Morse theory of the moment map for representations of quivers

The results of this paper concern the Morse theory of the norm-square of the moment map on the space of representations of a quiver. We show that the gradient flow of this function converges, and that the Morse stratification induced by the gradient flow co-incides with the Harder-Narasimhan stratification from algebraic geometry. Moreover, the limit of the gradient flow is isomorphic to the graded object of the Harder-Narasimhan-Jordan-H\"older filtration associated to the initial conditions for the flow. With a view towards applications to Nakajima quiver varieties we construct explicit local co-ordinates around the Morse strata and (under a technical hypothesis on the stability parameter) describe the negative normal space to the critical sets. Finally, we observe that the usual Kirwan surjectivity theorems in rational cohomology and integral K-theory carry over to this non-compact setting, and that these theorems generalize to certain equivariant contexts.Comment: 48 pages, small revisions from previous version based on referee's comments. To appear in Geometriae Dedicat

Viologen-immobilized 2D polymer film enabling highly efficient electrochromic device for solar-powered smart window

Electrochromic devices (ECDs) have emerged as a unique class of optoelectronic devices for the development of smart windows. However, current ECDs typically suffer from low coloration efficiency (CE) and high energy consumption, which have thus hindered their practical applications, especially as components in solar-powered EC windows. Here, the high-performance ECDs with a fully crystalline viologen-immobilized 2D polymer (V2DP) thin film as the color-switching layer is demonstrated. The high density of vertically oriented pore channels (pore size approximate to 4.5 nm; pore density approximate to 5.8 x 1016 m-2) in the synthetic V2DP film enables high utilization of redox-active viologen moieties and benefits for Li+ ion diffusion/transport. As a result, the as-fabricated ECDs achieve a rapid switching speed (coloration, 2.8 s; bleaching, 1.2 s), and a high CE (989 cm2 C-1, and low energy consumption (21.1 µW cm-2). Moreover, it is managed to fabricate transmission-tunable, self-sustainable EC window prototypes by vertically integrating the V2DP ECDs with transparent solar cells. This work sheds light on designing electroactive 2D polymers with molecular precision for optoelectronics and paves a practical route toward developing self-powered EC windows to offset the electricity consumption of buildings

Metabolism of 2,4-dichlorophenoxyacetic acid, 4-chloro-2-methylphenoxyacetic acid and 2-methylphenoxyacetic acid by Alcaligenes eutrophus JMP 134

Of eleven substituted phenoxyacetic acids tested, only three (2,4-dichloro-, 4-chloro-2-methyl- and 2-methylphenoxyacetic acid) served as growth substrates for Alcaligenes eutrophus JMP 134. Whereas only one enzyme seems to be responsible for the initial cleavage of the ether bond, there was evidence for the presence of three different phenol hydroxylases in this strain. 3,5-Dichlorocatechol and 5-chloro-3-methylcatechol, metabolites of the degradation of 2,4-dichlorophenoxyacetic acid and 4-chloro-2-methylphenoxyacetic acid, respectively, were exclusively metabolized via the ortho-cleavage pathway. 2-Methylphenoxyacetic acid-grown cells showed simultaneous induction of meta- and ortho-cleavage enzymes. Two catechol 1,2-dioxygenases responsible for ortho-cleavage of the intermediate catechols were partially purified and characterized. One of these enzymes converted 3,5-dichlorocatechol considerably faster than catechol or 3-chlorocatechol. A new enzyme for the cycloisomerisation of muconates was found, which exhibited high activity against the ring-cleavage products of 3,5-dichlorocatechol and 4-chlorocatechol, but low activities against 2-chloromuconate and muconate

Functional Scaffold‐Free Bone Equivalents Induce Osteogenic and Angiogenic Processes in a Human In Vitro Fracture Hematoma Model

After trauma, the formed fracture hematoma within the fracture gap contains all the important components (immune/stem cells, mediators) to initiate bone regeneration immediately. Thus, it is of great importance but also the most susceptible to negative influences. To study the interaction between bone and immune cells within the fracture gap, up-to-date in vitro systems should be capable of recapitulating cellular and humoral interactions and the physicochemical microenvironment (eg, hypoxia). Here, we first developed and characterized scaffold-free bone-like constructs (SFBCs), which were produced from bone marrow-derived mesenchymal stromal cells (MSCs) using a macroscale mesenchymal condensation approach. SFBCs revealed permeating mineralization characterized by increased bone volume (mu CT, histology) and expression of osteogenic markers (RUNX2, SPP1, RANKL). Fracture hematoma (FH) models, consisting of human peripheral blood (immune cells) mixed with MSCs, were co-cultivated with SFBCs under hypoxic conditions. As a result, FH models revealed an increased expression of osteogenic (RUNX2, SPP1), angiogenic (MMP2, VEGF), HIF-related (LDHA, PGK1), and inflammatory (IL6, IL8) markers after 12 and 48 hours co-cultivation. Osteogenic and angiogenic gene expression of the FH indicate the osteoinductive potential and, thus, the biological functionality of the SFBCs. IL-6, IL-8, GM-CSF, and MIP-1 beta were detectable within the supernatant after 24 and 48 hours of co-cultivation. To confirm the responsiveness of our model to modifying substances (eg, therapeutics), we used deferoxamine (DFO), which is well known to induce a cellular hypoxic adaptation response. Indeed, DFO particularly increased hypoxia-adaptive, osteogenic, and angiogenic processes within the FH models but had little effect on the SFBCs, indicating different response dynamics within the co-cultivation system. Therefore, based on our data, we have successfully modeled processes within the initial fracture healing phase in vitro and concluded that the cross-talk between bone and immune cells in the initial fracture healing phase is of particular importance for preclinical studies. (c) 2021 American Society for Bone and Mineral Research (ASBMR)

The Value of Early Tumor Size Response to Chemotherapy in Pediatric Rhabdomyosarcoma

Rhabdomyosarcoma is the most common soft tissue sarcoma in childhood. Results of clinical trials, with three-year event-free and overall survival as primary outcomes, often take 7 to 10 years. Identification of an early surrogate biomarker, predictive for survival, is therefore crucial. We conducted a systematic review to define the prognostic value of early tumor size response in children with IRSG group III rhabdomyosarcoma. The search included MEDLINE/EMBASE from inception to 18 November 2020. In total, six studies were included, describing 2010 patients, and assessed by the Quality in Prognosis Studies (QUIPS) instrument. Four studies found no prognostic value for tumor size response, whereas two studies reported a prognostic effect. In these two studies, the survival rate of patients with progressive disease was not separately analyzed from patients with stable disease, potentially explaining the difference in study outcome. In conclusion, our findings support that early progression of disease is associated with poorer survival, justifying adaptation of therapy. However, in patients with non-progressive disease, there is no evidence that the degree of response is a prognostic marker for survival. Because the vast majority of patients do not have progressive disease, early tumor size response should be reconsidered for assessment of treatment efficacy. Therefore, at present, early surrogate biomarkers for survival are still lacking

Volume loss from inaccurate sawing

This report originally published in Southern Lumberman, Sept. 15, 1954