global culture a noise induced transition in finite systems we analyze the effect of cultural drift modeled as noise in axelrod s model for the dissemination of culture the disordered multicultural frozen configurations are found not to be stable this general result is proven rigorously in d51 where the dynamics is described in terms of a lyapunov potential in d52 the dynamics is governed by the average relaxation time t of perturbations noise at a rate r t 21 induces monocultural configurations whereasr t 21 sustains disorder in the thermodynamic limit the relaxation time diverges and global polarization persists in spite of a dynamics of local convergence

detecting quantum entanglement we review the criteria for separability and quantum entanglement both in a bipartite as well as a multipartite setting we discuss bell inequalities entanglement witnesses entropic inequalities bound entanglement and several features of multipartite entanglement we indicate how these criteria bear on the experimental detection of quantum entanglement

cluster size entropy in the axelrod model of social influence small world networks and mass media we study the axelrod s cultural adaptation model using the concept of cluster size entropy s c which gives information on the variability of the cultural cluster size present in the system using networks of different topologies from regular to random we find that the critical point of the well known nonequilibrium monocultural multicultural order disorder transition of the axelrod model is given by the maximum of the s c q distributions the width of the cluster entropy distributions can be used to qualitatively determine whether the transition is first or second order by scaling the cluster entropy distributions we were able to obtain a relationship between the critical cultural trait q c and the number f of cultural features in two dimensional regular networks we also analyze the effect of the mass media external field on social systems within the axelrod model in a square network we find a partially ordered phase whose largest cultural cluster is not aligned with the external field in contrast with a recent suggestion that this type of phase cannot be formed in regular networks we draw a q b phase diagram for the axelrod model in regular networks

all teleportation and dense coding schemes we establish a one to one correspondence between 1 quantum teleportation schemes 2 dense coding schemes 3 orthonormal bases of maximally entangled vectors 4 orthonormal bases of unitary operators with respect to the hilbert schmidt scalar product and 5 depolarizing operations whose kraus operators can be chosen to be unitary the teleportation and dense coding schemes are assumed to be tight in the sense that all hilbert spaces involved have the same finite dimension d and the classical channel involved distinguishes d 2 signals a general construction procedure for orthonormal bases of unitaries involving latin squares and complex hadamard matrices is also presented

the classification of three parameter density matrices for a qutrit the properties and structure of the eight dimensional parameter space of three state density matrices are examined using the su 3 generator expansion three dimensional cross sections of the space of generalized bloch vectors are determined by the monte carlo sampling method and an appropriate classification of 56 different three parameter density matrices into ten types according to the shape of the corresponding region of allowed values of three relevant parameters is introduced positions of the representative points corresponding to the pure states are determined for all ten types

a special simplex in the state space for entangled qudits the focus is on two parties with hilbert spaces of dimension d i e qudits in the state space of these two possibly entangled qudits an analogue to the well known tetrahedron with the four qubit bell states at the vertices is presented the simplex analogue to this magic tetrahedron includes mixed states each of these states appears to each of the two parties as the maximally mixed state some studies on these states are performed and special elements of this set are identified a large number of them are included in the chosen simplex which fits exactly into conditions needed for teleportation and other applications its rich symmetry related to that of a classical phase space helps to study entanglement to construct witnesses and perform partial transpositions this simplex has been explored in detail for d 3 in this paper the mathematical background and extensions to arbitrary dimensions are analysed

l2 index formulae for perturbed dirac operators the callias index theorem is generalized from the euclidean case to certain spin manifolds with warped ends making use of certain index preserving deformations

geometry of two qubit states with negative conditional entropy we review the geometric features of negative conditional entropy and the properties of the conditional amplitude operator proposed by cerf and adami for two qubit states in comparison with entanglement and nonlocality of the states we identify the region of negative conditional entropy in the tetrahedron of locally maximally mixed two qubit states within this set of states negative conditional entropy implies nonlocality and entanglement but not vice versa and we show that the cerf adami conditional amplitude operator provides an entanglement witness equivalent to the peres horodecki criterion outside of the tetrahedron this equivalence is generally not true

entanglement reflected in wigner functions we construct an abelian algebra built by maximally entangled pure states the partial transposition maps this algebra for odd dimensions into a full matrix algebra ppt states are in one to one correspondence to states with a positive definite wigner function special extremal ppt states correspond to projections of various dimensions in particular we recover the projections corresponding to a complete set of mutually unbiased bases in prime dimensions

cluster diversity and entropy on the percolation model the lattice animal identification algorithm we present an algorithm to identify and count different lattice animals la s in the site percolation model this algorithm allows a definition of clusters based on the distinction of cluster shapes in contrast with the well known hoshen kopelman algorithm in which the clusters are differentiated by their sizes it consists in coding each unit cell of a cluster according to the nearest neighbors nn and ordering the codes in a proper sequence in this manner a la is represented by a specific code sequence in addition with some modification the algorithm is capable of differentiating between fixed and free la s the enhanced hoshen kopelman algorithm j hoshen m w berry and k s minser phys rev e 56 1455 1997 is used to compose the set of nn code sequences of each cluster using monte carlo simulations on planar square lattices up to 2000x2000 we apply this algorithm to the percolation model we calculate the cluster diversity and cluster entropy of the system which leads to the determination of probabilities associated with the maximum of these functions we show that these critical probabilities are associated with the percolation transition and with the complexity of the system

an equivariant index for proper actions i abstract equivariant indices taking values in group theoretic objects have previously been defined in cases where either the group acting or the orbit space of the action is compact in this paper we define an equivariant index without assuming the group or the orbit space to be compact this allows us to generalise an index of deformed dirac operators defined for compact groups by braverman in parts ii and iii of this series we explore some properties and applications of this index

nonequilibrium transitions in complex networks a model of social interaction we analyze the nonequilibrium order disorder transition of axelrod s model of social interaction in several complex networks in a small world network we find a transition between an ordered homogeneous state and a disordered state the transition point is shifted by the degree of spatial disorder of the underlying network the network disorder favoring ordered configurations in random scale free networks the transition is only observed for finite size systems showing system size scaling while in the thermodynamic limit only ordered configurations are always obtained thus in the thermodynamic limit the transition disappears however in structured scale free networks the phase transition between an ordered and a disordered phase is restored

bloch vectors for qudits we present three different matrix bases that can be used to decompose density matrices of d dimensional quantum systems so called qudits the generalized gell mann matrix basis the polarization operator basis and the weyl operator basis such a decomposition can be identified with a vector the bloch vector i e a generalization of the well known qubit case and is a convenient expression for comparison with measurable quantities and for explicit calculations avoiding the handling of large matrices we present a new method to decompose density matrices via so called standard matrices consider the important case of an isotropic two qudit state and decompose it according to each basis in the case of qutrits we show a representation of an entanglement witness in terms of expectation values of spin 1 measurements which is appropriate for an experimental realization

role of dimensionality in axelrod s model for the dissemination of culture we analyze a model of social interaction in one and two dimensional lattices for a moderate number of features we introduce an order parameter as a function of the overlap between neighboring sites in a one dimensional chain we observe that the dynamics is consistent with a second order transition where the order parameter changes continuously and the average domain diverges at the transition point however in a two dimensional lattice the order parameter is discontinuous at the transition point characteristic of a 4rst order transition between an ordered and a disordered state c

the physical modelling of society a historical perspective abstract by seeking to uncover the rules of collective human activities today s statistical physicists are aiming to return to their roots statistics originated in the study of social numbers in the 17th century and the discovery of statistical invariants in data on births and deaths crimes and marriages led some scientists and philosophers to conclude that society was governed by immutable natural laws beyond the reach of governments of which the gaussian error curve became regarded as the leitmotif while statistics flourished as a mathematical tool of all the sciences in the 19th century it provoked passionate responses from philosophers novelists and social commentators social statistics also guided maxwell and boltzmann towards the utilization of probability distributions in the development of the kinetic theory of gases the foundation of statistical mechanics

eta invariants and their adiabatic limits 0 introduction 1 algebraic preliminaries 2 the finite dimensional case superconnections a odd dimensional base spaces b even dimensional base spaces appendix 1 coupling to general superconnections 3 auxiliary grassman variables and auxiliary adiabatic limits 4 the infinite dimensional case fibrations a elementary geometry of fibrations b odd dimensional base spaces c even dimensional base spaces d the case in which the dirac operator on the fiber is not invertible appendix 2 multifibrations

bell inequalities for arbitrarily high dimensional systems we develop a novel approach to bell inequalities based on a constraint that the correlations exhibited by local variable theories must satisfy this is used to construct a family of bell inequalities for bipartite quantum systems of arbitrarily high dimensionality which are strongly resistant to noise in particular our work gives an analytic description of previous numerical results and generalizes them to arbitrarily high dimensionality

evaluating the holevo cramer rao bound for multiparameter quantum metrology only with the simultaneous estimation of multiple parameters are the quantum aspects of metrology fully revealed this is due to the incompatibility of observables the fundamental bound for multiparameter quantum estimation is the holevo cram er rao bound hcrb whose evaluation has so far remained elusive for finite dimensional systems we recast its evaluation as a semidefinite program with reduced size for rank deficient states we show that it also satisfies strong duality we use this result to study phase and loss estimation in optical interferometry and three dimensional magnetometry with noisy multiqubit systems for the former we show that in some regimes it is possible to attain the hcrb with the optimal single copy measurement for phase estimation for the latter we show a nontrivial interplay between the hcrb and incompatibility and provide numerical evidence that projective single copy measurements attain the hcrb in the noiseless 2 qubit case

local versus global interactions in nonequilibrium transitions a model of social dynamics a nonequilibrium system of locally interacting elements in a lattice with an absorbing order disorder phase transition is studied under the effect of additional interacting fields these fields are shown to produce interesting effects in the collective behavior of this system both for autonomous and external fields disorder grows in the system when the probability of the elements to interact with the field is increased there exists a threshold value of this probability beyond which the system is always disordered the domain of parameters of the ordered regime is larger for nonuniform local fields than for spatially uniform fields however the zero field limit is discontinous in the limit of vanishingly small probability of interaction with the field autonomous or external fields are able to order a system that would fall in a disordered phase under local interactions of the elements alone we consider different types of fields which are interpreted as forms of mass media acting on a social system in the context of axelrod s model for cultural dissemination

why two qubits are special we analyze some special properties of a system of two qubits and in particular of the so called bell basis for this system and discuss the possibility of extending these properties to higher dimensional systems we give a general construction for orthonormal bases of maximally entangled vectors which works in any dimension and is based on latin squares and complex hadamard matrices however for none of these bases the special properties of the operation of complex conjugation in bell basis hold namely that maximally entangled vectors have up to a phase real coefficients and that factorizable unitaries have real matrix elements

the existence of negative absolute temperatures in axelrod s social influence model abstract we introduce the concept of temperature as an order parameter in the standard axelrod s social influence model it is defined as the relation between suitably defined entropy and energy functions t s e 1 we show that at the critical point where the order disorder transition occurs this absolute temperature changes in sign at this point which corresponds to the transition homogeneous heterogeneous culture the entropy of the system shows a maximum we discuss the relationship between the temperature and other properties of the model in terms of cultural traits