arXiv subjects
Publications and source records attributed to Sergei Ivanov.
We prove that in a semi-dispersing Minkowski billiard, that is a billiard in the complement of a collection of convex sets in a normed space with a smooth strictly convex norm, any billiard trajectory of finite length has only finitely many reflections off the walls.
We investigate how magnetic fluctuations influence spin-orbit torque in ultrathin-film magnetic heterostructures whose Curie temperature $T_C$ is suppressed by confinement. Above $T_C$, the damping-like contribution to spin-orbit field is significantly enhanced while the field-like contribution is suppressed, with the two contributions exhibiting opposite field dependencies. We show that these behaviors are consistent with fluctuation driven mixing between the longitudinal and transverse interfacial spin conductances, which enhances absorption of transversely polarized spin current by the ferromagnet. This mechanism can be activated below $T_C$ by engineering the microscopic magnetic state and by harnessing spin current-generated short-wavelength magnons, suggesting a spintronic analog of heat-assisted magnetic recording.
Building infrastructure-as-code (IaC) in cloud computing is a critical task, underpinning the reliability, scalability, and security of modern software systems. Despite the remarkable progress of large language models (LLMs) in software engineering -- demonstrated across many dedicated benchmarks -- their capabilities in developing IaC remain underexplored. Unlike existing IaC benchmarks that predominantly center on declarative paradigms such as Terraform and involve generating entire codebases from scratch, our benchmark reflects the incremental code edits common in enterprise development with imperative tools like the AWS CDK. We present SWE-InfraBench, a diverse evaluation dataset sourced from dozens of real-world IaC codebases that challenge LLMs to perform realistic code modifications in AWS CDK repositories. Each example requires models to implement changes to existing codebases based on natural language instructions, with success determined by passing provided test cases. These tasks demand sophisticated reasoning about cloud resource dependencies and implementation patterns beyond conventional code generation challenges. Our evaluation results reveal significant limitations in current LLMs showing that even state-of-the-art systems struggle with many tasks -- the best model, Sonnet 3.7, succeeds in only 34\% of cases, while specialized reasoning models like DeepSeek R1 achieve just 24% success. The SWE-InfraBench dataset is available at: https://www.kaggle.com/datasets/64e59070fd51c0278560b01eb5dc4f3c447d5268cdabe5a350d2969e4413fea5
We consider how a closed Riemannian manifold $M$ and its metric tensor $g$ can be approximately reconstructed from local distance measurements. Moreover, we consider an inverse problem of determining $(M,g)$ from limited knowledge on the heat kernel. In the part 1 of the paper, we considered the approximate construction of a smooth manifold in the case when one is given the noisy distances $\tilde d(x,y)=d(x,y)+\varepsilon_{x,y}$ for all points $x,y\in X$, where $X$ is a $δ$-dense subset of $M$ and $|\varepsilon_{x,y}|<δ$. In this part 2 of the paper, we consider a similar problem with partial data, that is, the approximate construction of the manifold $(M,g)$ when we are given $\tilde d(x,y)$ for $x\in X$ and $y \in U\cap X$, where $U$ is an open subset of $M$. In addition, we consider the inverse problem of determining the manifold $(M,g)$ with non-negative Ricci curvature from noisy observations of the heat kernel $G(y,z,t)$. We show that a manifold approximating $(M,g)$ can be determined in a stable way, when for some unknown source points $z_j$ in $X\setminus U$, we are given the values of the heat kernel $G(y,z_k,t)$ for $y\in X\cap U$ and $t\in (0,1)$ with a multiplicative noise. We also give a uniqueness result for the inverse problem in the case when the data does not contain noise and consider applications in manifold learning. A novel feature of the inverse problem for the heat kernel is that the set $M\setminus U$ containing the sources and the observation set $U$ are disjoint.
We prove the following local version of Blaschke--Kakutani's characterization of ellipsoids: Let $V$ be a finite-dimensional real vector space, $B\subset V$ a convex body with 0 in its interior, and ${2\le k<\dim V}$ an integer. Suppose that the body $B$ is contained in a cylinder based on the cross-section $B \cap X$ for every $k$-plane $X$ from a connected open set of linear $k$-planes in $V$. Then in the region of $V$ swept by these $k$-planes $B$ coincides with either an ellipsoid, or a cylinder over an ellipsoid, or a cylinder over a $k$-dimensional base. For $k=2$ and $k=3$ we obtain as a corollary a local solution to Banach's isometric subspaces problem: If all cross-sections of $B$ by $k$-planes from a connected open set are linearly equivalent, then the same conclusion as above holds.
Both magnetism and spin-orbit coupling in systems with broken inversion symmetry lift the spin degeneracy of electronic bands, but the consequences of interplay between these mechanisms remain poorly understood. Here, we show that ultrathin transition ferromagnet-heavy metal bilayers exhibit anomalous temperature- and electric bias-dependent behaviors in the vicinity of the Curie temperature, inconsistent with the usual Weiss magnetism. Characterization by several complementary techniques and analysis of the dependence on composition reveal that these effects originate from interfacial spin-orbit interaction, which results in the emergence of a state with distinct magnetic and magnetoelectronic properties that can be described as Rashba magnetism. Our findings open a new route for the characterization and control of spin-orbit phenomena in heterostructures enabling the development of efficient spin-orbitronic devices.
SrIrO$_3$ is a metallic complex oxide with unusual electronic and magnetic properties believed to originate from electron correlations due to its proximity to Mott metal-insulator transition. However, the nature of its electronic state and the mechanism of metallic conduction remain poorly understood. We demonstrate that shot noise produced by nanoscale SrIrO$_3$ junctions is strongly suppressed, inconsistent with diffusive quasiparticle transport. Analysis of thermal effects and scaling with the junction length reveals that conduction is mediated by collective hopping of electrons almost localized by correlations. Our results provide insight into the non-Fermi liquid state close to Mott transition, and advance shot noise measurements as a powerful technique for the studies of quantum materials.
In Gel'fand's inverse problem, one aims to determine the topology, differential structure and Riemannian metric of a compact manifold $M$ with boundary from the knowledge of the boundary $\partial M,$ the Neumann eigenvalues $λ_j$ and the boundary values of the eigenfunctions $φ_j|_{\partial M}$. We show that this problem has a stable solution with quantitative stability estimates in a class of manifolds with bounded geometry. More precisely, we show that finitely many eigenvalues and the boundary values of corresponding eigenfunctions, known up to small errors, determine a metric space that is close to the manifold in the Gromov-Hausdorff sense. We provide an algorithm to construct this metric space. This result is based on an explicit estimate on the stability of the unique continuation for the wave operator.
Let $Δ$ be the Dirichlet Laplacian on the interval $(0,π)$. The null controllability properties of the equation $$u_{tt}+Δ^2 u+ρ(Δ)^αu_t=F(x,t)$$ are studied. Let $T>0$, and assume initial conditions $(u^0,u^1)\in Dom(Δ)\times L^2(0,π)$. We first prove finite dimensional null control results: suppose $F(x,t)=f^1(t)h^1(x)+f^2(t)h^2(x)$ with $h^1,h^2$ given functions. For $α\in [0,3/2)$, we prove that there exist $h^1,h^2\in L^2(0,π)$ such that for any $(u^0,u^1)$, there exist $L^2$ null controls $(f^1,f^2).$ For $α< 1$ and $ρ<2$, we prove null controllability with $f^2=0$ and $h^1$ belonging to a large class of functions. For $α\in [3/2,2)$, we prove spectral and null controllability both generally fail, but two dimensional weak controllability holds. Our second set of results pertains to $F(x,t)=χ_Ω(x)f(x,t)$, with $Ω$ any open subset of $(0,π)$. For any $α\in [0,3/2),$ we prove there exists a null control $f\in L^2(Ω\times(0,T))$ To prove our main results, we use the Fourier method to rewrite the control problems as moment problems. These are then solved by constructing biorthogonal sets to the associated exponential families. These constructions seem to be non-standard and may be of independent interest.
We assume that $M_0$ is a $d$-dimensional $C^{2,1}$-smooth submanifold of $R^n$. Let $K_0$ be the convex hull of $M_0,$ and $B^n_1(0)$ be the unit ball. We assume that $ M_0 \subseteq \partial K_0 \subseteq B^n_1(0).$ We also suppose that $M_0$ has volume ($d$-dimensional Hausdorff measure) less or equal to $V$, reach (i.e., normal injectivity radius) greater or equal to $τ$. Moreover, we assume that $M_0$ is $R$-exposed, that is, tangent to every point $x \in M$ there is a closed ball of radius $R$ that contains $M$. Let $x_1, \dots, x_N$ be independent random variables sampled from uniform distribution on $M_0$ and $ζ_1, \dots, ζ_N$ be a sequence of i.i.d Gaussian random variables in $R^n$ that are independent of $x_1, \dots, x_N$ and have mean zero and covariance $σ^2 I_n.$ We assume that we are given the noisy sample points $y_i$, given by $$ y_i = x_i + ζ_i,\quad \hbox{ for }i = 1, 2, \dots,N. $$ Let $ε,η>0$ be real numbers and $k\geq 2$. Given points $y_i$, $i=1,2,\dots,N$, we produce a $C^k$-smooth function which zero set is a manifold $M_{rec}\subseteq R^n$ such that the Hausdorff distance between $M_{rec}$ and $M_0$ is at most $ ε$ and $M_{rec}$ has reach that is bounded below by $cτ/d^6$ with probability at least $1 - η.$ Assuming $d < c \sqrt{\log \log n}$ and all the other parameters are positive constants independent of $n$, the number of the needed arithmetic operations is polynomial in $n$. In the present work, we allow the noise magnitude $σ$ to be an arbitrarily large constant, thus overcoming a drawback of previous work.
We prove that if all intersections of a convex body $B\subset\mathbb R^4$ with 3-dimensional linear subspaces are linearly equivalent then $B$ is a centered ellipsoid. This gives an affirmative answer to the case $n=3$ of the following question by Banach from 1932: Is a normed vector space $V$ whose $n$-dimensional linear subspaces are all isometric, for a fixed $2 \le n< \dim V$, necessarily Euclidean? The dimensions $n=3$ and $\dim V=4$ is the first case where the question was unresolved. Since the $3$-sphere is parallelizable, known global topological methods do not help in this case. Our proof employs a differential geometric approach.
We show that the mean-field resonating valence bond approximation proposed in 1987 by Baskaran, Zou, and Anderson describes gapless charge pair excitations confined to the boundaries of the spinon Brillouin zone. The existence of such pairs accounts for all the essential anomalous electronic properties of cuprates, with superconductivity arising due to the charge drag by the spinon superflow. This mechanism may be relevant to other unconventional superconductors.
We develop a two-orbital Hubbard model of electron correlations in ultrathin (111)-oriented fcc films of late transition metals such as Co and Ni. Our model indicates that the Mott-Hund's interaction results in ferromagnetic nearest-neighbor orbital correlations. Frustration associated with the mismatch between orbital and crystal symmetries prevents orbital ordering, resulting in the orbital liquid state. This state can be manifested in phenomena involving spin-orbit coupling, such as magnetic anisotropy.
Gradient Boosted Decision Trees (GBDTs) are dominant machine learning algorithms for modeling discrete or tabular data. Unlike neural networks with millions of trainable parameters, GBDTs optimize loss function in an additive manner and have a single trainable parameter per leaf, which makes it easy to apply high-order optimization of the loss function. In this paper, we introduce high-order optimization for GBDTs based on numerical optimization theory which allows us to construct trees based on high-order derivatives of a given loss function. In the experiments, we show that high-order optimization has faster per-iteration convergence that leads to reduced running time. Our solution can be easily parallelized and run on GPUs with little overhead on the code. Finally, we discuss future potential improvements such as automatic differentiation of arbitrary loss function and combination of GBDTs with neural networks.
In today's world, the presence of online disinformation and propaganda is more widespread than ever. Independent publishers are funded mostly via digital advertising, which is unfortunately also the case for those publishing disinformation content. The question of how to remove such publishers from advertising inventory has long been ignored, despite the negative impact on the open internet. In this work, we make the first step towards quickly detecting and red-flagging websites that potentially manipulate the public with disinformation. We build a machine learning model based on multilingual text embeddings that first determines whether the page mentions a topic of interest, then estimates the likelihood of the content being malicious, creating a shortlist of publishers that will be reviewed by human experts. Our system empowers internal teams to proactively, rather than defensively, blacklist unsafe content, thus protecting the reputation of the advertisement provider.
The problem of out-of-distribution detection for graph classification is far from being solved. The existing models tend to be overconfident about OOD examples or completely ignore the detection task. In this work, we consider this problem from the uncertainty estimation perspective and perform the comparison of several recently proposed methods. In our experiment, we find that there is no universal approach for OOD detection, and it is important to consider both graph representations and predictive categorical distribution.
Prediction of protein-ligand (PL) binding affinity remains the key to drug discovery. Popular approaches in recent years involve graph neural networks (GNNs), which are used to learn the topology and geometry of PL complexes. However, GNNs are computationally heavy and have poor scalability to graph sizes. On the other hand, traditional machine learning (ML) approaches, such as gradient-boosted decision trees (GBDTs), are lightweight yet extremely efficient for tabular data. We propose to use PL interaction features along with PL graph-level features in GBDT. We show that this combination outperforms the existing solutions.
Given any symplectomorphism on $D^{2n} (n\geq 1)$ which is $C^{\infty}$ close to the identity, and any completely integrable Hamiltonian system $Φ^t_H$ in the proper dimension, we construct a $C^{\infty}$ perturbation of $H$ such that the resulting Hamiltonian flow contains a "local Poincaré section" that "realizes" the symplectomorphism. As a (motivating) application, we show that there are arbitrarily small perturbations of any completely integrable Hamiltonian system which are entropy non-expansive (and, in particular, exhibit hyperbolic behavior on a set of positive measure).