Goodwillie calculus and I

We study the implications of using the indexing category of finite sets and injective maps in Goodwillie's calculus of homotopy functors. By careful analysis of the cross-effects of a reduced endofunctor of based spaces, this point of view leads to a monoidal model for the derivatives. Such structure induces operad and module structures for derivatives of monads and their modules, leading to a chain rule for higher derivatives. We also define a category through which n-excisive finitary functors to spectra factor, up to homotopy, and give a classification of such functors as modules over a certain spectral monoid

Unbased calculus for functors to chain complexes

Recently, the Johnson-McCarthy discrete calculus for homotopy functors was extended to include functors from an unbased simplicial model category to spectra. This paper completes the constructions needed to ensure that there exists a discrete calculus tower for functors from an unbased simplicial model category to chain complexes over a fixed commutative ring. Much of the construction of the Taylor tower for functors to spectra carries over to this context. However, one of the essential steps in the construction requires proving that a particular functor is part of a cotriple. For this, one needs to prove that certain identities involving homotopy limits hold up to isomorphism, rather than just up to weak equivalence. As the target category of chain complexes is not a simplicial model category, the arguments for functors to spectra need to be adjusted for chain complexes. In this paper, we take advantage of the fact that we can construct an explicit model for iterated fibers, and prove that the functor is a cotriple directly. We use related ideas to provide concrete infinite deloopings of the first terms in the resulting Taylor towers when evaluated at the initial object in the source category.Comment: 20 page

Classification of Cassini’s Orbit Regions as Magnetosphere, Magnetosheath, and Solar Wind via Machine Learning

Several machine learning algorithms and feature subsets from a variety of particle and magnetic field instruments on-board the Cassini spacecraft were explored for their utility in classifying orbit segments as magnetosphere, magnetosheath or solar wind. Using a list of manually detected magnetopause and bow shock crossings from mission scientists, random forest (RF), support vector machine (SVM), logistic regression (LR) and recurrent neural network long short-term memory (RNN LSTM) classification algorithms were trained and tested. A detailed error analysis revealed a RNN LSTM model provided the best overall performance with a 93.1% accuracy on the unseen test set and MCC score of 0.88 when utilizing 60 min of magnetometer data (|B|, Bθ, Bϕ and BR) to predict the region at the final time step. RF models using a combination of magnetometer and particle data, spanning H+, He+, He++ and electrons at a single time step, provided a nearly equivalent performance with a test set accuracy of 91.4% and MCC score of 0.84. Derived boundary crossings from each model’s region predictions revealed that the RNN model was able to successfully detect 82.1% of labeled magnetopause crossings and 91.2% of labeled bow shock crossings, while the RF model using magnetometer and particle data detected 82.4 and 74.3%, respectively

Isovariant homotopy theoy and fixed point invariants

An isovariant map is an equivariant map between G-spaces which strictly preserves isotropy groups. We consider an isovariant analogue of Klein–Williams equivariant intersection theory for a finite group G. We prove that under certain reasonable dimension and codimension conditions on H-fixed subspaces (for ), the fixed points of a self-map of a compact smooth G-manifold can be removed isovariantly if and only if the equivariant Reidemeister trace of the map vanishes. In doing so, we study isovariant maps between manifolds up to isovariant homotopy, yielding an isovariant Whitehead's theorem. In addition, we speculate on the role of isovariant homotopy theory in distinguishing manifolds up to homeomorphism

Single‐use versus reusable rhinolaryngoscopes for inpatient otorhinolaryngology consults: Resident and patient experience

Abstract Objectives Single‐use rhinolaryngoscopes were brought to market in 2019 as an alternative to traditional reusable scopes and have garnered interest across settings given portability and potential cost advantages. While single‐use was previously evaluated compared to traditional devices, the overall impact to the consult experience for both users and patients has not been captured. Methods Eighteen residents performed consults with both single‐use and reusable rhinolaryngoscope systems on alternating weeks. A five‐question cumulative survey administered across three assessment points over a 12‐week period using a five‐point rating system to rate favorability. Residents and patients also completed four‐point scale surveys following procedure(s) to capture the consult experience. Statistical analyses were performed to measure significance differences between survey responses between the two systems. Results Single‐use rhinolaryngoscopes received higher overall ratings compared with reusables across each metric captured including overall consult time (4.3 vs. 2.2, p < .001), multiscope consults (4.4 vs. 3.1, p < .001), patient communication (4.6 vs. 2.1, p < .001), teaching opportunities (4.6 vs. 2.1, p < .001), and overall ease of use (4.7 vs. 2.6, p < .001). Residents rated single‐use higher than reusable after each procedure in terms of ease of use (1.07 vs. 2.68, p < .001) and visual clarity (1.27 vs. 1.89, p = .003), while patients rated single‐use higher for understanding of illness (3.9 vs. 3.1, p < .001) and understanding of treatment rationale (3.9 vs. 3.1, p < .001). Conclusion Resident and patient experience feedback favored single‐use rhinolaryngoscopes compared to reusable scope technology across multiple surveyed measurables. Single‐use rhinolaryngoscopes provide a viable tool for otorhinolaryngologist and other clinicians to perform rhinolaryngoscopy consults. Level of Evidence 4

Decoding the dynamics of dental distributions: Insights from shark demography and dispersal

Shark teeth are one of the most abundant vertebrate fossils, and because tooth size generally correlates with body size, their accumulations document the size structure of populations. Understanding how ecological and environmental processes influence size structure, and how this extends to influence these dental distributions, may offer a window into the ecological and environmental dynamics of past and present shark populations. Here, we examine the dental distributions of sand tigers, including extant Carcharias taurus and extinct Striatolamia macrota, to reconstruct the size structure for a contemporary locality and four Eocene localities. We compare empirical distributions against expectations from a population simulation to gain insight into potential governing ecological processes. Specifically, we investigate the influence of dispersal flexibility to and from protected nurseries. We show that changing the flexibility of initial dispersal of juveniles from the nursery and annual migration of adults to the nursery explains a large amount of dental distribution variability. Our framework predicts dispersal strategies of an extant sand tiger population, and supports nurseries as important components of sand tiger life history in both extant and Eocene populations. These results suggest nursery protection may be vital for shark conservation with increasing anthropogenic impacts and climate change

Decoding the dynamics of dental distributions: insights from shark demography and dispersal.

Shark teeth are one of the most abundant vertebrate fossils, and because tooth size generally correlates with body size, their accumulations document the size structure of populations. Understanding how ecological and environmental processes influence size structure, and how this extends to influence these dental distributions, may offer a window into the ecological and environmental dynamics of past and present shark populations. Here, we examine the dental distributions of sand tigers, including extant Carcharias taurus and extinct Striatolamia macrota, to reconstruct the size structure for a contemporary locality and four Eocene localities. We compare empirical distributions against expectations from a population simulation to gain insight into potential governing ecological processes. Specifically, we investigate the influence of dispersal flexibility to and from protected nurseries. We show that changing the flexibility of initial dispersal of juveniles from the nursery and annual migration of adults to the nursery explains a large amount of dental distribution variability. Our framework predicts dispersal strategies of an extant sand tiger population, and supports nurseries as important components of sand tiger life history in both extant and Eocene populations. These results suggest nursery protection may be vital for shark conservation with increasing anthropogenic impacts and climate change