Cornerstones of Sampling of Operator Theory

This paper reviews some results on the identifiability of classes of operators whose Kohn-Nirenberg symbols are band-limited (called band-limited operators), which we refer to as sampling of operators. We trace the motivation and history of the subject back to the original work of the third-named author in the late 1950s and early 1960s, and to the innovations in spread-spectrum communications that preceded that work. We give a brief overview of the NOMAC (Noise Modulation and Correlation) and Rake receivers, which were early implementations of spread-spectrum multi-path wireless communication systems. We examine in detail the original proof of the third-named author characterizing identifiability of channels in terms of the maximum time and Doppler spread of the channel, and do the same for the subsequent generalization of that work by Bello. The mathematical limitations inherent in the proofs of Bello and the third author are removed by using mathematical tools unavailable at the time. We survey more recent advances in sampling of operators and discuss the implications of the use of periodically-weighted delta-trains as identifiers for operator classes that satisfy Bello's criterion for identifiability, leading to new insights into the theory of finite-dimensional Gabor systems. We present novel results on operator sampling in higher dimensions, and review implications and generalizations of the results to stochastic operators, MIMO systems, and operators with unknown spreading domains

Exactly solvable model of superstring in Ramond-Ramond plane wave background

We describe in detail the solution of type IIB superstring theory in the maximally supersymmetric plane-wave background with constant null Ramond-Ramond 5-form field strength. The corresponding light-cone Green-Schwarz action found in hep-th/0112044 is quadratic in both bosonic and fermionic coordinates. We find the spectrum of the light-cone Hamiltonian and the string representation of the supersymmetry algebra. The superstring Hamiltonian has a ``harmonic-oscillator'' form in both the string-oscillator and the zero-mode parts and thus has discrete spectrum in all 8 transverse directions. We analyze the structure of the zero-mode sector of the theory, establishing the precise correspondence between the lowest-lying ``massless'' string states and the type IIB supergravity fluctuation modes in the plane-wave background. The zero-mode spectrum has certain similarity to the supergravity spectrum in AdS_5 x S^5 of which the plane-wave background is a special limit. We also compare the plane-wave string spectrum with expected form of the light-cone gauge spectrum of superstring in AdS_5 x S^5.Comment: 33 pages, latex. v4: minor sign corrections in (1.5) and (3.62), to appear in PR

Four graviton scattering amplitude from SNR8S^N\large{{\bf R}}^{8} supersymmetric orbifold sigma model

In the IR limit the Matrix string theory is expected to be described by the $S^N\R^{8}$ supersymmetric orbifold sigma model. Recently Dijkgraaf, Verlinde and Verlinde proposed a vertex that may describe the type IIA string interaction. In this paper using this interaction vertex we derive the four graviton scattering amplitude from the orbifold model in the large $N$ limit.Comment: latex, 35 pages, misprints are corrected, the final version to appear in Nucl.Phys.

Thin film coatings which inhibit spin relaxation of polarized potassium atoms

A prototype of a polarized deuterium target which employs the spin exchange method is being developed. The mixing cell for mixing deuterium atoms and potassium vapor requires a surface that will reflect these atoms without being destroyed by the corrosive potassium. Thin film coating methods and a technique for coating pyrex are described. Results of spin relaxation measurements are given. (LEW

Electroproduction of the d* dibaryon

The unpolarized cross section for the electroproduction of the isoscalar $J^\pi = 3^+$ di-delta dibaryon $d^*$ is calculated for deuteron target using a simple picture of elastic electron-baryon scattering from the $\Delta \Delta (^7D_1)$ and the $NN (^3S_1)$ components of the deuteron. The calculated differential cross section at the electron lab energy of 1 GeV has the value of about 0.24 (0.05) nb/sr at the lab angle of 10$^\circ$ (30$^\circ$) for the Bonn B potential when the dibaryon mass is taken to be 2.1 GeV. The cross section decreases rapidly with increasing dibaryon mass. A large calculated width of 40 MeV for $d^*(\Delta\Delta ^7S_3)$ combined with a small experimental upper bound of 0.08 MeV for the $d^*$ decay width appears to have excluded any low-mass $d^*$ model containing a significant admixture of the $\Delta\Delta (^7S_3)$ configuration.Comment: 11 journal-style pages, 8 figure

Towards a population of HMXB/NS microquasars as counterparts of low-latitude unidentified EGRET sources

The discovery of the microquasar LS 5039 well within the 95% conficence contour of the Unidentified EGRET Source (UES) 3EG J1824-1514 was a major step towards the possible association between microquasars (MQs) and UESs. The recent discovery of precessing relativistic radio jets in LS I +61 303, a source associated for long time with 2CG 135+01 and with the UES 3EG J0241+6103, has given further support to this idea. Finally, the very recently proposed association between the microquasar candidate AX J1639.0-4642 and the UES 3EG J1639-4702 points towards a population of High Mass X-ray Binary (HMXB)/Neutron Star (NS) microquasars as counterparts of low-latitude unidentified EGRET sources.Comment: 12 pages, 7 figures. Proceedings of the Conference "The Multiwavelength Approach to Unidentified Gamma-ray Sources", to appear in the journal Astrophysics and Space Scienc

Gut Dysbiosis in Cutaneous T-Cell Lymphoma Is Characterized by Shifts in Relative Abundances of Specific Bacterial Taxa and Decreased Diversity in More Advanced Disease

Background Cutaneous T-cell lymphoma (CTCL) patients often suffer from recurrent skin infections and profound immune dysregulation in advanced disease. The gut microbiome has been recognized to influence cancers and cutaneous conditions; however, it has not yet been studied in CTCL.ObjectivesTo investigate the gut microbiome in patients with CTCL and in healthy controls.MethodsA case-control study was conducted between January 2019 and November 2020 at Northwestern’s busy multidisciplinary CTCL clinic (Chicago, Illinois, USA) utilizing 16S ribosomal RNA gene amplicon sequencing and bioinformatics analyses to characterize the microbiota present in fecal samples of CTCL patients (n = 38) and age-matched healthy controls (n = 13) from the same geographical region.ResultsGut microbial α-diversity trended lower in patients with CTCL and was significantly lower in patients with advanced CTCL relative to controls (P = 0.015). No differences in β-diversity were identified. Specific taxa were significantly reduced in patient samples; significance was determined using adjusted P-values (q-values) that accounted for a false discovery rate threshold of 0.05. Significantly reduced taxa in patient samples included the phylum Actinobacteria (q = 0.0002), classes Coriobacteriia (q = 0.002) and Actinobacteria (q = 0.03), order Coriobacteriales (q = 0.003), and genus Anaerotruncus (q = 0.01). The families Eggerthellaceae (q = 0.0007) and Lactobacillaceae (q = 0.02) were significantly reduced in patients with high skin disease burden.ConclusionsGut dysbiosis can be seen in patients with CTCL compared to healthy controls and is pronounced in more advanced CTCL. The taxonomic shifts associated with CTCL are similar to those previously reported in atopic dermatitis and opposite those of psoriasis, suggesting microbial parallels to the immune profile and skin barrier differences between these conditions. These findings may suggest new microbial disease biomarkers and reveal a new angle for intervention

Induced Parity Nonconserving Interaction and Enhancement of Two-Nucleon Parity Nonconserving Forces

Two-nucleon parity nonconserving (PNC) interaction induced by the single-particle PNC weak potential and the two-nucleon residual strong interaction is considered. An approximate analytical formula for this Induced PNC Interaction (IPNCI) between proton and neutron is derived ($Q({\bf r} {\bf \sigma}_{p} \times {\bf \sigma}_{n}) \delta({\bf r}_{p}-{\bf r}_{n})$), and the interaction constant is estimated. As a result of coherent contributions from the nucleons to the PNC potential, IPNCI is an order of magnitude stronger ($\sim A^{1/3}$) than the residual weak two-nucleon interaction and has a different coordinate and isotopic structure (e.g., the strongest part of IPNCI does not contribute to the PNC mean field). IPNCI plays an important role in the formation of PNC effects, e.g., in neutron-nucleus reactions. In that case, it is a technical way to take into account the contribution of the distant (small) components of a compound state which dominates the result. The absence of such enhancement ($\sim A^{1/3}$) in the case of T- and P-odd interaction completes the picture.Comment: Phys. Rev. C, to appear; 17 pages, revtex 3, no figure

Four-point correlators with higher weight superconformal primaries in the AdS/CFT Correspondence

The four-point correlation function of two 1/2 BPS primaries of conformal weight $\Delta=2$ and two 1/2-BPS primaries of conformal weight $\Delta=n$ is calculated in the large 't Hooft, large $N$ limit. These operators are dual to Kaluza-Klein supergravity fields $s_k$ with masses $m^2=-4$ and $m^2=n(n-4)$. Given that the existing formalism for evaluating sums of products of SO(6) tensors that determine the effective couplings is only suitable for primaries with small conformal dimensions, we make us of an alternative formalism based on harmonic polynomials introduced by Dolan and Osborn. We then show that the supergravity lagrangian relevant to the computation is of sigma-model type (i.e., the four-derivative couplings vanish) and that the final result for the connected amplitude splits into a free and an interacting part, as expected on general grounds.Comment: 31 pages, 4 figure