A User-Friendly Hybrid Sparse Matrix Class in C++

When implementing functionality which requires sparse matrices, there are numerous storage formats to choose from, each with advantages and disadvantages. To achieve good performance, several formats may need to be used in one program, requiring explicit selection and conversion between the formats. This can be both tedious and error-prone, especially for non-expert users. Motivated by this issue, we present a user-friendly sparse matrix class for the C++ language, with a high-level application programming interface deliberately similar to the widely used MATLAB language. The class internally uses two main approaches to achieve efficient execution: (i) a hybrid storage framework, which automatically and seamlessly switches between three underlying storage formats (compressed sparse column, coordinate list, Red-Black tree) depending on which format is best suited for specific operations, and (ii) template-based meta-programming to automatically detect and optimise execution of common expression patterns. To facilitate relatively quick conversion of research code into production environments, the class and its associated functions provide a suite of essential sparse linear algebra functionality (eg., arithmetic operations, submatrix manipulation) as well as high-level functions for sparse eigendecompositions and linear equation solvers. The latter are achieved by providing easy-to-use abstractions of the low-level ARPACK and SuperLU libraries. The source code is open and provided under the permissive Apache 2.0 license, allowing unencumbered use in commercial products

Heat Kernel Expansion and Extremal Kerr-Newmann Black Hole Entropy in Einstein-Maxwell Theory

We compute the second Seely-DeWitt coefficient of the kinetic operator of the metric and gauge fields in Einstein-Maxwell theory in an arbitrary background field configuration. We then use this result to compute the logarithmic correction to the entropy of an extremal Kerr-Newmann black hole.Comment: 12 page

Logarithmic Corrections to Schwarzschild and Other Non-extremal Black Hole Entropy in Different Dimensions

Euclidean gravity method has been successful in computing logarithmic corrections to extremal black hole entropy in terms of low energy data, and gives results in perfect agreement with the microscopic results in string theory. Motivated by this success we apply Euclidean gravity to compute logarithmic corrections to the entropy of various non-extremal black holes in different dimensions, taking special care of integration over the zero modes and keeping track of the ensemble in which the computation is done. These results provide strong constraint on any ultraviolet completion of the theory if the latter is able to give an independent computation of the entropy of non-extremal black holes from microscopic description. For Schwarzschild black holes in four space-time dimensions the macroscopic result seems to disagree with the existing result in loop quantum gravity.Comment: LaTeX, 40 pages; corrected small typos and added reference

Effects of APOE4 allelic dosage on lipidomic signatures in the entorhinal cortex of aged mice

Apolipoprotein E ε4 (APOE4) is the primary genetic risk factor for the late-onset form of Alzheimer's disease (AD). Although the reason for this association is not completely understood, researchers have uncovered numerous effects of APOE4 expression on AD-relevant brain processes, including amyloid beta (Aβ) accumulation, lipid metabolism, endosomal-lysosomal trafficking, and bioenergetics. In this study, we aimed to determine the effect of APOE4 allelic dosage on regional brain lipid composition in aged mice, as well as in cultured neurons. We performed a targeted lipidomic analysis on an AD-vulnerable brain region (entorhinal cortex; EC) and an AD-resistant brain region (primary visual cortex; PVC) from 14-15 month-old APOE3/3, APOE3/4, and APOE4/4 targeted replacement mice, as well as on neurons cultured with conditioned media from APOE3/3 or APOE4/4 astrocytes. Our results reveal that the EC possesses increased susceptibility to APOE4-associated lipid alterations compared to the PVC. In the EC, APOE4 expression showed a dominant effect in decreasing diacylglycerol (DAG) levels, and a semi-dominant, additive effect in the upregulation of multiple ceramide, glycosylated sphingolipid, and bis(monoacylglycerol)phosphate (BMP) species, lipids known to accumulate as a result of endosomal-lysosomal dysfunction. Neurons treated with conditioned media from APOE4/4 vs. APOE3/3 astrocytes showed similar alterations of DAG and BMP species to those observed in the mouse EC. Our results suggest that APOE4 expression differentially modulates regional neuronal lipid signatures, which may underlie the increased susceptibility of EC-localized neurons to AD pathology

On Invariant Structures of Black Hole Charges

We study "minimal degree" complete bases of duality- and "horizontal"- invariant homogeneous polynomials in the flux representation of two-centered black hole solutions in two classes of D=4 Einstein supergravity models with symmetric vector multiplets' scalar manifolds. Both classes exhibit an SL(2,R) "horizontal" symmetry. The first class encompasses N=2 and N=4 matter-coupled theories, with semi-simple U-duality given by SL(2,R) x SO(m,n); the analysis is carried out in the so-called Calabi-Vesentini symplectic frame (exhibiting maximal manifest covariance) and until order six in the fluxes included. The second class, exhibiting a non-trivial "horizontal" stabilizer SO(2), includes N=2 minimally coupled and N=3 matter coupled theories, with U-duality given by the pseudo-unitary group U(r,s) (related to complex flux representations). Finally, we comment on the formulation of special Kaehler geometry in terms of "generalized" groups of type E7.Comment: 1+24 pages; 1 Table. v2 : Eqs. (1.2) and (1.3) added; Eq. (2.87) change

Logarithmic Corrections to Extremal Black Hole Entropy from Quantum Entropy Function

We evaluate the one loop determinant of matter multiplet fields of N=4 supergravity in the near horizon geometry of quarter BPS black holes, and use it to calculate logarithmic corrections to the entropy of these black holes using the quantum entropy function formalism. We show that even though individual fields give non-vanishing logarithmic contribution to the entropy, the net contribution from all the fields in the matter multiplet vanishes. Thus logarithmic corrections to the entropy of quarter BPS black holes, if present, must be independent of the number of matter multiplet fields in the theory. This is consistent with the microscopic results. During our analysis we also determine the complete spectrum of small fluctuations of matter multiplet fields in the near horizon geometry.Comment: LaTeX file, 52 pages; v2: minor corrections, references adde

Adherence to treatment in children and adolescents with cystic fibrosis:a cross-sectional, multi-method study investigating the influence of beliefs about treatment and parental depressive symptoms

Background: Adherence to treatment is often reported to be low in children with cystic fibrosis. Adherence in cystic fibrosis is an important research area and more research is needed to better understand family barriers to adherence in order for clinicians to provide appropriate intervention. The aim of this study was to evaluate adherence to enzyme supplements, vitamins and chest physiotherapy in children with cystic fibrosis and to determine if any modifiable risk factors are associated with adherence. Methods: A sample of 100 children (≤18 years) with cystic fibrosis (44 male; median [range] 10.1 [0.2-18.6] years) and their parents were recruited to the study from the Northern Ireland Paediatric Cystic Fibrosis Centre. Adherence to enzyme supplements, vitamins and chest physiotherapy was assessed using a multi-method approach including; Medication Adherence Report Scale, pharmacy prescription refill data and general practitioner prescription issue data. Beliefs about treatments were assessed using refined versions of the Beliefs about Medicines Questionnaire-specific. Parental depressive symptoms were assessed using the Center for Epidemiologic Studies Depression Scale. Results: Using the multi-method approach 72% of children were classified as low-adherers to enzyme supplements, 59% low-adherers to vitamins and 49% low-adherers to chest physiotherapy. Variations in adherence were observed between measurement methods, treatments and respondents. Parental necessity beliefs and child age were significant independent predictors of child adherence to enzyme supplements and chest physiotherapy, but parental depressive symptoms were not found to be predictive of adherence. Conclusions: Child age and parental beliefs about treatments should be taken into account by clinicians when addressing adherence at routine clinic appointments. Low adherence is more likely to occur in older children, whereas, better adherence to cystic fibrosis therapies is more likely in children whose parents strongly believe the treatments are necessary. The necessity of treatments should be reinforced regularly to both parents and children

Stochastic Gravity: Theory and Applications

Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel.In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime: we compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations. Second, we discuss structure formation from the stochastic gravity viewpoint. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a quasi-static black hole.Comment: 75 pages, no figures, submitted to Living Reviews in Relativit

Stochastic Gravity: Theory and Applications

Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel. In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime, compute the two-point correlation functions of these perturbations and prove that Minkowski spacetime is a stable solution of semiclassical gravity. Second, we discuss structure formation from the stochastic gravity viewpoint. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a black hole and describe the metric fluctuations near the event horizon of an evaporating black holeComment: 100 pages, no figures; an update of the 2003 review in Living Reviews in Relativity gr-qc/0307032 ; it includes new sections on the Validity of Semiclassical Gravity, the Stability of Minkowski Spacetime, and the Metric Fluctuations of an Evaporating Black Hol