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.     

Improved osseointeraction of calcium phosphate-coated external fixation pins. Studies in calves

The analysis of health state of drivers sent for an extra health examination for the estimation of driving capability for the driving of motor vehicle in alcoholic state was presented. The study included 380 drivers who were found driving drunk by traffic police (studied group) and 180 drivers of control group sent for an extra health examination for some other reason. The disorders in psychomotor sphere were noticed in the drivers of studied group and it was determined that they had caused significantly larger number of traffic accidents in last five-year period compared to the drivers of control group. The alcohol consumption in driving population represents significant medical, social, economic and traffic problem. The control of driver's alcoholism, the sending of alcoholic drivers to an extra health examination for the repeated estimation of driving capability and including in therapeutic and health-educational program can present significant measure of the primary prevention of road traffic traumatism which is on the constant increase.     

Effect of percutaneous endoscopic gastrostomy on gastric emptying in clinically normal cats

OBJECTIVE: To assess the effect of percutaneous endoscopic gastrostomy (PEG) tube placement on gastric emptying in clinically normal cats. ANIMALS: 8 healthy adult 3- to 5-year-old cats. PROCEDURE: Cats were accommodated to the diet for 2 weeks prior to scintigraphy. Caloric needs were divided into 3 feedings/d. Food was withheld for 24 hours after tube placement, then was fed as a third of the caloric needs on day 1, two-thirds on day 2, and full caloric requirements thereafter. Gastric emptying was measured via nuclear scintigraphy. Labeled meals contained 111 MBq (3 mCi) of 99mTc-labeled disofenin. Sixty-second ventral scintigraphic images were acquired immediately, every 20 minutes for the first hour, then every 30 minutes for 4 hours after feeding. Each cat was evaluated 3 times prior to PEG tube placement. Cats were anesthetized, and 16-F mushroom-tipped Pezzar gastrostomy tubes were placed, using a video endoscope. Scintigraphy was repeated on days 1, 4, 7, 11, 14, and 21 after PEG tube placement. RESULTS: Gastric emptying was faster with a PEG tube in place. Percentage of retained gastric activity was significantly lower after PEG for 150, 180, 210, and 240 minutes versus time before PEG tube placement. CONCLUSION: Placement of a PEG tube does not delay gastric emptying in clinically normal cats. CLINICAL RELEVANCE: Gastric retention of food, vomiting, and aspiration pneumonia after PEG tube placement may not be related to delayed gastric emptying.     

Partial Order Reduction for Verification of Spatial Properties of Pi-Calculus Processes

Mechanical tools have recently been developed that enable computer-aided verification of spatial properties of concurrent systems. To be practical, these tools are expected to deal with the state- space explosion problem. In order to alleviate this problem, we develop partial order reduction for verification of spatial properties of pi-calculus processes. The main issue is that spatial logics are very expressive and some spatial formulas prevent partial order reduction. After discussing this issue, we propose a restricted spatial logic such that partial order reduction holds. Our approach relies on exploiting partially confluent communications and on identifying invisible communications in the pi-calculus, for which we propose a simple syntactic criterion.     

On construction of a library of formally verified low-level arithmetic functions

Arithmetic functions are used in many important computer programs such as computer algebra systems and cryptographic software. The latter are critical applications whose correct implementation deserves to be formally guaranteed. They are also computation-intensive applications, so that programmers often resort to low-level assembly code to implement arithmetic functions. We propose an approach for the construction of a library of formally verified low-level arithmetic functions. To build our library, we first introduce a formalization of data structures for signed multi-precision arithmetic in low-level programs. We use this formalization to verify the implementation of several primitive arithmetic functions using Separation logic, an extension of Hoare logic to deal with pointers. Since this direct style of formal verification leads to technically involved specifications, we also propose for larger functions to show a formal simulation relation between pseudo-code and assembly. This style of verification is illustrated with a concrete implementation of the binary extended gcd algorithm.     

The influence of gender, race, and menthol content on tobacco exposure measures.

Research has suggested that race, gender, and menthol cigarette use influence tobacco-smoke exposure measures and smoking-related disease risk. For example, a high proportion of Black smokers prefer menthol cigarettes and, despite smoking fewer cigarettes per day (CPD) than do Whites, tend to have higher cotinine levels. Additionally, Black males are more at risk for smoking-related lung cancer. High cotinine levels and smoking menthol cigarettes may lead to higher toxin intake, which contributes to increased disease risk. We explored the relationship between tobacco exposure variables (i.e., cotinine, CPD, carbon monoxide [CO], nicotine content, and nicotine dependence) with respect to race, gender, and menthol content in a sample of 307 smokers recruited from the greater Boston area to participate in a smoking cessation treatment trial. The pattern of correlations between tobacco exposure measures and cotinine showed a consistently positive correlation between cotinine and CO in all smokers and a correlation between cotinine and CPD in those who smoked nonmenthol cigarettes. Cotinine and CPD correlations varied by gender and race among menthol cigarette smokers. Consistently, we found a significant gender x race x menthol interaction on salivary cotinine level as well as cotinine/CPD ratio. These findings suggest that the relationship between number of cigarettes consumed and salivary cotinine is more complex than previously believed. It is not sufficient to look at race alone; researchers and clinicians need to look at race and gender concurrently, as well as type of cigarette consumed.     

A Progressive Algorithm for Three Point Transport

When computing global illumination in environments made up of surfaces with general Bidirectional Reflection Distribution Functions, a three point formulation of the rendering equation can be used. Brute-force algorithms can lead to a linear system of equations whose matrix is cubic, which is expensive in time and space. The hierarchical approach is more efficient. Aupperle et al . proposed a hierarchical three point algorithm to compute global illumination in the presence of glossy reflection. We present in this paper some improvements we brought to this method: shooting, "lazy" push-pull, photometric subdivision criterion, etc. Then we will show how our new method takes into account non-planar surfaces in the hierarchical resolution process.