Exact Results on Potts Model Partition Functions in a Generalized External Field and Weighted-Set Graph Colorings

We present exact results on the partition function of the $q$-state Potts model on various families of graphs $G$ in a generalized external magnetic field that favors or disfavors spin values in a subset $I_s = \{1,...,s\}$ of the total set of possible spin values, $Z(G,q,s,v,w)$, where $v$ and $w$ are temperature- and field-dependent Boltzmann variables. We remark on differences in thermodynamic behavior between our model with a generalized external magnetic field and the Potts model with a conventional magnetic field that favors or disfavors a single spin value. Exact results are also given for the interesting special case of the zero-temperature Potts antiferromagnet, corresponding to a set-weighted chromatic polynomial $Ph(G,q,s,w)$ that counts the number of colorings of the vertices of $G$ subject to the condition that colors of adjacent vertices are different, with a weighting $w$ that favors or disfavors colors in the interval $I_s$. We derive powerful new upper and lower bounds on $Z(G,q,s,v,w)$ for the ferromagnetic case in terms of zero-field Potts partition functions with certain transformed arguments. We also prove general inequalities for $Z(G,q,s,v,w)$ on different families of tree graphs. As part of our analysis, we elucidate how the field-dependent Potts partition function and weighted-set chromatic polynomial distinguish, respectively, between Tutte-equivalent and chromatically equivalent pairs of graphs.Comment: 39 pages, 1 figur

Perspective of monochromatic gamma-ray line detection with the High Energy cosmic-Radiation Detection (HERD) facility onboard China's Space Station

HERD is the High Energy cosmic-Radiation Detection instrument proposed to operate onboard China's space station in the 2020s. It is designed to detect energetic cosmic ray nuclei, leptons and photons with a high energy resolution ($\sim1\%$ for electrons and photons and $20\%$ for nuclei) and a large geometry factor ($>3\,{ m^2\,sr}$ for electrons and diffuse photons and $>2\,{ m^2\,sr}$ for nuclei). In this work we discuss the capability of HERD to detect monochromatic $\gamma$-ray lines, based on simulations of the detector performance. It is shown that HERD will be one of the most sensitive instruments for monochromatic $\gamma$-ray searches at energies between $\sim10$ to a few hundred GeV. Above hundreds of GeV, Cherenkov telescopes will be more sensitive due to their large effective area. As a specific example, we show that a good portion of the parameter space of a supersymmetric dark matter model can be probed with HERD.Comment: 9 pages, 7 figures, matches version published in Astropart.Phy

Quantum Dynamical Rˇ\check{R}- Matrix with Spectral Parameter from Fusion

A quantum dynamical $\check{R}$-matrix with spectral parameter is constructed by fusion procedure. This spin-1 $\check{R}$-matrix is connected with Lie algebra $so(3)$ and does not satisfy the condition of translation invariance.Comment: 6 pages, LaTeX, no figure

Association between right ventricular strain and outcomes in patients with dilated cardiomyopathy

Objective To explore the association between three-dimensional (3D) cardiac magnetic resonance (CMR) feature tracking (FT) right ventricular peak global longitudinal strain (RVpGLS) and major adverse cardiovascular events (MACEs) in patients with stage C or D heart failure (HF) with non-ischaemic dilated cardiomyopathy (NIDCM) but without atrial fibrillation (AF). Methods Patients with dilated cardiomyopathy were enrolled in this prospective cohort study. Comprehensive clinical and biochemical analysis and CMR imaging were performed. All patients were followed up for MACEs. Results A total of 192 patients (age 53±14 years) were eligible for this study. A combination of cardiovascular death and cardiac transplantation occurred in 18 subjects during the median follow-up of 567 (311, 920) days. Brain natriuretic peptide, creatinine, left ventricular (LV) end-diastolic volume, LV end-systolic volume, right ventricular (RV) end-diastolic volume and RVpGLS from CMR were associated with the outcomes. The multivariate Cox regression model adjusting for traditional risk factors and CMR variables detected a significant association between RVpGLS and MACEs in patients with stage C or D HF with NIDCM without AF. Kaplan-Meier analysis based on RVpGLS cut-off value revealed that patients with RVpGLS <−8.5% showed more favourable clinical outcomes than those with RVpGLS ≥−8.5% (p=0.0037). Subanalysis found that this association remained unchanged. Conclusions RVpGLS-derived from 3D CMR FT is associated with a significant prognostic impact in patients with NIDCM with stage C or D HF and without AF

Regularity of higher codimension area minimizing integral currents

This lecture notes are an expanded version of the course given at the ERC-School on Geometric Measure Theory and Real Analysis, held in Pisa, September 30th - October 30th 2013. The lectures aim to explain the main steps of a new proof of the partial regularity of area minimizing integer rectifiable currents in higher codimension, due originally to F. Almgren, which is contained in a series of papers in collaboration with C. De Lellis (University of Zurich).Comment: This text will appear in "Geometric Measure Theory and Real Analysis", pp. 131--192, Proceedings of the ERC school in Pisa (2013), L. Ambrosio Ed., Edizioni SNS (CRM Series

Degradation of the Separase-cleaved Rec8, a Meiotic Cohesin Subunit, by the N-end Rule Pathway

The Ate1 arginyltransferase (R-transferase) is a component of the N-end rule pathway, which recognizes proteins containing N-terminal degradation signals called N-degrons, polyubiquitylates these proteins, and thereby causes their degradation by the proteasome. Ate1 arginylates N-terminal Asp, Glu, or (oxidized) Cys. The resulting N-terminal Arg is recognized by ubiquitin ligases of the N-end rule pathway. In the yeast Saccharomyces cerevisiae, the separase-mediated cleavage of the Scc1/Rad21/Mcd1 cohesin subunit generates a C-terminal fragment that bears N-terminal Arg and is destroyed by the N-end rule pathway without a requirement for arginylation. In contrast, the separase-mediated cleavage of Rec8, the mammalian meiotic cohesin subunit, yields a fragment bearing N-terminal Glu, a substrate of the Ate1 R-transferase. Here we constructed and used a germ cell-confined Ate1−/− mouse strain to analyze the separase-generated C-terminal fragment of Rec8. We show that this fragment is a short-lived N-end rule substrate, that its degradation requires N-terminal arginylation, and that male Ate1−/− mice are nearly infertile, due to massive apoptotic death of Ate1−/− spermatocytes during the metaphase of meiosis I. These effects of Ate1 ablation are inferred to be caused, at least in part, by the failure to destroy the C-terminal fragment of Rec8 in the absence of N-terminal arginylation

Hyperactive transforming growth factor-β1 signaling potentiates skeletal defects in a neurofibromatosis type 1 mouse model

Dysregulated transforming growth factor beta (TGF-β) signaling is associated with a spectrum of osseous defects as seen in Loeys-Dietz syndrome, Marfan syndrome, and Camurati-Engelmann disease. Intriguingly, neurofibromatosis type 1 (NF1) patients exhibit many of these characteristic skeletal features, including kyphoscoliosis, osteoporosis, tibial dysplasia, and pseudarthrosis; however, the molecular mechanisms mediating these phenotypes remain unclear. Here, we provide genetic and pharmacologic evidence that hyperactive TGF-β1 signaling pivotally underpins osseous defects in Nf1(flox/-) ;Col2.3Cre mice, a model which closely recapitulates the skeletal abnormalities found in the human disease. Compared to controls, we show that serum TGF-β1 levels are fivefold to sixfold increased both in Nf1(flox/-) ;Col2.3Cre mice and in a cohort of NF1 patients. Nf1-deficient osteoblasts, the principal source of TGF-β1 in bone, overexpress TGF-β1 in a gene dosage-dependent fashion. Moreover, Nf1-deficient osteoblasts and osteoclasts are hyperresponsive to TGF-β1 stimulation, potentiating osteoclast bone resorptive activity while inhibiting osteoblast differentiation. These cellular phenotypes are further accompanied by p21-Ras-dependent hyperactivation of the canonical TGF-β1-Smad pathway. Reexpression of the human, full-length neurofibromin guanosine triphosphatase (GTPase)-activating protein (GAP)-related domain (NF1 GRD) in primary Nf1-deficient osteoblast progenitors, attenuated TGF-β1 expression levels and reduced Smad phosphorylation in response to TGF-β1 stimulation. As an in vivo proof of principle, we demonstrate that administration of the TGF-β receptor 1 (TβRI) kinase inhibitor, SD-208, can rescue bone mass deficits and prevent tibial fracture nonunion in Nf1(flox/-) ;Col2.3Cre mice. In sum, these data demonstrate a pivotal role for hyperactive TGF-β1 signaling in the pathogenesis of NF1-associated osteoporosis and pseudarthrosis, thus implicating the TGF-β signaling pathway as a potential therapeutic target in the treatment of NF1 osseous defects that are refractory to current therapie

The DArk Matter Particle Explorer mission

The DArk Matter Particle Explorer (DAMPE), one of the four scientific space science missions within the framework of the Strategic Pioneer Program on Space Science of the Chinese Academy of Sciences, is a general purpose high energy cosmic-ray and gamma-ray observatory, which was successfully launched on December 17th, 2015 from the Jiuquan Satellite Launch Center. The DAMPE scientific objectives include the study of galactic cosmic rays up to $\sim 10$ TeV and hundreds of TeV for electrons/gammas and nuclei respectively, and the search for dark matter signatures in their spectra. In this paper we illustrate the layout of the DAMPE instrument, and discuss the results of beam tests and calibrations performed on ground. Finally we present the expected performance in space and give an overview of the mission key scientific goals.Comment: 45 pages, including 29 figures and 6 tables. Published in Astropart. Phy