Lensless high-resolution on-chip optofluidic microscopes for Caenorhabditis elegans and cell imaging

Low-cost and high-resolution on-chip microscopes are vital for reducing cost and improving efficiency for modern biomedicine and bioscience. Despite the needs, the conventional microscope design has proven difficult to miniaturize. Here, we report the implementation and application of two high-resolution (≈0.9 μm for the first and ≈0.8 μm for the second), lensless, and fully on-chip microscopes based on the optofluidic microscopy (OFM) method. These systems abandon the conventional microscope design, which requires expensive lenses and large space to magnify images, and instead utilizes microfluidic flow to deliver specimens across array(s) of micrometer-size apertures defined on a metal-coated CMOS sensor to generate direct projection images. The first system utilizes a gravity-driven microfluidic flow for sample scanning and is suited for imaging elongate objects, such as Caenorhabditis elegans; and the second system employs an electrokinetic drive for flow control and is suited for imaging cells and other spherical/ellipsoidal objects. As a demonstration of the OFM for bioscience research, we show that the prototypes can be used to perform automated phenotype characterization of different Caenorhabditis elegans mutant strains, and to image spores and single cellular entities. The optofluidic microscope design, readily fabricable with existing semiconductor and microfluidic technologies, offers low-cost and highly compact imaging solutions. More functionalities, such as on-chip phase and fluorescence imaging, can also be readily adapted into OFM systems. We anticipate that the OFM can significantly address a range of biomedical and bioscience needs, and engender new microscope applications

Weighted Dirac combs with pure point diffraction

A class of translation bounded complex measures, which have the form of weighted Dirac combs, on locally compact Abelian groups is investigated. Given such a Dirac comb, we are interested in its diffraction spectrum which emerges as the Fourier transform of the autocorrelation measure. We present a sufficient set of conditions to ensure that the diffraction measure is a pure point measure. Simultaneously, we establish a natural link to the theory of the cut and project formalism and to the theory of almost periodic measures. Our conditions are general enough to cover the known theory of model sets, but also to include examples such as the visible lattice points.Comment: 44 pages; several corrections and improvement

Normal families of functions and groups of pseudoconformal diffeomorphisms of quaternion and octonion variables

This paper is devoted to the specific class of pseudoconformal mappings of quaternion and octonion variables. Normal families of functions are defined and investigated. Four criteria of a family being normal are proven. Then groups of pseudoconformal diffeomorphisms of quaternion and octonion manifolds are investigated. It is proven, that they are finite dimensional Lie groups for compact manifolds. Their examples are given. Many charactersitic features are found in comparison with commutative geometry over $\bf R$ or $\bf C$.Comment: 55 pages, 53 reference

International education: a force for peace and cross-cultural understanding?

This paper discusses the notion that the international sojourn has the potential to transform sojourners into cultural mediators who carry the power to improve global relations. A year-long ethnographic study of the adjustment experiences of international postgraduate students in England revealed a universal early enthusiasm for cross-cultural contact that was matched by a widespread adoption of segregated patterns of interacting. The most common friendship networks were described by bonds with conationals, and yet all students attested to an increase in their cultural learning and mindfulness by the end of the sojourn. Nevertheless, intercultural competence was maximised only in those few students who pursued a multicultural strategy of interaction, leading the researcher to call on Higher Education Institutions to instigate policies to encourage lasting cross-cultural contact

A dimensionally continued Poisson summation formula

We generalize the standard Poisson summation formula for lattices so that it operates on the level of theta series, allowing us to introduce noninteger dimension parameters (using the dimensionally continued Fourier transform). When combined with one of the proofs of the Jacobi imaginary transformation of theta functions that does not use the Poisson summation formula, our proof of this generalized Poisson summation formula also provides a new proof of the standard Poisson summation formula for dimensions greater than 2 (with appropriate hypotheses on the function being summed). In general, our methods work to establish the (Voronoi) summation formulae associated with functions satisfying (modular) transformations of the Jacobi imaginary type by means of a density argument (as opposed to the usual Mellin transform approach). In particular, we construct a family of generalized theta series from Jacobi theta functions from which these summation formulae can be obtained. This family contains several families of modular forms, but is significantly more general than any of them. Our result also relaxes several of the hypotheses in the standard statements of these summation formulae. The density result we prove for Gaussians in the Schwartz space may be of independent interest.Comment: 12 pages, version accepted by JFAA, with various additions and improvement

Quasi-analyticity and determinacy of the full moment problem from finite to infinite dimensions

This paper is aimed to show the essential role played by the theory of quasi-analytic functions in the study of the determinacy of the moment problem on finite and infinite-dimensional spaces. In particular, the quasi-analytic criterion of self-adjointness of operators and their commutativity are crucial to establish whether or not a measure is uniquely determined by its moments. Our main goal is to point out that this is a common feature of the determinacy question in both the finite and the infinite-dimensional moment problem, by reviewing some of the most known determinacy results from this perspective. We also collect some properties of independent interest concerning the characterization of quasi-analytic classes associated to log-convex sequences.Comment: 28 pages, Stochastic and Infinite Dimensional Analysis, Chapter 9, Trends in Mathematics, Birkh\"auser Basel, 201

Dynamical percolation on general trees

H\"aggstr\"om, Peres, and Steif (1997) have introduced a dynamical version of percolation on a graph $G$. When $G$ is a tree they derived a necessary and sufficient condition for percolation to exist at some time $t$. In the case that $G$ is a spherically symmetric tree, H\"aggstr\"om, Peres, and Steif (1997) derived a necessary and sufficient condition for percolation to exist at some time $t$ in a given target set $D$. The main result of the present paper is a necessary and sufficient condition for the existence of percolation, at some time $t\in D$, in the case that the underlying tree is not necessary spherically symmetric. This answers a question of Yuval Peres (personal communication). We present also a formula for the Hausdorff dimension of the set of exceptional times of percolation.Comment: 24 pages; to appear in Probability Theory and Related Field

A consideration of the challenges involved in supervising international masters students

This paper explores the challenges facing supervisors of international postgraduate students at the dissertation stage of the masters programme. The central problems of time pressure, language difficulties, a lack of critical analysis and a prevalence of personal problems among international students are discussed. This paper makes recommendations for the improvement of language and critical thinking skills, and questions the future policy of language requirements at HE for international Masters students