Low rank and sparse representation (LRSR) with dual-dictionaries-based methods for detecting anomalies in hyperspectral images (HSIs) are proven to be effective. However, the potential anomaly dictionary is vulnerable being contaminated by background pixels above methods, this limits effect of detection (HAD). In paper, a dual dictionaries construction method via two-stage complementary decisio...

The support function of a free-form–surface is closely related to the implicit equation of the dual surface, and the process of computing both the dual surface and the support function can be seen as dual implicitization. The support function can be used to parameterize a surface by its inverse Gauss map. This map makes it relatively simple to study isophotes (which are simply images of spheric...

We show that the 56-vertex Klein cubic graph Γ′ can be obtained from the 28-vertex Coxeter cubic graph Γ by ’zipping’ adequately the squares of the 24 7-cycles of Γ endowed with an orientation obtained by considering Γ as a C-ultrahomogeneous digraph, where C is the collection formed by both the oriented 7-cycles ~ C7 and the 2-arcs ~ P3 that tightly fasten those ~ C7 in Γ. In the process, it i...

Dual-process theories (DPT) of cognition posit that performance differences in reasoning stem from an interplay between heuristics-based processing (i.e., System 1) and more controlled, rule-based processing (System 2). Emerging evidence suggests that solving classic base-rate problems via Bayesian inference depends on adequately inhibiting the prepotent representations elicited by System 1 (De...

We consider the 3d dual of 1 + 1 dimensional large-Nc QCD with quarks in the fundamental representation, also known as the ’t Hooft model. ’t Hooft solved this model by deriving a Schrödinger equation for the wavefunction of a parton inside the meson. In the scale-invariant limit, we show how this equation is related by a transform to the equation of motion for a scalar field in AdS3. We thus f...

We extend the target map, together with the weighted barriers and the notions of weighted analytic centers, from linear programming to general convex conic programming. This extension is obtained from a novel geometrical perspective of the weighted barriers, that views a weighted barrier as a weighted sum of barriers for a strictly decreasing sequence of faces. Using the Euclidean Jordan-algebr...

Shadow maps are a widely used means for the generation of shadows although they exhibit aliasing artifacts and problems of numerical precision. In this paper we extend the concept of a single shadow map by introducing dual shadow maps, which are based on the two depth layers that are closest to the light source. Our shadow algorithm takes into account these two depth values and computes an adap...

Dual decomposition provides a tractable framework for designing algorithms for finding the most probable (MAP) configuration in graphical models. However, for many real-world inference problems, the typical decomposition has a large integrality gap, due to frustrated cycles. One way to tighten the relaxation is to introduce additional constraints that explicitly enforce cycle consistency. Earli...