On a Hierarchy of Means

For a class of partially ordered means we introduce a notion of the (nontrivial) cancelling mean. A simple method is given which helps to determine cancelling means for well known classes of Holder and Stolarsky means

Hyperparameter optimized classification pipeline for handling unbalanced urban and rural energy consumption patterns

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record Data availability: Data will be made available on request.Energy consumer locations are required for framing effective energy policies. However, due to privacy concerns, it is becoming increasingly difficult to obtain the locational data of the consumers. Machine learning (ML) based classification strategies can be used to find the locational information of the consumers based on their historical energy consumption patterns. The ML methods in this paper are applied to the Residential Energy Consumption Survey 2009 dataset. In this dataset, the number of consumers in the urban area is higher than the rural area, thus making the classification problem unbalanced. The unbalanced classification problem has been solved in original and transformed or reduced feature space using Monte Carlo based under-sampling of the majority class datapoints. The hyperparameters for each classification algorithm family is represented as an optimized pipeline, obtained using the genetic programming (GP) optimizer. The classification performance metrics are then obtained for different algorithm families on the original and transformed feature spaces. Performance comparisons have been reported using univariate and bivariate distributions of the classification metrics viz. accuracy, geometric mean score (GMS), F1 score, precision, area under the curve (AUC) of receiver operator characteristics (ROC). The energy policy aspects for the urban and rural residential consumers based on the classification results have also been discussed.European Regional Development Fund (ERDF

Features and New Physical Scales in Primordial Observables: Theory and Observation

All cosmological observations to date are consistent with adiabatic, Gaussian and nearly scale invariant initial conditions. These findings provide strong evidence for a particular symmetry breaking pattern in the very early universe (with a close to vanishing order parameter, $\epsilon$), widely accepted as conforming to the predictions of the simplest realizations of the inflationary paradigm. However, given that our observations are only privy to perturbations, in inferring something about the background that gave rise to them, it should be clear that many different underlying constructions project onto the same set of cosmological observables. Features in the primordial correlation functions, if present, would offer a unique and discriminating window onto the parent theory in which the mechanism that generated the initial conditions is embedded. In certain contexts, simple linear response theory allows us to infer new characteristic scales from the presence of features that can break the aforementioned degeneracies among different background models, and in some cases can even offer a limited spectroscopy of the heavier degrees of freedom that couple to the inflaton. In this review, we offer a pedagogical survey of the diverse, theoretically well grounded mechanisms which can imprint features into primordial correlation functions in addition to reviewing the techniques one can employ to probe observations. These observations include cosmic microwave background anisotropies and spectral distortions as well as the matter two and three point functions as inferred from large-scale structure and potentially, 21 cm surveys.Comment: Invited review to IJMPD, 101 pages + 2 appendices, 29 figures, references added, matches journal versio

DeepFRAP: Fast fluorescence recovery after photobleaching data analysis using deep neural networks

Conventional analysis of fluorescence recovery after photobleaching (FRAP) data for diffusion coefficient estimation typically involves fitting an analytical or numerical FRAP model to the recovery curve data using non-linear least squares. Depending on the model this can be time-consuming, especially for batch analysis of large numbers of data sets and if multiple initial guesses for the parameter vector are used to ensure convergence. In this work, we develop a completely new approach, DeepFRAP, utilizing machine learning for parameter estimation in FRAP. From a numerical FRAP model developed in previous work, we generate a very large set of simulated recovery curve data with realistic noise levels. The data is used for training different deep neural network regression models for prediction of several parameters, most importantly the diffusion coefficient. The neural networks are extremely fast and can estimate the parameters orders of magnitude faster than least squares. The performance of the neural network estimation framework is compared to conventional least squares estimation on simulated data, and found to be strikingly similar. Also, a simple experimental validation is performed, demonstrating excellent agreement between the two methods. We make the data and code used publicly available to facilitate further 34development of machine learning-based estimation in FRAP

The Planck mission

These lecture from the 100th Les Houches summer school on "Post-planck cosmology" of July 2013 discuss some aspects of the Planck mission, whose prime objective was a very accurate measurement of the temperature anisotropies of the Cosmic Microwave Background (CMB). We announced our findings a few months ago, on March 21$^{st}$, 2013. I describe some of the relevant steps we took to obtain these results, sketching the measurement process, how we processed the data to obtain full sky maps at 9 different frequencies, and how we extracted the CMB temperature anisotropies map and angular power spectrum. I conclude by describing some of the main cosmological implications of the statistical characteristics of the CMB we found. Of course, this is a very much shortened and somewhat biased view of the \Planck\ 2013 results, written with the hope that it may lead some of the students to consult the original papers.Comment: 53 p.-34 fig; for spacetime consideration, the file here is not paying justice to the actual thing; a closer approximation of it can be found at https://www.researchgate.net/profile/Francois_Bouchet/publication/262004262_The_Planck_Mission/file/e0b495363b042e81dd.pd