Miracle-dz/UniFAR-FTUs huggingface dataset:
Evaluating Restricted First-Order Counting Properties on Nowhere Dense Classes and Beyond

It is known that first-order logic with some counting extensions can be efficiently evaluated on graph classes with bounded expansion, where depth-$r$ minors have constant density. More precisely, the formulas are $\exists x_1 . x_k \#y \varphi(x_1,.,x_k, y)>N$, where $\varphi$ is an FO-formula. If $\varphi$ is quantifier-free, we can extend this result to nowhere dense graph classes with an almost linear FPT run time. Lifting this result further to slightly more general graph classes, namely almost nowhere dense classes, where the size of depth-$r$ clique minors is subpolynomial, is impossible unless FPT=W[1]. On the other hand, in almost nowhere dense classes we can approximate such counting formulas with a small additive error. Note those counting formulas are contained in FOC({<}) but not FOC1(P). In particular, it follows that partial covering problems, such as partial dominating set, have fixed parameter algorithms on nowhere dense graph classes with almost linear running time.
RaidEnv: Exploring New Challenges in Automated Content Balancing for Boss Raid Games

The balance of game content significantly impacts the gaming experience. Unbalanced game content diminishes engagement or increases frustration because of repetitive failure. Although game designers intend to adjust the difficulty of game content, this is a repetitive, labor-intensive, and challenging process, especially for commercial-level games with extensive content. To address this issue, the game research community has explored automated game balancing using artificial intelligence (AI) techniques. However, previous studies have focused on limited game content and did not consider the importance of the generalization ability of playtesting agents when encountering content changes. In this study, we propose RaidEnv, a new game simulator that includes diverse and customizable content for the boss raid scenario in MMORPG games. Additionally, we design two benchmarks for the boss raid scenario that can aid in the practical application of game AI. These benchmarks address two open problems in automatic content balancing, and we introduce two evaluation metrics to provide guidance for AI in automatic content balancing. This novel game research platform expands the frontiers of automatic game balancing problems and offers a framework within a realistic game production pipeline.
Large sample theory of spacings statistics for tests of fit for the composite hypothesis

SUMMARY Let X1, . , Xn be a sequence of independent and identically distributed random variables with an unknown underlying continuous cumulative distribution function F. Often we would like to test a null hypothesis concerning the goodness of fit of Fto some distribution function which is fully specified or belongs to some parametric family, i.e. in some applications the null hypothesis is simple whereas in others it may be composite. In this paper we present the large sample theory of tests based on non-symmetric functions of sample spacings under composite null hypotheses as well as under contiguous alternatives. Goodness-of-fit tests which are optimal within this class are constructed.
Fluctuation Theorem as a special case of Girsanov Theorem

Stochastic thermodynamics is an important development in the direction of finding general thermodynamic principles for non-equilibrium systems. We believe stochastic thermodynamics has the potential to benefit from the measure-theoretic framework of stochastic differential equations. Towards this, in this work, we show that Fluctuation Theorem (FT) is a special case of the Girsanov theorem, which is an important result in the theory of stochastic differential equations. We report that by employing Girsanov transformation of measures between the forward and the reversed dynamics of a general class of Langevin dynamic systems, we arrive at the Integral Fluctuation Relation. Following the same approach, we derive the FT also for the overdamped case. Our derivation is applicable to both transient and steady state conditions and can also incorporate diffusion coefficients varying as a function of state and time. We expect that the proposed method will be an easy route towards deriving the FT irrespective of the complexity and non-linearity of the system.
Dynamic Mobile Manipulation via Whole-Body Bilateral Teleoperation of a Wheeled Humanoid

Humanoid robots have the potential to help human workers by realizing physically demanding manipulation tasks such as moving large boxes within warehouses. We define such tasks as Dynamic Mobile Manipulation (DMM). This letter presents a framework for DMM via whole-body teleoperation, built upon three key contributions: Firstly, a teleoperation framework employing a Human Machine Interface (HMI) and a bi-wheeled humanoid, SATYRR, is proposed. Secondly, the study introduces a dynamic locomotion mapping, utilizing human-robot reduced order models, and a kinematic retargeting strategy for manipulation tasks. Additionally, the letter discusses the role of whole-body haptic feedback for wheeled humanoid control. Finally, the system's effectiveness and mappings for DMM are validated through locomanipulation experiments and heavy box pushing tasks. Here we show two forms of DMM: grasping a target moving at an average speed of 0.4 m/s, and pushing boxes weighing up to 105% of the robot's weight. By simultaneously adjusting their pitch and using their arms, the pilot adjusts the robot pose to apply larger contact forces and move a heavy box at a constant velocity of 0.2 m/s.
W 1, p -estimates for elliptic equations with lower order terms

We consider the Neumann and Dirichlet problems for second-order linear elliptic equations \begin{document}$ - {\rm{div}}{\mkern 1mu} (A\nabla u) - b \cdot \nabla u + \lambda u = f + {\rm{div}}{\mkern 1mu} F,\quad - {\rm{div}}{\mkern 1mu} ({A^t}\nabla v) + {\rm{div}}{\mkern 1mu} (vb) + \lambda v = g + {\rm{div}}{\mkern 1mu} G$ \end{document} in a bounded Lipschitz domain $\Omega \subset \mathbb{R}^n$, $n \geq 2$, where $A: \mathbb{R}^n \to \mathbb{R}^{n^2}$, $b: \Omega \to \mathbb{R}^n$ and $\lambda \geq 0$ are given. Some $W^{1, 2}$-estimates have been already known, provided that $A \in L^\infty(\Omega)^{n^2}$ and $b \in L^r(\Omega)^n$, where $n \leq r
Using Rewrite Strategies for Efficient Functional Automatic Differentiation

Automatic Differentiation (AD) has become a dominant technique in ML. AD frameworks have first been implemented for imperative languages using tapes. Meanwhile, functional implementations of AD have been developed, often based on dual numbers, which are close to the formal specification of differentiation and hence easier to prove correct. But these papers have focussed on correctness not efficiency. Recently, it was shown how an approach using dual numbers could be made efficient through the right optimizations. Optimizations are highly dependent on order, as one optimization can enable another. It can therefore be useful to have fine-grained control over the scheduling of optimizations. One method expresses compiler optimizations as rewrite rules, whose application can be combined and controlled using strategy languages. Previous work describes the use of term rewriting and strategies to generate high-performance code in a compiler for a functional language. In this work, we implement dual numbers AD in a functional array programming language using rewrite rules and strategy combinators for optimization. We aim to combine the elegance of differentiation using dual numbers with a succinct expression of the optimization schedule using a strategy language. We give preliminary evidence suggesting the viability of the approach on a micro-benchmark.
Simple and efficient improvement of spin image for three-dimensional object recognition

Abstract. This paper presents a highly distinctive and robust local three-dimensional (3-D) feature descriptor named longitude and latitude spin image (LLSI). The whole procedure has two modules: local reference frame (LRF) definition and LLSI feature description. We employ the same technique as Tombari to define the LRF. The LLSI feature descriptor is obtained by stitching the longitude and latitude (LL) image to the original spin image vertically, where the LL image was generated similarly with the spin image by mapping a two-tuple (θ,φ) into a discrete two-dimensional histogram. The performance of the proposed LLSI descriptor was rigorously tested on a number of popular and publicly available datasets. The results showed that our method is more robust with respect to noise and varying mesh resolution than existing techniques. Finally, we tested our LLSI-based algorithm for 3-D object recognition on two popular datasets. Our LLSI-based algorithm achieved recognition rates of 100%, 98.2%, and 96.2%, respectively, when tested on the Bologna, University of Western Australia (UWA) (up to 84% occlusion), UWA datasets (all). Moreover, our LLSI-based algorithm achieved 100% recognition rate on the whole UWA dataset when generating the LLSI descriptor with the LRF proposed by Guo.
On Optimal Finite-length Block Codes of Size Four for Binary Symmetric Channels

A binary code of blocklength $n$ and codebook size $M$ is called an $(n,M)$ code, which is studied for memoryless binary symmetric channels (BSCs) with the maximum likelihood (ML) decoding. For any $n \geq 2$, some optimal codes among the linear $(n,4)$ codes have been explicitly characterized in the previous study, but whether the optimal codes among the linear codes are better than all the nonlinear codes or not is unknown. In this paper, we first show that for any $n\geq 2$, there exists an optimal code (among all the $(n,4)$ codes) that is either linear or in a subset of nonlinear codes, called Class-I codes. We identified all the optimal codes among the linear $(n,4)$ codes for each blocklength $n\geq 2$, and found ones that were not given in literature. For any $n$ from $2$ to $300$, all the optimal $(n,4)$ codes are identified, where except for $n=3$, all the optimal $(n,4)$ codes are equivalent to linear codes. There exist optimal $(3,4)$ codes that are not equivalent to linear codes. Furthermore, we derive a subset of nonlinear codes called Class-II codes and justify that for any $n>300$, the set composed of linear, Class-I and Class-II codes and their equivalent codes contains all the optimal $(n,4)$ codes. Both Class-I and Class-II codes are close to linear codes in the sense that they involve only one type of columns that are not included in linear codes. Our results are obtained using a new technique to compare the ML decoding performance of two codes, featured by a partition of the entire range of the channel output.
A hybrid machine learning framework for clad characteristics prediction in metal additive manufacturing

During the past decade, metal additive manufacturing (MAM) has experienced significant developments and gained much attention due to its ability to fabricate complex parts, manufacture products with functionally graded materials, minimize waste, and enable low-cost customization. Despite these advantages, predicting the impact of processing parameters on the characteristics of an MAM printed clad is challenging due to the complex nature of MAM processes. Machine learning (ML) techniques can help connect the physics underlying the process and processing parameters to the clad characteristics. In this study, we introduce a hybrid approach which involves utilizing the data provided by a calibrated multi-physics computational fluid dynamic (CFD) model and experimental research for preparing the essential big dataset, and then uses a comprehensive framework consisting of various ML models to predict and understand clad characteristics. We first compile an extensive dataset by fusing experimental data into the data generated using the developed CFD model for this study. This dataset comprises critical clad characteristics, including geometrical features such as width, height, and depth, labels identifying clad quality, and processing parameters. Second, we use two sets of processing parameters for training the ML models: machine setting parameters and physics-aware parameters, along with versatile ML models and reliable evaluation metrics to create a comprehensive and scalable learning framework for predicting clad geometry and quality. This framework can serve as a basis for clad characteristics control and process optimization. The framework resolves many challenges of conventional modeling methods in MAM by solving t the issue of data scarcity using a hybrid approach and introducing an efficient, accurate, and scalable platform for clad characteristics prediction and optimization.
A Language Model for Grammatical Error Correction in L2 Russian

Grammatical error correction is one of the fundamental tasks in Natural Language Processing. For the Russian language, most of the spellcheckers available correct typos and other simple errors with high accuracy, but often fail when faced with non-native (L2) writing, since the latter contains errors that are not typical for native speakers. In this paper, we propose a pipeline involving a language model intended for correcting errors in L2 Russian writing. The language model proposed is trained on untagged texts of the Newspaper subcorpus of the Russian National Corpus, and the quality of the model is validated against the RULEC-GEC corpus.
Data-driven Predictive Latency for 5G: A Theoretical and Experimental Analysis Using Network Measurements

The advent of novel 5G services and applications with binding latency requirements and guaranteed Quality of Service (QoS) hastened the need to incorporate autonomous and proactive decision-making in network management procedures. The objective of our study is to provide a thorough analysis of predictive latency within 5G networks by utilizing real-world network data that is accessible to mobile network operators (MNOs). In particular, (i) we present an analytical formulation of the user-plane latency as a Hypoexponential distribution, which is validated by means of a comparative analysis with empirical measurements, and (ii) we conduct experimental results of probabilistic regression, anomaly detection, and predictive forecasting leveraging on emerging domains in Machine Learning (ML), such as Bayesian Learning (BL) and Machine Learning on Graphs (GML). We test our predictive framework using data gathered from scenarios of vehicular mobility, dense-urban traffic, and social gathering events. Our results provide valuable insights into the efficacy of predictive algorithms in practical applications.
Causal Reinforcement Learning: A Survey

Reinforcement learning is an essential paradigm for solving sequential decision problems under uncertainty. Despite many remarkable achievements in recent decades, applying reinforcement learning methods in the real world remains challenging. One of the main obstacles is that reinforcement learning agents lack a fundamental understanding of the world and must therefore learn from scratch through numerous trial-and-error interactions. They may also face challenges in providing explanations for their decisions and generalizing the acquired knowledge. Causality, however, offers a notable advantage as it can formalize knowledge in a systematic manner and leverage invariance for effective knowledge transfer. This has led to the emergence of causal reinforcement learning, a subfield of reinforcement learning that seeks to enhance existing algorithms by incorporating causal relationships into the learning process. In this survey, we comprehensively review the literature on causal reinforcement learning. We first introduce the basic concepts of causality and reinforcement learning, and then explain how causality can address core challenges in non-causal reinforcement learning. We categorize and systematically review existing causal reinforcement learning approaches based on their target problems and methodologies. Finally, we outline open issues and future directions in this emerging field.
A lower bound for the weighted-Hardy constant for domains satisfying a uniform exterior cone condition

We consider weighted Hardy inequalities involving the distance function to the boundary of a domain in the $N$-dimensional Euclidean space with nonempty boundary. We give a lower bound for the corresponding best Hardy constant for a domain satisfying a uniform exterior cone condition. This lower bound depends on the aperture of the corresponding infinite circular cone.
Cross-Element Combinatorial Selection for Multi-Element Creative in Display Advertising

The effectiveness of ad creatives is greatly influenced by their visual appearance. Advertising platforms can generate ad creatives with different appearances by combining creative elements provided by advertisers. However, with the increasing number of ad creative elements, it becomes challenging to select a suitable combination from the countless possibilities. The industry's mainstream approach is to select individual creative elements independently, which often overlooks the importance of interaction between creative elements during the modeling process. In response, this paper proposes a Cross-Element Combinatorial Selection framework for multiple creative elements, termed CECS. In the encoder process, a cross-element interaction is adopted to dynamically adjust the expression of a single creative element based on the current candidate creatives. In the decoder process, the creative combination problem is transformed into a cascade selection problem of multiple creative elements. A pointer mechanism with a cascade design is used to model the associations among candidates. Comprehensive experiments on real-world datasets show that CECS achieved the SOTA score on offline metrics. Moreover, the CECS algorithm has been deployed in our industrial application, resulting in a significant 6.02% CTR and 10.37% GMV lift, which is beneficial to the business.
Robust Graph Structure Learning with the Alignment of Features and Adjacency Matrix

To improve the robustness of graph neural networks (GNN), graph structure learning (GSL) has attracted great interest due to the pervasiveness of noise in graph data. Many approaches have been proposed for GSL to jointly learn a clean graph structure and corresponding representations. To extend the previous work, this paper proposes a novel regularized GSL approach, particularly with an alignment of feature information and graph information, which is motivated mainly by our derived lower bound of node-level Rademacher complexity for GNNs. Additionally, our proposed approach incorporates sparse dimensional reduction to leverage low-dimensional node features that are relevant to the graph structure. To evaluate the effectiveness of our approach, we conduct experiments on real-world graphs. The results demonstrate that our proposed GSL method outperforms several competitive baselines, especially in scenarios where the graph structures are heavily affected by noise. Overall, our research highlights the importance of integrating feature and graph information alignment in GSL, as inspired by our derived theoretical result, and showcases the superiority of our approach in handling noisy graph structures through comprehensive experiments on real-world datasets.
Direct electrical modulation of surface response in a single plasmonic nanoresonator

Classical electrodynamics describes the optical response of systems using bulk electronic properties and treats boundaries between two materials as infinitesimally thin. However, due to the quantum nature of electrons, interfaces have a finite thickness. Non-classical surface effects become increasingly important as ever smaller nanoscale systems are realized and eventually dominate over volume-related phenomena. Investigating the response of surface electrons in such systems, therefore, becomes imperative. One way to gain control over non-classical interface effects and study them is through electrical gating, as the static screening charges reside exclusively at the surface. Here, we investigate the modulation of the surface response upon direct electric charging of a single plasmonic nanoresonator by measuring the resulting changes in resonance. We analyze the observed effects within the general framework of surface-response functions and provide a basic model derived from electron spill-out within the local-response approximation (LRA). Our observed change in resonance frequency is well accounted for by assuming a modulation of the in-plane surface current. Surprisingly, we also measure a change in the resonance width, where adding electrons to the surface leads to a narrowing of the plasmonic resonance, i.e., reduced losses. The description of such effects requires considering nonlocal effects and the inclusion of a possible anisotropy of the perturbed surface permittivity. Our experiment, therefore, opens a vast field of investigations on how to gain control over the surface response in plasmonic resonators and to develop ultrafast and extremely small electrically driven plasmonic modulators and metasurfaces by leveraging electrical control over non-classical surface effects.
An Overview of the NET Playground - A Heterogeneous, Multi-Functional Network Test Bed

This paper provides an overview of the hardware and software components used in our test bed project the NET Playground. All source information is stored in the GitLab repository (https://gitlab.com/Paulteck/net-playground). In the Hardware section, we present sketches and 3D views of mechanical parts and technical drawings of printed boards. The Software section discusses relay control using shell scripts and the utilization of Ansible for automation. We also introduce a C++ framework for connecting with the INA231 energy sensor. This paper serves as a reference for understanding and replicating our project's hardware and software components.
The Erdős Pentagon Problem

The Erdős pentagon problem asks about the maximum number of copies of C5 that one can find in a triangle-free graph. This problem was posed in 1984, but was not resolved until 2012. In this thesis, we aim to capture the story of solving the pentagon problem as completely as possible. We provide a detailed exposition of the motivation behind and construction of flag algebras, and give a complete solution to the pentagon problem using flag algebra techniques. All known solutions of the pentagon problem to date have been computer-assisted; with the question of whether an elementary solution can be found in mind, we also investigate the pentagon problem and modifications of the problem from different elementary perspectives.
VertiBench: Advancing Feature Distribution Diversity in Vertical Federated Learning Benchmarks

Vertical Federated Learning (VFL) is a crucial paradigm for training machine learning models on feature-partitioned, distributed data. However, due to privacy restrictions, few public real-world VFL datasets exist for algorithm evaluation, and these represent a limited array of feature distributions. Existing benchmarks often resort to synthetic datasets, derived from arbitrary feature splits from a global set, which only capture a subset of feature distributions, leading to inadequate algorithm performance assessment. This paper addresses these shortcomings by introducing two key factors affecting VFL performance - feature importance and feature correlation - and proposing associated evaluation metrics and dataset splitting methods. Additionally, we introduce a real VFL dataset to address the deficit in image-image VFL scenarios. Our comprehensive evaluation of cutting-edge VFL algorithms provides valuable insights for future research in the field.