Efficient Maximum-Likelihood Decoding of Linear Block Codes on Binary Memoryless Channels

In this work, we consider efficient maximum-likelihood decoding of linear block codes for small-to-moderate block lengths. The presented approach is a branch-and-bound algorithm using the cutting-plane approach of Zhang and Siegel (IEEE Trans. Inf. Theory, 2012) for obtaining lower bounds. We have compared our proposed algorithm to the state-of-the-art commercial integer program solver CPLEX, and for all considered codes our approach is faster for both low and high signal-to-noise ratios. For instance, for the benchmark (155,64) Tanner code our algorithm is more than 11 times as fast as CPLEX for an SNR of 1.0 dB on the additive white Gaussian noise channel. By a small modification, our algorithm can be used to calculate the minimum distance, which we have again verified to be much faster than using the CPLEX solver.Comment: Submitted to 2014 International Symposium on Information Theory. 5 Pages. Accepte

Mathematical Programming Decoding of Binary Linear Codes: Theory and Algorithms

Mathematical programming is a branch of applied mathematics and has recently been used to derive new decoding approaches, challenging established but often heuristic algorithms based on iterative message passing. Concepts from mathematical programming used in the context of decoding include linear, integer, and nonlinear programming, network flows, notions of duality as well as matroid and polyhedral theory. This survey article reviews and categorizes decoding methods based on mathematical programming approaches for binary linear codes over binary-input memoryless symmetric channels.Comment: 17 pages, submitted to the IEEE Transactions on Information Theory. Published July 201

On a Cardinality Constrained Multicriteria Knapsack Problem

We consider a variant of a knapsack problem with a fixed cardinality constraint. There are three objective functions to be optimized: one real-valued and two integer-valued objectives. We show that this problem can be solved efficiently by a local search. The algorithm utilizes connectedness of a subset of feasible solutions and has optimal run-time

Efficiently Constructing Convex Approximation Sets in Multiobjective Optimization Problems

Convex approximation sets for multiobjective optimization problems are a well-studied relaxation of the common notion of approximation sets. Instead of approximating each image of a feasible solution by the image of some solution in the approximation set up to a multiplicative factor in each component, a convex approximation set only requires this multiplicative approximation to be achieved by some convex combination of finitely many images of solutions in the set. This makes convex approximation sets efficiently computable for a wide range of multiobjective problems - even for many problems for which (classic) approximations sets are hard to compute. In this article, we propose a polynomial-time algorithm to compute convex approximation sets that builds upon an exact or approximate algorithm for the weighted sum scalarization and is, therefore, applicable to a large variety of multiobjective optimization problems. The provided convex approximation quality is arbitrarily close to the approximation quality of the underlying algorithm for the weighted sum scalarization. In essence, our algorithm can be interpreted as an approximate variant of the dual variant of Benson's Outer Approximation Algorithm. Thus, in contrast to existing convex approximation algorithms from the literature, information on solutions obtained during the approximation process is utilized to significantly reduce both the practical running time and the cardinality of the returned solution sets while still guaranteeing the same worst-case approximation quality. We underpin these advantages by the first comparison of all existing convex approximation algorithms on several instances of the triobjective knapsack problem and the triobjective symmetric metric traveling salesman problem

Harnessing Large Language Models to Enhance Self-Regulated Learning via Formative Feedback

Effectively supporting students in mastering all facets of self-regulated learning is a central aim of teachers and educational researchers. Prior research could demonstrate that formative feedback is an effective way to support students during self-regulated learning (SRL). However, for formative feedback to be effective, it needs to be tailored to the learners, requiring information about their learning progress. In this work, we introduce LEAP, a novel platform that utilizes advanced large language models (LLMs), such as ChatGPT, to provide formative feedback to students. LEAP empowers teachers with the ability to effectively pre-prompt and assign tasks to the LLM, thereby stimulating students' cognitive and metacognitive processes and promoting self-regulated learning. We demonstrate that a systematic prompt design based on theoretical principles can provide a wide range of types of scaffolds to students, including sense-making, elaboration, self-explanation, partial task-solution scaffolds, as well as metacognitive and motivational scaffolds. In this way, we emphasize the critical importance of synchronizing educational technological advances with empirical research and theoretical frameworks.Comment: 9 pages, 3 Figures, 1 Tabl

Art Spiegelman, MetaMaus, Pantheon, 2011 (version française : Flammarion, 2012)Art Spiegelman, Co-Mix, A Retrospective of Comics, Graphics, and Scraps / Une rétrospective de bandes dessinées, graphisme et débris divers, Flammarion, 2012

Il n’est plus besoin à notre époque de présenter Art Spiegelman et son oeuvre-maîtresse, Maus, seule bande dessinée à avoir jamais obtenu un prix Pulitzer et devenue en un quart de siècleun des plus grands récits autour de la Shoah. Deux ouvrages récemment parus permettent de découvrir la genèse de cet ouvrage unique en son genre et de l’œuvre au sens large de son auteur. Publié à l’automne 2011 chez Pantheon, MetaMaus est un objet singulier. Sous-titré « A Look Inside a Modern Classic », il ..