of a base for g in this paper we prove that b g 6 if g is an almost simple group of exceptional lie type and is a primitive faithful g set an important consequence of this result when combined with other recent work is that b g 7 for any almost simple group g in a non standard action proving a conjecture of cameron the proof is probabilistic and uses bounds on fixed point ratios

monte carlo study of biased diffusion at the percolation threshold computer simulations confirm dhar s prediction ibid vol 17 p l257 1984 that the asymptotic exponent for the rms distance against time relation is zero right at the percolation threshold if a particle diffuses under the influence of a constant force in a random medium for intermediate times and weak force the exponent for the mean displacement as a function of time in the direction of the force confirms the prediction of ohtsuki and keyes phys rev lett vol 52 p 1177 1984

finite primitive permutation groups and regular cycles of their elements we conjecture that if g is a finite primitive group and if g is an element of g then either the element g has a cycle of length equal to its order or for some r m and k the group gsym m wrsym r preserving a prod uct structure of r direct copies of the natural action of sym m or alt m on k sets in this paper we reduce this conjecture to the case that g is an almost simple group with socle a classical group

behavioral estimation of mathematical programming objective function coefficients we propose a parameter estimation method based on what we call the minimum decisional regret principle we focus on mathematical programming models with objective functions that depend linearly on costs or other parameters the approach is illustrated for cost estimation in production planning using linear programming models the method uses past planning data to estimate costs that are otherwise difficult to estimate we define a monetary measure of distance between observed plans and optimal ones called decisional regret the proposed estimation algorithm finds parameter values for which the associated optimal plans are as near as possible to the observed ones on average such techniques may be called behavioral estimation because they are based on the observed planning or decision making behavior of managers or firms two numerical illustrations are given a supporting hyperplane algorithm is used to solve the estimation model a method is proposed for obtaining range estimates of the parameters when multiple alternative estimates exist we also propose a new validation approach for this estimation principle which we call the target mode agreement criterion

data driven inverse optimization with imperfect information in data driven inverse optimization an observer aims to learn the preferences of an agent who solves a parametric optimization problem depending on an exogenous signal thus the observer seeks the agent s objective function that best explains a historical sequence of signals and corresponding optimal actions we formalize this inverse optimization problem as a distributionally robust program minimizing the worst case risk that the estimated decision i e the decision implied by a particular candidate objective differs from the agent s actual response to a random signal we show that our framework offers attractive out of sample performance guarantees for different prediction errors and that the emerging inverse optimization problems can be reformulated as or approximated by tractable convex programs when the prediction error is measured in the space of objective values a main strength of the proposed approach is that it naturally generalizes to situations where the observer has imperfect information e g when the agent s true objective function is not contained in the space of candidate objectives when the agent suffers from bounded rationality or implementation errors or when the observed signal response pairs are corrupted by measurement noise

generalized inverse multiobjective optimization with application to cancer therapy we generalize the standard method of solving inverse optimization problems to allow for the solution of inverse problems that would otherwise be ill posed or infeasible in multiobjective linear optimization given a solution that is not a weakly efficient solution to the forward problem our method generates objective function weights that make the given solution a near weakly efficient solution our generalized inverse optimization model specializes to the standard model when the given solution is weakly efficient and retains the complexity of the underlying forward problem we provide a novel interpretation of our inverse formulation as the dual of the well known benson s method and by doing so develop a new connection between inverse optimization and pareto surface approximation techniques we apply our method to prostate cancer data obtained from princess margaret cancer centre in toronto canada we demonstrate that clinically acceptable treatments can be generated using a small number of objective

on restrictions of modular spin representations of symmetric and alternating groups let f be an algebraically closed field of characteristic p and h be an almost simple group or a central extension of an almost simple group an important problem in representation theory is to classify the subgroups g of h and fh modules v such that the restriction v g is irreducible for example this problem is a natural part of the program of describing maximal subgroups in finite classical groups in this paper we investigate the case of the problem where h is the schur s double cover n or s n

anisotropy in field assisted diffusion on a gasket fractal the random walk on the two dimensional gasket fractal has been studied with various forms of constant bias fields applied using the monte carlo method crossover from anomalous diffusion to drift was observed in the horizontal and upward bias fields while crossover from anomalous to normal diffusion was found in the downward bias field the scaling relation r bs t approximately tkf bstk was confirmed and the scaling exponent of f x approximately xbeta at large x was obtained as beta 1 175 or 0 004 for the horizontal bias field and beta 0 319 or 0 002 for the downward bias field in good agreement with the theoretical work by parrondo et al 1990

regular orbits of cyclic subgroups in permutation representations of certain simple groups if h acts on then an h orbit is regular if its cardinality is h the alternating groups already in their natural representation do not have the property of the theorem hence the exception the other known simple groups with a doubly transitive permutation representation are psl n q sp 2n 2 two representations u3 q b2 q g2 q and a short list of sporadic examples which are reproduced in section 5 if one assumes the completeness of the classification of finite simple groups then these are all doubly transitive representations of finite simple groups and the word known can be omitted in the theorem in our paper 8 the theorem 1 1 was proved for psl n q here we consider the remaining doubly transitive groups the same method can in

representations of the alternating group which are irreducible over subgroups ii nsf dms 1161094 dms 0901241 dms 1201374 humboldt foundation simons foundation 204181 simons foundation fellowship 305247

random walk on self avoiding walk a model for conductivity of linear polymers random walks on self avoiding walks saws are studied using monte carlo techniques on a square lattice with nearest neighbour hopping along the chain and between saw points which are nearest neighbours on the embedding lattice the average of the square of the end to end distance for random walks of t steps on saws of length n is fitted to the scaling forms rt2 varies as ndelta tk for t or approximately ntheta where theta approximately 2 nu s k nu s being the average end to end distance exponent for saws the observed value of the exponent delta is supported by the authors real space renormalisation group result for the conductivity of saw chains the exponent k has been related to the effective fractal dimension of the saw chain

ring theoretic aspects of quandles abstract we associate to every quandle x and an associative ring with unity k a nonassociative ring k x following 3 the basic properties of such rings are investigated in particular under the assumption that the inner automorphism group i n n x acts orbit 2 transitively on x a complete description of right or left ideals is provided the complete description of right ideals for the dihedral quandles r n is given it is also shown that if for two quandles x and y the inner automorphism groups act 2 transitively and k x is isomorphic to k y then the quandles are of the same partition type however we provide examples when the quandle rings k x and k y are isomorphic but the quandles x and y are not isomorphic these examples answer some open problems in 3

on a conjecture of g e wall abstract we prove that if g is a finite almost simple group having socle of lie type of rank r then the number of maximal subgroups of g is at most c r 2 3 g where c is an absolute constant this verifies a conjecture of wall for groups of sufficiently large rank using this we prove that any finite group g has at most 2 c g 3 2 maximal subgroups

walks trials and polymers with loops lattice models interpolating between free and self avoiding random walks are investigated generating functions are constructed for k tolerant walks various trail problems etc for trail problems the effective field theory describing the global behaviour is analysed in the vicinity of the upper critical dimension dc 4 their asymptotic large scale behaviours are the same as those of the self avoiding walk arguments are presented to support the same conclusion for much more general classes of walks including k tolerant walks one of the models exhibits a new tricritical point of order epsilon 1 2 if the fugacity for crossing is increased

multiplicity free kronecker products of characters of the symmetric groups we provide a classification of multiplicity free inner tensor products of irreducible characters of symmetric groups thus confirming a conjecture of bessenrodt concurrently we classify all multiplicity free inner tensor products of skew characters of the symmetric groups we also provide formulae for calculating the decomposition of these tensor products

two point stabilisers of partition actions of linear groups a partition of a kl dimensional vector space v is a set of l subspaces each of dimension k such that their direct sum is the original space v in this paper we show that unless l 2 the action of a group l such that psl v l pgl v on the set of partitions of v into l subspaces of dimension k is base two there exist two partitions v and w such that l v w 1 we will also show that given any finite group g there exist k l and partitions v w such that l v w g these results complement work the author has done with partition actions of the symmetric groups

fixed point ratios in actions of finite classical groups iii abstract this is the first in a series of four papers on fixed point ratios in actions of finite classical groups our main result states that if g is a finite almost simple classical group and is a faithful transitive non subspace g set then either fpr x x g 1 2 for all elements x g of prime order or g is one of a small number of known exceptions here fpr x denotes the proportion of points in which are fixed by x in this introductory note we present our results and describe an application to the study of minimal bases for primitive permutation groups a further application concerning monodromy groups of covers of riemann surfaces is also outlined

on almost extreme components in kronecker products of characters of the symmetric groups abstract using a recursion formula due to dvir we obtain information on maximal and almost maximal components in kronecker products of characters of the symmetric groups this is applied to confirm a conjecture made by bessenrodt and kleshchev in 1999 which classifies all such kronecker products with only three or four components