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Showing papers on "Distribution (differential geometry) published in 2014"


Journal ArticleDOI
TL;DR: In this paper, the authors proposed a method to compute the joint probability distribution of the eigenvalues of the one-body reduced density matrices of a random quantum state of multiple distinguishable or indistinguishable particles.
Abstract: Given a random quantum state of multiple distinguishable or indistinguishable particles, we provide an effective method, rooted in symplectic geometry, to compute the joint probability distribution of the eigenvalues of its one-body reduced density matrices. As a corollary, by taking the distribution’s support, which is a convex moment polytope, we recover a complete solution to the one-body quantum marginal problem. We obtain the probability distribution by reducing to the corresponding distribution of diagonal entries (i.e., to the quantitative version of a classical marginal problem), which is then determined algorithmically. This reduction applies more generally to symplectic geometry, relating invariant measures for the coadjoint action of a compact Lie group to their projections onto a Cartan subalgebra, and can also be quantized to provide an efficient algorithm for computing bounded height Kronecker and plethysm coefficients.

61 citations


Journal ArticleDOI
24 Aug 2014
TL;DR: In this paper, the authors employed physical and numerical models to study the uniformity of the flow distribution from manifold with various configurations, including tapered longitudinal section having inlet diameters of 10.16 cm and dead end diameter of 5.08 cm.
Abstract: The flow distribution in manifolds is highly dependent on inlet pressure, configuration, and total inlet flow to the manifold. The flow from a manifold has many applications and in various fields of engineering such as civil, mechanical, and chemical engineering. In this study, physical and numerical models were employed to study the uniformity of the flow distribution from manifold with various configurations. The physical model consists of main manifold with uniform longitudinal section having diameter of 10.16 cm (4 in), five laterals with diameter of 5.08 cm (2 in), and spacing of 22 cm. Different inlet flows were tested and the values of these flows are 500, 750, and 1000 L/min. A manifold with tapered longitudinal section having inlet diameters of 10.16 cm (4 in) and dead end diameter of 5.08 cm (2 in) with the same above later specifications and flow rates was tested for its uniformity too. The percentage of absolute mean deviation for manifold with uniform diameter was found to be 34% while its value for the manifold with nonuniform diameter was found to be 14%. This result confirms the efficiency of the nonuniform distribution of fluids.

38 citations


Journal ArticleDOI
TL;DR: The geometrical formulation of continuum mechanics provides a powerful approach to understand and solve problems in anelasticity where an elastic deformation is combined with a non-elastic component arising from defects, thermal stresses, growth effects or other effects leading to residual stresses.
Abstract: The geometrical formulation of continuum mechanics provides us with a powerful approach to understand and solve problems in anelasticity where an elastic deformation is combined with a non-elastic component arising from defects, thermal stresses, growth effects or other effects leading to residual stresses. The central idea is to assume that the material manifold, prescribing the reference configuration for a body, has an intrinsic, non-Euclidean, geometrical structure. Residual stresses then naturally arise when this configuration is mapped into Euclidean space. Here, we consider the problem of discombinations (a new term that we introduce in this paper), that is, a combined distribution of fields of dislocations, disclinations and point defects. Given a discombination, we compute the geometrical characteristics of the material manifold (curvature, torsion, non-metricity), its Cartan's moving frames and structural equations. This identification provides a powerful algorithm to solve semi-inverse problems with non-elastic components. As an example, we calculate the residual stress field of a cylindrically symmetric distribution of discombinations in an infinite circular cylindrical bar made of an incompressible hyperelastic isotropic elastic solid.

31 citations


Journal ArticleDOI
17 Jul 2014-Filomat
TL;DR: In this article, it was shown that if there exists a second order symmetric parallel tensor on an almost Kenmotsu manifold, whose characteristic vector field belongs to the $(k,\mu)'$-nullity distribution, then either the manifold is locally isometric to the Riemannian product of an n+1)$-dimensional manifold of constant sectional curvature, or the second order tensor is a constant multiple of the associated metric tensor of the manifold.
Abstract: In this paper, we prove that if there exists a second order symmetric parallel tensor on an almost Kenmotsu manifold $(M^{2n+1},\phi,\xi,\eta,g)$ whose characteristic vector field $\xi$ belongs to the $(k,\mu)'$-nullity distribution, then either $M^{2n+1}$ is locally isometric to the Riemannian product of an $(n+1)$-dimensional manifold of constant sectional curvature $-4$ and a flat $n$-dimensional manifold, or the second order parallel tensor is a constant multiple of the associated metric tensor of $M^{2n+1}$. Furthermore, some properties for an almost Kenmotsu manifold admitting a second order parallel tensor with $\xi$ belonging to the $(k,\mu)$-nullity distribution are also obtained.

26 citations


Posted Content
TL;DR: In this paper, Nevanlinna's theory for holomorphic maps f from Riemann surfaces to the projective line has been studied and a generalization of Bloch Theorem concerning the Zariski closure of maps f with values in a complex torus is presented.
Abstract: We survey several results in value distribution theory for parabolic Riemann surfaces. Let Y be a parabolic Riemann surface, i.e. subharmonic functions defined on Y are constant. We discuss Nevanlinna's theory for holomorphic maps f from Y to the projective line. The results we obtain parallel the classical case Y is the complex line, as we describe now. Let X be a manifold of general type, and let A be an ample line bundle on X. It is known that there exists a holomorphic jet differential P (of order k) with values in the dual of A. If the map f has infinite area and if Y has finite Euler characteristic, then we show that f satisfies the differential relation induced by P. As a consequence, we obtain a generalization of Bloch Theorem concerning the Zariski closure of maps f with values in a complex torus. An interesting corollary of these techniques is a refined Ax-Lindemann theorem, for which we give a quick proof. We then study the degree of Nevanlinna's current T[f] associated to a parabolic leaf of a foliation F by Riemann surfaces on a compact complex manifold. We show that the degree of T[f] on the tangent bundle of the foliation is bounded from below in terms of the counting function of f with respect to the singularities of F, and the Euler characteristic of Y. In the case of complex surfaces of general type, we obtain a complete analogue of McQuillan's result: a parabolic curve of infinite area and finite Euler characteristic tangent to F is not Zariski dense.

24 citations


Journal ArticleDOI
TL;DR: In this article, the distribution of eigenvalues of a random symmetric matrix in the Gaussian Orthogonal Ensemble (GOME) was shown to be a function of the dimension of the Riemann manifold.
Abstract: We relate the distribution of eigenvalues of a random symmetric matrix in the Gaussian Orthogonal Ensemble to the distribution of critical values of a random linear combination of eigenfunctions of the Laplacian on a compact Riemann manifold. We then prove a central limit theorem describing what happens when the dimension of the manifold is very large.

16 citations


Journal ArticleDOI
TL;DR: In this article, the asymptotic distribution of the non-discrete orbits of a finitely generated group acting linearly on the unitary tangent bundle of the associated surface was studied.
Abstract: In this work, we study the asymptotic distribution of the non-discrete orbits of a finitely generated group acting linearly on ${\Bbb R}^2$. To do this, we establish new equidistribution results for the horocyclic flow on the unitary tangent bundle of the associated surface.

16 citations


Journal ArticleDOI
Miao Qian1, Deqing Mei1, Zhehe Yao1, B.H. Liu1, Lou Xinyang1, Zichen Chen1 
TL;DR: In this article, the relationship between the flow manifold structure and the velocity distribution in the reaction channel with MPFAR was established by an equivalent electrical resistance network model validated via simulation.
Abstract: Velocity uniformity in reaction channels has a significant effect on the performance of laminated microreactors with micro-pin-fin arrays (MPFAR) for hydrogen production. The hydrogen production efficiency can be improved by optimizing the structure of flow manifolds. The relationship between the flow manifold structure and the velocity distribution in the reaction channel with MPFAR is established by an equivalent electrical resistance network model validated via simulation. The effects of the flow manifold structure on the velocity distribution are investigated. The results show that the velocity distribution can be improved by increasing the y-direction coordinate Ypi of the flow manifold inlet tube. The flow manifold structure is optimized for better velocity distribution in reaction channels with different MPFAR widths.

12 citations


Journal ArticleDOI
TL;DR: A novel projection method that can be combined with any manifold learning methods to improve their dimension reduction performance when applied to high-dimensional data with a high level of noise is proposed.
Abstract: The search for a low-dimensional structure in high-dimensional data is one of the fundamental tasks in machine learning and pattern recognition. Manifold learning algorithms have recently emerged as alternatives to traditional linear dimension reduction techniques. In this paper, we propose a novel projection method that can be combined with any manifold learning methods to improve their dimension reduction performance when applied to high-dimensional data with a high level of noise. The method first builds a dispersion function that describes the distribution of dispersed manifold where the data lie. It then projects the noisy data onto a region wrapping the true manifold sufficiently close to it by applying a dynamical projection system associated with the constructed dispersion function. The effectiveness of the proposed projection method is validated by applying it to some real-world data sets with promising results.

11 citations


Journal ArticleDOI
TL;DR: In this paper, the authors restrict their attention to sub-Riemannian manifolds where the associated distribution is an Engel distribution, which is a regular and bracket-generating distribution of codimension 2 in a four-dimensional manifold.
Abstract: A sub-Riemannian manifold is a smooth manifold which carries a metric defined only on a smooth distribution $\mbox{$\cal D$}$ . In this paper, we will restrict our attention to sub-Riemannian manifolds where the associated distribution is an Engel distribution which means that $\mbox{$\cal D$}$ is a regular and bracket-generating distribution of codimension 2 in a four-dimensional manifold. We obtain a parallelism on a sub-Riemannian structure of Engel type, and then, we classify all simply connected four-dimensional sub-Riemannian manifolds which are homogeneous spaces by using a canonical linearization of the structure.

10 citations


Journal ArticleDOI
TL;DR: In this paper, the authors investigated the asymptotic distribution of the zeros of polynomials Pn(x) satisfying a first-order differential-difference equation.
Abstract: In this paper, we investigate the asymptotic distribution of the zeros of polynomials Pn(x) satisfying a first-order differential-difference equation. We give several examples of orthogonal and non-orthogonal families.

Posted Content
TL;DR: In this article, the authors developed variation formulas for the quantities of extrinsic geometry for adapted variations of metrics on almost-product (e.g. foliated) Riemannian manifolds, and applied them to study the total mixed scalar curvature of a distribution.
Abstract: We develop variation formulas for the quantities of extrinsic geometry for adapted variations of metrics on almost-product (e.g. foliated) Riemannian manifolds, and apply them to study the total mixed scalar curvature of a distribution -- analogue of the classical Einstein-Hilbert action. The mixed scalar curvature ${\rm S}_{\,\rm mix}$ is the averaged sectional curvature over all planes that contain vectors from both distributions of an almost-product structure and the variations we consider preserve orthogonality of the distributions. We derive the directional derivative $D J_{\,\rm mix}$ (of the total ${\rm S}_{\,\rm mix}$) for adapted variations of metrics on closed almost-product manifolds and foliations of arbitrary dimension. The obtained Euler-Lagrange equations are presented in two equiva\-lent forms: in terms of extrinsic geometry and intrinsically using the partial Ricci tensor. Certainly, these mixed field equations admit amount of solutions (e.g., twisted products).

Patent
24 Sep 2014
TL;DR: In this paper, a finite element mesh is divided according to an assembly model of the exhaust manifold and the temperature and the convective heat transfer coefficient of the inner wall surface of the manifold are obtained.
Abstract: The invention relates to an engine exhaust manifold thermal stress analysis and structural optimization method. The method includes the following steps that 1 boundary conditions of an inlet and an outlet of an exhaust manifold under rated conditions are calculated; 2 transient liquidity of the exhaust manifold under the working cycle is calculated according to the boundary conditions, and the temperature and the convective heat transfer coefficient of the inner wall surface of the exhaust manifold are obtained; 3 a finite element mesh is divided according to an assembly model of the exhaust manifold; 4 temperature field distribution of the exhaust manifold is calculated according to the finite element mesh and the obtained temperature and the obtained convective heat transfer coefficient of the inner wall surface of the exhaust manifold; 5 equivalent plastic strain distribution in a test cycle of the exhaust manifold is solved according to temperature field distribution; 6 analysis and evaluation are conducted on equivalent plastic strain distribution; 7 structural adjustment is conducted on regions where analysis and evaluation do not meet design standard to enable the regions to meet the design standard, and digital analog derivation is completed. By the adoption of the engine exhaust manifold thermal stress analysis and structural optimization method, under the conditions that a geometry does not need to be modified repeatedly and the mesh does not need to be divided repeatedly, structural optimization of the exhaust manifold is achieved, the working efficiency is improved, and the working time is saved.

Journal ArticleDOI
TL;DR: In this paper, it was shown that the leaves of the time foliation do not have to be smooth manifolds but can be allowed to have kinks, and the trajectories are still well defined and the appropriate | ψ | 2 distribution is still equivariant so that the theory is empirically equivalent to standard quantum mechanics.

Journal ArticleDOI
TL;DR: Two methods that flexibly extend the Mahalanobis distance on the extended Grassmann manifolds can be used to measure pattern (dis)similarity on the basis of the pattern structure.
Abstract: In pattern classification problems, pattern variations are often modeled as a linear manifold or a low-dimensional subspace. Conventional methods use such models and define a measure of similarity or dissimilarity. However, these similarity measures are deterministic and do not take into account the distribution of linear manifolds or low-dimensional subspaces. Therefore, if the distribution is not isotopic, the distance measurements are not reliable, as well as vector-based distance measurement in the Euclidean space. We previously systematized the representations of variational patterns using the Grassmann manifold and introduce the Mahalanobis distance to the Grassmann manifold as a natural extension of Euclidean case. In this paper, we present two methods that flexibly extend the Mahalanobis distance on the extended Grassmann manifolds. These methods can be used to measure pattern (dis)similarity on the basis of the pattern structure. Experimental evaluation of the performance of the proposed methods demonstrated that they exhibit a lower error classification rate.

Journal ArticleDOI
TL;DR: In this paper, the existence of linear connections of Vranceanu type on Cartan spaces related to some foliated structures is studied. And the authors identify a certain (n, 2n-1)-codimensional subfoliation on T*M0 given by vertical foliation and the line foliation spanned by the vertical Liouville-Hamilton vector field C* and give a triplet of basic connections adapted to this subfoliations.
Abstract: In this paper, we study some problems related to a vertical Liouville distribution (called vertical Liouville–Hamilton distribution) on the cotangent bundle of a Cartan space. We study the existence of some linear connections of Vranceanu type on Cartan spaces related to some foliated structures. Also, we identify a certain (n, 2n-1)-codimensional subfoliation on T*M0 given by vertical foliation and the line foliation spanned by the vertical Liouville–Hamilton vector field C* and we give a triplet of basic connections adapted to this subfoliation. Finally, using the vertical Liouville foliation and the natural almost complex structure on T*M0 we study some aspects concerning the cohomology of c-indicatrix cotangent bundle.

Journal ArticleDOI
TL;DR: In this paper, the geometry of orbits of a family of Killing vector fields is studied and it is shown that the orbits are integral submanifolds of the distribution generated by the smallest Lie algebra containing this family of vector fields.
Abstract: We study the geometry of orbits of a family of Killing vector fields. We show that the orbits are integral submanifolds of the distribution generated by the smallest Lie algebra containing this family of Killing vector fields.

Journal ArticleDOI
TL;DR: In this paper, the authors show that some auto-encoder variants do a good job of capturing the local manifold structure of data, and that some of them even learn about the underlying data-generating distribution.
Abstract: What do auto-encoders learn about the underlying data-generating distribution? Recent work suggests that some auto-encoder variants do a good job of capturing the local manifold structure of data. ...

Journal ArticleDOI
TL;DR: In this paper, the authors studied pseudosymmetric light-like hypersurfaces of a semi-Riemannian manifold and showed a close relationship between the pseudoSymmetry condition of a light like hypersurface and its integrable screen distribution.
Abstract: We study lightlike hypersurfaces of a semi-Riemannian manifold satisfying pseudosymmetry conditions. We give sufficient conditions for a lightlike hypersurface to be pseudosymmetric and show that there is a close relationship of the pseudosymmetry condition of a lightlike hypersurface and its integrable screen distribution. We obtain that a pseudosymmetric lightlike hypersurface is a semisymmetric lightlike hypersurface or totally geodesic under certain conditions. Moreover, we give an example of pseudosymmetric lightlike hypersurfaces and investigate pseudoparallel lightlike hypersurfaces. Furthermore, we introduce Ricci-pseudosymmetric lightlike hypersurfaces, obtain characterizations, and give an example for such hypersurfaces.

Proceedings ArticleDOI
01 Jun 2014
TL;DR: The Locally Linear Embedding manifold learning method is modified to use an adaptive graph, and is used to extract low dimensional manifolds from hyperspectral image data collected during the SHARE 2012 campaign.
Abstract: Hyperspectral image data are traditionally analyzed using statistical models. However, as the spatial and spectral resolutions of the images improve as a result of advances in sensor technology, the data no longer maintain a Gaussian distribution; this is due to increased material diversity in the scene, i.e., clutter. This causes many statistical assumptions about the data — and subsequently, the algorithms based on those assumptions — to be flawed. In high dimensional data, manifold learning seeks to recover the embedded non-linear, lower-dimensional manifold upon which the data inherently lie. By recovering the lower-dimensional manifold, intrinsic structures and relationships within the data may be identified and exploited. Here, we consider the impacts of increasing material spectral clutter on the low dimensional manifolds recovered from high spatial resolution hyperspectral scenes for both single and multiple material classes. The Locally Linear Embedding manifold learning method is modified to use an adaptive graph, and is used to extract low dimensional manifolds from hyperspectral image data collected during the SHARE 2012 campaign.

Journal ArticleDOI
TL;DR: In this article, an equation for the effective tangent moduli for steel axial members of hot-rolled I-shaped section subjected to various residual stress distributions was presented. And the presented equations are extremely effective for accurately analyzing elastoplastic behavior of the axially loaded members in a simple manner without using complex shell element models.
Abstract: This paper presents an equation for the effective tangent moduli for steel axial members of hot-rolled I-shaped section subjected to various residual stress distributions. Because of the existence of residual stresses, the cross section yields gradually even when the member is subjected to uniform axial stresses. In the elasto-plastic stage, the structural response can be easily traced using rational tangent modulus of the member. In this study, the equations for rational tangent moduli for hot-rolled I-shaped steel members in the elasto-plastic stage were derived based on the general principle of force-equilibrium. For practical purpose, the equations for the tangent modulus were presented for conventional patterns of the residual stress distribution of hot-rolled I-shaped steel members. Through a series of material nonlinear analyses for steel axial members modeled by shell elements, the derived equations were numerically verified, and the presented equations were compared with the CRC tangent modulus equation, the most frequently used equation so far. The comparative study shows that the presented equations are extremely effective for accurately analyzing elasto-plastic behavior of the axially loaded members in a simple manner without using complex shell element models.

Posted Content
TL;DR: In this article, a natural condition of moderate growth along a closed submanifold of a Riemannian manifold is introduced, which is equivalent to the existence of an extension of a distribution in the Euclidean space.
Abstract: Let $M$ be a smooth manifold and $X\subset M$ a closed subset of $M$. In this paper, we introduce a natural condition of \emph{moderate growth} along $X$ for a distribution $t$ in $\mathcal{D}^\prime(M\setminus X)$ and prove that this condition is equivalent to the existence of an extension of $t$ in $\mathcal{D}^\prime(M)$ generalizing some previous results of Meyer and Brunetti--Fredenhagen. When $X$ is a closed submanifold of $M$, we show that the concept of distributions with moderate growth coincides with weakly homogeneous distributions of Meyer. Then we renormalize products of distributions with functions tempered along $X$ and finally, using the whole analytical machinery developed, we give an existence proof of perturbative quantum field theories on Riemannian manifolds.

Posted Content
TL;DR: In this article, a necessary and sufficient condition for a proper hemi-slant submanifold to be a proper Riemannian manifold is given, where the anti-invariant distribution is integrable.
Abstract: In the present paper, we study hemi-slant submanifolds of a locally product Riemannian manifold. We prove that the anti-invariant distribution which is involved in the definition of hemi-slant submanifold is integrable and give some applications of this result. We get a necessary and sufficient condition for a proper hemi-slant submanifold to be a hemi-slant product. We also study this type submanifolds with parallel canonical structures. Moreover, we give two characterization theorems for the totally umbilical proper hemi-slant submanifolds. Finally, we obtain a basic inequality involving Ricci curvature and the squared mean curvature of a hemi-slant submanifold of a certain type locally product Riemannian manifold.

Book ChapterDOI
01 Jan 2014
TL;DR: In this paper, the authors investigate generalizations of the ordinary Dirac operator to manifolds with additional structure, and apply the analysis to the settings of Riemannian foliations and of manifolds endowed with Lie group actions.
Abstract: In these lectures, we investigate generalizations of the ordinary Dirac operator to manifolds with additional structure. In particular, if the manifold comes equipped with a distribution and an associated Clifford algebra action on a bundle over the manifold, one may define a transversal Dirac operator associated to this structure. We investigate the geometric and analytic properties of these operators, and we apply the analysis to the settings of Riemannian foliations and of manifolds endowed with Lie group actions.

Journal ArticleDOI
TL;DR: In this article, the authors studied non-tangential light-like hypersurfaces of a semi-Riemannian space form admitting a semisymmetric non-metric connection.
Abstract: . We study lightlike hypersurfaces of a semi-Riemannian spaceform fM(c) admitting a semi-symmetric non-metric connection. First, weconstruct a type of lightlike hypersurfaces according to the form of thestructure vector field of Mf(c), which is called a ascreen lightlike hyper-surface. Next, we prove a characterization theorem for such an ascreenlightlike hypersurface endow with a totally geodesic screen distribution. 1. IntroductionThe theory of lightlike submanifolds is an important topic of research in dif-ferential geometry due to its application in mathematical physics, especially inthe electromagneticfield theory. The study ofsuch notion wasinitiated by Dug-gal and Bejancu [3] and later studied by many authors (see up-to date resultsin two books [4, 5]). The notion of a semi-symmetric non-metric connectionon a Riemannian manifold was introduced by Ageshe and Chafle [1]. Recentlyseveral authors ([9]-[13]) studied lightlike hypersurfaces in a semi-Riemannianmanifold admitting a semi-symmetric non-metric connection. Most of authorsthat wrote on either lightlike hypersurfaces M of semi-Riemannian manifoldsMfadmitting semi-symmetric non-metric connections or lightlike hypersurfacesM of indefinite almost contact manifolds Mffail to treat with the case the struc-ture vector field ζ of Mfis not tangent to M, but studied only to the case ζis tangent to M (such M is called tangential lightlike submanifold ([9]-[13]) ofMf). There are few papers on non-tangential lightlike submanifolds of indefinitealmost contact manifolds studied by Jin ([6]-[8]).In this paper, we study non-tangential lightlike hypersurfaces of a semi-Riemannian space form admitting a semi-symmetric non-metric connection.There are several different types of non-tangential lightlike hypersurfaces ac-cording to the form of the structure vector field of the ambient manifold. We

Journal ArticleDOI
TL;DR: In this paper, the intrinsic deformations of Levi flat structures on a smooth manifold were studied, and a complex whose cohomology group of order 1 contains the infinitesimal deformation of a Levi flat structure was defined.
Abstract: We study intrinsic deformations of Levi flat structures on a smooth manifold. A Levi flat structure on a smooth manifold L is a couple (ξ, J) where ξ ⊂ T(L) is an integrable distribution of codimension 1 and J : ξ → ξ is a bundle automorphism which defines a complex integrable structure on each leaf. A deformation of a Levi flat structure (ξ, J) is a smooth family {(ξt, Jt)}t∈]-e,e[ of Levi flat structures on L such that (ξ0, J0) = (ξ, J). We define a complex whose cohomology group of order 1 contains the infinitesimal deformations of a Levi flat structure. In the case of real analytic Levi flat structures, this cohomology group is where (𝒵*(L), δ, {⋅,⋅}) is the differential graded Lie algebra associated to ξ.

Journal ArticleDOI
TL;DR: In this paper, the authors introduce the Fisher information in the basis of decay modes of Markovian dynamics, arguing that it encodes important information about the behavior of nonequilibrium systems.
Abstract: We introduce the Fisher information in the basis of decay modes of Markovian dynamics, arguing that it encodes important information about the behavior of nonequilibrium systems. In particular we generalize an orthonormality relation between decay eigenmodes of detailed balanced systems to normal generators that commute with their time-reversal. Viewing such modes as tangent vectors to the manifold of statistical distributions, we relate the result to the choice of a coordinate patch that makes the Fisher-Rao metric Euclidean at the steady distribution, realizing a sort of statistical equivalence principle. We then classify nonequilibrium systems according to their spectrum, showing that a degenerate Fisher matrix is the signature of the insurgence of a class of dynamical phase transitions between nonequilibrium regimes, characterized by level crossing and power-law decay in time of suitable order parameters. An important consequence is that normal systems cannot manifest critical behavior. Finally, we study the Fisher matrix of systems with time-scale separation.

Posted Content
04 Jun 2014
TL;DR: In this article, it was shown that for a Riccati foliation associated to a branched projective structure over a finite type surface which is non-elementary and parabolic, all germs of holonomy between a fiber and a holomorphic section of the bundle are led to singularities by almost every developed geodesic ray.
Abstract: In this paper we study the problem of analytic extension of germs of holonomy of algebraic foliations. More precisely we prove that for a Riccati foliation associated to a branched projective structure over a finite type surface which is non-elementary and parabolic, all the germs of holonomy between a fiber and a holomorphic section of the bundle are led to singularities by almost every developed geodesic ray. We study in detail the distribution of these singularities and prove in particular that they are included and dense in the limit set and uncountable, giving another negative answer to a conjecture of Loray.

Posted Content
TL;DR: In this paper, the authors provide an exposition on the duality by abnormal geodesics in a wider framework, namely, in terms of quotients of control systems and sub-Riemannian pseudo-product structures.
Abstract: Given a five dimensional space endowed with a Cartan distribution, the abnormal geodesics form another five dimensional space with a cone structure. Then it is shown, if the cone structure is regarded as a control system, then, the space of abnormal geodesics of the cone structure is naturally identified with the original space. In this paper, we provide an exposition on the duality by abnormal geodesics in a wider framework, namely, in terms of quotients of control systems and sub-Riemannian pseudo-product structures. Also we consider the controllability of cone structures and describe the constrained Hamiltonian equations on normal and abnormal geodesics.

Proceedings ArticleDOI
13 Jul 2014
TL;DR: Three manifold regression approaches for estimating quantitative metrics characterizing subsurface zones contaminated by Dense Non-Aqueous Phase Liquids (DNAPLs) based on sparse down-gradient concentration data are developed.
Abstract: In this paper we develop three manifold regression approaches for estimating quantitative metrics characterizing subsurface zones contaminated by Dense Non-Aqueous Phase Liquids (DNAPLs) based on sparse down-gradient concentration data. We are particularly interested in estimating source zone characteristics related to the distribution of contaminant mass in highly saturated pool regions as well as more diffuse ganglia areas regions. Source zone characterization, a necessary first step in the development of any remediation strategy, is challenging due to practical constraints associated with the data available for processing. We use manifold methods for jointly representing labeled training data comprised of known metrics as well as features derived from the corresponding data sets. We then employ an integrated approach to the problems of (a) robustly embedding the sparse test data into the manifold when the metrics are not available and (b) constructing a regression function operating directly in manifold space for metric estimation. The utility of the approach is enhanced by the explicit incorporation of a physical constraint associated with the metrics into the problem formulation. We apply our manifold regression approaches to a simulated data set whose the hydraulic conductivity fields were generated using a Transition Probability Markov Chain (TP/MC) model. Using densely sampled concentration data for training but sparsely sampled data for testing, the results demonstrate the potential of our approaches.