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The two-body contact is a fundamental quantity of a dilute Bose gas which relates the thermodynamics to the short-distance two-body correlations. For a Bose gas in an optical lattice, near the superfluid--Mott-insulator transition, a ``universal'' contact $C_{\rm univ}$ can be defined from the singular part $P-P_{\rm MI}$ of the pressure ($P_{\rm MI}$ is the pressure of the Mott insulator). Its expression $C_{\rm univ}=C_{\rm DBG}(|n-n_{\rm MI}|,a^*)$ coincides with that of a dilute Bose gas provided we consider the effective ``scattering length'' $a^*$ of the quasi-particles at the quantum critical point (QCP) rather than the scattering length in vacuum, and the excess density $|n-n_{\rm MI}|$ of particles (or holes) with respect to the Mott insulator. Sufficiently close to the transition, there is a broad momentum range in the Brillouin zone where the singular part $n^{\rm sing}_{\bf k}=n_{\bf k}-n^{\rm MI}_{\bf k}$ of the momentum distribution exhibits the high-momentum tail $Z_{\rm QP} C_{\rm univ}/|{\bf k}|^4$, where $Z_{\rm QP}$ the quasi-particle weight of the elementary excitations at the QCP. We argue that the contact $C_{\rm univ}$ can be measured in state-of-the-art experiments on Bose gases in optical lattices, and in magnetic insulators., Comment: 6 pages, 4 figures; see also the companion paper submitted to arXiv on the same day

We present a strong-coupling expansion of the Bose-Hubbard model based on a mean-field treatment of the hopping term, while onsite fluctuations are taken into account exactly. This random phase approximation (RPA) describes the universal features of the generic Mott-insulator--superfluid transition (induced by a density change) and the superfluid phase near the phase transition. The critical quasi-particles at the quantum critical point have a quadratic dispersion with an effective mass $m^*$ and their mutual interaction is described by an effective $s$-wave scattering length $a^*$. The singular part of the pressure takes the same form as in a dilute Bose gas, provided we replace the boson mass $m$ and the scattering length in vacuum $a$ by $m^*$ and $a^*$, and the density $n$ by the excess density $|n-n_{\rm MI}|$ of particles (or holes) with respect to the Mott insulator. We define a ``universal'' two-body contact $C_{\rm univ}$ that controls the high-momentum tail $\sim 1/|{\bf k}|^4$ of the singular part $n^{\rm sing}_{\bf k}$ of the momentum distribution. We also apply the strong-coupling RPA to a lattice model of hard-core bosons and find that the high-momentum distribution is controlled by a universal contact, in complete agreement with the Bose-Hubbard model. Finally, we discuss a continuum model of bosons in an optical lattice and define two additional two-body contacts: a short-distance ``universal'' contact $C_{\rm univ}^{\rm sd}$ which controls the high-momentum tail of $n^{\rm sing}_{\bf k}$ at scales larger than the inverse lattice spacing, and a ``full'' contact $C$ which controls the high-momentum tail of the full momentum distribution $n_{\bf k}$., Comment: 20 pages, 6 figures; see also the companion paper submitted to arXiv on the same day

In machine learning, metric elicitation refers to the selection of performance metrics that best reflect an individual's implicit preferences for a given application. Currently, metric elicitation methods only consider metrics that depend on the accuracy values encoded within a given model's confusion matrix. However, focusing solely on confusion matrices does not account for other model feasibility considerations such as varied monetary costs or latencies. In our work, we build upon the multiclass metric elicitation framework of Hiranandani et al., extrapolating their proposed Diagonal Linear Performance Metric Elicitation (DLPME) algorithm to account for additional bounded costs and rewards. Our experimental results with synthetic data demonstrate our approach's ability to quickly converge to the true metric., Comment: Accompanying code at https://github.com/chethus/metric

We investigate granular flows over an inclined rigid base, which is vibrated externally in a direction normal to itself, through discrete element simulations. We vary the base inclination angle theta, vibration frequency f, and amplitude A to study changes in the granular flow profile and the mass flow rate Q. We find that the flow velocity profiles for the vibrated bases are nonlinear, unlike their fixed base counterparts. Our study reveals that Q may be maintained nearly constant in flows over vibrated bases utilizing appropriate combinations of theta, A, and f. At the same time, by vibrating the base at a fixed inclination, we may increase the mass flow rate by as much as 30 times the value found in flows over a stationary base. Finally, we show that Q depends upon a nondimensional number S obtained by taking the ratio of vibrational and gravitational energies., Comment: 10 Pages, 10 figures. Accepted for publication in Physical Review Fluids. Abstract link: https://journals.aps.org/prfluids/accepted/82079S10F3413d0c620b91674f996f03498146df0

Increasingly large imitation learning datasets are being collected with the goal of training foundation models for robotics. However, despite the fact that data selection has been of utmost importance in vision and natural language processing, little work in robotics has questioned what data such models should actually be trained on. In this work we investigate how to weigh different subsets or ``domains'' of robotics datasets for robot foundation model pre-training. Concrete, we use distributionally robust optimization (DRO) to maximize worst-case performance across all possible downstream domains. Our method, Re-Mix, addresses the wide range of challenges that arise when applying DRO to robotics datasets including variability in action spaces and dynamics across different datasets. Re-Mix employs early stopping, action normalization, and discretization to counteract these issues. Through extensive experimentation on the largest open-source robot manipulation dataset, the Open X-Embodiment dataset, we demonstrate that data curation can have an outsized impact on downstream performance. Specifically, domain weights learned by Re-Mix outperform uniform weights by 38\% on average and outperform human-selected weights by 32\% on datasets used to train existing generalist robot policies, specifically the RT-X models.

We investigate axial segregation of binary mixtures in a laterally shaken horizontal channel formed by ratchet-like sidewalls that appear as concatenated trapeziums when not offset axially. Grain mixtures shaken in such a channel are observed to segregate in two stages: they first separate rapidly into two vertically arranged layers and, then, these layers move axially in opposite directions, segregating the two species. Here, we conduct experiments to study the influence on the segregation process of various parameters: the size ratio of grains, the shaking frequency and the channel's geometry. We find that (a) segregation quality depends upon shaking frequency and it is possible to find a unique optimal frequency for segregation, (b) the optimal frequency lowers with increase in size ratio, (c) segregation is generally poorer when the sidewalls are more inclined to each other, and (d) segregation is improved when the sidewalls are axially offset from each other. We then carry out discrete element simulations of the segregation process in order to relate the experimental observations to the interfacial pressure gradient mechanism of Bhateja et al. [Bhateja, A., I. Sharma and J. K. Singh 2017. Segregation physics of a macroscale granular ratchet, Phys. Rev. Fluids 2, 052301]. We demonstrate that the segregation quality correlates well with the scaled interfacial pressure gradient, which is the ratio of the interfacial pressure gradient between the layers, formed in the first stage of the segregation process, to the axial body force provided by the tapered sidewalls., Comment: 40 pages, 30 figures. Submitted for review

Pre-training on Internet data has proven to be a key ingredient for broad generalization in many modern ML systems. What would it take to enable such capabilities in robotic reinforcement learning (RL)? Offline RL methods, which learn from datasets of robot experience, offer one way to leverage prior data into the robotic learning pipeline. However, these methods have a "type mismatch" with video data (such as Ego4D), the largest prior datasets available for robotics, since video offers observation-only experience without the action or reward annotations needed for RL methods. In this paper, we develop a system for leveraging large-scale human video datasets in robotic offline RL, based entirely on learning value functions via temporal-difference learning. We show that value learning on video datasets learns representations that are more conducive to downstream robotic offline RL than other approaches for learning from video data. Our system, called V-PTR, combines the benefits of pre-training on video data with robotic offline RL approaches that train on diverse robot data, resulting in value functions and policies for manipulation tasks that perform better, act robustly, and generalize broadly. On several manipulation tasks on a real WidowX robot, our framework produces policies that greatly improve over prior methods. Our video and additional details can be found at https://dibyaghosh.com/vptr/, Comment: First three authors contributed equally

During the COVID-19 pandemic, medical imaging techniques like computed tomography (CT) scans have demonstrated effectiveness in combating the rapid spread of the virus. Therefore, it is crucial to conduct research on computerized models for the detection of COVID-19 using CT imaging. A novel processing method has been developed, utilizing radiomic features, to assist in the CT-based diagnosis of COVID-19. Given the lower specificity of traditional features in distinguishing between different causes of pulmonary diseases, the objective of this study is to develop a CT-based radiomics framework for the differentiation of COVID-19 from other lung diseases. The model is designed to focus on outlining COVID-19 lesions, as traditional features often lack specificity in this aspect. The model categorizes images into three classes: COVID-19, non-COVID-19, or normal. It employs enhancement auto-segmentation principles using intensity dark channel prior (IDCP) and deep neural networks (ALS-IDCP-DNN) within a defined range of analysis thresholds. A publicly available dataset comprising COVID-19, normal, and non-COVID-19 classes was utilized to validate the proposed model's effectiveness. The best performing classification model, Residual Neural Network with 50 layers (Resnet-50), attained an average accuracy, precision, recall, and F1-score of 98.8%, 99%, 98%, and 98% respectively. These results demonstrate the capability of our model to accurately classify COVID-19 images, which could aid radiologists in diagnosing suspected COVID-19 patients. Furthermore, our model's performance surpasses that of more than 10 current state-of-the-art studies conducted on the same dataset., Comment: 8 pages, 2 figures, The 1st International Conference on Electronic and Computer Engineering, Universiti Teknologi Malaysia, "accept"

Passive observational data, such as human videos, is abundant and rich in information, yet remains largely untapped by current RL methods. Perhaps surprisingly, we show that passive data, despite not having reward or action labels, can still be used to learn features that accelerate downstream RL. Our approach learns from passive data by modeling intentions: measuring how the likelihood of future outcomes change when the agent acts to achieve a particular task. We propose a temporal difference learning objective to learn about intentions, resulting in an algorithm similar to conventional RL, but which learns entirely from passive data. When optimizing this objective, our agent simultaneously learns representations of states, of policies, and of possible outcomes in an environment, all from raw observational data. Both theoretically and empirically, this scheme learns features amenable for value prediction for downstream tasks, and our experiments demonstrate the ability to learn from many forms of passive data, including cross-embodiment video data and YouTube videos., Comment: Accompanying website at https://dibyaghosh.com/icvf/

We examine the gravity-induced flow of dry and cohesionless granular media through an outlet placed eccentrically in a planar silo, employing computations based on a soft-sphere discrete element method. The vertical velocity profiles, measured at the outlet, are self-similar when the eccentricity is given in terms of the gap ($s$) between the wall and the corner of the outlet nearest to the wall. On the other hand, the self-similarity of vertical velocity does not always hold for all eccentricities ($e$) given by the distance between the centers of an outlet and the silo base, which is a typical metric of eccentricity. Similar observations are noted for the profiles of solid fraction. For the former measure of eccentricity, the flow conditions are observed to be similar for different outlet sizes. In contrast, we observe, the latter leads to differing flow patterns for the highest eccentricity wherein the largest outlet touches the sidewall and the rest are located at a distance. This study establishes the importance of $s$ compared to $e$ from the viewpoint of the self-similarity of the vertical velocity and solid fraction profiles at the outlet, and generalizes the notion of the scaling of velocity and solid fraction reported by Janda et al. [Phys. Rev. Lett. 108, 248001 (2012)] in a silo with a centric exit to the one with eccentric granular discharge., Comment: Submitted to Physics of Fluids. 9 pages, 9 figures

This study utilizes computations based on soft-particle discrete element method for investigating the scaling of velocity in a two-dimensional silo draining under gravity. We focus on the region situated directly above and in proximity to the outlet, referred to as the region of orifice influence (ROI). The velocity at the exit scales with the outlet size, in agreement with previous studies. The velocity in the ROI upstream of the outlet, however, does not collapse to a single curve when scaled with the outlet size. We show that the height of an $\textit{equi-inertial}$ curve, which is defined to be a curve on which the inertial number is constant, can be employed for scaling the velocity in the ROI. The velocity corresponding to an equi-inertial curve, when measured relative to the outlet velocity, is considered for scaling. Results show that the scaling holds very well for low inertial number corresponding to the dense flow regime, whereas it breaks down for high inertial number region., Comment: 10 pages, 12 figures. Submitted for review

The steady flow of spherical particles in a rectangular bin is studied using the Discrete Element Method (DEM) for different flow rates of the particles from the bin, in the slow flow regime. The flow has two non-zero velocity components and is more complex than the widely studied unidirectional shear flows. The objective of the study is to characterize, in detail, the local rheology of the flowing material. The flow is shown to be nearly constant density, with a symmetric stress tensor and the principal directions of the stress and rate of strain tensors nearly colinear. The local rheology is analyzed using a coordinate transformation which enables direct computation of the viscosity and components of the pressure assuming the granular material to be a generalized Newtonian fluid. The scaled viscosity, fluctuation velocity and volume fraction are shown to follow power law relations with the inertial number, a scaled shear rate, and data for different flow rates collapse to a single curve in each case. Results for flow of the particles on an inclined surface, presented for comparison, are similar to those for the bin flow, but with a lower viscosity and a higher solid fraction due to layering of the particles. The in plane normal stresses are nearly equal and slightly larger than the third component. All three normal stresses correlate well with the corresponding fluctuation velocity components. Based on the empirical correlations obtained, a continuum model is presented for computation of granular flows., Comment: Under review in Physics of Fluids

Convolutional Neural Network (CNN) is achieving remarkable progress in various computer vision tasks. In the past few years, the remote sensing community has observed Deep Neural Network (DNN) finally taking off in several challenging fields. In this study, we propose a DNN to generate a predefined High Resolution (HR) synthetic spectral band using an ensemble of concurrent Low Resolution (LR) bands and existing HR bands. Of particular interest, the proposed network, namely DeepSWIR, synthesizes Short-Wave InfraRed (SWIR) band at 5m Ground Sampling Distance (GSD) using Green (G), Red (R) and Near InfraRed (NIR) bands at both 24m and 5m GSD, and SWIR band at 24m GSD. To our knowledge, the highest spatial resolution of commercially deliverable SWIR band is at 7.5m GSD. Also, we propose a Gaussian feathering based image stitching approach in light of processing large satellite imagery. To experimentally validate the synthesized HR SWIR band, we critically analyse the qualitative and quantitative results produced by DeepSWIR using state-of-the-art evaluation metrics. Further, we convert the synthesized DN values to Top Of Atmosphere (TOA) reflectance and compare with the corresponding band of Sentinel-2B. Finally, we show one real world application of the synthesized band by using it to map wetland resources over our region of interest.

This work utilizes soft-particle discrete element simulations to examine the rheology of steady two-dimensional granular flows with reference to a unidirectional shear flow, which has been extensively employed for validating the local visco-plastic model of Jop et al. [Nature 441, 727--730 (2006)]. The $\mu$-$I$ scaling proposed by Jop et al. is found to be valid in both two-dimensional and unidirectional flows, as observed in previous studies, however, each flow type results in a different curve. Here $\mu$, ratio of the shear stress magnitude to the pressure, is the friction coefficient and $I$ is the dimensionless inertial number, which is proportional to the ratio of the magnitude of the rate of strain tensor, $\dot{\gamma}$, to the square root of the pressure. The friction coefficient is found not to scale in a simple way with the flow classification parameter $\psi$, which characterizes the local flow type. All the data collapse to a single curve using the scaling proposed by Zhang and Kamrin [Phys. Rev. Lett. 118, 058001 (2017)], in which the scaled granular fluidity ($f=1/(\mu T)$, where $T \propto u/\dot{\gamma}$ and $u$ is the fluctuation velocity) is found to depend only on the solid fraction $\phi$. The data for variation of $\phi$ with inertial number $I$ collapse to a single curve for all the flows., Comment: 6 pages, 6 figures

The discharge of polydisperse grains in a two-dimensional silo, operating in a continuous-discharge mode, is studied with the help of soft-particle discrete element simulations. We find that the mass flow rate displays similar variation with vertical normal stress at the base and the transition-point in the bulk, signifying that the base normal stress can be considered as a representative of its bulk counterpart. The variation of the base and transition-point normal stresses with fill height follows the Janssen's model, with the former being larger than the latter. The transition-point ($y_t$) is defined as the vertical extent of Region of Orifice Influence (ROOI), which is situated directly above the orifice in its neighbourhood. The transition-point occurs largely at the same location irrespective of the fill height. It shifts, however, upon changing the orifice size, indicating its occurrence to be a localized phenomenon. Finally, the scaling of the vertical velocities at the transition-point and outlet uncovers $y_t$ to be a more relevant length scale than the orifice size $D$. This scaling provides a new insight into the dynamics of the silo discharge in the case where the flow rate varies but the normal stress stays largely invariant to change in the orifice size., Comment: 10 pages, 11 figures