The Complete Calibration of the Color-Redshift Relation (C3R2) Survey: Survey Overview and Data Release 1

A key goal of the Stage IV dark energy experiments Euclid, LSST and WFIRST is to measure the growth of structure with cosmic time from weak lensing analysis over large regions of the sky. Weak lensing cosmology will be challenging: in addition to highly accurate galaxy shape measurements, statistically robust and accurate photometric redshift (photo-z) estimates for billions of faint galaxies will be needed in order to reconstruct the three-dimensional matter distribution. Here we present an overview of and initial results from the Complete Calibration of the Color-Redshift Relation (C3R2) survey, designed specifically to calibrate the empirical galaxy color-redshift relation to the Euclid depth. These redshifts will also be important for the calibrations of LSST and WFIRST. The C3R2 survey is obtaining multiplexed observations with Keck (DEIMOS, LRIS, and MOSFIRE), the Gran Telescopio Canarias (GTC; OSIRIS), and the Very Large Telescope (VLT; FORS2 and KMOS) of a targeted sample of galaxies most important for the redshift calibration. We focus spectroscopic efforts on under-sampled regions of galaxy color space identified in previous work in order to minimize the number of spectroscopic redshifts needed to map the color-redshift relation to the required accuracy. Here we present the C3R2 survey strategy and initial results, including the 1283 high confidence redshifts obtained in the 2016A semester and released as Data Release 1.Comment: Accepted to ApJ. 11 pages, 5 figures. Redshifts can be found at http://c3r2.ipac.caltech.edu/c3r2_DR1_mrt.tx

Joint Hybrid Precoder and Combiner Design for mmWave Spatial Multiplexing Transmission

Millimeter-wave (mmWave) communications have been considered as a key technology for future 5G wireless networks because of the orders-of-magnitude wider bandwidth than current cellular bands. In this paper, we consider the problem of codebook-based joint analog-digital hybrid precoder and combiner design for spatial multiplexing transmission in a mmWave multiple-input multiple-output (MIMO) system. We propose to jointly select analog precoder and combiner pair for each data stream successively aiming at maximizing the channel gain while suppressing the interference between different data streams. After all analog precoder/combiner pairs have been determined, we can obtain the effective baseband channel. Then, the digital precoder and combiner are computed based on the obtained effective baseband channel to further mitigate the interference and maximize the sum-rate. Simulation results demonstrate that our proposed algorithm exhibits prominent advantages in combating interference between different data streams and offer satisfactory performance improvement compared to the existing codebook-based hybrid beamforming schemes

Cosmological Horizons, Uncertainty Principle and Maximum Length Quantum Mechanics

The cosmological particle horizon is the maximum measurable length in the Universe. The existence of such a maximum observable length scale implies a modification of the quantum uncertainty principle. Thus due to non-locality of quantum mechanics, the global properties of the Universe could produce a signature on the behaviour of local quantum systems. A Generalized Uncertainty Principle (GUP) that is consistent with the existence of such a maximum observable length scale $l_{max}$ is $\Delta x \Delta p \geq \frac{\hbar}{2}\;\frac{1}{1-\alpha \Delta x^2}$ where $\alpha = l_{max}^{-2}\simeq (H_0/c)^2$ ($H_0$ is the Hubble parameter and $c$ is the speed of light). In addition to the existence of a maximum measurable length $l_{max}=\frac{1}{\sqrt \alpha}$, this form of GUP implies also the existence of a minimum measurable momentum $p_{min}=\frac{3 \sqrt{3}}{4}\hbar \sqrt{\alpha}$. Using appropriate representation of the position and momentum quantum operators we show that the spectrum of the one dimensional harmonic oscillator becomes $\bar{\mathcal{E}}_n=2n+1+\lambda_n \bar{\alpha}$ where $\bar{\mathcal{E}}_n\equiv 2E_n/\hbar \omega$ is the dimensionless properly normalized $n^{th}$ energy level, $\bar{\alpha}$ is a dimensionless parameter with $\bar{\alpha}\equiv \alpha \hbar/m \omega$ and $\lambda_n\sim n^2$ for $n\gg 1$ (we show the full form of $\lambda_n$ in the text). For a typical vibrating diatomic molecule and $l_{max}=c/H_0$ we find $\bar{\alpha}\sim 10^{-77}$ and therefore for such a system, this effect is beyond reach of current experiments. However, this effect could be more important in the early universe and could produce signatures in the primordial perturbation spectrum induced by quantum fluctuations of the inflaton field.Comment: 11 pages, 7 Figures. The Mathematica file that was used for the production of the Figures may be downloaded from http://leandros.physics.uoi.gr/maxlenqm

Is "Better Data" Better than "Better Data Miners"? (On the Benefits of Tuning SMOTE for Defect Prediction)

We report and fix an important systematic error in prior studies that ranked classifiers for software analytics. Those studies did not (a) assess classifiers on multiple criteria and they did not (b) study how variations in the data affect the results. Hence, this paper applies (a) multi-criteria tests while (b) fixing the weaker regions of the training data (using SMOTUNED, which is a self-tuning version of SMOTE). This approach leads to dramatically large increases in software defect predictions. When applied in a 5*5 cross-validation study for 3,681 JAVA classes (containing over a million lines of code) from open source systems, SMOTUNED increased AUC and recall by 60% and 20% respectively. These improvements are independent of the classifier used to predict for quality. Same kind of pattern (improvement) was observed when a comparative analysis of SMOTE and SMOTUNED was done against the most recent class imbalance technique. In conclusion, for software analytic tasks like defect prediction, (1) data pre-processing can be more important than classifier choice, (2) ranking studies are incomplete without such pre-processing, and (3) SMOTUNED is a promising candidate for pre-processing.Comment: 10 pages + 2 references. Accepted to International Conference of Software Engineering (ICSE), 201

Discussion on "Sparse graphs using exchangeable random measures" by F. Caron and E. B. Fox

Discussion on "Sparse graphs using exchangeable random measures" by F. Caron and E. B. Fox. In this discussion we contribute to the analysis of the GGP model as compared to the Erdos-Renyi (ER) and the preferential attachment (AB) models, using different measures such as number of connected components, global clustering coefficient, assortativity coefficient and share of nodes in the core.Comment: 2 pages, 1 figur

Simulation Theorems via Pseudorandom Properties

We generalize the deterministic simulation theorem of Raz and McKenzie [RM99], to any gadget which satisfies certain hitting property. We prove that inner-product and gap-Hamming satisfy this property, and as a corollary we obtain deterministic simulation theorem for these gadgets, where the gadget's input-size is logarithmic in the input-size of the outer function. This answers an open question posed by G\"{o}\"{o}s, Pitassi and Watson [GPW15]. Our result also implies the previous results for the Indexing gadget, with better parameters than was previously known. A preliminary version of the results obtained in this work appeared in [CKL+17]

On the equivalence of Eulerian and Lagrangian variables for the two-component Camassa-Holm system

The Camassa-Holm equation and its two-component Camassa-Holm system generalization both experience wave breaking in finite time. To analyze this, and to obtain solutions past wave breaking, it is common to reformulate the original equation given in Eulerian coordinates, into a system of ordinary differential equations in Lagrangian coordinates. It is of considerable interest to study the stability of solutions and how this is manifested in Eulerian and Lagrangian variables. We identify criteria of convergence, such that convergence in Eulerian coordinates is equivalent to convergence in Lagrangian coordinates. In addition, we show how one can approximate global conservative solutions of the scalar Camassa-Holm equation by smooth solutions of the two-component Camassa-Holm system that do not experience wave breaking

Wireless Communication using Unmanned Aerial Vehicles (UAVs): Optimal Transport Theory for Hover Time Optimization

In this paper, the effective use of flight-time constrained unmanned aerial vehicles (UAVs) as flying base stations that can provide wireless service to ground users is investigated. In particular, a novel framework for optimizing the performance of such UAV-based wireless systems in terms of the average number of bits (data service) transmitted to users as well as UAVs' hover duration (i.e. flight time) is proposed. In the considered model, UAVs hover over a given geographical area to serve ground users that are distributed within the area based on an arbitrary spatial distribution function. In this case, two practical scenarios are considered. In the first scenario, based on the maximum possible hover times of UAVs, the average data service delivered to the users under a fair resource allocation scheme is maximized by finding the optimal cell partitions associated to the UAVs. Using the mathematical framework of optimal transport theory, a gradient-based algorithm is proposed for optimally partitioning the geographical area based on the users' distribution, hover times, and locations of the UAVs. In the second scenario, given the load requirements of ground users, the minimum average hover time that the UAVs need for completely servicing their ground users is derived. To this end, first, an optimal bandwidth allocation scheme for serving the users is proposed. Then, given this optimal bandwidth allocation, the optimal cell partitions associated with the UAVs are derived by exploiting the optimal transport theory. Results show that our proposed cell partitioning approach leads to a significantly higher fairness among the users compared to the classical weighted Voronoi diagram. In addition, our results reveal an inherent tradeoff between the hover time of UAVs and bandwidth efficiency while serving the ground users

How close are time series to power tail L\'evy diffusions?

This article presents a new and easily implementable method to quantify the so-called coupling distance between the law of a time series and the law of a differential equation driven by Markovian additive jump noise with heavy-tailed jumps, such as $\alpha$-stable L\'evy flights. Coupling distances measure the proximity of the empirical law of the tails of the jump increments and a given power law distribution. In particular they yield an upper bound for the distance of the respective laws on path space. We prove rates of convergence comparable to the rates of the central limit theorem which are confirmed by numerical simulations. Our method applied to a paleoclimate time series of glacial climate variability confirms its heavy tail behavior. In addition this approach gives evidence for heavy tails in data sets of precipitable water vapor of the Western Tropical Pacific.Comment: 30 pages, 10 figure

Bootstrapping 3D Fermions with Global Symmetries

We study the conformal bootstrap for 4-point functions of fermions $\langle \psi_i \psi_j \psi_k \psi_{\ell} \rangle$ in parity-preserving 3d CFTs, where $\psi_i$ transforms as a vector under an $O(N)$ global symmetry. We compute bounds on scaling dimensions and central charges, finding features in our bounds that appear to coincide with the $O(N)$ symmetric Gross-Neveu-Yukawa fixed points. Our computations are in perfect agreement with the $1/N$ expansion at large $N$ and allow us to make nontrivial predictions at small $N$. For values of $N$ for which the Gross-Neveu-Yukawa universality classes are relevant to condensed-matter systems, we compare our results to previous analytic and numerical results.Comment: 29 pages, 7 figure