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The equation of state for an ideal gas is simple, which is $P=nk_{\rm B}T$. In the case of imperfect gases where mutual interactions among the constituents are important, pressure $P$ can be expressed as the series expansion of density $n$ with appropriate coefficients, known as virial coefficients $B_m$. In this paper, we have obtained the first four virial coefficients for a model interaction potential $\Phi(r)$ using multidimensional Monte-Carlo integration and importance sampling methods. Next, we perform molecular dynamics simulations with the same $\Phi(r)$ for a many-particle system to obtain $P$ as a function of $T$ and $n$. We compare our numerical data with the virial equation of state., Comment: 15 Pages, 7 Figures

Multi-class cell detection and counting is an essential task for many pathological diagnoses. Manual counting is tedious and often leads to inter-observer variations among pathologists. While there exist multiple, general-purpose, deep learning-based object detection and counting methods, they may not readily transfer to detecting and counting cells in medical images, due to the limited data, presence of tiny overlapping objects, multiple cell types, severe class-imbalance, minute differences in size/shape of cells, etc. In response, we propose guided posterior regularization (DeGPR), which assists an object detector by guiding it to exploit discriminative features among cells. The features may be pathologist-provided or inferred directly from visual data. We validate our model on two publicly available datasets (CoNSeP and MoNuSAC), and on MuCeD, a novel dataset that we contribute. MuCeD consists of 55 biopsy images of the human duodenum for predicting celiac disease. We perform extensive experimentation with three object detection baselines on three datasets to show that DeGPR is model-agnostic, and consistently improves baselines obtaining up to 9% (absolute) mAP gains.

Contrastive Learning (CL) is a recent representation learning approach, which encourages inter-class separability and intra-class compactness in learned image representations. Since medical images often contain multiple semantic classes in an image, using CL to learn representations of local features (as opposed to global) is important. In this work, we present a novel semi-supervised 2D medical segmentation solution that applies CL on image patches, instead of full images. These patches are meaningfully constructed using the semantic information of different classes obtained via pseudo labeling. We also propose a novel consistency regularization (CR) scheme, which works in synergy with CL. It addresses the problem of confirmation bias, and encourages better clustering in the feature space. We evaluate our method on four public medical segmentation datasets and a novel histopathology dataset that we introduce. Our method obtains consistent improvements over state-of-the-art semi-supervised segmentation approaches for all datasets., Comment: The paper is withdrawn due to a bug in experimental protocol that renders its experimental results and observations invalid. All expts were conducted by the student authors. The roles of senior authors (Prasenjit Das, Govind Makharia, Prathosh, and Mausam) were in defining the problem statement, discussions of potential solutions and framing of the paper and not in performing experiments

We study the dynamics of an intruder moving through a fluidized granular medium in three dimensions ($d=3$). The intruder and grains have both translational and rotational degrees of freedom. The energy-dissipation mechanism is solid friction between all pairs of particles. We keep the granular system fluidized even at rather high densities by randomly perturbing the linear and angular velocities of the grains. We apply a constant external force of magnitude $F$ to the intruder, and obtain its steady state velocity $V_s$ in the center-of-mass frame of the grains. The $F$-$V_s$ relation is of great interest in the industrial processing of granular matter, and has been the subject of most experiments on this problem. We also obtain the mobility, which is proportional to the inverse viscosity, as a function of the volume fraction $\phi$. This is shown to diverge at the jamming volume fraction. For $\phi$ below the jamming fraction, we find that $V_s \sim F$ for small $F$ and $V_s \sim F^{1/2}$ for large $F$. The intruder shows diffusive motion in the plane perpendicular to the direction of the external force., Comment: 14 Pages, 5 Figs, and 1 Table, Accepted to Phys. Rev. E

This paper is the second in a two-part exposition on {\it surface-directed spinodal decomposition} (SDSD), i.e., the interplay of kinetics of wetting and phase separation at a surface which is wetted by one of the components of a binary mixture. In our first paper [P. Das, P.K. Jaiswal and S. Puri, Phys. Rev. E {\bf 102}, 012803 (2020)], we studied SDSD on chemically heterogeneous and physically flat substrates. In this paper, we study SDSD on a chemically homogeneous but morphologically patterned substrate. Such substrates arise in a vast variety of technological applications. Our goal is to provide a theoretical understanding of SDSD in this context. We present detailed numerical results for domain growth both inside and above the grooves in the substrate. The morphological evolution can be understood in terms of the interference of SDSD waves originating from the different surfaces comprising the substrate., Comment: 17Pages, 9 Figures, Accepted to Physical Review E

It has been established that the low frequency quasi-localized modes of amorphous solids at zero temperature exhibit universal density of states, depending on the frequencies as $D(\omega) \sim \omega^4$. It remains an open question whether this universal law extends to finite temperatures. In this Letter we show that well quenched model glasses at temperatures as high as $T_g/3$ possess the same universal density of states. The only condition required is that {\em average} particle positions stabilize before thermal diffusion destroys the cage structure of the material. The universal density of quasi-localized low frequency modes refers then to vibrations around the thermally averaged configuration of the material., Comment: 4 Pages, 4 Figs, Under Review

{\it Surface-directed spinodal decomposition} (SDSD) is the kinetic interplay of phase separation and wetting at a surface. This process is of great scientific and technological importance. In this paper, we report results from a numerical study of SDSD on a chemically patterned substrate. We consider simple surface patterns for our simulations, but most of the results apply for arbitrary patterns. In layers near the surface, we observe a dynamical crossover from a {\it surface-registry regime} to a {\it phase-separation regime}. We study this crossover using layer-wise correlation functions and structure factors, and domain length scales., Comment: 19 Pages, 11 Figs, Accepted to Physical Review E

Low frequency quasi-localized modes of amorphous glasses appear to exhibit universal density of states, depending on the frequencies as $D(\omega) \sim \omega^4$. To date various models of glass formers with short range binary interaction, and network glasses with both binary and ternary interactions, were shown to conform with this law. In this paper we examine granular amorphous solids with long-range electrostatic interactions, and find that they exhibit the same law. To rationalize this wide universality class we return to a model proposed by Gurevich, Parshin and Schober (GPS) and analyze its predictions for interaction laws with varying spatial decay, exploring this wider than expected universality class. Numerical and analytic results are provided for both the actual system with long range interaction and for the GPS model., Comment: 10 Pages, 7 Figures, Physical Review B

Electrostatic theory preserves charges, but allows dipolar excitations. Elasticity theory preserves dipoles, but allows quadrupolar (Eshelby like) plastic events. Charged amorphous granular systems are interesting in their own right; here we focus on their plastic instabilities and examine their mechanical response to external strain and to external electric field, to expose the competition between elasticity and electrostatics. In this paper a generic model is offered, its mechanical instabilities are examined and a theoretical analysis is presented. Plastic instabilities are discussed as saddle-node bifurcations that can be fully understood in terms of eigenvalues and eigenfunctions of the relevant Hessian matrix. This system exhibits moduli that describe how electric polarization and stress are influenced by strain and electric field. Theoretical expression for these moduli are offered and compared to the measurements in numerical simulations., Comment: 7 pages, 11 Figures

In amorphous solids at finite temperatures the particles follow chaotic trajectories which, at temperatures sufficiently lower than the glass transition, are trapped in "cages". Averaging their positions for times shorter than the diffusion time, one can define a time-averaged configuration. Under strain or stress, these {\em average} configurations undergo sharp plastic instabilities. In athermal glasses the understanding of plastic instabilities is furnished by the Hessian matrix, its eigenvalues and eigenfunctions. Here we propose an uplifting of Hessian methods to thermal glasses, with the aim of understanding the plastic responses in the time-averaged configuration. We discuss a number of potential definitions of Hessians and identify which of these can provide eigenvalues and eigenfunctions which can explain and predict the instabilities of the time-averaged configurations. The conclusion is that the non-affine changes in the average configurations during an instability is accurately predicted by the eigenfunctions of the low-lying eigenvalues of the chosen Hessian., Comment: 7 Pages, 6 Figures, Physical Review E

Shearing with a finite shear rate a compressed granular system results in a region of grains flowing over a compact, static assembly. Perforce this region is dilated to a degree that depends on the shear rate, the loading pressure, gravity, various material parameters, and the preparation protocol. In spite of numerous studies of granular flows a predictive theory of the amount of dilation is still lacking. Here, we offer a scaling theory that is focused on such a prediction as a function of shear rate and the dissipative parameters of the granular assembly. The resulting scaling laws are universal with respect to changing the interparticle force laws., Comment: 10 Figs and 6 Pages, published version