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We utilized steady-state, axisymmetric, viscous hydrodynamic fluid equations around a black hole in a Schwarzschild geometry background. Here, the relativistic Schwarzschild geometry is mimicked by the Paczy{\'n}sky-Wiita potential. We investigated two types of inflowing gases that can generate different kinds of accretion flows around the central objects. The inflowing gases are presented on the local energies ($B_{ob}$) of the gases versus the outermost accretion boundary locations ($r_{ob}$) plane we named it the outermost boundary condition (OBC)-plane. Based on the energies of the inflowing gases we found two types of inflowing gas classified as cold-mode and hot-mode inflowing gases in the OBC-plane. Doing so we have found the initial temperature of the inflowing gases can be a parameter for the study of the accretion process. As it can affect the disk structure and optical depth of the accretion flow, which in turn can impact the radiative emissions observed in many accreting sources., Comment: 11 pages, 5 figures, accepted for publication in Astrophysics and Space Science Proceedings, Springer Nature

Sgr~A* often shows bright, episodic flares observationally, the mechanism of the flares intermittent brightening is not very clear. Many people believe the flares may formed by the non-thermal particles, which can be a consequence of the magnetic reconnection and shock waves. In this work, we use the larger magnetic loop in the presence of pseudo-Newtonian potential which mimics general relativistic effects. The simulation results show that the reconnection of magnetic field lines passes through a current sheet, which bifurcates into two pairs of slow shocks. We also find the shock waves heat the plasma, especially when the plasma density is low. The shock wave heating effect by the magnetic reconnection is confirmed by the simulation results, and thus the process of instantaneous brightening of the flares on the accretion disk can be explained.

Immunohistochemistry (IHC) analysis is a well-accepted and widely used method for molecular subtyping, a procedure for prognosis and targeted therapy of breast carcinoma, the most common type of tumor affecting women. There are four molecular biomarkers namely progesterone receptor (PR), estrogen receptor (ER), antigen Ki67, and human epidermal growth factor receptor 2 (HER2) whose assessment is needed under IHC procedure to decide prognosis as well as predictors of response to therapy. However, IHC scoring is based on subjective microscopic examination of tumor morphology and suffers from poor reproducibility, high subjectivity, and often incorrect scoring in low-score cases. In this paper, we present, a deep learning-based semi-supervised trained, fully automatic, decision support system (DSS) for IHC scoring of invasive ductal carcinoma. Our system automatically detects the tumor region removing artifacts and scores based on Allred standard. The system is developed using 3 million pathologist-annotated image patches from 300 slides, fifty thousand in-house cell annotations, and forty thousand pixels marking of HER2 membrane. We have conducted multicentric trials at four centers with three different types of digital scanners in terms of percentage agreement with doctors. And achieved agreements of 95, 92, 88 and 82 percent for Ki67, HER2, ER, and PR stain categories, respectively. In addition to overall accuracy, we found that there is 5 percent of cases where pathologist have changed their score in favor of algorithm score while reviewing with detailed algorithmic analysis. Our approach could improve the accuracy of IHC scoring and subsequent therapy decisions, particularly where specialist expertise is unavailable. Our system is highly modular. The proposed algorithm modules can be used to develop DSS for other cancer types.

Digital pathology and microscopy image analysis are widely employed in the segmentation of digitally scanned IHC slides, primarily to identify cancer and pinpoint regions of interest (ROI) indicative of tumor presence. However, current ROI segmentation models are either stain-specific or suffer from the issues of stain and scanner variance due to different staining protocols or modalities across multiple labs. Also, tissues like Ductal Carcinoma in Situ (DCIS), acini, etc. are often classified as Tumors due to their structural similarities and color compositions. In this paper, we proposed a novel convolutional neural network (CNN) based Multi-class Tissue Segmentation model for histopathology whole-slide Breast slides which classify tumors and segments other tissue regions such as Ducts, acini, DCIS, Squamous epithelium, Blood Vessels, Necrosis, etc. as a separate class. Our unique pixel-aligned non-linear merge across spatial resolutions empowers models with both local and global fields of view for accurate detection of various classes. Our proposed model is also able to separate bad regions such as folds, artifacts, blurry regions, bubbles, etc. from tissue regions using multi-level context from different resolutions of WSI. Multi-phase iterative training with context-aware augmentation and increasing noise was used to efficiently train a multi-stain generic model with partial and noisy annotations from 513 slides. Our training pipeline used 12 million patches generated using context-aware augmentations which made our model stain and scanner invariant across data sources. To extrapolate stain and scanner invariance, our model was evaluated on 23000 patches which were for a completely new stain (Hematoxylin and Eosin) from a completely new scanner (Motic) from a different lab. The mean IOU was 0.72 which is on par with model performance on other data sources and scanners.

Let $R$ be a fibre product of standard graded algebras over a field. We study the structure of syzygies of finitely generated graded $R$-modules. As an application of this, we show that the existence of an $R$-module of finite regularity and infinite projective dimension forces $R$ to be Koszul. We also look at the extremal rays of the Betti cone of finitely generated graded $R$-modules, and show that when $\operatorname{depth}(R)=1$, they are spanned by the Betti tables of pure $R$-modules if and only if $R$ is Cohen-Macaulay with minimal multiplicity., Comment: Comments welcome!

In $2011$, Herzog, Hibi, and Ohsugi conjectured that if $J$ is the cover ideal of a chordal graph, then $J^s$ is componentwise linear for all $s \ge 1.$ In 2022, H\`a and Tuyl considered objects more general than chordal graphs and posed the following problem: Let $J(\Delta)$ be the cover ideal of a simplicial tree $\Delta.$ Is it true that $J(\Delta)^s$ is componentwise linear for all $s \geq 1$? In this article, we give an affirmative answer to this problem.

In large-scale multi-agent systems like taxi fleets, individual agents (taxi drivers) are self-interested (maximizing their own profits) and this can introduce inefficiencies in the system. One such inefficiency is with regard to the "required" availability of taxis at different time periods during the day. Since a taxi driver can work for a limited number of hours in a day (e.g., 8-10 hours in a city like Singapore), there is a need to optimize the specific hours, so as to maximize individual as well as social welfare. Technically, this corresponds to solving a large-scale multi-stage selfish routing game with transition uncertainty. Existing work in addressing this problem is either unable to handle ``driver" constraints (e.g., breaks during work hours) or not scalable. To that end, we provide a novel mechanism that builds on replicator dynamics through ideas from behavior cloning. We demonstrate that our methods provide significantly better policies than the existing approach in terms of improving individual agent revenue and overall agent availability., Comment: Accepted to the 22nd International Conference on Autonomous Agents and Multiagent Systems (AAMAS-23)

Change detection for aerial imagery involves locating and identifying changes associated with the areas of interest between co-registered bi-temporal or multi-temporal images of a geographical location. Farm ponds are man-made structures belonging to the category of minor irrigation structures used to collect surface run-off water for future irrigation purposes. Detection of farm ponds from aerial imagery and their evolution over time helps in land surveying to analyze the agricultural shifts, policy implementation, seasonal effects and climate changes. In this paper, we introduce a publicly available object detection and instance segmentation (OD/IS) dataset for localizing farm ponds from aerial imagery. We also collected and annotated the bi-temporal data over a time-span of 14 years across 17 villages, resulting in a binary change detection dataset called \textbf{F}arm \textbf{P}ond \textbf{C}hange \textbf{D}etection Dataset (\textbf{FPCD}). We have benchmarked and analyzed the performance of various object detection and instance segmentation methods on our OD/IS dataset and the change detection methods over the FPCD dataset. The datasets are publicly accessible at this page: \textit{\url{https://huggingface.co/datasets/ctundia/FPCD}}

Requirements of large amounts of data is a difficulty in training many GANs. Data efficient GANs involve fitting a generators continuous target distribution with a limited discrete set of data samples, which is a difficult task. Single image methods have focused on modeling the internal distribution of a single image and generating its samples. While single image methods can synthesize image samples with diversity, they do not model multiple images or capture the inherent relationship possible between two images. Given only a handful of images, we are interested in generating samples and exploiting the commonalities in the input images. In this work, we extend the single-image GAN method to model multiple images for sample synthesis. We modify the discriminator with an auxiliary classifier branch, which helps to generate a wide variety of samples and to classify the input labels. Our Data-Efficient GAN (DEff-GAN) generates excellent results when similarities and correspondences can be drawn between the input images or classes.

Modern-day reservoir management and monitoring of geological carbon storage increasingly call for costly time-lapse seismic data collection. In this letter, we show how techniques from graph theory can be used to optimize acquisition geometries for low-cost sparse 4D seismic. Based on midpoint-offset domain connectivity arguments, the proposed algorithm automatically produces sparse non-replicated time-lapse acquisition geometries that favor wavefield recovery.

There is a very popular two-zone accretion disk model that the inner part of the non-advective Keplerian disk (Shakura-Sunyaev disk) can produce hot advection-dominated accretion flow, which can generate high energy power-law radiation and outflows/jets. However, we find that this simple model is inadequate to automatically explain many properties of the sources (such as hysteresis effect, counter-clockwise traversal in a hardness-intensity diagram, peculiar variabilities, and association/non-association of jets in a black hole $X-$ray binary) without considering additional assumptions. We also find some theoretical issues in this model, such as understanding of variation of transition region and formation of an outer disk, which has only Keplerian distribution. Based on the recent theoretical studies on advective disk structures, as well as, many observational behaviors of the accreting black holes, we conclude that there should be a third component (TC) of accretion flow parallel to the two-zone disk model, which can naturally explain all above mentioned issues. Interestingly, this modified model also provides a new scenario for the jet generation and evolution with the TC flow during high energy states, which can make the jet close to the axis. We also find out an expression of jet kinetic power., Comment: 17 pages, 7 figures, comments are welcome