coherent states for the unitary symplectic group we present an explicit construction of coherent states for an arbitrary irreducible representation of the unitary symplectic group usp 4 three different families of coherent states are obtained corresponding to the subgroups u 1 u 1 u 2 and su 2 su 2 the symplectic structure on the manifold of coherent states is obtained and canonical coordinates are used to express the classical limit of quantum observables one of the families is seen to provide a trivial classical limit

how well does the owa operator represent real preferences we present the results of an empirical study in which we analyze the ability of the ordered weighted average owa operator to model actual preferences in a multi attribute ranking task we compare the owa to a competing model simple additive weighting saw and we also study whether its characteristic feature the ability to represent different attitudes toward compensation among attributes is reflected in the preferences provided by subjects we find that in general the owa model fits slightly less well to empirical data subjects whose preferences are better explained by the saw model are also more consistent in their choice behavior our results furthermore indicate that preferences of most subjects are not fully compensatory thus the ability of the owa operator to represent different attitudes toward compensation can be a useful feature in modeling actual preferences the structure of the weights estimated for the owa operator also suggests that it might provide a good approximation to certain types of decision heuristics

bi matching a new preference assessment method to reduce compatibility effects preference models and utility functions are often assessed by eliciting value trade offs among attributes prior research has shown that trade off judgments can be biased in systematic ways for example the attribute which is used as response receives more relative subjective weight i e the so called scale compatibility effects tversky et al tversky a s sattath p slovic 1988 contingent weighting in judgment and choice psych rev 95 371 384 this paper proposes a new procedure to elicit value trade offs called bidimensional matching or bi matching designed to alleviate this effect bi matching differs from traditional trade off judgments in that both attributes are adjusted simultaneously to reach indifference judgments bi matching is compared with simple matching and choice in four experimental studies to measure preferences for lotteries and riskless multiattribute alternatives the main results are 1 bi matching produces trade offs intermediate between those derived from matching on the more important attribute and matching on the less important attribute although closer to the former 2 the trade offs derived from choice reflect more relative weight on the more important dimension than those from bi matching 3 bi matching appears to reduce response error compared to standard matching these results are generally consistent with theoretical predictions we discuss the normative question of which preference assessment method is preferable the current results as a whole and the built in features of the bi matching procedure already position this elicitation method as a worthwhile alternative to traditional methods for helping decision makers introspect and construct their value trade offs

lottery equivalents reduction of the certainty effect problem in utility assessment this note describes a simple procedure for assessing utility functions which avoids many difficulties of the standard techniques the conventional methods suffer from at least three drawbacks they 1 generate utility functions that depend on the probability levels used 2 chain responses from one question to the next so that any bias is propagated and even magnified and 3 change ranges and reference points constantly introducing range effects and other distortions noting the evidence linking the dependence of utility functions on the certainty effect our method 1 compares lotteries with other lotteries rather than certain amounts 2 does not chain responses and 3 consistently uses elementary lotteries which control for range and reference points experimental work supports the proposed procedure

walks on graphs and their connections with tensor invariants and centralizer algebras abstract the number of walks of k steps from the node 0 to the node on the mckay quiver determined by a finite group g and a g module v is the multiplicity of the irreducible g module g in the tensor power v k and it is also the dimension of the irreducible module labeled by for the centralizer algebra z k g end g v k this paper explores ways to effectively calculate that number using the character theory of g we determine the corresponding poincare series the special case 0 gives the poincare series for the tensor invariants t v g k 0 v k g and a tensor analog of molien s formula for polynomial invariants when g is abelian we show that the exponential generating function for the number of walks is a product of generalized hyperbolic functions many graphs such as circulant graphs can be viewed as mckay quivers and the methods presented here provide efficient ways to compute the number of walks on them

matrix elements for the symplectic sp 4 lie algebra the closed gelfand tsetlin type formulae are constructed in this paper for the matrix elements of the symplectic sp 4 lie algebra in an arbitrary irreducible representation using the reduction chain sp 4 sp 2 sp 2 all resulting formulae for the matrix elements were obtained by directly solving the cartan weyl commutation relations of the sp 4 algebra

chip firing on dynkin diagrams and mckay quivers this paper establishes new connections between the representation theory of finite groups and sandpile dynamics two classes of avalanche finite matrices and their critical groups integer cokernels are studied from the viewpoint of chip firing sandpile dynamics namely the cartan matrices of finite root systems and the mckay cartan matrices for finite subgroups g of general linear groups in the root system case the recurrent and superstable configurations are identified explicitly and are related to minuscule dominant weights in the mckay cartan case for finite subgroups of the special linear group the cokernel is related to the abelianization of the subgroup g in the special case of the classical mckay correspondence the critical group and the abelianization are shown to be isomorphic

lie superalgebras and the multiplet structure of the genetic code ii branching schemes continuing our attempt to explain the degeneracy of the genetic code using basic classical lie superalgebras we present the branching schemes for the typical codon representations typical 64 dimensional irreducible representations of basic classical lie superalgebras and find three schemes that do reproduce the degeneracies of the standard code based on the orthosymplectic algebra osp 5 2 and differing only in details of the symmetry breaking pattern during the last step

static spherically symmetric solutions of the einstein yang mills equations we study the global behaviour of static spherically symmetric solutions of the einstein yang mills equations with gauge groupsu 2 our analysis results in three disjoint classes of solutions with a regular origin or a horizon the 3 spaces t const of the first generic class are compact and singular the second class consists of an infinite family of globally regular resp black hole solutions the third type is an oscillating solution which although regular is not asymptotically flat

a parameter free elicitation of the probability weighting function in medical decision analysis an important reason why people violate expected utility theory is probability weighting previous studies on the probability weighting function typically assume a specific parametric form exclude heterogeneity in individual preferences and exclusively consider monetary decision making this study presents a method to elicit the probability weighting function in rank dependent expected utility theory that makes no prior assumptions about the functional form of the probability weighting function we use both aggregate and individual subject data thereby allowing for heterogeneity of individual preferences and we examine probability weighting in a new domain medical decision making there is significant evidence of probability weighting both at the aggregate and at the individual subject level the modal probability weighting function is inverse s shaped displaying both lower subadditivity and upper subadditivity probability weighting is in particular relevant at the boundaries of the unit interval compared to studies involving monetary outcomes we generally find more elevation of the probability weighting function the robustness of the empirical findings on probability weighting indicates its importance ignoring probability weighting in modeling decision under risk and in utility measurement is likely to lead to descriptively invalid theories and distorted elicitations

enumerations of the hamiltonian walks on a cubic sublattice a massively parallel supercomputer was used to exhaustively enumerate all of the hamiltonian walks for simple cubic sublattices of four different sizes up to 3 4 4 the behaviour of the logarithm of the number of walks was found to be linear in the number of vertices in the lattice the linear fit is shown to agree also with the asymptotic limit of the flory mean field theoretical estimate thus we suggest that the fit obtained yields the number of walks for any size fragment of the cubic lattice to logarithmic accuracy the significance of this result to the validity of polymer models is also discussed

a generalized birkhoff theorem for the einstein yang mills system some results of a systematic study of the coupled einstein yang mills eym equations for arbitrary gauge groups are presented herein in a first step a group theoretical analysis of spherically symmetric eym fields is given this will lead to a concise description of a large class of principal bundles for which the spherically symmetric solutions of the eym equations have to be static generalized birkhoff theorem and the metric must be of the reissner nordstro m type

analysis of the static spherically symmetric su n einstein yang mills equations the singular boundary value problem that arises for the static spherically symmetricsu n einstein yang mills equations in the so called magnetic case is analyzed among the possible actions ofsu 2 on asu n principal bundles over space time there is one which appears to be the most natural if one assumes that no electrostatic type component is present in the yang mills fields and the gauge is suitably fixed a set ofn 1 second order and two first order differential equations is obtained forn 1 gauge potentials and two metric components as functions of the radial distance this system generalizes the one for the casen 2 that leads to the discrete series of the bartnick mckinnon and the corresponding black hole solutions it is highly nonlinear and singular atr and atr 0 or at the black hole horizon but it is known to admit at least one series of discrete solutions which are scaled versions of then 2 case in this paper local existence and uniqueness of solutions near these singular points is established which turns out to be a nontrivial problem for generaln moreover a number of new numerical soliton i e globally regular numerical solutions of thesu 3 eym equations are found that are not scaledn 2 solutions

lie superalgebras and the multiplet structure of the genetic code i codon representations it has been proposed by hornos and hornos phys rev lett 71 4401 4404 1993 that the degeneracy of the genetic code i e the phenomenon that different codons base triplets of dna are transcribed into the same amino acid may be interpreted as the result of a symmetry breaking process in their work this picture was developed in the framework of simple lie algebras here we explore the possibility of explaining the degeneracy of the genetic code using basic classical lie superalgebras whose representation theory is sufficiently well understood at least as far as typical representations are concerned in the present paper we give the complete list of all typical codon representations typical 64 dimensional irreducible representations whereas in the second part we shall present the corresponding branching rules and discuss which of them reproduce the multiplet structure of the genetic code

ultrametrics in the genetic code and the genome abstract ultrametric approach to the genetic code and the genome is considered and developed p adic degeneracy of the genetic code is pointed out ultrametric tree of the codon space is presented it is shown that codons and amino acids can be treated as p adic ultrametric networks ultrametric modification of the hamming distance is defined and noted how it can be useful ultrametric approach with p adic distance is an attractive and promising trend towards investigation of bioinformation

parameter free elicitation of utility and probability weighting functions this paper proposes a two step method to successively elicit utility functions and decision weights under rank dependent expected utility theory and its more descriptive version cumulative prospect theory the novelty of the method is that it is parameter free and thus elicits the whole individual preference functional without imposing any prior restriction this method is used in an experimental study to elicit individual utility and probability weighting functions for monetary outcomes in the gain and loss domains concave utility functions are obtained for gains and convex utility functions for losses the elicited weighting functions satisfy upper and lower subadditivity and are consistent with previous parametric estimations the data also show that the probability weighting function for losses is more elevated than for gains

static spherically symmetric solutions of the so 5 einstein yang mills equations globally regular ie asymptotically flat and regular interior spher ically symmetric and localised particle like solutions of the coupled ein stein yang mills eym equations with gauge group su 2 have been known for more than 20 years yet their properties are still not well understood spher ically symmetric yang mills fields are classified by a choice of isotropy genera tor and so 5 is distinguished as the simplest model with a non abelian resid ual little group su 2 u 1 and which admits globally regular particle like solutions we exhibit an algebraic gauge condition which normalises the resid ual gauge freedom to a finite number of discrete symmetries this generalises the well known reduction to the real magnetic potential w r t in the original su 2 ym model reformulating using gauge invariant polynomials dramat ically simplifies the system and makes numerical search techniques feasible we find three families of embedded su 2 eym equations within the so 5 system one of which was first detected only within the gauge invariant polyno mial reduced system numerical solutions representing mixtures of the three su 2 sub systems are found classified by a pair of positive integers

invariant polynomials and molien functions the molien function associated with a finite dimensional representation of a compact lie group is a useful tool in representation theory because it acts as a generating function for counting the number of invariant polynomials on the representation space the main purpose of this paper is to introduce a more general and apparently new generating function which in the same sense counts not only the number of invariant real polynomials in a real representation or the number of invariant complex polynomials in a complex representation as a function of their degree but encodes the number of invariant real polynomials in a complex representation as a function of their bidegree the first and second component of this bidegree being the number of variables in which the polynomial is holomorphic and antiholomorphic respectively this is obviously an additional and non trivial piece of information for representations which are truly complex i e not self conjugate or are pseudo real but it provides ad

the structure of spherically symmetric su n yang mills fields we summarize the algebraic structure of spherically symmetric yang mills potentials for a general compact gauge group and investigate the particular case of gauge groups with lie algebra su n in detail we develop techniques that lead to a complete classification of the possible spherical symmetry ansatze including descriptions of the reduced gauge group z the space of magnetic potentials h and for those ansatze that admit extensions across the symmetry axis a description of the space of vacuum potentials h0 and its little group z0 these results are illustrated by listing all irreducible models for su n n 6

on enumeration of hilbert like curves we present an analytical method to explicitly enumerate all self similar space filling curves similar to hilbert curve and find their number grows with length l as this presents a first step in the exact characterization of the crumpled globule ensemble relevant for dense topologically constrained polymer matter and dna folding moreover this result gives a stringent lower bound on the number of hamiltonian walks on a simple cubic lattice additionally we compute the exact number of crumpled curves with arbitrary endpoints and the closed crumpled curves on a cube

finite size scaling of the density of zeros of the partition function in first and second order phase transitions the finite size scaling form for the density of zeros of the partition function in first and second order phase transitions is derived using the finite size scaling of the density of zeros the order of a phase transition can be easily determined and the order parameter calculated from finite size data we illustrate the scaling theory using exact values for the zeros of the partition function of the two dimensional ising model in the complex magnetic field plane

exact enumeration of hamiltonian circuits walks and chains in two and three dimensions we present an algorithm for enumerating exactly the number of hamiltonian chains on regular lattices in low dimensions by definition these are sets of k disjoint paths whose union visits each lattice vertex exactly once the well known hamiltonian circuits and walks appear as the special cases k 0 and k 1 respectively in two dimensions we enumerate chains on l l square lattices up to l 12 walks up to l 17 and circuits up to l 20 some results for three dimensions are also given using our data we extract several quantities of physical interest

making descriptive use of prospect theory to improve the prescriptive use of expected utility this paper proposes a quantitative modification of standard utility elicitation procedures such as the probability and certainty equivalence methods to correct for commonly observed violations of expected utility traditionally decision analysis assumes expected utility not only for the prescriptive purpose of calculating optimal decisions but also for the descriptive purpose of eliciting utilities however descriptive violations of expected utility bias utility elicitations that such biases are effective became clear when systematic discrepancies were found between different utility elicitation methods that under expected utility should have yielded identical utilities as it is not clear how to correct for these biases without further knowledge of their size or nature most utility elicitations still calculate utilities by means of the expected utility formula this paper speculates on the biases and their sizes by using the quantitative assessments of probability transformation and loss aversion suggested by prospect theory it presents quantitative corrections for the probability and certainty equivalence methods if interactive sessions to correct for biases are not possible then the authors propose to use the corrected utilities rather than the uncorrected ones in prescriptions of optimal decisions in an experiment the discrepancies between the probability and certainty equivalence methods are removed by the authors proposal

invariants equivariants and characters in symmetric bifurcation theory in the analysis of stability in bifurcation problems it is often assumed that the appropriate reduced equations are in normal form in the presence of symmetry the truncated normal form is an equivariant polynomial map therefore the determination of invariants and equivariants of the group of symmetries of the problem is an important step in general these are hard problems of invariant theory and in most cases they are tractable only through symbolic computer programs nevertheless it is desirable to obtain some of the information about invariants and equivariants without actually computing them for example the number of linearly independent homogeneous invariants or equivariants of a certain degree generating functions for these dimensions are generally known as molien functions we obtain formulae for the number of linearly independent homogeneous invariants or equivariants for hopf bifurcation in terms of characters we also show how to construct molien functions for invariants and equivariants for hopf bifurcation our results are then applied to the computation of the number of invariants and equivariants for hopf bifurcation for several finite groups and the continuous group o 3

integrability versus non integrability hard hexagons and hard squares compared in this paper we compare the integrable hard hexagon model with the nonintegrable hard squares model by means of partition function roots and transfer matrix eigenvalues we consider partition functions for toroidal cylindrical and free free boundary conditions up to sizes 40 40 and transfer matrices up to 30 sites for all boundary conditions the hard squares roots are seen to lie in a bounded area of the complex fugacity plane along with the universal hard core line segment on the negative real fugacity axis the density of roots on this line segment matches the derivative of the phase difference between the eigenvalues of largest and equal moduli and exhibits much greater structure than the corresponding density of hard hexagons we also study the special point z 1 of hard squares where all eigenvalues have unit modulus and we give several conjectures for the value at z 1 of the partition functions

algebraic model for the evolution of the genetic code a search for symmetries based on the compact simple lie algebras is performed to verify to what extent the genetic code is a manifestation of some underlying symmetry an exact continuous symmetry group cannot be found to reproduce the present genetic code however a unique approximate symmetry group is compatible with codon assignment for the fundamental amino acids and the termination codon in order to obtain the actual genetic code the symmetry must be slightly broken

probability versus certainty equivalence methods in utility measurement are they equivalent certainty equivalence ce and probability equivalence pe methods are the two most frequently used procedures for constructing von neumann morgenstern utility functions in this paper we compare these methods experimentally using a two stage within subject design by asking subjects first for a ce judgment and later for a related pe judgment or vice versa a consistency test is devised which any deterministic expectation model including those allowing probability transformations should meet using four related experiments this consistency test is applied separately to gain and loss questions and to the two sequences of linked equivalence judgments namely ce pe and pe ce the empirical results reveal serious inconsistencies between the ce and pe responses for each of the four experiments the extent of discrepancy depends strongly on the subject s initial risk attitude and whether the gain or loss domain is examined to explain the complex pattern of results the second part of the paper explores several plausible hypotheses the first of these concerns the role of random error in either the responses or the utility function itself it is shown that both can lead to bias although not of a type that could explain our results thereafter shifts in reference points are examined a particular reframing of the pe response mode is postulated in which a pure gamble is psychologically translated into a mixed one leading to increased risk aversion this hypothesis which is also supported by other evidence offers a complete and simple explanation of the results finally several other behavioral hypotheses are examined after developing a weighted average model to simulate them they concern anchoring effects differences in salience between the probability and outcome dimensions strategic misrepresentation regret or rejoice influences and endowment effects although each hypothesis predicts some type of bias none of these five could singly explain the particular pattern of bias observed in general the study demonstrates 1 that serious discrepancies exist between the ce and pe methods of utility measurement 2 that the particular results are incompatible with traditional deterministic choice models 3 how random response errors through propagation can induce systematic biases in the utility function 4 that reframing of the pe mode offers a simple reference shift explanation of the complex findings and 5 how various heuristics and biases can be operationalized and simulated to assess their effects on utility measurement as such this study represents a further step toward a systematic investigation of response mode biases in utility measurement

self avoiding walks crossing a square we study a restricted class of self avoiding walks saws which start at the origin 0 0 end at l l and are entirely contained in the square 0 l 0 l on the square lattice z 2 the number of distinct walks is known to grow as l 2 o l 2 we estimate 1 744 550 0 000 005 as well as obtaining strict upper and lower bounds 1 628 1 it grows as l 2 h ere is the growth constant of unconstrained saws in z 2 f orx 1 we provide numerical evidence but no proof that the average walk length grows as l 4 3 another problem we study is that of saws as described above that pass through the central vertex of the square we estimate the proportion of such walks as a fraction of the total and find it to be just below 80 of the total number of saws we also consider hamiltonian walks under the same restriction they are known to grow as l 2 o l2

tensor product markov chains abstract we analyze families of markov chains that arise from decomposing tensor products of irreducible representations this illuminates the burnside brauer theorem for building irreducible representations the mckay correspondence and pitman s 2 m x theorem the chains are explicitly diagonalizable and we use the eigenvalues eigenvectors to give sharp rates of convergence for the associated random walks for modular representations the chains are not reversible and the analytical details are surprisingly intricate in the quantum group case the chains fail to be diagonalizable but a novel analysis using generalized eigenvectors proves successful

secondary structures in long compact polymers compact polymers are self avoiding random walks that visit every site on a lattice this polymer model is used widely for studying statistical problems inspired by protein folding one difficulty with using compact polymers to perform numerical calculations is generating a sufficiently large number of randomly sampled configurations we present a monte carlo algorithm that uniformly samples compact polymer configurations in an efficient manner allowing investigations of chains much longer than previously studied chain configurations generated by the algorithm are used to compute statistics of secondary structures in compact polymers we determine the fraction of monomers participating in secondary structures and show that it is self averaging in the long chain limit and strictly less than 1 comparison with results for lattice models of open polymer chains shows that compact chains are significantly more likely to form secondary structure

local existence proofs for the boundary value problem for static spherically symmetric einstein yang mills fields with compact gauge groups we prove local existence and uniqueness of static spherically symmetric solutions of the einstein yang mills eym equations for an arbitrary compact semisimple gauge group in the so called regular case by this we mean the equations obtained when the rotation group acts on the principal bundle on which the yang mills connection takes its values in a particularly simple way the only one ever considered in the literature the boundary value problem that results for possible asymptotically flat soliton or black hole solutions is very singular and just establishing that local power series solutions exist at the center and asymptotic solutions at infinity amounts to a nontrivial algebraic problem we discuss the possible field equations obtained for different group actions and solve the algebraic problem on how the local solutions depend on initial data at the center and at infinity

mckay centralizer algebras for a finite subgroup g of the special unitary group su2 we study the centralizer algebra zk g endg v k of g acting on the k fold tensor product of its defining representation v c2 the mckay corre spondence relates the representation theory of these groups to an associated affine dynkin diagram and we use this connection to study the structure and representation theory of zk g via the combinatorics of the dynkin diagram when g equals the binary tetrahedral octahedral or icosahedral group we exhibit remarkable connections between zk g and the martin jones set partition algebras

resolving inconsistencies in utility measurement under risk tests of generalizations of expected utility this paper explores inconsistencies that occur in utility measurement under risk when expected utility theory is assumed and the contribution that prospect theory and some other generalizations of expected utility can make to the resolution of these inconsistencies we used five methods to measure utilities under risk and found clear violations of expected utility of the theories studied prospect theory was the most consistent with our data the main improvement of prospect theory over expected utility was in comparisons between a riskless and a risky prospect riskless risk methods we observed no improvement over expected utility in comparisons between two risky prospects risk risk methods an explanation for the latter observation may be that there was less distortion in probability weighting in the interval 0 10 0 20 than has commonly been observed

curvature of the probability weighting function when individuals choose among risky alternatives the psychological weight attached to an outcome may not correspond to the probability of that outcome in rank dependent utility theories including prospect theory the probability weighting function permits probabilities to be weighted nonlinearly previous empirical studies of the weighting function have suggested an inverse s shaped function first concave and then convex however these studies suffer from a methodological shortcoming estimation procedures have required assumptions about the functional form of the value and or weighting functions we propose two preference conditions that are necessary and sufficient for concavity and convexity of the weighting function empirical tests of these conditions are independent of the form of the value function we test these conditions using preference ladders a series of questions that differ only by a common consequence the concavity convexity ladders validate previous findings of an s shaped weighting function concave up to p 0 40 and convex beyond that probability the tests also show significant nonlinearity away from the boundaries 0 and 1 finally we fit the ladder data with weighting functions proposed by tversky and kahneman tversky amos daniel kahneman 1992 advances in prospect theory cumulative representation of uncertainty j risk and uncertainty5 297 323 and prelec prelec dra en 1995 the probability weighting function unpublished paper

differential invariants for symplectic lie algebras realized by boson operators the study of algebraic symplectic models in high energy physics and even in molecular genetics has received much attention in the past decades in this paper we first survey one known bosonic realization with n types of bosons operators in a 2j 1 dimensional space with j being the semi integer then using the general theory of differential invariants we determine two sets of sp 2j 1 differential invariants in one set when n 2j 1 all independent invariants of any order are obtained in a simple closed form when n 2j 1 we could present only particular matrix forms in the latter case the differential invariants up to the second order are explicitly presented for the symplectic algebras sp 2 sp 4 and sp 6 realized by up to three types of bosons as applications we present the simplest sp 2 invariant lagrangians null lagrangians new solutions to the helmholtz inverse problem and evolution equations which will be of fundamental importance in the construction of dynamical systems invariant under the symplectic group

exact enumeration of hamiltonian walks on the 4 4 4 cube and applications to protein folding hamiltonian walks on lattices are model systems for compact polymers such as proteins here we enumerate exactly the number of hamiltonian walks on the 4 4 4 cube and give estimates up to the 7 7 7 cube through monte carlo methods we find that the number of configurations grows faster with chain length than previously anticipated finally we discuss uniqueness of ground states in the hp model for protein folding

poincare series for tensor invariants and the mckay correspondence abstract for a finite group g and a finite dimensional g module v we prove a general result on the poincare series for the g invariants in the tensor algebra t v k 0 v k we apply this result to the finite subgroups g of the 2 2 special unitary matrices and their natural module v of 2 1 column vectors because these subgroups are in one to one correspondence with the simply laced affine dynkin diagrams by the mckay correspondence the poincare series obtained are the generating functions for the number of walks on the simply laced affine dynkin diagrams

statistics of confined chains iii hamiltonian paths the entropy of self avoiding walks embedded in a square lattice has been monte carlo estimated inside plane squares of various side sizes r the length of the walks ranged from one to steps the maximum allowed length which corresponds to the so called hamiltonian paths it was found that if is the ratio of the occupied over the total number of available lattice sites inside the square the number of configurations scales to a good approximation as the limiting curve has then been estimated from the available data and expressed as a fourth degree polynomial in a table is given for z 1 that is hamiltonian paths comparing values obtained from the theoretical relationship given by orland et al from the exact enumeration data of mayer et al and from the monte carlo estimates of the present work

the predictive utility of generalized expected utility theories many alternative theories have been proposed to explain violations of expected utility eu theory observed in experiments several recent studies test some of these alternative theories against each other formal tests used to judge the theories usually count the number of responses consistent with the theory ignoring systematic variation in responses that are inconsistent we develop a maximum likelihood estimation method which uses all the information in the data creates test statistics that can be aggregated across studies and enables one to judge the predictive utility the fit and parsimony of utility theories analyses of 23 data sets using several thousand choices suggest a menu of theories which sacrifice the least parsimony for the biggest improvement in fit the menu is mixed fanning prospect theory eu and expected value which theories are best is highly sensitive to whether gambles in a pair have the same support eu fits better or not eu fits poorly our method may have application to other domains in which various theories predict different subsets of choices e g refinements of nash equilibrium in noncooperative games

the hard hexagon partition function for complex fugacity we study the analyticity of the partition function of the hard hexagon model in the complex fugacity plane by computing zeros and transfer matrix eigenvalues for large finite size systems we find that the partition function per site computed by baxter in the thermodynamic limit for positive real values of the fugacity is not sufficient to describe the analyticity in the full complex fugacity plane we also obtain a new algebraic equation for the low density partition function per site