Generalized Bloch analysis and propagators on Riemannian manifolds with a discrete symmetry

We consider an invariant quantum Hamiltonian $H=-\Delta_{LB}+V$ in the $L^{2}$ space based on a Riemannian manifold $\tilde{M}$ with a countable discrete symmetry group $\Gamma$. Typically, $\tilde{M}$ is the universal covering space of a multiply connected Riemannian manifold $M$ and $\Gamma$ is the fundamental group of $M$. On the one hand, following the basic step of the Bloch analysis, one decomposes the $L^{2}$ space over $\tilde{M}$ into a direct integral of Hilbert spaces formed by equivariant functions on $\tilde{M}$. The Hamiltonian $H$ decomposes correspondingly, with each component $H_{\Lambda}$ being defined by a quasi-periodic boundary condition. The quasi-periodic boundary conditions are in turn determined by irreducible unitary representations $\Lambda$ of $\Gamma$. On the other hand, fixing a quasi-periodic boundary condition (i.e., a unitary representation $\Lambda$ of $\Gamma$) one can express the corresponding propagator in terms of the propagator associated to the Hamiltonian $H$. We discuss these procedures in detail and show that in a sense they are mutually inverse

On twisted Fourier analysis and convergence of Fourier series on discrete groups

We study norm convergence and summability of Fourier series in the setting of reduced twisted group $C^*$-algebras of discrete groups. For amenable groups, F{\o}lner nets give the key to Fej\'er summation. We show that Abel-Poisson summation holds for a large class of groups, including e.g. all Coxeter groups and all Gromov hyperbolic groups. As a tool in our presentation, we introduce notions of polynomial and subexponential H-growth for countable groups w.r.t. proper scale functions, usually chosen as length functions. These coincide with the classical notions of growth in the case of amenable groups.Comment: 35 pages; abridged, revised and update

Differential diagnosis of neurodegenerative dementias with the explainable MRI based machine learning algorithm MUQUBIA

Biomarker-based differential diagnosis of the most common forms of dementia is becoming increasingly important. Machine learning (ML) may be able to address this challenge. The aim of this study was to develop and interpret a ML algorithm capable of differentiating Alzheimer’s dementia, frontotemporal dementia, dementia with Lewy bodies and cognitively normal control subjects based on sociodemographic, clinical, and magnetic resonance imaging (MRI) variables. 506 subjects from 5 databases were included. MRI images were processed with FreeSurfer, LPA, and TRACULA to obtain brain volumes and thicknesses, white matter lesions and diffusion metrics. MRI metrics were used in conjunction with clinical and demographic data to perform differential diagnosis based on a Support Vector Machine model called MUQUBIA (Multimodal Quantification of Brain whIte matter biomArkers). Age, gender, Clinical Dementia Rating (CDR) Dementia Staging Instrument, and 19 imaging features formed the best set of discriminative features. The predictive model performed with an overall Area Under the Curve of 98%, high overall precision (88%), recall (88%), and F1 scores (88%) in the test group, and good Label Ranking Average Precision score (0.95) in a subset of neuropathologically assessed patients. The results of MUQUBIA were explained by the SHapley Additive exPlanations (SHAP) method. The MUQUBIA algorithm successfully classified various dementias with good performance using cost-effective clinical and MRI information, and with independent validation, has the potential to assist physicians in their clinical diagnosis

Hair Trace Element and Electrolyte Content in Women with Natural and In Vitro Fertilization-Induced Pregnancy

The objective of the present study was to perform comparative analysis of hair trace element content in women with natural and in vitro fertilization (IVF)-induced pregnancy. Hair trace element content in 33 women with IVF-induced pregnancy and 99 age- and body mass index-matched control pregnant women (natural pregnancy) was assessed using inductively coupled plasma mass spectrometry. The results demonstrated that IVF-pregnant women are characterized by significantly lower hair levels of Cu, Fe, Si, Zn, Ca, Mg, and Ba at p < 0.05 or lower. Comparison of the individual levels with the national reference values demonstrated higher incidence of Fe and Cu deficiency in IVF-pregnant women in comparison to that of the controls. IVF pregnancy was also associated with higher hair As levels (p < 0.05). Multiple regression analysis revealed a significant interrelation between IVF pregnancy and hair Cu, Fe, Si, and As content. Hair Cu levels were also influenced by vitamin/mineral supplementation and the number of pregnancies, whereas hair Zn content was dependent on prepregnancy anthropometric parameters. In turn, planning of pregnancy had a significant impact on Mg levels in scalp hair. Generally, the obtained data demonstrate an elevated risk of copper, iron, zinc, calcium, and magnesium deficiency and arsenic overload in women with IVF-induced pregnancy. The obtained data indicate the necessity of regular monitoring of micronutrient status in IVF-pregnant women in order to prevent potential deleterious effects of altered mineral homeostasis

The "impact factor" in the evaluation of research

The "impact factor of journals", in brief IF, has become an important tool for the evaluation of research activities in certain disciplines, while it is gaining additional influence in others. Its widespread use is increasingly determining the fate of individuals, and academic departments. It is also contributing to restructuring of academic libraries and to reshaping the map of academic periodicals. There is no doubt that this index appears useful, and in many respects, attractive. It relieves faculty and administrators of the burden of reading and comparing papers and it seems to provide an ";objective"; criterion for judging scientific research. In this paper we present a different view and we argue that costs, in terms of potential damage to the scientific system, which are caused by an uncritical application of the IF, exceed by far its supposed merits. One purpose of this paper is to encourage scientists working in disciplines that have not yet been invaded by IF, (such as historians, jurists, social scientists and students of the humanities) not to be intimidated by the fact that other sciences are using IF to as a measure of research quality, and to carefully consider the implications of adopting such an index. This is not a study based on sophisticated statistical analysis. For such analysis we refer to the paper by Per O Seglen (a). Our criticism is based on ";political"; considerations, for which we deem observing reality with the naked eye to be sufficient