Concept

Upper and lower bounds

Related publications (171)

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Technical Brief: Knockdown Factor for the Buckling of Spherical Shells Containing Large-Amplitude Geometric Defects

Pedro Miguel Nunes Pereira de Almeida Reis, Anna Lee

We explore the effect of precisely defined geometric imperfections on the buckling load of spherical shells under external pressure loading, using finite-element analysis that was previously validated through precision experiments. Our numerical simulation ...

American Society of Mechanical Engineers2017

On The Least Squarefree Number In An Arithmetic Progression

Ramon Moreira Nunes

We prove an asymptotic formula for squarefree numbers in arithmetic progressions, improving previous results by Prachar and Hooley. As a consequence we improve a lower bound of Heath-Brown for the least squarefree number in an arithmetic progression. ...

London Math Soc2017

Bisector Energy and Few Distinct Distances

Frank de Zeeuw

We define the bisector energy E(P) of a set P in R-2 to be the number of quadruples (a, b, c, d) is an element of P-4 such that a, b determine the same perpendicular bisector as c, d. Equivalently, E(P) is the number of isosceles trapezoids determined by P ...

Springer2016

Lyapunov Exponents for Branching Processes in a Random Environment: The Effect of Information

Sophie Myriam Hautphenne

We consider multitype branching processes evolving in a Markovian random environment. To determine whether or not the branching process becomes extinct almost surely is akin to computing the maximal Lyapunov exponent of a sequence of random matrices, which ...

Springer Verlag2016

Partial Recovery Bounds for the Sparse Stochastic Block Model

Volkan Cevher, Jonathan Mark Scarlett

In this paper, we study the information-theoretic limits of community detection in the symmetric two-community stochastic block model, with intra-community and inter-community edge probabilities

\frac{a}{n}

and

\frac{b}{n}

respectively. We consider the ...

Ieee2016

Nonequilibrium localization and the interplay between disorder and interactions

Eduardo Carlo Mascarenhas Moraes

We study the nonequilibrium interplay between disorder and interactions in a closed quantum system. We base our analysis on the notion of dynamical state-space localization, calculated via the Loschmidt echo. Although real-space and state-space localizatio ...

Iop Publishing Ltd2016

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

Accelerated ADMM based on Accelerated Douglas-Rachford Splitting

Colin Neil Jones, Ivan Pejcic

Alternating direction method of multipliers (ADMM) is a form of augmented Lagrangian optimisation algorithm that found its place in many new applications in recent years. This paper explores a possibility for an upgrade of the ADMM by extrapolation-based a ...

Ieee2016

Computation in Multicast Networks: Function Alignment and Converse Theorems

Michael Christoph Gastpar, Naveen Goela

The classical problem in a network coding theory considers communication over multicast networks. Multiple transmitters send independent messages to multiple receivers that decode the same set of messages. In this paper, computation over multicast networks ...

Institute of Electrical and Electronics Engineers2016

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

Partial Recovery Bounds for the Sparse Stochastic Block Model

Volkan Cevher, Jonathan Mark Scarlett

In this paper, we study the information-theoretic limits of community detection in the symmetric two-community stochastic block model, with intra-community and inter-community edge probabilities

\frac{a}{n}

and

\frac{b}{n}

respectively. We consider the ...

Ieee2016