Faster algorithms for 1-mappability of a sequence

In the k-mappability problem, we are given a string x of length n and integers m and k, and we are asked to count, for each length-m factor y of x, the number of other factors of length m of x that are at Hamming distance at most k from y. We focus here on the version of the problem where k = 1. The fastest known algorithm for k = 1 requires time O(mn log n/ log log n) and space O(n). We present two algorithms that require worst-case time O(mn) and O(n log^2 n), respectively, and space O(n), thus greatly improving the state of the art. Moreover, we present an algorithm that requires average-case time and space O(n) for integer alphabets if m = {\Omega}(log n/ log {\sigma}), where {\sigma} is the alphabet size

Deciding Quantifier-Free Presburger Formulas Using Parameterized Solution Bounds

Given a formula in quantifier-free Presburger arithmetic, if it has a satisfying solution, there is one whose size, measured in bits, is polynomially bounded in the size of the formula. In this paper, we consider a special class of quantifier-free Presburger formulas in which most linear constraints are difference (separation) constraints, and the non-difference constraints are sparse. This class has been observed to commonly occur in software verification. We derive a new solution bound in terms of parameters characterizing the sparseness of linear constraints and the number of non-difference constraints, in addition to traditional measures of formula size. In particular, we show that the number of bits needed per integer variable is linear in the number of non-difference constraints and logarithmic in the number and size of non-zero coefficients in them, but is otherwise independent of the total number of linear constraints in the formula. The derived bound can be used in a decision procedure based on instantiating integer variables over a finite domain and translating the input quantifier-free Presburger formula to an equi-satisfiable Boolean formula, which is then checked using a Boolean satisfiability solver. In addition to our main theoretical result, we discuss several optimizations for deriving tighter bounds in practice. Empirical evidence indicates that our decision procedure can greatly outperform other decision procedures.Comment: 26 page

A fixed-target platform for serial femtosecond crystallography in a hydrated environment.

For serial femtosecond crystallography at X-ray free-electron lasers, which entails collection of single-pulse diffraction patterns from a constantly refreshed supply of microcrystalline sample, delivery of the sample into the X-ray beam path while maintaining low background remains a technical challenge for some experiments, especially where this methodology is applied to relatively low-ordered samples or those difficult to purify and crystallize in large quantities. This work demonstrates a scheme to encapsulate biological samples using polymer thin films and graphene to maintain sample hydration in vacuum conditions. The encapsulated sample is delivered into the X-ray beam on fixed targets for rapid scanning using the Roadrunner fixed-target system towards a long-term goal of low-background measurements on weakly diffracting samples. As a proof of principle, we used microcrystals of the 24 kDa rapid encystment protein (REP24) to provide a benchmark for polymer/graphene sandwich performance. The REP24 microcrystal unit cell obtained from our sandwiched in-vacuum sample was consistent with previously established unit-cell parameters and with those measured by us without encapsulation in humidified helium, indicating that the platform is robust against evaporative losses. While significant scattering from water was observed because of the sample-deposition method, the polymer/graphene sandwich itself was shown to contribute minimally to background scattering

Stable Noncrossing Matchings

Given a set of $n$ men represented by $n$ points lying on a line, and $n$ women represented by $n$ points lying on another parallel line, with each person having a list that ranks some people of opposite gender as his/her acceptable partners in strict order of preference. In this problem, we want to match people of opposite genders to satisfy people's preferences as well as making the edges not crossing one another geometrically. A noncrossing blocking pair w.r.t. a matching $M$ is a pair $(m,w)$ of a man and a woman such that they are not matched with each other but prefer each other to their own partners in $M$, and the segment $(m,w)$ does not cross any edge in $M$. A weakly stable noncrossing matching (WSNM) is a noncrossing matching that does not admit any noncrossing blocking pair. In this paper, we prove the existence of a WSNM in any instance by developing an $O(n^2)$ algorithm to find one in a given instance.Comment: This paper has appeared at IWOCA 201

Airborne observations of methane emissions from rice cultivation in the Sacramento Valley of California

Airborne measurements of methane (CH4) and carbon dioxide (CO2) were taken over the rice growing region of California's Sacramento Valley in the late spring of 2010 and 2011. From these and ancillary measurements, we show that CH4 mixing ratios were higher in the planetary boundary layer above the Sacramento Valley during the rice growing season than they were before it, which we attribute to emissions from rice paddies. We derive daytime emission fluxes of CH4 between 0.6 and 2.0% of the CO2 taken up by photosynthesis on a per carbon, or mole to mole, basis. We also use a mixing model to determine an average CH 4/CO2 flux ratio of -0.6% for one day early in the growing season of 2010. We conclude the CH4/CO2 flux ratio estimates from a single rice field in a previous study are representative of rice fields in the Sacramento Valley. If generally true, the California Air Resources Board (CARB) greenhouse gas inventory emission rate of 2.7×1010g CH4/yr is approximately three times lower than the range of probable CH4 emissions (7.8-9.3×10 10g CH4/yr) from rice cultivation derived in this study. We attribute this difference to decreased burning of the residual rice crop since 1991, which leads to an increase in CH4 emissions from rice paddies in succeeding years, but which is not accounted for in the CARB inventory. © 2012. American Geophysical Union. All Rights Reserved

Patterns of primary care and mortality among patients with schizophrenia or diabetes: a cluster analysis approach to the retrospective study of healthcare utilization

Abstract Background Patients with schizophrenia have difficulty managing their medical healthcare needs, possibly resulting in delayed treatment and poor outcomes. We analyzed whether patients reduced primary care use over time, differentially by diagnosis with schizophrenia, diabetes, or both schizophrenia and diabetes. We also assessed whether such patterns of primary care use were a significant predictor of mortality over a 4-year period. Methods The Veterans Healthcare Administration (VA) is the largest integrated healthcare system in the United States. Administrative extracts of the VA's all-electronic medical records were studied. Patients over age 50 and diagnosed with schizophrenia in 2002 were age-matched 1:4 to diabetes patients. All patients were followed through 2005. Cluster analysis explored trajectories of primary care use. Proportional hazards regression modelled the impact of these primary care utilization trajectories on survival, controlling for demographic and clinical covariates. Results Patients comprised three diagnostic groups: diabetes only (n = 188,332), schizophrenia only (n = 40,109), and schizophrenia with diabetes (Scz-DM, n = 13,025). Cluster analysis revealed four distinct trajectories of primary care use: consistent over time, increasing over time, high and decreasing, low and decreasing. Patients with schizophrenia only were likely to have low-decreasing use (73% schizophrenia-only vs 54% Scz-DM vs 52% diabetes). Increasing use was least common among schizophrenia patients (4% vs 8% Scz-DM vs 7% diabetes) and was associated with improved survival. Low-decreasing primary care, compared to consistent use, was associated with shorter survival controlling for demographics and case-mix. The observational study was limited by reliance on administrative data. Conclusion Regular primary care and high levels of primary care were associated with better survival for patients with chronic illness, whether psychiatric or medical. For schizophrenia patients, with or without comorbid diabetes, primary care offers a survival benefit, suggesting that innovations in treatment retention targeting at-risk groups can offer significant promise of improving outcomes.http://deepblue.lib.umich.edu/bitstream/2027.42/78274/1/1472-6963-9-127.xmlhttp://deepblue.lib.umich.edu/bitstream/2027.42/78274/2/1472-6963-9-127.pdfPeer Reviewe

Considering the Case for Biodiversity Cycles: Reexamining the Evidence for Periodicity in the Fossil Record

Medvedev and Melott (2007) have suggested that periodicity in fossil biodiversity may be induced by cosmic rays which vary as the Solar System oscillates normal to the galactic disk. We re-examine the evidence for a 62 million year (Myr) periodicity in biodiversity throughout the Phanerozoic history of animal life reported by Rohde & Mueller (2005), as well as related questions of periodicity in origination and extinction. We find that the signal is robust against variations in methods of analysis, and is based on fluctuations in the Paleozoic and a substantial part of the Mesozoic. Examination of origination and extinction is somewhat ambiguous, with results depending upon procedure. Origination and extinction intensity as defined by RM may be affected by an artifact at 27 Myr in the duration of stratigraphic intervals. Nevertheless, when a procedure free of this artifact is implemented, the 27 Myr periodicity appears in origination, suggesting that the artifact may ultimately be based on a signal in the data. A 62 Myr feature appears in extinction, when this same procedure is used. We conclude that evidence for a periodicity at 62 Myr is robust, and evidence for periodicity at approximately 27 Myr is also present, albeit more ambiguous.Comment: Minor modifications to reflect final published versio

Far-infrared spectroscopic images of M83

We have mapped the nearby face on barred spiral galaxy, M83 in the bright [CII] 158 μm, [OI] 63 and 146 μm, [NII] 122 μm, and [OIII] 88 μm fine-structure lines with the Long Wavelength Spectrometer (LWS) on ISO. The maps are nearly fully sampled, and cover the inner 6.75' x 6' region - essentially the entire optical disk. We also obtained a full LWS grating scan of the nucleus. The lines are detectable over the entire disk, and enhanced at the nucleus, where the [OI] 63 μm and [NII] lines are particularly strong. At the nucleus, the line ratios indicate a strong starburst headed by O9 stars. Surprisingly, the [OI] and [CII] line emission (from photodissociation regions) is not enhanced relative to [NII] (from low density HII regions) on the spiral arms. The line ratios are the same for the spiral arms and interarm regions. We find very strong emission in the [OIII] 88 μm, [OI] 146 μm, and [CII] lines at the intersection of the bar and spiral arm to the SW indicating particularly strong star formation activity there. The [OI] 63 μm/146 μm line ratio is quite small there likely the result of self absorption in the 63 μm line by enveloping clouds. The total luminosity of this emission peak is 1.2 x 109 Lodo

Revealing the electronic structure of a carbon nanotube carrying a supercurrent

Carbon nanotubes (CNTs) are not intrinsically superconducting but they can carry a supercurrent when connected to superconducting electrodes. This supercurrent is mainly transmitted by discrete entangled electron-hole states confined to the nanotube, called Andreev Bound States (ABS). These states are a key concept in mesoscopic superconductivity as they provide a universal description of Josephson-like effects in quantum-coherent nanostructures (e.g. molecules, nanowires, magnetic or normal metallic layers) connected to superconducting leads. We report here the first tunneling spectroscopy of individually resolved ABS, in a nanotube-superconductor device. Analyzing the evolution of the ABS spectrum with a gate voltage, we show that the ABS arise from the discrete electronic levels of the molecule and that they reveal detailed information about the energies of these levels, their relative spin orientation and the coupling to the leads. Such measurements hence constitute a powerful new spectroscopic technique capable of elucidating the electronic structure of CNT-based devices, including those with well-coupled leads. This is relevant for conventional applications (e.g. superconducting or normal transistors, SQUIDs) and quantum information processing (e.g. entangled electron pairs generation, ABS-based qubits). Finally, our device is a new type of dc-measurable SQUID