Optimal eigenvalues estimate for the Dirac operator on domains with boundary

We give a lower bound for the eigenvalues of the Dirac operator on a compact domain of a Riemannian spin manifold under the \MIT bag boundary condition. The limiting case is characterized by the existence of an imaginary Killing spinor.Comment: 10 page

Rigidity of compact Riemannian spin Manifolds with Boundary

In this article, we prove new rigidity results for compact Riemannian spin manifolds with boundary whose scalar curvature is bounded from below by a non-positive constant. In particular, we obtain generalizations of a result of Hang-Wang \cite{hangwang1} based on a conjecture of Schroeder and Strake \cite{schroeder}.Comment: English version of "G\'eom\'etrie spinorielle extrins\`eque et rigidit\'es", Corollary 6 in Section 3 added, to appear in Letters Math. Phy

Tautness and applications of the Alexander-Spanier cohomology of K

The aim of the present work is centered around the tautness property for the two K-types of Alexander-Spanier cohomology given by the authors. A version of the continuity property is proved, and some applications are given

Conservation of epigenetic regulation by the MLL3/4 tumour suppressor in planarian pluripotent stem cells

Currently, little is known about the evolution of epigenetic regulation in animal stem cells. Here we demonstrate, using the planarian stem cell system to investigate the role of the COMPASS family of MLL3/4 histone methyltransferases that their function as tumor suppressors in mammalian stem cells is conserved over a long evolutionary distance. To investigate the potential conservation of a genome-wide epigenetic regulatory program in animal stem cells, we assess the effects of Mll3/4 loss of function by performing RNA-seq and ChIP-seq on the G2/M planarian stem cell population, part of which contributes to the formation of outgrowths. We find many oncogenes and tumor suppressors among the affected genes that are likely candidates for mediating MLL3/4 tumor suppression function. Our work demonstrates conservation of an important epigenetic regulatory program in animals and highlights the utility of the planarian model system for studying epigenetic regulation

Nonexistence of Generalized Apparent Horizons in Minkowski Space

We establish a Positive Mass Theorem for initial data sets of the Einstein equations having generalized trapped surface boundary. In particular we answer a question posed by R. Wald concerning the existence of generalized apparent horizons in Minkowski space

A Reilly formula and eigenvalue estimates for differential forms

We derive a Reilly-type formula for differential p-forms on a compact manifold with boundary and apply it to give a sharp lower bound of the spectrum of the Hodge Laplacian acting on differential forms of an embedded hypersurface of a Riemannian manifold. The equality case of our inequality gives rise to a number of rigidity results, when the geometry of the boundary has special properties and the domain is non-negatively curved. Finally we also obtain, as a by-product of our calculations, an upper bound of the first eigenvalue of the Hodge Laplacian when the ambient manifold supports non-trivial parallel forms.Comment: 22 page

Regression Analysis of Rectal Cancer and Possible Application of Artificial Intelligence (AI) Utilization in Radiotherapy

Artificial Intelligence (AI) has been widely employed in the medical field in recent years in such areas as image segmentation, medical image registration, and computer-aided detection. This study explores one application of using AI in adaptive radiation therapy treatment planning by predicting the tumor volume reduction rate (TVRR). Cone beam computed tomography (CBCT) scans of twenty rectal cancer patients were collected to observe the change in tumor volume over the course of a standard five-week radiotherapy treatment. In addition to treatment volume, patient data including patient age, gender, weight, number of treatment fractions, and dose per fraction were also collected. Application of a stepwise regression model showed that age, dose per fraction and weight were the best predictors for tumor volume reduction rate

Strukturna i elektronska svojstva bbc selena pod visokim tlakom

Full-potential linearized augmented plane-wave method (FP-LAPW) within the density functional theory is applied to study the structural and electronic properties of selenium in the bcc phase at high pressures. We used local density approximation with and without generalized gradient correction based on exchange-correlation energy optimization. We have determined the full set of first-order elastic constants, which have not been established earlier experimentally or theoretically. The elastic moduli show linear dependence on pressure. The calculated energy allowed us to investigate several structural properties such as lattice parameter, bulk modulus and its pressure derivative. Our calculated lattice parameter is found to be in reasonable agreement with experimental result. The electronic band structure and the density of states at various pressures are also calculated to show that there is a possibility for these compounds to become metallic at high pressures. Further, we have calculated the electronic specific heat coefficient, which decreases with the increase of pressure.Primjenom metode lineariziranih proširenih ravnih valova s potpunim potencijalom, u okviru teorije funkcionala gustoće, proučavali smo strukturna i elektronska svojstva selena u bcc fazi na visokim tlakovima. Primijenili smo približenje lokalne gustoće sa i bez poopćene gradijentne popravke primjenom optimizacije energije korelacije i izmjene. Odredili smo potpun skup elestičnih konstanti prvog reda koje ranije nisu bile određene ni eksperimentalno ni teorijski. Moduli eleastičnosti pokazuju linearnu ovisnost o tlaku. Na osnovi izračunatih energija mogli smo istražiti više strukturnih svojstava, kao što su parametar rešetke, volumni modul stlačivosti i njegova derivacija po tlaku. Naš izračunat parametar rešetke je u dobrom slaganju s eksperimentalnim rezultatom. Također smo izračunali strukturu elekronskih vrpci i gustoće stanja da bismo ukazali na mogućnost da na visokim tlakovima selen u fazi bcc može postati metal. Nadalje, izračunali smo koeficijent elektronske specifične topline koji se smanjuje s porastom tlaka