AI pipeline for accurate retinal layer segmentation using OCT 3D images

Image data set from a multi-spectral animal imaging system is used to address two issues: (a) registering the oscillation in optical coherence tomography (OCT) images due to mouse eye movement and (b) suppressing the shadow region under the thick vessels/structures. Several classical and AI-based algorithms in combination are tested for each task to see their compatibility with data from the combined animal imaging system. Hybridization of AI with optical flow followed by Homography transformation is shown to be working (correlation value>0.7) for registration. Resnet50 backbone is shown to be working better than the famous U-net model for shadow region detection with a loss value of 0.9. A simple-to-implement analytical equation is shown to be working for brightness manipulation with a 1% increment in mean pixel values and a 77% decrease in the number of zeros. The proposed equation allows formulating a constraint optimization problem using a controlling factor {\alpha} for minimization of number of zeros, standard deviation of pixel value and maximizing the mean pixel value. For Layer segmentation, the standard U-net model is used. The AI-Pipeline consists of CNN, Optical flow, RCNN, pixel manipulation model, and U-net models in sequence. The thickness estimation process has a 6% error as compared to manual annotated standard data.Comment: 16 Page and 11 Figure

Relative estimation of scattering noise and its utility to select radiation detector for Gamma CT scanner

This study investigates two unavoidable noise factors: electronic noise and radiation scattering, associated with detectors and their electronics. This study proposes a novel methodology to estimate electronic and scattering noise separately. It utilizes mathematical tools, namely, Kanpur theorem-1, standard deviation, similarity dice coefficient parameters, and experimental Computerized Tomography technique. Four types of gamma detectors: CsI (Tl), LaBr_3 (Ce), NaI (Tl) and HPGe are used with their respective electronics. A detector having integrated circuit electronics is shown to impart significantly less (~33% less) electronic noise in data as compared to detectors with distributed electronics. Kanpur Theorem-1 signature is proposed as a scattering error estimate. An empirical expression is developed showing that scattering noise depends strongly on mass attenuation coefficients of detector crystal material and weakly on their active area. The difference between predicted and estimated relative scattering is 14.6%. The methodology presented in this study will assist the related industry in selecting the appropriate detector of optimal diameter, thickness, material composition, and hardware as per requirement.Comment: 9 Figures and 15 Page

Universal Sorting: Finding a DAG using Priced Comparisons

We resolve two open problems in sorting with priced information, introduced by [Charikar, Fagin, Guruswami, Kleinberg, Raghavan, Sahai (CFGKRS), STOC 2000]. In this setting, different comparisons have different (potentially infinite) costs. The goal is to sort with small competitive ratio (algorithmic cost divided by cheapest proof). 1) When all costs are in $\{0,1,n,\infty\}$, we give an algorithm that has $\widetilde{O}(n^{3/4})$ competitive ratio. Our algorithm generalizes the algorithms for generalized sorting (all costs are either $1$ or $\infty$), a version initiated by [Huang, Kannan, Khanna, FOCS 2011] and addressed recently by [Kuszmaul, Narayanan, FOCS 2021]. 2) We answer the problem of bichromatic sorting posed by [CFGKRS]: The input is split into $A$ and $B$, and $A-A$ and $B-B$ comparisons are more expensive than an $A-B$ comparisons. We give a randomized algorithm with a O(polylog n) competitive ratio. These results are obtained by introducing the universal sorting problem, which generalizes the existing framework in two important ways. We remove the promise of a directed Hamiltonian path in the DAG of all comparisons. Instead, we require that an algorithm outputs the transitive reduction of the DAG. For bichromatic sorting, when $A-A$ and $B-B$ comparisons cost $\infty$, this generalizes the well-known nuts and bolts problem. We initiate an instance-based study of the universal sorting problem. Our definition of instance-optimality is inherently more algorithmic than that of the competitive ratio in that we compare the cost of a candidate algorithm to the cost of the optimal instance-aware algorithm. This unifies existing lower bounds, and opens up the possibility of an $O(1)$-instance optimal algorithm for the bichromatic version.Comment: 40 pages, 5 figure

Awareness of Farmers about the Primary Agriculture Credit Societies (With Special Reference of Uttar Pradesh and Uttarakhand)

Primary Agriculture Credit Society is a basic unit and smallest cooperative credit institution in India. It works on the grass-root level (gram panchayat and village level). Primary Agriculture Credit Society is formed at the village or town level. It is the old cooperative credit system of India. Primary Agriculture Credit Society was designed to be a village-level credit society into which the farmers brought in share capital, deposits, and provide loans to each other. This study aims to assess the Awareness of Farmers about the Primary Agricultural Credit Societies with Special Reference to Uttar Pradesh and Uttarakhand. 58% of farmers know about primary agriculture credit societies and this study will useful for the rural areas policymakers and this study will also useful for many other stakeholders

An Algorithm for Bichromatic Sorting with Polylog Competitive Ratio

The problem of sorting with priced information was introduced by [Charikar, Fagin, Guruswami, Kleinberg, Raghavan, Sahai (CFGKRS), STOC 2000]. In this setting, different comparisons have different (potentially infinite) costs. The goal is to find a sorting algorithm with small competitive ratio, defined as the (worst-case) ratio of the algorithm's cost to the cost of the cheapest proof of the sorted order. The simple case of bichromatic sorting posed by [CFGKRS] remains open: We are given two sets $A$ and $B$ of total size $N$, and the cost of an $A-A$ comparison or a $B-B$ comparison is higher than an $A-B$ comparison. The goal is to sort $A \cup B$. An $\Omega(\log N)$ lower bound on competitive ratio follows from unit-cost sorting. Note that this is a generalization of the famous nuts and bolts problem, where $A-A$ and $B-B$ comparisons have infinite cost, and elements of $A$ and $B$ are guaranteed to alternate in the final sorted order. In this paper we give a randomized algorithm InversionSort with an almost-optimal w.h.p. competitive ratio of $O(\log^{3} N)$. This is the first algorithm for bichromatic sorting with a $o(N)$ competitive ratio.Comment: 18 pages, accepted to ITCS 2024. arXiv admin note: text overlap with arXiv:2211.0460

Computing Teichm\"{u}ller Maps between Polygons

By the Riemann-mapping theorem, one can bijectively map the interior of an $n$-gon $P$ to that of another $n$-gon $Q$ conformally. However, (the boundary extension of) this mapping need not necessarily map the vertices of $P$ to those $Q$. In this case, one wants to find the ``best" mapping between these polygons, i.e., one that minimizes the maximum angle distortion (the dilatation) over \textit{all} points in $P$. From complex analysis such maps are known to exist and are unique. They are called extremal quasiconformal maps, or Teichm\"{u}ller maps. Although there are many efficient ways to compute or approximate conformal maps, there is currently no such algorithm for extremal quasiconformal maps. This paper studies the problem of computing extremal quasiconformal maps both in the continuous and discrete settings. We provide the first constructive method to obtain the extremal quasiconformal map in the continuous setting. Our construction is via an iterative procedure that is proven to converge quickly to the unique extremal map. To get to within $\epsilon$ of the dilatation of the extremal map, our method uses $O(1/\epsilon^{4})$ iterations. Every step of the iteration involves convex optimization and solving differential equations, and guarantees a decrease in the dilatation. Our method uses a reduction of the polygon mapping problem to that of the punctured sphere problem, thus solving a more general problem. We also discretize our procedure. We provide evidence for the fact that the discrete procedure closely follows the continuous construction and is therefore expected to converge quickly to a good approximation of the extremal quasiconformal map.Comment: 28 pages, 6 figure