Traces, high powers and one level density for families of curves over finite fields

AbstractThe zeta function of a curve C over a finite field may be expressed in terms of the characteristic polynomial of a unitary matrix ΘC. We develop and present a new technique to compute the expected value of tr(ΘCn) for various moduli spaces of curves of genus g over a fixed finite field in the limit as g is large, generalising and extending the work of Rudnick [Rud10] and Chinis [Chi16]. This is achieved by using function field zeta functions, explicit formulae, and the densities of prime polynomials with prescribed ramification types at certain places as given in [BDF+16] and [Zha]. We extend [BDF+16] by describing explicit dependence on the place and give an explicit proof of the Lindelöf bound for function field Dirichlet L-functions L(1/2 + it, χ). As applications, we compute the one-level density for hyperelliptic curves, cyclic ℓ-covers, and cubic non-Galois covers.</jats:p

Anisotropic Electron Spin Lifetime in (In,Ga)As/GaAs (110) Quantum Wells

Anisotropic electron spin lifetimes in strained undoped (In,Ga)As/GaAs (110) quantum wells of different width and height are investigated by time-resolved Faraday rotation and time-resolved transmission and are compared to the (001)-orientation. From the suppression of spin precession, the ratio of in-plane to out-of-plane spin lifetimes is calculated. Whereas the ratio increases with In concentration in agreement with theory, a surprisingly high anisotropy of 480 is observed for the broadest quantum well, when expressed in terms of spin relaxation times.Comment: 4 pages, 4 figures, revise

Large magnetic circular dichroism in resonant inelastic x-ray scattering at the Mn L-edge of Mn-Zn ferrite

We report resonant inelastic x-ray scattering (RIXS) excited by circularly polarized x-rays on Mn-Zn ferrite at the Mn L2,3-resonances. We demonstrate that crystal field excitations, as expected for localized systems, dominate the RIXS spectra and thus their dichroic asymmetry cannot be interpreted in terms of spin-resolved partial density of states, which has been the standard approach for RIXS dichroism. We observe large dichroic RIXS at the L2-resonance which we attribute to the absence of metallic core hole screening in the insulating Mn-ferrite. On the other hand, reduced L3-RIXS dichroism is interpreted as an effect of longer scattering time that enables spin-lattice core hole relaxation via magnons and phonons occurring on a femtosecond time scale.Comment: 7 pages, 2 figures, http://link.aps.org/doi/10.1103/PhysRevB.74.17240

Dynamic quantum clustering: a method for visual exploration of structures in data

A given set of data-points in some feature space may be associated with a Schrodinger equation whose potential is determined by the data. This is known to lead to good clustering solutions. Here we extend this approach into a full-fledged dynamical scheme using a time-dependent Schrodinger equation. Moreover, we approximate this Hamiltonian formalism by a truncated calculation within a set of Gaussian wave functions (coherent states) centered around the original points. This allows for analytic evaluation of the time evolution of all such states, opening up the possibility of exploration of relationships among data-points through observation of varying dynamical-distances among points and convergence of points into clusters. This formalism may be further supplemented by preprocessing, such as dimensional reduction through singular value decomposition or feature filtering.Comment: 15 pages, 9 figure

Testing the accuracy of an observation-based classifier for rapid detection of autism risk

Current approaches for diagnosing autism have high diagnostic validity but are time consuming and can contribute to delays in arriving at an official diagnosis. In a pilot study, we used machine learning to derive a classifier that represented a 72% reduction in length from the gold-standard Autism Diagnostic Observation Schedule-Generic (ADOS-G), while retaining >97% statistical accuracy. The pilot study focused on a relatively small sample of children with and without autism. The present study sought to further test the accuracy of the classifier (termed the observation-based classifier (OBC)) on an independent sample of 2616 children scored using ADOS from five data repositories and including both spectrum (n=2333) and non-spectrum (n=283) individuals. We tested OBC outcomes against the outcomes provided by the original and current ADOS algorithms, the best estimate clinical diagnosis, and the comparison score severity metric associated with ADOS-2. The OBC was significantly correlated with the ADOS-G (r=−0.814) and ADOS-2 (r=−0.779) and exhibited >97% sensitivity and >77% specificity in comparison to both ADOS algorithm scores. The correspondence to the best estimate clinical diagnosis was also high (accuracy=96.8%), with sensitivity of 97.1% and specificity of 83.3%. The correlation between the OBC score and the comparison score was significant (r=−0.628), suggesting that the OBC provides both a classification as well as a measure of severity of the phenotype. These results further demonstrate the accuracy of the OBC and suggest that reductions in the process of detecting and monitoring autism are possible

Automatic Reconstruction of Fault Networks from Seismicity Catalogs: 3D Optimal Anisotropic Dynamic Clustering

We propose a new pattern recognition method that is able to reconstruct the 3D structure of the active part of a fault network using the spatial location of earthquakes. The method is a generalization of the so-called dynamic clustering method, that originally partitions a set of datapoints into clusters, using a global minimization criterion over the spatial inertia of those clusters. The new method improves on it by taking into account the full spatial inertia tensor of each cluster, in order to partition the dataset into fault-like, anisotropic clusters. Given a catalog of seismic events, the output is the optimal set of plane segments that fits the spatial structure of the data. Each plane segment is fully characterized by its location, size and orientation. The main tunable parameter is the accuracy of the earthquake localizations, which fixes the resolution, i.e. the residual variance of the fit. The resolution determines the number of fault segments needed to describe the earthquake catalog, the better the resolution, the finer the structure of the reconstructed fault segments. The algorithm reconstructs successfully the fault segments of synthetic earthquake catalogs. Applied to the real catalog constituted of a subset of the aftershocks sequence of the 28th June 1992 Landers earthquake in Southern California, the reconstructed plane segments fully agree with faults already known on geological maps, or with blind faults that appear quite obvious on longer-term catalogs. Future improvements of the method are discussed, as well as its potential use in the multi-scale study of the inner structure of fault zones

Blogging in the physics classroom: A research-based approach to shaping students' attitudes towards physics

Even though there has been a tremendous amount of research done in how to help students learn physics, students are still coming away missing a crucial piece of the puzzle: why bother with physics? Students learn fundamental laws and how to calculate, but come out of a general physics course without a deep understanding of how physics has transformed the world around them. In other words, they get the "how" but not the "why". Studies have shown that students leave introductory physics courses almost universally with decreased expectations and with a more negative attitude. This paper will detail an experiment to address this problem: a course weblog or "blog" which discusses real-world applications of physics and engages students in discussion and thinking outside of class. Specifically, students' attitudes towards the value of physics and its applicability to the real-world were probed using a 26-question Likert scale survey over the course of four semesters in an introductory physics course at a comprehensive Jesuit university. We found that students who did not participate in the blog study generally exhibited a deterioration in attitude towards physics as seen previously. However, students who read, commented, and were involved with the blog maintained their initially positive attitudes towards physics. Student response to the blog was overwhelmingly positive, with students claiming that the blog made the things we studied in the classroom come alive for them and seem much more relevant.Comment: 20 pages, 6 figure

Identification of network modules by optimization of ratio association

We introduce a novel method for identifying the modular structures of a network based on the maximization of an objective function: the ratio association. This cost function arises when the communities detection problem is described in the probabilistic autoencoder frame. An analogy with kernel k-means methods allows to develop an efficient optimization algorithm, based on the deterministic annealing scheme. The performance of the proposed method is shown on a real data set and on simulated networks

LOCOMOOR : a LOw-COst MOORing for the measurement of internal solitary waves

Presented at the ONR/MTS Buoy Workshop, May 9-11, 2000, Clark Laboratory, Woods Hole Oceanographic Institution, Woods Hole, MAIn order to supplement the ASIAEX field effort to measure the temporal and spatial structure of the internal solitary wave field in relationship to acoustic propagation and scattering studies, an array of low-cost temperature moorings (LOCOMOOR) has been developed. The basic concept is to provide spatial coverage as opposed to dense vertical resolution in temperature. Three temperature sensors on each mooring will adequately measure the time of passage of the internal solitary waves. A horizontal array of 20 of these moorings deployed for about three weeks will allow the internal solitary wave front geometry (curvature) and velocity to be measured as they propagate through the experiment region. The arrival time of each pulse within the packet of internal waves will be easily resolved, but the wave amplitude less exactly estimated. However, the amplitude will be very well measured by the velocity and density observations on the more heavily instrumented environmental moorings associated with the acoustic experiment