Minimax Estimation of Nonregular Parameters and Discontinuity in Minimax Risk

When a parameter of interest is nondifferentiable in the probability, the existing theory of semiparametric efficient estimation is not applicable, as it does not have an influence function. Song (2014) recently developed a local asymptotic minimax estimation theory for a parameter that is a nondifferentiable transform of a regular parameter, where the nondifferentiable transform is a composite map of a continuous piecewise linear map with a single kink point and a translation-scale equivariant map. The contribution of this paper is two fold. First, this paper extends the local asymptotic minimax theory to nondifferentiable transforms that are a composite map of a Lipschitz continuous map having a finite set of nondifferentiability points and a translation-scale equivariant map. Second, this paper investigates the discontinuity of the local asymptotic minimax risk in the true probability and shows that the proposed estimator remains to be optimal even when the risk is locally robustified not only over the scores at the true probability, but also over the true probability itself. However, the local robustification does not resolve the issue of discontinuity in the local asymptotic minimax risk

Adaptive Alert Management for Balancing Optimal Performance among Distributed CSOCs using Reinforcement Learning

Large organizations typically have Cybersecurity Operations Centers (CSOCs) distributed at multiple locations that are independently managed, and they have their own cybersecurity analyst workforce. Under normal operating conditions, the CSOC locations are ideally staffed such that the alerts generated from the sensors in a work-shift are thoroughly investigated by the scheduled analysts in a timely manner. Unfortunately, when adverse events such as increase in alert arrival rates or alert investigation rates occur, alerts have to wait for a longer duration for analyst investigation, which poses a direct risk to organizations. Hence, our research objective is to mitigate the impact of the adverse events by dynamically and autonomously re-allocating alerts to other location(s) such that the performances of all the CSOC locations remain balanced. This is achieved through the development of a novel centralized adaptive decision support system whose task is to re-allocate alerts from the affected locations to other locations. This re-allocation decision is non-trivial because the following must be determined: (1) timing of a re-allocation decision, (2) number of alerts to be re-allocated, and (3) selection of the locations to which the alerts must be distributed. The centralized decision-maker (henceforth referred to as agent) continuously monitors and controls the level of operational effectiveness-LOE (a quantified performance metric) of all the locations. The agent's decision-making framework is based on the principles of stochastic dynamic programming and is solved using reinforcement learning (RL). In the experiments, the RL approach is compared with both rule-based and load balancing strategies. By simulating real-world scenarios, learning the best decisions for the agent, and applying the decisions on sample realizations of the CSOC's daily operation, the results show that the RL agent outperforms both approaches by generating (near-) optimal decisions that maintain a balanced LOE among the CSOC locations. Furthermore, the scalability experiments highlight the practicality of adapting the method to a large number of CSOC locations

Derived categories of Burniat surfaces and exceptional collections

We construct an exceptional collection $\Upsilon$ of maximal possible length 6 on any of the Burniat surfaces with $K_X^2=6$, a 4-dimensional family of surfaces of general type with $p_g=q=0$. We also calculate the DG algebra of endomorphisms of this collection and show that the subcategory generated by this collection is the same for all Burniat surfaces. The semiorthogonal complement $\mathcal A$ of $\Upsilon$ is an "almost phantom" category: it has trivial Hochschild homology, and K_0(\mathcal A)=\bZ_2^6.Comment: 15 pages, 1 figure; further remarks expande

Topological Modes in One Dimensional Solids and Photonic Crystals

This is the final version of the article. Available from American Physical Society via the DOI in this record.It is shown theoretically that a one-dimensional crystal with time reversal symmetry is characterized by a Z_{2} topological invariant that predicts the existence or otherwise of edge states. This is confirmed experimentally through the construction and simulation of a photonic crystal analogue in the microwave regime.We thank an anonymous referee for helpful comments. The authors acknowledge financial support from the EPSRC through the QUEST program grant (Grant No. EP/I034548/1), C.A.M.B. was supported by QinetiQ and the EPSRC through the Industrial CASE scheme (Grant No. 08000346). H.M. is supported by a grant from the U. S. Department of Energy to the Particle Astrophysics Theory group at CWRU. T.J.A. is funded by the Research Corporation for Science Advancement through a Cottrell Award

Inconsistency of the MLE for the joint distribution of interval censored survival times and continuous marks

This paper considers the nonparametric maximum likelihood estimator (MLE) for the joint distribution function of an interval censored survival time and a continuous mark variable. We provide a new explicit formula for the MLE in this problem. We use this formula and the mark specific cumulative hazard function of Huang and Louis (1998) to obtain the almost sure limit of the MLE. This result leads to necessary and sufficient conditions for consistency of the MLE which imply that the MLE is inconsistent in general. We show that the inconsistency can be repaired by discretizing the marks. Our theoretical results are supported by simulations.Comment: 27 pages, 4 figure

Accelerating growth of HFC-227ea (1,1,1,2,3,3,3-heptafluoropropane) in the atmosphere

We report the first measurements of 1,1,1,2,3,3,3-heptafluoropropane (HFC-227ea), a substitute for ozone depleting compounds, in air samples originating from remote regions of the atmosphere and present evidence for its accelerating growth. Observed mixing ratios ranged from below 0.01 ppt in deep firn air to 0.59 ppt in the current northern mid-latitudinal upper troposphere. Firn air samples collected in Greenland were used to reconstruct a history of atmospheric abundance. Year-on-year increases were deduced, with acceleration in the growth rate from 0.029 ppt per year in 2000 to 0.056 ppt per year in 2007. Upper tropospheric air samples provide evidence for a continuing growth until late 2009. Furthermore we calculated a stratospheric lifetime of 370 years from measurements of air samples collected on board high altitude aircraft and balloons. Emission estimates were determined from the reconstructed atmospheric trend and suggest that current "bottom-up" estimates of global emissions for 2005 are too high by a factor of three

Bayesian estimation of one-parameter qubit gates

We address estimation of one-parameter unitary gates for qubit systems and seek for optimal probes and measurements. Single- and two-qubit probes are analyzed in details focusing on precision and stability of the estimation procedure. Bayesian inference is employed and compared with the ultimate quantum limits to precision, taking into account the biased nature of Bayes estimator in the non asymptotic regime. Besides, through the evaluation of the asymptotic a posteriori distribution for the gate parameter and the comparison with the results of Monte Carlo simulated experiments, we show that asymptotic optimality of Bayes estimator is actually achieved after a limited number of runs. The robustness of the estimation procedure against fluctuations of the measurement settings is investigated and the use of entanglement to improve the overall stability of the estimation scheme is also analyzed in some details.Comment: 10 pages, 5 figure

Investigating child participation in the everyday talk of a teacher and children in a preparatory year

In early years research, policy and education, a democratic perspective that positions children as participants and citizens is increasingly emphasized. These ideas take seriously listening to children’s opinions and respecting children’s influence over their everyday affairs. While much political and social investment has been paid to the inclusion of participatory approaches little has been reported on the practical achievement of such an approach in the day to day of early childhood education within school settings. This paper investigates talk and interaction in the everyday activities of a teacher and children in an Australian preparatory class (for children age 4-6 years) to see how ideas of child participation are experienced. We use an interactional analytic approach to demonstrate how participatory methods are employed in practical ways to manage routine interactions. Analysis shows that whilst the teacher seeks the children’s opinion and involves them in decision-making, child participation is at times constrained by the context and institutional categories of “teacher” and “student” that are jointly produced in their talk. The paper highlights tensions that arise for teachers as they balance a pedagogical intent of “teaching” and the associated institutional expectations, with efforts to engage children in decision-making. Recommendations include adopting a variety of conversational styles when engaging with children; consideration of temporal concerns and the need to acknowledge the culture of the school

Towards Machine Wald

The past century has seen a steady increase in the need of estimating and predicting complex systems and making (possibly critical) decisions with limited information. Although computers have made possible the numerical evaluation of sophisticated statistical models, these models are still designed \emph{by humans} because there is currently no known recipe or algorithm for dividing the design of a statistical model into a sequence of arithmetic operations. Indeed enabling computers to \emph{think} as \emph{humans} have the ability to do when faced with uncertainty is challenging in several major ways: (1) Finding optimal statistical models remains to be formulated as a well posed problem when information on the system of interest is incomplete and comes in the form of a complex combination of sample data, partial knowledge of constitutive relations and a limited description of the distribution of input random variables. (2) The space of admissible scenarios along with the space of relevant information, assumptions, and/or beliefs, tend to be infinite dimensional, whereas calculus on a computer is necessarily discrete and finite. With this purpose, this paper explores the foundations of a rigorous framework for the scientific computation of optimal statistical estimators/models and reviews their connections with Decision Theory, Machine Learning, Bayesian Inference, Stochastic Optimization, Robust Optimization, Optimal Uncertainty Quantification and Information Based Complexity.Comment: 37 page

Who knows best? A Q methodology study to explore perspectives of professional stakeholders and community participants on health in low-income communities

Abstract Background Health inequalities in the UK have proved to be stubborn, and health gaps between best and worst-off are widening. While there is growing understanding of how the main causes of poor health are perceived among different stakeholders, similar insight is lacking regarding what solutions should be prioritised. Furthermore, we do not know the relationship between perceived causes and solutions to health inequalities, whether there is agreement between professional stakeholders and people living in low-income communities or agreement within these groups. Methods Q methodology was used to identify and describe the shared perspectives (‘subjectivities’) that exist on i) why health is worse in low-income communities (‘Causes’) and ii) the ways that health could be improved in these same communities (‘Solutions’). Purposively selected individuals (n = 53) from low-income communities (n = 25) and professional stakeholder groups (n = 28) ranked ordered sets of statements – 34 ‘Causes’ and 39 ‘Solutions’ – onto quasi-normal shaped grids according to their point of view. Factor analysis was used to identify shared points of view. ‘Causes’ and ‘Solutions’ were analysed independently, before examining correlations between perspectives on causes and perspectives on solutions. Results Analysis produced three factor solutions for both the ‘Causes’ and ‘Solutions’. Broadly summarised these accounts for ‘Causes’ are: i) ‘Unfair Society’, ii) ‘Dependent, workless and lazy’, iii) ‘Intergenerational hardships’ and for ‘Solutions’: i) ‘Empower communities’, ii) ‘Paternalism’, iii) ‘Redistribution’. No professionals defined (i.e. had a significant association with one factor only) the ‘Causes’ factor ‘Dependent, workless and lazy’ and the ‘Solutions’ factor ‘Paternalism’. No community participants defined the ‘Solutions’ factor ‘Redistribution’. The direction of correlations between the two sets of factor solutions – ‘Causes’ and ‘Solutions’ – appear to be intuitive, given the accounts identified. Conclusions Despite the plurality of views there was broad agreement across accounts about issues relating to money. This is important as it points a way forward for tackling health inequalities, highlighting areas for policy and future research to focus on