practical global optimization for multiview geometry this paper presents a practical method for finding the provably globally optimal solution to numerous problems in projective geometry including multiview triangulation camera resectioning and homography estimation unlike traditional methods which may get trapped in local minima due to the non convex nature of these problems this approach provides a theoretical guarantee of global optimality the formulation relies on recent developments in fractional programming and the theory of convex underestimators and allows a unified framework for minimizing the standard l 2 norm of reprojection errors which is optimal under gaussian noise as well as the more robust l 1 norm which is less sensitive to outliers even though the worst case complexity of our algorithm is exponential the practical efficacy is empirically demonstrated by good performance on experiments for both synthetic and real data an open source matlab toolbox that implements the algorithm is also made available to facilitate further research

some finitely presented nilpotent by abelian groups this paper gives some sufficient conditions for the finite presentability of nilpotent by abelian groups the general question of deciding whether a particular soluble group admits a finite presentation has received considerable attention in recent years see the review article of strebel lo for a discussion of the work to 1984 in particular we want to draw attention to three papers particularly relevant to the topic of this paper firstly bieri and strebel have given in 4 a necessary and sufficient condition for the finite presentation of a metabelian group the present work is based on their methods the sufficient condition was extended by mcisaac in 7 to a condition for the finite presentation of a split extension of a group of nilpotency class 2 by an abelian group in a major work abels 2 deals with finite presentability of arithmetic groups his work shows for example that soluble arithmetic groups corresponding to connected algebraic groups are finitely presented if and only if the metabelian quotient is finitely presented and the multiplier the second homology with trivial coefficients of the derived group is finitely generated as a module for the group this therefore gives a superb answer to the question for arithmetic groups but it is not clear to what extent such results are available for general abstract groups we return briefly to this later in this introduction the aim of this paper is to carry the sufficient condition given by mcisaac considerably further we remove the restriction that the extension involved be split and widen the condition considerably in particular we make use of the jacobi identity which did not figure in mcisaac s treatment we also extend the results to the case where the nilpotent normal subgroup has arbitrary nilpotency class to describe our results we need to introduce some notation and to

multiple view geometry under the l_ infty norm this paper presents a new framework for solving geometric structure and motion problems based on the linfin norm instead of using the common sum of squares cost function that is the l2 norm the model fitting errors are measured using the linfin norm unlike traditional methods based on l2 our framework allows for the efficient computation of global estimates we show that a variety of structure and motion problems for example triangulation camera resectioning and homography estimation can be recast as quasi convex optimization problems within this framework these problems can be efficiently solved using second order cone programming socp which is a standard technique in convex optimization the methods have been implemented in matlab and the resulting toolbox has been made publicly available the algorithms have been validated on real data in different settings on problems with small and large dimensions and with excellent performance

quantum graphs a simple model for chaotic scattering we connect quantum graphs with infinite leads and turn them into scattering systems we show that they display all the features which characterize quantum scattering systems with an underlying classical chaotic dynamics typical poles delay time and conductance distributions ericson fluctuations and when considered statistically the ensemble of scattering matrices reproduces quite well the predictions of the appropriately defined random matrix ensembles the underlying classical dynamics can be defined and it provides important parameters which are needed for the quantum theory in particular we derive exact expressions for the scattering matrix and an exact trace formula for the density of resonances in terms of classical orbits analogous to the semiclassical theory of chaotic scattering we use this in order to investigate the origin of the connection between random matrix theory and the underlying classical chaotic dynamics being an exact theory and due to its relative simplicity it offers new insights into this problem which is at the forefront of the research in chaotic scattering and related fields

tropical varieties for non archimedean analytic spaces generalizing the construction from tropical algebraic geometry we associate to every irreducible d dimensional closed analytic subvariety of mathbb g m n a tropical variety in n with respect to a complete non archimedean place by methods of analytic and formal geometry we prove that the tropical variety is a totally concave locally finite union of d dimensional polytopes for an algebraic morphism f x a to a totally degenerate abelian variety a we give a bound for the dimension of f x in terms of the singularities of a strictly semistable model of x a closed d dimensional subvariety x of a induces a periodic tropical variety a generalization of mumford s construction yields models of x and a which can be handled with the theory of toric varieties for a canonically metrized line bundle l on a the measures c1 l x d are piecewise haar measures on x using methods of convex geometry we give an explicit description of these measures in terms of tropical geometry in a subsequent paper this is a key step in the proof of bogomolov s conjecture for totally degenerate abelian varieties over function fields

comparison of two notions of subharmonicity on non archimedean curves we show that a continuous function on the analytification of a smooth proper algebraic curve over a non archimedean field is subharmonic in the sense of thuillier if and only if it is psh i e subharmonic in the sense of chambert loir and ducros this equivalence implies that the property psh for continuous functions is stable under pullback with respect to morphisms of curves furthermore we prove an analogue of the monotone regularization theorem on the analytification of mathbb p 1 and mumford curves using this equivalence

tropicalization of the moduli space of stable maps let x be an algebraic variety and let s be a tropical variety associated to x we study the tropicalization map from the moduli space of stable maps into x to the moduli space of tropical curves in s we prove that it is a continuous map and that its image is compact and polyhedral loosely speaking when we deform algebraic curves in x the associated tropical curves in s deform continuously moreover the locus of realizable tropical curves inside the space of all tropical curves is compact and polyhedral our main tools are berkovich spaces formal models balancing conditions vanishing cycles and quantifier elimination for rigid subanalytic sets

virtual rational betti numbers of abelian by polycyclic groups abstract let 1 a g q 1 be an exact sequence of groups where a is abelian q is polycyclic and q k a z q is finitely generated as q q module via the diagonal q action for k 2 m moreover we assume that if g is not metabelian then it is of type fp 3 our main result is that sup u a dim q h j u q for 0 j m where a is the set of all subgroups of finite index in g

scattering reflection and impedance of waves in chaotic and disordered systems with absorption we review recent progress in analysing wave scattering in systems with both intrinsic chaos and or disorder and internal losses when the scattering matrix is no longer unitary by mapping the problem onto a nonlinear supersymmetric model we are able to derive closed form analytic expressions for the distribution of reflection probability in a generic disordered system one of the most important properties resulting from such an analysis is statistical independence between the phase and the modulus of the reflection amplitude in every perfectly open channel the developed theory has far reaching consequences for many quantities of interest including local green functions and time delays in particular we point out the role played by absorption as a sensitive indicator of mechanisms behind the anderson localization transition we also provide a random matrix based analysis of s matrix and impedance correlations for various symmetry classes as well as the distribution of transmitted power for systems with broken time reversal invariance completing previous works on the subject the results can be applied in particular to the experimentally accessible impedance and reflection in a microwave or an ultrasonic cavity attached to a system of antennas

fibers of tropicalization we use functoriality of tropicalization and the geometry of projections of subvarieties of tori to show that the fibers of the tropicalization map are dense in the zariski topology for subvarieties of tori over fields of generalized power series points in each tropical fiber are obtained constructively using kedlaya s transfinite version of newton s method

effective coupling for open billiards we derive an explicit expression for the coupling constants of individual eigenstates of a closed billiard that is opened by attaching a waveguide the wigner time delay and the resonance positions resulting from the coupling constants are compared to an exact numerical calculation deviations can be attributed to evanescent modes in the waveguide and to the finite number of eigenstates taken into account the influence of the shape of the billiard and of the boundary conditions at the mouth of the waveguide are also discussed finally we show that the mean value of the dimensionless coupling constants tends to the critical value when the eigenstates of the billiard follow random matrix theory

multiplicative structure of 2x2 tropical matrices we study the algebraic structure of the semigroup of all 2x2 tropical matrices under multiplication using ideas from tropical geometry we give a complete description of green s relations and the idempotents and maximal subgroups of this semigroup

computing tropical resultants abstract we fix the supports a a 1 a k of a list of tropical polynomials and define the tropical resultant tr a to be the set of choices of coefficients such that the tropical polynomials have a common solution we prove that tr a is the tropicalization of the algebraic variety of solvable systems and that its dimension can be computed in polynomial time the tropical resultant inherits a fan structure from the secondary fan of the cayley configuration of a and we present algorithms for the traversal of tr a in this structure we also present a new algorithm for recovering a newton polytope from the support of its tropical hypersurface we use this to compute the newton polytope of the sparse resultant polynomial in the case when tr a is of codimension 1 finally we consider the more general setting of specialized tropical resultants and report on experiments with our implementations

isomorphism rigidity of commuting automorphisms r let d 1 and let x and y be two zero entropy z d actions on compact abelian groups by d commuting automorphisms we show that if all lower rank subactions of and have completely positive entropy then any measurable equivariant map from x to y is an affine map in particular two such actions are measurably conjugate if and only if they are algebraically conjugate

on weak commutativity in groups abstract for a group g we study homological and homotopical properties of the group g g g g g 1 for g g in particular we show that the operator preserves the soluble of type f p property

tropical geometric interpretation of ultradiscrete singularity confinement using the interpretation of the ultradiscretization procedure as a non archimedean valuation we use results of tropical geometry to show how roots and poles manifest themselves in piece wise linear systems as points of non differentiability this will allow us to demonstrate a correspondence between singularity confinement for discrete integrable systems and ultradiscrete singularity confinement for ultradiscrete integrable systems

homogeneity and rigidity of the brookes groves invariant for the non commutative torus in 4 bieri and strebel defined a geometric invariant for finitely generated modules over the group algebras of finitely generated abelian groups they used this to define a criterion for when metabelian groups are finitely presented this invariant was further developed by bieri strebel and groves and has many interesting applications in 2 bieri and groves showed that when the group algebra is defined over a dedekind domain the complement of must be a closed rational spherical polyhedral cone in 6 7 brookes and groves defined a similar invariant for modules over the crossed product of a division ring by a free finitely generated abelian group such a crossed product is often known as the coordinate ring of the non commutative torus since in the special case where it is commutative it is the coordinate ring of an algebraic torus if in the commutative case we take the complement of and identify points that differ by a positive scalar multiple we obtain brookes and groves were unable to prove that their invariant must be a rational polyhedral cone although using the methods of 2 they do prove a weaker version of the result they show that for any finitely generated module m m must contain a rational polyhedral cone m of dimension equal to the gelfand kirillov dimension of m and moreover that the complement m m must be contained inside a rational polyhedral cone of strictly smaller dimension

pure dimension and projectivity of tropical polytopes abstract we study how geometric properties of tropical convex sets and polytopes which are of interest in many application areas manifest themselves in their algebraic structure as modules over the tropical semiring our main results establish a close connection between pure dimension of tropical convex sets and projectivity in the sense of ring theory these results lead to a geometric understanding of idempotency for tropical matrices as well as their direct interest our results suggest that there is substantial scope to apply ideas and techniques from abstract algebra in particular ring theory in tropical geometry

a rigidity property for the set of all characters induced by valuations if k is a field and g a finitely generated multiplicative subgroup of k then every real valuation on k induces a character g r it is known that the set ls g c r 1 of all characters induced by valuations is polyhedral we prove that a g satisfies a certain rigidity property and apply this to give a new and conceptual proof of the brewster roseblade result 4 on the group of automorphisms of k stabilizing g 1 lntroduction 1 1 let k be a field and k c k a subfield by a real valuation on k over k we mean a homomorphism w kx r of the multiplicative group of k into the additive group of the reals which is trivial on kx and satisfies w a b mint w a w b for all a b e kx with a b o throughout the paper g shall dersote a finitely generated multiplicative subgroup of k then w induces a character x wlc g 1t on g and so following g m bergman 1 we consider the set a g of all characters of g induced by real valuations on k over k thus a g is a

statistics of resonances and nonorthogonal eigenfunctions in a model for single channel chaotic scattering we describe analytical and numerical results on the statistical properties of complex eigenvalues and the corresponding nonorthogonal eigenvectors for non hermitian random matrices modeling one channel quantum chaotic scattering in systems with broken time reversal invariance

stable pair tropical and log canonical compactifications of moduli spaces of del pezzo surfaces we give a functorial normal crossing compactification of the moduli space of smooth cubic surfaces entirely analogous to the grothendieck knudsen compactification m 0 n subset overline m 0 n

experimental investigation of universal parametric correlators using a vibrating plate the parametric variation of the eigenfrequencies of a chaotic plate is measured and compared to random matrix theory using recently calculated universal correlation functions the sensitivity of the flexural modes of the plate to pressure is used to isolate this symmetry class of modes and simplify the data analysis the size of the plate is used as the external parameter and the eigenvalues are observed to undergo one or two oscillations in the experimental window the correlations of the eigenvalues are in good agreement with statistical measures such as the parametric number variance the velocity autocorrelation and the intralevel velocity autocorrelation derived for the gaussian orthogonal ensemble of random matrix theory our results show that the theory can be also applied to wave systems other than quantum systems

tensor powers of modules over finitely generated abelian groups in an earlier paper 11 the authors investigated as a major component of their final result a special case of the following question let r be a commutative ring with unity g a finitely generated abelian group and a4 a finitely generated rg module consider the tensor power m as an rg module via the diagonal action of g under what conditions is m a finitely generated rg module the answer obtained in 1 was for the case when r is a field and used an invariant z m introduced by the first author and strebel in 3 we briefly describe cl firstly if n is the torsion free rank of g we can identify hom g w with w defining two elements of hom g iw to be equivalent if they differ by a positive real multiple we obtain a natural projection of hom g w o onto the sphere s i denote the equivalence class of xe hom g 1w by x and define gcxi g ge g x g 30 then z is the subset of s consisting of all those x for which m is a finitely generated rg module and cl is the complement of c in s we say that m is k tame if there do not exist x i xk in zh such that x1 xk 0 then the partial answer referred to above theorem 3 4 of l is

faithful tropicalization of the grassmannian of planes we show that the tropical projective grassmannian of planes is homeomorphic to a closed subset of the analytic grassmannian in berkovich s sense by constructing a continuous section to the tropicalization map our main tool is an explicit description of the algebraic coordinate rings of the toric strata of the grassmannian we determine the fibers of the tropicalization map and compute the initial degenerations of all the toric strata as a consequence we prove that the tropical multiplicities of all points in the tropical projective grassmannian are equal to one finally we determine a piecewise linear structure on the image of our section that corresponds to the polyhedral structure on the tropical projective grassmannian

the bieri neumann strebel invariants via newton polytopes we study the newton polytopes of determinants of square matrices defined over rings of twisted laurent polynomials we prove that such newton polytopes are single polytopes rather than formal differences of two polytopes this result can be seen as analogous to the fact that determinants of matrices over commutative laurent polynomial rings are themselves polynomials rather than rational functions we also exhibit a relationship between the newton polytopes and invertibility of the matrices over novikov rings thus establishing a connection with the invariants of bieri neumann strebel bns via a theorem of sikorav we offer several applications we reprove thurston s theorem on the existence of a polytope controlling the bns invariants of a 3 manifold group we extend this result to free by cyclic groups and the more general descending hnn extensions of free groups we also show that the bns invariants of poincare duality groups of type mathtt f in dimension 3 and groups of deficiency one are determined by a polytope when the groups are assumed to be agrarian that is their integral group rings embed in skew fields the latter result partially confirms a conjecture of friedl we also deduce the vanishing of the newton polytopes associated to elements of the whitehead groups of many groups satisfying the atiyah conjecture we use this to show that the l 2 torsion polytope of friedl luck is invariant under homotopy we prove the vanishing of this polytope in the presence of amenability thus proving a conjecture of friedl luck tillmann

degenerations of amoebae and berkovich spaces we prove a continuity result for the fibers of the berkovich analytification of a complex algebraic variety with respect to the maximum of the archimedean norm and the trivial norm as a consequence we obtain generalizations of a result of mikhalkin and rullgard about degenerations of amoebae onto tropical varieties

interpolation formula for the reflection coefficient distribution of absorbing chaotic cavities in the presence of time reversal symmetry we propose an interpolation formula for the distribution of the reflection coefficient in the presence of time reversal symmetry for chaotic cavities with absorption this is done assuming a similar functional form as when time reversal invariance is absent the interpolation formula reduces to the analytical expressions for the strong and weak absorption limits our proposal is compared to the quite complicated exact result existing in the literature

universal results for correlations of characteristic polynomials riemann hilbert approach we prove that general correlation functions of both ratios and products of characteristic polynomials of hermitian random matrices are governed by integrable kernels of three different types a those constructed from orthogonal polynomials b those constructed from cauchy transforms of the same orthogonal polynomials and finally c those constructed from both orthogonal polynomials and their cauchy transforms these kernels are related with the riemann hilbert problem for orthogonal polynomials for the correlation functions we obtain exact expressions in the form of determinants of these kernels derived representations enable us to study asymptotics of correlation functions of characteristic polynomials via the deift zhou steepest descent stationary phase method for riemann hilbert problems and in particular to find negative moments of characteristic polynomials this reveals the universal parts of the correlation functions and moments of characteristic polynomials for an arbitrary invariant ensemble of 2 symmetry class

rank functions of tropical matrices abstract we consider rank functions important in tropical linear algebra the tropical rank equal to the topological dimension of the tropical linear span of the columns of a given matrix the factor rank equal to the smallest number of vectors containing these columns in their span the kapranov rank related to problems of tropical algebraic geometry and the determinantal and gondran minoux ranks which generalize the classical linear algebraic notion of rank we are interested in studying the arithmetic properties of the rank functions their mutual behavior and the related computational problems we discuss different open problems related to rank functions of tropical matrices and illustrate them by the number of examples

on the geometry of chemical reaction networks lyapunov function and large deviations in an earlier paper we proved the validity of large deviations theory for the particle approximation of quite general chemical reaction networks in this paper we extend its scope and present a more geometric insight into the mechanism of that proof exploiting the notion of spherical image of the reaction polytope this allows to view the asymptotic behavior of the vector field describing the mass action dynamics of chemical reactions as the result of an interaction between the faces of this polytope in different dimensions we also illustrate some local aspects of the problem in a discussion of wentzell freidlin theory together with some examples

polyhedrality of the brookes groves invariant for the non commutative torus in 3 bieri and strebel defined a geometric invariant for finitely generated modules over the group algebras of finitely generated abelian groups they used this to define a criterion for when metabelian groups are finitely presented this invariant was further developed by bieri strebel and groves and has many interesting applications in 2 bieri and groves showed that when the group algebra is defined over a dedekind domain the complement of must be a closed rational spherical polyhedral cone in 4 and 5 brookes and groves defined a similar invariant for modules over the crossed product of a division ring by a free finitely generated abelian group such a crossed product is often known as the coordinate ring of the non commutative torus since in the special case where it is commutative it is the coordinate ring of an algebraic torus if in the commutative case we take the complement of and identify points that differ by a positive scalar multiple we obtain brookes and groves were unable to prove that their invariant must be a rational polyhedral cone although using the methods of 2 they do prove a weaker version of the result they show that for any finitely generated module m m must contain a rational polyhedral cone m of dimension equal to the gelfand kirillov dimension of m and moreover that the complement m m must be contained inside a rational polyhedral cone of strictly smaller dimension in this paper we use grobner basis methods to prove the following theorem

random matrices close to hermitian or unitary overview of methods and results the paper discusses recent progress in understanding statistical properties of eigenvalues of weakly non hermitian and non unitary random matrices the first type of ensembles is of the form i with being a large random n n hermitian matrix with independent entries deformed by a certain anti hermitian n n matrix i satisfying in the limit of large dimension n the condition tr 2 n tr 2 here can be either a random or just a fixed given hermitian matrix ensembles of such a type with 0 emerge naturally when describing quantum scattering in systems with chaotic dynamics and serve to describe resonance statistics related models are used to mimic complex spectra of the dirac operator with chemical potential in the context of quantum chromodynamics ensembles of the second type arising naturally in scattering theory of discrete time systems are formed by n n matrices with complex entries such that i for 0 this coincides with the circular unitary ensemble and 0 i describes deviation from unitarity our result amounts to answering statistically the following old question given the singular values of a matrix describe the locus of its eigenvalues we systematically show that the obtained expressions for the correlation functions of complex eigenvalues describe a non trivial crossover from wigner dyson statistics of real unimodular eigenvalues typical of hermitian unitary matrices to ginibre statistics in the complex plane typical of ensembles with strong non hermiticity tr 2 tr 2 when n finally we discuss scarce results available on eigenvector statistics for weakly non hermitian random matrices

compactifications of subvarieties of tori we study compactifications of subvarieties of algebraic tori defined by imposing a sufficiently fine polyhedral structure on their non archimedean amoebas these compactifications have many nice properties for example any k boundary divisors intersect in codimension k we consider some examples including m 0 n subset overline m 0 n and more generally log canonical models of complements of hyperplane arrangements and compact quotients of grassmannians by a maximal torus

reducing nonideal to ideal coupling in random matrix description of chaotic scattering application to the time delay problem we write explicitly a transformation of the scattering phases reducing the problem of quantum chaotic scattering for systems with m statistically equivalent channels at nonideal coupling to that for ideal coupling unfolding the phases by their local density leads to universality of their local fluctuations for large m a relation between the partial time delays and diagonal matrix elements of the wigner smith matrix is revealed for ideal coupling this helped us in deriving the joint probability distribution of partial time delays and the distribution of the wigner time delay

the σ2 conjecture for metabelian groups the general case abstract the bieri neumann strebel invariant m g of a group g is a certain subset of a sphere that contains information about finiteness properties of subgroups of g in case of a metabelian group g the set 1 g completely characterizes finite presentability and it is conjectured that it also contains complete information about the higher finiteness properties fpm conjecture the m conjecture states how the higher invariants are obtained from 1 g in this paper we prove the 2 conjecture

linear multi view reconstruction and camera recovery using a reference plane this paper presents a linear algorithm for simultaneous computation of 3d points and camera positions from multiple perspective views based on having a reference plane visible in all views the reconstruction and camera recovery is achieved in a single step by finding the null space of a matrix built from image data using singular value decomposition contrary to factorization algorithms this approach does not need to have all points visible in all views this paper investigates two reference plane configurations finite reference planes defined by four coplanar points and infinite reference planes defined by vanishing points a further contribution of this paper is the study of critical configurations for configurations with four coplanar points by simultaneously reconstructing points and views we can exploit the numerical stabilizing effect of having wide spread cameras with large mutual baselines this is demonstrated by reconstructing the outside and inside courtyard of a building on the basis of 35 views in one single singular value decomposition

generic tropical varieties on subvarieties and in the non constant coefficient case abstract in earlier papers it was shown that the generic tropical variety of an ideal can contain information on algebraic invariants as for example the depth in a direct way the existence of generic tropical varieties has so far been proved in the constant coefficient case for the usual notion of genericity in this paper we generalize this existence result to include the case of non constant coefficients in certain settings moreover we extend the notion of genericity to arbitrary closed subvarieties of the general linear group in addition to including the concept of genericity on algebraic groups this yields structural results on the tropical variety of an ideal under an arbitrary linear coordinate change

experimental simulation of quantum graphs by microwave networks we present the results of experimental and theoretical study of irregular tetrahedral microwave networks consisting of coaxial cables annular waveguides connected by t joints the spectra of the networks were measured in the frequency range 0 0001 16 ghz in order to obtain their statistical properties such as the integrated nearest neighbor spacing distribution and the spectral rigidity d3sld the comparison of our experimental and theoretical results shows that microwave networks can simulate quantum graphs with time reversal symmetry in particular we use the spectra of the microwave networks to study the periodic orbits of the simulated quantum graphs we also present experimental study of directional microwave networks consisting of coaxial cables and faraday isolators for which the time reversal symmetry is broken in this case our experimental results indicate that spectral statistics of directional microwave networks deviate from predictions of gaussian orthogonal ensembles in random matrix theory approaching especially for small eigenfrequency spacing s results for gaussian unitary ensembles experimental results are supported by the theoretical analysis of directional graphs

distribution of reflection eigenvalues in many channel chaotic cavities with absorption the reflection matrix r s dagger s with s being the scattering matrix differs from the unit matrix when absorption is finite using the random matrix approach we calculate analytically the distribution function of its eigenvalues in the limit of a large number of propagating modes in the leads attached to a chaotic cavity the obtained result is independent of the presence of time reversal symmetry in the system being valid at finite absorption and arbitrary openness of the system the particular cases of perfectly and weakly open cavities are considered in detail an application of our results to the problem of thermal emission from random media is briefly discussed

quasiconvex optimization for robust geometric reconstruction geometric reconstruction problems in computer vision are often solved by minimizing a cost function that combines the reprojection errors in the 2d images in this paper we show that for various geometric reconstruction problems their reprojection error functions share a common and quasiconvex formulation based on the quasiconvexity we present a novel quasiconvex optimization framework in which the geometric reconstruction problems are formulated as a small number of small scale convex programs that are readily solvable our final reconstruction algorithm is simple and has intuitive geometric interpretation in contrast to existing local minimization approaches our algorithm is deterministic and guarantees a predefined accuracy of the minimization result the quasiconvexity also provides an intuitive method to handle directional uncertainties and outliers in measurements for a large scale problem or in a situation where computational resources are constrained we provide an efficient approximation that gives a good upper bound but not global minimum on the reconstruction error we demonstrate the effectiveness of our algorithm by experiments on both synthetic and real data

universal statistics of the scattering coefficient of chaotic microwave cavities we consider the statistics of the scattering coefficient s of a chaotic microwave cavity coupled to a single port we remove the nonuniversal effects of the coupling from the experimental s data using the radiation impedance obtained directly from the experiments we thus obtain the normalized scattering coefficient whose probability density function pdf is predicted to be universal in that it depends only on the loss quality factor of the cavity we compare experimental pdfs of the normalized scattering coefficients with those obtained from random matrix theory rmt and find excellent agreement the results apply to scattering measurements on any wave chaotic system

verifying global minima for l2 minimization problems in multiple view geometry we consider the least squares l2 minimization problems in multiple view geometry for triangulation homography camera resectioning and structure and motion with known rotation or known plane although optimal algorithms have been given for these problems under an l infinity cost function finding optimal least squares solutions to these problems is difficult since the cost functions are not convex and in the worst case may have multiple minima iterative methods can be used to find a good solution but this may be a local minimum this paper provides a method for verifying whether a local minimum solution is globally optimal by providing a simple and rapid test involving the hessian of the cost function the basic idea is that by showing that the cost function is convex in a restricted but large enough neighbourhood a sufficient condition for global optimality is obtained the method is tested on numerous problem instances of real data sets in the vast majority of cases we are able to verify that the solutions are optimal in particular for small to medium scale problems

tropical compactification in log regular varieties in this article we define a natural tropicalization procedure for closed subsets of log regular varieties in the case of constant coefficients and study its basic properties this framework allows us to generalize some of tevelev s results on tropical compactification as well as hacking s result on the cohomology of the link of a tropical variety to log regular varieties