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Construction of representations of braid group generators from $N$-state vertex models provide an elegant route to study knot and link invariants. Using such a braid group representation, an algebraic formula for the link invariants was put forth when the same spin $(N-1)/2$ are placed on all the component knots. In this paper, we generalise the procedure to deduce representations of braiding generators from bi-partite vertex models. Such a representation allows the study of multi-colored link invariants where the component knots carry different spins. We propose a multi-colored link invariant formula in terms of braiding generators derived from $R$ matrices of bi-partite vertex models., Comment: 18 pages, 2 figures, typos corrected

We discuss the equivalence of the standard covariant expressions and light-front expressions of the three fundamental one loop Feynman diagrams of Quantum Electrodynamics viz. vertex correction, fermion self-energy and vacuum polarization in the light-front gauge obtained using time-ordered Hamiltonian perturbation theory. Although this issue has been addressed by us and others previously, our emphasis in this article is to resolve any ambiguity regarding the correct form of the gauge boson propagator to be used in the light-front gauge. We show how integrating over the light-front energy consistently in the covariant expression of each of the three one loop corrections leads to the propagating as well as the instantaneous diagrams of the light-front theory. In doing so, we re-establish the necessity of using the doubly transverse gauge boson propagator., Comment: Major revisions made to the manuscript. Please refer arXiv:2003.10881 for the revised and updated version

Mammogram inspection in search of breast tumors is a tough assignment that radiologists must carry out frequently. Therefore, image analysis methods are needed for the detection and delineation of breast masses, which portray crucial morphological information that will support reliable diagnosis. In this paper, we proposed a conditional Generative Adversarial Network (cGAN) devised to segment a breast mass within a region of interest (ROI) in a mammogram. The generative network learns to recognize the breast mass area and to create the binary mask that outlines the breast mass. In turn, the adversarial network learns to distinguish between real (ground truth) and synthetic segmentations, thus enforcing the generative network to create binary masks as realistic as possible. The cGAN works well even when the number of training samples are limited. Therefore, the proposed method outperforms several state-of-the-art approaches. This hypothesis is corroborated by diverse experiments performed on two datasets, the public INbreast and a private in-house dataset. The proposed segmentation model provides a high Dice coefficient and Intersection over Union (IoU) of 94% and 87%, respectively. In addition, a shape descriptor based on a Convolutional Neural Network (CNN) is proposed to classify the generated masks into four mass shapes: irregular, lobular, oval and round. The proposed shape descriptor was trained on Digital Database for Screening Mammography (DDSM) yielding an overall accuracy of 80%, which outperforms the current state-of-the-art., Comment: 33 pages, Submitted to Expert Systems with Applications

In this paper, an optic disc and cup segmentation method is proposed using U-Net followed by a multi-scale feature matching network. The proposed method targets task 2 of the REFUGE challenge 2018. In order to solve the segmentation problem of task 2, we firstly crop the input image using single shot multibox detector (SSD). The cropped image is then passed to an encoder-decoder network with skip connections also known as generator. Afterwards, both the ground truth and generated images are fed to a convolution neural network (CNN) to extract their multi-level features. A dice loss function is then used to match the features of the two images by minimizing the error at each layer. The aggregation of error from each layer is back-propagated through the generator network to enforce it to generate a segmented image closer to the ground truth. The CNN network improves the performance of the generator network without increasing the complexity of the model., Comment: EYE REFUGE CHALLENGE 2018, submitted 7 Pages

This paper proposed a retinal image segmentation method based on conditional Generative Adversarial Network (cGAN) to segment optic disc. The proposed model consists of two successive networks: generator and discriminator. The generator learns to map information from the observing input (i.e., retinal fundus color image), to the output (i.e., binary mask). Then, the discriminator learns as a loss function to train this mapping by comparing the ground-truth and the predicted output with observing the input image as a condition.Experiments were performed on two publicly available dataset; DRISHTI GS1 and RIM-ONE. The proposed model outperformed state-of-the-art-methods by achieving around 0.96% and 0.98% of Jaccard and Dice coefficients, respectively. Moreover, an image segmentation is performed in less than a second on recent GPU., Comment: 8 pages, Submitted to 21st International Conference of the Catalan Association for Artificial Intelligence (CCIA 2018)

Skin lesion segmentation (SLS) in dermoscopic images is a crucial task for automated diagnosis of melanoma. In this paper, we present a robust deep learning SLS model, so-called SLSDeep, which is represented as an encoder-decoder network. The encoder network is constructed by dilated residual layers, in turn, a pyramid pooling network followed by three convolution layers is used for the decoder. Unlike the traditional methods employing a cross-entropy loss, we investigated a loss function by combining both Negative Log Likelihood (NLL) and End Point Error (EPE) to accurately segment the melanoma regions with sharp boundaries. The robustness of the proposed model was evaluated on two public databases: ISBI 2016 and 2017 for skin lesion analysis towards melanoma detection challenge. The proposed model outperforms the state-of-the-art methods in terms of segmentation accuracy. Moreover, it is capable to segment more than $100$ images of size 384x384 per second on a recent GPU., Comment: Accepted in MICCAI 2018, 9 pages

This paper proposes a novel approach based on conditional Generative Adversarial Networks (cGAN) for breast mass segmentation in mammography. We hypothesized that the cGAN structure is well-suited to accurately outline the mass area, especially when the training data is limited. The generative network learns intrinsic features of tumors while the adversarial network enforces segmentations to be similar to the ground truth. Experiments performed on dozens of malignant tumors extracted from the public DDSM dataset and from our in-house private dataset confirm our hypothesis with very high Dice coefficient and Jaccard index (>94% and >89%, respectively) outperforming the scores obtained by other state-of-the-art approaches. Furthermore, in order to detect portray significant morphological features of the segmented tumor, a specific Convolutional Neural Network (CNN) have also been designed for classifying the segmented tumor areas into four types (irregular, lobular, oval and round), which provides an overall accuracy about 72% with the DDSM dataset., Comment: 8 pages, Accepted at Medical Image Computing and Computer Assisted Intervention (MICCAI) 2018

Obtaining colored HOMFLY-PT polynomials for knots from 3-strand braid carrying arbitrary $SU(N)$ representation is still tedious. For a class of rank $r$ symmetric representations, $[r]$-colored HOMFLY-PT $H_{[r]}$ evaluation becomes simpler. Recently it was shown that $H_{[r]}$, for such knots from 3-strand braid, can be constructed using the quantum Racah coefficients (6j-symbols) of $U_q(sl_2)$. In this paper, we generalise it to links whose components carry different symmetric representations. We illustrate the technique by evaluating multi-colored link polynomials $H_{[r_1],[r_2]}$ for the two-component link L7a3 whose components carry $[r_1]$ and $[r_2]$ colors., Comment: 11 pages, 1 figure

We revisit the proof of equivalence of one loop expressions for fermion self-energy and vertex correction in light-front QED and Covariant QED at the Feynman diagram level and generalize, to all components, the proof of equivalence for the one loop vertex correction diagram which was presented earlier by us only for the $+$ component of $\Lambda^\mu$. We demonstrate, in the general case also, that the equivalence cannot be established without the third term in the three-term photon propagator in light cone gauge., Comment: 5 pages, 3 figures, Proceedings of Light Cone Conference 2017, September 2017, Mumbai, India. Published in Few Body Systems. Minor additions to previous version

Computing polynomial form of the colored HOMFLY-PT for non-arborescent knots obtained from three or more strand braids is still an open problem. One of the efficient methods suggested for the three-strand braids relies on the eigenvalue hypothesis which uses the Yang-Baxter equation to express the answer through the eigenvalues of the ${\cal R}$-matrix. In this paper, we generalize the hypothesis to higher number of strands in the braid where commuting relations of non-neighbouring $\mathcal{R}$ matrices are also incorporated. By solving these equations, we determine the explicit form for $\mathcal{R}$-matrices and the inclusive Racah matrices in terms of braiding eigenvalues (for matrices of size up to 6 by 6). For comparison, we briefly discuss the highest weight method for four-strand braids carrying fundamental and symmetric rank two $SU_q(N)$ representation. Specifically, we present all the inclusive Racah matrices for representation $[2]$ and compare with the matrices obtained from eigenvalue hypothesis., Comment: 23 pages

We study the entanglement for a state on linked torus boundaries in $3d$ Chern-Simons theory with a generic gauge group and present the asymptotic bounds of R\'enyi entropy at two different limits: (i) large Chern-Simons coupling $k$, and (ii) large rank $r$ of the gauge group. These results show that the R\'enyi entropies cannot diverge faster than $\ln k$ and $\ln r$, respectively. We focus on torus links $T(2,2n)$ with topological linking number $n$. The R\'enyi entropy for these links shows a periodic structure in $n$ and vanishes whenever $n = 0 \text{ (mod } \textsf{p})$, where the integer $\textsf{p}$ is a function of coupling $k$ and rank $r$. We highlight that the refined Chern-Simons link invariants can remove such a periodic structure in $n$., Comment: 31 pages, 5 figures

Tests of the integrality properties of a scalar operator in topological strings on a resolved conifold background or orientifold of conifold backgrounds have been performed for arborescent knots and some non-arborescent knots. The recent results on polynomials for those knots colored by SU(N) and SO(N) adjoint representations are useful to verify Marino's integrality conjecture up to two boxes in the Young diagram. In this paper, we review the salient aspects of the integrality properties and tabulate explicitly for an arborescent knot and a link. In our knotebook website, we have put these results for over 100 prime knots available in Rolfsen table and some links. The first application of the obtained results, an observation of the Gaussian distribution of the LMOV invariants is also reported., Comment: 28 pages