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Saptashwa Bhattacharyya

Understanding SVM Series: Part 1

In this post, I will give an introduction of Support Vector Machine classifier. This post will be a part of the series in which I will explain Support Vector Machine (SVM) including all the necessary minute details and mathematics behind it. It will be easy, believe me! Without any delay let’s begin —

Suppose we’re given these two samples of blue stars and purple hearts (just for schematic representation and no real data are used here), and our job is to find out a line that separates them best. What do we mean by best here ?

Figure 1: Samples in a 2D plane with some separation between them

Let’s see the…

Speeding Up Unstructured Search using Quantum Computer

Possible Circuit to Verify Grover’s Algorithm? (Source: Author)

After Deutsch-Jozsa algorithm, we will discuss Grover’s algorithm through which it was shown that Quantum Computers (QCs) can be substantially faster for searching databases than classical computers. The task that Grover’s algorithm aims to solve can be expressed as follows: given a classical function f(x):{0,1}ⁿ→{0,1}, where n is the bit-size of the search space, find an input x_0 for which f(x_0)=1. Our idea is to think about an oracle (black box) which has the ability to recognize the solution to the search problem and this recognition is signaled by making use of an oracle qubit. We will come to this…

Palomar 5 Cluster may Entirely Turn into Cluster of Black Holes

Black Hole? Artist’s Impression (Source: Pixabay)

Palomar 5 is a ‘fluffy’ cluster, spanning over 20 degrees across the sky and, it has very low density (0.1 times the solar mass over 1 cubic parsec), making it about 3,000 times less dense than average. Recently a study by a group of scientists from Spain, the UK and the Netherlands have published a research report in Nature Astronomy where they suggested that the sparse nature of Palomar 5 may be due to more than 100 black holes lurking within it. Let’s get a bit deeper !!!

Long Tail of Palomar 5:

Palomar 5 is a globular cluster (GC) in our own galaxy Milky…

Image Augmentation with Augly

Left: Original Image, Right: After augmentation with Augly (Image Created by Author)

Facebook recently released [1] an augmentation library, Augly, that combines several modalities (audio, image, video, and text) under the same roof. Data augmentation is quite a common technique for increasing both the size and the diversity of labeled training data which also helps to build robust models. Here I focus only on few of the augmentation functions I tested on an image but, this library can be used for text and audio too.

Augly is more dedicated towards transformations that happen in social media platforms, including Facebook. So apart from the usual crop, flip, other augmentation functions include very realistic…

Determine if a Function is Balanced or Constant

Verify DJ Algorithm for a balanced oracle. Image by Author created using Qiskit + Matplotlib.

Today we will learn and discuss about one of the most fundamental quantum algorithms, Deutsch-Jozsa algorithm, which was proposed by David Deutsch and Richard Jozsa in 1992 [1] and really showed the power of quantum algorithms over the classical ones. To discuss Deutsch-Jozsa algorithm, it is better to start from Deutsch algorithm where instead of n qubits, we just consider a single qubit. This will help us to ease our way towards understanding some of the hefty mathematics that will come later on. Before we start getting into detail, some of the important and necessary concepts like uniform superposition that…

Using Imgaug Library for Augmentation

Sunset ! Image by Author

Since Deep Neural Networks (DNN) have large set of learnable parameters, large amount of labeled data is necessary so that these parameters generalize well for our task in hand. Data augmentation is quite a common technique for increasing both the size and the diversity of labeled training data. In the Deep Learning Specialization course, Andrew Ng mentioned that unlike other domain, in computer vision it is almost always better to have more data. Image augmentations have also become a common implicit regularization technique to address over-fitting in DNNs. Usually in image augmentation we use combinations of flipping, rotating, scaling etc…

Searching Dark Matter Using James Webb Telescope

Sunrise ! (Image by Author).

Quite a while back , I wrote about how researchers proposed to look for Dark Matter signatures that could be hidden within the ancient rocks of the Earth. A new paper in the prestigious journal ‘Physical Review Letters’ came out yesterday where the researchers discussed how the exoplanets can be used to search Dark Matter (DM). This post is a review of this new and intriguing research paper. Let’s dive in —

How will Exoplanets Help Find Dark Matter?

So far researchers have been able to infer the existence of DM only from the gravitational effect that it seems to have on visible matter. Here, the researchers…

No Cloning Theorem and Bell States

Spring in Saitama, Japan (Image Credit: Author)

The idea if quantum teleportation is fascinating to say the least but it has been realized in real life by the scientists over large distance. This post will highlight how we can think and build intuition for quantum teleportation and discuss a simple quantum circuit to achieve such feat. Many of the concepts that will be introduced here, e.g. quantum gates, tensor product, Bell states and entanglement, are all discussed before in separate posts, so fell free to check them if you need.

Let’s introduce a story line so that our learning process will be way more fun. It’s a…

Stationary Hawking Radiation from Simulated Black Hole

Simulated view of a black hole in front of the Large Magellanic Cloud (Image Credit: Alain R)

‘Black Hole’, two words that fascinate all of us, a ‘place’ of no escape for anything that passes beyond the event horizon, a complex system like that has been created artificially in laboratory and, researchers observed stationary hawking radiation from it. This fascinating report has been published recently in the prestigious journal Nature. Let’s at least try to touch the surface of this extremely complicated laboratory model of black hole and some theories behind it.

Hawking Radiation: The concept behind Hawking Radiation relies on uncertainty principle in quantum mechanics. Large fluctuations in energy can happen for a brief period of…

Deep Learning with Class Imbalanced Data

Foggy Afternoon in Nagano, Japan (Image: Author’s Own Work)

Class Imbalance:

In machine learning sometimes we are dealt with a very good hand like MNIST fashion data or CIFAR-10 data where the examples of each class in the data-set are well balanced. What happens if in a classification problem the distribution of examples across the known classes are biased or skewed ? Such problems with severe to slight bias in the data-set are common and today we will discuss an approach to handle such class imbalanced data. Let’s consider an extreme case of imbalanced data-set of mails and we build a classifier to detect spam mails. Since spam mails are relatively…

Saptashwa Bhattacharyya

PhD, Astrophysics. Using Deep Learning, Searching Dark Matter!

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