An Equivariant Tamagawa Number Formula for Drinfeld Modules and Applications

We fix data $(K/F, E)$ consisting of a Galois extension $K/F$ of characteristic $p$ global fields with arbitrary abelian Galois group $G$ and a Drinfeld module $E$ defined over a certain Dedekind subring of $F$. For this data, we define a $G$-equivariant $L$-function $\Theta_{K/F}^E$ and prove an equivariant Tamagawa number formula for certain Euler-completed versions of its special value $\Theta_{K/F}^E(0)$. This generalizes Taelman's class number formula for the value $\zeta_F^E(0)$ of the Goss zeta function $\zeta_F^E$ associated to the pair $(F, E)$. Taelman's result is obtained from our result by setting $K=F$. As a consequence, we prove a perfect Drinfeld module analogue of the classical (number field) refined Brumer--Stark conjecture, relating a certain $G$-Fitting ideal of Taelman's class group $H(E/K)$ to the special value $\Theta_{K/F}^E(0)$ in question

Test and optimization of a multi-modal phase-based x-ray microscope for soft tissue imaging

Tissue imaging is a pivotal component of both biomedical research and clinical practice. In order to identify tissue structures down to the cellular level, it requires the capability to image mm-size unstained tissue specimens with micron to sub-micron resolution. Tissue imaging is normally performed either using x-rays or visible light. While the latter is limited by light scattering in relatively thick tissues, the former often suffers from poor contrast in absorption-based systems. Phase-contrast x-ray microscopes exist but they often lack the required quantitativeness, entail acquisition times of the order of tens of hours for 3-D imaging and are limited to narrow fields of view. We propose a novel multi-modal phase-based x-ray microscope capable of imaging mm-thick tissue samples on a mm-size field of view using intensity-modulation masks. They act as optical elements allowing the quantitative retrieval of tissue properties such as transmission, refraction and scattering. Additionally, given that the system’s spatial resolution depends only on the mask aperture size, a multi-resolution approach is possible by selecting masks with aperture size matching the resolution requirements (micron and sub-micron) of specific samples. The design and optimization of the x-ray microscope is presented in this paper together with exemplar images of a thin foam sample resulting from the retrieval of the three contrast channels. The final paper will include details of the system parameter optimization (e.g., propagation distance, mask aperture and period), their effect on the retrieval algorithm and imaging performance as well as the first images of biological samples

Visible Sector Supersymmetry Breaking Revisited

We revisit the possibility of "visible sector" SUSY models: models which are straightforward renormalizable extensions of the Minimal Supersymmetric Standard Model (MSSM), where SUSY is broken at tree level. Models of this type were abandoned twenty years ago due to phenomenological problems, which we review. We then demonstrate that it is possible to construct simple phenomenologically viable visible sector SUSY models. Such models are indeed very constrained, and have some inelegant features. They also have interesting and distinctive phenomenology. Our models predict light gauginos and very heavy squarks and sleptons. The squarks and sleptons may not be observable at the LHC. The LSP is a stable very light gravitino with a significant Higgsino admixture. The NLSP is mostly Bino. The Higgs boson is naturally heavy. Proton decay is sufficently and naturally suppressed, even for a cutoff scale as low as 10^8 GeV. The lightest particle of the O'Raifeartaigh sector (the LOP) is stable, and is an interesting cold dark matter candidate.Comment: 23 pages, 3 figures, LaTe

Structural and Biochemical Characterization of CIB1 Delineates a New Family of EF-hand-containing Proteins

CIB1 (CIB) is an EF-hand-containing protein that binds multiple effector proteins, including the platelet alphaIIbbeta3 integrin and several serine/threonine kinases and potentially modulates their function. The crystal structure for Ca(2+)-bound CIB1 has been determined at 2.0 A resolution and reveals a compact alpha-helical protein containing four EF-hands, the last two of which bind calcium ions in the standard fashion seen in many other EF-hand proteins. CIB1 shares high structural similarity with calcineurin B and the neuronal calcium sensor (NCS) family of EF-hand-containing proteins. Most importantly, like calcineurin B and NCS proteins, which possess a large hydrophobic pocket necessary for ligand binding, CIB1 contains a hydrophobic pocket that has been implicated in ligand binding by previous mutational analysis. However, unlike several NCS proteins, Ca(2+)-bound CIB1 is largely monomeric whether bound to a relevant peptide ligand or ligand-free. Differences in structure, oligomeric state, and phylogeny define a new family of CIB1-related proteins that extends from arthropods to humans

The linear multiplet and ectoplasm

In the framework of the superconformal tensor calculus for 4D N=2 supergravity, locally supersymmetric actions are often constructed using the linear multiplet. We provide a superform formulation for the linear multiplet and derive the corresponding action functional using the ectoplasm method (also known as the superform approach to the construction of supersymmetric invariants). We propose a new locally supersymmetric action which makes use of a deformed linear multiplet. The novel feature of this multiplet is that it corresponds to the case of a gauged central charge using a one-form potential not annihilated by the central charge (unlike the standard N=2 vector multiplet). Such a gauge one-form can be chosen to describe a variant nonlinear vector-tensor multiplet. As a byproduct of our construction, we also find a variant realization of the tensor multiplet in supergravity where one of the auxiliaries is replaced by the field strength of a gauge three-form.Comment: 31 pages; v3: minor corrections and typos fixed, version to appear in JHE

Multi-Messenger Gravitational Wave Searches with Pulsar Timing Arrays: Application to 3C66B Using the NANOGrav 11-year Data Set

When galaxies merge, the supermassive black holes in their centers may form binaries and, during the process of merger, emit low-frequency gravitational radiation in the process. In this paper we consider the galaxy 3C66B, which was used as the target of the first multi-messenger search for gravitational waves. Due to the observed periodicities present in the photometric and astrometric data of the source of the source, it has been theorized to contain a supermassive black hole binary. Its apparent 1.05-year orbital period would place the gravitational wave emission directly in the pulsar timing band. Since the first pulsar timing array study of 3C66B, revised models of the source have been published, and timing array sensitivities and techniques have improved dramatically. With these advances, we further constrain the chirp mass of the potential supermassive black hole binary in 3C66B to less than $(1.65\pm0.02) \times 10^9~{M_\odot}$ using data from the NANOGrav 11-year data set. This upper limit provides a factor of 1.6 improvement over previous limits, and a factor of 4.3 over the first search done. Nevertheless, the most recent orbital model for the source is still consistent with our limit from pulsar timing array data. In addition, we are able to quantify the improvement made by the inclusion of source properties gleaned from electromagnetic data to `blind' pulsar timing array searches. With these methods, it is apparent that it is not necessary to obtain exact a priori knowledge of the period of a binary to gain meaningful astrophysical inferences.Comment: 14 pages, 6 figures. Accepted by Ap

Phases of planar 5-dimensional supersymmetric Chern-Simons theory

In this paper we investigate the large-$N$ behavior of 5-dimensional $\mathcal{N}=1$ super Yang-Mills with a level $k$ Chern-Simons term and an adjoint hypermultiplet. As in three-dimensional Chern-Simons theories, one must choose an integration contour to completely define the theory. Using localization, we reduce the path integral to a matrix model with a cubic action and compute its free energy in various scenarios. In the limit of infinite Yang-Mills coupling and for particular choices of the contours, we find that the free-energy scales as $N^{5/2}$ for $U(N)$ gauge groups with large values of the Chern-Simons 't\,Hooft coupling, $\tilde\lambda\equiv N/k$. If we also set the hypermultiplet mass to zero, then this limit is a superconformal fixed point and the $N^{5/2}$ behavior parallels other fixed points which have known supergravity duals. We also demonstrate that $SU(N)$ gauge groups cannot have this $N^{5/2}$ scaling for their free-energy. At finite Yang-Mills coupling we establish the existence of a third order phase transition where the theory crosses over from the Yang-Mills phase to the Chern-Simons phase. The phase transition exists for any value of $\tilde\lambda$, although the details differ between small and large values of $\tilde\lambda$. For pure Chern-Simons theories we present evidence for a chain of phase transitions as $\tilde\lambda$ is increased. We also find the expectation values for supersymmetric circular Wilson loops in these various scenarios and show that the Chern-Simons term leads to different physical properties for fundamental and anti-fundamental Wilson loops. Different choices of the integration contours also lead to different properties for the loops.Comment: 40 pages, 17 figures, Minor corrections, Published versio

Astrophysical and Cosmological Implications of Large Volume String Compactifications

We study the spectrum, couplings and cosmological and astrophysical implications of the moduli fields for the class of Calabi-Yau IIB string compactifications for which moduli stabilisation leads to an exponentially large volume V ~ 10^{15} l_s^6 and an intermediate string scale m_s ~ 10^{11}GeV, with TeV-scale observable supersymmetry breaking. All K\"ahler moduli except for the overall volume are heavier than the susy breaking scale, with m ~ ln(M_P/m_{3/2}) m_{3/2} ~ (\ln(M_P/m_{3/2}))^2 m_{susy} ~ 500 TeV and, contrary to standard expectations, have matter couplings suppressed only by the string scale rather than the Planck scale. These decay to matter early in the history of the universe, with a reheat temperature T ~ 10^7 GeV, and are free from the cosmological moduli problem (CMP). The heavy moduli have a branching ratio to gravitino pairs of 10^{-30} and do not suffer from the gravitino overproduction problem. The overall volume modulus is a distinctive feature of these models and is an M_{planck}-coupled scalar of mass m ~ 1 MeV and subject to the CMP. A period of thermal inflation can help relax this problem. This field has a lifetime ~ 10^{24}s and can contribute to dark matter. It may be detected through its decays to 2\gamma or e^+e^-. If accessible the e^+e^- decay mode dominates, with Br(\chi \to 2 \gamma) suppressed by a factor (ln(M_P/m_{3/2}))^2. We consider the potential for detection of this field through different astrophysical sources and find that the observed gamma-ray background constrains \Omega_{\chi} <~ 10^{-4}. The decays of this field may generate the 511 keV emission line from the galactic centre observed by INTEGRAL/SPI.Comment: 31 pages, 2 figures; v2. refs adde

Catalytic intramolecular hydroamination of aminoallenes using titanium complexes of chiral, tridentate, dianionic imine-diol ligands

Alkylation of D- or L-phenylalanine or valine alkyl esters was carried out using methyl or phenyl Grignard reagents. Subsequent condensation with salicylaldehyde, 3,5-di-tert-butylsalicylaldehyde, or 5-fluorosalicylaldehyde formed tridentate, X_2L type, Schiff base ligands. Chiral shift NMR confirmed retention of stereochemistry during synthesis. X-ray crystal structures of four of the ligands show either inter- or intramolecular hydrogen bonding interactions. The ligands coordinate to the titanium reagents Ti(NMe_2)_4 or TiCl(NMe_2)_3 by protonolysis and displacement of two equivalents of HNMe_2. The crystal structure of one example of Ti(X_2L)Cl(NMe_2) was determined and the complex has a distorted square pyramidal geometry with an axial NMe_2 ligand. The bis-dimethylamide complexes are active catalysts for the ring closing hydroamination of di- and trisubstituted aminoallenes. The reaction of hepta-4,5-dienylamine at 135 °C with 5 mol% catalyst gives a mixture of 6-ethyl-2,3,4,5-tetrahydropyridine (40–72%) and both Z- and E-2-propenyl-pyrrolidine (25–52%). The ring closing reaction of 6-methyl-hepta-4,5-dienylamine at 135 °C with 5 mol% catalyst gives exclusively 2-(2-methyl-propenyl)-pyrrolidine. The pyrrolidine products are obtained with enantiomeric excesses up to 17%