Permutation Invariant Parking Assortments

We introduce parking assortments, a generalization of parking functions with cars of assorted lengths. In this setting, there are $n\in\mathbb{N}$ cars of lengths $\mathbf{y}=(y_1,y_2,\ldots,y_n)\in\mathbb{N}^n$ entering a one-way street with $m=\sum_{i=1}^ny_i$ parking spots. The cars have parking preferences $\mathbf{x}=(x_1,x_2,\ldots,x_n)\in[m]^n$, where $[m]:=\{1,2,\ldots,m\}$, and enter the street in order. Each car $i \in [n]$, with length $y_i$ and preference $x_i$, follows a natural extension of the classical parking rule: it begins looking for parking at its preferred spot $x_i$ and parks in the first $y_i$ contiguously available spots thereafter, if there are any. If all cars are able to park under the preference list $\mathbf{x}$, we say $\mathbf{x}$ is a parking assortment for $\mathbf{y}$. Parking assortments also generalize parking sequences, introduced by Ehrenborg and Happ, since each car seeks for the first contiguously available spots it fits in past its preference. Given a parking assortment $\mathbf{x}$ for $\mathbf{y}$, we say it is permutation invariant if all rearrangements of $\mathbf{x}$ are also parking assortments for $\mathbf{y}$. While all parking functions are permutation invariant, this is not the case for parking assortments in general, motivating the need for a characterization of this property. Although obtaining a full characterization for arbitrary $n\in\mathbb{N}$ and $\mathbf{y}\in\mathbb{N}^n$ remains elusive, we do so for $n=2,3$. Given the technicality of these results, we introduce the notion of minimally invariant car lengths, for which the only invariant parking assortment is the all ones preference list. We provide a concise, oracle-based characterization of minimally invariant car lengths for any $n\in\mathbb{N}$. Our results around minimally invariant car lengths also hold for parking sequences

The Mid-infrared Instrument for JWST and Its In-flight Performance

The Mid-Infrared Instrument (MIRI) extends the reach of the James Webb Space Telescope (JWST) to 28.5 μm. It provides subarcsecond-resolution imaging, high sensitivity coronagraphy, and spectroscopy at resolutions of λ/Δλ ∼ 100-3500, with the high-resolution mode employing an integral field unit to provide spatial data cubes. The resulting broad suite of capabilities will enable huge advances in studies over this wavelength range. This overview describes the history of acquiring this capability for JWST. It discusses the basic attributes of the instrument optics, the detector arrays, and the cryocooler that keeps everything at approximately 7 K. It gives a short description of the data pipeline and of the instrument performance demonstrated during JWST commissioning. The bottom line is that the telescope and MIRI are both operating to the standards set by pre-launch predictions, and all of the MIRI capabilities are operating at, or even a bit better than, the level that had been expected. The paper is also designed to act as a roadmap to more detailed papers on different aspects of MIRI

Health, education, and social care provision after diagnosis of childhood visual disability

Aim: To investigate the health, education, and social care provision for children newly diagnosed with visual disability.Method: This was a national prospective study, the British Childhood Visual Impairment and Blindness Study 2 (BCVIS2), ascertaining new diagnoses of visual impairment or severe visual impairment and blindness (SVIBL), or equivalent vi-sion. Data collection was performed by managing clinicians up to 1-year follow-up, and included health and developmental needs, and health, education, and social care provision.Results: BCVIS2 identified 784 children newly diagnosed with visual impairment/SVIBL (313 with visual impairment, 471 with SVIBL). Most children had associated systemic disorders (559 [71%], 167 [54%] with visual impairment, and 392 [84%] with SVIBL). Care from multidisciplinary teams was provided for 549 children (70%). Two-thirds (515) had not received an Education, Health, and Care Plan (EHCP). Fewer children with visual impairment had seen a specialist teacher (SVIBL 35%, visual impairment 28%, χ2p < 0.001), or had an EHCP (11% vs 7%, χ2p < 0 . 01).Interpretation: Families need additional support from managing clinicians to access recommended complex interventions such as the use of multidisciplinary teams and educational support. This need is pressing, as the population of children with visual impairment/SVIBL is expected to grow in size and complexity.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited

The Science Performance of JWST as Characterized in Commissioning

This paper characterizes the actual science performance of the James Webb Space Telescope (JWST), as determined from the six month commissioning period. We summarize the performance of the spacecraft, telescope, science instruments, and ground system, with an emphasis on differences from pre-launch expectations. Commissioning has made clear that JWST is fully capable of achieving the discoveries for which it was built. Moreover, almost across the board, the science performance of JWST is better than expected; in most cases, JWST will go deeper faster than expected. The telescope and instrument suite have demonstrated the sensitivity, stability, image quality, and spectral range that are necessary to transform our understanding of the cosmos through observations spanning from near-earth asteroids to the most distant galaxies.Comment: 5th version as accepted to PASP; 31 pages, 18 figures; https://iopscience.iop.org/article/10.1088/1538-3873/acb29

The James Webb Space Telescope Mission

Twenty-six years ago a small committee report, building on earlier studies, expounded a compelling and poetic vision for the future of astronomy, calling for an infrared-optimized space telescope with an aperture of at least $4m$. With the support of their governments in the US, Europe, and Canada, 20,000 people realized that vision as the $6.5m$ James Webb Space Telescope. A generation of astronomers will celebrate their accomplishments for the life of the mission, potentially as long as 20 years, and beyond. This report and the scientific discoveries that follow are extended thank-you notes to the 20,000 team members. The telescope is working perfectly, with much better image quality than expected. In this and accompanying papers, we give a brief history, describe the observatory, outline its objectives and current observing program, and discuss the inventions and people who made it possible. We cite detailed reports on the design and the measured performance on orbit.Comment: Accepted by PASP for the special issue on The James Webb Space Telescope Overview, 29 pages, 4 figure

Para-infectious brain injury in COVID-19 persists at follow-up despite attenuated cytokine and autoantibody responses

To understand neurological complications of COVID-19 better both acutely and for recovery, we measured markers of brain injury, inflammatory mediators, and autoantibodies in 203 hospitalised participants; 111 with acute sera (1–11 days post-admission) and 92 convalescent sera (56 with COVID-19-associated neurological diagnoses). Here we show that compared to 60 uninfected controls, tTau, GFAP, NfL, and UCH-L1 are increased with COVID-19 infection at acute timepoints and NfL and GFAP are significantly higher in participants with neurological complications. Inflammatory mediators (IL-6, IL-12p40, HGF, M-CSF, CCL2, and IL-1RA) are associated with both altered consciousness and markers of brain injury. Autoantibodies are more common in COVID-19 than controls and some (including against MYL7, UCH-L1, and GRIN3B) are more frequent with altered consciousness. Additionally, convalescent participants with neurological complications show elevated GFAP and NfL, unrelated to attenuated systemic inflammatory mediators and to autoantibody responses. Overall, neurological complications of COVID-19 are associated with evidence of neuroglial injury in both acute and late disease and these correlate with dysregulated innate and adaptive immune responses acutely

Minimal hypersurfaces of the round sphere

The purpose of this thesis is to discuss a conjectured classification concerning the index of non-totally geodesic minimal hypersurfaces of the n-dimensional standard sphere of radius one S^n. We briefly discuss the basic theory of minimal submanifolds before turning our attention to minimal submanifolds and hypersurfaces in S^n. We present some results of Simons which show that any minimal submanifold of S^n is unstable, and how the totally geodesic S^k ⊂ S^n are characterized by their index. We then present a related conjecture which claims that the Clifford hypersurfaces are also characterized by their index in a similar way, discuss the most recent developments related to the conjecture, and give Urbano’s proof of the conjecture for the special case when n = 3Science, Faculty ofMathematics, Department ofGraduat

Fiscal Year 2009

This report gives an overview of the U.S. research and development (R&D) enterprise and support for federal R&D activities, broken down by departments