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.     

Quantum dynamics of Friedmann’s universe

In the dynamics of three-dimensional space in global time, the global scale takes the form of a discrete variable whose dynamics is described by Friedmann models. Due to a nonzero Hamiltonian, a differential equation is formed for a vacuum configuration. This equation has exact discrete solutions with the spectrum ε _n = ±\(\sqrt {2n} \). Three Hilbert spaces are connected with this equation. We study the dynamics of wave packets on the basis of a small number of eigenfunctions.     

On Floridi’s Method of Levels of Abstraction

Abstraction is arguably one of the most important methods in modern science in analysing and understanding complex phenomena. In his book The Philosophy of Information, Floridi (The philosophy of information. Oxford University Press, Oxford, 2011) presents the method of levels of abstraction as the main method of the Philosophy of Information. His discussion of abstraction as a method seems inspired by the formal methods and frameworks of computer science, in which abstraction is operationalised extensively in programming languages and design methodologies. Is it really clear what we should understand by levels of abstraction? How should they be specified? We will argue that levels of abstraction should be augmented with annotations, in order to express semantic information for them and reconcile the method of level of abstraction (LoA’s) with other approaches. We discuss the extended method when applied e.g. to the analysis of abstract machines. This will lead to an example in which the number of LoA’s is unbounded.     

A Historical View of Studies of Women’s Work

Computer Supported Cooperative Work (CSCW) - This paper places observational studies of women’s work in historical perspective. We present some of the very early studies (carried out in the...     

Probabilistic verification of Herman’s self-stabilisation algorithm

Herman’s self-stabilisation algorithm provides a simple randomised solution to the problem of recovering from faults in an N-process token ring. However, a precise analysis of the algorithm’s maximum execution time proves to be surprisingly difficult. McIver and Morgan have conjectured that the worst-case behaviour results from a ring configuration of three evenly spaced tokens, giving an expected time of approximately 0.15N ². However, the tightest upper bound proved to date is 0.64N ². We apply probabilistic verification techniques, using the probabilistic model checker PRISM, to analyse the conjecture, showing it to be correct for all sizes of the ring that can be exhaustively analysed. We furthermore demonstrate that the worst-case execution time of the algorithm can be reduced by using a biased coin.     

Levi’s

从旧金山的金矿到伦敦的哈克逊广场（Hoxton Square），Levi’s品牌都是一流的。现在看看Graeme Aymer是如何解析这一品牌的发展过程的.[编者按]     

Realization of Seurat’s pointillism via non-photorealistic rendering

Photorealistic rendering is one of the oldest and most important research areas in computer graphics. More recently, the concept of non-photorealistic rendering has been proposed as an alternative with important advantages for numerous application areas. The popularity of non-photorealism can be mainly attributed to its simplicity, which could potentially lead to a state of aesthetics and succinctness. Reality often presents too many details and too much complexity, thus offsetting the observation of the essence of objects, and objects’ interaction with lights. Based on a similar belief, impressionism focuses primarily on conveying the interaction of light and shadows without emphasizing the fine details of a scene. In recent years, there has been a trend towards simulating impressionism with computers. Among the various styles of impressionism, we are particularly interested in simulating the style of pointillism, especially the style presented by Georges-Pierre Seurat, deemed the founder of pointillism. The reason his style attracts us is twofold. First, the painting process of pointillism is extremely laborious, so unloading the main proportion of the manual painting task is mostly desired. Second, though several existing general-purposed algorithms may be able to approximate pointillism with point-like strokes, some delicate features frequently observed in Seurat’s paintings are still not satisfactorily reflected. To achieve simulating Seurat’s painting style, we have made careful observations of all accessible Seurat’s paintings and extracted from them some important features, such as the relatively few primitive colors, color juxtaposition, point sizes, and, in particular, the effects of complementary colors and halos. These features have been more successfully simulated and results are comparable with not only Seurat’s existing paintings, but also with previous attempted simulations.     

Impulsive control and synchronization of Chua’s oscillators

Impulsive control of a chaotic system is ideal for designing digital control schemes where the control laws are generated by digital devices which are discrete in time. In this paper, several new theorems on the stability of impulsive control systems are presented. These theorems are then used to find the conditions under which the Chua’s oscillator can be asymptotically controlled to the origin by using impulsive control. Given the parameters of the Chua’s oscillator and the impulsive control law, an estimation of the upper bound of the impulse interval is given. We also present a theory of impulsive synchronization of two Chua’s oscillators. A numerical example and simulation illustrates the effectiveness of the proposed result. Compared with the existing results, these results are less conservative.     

Equiparadoxicality of Yablo’s Paradox and the Liar

It is proved that Yablo’s paradox and the Liar paradox are equiparadoxical, in the sense that their paradoxicality is based upon exactly the same circularity condition—for any frame ${\mathcal{K}}$ , the following are equivalent: (1) Yablo’s sequence leads to a paradox in ${\mathcal{K}}$ ; (2) the Liar sentence leads to a paradox in ${\mathcal{K}}$ ; (3) ${\mathcal{K}}$ contains odd cycles. This result does not conflict with Yablo’s claim that his sequence is non-self-referential. Rather, it gives Yablo’s paradox a new significance: his construction contributes a method by which we can eliminate the self-reference of a paradox without changing its circularity condition.     

Automatic Georeferencing of Images Acquired by UAV’s

This paper implements and evaluates experimentally a procedure for automatically georeferencing images acquired by unmanned aerial vehicles (UAV’s) in the sense that ground control points (GCP) are not necessary. Since the camera model is necessary for georeferencing, this paper also proposes a completely automatic procedure for collecting corner pixels in the model plane image to solve the camera calibration problem, i.e., to estimate the camera and the lens distortion parameters. The performance of the complete georeferencing system is evaluated with real flight data obtained by a typical UAV.     

Note on the Structure of Kruskal’s Algorithm

We study the merging process when Kruskal’s algorithm is run with random graphs as inputs. Our aim is to analyze this process when the underlying graph is the complete graph on n vertices lying in [0,1] ^d , and edge set weighted with the Euclidean distance. The height of the binary tree explaining the merging process is proved to be Θ(n) on average. On the way to the proof, we obtain similar results for the complete graph and the d-dimensional square lattice with i.i.d. edge weights.