a note on monopole moduli spaces we discuss the structure of the framed moduli space of bogomolny monopoles for arbitrary symmetry breaking and extend the definition of its stratification to the case of arbitrary compact lie groups we show that each stratum is a union of submanifolds for which we conjecture that the natural l2 metric is hyper kahler the dimensions of the strata and of these submanifolds are calculated and it is found that for the latter the dimension is always a multiple of four

information field dynamics for simulation scheme construction information field dynamics ifd is introduced here as a framework to derive numerical schemes for the simulation of physical and other fields without assuming a particular subgrid structure as many schemes do ifd constructs an ensemble of nonparametric subgrid field configurations from the combination of the data in computer memory representing constraints on possible field configurations and prior assumptions on the subgrid field statistics each of these field configurations can formally be evolved to a later moment since any differential operator of the dynamics can act on fields living in continuous space however these virtually evolved fields need again a representation by data in computer memory the maximum entropy principle of information theory guides the construction of updated data sets via entropic matching optimally representing these field configurations at the later time the field dynamics thereby become represented by a finite set of evolution equations for the data that can be solved numerically the subgrid dynamics is thereby treated within auxiliary analytic considerations the resulting scheme acts solely on the data space it should provide a more accurate description of the physical field dynamics than simulation schemes constructed ad hoc due to the more rigorous accounting of subgrid physics and the space discretization process assimilation of measurement data into an ifd simulation is conceptually straightforward since measurement and simulation data can just be merged the ifd approach is illustrated using the example of a coarsely discretized representation of a thermally excited classical klein gordon field this should pave the way towards the construction of schemes for more complex systems like turbulent hydrodynamics

monopoles and rational maps a note on a theorem of donaldson in a recent paper donaldson gave a description of the moduli space of su 2 monopoles in terms of rational maps this was done indirectly via the associated solution of nahm s equations we give here an interpretation of these rational maps in terms of the monopole s spectral curve and then as scattering data for the monopole itself

algebraic cycles and infinite loop spaces in this paper we use recent results about the topology of chow varieties to answer an open question in infinite loop space theory that is we construct an infinite loop space structure on a certain product of eilenberg maclane spaces so that the total chern map is an infinite loop map an analogous result for the total stiefel whitney map is also proved further results on the structure of stabilized spaces of alebraic cycles are obtained and computational consequences are also outlined

why instantons are monopoles it is shown that instantons are hyperbolic monopoles for the loop group with non maximal symmetry breaking at infinity

nahm s transformation for instantons we describe in mathematical detail the nahm transformation which maps anti self dual connections on the four torus s1 4 onto anti self dual connections on the dual torus this transformation induces a map between the relevant instanton moduli spaces and we show that this map is a hyperkahler isometry

stratifying monopoles and rational maps a stratification of the moduli space of monopoles and of the space of rational maps into a flag variety is presented it is shown that the map associating a rational map to a monopole preserves these strata these strata explain some problems in the intepretation of the parameters of the moduli space in terms of superpositions of fundamental monopoles this interpretation is not valid on the individual strata the space of fundamental monopoles is described and shown to be the same as the corresponding space of rational maps

monopoles non linear σ models and two fold loop spaces in this paper we study the topology of hat m k the moduli spaces ofsu 2 monopoles associated with the yang mills higgs and bogomol nyi equations and m k non linear models from quantum field theory beautiful work of donaldson 18 19 hitchin 24 25 and taubes 37 39 40 shows that gauge equivalence classes of monopoles correspond to based rational self maps of the riemann sphere similarly the non linear models we consider here are based harmonic maps from the riemann sphere to complex projectivem space in seminal work segal 35 studied m k the space of based rational maps from the riemann sphere to complex projectivem space of a fixed degreek any element of m k is clearly an element of k2cp m the space of all based continuous maps from the riemann sphere to complex projectivem space of a fixed degreek and this assignment gives rise to the natural inclusion of m k in k2cp m segal showed that these natural inclusions are homotopy equivalences through dimensionk 2m 1 as the topology of the two fold loop space 2cp m is well understood segal s result gives a very efficient way to explicitly determine the low dimensional topology of m k thus iterated loop spaces have much to say about the topology of monopoles and non linear models

nahm s equations singular point analysis and integrability a singular point analysis painleve test for certain special cases of nahm s equations is performed it is shown that there are cases in which the equations do not pass the test the laurent expansion does not contain the right number of arbitrary expansion coefficients nevertheless the systems under consideration are completely integrable

perron frobenius theorem for nonnegative multilinear forms and extensions we prove an analog of perron frobenius theorem for multilinear forms with nonnegative coefficients and more generally for polynomial maps with nonnegative coefficients we determine the geometric convergence rate of the power algorithm to the unique normalized eigenvector

monopoles and clusters we define and study certain hyperkahler manifolds which capture the asymptotic behaviour of the su 2 monopole metric in regions where monopoles break down into monopoles of lower charges the rate at which these new metrics approximate the monopole metric is exponential as for the gibbons manton metric

on the construction of monopoles we show that any self dual su 2 monopole may be constructed either by ward s twistor method or nahm s use of the adhm construction the common factor in both approaches is an algebraic curve whose jacobian is used to linearize the non linear ordinary differential equations which arise in nahm s method we derive the non singularity condition for the monopole in terms of this curve and apply the result to prove the regularity of axially symmetric solutions

continuation methods for computing z h eigenpairs of nonnegative tensors abstract in this paper a homotopy continuation method for the computation of nonnegative z h eigenpairs of a nonnegative tensor is presented we show that the homotopy continuation method is guaranteed to compute a nonnegative eigenpair additionally using degree analysis we show that the number of positive z eigenpairs of an irreducible nonnegative tensor is odd a novel homotopy continuation method is proposed to compute an odd number of positive z eigenpairs and some numerical results are presented

the level manifold of a generalized toda equation hierarchy the finite nonperiodic toda lattice equation induces a linear one parameter flow on a space of rational functions the level manifold of the toda equation hierarchy is shown to be a product of lines our main results establish a generalization of this toda hierarchy which will be called the cyclic toda hierarchy it is proved that the cyclic toda hierarchy is completely integrable and its level manifold is diffeomorphic to a disjoint union of cylinders

symmetric calorons and the rotation map we study su 2 calorons also known as periodic instantons and consider invariance under isometries of s1 r3 coupled with a non spatial isometry called the rotation map in particular we investigate the fixed points under various cyclic symmetry groups our approach utilises a construction akin to the adhm construction of instantons what we call the monad matrix data for calorons derived from the work of charbonneau and hurtubise to conclude we present an example of how investigating these symmetry groups can help to construct new calorons by deriving nahm data in the case of charge 2

adaptive mesh techniques for fronts in star formation abstract we present an implicit adaptive grid finite difference technique specifically designed to locate and track arbitrary fronts interfaces and structures in a radiation hydro flow the adaptive mesh is constructed in such a way that the average change of the flow variables per grid zone is the same throughout the entire grid a local grid refinement of up to a factor of 10 6 compared to an equidistant mesh has been obtained on a machine with 14 decimal digits per word crucial to this type of approach is the use of a stiffness operator which prevents tangling of the mesh the elliptic equation for the grid motion is solved implicitly coupled with the equations for the flow variables per timestep very steep and narrow flow features can travel many times their own width in true space however with respect to the adaptive mesh the motion of such flow features is always less than one zone thus the courant friedrichs lewy 1 cfl condition s accuracy limitation is always fulfilled although its stability criterion does not pose any timestep limitations for our implicit numerical method in fact the choice of timesteps is based purely on physical and accuracy considerations typical applications run on courant numbers ranging from 0 1 to 10 12 the performance of this numerical scheme is demonstrated on a planar 1 d shocktube and the formation of a one solar mass protostar in spherical symmetry

the topology of rational functions and divisors of surfaces segal studied the homotopy types of the spaces of holomorphic functions of the 2 sphere s 2 of closed surfaces of higher genus and of the spaces of divisors of these surfaces we continue segal s program by describing the entire stable homotopy types of these spaces in terms of the homotopy types of more familiar spaces

total decoupling of general quadratic pencils part ii structure preserving isospectral flows abstract quadratic pencils 2 m c k where m c and k are n n real matrices with or without some additional properties such as symmetry connectivity bandedness or positive definiteness arise in many important applications recently an existence theory has been established showing that almost all n degree of freedom second order systems can be reduced to n totally independent single degree of freedom second order subsystems by real valued isospectral transformations in contrast to the common knowledge that generally no three matrices can be diagonalized simultaneously by equivalence transformations these isospectral transformations endeavor to maintain a special linearization form called the lancaster structure and do break down m c and k into diagonal matrices simultaneously however these transformations depend on the matrices in a rather complicated way and hence are difficult to construct directly in this paper a second part of a continuing study a closed loop control system that preserves both the lancaster structure and the isospectrality is proposed as a means to achieve the diagonal reduction consequently these transformations are acquired

monopoles and baker functions the work in this paper pertains to the solutions of nahm s equations which arise in the atiyah drinfield hitchin manin nahm construction of solutions to the bogomol nyi equations for static monopoles this paper provides an explicit construction of the solution of nahm s equations which satisfy regularity and reality conditions the lax form of nahm s equations is reduced to a standard eigenvalue problem by a special gauge transformation these equations may then be solved by the method of baker krichever this leads to a compact representation of the solutions of nahm s equations the regularity condition is shown to be related to the monodromy of the gauge reduced linear operator hitchin showed that the solutions of nahm s equations can be characterized by an algebraic curve and some data on that curve here this characterization reduces to a transcendental equation involving certain loop integrals of a meromorphic differential donaldson coordinatized the moduli space ofk monopoles by a class of rational maps from the riemann sphere to itself the data of a baker function is equivalent to this map this method gives an apriori construction of the known two monopole solutions we also give a generalization of the two monopole solution to a class of elliptic solutions of arbitrary charge these solutions correspond to reducible curves with elliptic components and the associated donaldson rational function has a simple partial fraction expansion

classical solutions of the chiral model unitons and holomorphic vector bundles this paper deals with classical solutions of thesu 2 chiral model on 2 and of a generalized chiral model on 2 1 such solutions are shown to correspond to certain holomorphic vector bundles over minitwistor space with an appropriate boundary condition the solutions called 1 unitons in 9 correspond to bundles over a compact 2 dimensional complex manifold and the problem becomes one of algebraic geometry

on the estimates of the z eigenpair for an irreducible nonnegative tensor abstract in this paper we are concerned with the z eigenpair of a tensor in particular an irreducible nonnegative tensor some new lower and upper bounds for the eigenvector and z spectral radius of an irreducible weakly symmetric nonnegative tensors are provided our new bounds which mostly generalize the ones presented in li et al 2015 13 are closely related to the order of a tensor and proved to be tighter than those there a new bound for z 1 eigenvalue of general tensors is specifically presented some examples are given to show the sharpness of our new bounds in contrast with the known ones including the comparison results with the very recent research by other authors in the appendix

monopoles on asymptotically euclidean 3 manifolds on considere une generalisation de la theorie de yang mills higgs sur r 3 euclidien a des sommes convexes de r 3 avec des 3 varietes closes compactes

closed geodesics on the space of stable two monopoles we show that the atiyah hitchin metric on the space of stable two monopoles admits closed geodesics

inference with minimal gibbs free energy in information field theory non linear and non gaussian signal inference problems are difficult to tackle renormalization techniques permit us to construct good estimators for the posterior signal mean within information field theory ift but the approximations and assumptions made are not very obvious here we introduce the simple concept of minimal gibbs free energy to ift and show that previous renormalization results emerge naturally they can be understood as being the gaussian approximation to the full posterior probability which has maximal cross information with it we derive optimized estimators for three applications to illustrate the usage of the framework i reconstruction of a log normal signal from poissonian data with background counts and point spread function as it is needed for gamma ray astronomy and for cosmography using photometric galaxy redshifts ii inference of a gaussian signal with unknown spectrum and iii inference of a poissonian log normal signal with unknown spectrum the combination of i and ii finally we explain how gaussian knowledge states constructed by the minimal gibbs free energy principle at different temperatures can be combined into a more accurate surrogate of the non gaussian posterior

on the uniqueness of the positive z eigenvector for nonnegative tensors abstract the uniqueness of positive z eigenvector of nonnegative tensors has many important applications in both theory and practical application in this paper we give a sufficient condition that a nonnegative tensor has unique positive z eigenvector by using its entries for the third order transition probabilities tensor we show that its positive z eigenvector corresponding to eigenvalue 1 is unique

operator calculus for information field theory signal inference problems with non gaussian posteriors can be hard to tackle through using the concept of gibbs free energy these posteriors are rephrased as gaussian posteriors for the price of computing various expectation values with respect to a gaussian distribution we present a way of translating these expectation values to a language of operators which is similar to that in quantum mechanics this simplifies many calculations for instance such as those involving log normal priors the operator calculus is illustrated by deriving a self calibrating algorithm which is tested with mock data

infinite and finite dimensional generalized hilbert tensors abstract in this paper we introduce the concept of an m order n dimensional generalized hilbert tensor h n h i 1 i 2 i m h i 1 i 2 i m 1 i 1 i 2 i m m a a r z i 1 i 2 i m 1 2 n and show that its h spectral radius and its z spectral radius are smaller than or equal to m a n m 1 and m a n m 2 respectively here m a is a constant depending on a moreover both infinite and finite dimensional generalized hilbert tensors are positive definite for a 1 for an m order infinite dimensional generalized hilbert tensor h with a 0 we prove that h defines a bounded and positively m 1 homogeneous operator from l 1 into l p 1 p two upper bounds on the norms of corresponding positively homogeneous operators are obtained

instantons and geometric invariant theory we show that the yang mills instantons can be described in terms of certain holomorphic bundles on the projective plane the proof uses explicit matrix descriptions arising from monads and an analysis of the corresponding groups of symmetries

the classification of monopoles for the classical groups by studying a construction of nahm we compute the moduli spaces of monopoles with maximal symmetry breaking at infinity forsu n so n andsp n these are found to be equivalent to spaces of holomorphic maps from 1 into flag manifolds

instantons in two and four dimensions it is shown that yang mills instantons in four dimensions can naturally be identified with the instantons of a two dimensional theory with values in the loop group

monopoles and spectral curves for arbitrary lie groups the definition of the spectral curve of a monopole is extended to any connected compact simple lie groupk it is found there are rankk curves whose degrees are related to the topological weights of the monopole

some new inequalities for the minimum h eigenvalue of nonsingular m tensors abstract this paper is devoted to deriving some new upper and lower bounds for the minimum h eigenvalue of irreducible nonsingular m tensors we demonstrate that the proposed bounds improve some existing ones and numerical examples are given to illustrate this fact additionally we extend these bounds to general nonsingular m tensors the other main results in this paper is to provide sharper ky fan theorem and comparison theorem for nonsingular m tensors which are better than the corresponding ones obtained by he and huang 2014 12

on the uniqueness and non uniqueness of the positive z eigenvector for transition probability tensors abstract we study the basic properties of transition probability tensors we investigate sufficient conditions for this class of tensors to ensure the uniqueness of the positive z eigenvector we use three different methods contraction mappings monotone operators and the brouwer index of fixed points

eigenvalues and invariants of tensors abstract a tensor is represented by a supermatrix under a co ordinate system in this paper we define e eigenvalues and e eigenvectors for tensors and supermatrices by the resultant theory we define the e characteristic polynomial of a tensor an e eigenvalue of a tensor is a root of the e characteristic polynomial in the regular case a complex number is an e eigenvalue if and only if it is a root of the e characteristic polynomial we convert the e characteristic polynomial of a tensor to a monic polynomial and show that the coefficients of that monic polynomial are invariants of that tensor i e they are invariant under co ordinate system changes we call them principal invariants of that tensor the maximum number of principal invariants of mth order n dimensional tensors is a function of m and n we denote it by d m n and show that d 1 n 1 d 2 n n d m 2 m for m 3 and d m n m n 1 m for m n 3 we also define the rank of a tensor all real eigenvectors associated with nonzero e eigenvalues are in a subspace with dimension equal to its rank

monopoles braid groups and the dirac operator using the relation between the space of rational functions on the space ofsu 2 monopoles on 3 and the classifying space of the braid group see 10 we show how the index bundle of the family of real dirac operators coupled tosu 2 monopoles can be described using permutation representations of artin s braid groups we also show how this implies the existence of a pair consisting of a gauge fielda and a higgs field on 3 whose corresponding dirac equation has an arbitrarily large dimensional space of solutions

monopoles and geodesics using the holomorphic geometry of the space of straight lines in euclidean 3 space it is shown that every static monopole of chargek may be constructed canonically from an algebraic curve by means of the atiyah ward ansatz a k

asymptotic metrics for su n monopoles with maximal symmetry breaking we compute the asymptotic metrics for moduli spaces of su n monopoles with maximal symmetry breaking these metrics are exponentially close to the exact monopole metric1 as soon as for each simple root the individual monopoles corresponding to that root are well separated we also show that the estimates can be differentiated term by term in natural coordinates which is a new result even for su 2 monopoles

on eigenvalue problems of real symmetric tensors abstract we use variational methods to give a positive answer to a conjecture posed by liqun qi l qi eigenvalues of a real supersymmetric tensor j symbolic comput 40 2005 1302 1324 regarding the real eigenvalues of certain higher order tensors

the painleve property for partial differential equations in this paper we define the painleve property for partial differential equations and show how it determines in a remarkably simple manner the integrability the backlund transforms the linearizing transforms and the lax pairs of three well known partial differential equations burgers equation kdv equation and the modified kdv equation this indicates that the painleve property may provide a unified description of integrable behavior in dynamical systems ordinary and partial differential equations while at the same time providing an efficient method for determining the integrability of particular systems

some upper bounds on zt eigenvalues of tensors abstract in this paper we give upper bounds on zt spectral radius of a tensor a t 1 2 which extend the upper bounds of brauer to tensors moreover an upper bound on the z1 spectral radius is proposed via modulus sum of the entries of certain dimension of a which improves the upper bound given by li et al numerical experiments are given to illustrate the utility of the upper bound

calorons nahm s equations on s1 and bundles over mathbb p 1 times mathbb p 1 the moduli space of solutions to nahm s equations of rank k k j on the circle and hence of su 2 calorons of charge k j is shown to be equivalent to the moduli of holomorphic rank 2 bundles on mathbb p 1 times mathbb p 1 trivialized at infinity infty times mathbb p 1 cup mathbb p 1 times infty with c 2 k and equipped with a flag of degree j along mathbb p 1 times 0 an explicit matrix description of these spaces is given by a monad construction

reconstruction of gaussian and log normal fields with spectral smoothness we develop a method to infer log normal random fields from measurement data affected by gaussian noise the log normal model is well suited to describe strictly positive signals with fluctuations whose amplitude varies over several orders of magnitude we use the formalism of minimum gibbs free energy to derive an algorithm that uses the signal s correlation structure to regularize the reconstruction the correlation structure described by the signal s power spectrum is thereby reconstructed from the same data set we show that the minimization of the gibbs free energy corresponding to a gaussian approximation to the posterior marginalized over the power spectrum is equivalent to the empirical bayes ansatz in which the power spectrum is fixed to its maximum a posteriori value we further introduce a prior for the power spectrum that enforces spectral smoothness the appropriateness of this prior in different scenarios is discussed and its effects on the reconstruction s results are demonstrated we validate the performance of our reconstruction algorithm in a series of one and two dimensional test cases with varying degrees of non linearity and different noise levels

z eigenpair bounds for an irreducible nonnegative tensor abstract in this paper we consider the z eigenpair of a tensor in particular an irreducible nonnegative tensor we present some bounds for the eigenvector and z spectral radius the proposed bounds improve some existing ones an example with practical applications is given to show the proposed bound

upper bounds for h and z spectral radii of uniform hypergraphs abstract the h spectral radius and z spectral radius of a uniform hypergraph are the h spectral radius and the z spectral radius of its adjacency tensor respectively we give upper bounds for the h spectral radius and z spectral radius of uniform hypergraphs in terms of parameters such as number of vertices number of edges maximum degree and minimum degree and characterize the extremal hypergraphs some classical results on the spectral radius of an ordinary graph are generalized

min max theory for the yang mills higgs equations in each monopole sector there exist an infinite number of finite energy solutions to the prasad sommerfield limit of the su 2 yang mills higgs equations on 3 whose energy is greater than any finite number

reconstructing signals from noisy data with unknown signal and noise covariance we derive a method to reconstruct gaussian signals from linear measurements with gaussian noise this new algorithm is intended for applications in astrophysics and other sciences the starting point of our considerations is the principle of minimum gibbs free energy which was previously used to derive a signal reconstruction algorithm handling uncertainties in the signal covariance we extend this algorithm to simultaneously uncertain noise and signal covariances using the same principles in the derivation the resulting equations are general enough to be applied in many different contexts we demonstrate the performance of the algorithm by applying it to specific example situations and compare it to algorithms not allowing for uncertainties in the noise covariance the results show that the method we suggest performs very well under a variety of circumstances and is indeed qualitatively superior to the other methods in cases where uncertainty in the noise covariance is present

simulation of stochastic network dynamics via entropic matching the simulation of complex stochastic network dynamics arising for instance from models of coupled biomolecular processes remains computationally challenging often the necessity to scan a model s dynamics over a large parameter space renders full fledged stochastic simulations impractical motivating approximation schemes here we propose an approximation scheme which improves upon the standard linear noise approximation while retaining similar computational complexity the underlying idea is to minimize at each time step the kullback leibler divergence between the true time evolved probability distribution and a gaussian approximation entropic matching this condition leads to ordinary differential equations for the mean and the covariance matrix of the gaussian for cases of weak nonlinearity the method is more accurate than the linear method when both are compared to stochastic simulations

stochastic analysis of complex reaction networks using binomial moment equations the stochastic analysis of complex reaction networks is a difficult problem because the number of microscopic states in such systems increases exponentially with the number of reactive species direct integration of the master equation is thus infeasible and is most often replaced by monte carlo simulations while monte carlo simulations are a highly effective tool equation based formulations are more amenable to analytical treatment and may provide deeper insight into the dynamics of the network here we present a highly efficient equation based method for the analysis of stochastic reaction networks the method is based on the recently introduced binomial moment equations barzel and biham phys rev lett 106 150602 2011 the binomial moments are linear combinations of the ordinary moments of the probability distribution function of the population sizes of the interacting species they capture the essential combinatorics of the reaction processes reflecting their stoichiometric structure this leads to a simple and transparent form of the equations and allows a highly efficient and surprisingly simple truncation scheme unlike ordinary moment equations in which the inclusion of high order moments is prohibitively complicated the binomial moment equations can be easily constructed up to any desired order the result is a set of equations that enables the stochastic analysis of complex reaction networks under a broad range of conditions the number of equations is dramatically reduced from the exponential proliferation of the master equation to a polynomial and often quadratic dependence on the number of reactive species in the binomial moment equations the aim of this paper is twofold to present a complete derivation of the binomial moment equations to demonstrate the applicability of the moment equations for a representative set of example networks in which stochastic effects play an important role

on the complete integrability of the discrete nahm equations the discrete nahm equations a system of matrix valued difference equations arose in the work of braam and austin on half integral mass hyperbolic monopoles

spectral hypergraph theory of the adjacency hypermatrix and matroids abstract we define a matroid from an m uniform hypergraph spectral properties of the adjacency hypermatrix which can be deduced from the matroid are investigated in particular relationships between the coordinates of eigenvectors are revealed in terms of circuits of the matroid it is expected that these relationships will lead to a better initial input vector on the interior of the positive cone for numerical calculations of z eigenvalues using the ss hopm method and for h eigenvalues when using the nqz method

infinite and finite dimensional hilbert tensors abstract for an m order n dimensional hilbert tensor hypermatrix h n h i 1 i 2 i m h i 1 i 2 i m 1 i 1 i 2 i m m 1 i 1 i m 1 2 n its spectral radius is not larger than n m 1 sin n and an upper bound of its e spectral radius is n m 2 sin n moreover its spectral radius is strictly increasing and its e spectral radius is nondecreasing with respect to the dimension n when the order is even both infinite and finite dimensional hilbert tensors are positive definite we also show that the m order infinite dimensional hilbert tensor hypermatrix h h i 1 i 2 i m defines a bounded and positively m 1 homogeneous operator from l 1 into l p 1 p and the norm of corresponding positively homogeneous operator is smaller than or equal to 6

tensor norm and maximal singular vectors of nonnegative tensors a perron frobenius theorem a collatz wielandt characterization and a generalized power method abstract we study the l p 1 p m singular value problem for nonnegative tensors we prove a general perron frobenius theorem for weakly irreducible and irreducible nonnegative tensors and provide a collatz wielandt characterization of the maximal singular value additionally we propose a higher order power method for the computation of the maximal singular vectors and show that it has an asymptotic linear convergence rate

dynamic multiscale modes of resting state brain activity detected by entropy field decomposition the ability of functional magnetic resonance imaging fmri to noninvasively measure fluctuations in brain activity in the absence of an applied stimulus offers the possibility of discerning functional networks in the resting state of the brain however the reconstruction of brain networks from these signal fluctuations poses a significant challenge because they are generally nonlinear and nongaussian and can overlap in both their spatial and temporal extent moreover because there is no explicit input stimulus there is no signal model with which to compare the brain responses a variety of techniques have been devised to address this problem but the predominant approaches are based on the presupposition of statistical properties of complex brain signal parameters which are unprovable but facilitate the analysis in this article we address this problem with a new method entropy field decomposition for estimating structure within spatiotemporal data this method is based on a general information field theoretic formulation of bayesian probability theory incorporating prior coupling information that allows the enumeration of the most probable parameter configurations without the need for unjustified statistical assumptions this approach facilitates the construction of brain activation modes directly from the spatial temporal correlation structure of the data these modes and their associated spatial temporal correlation structure can then be used to generate space time activity probability trajectories called functional connectivity pathways which provide a characterization of functional brain networks

towards information optimal simulation of partial differential equations most simulation schemes for partial differential equations pdes focus on minimizing a simple error norm of a discretized version of a field this paper takes a fundamentally different approach the discretized field is interpreted as data providing information about a real physical field that is unknown this information is sought to be conserved by the scheme as the field evolves in time such an information theoretic approach to simulation was pursued before by information field dynamics ifd in this paper we work out the theory of ifd for nonlinear pdes in a noiseless gaussian approximation the result is an action that can be minimized to obtain an information optimal simulation scheme it can be brought into a closed form using field operators to calculate the appearing gaussian integrals the resulting simulation schemes are tested numerically in two instances for the burgers equation their accuracy surpasses finite difference schemes on the same resolution the ifd scheme however has to be correctly informed on the subgrid correlation structure in certain limiting cases we recover well known simulation schemes like spectral fourier galerkin methods we discuss implications of the approximations made

the bounds on spectral radius of nonnegative tensors via general product of tensors abstract in 1 j y shao proposed the general product of tensors based on this product the minc type bound on spectral radius of nonnegative tensors is given and the generalized minimax theorem of nonnegative tensors is presented moreover we give some bounds on the spectral radius of the general product of tensors

an always convergent algorithm for the largest eigenvalue of an irreducible nonnegative tensor in this paper we propose an iterative method to calculate the largest eigenvalue of a nonnegative tensor we prove this method converges for any irreducible nonnegative tensor we also apply this method to study the positive definiteness of a multivariate form

anti self dual yang mills connections over complex algebraic surfaces and stable vector bundles on presente une correspondance entre la geometrie algebrique et la geometrie differentielle des fibres vectoriels soit une surface algebrique projective x qui a un plongement donne x cp n et soit une metrique de kahler sur x dont la classe de cohomologie associee est duale a la classe de section d hyperplan h un fibre sur x est stable par rapport au plongement projectif si et seulement si il admet une connexion irreductible d hermite einstein par rapport a la metrique cette connexion est alors unique

toda flows inverse spectral transform and realization theory abstract in this paper we establish some new relationships between the solution techniques for completely integrable nonlinear differential equations of the toda type and topics in realization theory

some variational principles for z eigenvalues of nonnegative tensors many important spectral properties of nonnegative matrices have recently been successfully extended to higher order nonnegative tensors for example see chang et al 2008 2011 friedland et al in press lim 2005 liu et al 2010 ng et al 2010 qi et al 2007 yang and yang 2010 2 3 9 17 23 24 27 28 however most of these results focus on the h eigenvalues introduced by qi 2005 2007 25 26 the key results of this paper reveal some similarities as well as some crucial differences between z eigenvalues and h eigenvalues of a nonnegative tensor in particular neither the positive z eigenvalue nor the associated positive z eigenvector of an irreducible nonnegative tensor has to be unique in general as demonstrated by example 2 7 furthermore the collatz type min max characterizations of the largest positive z eigenvalue of an irreducible nonnegative tensor is only partially true in general as seen in theorem 4 7 and example 4 8

some bounds for h eigenpairs and z eigenpairs of a tensor abstract in this paper we consider the h eigenpairs and z eigenpairs of a tensor by estimating the ratio of the smallest and largest entries in the perron vector we present some sharper bounds for the h spectral radius of a nonnegative irreducible tensor similarly we also obtain some z spectral radius bounds of an irreducible weakly symmetric tensor in addition by using the technique of matricizing several bounds for the z spectrum are derived these proposed bounds improve some existing ones and some numerical examples are given to show the theoretical results

a note on the index bundle over the moduli space of monopoles donaldson has shown that the moduli space of monopolesmk is diffeomorphic to the spaceratk of based rational maps from the two sphere to itself we use this diffeomorphism to give an explicit description of the bundle onratk obtained by pushing out the index bundle frommk this gives an alternative and more explicit proof of some earlier results of cohen and jones

monopoles and the gibbons manton metric we show that in the region where monopoles are well separated the l 2 metric on the moduli space of n monopoles is exponentially close to the l 2 invariant hyperkahler metric proposed by gibbons and manton the proof is based on a description of the gibbons manton metric as a metric on a certain moduli space of solutions to nahm s equations and on twistor methods in particular we show how the twistor description of monopole metrics determines the asymptotic metric the construction of the gibbons manton metric in terms of nahm s equations yields a class of interesting pseudo hyperkahler metrics for example we show for each semisimple lie group g and a maximal torus t g the existence of a g t invariant pseudo hyperkahler manifold whose hyperkahler quotients by t are precisely kronheimer s hyperkahler metrics on g t a similar result holds for kronheimer s ale spaces

on the bilinear structure associated to bezoutians abstract this paper is partly a survey of known results on quadratic forms that are hard to find in the literature our main focus is a twisted form of a construction due to bezout this skew bezoutian is a symplectic resp quadratic space associated to a pair of reciprocal or skew reciprocal coprime polynomials of same degree the isometry group of this space turns out to contain a certain associated hypergeometric group using the skew bezoutian we construct explicit isometries of bilinear spaces with given invariants such as the characteristic polynomial or jordan form and in the quadratic case the spinor norm

on a painleve test of a coupled system of boussinesq and schrodinger equations the complete integrability of a new system of nonlinear equations using the technique of painleve analysis has been investigated the system essentially represents a coupling of boussinesq and schrodinger equations through nonlinear terms while the arbitrariness of the expansion coefficients are proved for a particular branch in the formalism of weiss et al j math phys 24 522 1983 with the reduced ansatz of kruskal the consistency of the truncation is proved by a combination of the methodology due to weiss j math phys 25 13 2226 1984 and hirota lecture notes in physics vol 515 springer berlin 1976 on the other hand the backlund transformation for the equations are obtained via the truncation procedure without the use of kruskal s simplification

comment on inference with minimal gibbs free energy in information field theory ensslin and weig phys rev e 82 051112 2010 have introduced a minimum gibbs free energy mgfe approach for estimation of the mean signal and signal uncertainty in bayesian inference problems it aims to combine the maximum a posteriori map and maximum entropy me principles we point out however that there are some important questions to be clarified before the new approach can be considered fully justified and therefore able to be used with confidence in particular after obtaining a gaussian approximation to the posterior in terms of the mgfe at some temperature t this approximation should always be raised to the power of t to yield a reliable estimate in addition we show explicitly that mgfe indeed incorporates the map principle as well as the mdi minimum discrimination information approach but not the well known me principle of jaynes e t jaynes phys rev 106 620 1957 we also illuminate some related issues and resolve apparent discrepancies finally we investigate the performance of mgfe estimation for different values of t and we discuss the advantages and shortcomings of the approach

the tensor splitting with application to solve multi linear systems abstract in this paper firstly we introduce the variant tensor splittings and present some equivalent conditions for a strong m tensor based on the tensor splitting secondly the existence and uniqueness conditions of the solution for multi linear systems are given thirdly we propose some tensor splitting algorithms for solving multi linear systems with coefficient tensor being a strong m tensor as an application a tensor splitting algorithm for solving the multi linear model of higher order markov chains is proposed numerical examples are given to demonstrate the efficiency of the proposed algorithms

on the z eigenvalues of the adjacency tensors for uniform hypergraphs abstract the adjacency matrices for graphs are generalized to the adjacency tensors for uniform hypergraphs and some fundamental properties for the adjacency tensor and its z eigenvalues of a uniform hypergraph are obtained in particular some bounds on the smallest and the largest z eigenvalues of the adjacency tensors for uniform hypergraphs are presented

moduli spaces of instantons on the taub nut space we present adhm nahm data for instantons on the taub nut space and encode these data in terms of bow diagrams we study the moduli spaces of the instantons and present these spaces as finite hyperkahler quotients as an example we find an explicit expression for the metric on the moduli space of one su 2 instanton

binomial moment equations for stochastic reaction systems a highly efficient formulation of moment equations for stochastic reaction networks is introduced it is based on a set of binomial moments that capture the combinatorics of the reaction processes the resulting set of equations can be easily truncated to include moments up to any desired order the number of equations is dramatically reduced compared to the master equation this formulation enables the simulation of complex reaction networks involving a large number of reactive species much beyond the feasibility limit of any existing method it provides an equation based paradigm to the analysis of stochastic networks complementing the commonly used monte carlo simulations

interval tensors and their application in solving multi linear systems of equations abstract in this paper we introduce interval tensors and present some results about their eigenvalues positive definiteness and application in solving multi linear systems it is proved that the set of maximum z eigenvalues of a symmetric interval tensor is a compact interval also several bounds for eigenvalues of an interval tensor are proposed in addition necessary and sufficient conditions for having a positive definite interval tensor are presented and investigated furthermore solving tensor equations using interval methods is presented and the interval jacobi and gauss seidel algorithms are extended for interval multi linear systems finally some numerical experiments are carried out to illustrate the methods

on the construction of monopoles for the classical groups forg a classical group an equivalence is exhibited between a g monopoles over 3 with maximal symmetry breaking at infinity b families of rank g algebraic curves int 1 along with divisors on those curves satisfying certain constraints c solutions of nahm s equations over rank g intervals satisfying the appropriate boundary conditions a and b are linked by twistor techniques b and c via the krichever method for solving non linear differential equations and a and c via the adhmn construction providing a unified picture of techniques for solution amongst other things an asymptotic formula for the higgs field of the monopole is computed

periodic instantons and the loop group we construct a large class of periodic instantons conjecturally we produce all periodic instantons this confirms a conjecture of garland and murray that relates periodic instantons to orbits of the loop group acting on an extension of its lie algebra

first integrals and yoshida analysis of nahm s equations first integrals of nahm s equations for monopole solutions in yang mills theories are explicitly given for various special cases taking into account the scale invariance all kowalewski exponents are determined both the polynomial first integrals and the kowalewski exponents are obtained with the help of a reduce program package this leads to a completely consistent picture in the sense of the analysis recently proposed by yoshida 1983

improving self calibration response calibration is the process of inferring how much the measured data depend on the signal one is interested in it is essential for any quantitative signal estimation on the basis of the data here we investigate self calibration methods for linear signal measurements and linear dependence of the response on the calibration parameters the common practice is to augment an external calibration solution using a known reference signal with an internal calibration on the unknown measurement signal itself contemporary self calibration schemes try to find a self consistent solution for signal and calibration by exploiting redundancies in the measurements this can be understood in terms of maximizing the joint probability of signal and calibration however the full uncertainty structure of this joint probability around its maximum is thereby not taken into account by these schemes therefore better schemes in sense of minimal square error can be designed by accounting for asymmetries in the uncertainty of signal and calibration we argue that at least a systematic correction of the common self calibration scheme should be applied in many measurement situations in order to properly treat uncertainties of the signal on which one calibrates otherwise the calibration solutions suffer from a systematic bias which consequently distorts the signal reconstruction furthermore we argue that nonparametric signal to noise filtered calibration should provide more accurate reconstructions than the common bin averages and provide a new improved self calibration scheme we illustrate our findings with a simplistic numerical example

the number of eigenvalues of a tensor abstract eigenvectors of tensors as studied recently in numerical multilinear algebra correspond to fixed points of self maps of a projective space we determine the number of eigenvectors and eigenvalues of a generic tensor and we show that the number of normalized eigenvalues of a symmetric tensor is always finite we also examine the characteristic polynomial and how its coefficients are related to discriminants and resultants

the geodesic approximation for the yang mills higgs equations in this paper we consider the dynamics of the monopole solutions of yang mills higgs theory on minkowski space the monopoles are solutions of the yang mills higgs equations on three dimensional euclidean space it is of interest to understand how they evolve in time when considered as solutions of the yang mills higgs equations on minkowski space i e the time dependent equations it was suggested by manton that in certain situations the monopole dynamics could be understood in terms of geodesics with respect to a certain metric on the space of guage equivalence classes of monopoles the moduli space the metric is defined by taking thel 2 inner product of tangent vectors to this space in this paper we will prove that manton s approximation is indeed valid in the right circumstances which correspond to the slow motion of monopoles the metric on the moduli space of monopoles was analysed in a book by atiyah and hitchin so together with the results of this paper a detailed and rigorous understanding of the low energy dynamics of monopoles in yang mills higgs theory is obtained the strategy of the proof is to develop asymptotic expansions using appropriate gauge conditions and then to use energy estimates to prove their validity for the case of monopoles to be considered here there is a technical obstacle to be overcome when the equations are linearised about the monopole the continuous spectrum extends all the way to the origin this is overcome by using a norm introduced by taubes in a discussion of index theory for the yang mills higgs functional

nahm s equations and the classification of monopoles solutions of nahm s system of ordinary differential equations are produced by variational methods this leads to an explicit parametrisation of the solutions to the bogomolny equation over 3

moduli space of su 2 monopoles and complex cyclic toda hierarchy we study the problem of complete parametrization of the moduli space ofsu 2 yang mills higgs monopoles in terms of a nonlinear integrable system it is shown that the moduli space is homeomorphic to the solution space of a new generalization of finite nonperiodic toda equation called the complex cyclic toda hierarchy