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Dynamical symmetries of laser-dressed matter determine selection rules that determine its absorption spectrum. We explore selection rules for polarization-sensitive absorption in Floquet matter, using Floquet group theory in synthetic dimensions. We present comprehensive tables of selection rules that polarization-structured light impose on Floquet dark states and Floquet dark bands. Notably, our tables encompass nonlinear absorption, to all nonlinear orders, revealing that different nonlinear orders follow distinct polarization selection rules, potentially leading to polarization-tunable optical filters.

This work concerns elementwise-transformations of spiked matrices: $Y_n = n^{-1/2} f( \sqrt{n} X_n + Z_n)$. Here, $f$ is a function applied elementwise, $X_n$ is a low-rank signal matrix, and $Z_n$ is white noise. We find that principal component analysis is powerful for recovering signal under highly nonlinear or discontinuous transformations. Specifically, in the high-dimensional setting where $Y_n$ is of size $n \times p$ with $n,p \rightarrow \infty$ and $p/n \rightarrow \gamma > 0$, we uncover a phase transition: for signal-to-noise ratios above a sharp threshold -- depending on $f$, the distribution of elements of $Z_n$, and the limiting aspect ratio $\gamma$ -- the principal components of $Y_n$ (partially) recover those of $X_n$. Below this threshold, the principal components of $Y_n$ are asymptotically orthogonal to the signal. In contrast, in the standard setting where $X_n + n^{-1/2}Z_n$ is observed directly, the analogous phase transition depends only on $\gamma$. A similar phenomenon occurs with $X_n$ square and symmetric and $Z_n$ a generalized Wigner matrix.

Modern datasets are trending towards ever higher dimension. In response, recent theoretical studies of covariance estimation often assume the proportional-growth asymptotic framework, where the sample size $n$ and dimension $p$ are comparable, with $n, p \rightarrow \infty $ and $\gamma_n = p/n \rightarrow \gamma > 0$. Yet, many datasets -- perhaps most -- have very different numbers of rows and columns. We consider instead the disproportional-growth asymptotic framework, where $n, p \rightarrow \infty$ and $\gamma_n \rightarrow 0$ or $\gamma_n \rightarrow \infty$. Either disproportional limit induces novel behavior unseen within previous proportional and fixed-$p$ analyses. We study the spiked covariance model, with theoretical covariance a low-rank perturbation of the identity. For each of 15 different loss functions, we exhibit in closed form new optimal shrinkage and thresholding rules. Our optimal procedures demand extensive eigenvalue shrinkage and offer substantial performance benefits over the standard empirical covariance estimator. Practitioners may ask whether to view their data as arising within (and apply the procedures of) the proportional or disproportional frameworks. Conveniently, it is possible to remain {\it framework agnostic}: one unified set of closed-form shrinkage rules (depending only on the aspect ratio $\gamma_n$ of the given data) offers full asymptotic optimality under either framework. At the heart of the phenomena we explore is the spiked Wigner model, in which a low-rank matrix is perturbed by symmetric noise. Exploiting a connection to the spiked covariance model as $\gamma_n \rightarrow 0$, we derive optimal eigenvalue shrinkage rules for estimation of the low-rank component, of independent and fundamental interest.

The behavior of the leading singular values and vectors of noisy low-rank matrices is fundamental to many statistical and scientific problems. Theoretical understanding currently derives from asymptotic analysis under one of two regimes: (1) the classical regime, with a fixed number of rows and large number of columns, or vice versa, and (2) the proportional regime, with large numbers of rows and columns, proportional to one another. This paper is concerned with the disproportional regime, where the matrix is either ``tall and narrow'' or ``short and wide'': we study sequences of matrices of size $n \times m_n$ with aspect ratio $ n/m_n \rightarrow 0$ or $n/m_n \rightarrow \infty$ as $n \rightarrow \infty$. This regime has important ``big data'' applications. Theory derived here shows that the displacement of the empirical singular values and vectors from their noise-free counterparts and the associated phase transitions -- well-known under proportional growth asymptotics -- still occur in the disproportionate setting. They must be quantified, however, on a novel scale of measurement that adjusts with the changing aspect ratio as the matrix size increases. In this setting, the top singular vectors corresponding to the longer of the two matrix dimensions are asymptotically uncorrelated with the noise-free signal.

The data-driven economy has led to a significant shortage of data scientists. To address this shortage, this study explores the prospects of outsourcing data analysis tasks to freelancers available on online labor markets (OLMs) by identifying the essential factors for this endeavor. Specifically, we explore the skills required from freelancers, collect information about the skills present on major OLMs, and identify the main hurdles for out-/crowd-sourcing data analysis. Adopting a sequential mixed-method approach, we interviewed 20 data scientists and subsequently surveyed 80 respondents from OLMs. Besides confirming the need for expected skills such as technical/mathematical capabilities, it also identifies less known ones such as domain understanding, an eye for aesthetic data visualization, good communication skills, and a natural understanding of the possibilities/limitations of data analysis in general. Finally, it elucidates obstacles for crowdsourcing like the communication overhead, knowledge gaps, quality assurance, and data confidentiality, which need to be mitigated.

Responding to calls from the National Science Foundation (NSF) for new proposals to measure the gravitational constant $G$, we offer an interesting experiment in deep space employing the classic gravity train mechanism. Our setup requires three bodies: a larger layered solid sphere with a cylindrical hole through its center, a much smaller retroreflector which will undergo harmonic motion within the hole and a host spacecraft with laser ranging capabilities to measure round trip light-times to the retroreflector but ultimately separated a significant distance away from the sphere-retroreflector apparatus. Measurements of the period of oscillation of the retroreflector in terms of host spacecraft clock time using existing technology could give determinations of $G$ nearly three orders of magnitude more accurate than current measurements here on Earth. However, significant engineering advances in the release mechanism of the apparatus from the host spacecraft will likely be necessary. Issues with regard to the stability of the system are briefly addressed., Comment: 13 pp, 3 figs, accepted CQG

We offer a response to recent claims that a constant $G$ measurement model with an additional Gaussian noise term fits the experimental data better than a model containing periodic terms., Comment: 2 pages, 3 figures, accepted for publication in EPL

We explore the possibility that the observed onset of the Pioneer anomaly after Saturn encounter by Pioneer 11 is not necessarily due to mismodeling of solar radiation pressure but instead reflects a physically relevant characteristic of the anomaly itself. We employ the principles of a recently proposed cosmological model termed "the theory of inertial centers" along with an understanding of the fundamental assumptions taken by the Deep Space Network (DSN) to attempt to model this sudden onset. Due to an ambiguity that arises from the difference in the DSN definition of expected light-time with light-time according to the theory of inertial centers, we are forced to adopt a seemingly arbitrary convention to relate DSN-assumed clock-rates to physical clock-rates for this model. We offer a possible reason for adopting the convention employed in our analysis; however, we remain skeptical. Nevertheless, with this convention, one finds that this theory is able to replicate the previously reported Hubble-like behavior of the "clock acceleration" for the Pioneer anomaly as well as the sudden onset of the anomalous acceleration after Pioneer 11 Saturn encounter. While oscillatory behavior with a yearly period is also predicted for the anomalous clock accelerations of both Pioneer 10 and Pioneer 11, the predicted amplitude is an order of magnitude too small when compared with that reported for Pioneer 10., Comment: 24+12 pages, 4 figures

About a dozen measurements of Newton's gravitational constant, G, since 1962 have yielded values that differ by far more than their reported random plus systematic errors. We find that these values for G are oscillatory in nature, with a period of P = 5.899 +/- 0.062 yr, an amplitude of (1.619 +/- 0.103) x 10^{-14} m^3 kg^{-1} s^{-2}, and mean-value crossings in 1994 and 1997. However, we do not suggest that G is actually varying by this much, this quickly, but instead that something in the measurement process varies. Of other recently reported results, to the best of our knowledge, the only measurement with the same period and phase is the Length of Day (LOD - defined as a frequency measurement such that a positive increase in LOD values means slower Earth rotation rates and therefore longer days). The aforementioned period is also about half of a solar activity cycle, but the correlation is far less convincing. The 5.9 year periodic signal in LOD has previously been interpreted as due to fluid core motions and inner-core coupling. We report the G/LOD correlation, whose statistical significance is 0.99764 assuming no difference in phase, without claiming to have any satisfactory explanation for it. Least unlikely, perhaps, are currents in the Earth's fluid core that change both its moment of inertia (affecting LOD) and the circumstances in which the Earth-based experiments measure G. In this case, there might be correlations with terrestrial magnetic field measurements., Comment: 6 pages, 4 figures, 1 table, added appendix in response to arXiv:1505.01774 [gr-qc]

What does it mean for an algorithm to be biased? In U.S. law, unintentional bias is encoded via disparate impact, which occurs when a selection process has widely different outcomes for different groups, even as it appears to be neutral. This legal determination hinges on a definition of a protected class (ethnicity, gender, religious practice) and an explicit description of the process. When the process is implemented using computers, determining disparate impact (and hence bias) is harder. It might not be possible to disclose the process. In addition, even if the process is open, it might be hard to elucidate in a legal setting how the algorithm makes its decisions. Instead of requiring access to the algorithm, we propose making inferences based on the data the algorithm uses. We make four contributions to this problem. First, we link the legal notion of disparate impact to a measure of classification accuracy that while known, has received relatively little attention. Second, we propose a test for disparate impact based on analyzing the information leakage of the protected class from the other data attributes. Third, we describe methods by which data might be made unbiased. Finally, we present empirical evidence supporting the effectiveness of our test for disparate impact and our approach for both masking bias and preserving relevant information in the data. Interestingly, our approach resembles some actual selection practices that have recently received legal scrutiny., Comment: Extended version of paper accepted at 2015 ACM SIGKDD Conference on Knowledge Discovery and Data Mining

In the following, we offer a novel approach to modeling the observed effects currently attributed to the theoretical concepts of `dark energy', `dark matter', and `dark flow'. Instead of assuming the existence of these theoretical concepts, we take an alternative route and choose to redefine what we consider to be inertial motion as well as what constitutes an inertial frame of reference in flat space-time. We adopt none of the features of our current cosmological models except for the requirement that special and general relativity be local approximations within our revised definition of inertial systems. Implicit in our ideas is the assumption that at "large enough" scales one can treat objects within these inertial systems as point-particles having an insignificant effect on the curvature of space-time. We then proceed under the assumption that time and space are fundamentally intertwined such that time- and spatial-translational invariance are not inherent symmetries of flat space-time (i.e. observable clock rates depend upon both relative velocity and spatial position within these inertial systems) and take the geodesics of this theory in the radial Rindler chart as the proper characterization of inertial motion. With this commitment, we are able to model solely with inertial motion the observed effects expected to be the result of `dark energy', `dark matter', and `dark flow'. In addition, we examine the potential observable implications of our theory in a gravitational system located within a confined region of an inertial reference frame, subsequently interpreting the Pioneer anomaly as support for our redefinition of inertial motion. As well, we extend our analysis into quantum mechanics by quantizing for a real scalar field and find a possible explanation for the asymmetry between matter and antimatter within the framework of these redefined inertial systems., Comment: 55 pages, 3 figures, 2 tables, 6 appendices; added two unpublished sections with supplementary material (see Comments section of PLoS ONE publication link). None of the physical content of the original article has changed

Juno Radio Science measures the frequency of X- and Ka-band radio links between the Juno spacecraft and the Earth-based observing stations of NASA’s Deep Space Network (DSN) in order to determine the gravitational field of Jupiter. The received frequency contains information on the gravitational field and is also perturbed by the propagation environment, including Earth troposphere and ionosphere, electrons in the solar plasma, electrons in the Io Plasma Torus around Jupiter, and instrumental effects on both the spacecraft and the ground electronics. Each of these effects must be calibrated out of the data to ensure an accurate estimation of the Jupiter gravitational field. This work discusses the data processing, calibration, and performance of the frequency measurements. The precision of the frequency measurements average 1.1 mHz (1σ standard deviation at 60 second integration time), or 5.3 microns/sec in units of velocity. The remaining noise sources are primarily from residual troposphere and charged particles. Further improvement could be made in future radio science experiments with the addition of a cross-link and stiffer ground antennas.

Perelman has discovered two integral quantities, the shrinker entropy $\cW$ and the (backward) reduced volume, that are monotone under the Ricci flow $\pa g_{ij}/\pa t=-2R_{ij}$ and constant on shrinking solitons. Tweaking some signs, we find similar formulae corresponding to the expanding case. The {\it expanding entropy} $\ctW$ is monotone on any compact Ricci flow and constant precisely on expanders; as in Perelman, it follows from a differential inequality for a Harnack-like quantity for the conjugate heat equation, and leads to functionals $\mu_+$ and $\nu_+$. The {\it forward reduced volume} $\theta_+$ is monotone in general and constant exactly on expanders. A natural conjecture asserts that $g(t)/t$ converges as $t\to\infty$ to a negative Einstein manifold in some weak sense (in particular ignoring collapsing parts). If the limit is known a-priori to be smooth and compact, this statement follows easily from any monotone quantity that is constant on expanders; these include $\Vol(g)/t^{n/2}$ (Hamilton) and $\bar\lambda$ (Perelman), as well as our new quantities. In general, we show that if $\Vol(g)$ grows like $t^{n/2}$ (maximal volume growth) then $\ctW$, $\theta_+$ and $\bar\lambda$ remain bounded (in their appropriate ways) for all time. We attempt a sharp formulation of the conjecture.

Juno Radio Science measures the frequency of X- and Ka-band radio links between the Juno spacecraft and the Earth-based observing stations of NASA’s Deep Space Network (DSN) in order to determine the gravitational field of Jupiter. The received frequency contains information on the gravitational field and is also perturbed by the propagation environment, including Earth troposphere and ionosphere, electrons in the solar plasma, electrons in the Io Plasma Torus around Jupiter, and instrumental effects on both the spacecraft and the ground electronics. Each of these effects must be calibrated out of the data to ensure an accurate estimation of the Jupiter gravitational field. This work discusses the data processing, calibration, and performance of the frequency measurements. The precision of the frequency measurements average 1.1 mHz (1σ standard deviation at 60 second integration time), or 5.3 microns/sec in units of velocity. The remaining noise sources are primarily from residual troposphere and charged particles. Further improvement could be made in future radio science experiments with the addition of a cross-link and stiffer ground antennas.

A new software tool was needed for flight planning of a high altitude, low speed unmanned aerial vehicle which would be flying in winds close to the actual airspeed of the vehicle. An energy modeled NLP (non-linear programming) formulation was used to obtain results for a variety of missions and wind profiles. The energy constraint derived included terms due to the wind field and the performance index was a weighted combination of the amount of fuel used and the final time. With no emphasis on time and with no winds the vehicle was found to fly at maximum lift to drag velocity, V(sub md). When flying in tail winds the velocity was less than V(sub md), while flying in head winds the velocity was higher than V(sub md). A family of solutions was found with varying times of flight and varying fuel amounts consumed which will aid the operator in choosing a flight plan depending on a desired landing time. At certain parts of the flight, the turning terms in the energy constraint equation were found to be significant. An analysis of a simpler vertical plane cruise optimal control problem was used to explain some of the characteristics of the vertical plane NLP results.

Digital Optics Corporation is a UNC-Charlotte spin-off company, established to transfer technology developed at UNC-Charlotte for the design and manufacture Computer Generated Holograms (CGH's) and to market products based on CGH technology. DOC acquired core technologies from UNC-Charlotte including: (1) a CGH encoding process that can provide holograms with extremely high diffraction efficiency; (2) a low cost, high precision CGH manufacturing process; and (3) extensive holographic and refractive element design capabilities for design and evaluation of complex optical systems. These technologies have been used to design and/or manufacture optical components for a variety of applications including: (1) generation of Spot arrays; (2) fiber optic coupling elements; (3) optical interconnects between VLSI chips within and between multichip modules; and (4) imaging systems for head-mounted displays (HMD's).

* Flash 5, software, 2000, Macromedia (800-326-2128, www.macromedia.com), $399; Flash 5 Freehand Studio, $599; Flash 5 Generator 2 Developer Edition, $648. Other material: user guide. Macromedia's Flash 5 is a [...]

E-learning involves choices--many of them. One of the most fundamental is, Make or buy? The learning organizations most need to teach can reside within the organization itself. It isn't going [...]

Computer Aided Design (CAD) systems that have been developed for electrical and mechanical design tasks are also effective tools for the process of designing Computer Generated Holograms (CGHs), particularly when these holograms are to be fabricated using electron beam lithography. CAD workstations provide efficient and convenient means of computing, storing, displaying, and preparing for fabrication many of the features that are common to CGH designs. Experience gained in the process of designing CGHs with various types of encoding methods is presented. Suggestions are made so that future workstations may further accommodate the CGH design process.