Motion of vortices implies chaos in Bohmian mechanics

Bohmian mechanics is a causal interpretation of quantum mechanics in which particles describe trajectories guided by the wave function. The dynamics in the vicinity of nodes of the wave function, usually called vortices, is regular if they are at rest. However, vortices generically move during time evolution of the system. We show that this movement is the origin of chaotic behavior of quantum trajectories. As an example, our general result is illustrated numerically in the two-dimensional isotropic harmonic oscillator.Comment: 7 pages 5 figure

Vortex interaction, chaos and quantum probabilities

The motion of a single vortex is able to originate chaos in the quantum trajectories defined in Bohm's interpretation of quantum mechanics. In this Letter, we show that this is also the case in the general situation, in which many interacting vortices exist. This result gives support to recent attempts in which Born's probability rule is derived in terms of an irreversible time evolution to equilibrium, rather than being postulated.Comment: 4 pages, 4 figure

Bifurcations of periodic and chaotic attractors in pinball billiards with focusing boundaries

We study the dynamics of billiard models with a modified collision rule: the outgoing angle from a collision is a uniform contraction, by a factor lambda, of the incident angle. These pinball billiards interpolate between a one-dimensional map when lambda=0 and the classical Hamiltonian case of elastic collisions when lambda=1. For all lambda<1, the dynamics is dissipative, and thus gives rise to attractors, which may be periodic or chaotic. Motivated by recent rigorous results of Markarian, Pujals and Sambarino, we numerically investigate and characterise the bifurcations of the resulting attractors as the contraction parameter is varied. Some billiards exhibit only periodic attractors, some only chaotic attractors, and others have coexistence of the two types.Comment: 30 pages, 17 figures. v2: Minor changes after referee comments. Version with some higher-quality figures available at http://sistemas.fciencias.unam.mx/~dsanders/publications.htm

Common polygenic risk for autism spectrum disorder (ASD) is associated with cognitive ability in the general population

Acknowledgements Generation Scotland has received core funding from the Chief Scientist Office of the Scottish Government Health Directorates CZD/16/6 and the Scottish Funding Council HR03006. We are grateful to all the families who took part, the general practitioners and the Scottish School of Primary Care for their help in recruiting them and the whole Generation Scotland team, which includes interviewers, computer and laboratory technicians, clerical workers, research scientists, volunteers, managers, receptionists, health-care assistants and nurses. We acknowledge with gratitude the financial support received for this work from the Dr Mortimer and Theresa Sackler Foundation. For the Lothian Birth Cohorts (LBC1921 and LBC1936), we thank Paul Redmond for database management assistance; Alan Gow, Martha Whiteman, Alison Pattie, Michelle Taylor, Janie Corley, Caroline Brett and Caroline Cameron for data collection and data entry; nurses and staff at the Wellcome Trust Clinical Research Facility, where blood extraction and genotyping was performed; staff at the Lothian Health Board; and the staff at the SCRE Centre, University of Glasgow. The research was supported by a program grant from Age UK (Disconnected Mind) and by grants from the Biotechnology and Biological Sciences Research Council (BBSRC). The work was undertaken by The University of Edinburgh Centre for Cognitive Ageing and Cognitive Epidemiology, part of the cross council Lifelong Health and Wellbeing Initiative (MR/K026992/1). Funding from the Medical Research Council (MRC) and BBSRC is gratefully acknowledged. DJM is an NRS Career Research Fellow funded by the CSO. BATS were funded by the Australian Research Council (A79600334, A79906588, A79801419, DP0212016, DP0664638, and DP1093900) and the National Health and Medical Research Council (389875) Australia. MKL is supported by a Perpetual Foundation Wilson Fellowship. SEM is supported by a Future Fellowship (FT110100548) from the Australian Research Council. GWM is supported by a National Health and Medical Research Council (NHMRC), Australia, Fellowship (619667). We thank the twins and siblings for their participation, Marlene Grace, Ann Eldridge and Natalie Garden for cognitive assessments, Kerrie McAloney, Daniel Park, David Smyth and Harry Beeby for research support, Anjali Henders and staff in the Molecular Epidemiology Laboratory for DNA sample processing and preparation and Scott Gordon for quality control and management of the genotypes. This work is supported by a Stragetic Award from the Wellcome Trust, reference 104036/Z/14/Z.Peer reviewedPublisher PD

Infinite ergodic theory and Non-extensive entropies

We bring into account a series of result in the infinite ergodic theory that we believe that they are relevant to the theory of non-extensive entropie

A striking correspondence between the dynamics generated by the vector fields and by the scalar parabolic equations

The purpose of this paper is to enhance a correspondence between the dynamics of the differential equations $\dot y(t)=g(y(t))$ on $\mathbb{R}^d$ and those of the parabolic equations $\dot u=\Delta u +f(x,u,\nabla u)$ on a bounded domain $\Omega$. We give details on the similarities of these dynamics in the cases $d=1$, $d=2$ and $d\geq 3$ and in the corresponding cases $\Omega=(0,1)$, $\Omega=\mathbb{T}^1$ and dim($\Omega$)$\geq 2$ respectively. In addition to the beauty of such a correspondence, this could serve as a guideline for future research on the dynamics of parabolic equations

Antimicrobial and cell-penetrating peptides induce lipid vesicle fusion by folding and aggregation

According to their distinct biological functions, membrane-active peptides are generally classified as antimicrobial (AMP), cell-penetrating (CPP), or fusion peptides (FP). The former two classes are known to have some structural and physicochemical similarities, but fusogenic peptides tend to have rather different features and sequences. Nevertheless, we found that many CPPs and some AMPs exhibit a pronounced fusogenic activity, as measured by a lipid mixing assay with vesicles composed of typical eukaryotic lipids. Compared to the HIV fusion peptide (FP23) as a representative standard, all designer-made peptides showed much higher lipid-mixing activities (MSI-103, MAP, transportan, penetratin, Pep1). Native sequences, on the other hand, were less fusogenic (magainin 2, PGLa, gramicidin S), and pre-aggregated ones were inactive (alamethicin, SAP). The peptide structures were characterized by circular dichroism before and after interacting with the lipid vesicles. A striking correlation between the extent of conformational change and the respective fusion activities was found for the series of peptides investigated here. At the same time, the CD data show that lipid mixing can be triggered by any type of conformation acquired upon binding, whether α-helical, β-stranded, or other. These observations suggest that lipid vesicle fusion can simply be driven by the energy released upon membrane binding, peptide folding, and possibly further aggregation. This comparative study of AMPs, CPPs, and FPs emphasizes the multifunctional aspects of membrane-active peptides, and it suggests that the origin of a peptide (native sequence or designer-made) may be more relevant to define its functional range than any given name

Deep learning-based phenotyping reclassifies combined hepatocellular-cholangiocarcinoma.

Primary liver cancer arises either from hepatocytic or biliary lineage cells, giving rise to hepatocellular carcinoma (HCC) or intrahepatic cholangiocarcinoma (ICCA). Combined hepatocellular- cholangiocarcinomas (cHCC-CCA) exhibit equivocal or mixed features of both, causing diagnostic uncertainty and difficulty in determining proper management. Here, we perform a comprehensive deep learning-based phenotyping of multiple cohorts of patients. We show that deep learning can reproduce the diagnosis of HCC vs. CCA with a high performance. We analyze a series of 405 cHCC-CCA patients and demonstrate that the model can reclassify the tumors as HCC or ICCA, and that the predictions are consistent with clinical outcomes, genetic alterations and in situ spatial gene expression profiling. This type of approach could improve treatment decisions and ultimately clinical outcome for patients with rare and biphenotypic cancers such as cHCC-CCA

A Combined Pathway and Regional Heritability Analysis Indicates NETRIN1 Pathway is Associated with Major Depressive Disorder

AbstractBackgroundGenome-wide association studies (GWASs) of major depressive disorder (MDD) have identified few significant associations. Testing the aggregation of genetic variants, in particular biological pathways, may be more powerful. Regional heritability analysis can be used to detect genomic regions that contribute to disease risk.MethodsWe integrated pathway analysis and multilevel regional heritability analyses in a pipeline designed to identify MDD-associated pathways. The pipeline was applied to two independent GWAS samples [Generation Scotland: The Scottish Family Health Study (GS:SFHS, N = 6455) and Psychiatric Genomics Consortium (PGC:MDD) (N = 18,759)]. A polygenic risk score (PRS) composed of single nucleotide polymorphisms from the pathway most consistently associated with MDD was created, and its accuracy to predict MDD, using area under the curve, logistic regression, and linear mixed model analyses, was tested.ResultsIn GS:SFHS, four pathways were significantly associated with MDD, and two of these explained a significant amount of pathway-level regional heritability. In PGC:MDD, one pathway was significantly associated with MDD. Pathway-level regional heritability was significant in this pathway in one subset of PGC:MDD. For both samples the regional heritabilities were further localized to the gene and subregion levels. The NETRIN1 signaling pathway showed the most consistent association with MDD across the two samples. PRSs from this pathway showed competitive predictive accuracy compared with the whole-genome PRSs when using area under the curve statistics, logistic regression, and linear mixed model.ConclusionsThese post-GWAS analyses highlight the value of combining multiple methods on multiple GWAS data for the identification of risk pathways for MDD. The NETRIN1 signaling pathway is identified as a candidate pathway for MDD and should be explored in further large population studies