Article the singular value expansion for arbitrary bounded linear operators

The singular value decomposition (SVD) is a basic tool for analyzing matrices. Regarding a general matrix as defining a linear operator and choosing appropriate orthonormal bases for the domain and co-domain allows the operator to be represented as multiplication by a diagonal matrix. It is well known that the SVD extends naturally to a compact linear operator mapping one Hilbert space to another; the resulting representation is known as the singular value expansion (SVE). It is less well known that a general bounded linear operator defined on Hilbert spaces also has a singular value expansion. This SVE allows a simple analysis of a variety of questions about the operator, such as whether it defines a well-posed linear operator equation and how to regularize the equation when it is not well posed

How to find discrete contact symmetries

This paper describes a new algorithm for determining all discrete contact symmetries of any differential equation whose Lie contact symmetries are known. The method is constructive and is easy to use. It is based upon the observation that the adjoint action of any contact symmetry is an automorphism of the Lie algebra of generators of Lie contact symmetries. Consequently, all contact symmetries satisfy various compatibility conditions. These conditions enable the discrete symmetries to be found systematically, with little effort

‘A storm of post-it notes’:experiences of perceptual capacity in autism and ADHD

Lab-based tasks suggest autistic people have increased perceptual capacity (i.e., process more information at any one time) compared to non-autistic people. Here, we explored whether this increase is reflected in autistic people’s day-to-day perceptual experiences and, when compared to those with ADHD/neurotypical people, whether commonalities/divergences in these experiences can illuminate differences between neurotypes. UK-based adults (108 autistic, 40 with ADHD, 79 autistic with ADHD, 85 neurotypical) completed an online survey about experiences of attention and distraction. Responses were analysed using thematic analysis. We found that participants of all neurotypes experienced periods of intense focus. Neurodivergent participants reported experiencing a barrage of information; autistic participants found this overwhelming, whereas those with ADHD referred to overload. This finding may reflect increased perceptual capacity for autistic people (adding ecological validity to previous findings regarding increased autistic perceptual capacity) vs. difficulties maintaining attentional priorities for those with ADHD. While differences between neurodivergent and neurotypical people were evident, discrepancies between experiences of neurodivergent groups were more subtle, suggesting that increased perceptual capacity may extend beyond autism. Consequently, perceptual capacity offers a useful framework to promote better understanding of one’s own perceptual experiences, and to guide strategies to ameliorate any challenges encountered

Systems Biology Approach to Late-Onset Alzheimer\u27s Disease Genome-Wide Association Study Identifies Novel Candidate Genes Validated Using Brain Expression Data and \u3cem\u3eCaenorhabditis elegans\u3c/em\u3e Experiments

Introduction—We sought to determine whether a systems biology approach may identify novel late-onset Alzheimer\u27s disease (LOAD) loci. Methods—We performed gene-wide association analyses and integrated results with human protein-protein interaction data using network analyses. We performed functional validation on novel genes using a transgenic Caenorhabditis elegans Aβ proteotoxicity model and evaluated novel genes using brain expression data from people with LOAD and other neurodegenerative conditions. Results—We identified 13 novel candidate LOAD genes outside chromosome 19. Of those, RNA interference knockdowns of the C. elegans orthologs of UBC, NDUFS3, EGR1, and ATP5H were associated with Aβ toxicity, and NDUFS3, SLC25A11, ATP5H, and APP were differentially expressed in the temporal cortex. Discussion—Network analyses identified novel LOAD candidate genes. We demonstrated a functional role for four of these in a C. elegans model and found enrichment of differentially expressed genes in the temporal cortex

Improving Depression Among HIV-Infected Adults: Transporting the Effect of a Depression Treatment Intervention to Routine Care

Depression affects 20-30% of people with HIV. Randomized controlled trials (RCTs) have demonstrated the effectiveness of interventions to improve depression among HIV-infected adults, but typically have highly selected populations which may limit generalizability. Inverse probability of sampling weights (IPSW) are a recently proposed method to transport (or standardize) findings from RCTs to a specific external target population

Multiple Imputation to Account for Measurement Error in Marginal Structural Models

Marginal structural models are an important tool for observational studies. These models typically assume that variables are measured without error. We describe a method to account for differential and non-differential measurement error in a marginal structural model

Ernst Freund as Precursor of the Rational Study of Corporate Law

Gindis, David, Ernst Freund as Precursor of the Rational Study of Corporate Law (October 27, 2017). Journal of Institutional Economics, Forthcoming. Available at SSRN: https://ssrn.com/abstract=2905547, doi: https://dx.doi.org/10.2139/ssrn.2905547The rise of large business corporations in the late 19th century compelled many American observers to admit that the nature of the corporation had yet to be understood. Published in this context, Ernst Freund's little-known The Legal Nature of Corporations (1897) was an original attempt to come to terms with a new legal and economic reality. But it can also be described, to paraphrase Oliver Wendell Holmes, as the earliest example of the rational study of corporate law. The paper shows that Freund had the intuitions of an institutional economist, and engaged in what today would be called comparative institutional analysis. Remarkably, his argument that the corporate form secures property against insider defection and against outsiders anticipated recent work on entity shielding and capital lock-in, and can be read as an early contribution to what today would be called the theory of the firm.Peer reviewe