Sum of Two Squares - Pair Correlation and Distribution in Short Intervals

In this work we show that based on a conjecture for the pair correlation of integers representable as sums of two squares, which was first suggested by Connors and Keating and reformulated here, the second moment of the distribution of the number of representable integers in short intervals is consistent with a Poissonian distribution, where "short" means of length comparable to the mean spacing between sums of two squares. In addition we present a method for producing such conjectures through calculations in prime power residue rings and describe how these conjectures, as well as the above stated result, may by generalized to other binary quadratic forms. While producing these pair correlation conjectures we arrive at a surprising result regarding Mertens' formula for primes in arithmetic progressions, and in order to test the validity of the conjectures, we present numericalz computations which support our approach.Comment: 3 figure

Research in interactive scene analysis

Cooperative (man-machine) scene analysis techniques were developed whereby humans can provide a computer with guidance when completely automated processing is infeasible. An interactive approach promises significant near-term payoffs in analyzing various types of high volume satellite imagery, as well as vehicle-based imagery used in robot planetary exploration. This report summarizes the work accomplished over the duration of the project and describes in detail three major accomplishments: (1) the interactive design of texture classifiers; (2) a new approach for integrating the segmentation and interpretation phases of scene analysis; and (3) the application of interactive scene analysis techniques to cartography

Concurrent Verbal Protocol Analysis in Sport: Illustration of Thought Processes during a Golf-Putting task

The purpose of this study was to examine the feasibility of concurrent verbal protocols to identify and map thought processes of players during a golf-putting task. Three novice golfers and three experienced golfers performed twenty 12-foot putts while thinking aloud. Verbalizations were transcribed verbatim and coded using an inductive method. Content analysis and event-sequence analysis were performed. Mapping of thought sequences indicated that experienced players’ cog­nitive processes centered on gathering information and planning, while beginners focused on technical aspects. Experienced players diagnosed current performance aspects more often than beginners did and were more likely to use this informa­tion to plan the next putt. These results are consistent with experienced players’ higher domain-specific knowledge and less reliance on step-by-step monitoring of motor performance than beginners. The methods used for recording, analyzing, and interpreting on-line thoughts of performers shed light on cognitive processes, which have implications for research

Generalization of the effective Wiener-Ikehara theorem

International audienceWe consider the classical Wiener–Ikehara Tauberian theorem, with a generalized condition of slow decrease and some additional poles on the boundary of convergence of the Laplace transform. In this generality, we prove the otherwise known asymptotic evaluation of the transformed function, when the usual conditions of the Wiener-Ikehara theorem hold. However, our version also provides an effective error term, not known thus far in this generality. The crux of the proof is a proper asymptotic variation of the lemmas of Ganelius and Tenenbaum, also constructed for the sake of an effective version of the Wiener–Ikehara theorem

Nulling Emittance Measurement Technique for CLIC Test Facility

In order to test the principle of Two-Beam-Acceleration (TBA), the CLIC Test Facility utilizes a high-intensity drive beam of 640 to 1000 nC to generate 30 GHz accelerating fields. To ensure that the beam is transported efficiently, a robust measurement of beam emittance and Twiss parameters is required. This is accomplished by measuring the beam size on a profile monitor, while scanning five or more upstream quadrupoles in such a fashion that the Twiss parameters at the profile monitor remain constant while the phase advance through the beam line changes. In this way the beam size can be sampled at different phases while a near-constant size is of such measurement devices, especially those associated with limited dynamic range. In addition, the beam size is explicitly constant for a matched beam, which provides a ``nulling'' measurement of the match. Details of the technique, simulations, and results of the measurements are discussed

Modulated Floquet Topological Insulators

Floquet topological insulators are topological phases of matter generated by the application of time-periodic perturbations on otherwise conventional insulators. We demonstrate that spatial variations in the time-periodic potential lead to localized quasi-stationary states in two-dimensional systems. These states include one-dimensional interface modes at the nodes of the external potential, and fractionalized excitations at vortices of the external potential. We also propose a setup by which light can induce currents in these systems. We explain these results by showing a close analogy to px+ipy superconductors

Improve deep learning with unsupervised objective

We propose a novel approach capable of embedding the unsupervised objective into hidden layers of the deep neural network (DNN) for preserving important unsupervised information. To this end, we exploit a very simple yet effective unsupervised method, i.e. principal component analysis (PCA), to generate the unsupervised “label" for the latent layers of DNN. Each latent layer of DNN can then be supervised not just by the class label, but also by the unsupervised “label" so that the intrinsic structure information of data can be learned and embedded. Compared with traditional methods which combine supervised and unsupervised learning, our proposed model avoids the needs for layer-wise pre-training and complicated model learning e.g. in deep autoencoder. We show that the resulting model achieves state-of-the-art performance in both face and handwriting data simply with learning of unsupervised “labels"

Functional neuroanatomy of intuitive physical inference

To engage with the world - to understand the scene in front of us, plan actions, and predict what will happen next - we must have an intuitive grasp of the world's physical structure and dynamics. How do the objects in front of us rest on and support each other, how much force would be required to move them, and how will they behave when they fall, roll, or collide? Despite the centrality of physical inferences in daily life, little is known about the brain mechanisms recruited to interpret the physical structure of a scene and predict how physical events will unfold. Here, in a series of fMRI experiments, we identified a set of cortical regions that are selectively engaged when people watch and predict the unfolding of physical events - a "physics engine" in the brain. These brain regions are selective to physical inferences relative to nonphysical but otherwise highly similar scenes and tasks. However, these regions are not exclusively engaged in physical inferences per se or, indeed, even in scene understanding; they overlap with the domain-general "multiple demand" system, especially the parts of that system involved in action planning and tool use, pointing to a close relationship between the cognitive and neural mechanisms involved in parsing the physical content of a scene and preparing an appropriate action.Eunice Kennedy Shriver National Institute of Child Health and Human Development (U.S.) (Grant F32-HD075427)National Eye Institute (Grant EY13455)National Science Foundation (U.S.) (Grant CCF-1231216