The Counting function for Elkies primes

Let $E$ be an elliptic curve over a finite field $\mathbb{F}_q$ where $q$ is a prime power. The Schoof--Elkies--Atkin (SEA) algorithm is a standard method for counting the number of $\mathbb{F}_q$-points on $E$. The asymptotic complexity of the SEA algorithm depends on the distribution of the so-called Elkies primes. Assuming GRH, we prove that the least Elkies prime is bounded by $(2\log 4q+4)^2$ when $q\geq 10^9$. This is the first such explicit bound in the literature. Previously, Satoh and Galbraith established an upper bound of $O((\log q)^{2+\varepsilon})$. Let $N_E(X)$ denote the number of Elkies primes less than $X$. Assuming GRH, we also show $$ N_E(X)=\frac{\pi(X)}{2}+O\left(\frac{\sqrt{X}(\log qX)^2}{\log X}\right)\,. $

Conformal Invariance and Shape-Dependent Conductance of Graphene Samples

For a sample of an arbitrary shape, the dependence of its conductance on the longitudinal and Hall conductivity is identical to that of a rectangle. We use analytic results for a conducting rectangle, combined with the semicircle model for transport coefficients, to study properties of the monolayer and bilayer graphene. A conductance plateau centered at the neutrality point, predicted for square geometry, is in agreement with recent experiments. For rectangular geometry, the conductance exhibits maxima at the densities of compressible quantum Hall states for wide samples, and minima for narrow samples. The positions and relative sizes of these features are different in the monolayer and bilayer cases, indicating that the conductance can be used as a tool for sample diagnostic.Comment: 9 pages, 6 figure

Ray-optical refraction with confocal lenslet arrays

Two parallel lenslet arrays with focal lengths f1 and f2 that share a common focal plane (that is, which are separated by a distance f1+f2) can refract transmitted light rays according to Snell's law, but with the 'sin's replaced with 'tan's. This is the case for a limited range of input angles and other conditions. Such confocal lenslet arrays can therefore simulate the interface between optical media with different refractive indices, n1 and n2, whereby the ratio η=-f2/f1 plays the role of the refractive-index ratio n2/n1. Suitable choices of focal lengths enable positive and negative refraction. In contrast to Snell's law, which leads to nontrivial geometric imaging by a planar refractive-index interface only for the special case of n1=±n2, the modified refraction law leads to geometric imaging by planar confocal lenslet arrays for any value of η. We illustrate some of the properties of confocal lenslet arrays with images rendered using ray-tracing software

Machine Learning and Irresponsible Inference: Morally Assessing the Training Data for Image Recognition Systems

Just as humans can draw conclusions responsibly or irresponsibly, so too can computers. Machine learning systems that have been trained on data sets that include irresponsible judgments are likely to yield irresponsible predictions as outputs. In this paper I focus on a particular kind of inference a computer system might make: identification of the intentions with which a person acted on the basis of photographic evidence. Such inferences are liable to be morally objectionable, because of a way in which they are presumptuous. After elaborating this moral concern, I explore the possibility that carefully procuring the training data for image recognition systems could ensure that the systems avoid the problem. The lesson of this paper extends beyond just the particular case of image recognition systems and the challenge of responsibly identifying a person’s intentions. Reflection on this particular case demonstrates the importance (as well as the difficulty) of evaluating machine learning systems and their training data from the standpoint of moral considerations that are not encompassed by ordinary assessments of predictive accuracy

A microscopic view on contact angle selection

We discuss the equilibrium condition for a liquid that partially wets a solid on the level of intermolecular forces. Using a mean field continuum description, we generalize the capillary pressure from variation of the free energy and show at what length scale the equilibrium contact angle is selected. After recovering Young's law for homogeneous substrates, it is shown how hysteresis of the contact angle can be incorporated in a self-consistent fashion. In all cases the liquid-vapor interface takes a nontrivial shape, which is compared to models using a disjoining pressure.Comment: 12 pages, 6 figure

Gray and white matter astrocytes differ in basal metabolism but respond similarly to neuronal activity

Astrocytes are a heterogeneous population of glial cells in the brain, which adapt their properties to the requirements of the local environment. Two major groups of astrocytes are protoplasmic astrocytes residing in gray matter as well as fibrous astrocytes of white matter. Here, we compared the energy metabolism of astrocytes in the cortex and corpus callosum as representative gray matter and white matter regions, in acute brain slices taking advantage of genetically encoded fluorescent nanosensors for the NADH/NAD+ redox ratio and for ATP. Astrocytes of the corpus callosum presented a more reduced basal NADH/NAD+ redox ratio, and a lower cytosolic concentration of ATP compared to cortical astrocytes. In cortical astrocytes, the neurotransmitter glutamate and increased extracellular concentrations of K+, typical correlates of neuronal activity, induced a more reduced NADH/NAD+ redox ratio. While application of glutamate decreased [ATP], K+ as well as the combination of glutamate and K+ resulted in an increase of ATP levels. Strikingly, a very similar regulation of metabolism by K+ and glutamate was observed in astrocytes in the corpus callosum. Finally, strong intrinsic neuronal activity provoked by application of bicuculline and withdrawal of Mg2+ caused a shift of the NADH/NAD+ redox ratio to a more reduced state as well as a slight reduction of [ATP] in gray and white matter astrocytes. In summary, the metabolism of astrocytes in cortex and corpus callosum shows distinct basal properties, but qualitatively similar responses to neuronal activity, probably reflecting the different environment and requirements of these brain regions

Wavelength-scale stationary-wave integrated Fourier-transform spectrometry

Spectrometry is a general physical-analysis approach for investigating light-matter interactions. However, the complex designs of existing spectrometers render them resistant to simplification and miniaturization, both of which are vital for applications in micro- and nanotechnology and which are now undergoing intensive research. Stationary-wave integrated Fourier-transform spectrometry (SWIFTS)-an approach based on direct intensity detection of a standing wave resulting from either reflection (as in the principle of colour photography by Gabriel Lippmann) or counterpropagative interference phenomenon-is expected to be able to overcome this drawback. Here, we present a SWIFTS-based spectrometer relying on an original optical near-field detection method in which optical nanoprobes are used to sample directly the evanescent standing wave in the waveguide. Combined with integrated optics, we report a way of reducing the volume of the spectrometer to a few hundreds of cubic wavelengths. This is the first attempt, using SWIFTS, to produce a very small integrated one-dimensional spectrometer suitable for applications where microspectrometers are essential

The roles of motivation and ability in controlling the consequences of stereotype suppression

Two experiments investigated the conditions under which previously suppressed stereotypes are applied in impression formation. In Experiment 1, the extent to which a previously suppressed racial stereotype influenced subsequent impressions depended on the race of the target who was subsequently encountered. Whereas impressions of race-unspecified targets were assimilated to the stereotype following its suppression, no such effects were observed when the target belonged to the racial group whose stereotype had been initially suppressed. These results demonstrate that when perceivers are motivated to avoid stereo-typing individuals, the influence of a stereotype that has been previously activated through suppression is minimized. Experiment 2 demonstrated that these processing goals effectively reduce the impact of suppression-activated stereotypes only when perceivers have sufficient capacity to enact the goals. These results suggest that both sufficient motivation and capacity are necessary to prevent heightened stereotyping following stereotype suppression

Cross‐scale seismic anisotropy analysis in metamorphic rocks from the COSC‐1 borehole in the Scandinavian Caledonides

Metamorphic and deformed rocks in thrust zones show particularly high seismic anisotropy causing challenges for seismic imaging and interpretation. A good example is the Seve Nappe Complex in central Sweden, an old exhumed orogenic thrust zone that is characterized by a strong but incoherent seismic reflectivity and considerable seismic anisotropy. However, only little is known about their origin in relation to composition and structural influences on measurements at different seismic scales. Here, we present a new integrative study of cross‐scale seismic anisotropy analyses combining mineralogical composition, microstructural analyses and seismic laboratory experiments from the COSC‐1 borehole, which sampled a 2.5 km‐deep section of metamorphic rocks deformed in an orogenic root now preserved in the Lower Seve Nappe. While there is strong crystallographic preferred orientation in most samples in general, variations in anisotropy depend mostly on bulk mineral composition and dominant core lithology as shown by a strong correlation between these. This relationship enables to identify three distinct seismic anisotropy facies providing a continuous anisotropy profile along the borehole. Moreover, comparison of laboratory seismic measurements and electron‐backscatter diffraction data reveals a strong scale‐dependence, which is more pronounced in the highly deformed, heterogeneous samples. This highlights the need for comprehensive cross‐validation of microscale anisotropy analyses with additional lithological data when integrating seismic anisotropy over seismic scales