An index theorem for higher orbital integrals

Recently, two of the authors of this paper constructed cyclic cocycles on Harish-Chandra's Schwartz algebra of linear reductive Lie groups that detect all information in the $K$-theory of the corresponding group $C^*$-algebra. The main result in this paper is an index formula for the pairings of these cocycles with equivariant indices of elliptic operators for proper, cocompact actions. This index formula completely determines such equivariant indices via topological expressions.Comment: 33 page

Heat kernels of perturbed operators and index theory on G-proper manifolds

Let G be a connected, linear real reductive group and let X be a G-proper manifold without boundary. We give a detailed account of both the large and small time behaviour of the heat-kernel of perturbed Dirac operators, as a map from the positive real line to the Lafforgue algebra. As a first application, we prove that certain delocalized eta invariants associated to perturbed Dirac operators are well defined. We then prove index formulas relating these delocalized eta invariants to Atiyah-Patodi-Singer delocalized indices on G-proper manifolds with boundary. We apply these results to the definition of rho-numbers associated to G-homotopy equivalences between closed G-proper manifolds and to the study of their bordism properties.Comment: This article contains an updated and extended version of part of arXiv:210800982(v2). It is independent of arXiv:210800982(v3), and the two papers together supersede arXiv:210800982(v2). The discussion of perturbations of Dirac operators in arXiv:210800982(v2) is corrected and included in this articl

Abietic acid attenuates LPS-induced acute lung injury by restoring Th17/Treg balance

Purpose: To investigate the mechanism of action and effects of abietic acid (AA) in a mouse acute lung injury (ALI) model. Methods: A mouse ALI model was established by lipopolysaccharide (LPS) induction. Lung tissues were examined for histological alterations and scored based on the degree of injury. Myeloperoxidase (MPO), IL-6, IL-1β, and TNF-α levels were measured by enzyme-linked immunosorbent assay (ELISA) while the numbers of Th17 and Treg cells were assessed by immunofluorescence. Protein expression levels of p-STAT3, p-STAT5, RORrt, and FOXP3 were analyzed by immunoblot assay. Expression of peroxisome proliferator-activated receptor γ (PPARγ) was assessed by immunoblot. Results: AA ameliorated LPS-induced lung injury in mice. Furthermore, AA ameliorated LPS-induced pneumonia in mice (p < 0.05) and restored Th17/Treg balance and Th17/Treg transcription factor expression that was altered by LPS induction. AA also activated PPARγ expression to restore Th17/Treg balance (p < 0.05). Conclusion: The results indicate that AA attenuates LPS-induced ALI in mice by restoring Th17/Treg balance. Thus, AA is a potential drug for the management of ALI; however, AA must first be evaluated in clinical studies

A Novel Model of Atherosclerosis in Rabbits Using Injury to Arterial Walls Induced by Ferric Chloride as Evaluated by Optical Coherence Tomography as well as Intravascular Ultrasound and Histology

This study aim was to develop a new model of atherosclerosis by FeCl3-induced injury to right common carotid arteries (CCAs) of rabbits. Right CCAs were induced in male New Zealand White rabbits (n = 15) by combination of a cholesterol-rich diet and FeCl3-induced injury to arterial walls. The right and left CCAs were evaluated by histology and in vivo intravascular ultrasound (IVUS) and optical coherence tomography (OCT) examinations of 24 hours (n = 3), 8 weeks (n = 6), and 12 weeks (n = 6) after injury. Each right CCA of the rabbits showed extensive white-yellow plaques. At eight and 12 weeks after injury, IVUS, OCT, and histological findings demonstrated that the right CCAs had evident eccentric plaques. Six plaques (50%) with evident positive remodeling were observed. Marked progression was clearly observed in the same plaque at 12 weeks after injury when it underwent repeat OCT and IVUS. We demonstrated, for the first time, a novel model of atherosclerosis induced by FeCl3. The model is simple, fast, inexpensive, and reproducible and has a high success rate. The eccentric plaques and remodeling of plaques were common in this model. We successfully carried out IVUS and OCT examinations twice in the same lesion within a relatively long period of time

Thermodynamic Stabilities of Perfect and Vacancy-Defected Li2 TiO3 (001) Surfaces From First-Principles Analyses

Lithium titanate (Li2TiO3) is an attractive ceramic material for various industrial applications, particularly as one of the most promising breeder blanket materials in future nuclear-fusion reactors. Previously reported studies mainly focus on sintered polycrystalline samples of Li2TiO3. Surface structure of the single-crystal form is rarely reported, although the information of surface structures and stabilities can be critical for further understanding the surface-associated processes. In this work, we perform extensive first-principles density-functional-theory (DFT) calculations to obtain the surface energies of Li2TiO3 (001) with different surface terminations. For four perfect (defect-free) Li-, O-, or LiTi-terminated (001) surfaces, Li- or O-terminated (001) surfaces can be most stable in limited chemical-potential ranges corresponding to certain experimental conditions, while a LiTi-terminated (001) surface is always unfavorable relative to Li or O terminations. By calculating the total energies of various possible configurations with surface vacancies, we determine the energetically most favorable vacancy-defected surface terminations. From the corresponding ternary phase diagram, we analyze the stability of a specific surface termination with vacancies as well as the possible formation of oxides. Our stability analysis together with DFT-simulated STM images reveals that a 1/3-monolayer-Li-terminated surface most likely corresponds to the ordered hexagonal-like pattern observed previously in STM experiments. For a 1/2-monolayer-Li-terminated surface, the most stable surface structure from our DFT calculations contrasts with previous results from an empirical-potential model

Accelerated Li⁺ Desolvation for Diffusion Booster Enabling Low‐Temperature Sulfur Redox Kinetics via Electrocatalytic Carbon‐Grazfted‐CoP Porous Nanosheets

Lithium–sulfur (Li–S) batteries are famous for their high energy density and low cost, but prevented by sluggish redox kinetics of sulfur species due to depressive Li ion diffusion kinetics, especially under low-temperature environment. Herein, a combined strategy of electrocatalysis and pore sieving effect is put forward to dissociate the Li+ solvation structure to stimulate the free Li+ diffusion, further improving sulfur redox reaction kinetics. As a protocol, an electrocatalytic porous diffusion-boosted nitrogen-doped carbon-grafted-CoP nanosheet is designed via forming the NCoP active structure to release more free Li+ to react with sulfur species, as fully investigated by electrochemical tests, theoretical simulations and in situ/ex situ characterizations. As a result, the cells with diffusion booster achieve desirable lifespan of 800 cycles at 2 C and excellent rate capability (775 mAh g−1 at 3 C). Impressively, in a condition of high mass loading or low-temperature environment, the cell with 5.7 mg cm−2 stabilizes an areal capacity of 3.2 mAh cm−2 and the charming capacity of 647 mAh g−1 is obtained under 0 °C after 80 cycles, demonstrating a promising route of providing more free Li ions toward practical high-energy Li–S batteries

Synthesis and Biological Evaluation of Novel Allobetulon/Allobetulin–Nucleoside Conjugates as AntitumorAgents

Allobetulin is structurally similar tobetulinic acid, inducing the apoptosis of cancer cells with low toxicity. However, both of them exhibited weak antiproliferation against several tumor cell lines. Therefore, the new series of allobetulon/allobetulin–nucleoside conjugates 9a–10i were designed and synthesized for potency improvement. Compounds 9b, 9e, 10a, and 10d showed promising antiproliferative activity toward six tested cell lines, compared to zidovudine, cisplatin, and oxaliplatin based on their antitumor activity results. Among them, compound 10d exhibited much more potent antiproliferative activity against SMMC-7721, HepG2, MNK-45, SW620, and A549 human cancer cell lines than cisplatin and oxaliplatin. In the preliminary study for the mechanism of action, compound 10d induced cell apoptosis and autophagy in SMMC cells, resulting in antiproliferation and G0/G1 cell cycle arrest by regulating protein expression levels of Bax, Bcl-2, and LC3. Consequently, the nucleoside-conjugated allobetulin (10d) evidenced that nucleoside substitution was a viable strategy to improve allobetulin/allobetulon’s antitumor activity based on our present study

ENIGMA and global neuroscience: A decade of large-scale studies of the brain in health and disease across more than 40 countries

This review summarizes the last decade of work by the ENIGMA (Enhancing NeuroImaging Genetics through Meta Analysis) Consortium, a global alliance of over 1400 scientists across 43 countries, studying the human brain in health and disease. Building on large-scale genetic studies that discovered the first robustly replicated genetic loci associated with brain metrics, ENIGMA has diversified into over 50 working groups (WGs), pooling worldwide data and expertise to answer fundamental questions in neuroscience, psychiatry, neurology, and genetics. Most ENIGMA WGs focus on specific psychiatric and neurological conditions, other WGs study normal variation due to sex and gender differences, or development and aging; still other WGs develop methodological pipelines and tools to facilitate harmonized analyses of "big data" (i.e., genetic and epigenetic data, multimodal MRI, and electroencephalography data). These international efforts have yielded the largest neuroimaging studies to date in schizophrenia, bipolar disorder, major depressive disorder, post-traumatic stress disorder, substance use disorders, obsessive-compulsive disorder, attention-deficit/hyperactivity disorder, autism spectrum disorders, epilepsy, and 22q11.2 deletion syndrome. More recent ENIGMA WGs have formed to study anxiety disorders, suicidal thoughts and behavior, sleep and insomnia, eating disorders, irritability, brain injury, antisocial personality and conduct disorder, and dissociative identity disorder. Here, we summarize the first decade of ENIGMA's activities and ongoing projects, and describe the successes and challenges encountered along the way. We highlight the advantages of collaborative large-scale coordinated data analyses for testing reproducibility and robustness of findings, offering the opportunity to identify brain systems involved in clinical syndromes across diverse samples and associated genetic, environmental, demographic, cognitive, and psychosocial factors