Solar Potential Analysis of Rooftops Using Satellite Imagery

Solar energy is one of the most important sources of renewable energy and the cleanest form of energy. In India, where solar energy could produce power around trillion kilowatt-hours in a year, our country is only able to produce power of around in gigawatts only. Many people are not aware of the solar potential of their rooftop, and hence they always think that installing solar panels is very much expensive. In this work, we introduce an approach through which we can generate a report remotely that provides the amount of solar potential of a building using only its latitude and longitude. We further evaluated various types of rooftops to make our solution more robust. We also provide an approximate area of rooftop that can be used for solar panels placement and a visual analysis of how solar panels can be placed to maximize the output of solar power at a location

Manin's b-constant in families

We show that the $b$-constant (appearing in Manin's conjecture) is constant on very general fibers of a family of algebraic varieties. If the fibers of the family are uniruled, then we show that the $b$-constant is constant on general fibers.Comment: 16 page

Counterexamples to Mercat's Conjecture

For any n>3, we provide examples of curves lying on K3 surfaces and vector bundles on those curves which invalidate Mercat's conjecture for rank n bundles.Comment: 6 pages, Proof of a lemma added in Section 2, Slight change in the proof of the main theorem, added reference

Manin's Conjecture and the Fujita invariant of finite covers

We prove a conjecture of Lehmann-Tanimoto about the behaviour of the Fujita invariant (or $a$-constant appearing in Manin's conjecture) under pull-back to generically finite covers. As a consequence we obtain results about geometric consistency of Manin's conjecture.Comment: Typos correcte

A Fourier extension based numerical integration scheme for fast and high-order approximation of convolutions with weakly singular kernels

Computationally efficient numerical methods for high-order approximations of convolution integrals involving weakly singular kernels find many practical applications including those in the development of fast quadrature methods for numerical solution of integral equations. Most fast techniques in this direction utilize uniform grid discretizations of the integral that facilitate the use of FFT for $O(n\log n)$ computations on a grid of size $n$. In general, however, the resulting error converges slowly with increasing $n$ when the integrand does not have a smooth periodic extension. Such extensions, in fact, are often discontinuous and, therefore, their approximations by truncated Fourier series suffer from Gibb's oscillations. In this paper, we present and analyze an $O(n\log n)$ scheme, based on a Fourier extension approach for removing such unwanted oscillations, that not only converges with high-order but is also relatively simple to implement. We include a theoretical error analysis as well as a wide variety of numerical experiments to demonstrate its efficacy

Bird Species Classification using Transfer Learning with Multistage Training

Bird species classification has received more and more attention in the field of computer vision, for its promising applications in biology and environmental studies. Recognizing bird species is difficult due to the challenges of discriminative region localization and fine-grained feature learning. In this paper, we have introduced a Transfer learning based method with multistage training. We have used both Pre-Trained Mask-RCNN and an ensemble model consisting of Inception Nets (InceptionV3 & InceptionResNetV2 ) to get localization and species of the bird from the images respectively. Our final model achieves an F1 score of 0.5567 or 55.67 % on the dataset provided in CVIP 2018 Challenge

Detecting 21 cm EoR Signal using Drift Scans: Correlation of Time-ordered Visibilities

We present a formalism to extract the EoR HI power spectrum for drift scans using radio interferometers. Our main aim is to determine the coherence time scale of time-ordered visibilities. We compute the two-point correlation function of the HI visibilities measured at different times to address this question. We determine, for a given baseline, the decorrelation of the amplitude and the phase of this complex function. Our analysis uses primary beams of four ongoing and future interferometers---PAPER, MWA, HERA, and SKA1-Low. We identify physical processes responsible for the decorrelation of the HI signal and isolate their impact by making suitable analytic approximations. The decorrelation time scale of the amplitude of the correlation function lies in the range of 2--20~minutes for baselines of interest for the extraction of the HI signal. The phase of the correlation function can be made small after scaling out an appropriate term, which also causes the coherence time scale of the phase to be longer than the amplitude of the correlation function. We find that our results are insensitive to the input HI power spectrum and therefore they are directly applicable to the analysis of the drift scan data. We also apply our formalism to a set of point sources and statistically homogeneous diffuse correlated foregrounds. We find that point sources decorrelate on a time scale much shorter than the HI signal. This provides a novel mechanism to partially mitigate the foregrounds in a drift scan.Comment: 22 pages and 5 figures. Accepted for publication in Ap

Random walks and forbidden minors II: A poly(dε−1)\text{poly}(d\varepsilon^{-1})-query tester for minor-closed properties of bounded-degree graphs

Let $G$ be a graph with $n$ vertices and maximum degree $d$. Fix some minor-closed property $\mathcal{P}$ (such as planarity). We say that $G$ is $\varepsilon$-far from $\mathcal{P}$ if one has to remove $\varepsilon dn$ edges to make it have $\mathcal{P}$. The problem of property testing $\mathcal{P}$ was introduced in the seminal work of Benjamini-Schramm-Shapira (STOC 2008) that gave a tester with query complexity triply exponential in $\varepsilon^{-1}$. Levi-Ron (TALG 2015) have given the best tester to date, with a quasipolynomial (in $\varepsilon^{-1}$) query complexity. It is an open problem to get property testers whose query complexity is $\text{poly}(d\varepsilon^{-1})$, even for planarity. In this paper, we resolve this open question. For any minor-closed property, we give a tester with query complexity $d\cdot \text{poly}(\varepsilon^{-1})$. The previous line of work on (independent of $n$, two-sided) testers is primarily combinatorial. Our work, on the other hand, employs techniques from spectral graph theory. This paper is a continuation of recent work of the authors (FOCS 2018) analyzing random walk algorithms that find forbidden minors

Finding forbidden minors in sublinear time: a n1/2+o(1)n^{1/2+o(1)}-query one-sided tester for minor closed properties on bounded degree graphs

Let $G$ be an undirected, bounded degree graph with $n$ vertices. Fix a finite graph $H$, and suppose one must remove $\varepsilon n$ edges from $G$ to make it $H$-minor free (for some small constant $\varepsilon > 0$). We give an $n^{1/2+o(1)}$-time randomized procedure that, with high probability, finds an $H$-minor in such a graph. As an application, suppose one must remove $\varepsilon n$ edges from a bounded degree graph $G$ to make it planar. This result implies an algorithm, with the same running time, that produces a $K_{3,3}$ or $K_5$ minor in $G$. No prior sublinear time bound was known for this problem. By the graph minor theorem, we get an analogous result for any minor-closed property. Up to $n^{o(1)}$ factors, this resolves a conjecture of Benjamini-Schramm-Shapira (STOC 2008) on the existence of one-sided property testers for minor-closed properties. Furthermore, our algorithm is nearly optimal, by an $\Omega(\sqrt{n})$ lower bound of Czumaj et al (RSA 2014). Prior to this work, the only graphs $H$ for which non-trivial one-sided property testers were known for $H$-minor freeness are the following: $H$ being a forest or a cycle (Czumaj et al, RSA 2014), $K_{2,k}$, $(k\times 2)$-grid, and the $k$-circus (Fichtenberger et al, Arxiv 2017).Comment: 31 page

Approximation Algorithms for Digraph Width Parameters

Several problems that are NP-hard on general graphs are efficiently solvable on graphs with bounded treewidth. Efforts have been made to generalize treewidth and the related notion of pathwidth to digraphs. Directed treewidth, DAG-width and Kelly-width are some such notions which generalize treewidth, whereas directed pathwidth generalizes pathwidth. Each of these digraph width measures have an associated decomposition structure. In this paper, we present approximation algorithms for all these digraph width parameters. In particular, we give an O(sqrt{logn})-approximation algorithm for directed treewidth, and an O({\log}^{3/2}{n})-approximation algorithm for directed pathwidth, DAG-width and Kelly-width. Our algorithms construct the corresponding decompositions whose widths are within the above mentioned approximation factors