Publications related to Sampling Curves with Finite Rate of Innovation

On some algebraic and extremal problems in discrete geometry

In the present thesis, we delve into different extremal and algebraic problems arising from combinatorial geometry. Specifically, we consider the following problems. For any integer

n\ge 3

, we define

e(n)

to be the minimum positive integer such that an ...

EPFL2017

Point and sensor estimation from images

Martin Vetterli, Adam James Scholefield, Alireza Ghasemi

System comprising at least one sensor configured to take a set of images from different viewpoints of a scene; a processor configured to identifying a point source represented in the images of a set of images; computing for each image of the set of images ...

2017

Incidences between points and generalized spheres over finite fields and related problems

Van Thang Pham

Let F-q be a finite field of q elements, where q is a large odd prime power and Q = a(1)x(1)(c1) + ..... + a(d)x(d)(cd) is an element of F-q[x(1) ,...,x(d)], where 2

Walter De Gruyter Gmbh2017

Distinct Distances on Algebraic Curves in the Plane

János Pach, Frank de Zeeuw

Let S be a set of n points in R-2 contained in an algebraic curve C of degree d. We prove that the number of distinct distances determined by S is at least c(d)n(4/3), unless C contains a line or a circle. We also prove the lower bound c(d)' min{m(2/3)n(2/ ...

Cambridge Univ Press2017

An Improved Upper Bound for the ErdAs-Szekeres Conjecture

Let ES(n) denote the minimum natural number such that every set of ES(n) points in general position in the plane contains n points in convex position. In 1935, ErdAs and Szekeres proved that ES. In 1961, they obtained the lower bound , which they conjectur ...

Springer2016

An Inner-Product Calculus for Periodic Functions and Curves

Michaël Unser, Daniel Andreas Schmitter, Anaïs Laure Marie-Thérèse Badoual

Our motivation is the design of efficient algorithms to process closed curves represented by basis functions or wavelets. To that end, we introduce an inner-product calculus to evaluate correlations and

L _{ 2 }

distances between such curves. In partic ...

2016

Few distinct distances implies no heavy lines or circles

Frank de Zeeuw

We study the structure of planar point sets that determine a small number of distinct distances. Specifically, we show that if a set of n points determines o(n) distinct distances, then no line contains Omega(n (7/8)) points of and no circle contains Omega ...

Springer Heidelberg2016

On the Richter-Thomassen Conjecture about Pairwise Intersecting Closed Curves

János Pach, Gábor Tardos

A long-standing conjecture of Richter and Thomassen states that the total number of intersection points between any n simple closed Jordan curves in the plane, so that any pair of them intersect and no three curves pass through the same point, is at least ...

Cambridge Univ Press2016

Minimizing movements along a sequence of functionals and curves of maximal slope

Maria Colombo

We prove that a general condition introduced by Colombo and Gobbino to study limits of curves of maximal slope allows us to characterize also minimizing movements along a sequence of functionals as curves of maximal slope of a limit functional. ...

2016

Stochastic frequency reserve provision by chance-constrained control of commercial buildings

Maryam Kamgarpour, Xiuwei Zhang

Robust programs with modulated uncertainty sets are problems in which the uncertainty sets are treated as optimization variables. In many applications, these uncertainty sets can be interpreted as reserve capacities for which rewards are offered. One examp ...

IEEE2015

Sampling Curves with Finite Rate of Innovation

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On some algebraic and extremal problems in discrete geometry

Point and sensor estimation from images

Incidences between points and generalized spheres over finite fields and related problems

Distinct Distances on Algebraic Curves in the Plane

An Improved Upper Bound for the ErdAs-Szekeres Conjecture

An Inner-Product Calculus for Periodic Functions and Curves

Few distinct distances implies no heavy lines or circles

On the Richter-Thomassen Conjecture about Pairwise Intersecting Closed Curves

Minimizing movements along a sequence of functionals and curves of maximal slope

Stochastic frequency reserve provision by chance-constrained control of commercial buildings

On some algebraic and extremal problems in discrete geometry

On the Richter-Thomassen Conjecture about Pairwise Intersecting Closed Curves

Incidences between points and generalized spheres over finite fields and related problems

Distinct Distances on Algebraic Curves in the Plane

An Improved Upper Bound for the ErdAs-Szekeres Conjecture

Few distinct distances implies no heavy lines or circles

Point and sensor estimation from images

Minimizing movements along a sequence of functionals and curves of maximal slope

An Inner-Product Calculus for Periodic Functions and Curves

Stochastic frequency reserve provision by chance-constrained control of commercial buildings