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

Modulational Instability in Equations of KdV Type

It is a matter of experience that nonlinear waves in dispersive media, propagating primarily in one direction, may appear periodic in small space and time scales, but their characteristics --- amplitude, phase, wave number, etc. --- slowly vary in large space and time scales. In the 1970's, Whitham developed an asymptotic (WKB) method to study the effects of small "modulations" on nonlinear periodic wave trains. Since then, there has been a great deal of work aiming at rigorously justifying the predictions from Whitham's formal theory. We discuss recent advances in the mathematical understanding of the dynamics, in particular, the instability of slowly modulated wave trains for nonlinear dispersive equations of KdV type.Comment: 40 pages. To appear in upcoming title in Lecture Notes in Physic

Toward a 21st-century health care system: Recommendations for health care reform

The coverage, cost, and quality problems of the U.S. health care system are evident. Sustainable health care reform must go beyond financing expanded access to care to substantially changing the organization and delivery of care. The FRESH-Thinking Project (www.fresh-thinking.org) held a series of workshops during which physicians, health policy experts, health insurance executives, business leaders, hospital administrators, economists, and others who represent diverse perspectives came together. This group agreed that the following 8 recommendations are fundamental to successful reform: 1. Replace the current fee-for-service payment system with a payment system that encourages and rewards innovation in the efficient delivery of quality care. The new payment system should invest in the development of outcome measures to guide payment. 2. Establish a securely funded, independent agency to sponsor and evaluate research on the comparative effectiveness of drugs, devices, and other medical interventions. 3. Simplify and rationalize federal and state laws and regulations to facilitate organizational innovation, support care coordination, and streamline financial and administrative functions. 4. Develop a health information technology infrastructure with national standards of interoperability to promote data exchange. 5. Create a national health database with the participation of all payers, delivery systems, and others who own health care data. Agree on methods to make de-identified information from this database on clinical interventions, patient outcomes, and costs available to researchers. 6. Identify revenue sources, including a cap on the tax exclusion of employer-based health insurance, to subsidize health care coverage with the goal of insuring all Americans. 7. Create state or regional insurance exchanges to pool risk, so that Americans without access to employer-based or other group insurance could obtain a standard benefits package through these exchanges. Employers should also be allowed to participate in these exchanges for their employees' coverage. 8. Create a health coverage board with broad stakeholder representation to determine and periodically update the affordable standard benefit package available through state or regional insurance exchanges

Shared genetic risk between eating disorder- and substance-use-related phenotypes:Evidence from genome-wide association studies

First published: 16 February 202

Age at first birth in women is genetically associated with increased risk of schizophrenia

Prof. Paunio on PGC:n jäsenPrevious studies have shown an increased risk for mental health problems in children born to both younger and older parents compared to children of average-aged parents. We previously used a novel design to reveal a latent mechanism of genetic association between schizophrenia and age at first birth in women (AFB). Here, we use independent data from the UK Biobank (N = 38,892) to replicate the finding of an association between predicted genetic risk of schizophrenia and AFB in women, and to estimate the genetic correlation between schizophrenia and AFB in women stratified into younger and older groups. We find evidence for an association between predicted genetic risk of schizophrenia and AFB in women (P-value = 1.12E-05), and we show genetic heterogeneity between younger and older AFB groups (P-value = 3.45E-03). The genetic correlation between schizophrenia and AFB in the younger AFB group is -0.16 (SE = 0.04) while that between schizophrenia and AFB in the older AFB group is 0.14 (SE = 0.08). Our results suggest that early, and perhaps also late, age at first birth in women is associated with increased genetic risk for schizophrenia in the UK Biobank sample. These findings contribute new insights into factors contributing to the complex bio-social risk architecture underpinning the association between parental age and offspring mental health.Peer reviewe

The genetics of the mood disorder spectrum:genome-wide association analyses of over 185,000 cases and 439,000 controls

Background Mood disorders (including major depressive disorder and bipolar disorder) affect 10-20% of the population. They range from brief, mild episodes to severe, incapacitating conditions that markedly impact lives. Despite their diagnostic distinction, multiple approaches have shown considerable sharing of risk factors across the mood disorders. Methods To clarify their shared molecular genetic basis, and to highlight disorder-specific associations, we meta-analysed data from the latest Psychiatric Genomics Consortium (PGC) genome-wide association studies of major depression (including data from 23andMe) and bipolar disorder, and an additional major depressive disorder cohort from UK Biobank (total: 185,285 cases, 439,741 controls; non-overlapping N = 609,424). Results Seventy-three loci reached genome-wide significance in the meta-analysis, including 15 that are novel for mood disorders. More genome-wide significant loci from the PGC analysis of major depression than bipolar disorder reached genome-wide significance. Genetic correlations revealed that type 2 bipolar disorder correlates strongly with recurrent and single episode major depressive disorder. Systems biology analyses highlight both similarities and differences between the mood disorders, particularly in the mouse brain cell-types implicated by the expression patterns of associated genes. The mood disorders also differ in their genetic correlation with educational attainment – positive in bipolar disorder but negative in major depressive disorder. Conclusions The mood disorders share several genetic associations, and can be combined effectively to increase variant discovery. However, we demonstrate several differences between these disorders. Analysing subtypes of major depressive disorder and bipolar disorder provides evidence for a genetic mood disorders spectrum