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We relate Hilbert schemes of points and Fulton-MacPherson compactifications by an interpolating stability condition. We then derive wall-crossings formulas and some applications for the enumerative geometry of Hilbert schemes., Comment: 46 pages

The asymptotics of a singularly perturbed problem is constructed. describing the transport of a polydisperse impurity in the atmosphere, taking into account the processes of precipitation and wind pick-up, as well as the processes of coagulation - dissociation. The mathematical model of this process represents a differential-operator equation of turbulent diffusion with a non-standard boundary condition containing two components - atmospheric and soil. The asymptotics of the solution is constructed by the method of boundary functions. Problems that do not contain small parameters are obtained for the main terms of the asymptotic equation., Comment: 12 pages, 1 figur

We present an alternative formulation of generalized unimodular gravity (GUMG), extending the Henneaux-Teitelboim approach to unimodular gravity (UMG). The central feature of this formulation is the consistent incorporation of time reparameterization, which enhances the gauge structure and reveals a spatial nonlocality hidden in the dynamics of the original formulation. We examine the resulting dynamics, emphasizing the effects of spatial nonlocality, and outline the constraint structure. In particular, we show that the gauge symmetry in the gravitational sector is extended by a functionally incomplete symmetry, as occurs in the unimodular gravity. Furthermore, we identify a subset of GUMG models for which the alternative formulation preserves manifest locality., Comment: 5 pages

In the first part of this paper, we prove that, under some natural non-degeneracy assumptions, the Greedy Parabolic Target-Following Method, based on {\em universal tangent direction} has a favorable local behavior. In view of its global complexity bound of the order $O(\sqrt{n} \ln {1 \over \epsilon})$, this fact proves that the functional proximity measure, used for controlling the closeness to Greedy Central Path, is large enough for ensuring a local super-linear rate of convergence, provided that the proximity to the path is gradually reduced. This requirement is eliminated in our second algorithm based on a new auto-correcting predictor direction. This method, besides the best-known polynomial-time complexity bound, ensures an automatic switching onto the local quadratic convergence in a small neighborhood of solution. Our third algorithm approximates the path by quadratic curves. On the top of the best-known global complexity bound, this method benefits from an unusual local cubic rate of convergence. This amelioration needs no serious increase in the cost of one iteration. We compare the advantages of these local accelerations with possibilities of finite termination. The conditions allowing the optimal basis detection sometimes are even weaker than those required for the local superlinear convergence. Hence, it is important to endow the practical optimization schemes with both abilities. The proposed methods have a very interesting combination of favorable properties, which can be hardly found in the most of existing Interior-Point schemes. As all other parabolic target-following schemes, the new methods can start from an arbitrary strictly feasible primal-dual pair and go directly towards the optimal solution of the problem in a single phase. The preliminary computational experiments confirm the advantage of the second-order prediction.

The yields of the inverse beta decay events produced by antineutrinos from a certain nuclear reactor fuel component are used by many experiments to check various model predictions. Yet measurements of the absolute yields feature significant uncertainties coming, mainly, from the understanding of the antineutrino detection efficiency. This work presents a simple novel approach to directly determine the $^{235}$U to $^{239}$Pu inverse beta decay yield ratio using the fuel evolution analysis. This ratio can be used for a sensitive test of reactor models, while the proposed method, results in smaller systematic uncertainties., Comment: 5 pages, 2 figures

Electron antineutrinos are emitted in the decay chains of the fission products inside a reactor core and could be used for remote monitoring of nuclear reactors. The DANSS detector is placed under the core of the 3.1 GW power reactor at the Kalinin Nuclear Power Plant (KNPP) and collects up to 5000 antineutrino events per day. DANSS measured changes of the reactor power by antineutrino counting rates over 7 years with 1.0% accuracy in one week periods. The systematic uncertainty of this measurement is less than 0.8%. It is comparable to the accuracy of conventional methods of the reactor power measurements while it is based on completely different approach. For the first time the 239Pu and 235U fission fractions were reconstructed using antineutrino inverse beta-decay spectrum which is a completely new technique. This method was applied to the data from three reactor fuel campaigns (approximately 1.5 year each). The reconstructed fission fractions in about one week measurements and the fission fractions provided by KNPP coincide within about 3% accuracy. This provides confidence in both completely different approaches of the fission fraction determination.

In this paper, we attempt to compare two distinct branches of research on second-order optimization methods. The first one studies self-concordant functions and barriers, the main assumption being that the third derivative of the objective is bounded by the second derivative. The second branch studies cubic regularized Newton methods (CRNMs) with the main assumption that the second derivative is Lipschitz continuous. We develop a new theoretical analysis for a path-following scheme (PFS) for general self-concordant functions, as opposed to the classical path-following scheme developed for self-concordant barriers. We show that the complexity bound for this scheme is better than that of the Damped Newton Method (DNM) and show that our method has global superlinear convergence. We propose also a new predictor-corrector path-following scheme (PCPFS) that leads to further improvement of constant factors in the complexity guarantees for minimizing general self-concordant functions. We also apply path-following schemes to different classes of constrained optimization problems and obtain the resulting complexity bounds. Finally, we analyze an important subclass of general self-concordant functions, namely a class of strongly convex functions with Lipschitz continuous second derivative, and show that for this subclass CRNMs give even better complexity bounds.

This paper develops the novel convergence analysis of a generic class of descent methods in nonsmooth and nonconvex optimization under several versions of the Kurdyka-\L ojasiewicz (KL) property. Along other results, we prove the finite termination of generic algorithms under the KL property with lower exponents. Specifications are given to convergence rates of some particular algorithms including inexact reduced gradient methods and the boosted algorithm in DC programming. It revealed, e.g., that the lower exponent KL property in the DC framework is incompatible with the gradient Lipschitz continuity for the plus function around a local minimizer. On the other hand, we show that the above inconsistency observation may fail if the Lipschitz continuity is replaced by merely the gradient continuity., Comment: 12 pages

Kim, Kresch and Oh defined unramified Gromov-Witten invariants. For a threefold, Pandharipande conjectured that they are equal to Gopakumar-Vafa invariants (BPS invariants) in the case of Fano classes and primitive Calabi-Yau classes. We prove the conjecture using a wall-crossing technique. This provides an algebro-geometric construction of Gopakumar-Vafa invariants in these cases., Comment: Some minor changes, more details are added, 67 pages, 3 figures

The relaxation time of several second generation molecular motors is analysed by calculating the minimum energy path between the metastable and stable states and evaluating the transition rate within harmonic transition state theory based on energetics obtained from density functional theory. Comparison with published experimental data shows remarkably good agreement and demonstrates the predictive capability of the theoretical approach. While previous measurements by Feringa and coworkers [Chem.\,Eur.\,J.\,(2017) 23, 6643] have shown that a replacement of the stereogenic hydrogen by a fluorine atom increases the relaxation time because of destabilization of the transition state for the thermal helix inversion, we find that a replacement of CH$_3$ by a CF$_3$ group at the same site shortens the relaxation time because of elevated energy of the metastable state without a significant shift in the transition state energy. Since these two fluorine substitutions have an opposite effect on the relaxation time, the two combined can provide a way to fine tune the rotational speed of a molecular motor.

First order methods endowed with global convergence guarantees operate using global lower bounds on the objective. The tightening of the bounds has been shown to increase both the theoretical guarantees and the practical performance. In this work, we define a global lower bound for smooth differentiable objectives that is optimal with respect to the collected oracle information. The bound can be readily employed by the Gradient Method with Memory to improve its performance. Further using the machinery underlying the optimal bounds, we introduce a modified version of the estimate sequence that we use to construct an Optimized Gradient Method with Memory possessing the best known convergence guarantees for its class of algorithms, even in terms of the proportionality constant. We additionally equip the method with an adaptive convergence guarantee adjustment procedure that is an effective replacement for line-search. Simulation results on synthetic but otherwise difficult smooth problems validate the theoretical properties of the bound and proposed methods., Comment: 29 pages, 1 figure

The Spin Physics Detector collaboration proposes to install a universal detector in the second interaction point of the NICA collider under construction (JINR, Dubna) to study the spin structure of the proton and deuteron and other spin-related phenomena using a unique possibility to operate with polarized proton and deuteron beams at a collision energy up to 27 GeV and a luminosity up to $10^{32}$ cm$^{-2}$ s$^{-1}$. As the main goal, the experiment aims to provide access to the gluon TMD PDFs in the proton and deuteron, as well as the gluon transversity distribution and tensor PDFs in the deuteron, via the measurement of specific single and double spin asymmetries using different complementary probes such as charmonia, open charm, and prompt photon production processes. Other polarized and unpolarized physics is possible, especially at the first stage of NICA operation with reduced luminosity and collision energy of the proton and ion beams. This document is dedicated exclusively to technical issues of the SPD setup construction.

The dispersive-readout scheme enables quantum nondemolition measurement of superconducting qubits. An increased readout power can shorten the readout time and reduce the state discrimination error but can promote qubit transitions into higher noncomputational states. The ability to predict the onset of these measurement-induced state transitions can aid the optimization of qubit circuits and provide means for comparing the readout performance of different qubit types. Building upon the concept of dressed coherent states, we consider two straightforward metrics for determining the maximum number of photons that can be used for dispersive readout without causing state transitions. We focus on the fluxonium readout to demonstrate the independence of the metrics from any qubit-type-specific approximations. The dispersive readout of transmons and other superconducting qubits can be treated universally in the same fashion., Comment: 18 pages, 11 figures; accepted version

The cosmological constant problem is a fundamental issue that has puzzled researchers in the fields of theoretical physics and cosmology for a long time. It arises from the discrepancy between the observed value of the cosmological constant and the value predicted by quantum field theory. A new spacetime model based on nonassociative geometry and statistical physics of complex networks offers a fresh perspective on the problem. Our research indicates that spacetime topology plays a crucial role in solving the cosmological constant problem and addressing the dark energy issue. We discovered that spacetime foam significantly impacts the effective cosmological constant, which is determined by the density of topological geons. Furthermore, we demonstrate that the source of dark energy is topological geons, Comment: 8 pages

The clustering coefficient is a valuable tool for understanding the structure of complex networks. It is widely used to analyze social networks, biological networks, and other complex systems. While there is generally a single common definition for the local clustering coefficient, there are two different ways to calculate the global clustering coefficient. The first approach takes the average of the local clustering coefficients for each node in the network. The second one is based on the ratio of closed triplets to all triplets. It is shown that these two definitions of the global clustering coefficients are strongly inequivalent and may significantly impact the accuracy of the outcome., Comment: 4 pages, 5 figures

This paper can be seen as an attempt of rethinking the {\em Extra-Gradient Philosophy} for solving Variational Inequality Problems. We show that the properly defined {\em Reduced Gradients} can be used instead for finding approximate solutions to Composite Variational Inequalities by the higher-order schemes. Our methods are optimal since their performance is proportional to the lower worst-case complexity bounds for corresponding problem classes. They enjoy the provable hot-start capabilities even being applied to minimization problems. The primal version of our schemes demonstrates a linear rate of convergence under an appropriate uniform monotonicity assumption.

DANSS is a spectrometer of reactor antineutrino based on plastic scintillator. The sensitive volume of the detector is made of 2500 polystyrene based scintillator plates with wavelength shifting (WLS) fiber readout (strips). We present a study of the strips light yield during 6.5 years of DANSS continuous running. Overall ageing at the rate $0.55 \pm 0.05(syst.)$ % per year is observed that is considerably smaller than in other similar experiments. We also observe the WLS fiber attenuation length shortening at the rate $0.26 \pm 0.04(stat.)$ % per year., Comment: 9 pages, 7 figures, to be submitted to JINST

In this paper, we suggest a new framework for analyzing primal subgradient methods for nonsmooth convex optimization problems. We show that the classical step-size rules, based on normalization of subgradient, or on the knowledge of optimal value of the objective function, need corrections when they are applied to optimization problems with constraints. Their proper modifications allow a significant acceleration of these schemes when the objective function has favorable properties (smoothness, strong convexity). We show how the new methods can be used for solving optimization problems with functional constraints with possibility to approximate the optimal Lagrange multipliers. One of our primal-dual methods works also for unbounded feasible set.

Web resources in linked open data (LOD) are comprehensible to humans through literal textual values attached to them, such as labels, notes, or comments. Word choices in literals may not always be neutral. When outdated and culturally stereotyping terminology is used in literals, they may appear as offensive to users in interfaces and propagate stereotypes to algorithms trained on them. We study how frequently and in which literals contentious terms about people and cultures occur in LOD and whether there are attempts to mark the usage of such terms. For our analysis, we reuse English and Dutch terms from a knowledge graph that provides opinions of experts from the cultural heritage domain about terms' contentiousness. We inspect occurrences of these terms in four widely used datasets: Wikidata, The Getty Art & Architecture Thesaurus, Princeton WordNet, and Open Dutch WordNet. Some terms are ambiguous and contentious only in particular senses. Applying word sense disambiguation, we generate a set of literals relevant to our analysis. We found that outdated, derogatory, stereotyping terms frequently appear in descriptive and labelling literals, such as preferred labels that are usually displayed in interfaces and used for indexing. In some cases, LOD contributors mark contentious terms with words and phrases in literals (implicit markers) or properties linked to resources (explicit markers). However, such marking is rare and non-consistent in all datasets. Our quantitative and qualitative insights could be helpful in developing more systematic approaches to address the propagation of stereotypes via LOD.

Electrical current rectification is an interesting electronic feature, popularly known as a diode. Achieving a high rectification ratio in a molecular junction has been a long-standing goal in molecular electronics. The present work describes mimicking electrical current rectification with pi-stacked rhenium(I) compound sandwiched between two electrical contacts. Among the two mononuclear rhenium compounds studied here, [Re(CO)4(PPh3){(N)-saccharinate}] (1) and [Re(CO)3(phen){(N)-saccharinate}] (2), the latter show strong pi-pi interactions-induced high rectification ratio of ~ 4000 at 2.0 V at room temperature. Alternating current (AC)-based electrical measurements ensuring AC to DC electrical signal conversion at a frequency f of 1 KHz showing 2 can act as an excellent half-wave rectifier. Asymmetric charge injection barrier height at the electrode/Re(I) interfaces of the devices with a stacking configuration of p++-Si/Re compound31nm(2)/ITO originates the flow of electrical current unidirectionally. The charge transport mechanism governed by thermally activated hopping phenomena, and charge carrier propagation is explained through an energy profile considering the Fermi levels of two electrodes, and the energy of frontier molecular orbitals, HOMO, and LUMO, confirming rectification is of a molecular origin. The present work paves the way to combine different organometallic compounds as circuit elements in nanoelectronic devices to achieve numerous exciting electronic features., Comment: 16 pages, 5 figures

The Micius satellite is the pioneering initiative to demonstrate quantum teleportation, entanglement distribution, quantum key distribution (QKD), and quantum-secured communications experiments at the global scale. In this work, we report on the results of the 600-mm-aperture ground station design which has enabled the establishment of a quantum-secured link between the Zvenigorod and Nanshan ground stations using the Micius satellite. As a result of a quantum communications session, an overall sifted key of 2.5 Mbits and a total final key length of 310 kbits have been obtained. We present an extension of the security analysis of the realization of satellite-based QKD decoy-state protocol by taking into account the effect of the detection-efficiency mismatch for four detectors. We also simulate the QKD protocol for the satellite passage and by that validate our semi-empirical model for a realistic receiver, which is in good agreement with the experimental data. Our results pave the way to the considerations of realistic imperfection of the QKD systems, which are important in the context of their practical security., Comment: 8+2 pages, 5+2 figures

Clinical Decision Support Systems (CDSS) utilize evidence-based knowledge and patient data to offer real-time recommendations, with Large Language Models (LLMs) emerging as a promising tool to generate plain-text explanations for medical decisions. This study explores the effectiveness and reliability of LLMs in generating explanations for diagnoses based on patient complaints. Three experienced doctors evaluated LLM-generated explanations of the connection between patient complaints and doctor and model-assigned diagnoses across several stages. Experimental results demonstrated that LLM explanations significantly increased doctors' agreement rates with given diagnoses and highlighted potential errors in LLM outputs, ranging from 5% to 30%. The study underscores the potential and challenges of LLMs in healthcare and emphasizes the need for careful integration and evaluation to ensure patient safety and optimal clinical utility.

Simulation tools have become an integral tool in the analysis of neutronic parameters of reactor units. These simulation tools are built to solve the neutron transport equation. In this article, the MCU-PTR simulation tool is used in the evaluation of the possibility of achieving extra-long fuel lifetime in the RITM-200 reactor unit with consideration to the fuel composition. The three dispersed fuel compositions (238U+235U)O2, (232Th+235U)O2 and (232Th+233U)O2 are simulated at varying fuel element diameter of 4.9 mm to 8.9 mm with 1 mm interval. From the simulation, the dependence of reactivity margin on the fuel burnup of the three dispersed fuels were established. The dependence of the effective multiplication factor (keff) on the reactor operation time for the three dispersed fuel composition were also determined. From the results, it can be deduced that transition of the fuel from (238U + 235U)O2 to (232Th + 235U)O2 results in a 12% increase in the fuel burnup and no change in fuel campaign. While the transition from (238U + 235U)O2 to (232Th + 233U)O2 leads to a 32.4% increase in the fuel campaign and 45.6% increase in the fuel burnup. It has also been shown that the optimal fuel element diameter is 7.9 mm for (232Th + 233U)O2 dispersed fuel. At this diameter, it is possible to increase the duration of the fuel campaign by 85.3% and achieve a fuel burnup of 51.9% in comparison to the design fuel diameter of 6.9 mm for (238U + 235U)O2 dispersed fuel., Comment: The 5 pages and 5 figures for this manuscript as published as conference proceeding at the International Youth Forum Russia - Africa: Nuclear education-potential for successful regional development

An asymptotic expansion with respect to a small parameter of the solution of the Cauchy problem is constructed for a system of three transfer equations, two of which are singularly perturbed by the degeneracy of the entire senior part of the transfer operator, and the third equation clearly does not contain a small parameter. The peculiarity of the problem is that it belongs to the so-called critical case: the solution of a degenerate problem is a one-parameter family. The asymptotic expansion of the solution under smooth initial conditions is constructed as the sum of the regular part and boundary functions.