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This paper presents an exposition of Rio's proof of the strong law of large numbers and extends his method to random fields. In addition to considering the rate of convergence in the Marcinkiewicz--Zygmund strong law of large numbers, we go a step further by establishing (i) the Hsu--Robbins--Erd\"{o}s--Spitzer--Baum--Katz theorem, (ii) the Feller weak law of large numbers, and (iii) the Pyke--Root theorem on mean convergence for dependent random fields. These results significantly improve several particular cases in the literature. The proof is based on new maximal inequalities that hold for random fields satisfying a very general dependence structure.

Financial analysis heavily relies on the evaluation of earnings reports to gain insights into company performance. Traditional generation of these reports requires extensive financial expertise and is time-consuming. With the impressive progress in Large Language Models (LLMs), a wide variety of financially focused LLMs has emerged, addressing tasks like sentiment analysis and entity recognition in the financial domain. This paper presents a novel challenge: developing an LLM specifically for automating the generation of earnings reports analysis. Our methodology involves an in-depth analysis of existing earnings reports followed by a unique approach to fine-tune an LLM for this purpose. This approach combines retrieval augmentation and the generation of instruction-based data, specifically tailored for the financial sector, to enhance the LLM's performance. With extensive financial documents, we construct financial instruction data, enabling the refined adaptation of our LLM to financial contexts. Preliminary results indicate that our augmented LLM outperforms general open-source models and rivals commercial counterparts like GPT-3.5 in financial applications. Our research paves the way for streamlined and insightful automation in financial report generation, marking a significant stride in the field of financial analysis., Comment: 8 pages, 1 figure, 4 tables

We propose the joint dynamic power allocation and multi-relay selection for the cohabitation of high-priority military radar and low-priority commercial 5G communication. To improve the 5G network performance, we design the full-duplex underlay cognitive radio network for the low-priority commercial 5G network, where multiple relays are selected for concurrently receive the signal from the source and send it to the destination. Then, we propose the interference suppression at the high-priority radar system by using both non-coherent and coherent relay cases. In particular, we formulate the optimization problem for maximizing the system rate, with the consideration of the power constraints at the 5G users and the interference constraint at the radar system. Then, we propose the mathematical analysis model to evaluate the rate performance, considering the impacts of self-interference at the relays and derive the algorithms of joint power allocation and relay selection. Our numerical results demonstrate the characteristic of the optimal configuration and the significant performance gain of coherent case with respect to the non-coherent case and the existing algorithms with single relay selections., Comment: 11th Annual Conference on Computational Science & Computational Intelligence (CSCI'24)

Enhancing light emission from perovskite nanocrystal (NC) films is essential in light-emitting devices, as their conventional stacks often restrict the escape of emitted light. This work addresses this challenge by employing a TiO$_2$ grating to enhance light extraction and shape the emission of CsPbBr$_3$ nanocrystal films. Angle-resolved photoluminescence (PL) demonstrated a tenfold increase in emission intensity by coupling the Bloch resonances of the grating with the spontaneous emission of the perovskite NCs. Fluorescence lifetime imaging microscopy (FLIM) provided micrometer-resolution mapping of both PL intensity and lifetime across a large area, revealing a decrease in PL lifetime from 8.2 ns for NC films on glass to 6.1 ns on the TiO$_2$ grating. Back focal plane (BFP) spectroscopy confirmed how the Bloch resonances transformed the unpolarized, spatially incoherent emission of NCs into polarized and directed light. These findings provide further insights into the interactions between dielectric nanostructures and perovskite NC films, offering possible pathways for designing better performing perovskite optoelectronic devices.

Creating soft-Coulomb-type (SC) molecular potential within single-active-electron approximation (SAE) is essential since it allows solving time-dependent Schr\"odinger equations with fewer computational resources compared to other multielectron methods. The current available SC potentials can accurately reproduce the energy of the highest occupied molecular orbital (HOMO), which is sufficient for analyzing nonlinear effects in laser-molecule interactions like high-order harmonic generation (HHG). However, recent discoveries of significant effects of deep-lying molecular orbitals call for more precise potentials to analyze them. In this study, we present a fast and accurate method based on machine learning to construct SC potentials that simultaneously reproduce various molecular features, including energies, symmetries, and dipole moments of HOMO, HOMO-1, and HOMO-2. We use this ML model to create SC SAE potentials of the HCN molecule and then comprehensively analyze the fingerprints of lower-lying orbitals in HHG spectra emitted during the H-CN stretching. Our findings reveal that HOMO-1 plays a role in forming the second HHG plateau. Additionally, as the H-C distance increases, the plateau structure and the smoothness of HHG spectra are altered due to the redistribution of orbital electron density. These results are in line with other experimental and theoretical studies. Lastly, the machine learning approach using deconvolution and convolution neural networks in the present study is so general that it can be applied to construct molecular potential for other molecules and molecular dynamic processes.

We study a new variant of graph coloring by adding a connectivity constraint. A path in a vertex-colored graph is called conflict-free if there is a color that appears exactly once on its vertices. A connected graph $G$ is said to be strongly conflict-free vertex-connection $k$-colorable if $G$ admits a vertex $k$-coloring such that any two distinct vertices of $G$ are connected by a conflict-free $shortest$ path. Among others, we show that deciding whether a given graph is strongly conflict-free vertex-connection $3$-colorable is NP-complete even when restricted to $3$-colorable graphs with diameter $3$, radius $2$ and domination number $3$, and, assuming the Exponential Time Hypothesis (ETH), cannot be solved in $2^{o(n)}$ time on such restricted input graphs with $n$ vertices. This hardness result is quite strong when compared to the ordinary $3$-COLORING problem: it is known that $3$-COLORING is solvable in polynomial time in graphs with bounded domination number, and assuming ETH, cannot be solved in $2^{o(\sqrt{n})}$ time in $n$-vertex graphs with diameter $3$ and radius $2$. On the positive side, we point out that a strong conflict-free vertex-connection coloring with minimum color number of a given split graph or a co-bipartite graph can be computed in polynomial time., Comment: The full version of a COCOON 2024 paper

This paper presents a space-time interface-fitted finite element method for solving a parabolic advection-diffusion problem with a nonstationary interface. The jumping diffusion coefficient gives rise to the discontinuity of the solution gradient across the interface. We use the Banach-Necas-Babuska theorem to show the well-posedness of the continuous variational problem. A fully discrete finite-element based scheme is analyzed using the Galerkin method and unstructured interface-fitted meshes. An optimal error estimate is established in a discrete energy norm under a globally low but locally high regularity condition. Some numerical results corroborate our theoretical results., Comment: 20 pages

A stable cutset in a graph $G$ is a set $S\subseteq V(G)$ such that vertices of $S$ are pairwise non-adjacent and such that $G-S$ is disconnected, i.e., it is both stable (or independent) set and a cutset (or separator). Unlike general cutsets, it is $NP$-complete to determine whether a given graph $G$ has any stable cutset. Recently, Rauch et al.\ [FCT 2023] gave a number of fixed-parameter tractable (FPT) algorithms, time $f(k)\cdot |V(G)|^c$, for Stable Cutset under a variety of parameters $k$ such as the size of a (given) dominating set, the size of an odd cycle transversal, or the deletion distance to $P_5$-free graphs. Earlier works imply FPT algorithms relative to clique-width and relative to solution size. We complement these findings by giving the first results on the existence of polynomial kernelizations for \stablecutset, i.e., efficient preprocessing algorithms that return an equivalent instance of size polynomial in the parameter value. Under the standard assumption that $NP\nsubseteq coNP/poly$, we show that no polynomial kernelization is possible relative to the deletion distance to a single path, generalizing deletion distance to various graph classes, nor by the size of a (given) dominating set. We also show that under the same assumption no polynomial kernelization is possible relative to solution size, i.e., given $(G,k)$ answering whether there is a stable cutset of size at most $k$. On the positive side, we show polynomial kernelizations for parameterization by modulators to a single clique, to a cluster or a co-cluster graph, and by twin cover., Comment: For Dieter Kratsch on his 65th birthday

We derive an analytical expression for $s$-state exciton energies in monolayer transition-metal dichalcogenides (TMDCs): $E_{\text{ns}}=-{\text{Ry}}^*\times P_n/{(n-1/2+0.479\, r^*_0/\kappa)^2}$, $n=1,2,...$, where $r^*_0$ and $\kappa$ are the dimensionless screening length and dielectric constant of the surrounding medium; $\text{Ry}^*$ is an effective Rydberg energy scaled by the dielectric constant and exciton reduced mass; $P_n(r^*_0/\kappa)$ is a function of variables $n$ and $r^*_0/\kappa$. Its values are around 1.0 so we consider it a term that corrects the Rydberg energy. Despite the simple form, the suggested formula gives exciton energies with high precision compared to the exact numerical solutions that accurately describe recent experimental data for a large class of TMDC materials, including WSe$_2$, WS$_2$, MoSe$_2$, MoS$_2$, and MoTe$_2$. To achieve these results, we have developed a so-called regulated perturbation theory by combining the conventional perturbation method with several elements of the Feranchuk-Komarov operator method, including the Levi-Civita transformation, the algebraic calculation technique via the annihilation and creation operators, and the introduction of a free parameter to optimize the convergence rate of the perturbation series. This universal form of exciton energies could be helpful in various physical analyses, including retrieval of the material parameters such as reduced exciton mass and screening length from the available measured exciton energies., Comment: 5 pages, 1 figure, 3 tables, 1 supplementary

In this paper, we study a Dirichlet type problem for the non-pluripolar complex Monge - Amp\`ere equation with prescribed singularity on a bounded domain of $\mathbb{C}^n$. We provide a local version for an existence and uniqueness theorem proved by Darvas, Di Nezza and Lu. Our work also extends a result of Ahag, Cegrell, Czyz and Pham., Comment: 23 pages. In this version, we fixed some minor errors and added some content to the introduction

Although the frequency shift and odd-even intensity modulation in high-order harmonic generation (HHG) have both been observed for asymmetric laser-target systems, they are typically studied as two separate phenomena. In this Letter, we provide a comprehensive picture of these two nonlinear optical phenomena, unifying them through a common origin - asymmetry of the laser-target system. By tuning asymmetric laser-target systems, we discover a transition from the harmonic frequency shift to the odd-even intensity modulation upon increasing the duration of the driving laser pulse. Specifically, these phenomena are observed simultaneously for laser pulses with intermediate pulse duration. For numerical evidence, we solve the time-dependent Schr\"{o}dinger equation, while insight into the underlying physics is obtained from a simplified analytically tractable model. Understanding the asymmetric characteristics reflected in the HHG as provided is crucial for retrieving laser-target information, sampling external fields, and probing molecular dynamics., Comment: 6 pages, 4 figures

Log parsing, the process of converting raw log messages into structured formats, is an important initial step for automated analysis of logs of large-scale software systems. Traditional log parsers often rely on heuristics or handcrafted features, which may not generalize well across diverse log sources or require extensive model tuning. Recently, some log parsers have utilized powerful generative capabilities of large language models (LLMs). However, they heavily rely on demonstration examples, resulting in substantial overhead in LLM invocations. To address these issues, we propose LogBatcher, a cost-effective LLM-based log parser that requires no training process or labeled data. To leverage latent characteristics of log data and reduce the overhead, we divide logs into several partitions through clustering. Then we perform a cache matching process to match logs with previously parsed log templates. Finally, we provide LLMs with better prompt context specialized for log parsing by batching a group of logs from each partition. We have conducted experiments on 16 public log datasets and the results show that LogBatcher is effective and efficient for log parsing.

Large Language Models (LLMs) have garnered considerable attention owing to their remarkable capabilities, leading to an increasing number of companies offering LLMs as services. Different LLMs achieve different performance at different costs. A challenge for users lies in choosing the LLMs that best fit their needs, balancing cost and performance. In this paper, we propose a framework for addressing the cost-effective query allocation problem for LLMs. Given a set of input queries and candidate LLMs, our framework, named OptLLM, provides users with a range of optimal solutions to choose from, aligning with their budget constraints and performance preferences, including options for maximizing accuracy and minimizing cost. OptLLM predicts the performance of candidate LLMs on each query using a multi-label classification model with uncertainty estimation and then iteratively generates a set of non-dominated solutions by destructing and reconstructing the current solution. To evaluate the effectiveness of OptLLM, we conduct extensive experiments on various types of tasks, including text classification, question answering, sentiment analysis, reasoning, and log parsing. Our experimental results demonstrate that OptLLM substantially reduces costs by 2.40% to 49.18% while achieving the same accuracy as the best LLM. Compared to other multi-objective optimization algorithms, OptLLM improves accuracy by 2.94% to 69.05% at the same cost or saves costs by 8.79% and 95.87% while maintaining the highest attainable accuracy., Comment: This paper is accepted by ICWS 2024

Precise control of the electron phase accumulated during its sub-cycle motion within intense laser fields is essential in strong-field physics, yet remains mostly indirect and complicated so far. In this Letter, we develop a novel approach to control this sub-cycle electron phase by tuning a low-frequency electric field applied on a centrosymmetric gaseous target during its interaction with a few-cycle infrared laser pulse. Our method is based on a universal analytical relation between the low-frequency electric field and its induced harmonic frequency shift, derived by the strong-field approximation. This simple relation and its universality are confirmed numerically by directly solving the time-dependent Schr\"odinger equation. Moreover, we discuss the benefits of the discovered relation in \textit{in situ} applications, including continuously and precisely tuning XUV waves and developing a new method of comprehensively sampling THz pulse., Comment: 6 pages, 3 figures

This paper provides a rigorous analysis of boundary element methods for the magnetic field integral equation on Lipschitz polyhedra. The magnetic field integral equation is widely used in practical applications to model electromagnetic scattering by a perfectly conducting body. The governing operator is shown to be coercive by means of the electric field integral operator with a purely imaginary wave number. Consequently, the continuous variational problem is uniquely solvable, given that the wave number does not belong to the spectrum of the interior Maxwell's problem. A Petrov-Galerkin discretization scheme is then introduced, employing Raviart-Thomas boundary elements for the solution space and Buffa-Christiansen boundary elements for the test space. Under a mild assumption depending only on the geometrical domain, the corresponding discrete inf-sup condition is proven, implying the unique solvability of the discrete problem. An asymptotically quasi-optimal error estimate for numerical solutions is established, and the convergence rate of the numerical scheme is examined. In addition, the resulting matrix system is shown to be well-conditioned regardless of the mesh refinement. Some numerical results are presented to support the theoretical analysis., Comment: 21 pages, 5 figures

We investigate the effects of broken scale invariant unparticle at the MUonE experiment. The choice of the broken model is because the original scale-invariant model is severely suppressed by constraints from cosmology and low-energy experiments. Broken scale invariant unparticle model is categorized into four types: pseudoscalar, scalar, axial-vector, and vector unparticle. Each uparticle type is characterized by three free parameters: coupling constant $\lambda$, scaling dimension $d$, and energy scale $\mu$ at which the scale-invariance is broken. After considering all of the available constraints on the model, we find that the MUonE experiment is sensitive to (axial-)vector unparticle with $1 < d < 1.4$ and $1\le \mu \le 12$ GeV., Comment: 5 pages, 3 figs, contribution to the proceedings of Windows on the Universe conference, August 2023, Quy Nhon, Vietnam

The well-known Cluster Vertex Deletion problem (CVD) asks for a given graph $G$ and an integer $k$ whether it is possible to delete a set $S$ of at most $k$ vertices of $G$ such that the resulting graph $G-S$ is a cluster graph (a disjoint union of cliques). We give a complete characterization of graphs $H$ for which CVD on $H$-free graphs is polynomially solvable and for which it is NP-complete. Moreover, in the NP-completeness cases, CVD cannot be solved in sub-exponential time in the vertex number of the $H$-free input graphs unless the Exponential-Time Hypothesis fails. We also consider the connected variant of CVD, the Connected Cluster Vertex Deletion problem (CCVD), in which the set $S$ has to induce a connected subgraph of $G$. It turns out that CCVD admits the same complexity dichotomy for $H$-free graphs. Our results enlarge a list of rare dichotomy theorems for well-studied problems on $H$-free graphs., Comment: Extended version of a MFCS 2022 paper. To appear in Theory of Computing Systems

A matching cut in a graph G is an edge cut of G that is also a matching. This short survey gives an overview of old and new results and open problems for Maximum Matching Cut, which is to determine the size of a largest matching cut in a graph. We also compare this problem with the related problems Matching Cut, Minimum Matching Cut, and Perfect Matching Cut, which are to determine if a graph has a matching cut; the size of a smallest matching cut in a graph; and if a graph has a matching cut that is a perfect matching, respectively. Moreover, we discuss a relationship between Maximum Matching Cut and Max Cut, which is to determine the size of a largest edge cut in a graph, as well as a relationship between Minimum Matching Cut and Min Cut, which is to determine the size of a smallest edge cut in a graph.

We perform an extensive survey of rare and exclusive few-body decays -- defined as those with branching fractions $\mathcal{B} \lesssim 10^{-5}$ and two or three final particles -- of the Higgs, Z, W bosons, and the top quark. Such rare decays can probe physics beyond the Standard Model (BSM), constitute a background for exotic decays into new BSM particles, and provide precise information on quantum chromodynamics factorization with small nonperturbative corrections. We tabulate the theoretical $\mathcal{B}$ values for almost 200 rare decay channels of the four heaviest elementary particles, indicating the current experimental limits in their observation. Among those, we have computed for the first time ultrarare Higgs boson decays into photons and/or neutrinos, H and Z radiative decays into leptonium states, radiative H and Z quark-flavour-changing decays, and semiexclusive top-quark decays into a quark plus a meson, while updating predictions for a few other rare H, Z, and top quark partial widths. The feasibility of measuring each of these unobserved decays is estimated for p-p collisions at the high-luminosity Large Hadron Collider (HL-LHC), and for $e^+e^-$ and p-p collisions at the future circular collider (FCC)., Comment: 56 pages, 34 figs. Extended description of theoretical models. New subsection added with Z boson exclusive FCNC decays. Refs. added

This paper introduces a time-domain combined field integral equation for electromagnetic scattering by a perfect electric conductor. The new equation is obtained by leveraging the quasi-Helmholtz projectors, which separate both the unknown and the source fields into solenoidal and irrotational components. These two components are then appropriately rescaled to cure the solution from a loss of accuracy occurring when the time step is large. Yukawa-type integral operators of a purely imaginary wave number are also used as a Calderon preconditioner to eliminate the ill-conditioning of matrix systems. The stabilized time-domain electric and magnetic field integral equations are linearly combined in a Calderon-like fashion, then temporally discretized using an appropriate pair of trial functions, resulting in a marching-on-in-time linear system. The novel formulation is immune to spurious resonances, dense discretization breakdown, large-time step breakdown and dc instabilities stemming from non-trivial kernels. Numerical results for both simply-connected and multiply-connected scatterers corroborate the theoretical analysis., Comment: 13 pages