Strichartz Estimates for the Vibrating Plate Equation

We study the dispersive properties of the linear vibrating plate (LVP) equation. Splitting it into two Schr\"odinger-type equations we show its close relation with the Schr\"odinger equation. Then, the homogeneous Sobolev spaces appear to be the natural setting to show Strichartz-type estimates for the LVP equation. By showing a Kato-Ponce inequality for homogeneous Sobolev spaces we prove the well-posedness of the Cauchy problem for the LVP equation with time-dependent potentials. Finally, we exhibit the sharpness of our results. This is achieved by finding a suitable solution for the stationary homogeneous vibrating plate equation.Comment: 18 pages, 4 figures, some misprints correcte

Air and water pollution over time and industries with stochastic dominance

We employ a stochastic dominance (SD) approach to analyze the components that contribute to environmental degradation over time. The variables include countries\u2019 greenhouse gas (GHG) emissions and water pollution. Our approach is based on pair-wise SD tests. First, we study the dynamic progress of each separate variable over time, from 1990 to 2005, within 5-year horizons. Then, pair-wise SD tests are used to study the major industry contributors to the overall GHG emissions and water pollution at any given time, to uncover the industry which contributes the most to total emissions and water pollution. While CO2 emissions increased in the first order SD sense over 15 years, water pollution increased in a second-order SD sense. Electricity and heat production were the major contributors to the CO2 emissions, while the food industry gradually became the major water polluting industry over time. SD sense over 15 years, water pollution increased in a second-order SD sense. Electricity and heat production were the major contributors to the CO2 emissions, while the food industry gradually

Tunable control of CAR T cell activity through tetracycline mediated disruption of protein-protein interaction

Chimeric antigen receptor (CAR) T cells are a promising form of cancer immunotherapy, although they are often associated with severe toxicities. Here, we present a split-CAR design incorporating separate antigen recognition and intracellular signaling domains. These exploit the binding between the tetracycline repressor protein and a small peptide sequence (TIP) to spontaneously assemble as a functional CAR. Addition of the FDA-approved, small molecule antibiotic minocycline, acts as an "off-switch" by displacing the signaling domain and down-tuning CAR T activity. Here we describe the optimization of this split-CAR approach to generate a CAR in which cytotoxicity, cytokine secretion and proliferation can be inhibited in a dose-dependent and reversible manner. Inhibition is effective during on-going CAR T cell activation and inhibits activation and tumor control in vivo. This work shows how optimization of split-CAR structure affects function and adds a novel design allowing easy CAR inhibition through an FDA-approved small molecule

Potential of Magnetic Hyperthermia to Stimulate Localized Immune Activation

Magnetic hyperthermia (MH) harnesses the heat-releasing properties of superparamagnetic iron oxide nanoparticles (SPIONs) and has potential to stimulate immune activation in the tumor microenvironment whilst sparing surrounding normal tissues. To assess feasibility of localized MH in vivo, SPIONs are injected intratumorally and their fate tracked by Zirconium-89-positron emission tomography, histological analysis, and electron microscopy. Experiments show that an average of 49% (21-87%, n = 9) of SPIONs are retained within the tumor or immediately surrounding tissue. In situ heating is subsequently generated by exposure to an externally applied alternating magnetic field and monitored by thermal imaging. Tissue response to hyperthermia, measured by immunohistochemical image analysis, reveals specific and localized heat-shock protein expression following treatment. Tumor growth inhibition is also observed. To evaluate the potential effects of MH on the immune landscape, flow cytometry is used to characterize immune cells from excised tumors and draining lymph nodes. Results show an influx of activated cytotoxic T cells, alongside an increase in proliferating regulatory T cells, following treatment. Complementary changes are found in draining lymph nodes. In conclusion, results indicate that biologically reactive MH is achievable in vivo and can generate localized changes consistent with an anti-tumor immune response

Debt Maturity Choices, Multi-stage Investments and Financing Constraints

We develop a dynamic investment options framework with optimal capital structure and analyze the effect of debt maturity. We find that in the absence of financing constraints short-term debt maximizes firm value. In contrast with most literature results, in the absence of constraints, higher volatility may increase initial debt for firms with low initial revenues, issuing long term debt that expires after the investment option maturity. This effect, which is due to the option value of receiving the value of assets and remaining tax savings, does not hold for short term debt and firms with high profitability, where an increase in volatility reduces the firm value. The importance of short-term debt is reduced in the presence of non-negative equity net worth or debt financing constraints and firms behave more conservatively in the use of initial debt. With non-negative equity net worth, higher volatility has adverse effects on the firm value, while with debt financing constraints higher volatility may enhance firm value for firms with relatively low revenue that have out-of-the-money investment options