A generalization of a result of Minakshisundaram and Pleijel

Minakshisundaram and Pleijel gave an asymptotic formula for the sum of squares of the pointwise values of the eigenfunctions of the Laplace-Beltrami operator on a compact Riemannian manifold, with eigenvalues less than a fixed number. Here, a generalization is given, where the pointwise values are replaced by the Fourier coefficients of a smooth measure supported on a compact submanifold.Comment: 13 page

Self-dual gravitational instantons and geometric flows of all Bianchi types

We investigate four-dimensional, self-dual gravitational instantons endowed with a product structure RxM_3, where M_3 is homogeneous of Bianchi type. We analyze the general conditions under which Euclidean-time evolution in the gravitational instanton can be identified with a geometric flow of a metric on M_3. This includes both unimodular and non-unimodular groups, and the corresponding geometric flow is a general Ricci plus Yang-Mills flow accompanied by a diffeomorphism.Comment: Latex, 12 pages; Final versio

A new ⁶⁸Ga-labeled somatostatin analog containing two iodo-amino acids for dual somatostatin receptor subtype 2 and 5 targeting.

Somatostatin receptor (SST) targeting, specifically of the subtype 2 (SST2), with radiolabeled somatostatin analogs, is established for imaging and treatment of neuroendocrine tumors. Owing to the concomitant and heterogeneous expression of several subtypes on the same tumor, analogs targeting more subtypes than SST2 potentially target a broader spectrum of tumors and/or increase the uptake of a given tumor. The analog ST8950 ((4-amino-3-iodo)-D-Phe-c[Cys-(3-iodo)-Tyr-D-Trp-Lys-Val-Cys]-Thr-NH <sub>2</sub> ), bearing 2 iodo-amino acids, exhibits sub-nanomolar affinity to SST2 and SST5. We report herein the development and preclinical evaluation of DOTA-ST8950 labeled with <sup>68</sup> Ga, for imaging SST2- and SST5-expressing tumors. Comparative in vitro and in vivo studies were performed with the de-iodinated DOTA-ST8951 ((4-amino)-D-Phe-c[Cys-Tyr-D-Trp-Lys-Val-Cys]-Thr-NH <sub>2</sub> ) and with the reference compounds DOTA-TATE (SST2 selective) and DOTA-NOC (for SST2 and SST5). Compared with <sup>nat</sup> Ga-DOTA-NOC, <sup>nat</sup> Ga-DOTA-ST8950 exhibited higher affinity to SST2 and SST5 (IC <sub>50</sub> (95%CI), nM = 0.32 (0.20-0.50) and 1.9 (1.1-3.1) vs 0.70 (0.50-0.96) and 3.4 (1.8-6.2), respectively), while <sup>nat</sup> Ga-DOTA-ST8951 lost affinity for both subtypes. <sup>nat</sup> Ga-DOTA-ST8950 had the same potency for inducing SST2-mediated cAMP accumulation as <sup>nat</sup> Ga-DOTA-TATE and slightly better than <sup>nat</sup> Ga-DOTA-NOC (EC <sub>50</sub> , nM = 0.46 (0.23-0.92) vs 0.47 (0.15-1.5) vs 0.59 (0.18-1.9), respectively). [ <sup>67</sup> Ga]Ga-DOTA-ST8950 had a similar internalization rate as [ <sup>67</sup> Ga]Ga-DOTA-NOC in SST2-expressing cells (12.4 ± 1.6% vs 16.6 ± 2.2%, at 4 h, p = 0.0586). In vivo, [ <sup>68</sup> Ga]Ga-DOTA-ST8950 showed high and specific accumulation in SST2- and SST5-expressing tumors, comparable with [ <sup>68</sup> Ga]Ga-DOTA-NOC (26 ± 8 vs 30 ± 8 %IA/g, p = 0.4630 for SST2 and 15 ± 6 vs 12 ± 5 %IA/g, p = 0.3282, for SST5, 1 h p.i.) and accumulation in the SST-positive tissues, the kidneys and the liver. PET/CT images of [ <sup>68</sup> Ga]Ga-DOTA-ST8950, performed in a dual HEK-SST2 and HEK-SST5 tumor xenografted model, clearly visualized both tumors and illustrated high tumor-to-background contrast. [ <sup>68</sup> Ga]Ga-DOTA-ST8950 reveals its potential for PET imaging SST2- and SST5-expressing tumors. It compares favorably with the clinically used [ <sup>68</sup> Ga]Ga-DOTA-NOC in terms of tumor uptake; however, its uptake in the liver remains a challenge for clinical translation. In addition, this study reveals the essential role of the iodo-substitutions in positions 1 and 3 of [ <sup>68</sup> Ga]Ga-DOTA-ST8950 for maintaining affinity to SST2 and SST5, as the de-iodinated [ <sup>68</sup> Ga]Ga-DOTA-ST8951 lost affinity for both receptor subtypes

Identification of New Drug Candidates Against \u3cem\u3eBorrelia burgdorferi\u3c/em\u3e Using High-Throughput Screening

Lyme disease is the most common zoonotic bacterial disease in North America. It is estimated that .300,000 cases per annum are reported in USA alone. A total of 10%–20% of patients who have been treated with antibiotic therapy report the recrudescence of symptoms, such as muscle and joint pain, psychosocial and cognitive difficulties, and generalized fatigue. This condition is referred to as posttreatment Lyme disease syndrome. While there is no evidence for the presence of viable infectious organisms in individuals with posttreatment Lyme disease syndrome, some researchers found surviving Borrelia burgdorferi population in rodents and primates even after antibiotic treatment. Although such observations need more ratification, there is unmet need for developing the therapeutic agents that focus on removing the persisting bacterial form of B. burgdorferi in rodent and nonhuman primates. For this purpose, high-throughput screening was done using BacTiter-Glo assay for four compound libraries to identify candidates that stop the growth of B. burgdorferi in vitro. The four chemical libraries containing 4,366 compounds (80% Food and Drug Administration [FDA] approved) that were screened are Library of Pharmacologically Active Compounds (LOPAC1280), the National Institutes of Health Clinical Collection, the Microsource Spectrum, and the Biomol FDA. We subsequently identified 150 unique compounds, which inhibited .90% of B. burgdorferi growth at a concentration of ,25 µM. These 150 unique compounds comprise many safe antibiotics, chemical compounds, and also small molecules from plant sources. Of the 150 unique compounds, 101 compounds are FDA approved. We selected the top 20 FDA-approved molecules based on safety and potency and studied their minimum inhibitory concentration and minimum bactericidal concentration. The promising safe FDA-approved candidates that show low minimum inhibitory concentration and minimum bactericidal concentration values can be chosen as lead molecules for further advanced studies

Torsion and the Gravity Dual of Parity Symmetry Breaking in AdS4/CFT3 Holography

We study four dimensional gravity with a negative cosmological constant deformed by the Nieh-Yan torsional topological invariant with a spacetime-dependent coefficient. We find an exact solution of the Euclidean system, which we call the torsion vortex, having two asymptotic AdS4 regimes supported by a pseudoscalar with a kink profile. We propose that the torsion vortex is the holographic dual of a three dimensional system that exhibits distinct parity breaking vacua. The torsion vortex represents a (holographic) transition between these distinct vacua. We expect that from the boundary point of view, the torsion vortex represents a `domain wall' between the two distinct vacua. From a bulk point of view, we point out an intriguing identification of the parameters of the torsion vortex with those of an Abrikosov vortex in a Type I superconductor. Following the analogy, we find that external Kalb-Ramond flux then appears to support bubbles of flat spacetime within an asymptotically AdS geometry.Comment: 26 pages, 4 figures; v2: minor improvements, references adde

The Massive Progenitor of the Type II-Linear Supernova 2009kr

We present early-time photometric and spectroscopic observations of supernova (SN) 2009kr in NGC 1832. We find that its properties to date support its classification as Type II-linear (SN II-L), a relatively rare subclass of core-collapse supernovae (SNe). We have also identified a candidate for the SN progenitor star through comparison of pre-explosion, archival images taken with WFPC2 on board the Hubble Space Telescope with SN images obtained using adaptive optics plus NIRC2 on the 10 m Keck-II telescope. Although the host galaxy's substantial distance (similar to 26 Mpc) results in large uncertainties in the relative astrometry, we find that if this candidate is indeed the progenitor, it is a highly luminous (M(V)(0) = -7.8 mag) yellow supergiant with initial mass similar to 18-24 M(circle dot). This would be the first time that an SN II-L progenitor has been directly identified. Its mass may be a bridge between the upper initial mass limit for the more common Type II-plateau SNe and the inferred initial mass estimate for one Type II-narrow SN.Hungarian OTKA K76816NSF AST-0707769, AST-0908886Sylvia & Jim Katzman FoundationTABASGO FoundationNASA through STScI AR-11248, GO-10877Harvard UniversityUC BerkeleyUniversity of VirginiaNASA/Swift NNX09AQ66GDOEAstronom

Black hole entropy in 3D gravity with torsion

The role of torsion in quantum three-dimensional gravity is investigated by studying the partition function of the Euclidean theory in Riemann-Cartan spacetime. The entropy of the black hole with torsion is found to differ from the standard Bekenstein-Hawking result, but its form is in complete agreement with the first law of black hole thermodynamics.Comment: 17 pages, RevTeX, minor revision

Holographic renormalization as a canonical transformation

The gauge/string dualities have drawn attention to a class of variational problems on a boundary at infinity, which are not well defined unless a certain boundary term is added to the classical action. In the context of supergravity in asymptotically AdS spaces these problems are systematically addressed by the method of holographic renormalization. We argue that this class of a priori ill defined variational problems extends far beyond the realm of holographic dualities. As we show, exactly the same issues arise in gravity in non asymptotically AdS spaces, in point particles with certain unbounded from below potentials, and even fundamental strings in flat or AdS backgrounds. We show that the variational problem in all such cases can be made well defined by the following procedure, which is intrinsic to the system in question and does not rely on the existence of a holographically dual theory: (i) The first step is the construction of the space of the most general asymptotic solutions of the classical equations of motion that inherits a well defined symplectic form from that on phase space. The requirement of a well defined symplectic form is essential and often leads to a necessary repackaging of the degrees of freedom. (ii) Once the space of asymptotic solutions has been constructed in terms of the correct degrees of freedom, then there exists a boundary term that is obtained as a certain solution of the Hamilton-Jacobi equation which simultaneously makes the variational problem well defined and preserves the symplectic form. This procedure is identical to holographic renormalization in the case of asymptotically AdS gravity, but it is applicable to any Hamiltonian system.Comment: 37 pages; v2 minor corrections in section 2, 2 references and a footnote on Palatini gravity added. Version to appear in JHE

Gravity in the 3+1-Split Formalism I: Holography as an Initial Value Problem

We present a detailed analysis of the 3+1-split formalism of gravity in the presence of a cosmological constant. The formalism helps revealing the intimate connection between holography and the initial value formulation of gravity. We show that the various methods of holographic subtraction of divergences correspond just to different transformations of the canonical variables, such that the initial value problem is properly set up at the boundary. The renormalized boundary energy momentum tensor is a component of the Weyl tensor.Comment: 28 pages; v2: minor improvements, references adde