A topological realization of the congruence subgroup Kernel A

A number of years ago, Kumar Murty pointed out to me that the computation of the fundamental group of a Hilbert modular surface ([7],IV,${\S}$6), and the computation of the congruence subgroup kernel of SL(2) ([6]) were surprisingly similar. We puzzled over this, in particular over the role of elementary matrices in both computations. We formulated a very general result on the fundamental group of a Satake compactification of a locally symmetric space. This lead to our joint paper [1] with Lizhen Ji and Les Saper on these fundamental groups. Although the results in it were intriguingly similar to the corresponding calculations of the congruence subgroup kernel of the underlying algebraic group in [5], we were not able to demonstrate a direct connection (cf. [1], ${\S}$7). The purpose of this note is to explain such a connection. A covering space is constructed from inverse limits of reductive Borel-Serre compactifications. The congruence subgroup kernel then appears as the group of deck transformations of this covering. The key to this is the computation of the fundamental group in [1]

Spin-orbit interaction and spin relaxation in a two-dimensional electron gas

Using time-resolved Faraday rotation, the drift-induced spin-orbit Field of a two-dimensional electron gas in an InGaAs quantum well is measured. Including measurements of the electron mobility, the Dresselhaus and Rashba coefficients are determined as a function of temperature between 10 and 80 K. By comparing the relative size of these terms with a measured in-plane anisotropy of the spin dephasing rate, the D'yakonv-Perel' contribution to spin dephasing is estimated. The measured dephasing rate is significantly larger than this, which can only partially be explained by an inhomogeneous g-factor.Comment: 6 pages, 5 figure

An integrated uncertainty and ensemble-based data assimilation approach for improved operational streamflow predictions

The current study proposes an integrated uncertainty and ensemble-based data assimilation framework (ICEA) and evaluates its viability in providing operational streamflow predictions via assimilating snow water equivalent (SWE) data. This step-wise framework applies a parameter uncertainty analysis algorithm (ISURF) to identify the uncertainty structure of sensitive model parameters, which is subsequently formulated into an Ensemble Kalman Filter (EnKF) to generate updated snow states for streamflow prediction. The framework is coupled to the US National Weather Service (NWS) snow and rainfall-runoff models. Its applicability is demonstrated for an operational basin of a western River Forecast Center (RFC) of the NWS. Performance of the framework is evaluated against existing operational baseline (RFC predictions), the stand-alone ISURF and the stand-alone EnKF. Results indicate that the ensemble-mean prediction of ICEA considerably outperforms predictions from the other three scenarios investigated, particularly in the context of predicting high flows (top 5th percentile). The ICEA streamflow ensemble predictions capture the variability of the observed streamflow well, however the ensemble is not wide enough to consistently contain the range of streamflow observations in the study basin. Our findings indicate that the ICEA has the potential to supplement the current operational (deterministic) forecasting method in terms of providing improved single-valued (e.g., ensemble mean) streamflow predictions as well as meaningful ensemble predictions

Property (T) and rigidity for actions on Banach spaces

We study property (T) and the fixed point property for actions on $L^p$ and other Banach spaces. We show that property (T) holds when $L^2$ is replaced by $L^p$ (and even a subspace/quotient of $L^p$), and that in fact it is independent of $1\leq p<\infty$. We show that the fixed point property for $L^p$ follows from property (T) when 1. For simple Lie groups and their lattices, we prove that the fixed point property for $L^p$ holds for any $1< p<\infty$ if and only if the rank is at least two. Finally, we obtain a superrigidity result for actions of irreducible lattices in products of general groups on superreflexive Banach spaces.Comment: Many minor improvement

Stochastic make-to-stock inventory deployment problem: an endosymbiotic psychoclonal algorithm based approach

Integrated steel manufacturers (ISMs) have no specific product, they just produce finished product from the ore. This enhances the uncertainty prevailing in the ISM regarding the nature of the finished product and significant demand by customers. At present low cost mini-mills are giving firm competition to ISMs in terms of cost, and this has compelled the ISM industry to target customers who want exotic products and faster reliable deliveries. To meet this objective, ISMs are exploring the option of satisfying part of their demand by converting strategically placed products, this helps in increasing the variability of product produced by the ISM in a short lead time. In this paper the authors have proposed a new hybrid evolutionary algorithm named endosymbiotic-psychoclonal (ESPC) to decide what and how much to stock as a semi-product in inventory. In the proposed theory, the ability of previously proposed psychoclonal algorithms to exploit the search space has been increased by making antibodies and antigen more co-operative interacting species. The efficacy of the proposed algorithm has been tested on randomly generated datasets and the results compared with other evolutionary algorithms such as genetic algorithms (GA) and simulated annealing (SA). The comparison of ESPC with GA and SA proves the superiority of the proposed algorithm both in terms of quality of the solution obtained and convergence time required to reach the optimal/near optimal value of the solution

Fano resonances in a three-terminal nanodevice

The electron transport through a quantum sphere with three one-dimensional wires attached to it is investigated. An explicit form for the transmission coefficient as a function of the electron energy is found from the first principles. The asymmetric Fano resonances are detected in transmission of the system. The collapse of the resonances is shown to appear under certain conditions. A two-terminal nanodevice with an additional gate lead is studied using the developed approach. Additional resonances and minima of transmission are indicated in the device.Comment: 11 pages, 5 figures, 2 equations are added, misprints in 5 equations are removed, published in Journal of Physics: Condensed Matte

Linear-time list recovery of high-rate expander codes

We show that expander codes, when properly instantiated, are high-rate list recoverable codes with linear-time list recovery algorithms. List recoverable codes have been useful recently in constructing efficiently list-decodable codes, as well as explicit constructions of matrices for compressive sensing and group testing. Previous list recoverable codes with linear-time decoding algorithms have all had rate at most 1/2; in contrast, our codes can have rate $1 - \epsilon$ for any $\epsilon > 0$. We can plug our high-rate codes into a construction of Meir (2014) to obtain linear-time list recoverable codes of arbitrary rates, which approach the optimal trade-off between the number of non-trivial lists provided and the rate of the code. While list-recovery is interesting on its own, our primary motivation is applications to list-decoding. A slight strengthening of our result would implies linear-time and optimally list-decodable codes for all rates, and our work is a step in the direction of solving this important problem

Chaotic maps and flows: Exact Riemann-Siegel lookalike for spectral fluctuations

To treat the spectral statistics of quantum maps and flows that are fully chaotic classically, we use the rigorous Riemann-Siegel lookalike available for the spectral determinant of unitary time evolution operators $F$. Concentrating on dynamics without time reversal invariance we get the exact two-point correlator of the spectral density for finite dimension $N$ of the matrix representative of $F$, as phenomenologically given by random matrix theory. In the limit $N\to\infty$ the correlator of the Gaussian unitary ensemble is recovered. Previously conjectured cancellations of contributions of pseudo-orbits with periods beyond half the Heisenberg time are shown to be implied by the Riemann-Siegel lookalike

Sonoluminescing air bubbles rectify argon

The dynamics of single bubble sonoluminescence (SBSL) strongly depends on the percentage of inert gas within the bubble. We propose a theory for this dependence, based on a combination of principles from sonochemistry and hydrodynamic stability. The nitrogen and oxygen dissociation and subsequent reaction to water soluble gases implies that strongly forced air bubbles eventually consist of pure argon. Thus it is the partial argon (or any other inert gas) pressure which is relevant for stability. The theory provides quantitative explanations for many aspects of SBSL.Comment: 4 page