new examples of willmore tori in s4 using the generalized darboux transformation in the case of the clifford torus we construct for all pythagorean triples a family of willmore tori in s4 with willmore energy 2 n 2

modeling for dynamic ordinal regression relationships an application to estimating maturity of rockfish in california abstractwe develop a bayesian nonparametric framework for modeling ordinal regression relationships which evolve in discrete time the motivating application involves a key problem in fisheries research on estimating dynamically evolving relationships between age length and maturity the latter recorded on an ordinal scale the methodology builds from nonparametric mixture modeling for the joint stochastic mechanism of covariates and latent continuous responses this approach yields highly flexible inference for ordinal regression functions while at the same time avoiding the computational challenges of parametric models that arise from estimation of cut off points relating the latent continuous and ordinal responses a novel dependent dirichlet process prior for time dependent mixing distributions extends the model to the dynamic setting the methodology is used for a detailed study of relationships between maturity age and length for chilipepper rockfish using data collected over 15 years along th

correlated random measures abstractwe develop correlated random measures random measures where the atom weights can exhibit a flexible pattern of dependence and use them to develop powerful hierarchical bayesian nonparametric models hierarchical bayesian nonparametric models are usually built from completely random measures a poisson process based construction in which the atom weights are independent completely random measures imply strong independence assumptions in the corresponding hierarchical model and these assumptions are often misplaced in real world settings correlated random measures address this limitation they model correlation within the measure by using a gaussian process in concert with the poisson process with correlated random measures for example we can develop a latent feature model for which we can infer both the properties of the latent features and their dependency pattern we develop several other examples as well we study a correlated random measure model of pairwise count data we derive an eff

distributed average consensus with dithered quantization in this paper we develop algorithms for distributed computation of averages of the node data over networks with bandwidth power constraints or large volumes of data distributed averaging algorithms fail to achieve consensus when deterministic uniform quantization is adopted we propose a distributed algorithm in which the nodes utilize probabilistically quantized information i e dithered quantization to communicate with each other the algorithm we develop is a dynamical system that generates sequences achieving a consensus at one of the quantization values almost surely in addition we show that the expected value of the consensus is equal to the average of the original sensor data we derive an upper bound on the mean square error performance of the probabilistically quantized distributed averaging pqda moreover we show that the convergence of the pqda is monotonic by studying the evolution of the minimum length interval containing the node values we reveal that the length of this interval is a monotonically nonincreasing function with limit zero we also demonstrate that all the node values in the worst case converge to the final two quantization bins at the same rate as standard unquantized consensus finally we report the results of simulations conducted to evaluate the behavior and the effectiveness of the proposed algorithm in various scenarios

variational inference for large scale models of discrete choice discrete choice models are commonly used by applied statisticians in numerous fields such as marketing economics finance and operations research when agents in discrete choice models are assumed to have differing preferences exact inference is often intractable markov chain monte carlo techniques make approximate inference possible but the computational cost is prohibitive on the large datasets now becoming routinely available variational methods provide a deterministic alternative for approximation of the posterior distribution we derive variational procedures for empirical bayes and fully bayesian inference in the mixed multinomial logit model of discrete choice the algorithms require only that we solve a sequence of unconstrained optimization problems which are shown to be convex one version of the procedures relies on a new approximation to the variational objective function based on the multivariate delta method extensive simulations along with an analysis of real world data demonstr

stochastic variational inference we develop stochastic variational inference a scalable algorithm for approximating posterior distributions we develop this technique for a large class of probabilistic models and we demonstrate it with two probabilistic topic models latent dirichlet allocation and the hierarchical dirichlet process topic model using stochastic variational inference we analyze several large collections of documents 300k articles from nature 1 8m articles from the new york times and 3 8m articles from wikipedia stochastic inference can easily handle data sets of this size and outperforms traditional variational inference which can only handle a smaller subset we also show that the bayesian nonparametric topic model outperforms its parametric counterpart stochastic variational inference lets us apply complex bayesian models to massive data sets

nonconcurrent error detection and correction in fault tolerant linear finite state machines in this paper we construct fault tolerant linear finite state machines lfsms in which error detection and correction can be performed nonconcurrently e g periodically more specifically by jointly choosing the state encoding constraints and the redundant dynamics of the fault tolerant lfsm we enable an external checker to detect and identify errors due to past faults based on the current possibly corrupted state of the lfsm the paper presents systematic constructions of fault tolerant lfsms based on a characterization of nonconcurrent error detection correction in terms of state encoding constraints and redundant dynamics in particular we develop a scheme that uses bose chaudhuri hocquenghem bch coding and obtains fault tolerant lfsms that require 2d additional state variables and have the ability to correct up to d errors in any state variable at any time step in the time interval consisting of the latest n time steps of operation the construction uses the minimum possible number of additional state variables and requires an error detecting correcting mechanism with computational complexity that is only linear in n

nonparametric bayes estimators based on beta processes in models for life history data the article studies the problem of finding bayes estimators for cumulative hazard rates and related quantities w r t prior distributions that correspond to cumulative hazard rate processes with nonnegative independent increments a particular class of prior processes termed beta processes is introduced and is shown to constitute a conjugate class an important bonus of the approach based on cumulative hazards is that more complicated models for life history data than the simple life table situation can be treated for example time inhomogeneous markov chains we find posterior distributions and derive bayes estimators in such models and present a semiparametric bayesian analysis of the cox regression model

a first eigenvalue estimate for minimal hypersurfaces on obtient une borne inferieure pour la premiere valeur propre d une hypersurface orientable compacte plongee de facon minimale dans une variete orientable compacte a courbure de ricci positive

survey generic properties and control of linear structured systems a survey in this survey paper we consider linear structured systems in state space form where a linear system is structured when each entry of its matrices like a b c and d is either a fixed zero or a free parameter the location of the fixed zeros in these matrices constitutes the structure of the system indeed a lot of man made physical systems which admit a linear model are structured a structured system is representative of a class of linear systems in the usual sense it is of interest to investigate properties of structured systems which are true for almost any value of the free parameters therefore also called generic properties interestingly a lot of classical properties of linear systems can be studied in terms of genericity moreover these generic properties can in general be checked by means of directed graphs that can be associated to a structured system in a natural way we review here a number of results concerning generic properties of structured systems expressed in graph theoretic terms by properties we mean here system specific properties like controllability the finite and infinite zero structure and so on as well as solvability issues of certain classical control problems like disturbance rejection input output decoupling and so on in this paper we do not try to be exhaustive but instead by a selection of results we would like to motivate the reader to appreciate what we consider as a wonderful modelling and analysis tool we emphasize the fact that this modelling technique allows us to get a number of important results based on poor information on the system only moreover the graph theoretic conditions are intuitive and are easy to check by hand for small systems and by means of well known polynomially bounded combinatorial techniques for larger systems

harmonic maps into lie groups classical solutions of the chiral model on considere deux aspects de la structure algebrique de 7b m l espace des applications harmoniques d un domaine a 2 dimensions simplement connexe dans un groupe de lie reel g r la forme reelle d un groupe complexe g on construit une representation du groupe boucle 7b a s 1 g r sur 7b m correspondant a l algebre de lie de kacmoody des deformations infinitesimales on decrit l action sur 7b m et l action d un sous groupe sur l espace des applications harmoniques dans des gaussmanniens dans une seconde partie on se restreint a une theorie qui s applique seulement quand est un domaine riemannien a 2 dimensions simplement connexe et le groupe est g r u n

equivariant constrained willmore tori in the 3 sphere in this paper we study equivariant constrained willmore tori in the 3 sphere these tori admit a 1 parameter group of mobius symmetries and are critical points of the willmore energy under conformal variations we show that the spectral curve associated to an equivariant torus is given by a double covering of mathbb c and classify equivariant constrained willmore tori by the genus g of their spectral curve in this case the spectral genus satisfies g le 3

a new conformal invariant and its applications to the willmore conjecture and the first eigenvalue of compact surfaces let m be a compact riemannian manifold with a fixed conformal structure then we introduce the concept of conformal volume of m in the following manner for each branched conformal immersion q9 of m into the unit sphere s n we consider the set of all branched conformal immersions obtained by composi t ion of qo with the conformal automorphisms of s we let vc n qg be the max imum volume of these branched immersions the conformal volume of m is defined to be the infimum of v n q0 where qo ranges over all branched conformal immersions of m into the unit sphere s in this paper we study the case when m is a compact surface and we call the conformal volume of m to be the conformal area of m we demonst ra te that this conformal invariant is non trivial in fact we prove that if there exists a minimal immersion of m into s where coordinate functions are first eigenfunctions then the conformal area of m is given by the area of m with respect to the induced metric this enables us to compute the conformal area for several surfaces for example the conformal area of r p z is 6n and the conformal area of the square torus is 27c 2 we believe that the computa t ion of the conformal area for general surfaces will be very impor tant in studying the geometry of compact surfaces we demonstrate this claim by applying the concept of conformal area to two different branches of surface theory the first application is to study the total curvature of a compact surface in r this problem has a long history fenchel and fary 9 proved that for a closed curve o in r slk 27c where k is its curvature then milnor 12

on otsuki tori and their willmore energy abstract otsuki tori in the three dimensional unit sphere are studied from calculations of the willmore energy the lower and upper bound estimates for the otsuki tori are established invariance of the otsuki tori under antipodal maps is also considered and in such cases better lower bound estimates of their willmore energies are obtained

hierarchical dirichlet processes we consider problems involving groups of data where each observation within a group is a draw from a mixture model and where it is desirable to share mixture components between groups we assume that the number of mixture components is unknown a priori and is to be inferred from the data in this setting it is natural to consider sets of dirichlet processes one for each group where the well known clustering property of the dirichlet process provides a nonparametric prior for the number of mixture components within each group given our desire to tie the mixture models in the various groups we consider a hierarchical model specifically one in which the base measure for the child dirichlet processes is itself distributed according to a dirichlet process such a base measure being discrete the child dirichlet processes necessarily share atoms thus as desired the mixture models in the different groups necessarily share mixture components we discuss representations of hierarchical dirichlet processes

on the number of controllable linear systems over a finite field it is shown that over a finite field there are more controllable systems than uncontrollable ones if and only if the number of system inputs is greater than one or the field contains at least three elements

the geometry of minimal surfaces of finite genus i curvature estimates and quasiperiodicity let mathcal m be the space of properly embedded minimal surfaces in 3 with genus zero and two limit ends normalized so that every surface m mathcal m has horizontal limit tangent plane at infinity and the vertical component of its flux equals one we prove that if a sequence m i i mathcal m has the horizontal part of the flux bounded from above then the gaussian curvature of the sequence is uniformly bounded this curvature estimate yields compactness results and the techniques in its proof lead to a number of consequences concerning the geometry of any properly embedded minimal surface in 3 with finite genus and the possible limits through a blowing up process on the scale of curvature of a sequence of properly embedded minimal surfaces with locally bounded genus in a homogeneously regular riemannian 3 manifold

variational bayesian inference for parametric and nonparametric regression with missing data bayesian hierarchical models are attractive structures for conducting regression analyses when the data are subject to missingness however the requisite probability calculus is challenging and monte carlo methods typically are employed we develop an alternative approach based on deterministic variational bayes approximations both parametric and nonparametric regression are considered attention is restricted to the more challenging case of missing predictor data we demonstrate that variational bayes can achieve good accuracy but with considerably less computational overhead the main ramification is fast approximate bayesian inference in parametric and nonparametric regression models with missing data supplemental materials accompany the online version of this article

symmetry of embedded genus 1 helicoids in this note we use the lopez ros deformation introduced in 9 to show that any embedded genus one helicoid must be symmetric with respect to rotation by 180 around a normal line this partially answers a conjecture of bobenko from 3 we also show this symmetry holds for an embedded genus k helicoid provided the underlying conformal structure of is hyperelliptic in 3 bobenko conjectures that any immersed genus k helicoid i e a minimally immersed once punctured genus k surface with helicoid like behavior at the puncture is symmetric with respect to rotation by 180 around a line perpendicular to the surface this conjecture is motivated by the observation in 3 that the period problem for these surfaces is algebraically well posed when there is such a symmetry but is over determined without it in this note we verify bobenko s conjecture for embedded genus one helicoids that is theorem 0 1 let be an embedded genus one helicoid then there is a line l normal to so that rotation by 180 about l acts as an orientation preserving isometry on we define a genus k helicoid to be a complete minimal surface immersed in r which has genus k one end and is asymptotic to a helicoid a consequence of theorem 3 of 5 is that any immersed minimal surface which is conformally a once punctured compact genus k riemann surface with helicoid like weierstrass data at the puncture is a genus k helicoid in this sense in particular the above definition encompasses the surfaces studied by bobenko importantly by theorem 1 1 of 2 any complete embedded minimal surface in r with genus k and one end has helicoid like weierstrass data and hence is a genus k helicoid the space of such objects is not vacuous weber hoffman and wolf 12 and hoffman and white 7 have given very different constructions of embedded genus one helicoids at present it is unknown whether the two constructions give the same surface both constructions produce a genus one helicoid that has in addition to the orientation preserving symmetry of theorem 0 1 two orientation reversing symmetries whether all genus one helicoids possess these additional symmetries is also unknown we emphasize that our argument does not generalize to genus k 1 because we crucially use the fact that every genus one riemann surface admits a large number of biholomorphic involutions more precisely that any once punctured genus one riemann surface admits a non trivial biholomorphic involution this need not be true for higher genus indeed a priori there may fail to be any nontrivial biholomorphic automorphisms however if we restrict attention to genus k 2000 mathematics subject classification 53a10 the authors were supported respectively by the nsf grants dms 0902721 and dms 0902718

controllability of discrete time multi agent systems with directed topology and input delay this paper investigates the controllability of first order and second order discrete time multi agent systems with directed topology and input delay the problem is studied in the leader follower framework where a number of agents are selected to be leaders and serve as control inputs to all other agents sufficient and necessary conditions are derived for the controllability of first order discrete time multi agent systems with sampling period and feedback gain satisfying certain conditions it is proved under three different protocols that the controllability of second order discrete time multi agent systems is equivalent to that of a pair of submatrices of laplacian matrix in addition the controllability of both first order and second order discrete time multi agent systems with input delay is shown through some transformations to be equivalent to that of the transformed non delayed systems finally some simulation examples are given to illustrate the theoretical results

simple factor dressing and the lopez ros deformation of minimal surfaces in euclidean 3 space the aim of this paper is to investigate a new link between integrable systems and minimal surface theory the dressing operation uses the associated family of flat connections of a harmonic map to construct new harmonic maps since a minimal surface in 3 space is a willmore surface its conformal gauss map is harmonic and a dressing on the conformal gauss map can be defined we study the induced transformation on minimal surfaces in the simplest case the simple factor dressing and show that the well known lopez ros deformation of minimal surfaces is a special case of this transformation we express the simple factor dressing and the lopez ros deformation explicitly in terms of the minimal surface and its conjugate surface in particular we can control periods and end behaviour of the simple factor dressing this allows to construct new examples of doubly periodic minimal surfaces arising as simple factor dressings of scherk s first surface

two dimensional cellular automata a largely phenomenological study of two dimensional cellular automata is reported qualitative classes of behavior similar to those in one dimensional cellular automata are found growth from simple seeds in two dimensiona cellular automata can produce patterns with complicated boundaries characterized by a variety of growth dimensions evolution from disordered states can give domains with boundaries that execute effectively continuous motions some global properties of cellular automata can be described by entropies and lyapunov exponents others are undecidable

consensus networks with time delays over finite fields abstractin this paper we investigate the consensus problem in networks with time delays over finite fields the delays are categorised into three cases single constant delay multiple constant delays and time varying bounded delays for all cases some sufficient and necessary conditions for consensus are derived furthermore assuming that the communication graph is strongly connected some of the obtained necessary conditions reveal that the conditions for consensus with time delays over finite fields depend not only on the diagonal entries but also on the off diagonal entries something that is intrinsically distinct from the case over real numbers where having at least one nonzero diagonal entry is a sufficient and necessary condition to guarantee consensus in addition it is shown that delayed networks cannot achieve consensus when the interaction graph is a tree if the corresponding delay free networks cannot reach consensus which is consistent with the result over real numbers as for averag

spike and slab variable selection frequentist and bayesian strategies variable selection in the linear regression model takes many apparent faces from both frequentist and bayesian standpoints in this paper we introduce a variable selection method referred to as a rescaled spike and slab model we study the importance of prior hierarchical specifications and draw connections to frequentist generalized ridge regression estimation specifically we study the usefulness of continuous bimodal priors to model hypervariance parameters and the effect scaling has on the posterior mean through its relationship to penalization several model selection strategies some frequentist and some bayesian in nature are developed and studied theoretically we demonstrate the importance of selective shrinkage for effective variable selection in terms of risk misclassification and show this is achieved using the posterior from a rescaled spike and slab model we also show how to verify a procedure s ability to reduce model uncertainty in finite samples using a specialized forward selection strategy using this tool we illustrate the effectiveness of rescaled spike and slab models in reducing model uncertainty

on persistent excitations for the identification of switched linear dynamical systems over finite fields this paper discusses the issue of the persistent excitation pe conditions in the context of identification for dynamical systems defined over a finite field the work is motivated by the fact that the asymptotical property of the pe conditions for dynamical systems defined over the field of real numbers is no longer valid in the case of systems defined over finite fields the special class of switched linear discrete time systems for which the mode is assumed to be unknown is considered a necessary and sufficient condition that provides the minimum amount of data required for the identification is first proposed next a necessary condition is derived that gives the structural condition the system must satisfy regardless of the availability of data finally some computational aspects are discussed and examples are given to illustrate the validity of the proposed results

negative binomial process count and mixture modeling the seemingly disjoint problems of count and mixture modeling are united under the negative binomial nb process a gamma process is employed to model the rate measure of a poisson process whose normalization provides a random probability measure for mixture modeling and whose marginalization leads to an nb process for count modeling a draw from the nb process consists of a poisson distributed finite number of distinct atoms each of which is associated with a logarithmic distributed number of data samples we reveal relationships between various count and mixture modeling distributions and construct a poisson logarithmic bivariate distribution that connects the nb and chinese restaurant table distributions fundamental properties of the models are developed and we derive efficient bayesian inference it is shown that with augmentation and normalization the nb process and gamma nb process can be reduced to the dirichlet process and hierarchical dirichlet process respectively these relationships highlight theoretical structural and computational advantages of the nb process a variety of nb processes including the beta geometric beta nb marked beta nb marked gamma nb and zero inflated nb processes with distinct sharing mechanisms are also constructed these models are applied to topic modeling with connections made to existing algorithms under poisson factor analysis example results show the importance of inferring both the nb dispersion and probability parameters

consensus networks with switching topology and time delays over finite fields the consensus problem in networks with both switching topology and time delays over finite fields is investigated in this paper the finite field which is a kind of finite alphabet is considered due to the fact that networks often possess limited computation memory and capabilities of communication first by graph theoretic method one necessary and sufficient condition is derived for finite field consensus of switching networks without time delays subsequently another necessary and sufficient condition on finite field consensus without time delays is provided based on ffc property of matrices associated with switching networks moreover by means of the results on delay free networks some necessary and sufficient conditions for finite field consensus of networks with both switching topology and time delays are obtained additionally it can be shown that switching networks with time delays present in each self transmission cannot achieve consensus

the single input minimal controllability problem for structured systems abstract this paper considers the minimal controllability problem mcp i e the problem of controlling a linear system with an input vector having as few non zero entries as possible we focus on structured systems which represent an interesting class of parameter dependent linear systems and look for structural controllability properties based on the sparsity pattern of the input vector we show first that the mcp is solvable when a rank condition is satisfied and show that generically one non zero entry in the input vector is sufficient to achieve controllability when there is no specific system structure according to the fixed zero non zero pattern of the state matrix entries we give an explicit characterization of the minimum number and the possible location of non zero entries in the input vector to ensure generic controllability the analysis based on graph tools provides with a simple polynomial mcp solution and highlights the structural mechanisms that make it useful to act on some variables to ensure controllability

compound random measures and their use in bayesian non parametrics summary a new class of dependent random measures which we call compound random measures is proposed and the use of normalized versions of these random measures as priors in bayesian non parametric mixture models is considered their tractability allows the properties of both compound random measures and normalized compound random measures to be derived in particular we show how compound random measures can be constructed with gamma stable and generalized gamma process marginals we also derive several forms of the laplace exponent and characterize dependence through both the levy copula and the correlation function an augmented polya urn scheme sampler and a slice sampler are described for posterior inference when a normalized compound random measure is used as the mixing measure in a non parametric mixture model and a data example is discussed

the two parameter poisson dirichlet distribution derived from a stable subordinator the two parameter poisson dirichlet distribution denoted mathsf pd alpha theta is a probability distribution on the set of decreasing positive sequences with sum 1 the usual poisson dirichlet distribution with a single parameter theta introduced by kingman is mathsf pd 0 theta known properties of mathsf pd 0 theta including the markov chain description due to vershik shmidt and ignatov are generalized to the two parameter case the size biased random permutation of mathsf pd alpha theta is a simple residual allocation model proposed by engen in the context of species diversity and rediscovered by perman and the authors in the study of excursions of brownian motion and bessel processes for 0 alpha 1 mathsf pd alpha 0 is the asymptotic distribution of ranked lengths of excursions of a markov chain away from a state whose recurrence time distribution is in the domain of attraction of a stable law of index alpha formulae in this case trace back to work of darling lamperti and wendel in the 1950s and 1960s the distribution of ranked lengths of excursions of a one dimensional brownian motion is mathsf pd 1 2 0 and the corresponding distribution for a brownian bredge is mathsf pd 1 2 1 2 the mathsf pd alpha 0 and mathsf pd alpha alpha distributions admit a similar interpretation in terms of the ranked lengths of excursions of a semistable markov process whose zero set is the range of a stable subordinator of index alpha

bayesian density estimation and inference using mixtures abstract we describe and illustrate bayesian inference in models for density estimation using mixtures of dirichlet processes these models provide natural settings for density estimation and are exemplified by special cases where data are modeled as a sample from mixtures of normal distributions efficient simulation methods are used to approximate various prior posterior and predictive distributions this allows for direct inference on a variety of practical issues including problems of local versus global smoothing uncertainty about density estimates assessment of modality and the inference on the numbers of components also convergence results are established for a general class of normal mixture models

a new generalized consensus problem and its crt based solution this technical note introduces a new generalized consensus problem where nodes in a network are guaranteed to reach the final consensus on a common vector whose elements are exactly the initial values arbitrarily chosen by nodes we propose a fully decentralized algorithm able to solve the above problem and derive conditions to guarantee that consensus is reached in a finite number of steps in particular we prove that in a network composed by n nodes the proposed consensus problem is solvable in at most 2n steps moreover we introduce a finite field solution based on the chinese remainder theorem crt able to reduce the complexity of the proposed approach in the case of capacity constraints and we discuss an illustrative case study

sequences of willmore surfaces in this paper we develop the theory of willmore sequences for willmore surfaces in the 4 sphere we show that under appropriate conditions this sequence has to terminate in this case the willmore surface either is the twistor projection of a holomorphic curve into mathbb c mathbb p 3 or the inversion of a minimal surface with planar ends in mathbb r 4 these results give a unified explanation of previous work on the characterization of willmore spheres and willmore tori with non trivial normal bundles by various authors

discrete holomorphic geometry i darboux transformations and spectral curves finding appropriate notions of discrete holomorphic maps and more generally conformal immersions of discrete riemann surfaces into 3 space is an important problem of discrete differential geometry and computer visualization we propose an approach to discrete conformality that is based on the concept of holomorphic line bundles over discrete surfaces by which we mean the vertex sets of triangulated surfaces with bi colored set of faces the resulting theory of discrete conformality is simultaneously mobius invariant and based on linear equations in the special case of maps into the 2 sphere we obtain a reinterpretation of the theory of complex holomorphic functions on discrete surfaces introduced by dynnikov and novikov as an application of our theory we introduce a darboux transformation for discrete surfaces in the conformal 4 sphere this darboux transformation can be interpreted as the space and time discrete davey stewartson flow of konopelchenko and schief for a generic map of a discrete torus with regular combinatorics the space of all darboux transforms has the structure of a compact riemann surface the spectral curve this makes contact to the theory of algebraically completely integrable systems and is the starting point of a soliton theory for triangulated tori in 3 and 4 space devoid of special assumptions on the geometry of the surface

curved flats and isothermic surfaces we show how pairs of isothermic surfaces are given by curved flats in a pseudo riemannian symmetric space and vice versa calapso s fourth order partial differential equation is derived and using a solution of this equation a mobius invariant frame for an isothermic surface is built

the geometric complexity of special lagrangian t2 cones we prove a number of results on the geometric complexity of special lagrangian slg t2 cones in 3 every slg t2 cone has a fundamental integer invariant its spectral curve genus we prove that the spectral curve genus of an slg t2 cone gives a lower bound for its geometric complexity i e the area the stability index and the legendrian index of any slg t2 cone are all bounded below by explicit linearly growing functions of the spectral curve genus we prove that the cone on the clifford torus which has spectral curve genus zero in s5 is the unique slg t2 cone with the smallest possible legendrian index and hence that it is the unique stable slg t2 cone this leads to a classification of all rigid index 1 slg cone types in dimension three for cones with spectral curve genus two we give refined lower bounds for the area the legendrian index and the stability index one consequence of these bounds is that there exist s1 invariant slg torus cones of arbitrarily large area legendrian and stability indices we explain some consequences of our results for the programme due to joyce to understand the most common three dimensional isolated singularities of generic families of slg submanifolds in almost calabi yau manifolds

some results about the existence of critical points for the willmore functional using a perturbative approach it is shown existence and multiplicity of critical points for the willmore functional in ambient manifold mathbb r 3 g epsilon where g epsilon is a metric close and asymptotic to the euclidean one with the same technique it is proved a non existence result in general riemannian manifold m g of dimension three

energy of sections of the deligne hitchin twistor space we study a natural functional on the space of holomorphic sections of the deligne hitchin moduli space of a compact riemann surface generalizing the energy of equivariant harmonic maps corresponding to twistor lines we show that the energy is the residue of the pull back along the section of a natural meromorphic connection on the hyperholomorphic line bundle recently constructed by hitchin as a byproduct we show the existence of a hyper kahler potentials for new components of real holomorphic sections of twistor spaces of hyper kahler manifolds with rotating s 1 action additionally we prove that for a certain class of real holomorphic sections of the deligne hitchin moduli space the energy functional is basically given by the willmore energy of corresponding equivariant conformal map to the 3 sphere as an application we use the functional to distinguish new components of real holomorphic sections of the deligne hitchin moduli space from the space of twistor lines

lower eigenvalue estimates for dirac operators we derive upper eigenvalue estimates for generalized dirac operators on closed riemannian manifolds in the case of the classical dirac operator the estimates on the first eigenvalues are sharp for spheres of constant curvature

variational inference in nonconjugate models mean field variational methods are widely used for approximate posterior inference in many probabilistic models in a typical application mean field methods approximately compute the posterior with a coordinate ascent optimization algorithm when the model is conditionally conjugate the coordinate updates are easily derived and in closed form however many models of interest like the correlated topic model and bayesian logistic regression are nonconjugate in these models mean field methods cannot be directly applied and practitioners have had to develop variational algorithms on a case by case basis in this paper we develop two generic methods for nonconjugate models laplace variational inference and delta method variational inference our methods have several advantages they allow for easily derived variational algorithms with a wide class of nonconjugate models they extend and unify some of the existing algorithms that have been derived for specific models and they work well on real world data sets we studied our methods on the correlated topic model bayesian logistic regression and hierarchical bayesian logistic regression

structural controllability and observability of linear systems over finite fields with applications to multi agent systems we develop a graph theoretic characterization of controllability and observability of linear systems over finite fields specifically we show that a linear system will be structurally controllable and observable over a finite field if the graph of the system satisfies certain properties and the size of the field is sufficiently large we also provide graph theoretic upper bounds on the controllability and observability indices for structured linear systems over arbitrary fields we then use our analysis to design nearest neighbor rules for multi agent systems where the state of each agent is constrained to lie in a finite set we view the discrete states of each agent as elements of a finite field and employ a linear iterative strategy whereby at each time step each agent updates its state to be a linear combination over the finite field of its own state and the states of its neighbors using our results on structural controllability and observability we show how a set of leader agents can use this strategy to place all agents into any desired state within the finite set and how a set of sink agents can recover the set of initial values held by all of the agents