On Multiphase-Linear Ranking Functions

Multiphase ranking functions ($\mathit{M{\Phi}RFs}$) were proposed as a means to prove the termination of a loop in which the computation progresses through a number of "phases", and the progress of each phase is described by a different linear ranking function. Our work provides new insights regarding such functions for loops described by a conjunction of linear constraints (single-path loops). We provide a complete polynomial-time solution to the problem of existence and of synthesis of $\mathit{M{\Phi}RF}$ of bounded depth (number of phases), when variables range over rational or real numbers; a complete solution for the (harder) case that variables are integer, with a matching lower-bound proof, showing that the problem is coNP-complete; and a new theorem which bounds the number of iterations for loops with $\mathit{M{\Phi}RFs}$. Surprisingly, the bound is linear, even when the variables involved change in non-linear way. We also consider a type of lexicographic ranking functions, $\mathit{LLRFs}$, more expressive than types of lexicographic functions for which complete solutions have been given so far. We prove that for the above type of loops, lexicographic functions can be reduced to $\mathit{M{\Phi}RFs}$, and thus the questions of complexity of detection and synthesis, and of resulting iteration bounds, are also answered for this class.Comment: typos correcte

Ranking Templates for Linear Loops

We present a new method for the constraint-based synthesis of termination arguments for linear loop programs based on linear ranking templates. Linear ranking templates are parametrized, well-founded relations such that an assignment to the parameters gives rise to a ranking function. This approach generalizes existing methods and enables us to use templates for many different ranking functions with affine-linear components. We discuss templates for multiphase, piecewise, and lexicographic ranking functions. Because these ranking templates require both strict and non-strict inequalities, we use Motzkin's Transposition Theorem instead of Farkas Lemma to transform the generated $\exists\forall$-constraint into an $\exists$-constraint.Comment: TACAS 201

Hyaluronan concentration and size distribution in human knee synovial fluid: variations with age and cartilage degeneration.

BackgroundOne potential mechanism for early superficial cartilage wear in normal joints is alteration of the lubricant content and quality of synovial fluid. The purpose of this study was to determine if the concentration and quality of the lubricant, hyaluronan, in synovial fluid: (1) was similar in left and right knees; (2) exhibited similar age-associated trends, whether collected postmortem or antemortem; and (3) varied with age and grade of joint degeneration.MethodsHuman synovial fluid of donors (23-91 years) without osteoarthritis was analyzed for the concentrations of protein, hyaluronan, and hyaluronan in the molecular weight ranges of 2.5-7 MDa, 1-2.5 MDa, 0.5-1 MDa, and 0.03-0.5 MDa. Similarity of data between left and right knees was assessed by reduced major axis regression, paired t-test, and Bland-Altman analysis. The effect of antemortem versus postmortem collection on biochemical properties was assessed for age-matched samples by unpaired t-test. The relationships between age, joint grade, and each biochemical component were assessed by regression analysis.ResultsJoint grade and the concentrations of protein, hyaluronan, and hyaluronan in the molecular weight ranges of 2.5-7 MDa, 1-2.5 MDa, and 0.5-1 MDa in human synovial fluid showed good agreement between left and right knees and were similar between age-matched patient and cadaver knee joints. There was an age-associated decrease in overall joint grade (-15 %/decade) and concentrations of hyaluronan (-10.5 %/decade), and hyaluronan in the molecular weight ranges of 2.5-7 MDa (-9.4 %/decade), 1-2.5 MDa (-11.3 %/decade), 0.5-1 MDa (-12.5 %/decade), and 0.03-0.5 MDa (-13.0 %/decade). Hyaluronan concentration and quality was more strongly associated with age than with joint grade.ConclusionsThe age-related increase in cartilage wear in non-osteoarthritic joints may be related to the altered hyaluronan content and quality of synovial fluid

Autonomous and remotely operated vehicle technology for hydrothermal vent discovery, exploration, and sampling

Author Posting. © Oceanography Society, 2007. This article is posted here by permission of Oceanography Society for personal use, not for redistribution. The definitive version was published in Oceanography 20, 1 (2007): 152-161.Autonomous and remotely operated underwater vehicles play complementary roles in the discovery, exploration, and detailed study of hydrothermal vents. Beginning with clues provided by towed or lowered instruments, autonomous underwater vehicles (AUVs) can localize and make preliminary photographic surveys of vent fields. In addition to finding and photographing such sites, AUVs excel at providing regional context through fine-scale bathymetric and magnetic field mapping. Remotely operated vehicles (ROVs) enable close-up inspection, photomosaicking, and tasks involving manipulation of samples and instruments. Increasingly, ROVs are used to conduct in situ seafloor experiments. ROVs can also be used for fine-scale bathymetric mapping with excellent results, although AUVs are usually more efficient in such tasks

Proving Termination Starting from the End

We present a novel technique for proving program termination which introduces a new dimension of modularity. Existing techniques use the program to incrementally construct a termination proof. While the proof keeps changing, the program remains the same. Our technique goes a step further. We show how to use the current partial proof to partition the transition relation into those behaviors known to be terminating from the current proof, and those whose status (terminating or not) is not known yet. This partition enables a new and unexplored dimension of incremental reasoning on the program side. In addition, we show that our approach naturally applies to conditional termination which searches for a precondition ensuring termination. We further report on a prototype implementation that advances the state-of-the-art on the grounds of termination and conditional termination.Comment: 16 page

The Spectrum of the Black Hole X-ray Nova V404 Cygni in Quiescence as Measured by XMM-Newton

We present XMM observations of the black hole X-ray nova V404 Cygni in quiescence. Its quiescent spectrum can be best fitted by a simple power-law with slope 2. The spectra are consistent with that expected for the advection-dominated accretion flow (ADAF). V404 Cyg was roughly equal in luminosity compared to the previous observation of Chandra. We see variability of a factor of 4 during the observation. We find no evidence for the presence of fluorescent or H-like/He-like iron emission, with upper limits of 52 eV and 110 eV respectively. The limit on the fluorescent emission is improved by a factor of 15 over the previous estimate, and the restriction on H-like/He-like emission is lower than predicted from models by a factor of roughly 2.Comment: 6 pages, 7 figures, ApJ accepte

Mid-ocean ridge exploration with an autonomous underwater vehicle

Author Posting. © Oceanography Society, 2007. This article is posted here by permission of Oceanography Society for personal use, not for redistribution. The definitive version was published in Oceanography 20, 4 (2007): 52-61.Human-occupied submersibles, towed vehicles, and tethered remotely operated vehicles (ROVs) have traditionally been used to study the deep seafloor. In recent years, however, autonomous underwater vehicles (AUVs) have begun to replace these other vehicles for mapping and survey missions. AUVs complement the capabilities of these pre-existing systems, offering superior mapping capabilities, improved logistics, and better utilization of the surface support vessel by allowing other tasks such as submersible operations, ROV work, CTD stations, or multibeam surveys to be performed while the AUV does its work. AUVs are particularly well suited to systematic preplanned surveys using sonars, in situ chemical sensors, and cameras in the rugged deep-sea terrain that has been the focus of numerous scientific expeditions (e.g., those to mid-ocean ridges and ocean margin settings). The Autonomous Benthic Explorer (ABE) is an example of an AUV that has been used for over 20 cruises sponsored by the National Science Foundation (NSF), the National Oceanic and Atmospheric Administration (NOAA) Office of Ocean Exploration (OE), and international and private sources. This paper summarizes NOAA OE-sponsored cruises made to date using ABE

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

Measuring Cation Dependent DNA Polymerase Fidelity Landscapes by Deep Sequencing

High-throughput recording of signals embedded within inaccessible micro-environments is a technological challenge. The ideal recording device would be a nanoscale machine capable of quantitatively transducing a wide range of variables into a molecular recording medium suitable for long-term storage and facile readout in the form of digital data. We have recently proposed such a device, in which cation concentrations modulate the misincorporation rate of a DNA polymerase (DNAP) on a known template, allowing DNA sequences to encode information about the local cation concentration. In this work we quantify the cation sensitivity of DNAP misincorporation rates, making possible the indirect readout of cation concentration by DNA sequencing. Using multiplexed deep sequencing, we quantify the misincorporation properties of two DNA polymerases – Dpo4 and Klenow exo[subscript −] – obtaining the probability and base selectivity of misincorporation at all positions within the template. We find that Dpo4 acts as a DNA recording device for Mn[superscript 2+] with a misincorporation rate gain of ~2%/mM. This modulation of misincorporation rate is selective to the template base: the probability of misincorporation on template T by Dpo4 increases >50-fold over the range tested, while the other template bases are affected less strongly. Furthermore, cation concentrations act as scaling factors for misincorporation: on a given template base, Mn[superscript 2+] and Mg[superscript 2+] change the overall misincorporation rate but do not alter the relative frequencies of incoming misincorporated nucleotides. Characterization of the ion dependence of DNAP misincorporation serves as the first step towards repurposing it as a molecular recording device.Damon Runyon Cancer Research FoundationNational Institutes of Health (U.S.)National Science Foundation (U.S.)McGovern Institute for Brain Research at MITMassachusetts Institute of Technology. Media LaboratoryNew York Stem Cell Foundation (Robertson Neuroscience Investigator Award)Paul G. Allen Family Foundation (Distinguished Investigator in Neuroscience Award

Alternating runtime and size complexity analysis of integer programs

We present a modular approach to automatic complexity analysis. Based on a novel alternation between finding symbolic time bounds for program parts and using these to infer size bounds on program variables, we can restrict each analysis step to a small part of the program while maintaining a high level of precision. Extensive experiments with the implementation of our method demonstrate its performance and power in comparison with other tools