Filtering smooth concordance classes of topologically slice knots

We propose and analyze a structure with which to organize the difference between a knot in the 3-sphere bounding a topologically embedded 2-disk in the 4-ball and it bounding a smoothly embedded disk. The n-solvable filtration of the topological knot concordance group, due to Cochran-Orr-Teichner, may be complete in the sense that any knot in the intersection of its terms may well be topologically slice. However, the natural extension of this filtration to what is called the n-solvable filtration of the smooth knot concordance group, is unsatisfactory because any topologically slice knot lies in every term of the filtration. To ameliorate this we investigate a new filtration, {B_n}, that is simultaneously a refinement of the n-solvable filtration and a generalization of notions of positivity studied by Gompf and Cochran. We show that each B_n/B_{n+1} has infinite rank. But our primary interest is in the induced filtration, {T_n}, on the subgroup, T, of knots that are topologically slice. We prove that T/T_0 is large, detected by gauge-theoretic invariants and the tau, s, and epsilon-invariants; while the non-triviliality of T_0/T_1 can be detected by certain d-invariants. All of these concordance obstructions vanish for knots in T_1. Nonetheless, going beyond this, our main result is that T_1/T_2 has positive rank. Moreover under a "weak homotopy-ribbon" condition, we show that each T_n/T_{n+1} has positive rank. These results suggest that, even among topologically slice knots, the fundamental group is responsible for a wide range of complexity.Comment: 41 pages, slightly revised introduction, minor corrections and up-dated references, this is the final version to appear in Geometry and Topolog

Approaching the basis set limit for DFT calculations using an environment-adapted minimal basis with perturbation theory: formulation, proof of concept, and a pilot implementation

Recently developed density functionals have good accuracy for both thermochemistry (TC) and non-covalent interactions (NC) if very large atomic orbital basis sets are used. To approach the basis set limit with potentially lower computational cost, a new self-consistent field (SCF) scheme is presented that employs minimal adaptive basis (MAB) functions. The MAB functions are optimized on each atomic site by minimizing a surrogate function. High accuracy is obtained by applying a perturbative correction (PC) to the MAB calculation, similar to dual basis approaches. Compared to exact SCF results, using this MAB-SCF?(PC) approach with the same large target basis set produces <0.15 kcal/mol root-mean-square deviations for most of the tested TC datasets, and <0.1 kcal/mol for most of the NC datasets. The performance of density functionals near the basis set limit can be even better reproduced. With further improvement to its implementation, MAB-SCF?(PC) is a promising lower-cost substitute for conventional large-basis calculations as a method to approach the basis set limit of modern density functionals

EFSA NDA Panel (EFSA Panel on Dietetic Products, Nut rition and Allergies ) , 2013. Scientific Opinion on the substantiation of a health claim related to the c onsum ption of 2 g/day of plant stanols (as plant stanol ester s ) as part of a diet low in saturated fat and a two - fold greater reduction in blood LDL - chol esterol concentrations compared to the consumption of a diet low in saturated fat alone pursuant to Article 14 of Regulation (EC) No 1924/2006

Following an application from McNeil Nutritionals and Raisio Nutrition Ltd, submitted for authorisation of a health claim pursuant to Article 14 of Regulation (EC) No 1924/2006 via the Competent Authority of the United Kingdom, the Panel on Dietetic Products, Nutrition and Allergies (NDA) was asked to deliver an opinion on the scientific substantiation of a health claim related to the consumption of 2 g/day of plant stanols (as plant stanol esters) as part of a diet low in saturated fat and a two-fold greater reduction in blood LDL-cholesterol concentrations compared to the consumption of a diet low in saturated fat alone. The food that is the subject of the health claim, plant stanol esters, is sufficiently characterised. The applicant provided five human intervention studies for the scientific substantiation of the claim. The Panel notes that the design of the studies submitted did not allow an evaluation of the quantitative effects of diets low in saturated fat per se on blood LDL-cholesterol concentrations. Therefore, the effect of consuming 2 g/day plant stanols as part of a diet low in saturated fat relative to the effect of consuming a diet low in saturated fat alone cannot be determined on a quantitative basis. The Panel considers that the evidence provided by the applicant does not establish that the consumption of 2 g/day of plant stanols (as plant stanol esters) as part of a diet low in saturated fat results in a two-fold greater reduction in LDL-cholesterol concentrations compared with consuming a diet low in saturated fat alone. A claim on plant stanol esters and reduction of blood LDL-cholesterol concentrations (irrespective of the background diet) has already been authorised in the European Union

A Non-Perturbative Pairwise-Additive Analysis of Charge Transfer Contributions to Intermolecular Interaction Energies

Energy decomposition analysis (EDA) based on absolutely localized molecular orbitals (ALMOs) decomposes the interaction energy between molecules into physically interpretable components like geometry distortion, frozen interactions, polarization, and charge transfer (CT, also sometimes called charge delocalization) interactions. In this work, a numerically exact scheme to decompose the CT interaction energy into pairwise additive terms is introduced for the ALMO-EDA using density functional theory. Unlike perturbative pairwise charge-decomposition analysis, the new approach does not break down for strongly interacting systems, or show significant exchange-correlation functional dependence in the decomposed energy components. Both the energy lowering and the charge flow associated with CT can be decomposed. Complementary occupied-virtual orbital pairs (COVPs) that capture the dominant donor and acceptor CT orbitals are obtained for the new decomposition. It is applied to systems with different types of interactions including DNA base-pairs, borane-ammonia adducts, and transition metal hexacarbonyls. While consistent with most existing understanding of the nature of CT in these systems, the results also reveal some new insights into the origin of trends in donor-acceptor interactions

User-friendly tail bounds for sums of random matrices

This paper presents new probability inequalities for sums of independent, random, self-adjoint matrices. These results place simple and easily verifiable hypotheses on the summands, and they deliver strong conclusions about the large-deviation behavior of the maximum eigenvalue of the sum. Tail bounds for the norm of a sum of random rectangular matrices follow as an immediate corollary. The proof techniques also yield some information about matrix-valued martingales. In other words, this paper provides noncommutative generalizations of the classical bounds associated with the names Azuma, Bennett, Bernstein, Chernoff, Hoeffding, and McDiarmid. The matrix inequalities promise the same diversity of application, ease of use, and strength of conclusion that have made the scalar inequalities so valuable.Comment: Current paper is the version of record. The material on Freedman's inequality has been moved to a separate note; other martingale bounds are described in Caltech ACM Report 2011-0

The 'not-so-strange' body in the mirror: : A principal components analysis of direct and mirror self-observation

This document is the Accepted Manuscript version of the following article: Paul M. Jenkinson, and Catherine Preston, ‘The “not-so-strange” body in the mirror: A principal components analysis of direct and mirror self-observation’, Consciousness and Cognition, Vol. 48, pp. 262-272, first published online 4 January 2017, doi: http://dx.doi.org/10.1016/j.concog.2016.12.007 This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/.In this study we adopted a psychometric approach to examine how the body is subjectively experienced in a mirror. One hundred and twenty-four healthy participants viewed their body for five minutes directly or via a mirror, and then completed a 20-item questionnaire designed to capture subjective experiences of the body. PCA revealed a two-component structure for both direct and mirror conditions, comprising body evaluations (and alienation) and unusual feelings and perceptions. The relationship between these components and pre-existing tendencies for appearance anxiety, body dysmorphic-type beliefs, dissociative symptomatology, self-objectification and delusion ideation further supported the similarity between direct and mirror conditions; however, the occurrence of strange experiences like those reported to occur during prolonged face viewing was not confirmed. These results suggest that, despite obvious differences in visual feedback, observing the body via a mirror (as an outside observer) is subjectively equivalent to observing the body directly (from our own viewpoint).Peer reviewedFinal Accepted Versio

Assessment and weighting of meteorological ensemble forecast members based on supervised machine learning with application to runoff simulations and flood warning

Numerical weather forecasts, such as meteorological forecasts of precipitation, are inherently uncertain. These uncertainties depend on model physics as well as initial and boundary conditions. Since precipitation forecasts form the input into hydrological models, the uncertainties of the precipitation forecasts result in uncertainties of flood forecasts. In order to consider these uncertainties, ensemble prediction systems are applied. These systems consist of several members simulated by different models or using a single model under varying initial and boundary conditions. However, a too wide uncertainty range obtained as a result of taking into account members with poor prediction skills may lead to underestimation or exaggeration of the risk of hazardous events. Therefore, the uncertainty range of model-based flood forecasts derived from the meteorological ensembles has to be restricted. In this paper, a methodology towards improving flood forecasts by weighting ensemble members according to their skills is presented. The skill of each ensemble member is evaluated by comparing the results of forecasts corresponding to this member with observed values in the past. Since numerous forecasts are required in order to reliably evaluate the skill, the evaluation procedure is time-consuming and tedious. Moreover, the evaluation is highly subjective, because an expert who performs it makes his decision based on his implicit knowledge. Therefore, approaches for the automated evaluation of such forecasts are required. Here, we present a semi automated approach for the assessment of precipitation forecast ensemble members. The approach is based on supervised machine learning and was tested on ensemble precipitation forecasts for the area of the Mulde river basin in Germany. Based on the evaluation results of the specific ensemble members, weights corresponding to their forecast skill were calculated. These weights were then successfully used to reduce the uncertainties within rainfall-runoff simulations and flood risk predictions

Single electron emission in two-phase xenon with application to the detection of coherent neutrino-nucleus scattering

We present an experimental study of single electron emission in ZEPLIN-III, a two-phase xenon experiment built to search for dark matter WIMPs, and discuss applications enabled by the excellent signal-to-noise ratio achieved in detecting this signature. Firstly, we demonstrate a practical method for precise measurement of the free electron lifetime in liquid xenon during normal operation of these detectors. Then, using a realistic detector response model and backgrounds, we assess the feasibility of deploying such an instrument for measuring coherent neutrino-nucleus elastic scattering using the ionisation channel in the few-electron regime. We conclude that it should be possible to measure this elusive neutrino signature above an ionisation threshold of $\sim$3 electrons both at a stopped pion source and at a nuclear reactor. Detectable signal rates are larger in the reactor case, but the triggered measurement and harder recoil energy spectrum afforded by the accelerator source enable lower overall background and fiducialisation of the active volume

Identification of Genes Affecting the Toxicity of Anti-Cancer Drug Bortezomib by Genome-Wide Screening in S. pombe

Bortezomib/PS-341/Velcade, a proteasome inhibitor, is widely used to treat multiple myeloma. While several mechanisms of the cytotoxicity of the drug were proposed, the actual mechanism remains elusive. We aimed to identify genes affecting the cytotoxicity of Bortezomib in the fission yeast S.pombe as the drug inhibits this organism's cell division cycle like proteasome mutants. Among the 2815 genes screened (covering 56% of total ORFs), 19 genes, whose deletions induce strong synthetic lethality with Bortezomib, were identified. The products of the 19 genes included four ubiquitin enzymes and one nuclear proteasome factor, and 13 of them are conserved in humans. Our results will provide useful information for understanding the actions of Bortezomib within cells