Reconstruction of Nonunion Tibial Fractures in War-Wounded Iraqi Civilians, 2006-2008: Better Late Than Never

OBJECTIV

Formal Verification of Nonlinear Inequalities with Taylor Interval Approximations

We present a formal tool for verification of multivariate nonlinear inequalities. Our verification method is based on interval arithmetic with Taylor approximations. Our tool is implemented in the HOL Light proof assistant and it is capable to verify multivariate nonlinear polynomial and non-polynomial inequalities on rectangular domains. One of the main features of our work is an efficient implementation of the verification procedure which can prove non-trivial high-dimensional inequalities in several seconds. We developed the verification tool as a part of the Flyspeck project (a formal proof of the Kepler conjecture). The Flyspeck project includes about 1000 nonlinear inequalities. We successfully tested our method on more than 100 Flyspeck inequalities and estimated that the formal verification procedure is about 3000 times slower than an informal verification method implemented in C++. We also describe future work and prospective optimizations for our method.Comment: 15 page

Intravascular Papillary Endothelial Hyperplasia : report of 4 cases with immunohistochemical findings

Intravascular papillary endothelial hyperplasia (IPEH) is a benign endothelial proliferation, usually intravascular, that may mimic angiosarcoma. In this report, four new cases of IPEH involving the oral region are described. The affected sites were the lower lip, labial comissure and the submandibular region. After clinical evaluation, the complete removal of the lesions showed a circumscribed and soft mass. Histologically, the major feature was a reactive proliferation of endothelial cells composed of small papillary structures with hypocellular and hyalinized cores arising in an organized thrombus. Immunohistochemical staining for CD34 was strongly positive in endothelial cells. Vimentin and laminin immunolabelling were also consistent with a vascular origin. In order to verify the proliferative potential of the lesions, the Ki-67 antibody was used, revealing low percentage of labeled cells (<20%). No immunoreactivity for GLUT-1 was observed. Since the complete removal is curative, no additional treatment was necessary, and no signs of recurrence had been observed until now. Due to the particular features of IPEH, it is important for pathologists and clinicians to become familiar with this lesion. Additionally, the specific histological arrangement, including the absence of cellular pleomorphism, mitotic activity and necrosis, represents a guide to help in the differential diagnosis. Moreover, the vascular origin and the proliferative index should be assessed by immunohistochemistry in order to provide an accurate diagnosis

Electrochemical deprotonation of phosphate on stainless steel

Voltammetric experiments performed in phosphate buffer at constant pH 8.0 on platinum and stainless steel revealed clear reduction currents, which were correlated to the concentrations of phosphate. On the basis of the reactions proposed previously, a model was elaborated, assuming that both H2PO4 and HPO4 2 underwent cathodic deprotonation, and including the acid–base equilibriums. A kinetic model was derived by analogy with the equations generally used for hydrogen evolution. Numerical fitting of the experimental data confirmed that the phosphate species may act as an efficient catalyst of hydrogen evolution via electrochemical deprotonation. This reaction may introduce an unexpected reversible pathway of hydrogen formation in the mechanisms of anaerobic corrosion. The possible new insights offered by the electrochemical deprotonation of phosphate in microbially influenced corrosion was finally discussed

Proving Tight Bounds on Univariate Expressions with Elementary Functions in Coq

International audienceThe verification of floating-point mathematical libraries requires computing numerical bounds on approximation errors. Due to the tightness of these bounds and the peculiar structure of approximation errors, such a verification is out of the reach of generic tools such as computer algebra systems. In fact, the inherent difficulty of computing such bounds often mandates a formal proof of them. In this paper, we present a tactic for the Coq proof assistant that is designed to automatically and formally prove bounds on univariate expressions. It is based on a formalization of floating-point and interval arithmetic, associated with an on-the-fly computation of Taylor expansions. All the computations are performed inside Coq's logic, in a reflexive setting. This paper also compares our tactic with various existing tools on a large set of examples

Automatic Estimation of Verified Floating-Point Round-Off Errors via Static Analysis

This paper introduces a static analysis technique for computing formally verified round-off error bounds of floating-point functional expressions. The technique is based on a denotational semantics that computes a symbolic estimation of floating-point round-o errors along with a proof certificate that ensures its correctness. The symbolic estimation can be evaluated on concrete inputs using rigorous enclosure methods to produce formally verified numerical error bounds. The proposed technique is implemented in the prototype research tool PRECiSA (Program Round-o Error Certifier via Static Analysis) and used in the verification of floating-point programs of interest to NASA

Influences of Excluded Volume of Molecules on Signaling Processes on Biomembrane

We investigate the influences of the excluded volume of molecules on biochemical reaction processes on 2-dimensional surfaces using a model of signal transduction processes on biomembranes. We perform simulations of the 2-dimensional cell-based model, which describes the reactions and diffusion of the receptors, signaling proteins, target proteins, and crowders on the cell membrane. The signaling proteins are activated by receptors, and these activated signaling proteins activate target proteins that bind autonomously from the cytoplasm to the membrane, and unbind from the membrane if activated. If the target proteins bind frequently, the volume fraction of molecules on the membrane becomes so large that the excluded volume of the molecules for the reaction and diffusion dynamics cannot be negligible. We find that such excluded volume effects of the molecules induce non-trivial variations of the signal flow, defined as the activation frequency of target proteins, as follows. With an increase in the binding rate of target proteins, the signal flow varies by i) monotonically increasing; ii) increasing then decreasing in a bell-shaped curve; or iii) increasing, decreasing, then increasing in an S-shaped curve. We further demonstrate that the excluded volume of molecules influences the hierarchical molecular distributions throughout the reaction processes. In particular, when the system exhibits a large signal flow, the signaling proteins tend to surround the receptors to form receptor-signaling protein clusters, and the target proteins tend to become distributed around such clusters. To explain these phenomena, we analyze the stochastic model of the local motions of molecules around the receptor.Comment: 31 pages, 10 figure

Insulin and Glucagon Impairments in Relation with Islet Cells Morphological Modifications Following Long Term Pancreatic Duct Ligation in the Rabbit – A Model of Non-insulin-dependent Diabete

Plasma levels of glucose, insulin and glucagon were measured at various time intervals after pancreatic duct ligation (PDL) in rabbits. Two hyperglycemic periods were observed: one between 15–90 days (peak at 30 days of 15.1 ± 1.2mmol/l, p < 0.01), and the other at 450 days (11.2 ± 0.5 mmol/l, p < 0.02). The first hyperglycemic episode was significantly correlated with both hypoinsulinemia (41.8 ± 8pmol/l, r= –0.94, p < 0.01) and hyperglucagonemia (232 ± 21ng/l, r=0.95, p < 0.01). However, the late hyperglycemic phase (450 days), which was not accompanied by hypoinsulinemia, was observed after the hyperglucagonemia (390 days) produced by abundant immunostained A-cells giving rise to a 3-fold increase in pancreatic glucagon stores. The insulin and glucagon responses to glucose loading at 180, 270 and 450 days reflected the insensitivity of B- and A-cells to glucose. The PDL rabbit model with chronic and severe glycemic disorders due to the predominant role of glucagon mimicked key features of the NIDDM syndrome secondary to exocrine disease

Ammonium regeneration: Its contribution to phytoplankton nitrogen requirements in a eutrophic environment

Ammonium regeneration, nutrient uptake, bacterial activity and primary production were measured from March to August 1980 in Bedford Basin, Nova Scotia, Canada, a eutrophic environment. Rates of regeneration and nutrient uptake were determined using 15N isotope dilution and tracer methodology. Although primary production, nutrient uptake and ammonium regeneration were significantly intercorrelated, no relationship was detected between these parameters and heterotrophic activity. The average contribution of ammonium to total nitrogen (ammonium+nitrate) uptake was similar in the spring and in the summer (approximately 60%). On a seasonal average basis, 36% of the phytoplankton ammonium uptake could be supplied by rapid remineralization processes. In spite of the high average contribution of NH4 regeneration to phytoplankton ammonia uptake, there is indirect evidence suggesting that other NH4 sources may occasionally be important