Detecting orbits along subvarieties via the moment map

Let G be a (real or complex) linear reductive algebraic group acting on an affine variety V . Let W be a subvariety. In this work we study how the G-orbits intersect W. We develop a criterion to determine when the intersection can be described as a finite union of orbits of a reductive subgroup. The conditions of the criterion are easily verified in practice and are used to develop techniques to study left-invariant Ricci soliton metrics on nilpotent Lie groups. A nilpotent Lie group is called an Einstein nilradical if it admits a left-invariant Ricci soliton metric. Applying the techniques developed, we show that the classification of Einstein nilradicals can be reduced to the class of so-called indecomposable groups. Among other applications, we construct arbitrarily large continuous families of (non-isomorphic) nilpotent Lie groups which do not admit left-invariant Ricci soliton metrics. The note finishes by applying our techniques to the adjoint representation of reductive Lie groups. The classical result of finiteness of nilpotent orbits is reproved and it is shown that each of these orbits contains a critical point of the norm squared of the moment map

Drawing Upon Our Roots and Charism to Address Climate Change and Build Bridges of Dialogue in Addressing Human Rights and Achieving an Integral Ecology

Although sustainability and human rights are interconnected expressions of Catholic social teaching, the fields and praxis have developed independently. Human rights and other justice issues are rooted in the humanities and social sciences. The idea of sustainability has roots in the humanities and social sciences, but also in natural science and engineering. While sustainability research by scientists and engineers receives support, it is lacking for consideration of human rights and justice concerns, largely because these are viewed as advocacy. More recently, the intersection of these areas, particularly in the examination of the impacts of global climate change, has provided an opportunity for unification, especially when human stories lend empathy to observations, provide motivation to action, and allow technical expertise to help alleviate injustice. Faith-based organizations are positioned to be bridge-builders by inviting the expertise of environmental scientists in educational programs. Pope Francis’ Laudato Si\u27 received warm reception by numerous scientific organizations, and its call for all fields to work towards an integral ecology through dialogue is an impetus for interconnection. The longstanding tradition of Catholic institutions in addressing social concerns and the integration inherent in Catholic intellectual tradition invite opportunities for the integration of divergent fields of knowledge in the practices of sustainability and human rights. As a Catholic and Marianist institution, the University of Dayton draws on its founding charism by seeing all as members of one global family and by extending the concept of community from people to ecosystems. We offer opportunities to engage in dialogues among expert panelists, a diverse campus, and the local community to explore justice issues like hunger, environmental racism, and peace. Applying the spiritualities, vision, and behavior of the founders of our religious institutions to today’s needs can help us to educate, act, and advocate for an integral ecological future together

Assessment of institutional barriers to the use of natural gas fuel in automotive vehicle fleets

Institutional barriers to the use of natural gas as a fuel for motor vehicle fleets were identified. Recommendations for barrier removal were developed. Eight types of institutional barriers were assessed: (1) lack of a national standard for the safe design and certification of natural gas vehicles and refueling stations; (2) excessively conservative or misapplied state and local regulations, including bridge and tunnel restrictions, restrictions on types of vehicles that may be fueled by natural gas, zoning regulations that prohibit operation of refueling stations, parking restrictions, application of LPG standards to LNG vehicles, and unintentionally unsafe vehicle or refueling station requirements; (3) need for clarification of EPA's tampering enforcement policy; (4) the U.S. hydrocarbon standard; (5) uncertainty concerning state utility commission jurisdiction; (6) sale for resale prohibitions imposed by natural gas utility companies or state utility commissions; (7) uncertainty of the effects of conversions to natural gas on vehicle manufactures warranties; and (8) need for a natural gas to gasoline equivalent units conversion factor for use in calculation of state road use taxes

Presence of rd8 mutation does not alter the ocular phenotype of late-onset retinal degeneration mouse model.

PurposeA spontaneous frameshift mutation, c.3481delC, in the Crb1 gene is the underlying cause of dysplasia and retinal degeneration in rd8 mice. The rd8 mutation is found in C57BL/6N but not in C57BL/6J mouse sub-strains. The development of ocular pathology in single knockout Ccl2-/-, Cx3cr1-/- and in double knockout Ccl2-/-, Cx3cr1-/- mice raised on a C57BL/6 background has been reported to depend on the presence of a rd8 mutation. In this study, we investigated the influence of the rd8 mutation on the retinal pathology that we previously described in the late-onset retinal degeneration (L-ORD) mouse model with a heterozygous S163R mutation in the C1q-tumor necrosis factor-related protein-5Ctrp5+/- gene that was generated on a C57BL/6J background.MethodsMouse lines carrying the Ctrp5 S163R and rd8 mutations (Ctrp5+/-;rd8/rd8), corresponding controls without the rd8 mutation (Ctrp5+/-;wt/wt), and wild-type mice with and without the rd8 mutation (Wtrd8/rd8 and Wtwt/wt, respectively) were generated by systematic breeding of mice in our L-ORD mouse colony. Genotyping the mice for the rd8 (del C at nt3481 in Crb1) and Ctrp5 S163R mutations was performed with allelic PCR or sequencing. Retinal morphology was studied with fundus imaging, histology, light microscopy, electron microscopy, and immunohistochemistry.ResultsGenotype analysis of the mice in L-ORD mouse colony detected the rd8 mutation in the homozygous and heterozygous state. Fundus imaging of wild-type mice without the rd8 mutation (Wtwt/wt) revealed no autofluorescence (AF) spots up to 6-8 months and few AF spots at 21 months. However, the accumulation of AF lesions accelerated with age in the Ctrp5+/- mice that lack the rd8 mutation (Ctrp5+/-;wt/wt). The number of AF lesions was significantly increased (p<0.001), and they were small and uniformly distributed throughout the retina in the 21-month-old Ctrp5+/-;wt/wt mice when compared to the age-matched controls. Wild-type and Ctrp5+/- mice with the rd8 mutation (Wtrd8/rd8 and Ctrp5+/-;rd8/rd8, respectively) revealed an integrated retinal architecture with well-defined outer segments/inner segments (OS/IS), outer nuclear layer (ONL), outer plexiform layer (OPL), and inner nuclear layer (INL). The presence of pseudorosette structures reported in the rd8 mice between the ONL and the INL in the ventral quadrant of the retina was not observed in all genotypes studied. Further, the external limiting membrane was continuous in the Ctrp5+/-;rd8/rd8 and Wtrd8/rd8 mice. Evaluation of the retinal phenotype revealed that the Ctrp5+/-;wt/wt mice developed characteristic L-ORD pathology including age-dependent accumulation of AF spots, development of sub-retinal, sub-RPE, and basal laminar deposits, and Bruch's membrane abnormalities at older age, while these changes were not observed in the age-matched littermate WTwt/wt mice.ConclusionsThe Wtrd8/rd8 and Ctrp5+/-;rd8/rd8 mice raised on C57BL/6J did not develop early onset retinal changes that are characteristic of the rd8 phenotype, supporting the hypothesis that manifestation of rd8-associated pathology depends on the genetic background. The retinal pathology observed in mice with the Ctrp5+/-;wt/wt genotype is consistent with the L-ORD phenotype observed in patients and with the phenotype we described previously. The lack of rd8-associated retinal pathology in the Ctrp5+/-;wt/wt mouse model raised on the C57BL/6J background and the development of the L-ORD phenotype in these mice in the presence and absence of the rd8 mutation suggests that the pathology observed in the Ctrp5+/-;wt/wt mice is primarily associated with the S163R mutation in the Ctrp5 gene

Ecological structure of diversity-dependent diversification in Phanerozoic marine bivalves

Rigorous analysis of diversity-dependence—the hypothesis that the rate of proliferation of new species is inversely related to standing diversity—requires consideration of the ecology of the organisms in question. Differences between infaunal marine bivalves (living entirely within the sediment) and epifaunal forms (living partially or completely above the sediment–water interface) predict that these major ecological groups should have different diversity dynamics: epifaunal species may compete more intensely for space and be more susceptible to predation and physical disturbance. By comparing detrended standing diversity with rates of diversification, origination, and extinction in this exceptional fossil record, we find that epifaunal bivalves experienced significant, negative diversity-dependence in origination and net diversification, whereas infaunal forms show little appreciable relationship between diversity and evolutionary rates. This macroevolutionary contrast is robust to the time span over which dynamics are analysed, whether mass-extinction rebounds are included in the analysis, the treatment of stratigraphic ranges that are not maximally resolved, and the details of detrending. We also find that diversity-dependence persists over hundreds of millions of years, even though diversity itself rises nearly exponentially, belying the notion that diversity-dependence must imply equilibrial diversity dynamics

Automatic detection and counting of retina cell nuclei using deep learning

The ability to automatically detect, classify, calculate the size, number, and grade of retinal cells and other biological objects is critically important in eye disease like age-related macular degeneration (AMD). In this paper, we developed an automated tool based on deep learning technique and Mask R-CNN model to analyze large datasets of transmission electron microscopy (TEM) images and quantify retinal cells with high speed and precision. We considered three categories for outer nuclear layer (ONL) cells: live, intermediate, and pyknotic. We trained the model using a dataset of 24 samples. We then optimized the hyper-parameters using another set of 6 samples. The results of this research, after applying to the test datasets, demonstrated that our method is highly accurate for automatically detecting, categorizing, and counting cell nuclei in the ONL of the retina. Performance of our model was tested using general metrics: general mean average precision (mAP) for detection; and precision, recall, F1-score, and accuracy for categorizing and counting.Comment: 13 pages, 11 figures, 2 tables, SPIE. Medical Imaging 2020 Conferenc