Formalization of Shannon’s Theorems

The most fundamental results of information theory are Shannon’s theorems. These theorems express the bounds for (1) reliable data compression and (2) data transmission over a noisy channel. Their proofs are non-trivial but are rarely detailed, even in the introductory literature. This lack of formal foundations is all the more unfortunate that crucial results in computer security rely solely on information theory: this is the so-called “unconditional security”. In this article, we report on the formalization of a library for information theory in the SSReflect extension of the Coq proof-assistant. In particular, we produce the first formal proofs of the source coding theorem, that introduces the entropy as the bound for lossless compression, and of the channel coding theorem, that introduces the capacity as the bound for reliable communication over a noisy channel.     

Effect of molybdenum,niobium, and vanadium on static recovery and recrystallization and on solute strengthening in microalloyed steels

The effect of molybdenum, niobium, and vanadium on the occurrence of static recovery and recrystallization after high temperature deformation was investigated in a series of microalloyed steels. The steels had a base composition of 0.05 pct C and 1.40 pct Mn. To this, single additions of 0.30 pct Mo, 0.035 pct Nb, and 0.115 pct V were made. Interrupted hot compression tests were performed at 900 and 1000 °C, and at a constant true strain rate of 2 s^-1. The load-free time was decreased from 5000 s to 50 ms, and the degree of static softening during this period was determined. Both graphite and glass were used as lubricants. Percent softeningvs delay time curves are presented and the retarding effect of molybdenum, niobium, and vanadium addition on the rate of static recovery and recrystallization is discussed. The greatest solute retardation of static recovery and recrystallization is produced by niobium addition, followed by that of molybdenum, vanadium leading to the smallest delay. Although the rank order of this effect is the same as found under dynamic softening conditions, the relative contribution of niobium is more profound for the static condition. The solute strengthening attributable to each element was also assessed, and found to follow the same order as for the recovery and recrystallization results. At 900 °C, the onset of the static precipitation of Nb (CN) was detected at approximately 10 seconds, somewhat earlier than previously reported. Formerly Graduate Student at McGill University, Montreal, Quebec.     

Uzawa Conjugate Gradient Domain Decomposition Methods for Coupled Stokes Flows

This paper deals with nonoverlapping domain decomposition methods for two coupled Stokes flows, based on the duality theory. By introducing a fictitious variable in the transmission condition and using saddle-point equations, the problem is restated as a linearly constrained maximization problem. According to whether constraints are uncoupled Stokes problems or uncoupled Poisson problems, two Uzawa-type domain decomposition algorithms are proposed. The results of some numerical experiments on a model problem are given.     

Creep and rupture behaviour in fibre bundles

The time dependent rupture of a fibre bundle under constant tensile load and with scatter in fibre stiffness and fibre strength is analysed using a general formulation of the creep law. The total rupture time is divided into an incubation time, with all fibres intact, and a failure propagation time where fibres fail progressively. Governing equations are given for both time intervals. It is shown that the failure propagation time interval is independent of the load if no spatial stress redistribution occurs and all fibres remain intact upon loading. For a bundle consisting of originally uniform fibres where a fraction is afflicted with a certain defect, the time intervals are calculated assuming Norton's non linear creep law.     

Numerical simulation of segmented penetrator impact

The performance of segmented and continuous penetrators impacting semi-infinite and spaced armor is studied using both the EPIC-2 and HULL hydrocodes. First the performance of a segmented rod is studied, striking semi-infinite armor, for various parameters such as striking velocity, segment spacing and number of segments. Then an actual penetrator configuration proposed by A. Charters is analyzed and the use of normalized penetration is discussed. Finally three-dimensional simulations are presented for segmented and continuous penetrators impacting oblique spaced armor varying such parameters as striking velocity, segment spacing, number of segments, and target thickness.     

Abstraction paradigms for computer graphics

In computer graphics we use techniques from different areas of mathematics. Mathematical models are used to simulate real-world objects, as well as natural phenomena. In order to understand these models and pose relevant problems in each particular field of this area, it is important to create levels of abstraction. These levels encapsulate common properties of the different models and allow us to have a global, conceptual view of the methods and techniques in each field. In this paper we study a paradigm for creating abstraction levels that can also be used to characterize more general problems in computational applied mathematics. We apply this paradigm to different areas of computer graphics: modeling, animation, illumination, color theory, image processing and human-computer interface.     

Nonlinear black-box modeling in system identification: a unified overview

A nonlinear black-box structure for a dynamical system is a model structure that is prepared to describe virtually any nonlinear dynamics. There has been considerable recent interest in this area, with structures based on neural networks, radial basis networks, wavelet networks and hinging hyperplanes, as well as wavelet-transform-based methods and models based on fuzzy sets and fuzzy rules. This paper describes all these approaches in a common framework, from a user's perspective. It focuses on what are the common features in the different approaches, the choices that have to be made and what considerations are relevant for a successful system-identification application of these techniques. It is pointed out that the nonlinear structures can be seen as a concatenation of a mapping form observed data to a regression vector and a nonlinear mapping from the regressor space to the output space. These mappings are discussed separately. The latter mapping is usually formed as a basis function expansion. The basis functions are typically formed from one simple scalar function, which is modified in terms of scale and location. The expansion from the scalar argument to the regressor space is achieved by a radial- or a ridge-type approach. Basic techniques for estimating the parameters in the structures are criterion minimization, as well as two-step procedures, where first the relevant basis functions are determined, using data, and then a linear least-squares step to determine the coordinates of the function approximation. A particular problem is to deal with the large number of potentially necessary parameters. This is handled by making the number of ‘used’ parameters considerably less than the number of ‘offered’ parameters, by regularization, shrinking, pruning or regressor selection.     

Reduced autonomy workspace (RAW)—an interaction design approach for human-automation cooperation

Cognition, Technology & Work - Lack of support for handling a reduction of autonomy in a highly autonomous automation may lead to a stressful situation for a human when forced to take over. We...     

The business model concept: theoretical underpinnings and empirical illustrations

The business model concept is becoming increasingly popular within IS, management and strategy literature. It is used within many fields of research, including both traditional strategy theory and in the emergent body of literature on e-business. However, the concept is often used independently from theory, meaning model components and their interrelations are relatively obscure. Nonetheless, we believe that the business model concept is useful in explaining the relation between IS and strategy. This paper offers an outline for a conceptual business model, and proposes that it should include customers and competitors, the offering, activities and organisation, resources and factor market interactions. The causal inter-relations and the longitudinal processes by which business models evolve should also be included. The model criticises yet draws on traditional strategy theory and on the literature that addresses business models directly. The business model is illustrated by an ERP implementation in a European multi-national company.     

A Modeling Framework for Troubleshooting Automotive Systems

This article presents a novel framework for modeling the troubleshooting process for automotive systems such as trucks and buses. We describe how a diagnostic model of the troubleshooting process can be created using event-driven, nonstationary, dynamic Bayesian networks. Exact inference in such a model is in general not practically possible. Therefore, we evaluate different approximate methods for inference based on the Boyen–Koller algorithm. We identify relevant model classes that have particular structure such that inference can be made with linear time complexity. We also show how models created using expert knowledge can be tuned using statistical data. The proposed learning mechanism can use data that is collected from a heterogeneous fleet of modular vehicles that can consist of different components. The proposed framework is evaluated both theoretically and experimentally on an application example of a fuel injection system.