Stochastic Invariants for Probabilistic Termination

Termination is one of the basic liveness properties, and we study the termination problem for probabilistic programs with real-valued variables. Previous works focused on the qualitative problem that asks whether an input program terminates with probability~1 (almost-sure termination). A powerful approach for this qualitative problem is the notion of ranking supermartingales with respect to a given set of invariants. The quantitative problem (probabilistic termination) asks for bounds on the termination probability. A fundamental and conceptual drawback of the existing approaches to address probabilistic termination is that even though the supermartingales consider the probabilistic behavior of the programs, the invariants are obtained completely ignoring the probabilistic aspect. In this work we address the probabilistic termination problem for linear-arithmetic probabilistic programs with nondeterminism. We define the notion of {\em stochastic invariants}, which are constraints along with a probability bound that the constraints hold. We introduce a concept of {\em repulsing supermartingales}. First, we show that repulsing supermartingales can be used to obtain bounds on the probability of the stochastic invariants. Second, we show the effectiveness of repulsing supermartingales in the following three ways: (1)~With a combination of ranking and repulsing supermartingales we can compute lower bounds on the probability of termination; (2)~repulsing supermartingales provide witnesses for refutation of almost-sure termination; and (3)~with a combination of ranking and repulsing supermartingales we can establish persistence properties of probabilistic programs. We also present results on related computational problems and an experimental evaluation of our approach on academic examples.Comment: Full version of a paper published at POPL 2017. 20 page

Quantitative Regular Expressions for Arrhythmia Detection Algorithms

Motivated by the problem of verifying the correctness of arrhythmia-detection algorithms, we present a formalization of these algorithms in the language of Quantitative Regular Expressions. QREs are a flexible formal language for specifying complex numerical queries over data streams, with provable runtime and memory consumption guarantees. The medical-device algorithms of interest include peak detection (where a peak in a cardiac signal indicates a heartbeat) and various discriminators, each of which uses a feature of the cardiac signal to distinguish fatal from non-fatal arrhythmias. Expressing these algorithms' desired output in current temporal logics, and implementing them via monitor synthesis, is cumbersome, error-prone, computationally expensive, and sometimes infeasible. In contrast, we show that a range of peak detectors (in both the time and wavelet domains) and various discriminators at the heart of today's arrhythmia-detection devices are easily expressible in QREs. The fact that one formalism (QREs) is used to describe the desired end-to-end operation of an arrhythmia detector opens the way to formal analysis and rigorous testing of these detectors' correctness and performance. Such analysis could alleviate the regulatory burden on device developers when modifying their algorithms. The performance of the peak-detection QREs is demonstrated by running them on real patient data, on which they yield results on par with those provided by a cardiologist.Comment: CMSB 2017: 15th Conference on Computational Methods for Systems Biolog

What is the potential of p53 isoforms as a predictive biomarker in the treatment of cancer?

Introduction: For decades, p53 was researched as a single protein with alterations described as mutants. The discovery of 12 human p53 isoforms expressed from 9 transcripts changed this perception, eloquently explaining the numerous roles p53 plays, including apoptosis, senescence, and regeneration. Area covered: Here, we summarise the p53 isoforms and their relevance to cancer to establish an understanding and theorise on potential applications of the isoforms in clinical practice. Expert commentary: Pertaining to the different expression of isoforms in different tumors, it is concluded that the clinical use of isoforms as prognostic and predictive biomarkers will be different depending on the cell type, the tissue origin of the tumors, the position of the TP53 mutation and the driver-oncogene.</p

Counterexample-Guided Polynomial Loop Invariant Generation by Lagrange Interpolation

We apply multivariate Lagrange interpolation to synthesize polynomial quantitative loop invariants for probabilistic programs. We reduce the computation of an quantitative loop invariant to solving constraints over program variables and unknown coefficients. Lagrange interpolation allows us to find constraints with less unknown coefficients. Counterexample-guided refinement furthermore generates linear constraints that pinpoint the desired quantitative invariants. We evaluate our technique by several case studies with polynomial quantitative loop invariants in the experiments

Non-polynomial Worst-Case Analysis of Recursive Programs

We study the problem of developing efficient approaches for proving worst-case bounds of non-deterministic recursive programs. Ranking functions are sound and complete for proving termination and worst-case bounds of nonrecursive programs. First, we apply ranking functions to recursion, resulting in measure functions. We show that measure functions provide a sound and complete approach to prove worst-case bounds of non-deterministic recursive programs. Our second contribution is the synthesis of measure functions in nonpolynomial forms. We show that non-polynomial measure functions with logarithm and exponentiation can be synthesized through abstraction of logarithmic or exponentiation terms, Farkas' Lemma, and Handelman's Theorem using linear programming. While previous methods obtain worst-case polynomial bounds, our approach can synthesize bounds of the form $\mathcal{O}(n\log n)$ as well as $\mathcal{O}(n^r)$ where $r$ is not an integer. We present experimental results to demonstrate that our approach can obtain efficiently worst-case bounds of classical recursive algorithms such as (i) Merge-Sort, the divide-and-conquer algorithm for the Closest-Pair problem, where we obtain $\mathcal{O}(n \log n)$ worst-case bound, and (ii) Karatsuba's algorithm for polynomial multiplication and Strassen's algorithm for matrix multiplication, where we obtain $\mathcal{O}(n^r)$ bound such that $r$ is not an integer and close to the best-known bounds for the respective algorithms.Comment: 54 Pages, Full Version to CAV 201

The complex TIE between macrophages and angiogenesis

Macrophages are primarily known as phagocytic immune cells, but they also play a role in diverse processes, such as morphogenesis, homeostasis and regeneration. In this review, we discuss the influence of macrophages on angiogenesis, the process of new blood vessel formation from the pre-existing vasculature. Macrophages play crucial roles at each step of the angiogenic cascade, starting from new blood vessel sprouting to the remodelling of the vascular plexus and vessel maturation. Macrophages form promising targets for both pro- and anti-angiogenic treatments. However, to target macrophages, we will first need to understand the mechanisms that control the functional plasticity of macrophages during each of the steps of the angiogenic cascade. Here, we review recent insights in this topic. Special attention will be given to the TIE2-expressing macrophage (TEM), which is a subtype of highly angiogenic macrophages that is able to influence angiogenesis via the angiopoietin-TIE pathway

PrIC3: Property Directed Reachability for MDPs

IC3 has been a leap forward in symbolic model checking. This paper proposes PrIC3 (pronounced pricy-three), a conservative extension of IC3 to symbolic model checking of MDPs. Our main focus is to develop the theory underlying PrIC3. Alongside, we present a first implementation of PrIC3 including the key ingredients from IC3 such as generalization, repushing, and propagation

SPECIFICITY AND POSSIBLE MECHANISM OF REACTION BETWEEN 9-ANTHRALDEHYDE AND UNSATURATED ALIPHATIC COMPOUNDS DURING ULTRA-VIOLET IRRADIATION

No abstract

De novo assembly of the dual transcriptomes of a polymorphic raptor species and its malarial parasite

Pauli M, Chakarov N, Rupp O, et al. De novo assembly of the dual transcriptomes of a polymorphic raptor species and its malarial parasite. BMC Genomics. 2015;16(1): 1038