Ground states and formal duality relations in the Gaussian core model

We study dimensional trends in ground states for soft-matter systems. Specifically, using a high-dimensional version of Parrinello-Rahman dynamics, we investigate the behavior of the Gaussian core model in up to eight dimensions. The results include unexpected geometric structures, with surprising anisotropy as well as formal duality relations. These duality relations suggest that the Gaussian core model possesses unexplored symmetries, and they have implications for a broad range of soft-core potentials.Comment: 7 pages, 1 figure, appeared in Physical Review E (http://pre.aps.org

Bias Analysis in Entropy Estimation

We consider the problem of finite sample corrections for entropy estimation. New estimates of the Shannon entropy are proposed and their systematic error (the bias) is computed analytically. We find that our results cover correction formulas of current entropy estimates recently discussed in literature. The trade-off between bias reduction and the increase of the corresponding statistical error is analyzed.Comment: 5 pages, 3 figure

Neuroactive compounds in the brain of the honeybee during imaginal life.

1. In the brains of worker honeybees (Apis mellifera carnica) corresponding to different stages in the life span, we measured the content of GABA, glutamate, acetylcholine, eholine, norepinephrine, dopamine and serotonin. 2. The highest concentrations were found for GABA, glutamate and acetylcholine. 3. Biogenic amines occur in considerably lower concentrations in comparison to the above mentioned transmitters. 4. Age-correlated changes were found for different neuroactive substances. 5. GABA and glutamate show a well marked rise and fall of their concentrations with a maximum at day 10. 6. The results are discussed in comparison to other species and with respect to age polyethism of worker honeybees

Equivariant toric geometry and Euler-Maclaurin formulae -- an overview

We survey recent developments in the study of torus equivariant motivic Chern and Hirzebruch characteristic classes of projective toric varieties, with applications to calculating equivariant Hirzebruch genera of torus-invariant Cartier divisors in terms of torus characters, as well as to general Euler-Maclaurin type formulae for full-dimensional simple lattice polytopes. We present recent results by the authors, emphasizing the main ideas and some key examples. This includes global formulae for equivariant Hirzebruch classes in the simplicial context proved by localization at the torus fixed points, a weighted versions of a classical formula of Brion, as well as of the Molien formula of Brion-Vergne. Our Euler-Maclaurin type formulae provide generalizations to arbitrary coherent sheaf coefficients of the Euler-Maclaurin formulae of Cappell-Shaneson, Brion-Vergne, Guillemin, etc., via the equivariant Hirzebruch-Riemann-Roch formalism. Our approach, based on motivic characteristic classes, allows us, e.g., to obtain such Euler-Maclaurin formulae also for (the interior of) a face. We obtain such results also in the weighted context, and for Minkovski summands of the given full-dimensional lattice polytope.Comment: survey paper overviewing recent results by the authors from arXiv:2303.16785, emphasizing the main ideas and some key example

Equivariant toric geometry and Euler-Maclaurin formulae

We consider equivariant versions of the motivic Chern and Hirzebruch characteristic classes of a quasi-projective toric variety, and extend many known results from non-equivariant to the equivariant setting. The corresponding generalized equivariant Hirzebruch genus of a torus-invariant Cartier divisor is also calculated. Further global formulae for equivariant Hirzebruch classes are obtained in the simplicial context by using the Cox construction and the equivariant Lefschetz-Riemann-Roch theorem. Alternative proofs of all these results are given via localization at the torus fixed points in equivariant $K$- and homology theories. In localized equivariant $K$-theory, we prove a weighted version of a classical formula of Brion for a full-dimensional lattice polytope. We also generalize to the context of motivic Chern classes the Molien formula of Brion-Vergne. Similarly, we compute the localized Hirzebruch class, extending results of Brylinski-Zhang for the localized Todd class. We also elaborate on the relation between the equivariant toric geometry via the equivariant Hirzebruch-Riemann-Roch and Euler-Maclaurin type formulae for full-dimensional simple lattice polytopes. Our results provide generalizations to arbitrary coherent sheaf coefficients, and algebraic geometric proofs of (weighted versions of) the Euler-Maclaurin formulae of Cappell-Shaneson, Brion-Vergne, Guillemin, etc., via the equivariant Hirzebruch-Riemann-Roch formalism. Our approach, based on motivic characteristic classes, allows us to obtain such Euler-Maclaurin formulae also for (the interior of) a face, or for the polytope with several facets removed. We also prove such results in the weighted context, and for Minkovski summands of the given full-dimensional lattice polytope. Some of these results are extended to local Euler-Maclaurin formulas for the tangent cones at the vertices of the given lattice polytope.Comment: 93 pages, comments are very welcom

Measuring out-of-field dose to the hippocampus in common radiotherapy indications

Background The high susceptibility of the hippocampus region to radiation injury is likely the causal factor of neurocognitive dysfunctions after exposure to ionizing radiation. Repetitive exposures with even low doses have been shown to impact adult neurogenesis and induce neuroinfammation. We address the question whether the out-offeld doses during radiotherapy of common tumour entities may pose a risk for the neuronal stem cell compartment in the hippocampus. Methods The dose to the hippocampus was determined for a single fraction according to diferent treatment plans for the selected tumor entities: Point dose measurements were performed in an anthropomorphic Alderson phantom and the out-of-feld dose to the hippocampus was measured using thermoluminescence dosimeters. Results For carcinomas in the head and neck region the dose exposure to the hippocampal region for a single fraction ranged from to 37.4 to 154.8 mGy. The hippocampal dose was clearly diferent for naso-, oro- and hypopharynx, with maximal values for nasopharynx carcinoma. In contrast, hippocampal dose levels for breast and prostate cancer ranged between 2.7 and 4.1 mGy, and therefore signifcantly exceeded the background irradiation level. Conclusion The mean dose to hippocampus for treatment of carcinomas in the head and neck region is high enough to reduce neurocognitive functions. In addition, care must be taken regarding the out of feld doses. The mean dose is mainly related to scattering efects, as is confrmed by the data from breast or prostate treatments, with a very diferent geometrical set-up but similar dosimetric results

Excision for simplicial sheaves on the Stein site and Gromov's Oka principle

A complex manifold $X$ satisfies the Oka-Grauert property if the inclusion \Cal O(S,X) \hookrightarrow \Cal C(S,X) is a weak equivalence for every Stein manifold $S$, where the spaces of holomorphic and continuous maps from $S$ to $X$ are given the compact-open topology. Gromov's Oka principle states that if $X$ has a spray, then it has the Oka-Grauert property. The purpose of this paper is to investigate the Oka-Grauert property using homotopical algebra. We embed the category of complex manifolds into the model category of simplicial sheaves on the site of Stein manifolds. Our main result is that the Oka-Grauert property is equivalent to $X$ representing a finite homotopy sheaf on the Stein site. This expresses the Oka-Grauert property in purely holomorphic terms, without reference to continuous maps.Comment: Version 3 contains a few very minor improvement