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Learning from label proportions (LLP) is a kind of weakly supervised learning that trains an instance-level classifier from label proportions of bags, which consist of sets of instances without using instance labels. A challenge in LLP arises when the number of instances in a bag (bag size) is numerous, making the traditional LLP methods difficult due to GPU memory limitations. This study aims to develop an LLP method capable of learning from bags with large sizes. In our method, smaller bags (mini-bags) are generated by sampling instances from large-sized bags (original bags), and these mini-bags are used in place of the original bags. However, the proportion of a mini-bag is unknown and differs from that of the original bag, leading to overfitting. To address this issue, we propose a perturbation method for the proportion labels of sampled mini-bags to mitigate overfitting to noisy label proportions. This perturbation is added based on the multivariate hypergeometric distribution, which is statistically modeled. Additionally, loss weighting is implemented to reduce the negative impact of proportions sampled from the tail of the distribution. Experimental results demonstrate that

Magnetic skyrmions are topologically nontrivial spin configurations that possess particle-like properties. Earlier research was mainly focused on a specific type of skyrmion with topological charge Q = -1. However, theoretical analyses of two-dimensional chiral magnets have predicted the existence of skyrmion bags -- solitons with arbitrary positive or negative topological charge. Although such spin textures are metastable states, recent experimental observations have confirmed the stability of isolated skyrmion bags in a limited range of applied magnetic fields. Here, by utilizing Lorentz transmission electron microscopy, we show the extraordinary stability of skyrmion bags in thin plates of B20-type FeGe. In particular, we show that skyrmion bags embedded within a skyrmion lattice remain stable even in zero or inverted external magnetic fields. A robust protocol for nucleating such embedded skyrmion bags is provided. Our results agree perfectly with micromagnetic simulations and establish thin plates of cubic chiral magnets as a powerful platform for exploring a broad spectrum of topological magnetic solitons.

We prove that several natural graph classes have tree-decompositions with minimum width such that each bag has bounded treewidth. For example, every planar graph has a tree-decomposition with minimum width such that each bag has treewidth at most 3. This treewidth bound is best possible. More generally, every graph of Euler genus $g$ has a tree-decomposition with minimum width such that each bag has treewidth in $O(g)$. This treewidth bound is best possible. Most generally, every $K_p$-minor-free graph has a tree-decomposition with minimum width such that each bag has treewidth at most some polynomial function $f(p)$. In such results, the assumption of an excluded minor is justified, since we show that analogous results do not hold for the class of 1-planar graphs, which is one of the simplest non-minor-closed monotone classes. In fact, we show that 1-planar graphs do not have tree-decompositions with width within an additive constant of optimal, and with bags of bounded treewidth. On the other hand, we show that 1-planar $n$-vertex graphs have tree-decompositions with width $O(\sqrt{n})$ (which is the asymptotically tight bound) and with bounded treewidth bags. Moreover, this resu

Skyrmions as well as skyrmion bags in magnetic thin films are promising candidates for future high-density memory devices. The observation of skyrmion bags in liquid crystals and their predicted existence in ferromagnetic films has sparked theoretical studies on current induced dynamics of these topological charges. Here using micromagnetism, we study the impact of out of plane strain on the stability of skyrmion and skyrmion bags in ferromagnetic thin film. We further studied the current induced dynamics in the presence of out of plane strain gradient. We demonstrate that out of plane strain gradient direction with respect to the electron flow can be an efficient way to control the dynamics of topological charges. Specifically, the deflection of skyrmion bags correlates with their topological degree, and an appropriate strain gradient can counteract skyrmion Hall effects, enabling straight-line movement. Our micromagnetic simulations align well with theoretical predictions from the Thiele equation.

Skyrmion bags as spin textures with arbitrary topological charge are expected to be the carriers in racetrack memory. Here, we theoretically and numerically investigated the dynamics of skyrmion bags in an anisotropy gradient. It is found that, without the boundary potential, the dynamics of skyrmion bags are dependent on the spin textures, and the velocity of skyrmionium with $Q = 0$ is faster than other skyrmion bags. However, when the skyrmion bags move along the boundary, the velocities of all skyrmion bags with different $Q$ are same. This can be attributed to the same value of $u/η_{xx}$, where the $u$ and $η_{xx}$ are the terms related to the magnetization distribution of skyrmion bag. In addition, we theoretically derived the dynamics of skyrmion bags in the two cases using the Thiele approach and discussed the scope of Thiele equation. Within a certain range, the simulation results are in good agreement with the analytically calculated results. Our findings provide an alternative way to manipulate the racetrack memory based on the skyrmion bags.

Magnetic skyrmion bags are composite topological spin textures with arbitrary topological charges. Here, we computationally study the transient rotational motion of skyrmion bags, which is characterized by a global rotation of the inner skyrmions around the central point. Distinct from conventional rotational modes found in skyrmions, the observed rotation is a forced motion associated with the breathing mode induced solely by vertical microwave fields. The driving force behind this rotation originates from the interactions between outer and inner skyrmions, with the angular velocity determined by the phase difference resulting from their asynchronous breathing behaviors. It is also found that skyrmion bags with larger skyrmion numbers are more conducive to the occurrence of the rotation. Our results are useful for understanding the cluster dynamics of complex topological spin textures driven by dynamic fields.

Skyrmion bags are composed of an outer skyrmion and arbitrary inner skyrmions, which have recently been observed in bulk chiral magnets, but still remain elusive in magnetic films. Here, we propose a method of creating skyrmion bags in a thin-film nanodisk, which includes three steps. Firstly, the size of outer skyrmion is enlarged by a vertical magnetic field, then inner skyrmions are nucleated at an off-center area by local current injection, and the system is finally reconstructed due to multiple inter-skyrmion potentials. Thus, skyrmion bags with topological charge up to forty can be created. Simulated Lorentz transmission electron microscopy images are given to facilitate the experimental demonstration. Our proposal is expected to inspire relevant experiments in magnetic films, and pave the way for potential spintronic applications based on skyrmion bags.

Bagging tasks, commonly found in industrial scenarios, are challenging considering deformable bags' complicated and unpredictable nature. This paper presents an automated bagging system from the proposed adaptive Structure-of-Interest (SOI) manipulation strategy for dual robot arms. The system dynamically adjusts its actions based on real-time visual feedback, removing the need for pre-existing knowledge of bag properties. Our framework incorporates Gaussian Mixture Models (GMM) for estimating SOI states, optimization techniques for SOI generation, motion planning via Constrained Bidirectional Rapidly-exploring Random Tree (CBiRRT), and dual-arm coordination using Model Predictive Control (MPC). Extensive experiments validate the capability of our system to perform precise and robust bagging across various objects, showcasing its adaptability. This work offers a new solution for robotic deformable object manipulation (DOM), particularly in automated bagging tasks. Video of this work is available at https://youtu.be/6JWjCOeTGiQ.

Thin plastic bags are ubiquitous in retail stores, healthcare, food handling, recycling, homes, and school lunchrooms. They are challenging both for perception (due to specularities and occlusions) and for manipulation (due to the dynamics of their 3D deformable structure). We formulate the task of "bagging:" manipulating common plastic shopping bags with two handles from an unstructured initial state to an open state where at least one solid object can be inserted into the bag and lifted for transport. We propose a self-supervised learning framework where a dual-arm robot learns to recognize the handles and rim of plastic bags using UV-fluorescent markings; at execution time, the robot does not use UV markings or UV light. We propose the AutoBag algorithm, where the robot uses the learned perception model to open a plastic bag through iterative manipulation. We present novel metrics to evaluate the quality of a bag state and new motion primitives for reorienting and opening bags based on visual observations. In physical experiments, a YuMi robot using AutoBag is able to open bags and achieve a success rate of 16/30 for inserting at least one item across a variety of initial bag co

Using an exactly solvable statistical model we discuss the equation of state of large/heavy and short-living quark gluon plasma (QGP) bags. We argue that the large width of the QGP bags explains not only the observed deficit in the number of hadronic resonances, but also clarifies the reason why the heavy QGP bags cannot be directly observed even as metastable states in a hadronic phase. Also the Regge trajectories of large and heavy QGP bags are established both in a vacuum and in a strongly interacting medium. It is shown that at high temperatures the average mass and width of the QGP bags behave in accordance with the upper bound of the Regge trajectory asymptotics (the linear asymptotics), whereas for temperatures below T_H/2 (T_H is the Hagedorn temperature) they obey the lower bound of the Regge trajectory asymptotics (the square root one). Thus, for T < T_H/2 the spin of the QGP bags is restricted from above, whereas for T> T_H/2 these bags demonstrate the standard Regge behavior consistent with the string models.

Within an exactly solvable model I discuss the influence of the medium dependent finite width of quark gluon plasma (QGP) bags on their equation of state. It is shown that the large width of the QGP bags not only explains the observed deficit in the number of hadronic resonances, but also clarifies the reason why the heavy QGP bags cannot be directly observed as metastable states in a hadronic phase. I show how the model allows one to estimate the minimal value of the width of QGP bags being heavier than 2.5 GeV from a variety of the lattice QCD data and to get the minimal resonance width at zero temperature of about 600 MeV. The Regge trajectories of large and heavy QGP bags are established both in a vacuum and in a strongly interacting medium. It is shown that at high temperatures the average mass and width of the QGP bags behave in accordance with the upper bound of the Regge trajectory asymptotics (the linear asymptotics), whereas at low temperatures (below a half of the Hagedorn temperature T_H [1] they obey the lower bound of the Regge trajectory asymptotics (the square root one). Thus, for temperatures below T_H/2 the spin of the QGP bags is restricted from above, whereas fo

We discuss a new family of multi-quanta bound states in the Standard Model, which exist due to the mutual Higgs-based attraction of the heaviest members of the SM, namely, gauge quanta $W,Z$ and (anti)top quarks, $\bar t, t $. We use a self-consistent mean-field approximation, up to a rather large particle number $N$. In this paper we do not focus on weakly-bound, non-relativistic bound states, but rather on "bags" in which the Higgs VEV is significantly modified/depleted. The minimal number $N$ above which such states appear strongly depends on the ratio of the Higgs mass to the masses of $W,Z,\bar{t}, t $: For a light Higgs mass $m_H \sim 50\, GeV$ bound states start from $N\sim O(10)$, but for a "realistic" Higgs mass, $m_H\sim 100\, GeV$, one finds metastable/bound $W,Z$ bags only for $N\sim O(1000)$. We also found that in the latter case pure top bags disappear for all N, although top quarks can still be well bound to the W-bags. Anticipating cosmological applications (discussed in a companion paper) of these bags as "doorway states" for baryosynthesis, we also consider the existence of such metastable bags at finite temperatures, when SM parameters such as Higgs, gauge and to

Protecting user privacy is a major concern for many machine learning systems that are deployed at scale and collect from a diverse set of population. One way to address this concern is by collecting and releasing data labels in an aggregated manner so that the information about a single user is potentially combined with others. In this paper, we explore the possibility of training machine learning models with aggregated data labels, rather than individual labels. Specifically, we consider two natural aggregation procedures suggested by practitioners: curated bags where the data points are grouped based on common features and random bags where the data points are grouped randomly in bag of similar sizes. For the curated bag setting and for a broad range of loss functions, we show that we can perform gradient-based learning without any degradation in performance that may result from aggregating data. Our method is based on the observation that the sum of the gradients of the loss function on individual data examples in a curated bag can be computed from the aggregate label without the need for individual labels. For the random bag setting, we provide a generalization risk bound based

The influence of the medium dependent finite width of QGP bags on their equation of state is analyzed within an exactly solvable model. It is argued that the large width of the QGP bags not only explains the observed deficit in the number of hadronic resonances, but also clarifies the reason why the heavy QGP bags cannot be directly observed as metastable states in a hadronic phase. The model allows us to estimate the minimal value of the width of QGP bags from a variety of the lattice QCD data and get that the minimal resonance width at zero temperature is about 600 MeV, whereas the minimal resonance width at the Hagedorn temperature is about 2000 MeV. As shown these estimates are almost insensitive to the number of the elementary degrees of freedom. The recent lattice QCD data are analyzed and it is found that besides sigma T**4 term the lattice QCD pressure contains T-linear and T**4 ln T terms in the range of temperatures between 240 MeV and 420 MeV. The presence of the last term in the pressure bears almost no effect on the width estimates. Our analysis shows that at hight temperatures the average mass and width of the QGP bags behave in accordance with the upper bound of the

Nontopological solitons, or ``bags,'' can arise when fermions acquire their mass through a Yukawa coupling to some scalar field. Bags have played an important role in models of baryons, nuclei, and more recently, in the idea that a Higgs condensate may form around a very heavy top quark. It has been claimed that deep bags, which correspond to tightly-bound states of fermions, will form when the Yukawa coupling is strong. Quantum corrections, however, are significant in this regime. We examine the effects of these quantum corrections on the formation of nontopological solitons in an exactly solvable large-$N$ model. We find that quantum bags differ dramatically from those of the classical theory. In particular, for large Yukawa coupling, the bags remain shallow and the fermions weakly bound.

Because strongly-linearizable objects provide stronger guarantees than linearizability, they serve as valuable building blocks for the design of concurrent data structures. Yet, many objects that have linearizable implementations from base objects weaker than compare&swap objects do not have strongly-linearizable implementations from the same base objects. We focus on one such object: the bag, a multiset from which processes can take unspecified elements. We present the first lock-free, strongly-linearizable implementation of a bag from interfering objects (specifically, registers, and test&set objects). This may be surprising, since there are provably no such implementations of stacks or queues. Since a bag can contain arbitrarily many elements, an unbounded amount of space must be used to implement it. Hence, it makes sense to also consider a bag with a bound on its capacity. However, like stacks and queues, a bag with capacity $b$ shared by more than $2b$ processes has no lock-free, strongly-linearizable implementation from interfering objects. If we further restrict a bounded bag so that only one process can insert into it, we are able to obtain a lock-free, strongly-li

Multiple instance learning (MIL) is a variation of traditional supervised learning problems where data (referred to as bags) are composed of sub-elements (referred to as instances) and only bag labels are available. MIL has a variety of applications such as content-based image retrieval, text categorization and medical diagnosis. Most of the previous work for MIL assume that the training bags are fully labeled. However, it is often difficult to obtain an enough number of labeled bags in practical situations, while many unlabeled bags are available. A learning framework called PU learning (positive and unlabeled learning) can address this problem. In this paper, we propose a convex PU learning method to solve an MIL problem. We experimentally show that the proposed method achieves better performance with significantly lower computational costs than an existing method for PU-MIL.

We combine experiments and numerical computations to examine underlying fluid mechanical processes associated with bioaerosol generation during violent respiratory manoeuvres, such as coughing or sneezing. Analogous experiments performed in a cough machine -- consisting of a strong shearing airflow over a thin liquid film, allow us to illustrate the changes in film topology as it disintegrates into small droplets. We identify that aerosol generation during the shearing of the liquid film is mediated by the formation of inflated bag-like structures. The breakup of these bags is triggered by the appearance of retracting holes that puncture the bag surface. Consequently, the cascade from inflated bags to droplets is primarily controlled by the dynamics and stability of liquid rims bounding these retracting holes. We also reveal the stabilizing role of fluid viscosity that eventually leads to the generation of smaller droplets.