CR-Invariants and the Scattering Operator for Complex Manifolds with Boundary

The purpose of this paper is to describe certain CR-covariant differential operators on a strictly pseudoconvex CR manifold $M$ as residues of the scattering operator for the Laplacian on an ambient complex K\"{a}hler manifold $X$ having $M$ as a `CR-infinity.' We also characterize the CR $Q$-curvature in terms of the scattering operator. Our results parallel earlier results of Graham and Zworski \cite{GZ:2003}, who showed that if $X$ is an asymptotically hyperbolic manifold carrying a Poincar\'{e}-Einstein metric, the $Q$-curvature and certain conformally covariant differential operators on the `conformal infinity' $M$ of $X$ can be recovered from the scattering operator on $X$. The results in this paper were announced in \cite{HPT:2006}.Comment: 32 page

Dependence of the density of states outer measure on the potential for deterministic Schr\"odinger operators on graphs with applications to ergodic and random models

We continue our study of the dependence of the density of states measure and related spectral functions of Schr\"odinger operators on the potential. Whereas our earlier work focused on random Schr\"odinger operators, we extend these results to Schr\"odinger operators on infinite graphs with deterministic potentials and ergodic potentials, and improve our results for random potentials. In particular, we prove the Lipschitz continuity of the DOSm for random Schr\"odinger operators on the lattice, recovering results of \cite{kachkovskiy, shamis}. For our treatment of deterministic potentials, we first study the density of states outer measure (DOSoM), defined for all Schr\"odinger operators, and prove a deterministic result of the modulus of continuity of the DOSoM with respect to the potential. We apply these results to Schr\"odinger operators on the lattice $Z^d$ and the Bethe lattice. In the former case, we prove the Lipschitz continuity of the DOSoM, and in the latter case, we prove that the DOSoM is $\frac{1}{2}$-log-H\"older continuous. Our technique combines the abstract Lipschitz property of one-parameter families of self-adjoint operators with a new finite-range reduction that allows us to study the dependency of the DOSoM and related functions on only finitely-many variables and captures the geometry of the graph at infinity.Comment: Related to arXiv:1804.02444 and arXiv:1904.01118 by the authors; New appendices C and D are added and typos corrected. Appendix C discusses inequalities between the metric of weak convergence of measures and the Kantorovich-Rubinstein-Wasserstein metric. Appendix D presents results on continuity of the Hausdorff distance between two spectra with respect to the potential

CD8+ immunodominance among Epstein-Barr virus lytic cycle antigens directly reflects the efficiency of antigen presentation in lytically infected cells

Antigen immunodominance is an unexplained feature of CD8+ T cell responses to herpesviruses, which are agents whose lytic replication involves the sequential expression of immediate early (IE), early (E), and late (L) proteins. Here, we analyze the primary CD8 response to Epstein-Barr virus (EBV) infection for reactivity to 2 IE proteins, 11 representative E proteins, and 10 representative L proteins, across a range of HLA backgrounds. Responses were consistently skewed toward epitopes in IE and a subset of E proteins, with only occasional responses to novel epitopes in L proteins. CD8+ T cell clones to representative IE, E, and L epitopes were assayed against EBV-transformed lymphoblastoid cell lines (LCLs) containing lytically infected cells. This showed direct recognition of lytically infected cells by all three sets of effectors but at markedly different levels, in the order IE > E ≫ L, indicating that the efficiency of epitope presentation falls dramatically with progress of the lytic cycle. Thus, EBV lytic cycle antigens display a hierarchy of immunodominance that directly reflects the efficiency of their presentation in lytically infected cells; the CD8+ T cell response thereby focuses on targets whose recognition leads to maximal biologic effect

Use of methods for specifying the target difference in randomised controlled trial sample size calculations : Two surveys of trialists' practice

© The Author(s), 2014.Peer reviewedPublisher PD

Shapes of leading tunnelling trajectories for single-electron molecular ionization

Based on the geometrical approach to tunnelling by P.D. Hislop and I.M. Sigal [Memoir. AMS 78, No. 399 (1989)], we introduce the concept of a leading tunnelling trajectory. It is then proven that leading tunnelling trajectories for single-active-electron models of molecular tunnelling ionization (i.e., theories where a molecular potential is modelled by a single-electron multi-centre potential) are linear in the case of short range interactions and "almost" linear in the case of long range interactions. The results are presented on both the formal and physically intuitive levels. Physical implications of the obtained results are discussed.Comment: 14 pages, 5 figure

Anomalous Scale Dimensions from Timelike Braiding

Using the previously gained insight about the particle/field relation in conformal quantum field theories which required interactions to be related to the existence of particle-like states associated with fields of anomalous scaling dimensions, we set out to construct a classification theory for the spectra of anomalous dimensions. Starting from the old observations on conformal superselection sectors related to the anomalous dimensions via the phases which appear in the spectral decomposition of the center of the conformal covering group $Z(\widetilde{SO(d,2)}),$ we explore the possibility of a timelike braiding structure consistent with the timelike ordering which refines and explains the central decomposition. We regard this as a preparatory step in a new construction attempt of interacting conformal quantum field theories in D=4 spacetime dimensions. Other ideas of constructions based on the $AdS_{5}$-$CQFT_{4}$ or the perturbative SYM approach in their relation to the present idea are briefly mentioned.Comment: completely revised, updated and shortened replacement, 24 pages tcilatex, 3 latexcad figure

Singular Modes of the Electromagnetic Field

We show that the mode corresponding to the point of essential spectrum of the electromagnetic scattering operator is a vector-valued distribution representing the square root of the three-dimensional Dirac's delta function. An explicit expression for this singular mode in terms of the Weyl sequence is provided and analyzed. An essential resonance thus leads to a perfect localization (confinement) of the electromagnetic field, which in practice, however, may result in complete absorption.Comment: 14 pages, no figure