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We propose a self-supervised model producing 3D anatomical positional embeddings (APE) of individual medical image voxels. APE encodes voxels' anatomical closeness, i.e., voxels of the same organ or nearby organs always have closer positional embeddings than the voxels of more distant body parts. In contrast to the existing models of anatomical positional embeddings, our method is able to efficiently produce a map of voxel-wise embeddings for a whole volumetric input image, which makes it an optimal choice for different downstream applications. We train our APE model on 8400 publicly available CT images of abdomen and chest regions. We demonstrate its superior performance compared with the existing models on anatomical landmark retrieval and weakly-supervised few-shot localization of 13 abdominal organs. As a practical application, we show how to cheaply train APE to crop raw CT images to different anatomical regions of interest with 0.99 recall, while reducing the image volume by 10-100 times. The code and the pre-trained APE model are available at https://github.com/mishgon/ape .

Understanding body part geometry is crucial for precise medical diagnostics. Curves effectively describe anatomical structures and are widely used in medical imaging applications related to cardiovascular, respiratory, and skeletal diseases. Traditional curve detection methods are often task-specific, relying heavily on domain-specific features, limiting their broader applicability. This paper introduces a novel approach for detecting non-branching curves, which does not require prior knowledge of the object's orientation, shape, or position. Our method uses neural networks to predict (1) an attraction field, which offers subpixel accuracy, and (2) a closeness map, which limits the region of interest and essentially eliminates outliers far from the desired curve. We tested our curve detector on several clinically relevant tasks with diverse morphologies and achieved impressive subpixel-level accuracy results that surpass existing methods, highlighting its versatility and robustness. Additionally, to support further advancements in this field, we provide our private annotations of aortic centerlines and masks, which can serve as a benchmark for future research. The dataset can be found at https://github.com/neuro-ml/curve-detection., Comment: Accepted to ShapeMI MICCAI 2024

This paper constructs a full exceptional collection in the bounded derived category of coherent sheaves on a generalized flag scheme G/P over Z, by means of a G-linear semiorthogonal decomposition of the bounded derived category of noetherian representations of P . The ensuing semiorthogonal decompositions are compatible with the Bruhat order on cosets of the Weyl group of P in the Weyl group of G. The construction builds upon the foundational results on B-modules from the works of Mathieu, Polo, and van der Kallen, and upon properties of the Steinberg basis of the T-equivariant K-theory of G/B., Comment: 75 pages; Main result now covers G/P

Interpretation of chest computed tomography (CT) is time-consuming. Previous studies have measured the time-saving effect of using a deep-learning-based aid (DLA) for CT interpretation. We evaluated the joint impact of a multi-pathology DLA on the time and accuracy of radiologists' reading. 40 radiologists were randomly split into three experimental arms: control (10), who interpret studies without assistance; informed group (10), who were briefed about DLA pathologies, but performed readings without it; and the experimental group (20), who interpreted half studies with DLA, and half without. Every arm used the same 200 CT studies retrospectively collected from BIMCV-COVID19 dataset; each radiologist provided readings for 20 CT studies. We compared interpretation time, and accuracy of participants diagnostic report with respect to 12 pathological findings. Mean reading time per study was 15.6 minutes [SD 8.5] in the control arm, 13.2 minutes [SD 8.7] in the informed arm, 14.4 [SD 10.3] in the experimental arm without DLA, and 11.4 minutes [SD 7.8] in the experimental arm with DLA. Mean sensitivity and specificity were 41.5 [SD 30.4], 86.8 [SD 28.3] in the control arm; 53.5 [SD 22.7], 92.3 [SD 9.4] in the informed non-assisted arm; 63.2 [SD 16.4], 92.3 [SD 8.2] in the experimental arm without DLA; and 91.6 [SD 7.2], 89.9 [SD 6.0] in the experimental arm with DLA. DLA speed up interpretation time per study by 2.9 minutes (CI95 [1.7, 4.3], p<0.0005), increased sensitivity by 28.4 (CI95 [23.4, 33.4], p<0.0005), and decreased specificity by 2.4 (CI95 [0.6, 4.3], p=0.13). Of 20 radiologists in the experimental arm, 16 have improved reading time and sensitivity, two improved their time with a marginal drop in sensitivity, and two participants improved sensitivity with increased time. Overall, DLA introduction decreased reading time by 20.6%., Comment: 17 pages, 6 figures, 8 tables

Berry curvature, a momentum space property, can manifest itself in current responses. The well-known anomalous Hall effect in time-reversal-breaking systems arises from a Berry curvature monopole. In time-reversal-invariant materials, a second-order Hall conductivity emerges from a Berry curvature dipole. Recently, it has been shown that a Berry curvature quadrupole induces a third-order ac Hall response in systems that break time reversal ($K$) and a fourfold rotational ($C_{4}$) symmetry, while remaining invariant under the combination of the two ($C_{4}K$). In this letter, we demonstrate that incident light can induce a $\rm dc$ Hall current in such systems, driven by the Berry curvature quadrupole. We consider a combination of a static $\rm dc$ electric field and an ac light-induced electric field. We calculate the current perpendicular to both the static electric field and the fourfold axis. Remarkably, the induced current is generically spin-polarized. A net charge current appears for light that is linearly or elliptically polarized, but not for circular polarization. In contrast, the spin current remains unchanged when the polarization of light is varied. This allows for rich possibilities such as generating a spin current by shining circularly polarized light on an altermagnetic material. We demonstrate this physics using a two-dimensional toy model for altermagnets.

In this paper, we carry out experimental research on Grammatical Error Correction, delving into the nuances of single-model systems, comparing the efficiency of ensembling and ranking methods, and exploring the application of large language models to GEC as single-model systems, as parts of ensembles, and as ranking methods. We set new state-of-the-art performance with F_0.5 scores of 72.8 on CoNLL-2014-test and 81.4 on BEA-test, respectively. To support further advancements in GEC and ensure the reproducibility of our research, we make our code, trained models, and systems' outputs publicly available.

We derive microscopically the Ginzburg-Landau free energy functional for a superconductor in which the Cooper pairs are formed not only by quasiparticles from the same band, but also by quasiparticles from different bands. In the simplest case of an s-wave or d-wave pairing in a two-band system, the order parameter has three components describing two intraband and one interband pair condensates. The interband pairing-specific terms in the free energy bring about some qualitative changes in the phase diagram, for example, time-reversal symmetry breaking superconducting states are stabilized at low temperatures., Comment: 21 pages, 6 figures

We study the effects of interband pairing in two-band s-wave and d-wave superconductors with D4h symmetry in both time-reversal invariant as well as time-reversal symmetry breaking states. The presence of interband pairing qualitatively changes the nodal structure of the superconductor: nodes can (dis)appear, merge, and leave high-symmetry locations when interband pairing is tuned. Furthermore, in the d-wave case, we find that also the boundary modes change qualitatively when interband pairing increases: flat zero-energy Andreev bound states gap out and transition to helical edge states., Comment: 19 pages, 11 figures

In this paper we show that GEC systems display gender bias related to the use of masculine and feminine terms and the gender-neutral singular "they". We develop parallel datasets of texts with masculine and feminine terms and singular "they" and use them to quantify gender bias in three competitive GEC systems. We contribute a novel data augmentation technique for singular "they" leveraging linguistic insights about its distribution relative to plural "they". We demonstrate that both this data augmentation technique and a refinement of a similar augmentation technique for masculine and feminine terms can generate training data that reduces bias in GEC systems, especially with respect to singular "they" while maintaining the same level of quality., Comment: 15 pages. Accepted for publication in BEA workshop (18th Workshop on Innovative Use of NLP for Building Educational Applications; co-located with ACL)

The paper deals with perturbations of the equation that have a number of conservation laws. When a small term is added to the equation its conserved quantities usually decay at individual rates, a phenomenon known as a selective decay. These rates are described by the simple law using the conservation laws' generating functions and the added term. Yet some perturbation may retain a specific quantity(s), such as energy, momentum and other physically important characteristics of solutions. We introduce a procedure for finding such perturbations and demonstrate it by examples including the KdV-Burgers equation and a system from magnetodynamics. Some interesting properties of solutions of such perturbed equations are revealed and discussed., Comment: 9 pages, 3 figures

We use the method of invariants to derive one- and two-band effective Hamiltonians of a noncentrosymmetric two-dimensional electron gas, in the presence of magnetic field. A complete classification of the antisymmetric spin-orbit and magnetic coupling terms near the $\Gamma$ point is developed for all two-dimensional crystal symmetries. The effective Hamiltonian depends on the symmetry of the Bloch bands at the $\Gamma$ point, which is described by one of the double-valued corepresentations of the two-dimensional magnetic point group. In some bands, the spin-orbit coupling is cubic in the electron momentum and the effective Zeeman interaction is strongly anisotropic. As an example of a two-band effective Hamiltonian, we introduce a simple model of a topological insulator with the intraband and interband spin-orbit coupling and investigate its bulk and boundary properties., Comment: 24 pages, 2 figures

This study focuses on open quasispecies systems with competition and death flow, described by modified Eigen and Crow-Kimura models. We examine the evolutionary adaptation process as a reaction to changes in rates. One of the fundamental assumptions, which forms the basis of our mathematical model, is the existence of two different timescales: internal dynamics time and evolutionary time. The latter is much slower and exhibits significant adaptation events. These conditions allow us to represent the whole evolutionary process through a series of steady-state equations, where all the elements continuously depend on the evolutionary parameter.

We consider distributed stochastic variational inequalities (VIs) on unbounded domains with the problem data that is heterogeneous (non-IID) and distributed across many devices. We make a very general assumption on the computational network that, in particular, covers the settings of fully decentralized calculations with time-varying networks and centralized topologies commonly used in Federated Learning. Moreover, multiple local updates on the workers can be made for reducing the communication frequency between the workers. We extend the stochastic extragradient method to this very general setting and theoretically analyze its convergence rate in the strongly-monotone, monotone, and non-monotone (when a Minty solution exists) settings. The provided rates explicitly exhibit the dependence on network characteristics (e.g., mixing time), iteration counter, data heterogeneity, variance, number of devices, and other standard parameters. As a special case, our method and analysis apply to distributed stochastic saddle-point problems (SPP), e.g., to the training of Deep Generative Adversarial Networks (GANs) for which decentralized training has been reported to be extremely challenging. In experiments for the decentralized training of GANs we demonstrate the effectiveness of our proposed approach., Comment: Appears in: Advances in Neural Information Processing Systems 35 (NeurIPS 2022). Minor modifications with respect to the NeurIPS version. 43 pages, 1 algorithm, 6 figures, 2 tables

We show that in some trigonal and hexagonal crystals the Zeeman coupling of band electrons with an external magnetic field is strongly anisotropic and necessarily vanishes along the main symmetry axis. This leads to qualitative changes in the temperature dependence of the electron spin susceptibility in the superconducting state. In particular, the power-law exponents at low temperatures due to the contribution of the nodal quasiparticles are considerably modified compared to their textbook values., Comment: 15 pages

For the KdV-Burgers equations for cylindrical and spherical waves the development of a regular profile starting from an equilibrium under a periodic perturbation at the boundary is studied. The equation describes a medium which is both dissipative and dispersive. For an appropriate combination of dispersion and dissipation the asymptotic profile looks like a periodical chain of shock fronts with a decreasing amplitude (sawtooth waves). The development of such a profile is preceded by a head shock of a constant height and equal velocity which depends on spatial dimension as well as on integral characteristics of boundary condition; an explicit asymptotic for this head shock is found., Comment: 11 pages, 6figures

Consider a mathematical model of evolutionary adaptation of fitness landscape and mutation matrix as a reaction to population changes. As a basis, we use an open quasispecies model, which is modified to include explicit death flow. We assume that evolutionary parameters of mutation and selection processes vary in a way to maximize the mean fitness of the system. From this standpoint, Fisher's theorem of natural selection is being rethought and discussed. Another assumption is that system dynamics has two significant timescales. According to our central hypothesis, major evolutionary transitions happen in the steady-state of the corresponding dynamical system, so the evolutionary time is much slower than the one of internal dynamics. For the specific cases of quasispecies systems, we show how our premises form the fitness landscape adaptation process.

This paper focuses on the distributed optimization of stochastic saddle point problems. The first part of the paper is devoted to lower bounds for the cenralized and decentralized distributed methods for smooth (strongly) convex-(strongly) concave saddle-point problems as well as the near-optimal algorithms by which these bounds are achieved. Next, we present a new federated algorithm for cenralized distributed saddle point problems - Extra Step Local SGD. Theoretical analysis of the new method is carried out for strongly convex-strongly concave and non-convex-non-concave problems. In the experimental part of the paper, we show the effectiveness of our method in practice. In particular, we train GANs in a distributed manner., Comment: 52 pages, 9 figures, 1 table, 4 algorithms (3 new)

The energy dependence of the differential cross-section of elastic proton-proton scattering in the ISR--LHC energy range is discussed for fixed values of momentum transfer in the region of the forward diffraction cone, in the region beyond the second maximum of $d\sigma/dt$ and in the vicinity of the dip-bump structure. As can be seen from the currently available experimental data, the differential cross-section in the region beyond the second maximum has exactly the same properties as in the forward diffraction cone, including the existence of a stationary point, that is, we observe a second diffraction cone, which has the same origin as the forward peak. The simplest natural explanation for this experimental fact is that the amplitude of high energy elastic scattering is the sum of two similar terms that have the same status and differ only in the values of parameters. The energy dependence of $d\sigma/dt$ for a fixed $t$ in the region of the dip-bump structure, where these two terms interfere, confirms the above observations. We discuss the possible origin of the two-component structure of the high energy elastic scattering amplitude and explain this by the structural symmetry of the amplitude., Comment: 23 pages, 7 figures