Ribbon braids and related operads

This thesis consists of two parts, both being concerned with operads related to the ribbon braid groups. In the first part, we define a notion of semidirect product for operads and use it to study the framed $n$-discs operad (the semidirect product $f\mathcal{D}_n=\mathcal{D}_n\rtimes SO(n)$ of the little $n$-discs operad with the special orthogonal group). This enables us to deduce properties of $f\mathcal{D}_n$ from the corresponding properties for $\mathcal{D}_n$. We prove an equivariant recognition principle saying that algebras over the framed $n$-discs operad are $n$-fold loop spaces on $SO(n)$-spaces. We also study the operations induced on homology, showing that an $H(f\mathcal{D}_n)$-algebra is a higher dimensional Batalin-Vilkovisky algebra with some additional operators when $n$ is even. Contrastingly, for $n$ odd, we show that the Gerstenhaber structure coming from the little $n$-discs does not give rise to a Batalin-Vilkovisky structure. We give a general construction of operads from families of groups. We then show that the operad obtained from the ribbon braid groups is equivalent to the framed 2-discs operad. It follows that the classifying spaces of ribbon braided monoidal categories are double loop spaces on $S^1$-spaces. The second part of this thesis is concerned with infinite loop space structures on the stable mapping class group. Two such structures were discovered by Tillmann. We show that they are equivalent, constructing a map between the spectra of deloops. We first construct an `almost map', i.e a map between simplicial spaces for which one of the simplicial identities is satisfied only up to homotopy. We show that there are higher homotopies and deduce the existence of a rectification. We then show that the rectification gives an equivalence of spectra

Projected entangled-pair states can describe chiral topological states

We show that Projected Entangled-Pair States (PEPS) in two spatial dimensions can describe chiral topological states by explicitly constructing a family of such states with a non-trivial Chern number. They are ground states of two different kinds of free-fermion Hamiltonians: (i) local and gapless; (ii) gapped, but with hopping amplitudes that decay according to a power law. We derive general conditions on topological free fermionic PEPS which show that they cannot correspond to exact ground states of gapped, local parent Hamiltonians, and provide numerical evidence demonstrating that they can nevertheless approximate well the physical properties of topological insulators with local Hamiltonians at arbitrary temperatures.Comment: v2: minor changes, references added. v3: accepted version, Journal-Ref adde

Extraction efficiency of drifting electrons in a two-phase xenon time projection chamber

We present a measurement of the extraction efficiency of quasi-free electrons from the liquid into the gas phase in a two-phase xenon time-projection chamber. The measurements span a range of electric fields from 2.4 to 7.1 kV/cm in the liquid xenon, corresponding to 4.5 to 13.1 kV/cm in the gaseous xenon. Extraction efficiency continues to increase at the highest extraction fields, implying that additional charge signal may be attained in two-phase xenon detectors through careful high-voltage engineering of the gate-anode region

Redefining Freedom Of Speech Under International Space Law: The Need For Bilateral Communications Alliances To Resolve The Debate Between The Free Flow Of Information And Prior Consent Schools Of Thought

The International Court of Justice (ICJ) has a dilemma. Imagine the Utopian States\u27 positions a $236 million satellite system in the geosynchronous orbit to broadcast Utopian programming into Atlantis. Atlantis is outraged. Atlantis believes that Utopian programming not only destroys the cultural identity of Atlantis, but also advocates the overthrow of the Atlantian government. Despite protests by Atlantis, the Utopian States assert that international freedom of speech protects the broadcast

Calibration of a two-phase xenon time projection chamber with a 37^{37}Ar source

We calibrate a two-phase xenon detector at 0.27 keV in the charge channel and at 2.8 keV in both the light and charge channels using a $^{37}$Ar source that is directly released into the detector. We map the light and charge yields as a function of electric drift field. For the 2.8 keV peak, we calculate the Thomas-Imel box parameter for recombination and determine its dependence on drift field. For the same peak, we achieve an energy resolution, $E_{\sigma}/E_{mean}$, between 9.8% and 10.8% for 0.1 kV/cm to 2 kV/cm electric drift fields.Comment: 12 pages, 7 figure

Structural basis for dual roles of Aar2p in U5 snRNP assembly

Yeast U5 small nuclear ribonucleoprotein particle (snRNP) is assembled via a cytoplasmic precursor that contains the U5-specific Prp8 protein but lacks the U5-specific Brr2 helicase. Instead, pre-U5 snRNP includes the Aar2 protein not found in mature U5 snRNP or spliceosomes. Aar2p and Brr2p bind competitively to a C-terminal region of Prp8p that comprises consecutive RNase H-like and Jab1/MPN-like domains. To elucidate the molecular basis for this competition, we determined the crystal structure of Aar2p in complex with the Prp8p RNase H and Jab1/MPN domains. Aar2p binds on one side of the RNase H domain and extends its C terminus to the other side, where the Jab1/MPN domain is docked onto a composite Aar2p–RNase H platform. Known Brr2p interaction sites of the Jab1/MPN domain remain available, suggesting that Aar2p-mediated compaction of the Prp8p domains sterically interferes with Brr2p binding. Moreover, Aar2p occupies known RNA-binding sites of the RNase H domain, and Aar2p interferes with binding of U4/U6 di-snRNA to the Prp8p C-terminal region. Structural and functional analyses of phospho-mimetic mutations reveal how phosphorylation reduces affinity of Aar2p for Prp8p and allows Brr2p and U4/U6 binding. Our results show how Aar2p regulates both protein and RNA binding to Prp8p during U5 snRNP assembly

Anveshak - A Groundtruth Generation Tool for Foreground Regions of Document Images

We propose a graphical user interface based groundtruth generation tool in this paper. Here, annotation of an input document image is done based on the foreground pixels. Foreground pixels are grouped together with user interaction to form labeling units. These units are then labeled by the user with the user defined labels. The output produced by the tool is an image with an XML file containing its metadata information. This annotated data can be further used in different applications of document image analysis.Comment: Accepted in DAR 201

Local-regional richness relationship in fouling assemblages - Effects of succession

The number of species in a local habitat depends on local and regional processes. One common approach to explore ecological saturation of local richness has been to plot local versus regional richness. We expand this approach by incorporating two dimensions of diversity - taxonomic and functional - and different successional ages of marine fouling communities. In four different biogeographic regions (Mediterranean Sea, NE Atlantic, Western Baltic Sea and North Sea) 60 experimental units made from artificial substratum were deployed for colonization. Local richness was assessed as the average number of species and functional groups (FG) per unit area while regional richness was estimated as the estimated (Jack 2) asymptote of the accumulation curves for species or FG in local panel communities. Our findings indicate that the nature of the relationship between local and regional diversity is sensitive to successional stage and the dimension of diversity considered. However, as a general pattern, for taxonomic and functional richness, the slope of the local-regional relationship increased in the course of succession. We discuss how this pattern could have been produced by a combination of low number of recruiting species and incomplete competitive exclusion as is typical for early Successio