Deliberately Indifferent: Institutional Liability for Further Harassment in Student-on-Student Title IX Cases

Sexual harassment is an unfortunate problem far too many have experienced. Universities and other educational institutions owe a duty, both legal and moral, to protect students from sexual harassment, and in turn to allow students to receive the full benefits of their education. But a circuit split has limited students\u27 ability to hold educational institutions liable. This circuit split results in the absurd scenario where an individual must experience sexual harassment more than one time to hold their educational institution liable. This Note attempts to fix that by proposing Title IX (the law governing sexual harassment at educational institutions) adopt the hostile work environment analysis from Title VII (an employment law statute) in further harassment claims. This solution balances the interests of students in receiving the full benefits of their education in a safe environment with the interests of educational institutions to not be held liable for issues these universities may not know exist

Geometric Control of two Quadrotors Carrying a Rigid Rod with Elastic Cables

This paper presents the design of a geometric trajectory tracking controller for the cooperative task of two quadrotor UAVs (unmanned aerial vehicles) carrying and transporting a rigid bar, which is attached to the quadrotors via inflexible elastic cables. The elasticity of the cables together with techniques of singular perturbation allows a reduction in the model to that of a similar model with inelastic cables. In this reduced model, we design a controller such that the rod exponentially tracks a given desired trajectory for its position and attitude, under some assumptions on initial error. We then show that exponential tracking in the reduced model corresponds to exponential tracking of the original elastic model. We also show that the previously defined control scheme provides uniform ultimate boundedness in the presence of unstructured bounded disturbances.Comment: 20 pages, 3 figure

Reduction of Sufficient Conditions in Variational Obstacle Avoidance Problems

This paper studies sufficient conditions in a variational obstacle avoidance problem on complete Riemannian manifolds. That is, we minimize an action functional, among a set of admissible curves, which depends on an artificial potential function used to avoid obstacles. We provide necessary and sufficient conditions under which the resulting critical points, the so-called modified Riemannian cubics, are local minimizers. We then study the theory of reduction by symmetries of sufficient conditions for optimality in variational obstacle avoidance problems on Lie groups endowed with a left-invariant metric. This amounts to left-translating the Bi-Jacobi fields described to the Lie algebra, and studying the corresponding bi-conjugate points. New conditions are provided in terms of the invertibility of a certain matrix.Comment: 9 pages, 8th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control. arXiv admin note: text overlap with arXiv:2207.1357

Reduction of Necessary Conditions for the Variational Collision Avoidance Problem

In this work, we study the reduction by a Lie group of symmetries of variational collision avoidance probelms of multiple agents evolving on a Riemannian manifold and derive necessary conditions for the reduced extremals. The problem consists of finding non-intersecting trajectories of a given number of agents, among a set of admissible curves, to reach a specified configuration, based on minimizing an energy functional that depends on the velocity, covariant acceleration and an artificial potential function used to prevent collision among the agents.Comment: 7 pages, 8th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, LHMNC 2024. arXiv admin note: text overlap with arXiv:2310.18057, arXiv:2207.1357

Adult hypertension referral pathway and therapeutic management:British and Irish Hypertension Society position statement

In the UK, most adults with hypertension are managed in Primary Care. Referrals to Secondary Care Hypertension Specialists are targeted to patients in whom further investigations are likely to change management decisions. In this position statement the British and Irish Hypertension Society provide clinicians with a framework for referring patients to Hypertension Specialists. Additional therapeutic advice is provided to optimise patient management whilst awaiting specialist review. Our aim is to ensure that referral criteria to Hypertension Specialists are consistent across the UK and Ireland to ensure equitable access for all patients

Is early center-based child care associated with tantrums and unmanageable behavior over time up to school entry?

Background. Existing research suggests that there is a relationship between greater exposure to center-based child care and child behavioral problems though the mechanism for the impact is unclear. However the measure used to document child care has usually been average hours, which may be particularly unreliable in the early months when fewer children are in center care. In addition individual trajectories for behavior difficulties have not been studied. Objective. The purpose of the current study was to examine whether the extent of exposure to center-based child care before two years predicted the trajectory of children’s difficult behavior (i.e., tantrums and unmanageable behavior) from 30 to 51 months controlling for child and maternal characteristics. Method. Data were drawn from UK-based Families, Children and Child Care (FCCC) study (n=1201). Individual growth models were fitted to test the relation between early center-based child care experiences and subsequent difficult behavior. Results. Children with more exposure to center-based care before two had less difficult behavior at 30 months, but more increase over time. Initial levels were predicted by higher difficult temperament and lower verbal ability. Higher difficult temperament and lower family socio-economic status predicted its change over time. Conclusion. Findings suggest that early exposure to center-based care before two years old is a risk factor for subsequent behavior problems especially when children have a longer period of exposure. A possible explanatory process is that child coping strategies to manage frustration are less well developed in a group context, especially when they lag behind in expressive language

The critical window for the classical Ramsey-Tur\'an problem

The first application of Szemer\'edi's powerful regularity method was the following celebrated Ramsey-Tur\'an result proved by Szemer\'edi in 1972: any K_4-free graph on N vertices with independence number o(N) has at most (1/8 + o(1)) N^2 edges. Four years later, Bollob\'as and Erd\H{o}s gave a surprising geometric construction, utilizing the isoperimetric inequality for the high dimensional sphere, of a K_4-free graph on N vertices with independence number o(N) and (1/8 - o(1)) N^2 edges. Starting with Bollob\'as and Erd\H{o}s in 1976, several problems have been asked on estimating the minimum possible independence number in the critical window, when the number of edges is about N^2 / 8. These problems have received considerable attention and remained one of the main open problems in this area. In this paper, we give nearly best-possible bounds, solving the various open problems concerning this critical window.Comment: 34 page

Multimodal Management of Atrophic Acne Scarring in the Aging Face

Atrophic facial acne scarring is a widely prevalent condition that can have a negative impact on a patient’s quality of life. The appearance of these scars is often worsened by the normal effects of aging. A number of options are available for the treatment of acne scarring, including chemical peeling, dermabrasion, ablative or nonablative laser resurfacing, dermal fillers, and surgical techniques such as subcision or punch excision. Depending on the type and extent of scarring, a multimodal approach is generally necessary to provide satisfactory results. Resurfacing techniques correct surface irregularities, long-lasting dermal fillers address the volume loss resulting from acne, and sub-superficial musculoaponeurotic system (SMAS) face-lift procedures counter the soft tissue laxity and ptosis associated with aging. This article briefly reviews the evolution of individual approaches to treating atrophic acne scarring, followed by case examples illustrating results that can be achieved using a multimodal approach. Representative cases from patients in their 30s, 40s, and 50s are presented. In the author’s clinical practice, multimodal approaches incorporating fractionated laser, injectable poly-l-lactic acid, and sub-SMAS face-lift procedures have achieved optimal aesthetic outcomes, high patient satisfaction, and durability of aesthetic effect over time