Algorithmic Analysis of Qualitative and Quantitative Termination Problems for Affine Probabilistic Programs

In this paper, we consider termination of probabilistic programs with real-valued variables. The questions concerned are: 1. qualitative ones that ask (i) whether the program terminates with probability 1 (almost-sure termination) and (ii) whether the expected termination time is finite (finite termination); 2. quantitative ones that ask (i) to approximate the expected termination time (expectation problem) and (ii) to compute a bound B such that the probability to terminate after B steps decreases exponentially (concentration problem). To solve these questions, we utilize the notion of ranking supermartingales which is a powerful approach for proving termination of probabilistic programs. In detail, we focus on algorithmic synthesis of linear ranking-supermartingales over affine probabilistic programs (APP's) with both angelic and demonic non-determinism. An important subclass of APP's is LRAPP which is defined as the class of all APP's over which a linear ranking-supermartingale exists. Our main contributions are as follows. Firstly, we show that the membership problem of LRAPP (i) can be decided in polynomial time for APP's with at most demonic non-determinism, and (ii) is NP-hard and in PSPACE for APP's with angelic non-determinism; moreover, the NP-hardness result holds already for APP's without probability and demonic non-determinism. Secondly, we show that the concentration problem over LRAPP can be solved in the same complexity as for the membership problem of LRAPP. Finally, we show that the expectation problem over LRAPP can be solved in 2EXPTIME and is PSPACE-hard even for APP's without probability and non-determinism (i.e., deterministic programs). Our experimental results demonstrate the effectiveness of our approach to answer the qualitative and quantitative questions over APP's with at most demonic non-determinism.Comment: 24 pages, full version to the conference paper on POPL 201

Strong, Weak and Branching Bisimulation for Transition Systems and Markov Reward Chains: A Unifying Matrix Approach

We first study labeled transition systems with explicit successful termination. We establish the notions of strong, weak, and branching bisimulation in terms of boolean matrix theory, introducing thus a novel and powerful algebraic apparatus. Next we consider Markov reward chains which are standardly presented in real matrix theory. By interpreting the obtained matrix conditions for bisimulations in this setting, we automatically obtain the definitions of strong, weak, and branching bisimulation for Markov reward chains. The obtained strong and weak bisimulations are shown to coincide with some existing notions, while the obtained branching bisimulation is new, but its usefulness is questionable

Value Iteration for Long-run Average Reward in Markov Decision Processes

Markov decision processes (MDPs) are standard models for probabilistic systems with non-deterministic behaviours. Long-run average rewards provide a mathematically elegant formalism for expressing long term performance. Value iteration (VI) is one of the simplest and most efficient algorithmic approaches to MDPs with other properties, such as reachability objectives. Unfortunately, a naive extension of VI does not work for MDPs with long-run average rewards, as there is no known stopping criterion. In this work our contributions are threefold. (1) We refute a conjecture related to stopping criteria for MDPs with long-run average rewards. (2) We present two practical algorithms for MDPs with long-run average rewards based on VI. First, we show that a combination of applying VI locally for each maximal end-component (MEC) and VI for reachability objectives can provide approximation guarantees. Second, extending the above approach with a simulation-guided on-demand variant of VI, we present an anytime algorithm that is able to deal with very large models. (3) Finally, we present experimental results showing that our methods significantly outperform the standard approaches on several benchmarks

Seeding systems and cropping trends in Saskatchewan results of a PFRA survey, 1997-2002

Non-Peer ReviewedFrom 1997 to 2002, Agriculture & Agri-Food Canada’s (AAFC) PFRA Branch conducted a survey of over 4000 annually cropped fields in Saskatchewan. Each year the same fields were visited shortly after crop emergence to collect information on crop type, row spacing, opener type, packing system, amount of previous crop residue, orientation of previous crop stubble, and adoption of low soil disturbance seeding. Key results are the increasing trend toward lower soil disturbance seeding, and the high incidence of pulse crops associated with low disturbance seeding. In depth analysis of trends on individual fields suggest that very few producers are able to maintain low disturbance seeding every year on the same field. This suggests that some flexibility is required to allow for periodic soil disturbance to address issues such as perennial weeds

Bioactivity of the Murex Homeopathic Remedy and of Extracts from an Australian Muricid Mollusc against Human Cancer Cells

Marine molluscs from the family Muricidae are the source of a homeopathic remedy Murex, which is used to treat a range of conditions, including cancer. The aim of this study was to evaluate the in vitro bioactivity of egg mass extracts of the Australian muricid Dicathais orbita, in comparison to the Murex remedy, against human carcinoma and lymphoma cells. Liquid chromatography coupled with mass spectrometry (LC-MS) was used to characterize the chemical composition of the extracts and homeopathic remedy, focusing on biologically active brominated indoles. The MTS (tetrazolium salt) colorimetric assay was used to determine effects on cell viability, while necrosis and apoptosis induction were investigated using flow cytometry (propidium iodide and Annexin-V staining, resp.). Cells were treated with varying concentrations (1–0.01 mg/mL) of crude and semi-purified extracts or preparations (dilute 1 M and concentrated 4 mg/mL) from the Murex remedy (4 h). The Murex remedy showed little biological activity against the majority of cell lines tested. In contrast, the D. orbita egg extracts significantly decreased cell viability in the majority of carcinoma cell lines. Flow cytometry revealed these extracts induce necrosis in HT29 colorectal cancer cells, whereas apoptosis was induced in Jurkat cells. These findings highlight the biomedical potential of Muricidae extracts in the development of a natural therapy for the treatment of neoplastic tumors and lymphomas

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

The scattering properties of a system of structures in water waves

This is a pre-copyedited, author-produced PDF of an article accepted for publication in Quarterly Journal of Mechanics and Applied Mathematics following peer review. The version of record MCIVER, M., 2013. The scattering properties of a system of structures in water waves. Quarterly Journal of Mechanics and Applied Mathematics, 67(4), pp. 631-639 is available online at: http://dx.doi.org/10.1093/qjmam/hbu021A fixed, rigid structure is said to be cloaked in small amplitude, time-harmonic water waves if it is possible to surround it with other fixed or moving structures or variations in the sea-bed topography in such a way that there are no scattered waves in the far field. The resulting system of structures is said to be transparent to the incident wave field. By finding inequalities which the kinetic and potential energy in the total wave field for such a system must satisfy, it is shown that transparency is impossible for a system of structures which has non-zero volume and satisfies the condition that the free surface is connected and a vertical line drawn from every point on the free surface does not intersect another structure but intersects the sea bed at a point at which the bed is horizontal

Far-field representation for the vertical force on a floating structure

This article is closed access.Equations are derived that relate the vertical hydrodynamic force on two- and threedimensional structures that are floating in a fluid of infinite depth to the far-field dipole coefficient in the velocity potential. By an application of Green’s theorem to the radiation or scattering potential and a suitable test potential, the heave added mass, the heave damping and the vertical exciting force are shown to be expressible in terms of the dipole coefficient in the relevant potential. The results add to the known reciprocity relations, which relate quantities such as the damping and the exciting force to the amplitude of the far-field radiated wave. The expressions are valid at all frequencies, and their high- and low-frequency asymptotics are investigated

Ranking and Repulsing Supermartingales for Reachability in Probabilistic Programs

Computing reachability probabilities is a fundamental problem in the analysis of probabilistic programs. This paper aims at a comprehensive and comparative account on various martingale-based methods for over- and under-approximating reachability probabilities. Based on the existing works that stretch across different communities (formal verification, control theory, etc.), we offer a unifying account. In particular, we emphasize the role of order-theoretic fixed points---a classic topic in computer science---in the analysis of probabilistic programs. This leads us to two new martingale-based techniques, too. We give rigorous proofs for their soundness and completeness. We also make an experimental comparison using our implementation of template-based synthesis algorithms for those martingales

Microscopic theory for the light-induced anomalous Hall effect in graphene

We employ a quantum Liouville equation with relaxation to model the recently observed anomalous Hall effect in graphene irradiated by an ultrafast pulse of circularly polarized light. In the weak-field regime, we demonstrate that the Hall effect originates from an asymmetric population of photocarriers in the Dirac bands. By contrast, in the strong-field regime, the system is driven into a non-equilibrium steady state that is well-described by topologically non-trivial Floquet-Bloch bands. Here, the anomalous Hall current originates from the combination of a population imbalance in these dressed bands together with a smaller anomalous velocity contribution arising from their Berry curvature. This robust and general finding enables the simulation of electrical transport from light-induced Floquet-Bloch bands in an experimentally relevant parameter regime and creates a pathway to designing ultrafast quantum devices with Floquet-engineered transport properties