We compute Seshadri constants of a torus equivariant nef vector bundle on a projective space satisfying certain conditions. As an application, we compute Seshadri constants of tangent bundles on projective spaces. We also consider equivariant nef vector bundles on Bott towers of height 2 (i.e. Hirzebruch surfaces) and Bott towers of height 3 respectively. Assuming some conditions on the minimal slope of the restrictions of these bundles to invariant curves, we give precise values of Seshadri constant at an arbitrary point. We also give several examples illustrating our results.
Last year, the Institute of Mental Health (IMH) celebrated its 85 th anniversary. From its origins in 1928 as what was then simply called The Mental Hospital, this nondescript name was later changed in 1950 to Woodbridge Hospital. 1 The establishment of the Mental Hospital was at a time when there was no effective treatment for mental illness. The only humane option at the time was "moral treatment", which meant kind, individualised treatment in the form of occupational therapy, exercise, and recreation in a sheltered environment. The hospital was, in fact, an asylum in the original meaning of the word: "a refuge, protection, or sanctuary".This humane idea of looking after the mentally ill reached its apotheosis in America when the early mental hospitals built in the 19 th century took the form of large, stately buildings, with large sprawling grounds and comfortable accommodation that also created a sense of community and companionship for the patients. There were farms and dairies that provided therapy for the patients in the form of work, and these agricultural activities also helped to sustain the running of the hospitals. Antipsychiatry MovementHowever, it was also in America where the page turned with the precipitate decline of this high-minded ideal. An infl ux of an increasing number of patients and shortage of funds strained these mental hospitals to their limits and forced them to closure. Within a few decades, most morphed into "warehouses" for the mentally ill, and became synonymous with neglect, misery and abuse.Journalistic exposé of the appalling conditions of these hospitals whipped up a sense of public revulsion and outrage, which was further stoked by Ken Kesey's novel 'One Flew Over the Cuckoo's Nest' and the subsequent blockbuster movie with its graphic depiction of the sequential brutalisation of a wayward patient at the hands of the staff of a mental hospital.
The focus of this paper is on a gesture-based interface designed for controlling a mobile robot equipped with a manipulator. This interface employs a camera to track a person's movements and recognize gestures that involve arm motion. To enable the robot to follow a person reliably through environments with changing lighting conditions, a fast, adaptive tracking algorithm is utilized. The paper compares two alternative approaches for gesture recognition: a template-based approach and a neural network approach. Both methods are combined with the Viterbi algorithm to recognize arm motion-based gestures in addition to static arm poses. The results of this study are presented in the context of an interactive clean-up task, where a person directs the robot to specific locations that require cleaning and instructs it to pick up trash. Service robotics is currently an important area of research, with significant potential for societal impact. As service robots interact directly with people, developing intuitive and user-friendly interfaces is crucial. While prior work has primarily focused on navigation and manipulation, few robotic systems possess flexible user interfaces that enable natural and easy-to-use control of the robot.
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