Homotopy classification of ribbon tubes and welded string links

Ribbon 2-knotted objects are locally flat embeddings of surfaces in 4-space which bound immersed 3-manifolds with only ribbon singularities. They appear as topological realizations of welded knotted objects, which is a natural quotient of virtual knot theory. In this paper we consider ribbon tubes and ribbon torus-links, which are natural analogues of string links and links, respectively. We show how ribbon tubes naturally act on the reduced free group, and how this action classifies ribbon tubes up to link-homotopy, that is when allowing each component to cross itself. At the combinatorial level, this provides a classification of welded string links up to self-virtualization. This generalizes a result of Habegger and Lin on usual string links, and the above-mentioned action on the reduced free group can be refined to a general "virtual extension" of Milnor invariants. As an application, we obtain a classification of ribbon torus-links up to link-homotopy.Comment: 33p. ; v2: typos and minor corrections ; v3: Introduction rewritten, exposition revised, references added. Section 5 of the previous version was significantly expanded and was separated into another paper (arXiv:1507.00202) ; v4: typos and minor corrections ; to appear in Annali della scuola Normale Superiore de Pisa (classe de scienze

Extensions of some classical local moves on knot diagrams

In the present paper, we consider local moves on classical and welded diagrams: (self-)crossing change, (self-)virtualization, virtual conjugation, Delta, fused, band-pass and welded band-pass moves. Interrelationship between these moves is discussed and, for each of these move, we provide an algebraic classification. We address the question of relevant welded extensions for classical moves in the sense that the classical quotient of classical object embeds into the welded quotient of welded objects. As a by-product, we obtain that all of the above local moves are unknotting operations for welded (long) knots. We also mention some topological interpretations for these combinatorial quotients.Comment: 18 pages; this paper is an entirely new version of "On forbidden moves and the Delta move": the exposition has been totally revised, and several new results have been added; to appear in Michigan Math.

On Usual, Virtual and Welded knotted objects up to homotopy

We consider several classes of knotted objects, namely usual, virtual and welded pure braids and string links, and two equivalence relations on those objects, induced by either self-crossing changes or self-virtualizations. We provide a number of results which point out the differences between these various notions. The proofs are mainly based on the techniques of Gauss diagram formulae.Comment: 14 pages. This paper is an expanded version of a former section, now removed (section 5 in versions 1 and 2) of arXiv:1407.0184. To appear in Journal of the Mathematical Society of Japa

Targeting the poor in Mexico

This report reevaluates PROGRESA's targeting methods since the program began adding beneficiary households through a process called “densification.” The authors first evaluate PROGRESA's accuracy in targeting both at the community and household levels. Second, they evaluate the targeting in terms of its impact on poverty alleviation relative to other feasible methods assuming the same total budget.Education ,Mexico ,

Growth and applications of carbon nanotube-based nanosponge sheets

M.S. University of Hawaii at Manoa 2012.Includes bibliographical references.Recently, while trying to replicate research results from Gui et al. [1], via liquid-injection chemical vapor deposition, an unexpected result was recorded-instead of growing a carbon nanotube sponge on the sample slide as expected, a thin, paper-like film was discovered on the furnace sidewalls. This material was found to have a flexibility and thickness comparable to Teflon tape, capable of being easily handled without tearing. Later SEM analysis showed that this new material was indeed comprised entirely of carbon nanotubes, but with a higher degree of long-range order, flexibility and toughness than the structures reported by Gui et al. indicating that this might be a new material type entirely, and hence is called NanoSponge Sheets (NSSs). After repeating the conditions responsible for the initial discovery, it was determined that the major influencing factor was the addition of xylene to the precursor mix. Further experimentation yielded a functional set of growth parameters, which are still being further refined. Currently, the growth process is being developed to grow larger sizes of the NSSs for further applications testing. The growth process is based on liquid-injection chemical vapor deposition, with a 2" diameter quartz furnace tube. A 6" diameter furnace is currently under development for use in other projects, but can be easily refitted for growing larger NSS samples for larger-scale applications and testing. This "Nano Sponge Sheet" or NSS material has already displayed numerous interesting properties which may make it useful for a range of applications, including but not limited to: supercapacitors, energy storage, water desalination filters, composites/armor, EMF shielding, photovoltaics, and heat sinks

Superconducting quantum node for entanglement and storage of microwave radiation

Superconducting circuits and microwave signals are good candidates to realize quantum networks, which are the backbone of quantum computers. We have realized a quantum node based on a 3D microwave superconducting cavity parametrically coupled to a transmission line by a Josephson ring modulator. We first demonstrate the time-controlled capture, storage and retrieval of an optimally shaped propagating microwave field, with an efficiency as high as 80%. We then demonstrate a second essential ability, which is the timed-controlled generation of an entangled state distributed between the node and a microwave channel.Comment: 6 pages, 4 figures. Supplementary information can be downloaded as the ancillary file her

Short Message Service (SMS) Technology in Alcohol Research—A Feasibility Study

Aim: The aim of this study was to describe the feasibility, advantages and limitations of the combined use of Internet and SMS technology to assess alcohol use, and to test whether an SMS sent in the evening (i.e. prior to a possible drinking event) changed the respondents' assessment, made on the following day, of the number of drinks consumed. Participants: Seventy young adults (mean age 22.7) were recruited through face-to-face contacts, e-mails and Internet advertisements. Design and setting: Participants completed a baseline assessment via Internet and were randomly assigned to two conditions (with and without evening SMS). Over four weekends, both Friday and Saturday night, drinking was assessed via SMS questions sent the next day to the participants' cell phones. Results: A high retention rate (75% in total) was obtained across all three recruitment conditions. The number of drinks indicated in the SMS survey was strongly correlated with the usual quantity assessed via Internet and did not differ depending on whether an additional SMS question was sent in the evening or not. Conclusion: The new method shares some of the advantages of conventional diaries but overcomes most of the limitations: it is easy to use, cost-effective and suitable for large-scale surveys. Application restrictions and further developments are discusse

Simple Bounds for Recovering Low-complexity Models

This note presents a unified analysis of the recovery of simple objects from random linear measurements. When the linear functionals are Gaussian, we show that an s-sparse vector in R^n can be efficiently recovered from 2s log n measurements with high probability and a rank r, n by n matrix can be efficiently recovered from r(6n-5r) with high probability. For sparse vectors, this is within an additive factor of the best known nonasymptotic bounds. For low-rank matrices, this matches the best known bounds. We present a parallel analysis for block sparse vectors obtaining similarly tight bounds. In the case of sparse and block sparse signals, we additionally demonstrate that our bounds are only slightly weakened when the measurement map is a random sign matrix. Our results are based on analyzing a particular dual point which certifies optimality conditions of the respective convex programming problem. Our calculations rely only on standard large deviation inequalities and our analysis is self-contained

Wireless indoor localisation within the 5G internet of radio light

This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University LondonNumerous applications can be enhanced by accurate and efficient indoor localisation using wireless sensor networks, however trade-offs often exist between these two parameters. In this thesis, realworld and simulation data is used to examine the hybrid millimeter wave and Visible Light Communications (VLC) architecture of the 5G Internet of Radio Light (IoRL) Horizon 2020 project. Consequently, relevant localisation challenges within Visible Light Positioning (VLP) and asynchronous sampling networks are identified, and more accurate and efficient solutions are developed. Currently, VLP relies strongly on the assumed Lambertian properties of light sources. However, in practice, not all lights are Lambertian. To support the widespread deployment of VLC technology in numerous environments, measurements from non-Lambertian sources are analysed to provide new insights into the limitations of existing VLP techniques. Subsequently, a novel VLP calibration technique is proposed, and results indicate a 59% accuracy improvement against existing methods. This solution enables high accuracy centimetre level VLP to be achieved with non- Lambertian sources. Asynchronous sampling of range-based measurements is known to impact localisation performance negatively. Various Asynchronous Sampling Localisation Techniques (ASLT) exist to mitigate these effects. While effective at improving positioning performance, the exact suitability of such solutions is not evident due to their additional processes, subsequent complexity, and increased costs. As such, extensive simulations are conducted to study the effectiveness of ASLT under variable sampling latencies, sensor measurement noise, and target trajectories. Findings highlight the computational demand of existing ASLT and motivate the development of a novel solution. The proposed Kalman Extrapolated Least Squares (KELS) method achieves optimal localisation performance with a significant energy reduction of over 50% when compared to current leading ASLT. The work in this thesis demonstrates both the capability for high performance VLP from non- Lambertian sources as well as the potential for energy efficient localisation for sequentially sampled range measurements.Horizon 202