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Concept

Set function

Related publications (6)

Neural Set Function Extensions: Learning with Discrete Functions in High Dimensions

Andreas Loukas, Nikolaos Karalias

Integrating functions on discrete domains into neural networks is key to developing their capability to reason about discrete objects. But, discrete domains are (I) not naturally amenable to gradient-based optimization, and (II) incompatible with deep lear ...

2022

The hamburger theorem

Jan Kyncl

We generalize the ham sandwich theorem to d +1 measures on R-d as follows. Let mu(1), mu(2),..., mu(d+1) be absolutely continuous finite Borel measures on R-d. Let omega(i) = mu(i) (R-d) for i is an element of [d + 1], omega = min{omega(i) : i is an elemen ...

Elsevier Science Bv2018

Combinatorial Penalties: Which structures are preserved by convex relaxations?

Volkan Cevher, Marwa El Halabi

We consider the homogeneous and the non-homogeneous convex relaxations for combinatorial penalty functions defined on support sets. Our study identifies key differences in the tightness of the resulting relaxations through the notion of the lower combinato ...

2017

Families with no s pairwise disjoint sets

Andrei Kupavskii

For integers n >= s >= 2 let e (n, s) denote the maximum of vertical bar F vertical bar, where F is a family of subsets of an n- element set and F contains no s pairwise disjoint members. Half a century ago, solving a conjecture of Erd. os, Kleitman determ ...

Wiley2017

Discarding low quality Minutia Cylinder-Code pairs for improved fingerprint comparison

Andrzej Drygajlo, Mohammad Hamed Izadi

Local minutiae descriptors such as Minutia Cylinder-Code (MCC) are becoming more popular in modern fingerprint matching systems. The matching performance depends a lot on the fingerprint image quality in global and local levels. Rejecting part of the lowes ...

2015

Tangencies between families of disjoint regions in the plane

János Pach

Let C be a family of n convex bodies in the plane, which can be decomposed into k subfamilies of pairwise disjoint sets. It is shown that the number of tangencies between the members of C is at most O(kn), and that this bound cannot be improved. If we only ...

2010

Related publications (6)