A certain constrained vector-valued dynamic game is formulated and shown to be equivalent to a pair of multiobjective symmetric dual variational problems which have more general formulations than those studied earlier. A number of duality theorems, are established under suitable generalized convexity assumptions on the functionals. Selfduality reflecting symmetric dynamic games is investigated....

This paper is devoted to the construction of projective actions of certain arithmetic groups on the derived categories of coherent sheaves on abelian schemes over a normal base S. These actions are constructed by mimicking the construction of Weil in [27] of a projective representation of the symplectic group Sp(V ∗ ⊕ V ) on the space of smooth functions on the lagrangian subspace V . Namely, w...

We propose a fast algorithm for image denoising, which is based on a dual formulation of a recent denoising model involving the total variation minimization of the tangential vector field under the incompressibility condition stating that the tangential vector field should be divergence free. The model turns noisy images into smooth and visually pleasant ones and preserves the edges quite well....

A discussion of duality continues the development of a mathematical theory for bond graphs as combinatorial structures. The dual of a bondgraph is de$ned and its associated vector spaces are the co-spaces of the original bond graph. The relationship between the algebraic structures and their duals is explored. The theory is used to justfy the construction of a simplified bond graph, the proper ...

We consider the minimization problem of φ-divergences between a given probability measure P and subsets Ω of the vector space MF of all signed finite measures which integrate a given class F of bounded or unbounded measurable functions. The vector space MF is endowed with the weak topology induced by the class F ∪Bb where Bb is the class of all bounded measurable functions. We treat the problem...

Knowledge of the transcriptional responses of vector-borne pathogens at the vector-pathogen interface is critical for understanding disease transmission. Borrelia (Borreliella) burgdorferi, the causative agent of Lyme disease in the United States, is transmitted by the bite of infected Ixodes sp. ticks. It is known that B. burgdorferi has altered patterns of gene expression during tick acquisit...

In relation to the vector optimization problem v-minx∈X(f + g ◦ A)(x), with f, g proper and cone-convex functions and A : X → Y a linear continuous operator between separated locally convex spaces, we define a general vector Fenchel-type dual problem. For the primal-dual pair we prove weak, and under appropriate regularity conditions, strong and converse duality. In the particular case when the...

The standard SVM formulation for binary classification is based on the Hinge loss function, where errors are considered not correlated. Due to this, local information in the feature space which can be useful to improve the prediction model is disregarded. In this paper we address this problem by defining a generalized quadratic loss where the co-occurrence of errors is weighted according to a k...

We compare L1 and L2 soft margin support vector machines from the standpoint of positive definiteness, the number of support vectors, and uniqueness and degeneracy of solutions. Since the Hessian matrix of L2 SVMs is positive definite, the number of support vectors for L2 SVMs is larger than or equal to the number of L1 SVMs. For L1 SVMs, if there are plural irreducible sets of support vectors,...

We present a new technique for 3D surface object classification that combines a powerful shape representation approach with suitable pattern classification techniques. Spherical harmonic parameterization and normalization techniques are used to describe a surface shape and derive a dual high dimensional landmark representation. A point distribution model is applied to reduce the dimensionality....