arXiv subjects
Publications and source records attributed to Hoang Truong.
This paper investigates mapping spaces between enriched operads and relates these spaces to those between operadic bimodules via convenient fiber sequences. The main statements hold for simplicial operads, operads enriched in simplicial modules over a commutative ring, and for connective dg operads, with the last case relying on an operadic version of the Dold-Kan correspondence.
A modern insight due to Quillen, which is further developed by Lurie, asserts that many cohomology theories of interest are particular cases of a single construction, which allows one to define cohomology groups in an abstract setting using only intrinsic properties of the category (or $\infty$-category) at hand. This universal cohomology theory is known as Quillen cohomology. In any setting, Quillen cohomology of a given object is classified by its cotangent complex. The main purpose of this paper is to study Quillen cohomology of operads enriched over a general base category. Our main result provides an explicit formula for computing Quillen cohomology of enriched operads, based on a procedure of taking certain infinitesimal models of their cotangent complexes. Furthermore, we propose a natural construction of the twisted arrow $\infty$-categories of simplicial operads. We then assert that the cotangent complex of a simplicial operad can be represented as a spectrum valued functor on its twisted arrow $\infty$-category. When working in stable base categories such as chain complexes and spectra, Francis and Lurie proved the existence of a fiber sequence relating the cotangent complex and Hochschild complex of an $E_n$-algebra, from which a conjecture of Kontsevich is verified. We establish an analogous fiber sequence for the operad $E_n$ itself, in the topological setting.
Various intervention therapies ranging from pharmaceutical to hi-tech tailored solutions have been available to treat difficulty in falling asleep commonly caused by insomnia in modern life. However, current techniques largely remain ill-suited, ineffective, and unreliable due to their lack of precise real-time sleep tracking, in-time feedback on the therapies, an ability to keep people asleep during the night, and a large-scale effectiveness evaluation. Here, we introduce a novel sleep aid system, called Earable, that can continuously sense multiple head-based physiological signals and simultaneously enable closed-loop auditory stimulation to entrain brain activities in time for effective sleep promotion. We develop the system in a lightweight, comfortable, and user-friendly headband with a comprehensive set of algorithms and dedicated own-designed audio stimuli. We conducted multiple protocols from 883 sleep studies on 377 subjects (241 women, 119 men) wearing either a gold-standard device (PSG), Earable, or both concurrently. We demonstrate that our system achieves (1) a strong correlation (0.89 +/- 0.03) between the physiological signals acquired by Earable and those from the gold-standard PSG, (2) an 87.8 +/- 5.3% agreement on sleep scoring using our automatic real-time sleep staging algorithm with the consensus scored by three sleep technicians, and (3) a successful non-pharmacological stimulation alternative to effectively shorten the duration of sleep falling by 24.1 +/- 0.1 minutes. These results show that the efficacy of Earable exceeds existing techniques in intentions to promote fast falling asleep, track sleep state accurately, and achieve high social acceptance for real-time closed-loop personalized neuromodulation-based home sleep care.