Publications related to Logarithm

Asymptotics of action variables near semi-toric singularities

The presence of focus-focus singularities in semi-toric integrables Hamiltonian systems is one of the reasons why there cannot exist global Action-Angle coordinates on such systems. At focus-focus critical points, the Liouville-Arnold-Mineur theorem does n ...

Elsevier2015

MATHICSE Technical Report : Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

Fabio Nobile, Giovanni Migliorati

We analyze the accuracy of the discrete least-squares approximation of a function u in multivariate polynomial spaces

P_\Lambda := span\{y \mapsto y^\nu | \nu \in \Lambda\}

with

\Lambda\subset N_0^d

over the domain

\Gamma := [-1,1]^d

, based on the sa ...

MATHICSE2015

Analysis of discrete least squares on multivariate polynomial spaces with evaluations at low-discrepancy point sets

Fabio Nobile, Giovanni Migliorati

We analyze the stability and accuracy of discrete least squares on multivariate polynomial spaces to approximate a given function depending on a multivariate random variable uniformly distributed on a hypercube. The polynomial approximation is calculated s ...

2015

MATHICSE Technical Report : Analysis of discrete least squares on multivariate polynomial spaces with evaluations at low-discrepancy point sets

Fabio Nobile, Giovanni Migliorati

We analyze the stability and accuracy of discrete least squares on multivariate poly- nomial spaces to approximate a given function depending on a multivariate random variable uniformly distributed on a hypercube. The polynomial approximation is calculated ...

MATHICSE2015

A Tale of Two Quasi-Polynomial Algorithms

Robert Granger

In 2013 the Discrete Logarithm Problem in finite fields of small characteristic enjoyed a rapid series of developments, starting with the heuristic polynomial-time relation generation method due to Gologlu, Granger, McGuire and Zumbragel, and culminating w ...

2015

Predicting aqueous speciation of environmentally relevant halogen oxidants: chloramines, bromamines, and bromochloramines

Jeremy Samuel Arey, Daniela Trogolo

Chloramines, bromamines, and bromochloramines are halogen-containing oxidants that arise from the reaction between ammonia and hypohalous acids during the disinfection of drinking and wastewaters. Although involved in the formation of toxic disinfection by ...

2015

On the discrete logarithm problem in finite fields of fixed characteristic

Robert Granger, Thorsten Kleinjung, Jens Markus Zumbrägel

For

q

a prime power, the discrete logarithm problem (DLP) in

\mathbb{F}_q

consists in finding, for any

g \in \mathbb{F}_{q}^{\times}

and

h \in \langle g \rangle

, an integer

x

such that

g^x = h

. We present an algorithm for computing discrete log ...

2015

Improved Masking for Tweakable Blockciphers with Applications to Authenticated Encryption

Robert Granger, Philipp Svetolik Jovanovic

A popular approach to tweakable blockcipher design is via masking, where a certain primitive (a blockcipher or a permutation) is preceded and followed by an easy-to-compute tweak-dependent mask. In this work, we revisit the principle of masking. We do so a ...

2015

LLR-Based Successive Cancellation List Decoding of Polar Codes

Andreas Peter Burg, Alexios Konstantinos Balatsoukas Stimming

We show that successive cancellation list decoding can be formulated exclusively using log-likelihood ratios. In addition to numerical stability, the log-likelihood ratio based formulation has useful properties that simplify the sorting step involved in su ...

Institute of Electrical and Electronics Engineers2015

Analysis of Discrete L2 Projection on Polynomial Spaces with Random Evaluations

Fabio Nobile, Giovanni Migliorati, Erik Gustaf Bogislaw Von Schwerin

We analyse the problem of approximating a multivariate function by discrete least-squares projection on a polynomial space starting from random, noise-free observations. An area of possible application of such technique is Uncertainty Quantification (UQ) f ...

2014

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Asymptotics of action variables near semi-toric singularities

MATHICSE Technical Report : Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

Analysis of discrete least squares on multivariate polynomial spaces with evaluations at low-discrepancy point sets

MATHICSE Technical Report : Analysis of discrete least squares on multivariate polynomial spaces with evaluations at low-discrepancy point sets

A Tale of Two Quasi-Polynomial Algorithms

Predicting aqueous speciation of environmentally relevant halogen oxidants: chloramines, bromamines, and bromochloramines

On the discrete logarithm problem in finite fields of fixed characteristic

Improved Masking for Tweakable Blockciphers with Applications to Authenticated Encryption

LLR-Based Successive Cancellation List Decoding of Polar Codes

Analysis of Discrete L2 Projection on Polynomial Spaces with Random Evaluations

Asymptotics of action variables near semi-toric singularities

Improved Masking for Tweakable Blockciphers with Applications to Authenticated Encryption

MATHICSE Technical Report : Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

MATHICSE Technical Report : Analysis of discrete least squares on multivariate polynomial spaces with evaluations at low-discrepancy point sets

On the discrete logarithm problem in finite fields of fixed characteristic

A Tale of Two Quasi-Polynomial Algorithms

Analysis of discrete least squares on multivariate polynomial spaces with evaluations at low-discrepancy point sets

LLR-Based Successive Cancellation List Decoding of Polar Codes

Predicting aqueous speciation of environmentally relevant halogen oxidants: chloramines, bromamines, and bromochloramines

Analysis of Discrete L2 Projection on Polynomial Spaces with Random Evaluations