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On Polygons Excluding Point Sets

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On some algebraic and extremal problems in discrete geometry

Seyed Hossein Nassajianmojarrad

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

On the existence of ordinary triangles

Sebastian Urban Stich, Radoslav Fulek, Márton Naszódi

Let P be a finite point set in the plane. A \emph{c-ordinary triangle} in P is a subset of P consisting of three non-collinear points such that each of the three lines determined by the three points contains at most c points of P. Motivated by a question o ...

Elsevier2017

Superpixels and Polygons using Simple Non-Iterative Clustering

Sabine Süsstrunk, Radhakrishna Achanta

We present an improved version of the Simple Linear Iterative Clustering (SLIC) superpixel segmentation. Unlike SLIC, our algorithm is non-iterative, enforces connectivity from the start, requires lesser memory, and is faster. Relying on the superpixel bou ...

Ieee2017

Comment on "Room Temperature Electrically Injected Polariton Laser"

Benoît Marie Joseph Deveaud

In this Comment I challenge the main conclusions of Ref. [1]. The main reason for this Comment is the large number of questions on the details of the experiment that led me to request the raw data. I have obtained two sets of raw data. After a long discuss ...

American Physical Society2016

Search for the decay B-0 -> phi gamma

Olivier Schneider, Yiming Li, Mingkui Wang, Chao Wang, Tagir Aushev, Ho Ling Li, Sun Hee Kim, Tara Nanut, Jun Yong Kim, Ji Hyun Kim, Donghyun Kim, Dipanwita Dutta

We have searched for the decay B-0 -> phi gamma sing the full Belle data set of 772 x 10(6) B (B) over bar pairs collected at the gamma(4S) resonance with the Belle detector at the KEKB e(+)e(-) collider. No signal is observed, and we set an upper limit on ...

Amer Physical Soc2016

Separation with restricted families of sets

János Pach, Gábor Tardos, Márton Naszódi, Zsolt Langi

Given a finite n-element set X, a family of subsets F subset of 2(X) is said to separate X if any two elements of X are separated by at least one member of F. It is shown that if vertical bar F vertical bar > 2(n-1), then one can select vertical bar log n ...

Academic Press Inc Elsevier Science2016

Decomposition of Multiple Packings with Subquadratic Union Complexity

János Pach, Bartosz Maria Walczak

Suppose k is a positive integer and X is a k-fold packing of the plane by infinitely many arc-connected compact sets, which means that every point of the plane belongs to at most k sets. Suppose there is a function f(n) = o(n(2)) with the property that any ...

Cambridge Univ Press2016

Multi-Label Answer Aggregation for Crowdsourcing

Thành Tâm Nguyên

Crowdsourcing has been widely established as a means to enable human computation at large scale, in particular for tasks that require manual labelling of large sets of data items. Answers obtained from heterogeneous crowd workers are aggregated to obtain a ...

2016

On The Number Of Ordinary Conics

Frank de Zeeuw, Adrian Claudiu Valculescu

We prove a lower bound on the number of ordinary conics determined by a finite point set in R-2. An ordinary conic for S subset of R-2 is a conic that is determined by five points of S and contains no other points of S. Wiseman and Wilson proved the Sylves ...

Siam Publications2016

Progressive Geometric Algorithms

Timur Bagautdinov

Progressive algorithms are algorithms that, on the way to computing a complete solution to the problem at hand, output intermediate solutions that approximate the complete solution increasingly well. We present a framework for analyzing such algorithms, an ...

Carleton Univ, Dept Mathematics & Statistics2015