Lines pinning lines

A line g is a transversal to a family F of convex polytopes in 3-dimensional space if it intersects every member of F. If, in addition, g is an isolated point of the space of line transversals to F, we say that F is a pinning of g. We show that any minimal pinning of a line by convex polytopes such that no face of a polytope is coplanar with the line has size at most eight. If, in addition, the polytopes are disjoint, then it has size at most six. We completely characterize configurations of disjoint polytopes that form minimal pinnings of a line.Comment: 27 pages, 10 figure

The consequences of SU(3) colorsingletness, Polyakov Loop and Z(3) symmetry on a quark-gluon gas

Based on quantum statistical mechanics we show that the $SU(3)$ color singlet ensemble of a quark-gluon gas exhibits a $Z(3)$ symmetry through the normaized character in fundamental representation and also becomes equivalent, within a stationary point approximation, to the ensemble given by Polyakov Loop. Also Polyakov Loop gauge potential is obtained by considering spatial gluons along with the invariant Haar measure at each space point. The probability of the normalized character in $SU(3)$ vis-a-vis Polyakov Loop is found to be maximum at a particular value exhibiting a strong color correlation. This clearly indicates a transition from a color correlated to uncorrelated phase or vise-versa. When quarks are included to the gauge fields, a metastable state appears in the temperature range $145\le T({\rm{MeV}}) \le 170$ due to the explicit $Z(3)$ symmetry breaking in the quark-gluon system. Beyond $T\ge 170$ MeV the metastable state disappears and stable domains appear. At low temperature a dynamical recombination of ionized $Z(3)$ color charges to a color singlet $Z(3)$ confined phase is evident along with a confining background that originates due to circulation of two virtual spatial gluons but with conjugate $Z(3)$ phases in a closed loop. We also discuss other possible consequences of the center domains in the color deconfined phase at high temperature.Comment: Version published in J. Phys.

Acute Sets of Exponentially Optimal Size

We present a simple construction of an acute set of size (Formula presented.) in (Formula presented.) for any dimension d. That is, we explicitly give (Formula presented.) points in the d-dimensional Euclidean space with the property that any three points form an acute triangle. It is known that the maximal number of such points is less than (Formula presented.). Our result significantly improves upon a recent construction, due to Dmitriy Zakharov, with size of order (Formula presented.) where (Formula presented.) is the golden ratio. © 2018 Springer Science+Business Media, LLC, part of Springer Natur

Hadron Spectroscopy with Dynamical Chirally Improved Fermions

We simulate two dynamical, mass degenerate light quarks on 16^3x32 lattices with a spatial extent of 2.4 fm using the Chirally Improved Dirac operator. The simulation method, the implementation of the action and signals of equilibration are discussed in detail. Based on the eigenvalues of the Dirac operator we discuss some qualitative features of our approach. Results for ground state masses of pseudoscalar and vector mesons as well as for the nucleon and delta baryons are presented.Comment: 26 pages, 17 figures, 10 table

The Fermat-Torricelli problem in normed planes and spaces

We investigate the Fermat-Torricelli problem in d-dimensional real normed spaces or Minkowski spaces, mainly for d=2. Our approach is to study the Fermat-Torricelli locus in a geometric way. We present many new results, as well as give an exposition of known results that are scattered in various sources, with proofs for some of them. Together, these results can be considered to be a minitheory of the Fermat-Torricelli problem in Minkowski spaces and especially in Minkowski planes. This demonstrates that substantial results about locational problems valid for all norms can be found using a geometric approach

The strong thirteen spheres problem

The thirteen spheres problem is asking if 13 equal size nonoverlapping spheres in three dimensions can touch another sphere of the same size. This problem was the subject of the famous discussion between Isaac Newton and David Gregory in 1694. The problem was solved by Schutte and van der Waerden only in 1953. A natural extension of this problem is the strong thirteen spheres problem (or the Tammes problem for 13 points) which asks to find an arrangement and the maximum radius of 13 equal size nonoverlapping spheres touching the unit sphere. In the paper we give a solution of this long-standing open problem in geometry. Our computer-assisted proof is based on a enumeration of the so-called irreducible graphs.Comment: Modified lemma 2, 16 pages, 12 figures. Uploaded program packag

Multimodal imaging of pancreatic beta cells in vivo by targeting transmembrane protein 27 (TMEM27)

Aims/hypothesis: Non-invasive diagnostic tools specific for pancreatic beta cells will have a profound impact on our understanding of the pathophysiology of metabolic diseases such as diabetes. The objective of this study was to use molecular imaging probes specifically targeting beta cells on human samples and animal models using state-of-the-art imaging modalities (fluorescence and PET) with preclinical and clinical perspective. Methods: We generated a monoclonal antibody, 8/9-mAb, targeting transmembrane protein 27 (TMEM27; a surface N-glycoprotein that is highly expressed on beta cells), compared its expression in human and mouse pancreas, and demonstrated beta cell-specific binding in both. In vivo imaging was performed in mice with subcutaneous insulinomas overexpressing the human TMEM27 gene, or transgenic mice with beta cell-specific hTMEM27 expression under the control of rat insulin promoter (RIP-hTMEM27-tg), using fluorescence and radioactively labelled antibody, followed by tissue ex vivo analysis and fluorescence microscopy. Results: Fluorescently labelled 8/9-mAb showed beta cell-specific staining on human and mouse pancreatic sections. Real-time PCR on islet cDNA indicated about tenfold higher expression of hTMEM27 in RIP-hTMEM27-tg mice than in humans. In vivo fluorescence and PET imaging in nude mice with insulinoma xenografts expressing hTMEM27 showed high 8/9-mAb uptake in tumours after 72h. Antibody homing was also observed in beta cells of RIP-hTMEM27-tg mice by in vivo fluorescence imaging. Ex vivo analysis of intact pancreas and fluorescence microscopy in beta cells confirmed these findings. Conclusions/interpretation: hTMEM27 constitutes an attractive target for in vivo visualisation of pancreatic beta cells. Studies in mouse insulinoma models and mice expressing hTMEM27 demonstrate the feasibility of beta cell-targeted in vivo imaging, which is attractive for preclinical investigations and holds potential in clinical diagnostic

Decarbonizing conference travel: testing a multi-hub approach

As the global research enterprise grapples with the challenge of a low carbon future, a key challenge is the future of international conferences. An emerging initiative which combines elements of the traditional in-person and virtual conference is a multi-hub approach. Here we report on a real-world trial of a multi-hub approach, the World Climate Research Programme/Stratosphere-troposphere Processes And their Role in Climate (WCRP/SPARC) General Assembly held in Qingdao-Reading-Boulder during the last week of October 2022 with more than 400 participants. While there are other examples of conferences run in dual-hub or hybrid online and in-person formats, we are not aware of other large atmospheric science conferences held in this format. Based on travel surveys of participants, we estimate that the multi-hub approach reduced the carbon footprint from travel by between a factor of 2.3 and 4.1 times the footprint when hosting the conference in a single location. This resulted in a saving of at least 288 tonnes of carbon dioxide equivalent (tCO2eq) and perhaps as much as 683 tCO2eq, compared to having the conference in one location only. Feedback from participants, collected immediately after the conference, showed that the majority (85%) would again attend another conference in a similar format. There are many ways that the format of the SPARC General Assembly could have been improved, but this proof-of-concept provides an inspiration to other groups to give the multi-hub format a try

The sign problem across the QCD phase transition

The average phase factor of the QCD fermion determinant signals the strength of the QCD sign problem. We compute the average phase factor as a function of temperature and baryon chemical potential using a two-flavor NJL model. This allows us to study the strength of the sign problem at and above the chiral transition. It is discussed how the $U_A(1)$ anomaly affects the sign problem. Finally, we study the interplay between the sign problem and the endpoint of the chiral transition.Comment: 9 pages and 9 fig