We get the algorithms of our ground truths: Designing referential databases in digital image processing

This article documents the practical efforts of a group of scientists designing an imageprocessing algorithm for saliency detection. By following the actors of this computer science project, the article shows that the problems often considered to be the starting points of computational models are in fact provisional results of time-consuming, collective and highly material processes that engage habits, desires, skills and values. In the project being studied, problematization processes lead to the constitution of referential databases called ‘ground truths’ that enable both the effective shaping of algorithms and the evaluation of their performances. Working as important common touchstones for research communities in image processing, the ground truths are inherited from prior problematization processes and may be imparted to subsequent ones. The ethnographic results of this study suggest two complementary analytical perspectives on algorithms: (1) an ‘axiomatic’ perspective that understands algorithms as sets of instructions designed to solve given problems computationally in the best possible way, and (2) a ‘problem-oriented’ perspective that understands algorithms as sets of instructions designed to computationally retrieve outputs designed and designated during specific problematization processes. If the axiomatic perspective on algorithms puts the emphasis on the numerical transformations of inputs into outputs, the problem-oriented perspective puts the emphasis on the definition of both inputs and outputs

Object-oriented finite element programming

New technologies in computer science applied to numerical computations open the door to alternative approaches to mechanical problems using the finite element method. In classical approaches, theoretical developments often become cumbersome and the computer model which follows shows resemblance with the initial problem statement. The first step in the development consists usually in the analysis of the physics of the problem to simulate. The problem is generally described by a set of equations including partial differential equations. This first model is then replaced by successive equivalent or approximated models. The final result consists in a mathematical description of elemental matrices and algorithms describing the matrix form of the problem. The traditional approach consists then in constructing a computer model, generally complex and often quite different from the original mathematical description, thus making further corrections difficult. Therefore, the crucial problem of both the software architecture and the choice of the appropriate programming language is raised. Partially breaking with this approach, we propose a new approach to develop and program finite element formulations. The approach is based on a hybrid symbolic/numerical approach on the one hand, and on a high level software tool, object-oriented programming (supported here by the languages Smalltalk and C++) on the other hand. The aim of this work is to develop an appropriate environment for the algebraic manipulations needed for a finite element formulation applied to an initial boundary value problem, and also to perform efficient numerical computations. The new environment should make it possible to manage al1 the concepts necessary to solve a physical problem: manipulation of partial differential equations, variational formulations, integration by parts, weak forms, finite element approximations… The concepts manipulated therefore remain closely related to the original mathematical framework. The result of these symbolic manipulations is a set of elemental data (mass matrix, stiffness matrix, tangent stiffness matrix,…) to be introduced in a classical numerical code. The object-oriented paradigm is essential to the success of the implementation. In the context of the finite element codes, the object-oriented approach has already proved its capacity to represent and handle complex structures and phenomena. This is confirmed here with the symbolic environment for derivation of finite element formulations in which objects such as expression, integral and variational formulation appear. The link between both the numerical world and the symbolic world is based on an object-oriented concept for automatic programmation of matrix forms derived from the finite element method. As a result, a global environment in which the numerical is capable of evolving, using a language close to the natural mathematical one, is achieved. The potential of the approach is further demonstrated, on the one hand, by the wide range of problems solved in linear mechanics (electrodynamics in 1 and 2D, heat diffusion,…) as well as in nonlinear mechanics (advection dominated 1D problem, Navier Stokes problem), and, on the other hand by the diversity of the formulations manipulated (Galerkin formulations, space-time Galerkin formulations continuous in space and discontinuous in time, generalized Galerkin least-squares formulations).

EPFL1997

A formal approach to fault tolerant distributed consensus

Rachele Fuzzati

The term distributed Consensus denotes the problem of getting a certain number of processes, that could be far away from each other and that exchange messages through some communication means, to all agree on the same value. This problem has been proved impossible to solve in asynchronous settings when at least one process can crash, i.e., stop working. Since the problem of reaching Consensus among processes is recurrent in the domain of distributed computation, many algorithms have been proposed for solving it, circumventing the impossibility result through the introduction of some kind of synchrony in the system. Such algorithms are traditionally expressed in natural language or in pseudocode, thus sometimes generating ambiguities on their contents and on their correctness proofs. In this thesis, we propose a simple, yet efficient way of providing formal descriptions and proofs of distributed Consensus algorithms. Such method is based on the use of inference rules, it requires very little prior knowledge in order to be understood, and follows closely the way algorithms are expressed in pseudocode, thus being intuitive for the users. To show the validity of our claims, we use our method to formalize two of the major distributed Consensus algorithms, namely the Chandra-Toueg and the Paxos algorithms. Using our rigorous description, we then formally prove that such algorithms guarantee the respect of the Validity, Agreement and Termination properties that every solution to the Consensus problem should provide. This proving exercise actually reveals interesting results. We see that the Chandra-Toueg and the Paxos algorithms have strong points of resemblance and their correctness proofs can be carried out in very similar manners. However, while the Chandra-Toueg algorithm proves to be correct under the point of view of the three properties, we discover that Paxos does not give any guarantee of terminating. This generates a philosophical question: should such algorithm be considered a Consensus algorithm or not?

EPFL2008

Subdeterminant Maximization via Nonconvex Relaxations and Anti-Concentration

Javad Ebrahimi Boroojeni, Damian Mateusz Straszak, Nisheeth Vishnoi

Several fundamental problems that arise in optimization and computer science can be cast as follows: Given vectors v(1), ..., v(m) is an element of R-d and a constraint family B subset of 2([m]), find a set S. B that maximizes the squared volume of the simplex spanned by the vectors in S. A motivating example is the ubiquitous data-summarization problem in machine learning and information retrieval where one is given a collection of feature vectors that represent data such as documents or images. The volume of a collection of vectors is used as a measure of their diversity, and partition or matroid constraints over [m] are imposed in order to ensure resource or fairness constraints. Even with a simple cardinality constraint (B = (([m])(r))), the problem becomes NP-hard and has received much attention starting with a result by Khachiyan [1] who gave an r(O(r)) approximation algorithm for this problem. Recently, Nikolov and Singh [2] presented a convex program and showed how it can be used to estimate the value of the most diverse set when there are multiple cardinality constraints (i.e., when B corresponds to a partition matroid). Their proof of the integrality gap of the convex program relied on an inequality by Gurvits [3], and was recently extended to regular matroids [4], [5]. The question of whether these estimation algorithms can be converted into the more useful approximation algorithms - that also output a set - remained open. The main contribution of this paper is to give the first approximation algorithms for both partition and regular matroids. We present novel formulations for the subdeterminant maximization problem for these matroids; this reduces them to the problem of finding a point that maximizes the absolute value of a nonconvex function over a Cartesian product of probability simplices. The technical core of our results is a new anti-concentration inequality for dependent random variables that arise from these functions which allows us to relate the optimal value of these nonconvex functions to their value at a random point. Unlike prior work on the constrained subdeterminant maximization problem, our proofs do not rely on real-stability or convexity and could be of independent interest both in algorithms and complexity where anti-concentration phenomena has recently been deployed.

Ieee2017