Fourier duality in the Brascamp-Lieb inequality

It was observed recently in work of Bez, Buschenhenke, Cowling, Flock and the first author, that the euclidean Brascamp-Lieb inequality satisfies a natural and useful Fourier duality property. The purpose of this paper is to establish an appropriate discrete analogue of this. Our main result identifies the Brascamp-Lieb constants on (finitely-generated) discrete abelian groups with Brascamp-Lieb constants on their (Pontryagin) duals. As will become apparent, the natural setting for this duality principle is that of locally compact abelian groups, and this raises basic questions about Brascamp-Lieb constants formulated in this generality.Comment: 22 page

Bochner-Riesz mean for the twisted Laplacian in R2\mathbb R^2

We study the Bochner-Riesz problem for the twisted Laplacian $\mathcal L$ on $\mathbb R^2$. For $p\in [1, \infty]\setminus\{2\}$, it has been conjectured that the Bochner-Riesz means $S_\lambda^\delta(\mathcal L) f$ of order $\delta$ converges in $L^p$ for every $f\in L^p$ if and only if $\delta> \max(0,|(p-2)/p|-1/2)$. We prove the conjecture by obtaining uniform $L^p$ bounds on $S_\lambda^\delta(\mathcal L)$ up to the sharp summability indices.Comment: 15 page

Bounds on the Hermite spectral projection operator

We study $L^p$-$L^q$ bounds on the spectral projection operator $\Pi_\lambda$ associated to the Hermite operator $H=|x|^2-\Delta$ in $\mathbb R^d$. We are mainly concerned with a localized operator $\chi_E\Pi_\lambda\chi_E$ for a subset $E\subset\mathbb R^d$ and undertake the task of characterizing the sharp $L^p$--$L^q$ bounds. We obtain sharp bounds in extended ranges of $p,q$. First, we provide a complete characterization of the sharp $L^p$--$L^q$ bounds when $E$ is away from $\sqrt{\lambda}\mathbb S^{d-1}$. Secondly, we obtain the sharp bounds as the set $E$ gets close to $\sqrt\lambda\mathbb S^{d-1}$. Thirdly, we extend the range of $p,q$ for which the operator $\Pi_\lambda$ is uniformly bounded from $L^p(\mathbb R^d)$ to $L^q(\mathbb R^d)$.Comment: The paper is a modified version of a part of the paper Hermite spectral projection operator (arXiv:2006.11762v3). The previous paper will remain unpublishe

Multisensory Facial Stimulation Implicitly Improves Evaluations of the Goodness of Attractive Others

It has been well demonstrated that shared multisensory experiences between the self and others can influence the social perception of out-group members. Previous research has shown that the illusion of ownership over a dark-skinned rubber hand or full virtual body generated less negative implicit bias against people with dark skin. However, less is known about how perceived attractiveness difference between self and other affects social perception toward those others after shared multisensory experience. The present study assessed whether shared multisensory experience between the self and attractive others would affect the implicit evaluation of goodness of others. Seventy-three women participated in the study. After the visuotactile multisensory stimulation procedure, participants were administered the Single Category Implicit Association Test (SC-IAT), which presents two attributes (good and bad) and one concept (other). Results showed that the more attractive the faces are, the more positive their implicit evaluation becomes after the synchronous tactile stimulation. This result suggests that shared multisensory experience makes people feel more positive toward others who have positive attribute. This finding suggests that self-other blurring in social contexts might be a compelling factor in evaluating other people positively

Lactate oxidase/catalase-displaying nanoparticles efficiently consume lactate in the tumor microenvironment to effectively suppress tumor growth

<jats:title>Abstract</jats:title><jats:p>The aggressive proliferation of tumor cells often requires increased glucose uptake and excessive anaerobic glycolysis, leading to the massive production and secretion of lactate to form a unique tumor microenvironment (TME). Therefore, regulating appropriate lactate levels in the TME would be a promising approach to control tumor cell proliferation and immune suppression. To effectively consume lactate in the TME, lactate oxidase (LOX) and catalase (CAT) were displayed onto <jats:italic>Aquifex aeolicus</jats:italic> lumazine synthase protein nanoparticles (AaLS) to form either AaLS/LOX or AaLS/LOX/CAT. These complexes successfully consumed lactate produced by CT26 murine colon carcinoma cells under both normoxic and hypoxic conditions. Specifically, AaLS/LOX generated a large amount of H<jats:sub>2</jats:sub>O<jats:sub>2</jats:sub> with complete lactate consumption to induce drastic necrotic cell death regardless of culture condition. However, AaLS/LOX/CAT generated residual H<jats:sub>2</jats:sub>O<jats:sub>2</jats:sub>, leading to necrotic cell death only under hypoxic condition similar to the TME. While the local administration of AaLS/LOX to the tumor site resulted in mice death, that of AaLS/LOX/CAT significantly suppressed tumor growth without any severe side effects. AaLS/LOX/CAT effectively consumed lactate to produce adequate amounts of H<jats:sub>2</jats:sub>O<jats:sub>2</jats:sub> which sufficiently suppress tumor growth and adequately modulate the TME, transforming environments that are favorable to tumor suppressive neutrophils but adverse to tumor-supportive tumor-associated macrophages. Collectively, these findings showed that the modular functionalization of protein nanoparticles with multiple metabolic enzymes may offer the opportunity to develop new enzyme complex-based therapeutic tools that can modulate the TME by controlling cancer metabolism.</jats:p> <jats:p><jats:bold>Graphical Abstract</jats:bold></jats:p&gt