Modularity of nearly ordinary 2-adic residually dihedral Galois representations

We prove modularity of some two dimensional, 2-adic Galois representations over totally real fields that are nearly ordinary and that are residually dihedral. We do this by employing the strategy of Skinner and Wiles, using Hida families, together with the 2-adic patching method of Khare and Wintenberger. As an application we deduce modularity of some elliptic curves over totally real fields that have good ordinary or multiplicative reduction at places above 2.Comment: 87 pages. Typos correcte

Deformations of polarized automorphic Galois representations and adjoint Selmer groups

We prove the vanishing of the geometric Bloch-Kato Selmer group for the adjoint representation of a Galois representation associated to regular algebraic polarized cuspidal automorphic representations under an assumption on the residual image. Using this, we deduce that the localization and completion of a certain universal deformation ring for the residual representation at the characteristic zero point induced from the automorphic representation is formally smooth of the correct dimension. We do this by employing the Taylor-Wiles-Kisin patching method together with Kisin's technique of analyzing the generic fibre of universal deformation rings. Along the way we give a characterization of smooth closed points on the generic fibre of Kisin's potentially semistable local deformation rings in terms of their Weil-Deligne representations.Comment: Added reference to work of Breuil-Hellmann-Schraen. Minor change in assumption (b) of Theorems C and 3.1.3. Added Theorem 3.2.3 and subsection 3.3. Corrected typos and incorporated suggestions of the referee. To appear in Duke Math.

Phosphorylation of Spinophilin Modulates Its Interaction with Actin Filaments

Spinophilin is a protein phosphatase 1 (PP1)- and actin-binding protein that modulates excitatory synaptic transmission and dendritic spine morphology. We report that spinophilin is phosphorylated in vitro by protein kinase A (PKA). Phosphorylation of spinophilin was stimulated by treatment of neostriatal neurons with a dopamine D1 receptor agonist or with forskolin, consistent with spinophilin being a substrate for PKA in intact cells. Using tryptic phosphopeptide mapping, site-directed mutagenesis, and microsequencing analysis, we identified two major sites of phosphorylation, Ser-94 and Ser-177, that are located within the actin-binding domain of spinophilin. Phosphorylation of spinophilin by PKA modulated the association between spinophilin and the actin cytoskeleton. Following subcellular fractionation, unphosphorylated spinophilin was enriched in the postsynaptic density, whereas a pool of phosphorylated spinophilin was found in the cytosol. F-actin co-sedimentation and overlay analysis revealed that phosphorylation of spinophilin reduced the stoichiometry of the spinophilin-actin interaction. In contrast, the ability of spinophilin to bind to PP1 remained unchanged. Taken together, our studies suggest that phosphorylation of spinophilin by PKA modulates the anchoring of the spinophilin-PP1 complex within dendritic spines, thereby likely contributing to the efficacy and plasticity of synaptic transmission

Potential automorphy over CM fields

Let $F$ be a CM number field. We prove modularity lifting theorems for regular $n$-dimensional Galois representations over $F$ without any self-duality condition. We deduce that all elliptic curves $E$ over $F$ are potentially modular, and furthermore satisfy the Sato--Tate conjecture. As an application of a different sort, we also prove the Ramanujan Conjecture for weight zero cuspidal automorphic representations for $\mathrm{GL}_2(\mathbf{A}_F)$.Comment: A number of details have been included to address the concerns of the referees. The definition of decomposed generic (Def 4.3.1) has been weakened slightly to be in line with the current version of arxiv.org/abs/1909.01898, resulting in a strengthening of a number of our theorems. This is the accepted version of the pape

Cosmology and Astrophysics from Relaxed Galaxy Clusters II: Cosmological Constraints

We present cosmological constraints from measurements of the gas mass fraction, $f_{gas}$, for massive, dynamically relaxed galaxy clusters. Our data set consists of Chandra observations of 40 such clusters, identified in a comprehensive search of the Chandra archive, as well as high-quality weak gravitational lensing data for a subset of these clusters. Incorporating a robust gravitational lensing calibration of the X-ray mass estimates, and restricting our measurements to the most self-similar and accurately measured regions of clusters, significantly reduces systematic uncertainties compared to previous work. Our data for the first time constrain the intrinsic scatter in $f_{gas}$, $(7.4\pm2.3)$% in a spherical shell at radii 0.8-1.2 $r_{2500}$, consistent with the expected variation in gas depletion and non-thermal pressure for relaxed clusters. From the lowest-redshift data in our sample we obtain a constraint on a combination of the Hubble parameter and cosmic baryon fraction, $h^{3/2}\Omega_b/\Omega_m=0.089\pm0.012$, that is insensitive to the nature of dark energy. Combined with standard priors on $h$ and $\Omega_b h^2$, this provides a tight constraint on the cosmic matter density, $\Omega_m=0.27\pm0.04$, which is similarly insensitive to dark energy. Using the entire cluster sample, extending to $z>1$, we obtain consistent results for $\Omega_m$ and interesting constraints on dark energy: $\Omega_\Lambda=0.65^{+0.17}_{-0.22}$ for non-flat $\Lambda$CDM models, and $w=-0.98\pm0.26$ for flat constant-$w$ models. Our results are both competitive and consistent with those from recent CMB, SNIa and BAO data. We present constraints on models of evolving dark energy from the combination of $f_{gas}$ data with these external data sets, and comment on the possibilities for improved $f_{gas}$ constraints using current and next-generation X-ray observatories and lensing data. (Abridged)Comment: 25 pages, 14 figures, 8 tables. Accepted by MNRAS. Code and data can be downloaded from http://www.slac.stanford.edu/~amantz/work/fgas14/ . v2: minor fix to table 1, updated bibliograph

Mechanically-stacked tandem solar cells with GaAsP on GaP and silicon

Preliminary results are encouraging for the achievement of high conversion efficiencies using a GaAsP top solar cell mechanically stacked on a conventional silicon solar cell. A realistic maximum of 29.4 percent is suggested when both the top and bottom solar cells are state of the art. Practical system efficiencies greater than 25 percent are attainable in the near future with the use of a state of the art bottom solar cell

Sampling rare switching events in biochemical networks

Bistable biochemical switches are ubiquitous in gene regulatory networks and signal transduction pathways. Their switching dynamics, however, are difficult to study directly in experiments or conventional computer simulations, because switching events are rapid, yet infrequent. We present a simulation technique that makes it possible to predict the rate and mechanism of flipping of biochemical switches. The method uses a series of interfaces in phase space between the two stable steady states of the switch to generate transition trajectories in a ratchet-like manner. We demonstrate its use by calculating the spontaneous flipping rate of a symmetric model of a genetic switch consisting of two mutually repressing genes. The rate constant can be obtained orders of magnitude more efficiently than using brute-force simulations. For this model switch, we show that the switching mechanism, and consequently the switching rate, depends crucially on whether the binding of one regulatory protein to the DNA excludes the binding of the other one. Our technique could also be used to study rare events and non-equilibrium processes in soft condensed matter systems.Comment: 9 pages, 6 figures, last page contains supplementary informatio

Screening properties of Gaussian electrolyte models, with application to dissipative particle dynamics

We investigate the screening properties of Gaussian charge models of electrolyte solutions by analysing the asymptotic behaviour of the pair distribution functions. We use a combination of Monte-Carlo simulations with the hyper-netted chain integral equation closure, and the random phase approximation, to establish the conditions under which a screening length is well defined and the extent to which it matches the expected Debye length. For practical applications, for example in dissipative particle dynamics, we are able to summarise our results in succinct rules-of-thumb which can be used for mesoscale modeling of electrolyte solutions. We thereby establish a solid foundation for future work, such as the systematic incorporation of specific ion effects.Comment: 9 pages, 9 figures, 1 table, RevTeX4-