Complex-Distance Potential Theory and Hyperbolic Equations

An extension of potential theory in R^n is obtained by continuing the Euclidean distance function holomorphically to C^n. The resulting Newtonian potential is generated by an extended source distribution D(z) in C^n whose restriction to R^n is the delta function. This provides a natural model for extended particles in physics. In C^n, interpreted as complex spacetime, D(z) acts as a propagator generating solutions of the wave equation from their initial values. This gives a new connection between elliptic and hyperbolic equations that does not assume analyticity of the Cauchy data. Generalized to Clifford analysis, it induces a similar connection between solutions of elliptic and hyperbolic Dirac equations. There is a natural application to the time-dependent, inhomogeneous Dirac and Maxwell equations, and the `electromagnetic wavelets' introduced previously are an example.Comment: 25 pages, submited to Proceedings of 5th Intern. Conf. on Clifford Algebras, Ixtapa, June 24 - July 4, 199

Antipsychotic prescribing for vulnerable populations: a clinical audit at an acute Australian mental health unit at two-time points

Background: Antipsychotics are recognised as a critical intervention for schizophrenia and bipolar disorder. Guidelines globally endorse the routine practice of antipsychotic monotherapy, at the minimum effective dose. Even in treatmentresistant schizophrenia, clozapine use is endorsed before combining antipsychotics. This aim of this study was to review antipsychotic polytherapy alone, high-dose therapy alone, polytherapy and highdose prescribing patterns in adults discharged from an inpatient mental health unit at two time-points, and the alignment of this prescribing with clinical guideline recommendations. Additionally, associations with polytherapy and high-dose antipsychotic prescribing, including patient and clinical characteristics, were explored. Methods: A retrospective clinical audit of 400 adults (200 patients at two different time-points) discharged with at least one antipsychotic. Preliminary findings and education sessions were provided to physicians between Cohorts. Outcomes (polytherapy alone, high-dose therapy alone, polytherapy and high-dose therapy) were compared between study Cohorts using chi-squared and rank-sum tests. Associations between outcomes and covariates were assessed using multivariable logistic regression. Results: Most patients (62.5%) were discharged on a single antipsychotic within the recommended dose range. There was a clear preference for prescribing second generation antipsychotics, and in this respect, prescribing is aligned with current evidence-based guidelines. However, sub-optimal prescribing practices were identified for both Cohorts in relation to polytherapy and high-dose antipsychotic rates. Involuntary treatment, frequent hospitalisations and previous clozapine use significantly increased the risk of all three prescribing outcomes at discharge. Conclusions: In a significant minority, antipsychotic prescribing did not align with clinical guidelines despite increased training, indicating that the education program alone was ineffective at positively influencing antipsychotic prescribing practices. Further consideration should be given when prescribing antipsychotics for involuntary patients, people with frequent hospitalisations, and those who have previously trialled clozapine

Medical Informatics Platform (MIP): A Pilot Study Across Clinical Italian Cohorts

Introduction: With the shift of research focus to personalized medicine in Alzheimer's Dementia (AD), there is an urgent need for tools that are capable of quantifying a patient's risk using diagnostic biomarkers. The Medical Informatics Platform (MIP) is a distributed e-infrastructure federating large amounts of data coupled with machine-learning (ML) algorithms and statistical models to define the biological signature of the disease. The present study assessed (i) the accuracy of two ML algorithms, i.e., supervised Gradient Boosting (GB) and semi-unsupervised 3C strategy (Categorize, Cluster, Classify—CCC) implemented in the MIP and (ii) their contribution over the standard diagnostic workup. / Methods: We examined individuals coming from the MIP installed across 3 Italian memory clinics, including subjects with Normal Cognition (CN, n = 432), Mild Cognitive Impairment (MCI, n = 456), and AD (n = 451). The GB classifier was applied to best discriminate the three diagnostic classes in 1,339 subjects, and the CCC strategy was used to refine the classical disease categories. Four dementia experts provided their diagnostic confidence (DC) of MCI conversion on an independent cohort of 38 patients. DC was based on clinical, neuropsychological, CSF, and structural MRI information and again with addition of the outcome from the MIP tools. / Results: The GB algorithm provided a classification accuracy of 85% in a nested 10-fold cross-validation for CN vs. MCI vs. AD discrimination. Accuracy increased to 95% in the holdout validation, with the omission of each Italian clinical cohort out in turn. CCC identified five homogeneous clusters of subjects and 36 biomarkers that represented the disease fingerprint. In the DC assessment, CCC defined six clusters in the MCI population used to train the algorithm and 29 biomarkers to improve patients staging. GB and CCC showed a significant impact, evaluated as +5.99% of increment on physicians' DC. The influence of MIP on DC was rated from “slight” to “significant” in 80% of the cases. / Discussion: GB provided fair results in classification of CN, MCI, and AD. CCC identified homogeneous and promising classes of subjects via its semi-unsupervised approach. We measured the effect of the MIP on the physician's DC. Our results pave the way for the establishment of a new paradigm for ML discrimination of patients who will or will not convert to AD, a clinical priority for neurology

Isolated and dynamical horizons and their applications

Over the past three decades, black holes have played an important role in quantum gravity, mathematical physics, numerical relativity and gravitational wave phenomenology. However, conceptual settings and mathematical models used to discuss them have varied considerably from one area to another. Over the last five years a new, quasi-local framework was introduced to analyze diverse facets of black holes in a unified manner. In this framework, evolving black holes are modeled by dynamical horizons and black holes in equilibrium by isolated horizons. We review basic properties of these horizons and summarize applications to mathematical physics, numerical relativity and quantum gravity. This paradigm has led to significant generalizations of several results in black hole physics. Specifically, it has introduced a more physical setting for black hole thermodynamics and for black hole entropy calculations in quantum gravity; suggested a phenomenological model for hairy black holes; provided novel techniques to extract physics from numerical simulations; and led to new laws governing the dynamics of black holes in exact general relativity.Comment: 77 pages, 12 figures. Typos and references correcte

MSH3 polymorphisms and protein levels affect CAG repeat instability in huntington's disease mice

Expansions of trinucleotide CAG/CTG repeats in somatic tissues are thought to contribute to ongoing disease progression through an affected individual's life with Huntington's disease or myotonic dystrophy. Broad ranges of repeat instability arise between individuals with expanded repeats, suggesting the existence of modifiers of repeat instability. Mice with expanded CAG/CTG repeats show variable levels of instability depending upon mouse strain. However, to date the genetic modifiers underlying these differences have not been identified. We show that in liver and striatum the R6/1 Huntington's disease (HD) (CAG)~100 transgene, when present in a congenic C57BL/6J (B6) background, incurred expansion-biased repeat mutations, whereas the repeat was stable in a congenic BALB/cByJ (CBy) background. Reciprocal congenic mice revealed the Msh3 gene as the determinant for the differences in repeat instability. Expansion bias was observed in congenic mice homozygous for the B6 Msh3 gene on a CBy background, while the CAG tract was stabilized in congenics homozygous for the CBy Msh3 gene on a B6 background. The CAG stabilization was as dramatic as genetic deficiency of Msh2. The B6 and CBy Msh3 genes had identical promoters but differed in coding regions and showed strikingly different protein levels. B6 MSH3 variant protein is highly expressed and associated with CAG expansions, while the CBy MSH3 variant protein is expressed at barely detectable levels, associating with CAG stability. The DHFR protein, which is divergently transcribed from a promoter shared by the Msh3 gene, did not show varied levels between mouse strains. Thus, naturally occurring MSH3 protein polymorphisms are modifiers of CAG repeat instability, likely through variable MSH3 protein stability. Since evidence supports that somatic CAG instability is a modifier and predictor of disease, our data are consistent with the hypothesis that variable levels of CAG instability associated with polymorphisms of DNA repair genes may have prognostic implications for various repeat-associated diseases

Sex-biased parental care and sexual size dimorphism in a provisioning arthropod

The diverse selection pressures driving the evolution of sexual size dimorphism (SSD) have long been debated. While the balance between fecundity selection and sexual selection has received much attention, explanations based on sex-specific ecology have proven harder to test. In ectotherms, females are typically larger than males, and this is frequently thought to be because size constrains female fecundity more than it constrains male mating success. However, SSD could additionally reflect maternal care strategies. Under this hypothesis, females are relatively larger where reproduction requires greater maximum maternal effort – for example where mothers transport heavy provisions to nests. To test this hypothesis we focussed on digger wasps (Hymenoptera: Ammophilini), a relatively homogeneous group in which only females provision offspring. In some species, a single large prey item, up to 10 times the mother’s weight, must be carried to each burrow on foot; other species provide many small prey, each flown individually to the nest. We found more pronounced female-biased SSD in species where females carry single, heavy prey. More generally, SSD was negatively correlated with numbers of prey provided per offspring. Females provisioning multiple small items had longer wings and thoraxes, probably because smaller prey are carried in flight. Despite much theorising, few empirical studies have tested how sex-biased parental care can affect SSD. Our study reveals that such costs can be associated with the evolution of dimorphism, and this should be investigated in other clades where parental care costs differ between sexes and species

Stoichiometry of Base Excision Repair Proteins Correlates with Increased Somatic CAG Instability in Striatum over Cerebellum in Huntington's Disease Transgenic Mice

Huntington's disease (HD) is a progressive neurodegenerative disorder caused by expansion of an unstable CAG repeat in the coding sequence of the Huntingtin (HTT) gene. Instability affects both germline and somatic cells. Somatic instability increases with age and is tissue-specific. In particular, the CAG repeat sequence in the striatum, the brain region that preferentially degenerates in HD, is highly unstable, whereas it is rather stable in the disease-spared cerebellum. The mechanisms underlying the age-dependence and tissue-specificity of somatic CAG instability remain obscure. Recent studies have suggested that DNA oxidation and OGG1, a glycosylase involved in the repair of 8-oxoguanine lesions, contribute to this process. We show that in HD mice oxidative DNA damage abnormally accumulates at CAG repeats in a length-dependent, but age- and tissue-independent manner, indicating that oxidative DNA damage alone is not sufficient to trigger somatic instability. Protein levels and activities of major base excision repair (BER) enzymes were compared between striatum and cerebellum of HD mice. Strikingly, 5′-flap endonuclease activity was much lower in the striatum than in the cerebellum of HD mice. Accordingly, Flap Endonuclease-1 (FEN1), the main enzyme responsible for 5′-flap endonuclease activity, and the BER cofactor HMGB1, both of which participate in long-patch BER (LP–BER), were also significantly lower in the striatum compared to the cerebellum. Finally, chromatin immunoprecipitation experiments revealed that POLβ was specifically enriched at CAG expansions in the striatum, but not in the cerebellum of HD mice. These in vivo data fit a model in which POLβ strand displacement activity during LP–BER promotes the formation of stable 5′-flap structures at CAG repeats representing pre-expanded intermediate structures, which are not efficiently removed when FEN1 activity is constitutively low. We propose that the stoichiometry of BER enzymes is one critical factor underlying the tissue selectivity of somatic CAG expansion

Bidirectional switch of the valence associated with a hippocampal contextual memory engram

The valence of memories is malleable because of their intrinsic reconstructive property. This property of memory has been used clinically to treat maladaptive behaviours. However, the neuronal mechanisms and brain circuits that enable the switching of the valence of memories remain largely unknown. Here we investigated these mechanisms by applying the recently developed memory engram cell- manipulation technique. We labelled with channelrhodopsin-2 (ChR2) a population of cells in either the dorsal dentate gyrus (DG) of the hippocampus or the basolateral complex of the amygdala (BLA) that were specifically activated during contextual fear or reward conditioning. Both groups of fear-conditioned mice displayed aversive light-dependent responses in an optogenetic place avoidance test, whereas both DG- and BLA-labelled mice that underwent reward conditioning exhibited an appetitive response in an optogenetic place preference test. Next, in an attempt to reverse the valence of memory within a subject, mice whose DG or BLA engram had initially been labelled by contextual fear or reward conditioning were subjected to a second conditioning of the opposite valence while their original DG or BLA engram was reactivated by blue light. Subsequent optogenetic place avoidance and preference tests revealed that although the DG-engram group displayed a response indicating a switch of the memory valence, the BLA-engram group did not. This switch was also evident at the cellular level by a change in functional connectivity between DG engram-bearing cells and BLA engram-bearing cells. Thus, we found that in the DG, the neurons carrying the memory engram of a given neutral context have plasticity such that the valence of a conditioned response evoked by their reactivation can be reversed by re-associating this contextual memory engram with a new unconditioned stimulus of an opposite valence. Our present work provides new insight into the functional neural circuits underlying the malleability of emotional memory.RIKEN Brain Science InstituteHoward Hughes Medical InstituteJPB FoundationNational Institutes of Health (U.S.) (Pre-doctoral Training Grant T32GM007287

Gravitational Waves from Gravitational Collapse

Gravitational wave emission from the gravitational collapse of massive stars has been studied for more than three decades. Current state of the art numerical investigations of collapse include those that use progenitors with realistic angular momentum profiles, properly treat microphysics issues, account for general relativity, and examine non--axisymmetric effects in three dimensions. Such simulations predict that gravitational waves from various phenomena associated with gravitational collapse could be detectable with advanced ground--based and future space--based interferometric observatories.Comment: 68 pages including 13 figures; revised version accepted for publication in Living Reviews in Relativity (http://www.livingreviews.org

Dynamical Boson Stars

The idea of stable, localized bundles of energy has strong appeal as a model for particles. In the 1950s John Wheeler envisioned such bundles as smooth configurations of electromagnetic energy that he called {\em geons}, but none were found. Instead, particle-like solutions were found in the late 1960s with the addition of a scalar field, and these were given the name {\em boson stars}. Since then, boson stars find use in a wide variety of models as sources of dark matter, as black hole mimickers, in simple models of binary systems, and as a tool in finding black holes in higher dimensions with only a single killing vector. We discuss important varieties of boson stars, their dynamic properties, and some of their uses, concentrating on recent efforts.Comment: 79 pages, 25 figures, invited review for Living Reviews in Relativity; major revision in 201