Exploring Photometric Redshifts as an Optimization Problem: An Ensemble MCMC and Simulated Annealing-Driven Template-Fitting Approach

Using a grid of $\sim 2$ million elements ($\Delta z = 0.005$) adapted from COSMOS photometric redshift (photo-z) searches, we investigate the general properties of template-based photo-z likelihood surfaces. We find these surfaces are filled with numerous local minima and large degeneracies that generally confound rapid but "greedy" optimization schemes, even with additional stochastic sampling methods. In order to robustly and efficiently explore these surfaces, we develop BAD-Z [Brisk Annealing-Driven Redshifts (Z)], which combines ensemble Markov Chain Monte Carlo (MCMC) sampling with simulated annealing to sample arbitrarily large, pre-generated grids in approximately constant time. Using a mock catalog of 384,662 objects, we show BAD-Z samples $\sim 40$ times more efficiently compared to a brute-force counterpart while maintaining similar levels of accuracy. Our results represent first steps toward designing template-fitting photo-z approaches limited mainly by memory constraints rather than computation time.Comment: 14 pages, 8 figures; submitted to MNRAS; comments welcom

Landscape statistics of the low autocorrelated binary string problem

The statistical properties of the energy landscape of the low autocorrelated binary string problem (LABSP) are studied numerically and compared with those of several classic disordered models. Using two global measures of landscape structure which have been introduced in the Simulated Annealing literature, namely, depth and difficulty, we find that the landscape of LABSP, except perhaps for a very large degeneracy of the local minima energies, is qualitatively similar to some well-known landscapes such as that of the mean-field 2-spin glass model. Furthermore, we consider a mean-field approximation to the pure model proposed by Bouchaud and Mezard (1994, J. Physique I France 4 1109) and show both analytically and numerically that it describes extremely well the statistical properties of LABSP

Effects of temperature on thick branes and the fermion (quasi-)localization

Following Campos's work [Phys. Rev. Lett. 88, 141602 (2002)], we investigate the effects of temperature on flat, de Sitter (dS), and anti-de Following Campos's work [Phys. Rev. Lett. \textbf{88}, 141602 (2002)], we investigate the effects of temperature on flat, de Sitter (dS), and anti-de Sitter (AdS) thick branes in five-dimensional (5D) warped spacetime, and on the fermion (quasi-)localization. First, in the case of flat brane, when the critical temperature reaches, the solution of the background scalar field and the warp factor is not unique. So the thickness of the flat thick brane is uncertain at the critical value of the temperature parameter, which is found to be lower than the one in flat 5D spacetime. The mass spectra of the fermion Kaluza-Klein (KK) modes are continuous, and there is a series of fermion resonances. The number and lifetime of the resonances are finite and increase with the temperature parameter, but the mass of the resonances decreases with the temperature parameter. Second, in the case of dS brane, we do not find such a critical value of the temperature parameter. The mass spectra of the fermion KK modes are also continuous, and there is a series of fermion resonances. The effects of temperature on resonance number, lifetime, and mass are the same with the case of flat brane. Last, in the case of AdS brane, {the critical value of the temperature parameter can less or greater than the one in the flat 5D spacetime.} The spectra of fermion KK modes are discrete, and the mass of fermion KK modes does not decrease monotonically with increasing temperature parameter.Comment: 24 pages, 15 figures, published versio

Memory Augmented Control Networks

Planning problems in partially observable environments cannot be solved directly with convolutional networks and require some form of memory. But, even memory networks with sophisticated addressing schemes are unable to learn intelligent reasoning satisfactorily due to the complexity of simultaneously learning to access memory and plan. To mitigate these challenges we introduce the Memory Augmented Control Network (MACN). The proposed network architecture consists of three main parts. The first part uses convolutions to extract features and the second part uses a neural network-based planning module to pre-plan in the environment. The third part uses a network controller that learns to store those specific instances of past information that are necessary for planning. The performance of the network is evaluated in discrete grid world environments for path planning in the presence of simple and complex obstacles. We show that our network learns to plan and can generalize to new environments