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Component separation is one of the key stages of any modern cosmic microwave background data analysis pipeline. It is an inherently nonlinear procedure and typically involves a series of sequential solutions of linear systems with similar but not identical system matrices, derived for different data models of the same data set. Sequences of this type arise, for instance, in the maximization of the data likelihood with respect to foreground parameters or sampling of their posterior distribution. However, they are also common in many other contexts. In this work we consider solving the component separation problem directly in the measurement (time-) domain. This can have a number of important benefits over the more standard pixel-based methods, in particular if non-negligible time-domain noise correlations are present, as is commonly the case. The approach based on the time-domain, however, implies significant computational effort because the full volume of the time-domain data set needs to be manipulated. To address this challenge, we propose and study efficient solvers adapted to solving time-domain-based component separation systems and their sequences, and which are capable of capitalizing on information derived from the previous solutions. This is achieved either by adapting the initial guess of the subsequent system or through a so-called subspace recycling, which allows constructing progressively more efficient two-level preconditioners. We report an overall speed-up over solving the systems independently of a factor of nearly 7, or 5, in our numerical experiments, which are inspired by the likelihood maximization and likelihood sampling procedures, respectively.

We present selected known results and some new observations, involving Gurariĭ Spaces. A Banach space is Gurariĭ Spaces if it has certain natural extension property for almost isometric embeddings of finite-dimensional spaces. Deleting the word \almost", we get the notion of a strong Gurariĭ Spaces. There exists a unique (up to isometry) separable Gurariĭ Spaces, however strong Gurariĭ Spaces cannot be separable. The structure of the class of non-separable Gurariĭ Spaces seems to be not very well understood. We discuss some of their properties and state some open questions. In particular, we characterize nonseparable Gurariĭ Spaces in terms of skeletons of separable subspaces, we construct a nonseparable Gurariĭ Spaces with a projectional resolution of the identity and we show that no strong Gurariĭ Spaces can be weakly Lindelӧf determined. Research of the first author is supported by the ESF Human Capital Operational Program grant 6/1/8.2.1./POKL/2009. peerReviewed

A tower between two regular languages is a sequence of strings such that all strings on odd positions belong to one of the languages, all strings on even positions belong to the other language, and each string can be embedded into the next string in the sequence. It is known that if there are towers of any length, then there also exists an infinite tower. We investigate upper and lower bounds on the length of finite towers between two regular languages with respect to the size of the automata representing the languages in the case there is no infinite tower. This problem is relevant to the separation problem of regular languages by piecewise testable languages.

Human perceptions of nature and the environment are increasingly being recognised as important for environmental management and conservation. Understanding people's perceptions is crucial for understanding behaviour and developing effective management strategies to maintain, preserve and improve biodiversity, ecosystem services and human well-being. As an interdisciplinary team, we produced a synthesis of the key factors that influence people's perceptions of invasive alien species, and ordered them in a conceptual framework. In a context of considerable complexity and variation across time and space, we identified six broad-scale dimensions: (1) attributes of the individual perceiving the invasive alien species; (2) characteristics of the invasive alien species itself; (3) effects of the invasion (including negative and positive impacts, i.e. benefits and costs); (4) socio-cultural context; (5) landscape context; and (6) institutional and policy context. A number of underlying and facilitating aspects for each of these six overarching dimensions are also identified and discussed. Synthesising and understanding the main factors that influence people's perceptions is useful to guide future research, to facilitate dialogue and negotiation between actors, and to aid management and policy formulation and governance of invasive alien species. This can help to circumvent and mitigate conflicts, support prioritisation plans, improve stakeholder engagement platforms, and implement control measures.

Phage therapy could offer a safe and effective alternative to antibiotic treatment of infections caused by Gram-positive bacterium Staphylococcus aureus that have emerged as a significant threat in hospital and community environment and is attracting growing interest among clinicians. The legislation process of approving the phage therapeutics by pharmaceutical authorities requires rapid analytical techniques for assessment of phage activity. Here, we present a three-step method for on-line monitoring the phage effect on bacterial cells dynamically adhered from microliter volumes of high conductivity matrix onto the inner surface of fused silica capillary with a part etched with supercritical water. Phage K1/420 particles of the Kayvirus genus generated by propagation on the host S. aureus cells together with the uninfected cells were concentrated, separated and detected using capillary electrophoretic methods. The phage interactions with selected S. aureus strains exhibiting differences in phage susceptibility were compared. The method allowed determination of the phage burst size and time of phage latent period in analyzed strains. Apart from enumeration of bacteriophages by the plaque assays, the proposed method is suitable for phage activity testing.

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We propose a computational model to study (the evolution of) post-secondary education. “Consumers” who differ in quality shop around for desirable colleges or universities. “Firms” that differ in quality signal the availability of their services to desirable students. As long as they have capacity, colleges and universities make offers to students, who apply and qualify. Our model generalizes an earlier literature (namely, Vriend 1995) in an important dimension: quality, the model confirms key predictions of an analytical model that we also supply, and the model allows us to systematically explore the emergence of macro regularities and the consequences of various strategies that sellers might try. We supply three such exercises. In our baseline treatment we establish the dynamics and asymptotics of our generalized matching model. In the second treatment we study the consequences of opportunistic behavior of firms and thus demonstrate the usefulness of our computational laboratory for the analysis of this or similar questions (e.g., the problem of early admission). In the third treatment we equip some firms with economies of scale. This variant of our matching model is motivated by the entry of for-profit providers into low-quality segments of post-secondary education in the USA and by empirical evidence that, while traditional nonprofit or state-supported providers of higher education do not have significant economies of scale, the new breed of for-profit providers seems to capture economies in core functions such as curricular design, advertising, informational infrastructure, and regulatory compliance. Our computational results suggest that this new breed of providers is likely to continue to move up the quality ladder, albeit not necessarily all the way up to the top.