Locating regions in a sequence under density constraints

Several biological problems require the identification of regions in a sequence where some feature occurs within a target density range: examples including the location of GC-rich regions, identification of CpG islands, and sequence matching. Mathematically, this corresponds to searching a string of 0s and 1s for a substring whose relative proportion of 1s lies between given lower and upper bounds. We consider the algorithmic problem of locating the longest such substring, as well as other related problems (such as finding the shortest substring or a maximal set of disjoint substrings). For locating the longest such substring, we develop an algorithm that runs in O(n) time, improving upon the previous best-known O(n log n) result. For the related problems we develop O(n log log n) algorithms, again improving upon the best-known O(n log n) results. Practical testing verifies that our new algorithms enjoy significantly smaller time and memory footprints, and can process sequences that are orders of magnitude longer as a result.Comment: 17 pages, 8 figures; v2: minor revisions, additional explanations; to appear in SIAM Journal on Computin

Planet Formation in the Outer Solar System

This paper reviews coagulation models for planet formation in the Kuiper Belt, emphasizing links to recent observations of our and other solar systems. At heliocentric distances of 35-50 AU, single annulus and multiannulus planetesimal accretion calculations produce several 1000 km or larger planets and many 50-500 km objects on timescales of 10-30 Myr in a Minimum Mass Solar Nebula. Planets form more rapidly in more massive nebulae. All models yield two power law cumulative size distributions, N_C propto r^{-q} with q = 3.0-3.5 for radii larger than 10 km and N_C propto r^{-2.5} for radii less than 1 km. These size distributions are consistent with observations of Kuiper Belt objects acquired during the past decade. Once large objects form at 35-50 AU, gravitational stirring leads to a collisional cascade where 0.1-10 km objects are ground to dust. The collisional cascade removes 80% to 90% of the initial mass in the nebula in roughly 1 Gyr. This dust production rate is comparable to rates inferred for alpha Lyr, beta Pic, and other extrasolar debris disk systems.Comment: invited review for PASP, March 2002. 33 pages of text and 12 figure

Searching a bitstream in linear time for the longest substring of any given density

Given an arbitrary bitstream, we consider the problem of finding the longest substring whose ratio of ones to zeroes equals a given value. The central result of this paper is an algorithm that solves this problem in linear time. The method involves (i) reformulating the problem as a constrained walk through a sparse matrix, and then (ii) developing a data structure for this sparse matrix that allows us to perform each step of the walk in amortised constant time. We also give a linear time algorithm to find the longest substring whose ratio of ones to zeroes is bounded below by a given value. Both problems have practical relevance to cryptography and bioinformatics.Comment: 22 pages, 19 figures; v2: minor edits and enhancement

Endothelial cell-surface tissue transglutaminase inhibits neutrophil adhesion by binding and releasing nitric oxide

Nitric oxide (NO) produced by endothelial cells in response to cytokines displays anti-inflammatory activity by preventing the adherence, migration and activation of neutrophils. The molecular mechanism by which NO operates at the blood-endothelium interface to exert anti-inflammatory properties is largely unknown. Here we show that on endothelial surfaces, NO is associated with the sulfhydryl-rich protein tissue transglutaminase (TG2), thereby endowing the membrane surfaces with anti-inflammatory properties. We find that tumor necrosis factor-α-stimulated neutrophil adherence is opposed by TG2 molecules that are bound to the endothelial surface. Alkylation of cysteine residues in TG2 or inhibition of endothelial NO synthesis renders the surface-bound TG2 inactive, whereas specific, high affinity binding of S-nitrosylated TG2 (SNO-TG2) to endothelial surfaces restores the anti-inflammatory properties of the endothelium, and reconstitutes the activity of endothelial-derived NO. We also show that SNO-TG2 is present in healthy tissues and that it forms on the membranes of shear-activated endothelial cells. Thus, the anti-inflammatory mechanism that prevents neutrophils from adhering to endothelial cells is identified with TG2 S-nitrosylation at the endothelial cell-blood interface

Results of a Feasibility Randomized Controlled Trial (RCT) of the Toolkit for Optimal Recovery (TOR): A Live Video Program to Prevent Chronic Pain in At-Risk Adults with Orthopedic Injuries

Background: Orthopedic injuries are the leading cause of hospital admissions in the USA, and many of these patients transition into chronic pain. Currently, there are no evidence-based interventions targeting prevention of chronic pain in patients with orthopedic injuries. We iteratively developed a four-session intervention “The Toolkit for Optimal Recovery” (TOR) which we plan to subsequently test for efficacy in a phase III hybrid efficacy-effectiveness multi-site clinical trial. In order to prevent methodological weaknesses in the subsequent trial, we conducted a feasibility pilot to evaluate the TOR delivered via secure live video versus usual care (UC) in patients with orthopedic injuries from an urban, level I trauma clinic, who screen in as at risk for chronic pain and disability. We tested the feasibility of recruitment, acceptability of screening, and randomization methods; acceptability of the intervention, treatment adherence, and treatment fidelity; satisfaction with the intervention; feasibility of the assessment process at all time points; acceptability of outcome measures for the definitive trial; and within-treatment effect sizes. Methods: We aimed to recruit 50–60 participants, randomize, and retain them for ~ 4 months. Assessments were done electronically via REDCap at baseline, post-intervention (approximately 5 weeks after baseline), and 3 months later. We followed procedures we intend to implement in the full-scale hybrid efficacy-effectiveness trial. Results: We recruited 54 participants and found that randomization and data collection procedures were generally acceptable. The majority of participants were white, educated, and employed. Warm hand-off referrals were more effective than research assistants directly approaching patients for participation without their providers’ engagement. Feasibility of recruitment, acceptability of screening, and randomization were good. Satisfaction with the program, adherence to treatment sessions, and treatment fidelity were all high. There were no technical issues associated with the live video delivery of the TOR. There was minimal missing data and outcome measures were deemed appropriate. Effect sizes for improvement after participation in TOR were moderate to large. There were many lessons learned for future trials. Conclusions: This study provided evidence of the feasibility of the planned hybrid efficacy-effectiveness trial design when implemented at our home institution. Establishing feasibility of the intervention and study procedures at other trauma centers with more diverse patient populations and different clinical practices is required before a multi-site phase III efficacy-effectiveness trial. Trial registration: ClinicalTrials.gov ID: NCT03405610. Registered on January 28, 2018—retrospectively registered

SARS-CoV-2 infects human engineered heart tissues and models COVID-19 myocarditis

There is ongoing debate as to whether cardiac complications of coronavirus disease-2019 (COVID-19) result from myocardial viral infection or are secondary to systemic inflammation and/or thrombosis. We provide evidence that cardiomyocytes are infected in patients with COVID-19 myocarditis and are susceptible to severe acute respiratory syndrome coronavirus 2. We establish an engineered heart tissue model of COVID-19 myocardial pathology, define mechanisms of viral pathogenesis, and demonstrate that cardiomyocyte severe acute respiratory syndrome coronavirus 2 infection results in contractile deficits, cytokine production, sarcomere disassembly, and cell death. These findings implicate direct infection of cardiomyocytes in the pathogenesis of COVID-19 myocardial pathology and provides a model system to study this emerging disease

Statistics of Q-Oscillators, Quons and Relation to Fractional Satistics

The statistics of $q$-oscillators, quons and to some extent, of anyons are studied and the basic differences among these objects are pointed out. In particular, the statistical distributions for different bosonic and fermionic $q$-oscillators are found for their corresponding Fock space representations in the case when the hamiltonian is identified with the number operator. In this case and for nonrelativistic particles, the single-particle temperature Green function is defined with $q$-deformed periodicity conditions. The equations of state for nonrelativistic and ultrarelativistic bosonic $q$-gases in an arbitrary space dimension are found near Bose statistics, as well as the one for an anyonic gas near Bose and Fermi statistics. The first corrections to the second virial coefficients are also evaluated. The phenomenon of Bose-Einstein condensation in the $q$-deformed gases is also discussed.Comment: 21 pages, Latex, HU-TFT-93-2

Scattering Theory and PT\mathcal{P}\mathcal{T}-Symmetry

We outline a global approach to scattering theory in one dimension that allows for the description of a large class of scattering systems and their $\mathcal{P}$-, $\mathcal{T}$-, and $\mathcal{P}\mathcal{T}$-symmetries. In particular, we review various relevant concepts such as Jost solutions, transfer and scattering matrices, reciprocity principle, unidirectional reflection and invisibility, and spectral singularities. We discuss in some detail the mathematical conditions that imply or forbid reciprocal transmission, reciprocal reflection, and the presence of spectral singularities and their time-reversal. We also derive generalized unitarity relations for time-reversal-invariant and $\mathcal{P}\mathcal{T}$-symmetric scattering systems, and explore the consequences of breaking them. The results reported here apply to the scattering systems defined by a real or complex local potential as well as those determined by energy-dependent potentials, nonlocal potentials, and general point interactions.Comment: Slightly expanded revised version, 38 page