Publications related to Unit circle

On Sets Defining Few Ordinary Circles

An ordinary circle of a set P of n points in the plane is defined as a circle that contains exactly three points of P. We show that if P is not contained in a line or a circle, then P spans at least ordinary circles. Moreover, we determine the exact minimu ...

Springer2018

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

Periodic population codes: From a single circular variable to higher dimensions, multiple nested scales, and conceptual spaces

Alexander Mathis

Across the nervous system, neurons often encode circular stimuli using tuning curves that are not sine or cosine functions, but that belong to the richer class of von Mises functions, which are periodic variants of Gaussians. For a population of neurons en ...

2017

Exact Algorithms for $ L ^{ 1 } $ -TV Regularization of Real-Valued or Circle-Valued Signals

Michaël Unser, Martin Kurt Storath

We consider

L ^{ 1 }

-TV regularization of univariate signals with values on the real line or on the unit circle. While the real data space leads to a convex optimization problem, the problem is nonconvex for circle-valued data. In this paper, we deriv ...

SIAM2016

Intrachain antiferromagnetic exchange in a 1D branched-chain built of two different copper(II) centres interlinked by end-on azido and phenoxo bridges: electron density map, electrochemical and magnetic properties

Henrik Moodysson Rønnow, Kurt Schenk, Philip Pattison, Krunoslav Prsa, Arash Alahgholipour Omrani, Noore Elahi Shaik

A 1D, end-on azido- and phenoxo-bridged, coordination polymer, Cu-2(mu-NAPPR)(mu(1,1)-N-3)(2) (1), (NAPPR(2-) = 1,3-bis(naphthylideneimino) propane dianion), was synthesized and characterized. The 1D branched-chain is built of two types of slightly di ...

2015

Computing Extremal Points Of Symplectic Pseudospectra And Solving Symplectic Matrix Nearness Problems

Daniel Kressner

We study differential equations that lead to extremal points in symplectic pseudospectra. In a two-level approach, where on the inner level we compute extremizers of the symplectic epsilon-pseudospectrum for a given epsilon and on the outer level we optimi ...

Siam Publications2014

Phase extraction in speckle interferometry by a circle fitting procedure in the complex plane

Pierre Jacquot, Sébastien Equis

In speckle interferometry (SI), temporal signals are amplitude- and frequency-modulated signals and exhibit a fluctuating background. Prior to phase computation, this background intensity must be eliminated. Here our approach is to build a complex signal f ...

Optical Society of America2011

Phase transitions in full counting statistics for periodic pumping

Dmitri Ivanov

We discuss the problem of full counting statistics for periodic pumping. The probability generating function is usually defined on a circle of the "physical" values of the counting parameter, with its periodicity corresponding to charge quantization. The e ...

2010

Bit Precision Analysis for Compressed Sensing

Mohammad Amin Shokrollahi, Mahdi Cheraghchi Bashi Astaneh

This paper studies the stability of some reconstruction algorithms for compressed sensing in terms of the bit precision. Considering the fact that practical digital systems deal with discretized signals, we motivate the importance of the total number of ac ...

2009

Unit circle

Graph Chatbot

Chat with Graph Search

On Sets Defining Few Ordinary Circles

On some algebraic and extremal problems in discrete geometry

Periodic population codes: From a single circular variable to higher dimensions, multiple nested scales, and conceptual spaces

Exact Algorithms for $ L ^{ 1 } $ -TV Regularization of Real-Valued or Circle-Valued Signals

Intrachain antiferromagnetic exchange in a 1D branched-chain built of two different copper(II) centres interlinked by end-on azido and phenoxo bridges: electron density map, electrochemical and magnetic properties

Computing Extremal Points Of Symplectic Pseudospectra And Solving Symplectic Matrix Nearness Problems

Phase extraction in speckle interferometry by a circle fitting procedure in the complex plane

Phase transitions in full counting statistics for periodic pumping

Bit Precision Analysis for Compressed Sensing

On some algebraic and extremal problems in discrete geometry

On Sets Defining Few Ordinary Circles

Periodic population codes: From a single circular variable to higher dimensions, multiple nested scales, and conceptual spaces

Exact Algorithms for $ L ^{ 1 } $ -TV Regularization of Real-Valued or Circle-Valued Signals

Intrachain antiferromagnetic exchange in a 1D branched-chain built of two different copper(II) centres interlinked by end-on azido and phenoxo bridges: electron density map, electrochemical and magnetic properties

Computing Extremal Points Of Symplectic Pseudospectra And Solving Symplectic Matrix Nearness Problems

Phase transitions in full counting statistics for periodic pumping

Bit Precision Analysis for Compressed Sensing

Phase extraction in speckle interferometry by a circle fitting procedure in the complex plane