rational group decision making a random field ising model at t 0 abstract a modified version of a finite random field ising ferromagnetic model in an external magnetic field at zero temperature is presented to describe group decision making fields may have a non zero average a postulate of minimum inter individual conflicts is assumed interactions then produce a group polarization along one very choice which is however randomly selected a small external social pressure is shown to have a drastic effect on the polarization individual bias related to personal backgrounds cultural values and past experiences are introduced via quenched local competing fields they are shown to be instrumental in generating a larger spectrum of collective new choices beyond initial ones in particular compromise is found to results from the existence of individual competing bias conflict is shown to weaken group polarization the model yields new psychosociological insights about consensus and compromise in groups

ising model susceptibility the fuchsian differential equation for χ 4 and its factorization properties we give the fuchsian linear differential equation satisfied by x 4 the four particle contribution to the susceptibility of the isotropic square lattice ising model this fuchsian differential equation is deduced from a series expansion method introduced in two previous papers and is applied with some symmetries and tricks specific to x 4 the corresponding order ten linear differentia operator exhibits a large set of factorization properties among these factorizations one is highly remarkable it corresponds to the fact that the two particle contribution x 2 is actually a solution of this order ten linear differential operator this result together with a similar one for the order seven differential operator corresponding to the three particle contribution x 3 leads us to a conjecture on the structure of all the n particle contributions x n

a statistical mechanics approach to granovetter theory abstract in this paper we try to bridge breakthroughs in quantitative sociology econometrics pioneered during the last decades by mac fadden brock durlauf granovetter and watts strogatz by introducing a minimal model able to reproduce essentially all the features of social behavior highlighted by these authors our model relies on a pairwise hamiltonian for decision maker interactions which naturally extends the multi populations approaches by shifting and biasing the pattern definitions of a hopfield model of neural networks once introduced the model is investigated through graph theory to recover granovetter and watts strogatz results and statistical mechanics to recover mac fadden and brock durlauf results due to the internal symmetries of our model the latter is obtained as the relaxation of a proper markov process allowing even to study its out of equilibrium properties the method used to solve its equilibrium is an adaptation of the hamilton jacobi technique recently introduced by guerra in the spin glass scenario and the picture obtained is the following shifting the patterns from 1 1 0 1 implies that the larger the amount of similarities among decision makers the stronger their relative influence and this is enough to explain both the different role of strong and weak ties in the social network as well as its small world properties as a result imitative interaction strengths seem essentially a robust request enough to break the gauge symmetry in the couplings furthermore this naturally leads to a discrete choice modelization when dealing with the external influences and to imitative behavior a la curie weiss as the one introduced by brock and durlauf

exact expressions for row correlation functions in the isotropic d 2 ising model we present exact explicit expressions for the row spin spin correlation functions 00 n0 in the isotropicd 2 ising model in terms of elliptic integrals forn 5 we also give a general structural formula for 00 n0

the susceptibility of the square lattice ising model new developments we have made substantial advances in elucidating the properties of the susceptibility of the square lattice ising model we discuss its analyticity properties certain closed form expressions for subsets of the coefficients and give an algorithm of complexity o n6 to determine its first n coefficients as a result we have generated and analyzed series with more than 300 terms in both the high and low temperature regime we quantify the effect of irrelevant variables to the scaling amplitude functions in particular we find and quantify the breakdown of simple scaling in the absence of irrelevant scaling fields arising first at order t tc 9 4 though high low temperature symmetry is still preserved at terms of order t tc 17 4 and beyond this symmetry is no longer present the short distance terms are shown to have the form t tc p log t tc q with p q2 conjectured exact expressions for some correlation functions and series coefficients in terms of elliptic theta functions also foreshadow future developments

statistical mechanics for natural flocks of birds flocking is a typical example of emergent collective behavior where interactions between individuals produce collective patterns on the large scale here we show how a quantitative microscopic theory for directional ordering in a flock can be derived directly from field data we construct the minimally structured maximum entropy model consistent with experimental correlations in large flocks of starlings the maximum entropy model shows that local pairwise interactions between birds are sufficient to correctly predict the propagation of order throughout entire flocks of starlings with no free parameters we also find that the number of interacting neighbors is independent of flock density confirming that interactions are ruled by topological rather than metric distance finally by comparing flocks of different sizes the model correctly accounts for the observed scale invariance of long range correlations among the fluctuations in flight direction

painleve versus fuchs the sigma form of the painleve vi pvi equation contains four arbitrary parameters and generically the solutions can be said to be genuinely nonlinear because they do not satisfy linear differential equations of finite order however when there are certain restrictions on the four parameters there exist one parameter families of solutions which do satisfy fuchsian differential equations of finite order we study this phenomenon of fuchsian solutions to the painleve equation with a focus on the particular pvi equation which is satisfied by the diagonal correlation function c n n of the ising model we obtain fuchsian equations of order n i for c n n and show that the equation for c n n is equivalent to the nth symmetric power of the equation for the elliptic integral e we show that these fuchsian equations correspond to rational algebraic curves with an additional riccati structure and we show that the malmquist hamiltonian p q variables are rational functions in complete elliptic integrals fuchsian equations for off diagonal correlations c n m are given which extend our considerations to discrete generalizations of painleve

singularities of n fold integrals of the ising class and the theory of elliptic curves we introduce some multiple integrals that are expected to have the same singularities as the singularities of the n particle contributions n to the susceptibility of the square lattice ising model we find the fuchsian linear differential equation satisfied by these multiple integrals for n 1 2 3 4 and only modulo some primes for n 5 and 6 thus providing a large set of possible new singularities of n we discuss the singularity structure for these multiple integrals by solving the landau conditions we find that the singularities of the associated odes identify up to n 6 with the leading pinch landau singularities the second remarkable obtained feature is that the singularities of the odes associated with the multiple integrals reduce to the singularities of the odes associated with a finite number of one dimensional integrals among the singularities found we underline the fact that the quadratic polynomial condition 1 3w 4w2 0 that occurs in the linear differential equation of 3 actually corresponds to a remarkable property of selected elliptic curves namely the occurrence of complex multiplication the interpretation of complex multiplication for elliptic curves as complex fixed points of the selected generators of the renormalization group namely isogenies of elliptic curves is sketched most of the other singularities occurring in our multiple integrals are not related to complex multiplication situations suggesting an interpretation in terms of motivic mathematical structures beyond the theory of elliptic curves

globally nilpotent differential operators and the square ising model we recall various multiple integrals with one parameter related to the isotropic square ising model and corresponding respectively to the n particle contributions of the magnetic susceptibility to the lattice form factors to the two point correlation functions and to their extensions the univariate analytic functions defined by these integrals are holonomic and even g functions they satisfy fuchsian linear differential equations with polynomial coefficients and have some arithmetic properties we recall the explicit forms found in previous work of these fuchsian equations as well as their russian doll and direct sum structures these differential operators are selected fuchsian linear differential operators and their remarkable properties have a deep geometrical origin they are all globally nilpotent or sometimes even have zero p curvature we also display miscellaneous examples of globally nilpotent operators emerging from enumerative combinatorics problems for which no integral representation is yet known focusing on the factorized parts of all these operators we find out that the global nilpotence of the factors resp p curvature nullity corresponds to a set of selected structures of algebraic geometry elliptic curves modular curves curves of genus five six and even a remarkable weight 1 modular form emerging in the three particle contribution 3 of the magnetic susceptibility of the square ising model noticeably this associated weight 1 modular form is also seen in the factors of the differential operator for another n fold integral of the ising class 3 h for the staircase polygons counting and in ap ry s study of 3 g functions naturally occur as solutions of globally nilpotent operators in the case where we do not have g functions but hamburger functions one irregular singularity at 0 or that correspond to the confluence of singularities in the scaling limit the p curvature is also found to verify new structures associated with simple deformations of the nilpotent property

ising model for neural data model quality and approximate methods for extracting functional connectivity we study pairwise ising models for describing the statistics of multineuron spike trains using data from a simulated cortical network we explore efficient ways of finding the optimal couplings in

inverse problem robustness for multi species mean field spin models the inverse problem method is tested for a class of mean field statistical mechanics models representing a mixture of particles of different species the robustness of the inversion is investigated for different values of the physical parameters systemsizesandindependentsamples weshowhowtoreconstruct the parameter values with a precision of a few per cent

square lattice ising model susceptibility connection matrices and singular behaviour of χ 3 and χ 4 we present a simple but efficient way to calculate connection matrices between sets of independent local solutions defined at two neighbouring singular points of fuchsian differential equations of quite large orders such as those found for the third and fourth contribution 3 and 4 to the magnetic susceptibility of the square lattice ising model we deduce all the critical behaviours of the solutions 3 and 4 as well as the asymptotic behaviour of the coefficients in the corresponding series expansions we confirm that the newly found quadratic singularities of the fuchsian ode associated with 3 are not singularities of the particular solution 3 itself we use the previous connection matrices to get the exact expressions of all the monodromy matrices of the fuchsian differential equation for 3 and 4 expressed in the same basis of solutions these monodromy matrices are the generators of the differential galois group of the fuchsian differential equations for 3 and 4 whose analysis is just sketched here as far as the physics implications of the solutions are concerned we find challenging qualitative differences when comparing the corrections to scaling for the full susceptibility at high temperature respectively low temperature and the first two terms 1 and 3 respectively 2 and 4

holonomy of the ising model form factors we study the ising model two point diagonal correlation function c n n by presenting an exponential and form factor expansion in an integral representation which differs from the known expansion of wu mccoy tracy and barouch we extend this expansion weighting by powers of a variable the j particle contributions f j n n in the form factor expansion the corresponding extension of the two point diagonal correlation function c n n is shown for arbitrary to be a solution of the sigma form of the painleve vi equation introduced by jimbo and miwa in their isomonodromic approach to the ising model fuchsian linear differential equations for the form factors f j n n are obtained for j 9 and shown to have both a russian doll nesting and a decomposition of the corresponding linear differential operators as a direct sum of operators equivalent to symmetric powers of the second order linear differential operator associated with the elliptic integral e from this we show that each f j n n is unexpectedly simple being expressed polynomially in terms of the elliptic integrals e and k in contrast we exhibit some mathematical objects built from these form factors f j n n which break the direct sum of symmetric powers decomposition with its associated polynomial expressions first we show that the scaling limit of these differential operators and form factors breaks the direct sum structure but not the russian doll structure secondly we show that the previous extension of two point diagonal correlation functions c n n is for singled out values cos m n m n integers also solutions of fuchsian linear differential equations these solutions of painleve vi are not polynomial in e and k but are actually algebraic functions being associated with modular curves

stochastic algorithms for markov models estimation with intermittent missing data summary multistate markov models are frequently used to characterize disease processes but their estimation from longitudinal data is often hampered by complex patterns of incompleteness two algorithms for estimating markov chain models in the case of intermittent missing data in longitudinal studies a stochastic em algorithm and the gibbs sampler are described the first can be viewed as a random perturbation of the em algorithm and is appropriate when the m step is straightforward but the e step is computationally burdensome it leads to a good approximation of the maximum likelihood estimates the gibbs sampler is used for a full bayesian inference the performances of the two algorithms are illustrated on two simulated data sets a motivating example concerned with the modelling of the evolution of parasitemia by plasmodium falciparum malaria in a cohort of 105 young children in cameroon is described and briefly analyzed

fuchs versus painleve we briefly recall the fuchs painleve elliptic representation of painleve vi we then show that the polynomiality of the expressions of the correlation functions and form factors in terms of the complete elliptic integral of the first and second kinds k and e is a straight consequence of the fact that the differential operators corresponding to the entries of toeplitz like determinants are equivalent to the second order operator l e which has e as solution or for off diagonal correlations to the direct sum of l e and d dt we show that this can be generalized mutatis mutandis to the anisotropic ising model the singled out second order linear differential operator l e is replaced by an isomonodromic system of two third order linear partial differential operators associated with 1 the jacobi s form of the complete elliptic integral of the third kind or equivalently two second order linear partial differential operators associated with appell functions where one of these operators can be seen as a deformation of l e we finally explore the generalizations to the anisotropic ising models of the links we made in two previous papers between painleve nonlinear odes fuchsian linear odes and elliptic curves in particular the elliptic representation of painleve vi has to be generalized to an appellian representation of gamier systems

small correlation expansions for the inverse ising problem we present a systematic small correlation expansion to solve the inverse ising problem and find a set of couplings and fields corresponding to a given set of correlations and magnetizations couplings are calculated up to the third order in the correlations for generic magnetizations and to the seventh order in the case of zero magnetizations in addition we show how to sum some useful classes of diagrams exactly the resulting expansion outperforms existing algorithms on the sherrington kirkpatrick spin glass model

rescaled magnetization for critical bipartite curie weiss models we consider a bipartite generalization of the curie weiss model in a critical regime in order to study the asymptotic behavior of the random vector of the total magnetization we apply the change of variables that diagonalizes the hessian matrix of the pressure functional associated to the model we obtain a new vector that suitably rescaled weakly converges to the product of a gaussian distribution and a distribution proportional to exp xi x 4 where the positive constant xi can be computed from the pressure functional

scaling functions in the square ising model we show and give the linear differential operators of order for the integrals which appear in the two point correlation scaling function of ising model the integrals are given in expansion around in the basis of the formal solutions of with transcendental combination coefficients we find that the expression is a solution of the painleve vi equation in the scaling limit combinations of the analytic at solutions of sum to we show that the expression is the scaling limit of the correlation function and the differential galois groups of the factors occurring in the operators are given

the fuchsian differential equation of the square lattice ising model χ 3 susceptibility using an expansion method in the variables xi that appear in n 1 dimensional integrals representing the n particle contribution to the ising square lattice model susceptibility we generate a long series of coefficients for the three particle contribution 3 using an n4 polynomial time algorithm we give the fuchsian differential equation of order 7 for 3 that reproduces all the terms of our long series an analysis of the properties of this fuchsian differential equation is performed

square lattice ising model susceptibility series expansion method and differential equation for χ 3 in a previous paper 2004 j phys a math gen 37 9651 68 we have given the fuchsian linear differential equation satisfied by 3 the three particle contribution to the susceptibility of the isotropic square lattice ising model this paper gives the details of the calculations with some useful tricks and tools allowing one to obtain long series in polynomial time the method is based on series expansion in the variables that appear in the n 1 dimensional integrals representing the n particle contribution to the isotropic square lattice ising model susceptibility the integration rules are straightforward due to remarkable formulae we derived for these variables we obtain without any numerical approximation 3 as a fully integrated series in the variable w s 2 1 s2 where s sh 2k with k j kt the conventional ising model coupling constant we also give some perspectives and comments on these results