Loss of Precision in Implementations of the Toom-Cook Algorithm

Historically, polynomial multiplication has required a quadratic number of operations. Several algorithms in the past century have improved upon this. In this work, we focus on the Toom-Cook algorithm. Devised by Toom in 1963, it is a family of algorithms parameterized by an integer, n. The algorithm multiplies two polynomials by recursively dividing them into smaller polynomials, multiplying many small polynomials, and interpolating to obtain the product. While it is no longer the asymptotically fastest method of multiplying, there is a range of intermediate degrees (typically less than 1000) where it performs the best. Some applications, like quantum-resistant cryptosystems, require the use of polynomials whose coefficients belong to the ring of integers modulo a power of 2. A problem arises with using the Toom-Cook algorithm to multiply these polynomials because the interpolation step of the algorithm requires division by even numbers. This results in a loss of 2-adic precision. If too many bits of precision are lost, the product will be incorrect. Interpolating a polynomial from some of its values is generally easy, and different works have solved the interpolation step of the Toom-Cook algorithm with different equations. In order to track the loss of precision, it is necessary to establish and prove the general form of the solution to the system of equations. We present three sets of interpolation formulas: the matrix, natural, and efficient formulas. For any integer n \u3e 2, we seek to find a general expression for each of the three sets of formulas, and to prove the respective loss of precision. First, for the efficient interpolation, we prove the general set of formulas. Then, for the natural interpolation, we conjecture a general set of formulas that depends on two combinatorial identities. We prove the first identity and some cases of the second identity. Finally, we prove the loss of precision of the matrix interpolation formulas

Flexibility in Problem Solving: Analogical Transfer of Tool Use in Toddlers Is Immune to Delay

Solving problems that are perceptually dissimilar but require similar solutions is a key skill in everyday life. In adults, this ability, termed analogical transfer, draws on memories of relevant past experiences that partially overlap with the present task at hand. Thanks to this support from long-term memory, analogical transfer allows remarkable behavioral flexibility beyond immediate situations. However, little is known about the interaction between long-term memory and analogical transfer in development as, to date, they have been studied separately. Here, for the first time, effects of age and memory on analogical transfer were investigated in 2-to-4.5-olds in a simple tool-use setup. Children attempted to solve a puzzle box after training the correct solution on a different looking box, either right before the test or 24 hours earlier. We found that children (N = 105) could transfer thesolution regardless of the delay and a perceptual conflict introduced in the tool set. For children who failed to transfer (N = 54) and repeated the test without a perceptual conflict, the odds of success did not improve. Our findings suggest that training promoted the detection of functional similarities between boxes and, thereby, flexible transfer both in the short and the long term

Declínio cognitivo, depressão e qualidade de vida em pacientes de diferentes estágios da doença renal crônica

Introduction: Patients with chronic kidney disease constitute a population at high risk for cognitive decline. Therefore they are often users of “polypharmacy” and present comorbidities such as diabetes and hypertension. Objective: To evaluate cognitive function, depression and quality of life in patients at different stages of chronic kidney disease. Method: Cross-sectional study carried out from June to December 2007 in 119 patients: 27 in peritoneal dialysis, 30 in hemodialysis, 32 in pre-dialysis and 30 with arterial hypertension. Several tests were performed: Mini-Mental State Examination (MMSE), Verbal Fluency Test, Digits, Clock Test, Codes, SF-36 (Quality of Life) and the Beck Depression Inventory. Additionally, clinical and laboratory data of the patients were collected and medication use was recorded. Results: There was no difference in mean age of the patients among the groups. There was no statistical difference when cognitive impairment was assessed by the Mini-mental test (p = 0.558). The Digit Span test (p = 0.01) and Clock test (p = 0.02) were significantly worse in the hemodialysis patients, and there was a trend with Code test (p = 0.09) in these patients. There was no difference between groups in the level of depression and Quality of Life. Conclusion: These results show that cognitive impairment is frequent among patients in with CKD, particularly in those undergoing hemodialysis and suggest the need to conduct longitudinal studies to confirm whether or not there is an influence of dialysis treatment on the cognitive decline.INTRODUÇÃO: Os pacientes portadores de doença renal crônica constituem uma população de alto risco para o declínio cognitivo, pois, frequentemente, são usuários de "polifarmácias" e apresentam comorbidades como diabetes e hipertensão arterial. OBJETIVO: Avaliar a função cognitiva, a depressão e a qualidade de vida de pacientes em diferentes estágios da doença renal crônica. MÉTODO: Estudo transversal realizado nos meses de junho a dezembro de 2007, em 119 pacientes, sendo 27 em diálise peritoneal, 30 em hemodiálise, 32 em pré-diálise e 30 com hipertensão arterial. Realizou-se bateria de testes: Mini-mental, Teste de Fluência Verbal, Dígitos, Teste do Relógio, Códigos, SF-36 (Qualidade de Vida) e Inventário Beck de Depressão. Coletaram-se dados clínicos e laboratoriais dos pacientes e foi feita sondagem, análise de prontuário, sobre uso de medicamentos. RESULTADOS: Não se observou diferença na média de idade dos pacientes nos diferentes grupos. Não houve diferença estatística na avaliação do MEEM (p = 0,558). Os pacientes em hemodiálise apresentaram pior performance nos testes de avaliação cognitiva Dígitos ordem direta (p = 0,01) e Relógio (0,02) e, no teste Código (p = 0,09), houve uma tendência de pior desempenho. O pior resultado no teste de Fluência Verbal foi observado nos pacientes do grupo da pré-diálise. Não houve diferença entre os grupos quanto ao nível de depressão e qualidade de vida. CONCLUSÃO: Esses resultados evidenciam a ocorrência de déficit cognitivo nos pacientes com DRC, notadamente naqueles tratados pela hemodiálise, e sugerem a necessidade de se realizar estudos longitudinais para confirmar ou não a influência do tratamento dialítico no declínio cognitivo

MicroRNAs in vascular tissue engineering and post-ischemic neovascularization

Increasing numbers of paediatric patients with congenital heart defects are surviving to adulthood, albeit with continuing clinical needs. Hence, there is still scope for revolutionary new strategies to correct vascular anatomical defects. Adult patients are also surviving longer with the adverse consequences of ischemic vascular disease, especially after acute coronary syndromes brought on by plaque erosion and rupture. Vascular tissue engineering and therapeutic angiogenesis provide new hope for these patients. Both approaches have shown promise in laboratory studies, but have not yet been able to deliver clear evidence of clinical success. More research into biomaterials, molecular medicine and cell and molecular therapies is necessary. This review article focuses on the new opportunities offered by targeting microRNAs for the improved production and greater empowerment of vascular cells for use in vascular tissue engineering or for increasing blood perfusion of ischemic tissues by amplifying the resident microvascular network

Report on the sixth blind test of organic crystal structure prediction methods.

The sixth blind test of organic crystal structure prediction (CSP) methods has been held, with five target systems: a small nearly rigid molecule, a polymorphic former drug candidate, a chloride salt hydrate, a co-crystal and a bulky flexible molecule. This blind test has seen substantial growth in the number of participants, with the broad range of prediction methods giving a unique insight into the state of the art in the field. Significant progress has been seen in treating flexible molecules, usage of hierarchical approaches to ranking structures, the application of density-functional approximations, and the establishment of new workflows and `best practices' for performing CSP calculations. All of the targets, apart from a single potentially disordered Z' = 2 polymorph of the drug candidate, were predicted by at least one submission. Despite many remaining challenges, it is clear that CSP methods are becoming more applicable to a wider range of real systems, including salts, hydrates and larger flexible molecules. The results also highlight the potential for CSP calculations to complement and augment experimental studies of organic solid forms.The organisers and participants are very grateful to the crystallographers who supplied the candidate structures: Dr. Peter Horton (XXII), Dr. Brian Samas (XXIII), Prof. Bruce Foxman (XXIV), and Prof. Kraig Wheeler (XXV and XXVI). We are also grateful to Dr. Emma Sharp and colleagues at Johnson Matthey (Pharmorphix) for the polymorph screening of XXVI, as well as numerous colleagues at the CCDC for assistance in organising the blind test. Submission 2: We acknowledge Dr. Oliver Korb for numerous useful discussions. Submission 3: The Day group acknowledge the use of the IRIDIS High Performance Computing Facility, and associated support services at the University of Southampton, in the completion of this work. We acknowledge funding from the EPSRC (grants EP/J01110X/1 and EP/K018132/1) and the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC through grant agreements n. 307358 (ERC-stG- 2012-ANGLE) and n. 321156 (ERC-AG-PE5-ROBOT). Submission 4: I am grateful to Mikhail Kuzminskii for calculations of molecular structures on Gaussian 98 program in the Institute of Organic Chemistry RAS. The Russian Foundation for Basic Research is acknowledged for financial support (14-03-01091). Submission 5: Toine Schreurs provided computer facilities and assistance. I am grateful to Matthew Habgood at AWE company for providing a travel grant. Submission 6: We would like to acknowledge support of this work by GlaxoSmithKline, Merck, and Vertex. Submission 7: The research was financially supported by the VIDI Research Program 700.10.427, which is financed by The Netherlands Organisation for Scientific Research (NWO), and the European Research Council (ERC-2010-StG, grant agreement n. 259510-KISMOL). We acknowledge the support of the Foundation for Fundamental Research on Matter (FOM). Supercomputer facilities were provided by the National Computing Facilities Foundation (NCF). Submission 8: Computer resources were provided by the Center for High Performance Computing at the University of Utah and the Extreme Science and Engineering Discovery Environment (XSEDE), supported by NSF grant number ACI-1053575. MBF and GIP acknowledge the support from the University of Buenos Aires and the Argentinian Research Council. Submission 9: We thank Dr. Bouke van Eijck for his valuable advice on our predicted structure of XXV. We thank the promotion office for TUT programs on advanced simulation engineering (ADSIM), the leading program for training brain information architects (BRAIN), and the information and media center (IMC) at Toyohashi University of Technology for the use of the TUT supercomputer systems and application software. We also thank the ACCMS at Kyoto University for the use of their supercomputer. In addition, we wish to thank financial supports from Conflex Corp. and Ministry of Education, Culture, Sports, Science and Technology. Submission 12: We thank Leslie Leiserowitz from the Weizmann Institute of Science and Geoffrey Hutchinson from the University of Pittsburgh for helpful discussions. We thank Adam Scovel at the Argonne Leadership Computing Facility (ALCF) for technical support. Work at Tulane University was funded by the Louisiana Board of Regents Award # LEQSF(2014-17)-RD-A-10 “Toward Crystal Engineering from First Principles”, by the NSF award # EPS-1003897 “The Louisiana Alliance for Simulation-Guided Materials Applications (LA-SiGMA)”, and by the Tulane Committee on Research Summer Fellowship. Work at the Technical University of Munich was supported by the Solar Technologies Go Hybrid initiative of the State of Bavaria, Germany. Computer time was provided by the Argonne Leadership Computing Facility (ALCF), which is supported by the Office of Science of the U.S. Department of Energy under contract DE-AC02-06CH11357. Submission 13: This work would not have been possible without funding from Khalifa University’s College of Engineering. I would like to acknowledge Prof. Robert Bennell and Prof. Bayan Sharif for supporting me in acquiring the resources needed to carry out this research. Dr. Louise Price is thanked for her guidance on the use of DMACRYS and NEIGHCRYS during the course of this research. She is also thanked for useful discussions and numerous e-mail exchanges concerning the blind test. Prof. Sarah Price is acknowledged for her support and guidance over many years and for providing access to DMACRYS and NEIGHCRYS. Submission 15: The work was supported by the United Kingdom’s Engineering and Physical Sciences Research Council (EPSRC) (EP/J003840/1, EP/J014958/1) and was made possible through access to computational resources and support from the High Performance Computing Cluster at Imperial College London. We are grateful to Professor Sarah L. Price for supplying the DMACRYS code for use within CrystalOptimizer, and to her and her research group for support with DMACRYS and feedback on CrystalPredictor and CrystalOptimizer. Submission 16: R. J. N. acknowledges financial support from the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. [EP/J017639/1]. R. J. N. and C. J. P. acknowledge use of the Archer facilities of the U.K.’s national high-performance computing service (for which access was obtained via the UKCP consortium [EP/K014560/1]). C. J. P. also acknowledges a Leadership Fellowship Grant [EP/K013688/1]. B. M. acknowledges Robinson College, Cambridge, and the Cambridge Philosophical Society for a Henslow Research Fellowship. Submission 17: The work at the University of Delaware was supported by the Army Research Office under Grant W911NF-13-1- 0387 and by the National Science Foundation Grant CHE-1152899. The work at the University of Silesia was supported by the Polish National Science Centre Grant No. DEC-2012/05/B/ST4/00086. Submission 18: We would like to thank Constantinos Pantelides, Claire Adjiman and Isaac Sugden of Imperial College for their support of our use of CrystalPredictor and CrystalOptimizer in this and Submission 19. The CSP work of the group is supported by EPSRC, though grant ESPRC EP/K039229/1, and Eli Lilly. The PhD students support: RKH by a joint UCL Max-Planck Society Magdeburg Impact studentship, REW by a UCL Impact studentship; LI by the Cambridge Crystallographic Data Centre and the M3S Centre for Doctoral Training (EPSRC EP/G036675/1). Submission 19: The potential generation work at the University of Delaware was supported by the Army Research Office under Grant W911NF-13-1-0387 and by the National Science Foundation Grant CHE-1152899. Submission 20: The work at New York University was supported, in part, by the U.S. Army Research Laboratory and the U.S. Army Research Office under contract/grant number W911NF-13-1-0387 (MET and LV) and, in part, by the Materials Research Science and Engineering Center (MRSEC) program of the National Science Foundation under Award Number DMR-1420073 (MET and ES). The work at the University of Delaware was supported by the U.S. Army Research Laboratory and the U.S. Army Research Office under contract/grant number W911NF-13-1- 0387 and by the National Science Foundation Grant CHE-1152899. Submission 21: We thank the National Science Foundation (DMR-1231586), the Government of Russian Federation (Grant No. 14.A12.31.0003), the Foreign Talents Introduction and Academic Exchange Program (No. B08040) and the Russian Science Foundation, project no. 14-43-00052, base organization Photochemistry Center of the Russian Academy of Sciences. Calculations were performed on the Rurik supercomputer at Moscow Institute of Physics and Technology. Submission 22: The computational results presented have been achieved in part using the Vienna Scientific Cluster (VSC). Submission 24: The potential generation work at the University of Delaware was supported by the Army Research Office under Grant W911NF-13-1-0387 and by the National Science Foundation Grant CHE-1152899. Submission 25: J.H. and A.T. acknowledge the support from the Deutsche Forschungsgemeinschaft under the program DFG-SPP 1807. H-Y.K., R.A.D., and R.C. acknowledge support from the Department of Energy (DOE) under Grant Nos. DE-SC0008626. This research used resources of the Argonne Leadership Computing Facility at Argonne National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-06CH11357. This research used resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DEAC02-05CH11231. Additional computational resources were provided by the Terascale Infrastructure for Groundbreaking Research in Science and Engineering (TIGRESS) High Performance Computing Center and Visualization Laboratory at Princeton University.This is the final version of the article. It first appeared from Wiley via http://dx.doi.org/10.1107/S2052520616007447

Report on the sixth blind test of organic crystal-structure prediction methods

The sixth blind test of organic crystal-structure prediction (CSP) methods has been held, with five target systems: a small nearly rigid molecule, a polymorphic former drug candidate, a chloride salt hydrate, a co-crystal, and a bulky flexible molecule. This blind test has seen substantial growth in the number of submissions, with the broad range of prediction methods giving a unique insight into the state of the art in the field. Significant progress has been seen in treating flexible molecules, usage of hierarchical approaches to ranking structures, the application of density-functional approximations, and the establishment of new workflows and "best practices" for performing CSP calculations. All of the targets, apart from a single potentially disordered Z` = 2 polymorph of the drug candidate, were predicted by at least one submission. Despite many remaining challenges, it is clear that CSP methods are becoming more applicable to a wider range of real systems, including salts, hydrates and larger flexible molecules. The results also highlight the potential for CSP calculations to complement and augment experimental studies of organic solid forms

Genomic Relationships, Novel Loci, and Pleiotropic Mechanisms across Eight Psychiatric Disorders

Genetic influences on psychiatric disorders transcend diagnostic boundaries, suggesting substantial pleiotropy of contributing loci. However, the nature and mechanisms of these pleiotropic effects remain unclear. We performed analyses of 232,964 cases and 494,162 controls from genome-wide studies of anorexia nervosa, attention-deficit/hyper-activity disorder, autism spectrum disorder, bipolar disorder, major depression, obsessive-compulsive disorder, schizophrenia, and Tourette syndrome. Genetic correlation analyses revealed a meaningful structure within the eight disorders, identifying three groups of inter-related disorders. Meta-analysis across these eight disorders detected 109 loci associated with at least two psychiatric disorders, including 23 loci with pleiotropic effects on four or more disorders and 11 loci with antagonistic effects on multiple disorders. The pleiotropic loci are located within genes that show heightened expression in the brain throughout the lifespan, beginning prenatally in the second trimester, and play prominent roles in neurodevelopmental processes. These findings have important implications for psychiatric nosology, drug development, and risk prediction.Peer reviewe

Impact of COVID-19 on cardiovascular testing in the United States versus the rest of the world

Objectives: This study sought to quantify and compare the decline in volumes of cardiovascular procedures between the United States and non-US institutions during the early phase of the coronavirus disease-2019 (COVID-19) pandemic. Background: The COVID-19 pandemic has disrupted the care of many non-COVID-19 illnesses. Reductions in diagnostic cardiovascular testing around the world have led to concerns over the implications of reduced testing for cardiovascular disease (CVD) morbidity and mortality. Methods: Data were submitted to the INCAPS-COVID (International Atomic Energy Agency Non-Invasive Cardiology Protocols Study of COVID-19), a multinational registry comprising 909 institutions in 108 countries (including 155 facilities in 40 U.S. states), assessing the impact of the COVID-19 pandemic on volumes of diagnostic cardiovascular procedures. Data were obtained for April 2020 and compared with volumes of baseline procedures from March 2019. We compared laboratory characteristics, practices, and procedure volumes between U.S. and non-U.S. facilities and between U.S. geographic regions and identified factors associated with volume reduction in the United States. Results: Reductions in the volumes of procedures in the United States were similar to those in non-U.S. facilities (68% vs. 63%, respectively; p = 0.237), although U.S. facilities reported greater reductions in invasive coronary angiography (69% vs. 53%, respectively; p < 0.001). Significantly more U.S. facilities reported increased use of telehealth and patient screening measures than non-U.S. facilities, such as temperature checks, symptom screenings, and COVID-19 testing. Reductions in volumes of procedures differed between U.S. regions, with larger declines observed in the Northeast (76%) and Midwest (74%) than in the South (62%) and West (44%). Prevalence of COVID-19, staff redeployments, outpatient centers, and urban centers were associated with greater reductions in volume in U.S. facilities in a multivariable analysis. Conclusions: We observed marked reductions in U.S. cardiovascular testing in the early phase of the pandemic and significant variability between U.S. regions. The association between reductions of volumes and COVID-19 prevalence in the United States highlighted the need for proactive efforts to maintain access to cardiovascular testing in areas most affected by outbreaks of COVID-19 infection