(in alphabetic order by speaker surname) Speaker: Judit Abardia (Frankfurt University) Title: Projection bodies in complex vector spaces Abstract: The projection body of a convex body in the Euclidean space was characterized by Monika Ludwig as the unique Minkowski valuation which is continuous, translation invariant and contravariant under the (real) special linear group. In a joint work with ...

Knowing the fact that the main weakness of the most standard methods including k-means and hierarchical data clustering is their sensitivity to initialization and trapping to local minima, this paper proposes a modification of convex data clustering  in which there is no need to  be peculiar about how to select initial values. Due to properly converting the task of optimization to an equivalent...

We consider the inverse conductivity problem in a strictly convex domain whose boundary is not known. Usually the numerical reconstruction from the measured current and voltage data is done assuming the domain has a known fixed geometry. However, in practical applications the geometry of the domain is usually not known. This introduces an error, and effectively changes the problem into an aniso...

In this paper, we study convex analysis and its theoretical applications. We first apply important tools of convex analysis to Optimization and to Analysis. We then show various deep applications of convex analysis and especially infimal convolution in Monotone Operator Theory. Among other things, we recapture the Minty surjectivity theorem in Hilbert space, and present a new proof of the sum t...

The concepts of M-convex functions and M^-convex functions play central roles in the theory of discrete convex analysis which has been applied to mathematical economics. On the other hand, substitutability, which is a key property guaranteeing the existence of a stable matching in generalized stable marriage models, is known as a nice property in mathematical economics. In this paper, we introd...

In the main theorem of this paper we show that any involution on the class of lower semi-continuous convex functions which is order-reversing, must be, up to linear terms, the well known Legendre transform.

The purpose of this work is to carry out a systematic study of a special class of convex functions defined over the space Sn of symmetric matrices of order n×n. The functions under consideration (Φ : Sn → R∪ {+∞}) are spectrally defined in the sense that the value Φ(A) depends only on the spectrum {λ1(A), . . . , λn(A)} of the matrix A ∈ Sn. Fenchel–Legendre conjugation, firstand second-order s...

In this paper, the error performance achieved by cooperative detection among K distributed receivers in a diffusionbased molecular communication (MC) system is analyzed and optimized. In this system, the receivers first make local hard decisions on the transmitted symbol and then report these decisions to a fusion center (FC). The FC combines the local hard decisions to make a global decision u...

We deal with duality for almost convex finite dimensional optimization problems by means of the classical perturbation approach. To this aim some standard results from the convex analysis are extended to the case of almost convex sets and functions. The duality for some classes of primal-dual problems is derived as a special case of the general approach. The sufficient regularity conditions we ...

CCA can be seen as a multiview extension of PCA, in which information from two sources is used for learning by finding a subspace in which the two views are most correlated. However PCA, and by extension CCA, does not use label information. Fisher Discriminant Analysis uses label information to find informative projections, which can be more informative in supervised learning settings. We deriv...