On the convergence of mirror descent beyond stochastic convex programming

In this paper, we examine the convergence of mirror descent in a class of stochastic optimization problems that are not necessarily convex (or even quasi-convex), and which we call variationally coherent. Since the standard technique of "ergodic averaging" offers no tangible benefits beyond convex programming, we focus directly on the algorithm's last generated sample (its "last iterate"), and we show that it converges with probabiility $1$ if the underlying problem is coherent. We further consider a localized version of variational coherence which ensures local convergence of stochastic mirror descent (SMD) with high probability. These results contribute to the landscape of non-convex stochastic optimization by showing that (quasi-)convexity is not essential for convergence to a global minimum: rather, variational coherence, a much weaker requirement, suffices. Finally, building on the above, we reveal an interesting insight regarding the convergence speed of SMD: in problems with sharp minima (such as generic linear programs or concave minimization problems), SMD reaches a minimum point in a finite number of steps (a.s.), even in the presence of persistent gradient noise. This result is to be contrasted with existing black-box convergence rate estimates that are only asymptotic.Comment: 30 pages, 5 figure

Sources and Occurrences of Nonpoint-Source Chemicals in Groundwater, Jackson Purchase Region, Kentucky

Nitrate concentrations that exceed U.S. Environmental Protection Agency drinking-water standards have been reported in Jackson Purchase Region groundwater since the 1960\u27s. More recently, other nonpoint-source chemicals such as pesticides and volatile organic compounds have also been found. The sources of these chemicals and the pathways by which they reach domestic groundwater supplies must be determined to protect human health and to design effective land-management practices. To investigate the occurrence of nonpoint-source chemicals in Jackson Purchase groundwater, 60 wells were selected on the basis of geographic location, hydrostratigraphic unit penetrated, and well type (bored or drilled); distances to row crops, known septic systems, and active and abandoned feedlots were recorded for each well. Groundwater was sampled in the spring and fall of 2005 for field measurements, water properties, major and minor solutes, nutrients, metals, pesticides, volatile organic compounds, caffeine, and bacteria. Nitrate concentrations exceeded EPA maximum contaminant levels in three wells, and exceeded half the MCL in three other wells. High nitrate concentrations were found mainly in samples from shallow wells in the Continental Gravel hydrostratigraphic unit near row crops. The combination of the permeable gravel and proximity to fertilizer applications makes these wells highly susceptible to nitrate contamination. Pesticides and caffeine were most commonly detected in Continental Gravel samples, but also in other units throughout the area. Total coliform bacteria were found throughout the region from all hydrostratigraphic units and all well types. High nitrate concentrations and detectable caffeine and pesticides are most often found in shallow wells regardless of whether the well was drilled or bored. Shallow wells, bored wells, and those near septic systems were most likely to produce water containing total coliform bacteria, however. The occurrence of high nitrate concentrations and detectable amounts of pesticides and caffeine shows that groundwater contamination is occurring in the Jackson Purchase. Land management practices that take into account the different hydrologic properties of hydrostratigraphic units and bored wells\u27 greater susceptibility to annular leakage are needed to protect groundwater quality from further degradation. The occurrence of total coliform bacteria in groundwater samples indicates contamination of either the well or water delivery system (or both) or the water-producing aquifer. More extensive testing is needed to determine exactly where the bacteria reside. This study was one of the first to consider well types and distances to potential sources of nonpoint groundwater contaminants with water-chemistry investigations. Future studies of nonpoint-source groundwater contamination must first establish that pollutants are not entering the well via local pathways such as leaky well casings or near-wellhead surface sources of chemicals, but rather that the local or regional groundwater system is affected. Second, future studies must carefully document distances from wells to potential sources of contaminants. In many cases this will require historical investigations to locate abandoned confined-animal feeding operations or on-site waste-disposal systems

Distributed integrated product teams

Thesis (S.M.)--Massachusetts Institute of Technology, System Design & Management Program, 2000.Includes bibliographical references (p. 134-135).Two major organizational tools, Integrated Process and Product Development (IPPD) and co-location, have been key initiatives in many corporate knowledge management and information flow strategies. The benefits of IPPD and co-location are well documented, and central to the success of these tools is the increased information flow and knowledge transfer across organizational boundaries. The fundamental knowledge management philosophy of IPPD is person-to-person tacit knowledge sharing and capture through the establishment of multi-disciplined Integrated Product Teams (IPT). Co-location of the integrated product team members has facilitated frequent informal face-to-face information flow outside of the structured meetings typical of IPPD processes. In today's global environment, the development and manufacture of large complex systems can involve hundreds, if not thousands, of geographically dispersed engineers often from different companies working on IPTs. In such an environment, the implementation of IPPD is challenging, and co-location is not feasible across the entire enterprise. The development of a comprehensive knowledge capture and information flow strategy aligned to the organizational architecture and processes involved with proper utilization of available information technologies is critical in facilitating information flow and knowledge transfer between dispersed IPTs. In this thesis we provide a case study of the knowledge capture and information flow issues that have arisen with the recent transition to the Module Center organization at Pratt & Whitney. We identify several critical enablers for efficient information flow and knowledge capture in a dispersed IPT environment by analyzing qualitative and quantitative survey data obtained at Pratt & Whitney, existing research in this area, and our own observations as participants in this environment. From this analysis, we identify key information flow and knowledge capture issues and provide recommendations for potential improvement. The Design Structures Matrix (DSM) methodology is used to understand the complex, tightly coupled information flow between the IPTs that exist at Pratt & Whitney. We build upon the previous Pratt & Whitney DSM work. The proposed DSM is not only a valuable tool identifying the information flow paths that exist between part level and system level attributes, but also can be utilized as an information technology tool to capture the content or knowledge contained in the information flow paths identified.by Stephen V. Glynn [and] Thomas G. Pelland.S.M

The floods: Where do we go from here?

"Support, recovery and lessons learned" from 2015 Cumbria floods. Two months on from devastating flooding in the county various key figures and leaders give their responses to the next stage of recovery, including looking towards strategic solutions for flood prevention

Real-Time Feedback of Air Quality in Children’s Bedrooms Reduces Exposure to Secondhand Smoke

Introduction:Secondhand smoke (SHS) exposure creates health risks for nonsmokers and is especially detrimental to children. This study evaluated whether immediate feedback in response to poor indoor air quality in children’s bedrooms can reduce the potential for SHS exposure, as measured by adherence to a World Health Organization (WHO) indoor air standard.Methods:Homes that contained children and an adult who regularly smoked inside (n=298) had an air particle monitor installed in the child’s bedroom. These devices measured the concentration of particulate matter (PM2.5) for approximately three months and, for half of the participants, immediately provided aversive feedback in response to elevated PM2.5. Hierarchical linear models were fit to the data to assess whether the intervention increased the probability that: 1) a given day was below the WHO guideline for daily exposure, and 2) a household established and maintained a smoke-free home (SFH), operationalized as achieving 30 consecutive days below the WHO guideline. The intervention’s impact was calculated as groupby- time effects.Results:The likelihood that a child’s bedroom met the WHO indoor air quality standard on a given day increased such that the baseline versus post-baseline odds ratio (OR) of maintaining indoor PM2.5 levels below the WHO guideline was 2.38 times larger for participants who received the intervention. Similarly, the baseline versus post-baseline OR associated with achieving an SFH was 3.49 times larger for participants in the intervention group.Conclusions:The real-time intervention successfully drove clinically meaningful changes in smoking behavior that mitigated indoor PM2.5 levels in children’s bedrooms and thereby reduced SHS exposure. These results demonstrate the effectiveness of targeting sensitive microenvironments by giving caregivers actionable information about children’s SHS risks. Future extensions should examine additional microenvironments and focus on identifying the potential for SHS exposure before it occurs

KINEMATIC DIFFERENCES BETWEEN ‘ONE-FOOTED’ AND ‘TWO-FOOTED’ YOUNG SOCCER PLAYERS KICKING WITH THE NON-PREFERRED LEG

The purpose of this study was to examine kinematic differences between ‘one-footed’ and ‘two-footed’ players when kicking with the non-preferred leg at a target and with maximal effort. Eighteen highly-trained young soccer players were categorised as one-footed (n=9) and two-footed (n=9) based on results of a kicking test. Motion analysis data showed that two-footed players run-up straighter and have less pelvic rotation at ball-foot impact than one-footed players and the differences are likely to be meaningful (ES differences of 0.89 and 0.99 respectively). Run-up angle and pelvic rotation angle are significantly correlated (P < 0.1). The study found that two-footed players are significantly smaller in stature than one-footed players (P < 0.1). Practical implications for soccer coaches arose from the study

Antiretroviral Treatment Cohort Analysis Using Time-Updated CD4 Counts: Assessment of Bias with Different Analytic Methods

BACKGROUND: Survival analysis using time-updated CD4+ counts during antiretroviral therapy is frequently employed to determine risk of clinical events. The time-point when the CD4+ count is assumed to change potentially biases effect estimates but methods used to estimate this are infrequently reported. METHODS: This study examined the effect of three different estimation methods: assuming i) a constant CD4+ count from date of measurement until the date of next measurement, ii) a constant CD4+ count from the midpoint of the preceding interval until the midpoint of the subsequent interval and iii) a linear interpolation between consecutive CD4+ measurements to provide additional midpoint measurements. Person-time, tuberculosis rates and hazard ratios by CD4+ stratum were compared using all available CD4+ counts (measurement frequency 1-3 months) and 6 monthly measurements from a clinical cohort. Simulated data were used to compare the extent of bias introduced by these methods. RESULTS: The midpoint method gave the closest fit to person-time spent with low CD4+ counts and for hazard ratios for outcomes both in the clinical dataset and the simulated data. CONCLUSION: The midpoint method presents a simple option to reduce bias in time-updated CD4+ analysis, particularly at low CD4 cell counts and rapidly increasing counts after ART initiation

Conference report:Improving outcomes for gastrointestinal cancer in the UK

Substantial steps are being made towards early diagnosis. A range of tools are available to help GPs appropriately categorise early symptoms during routine consultations. Various promising new tests and devices are being explored, especially for cancers that frequently present at late stages. The continuing increase in demand on endoscopy services is a major concern, not least because of the shortage of trained practitioners and other healthcare staff. However, screening and collaborative streamlining initiatives might help to improve the relevance of referrals. The question posed in the title of the conference was rhetorical, but a positive answer seems potentially achievable, even in austere times, through facilitating uptake of screening, working to develop the primary-secondary care interface, educating the public and by protecting funds for research