Mixture Selection, Mechanism Design, and Signaling

We pose and study a fundamental algorithmic problem which we term mixture selection, arising as a building block in a number of game-theoretic applications: Given a function $g$ from the $n$-dimensional hypercube to the bounded interval $[-1,1]$, and an $n \times m$ matrix $A$ with bounded entries, maximize $g(Ax)$ over $x$ in the $m$-dimensional simplex. This problem arises naturally when one seeks to design a lottery over items for sale in an auction, or craft the posterior beliefs for agents in a Bayesian game through the provision of information (a.k.a. signaling). We present an approximation algorithm for this problem when $g$ simultaneously satisfies two smoothness properties: Lipschitz continuity with respect to the $L^\infty$ norm, and noise stability. The latter notion, which we define and cater to our setting, controls the degree to which low-probability errors in the inputs of $g$ can impact its output. When $g$ is both $O(1)$-Lipschitz continuous and $O(1)$-stable, we obtain an (additive) PTAS for mixture selection. We also show that neither assumption suffices by itself for an additive PTAS, and both assumptions together do not suffice for an additive FPTAS. We apply our algorithm to different game-theoretic applications from mechanism design and optimal signaling. We make progress on a number of open problems suggested in prior work by easily reducing them to mixture selection: we resolve an important special case of the small-menu lottery design problem posed by Dughmi, Han, and Nisan; we resolve the problem of revenue-maximizing signaling in Bayesian second-price auctions posed by Emek et al. and Miltersen and Sheffet; we design a quasipolynomial-time approximation scheme for the optimal signaling problem in normal form games suggested by Dughmi; and we design an approximation algorithm for the optimal signaling problem in the voting model of Alonso and C\^{a}mara

Manipulating dc currents with bilayer bulk natural materials

The principle of transformation optics has been applied to various wave phenomena (e.g., optics, electromagnetics, acoustics and thermodynamics). Recently, metamaterial devices manipulating dc currents have received increasing attention which usually adopted the analogue of transformation optics using complicated resistor networks to mimic the inhomogeneous and anisotropic conductivities. We propose a distinct and general principle of manipulating dc currents by directly solving electric conduction equations, which only needs to utilize two layers of bulk natural materials. We experimentally demonstrate dc bilayer cloak and fan-shaped concentrator, derived from the generalized account for cloaking sensor. The proposed schemes have been validated as exact devices and this opens a facile way towards complete spatial control of dc currents. The proposed schemes may have vast potentials in various applications not only in dc, but also in other fields of manipulating magnetic field, thermal heat, elastic mechanics, and matter waves

Gray and White Matter Abnormality in Patients With T2DM-Related Cognitive Dysfunction: A Systemic Review and Meta-Analysis

Aims/hypothesis Brain structure abnormality in patients with type 2 diabetes mellitus (T2DM)-related cognitive dysfunction (T2DM-CD) has been reported for decades in magnetic resonance imaging (MRI) studies. However, the reliable results were still unclear. This study aimed to make a systemic review and meta-analysis to find the significant and consistent gray matter (GM) and white matter (WM) alterations in patients with T2DM-CD by comparing with the healthy controls (HCs). Methods Published studies were systemically searched from PubMed, MEDLINE, Cochrane Library and Web of Science databases updated to November 14, 2021. Studies reporting abnormal GM or WM between patients with T2DM-CD and HCs were selected, and their significant peak coordinates (x, y, z) and effect sizes (z-score or t-value) were extracted to perform a voxel-based meta-analysis by anisotropic effect size-signed differential mapping (AES-SDM) 5.15 software. Results Total 15 studies and 16 datasets (1550 participants) from 7531 results were involved in this study. Compared to HCs, patients with T2DM-CD showed significant and consistent decreased GM in right superior frontal gyrus, medial orbital (PFCventmed. R, BA 11), left superior temporal gyrus (STG. L, BA 48), and right calcarine fissure / surrounding cortex (CAL. R, BA 17), as well as decreased fractional anisotropy (FA) in right inferior network, inferior fronto-occipital fasciculus (IFOF. R), right inferior network, longitudinal fasciculus (ILF. R), and undefined area (32, −60, −42) of cerebellum. Meta-regression showed the positive relationship between decreased GM in PFCventmed.R and MoCA score, the positive relationship between decreased GM in STG.L and BMI, as well as the positive relationship between the decreased FA in IFOF.R and age or BMI. Conclusions/interpretation T2DM impairs the cognitive function by affecting the specific brain structures. GM atrophy in PFCventmed. R (BA 11), STG. L (BA 48), and CAL. R (BA 17), as well as WM injury in IFOF. R, ILF. R, and undefined area (32, −60, −42) of cerebellum. And those brain regions may be valuable targets for future researches. Age, BMI, and MoCA score have a potential influence on the altered GM or WM in T2DM-CD

Interplay between Cell Migration and Neurite Outgrowth Determines SH2B1β-Enhanced Neurite Regeneration of Differentiated PC12 Cells

The regulation of neurite outgrowth is crucial in developing strategies to promote neurite regeneration after nerve injury and in degenerative diseases. In this study, we demonstrate that overexpression of an adaptor/scaffolding protein SH2B1β promotes neurite re-growth of differentiated PC12 cells, an established neuronal model, using wound healing (scraping) assays. Cell migration and the subsequent remodeling are crucial determinants during neurite regeneration. We provide evidence suggesting that overexpressing SH2B1β enhances protein kinase C (PKC)-dependent cell migration and phosphatidylinositol 3-kinase (PI3K)-AKT-, mitogen activated protein kinase (MAPK)/extracellular signal-regulated protein kinase (ERK) kinase (MEK)-ERK-dependent neurite re-growth. Our results further reveal a cross-talk between pathways involving PKC and ERK1/2 in regulating neurite re-growth and cell migration. We conclude that temporal regulation of cell migration and neurite outgrowth by SH2B1β contributes to the enhanced regeneration of differentiated PC12 cells

Enhancement of the superconductivity and quantum metallic state in the thin film of superconducting Kagome metal KV3_3Sb5_5

Recently V-based Kagome metal attracted intense attention due to the emergence of superconductivity in the low temperature. Here we report the fabrication and physical investigations of the high quality single-crystalline thin films of the Kagome metal KV$_3$Sb$_5$. For the sample with the thickness of about 15 nm, the temperature dependent resistance reveals a Berezinskii-Kosterlitz-Thouless (BKT) type behavior, indicating the presence of two-dimensional superconductivity. Compared with the bulk sample, the onset transition temperature $T^{onset}_{c}$ and the out-of-plane upper critical field $H_{c2}$ are enhanced by 15\% and more than 10 times respectively. Moreover, the zero-resistance state is destroyed by a magnetic field as low as 50 Oe. Meanwhile, the temperature-independent resistance is observed in a wide field region, which is the hallmark of quantum metallic state. Our results provide evidences for the existence of unconventional superconductivity in this material.Comment: 5 pages, 4 figure

Consecutive Tumor Lysis Syndrome and Hepatic Failure after Transarterial Chemoembolization for Treatment of Hepatocellular Aarcinoma: A Case Report and Literature Review

Introduction: Acute tumor lysis syndrome (ATLS) and hepatic failure are fatal complications that can occur in patients with hepatocellular carcinoma (HCC) who undergo transarterial chemoembolization (TACE).Presentation of Case: We report the case of a 78-year-old man with HCC who had successive ATLS and hepatic failure after the first course of TACE. He succumbed due to rapid deterioration of his condition.Conclusion: We therefore concluded that awareness of the risks of ATLS and hepatic failure before administration of TACE is crucial in patients with HCC