Combinatorial classification of quantum lens spaces

We answer the question of how large the dimension of a quantum lens space must be, compared to the primary parameter $r$, for the isomorphism class to depend on the secondary parameters. Since classification results in C*-algebra theory reduces this question to one concerning a certain kind of $SL$-equivalence of integer matrices of a special form, our approach is entirely combinatorial and based on the counting of certain paths in the graphs shown by Hong and Szyma\'nski to describe the quantum lens spaces.Comment: 27 pages, 2 figure

Kennedy Channel and its geophysical lineaments: new evidence that the Wegener Fault is a myth

2010, the year under review, marks the centennial of perhaps the most controversial structure in the Arctic: the Wegener Fault, the 1000-km long fracture that is supposed to underlie Nares Strait and define the north-western margin of an independent Greenland plate (Fig. 1). The seaway between Greenland and Ellesmere Island, Canada, was branded a megashear by Frank Taylor who, purely on physiographic expression, postulated massive Tertiary strike-slip (Taylor 1910). This revolutionary idea fittingly found a place in Alfred Wegener’s theory of continental drift and thereafter in plate-tectonic theory with Greenland drifting hundreds of kilometres from North America along what Tuzo Wilson subsequently dubbed the ‘Wegener Fault’ (Wilson 1963). Today, the concept lives on. In modern palaeogeography, Nares Strait is given a long multiphase dynamic history with collision of Greenland and Canada in the Palaeogene (Fig. 1). A freely drifting Greenland plate unconstrained by ties to North America is now part of conventional wisdom as related in textbooks, review articles and educational material available on the internet. Accordingly, the Wegener Fault is a standard feature in international compilations of world geology (e.g. UNESCO 2010; Fig. 2). Unfortunately, this 100-year acclamation from Taylor (1910) to UNESCO (2010) is fundamentally flawed: the rocks and their relationships at Nares Strait flatly contradict the existence of the structure

Support of Closed Walks and Second Eigenvalue Multiplicity of the Normalized Adjacency Matrix

We show that the multiplicity of the second normalized adjacency matrix eigenvalue of any connected graph of maximum degree $\Delta$ is bounded by $O(n \Delta^{7/5}/\log^{1/5-o(1)}n)$ for any $\Delta$, and by $O(n\log^{1/2}d/\log^{1/4-o(1)}n)$ for simple $d$-regular graphs when $d\ge \log^{1/4}n$. In fact, the same bounds hold for the number of eigenvalues in any interval of width $\lambda_2/\log_\Delta^{1-o(1)}n$ containing the second eigenvalue $\lambda_2$. The main ingredient in the proof is a polynomial (in $k$) lower bound on the typical support of a closed random walk of length $2k$ in any connected graph, which in turn relies on new lower bounds for the entries of the Perron eigenvector of submatrices of the normalized adjacency matrix.Comment: A previous version of this paper proved the main result for d-regular graphs. The current version proves a more general result for the normalized adjacency matrix of bounded degree graphs. 24pp, 3 figure

Threshold Fully Homomorphic Encryption

We formally define and give the first construction of (leveled) threshold fully homomorphic encryption for any access structure induced by a monotone boolean formula and in particular for the threshold access structure. Our construction is based on the learning with errors assumption and can be instantiated with any existing homomorphic encryption scheme that satisfies fairly general conditions, such as Gentry, Sahai, Waters (CRYPTO 2013) and Brakerski, Gentry, Vaikuntanathan (ITCS 2012). From threshold homomorphic encryption, we construct function secret sharing and distributed pseudorandom functions for the aforementioned access structures. No such constructions were known prior to this work

Empowerment for Continuous Agent-Environment Systems

This paper develops generalizations of empowerment to continuous states. Empowerment is a recently introduced information-theoretic quantity motivated by hypotheses about the efficiency of the sensorimotor loop in biological organisms, but also from considerations stemming from curiosity-driven learning. Empowemerment measures, for agent-environment systems with stochastic transitions, how much influence an agent has on its environment, but only that influence that can be sensed by the agent sensors. It is an information-theoretic generalization of joint controllability (influence on environment) and observability (measurement by sensors) of the environment by the agent, both controllability and observability being usually defined in control theory as the dimensionality of the control/observation spaces. Earlier work has shown that empowerment has various interesting and relevant properties, e.g., it allows us to identify salient states using only the dynamics, and it can act as intrinsic reward without requiring an external reward. However, in this previous work empowerment was limited to the case of small-scale and discrete domains and furthermore state transition probabilities were assumed to be known. The goal of this paper is to extend empowerment to the significantly more important and relevant case of continuous vector-valued state spaces and initially unknown state transition probabilities. The continuous state space is addressed by Monte-Carlo approximation; the unknown transitions are addressed by model learning and prediction for which we apply Gaussian processes regression with iterated forecasting. In a number of well-known continuous control tasks we examine the dynamics induced by empowerment and include an application to exploration and online model learning

Osteoprotegerin and coronary artery disease in type 2 diabetic patients with microalbuminuria

<p>Abstract</p> <p>Objective</p> <p>Plasma osteoprotegerin (P-OPG) is an independent predictor of cardiovascular disease in diabetic and other populations. OPG is a bone-related glycopeptide produced by vascular smooth muscle cells and increased P-OPG may reflect arterial damage. We investigated the correlation between P-OPG and coronary artery disease (CAD) in asymptomatic type 2 diabetic patients with microalbuminuria.</p> <p>Methods</p> <p>P-OPG was measured in 200 asymptomatic diabetic patients without known cardiac disease. Patients with P-NT-proBNP >45.2 ng/l and/or coronary calcium score (CCS) ≥400 were stratified as high risk of CAD (n = 133), and all other patients as low risk patients (n = 67). High risk patients were examined by myocardial perfusion imaging (MPI; n = 109), and/or CT-angiography (n = 20), and/or coronary angiography (CAG; n = 86). Significant CAD was defined by presence of significant myocardial perfusion defects at MPI and/or >70% coronary artery stenosis at CAG.</p> <p>Results</p> <p>Significant CAD was demonstrated in 70 of the high risk patients and of these 23 patients had >70% coronary artery stenosis at CAG. Among high risk patients, increased P-OPG was an independent predictor of significant CAD (adjusted odds ratio [CI] 3.11 [1.01-19.54] and 3.03 [1.00-9.18] for second and third tertile vs.first tertile P-OPG, respectively) and remained so after adjustments for NT-proBNP and CCS. High P-OPG was also associated with presence of >70% coronary artery stenosis(adjusted odds ratio 14.20 [1.35-148.92] for third vs. first tertile P-OPG), and 91% of patients with low (first tertile) P-OPG did not have >70% coronary artery stenosis.</p> <p>Conclusions</p> <p>Elevated P-OPG is an independent predictor of the presence of CAD in asymptomatic type 2 diabetic patients with microalbuminuria.</p

Model-based inference from microvascular measurements: Combining experimental measurements and model predictions using a Bayesian probabilistic approach

Objective: In vivo imaging of the microcirculation and network-oriented modeling have emerged as powerful means of studying microvascular function and understanding its physiological significance. Network-oriented modeling may provide the means of summarizing vast amounts of data produced by high-throughput imaging techniques in terms of key, physiological indices. To estimate such indices with sufficient certainty, however, network-oriented analysis must be robust to the inevitable presence of uncertainty due to measurement errors as well as model errors. Methods: We propose the Bayesian probabilistic data analysis framework as a means of integrating experimental measurements and network model simulations into a combined and statistically coherent analysis. The framework naturally handles noisy measurements and provides posterior distributions of model parameters as well as physiological indices associated with uncertainty. Results: We applied the analysis framework to experimental data from three rat mesentery networks and one mouse brain cortex network. We inferred distributions for more than 500 unknown pressure and hematocrit boundary conditions. Model predictions were consistent with previous analyses, and remained robust when measurements were omitted from model calibration. Conclusion: Our Bayesian probabilistic approach may be suitable for optimizing data acquisition and for analyzing and reporting large data sets acquired as part of microvascular imaging studies

A North Atlantic tephrostratigraphical framework for 130-60 ka b2k:new tephra discoveries, marine-based correlations, and future challenges

Building chronological frameworks for proxy sequences spanning 130–60 ka b2k is plagued by difficulties and uncertainties. Recent developments in the North Atlantic region, however, affirm the potential offered by tephrochronology and specifically the search for cryptotephra. Here we review the potential offered by tephrostratigraphy for sequences spanning 130–60 ka b2k. We combine newly identified cryptotephra deposits from the NGRIP ice-core and a marine core from the Iceland Basin with previously published data from the ice and marine realms to construct the first tephrostratigraphical framework for this time-interval. Forty-three tephra or cryptotephra deposits are incorporated into this framework; twenty three tephra deposits are found in the Greenland ice-cores, including nine new NGRIP tephras, and twenty separate deposits are preserved in various North Atlantic marine sequences. Major, minor and trace element results are presented for the new NGRIP horizons together with age estimates based on their position within the ice-core record. Basaltic tephras of Icelandic origin dominate the framework with only eight tephras of rhyolitic composition found. New results from marine core MD99-2253 also illustrate some of the complexities and challenges of assessing the depositional integrity of marine cryptotephra deposits. Tephra-based correlations in the marine environment provide independent tie-points for this time-interval and highlight the potential of widening the application of tephrochronology. Further investigations, however, are required, that combine robust geochemical fingerprinting and a rigorous assessment of tephra depositional processes, in order to trace coeval events between the two depositional realms