Criteria of efficiency for conformal prediction

We study optimal conformity measures for various criteria of efficiency of classification in an idealised setting. This leads to an important class of criteria of efficiency that we call probabilistic; it turns out that the most standard criteria of efficiency used in literature on conformal prediction are not probabilistic unless the problem of classification is binary. We consider both unconditional and label-conditional conformal prediction.Comment: 31 page

Decentralized Estimation over Orthogonal Multiple-access Fading Channels in Wireless Sensor Networks - Optimal and Suboptimal Estimators

Optimal and suboptimal decentralized estimators in wireless sensor networks (WSNs) over orthogonal multiple-access fading channels are studied in this paper. Considering multiple-bit quantization before digital transmission, we develop maximum likelihood estimators (MLEs) with both known and unknown channel state information (CSI). When training symbols are available, we derive a MLE that is a special case of the MLE with unknown CSI. It implicitly uses the training symbols to estimate the channel coefficients and exploits the estimated CSI in an optimal way. To reduce the computational complexity, we propose suboptimal estimators. These estimators exploit both signal and data level redundant information to improve the estimation performance. The proposed MLEs reduce to traditional fusion based or diversity based estimators when communications or observations are perfect. By introducing a general message function, the proposed estimators can be applied when various analog or digital transmission schemes are used. The simulations show that the estimators using digital communications with multiple-bit quantization outperform the estimator using analog-and-forwarding transmission in fading channels. When considering the total bandwidth and energy constraints, the MLE using multiple-bit quantization is superior to that using binary quantization at medium and high observation signal-to-noise ratio levels

High-fidelity multimode fibre-based endoscopy for deep brain in vivo imaging

Progress in neuroscience constantly relies on the development of new techniques to investigate the complex dynamics of neuronal networks. An ongoing challenge is to achieve minimally-invasive and high-resolution observations of neuronal activity in vivo inside deep brain areas. A perspective strategy is to utilise holographic control of light propagation in complex media, which allows converting a hair-thin multimode optical fibre into an ultra-narrow imaging tool. Compared to current endoscopes based on GRIN lenses or fibre bundles, this concept offers a footprint reduction exceeding an order of magnitude, together with a significant enhancement in resolution. We designed a compact and high-speed system for fluorescent imaging at the tip of a fibre, achieving micron-scale resolution across a 50 um field of view, and yielding 7-kilopixel images at a rate of 3.5 frames/s. Furthermore, we demonstrate in vivo observations of cell bodies and processes of inhibitory neurons within deep layers of the visual cortex and hippocampus of anesthetised mice. This study forms the basis for several perspective techniques of modern microscopy to be delivered deep inside the tissue of living animal models while causing minimal impact on its structural and functional properties.Comment: 10 pages, 2 figures, Supplementary movie: https://drive.google.com/file/d/1Fm0G3TAIC49LVX6FaEiAtlefkWx1T2a5/vie

Looking backward: From Euler to Riemann

We survey the main ideas in the early history of the subjects on which Riemann worked and that led to some of his most important discoveries. The subjects discussed include the theory of functions of a complex variable, elliptic and Abelian integrals, the hypergeometric series, the zeta function, topology, differential geometry, integration, and the notion of space. We shall see that among Riemann's predecessors in all these fields, one name occupies a prominent place, this is Leonhard Euler. The final version of this paper will appear in the book \emph{From Riemann to differential geometry and relativity} (L. Ji, A. Papadopoulos and S. Yamada, ed.) Berlin: Springer, 2017

Nonlinear Supersymmetry as a Hidden Symmetry

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Structure in 6D and 4D N=1 supergravity theories from F-theory

We explore some aspects of 4D supergravity theories and F-theory vacua that are parallel to structures in the space of 6D theories. The spectrum and topological terms in 4D supergravity theories correspond to topological data of F-theory geometry, just as in six dimensions. In particular, topological axion-curvature squared couplings appear in 4D theories; these couplings are characterized by vectors in the dual to the lattice of axion shift symmetries associated with string charges. These terms are analogous to the Green-Schwarz terms of 6D supergravity theories, though in 4D the terms are not generally linked with anomalies. We outline the correspondence between F-theory topology and data of the corresponding 4D supergravity theories. The correspondence of geometry with structure in the low-energy action illuminates topological aspects of heterotic-F-theory duality in 4D as well as in 6D. The existence of an F-theory realization also places geometrical constraints on the 4D supergravity theory in the large-volume limit.Comment: 63 page

Three-dimensional holographic optical manipulation through a high-numerical-aperture soft-glass multimode fibre

Holographic optical tweezers (HOT) hold great promise for many applications in biophotonics, allowing the creation and measurement of minuscule forces on biomolecules, molecular motors and cells. Geometries used in HOT currently rely on bulk optics, and their exploitation in vivo is compromised by the optically turbid nature of tissues. We present an alternative HOT approach in which multiple three-dimensional (3D) traps are introduced through a high-numerical-aperture multimode optical fibre, thus enabling an equally versatile means of manipulation through channels having cross-section comparable to the size of a single cell. Our work demonstrates real-time manipulation of 3D arrangements of micro-objects, as well as manipulation inside otherwise inaccessible cavities. We show that the traps can be formed over fibre lengths exceeding 100 mm and positioned with nanometric resolution. The results provide the basis for holographic manipulation and other high-numerical-aperture techniques, including advanced microscopy, through single-core-fibre endoscopes deep inside living tissues and other complex environments

Genomic and neural analysis of the estradiol-synthetic pathway in the zebra finch

<p>Abstract</p> <p>Background</p> <p>Steroids are small molecule hormones derived from cholesterol. Steroids affect many tissues, including the brain. In the zebra finch, estrogenic steroids are particularly interesting because they masculinize the neural circuit that controls singing and their synthesis in the brain is modulated by experience. Here, we analyzed the zebra finch genome assembly to assess the content, conservation, and organization of genes that code for components of the estrogen-synthetic pathway and steroid nuclear receptors. Based on these analyses, we also investigated neural expression of a cholesterol transport protein gene in the context of song neurobiology.</p> <p>Results</p> <p>We present sequence-based analysis of twenty steroid-related genes using the genome assembly and other resources. Generally, zebra finch genes showed high homology to genes in other species. The diversity of steroidogenic enzymes and receptors may be lower in songbirds than in mammals; we were unable to identify all known mammalian isoforms of the 3β-hydroxysteroid dehydrogenase and 17β-hydroxysteroid dehydrogenase families in the zebra finch genome assembly, and not all splice sites described in mammals were identified in the corresponding zebra finch genes. We did identify two factors, Nobox and NR1H2-RXR, that may be important for coordinated transcription of multiple steroid-related genes. We found very little qualitative overlap in predicted transcription factor binding sites in the genes for two cholesterol transport proteins, the 18 kDa cholesterol transport protein (TSPO) and steroidogenic acute regulatory protein (StAR). We therefore performed in situ hybridization for TSPO and found that its mRNA was not always detected in brain regions where StAR and steroidogenic enzymes were previously shown to be expressed. Also, transcription of TSPO, but not StAR, may be regulated by the experience of hearing song.</p> <p>Conclusions</p> <p>The genes required for estradiol synthesis and action are represented in the zebra finch genome assembly, though the complement of steroidogenic genes may be smaller in birds than in mammals. Coordinated transcription of multiple steroidogenic genes is possible, but results were inconsistent with the hypothesis that StAR and TSPO mRNAs are co-regulated. Integration of genomic and neuroanatomical analyses will continue to provide insights into the evolution and function of steroidogenesis in the songbird brain.</p

The stellar and sub-stellar IMF of simple and composite populations

The current knowledge on the stellar IMF is documented. It appears to become top-heavy when the star-formation rate density surpasses about 0.1Msun/(yr pc^3) on a pc scale and it may become increasingly bottom-heavy with increasing metallicity and in increasingly massive early-type galaxies. It declines quite steeply below about 0.07Msun with brown dwarfs (BDs) and very low mass stars having their own IMF. The most massive star of mass mmax formed in an embedded cluster with stellar mass Mecl correlates strongly with Mecl being a result of gravitation-driven but resource-limited growth and fragmentation induced starvation. There is no convincing evidence whatsoever that massive stars do form in isolation. Various methods of discretising a stellar population are introduced: optimal sampling leads to a mass distribution that perfectly represents the exact form of the desired IMF and the mmax-to-Mecl relation, while random sampling results in statistical variations of the shape of the IMF. The observed mmax-to-Mecl correlation and the small spread of IMF power-law indices together suggest that optimally sampling the IMF may be the more realistic description of star formation than random sampling from a universal IMF with a constant upper mass limit. Composite populations on galaxy scales, which are formed from many pc scale star formation events, need to be described by the integrated galactic IMF. This IGIMF varies systematically from top-light to top-heavy in dependence of galaxy type and star formation rate, with dramatic implications for theories of galaxy formation and evolution.Comment: 167 pages, 37 figures, 3 tables, published in Stellar Systems and Galactic Structure, Vol.5, Springer. This revised version is consistent with the published version and includes additional references and minor additions to the text as well as a recomputed Table 1. ISBN 978-90-481-8817-