Geology of the Northern Part of the Fra Cristobal Range, Sierra and Socorro Counties, New Mexico

The northern part of the Fra Cristobal Range contains rocks of Precambrian, Cambrian, Pennsylvanian, Permian, Cretaceous, Tertiary and Quaternary age. One of the northernmost exposures in New Mexico of the Cambrian Bliss formation occurs in the central part of the range. Here the bliss formation wedges out due to widespread pre-Pennsylvanian erosion which removed all the other lower Paleozoic rocks. The Pennsylvanian Magdalena group, which is predominately limestone, rests uncomformably on Precambrian rock and the Bliss Formation. It forms the greatest part of the sedimentary sequence and is divided into three formations; the Red House, Nakaye, and Bar B formations which represent marine transgression, maximum transgression, and marine regression respectively. Permian time is represented by the predominately clastic Abo and Yeso formations. Triassic, Jurassic, and early Cretaceous rocks are not present in the mapped area. At the north end of the Fra Cristobal Range, the Jose Creek beds of the Upper Cretacious McRae formation form a course of fanglomerate of gneissic boulders on the Precambrian granite gneiss. Northward the fanglomerate grades into the ordinary Jose Creek beds of sandstone and mudstone. These relationships indicate profound deformation and deep erosion in pre-McRae time. This area probably provides the best evidence found so far of a pre-McRae age for the beginning of strong orogeny in south-central New Mexico. At least three periods of orogeny have affected the area. These took place in Precambrian, late Cretaceous and middle and late Tertiary time. Little is known of the Precambrian deformation. The structural features which are considered to be of Laramide age form a northward-trending belt of intense deformation along the west side of the range. This belt consists of overturned folds and associate thrust faults which have been highly modified by subsequent normal and faulting erosion. The tertiary structures include open folds and high-angle normal faults trending predominately northwesterly. Later movement on the Hot Springs and Fra Cristobal faults elevated the range to its present prominence. No mining is being done within the mapped area at the present time; however, mineral deposits including a manganese deposit adjacent to the Hot Springs fault and an old mine at the head of Spring Canyon which probably produced copper. Galena is present in some of the quartz veins

Configuration Spaces, Multijet Transversality, and the Square-Peg Problem

We prove a transversality "lifting property" for compactified configuration spaces as an application of the multijet transversality theorem: given a submanifold of configurations of points on an embedding of a compact manifold $M$ in Euclidean space, we can find a dense set of smooth embeddings of $M$ for which the corresponding configuration space of points is transverse to any submanifold of the configuration space of points in Euclidean space, as long as the two submanifolds of compactified configuration space are boundary-disjoint. We use this setup to provide an attractive proof of the square-peg problem: there is a dense family of smoothly embedded circles in the plane where each simple closed curve has an odd number of inscribed squares, and there is a dense family of smoothly embedded circles in $\R^n$ where each simple closed curve has an odd number of inscribed square-like quadrilaterals.Comment: 30 pages, 5 figures. arXiv admin note: text overlap with arXiv:1402.617

Families of similar simplices inscribed in most smoothly embedded spheres

Let $\Delta$ denote a non-degenerate $k$-simplex in $\mathbb{R}^k$. The set $\text{Sim}(\Delta)$ of simplices in $\mathbb{R}^k$ similar to $\Delta$ is diffeomorphic to $O(k)\times [0,\infty)\times \mathbb{R}^k$, where the factor in $O(k)$ is a matrix called the {\em pose}. Among $(k-1)$-spheres smoothly embedded in $\mathbb{R}^k$ and isotopic to the identity, there is a dense family of spheres, for which the subset of $\text{Sim}(\Delta)$ of simplices inscribed in each embedded sphere contains a similar simplex of every pose $U\in O(k)$. Further, the intersection of $\text{Sim}(\Delta)$ with the configuration space of $k+1$ distinct points on an embedded sphere is a manifold whose top homology class maps to the top class in $O(k)$ via the pose map. This gives a high dimensional generalization of classical results on inscribing families of triangles in plane curves. We use techniques established in our previous paper on the square-peg problem where we viewed inscribed simplices in spheres as transverse intersections of submanifolds of compactified configuration spaces.Comment: 20 pages, 2 figures. arXiv admin note: text overlap with arXiv:2103.07506 New version has correct term for $k$-simplex and other minor correction

Differentials in the homological homotopy fixed point spectral sequence

We analyze in homological terms the homotopy fixed point spectrum of a T-equivariant commutative S-algebra R. There is a homological homotopy fixed point spectral sequence with E^2_{s,t} = H^{-s}_{gp}(T; H_t(R; F_p)), converging conditionally to the continuous homology H^c_{s+t}(R^{hT}; F_p) of the homotopy fixed point spectrum. We show that there are Dyer-Lashof operations beta^epsilon Q^i acting on this algebra spectral sequence, and that its differentials are completely determined by those originating on the vertical axis. More surprisingly, we show that for each class x in the $^{2r}-term of the spectral sequence there are 2r other classes in the E^{2r}-term (obtained mostly by Dyer-Lashof operations on x) that are infinite cycles, i.e., survive to the E^infty-term. We apply this to completely determine the differentials in the homological homotopy fixed point spectral sequences for the topological Hochschild homology spectra R = THH(B) of many S-algebras, including B = MU, BP, ku, ko and tmf. Similar results apply for all finite subgroups C of T, and for the Tate- and homotopy orbit spectral sequences. This work is part of a homological approach to calculating topological cyclic homology and algebraic K-theory of commutative S-algebras.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-27.abs.htm

Spectral sequences in combinatorial geometry: Cheeses, Inscribed sets, and Borsuk-Ulam type theorems

Algebraic topological methods are especially suited to determining the nonexistence of continu- ous mappings satisfying certain properties. In combinatorial problems it is sometimes possible to define a mapping from a space X of configurations to a Euclidean space Rm in which a subspace, a discriminant, often an arrangement of linear subspaces A, expresses a desirable condition on the configurations. Add symmetries of all these data under a group G for which the mapping is equivariant. Removing the discriminant leads to the problem of the existence of an equivariant mapping from X to Rm - the discriminant. Algebraic topology may be applied to show that no such mapping exists, and hence the original equivariant mapping must meet the discriminant. We introduce a general framework, based on a comparison of Leray-Serre spectral sequences. This comparison can be related to the theory of the Fadell-Husseini index. We apply the framework to: - solve a mass partition problem (antipodal cheeses) in Rd, - determine the existence of a class of inscribed 5-element sets on a deformed 2-sphere, - obtain two different generalizations of the theorem of Dold for the nonexistence of equivariant maps which generalizes the Borsuk-Ulam theorem

Spectral sequences in combinatorial geometry: Cheeses, Inscribed sets, and Borsuk-Ulam type theorems

Algebraic topological methods are especially suited to determining the nonexistence of continu- ous mappings satisfying certain properties. In combinatorial problems it is sometimes possible to define a mapping from a space X of configurations to a Euclidean space Rm in which a subspace, a discriminant, often an arrangement of linear subspaces A, expresses a desirable condition on the configurations. Add symmetries of all these data under a group G for which the mapping is equivariant. Removing the discriminant leads to the problem of the existence of an equivariant mapping from X to Rm - the discriminant. Algebraic topology may be applied to show that no such mapping exists, and hence the original equivariant mapping must meet the discriminant. We introduce a general framework, based on a comparison of Leray-Serre spectral sequences. This comparison can be related to the theory of the Fadell-Husseini index. We apply the framework to: - solve a mass partition problem (antipodal cheeses) in Rd, - determine the existence of a class of inscribed 5-element sets on a deformed 2-sphere, - obtain two different generalizations of the theorem of Dold for the nonexistence of equivariant maps which generalizes the Borsuk-Ulam theorem

Vermont School Districts Meal Service Response to COVID-19

The COVID-19 pandemic has posed many challenges worldwide, including lack of food access and security. Food insecurity in Vermont has increased from 18% to 24% since the outbreak of the pandemic. Food insecurity among families with school-aged children puts children at risk for developmental delays, poor social functioning, and poor academic performance. The goal of this project is to identify the challenges that the COVID-19 pandemic has posed for meal distribution services in school districts across Vermont, recognize the adaptations that were made by schools to address these challenges, and determine which adaptations had positive effects to encourage widespread implementation of these and other strategies to maximize food security for school-aged children nationwide.https://scholarworks.uvm.edu/comphp_gallery/1312/thumbnail.jp

Metastatic Colorectal Cancer Outcomes by Age Among ARCAD First- and Second-Line Clinical Trials

Metastatic Colorectal Cancer; OutcomesCáncer colorrectal metastásico; ResultadosCàncer colorrectal metastàtic; ResultatsBackground We evaluated the time to progression (TTP) and survival outcomes of second-line therapy for metastatic colorectal cancer among adults aged 70 years and older compared with younger adults following progression on first-line clinical trials. Methods Associations between clinical and disease characteristics, time to initial progression, and rate of receipt of second-line therapy were evaluated. TTP and overall survival (OS) were compared between older and younger adults in first- and second-line trials by Cox regression, adjusting for age, sex, Eastern Cooperative Oncology Group Performance Status, number of metastatic sites and presence of metastasis in the lung, liver, or peritoneum. All statistical tests were 2-sided. Results Older adults comprised 16.4% of patients on first-line trials (870 total older adults aged >70 years; 4419 total younger adults aged ≤70 years, on first-line trials). Older adults and those with Eastern Cooperative Oncology Group Performance Status >0 were less likely to receive second-line therapy than younger adults. Odds of receiving second-line therapy decreased by 11% for each additional decade of life in multivariable analysis (odds ratio = 1.11, 95% confidence interval = 1.02 to 1.21, P = .01). Older and younger adults enrolled in second-line trials experienced similar median TTP and median OS (median TTP = 5.1 vs 5.2 months, respectively; median OS = 11.6 vs 12.4 months, respectively). Conclusions Older adults were less likely to receive second-line therapy for metastatic colorectal cancer, though we did not observe a statistical difference in survival outcomes vs younger adults following second-line therapy. Further study should examine factors affecting decisions to treat older adults with second-line therapy. Inclusion of geriatric assessment may provide better criteria regarding the risks and benefits of second-line therapy.The National Cancer Institute Gastrointestinal Cancer Center Specialized Programs of Research Excellence (SPORE) Career Development Award (5P50CA127003-08) funded Dr McCleary’s effort. The ARCAD Foundation funded data collection and analysis