Finding polynomial loop invariants for probabilistic programs

Quantitative loop invariants are an essential element in the verification of probabilistic programs. Recently, multivariate Lagrange interpolation has been applied to synthesizing polynomial invariants. In this paper, we propose an alternative approach. First, we fix a polynomial template as a candidate of a loop invariant. Using Stengle's Positivstellensatz and a transformation to a sum-of-squares problem, we find sufficient conditions on the coefficients. Then, we solve a semidefinite programming feasibility problem to synthesize the loop invariants. If the semidefinite program is unfeasible, we backtrack after increasing the degree of the template. Our approach is semi-complete in the sense that it will always lead us to a feasible solution if one exists and numerical errors are small. Experimental results show the efficiency of our approach.Comment: accompanies an ATVA 2017 submissio

Galectin-4 Controls Intestinal Inflammation by Selective Regulation of Peripheral and Mucosal T Cell Apoptosis and Cell Cycle

Galectin-4 is a carbohydrate-binding protein belonging to the galectin family. Here we provide novel evidence that galectin-4 is selectively expressed and secreted by intestinal epithelial cells and binds potently to activated peripheral and mucosal lamina propria T-cells at the CD3 epitope. The carbohydrate-dependent binding of galectin-4 at the CD3 epitope is fully functional and inhibited T cell activation, cycling and expansion. Galectin-4 induced apoptosis of activated peripheral and mucosal lamina propria T cells via calpain-, but not caspase-dependent, pathways. Providing further evidence for its important role in regulating T cell function, galectin-4 blockade by antisense oligonucleotides reduced TNF-alpha inhibitor induced T cell death. Furthermore, in T cells, galectin-4 reduced pro-inflammatory cytokine secretion including IL-17. In a model of experimental colitis, galectin-4 ameliorated mucosal inflammation, induced apoptosis of mucosal T-cells and decreased the secretion of pro-inflammatory cytokines. Our results show that galectin-4 plays a unique role in the intestine and assign a novel role of this protein in controlling intestinal inflammation by a selective induction of T cell apoptosis and cell cycle restriction. Conclusively, after defining its biological role, we propose Galectin-4 is a novel anti-inflammatory agent that could be therapeutically effective in diseases with a disturbed T cell expansion and apoptosis such as inflammatory bowel disease

Gauge-independent MS‾\overline{MS} renormalization in the 2HDM

We present a consistent renormalization scheme for the CP-conserving Two-Higgs-Doublet Model based on $\overline{MS}$ renormalization of the mixing angles and the soft-$Z_2$-symmetry-breaking scale $M_{sb}$ in the Higgs sector. This scheme requires to treat tadpoles fully consistently in all steps of the calculation in order to provide gauge-independent $S$-matrix elements. We show how bare physical parameters have to be defined and verify the gauge independence of physical quantities by explicit calculations in a general $R_{\xi}$-gauge. The procedure is straightforward and applicable to other models with extended Higgs sectors. In contrast to the proposed scheme, the $\overline{MS}$ renormalization of the mixing angles combined with popular on-shell renormalization schemes gives rise to gauge-dependent results already at the one-loop level. We present explicit results for electroweak NLO corrections to selected processes in the appropriately renormalized Two-Higgs-Doublet Model and in particular discuss their scale dependence.Comment: 52 pages, PDFLaTeX, PDF figures, JHEP version with Eq. (5.23) correcte

Biomarker discovery and redundancy reduction towards classification using a multi-factorial MALDI-TOF MS T2DM mouse model dataset

Diabetes like many diseases and biological processes is not mono-causal. On the one hand multifactorial studies with complex experimental design are required for its comprehensive analysis. On the other hand, the data from these studies often include a substantial amount of redundancy such as proteins that are typically represented by a multitude of peptides. Coping simultaneously with both complexities (experimental and technological) makes data analysis a challenge for Bioinformatics

The Borwein brothers, Pi and the AGM

We consider some of Jonathan and Peter Borweins' contributions to the high-precision computation of $\pi$ and the elementary functions, with particular reference to their book "Pi and the AGM" (Wiley, 1987). Here "AGM" is the arithmetic-geometric mean of Gauss and Legendre. Because the AGM converges quadratically, it can be combined with fast multiplication algorithms to give fast algorithms for the $n$-bit computation of $\pi$, and more generally the elementary functions. These algorithms run in almost linear time $O(M(n)\log n)$, where $M(n)$ is the time for $n$-bit multiplication. We outline some of the results and algorithms given in Pi and the AGM, and present some related (but new) results. In particular, we improve the published error bounds for some quadratically and quartically convergent algorithms for $\pi$, such as the Gauss-Legendre algorithm. We show that an iteration of the Borwein-Borwein quartic algorithm for $\pi$ is equivalent to two iterations of the Gauss-Legendre quadratic algorithm for $\pi$, in the sense that they produce exactly the same sequence of approximations to $\pi$ if performed using exact arithmetic.Comment: 24 pages, 6 tables. Changed style file and reformatted algorithms in v

Credible Autocoding of Convex Optimization Algorithms

International audienceThe efficiency of modern optimization methods, coupled with increasing computational resources, has led to the possibility of real-time optimization algorithms acting in safety critical roles. There is a considerable body of mathematical proofs on on-line optimization programs which can be leveraged to assist in the development and verification of their implementation. In this paper, we demonstrate how theoretical proofs of real-time optimization algorithms can be used to describe functional properties at the level of the code, thereby making it accessible for the formal methods community. The running example used in this paper is a generic semi-definite programming (SDP) solver. Semi-definite programs can encode a wide variety of optimization problems and can be solved in polynomial time at a given accuracy. We describe a top-to-down approach that transforms a high-level analysis of the algorithm into useful code annotations. We formulate some general remarks about how such a task can be incorporated into a convex programming autocoder. We then take a first step towards the automatic verification of the optimization program by identifying key issues to be adressed in future work

A semidefinite programming approach for solving multiobjective linear programming

Several algorithms are available in the literature for finding the entire set of Pareto-optimal solutions in MultiObjective Linear Programming (MOLP). However, it has not been proposed so far an interior point algorithm that finds all Pareto-optimal solutions of MOLP. We present an explicit construction, based on a transformation of any MOLP into a finite sequence of SemiDefinite Programs (SDP), the solutions of which give the entire set of Pareto-optimal extreme points solutions of MOLP. These SDP problems are solved by interior point methods; thus our approach provides a pseudopolynomial interior point methodology to find the set of Pareto-optimal solutions of MOLP.Junta de AndalucíaFondo Europeo de Desarrollo RegionalMinisterio de Ciencia e Innovació

Effect of commercial rye whole-meal bread on postprandial blood glucose and gastric emptying in healthy subjects

<p>Abstract</p> <p>Background</p> <p>The intake of dietary fibre has been shown to reduce the risk of developing diabetes mellitus. The aim of this study was to compare the effects of commercial rye whole-meal bread containing whole kernels and white wheat bread on the rate of gastric emptying and postprandial glucose response in healthy subjects.</p> <p>Methods</p> <p>Ten healthy subjects took part in a blinded crossover trial. Blood glucose level and gastric emptying rate (GER) were determined after the ingestion of 150 g white wheat bread or 150 g whole-meal rye bread on two different occasions after fasting overnight. The GER was measured using real-time ultrasonography, and was calculated as the percentage change in antral cross-sectional area 15 and 90 minutes after completing the meal.</p> <p>Results</p> <p>No statistically significant difference was found between the GER values or the blood glucose levels following the two meals when evaluated with the Wilcoxon signed rank sum test.</p> <p>Conclusion</p> <p>The present study revealed no difference in postprandial blood glucose response or gastric emptying after the ingestion of rye whole-meal bread compared with white wheat bread.</p> <p>Trial registration</p> <p>NCT00779298</p

The botanical integrity of wheat products influences the gastric distention and satiety in healthy subjects

<p>Abstract</p> <p>Background</p> <p>Maintenance of the botanical integrity of cereal kernels and the addition of acetic acid (as vinegar) in the product or meal has been shown to lower the postprandial blood glucose and insulin response and to increase satiety. However, the mechanism behind the benefits of acetic acid on blood glucose and satiety is not clear. We hypothesized that the gastric emptying rate could be involved. Thus, the aim of this study was to evaluate the possible influence of maintained botanical integrity of cereals and the presence of acetic acid (vinegar) on gastric emptying rate (GER), postprandial blood glucose and satiety.</p> <p>Methods</p> <p>Fifteen healthy subjects were included in a blinded crossover trial, and thirteen of the subjects completed the study. Equicarbohydrate amounts of the following wheat-based meals were studied: white wheat bread, whole-kernel wheat bread or wholemeal wheat bread served with white wine vinegar. The results were compared with a reference meal consisting of white wheat bread without vinegar. The GER was measured with standardized real-time ultrasonography using normal fasting blood glucose <6.1 mmol/l or plasma glucose <7.0 mmol/l as an inclusion criterion. The GER was calculated as the percentage change in the antral cross-sectional area 15 and 90 minutes after ingestion of the various meals. Satiety scores were estimated and blood glucose was measured before and 15, 30, 45, 60, 90 and 120 min after the start of the meal.</p> <p>Results</p> <p>The whole-kernel wheat bread with vinegar resulted in significantly higher (<0.05) satiety than the wholemeal wheat bread and white wheat bread with vinegar and the reference bread. Wheat fiber present in the wholemeal wheat bread, or the presence of wheat kernels per se, did not affect the postprandial blood glucose or GER significantly compared with white wheat bread, neither did the addition of vinegar to white bread affect these variables. There was no correlation found between the satiety with antral areas or GER</p> <p>Conclusion</p> <p>The present study shows higher satiety after a whole-kernel wheat bread meal with vinegar. This may be explained by increased antral distension after ingestion of intact cereal kernels but, in this study, not by a lower gastric emptying rate or higher postprandial blood glucose response.</p> <p>Trial registration</p> <p>NTR1116</p

The prognostic role of intragenic copy number breakpoints and identification of novel fusion genes in paediatric high grade glioma

BACKGROUND: Paediatric high grade glioma (pHGG) is a distinct biological entity to histologically similar tumours arising in older adults, and has differing copy number profiles and driver genetic alterations. As functionally important intragenic copy number aberrations (iCNA) and fusion genes begin to be identified in adult HGG, the same has not yet been done in the childhood setting. We applied an iCNA algorithm to our previously published dataset of DNA copy number profiling in pHGG with a view to identify novel intragenic breakpoints. RESULTS: We report a series of 288 iCNA events in pHGG, with the presence of intragenic breakpoints itself a negative prognostic factor. We identified an increased number of iCNA in older children compared to infants, and increased iCNA in H3F3A K27M mutant tumours compared to G34R/V and wild-type. We observed numerous gene disruptions by iCNA due to both deletions and amplifications, targeting known HGG-associated genes such as RB1 and NF1, putative tumour suppressors such as FAF1 and KIDINS220, and novel candidates such as PTPRE and KCND2. We further identified two novel fusion genes in pHGG - CSGALNACT2:RET and the complex fusion DHX57:TMEM178:MAP4K3. The latter was sequence-validated and appears to be an activating event in pHGG. CONCLUSIONS: These data expand upon our understanding of the genomic events driving these tumours and represent novel targets for therapeutic intervention in these poor prognosis cancers of childhood.We are grateful for support from the Rosetrees Trust, the Brain Tumour Charity and Fundacao para a Ciencia e Tecnologia, Portugal (PhD Studentship SFRH/BD/33473/2008). DC, AM, LB and CJ acknowledge NHS funding to the Biomedical Research Centre