Ghost numbers of Group Algebras

Motivated by Freyd's famous unsolved problem in stable homotopy theory, the generating hypothesis for the stable module category of a finite group is the statement that if a map in the thick subcategory generated by the trivial representation induces the zero map in Tate cohomology, then it is stably trivial. It is known that the generating hypothesis fails for most groups. Generalizing work done for $p$-groups, we define the ghost number of a group algebra, which is a natural number that measures the degree to which the generating hypothesis fails. We describe a close relationship between ghost numbers and Auslander-Reiten triangles, with many results stated for a general projective class in a general triangulated category. We then compute ghost numbers and bounds on ghost numbers for many families of $p$-groups, including abelian $p$-groups, the quaternion group and dihedral $2$-groups, and also give a general lower bound in terms of the radical length, the first general lower bound that we are aware of. We conclude with a classification of group algebras of $p$-groups with small ghost number and examples of gaps in the possible ghost numbers of such group algebras.Comment: 28 pages; v2 improves introduction and has many other minor changes throughout. appears in Algebras and Representation Theory, 201

Ghost number of group algebras

The generating hypothesis for the stable module category of a finite group is the statement that if a map in the thick subcategory generated by the trivial representation induces the zero map in Tate cohomology, then it is stably trivial. It is known that the generating hypothesis fails for most groups. Generalizing work done for p-groups, we define the ghost number of a group algebra, which is a natural number that measures the degree to which the generating hypothesis fails. We describe a close relationship between ghost numbers and Auslander-Reiten triangles, with many results stated for a general projective class in a general triangulated category. We then compute ghost numbers and bounds on ghost numbers for many families of p-groups. For non-p-groups, we introduce two other closely related invariants, the simple ghost number, which considers maps which are stably trivial when composed with any map from a simple module, and the strong ghost number, which considers maps which are ghosts after restriction to every subgroup of G. We produce the first computations of the ghost number for non-p-groups. We prove that there are close relationships between the three invariants, and make computations of the new invariants for many families of groups. We also discuss how computational algebra can be applied to calculate the ghost number

Adjusting win statistics for dependent censoring

For composite outcomes whose components can be prioritized on clinical importance, the win ratio, the net benefit and the win odds apply that order in comparing patients pairwise to produce wins and subsequently win proportions. Because these three statistics are derived using the same win proportions and they test the same hypothesis of equal win probabilities in the two treatment groups, we refer to them as win statistics. These methods, particularly the win ratio and the net benefit, have received increasing attention in methodological research and in design and analysis of clinical trials. For time‐to‐event outcomes, however, censoring may introduce bias. Previous work has shown that inverse‐probability‐of‐censoring weighting (IPCW) can correct the win ratio for bias from independent censoring. The present article uses the IPCW approach to adjust win statistics for dependent censoring that can be predicted by baseline covariates and/or time‐dependent covariates (producing the CovIPCW‐adjusted win statistics). Theoretically and with examples and simulations, we show that the CovIPCW‐adjusted win statistics are unbiased estimators of treatment effect in the presence of dependent censoring

Efficacy and Safety of Low-Dose Cyclosporine with Everolimus and Steroids in de novo Heart Transplant Patients: A Multicentre, Randomized Trial

A six-month, multicenter, randomized, open-label study was undertaken to determine whether renal function is improved using reduced-exposure cyclosporine (CsA) versus standard-exposure CsA in 199 de novo heart transplant patients receiving everolimus and steroids ± induction therapy. Mean C2 levels were at the low end of the target range in standard-exposure patients (n = 100) and exceeded target range in reduced-exposure patients (n = 99) throughout the study. Mean serum creatinine at Month 6 (the primary endpoint) was 141.0 ± 53.1 μmol/L in standard-exposure patients versus 130.1 ± 53.7 μmol/L in reduced-exposure patients (P = 0.093). The incidence of biopsy-proven acute rejection ≥3A at Month 6 was 21.0% (21/100) in the standard-exposure group and 16.2% (16/99) in the reduced-exposure group (n.s.). Adverse events and infections were similar between treatment groups. Thus, everolimus with reduced-exposure CsA resulted in comparable efficacy compared to standard-exposure CsA. No renal function benefits were demonstrated; that is possibly related to poor adherence to reduced CsA exposure

Flavokawain A alleviates the progression of mouse osteoarthritis: An in vitro and in vivo study

Osteoarthritis (OA) is one of the most prevalent chronic degenerative joint diseases affecting adults in their middle or later years. It is characterized by symptoms such as joint pain, difficulty in movement, disability, and even loss of motion. Moreover, the onset and progression of inflammation are directly associated with OA. In this research, we evaluated the impact of Flavokawain A (FKA) on osteoarthritis. In-vitro effects of FKA on murine chondrocytes have been examined using cell counting kit-8 (CCK-8), safranin o staining, western blot, immunofluorescence staining, senescence β-galactosidase staining, flow cytometry analysis, and mRFP-GFP-LC3 adenovirus infection. An in-vivo model of destabilization of the medial meniscus (DMM) was employed to investigate FKA’s effect on OA mouse. An analysis of bioinformatics was performed on FKA and its potential role in OA. It was observed that FKA blocked interleukin (IL)-1β-induced expression of inflammatory factors, i.e., cyclooxygenase-2 (COX2) and inducible nitric oxide synthase (iNOS) in chondrocytes. In addition, FKA also downregulated the catabolic enzyme expression, i.e., aggrecanase-2 (ADAMTS5) and matrix metalloproteinases (MMPs), and helped in the upregulation of the anabolic protein expression, i.e., type II collagen (Col2), Aggrecan, and sry-box transcription factor 9 (SOX9). Moreover, FKA ameliorated IL-1β-triggered autophagy in chondrocytes, and it was observed that the FKA causes anti-inflammatory effects by the mitogen-activated protein kinase (MAPK) and phosphoinositide-3-kinase/Akt/mammalian target of rapamycin (PI3K/AKT/mTOR) signaling pathways inhibition. The results of immunohistochemical analysis and microcomputed tomography from the in vivo OA mouse model confirmed the therapeutic effect of FKA. Finally, we assessed the anti-arthritic impacts of FKA by conducting in vivo and in vitro analyses. We concluded that FKA can be employed as a useful therapeutic agent for OA therapy, but the findings require needs further clinical investigation

Control of lunar and Martian dust - experimental insights from artificial and natural cyanobacterial and algal crusts in the Desert of Inner Mongolia, China

Studies on the colonization of environmentally extreme ground surfaces were conducted in a Mars-like desert area of Inner Mongolia, People's Republic of China, with microalgae and cyanobacteria. We collected and mass-cultured cyanobacterial strains from these regions and investigated their ability to form desert crusts artificially. These crusts had the capacity to resist sand wind erosion after just 15 days of growth. Similar to the surface of some Chinese deserts, the surface of Mars is characterized by a layer of fine dust, which will challenge future human exploration activities, particularly in confined spaces that will include greenhouses and habitats. We discuss the use of such crusts for the local control of desert sands in enclosed spaces on Mars. These experiments suggest innovative new directions in the applied use of microbe-mineral interactions to advance the human exploration and settlement of space

Controlling fuel crossover and hydration in ultra-thin proton exchange membrane-based fuel cells using Pt-nanosheet catalysts

An ultra-thin proton exchange membrane with Pt-nanosheet catalysts was designed for a self-humidifying fuel cell running on H-2 and O-2. In this design, an ultra-thin Nation membrane was used to reduce ohmic resistance. Pt nanocatalysts were uniformly anchored on exfoliated, layered double hydroxide (LDH) nanosheets by chemical vapor deposition. After embedding Pt-LDH nanocatalysts in 9 mu m-thick Nation membranes, exfoliated LDH nanosheets effectively captured crossovered H-2 and O-2 through the membranes. Meanwhile, Pt nanocatalysts on LDH nanosheets catalyzed reactions between captured H-2 and O-2 and provided in situ hydration inside Nation membranes to maintain their proton conductivity level. Furthermore, LDH nanosheets reinforced the Nation membranes, with 181% improvement in tensile modulus and 166% improvement in yield strength. In a hydrogen fuel cell running with dry fuel, the membrane-electrode assembly employing the Pt-LDH/Nafion membrane showed an improvement of 200% in maximum power density, an increase of 197% in current density at 0.3 V and an improvement of 497% in current density at 0.5 V as compared to those with Nation 211. The Pt-LDH/Nafion membrane with a thickness of 9 mu m exhibited a combination of desirable properties for the development of affordable and durable hydrogen fuel cell technology, including better mechanical properties, higher open-circuit voltage, lower ohmic resistance and enhanced water management in a hydrogen fuel cell without external humidification