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The fundamental quantum Coulomb problem in the momentum space is considered. A differential equation with SO(4) simmetry has been obtained in the momentum space instead of the integral Fock equation. The corresponding equation in the coordinate space is the sum of the squares of the angular momentum and the Runge-Lenz operators.This approach is unknown in the momentum space where the Runge-Lenz operator is not applied in the existing theory. The Runge-Lenz operator obtained in the momentum space is simplier than that in the coordinate space and allows one to effectively consider the Coulomb problem in the momentum space. A relation of new operator to the infinitesimal rotation operator of the three-dimensional the Fock sphere has been determined., Comment: 5 pages

The study aimed at detecting cartel collusion involved analyzing decisions of the Russian Federal Antimonopoly Service and data on auctions. As a result, a machine learning model was developed that predicts with 91% accuracy the signs of collusion between bidders based on their history after dividing 40 auctions into test and training samples in a 30/70 ratio. Decomposition of the model using the Shepley vector allowed the interpretation of the decision-making process. The behavior of honest companies in auctions was also studied, confirmed by independent simulation validation., Comment: 22 pages, 9 figures. in Russian language

Demand forecasting faces challenges induced by Peak Events (PEs) corresponding to special periods such as promotions and holidays. Peak events create significant spikes in demand followed by demand ramp down periods. Neural networks like MQCNN and MQT overreact to demand peaks by carrying over the elevated PE demand into subsequent Post-Peak-Event (PPE) periods, resulting in significantly over-biased forecasts. To tackle this challenge, we introduce a neural forecasting model called Split Peak Attention DEcomposition, SPADE. This model reduces the impact of PEs on subsequent forecasts by modeling forecasting as consisting of two separate tasks: one for PEs; and the other for the rest. Its architecture then uses masked convolution filters and a specialized Peak Attention module. We show SPADE's performance on a worldwide retail dataset with hundreds of millions of products. Our results reveal a reduction in PPE degradation by 4.5% and an improvement in PE accuracy by 3.9%, relative to current production models.

We investigate correlated three-electron escape in Ne when driven by an intense, infrared laser field. We do so by employing a reduced-dimensionality quantum-mechanical model and two three-dimensional semi-classical models. One semi-classical model is a recently developed one that accounts with effective coulomb potentials for the interaction between two bound electrons (ECBB) while it fully accounts for all other interactions. The other semi-classical model is the Heisenberg one, which effectively accounts for the interaction of each electron with the core via a soft-core potential. We identify and compare the signatures of correlated three-electron escape for both quantum and semi-classical models on Dalitz plots and find a better agreement between the quantum and the ECBB model. We also show that a central ``spot'' on the Dalitz plots is reproduced by all models. Using the ECBB model we associate this ``spot'' with the direct triple ionization pathway and argue this to be the case also for the quantum model. Devising a simple classical model that accounts for the direct pathway of triple ionization, we show that the width of this spot in the Dalitz plots solely depends on the time of tunnel-ionization., Comment: 11 pages, 6 figures, original article

Diffusion models have found phenomenal success as expressive priors for solving inverse problems, but their extension beyond natural images to more structured scientific domains remains limited. Motivated by applications in materials science, we aim to reduce the number of measurements required from an expensive imaging modality of interest, by leveraging side information from an auxiliary modality that is much cheaper to obtain. To deal with the non-differentiable and black-box nature of the forward model, we propose a framework to train a multimodal diffusion model over the joint modalities, turning inverse problems with black-box forward models into simple linear inpainting problems. Numerically, we demonstrate the feasibility of training diffusion models over materials imagery data, and show that our approach achieves superior image reconstruction by leveraging the available side information, requiring significantly less amount of data from the expensive microscopy modality.

Cascade multiplication is a common technique to enhance the sensitivity of photon detectors. In this study, we demonstrate novel cascade-amplified superconducting detectors utilizing arrays of Josephson junctions. The mutual coupling between junctions induces avalanche-like switching of multiple junctions upon photon absorption, leading to cascade amplification of the readout voltage. We present two prototypes featuring either low-Tc linear Nb/NbxSi1-x/Nb arrays, or high-Tc stacked intrinsic Josephson junctions. Both devices exhibit clear antenna effects in microwave directivities, indicating good impedance matching and absorption efficiency. The combination of high absorption efficiency and large cascade amplification has the potential to produce broadband THz sensors with sensitivity exceeding 10^13 V/W., Comment: 9 pages, 3 figures

As digital twins (DTs) to physical communication systems, network simulators can aid the design and deployment of communication networks. However, time-consuming simulations must be run for every new set of network configurations. Learnable digital twins (LDTs), in contrast, can be trained offline to emulate simulation outcomes and serve as a more efficient alternative to simulation-based DTs at runtime. In this work, we propose GLANCE, a communication LDT that learns from the simulator ns-3. It can evaluate network key performance indicators (KPIs) and assist in network management with exceptional efficiency. Leveraging graph learning, we exploit network data characteristics and devise a specialized architecture to embed sequential and topological features of traffic flows within the network. In addition, multi-task learning (MTL) and transfer learning (TL) are leveraged to enhance GLANCE's generalizability to unseen inputs and efficacy across different tasks. Beyond end-to-end KPI prediction, GLANCE can be deployed within an optimization framework for network management. It serves as an efficient or differentiable evaluator in optimizing network configurations such as traffic loads and flow destinations. Through numerical experiments and benchmarking, we verify the effectiveness of the proposed LDT architecture, demonstrate its robust generalization to various inputs, and showcase its efficacy in network management applications.

In this paper, for the first time, analytical expressions for determination of the wavelength of defect modes (DMs) in one-dimensional (1D) photonic crystals (PCs) with two defect layers (DLs) were obtained from the condition of zero reflection. Analytical formulas on the conditions for the merging of two DMs and on the DMs with zero value of the reflection coefficient were obtained. Different typical 1D PC structures with two DLs were considered and compared, including their DMs behavior. The distribution of electromagnetic field within the first photonic bandgap (PBG) was analyzed for several cases of DM merging and for the different orders of DMs. The results of this research permit the simplification of the analysis of optical sensors and filters based on 1D PCs with two DLs, as well as a more comprehensive understanding of the DM behavior within the PBGs of such PC structures. Furthermore, this paper helps to explain the results obtained by other researchers earlier in this field, too.

The paper considers the observer synthesis for nonlinear, time-varying plants with uncertain parameters under multiharmonic disturbance. It is assumed that the relative degree of the plant is known, the regressor linearly depends on the state vector and may have a nonlinear relationship with the output signal. The proposed solution consists of three steps. Initially, an unknown input state observer is synthesized. This observer, however, necessitates the measurement of output derivatives equal to the plant's relative degree. To relax this limitation, an alternative representation of the observer is introduced. Further, based on this observer, the unknown parameters and disturbances are reconstructed using an autoregression model and the dynamic regressor extension and mixing (DREM) approach. This approach allows the estimates to be obtained in a finite time. Finally, based on these estimates, an observer has been constructed that does not require measurements of the output derivatives. The effectiveness and efficiency of this solution are demonstrated through a computer simulation.

In this paper we study the field of Hahn-Witt series $HW(\overline{\mathbb{F}}_p)$ with residue field $\overline{\mathbb{F}}_p$ (also known as a $p$-adic Malcev-Neumann field \cite{La86, P93}), and its generalizations. Informally, the Hahn-Witt series are possibly infinite linear combinations of rational powers of $p,$ in which the coefficients are Teichm\"uller representatives, and the set of exponents is well-ordered. They form an algebraically closed extension of $\mathbb{Q}_p,$ with a canonical automorphism $\varphi,$ coming from the absolute Frobenius of $\overline{\mathbb{F}}_p.$ We prove that the action of $\varphi$ on the $p$-power roots of unity is given by $\varphi(\zeta)=\zeta^{-1},$ answering a question of Kontsevich. More generally, we consider the $\pi$-typical Hahn-Witt series $HW_{(K,\pi)}(\overline{\mathbb{F}}_q)$, where $\pi$ is a uniformizer in a local field $K$ with residue field $\mathbb{F}_q.$ Again, this field is an algebraically closed extension of $K,$ and it has a canonical automorphism $\varphi_{\pi},$ coming from the relative Frobenius of $\overline{\mathbb{F}}_q$ over $\mathbb{F}_q.$ We prove that the action of $\varphi_{\pi}$ on the maximal abelian extension $K^{ab}$ corresponds via local class field theory to the uniformizer $-\pi\in K^*.$, Comment: 19 pages

This note proposes a novel nonlinear state feedback controller for perturbed second-order systems. In analogy to a linear proportional-derivative (PD) feedback control, the proposed nonlinear scheme uses the output state of interest and its time derivative, while achieving robust control in a finite time. The control has only one free design parameter, and the closed-loop system is shown to be uniformly asymptotically stable in the presence of matched disturbances. We derive a strict Lyapunov function for the closed-loop control system with a bounded exogenous perturbation, and use it for both the control parameter tuning and analysis of the finite-time convergence. Apart from the numerical results, a revealing experimental example is also shown in favor of the proposed control and in comparison with PD and sub-optimal nonlinear damping regulators., Comment: 7 pages, 7 figures

In this paper we introduce and study the so-called continuous $K$-theory for a certain class of "large" stable $\infty$-categories, more precisely, for dualizable presentable categories. For compactly generated categories, the continuous $K$-theory is simply the usual (non-connective) $K$-theory of the full subcategory of compact objects. More generally, we show that any localizing invariant of small stable $\infty$-categories can be uniquely extended to a localizing invariant of dualizable categories. We compute the continuous $K$-theory for categories of sheaves on locally compact Hausdorff spaces. Using the special case for sheaves on the real line, we give an alternative proof of the theorem of Kasprowski and Winges \cite{KW19} on the commutation of $K$-theory with infinite products for small stable $\infty$-categories. We also study the general theory of dualizable categories. In particular, we give an "explicit" proof of Ramzi's theorem \cite{Ram} on the $\omega_1$-presentability of the category of dualizable categories. Among other things, we prove that dualizability is equivalent to "flatness" in the category of presentable stable categories., Comment: 123 pages; v2: minor changes, some typos corrected, a reference added

We introduce KazQAD -- a Kazakh open-domain question answering (ODQA) dataset -- that can be used in both reading comprehension and full ODQA settings, as well as for information retrieval experiments. KazQAD contains just under 6,000 unique questions with extracted short answers and nearly 12,000 passage-level relevance judgements. We use a combination of machine translation, Wikipedia search, and in-house manual annotation to ensure annotation efficiency and data quality. The questions come from two sources: translated items from the Natural Questions (NQ) dataset (only for training) and the original Kazakh Unified National Testing (UNT) exam (for development and testing). The accompanying text corpus contains more than 800,000 passages from the Kazakh Wikipedia. As a supplementary dataset, we release around 61,000 question-passage-answer triples from the NQ dataset that have been machine-translated into Kazakh. We develop baseline retrievers and readers that achieve reasonable scores in retrieval (NDCG@10 = 0.389 MRR = 0.382), reading comprehension (EM = 38.5 F1 = 54.2), and full ODQA (EM = 17.8 F1 = 28.7) settings. Nevertheless, these results are substantially lower than state-of-the-art results for English QA collections, and we think that there should still be ample room for improvement. We also show that the current OpenAI's ChatGPTv3.5 is not able to answer KazQAD test questions in the closed-book setting with acceptable quality. The dataset is freely available under the Creative Commons licence (CC BY-SA) at https://github.com/IS2AI/KazQAD., Comment: To appear in Proceedings of the 2024 Joint International Conference on Computational Linguistics, Language Resources and Evaluation (LREC-COLING 2024)

In this paper, an analytical formula for the sensitivity of optical sensors based on one-dimensional photonic crystals (PCs) with a defect was derived for the first time. Based on this formula, a comparative analysis of the sensitivity of defected PCs with and without mirror symmetry was carried out. In addition, the exact values of sensitivity in the limit of an infinite PC with a quarter-wave unit cell were obtained. It was shown that the sensitivity of a defective PC with an infinitely thick defect layer is equal to that of a perfectly reflecting Fabry-Perot resonator and does not depend on the specific structure of the PC. The results of this work provide a significant simplification of the analysis and optimization of optical sensors based on defective PCs, as well as a better understanding of the numerous numerical results obtained previously., Comment: 13 pages, 3 figures

Score-based diffusion models, while achieving remarkable empirical performance, often suffer from low sampling speed, due to extensive function evaluations needed during the sampling phase. Despite a flurry of recent activities towards speeding up diffusion generative modeling in practice, theoretical underpinnings for acceleration techniques remain severely limited. In this paper, we design novel training-free algorithms to accelerate popular deterministic (i.e., DDIM) and stochastic (i.e., DDPM) samplers. Our accelerated deterministic sampler converges at a rate $O(1/{T}^2)$ with $T$ the number of steps, improving upon the $O(1/T)$ rate for the DDIM sampler; and our accelerated stochastic sampler converges at a rate $O(1/T)$, outperforming the rate $O(1/\sqrt{T})$ for the DDPM sampler. The design of our algorithms leverages insights from higher-order approximation, and shares similar intuitions as popular high-order ODE solvers like the DPM-Solver-2. Our theory accommodates $\ell_2$-accurate score estimates, and does not require log-concavity or smoothness on the target distribution., Comment: The first two authors contributed equally

Homogeneous observer for linear multi-input multi-output (MIMO) system is designed. A prefilter of the output is utilized in order to improve robustness of the observer with respect to measurement noises. The use of such a prefilter also simplifies tuning, since the observer gains in this case are parameterized by a linear matrix inequality (LMI) being always feasible for observable system. In particular case, the observer is shown to be applicable in the presence of the state and the output bounded perturbations. Theoretical results are supported by numerical simulations.

Extension of coherent response time is a desired goal in the field of all-optical information processing implemented in classical and quantum ways. Here we demonstrate how spin-dependent stimulated photon echo can be used to extend decay time of coherent signal from exciton ensemble. We experimentally studied photon echoes from excitons in a model single InGaAs/GaAs quantum well subject to transverse magnetic field. Field-induced quantum beats lead to oscillation of exciton population between bright and long-lived dark excitons. As a result, photon echo decays much longer with decay time attaining dark exciton lifetime in case of non-oscillatory regime.

We investigated the absence of certain bright peaks in Autler-Townes laser excitation spectra of alkali metal atoms. Our research revealed that these dips in the spectra are caused by a specific architecture of adiabatic (or ``laser-dressed'') states in hyperfine (HF) components. The dressed states' analysis pinpointed several cases where constructive and destructive interference between HF excitation pathways in a two-photon excitation scheme limits the available two-photon transitions. This results in a reduction of the conventional two-photon selection rule for the total angular momentum $F$, from $\Delta F= 0,\pm 1$ to $\Delta F\equiv 0$. Our discovery presents practical methods for selectively controlling the populations of unresolvable HF $F$-components of $ns_{1/2}$ Rydberg states in alkali metal atoms. Using numerical simulations with sodium and rubidium atoms, we demonstrate that by blocking the effects of HF interaction with a specially tuned auxiliary control laser field, the deviations from the ideal selectivity of the HF components population can be lower than $0.01\%$ for Na and $0.001\%$ for Rb atoms., Comment: 20 pages, 14 figures, to be submitted to PRA. Changelog: * added missing ORCID iDs; * Notation used in figures 4,6 is now consistent with the rest of the manuscript: Pump paser -> S-laser; * corrected typos, more precise language througout the paper; * improved legibility of labels in figures 4-8

Let $\mathbb K$ be an algebraically closed field of characteristic zero, $\mathbb K[x, y]$ the polynonial ring in variables $x$, $y$ and let $W_2(\mathbb K)$ be the Lie algebra of all $\mathbb K$-derivations on $\mathbb K[x, y]$. A derivation $D \in W_2(\mathbb K)$ is called a Jacobian derivation if there exists $f \in \mathbb K[x, y]$ such that $D(h) = \det J(f, h)$ for any $h \in \mathbb K[x, y]$ (here $J(f, h)$ is the Jacobian matrix for $f$ and $h$). Such a derivation is denoted by $D_f$. The kernel of $D_f$ in $\mathbb K[x, y]$ is a subalgebra $\mathbb K[p]$ where $p=p(x, y)$ is a polynomial of smallest degree such that $f(x, y) = \varphi (p(x, y)$ for some $\varphi (t) \in \mathbb K[t]$. Let $C = C_{W_2(\mathbb K)} (D_f)$ be the centralizer of $D_f$ in $W_2(\mathbb K)$. We prove that $C$ is the free $\mathbb K[p]$-module of rank 1 or 2 over $\mathbb K[p]$ and point out a criterion of being a module of rank $2$. These results are used to obtain a class of integrable autonomous systems of differential equations., Comment: 7 pages

Let $K$ be an algebraically closed field of characteristic zero, $P_n=K[x_1, ..., x_n]$ the polynomial ring, and $W_n(K)$ the Lie algebra of all $K$-derivations on $P_n$. One of the most important subalgebras of $W_n(K)$ is the triangular subalgebra $u_n(K) = P_0\partial_1+\cdots+P_{n-1}\partial_n$, where $\partial_i:=\partial/\partial x_i$ are partial derivatives on $P_n$. This subalgebra consists of locally nilpotent derivations on $P_n.$ Such derivations define automorphisms of the ring $P_n$ and were studied by many authors. The subalgebra $u_n(K) $ is contained in another interesting subalgebra $s_n(K)=(P_0+x_1P_0)\partial_1+\cdots +(P_{n-1}+x_nP_{n-1})\partial_n,$ which is solvable of the derived length $2n$ that is the maximum derived length of solvable subalgebras of $W_n(K).$ It is proved that $u_n(K)$ is a maximal locally nilpotent subalgebra and $s_n(K)$ is a maximal solvable subalgebra of the Lie algebra $W_n(K).$, Comment: 8 pages