Quantum speed limit for noisy dynamics

The laws of quantum physics place a limit on the speed of computation, in particular the evolution time of a system cannot be arbitrarily fast. Bounds on the speed of evolution for unitary dynamics have been long studied. A few bounds on the speed of evolution for noisy dynamics have also been obtained recently, these bounds, however, are in general not tight. In this article we present a new framework for quantum speed limit of noisy dynamics. With this framework we obtain the exact maximal angle that a noisy dynamics can achieve at any given time, this then provides tight bounds on the evolution time for noisy dynamics. The obtained bound reveals that noisy dynamics are generically different from unitary dynamics, in particular we show that the 'orthogonalization' time, which is the minimum time needed to evolve any state to its orthogonal states, is in general not applicable to noisy dynamics.Comment: 6 pages. Comments are welcom

International diffusion and response : the social dimension of the EU-China relationship

The studies of political science and social policy have a strong tradition of analyzing the role of developed countries and the organizations like the European Union (EU) in shaping international diffusion of social policy. However, in-depth research focusing on the response of developing and emerging countries, in particular China, is lacking. Therefore, this dissertation presents an original analysis of the involvement of EU and China in bilateral and international social policy diffusion/transfer. It highlights the relational nature of the normative power Europe (NPE) and the impact of the recipient country China on the NPE. The dissertation conceptualizes the response of recipient countries to international diffusion and develops a typological framework of it. The dissertation refines the existing theoretical framework of policy learning by highlighting the complexity of learning through trial-and-error processes. It also illustrates the usefulness of careful case study design and content analysis in researching bilateral relations and refining the conceptual and theoretical frameworks of international diffusion. The analysis of the social dimension of the EU-China relations indicates that the EU’s mixed approaches combine pragmatic and normative concerns. The typological framework of the variability of response (VOR) introduced and developed in this dissertation is more capable of mapping China’s mixed response than the existing linear conceptual frameworks. China’s learning from European expertise in social security since late 1990s results from its reflections on the undesirable social consequences of neoliberal-oriented reforms since 1970s and has been reinforced by its successful cooperation with the EU in the past decade. The labour provisions travelling though free trade agreements from the EU has been restrained by some recipient countries including China. The findings unveil the complexity of the social dimension of the EU-China relationship due to each party’s mixed approaches. The findings indicate that the others’ positive perceptions of the EU are crucial for the success of the NPE. The dissertation accentuates complex causality in international diffusion including policy learning, which requires better understanding by taking different causal factors into consideration and refining existing theoretical frameworks including typological theories

Family Floer mirror space and SYZ singularities for the conifold

We show a mathematically precise version of the SYZ conjecture, proposed in the family Floer context, for the conifold with a conjectural mirror relation between smoothing and crepant resolution. The singular T-duality fibers are explicitly written and exactly correspond to the codimension-2 `missing points' in the mirror cluster variety, which confirms the speculation of Chan, Pomerleano, and Ueda but only in the non-archimedean setting. Concerning purely the area of Berkovich geometry and forgetting all the mirror symmetry background, our B-side analytic fibration is also a new explicit example of affinoid torus fibration with singular extension.Comment: 20 pages, 1 figure. Comments welcom

Using machine learning for wearables to understand the association of sleep with future morbidity

Sleep is essential to life and is structurally complex. Our understanding of how sleep is associated with health and morbidity primarily draws on studies that use self-report sleep diaries, which capture the subjective experience. However, sleep diaries are limited because they are measured at one point in time, single dimensional, often only capturing sleep duration, and have a low correlation with objective device-measured sleep parameters. The accepted standard for sleep measurement is laboratory-based polysomnography, which is not feasible for use at scale due to its high cost and technical complexity. Instead, wrist-worn accelerometers are more viable to deploy in large-scale epidemiological studies because of their portability and low user burden. Therefore, I aimed to develop a machine learning method for sleep stage classification and evaluate its utility to provide insights into the association between sleep and health outcomes. I conducted a systematic review to assess the agreement between accelerometer-based sleep staging and polysomnography with a secondary aim of understanding the agreement level from different methods used. This review found that existing sleep staging methods were limited by a reliance on hand-crafted features and the use of labelled datasets of small sizes, highlighting the need to improve accelerometer-based sleep staging. A self-supervised deep neural network was first developed to automatically extract features from 700,000 person-days of unlabelled raw accelerometry. To systematically evaluate the generalisability of the self-supervised features, the pre-trained network was tested in seven human activity recognition datasets, for which more open-access benchmark datasets were available. The self-supervised network showed generalisability across activity classes, devices, device placements and populations with an F1 relative improvement of 2.5%-100% (median: 18.4%) compared to the network without self-supervision. The self-supervised feature extractor was then used to develop a sleep stage classifier (SleepNet) using a deep recurrent neural network. The SleepNet was able to obtain a state-of-the-art performance for the classification of sleep and the stages of sleep using ~1,500 nights of multi-centre polysomnography as the ground truth. Overall, the derived sleep parameters had a fair agreement with polysomnography with a Kappa score of 0.37 (SD: 0.16) for three-class classification between wake, rapid-eye-movement sleep (REM), and non-rapid-eye-movement sleep (NREM). The difference between polysomnography and the model classifications on the external validation was 34.7 minutes (95% limits of agreement (LoA): -37.8 to 107.2 minutes) for total sleep duration, 2.6 minutes for REM duration (95% LoA: -68.4 to 73.4 minutes) and 32.1 minutes (95% LoA: -54.4 to 118.5 minutes) for NREM duration. Finally, SleepNet was used to infer overnight sleep duration and sleep efficiency (the proportion of time asleep when in bed) in the UK Biobank accelerometer dataset to understand the associations with mortality outcomes. Short sleepers (<6 hours) had a higher risk of mortality compared to participants with normal sleep duration 6 to 7.9 hours, regardless of whether they had low sleep efficiency (Hazard ratios (HRs): 1.58; 95% confidence intervals (CIs): 1.19 to 2.11) or high sleep efficiency (HRs: 1.45; 95% CIs: 1.16 to 1.81). In conclusion, accelerometer-based sleep classification had a fair agreement with polysomnography. Using the derived sleep parameters on datasets with longitudinal follow-up could transform our understanding of how sleep contributes to human health and well-being

Disk counting and wall-crossing phenomenon via family Floer theory

We use the wall-crossing formula in the non-archimedean SYZ mirror construction (arXiv: 2003.06106) to compute the Landau-Ginzburg superpotential and the one-pointed open Gromov-Witten invariants for a Chekanov-type Lagrangian torus in any smooth toric Fano compactification of C^n. It agrees with the works of Auroux, Chekanov-Schlenk, and Pascaleff-Tonkonog.Comment: 22 Pages (The main body only has 9 pages). We move all the review parts to the appendix to highlight the key points. The exposition is much more concise. The result is also much more general than befor

Family Floer SYZ conjecture for AnA_n singularity

We resolve a mathematically precise SYZ conjecture for $A_n$ singularity by building a quantum-corrected T-duality between two singular torus fibrations related to the Kahler geometry of the $A_n$-smoothing and the Berkovich geometry of the $A_n$-resolution, respectively. Our approach involves heavy computations that embody a non-archimedean version of the partition of unity, and it confirms the strategy that patching verified local singularity models brings global SYZ conjecture solutions (like K3 surfaces) within reach. There is also remarkably explicit extra evidence concerning the collision of singular fibers and braid group actions. On one hand, we address the central challenge of matching SYZ singular loci identified by Joyce. In reality, we construct not merely an isolated SYZ mirror fibration partner, but a parameter-dependent one that always keeps the matching singular loci plus integral affine structure, even when the collision of singular fibers occurs. On the other hand, our SYZ result surprisingly displays a visible tie, regardless of the parameter choice, between the $(A_n)$-configuration of Lagrangian spheres occurred as vanishing cycles in the $A_n$-smoothing and the exceptional locus of rational $(-2)$-curves in the $A_n$-resolution. It closely aligns with the celebrated works of Khovanov, Seidel, and Thomas from around 20 years ago in a somewhat distant subject, providing geometric evidence for the family Floer functor approach explored by Abouzaid and Fukaya. Intriguingly, these discoveries use certain explicit realizations by order statistics.Comment: 53 pages, 12 figure