A convolution estimate for two-dimensional hypersurfaces

Given three transversal and sufficiently regular hypersurfaces in R^3 it follows from work of Bennett-Carbery-Wright that the convolution of two L^2 functions supported of the first and second hypersurface, respectively, can be restricted to an L^2 function on the third hypersurface, which can be considered as a nonlinear version of the Loomis-Whitney inequality. We generalize this result to a class of C^{1,beta} hypersurfaces in R^3, under scaleable assumptions. The resulting uniform L^2 estimate has applications to nonlinear dispersive equations.Comment: 21 pages, 1 figur

Global well-posedness of the energy critical Nonlinear Schr\"odinger equation with small initial data in H^1(T^3)

A refined trilinear Strichartz estimate for solutions to the Schr\"odinger equation on the flat rational torus T^3 is derived. By a suitable modification of critical function space theory this is applied to prove a small data global well-posedness result for the quintic Nonlinear Schr\"odinger Equation in H^s(T^3) for all s \geq 1. This is the first energy-critical global well-posedness result in the setting of compact manifolds.Comment: v3: 19 page

Strichartz estimates for partially periodic solutions to Schr\"odinger equations in 4d and applications

We consider the energy critical nonlinear Schr\"odinger equation on periodic domains of the form R^m x T^{4-m} with m=0,1,2,3. Assuming that a certain L^4 Strichartz estimate holds for solutions to the corresponding linear Schr\"odinger equation, we prove that the nonlinear problem is locally well-posed in the energy space. Then we verify that the L^4 estimate holds if m=2,3, leaving open the cases m=0,1.Comment: 15 page

Table of Contents and Prologue

Editorial board, Table of contents, and Prologue, an introduction to volume 1

Project for the Architecture of Transition

Death as a subject of architecture is the art of the depiction of the invisible. It transgresses the field of architectural signification delineated by utility and purpose and imposes an unavoidable need to examine and question expressive limits of architecture

eXplainable AI for Quantum Machine Learning

Parametrized Quantum Circuits (PQCs) enable a novel method for machine learning (ML). However, from a computational point of view they present a challenge to existing eXplainable AI (xAI) methods. On the one hand, measurements on quantum circuits introduce probabilistic errors which impact the convergence of these methods. On the other hand, the phase space of a quantum circuit expands exponentially with the number of qubits, complicating efforts to execute xAI methods in polynomial time. In this paper we will discuss the performance of established xAI methods, such as Baseline SHAP and Integrated Gradients. Using the internal mechanics of PQCs we study ways to speed up their computation

Aryl Ethers from Arenediazonium Tetrafluoroborate Salts: from Neat Reactions to Solvent-mediated Effects

A general procedure for the synthesis of various aryl ethers via the thermal decomposition of benzenediazonium tetrafluoroborate salts is described. Studies performed in neat alcohol at 60°C gave aryl ethers in yields ranging from 0-73%. Upon completion of a series of reactions, the effect of solvent was explored to expand the scope and relevance of this procedure. It was found that even solvents that are traditionally non-nucleophilic gave rise to products including bi-aryls and N-aryl acetamides. The utilization of an ionic liquid, l-butyl-4-methylpyridinium tetrafluoroborate, resulted in yields comparable to reactions performed in neat alcoholic solvents

Successful Treatment of Early Relapsed High-Risk AML After Allogeneic Hematopoietic Stem Cell Transplantation With Biomodulatory Therapy

Early relapse of acute myeloid leukemia (AML) after allogeneic hematopoietic stem cell transplantation (allo-HSCT) is an often unsuccessful therapeutic challenge. Since treatment options are few and efficacy is low, new approaches such as de novo allo-HSCT, targeted therapies and biomodulatory drugs have been developed, albeit prognosis is very poor. In this manuscript we present an unusual case of a patient with high-risk AML with an unbalanced jumping translocation and FLT3-TKD (low) mutation who presented with early relapse (FLT3 negative) after allo-HSCT, refractory to one cycle of azacytidine and discontinuation of immunosuppression (IS). As salvage therapy, the patient received a biomodulatory therapy consisting of low-dose azacytidine 75 mg/day (given s.c. d1-7 of 28), pioglitazone 45 mg/day orally, and all-trans-retinoic acid (ATRA) 45 mg/m(2)/day orally achieving a complete remission after two cycles of therapy. Even after cessation of treatment after 5 cycles, the patient remained in complete remission with full chimerism in peripheral blood and bone marrow for another 7 months. In conclusion, we report about an unusual case of long-lasting complete remission of early relapsed high-risk AML after allo-HSCT treated with azacytidine, pioglitazone and ATRA after standard of care treatment with HMA and discontinuation of IS failed