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

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

Constraining Unmodeled Physics with Compact Binary Mergers from GWTC-1

We present a flexible model to describe the effects of generic deviations of observed gravitational wave signals from modeled waveforms in the LIGO and Virgo gravitational wave detectors. With the detection of 11 gravitational wave events from the GWTC-1 catalog, we are able to constrain possible deviations from our modeled waveforms. In this paper we present our coherent spline model that describes the deviations, then choose to validate our model on an example phenomenological and astrophysically motivated departure in waveforms based on extreme spontaneous scalarization. We find that the model is capable of recovering the simulated deviations. By performing model comparisons we observe that the spline model effectively describes the simulated departures better than a normal compact binary coalescence (CBC) model. We analyze the entire GWTC-1 catalog of events with our model and compare it to a normal CBC model, finding that there are no significant departures from the modeled template gravitational waveforms used

Bandgaps in the propagation and scattering of surface water waves over cylindrical steps

Here we investigate the propagation and scattering of surface water waves by arrays of bottom-mounted cylindrical steps. Both periodic and random arrangements of the steps are considered. The wave transmission through the arrays is computed using the multiple scattering method based upon a recently derived formulation. For the periodic case, the results are compared to the band structure calculation. We demonstrate that complete band gaps can be obtained in such a system. Furthermore, we show that the randomization of the location of the steps can significantly reduce the transmission of water waves. Comparison with other systems is also discussed.Comment: 4 pages, 3 figure

Emergent Phenomena Induced by Spin-Orbit Coupling at Surfaces and Interfaces

Spin-orbit coupling (SOC) describes the relativistic interaction between the spin and momentum degrees of freedom of electrons, and is central to the rich phenomena observed in condensed matter systems. In recent years, new phases of matter have emerged from the interplay between SOC and low dimensionality, such as chiral spin textures and spin-polarized surface and interface states. These low-dimensional SOC-based realizations are typically robust and can be exploited at room temperature. Here we discuss SOC as a means of producing such fundamentally new physical phenomena in thin films and heterostructures. We put into context the technological promise of these material classes for developing spin-based device applications at room temperature

A case study evaluation of competitors undertaking an antarctic ultra-endurance event: nutrition, hydration and body composition variables

Background: The nutritional demands of ultra-endurance racing are well documented. However, the relationship between nutritional consumption and performance measures are less obvious for athletes competing in Polar conditions. Therefore, the aim of this study was to evaluate dietary intake, hydration status, body composition and performance times throughout an 800-km Antarctic race. Methods: The event organisers declared that 17 competitors would participate in the South Pole race. Of the 17 competitors, pre-race data were collected from 13 participants (12 males and 1 female (M±SD): age: 40.1±8.9 years; weight 83.9±10.3kg; and body fat percentage: 21.9±3.8%). Dietary recall, body composition and urinary osmolarity were assessed pre-race, midway checkpoint and end race. Data were compared on the basis of fast finishers (the Norwegian team (n=3) who won in a record of 14 day) and slower finishers (the remaining teams (n=10) reaching the South Pole between 22 and 28 days). Results: The percentage contribution of macronutrients to daily energy intake for all participants was as follows: carbohydrate (CHO) - 23.7% (221±82 g.day-1), fat = 60.6% (251±127g.day-1) and protein = 15.7% (117±52g.day-1). Energy demands were closer met by faster finishers compared to slower finishers (5,332±469 vs. 3,048±1,140kcal.day-1, p=0.02). Average reduction in body mass throughout the race was 8.3±5.5kg, with an average loss of lean mass of 2.0±4.1kg. There as a significant negative correlation between changes in lean mass and protein intake (p=0.03), and lean mass and energy intake (p=0.03). End-race urinary osmolarity was significantly elevated for faster finishers compared to slower finishers and control volunteers (faster finishers: 933±157mOsmol.L-1; slower finishers: 543±92mOsmol.L-1; control: 515±165mOsmol.L-1, p+0.04). Conclusions: Throughout the race, both groups were subjected to a negative change in energy balance which partly explained reduced body mass. Carbohydrate availability was limited inferring a greater reliance on fat and protein metabolism. Consequently, loss in fat-free mass was more prevalent with insufficient protein and caloric intake, which may relate to performance

Down-Regulation of miR-92 in Human Plasma Is a Novel Marker for Acute Leukemia Patients

BACKGROUND: MicroRNAs are a family of 19- to 25-nucleotides noncoding small RNAs that primarily function as gene regulators. Aberrant microRNA expression has been described for several human malignancies, and this new class of small regulatory RNAs has both oncogenic and tumor suppressor functions. Despite this knowledge, there is little information regarding microRNAs in plasma especially because microRNAs in plasma, if exist, were thought to be digested by RNase. Recent studies, however, have revealed that microRNAs exist and escape digestion in plasma. METHODOLOGY/PRINCIPAL FINDINGS: We performed microRNA microaray to obtain insight into microRNA deregulation in the plasma of a leukemia patient. We have revealed that microRNA-638 (miR-638) is stably present in human plasmas, and microRNA-92a (miR-92a) dramatically decreased in the plasmas of acute leukemia patients. Especially, the ratio of miR-92a/miR-638 in plasma was very useful for distinguishing leukemia patients from healthy body. CONCLUSIONS/SIGNIFICANCE: The ratio of miR-92a/miR-638 in plasma has strong potential for clinical application as a novel biomarker for detection of leukemia

Control over topological insulator photocurrents with light polarization

Three-dimensional topological insulators represent a new quantum phase of matter with spin-polarized surface states that are protected from backscattering. The static electronic properties of these surface states have been comprehensively imaged by both photoemission and tunneling spectroscopies. Theorists have proposed that topological surface states can also exhibit novel electronic responses to light, such as topological quantum phase transitions and spin-polarized electrical currents. However, the effects of optically driving a topological insulator out of equilibrium have remained largely unexplored experimentally, and no photocurrents have been measured. Here we show that illuminating the topological insulator Bi2Se3 with circularly polarized light generates a photocurrent that originates from topological helical Dirac fermions, and that reversing the helicity of the light reverses the direction of the photocurrent. We also observe a photocurrent that is controlled by the linear polarization of light, and argue that it may also have a topological surface state origin. This approach may allow the probing of dynamic properties of topological insulators and lead to novel opto-spintronic devices.Comment: Accepted in Nature Nanotechnology, November 2 201