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The search for life on the planets outside the Solar System can be broadly classified into the following: looking for Earth-like conditions or the planets similar to the Earth (Earth similarity), and looking for the possibility of life in a form known or unknown to us (habitability). The two frequently used indices, Earth Similarity Index (ESI) and Planetary Habitability Index (PHI), describe heuristic methods to score similarity/habitability in the efforts to categorize different exoplanets or exomoons. ESI, in particular, considers Earth as the reference frame for habitability and is a quick screening tool to categorize and measure physical similarity of any planetary body with the Earth. The PHI assesses the probability that life in some form may exist on any given world, and is based on the essential requirements of known life: a stable and protected substrate, energy, appropriate chemistry and a liquid medium. We propose here a different metric, a Cobb-Douglas Habitability Score (CDHS), based on Cobb-Douglas habitability production function (CD-HPF), which computes the habitability score by using measured and calculated planetary input parameters. As an initial set, we used radius, density, escape velocity and surface temperature of a planet. The values of the input parameters are normalized to the Earth Units (EU). The proposed metric, with exponents accounting for metric elasticity, is endowed with verifiable analytical properties that ensure global optima, and is scalable to accommodate finitely many input parameters. The model is elastic, does not suffer from curvature violations and, as we discovered, the standard PHI is a special case of CDHS. Computed CDHS scores are fed to K-NN (K-Nearest Neighbour) classification algorithm with probabilistic herding that facilitates the assignment of exoplanets to appropriate classes via supervised feature learning methods, producing granular clusters of habitability. The proposed work describes a decision-theoretical model using the power of convex optimization and algorithmic machine learning.

Predicting trends in stock market prices has been an area of interest for researchers for many years due to its complex and dynamic nature. Intrinsic volatility in stock market across the globe makes the task of prediction challenging. Forecasting and diffusion modeling, although effective can't be the panacea to the diverse range of problems encountered in prediction, short-term or otherwise. Market risk, strongly correlated with forecasting errors, needs to be minimized to ensure minimal risk in investment. The authors propose to minimize forecasting error by treating the forecasting problem as a classification problem, a popular suite of algorithms in Machine learning. In this paper, we propose a novel way to minimize the risk of investment in stock market by predicting the returns of a stock using a class of powerful machine learning algorithms known as ensemble learning. Some of the technical indicators such as Relative Strength Index (RSI), stochastic oscillator etc are used as inputs to train our model. The learning model used is an ensemble of multiple decision trees. The algorithm is shown to outperform existing algorithms found in the literature. Out of Bag (OOB) error estimates have been found to be encouraging.

Seven Earth-sized planets, known as the TRAPPIST-1 system was discovered with great fanfare in the last week of February 2017. Three of these planets are in the habitable zone of their star, making them potentially habitable planets a mere 40 light years away. Discovery of the closest potentially habitable planet to us just a year before -Proxima b and a realization that Earth-type planets in circumstellar habitable zones are a common occurrence provides the impetus to the existing pursuit for life outside the Solar System. The search for life has two goals essentially: Earth similarity and habitability. An index was recently proposed, Cobb-Douglas Habitability Score (CDHS), based on Cobb-Douglas habitability production function, which computes the habitability score by using measured and estimated planetary parameters like radius, density, escape velocity and surface temperature of a planet. The proposed metric, with exponents accounting for metric elasticity, is endowed with analytical properties that ensure global optima and can be scaled to accommodate a finite number of input parameters. We show here that the model is elastic, and the conditions on elasticity to ensure global maxima can scale as the number of predictor parameters increase. K-Nearest Neighbor classification algorithm, embellished with probabilistic herding and thresholding restriction, utilizes CDHS scores and labels exoplanets to appropriate classes via feature-learning methods. The algorithm works on top of a decision-theoretical model using the power of convex optimization and machine learning. The goal is to classify the recently discovered exoplanets into the "Earth League" and other classes. A second approach, based on a novel feature-learning and tree-building method classifies the same planets without computing the CDHS of the planets and produces a similar outcome. The convergence of the two different approaches indicates the strength of the proposed scheme and the likelihood of the potential habitability of the recent discoveries. 2016). This planet generated a lot of stir in the news (Witze, 2016) because it is located in the habitable zone and its mass is in the Earth's mass range: 1.27 − 3 M ⊕ , making it a potentially habitable planet (PHP) and an immediate destination for the Breakthrough Starshot initiative (Starshot, 2016). A few months after the announcement of Proxima b, another family of terrestrial-size exoplanets -the TRAPPIST-1 systemwas discovered (Gillon, 2016).This work is motivated by testing the efficacy of the suggested model, CDHS, in determining the habitability score, the proximity to the "Earth-League", of the recently discovered Proxima b. The habitability score model has been found to work well in classifying previously known exoplanets in terms of potential habitability. Therefore it was natural to test whether the model can also classify it as potentially habitable by computing its habitability score. This could indicate whether the model may be extended for a quick check of the potential habitability of n...

Enterprises are enhancing investments in cloud services setting up data centers to meet growing demand. A typical investment is of the order of millions of dollars, infrastructure and recurring cost included. This paper proposes an algorithmic/analytical approach to address the issues of optimal utilization of the resources towards a feasible and profitable model. The economic sustainability of such a model is accomplished via Cobb-Douglas production function. The production model seeks to answer questions on maximal revenue given a set of budgetary constraints. The model suggests minimum investments needed to achieve target output.

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Inspired by chaotic firing of neurons in the brain, we propose ChaosNet -a novel chaos based artificial neural network architecture for classification tasks. ChaosNet is built using layers of neurons, each of which is a 1D chaotic map known as the Generalized Luröth Series (GLS) which has been shown in earlier works to possess very useful properties for compression, cryptography and for computing XOR and other logical operations. In this work, we design a novel learning algorithm on ChaosNet that exploits the topological transitivity property of the chaotic GLS neurons. The proposed learning algorithm gives consistently good performance accuracy in a number of classification tasks on well known publicly available datasets with very limited training samples. Even with as low as 7 (or fewer) training samples/class (which accounts for less than 0.05% of the total available data), ChaosNet yields performance accuracies in the range 73.89% − 98.33%. We demonstrate the robustness of ChaosNet to additive parameter noise and also provide an example implementation of a 2-layer ChaosNet for enhancing classification accuracy. We envisage the development of several other novel learning algorithms on ChaosNet in the near future.Chaos has been empirically found in the brain at several spatio-temporal scales [1,2]. In fact, individual neurons in the brain are known to exhibit chaotic bursting activity and several neuronal models such as the Hindmarsh-Rose neuron model exhibit complex chaotic dynamics [3]. Though Artificial Neural Networks (ANN) such as Recurrent Neural Networks exhibit chaos, to our knowledge, there have been no successful attempts in building an ANN for classification tasks which is entirely comprised of neurons which are individually chaotic. Building on our earlier research, in this work, we propose ChaosNet -an ANN built out of neurons -each of which is a 1D chaotic map known as Generalized Luröth Series (GLS). GLS has been shown to have salient properties such as ability to encode and decode information losslessly with Shannon optimality, computing logical operations (XOR, AND etc.), universal approximation property and ergodicity (mixing) for cryptography applications. In this work, ChaosNet exploits the topological transitivity property of chaotic GLS neurons for classification tasks with state-of-the art accuracies in the low training sample regime. This work, inspired by the chaotic nature of neurons in the brain, demonstrates the unreasonable effectiveness of chaos and its properties for machine learning. It also paves the way for designing and implementing other novel learning algorithms on the ChaosNet architecture.