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Properties of Network Polynomials

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Solving Stochastic Ordinary Differential Equations by Monte Carlo and Polynomial Chaos

Gilles Brunner

In this project, we study and compare two methods to solve stochastic ordinary differential equations. The first is the Monte Carlo method and the second uses Polynomial Chaos. In the first part, we will solve a stochastic ordinary differential equation by ...

2013

Algebraic algorithms for network information flow

Javad Ebrahimi Boroojeni

Ahlswede et al. in the seminal paper [1] have shown that in data transfer over networks, processing the data at the nodes can significantly improve the throughput. As proved by Li et al. in [2], even with a simple type of operation, namely linear operation ...

EPFL2013

Properties of Network Polynomials

Christina Fragouli, Javad Ebrahimi Boroojeni

It is well known that transfer polynomials play an important role in the network code design problem. In this paper we provide a graph theoretical description of the terms of such polynomials. We consider acyclic networks with arbitrary number of receivers ...

2012

A Probabilistic Approach of Sum Rules for Heat Polynomials

Olivier Lévêque

In this paper, we show that the sum rules for generalized Hermite polynomials derived by Daboul and Mizrahi (2005 J. Phys. A: Math. Gen. 38 427-48) and by Graczyk and Nowak (2004 C. R. Acad. Sci., Ser. 1 338 849) can be interpreted and easily recovered usi ...

2012

Computation of connection coefficients and measure modifications for orthogonal polynomials

Jan Sickmann Hesthaven

We observe that polynomial measure modifications for families of univariate orthogonal polynomials imply sparse connection coefficient relations. We therefore propose connecting L (2) expansion coefficients between a polynomial family and a modified family ...

Springer Verlag2012

Implementation of optimal Galerkin and Collocation approximations of PDEs with Random Coefficients

Fabio Nobile, Lorenzo Tamellini

In this work we first focus on the Stochastic Galerkin approximation of the solution u of an elliptic stochastic PDE. We rely on sharp estimates for the decay of the coefficients of the spectral expansion of u on orthogonal polynomials to build a sequence ...

2011

Efficient multiplication using type $2$ optimal normal bases

Mohammad Amin Shokrollahi

In this paper we propose a new structure for multiplication using optimal normal bases of type

2

. The multiplier uses an efficient linear transformation to convert the normal basis representations of elements of

F_{q^{n}}

to suitable polynomials of deg ...

2007

Information flow decomposiiton for network coding

Christina Fragouli, Emina Soljanin

The famous min-cut, max-flow theorem states that a source node can send a commodity through a network to a sink node at the rate determined by the flow of the min-cut separating the source and the sink. Recently it has been shown that by linear re-encoding ...

Institute of Electrical and Electronics Engineers2006

2

. The multiplier uses an efficient linear transformation to convert the normal basis representations of elements of

F_{q^{n}}

to suitable polynomials of deg ...

2007

Properties of Network Polynomials

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Solving Stochastic Ordinary Differential Equations by Monte Carlo and Polynomial Chaos

Algebraic algorithms for network information flow

Properties of Network Polynomials

A Probabilistic Approach of Sum Rules for Heat Polynomials

Computation of connection coefficients and measure modifications for orthogonal polynomials

Implementation of optimal Galerkin and Collocation approximations of PDEs with Random Coefficients

Efficient multiplication using type $2$ optimal normal bases

Information flow decomposiiton for network coding

Information Flow Decomposition for Network Coding

Information Flow Decomposition for Network Coding

Algebraic algorithms for network information flow

Solving Stochastic Ordinary Differential Equations by Monte Carlo and Polynomial Chaos

Information Flow Decomposition for Network Coding

Properties of Network Polynomials

A Probabilistic Approach of Sum Rules for Heat Polynomials

Computation of connection coefficients and measure modifications for orthogonal polynomials

Implementation of optimal Galerkin and Collocation approximations of PDEs with Random Coefficients

Efficient multiplication using type $2$ optimal normal bases

Information Flow Decomposition for Network Coding

Information flow decomposiiton for network coding