Hook Interpolations

The hook components of $V^{\otimes n}$ interpolate between the symmetric power \sym^n(V) and the exterior power $\wedge^n(V)$. When $V$ is the vector space of $k\times m$ matrices over \bbc, we decompose the hook components into irreducible GL_k(\bbc)\times GL_m(\bbc)-modules. In particular, classical theorems are proved as boundary cases. For the algebra of square matrices over \bbc, a bivariate interpolation is presented and studied.Comment: 23 pages; small change

Marital Status as a Categoric Risk in Major Mental Disorders

Author Institution: Bureau of Research and Statistics, Ohio Department of Public Welfare, Columbu

A hydrodynamic analog of interaction-free measurement

Interaction-free measurement allows for quantum particles to detect objects along paths they never traveled. As such, it represents one of the most beguiling of quantum phenomena. Here, we present a classical analog of interaction-free measurement using the hydrodynamic pilot-wave system, in which a droplet self-propels across a vibrating fluid surface, guided by a wave of its own making. We argue that existing rationalizations of interaction-free quantum measurement in terms of particles being guided by wave forms allow for a classical description manifest in our hydrodynamic system, wherein the measurement is decidedly not interaction-free

Nonlinear Dynamics of Capacitive Charging and Desalination by Porous Electrodes

The rapid and efficient exchange of ions between porous electrodes and aqueous solutions is important in many applications, such as electrical energy storage by super-capacitors, water desalination and purification by capacitive deionization (or desalination), and capacitive extraction of renewable energy from a salinity difference. Here, we present a unified mean-field theory for capacitive charging and desalination by ideally polarizable porous electrodes (without Faradaic reactions or specific adsorption of ions) in the limit of thin double layers (compared to typical pore dimensions). We illustrate the theory in the case of a dilute, symmetric, binary electrolyte using the Gouy-Chapman-Stern (GCS) model of the double layer, for which simple formulae are available for salt adsorption and capacitive charging of the diffuse part of the double layer. We solve the full GCS mean-field theory numerically for realistic parameters in capacitive deionization, and we derive reduced models for two limiting regimes with different time scales: (i) In the "super-capacitor regime" of small voltages and/or early times where the porous electrode acts like a transmission line, governed by a linear diffusion equation for the electrostatic potential, scaled to the RC time of a single pore. (ii) In the "desalination regime" of large voltages and long times, the porous electrode slowly adsorbs neutral salt, governed by coupled, nonlinear diffusion equations for the pore-averaged potential and salt concentration

Superradiant droplet emission from parametrically excited cavities

Superradiance occurs when a collection of atoms exhibits cooperative, spontaneous emission of photons at a rate that exceeds that of its component parts. Here, we reveal a similar phenomenon in a hydrodynamic system consisting of a pair of vibrationally-excited cavities, coupled through their common wavefield, that spontaneously emit droplets via interfacial fracture. We show that the droplet emission rate of two coupled cavities is higher than the emission rate of two isolated cavities. We further show that the amplified emission rate varies sinusoidally with distance between the cavities, thus demonstrating a hydrodynamic phenomenon that captures the essential features of superradiance in optical systems

Egg-derived anti-SARS-CoV-2 Immunoglobulin Y (IgY) with broad variant activity as intranasal prophylaxis against COVID-19

UNLABELLED: COVID-19 emergency use authorizations and approvals for vaccines were achieved in record time. However, there remains a need to develop additional safe, effective, easy-to-produce, and inexpensive prevention to reduce the risk of acquiring SARS-CoV-2 infection. This need is due to difficulties in vaccine manufacturing and distribution, vaccine hesitancy, and, critically, the increased prevalence of SARS-CoV-2 variants with greater contagiousness or reduced sensitivity to immunity. Antibodies from eggs of hens (immunoglobulin Y; IgY) that were administered the receptor-binding domain (RBD) of the SARS-CoV-2 spike protein were developed for use as nasal drops to capture the virus on the nasal mucosa. Although initially raised against the 2019 novel coronavirus index strain (2019-nCoV), these anti-SARS-CoV-2 RBD IgY surprisingly had indistinguishable enzyme-linked immunosorbent assay binding against variants of concern that have emerged, including Alpha (B.1.1.7), Beta (B.1.351), Delta (B.1.617.2), and Omicron (B.1.1.529). This is different from sera of immunized or convalescent patients. Culture neutralization titers against available Alpha, Beta, and Delta were also indistinguishable from the index SARS-CoV-2 strain. Efforts to develop these IgY for clinical use demonstrated that the intranasal anti-SARS-CoV-2 RBD IgY preparation showed no binding (cross-reactivity) to a variety of human tissues and had an excellent safety profile in rats following 28-day intranasal delivery of the formulated IgY. A double-blind, randomized, placebo-controlled phase 1 study evaluating single-ascending and multiple doses of anti-SARS-CoV-2 RBD IgY administered intranasally for 14 days in 48 healthy adults also demonstrated an excellent safety and tolerability profile, and no evidence of systemic absorption. As these antiviral IgY have broad selectivity against many variants of concern, are fast to produce, and are a low-cost product, their use as prophylaxis to reduce SARS-CoV-2 viral transmission warrants further evaluation. CLINICAL TRIAL REGISTRATION: https://www.clinicaltrials.gov/ct2/show/NCT04567810, identifier NCT04567810