Uniform coverage designs for mixture experiments

We investigate an optimization problem for mixture experiments. We consider the case when a large number of ingredients are available but mixtures can contain only a few number of ingredients. These conditions are held in experiments for self assembling molecular systems. First, we introduce a concept of uniform coverage design specialized for the situation. Next, we propose to use the stepwise technique for estimating coefficients of third-order Scheffe model which describes a response surface. After that, we propose a method of adding new mixtures for a movement to an extremum region. By this method, additional mixtures of experiments are extremum points of current estimated model and points which lead to more accurate estimation of current model prediction. This methodology is studied numerically for a model constructed from real data.     

The guaranteed estimation of the Lipschitz classifier accuracy: Confidence set approach

This paper introduces an original method for the guaranteed estimation of the Lipschitz classifier accuracy in the case of a large number of classes. The solution was obtained as a finite closed set of alternative hypotheses, which contains an object of classification with probability of not less than the specified value. Thus, the classification is represented by a set of hypothetical classes. In this case, the smaller the cardinality of the discrete set of hypothetical classes is, the higher is the classification accuracy. This problem is relevant in practical biometrics, when the number of analyzed samples amounts to tens of thousands, and many of them are distinguished vaguely in the primary feature space.     

Digital platforms and the changing freelance workforce in the Russian Federation: A ten-year perspective

This article traces the development of the online labour market in the Russian Federation and across the wider post-Soviet space. The authors draw on the unique data of four waves of an online survey for 2009, 2011, 2014 and 2019 on the leading Russian-speaking general-purpose platform for creative and knowledge-based work. The results shed light on key trends, such as spatial decentralization, occupational diversification, feminization, maturing, rising educational attainment and educational mismatch, the consolidation of freelance careers, platformization and legalization. The article discusses these findings and their potential policy implications for the future development of online platform work in the Russian Federation.     

‘I'm Home for the Kids’: Contradictory Implications for Work–Life Balance of Teleworking Mothers

This study explores the experience of time flexibility and its relationship to work–life balance among married female teleworkers with school‐aged children. Drawing from a larger study of teleworkers from a Canadian financial corporation, 18 mothers employed in professional positions discussed work, leisure and their perceptions of work–life balance in in‐depth interviews. Telework was viewed positively because flexible scheduling facilitated optimal time management. A key factor was the pervasiveness of caregiving, which could result in ongoing tensions and contradictions between the ethic of care and their employment responsibilities. The ideology of ‘intensive mothering’ meant that work schedules were closely tied to the rhythms of children's school and leisure activities. The different temporal demands of motherhood and employment resulted in little opportunity for personal leisure. Time ‘saved’ from not having to commute to an office was reallocated to caregiving, housework or paid employment rather than to time for their self. The women also experienced a traditional gendered division of household labour and viewed telework as a helpful tool for combining their dual roles. Time flexibility enhanced their sense of balancing work and life and their perceived quality of life. At the same time, they did not question whether having the primary responsibility for caregiving while engaged in paid employment at home was fair or whether it was a form of exploitation.     

Relative blocking in posets

Poset-theoretic generalizations of set-theoretic committee constructions are presented. The structure of the corresponding subposets is described. Sequences of irreducible fractions associated to the principal order ideals of finite bounded posets are considered and those related to the Boolean lattices are explored; it is shown that such sequences inherit all the familiar properties of the Farey sequences. 2000 Mathematics Subject Classification 05A05, 06A07, 11B57, 90C27     

Achieving limiting distributions for Markov chains using back buttons

As a simple model for browsing the World Wide Web, we consider Markov chains with the option of moving back to the previous state. We develop an algorithm which uses back buttons to achieve essentially any limiting distribution on the state space. This corresponds to spending the desired total fraction of time at each web page. On finite state spaces, our algorithm always succeeds. On infinite state spaces the situation is more complicated, and is related to both the tail behaviour of the distributions, and the properties of convolution equations.     

Optimal designs for statistical analysis with Zernike polynomials

The Zernike polynomials arise in several applications such as optical metrology or image analysis on a circular domain. In the present paper, we determine optimal designs for regression models which are represented by expansions in terms of Zernike polynomials. We consider two estimation methods for the coefficients in these models and determine the corresponding optimal designs. The first one is the classical least squares method and Φ _p -optimal designs in the sense of Kiefer [Kiefer, J., 1974, General equivalence theory for optimum designs (approximate theory). Annals of Statistics, 2 849–879.] are derived, which minimize an appropriate functional of the covariance matrix of the least squares estimator. It is demonstrated that optimal designs with respect to Kiefer's Φ _p -criteria (p>?∞) are essentially unique and concentrate observations on certain circles in the experimental domain. E-optimal designs have the same structure but it is shown in several examples that these optimal designs are not necessarily uniquely determined. The second method is based on the direct estimation of the Fourier coefficients in the expansion of the expected response in terms of Zernike polynomials and optimal designs minimizing the trace of the covariance matrix of the corresponding estimator are determined. The designs are also compared with the uniform designs on a grid, which is commonly used in this context.     

A geometric characterization of optimal designs for regression models with correlated observations

We consider the problem of optimal design of experiments for random effects models, especially population models, where a small number of correlated observations can be taken on each individual, while the observations corresponding to different individuals are assumed to be uncorrelated. We focus on c-optimal design problems and show that the classical equivalence theorem and the famous geometric characterization of Elfving (1952) from the case of uncorrelated data can be adapted to the problem of selecting optimal sets of observations for the n individual patients. The theory is demonstrated by finding optimal designs for a linear model with correlated observations and a nonlinear random effects population model, which is commonly used in pharmacokinetics.