On space-time quasiconcave solutions of the heat equation

In this paper we first obtain a constant rank theorem for the second fundamental form of the space-time level sets of a space-time quasiconcave solution of the heat equation. Utilizing this constant rank theorem, we can obtain some strictly convexity results of the spatial and space-time level sets of the space-time quasiconcave solution of the heat equation in a convex ring. To explain our ideas and for completeness, we also review the constant rank theorem technique for the space-time Hessian of space-time convex solution of heat equation and for the second fundamental form of the convex level sets for harmonic function

Aspects of higher-point functions in BCFTd_d

We study three-point correlation functions of scalar operators in conformal field theories with boundaries and interfaces. We focus on two cases where there are one bulk and two boundary operators (B$\partial\partial$), or two bulk and one boundary operators (BB$\partial$). We perform a detailed analysis of the conformal blocks in different OPE channels. In particular, we obtain the bulk channel conformal blocks of the BB$\partial$ three-point functions for arbitrary exchanged spins in a series expansion with respect to the radial coordinates. We also study examples of such three-point functions in the simplest holographic dual where the $AdS_{d+1}$ space contains a brane filling an $AdS_d$ subspace. Such a setup arises in top-down models with probe branes and is also relevant for the functional approach to boundary and interface CFT correlators. We systematically study the Witten diagrams in this setup both in position space and in Mellin space. We also discuss in detail how to decompose these Witten diagrams into conformal blocks.Comment: v1: 69 pages, 10 figures, 1 Mathematica notebook; v2: published versio

Defect two-point functions in 6d (2,0) theories

We consider correlation functions in 6d $(2,0)$ theories of two $\frac{1}{2}$-BPS operators inserted away from a $\frac{1}{2}$-BPS surface defect. In the large central charge limit the leading connected contribution corresponds to sums of tree-level Witten diagram in AdS$_7\times$S$^4$ in the presence of an AdS$_3$ defect. We show that these correlators can be uniquely determined by imposing only superconformal symmetry and consistency conditions, eschewing the details of the complicated effective Lagrangian. We explicitly compute all such two-point functions. The result exhibits remarkable hidden simplicity.Comment: 7 pages, 1 figure, 1 table, 1 ancillary Mathematica noteboo

Generative artificial intelligence-enabled dynamic detection of nicotine-related circuits

The identification of addiction-related circuits is critical for explaining addiction processes and developing addiction treatments. And models of functional addiction circuits developed from functional imaging are an effective tool for discovering and verifying addiction circuits. However, analyzing functional imaging data of addiction and detecting functional addiction circuits still have challenges. We have developed a data-driven and end-to-end generative artificial intelligence(AI) framework to address these difficulties. The framework integrates dynamic brain network modeling and novel network architecture networks architecture, including temporal graph Transformer and contrastive learning modules. A complete workflow is formed by our generative AI framework: the functional imaging data, from neurobiological experiments, and computational modeling, to end-to-end neural networks, is transformed into dynamic nicotine addiction-related circuits. It enables the detection of addiction-related brain circuits with dynamic properties and reveals the underlying mechanisms of addiction

Stromal microenvironment processes unveiled by biological component analysis of gene expression in xenograft tumor models

<p>Abstract</p> <p>Background</p> <p>Mouse xenograft models, in which human cancer cells are implanted in immune-suppressed mice, have been popular for studying the mechanisms of novel therapeutic targets, tumor progression and metastasis. We hypothesized that we could exploit the interspecies genetic differences in these experiments. Our purpose is to elucidate stromal microenvironment signals from probes on human arrays unintentionally cross-hybridizing with mouse homologous genes in xenograft tumor models.</p> <p>Results</p> <p>By identifying cross-species hybridizing probes from sequence alignment and cross-species hybridization experiment for the human whole-genome arrays, deregulated stromal genes can be identified and then their biological significance were predicted from enrichment studies. Comparing these results with those found by the laser capture microdissection of stromal cells from tumor specimens resulted in the discovery of significantly enriched stromal biological processes.</p> <p>Conclusions</p> <p>Using this method, in addition to their primary endpoints, researchers can leverage xenograft experiments to better characterize the tumor microenvironment without additional costs. The Xhyb probes and R script are available at <url>http://www.lussierlab.org/publications/Stroma</url></p