Set Of Problems Research Articles

The Perception of Eponym in Modern Linguistics: Dynamics of Concepts and Definitions

Key words: eponymization, onimization, transonimization, signified, signifier, anthroponym, toponym, semanticization, desemanticization In the article, the perception of the linguistic reality of eponym in modern linguistics has been studied. On the basis of it the term eponym and the process of eponymization have been characterized and clarified. The study was conducted by comparative analysis. In the work, due to the need to solve the set problems, an examination and analysis of the linguistic observations of the concept of eponym has been performed. As a result, the proposed views have been grouped into three main groups: 1. the starting unit of the eponymization process is considered an eponym, 2. the word generated in the end result of the eponymization process is considered an eponym, 3. both sides of the eponymization process are considered eponyms – both the starting unit and the final word. It has been considered acceptable to use the term eponym only for the linguistic unit resulting from the process of eponymization, since theoretically all proper names can become eponyms. In the work, an attempt has been made to clarify the characteristics of the concept of eponym. Thus, it has been defined as a proper or common name, which emerged as a result of the semanticization or polyfunctionalization of the homonymous proper name. It has been noted that an eponym is a word created as a result of the process of eponymization, which has the primary function for a linguistic sign unit, i. e., to name the phenomenon by reflecting it in the system of linguistic sign units. For the process of eponymization, which has been considered beyond the limits of the change of lexical meaning, two main ways have been put forward: semanticization and polyfunctionalization of the proper name. The process of eponymization, which is related to the development of various social spheres that determine human activity, has been evaluated as an important means of enriching the vocabulary of the language, examination of which leads to the necessity for intercultural, sociolinguistic and interdisciplinary studies.

Exploration in Deep Reinforcement Learning: From Single-Agent to Multiagent Domain.

Deep reinforcement learning (DRL) and deep multiagent reinforcement learning (MARL) have achieved significant success across a wide range of domains, including game artificial intelligence (AI), autonomous vehicles, and robotics. However, DRL and deep MARL agents are widely known to be sample inefficient that millions of interactions are usually needed even for relatively simple problem settings, thus preventing the wide application and deployment in real-industry scenarios. One bottleneck challenge behind is the well-known exploration problem, i.e., how efficiently exploring the environment and collecting informative experiences that could benefit policy learning toward the optimal ones. This problem becomes more challenging in complex environments with sparse rewards, noisy distractions, long horizons, and nonstationary co-learners. In this article, we conduct a comprehensive survey on existing exploration methods for both single-agent RL and multiagent RL. We start the survey by identifying several key challenges to efficient exploration. Then, we provide a systematic survey of existing approaches by classifying them into two major categories: uncertainty-oriented exploration and intrinsic motivation-oriented exploration. Beyond the above two main branches, we also include other notable exploration methods with different ideas and techniques. In addition to algorithmic analysis, we provide a comprehensive and unified empirical comparison of different exploration methods for DRL on a set of commonly used benchmarks. According to our algorithmic and empirical investigation, we finally summarize the open problems of exploration in DRL and deep MARL and point out a few future directions.

Approximation Algorithms for the Submodular Hitting Set Problem

In this paper, we study the submodular hitting set problem (SHSP), which is a variant of the hitting set problem. In the SHSP, we are given a supergraph H = ( V , C ) and a nonnegative submodular function on the set 2 V . The objective is to determine a vertex subset to cover all hyperedges such that the cost of submodular covering is minimized. Our main work is to present a rounding algorithm and a primal-dual algorithm respectively for the SHSP and prove that they both have the approximation ratio k , where k is the maximum number of vertices in all hyperedges.

Uniqueness and reconstruction of finite lattice sets from their line sums

If an unknown finite set C⊂Z2 is cut by lines parallel to given directions, then one may count the number of points of C that are intercepted by each line, that is, the projections of C in the given directions. The inverse problem consists in reconstructing the set C, interpreted as a binary image, from the knowledge of its projections.In general, this challenging combinatorial problem, also related to the tomographic reconstruction of an unknown homogeneous object by means of X-rays, is ill-posed, meaning that different binary images exist that match the available projections. Therefore, as a preliminary step, one can try to find conditions to be imposed on the considered directions in order to limit the number of allowed solutions.In this paper we address the above problems for sets C contained in a finite assigned lattice grid, and generalize some results known in literature.First, we describe special sets of lattice directions, called simple cycles, and focus on some of their properties. Then we prove that uniqueness of reconstruction for binary images is guaranteed if and only if the line sums are computed along suitable simple cycles having even cardinality.As a second item, we prove that the unique binary solution can be explicitly reconstructed from a real-valued solution having minimal Euclidean norm. This leads to an explicit reconstruction algorithm, tested on four different phantoms and compared with previous results, which points out a significant improvement of the corresponding performance.

On the Local Fourier Uniformity Problem for Small Sets

Abstract We consider vanishing properties of exponential sums of the Liouville function $\boldsymbol{\lambda }$ of the form $$ \begin{align*} & \lim_{H\to\infty}\limsup_{X\to\infty}\frac{1}{\log X}\sum_{m\leq X}\frac{1}{m}\sup_{\alpha\in C}\bigg|\frac{1}{H}\sum_{h\leq H}\boldsymbol{\lambda}(m+h)e^{2\pi ih\alpha}\bigg|=0, \end{align*} $$ where $C\subset{{\mathbb{T}}}$. The case $C={{\mathbb{T}}}$ corresponds to the local $1$-Fourier uniformity conjecture of Tao, a central open problem in the study of multiplicative functions with far-reaching number-theoretic applications. We show that the above holds for any closed set $C\subset{{\mathbb{T}}}$ of zero Lebesgue measure. Moreover, we prove that extending this to any set $C$ with non-empty interior is equivalent to the $C={{\mathbb{T}}}$ case, which shows that our results are essentially optimal without resolving the full conjecture. We also consider higher-order variants. We prove that if the linear phase $e^{2\pi ih\alpha }$ is replaced by a polynomial phase $e^{2\pi ih^{t}\alpha }$ for $t\geq 2$ then the statement remains true for any set $C$ of upper box-counting dimension $< 1/t$. The statement also remains true if the supremum over linear phases is replaced with a supremum over all nilsequences coming form a compact countable ergodic subsets of any $t$-step nilpotent Lie group. Furthermore, we discuss the unweighted version of the local $1$-Fourier uniformity problem, showing its validity for a class of “rigid” sets (of full Hausdorff dimension) and proving a density result for all closed subsets of zero Lebesgue measure.

Web-Based, Human-Guided, or Computer-Guided Transdiagnostic Cognitive Behavioral Therapy in University Students With Anxiety and Depression: Randomized Controlled Trial.

Internet-based cognitive behavioral interventions (iCBTs) are efficacious treatments for depression and anxiety. However, it is unknown whether adding human guidance is feasible and beneficial within a large educational setting. This study aims to potentially demonstrate the superiority of 2 variants of a transdiagnostic iCBT program (human-guided and computer-guided iCBT) over care as usual (CAU) in a large sample of university students and the superiority of human-guided iCBT over computer-guided iCBT. A total of 801 students with elevated levels of anxiety, depression, or both from a large university in the Netherlands were recruited as participants and randomized to 1 of 3 conditions: human-guided iCBT, computer-guided iCBT, and CAU. The primary outcome measures were depression (Patient Health Questionnaire) and anxiety (Generalized Anxiety Disorder scale). Secondary outcomes included substance use-related problems (Alcohol Use Disorder Identification Test and Drug Abuse Screening Test-10 items). Linear mixed models were used to estimate the effects of time, treatment group, and their interactions (slopes). The primary research question was whether the 3 conditions differed in improvement over 3 time points (baseline, midtreatment, and after treatment) in terms of depression and anxiety symptoms. Results were analyzed according to the intention-to-treat principle using multiple imputation. Patients were followed exploratively from baseline to 6 and 12 months. In both short-term and long-term analyses, the slopes for the 3 conditions did not differ significantly in terms of depression and anxiety, although both web-based interventions were marginally more efficacious than CAU over 6 months (P values between .02 and .03). All groups showed significant improvement over time (P<.001). For the secondary outcomes, only significant improvements over time (across and not between groups) were found for drug use (P<.001). Significant differences were found in terms of adherence, indicating that participants in the human-guided condition did more sessions than those in the computer-guided condition (P=.002). The transdiagnostic iCBT program offers a practical, feasible, and efficacious alternative to usual care to tackle mental health problems in a large university setting. There is no indication that human guidance should be preferred over technological guidance. The potential preference of human support also depends on the scale of implementation and cost-effectiveness, which need to be addressed in future trials. International Clinical Trials Registry Platform NL7328/NTR7544; https://trialsearch.who.int/Trial2.aspx?TrialID=NL-OMON26795.

Resistance to Targeted Inhibitors of the PI3K/AKT/mTOR Pathway in Advanced Oestrogen-Receptor-Positive Breast Cancer.

The PI3K/AKT/mTOR signalling pathway is one of the most frequently activated pathways in breast cancer and also plays a central role in the regulation of several physiologic functions. There are major efforts ongoing to exploit precision medicine by developing inhibitors that target the three kinases (PI3K, AKT, and mTOR). Although multiple compounds have been developed, at present, there are just three inhibitors approved to target this pathway in patients with advanced ER-positive, HER2-negative breast cancer: everolimus (mTOR inhibitor), alpelisib (PIK3CA inhibitor), and capivasertib (AKT inhibitor). Like most targeted cancer drugs, resistance poses a major problem in the clinical setting and is a factor that has frequently limited the overall efficacy of these agents. Drug resistance can be categorised into intrinsic or acquired resistance depending on the timeframe it has developed within. Whereas intrinsic resistance exists prior to a specific treatment, acquired resistance is induced by a therapy. The majority of patients with ER-positive, HER2-negative advanced breast cancer will likely be offered an inhibitor of the PI3K/AKT/mTOR pathway at some point in their cancer journey, with the options available depending on the approval criteria in place and the cancer's mutation status. Within this large cohort of patients, it is likely that most will develop resistance at some point, which makes this an area of interest and an unmet need at present. Herein, we review the common mechanisms of resistance to agents that target the PI3K/AKT/mTOR signalling pathway, elaborate on current management approaches, and discuss ongoing clinical trials attempting to mitigate this significant issue. We highlight the need for additional studies into AKT1 inhibitor resistance in particular.

Missing data in amortized simulation-based neural posterior estimation.

Amortized simulation-based neural posterior estimation provides a novel machine learning based approach for solving parameter estimation problems. It has been shown to be computationally efficient and able to handle complex models and data sets. Yet, the available approach cannot handle the in experimental studies ubiquitous case of missing data, and might provide incorrect posterior estimates. In this work, we discuss various ways of encoding missing data and integrate them into the training and inference process. We implement the approaches in the BayesFlow methodology, an amortized estimation framework based on invertible neural networks, and evaluate their performance on multiple test problems. We find that an approach in which the data vector is augmented with binary indicators of presence or absence of values performs the most robustly. Indeed, it improved the performance also for the simpler problem of data sets with variable length. Accordingly, we demonstrate that amortized simulation-based inference approaches are applicable even with missing data, and we provide a guideline for their handling, which is relevant for a broad spectrum of applications.

Investment–consumption optimization with transaction cost and learning about return predictability

In this paper, we investigate an investment–consumption optimization problem in continuous-time settings, where the expected rate of return from a risky asset is predictable with an observable factor and an unobservable factor. Based on observable information, a decision-maker learns about the unobservable factor while making investment–consumption decisions. Both factors are supposed to follow a mean-reverting process. Also, we relax the assumption for perfect liquidity of the risky asset through incorporating proportional transaction costs that are incurred in trading the risky asset. In such way, a form of friction posing liquidity risk to the investor is examined. Dynamic programming principle coupled with an Hamilton–Jacobi–Bellman (HJB) equation are adopted to discuss the problem. Applying an asymptotic method with small transaction costs being taken as a perturbation parameter, we determine the frictional value function by solving the first and second corrector equations. For the numerical implementation of the proposed approach, a Monte-Carlo-simulation-based approximation algorithm is adopted to solve the second corrector equation. Finally, numerical examples and their economic interpretations are discussed.

A practical and robust approach for solving the multi‐compartment vehicle routing problem under demand uncertainty using machine learning

AbstractThe multi‐compartment vehicle routing problem is an extension of the vehicle routing problem and consists of designing a set of routes to perform the collection or delivery of different product types from customers with minimal costs. The product types are incompatible with each other and must be transported separately in multiple compartments. In practice, several uncertainties such as uncertainty in demands can arise, where the exact demand of customers is not known at the time of planning. To deal with these uncertainties, decision‐makers have to rely on robust solutions. A solution is considered robust when it can resist perturbations in every possible demand scenario as much as possible. In the day to day business of most logistic companies, historical data about each customer can be stored and used to make intelligent decisions regarding the expected demands. In this article, we propose an adaptive large neighborhood search for solving the robust multi‐compartment vehicle routing problem under demand uncertainty and present a robust solution approach for the problem in practical settings by employing machine learning. We show that by using our approach, the solutions obtained have lower recourse costs and have a lower gap between expected and actual costs, which is a favorable outcome to have in practice.

Decidability bounds for Presburger arithmetic extended by sine

We consider Presburger arithmetic extended by the sine function, call this extension sine-Presburger arithmetic (sin-PA), and systematically study decision problems for sets of sentences in sin-PA. In particular, we detail a decision algorithm for existential sin-PA sentences under assumption of Schanuel's conjecture. This procedure reduces decisions to the theory of the ordered additive group of real numbers extended by sine, which is decidable under Schanuel's conjecture. On the other hand, we prove that four alternating quantifier blocks suffice for undecidability of sin-PA sentences. To do so, we explicitly interpret the weak monadic second-order theory of the grid, which is undecidable, in sin-PA.

Near-Optimal Packet Scheduling in Multihop Networks with End-to-End Deadline Constraints

Scheduling packets with end-to-end deadline constraints in multihop networks is an important problem that has been notoriously difficult to tackle. Recently, there has been progress on this problem in the worst-case traffic setting, with the objective of maximizing the number of packets delivered within their deadlines. Specifically, the proposed algorithms were shown to achieve Ω(1/log(L)) fraction of the optimal objective value if the minimum link capacity in the network is C min = Ω(log (L)), where L is the maximum length of a packet's route in the network (which is bounded by the packet's maximum deadline). However, such guarantees can be quite pessimistic due to the strict worst-case traffic assumption and may not accurately reflect real-world settings. In this work, we aim to address this limitation by exploring whether it is possible to design algorithms that achieve a constant fraction of the optimal value while relaxing the worst-case traffic assumption. We provide a positive answer by demonstrating that in stochastic traffic settings, such as i.i.d. packet arrivals, near-optimal, (1-ε)-approximation algorithms can be designed if C min = Ω((over (logL/ε) Ω 2 ). To the best of our knowledge, this is the first result that shows this problem can be solved near-optimally under nontrivial assumptions on traffic and link capacity.

Identifying critical demand scenarios for the robust capacitated network design problem using principal component analysis

AbstractIn this paper, we consider the single‐commodity robust network design problem. Given an undirected graph with capacity installation costs on its edges and a set of scenarios with associated flow balance vectors that represent different scenarios of node supplies and demands, the goal is to find integer edge capacities that minimize the total installation cost and permit a feasible single commodity flow for each scenario. This problem arises, for example, in the design of power networks, which are dimensioned to accommodate many different load scenarios. We propose a new method to identify a small subset of the given scenarios, such that solving the robust network design problem for the smaller scenario set leads to almost the same capacities as solving it for the full scenario set . By considering only the scenarios in , the size of the model that needs to be solved can be reduced substantially, while the error introduced by neglecting the remaining scenarios is kept very small. Our method only employs simple techniques from statistical data analysis, namely principal component analysis (PCA), and convex hull computations in low dimensions. Thus, its computational effort is very small and it is easily applicable to more complex network design problems. We evaluate the effectiveness of the method in computational experiments for instances stemming from offshore power grid planning and telecommunication networks. Our results show that the proposed techniques are indeed well suited to identify small scenario subsets that lead to significantly reduced models with high quality solutions.

On a sumset problem for dilated integer sets

Let [Formula: see text] be a non-empty finite set of integers. For any integer [Formula: see text], let [Formula: see text]. One of the important problems in additive combinatorics is to find the optimal lower bound for the cardinality of the sumset [Formula: see text]. Cilleruelo, Silva, and Vinuesa conjectured that, if [Formula: see text] is a positive integer and [Formula: see text] is a finite set of integers with sufficiently large cardinality, then [Formula: see text]. For some values of [Formula: see text] this conjecture is already confirmed. In this article, under certain restrictions on set [Formula: see text], we confirm this conjecture for all positive integers [Formula: see text] except for those of the form [Formula: see text] or [Formula: see text] where [Formula: see text] is an odd prime number and [Formula: see text] for [Formula: see text].

Minimum connected dominating set and backbone of a random graph

We study the minimum dominating set problem as a representative combinatorial optimization challenge with a global topological constraint. The requirement that the backbone induced by the vertices of a dominating set should be a connected subgraph makes the problem rather nontrivial to investigate by statistical physics methods. Here, we convert this global connectivity constraint into a set of local vertex constraints and build a spin glass model with only five coarse-grained vertex states. We derive a set of coarse-grained belief-propagation equations and obtain theoretical predictions of the relative sizes of the minimum dominating sets for regular random and Erdös–Rényi random graph ensembles. We also implement an efficient message-passing algorithm to construct close-to-minimum connected dominating sets and backbone subgraphs for single random graph instances. Our theoretical strategy may also be applicable to some other global topological constraints.

Finding small feedback arc sets on large graphs

The minimum feedback arc set problem (FASP), which seeks to remove a minimum set of arcs from a directed graph to make the remaining graph acyclic, is fundamental in graph algorithms with many applications in social network analysis, circuit testing, deadlock resolution, algorithmic games, and other fields. However, in theory, FASP is NP-Hard and cannot be approximated within any constant under the Unique-Games Conjecture. In practice, the performance of existing algorithms on large graphs is still unsatisfactory. To solve FASP on large graphs, we propose two novel methods in this paper. First, we systematically study the reduction rules for FASP that can quickly reduce the scale of input graphs without losing optimality. We integrate the reduction rules into an algorithm that can be used as a preprocessor for all existing FASP algorithms to simplify the input graphs. Second, we provide a scalable heuristic algorithm based on the divide-and-conquer method for better solution quality. Extensive experiments on a wide range of real-world graphs show that the reduction algorithm effectively reduces the size of input instances. Furthermore, for half of the circuit benchmark graphs, our final algorithm improves the quality of the existing heuristic solution by 24% to 40% within an acceptable running time.

A two-species diffusion-advection competition model with protection zones

In this paper, we study a two-species reaction-diffusion-advection competition model imposed the Danckwerts boundary conditions and with boundary protection zones. Some special cases have been extensively studied, which include reaction-diffusion-advection competition models without protection zones [25,29] and reaction-diffusion competition models with protection zones in non-advective environments [7]. If the product of the two competition rates in the unprotected zone is less than a given value, by establishing a prior estimate and applying the monotone dynamical system theory, we completely characterize the global dynamics, which extends some existing ones. If the product is bigger than the above mentioned value, we find that the size of the protection zone plays an important role in determining the global dynamics. We also discuss the problem of optimal protection zone setting and investigate the effect of advection on the critical size of the protection zone.

A framework for neurosymbolic robot action planning using large language models.

Symbolic task planning is a widely used approach to enforce robot autonomy due to its ease of understanding and deployment in engineered robot architectures. However, techniques for symbolic task planning are difficult to scale in real-world, highly dynamic, human-robot collaboration scenarios because of the poor performance in planning domains where action effects may not be immediate, or when frequent re-planning is needed due to changed circumstances in the robot workspace. The validity of plans in the long term, plan length, and planning time could hinder the robot's efficiency and negatively affect the overall human-robot interaction's fluency. We present a framework, which we refer to as Teriyaki, specifically aimed at bridging the gap between symbolic task planning and machine learning approaches. The rationale is training Large Language Models (LLMs), namely GPT-3, into a neurosymbolic task planner compatible with the Planning Domain Definition Language (PDDL), and then leveraging its generative capabilities to overcome a number of limitations inherent to symbolic task planners. Potential benefits include (i) a better scalability in so far as the planning domain complexity increases, since LLMs' response time linearly scales with the combined length of the input and the output, instead of super-linearly as in the case of symbolic task planners, and (ii) the ability to synthesize a plan action-by-action instead of end-to-end, and to make each action available for execution as soon as it is generated instead of waiting for the whole plan to be available, which in turn enables concurrent planning and execution. In the past year, significant efforts have been devoted by the research community to evaluate the overall cognitive capabilities of LLMs, with alternate successes. Instead, with Teriyaki we aim to providing an overall planning performance comparable to traditional planners in specific planning domains, while leveraging LLMs capabilities in other metrics, specifically those related to their short- and mid-term generative capabilities, which are used to build a look-ahead predictive planning model. Preliminary results in selected domains show that our method can: (i) solve 95.5% of problems in a test data set of 1,000 samples; (ii) produce plans up to 13.5% shorter than a traditional symbolic planner; (iii) reduce average overall waiting times for a plan availability by up to 61.4%.

Construction of "Professional-Entrepreneurial Integration" Education System of Musicology in Local Applied Universities

With the vigorous promotion of supply-side structural reform in China, it has become necessary for application-oriented undergraduate universities to cultivate high-quality talents with both innovative spirit and entrepreneurial ability in the new era. The curriculum reform and construction of "professional and entrepreneurship integration" in applied colleges and universities is a response to the existing social talent demand and problems in the curriculum setting of colleges and universities majoring in music. This paper examines the status of music colleges at various applied universities in Anhui province through interviews and investigations. According to the survey results， musicology majors in applied colleges and universities have established a multifaceted system for evaluating teaching and have achieved a hierarchical development of students' abilities. They have fully implemented a project-based results process rating system. This is highly significant in constructing a "Professional-Entrepreneurship Integration" education system for musicology majors in local applied colleges and universities, which can serve the development of regional culture.

Leveraging Reviews: Learning to Price with Buyer and Seller Uncertainty

Customers can access hundreds of reviews for a single product in online marketplaces. Buyers often use reviews from other customers that share their type---such as height for clothing or skin type for skincare products---to estimate their values, which they may not know a priori. Customers with few relevant reviews may hesitate to purchase except at a low price, so for the seller, there is a tension between setting high prices and ensuring that there are enough reviews so buyers can confidently estimate their values. Simultaneously, sellers may use reviews to gauge the demand for items they wish to sell. In this work, we study this pricing problem in an online setting where the seller interacts with a set of buyers of finitely many types, one by one, over a series of T rounds. At each round, the seller first sets a price. Then, a buyer arrives and examines the reviews of the previous buyers with the same type, which reveal those buyers' ex-post values. Based on the reviews, the buyer decides to purchase if they have good reason to believe their ex-ante utility is positive. Crucially, the seller does not know the buyer's type when setting the price, nor even the distribution over types. We provide a no-regret algorithm that the seller can use to obtain high revenue. When there are d types, after T rounds, our algorithm achieves a problem-independent Õ ( T 2/3 d 1/3 ) regret bound. However, when the smallest probability q min that any given type appears is large, specifically when q min ∈ Ω( d −2/3 T −1/3 ), the same algorithm achieves a [EQUATION] regret bound. We complement these upper bounds with matching lower bounds in both regimes, showing that our algorithm is minimax optimal up to lower-order terms. This is a summary of work that won the Exemplary AI Track Paper Award at EC'24.