Reflection groups in hyperbolic spaces and the denominator formula for Lorentzian Kac--Moody Lie algebras

This is a continuation of our "Lecture on Kac--Moody Lie algebras of the arithmetic type" \cite{25}. We consider hyperbolic (i.e. signature $(n,1)$) integral symmetric bilinear form $S:M\times M \to {\Bbb Z}$ (i.e. hyperbolic lattice), reflection group $W\subset W(S)$, fundamental polyhedron \Cal M of $W$ and an acceptable (corresponding to twisting coefficients) set P({\Cal M})\subset M of vectors orthogonal to faces of \Cal M (simple roots). One can construct the corresponding Lorentzian Kac--Moody Lie algebra {\goth g}={\goth g}^{\prime\prime}(A(S,W,P({\Cal M}))) which is graded by $M$. We show that \goth g has good behavior of imaginary roots, its denominator formula is defined in a natural domain and has good automorphic properties if and only if \goth g has so called {\it restricted arithmetic type}. We show that every finitely generated (i.e. P({\Cal M}) is finite) algebra {\goth g}^{\prime\prime}(A(S,W_1,P({\Cal M}_1))) may be embedded to {\goth g}^{\prime\prime}(A(S,W,P({\Cal M}))) of the restricted arithmetic type. Thus, Lorentzian Kac--Moody Lie algebras of the restricted arithmetic type is a natural class to study. Lorentzian Kac--Moody Lie algebras of the restricted arithmetic type have the best automorphic properties for the denominator function if they have {\it a lattice Weyl vector $\rho$}. Lorentzian Kac--Moody Lie algebras of the restricted arithmetic type with generalized lattice Weyl vector $\rho$ are called {\it elliptic}Comment: Some corrections in Sects. 2.1, 2.2 were done. They don't reflect on results and ideas. 31 pages, no figures. AMSTe

Comment on "Quantitative x-ray photoelectron spectroscopy: Quadrupole effects, shake up, Shirley background, and relative sensitivity factors from a database of true x-ray photoelectron spectra"

This Comment demonstrates that a comparison analysis by Seah and Gilmore between experimental data on the X-ray photoelectron spectroscopy intensities and theoretical data by Trzhaskovskaya et al. is misleading due to a number of serious errors made by Seah and Gilmore (Phys. Rev. B, 73, 174113).Comment: 7 pages, 3 figures, submitted to Phys. Rev.

The Geometry and Moduli of K3 Surfaces

These notes will give an introduction to the theory of K3 surfaces. We begin with some general results on K3 surfaces, including the construction of their moduli space and some of its properties. We then move on to focus on the theory of polarized K3 surfaces, studying their moduli, degenerations and the compactification problem. This theory is then further enhanced to a discussion of lattice polarized K3 surfaces, which provide a rich source of explicit examples, including a large class of lattice polarizations coming from elliptic fibrations. Finally, we conclude by discussing the ample and Kahler cones of K3 surfaces, and give some of their applications.Comment: 34 pages, 2 figures. (R. Laza, M. Schutt and N. Yui, eds.

Remarques sur le maximum de vraisemblance

Some paradoxes on the maximum likelihood principle are presented and commented. We consider the properties of the maximum likelihood estimators as a particular case of the M-estimators. We propose a unified theory which includes non-dominated models. Several examples are given

Statistical analysis of the generalized additive semiparametric survival model with random covariate

Generalizations of the additive hazards model are considered. Estimates of the regression parameters and baseline function are proposed, when covariates are random. The asymptotic properties of estimators are considered

Del Pezzo surfaces with 1/3(1,1) points

We classify del Pezzo surfaces with 1/3(1,1) points in 29 qG-deformation families grouped into six unprojection cascades (this overlaps with work of Fujita and Yasutake), we tabulate their biregular invariants, we give good model constructions for surfaces in all families as degeneracy loci in rep quotient varieties and we prove that precisely 26 families admit qG-degenerations to toric surfaces. This work is part of a program to study mirror symmetry for orbifold del Pezzo surfaces.Comment: 42 pages. v2: model construction added of last remaining surface, minor corrections, minor changes to presentation, references adde

Neurophysiophenomenology – predicting emotional arousal from brain arousal in a virtual reality roller coaster

Arousal is a core affect constituted of both bodily and subjective states that prepares an agent to respond to events of the natural environment. While the peripheral physiological components of arousal have been examined also under naturalistic conditions, its neural correlates were suggested mainly on the basis of simplifed experimental designs.   We used virtual reality (VR) to present a highly immersive and contextually rich scenario of roller coaster rides to evoke naturalistic states of emotional arousal. Simultaneously, we recorded EEG to validate the suggested neural correlates of arousal in alpha frequency oscillations (8-12Hz) over temporo-parietal cortical areas. To fnd the complex link between these alpha components and the participants’ continuous subjective reports of arousal, we employed a set of complementary analytical methods coming from machine learning and deep learning

Statistical analysis of the generalized additive semiparametric survival model with random covariate

Generalizations of the additive hazards model are considered. Estimates of the regression parameters and baseline function are proposed, when covariates are random. The asymptotic properties of estimators are considered

Integral constraints on the monodromy group of the hyperkahler resolution of a symmetric product of a K3 surface

Let M be a 2n-dimensional Kahler manifold deformation equivalent to the Hilbert scheme of length n subschemes of a K3 surface S. Let Mon be the group of automorphisms of the cohomology ring of M, which are induced by monodromy operators. The second integral cohomology of M is endowed with the Beauville-Bogomolov bilinear form. We prove that the restriction homomorphism from Mon to the isometry group O[H^2(M)] is injective, for infinitely many n, and its kernel has order at most 2, in the remaining cases. For all n, the image of Mon in O[H^2(M)] is the subgroup generated by reflections with respect to +2 and -2 classes. As a consequence, we get counter examples to a version of the weight 2 Torelli question, when n-1 is not a prime power.Comment: Version 3: Latex, 54 pages. Expository change

Predicting the effects of climate change on Schistosoma mansoni transmission in eastern Africa

Background: Survival and fitness attributes of free-living and sporocyst schistosome life-stages and their intermediate host snails are sensitive to water temperature. Climate change may alter the geographical distribution of schistosomiasis by affecting the suitability of freshwater bodies for hosting parasite and snail populations. Methods: We have developed an agent-based model of the temperature-sensitive stages of the Schistosoma mansoni and intermediate host snail lifecycles. The model was run using low, moderate and high warming climate projections over eastern Africa. For each climate projection, eight model scenarios were used to determine the sensitivity of predictions to different relationships between air and water temperature, and different snail mortality rates. Maps were produced showing predicted changes in risk as a result of increasing temperatures over the next 20 and 50 years. Results Baseline model output compared to prevalence data indicates suitable temperatures are necessary but not sufficient for both S. mansoni transmission and high infection prevalences. All else being equal, infection risk may increase by up to 20% over most of eastern Africa over the next 20 and 50 years. Increases may be higher in Rwanda, Burundi, south-west Kenya and eastern Zambia, and S. mansoni may become newly endemic in some areas. Results for 20-year projections are robust to changes in simulated intermediate host snail habitat conditions. There is greater uncertainty about the effects of different habitats on changes in risk in 50 years’ time. Conclusions: Temperatures are likely to become suitable for increased S. mansoni transmission over much of eastern Africa. This may reduce the impact of control and elimination programmes. S. mansoni may also spread to new areas outside existing control programmes. We call for increased surveillance in areas defined as potentially suitable for emergent transmission