Gaussian Approximation for Tracking Occluding and Interacting Targets

In this paper, we show how interacting and occluding targets can be tackled successfully within a Gaussian approximation. For that purpose, we develop a general expansion of the mean and covariance of the posterior and we consider a first order approximation of it. The proposed method differs from EKF in that neither a non-linear dynamical model nor a non-linear measurement vector to state relation have to be defined, so it works with any kind of interaction potential and likelihood. The approach has been tested on three sequences (10400, 2500, and 400 frames each one). The results show that our approach helps to reduce the number of failures without increasing too much the computation time with respect to methods that do not take into account target interactions.

A Probe-Goal Approach to Agreement and Incorporation Restrictions in Southern Tiwa

Southern Tiwa (Tanoan) exhibits agreement with up to three arguments (ergative, absolutive, dative). This agreement is subject to certain restrictions resembling the Person-Case Constraint paradigm (Bonet 1991). Moreover, there is a correlation between agreement restrictions and conditions on (the obviation of) noun-incorporation in Southern Tiwa, as explicitly and elegantly captured by Rosen (1990) in terms of a heterogeneous feature hierarchy and rules of association. We attempt to recast Rosen’s central insights in terms of Anagnostopoulou’s probe-sharing model of Person-Case Constraint effects (Anagnostopoulou 2003, 2006), to show that the full range of Southern Tiwa agreement and (non-)incorporation restrictions can be given a single, unified analysis within the probe-goal-Agree framework of Chomsky (2001). In particular, we argue that Southern Tiwa’s triple-agreement system is characterized by (a) an independent class probe located on the heads T and v, and (b) a rule that allows this class probe to be deleted in the context of local-person T-agreement. The various restrictions on agreement and non-incorporation then reduce to a single source: failure of class-valuation with DP (as opposed to NP) arguments.

Tailoring Alphabetical Metamaterials in Optical Frequency: Plasmonic Coupling, Dispersion, and Sensing

Tailoring optical properties of artificial metamaterials, whose optical properties go beyond the limitations of conventional and naturally occurring materials, is of importance in fundamental research and has led to many important applications such as security imaging, invisible cloak, negative refraction, ultrasensitive sensing, transformable and switchable optics. Herein, by precisely controlling the size, symmetry and topology of alphabetical metamaterials with U, S, Y, H, U-bar and V shapes, we have obtained highly tunable optical response covering visible-to-infrared (Vis-NIR) optical frequency. In addition, we show a detailed study on the physical origin of resonance modes, plasmonic coupling, the dispersion of electronic and magnetic surface plasmon polaritons, and the possibility of negative refraction. We have found that all the electronic and magnetic modes follow the dispersion of surface plasmon polaritons thus essentially they are electronic- and magnetic-surface-plasmon-polaritons-like (ESPP-like and MSPP-like) modes resulted from diffraction coupling between localized surface plasmon and freely-propagating light. Based on the fill factor and formula of magnetism permeability, we predict that the alphabetical metamaterials should show the negative refraction capability in visible optical frequency. Furthermore, we have demonstrated the specific ultrasensitive surface enhanced Raman spectroscopy (SERS) sensing of monolayer molecules and femtomolar food contaminants by tuning their resonance to match the laser wavelength, or by tuning the laser wavelength to match the plasmon resonance of metamaterials. Our tunable alphabetical metamaterials provide a generic platform to study the electromagnetic properties of metamaterials and explore the novel applications in optical frequency.

The Cyrenaican Prehistory Project 2011: Late-Holocene environments and human activity from a cave fill in Cyrenaica, Libya

Little is known about late Holocene environmental change in Cyrenaica. The late Holocene sequence in the Haua Fteah, the key regional site, is highly discontinuous and characterised by stable-burning deposits. The geoarchaeology of the late-Holocene cave fill of a small cave, CP1565, located close to the Haua Fteah, is described. The well-stratified sequence, dating from the fourth century AD to the present day, provides a glimpse of life at the bottom of the settlement hierarchy and of changing environments over the last 1600 years, with degraded vegetation and aridity in the ‘Little Ice Age’.

Isometric embedding of finite ultrametric spaces in Banach spaces

We prove that for any finite ultrametric space M and any infinite-dimensional Banach space B there exists an isometric embedding of M into B.

Monotonically normal topological vector spaces are stratifiable

We prove that for any Hausdorff topological vector space E over the field R there exists A subset of E such that E is homeomorphic to a subset of A x R and A x R is homeomorphic to a subset of E. Using this fact we prove that E is monotonically normal if and only if E is stratifiable.

Two-dimensional Banach spaces with polynomial numerical index zero

We study two-dimensional Banach spaces with polynomial numerical indices equal to zero.

A hierarchical multiclass support vector machine incorporated with holistic triple learning units

This paper proposes a new hierarchical learning structure, namely the holistic triple learning (HTL), for extending the binary support vector machine (SVM) to multi-classification problems. For an N-class problem, a HTL constructs a decision tree up to a depth of A leaf node of the decision tree is allowed to be placed with a holistic triple learning unit whose generalisation abilities are assessed and approved. Meanwhile, the remaining nodes in the decision tree each accommodate a standard binary SVM classifier. The holistic triple classifier is a regression model trained on three classes, whose training algorithm is originated from a recently proposed implementation technique, namely the least-squares support vector machine (LS-SVM). A major novelty with the holistic triple classifier is the reduced number of support vectors in the solution. For the resultant HTL-SVM, an upper bound of the generalisation error can be obtained. The time complexity of training the HTL-SVM is analysed, and is shown to be comparable to that of training the one-versus-one (1-vs.-1) SVM, particularly on small-scale datasets. Empirical studies show that the proposed HTL-SVM achieves competitive classification accuracy with a reduced number of support vectors compared to the popular 1-vs-1 alternative.

On the derived category of a regular toric scheme

Let X be a quasi-compact scheme, equipped with an open covering by affine schemes U s = Spec A s . A quasi-coherent sheaf on X gives rise, by taking sections over the U s , to a diagram of modules over the coordinate rings A s , indexed by the intersection poset S of the covering. If X is a regular toric scheme over an arbitrary commutative ring, we prove that the unbounded derived category of quasi-coherent sheaves on X can be obtained from a category of Sop-diagrams of chain complexes of modules by inverting maps which induce homology isomorphisms on hyper-derived inverse limits. Moreover, we show that there is a finite set of weak generators, one for each cone in the fan S. The approach taken uses the machinery of Bousfield–Hirschhorn colocalisation of model categories. The first step is to characterise colocal objects; these turn out to be homotopy sheaves in the sense that chain complexes over different open sets U s agree on intersections up to quasi-isomorphism. In a second step it is shown that the homotopy category of homotopy sheaves is equivalent to the derived category of X.