Open Set Recognition (OSR) has been an emerging topic. Besides recognizing predefined classes, the system needs to reject unknowns. Prototype learning is a potential manner handle problem, as its ability improve intra-class compactness of representations much needed in discrimination between known and In this work, we propose novel Mining And Learning (PMAL) framework. It prototype mining mecha...

In inference, open-set classification is to either classify a sample into known class from training or reject it as an unknown class. Existing deep classifiers train explicit closed-set classifiers, in some cases disjointly utilizing reconstruction, which we find dilutes the latent representation's ability distinguish classes. contrast, our model cooperatively learn reconstruction and perform c...

Let P be a set of m points and L a set of n lines in R, such that the points of P lieon an algebraic three-dimensional surface of degree D that does not contain hyperplaneor quadric components, and no 2-flat contains more than s lines of L. We show thatthe number of incidences between P and L is

Let Ω ⊆ R be a non-empty open set for which the Sobolev embedding H 0 (Ω) −→ L(Ω) is compact, and let V ∈ L∞(Ω) be a potential taking only positive real values and satisfying the asymptotics V (·) 〈·〉 for some α ∈ ]3,∞[. We establish the discreteness of the set of real transmission eigenvalues for both Schrödinger and Helmholtz scattering with these potentials.

We investigate whether K,-free graphs with few repetitions in the degree sequence may have independence number o(n). We settle the cases r = 3 and r >/5, and give partial results for the very interesting case r=4 . In an earl ier art icle I-4] it is shown that t r iangle-free graphs in which no term of the degree sequence occurs more than twice must be bipar t i te , but that there exist t r ia...

Motivated by phylogenetics, our aim is to obtain a system of equations that define a phylogenetic variety on an open set containing the biologically meaningful points. In this paper we consider phylogenetic varieties defined via group-based models. For any finite abelian group G, we provide an explicit construction of codimX phylogenetic invariants (polynomial equations) of degree at most |G| t...

the reciprocal degree distance (rdd)‎, ‎defined for a connected graph $g$ as vertex-degree-weighted sum of the reciprocal distances‎, ‎that is‎, ‎$rdd(g) =sumlimits_{u,vin v(g)}frac{d_g(u)‎ + ‎d_g(v)}{d_g(u,v)}.$ the reciprocal degree distance is a weight version of the harary index‎, ‎just as the degree distance is a weight version of the wiener index‎. ‎in this paper‎, ‎we present exact formu...

This paper characterizes all controllers to a problem of simultaneous robust regulation and robust stabilization, which was left open by Cevik and Schumacher. The characterization is based on a combination of their results, i.e., the controller parameterization of robust regulation with nominal internal stability and the stability margin given by an internally stabilizing controller. The contro...