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The article discusses the study of conic sections in mathematics and introduces a new class of curves called haricoids. It explains the definition of a conic in terms of its focus, directrix, and eccentricity. The article explores the concept of using a circle as a directrix for ellipses and hyperbolas, noting that the position of the focus relative to the circle determines the shape of the conic. The text then delves into the properties and equations of haricoids, including their construction and behavior as parameters vary. The author presents examples and graphs to illustrate these concepts and suggests further research on the applications and connections of haricoids. [Extracted from the article]

Using assembly theory, we investigate the assembly pathways of binary strings (bitstrings) of length N formed by joining bits present in the assembly pool and the bitstrings that entered the pool as a result of previous joining operations. We show that the bitstring assembly index is bounded from below by the shortest addition chain for N, and we conjecture about the form of the upper bound. We define the degree of causation for the minimum assembly index and show that, for certain N values, it has regularities that can be used to determine the length of the shortest addition chain for N. We show that a bitstring with the smallest assembly index for N can be assembled via a binary program of a length equal to this index if the length of this bitstring is expressible as a product of Fibonacci numbers. Knowing that the problem of determining the assembly index is at least NP-complete, we conjecture that this problem is NP-complete, while the problem of creating the bitstring so that it would have a predetermined largest assembly index is NP-hard. The proof of this conjecture would imply P ≠ NP since every computable problem and every computable solution can be encoded as a finite bitstring. The lower bound on the bitstring assembly index implies a creative path and an optimization path of the evolution of information, where only the latter is available to Turing machines (artificial intelligence). Furthermore, the upper bound hints at the role of dissipative structures and collective, in particular human, intelligence in this evolution. [ABSTRACT FROM AUTHOR]

Given a family F of graphs, we say that a graph G is F -saturated if G does not contain any member of F , but for any edge e ∈ E (G ¯) the graph G + e does contain a member of F . The F -saturation game is played by two players starting with an empty graph and adding an edge on their turn without making a member of F . The game ends when the graph is F -saturated. One of the players wants to maximize the number edges in the final graph, while the other wants to minimize it. The game saturation number is the number of edges in the final graph given the optimal play by both players. In the present paper we study F -saturation game when F = { P 6 } consists of the single path on 6 vertices. [ABSTRACT FROM AUTHOR]

Given two graphs F and H, Constructor and Blocker alternately claim unclaimed edges of the complete graph Kn. Constructor's graph must remain F-free, while Blocker claims edges without restrictions. The game ends when Constructor cannot claim further edges or when all edges have been claimed. The score of the game is the number of H's in Constructor's graph. Constructor's aim is to maximize the score, while Blocker tries to minimize it. We study this game for several choices of F and H. [ABSTRACT FROM AUTHOR]

Early numerical skills are important not only for later mathematical achievement but for overall achievement and are associated with later income, health, and quality of life. Socioeconomic disparities in numerical skills are visible before children begin school, and widen throughout schooling. It is, therefore, important to support the development of early numerical skills in children from lower socioeconomic backgrounds. Previous studies have highlighted the effectiveness of linear number board games for improving early numerical skills, and the beneficial effect of counting backward as well as forward. We designed a number board game that required children to place number cards in order on a line, either forward-only or forward and backward in small groups in the classroom. The game's effectiveness was evaluated in 4- to 5-year-old children from schools located in socioeconomically disadvantaged areas. Children were randomly allocated to one of three conditions: playing the number game forward-only (n = 82), playing the number game forward and backward (i.e., bidirectional condition; n = 82), or an alphabet game (active control, n = 85). After eight gameplay sessions across 5 weeks, children's numerical and letter-sound knowledge skills improved, but there was no significant effect of the intervention condition. Neither forward nor bidirectional number line games (nor the alphabet game) added benefits beyond the learning already happening in the classroom. Short linear board game interventions may be effective compared to control groups who received minimal or absent numerical education, but they fail to provide an additional advantage when children are already learning mathematics in school. Educational Impact and Implications Statement: The study investigated the effectiveness of a brief number board game intervention aimed at enhancing early numerical skills in young children. Low attrition, high engagement, and enjoyment were observed among the children during the game sessions, demonstrating the game's potential in terms of usability. However, the game did not provide additional benefits beyond regular classroom learning. Short game-based interventions may not always improve numerical skills beyond the learning already happening in the classroom. [ABSTRACT FROM AUTHOR]

We study queueing problems with an endogenous number of machines, the novelty being that coalitions not only choose how to queue, but on how many machines. After minimizing the processing costs and machine costs, we share the proceeds of this cooperation, and study the existence of stable allocations. First, we study queueing problems, and examine how to share the total cost. We provide an upper bound and a lower bound on the cost of a machine to guarantee the non-emptiness of the core. Next, we study requeueing problems, where there is an existing queue. We examine how to share the cost savings compared to the initial situation, when optimally requeueing/changing the number of machines. Although stable allocations may not exist, we guarantee their existence when all machines are considered public goods, and we start with an initial queue in which agents with larger waiting costs are processed first. [ABSTRACT FROM AUTHOR]

Cops and Robber is a well-studied two player pursuit-evasion game played on a graph. In this game, a set of cops, controlled by the first player, tries to capture the position of a robber, controlled by the second player. The cop number of a graph is the minimum number of cops required to capture the robber in the graph. A group of cops guard a subgraph if they can ensure that the robber cannot enter the subgraph without getting captured immediately. We study the applications of guarding to provide new bounds and improve existing bounds for several graph classes. In particular, we show that the cop number for butterfly networks and for solid grids is two. We also construct a partial grid with cop number 3 establishing that partial grids have same cop number as their superclass planar graphs. We also consider three well-studied variants of Cops and Robber : Cops and Fast Robber , Cops and Attacking Robber , and Surrounding CnR. We improve the existing bounds for the cop number of multidimensional grids for both Cops and Attacking Robber and Surrounding CnR. Finally, we consider Cops and Fast Robber on AT-free graphs to improve the existing bounds on the cop number for this game. [ABSTRACT FROM AUTHOR]

Just as mathematics helps us to represent and reason about the natural world, in its internal applications one branch of mathematics helps us to represent and reason about the subject matter of another. Recognition of the close analogy between internal and external applications of mathematics can help resolve two persistent philosophical puzzles concerning its applicability: a platonist puzzle arising from the abstractness of mathematical objects; and an empiricist puzzle arising from mathematical propositions' lack of empirical factual content. In order to see how this is the case, we will examine what it is to apply mathematics internally and describe examples. [ABSTRACT FROM AUTHOR]

Giardiasis is among the ignored zoonotic illnesses accorded by the World Health Organization that is caused by Giardia duodenalis. The disease is ignored regardless of the harm it causes to people and other creatures. In this paper, a mathematical model for giardiasis illness transmission is formed, which considers sickness carriers and control measures such as screening, treatment, and sanitation of the environment around people. In the assessment, the basic reproduction number, R 0 , which is used for analyzing the local stability of the equilibria is determined using the state-of-the-art next-generation matrix, while the Metzler constancy speculation is used to show the overall adequacy of the global stability of the equilibrium point free from the disease. In addition, a Lyapunov function has been used to study the stability of the endemic equilibrium point. The assessment of parameters is performed to explore the limits that significantly influence the transmission components of the disease disorders using the normalizing sensitivity index method. The result revealed that the recruitment rate is the most sensitive limit to the reproduction number. The environment-human interaction parameter is the second influential factor in the transmission of giardiasis in the community. In the same manner, the outcomes recommend that carriers assume an expected part in the rate of giardiasis subsequently; disregarding them could risk endeavors to control the pestilence. Besides, the mathematical recreation of the model shows that a mix of each of the three interventions fundamentally affects the control of giardiasis. In this way, we advise implementing the strategies simultaneously in endemic areas to effectively stop the spread of the giardiasis disease in humans. [ABSTRACT FROM AUTHOR]

A generalization of mixed strategy equilibrium is proposed, where mixed strategies need only be finitely additive and payoff functions are not required to be integrable or bounded. This notion of best-response equilibrium is based on an extension of the idea that an equilibrium strategy is supported in the player's set of best-response actions, but is applicable also when no best-response actions exist. It yields simple, natural equilibria in a number of well-known games where other kinds of mixed equilibrium are complicated, not compelling or do not exist. [ABSTRACT FROM AUTHOR]

Sharing resources among cloudlets can significantly reduce deployment and management costs and improve the quality of edge services in the CloudLet Federation (CLF). To balance the interests of Cloudlet Infrastructure Providers (CIPs) and enhance the overall profits of the federation, this paper presents a fair pricing strategy for cloudlet resources using a game model. The game model designs the initial quotes from both sides of the game, considering the idle resource rate of CIPs and the overall profit of the CLF. Additionally, the price adjustment strategy considers the psychology of the demand side and the convergence rate of the game process. The paper proves the existence of the Nash equilibrium solution of the game model by selecting the number of game rounds as a critical factor. Furthermore, an algorithm, Game Pricing Approach based on Selection Times, is proposed to solve the model. Simulation results show that the proposed method can improve the total profit by more than 20 % and resource utilization by over 50 % compared to the existing methods. [ABSTRACT FROM AUTHOR]

Despite the indisputable progresses of artificial intelligence, some tasks that are rather easy for a human being are still challenging for a machine. An emblematic example is the resolution of mathematical puzzles with diagrams. Sub-symbolical approaches have proven successful in fields like image recognition and natural language processing, but the combination of these techniques into a multimodal approach towards the identification of the puzzle's answer appears to be a matter of reasoning, more suitable for the application of a symbolic technique. In this work, we employ logic programming to perform spatial reasoning on the puzzle's diagram and integrate the deriving knowledge into the solving process. Analysing the resolution strategies required by the puzzles of an international competition for humans, we draw the design principles of a Prolog reasoning library, which interacts with image processing software to formulate the puzzle's constraints. The library integrates the knowledge from different sources, and relies on the Prolog inference engine to provide the answer. This work can be considered as a first step towards the ambitious goal of a machine autonomously solving a problem in a generic context starting from its textual-graphical presentation. An ability that can help potentially every human–machine interaction. [ABSTRACT FROM AUTHOR]

In this paper, we continue the study of the domination game on graphs introduced by Brešar et al. (2010). Haynes and Henning in 2009 introduced a paired-domination version of the domination game. We study an alternative paired-domination version of the domination game played on a graph G by two players, named Dominator and Staller. The players take turns choosing a pair of adjacent vertices of G such that neither vertex in the pair has yet been chosen and the vertices in the pair must dominate at least one vertex not dominated by the previously chosen vertices. This process eventually produces a paired-dominating set of vertices of G ; that is, a dominating set in G that induces a subgraph that contains a perfect matching. Dominator wishes to minimize the number of vertices chosen, while Staller wishes to maximize it. The game paired-domination number γ gpr (G) of G is the number of vertices chosen when Dominator starts the game and both players play optimally, and the Staller-start game paired-domination number γ gpr ′ (G) of G is the number of vertices chosen when Staller starts the game and both players play optimally. In this paper, we determine the paired-domination numbers γ gpr (G) and γ gpr ′ (G) when the graph G is a cycle. [ABSTRACT FROM AUTHOR]

We consider misinformation propagating through a social network and study the problem of its prevention. The goal is to identify a set of |$k$| users that need to be convinced to adopt a limiting campaign so as to minimize the number of people that end up adopting the misinformation. This work presents Reverse Prevention Sampling (RPS), an algorithm that provides a scalable solution to the misinformation mitigation problem. Our theoretical analysis shows that RPS runs in |$O((k + l)(n + m)(\frac{1}{1 - \gamma }) \log n / \epsilon ^2)$| expected time and returns a |$(1 - 1/e - \epsilon)$| -approximate solution with at least |$1 - n^{-l}$| probability (where |$\gamma $| is a typically small network parameter and |$l$| is a confidence parameter). The time complexity of RPS substantially improves upon the previously best-known algorithms that run in time |$\Omega (m n k \cdot POLY(\epsilon ^{-1}))$|⁠. We experimentally evaluate RPS on large datasets and show that it outperforms the state-of-the-art solution by several orders of magnitude in terms of running time. This demonstrates that misinformation mitigation can be made practical while still offering strong theoretical guarantees. [ABSTRACT FROM AUTHOR]

The best allocation of limited resources to activities with the aim of accomplishing the desired goal, such as maximization of profit or minimization of cost, is the focus of linear programming. The relationships between activities in linear programming models satisfy the proportionality and additivity requirements since they are linear interactions. This feature of linear programming is extended to the tourism industry which is one of the major industries in the global economy with respect to invested capital and earnings of foreign currencies. In todays era of design thinking, automation, and met averse, there is a very close margin between solutions to similar real-world problems. This is where the need and demand for fuzzy and imprecise linear programming arises. The membership functions provide the model developer the freedom to grade the imprecision as per his/her preference, thereby enabling a unique solution for each problem. While considering the tourism problem a number of factors like natural resources, people, history, culture, security, accommodation, entertainment, political stability, cost of services, tour operator, tour information, and advertisement play an important role in enhancing the sector to a large extent. Combined and classified they come under the following categories like leisure tourism, therapeutic/spa tourism, conference tourism, political tourism, sports/recreational tourism, cultural tourism, social tourism, conference tourism, recreational tourism, sports tourism, religious tourism, health tourism, etc. Each of these sectors requires careful investment on the part of the Government and other stake holders for development purpose. i.e. only a proper marketing mix will ensure a better return for the state. Taking this aspect into consideration the authors decided to introduce a hypothetical LP maximization model for the tourism industry in North East. Cost and space allocation are the constraints in the model. Among the various categories, three tourism forms (heritage, eco-tourism, and pilgrimage tourism) are considered which are used to optimize the allocation of the States marketing budget in tourism in such a way that the appropriate sector provides the greatest likelihood of producing the strongest return on investment. The maximization of profit has been done using various methods, like Werner's, Verdegay's, and Zimmermans. The authors have concluded the results based on the sensitivity analysis that has been done in the process of maximizing profit along with a maximal satisfaction level. [ABSTRACT FROM AUTHOR]

Winning accolades including "the most fascinating museum in New York State worth traveling for" and the "best museum for kids", the National Museum of Mathematics, or MoMath as it was affectionately called, was on its way. Graph: The Math Encounters (mathencounters.org) public presentation series celebrates the wonder of mathematics, bringing serious math researchers to the stage to share what they do with a general audience. Additionally, mathematics has historically not been equally welcoming to all groups, and the math community as a whole is focused on improving diversity - how can MoMath continue to participate in this effort in its second decade?. [Extracted from the article]

This article explores the social lives of gaming stones, a significant number of which have been found at the Late Bronze Age farming settlement of Aredhiou Vouppes , Cyprus. The number of gaming stones found at the site is unprecedented within a Late Cypriot context. Comparatively few are found in the contemporary urban centers, and in general they appear to be more typical of the Middle Cypriot social world. The purpose of this article is to investigate the agency of these gaming stones, and to consider them as social mediators within the community of Aredhiou. It explores the social and cognitive lives of these objects, examining how they might be transformed and reimagined as they moved through myriad states of existence throughout their object-life, and thus the various ways in which they were entangled in the social life of the settlement. [ABSTRACT FROM AUTHOR]

In this work, we introduce an innovative Markov Chain Monte Carlo (MCMC) classifier, a synergistic combination of Bayesian machine learning and Apache Spark, highlighting the novel use of this methodology in the spectrum of big data management and environmental analysis. By employing a large dataset of air pollutant concentrations in Madrid from 2001 to 2018, we developed a Bayesian Logistic Regression model, capable of accurately classifying the Air Quality Index (AQI) as safe or hazardous. This mathematical formulation adeptly synthesizes prior beliefs and observed data into robust posterior distributions, enabling superior management of overfitting, enhancing the predictive accuracy, and demonstrating a scalable approach for large-scale data processing. Notably, the proposed model achieved a maximum accuracy of 87.91% and an exceptional recall value of 99.58% at a decision threshold of 0.505, reflecting its proficiency in accurately identifying true negatives and mitigating misclassification, even though it slightly underperformed in comparison to the traditional Frequentist Logistic Regression in terms of accuracy and the AUC score. Ultimately, this research underscores the efficacy of Bayesian machine learning for big data management and environmental analysis, while signifying the pivotal role of the first-ever MCMC Classifier and Apache Spark in dealing with the challenges posed by large datasets and high-dimensional data with broader implications not only in sectors such as statistics, mathematics, physics but also in practical, real-world applications. [ABSTRACT FROM AUTHOR]

We consider the connected game coloring number of a graph, introduced by Charpentier et al. as a game theoretic graph parameter that measures the degeneracy of a graph with respect to a connected version of the graph marking game. We establish bounds for the connected game coloring number of graphs of bounded treedepth and of k -trees. We also show that there exists an outerplanar 2-tree with connected game coloring number 5, which answers a question from Charpentier et al., (2020). [ABSTRACT FROM AUTHOR]

It selected three different points in Qingshan Lake Greenway (Mid-lake Square, Lawn Park, Water Forest), and measured the microclimate factors in 3 sunny days and 3 cloudy days in summer and autumn respectively. At the same time, the number and behavior characteristics of visitors were observed and recorded in unit time. Comparing the difference and relationship between microclimate factors and visitors’ behavior in three points, it aimed to provide some reference for the improvement of the future recreation space and landscape service facilities of the greenway. The results showed that: (1) The daily average temperature of the Water Forest was lower than Lawn Park by 1.6℃ and lower than Mid-lake Square by 3.2℃ in summer. It was 1.5℃ lower than Lawn Park and 2℃ lower than Mid-lake Square in autumn. The daily average relative humidity of Water Forest was higher than Lawn Park by 8.88% and higher than Mid-lake Square by 11.92% in summer. It was 7.92% higher than Lawn Park, and 10.48% higher than Mid-lake Square in autumn. The wind speed in Mid-lake Square and Lawn Park was remarkable changing, and the Water Forest was basically windless. The average daily UV radiation intensity and light quantum showed a single peak type curves and reached the peak at 12: 00 and then decreased. (2) The comfort index of microclimate reached Grade I in Lawn Park at 8: 00 in summer and 12: 00-16: 00 in autumn, in Mid-lake Square at 12: 00-16: 00 in autumn, and in Water Forest at 8: 00-10: 00 in summer and at 12: 00 in autumn. (3) In summer, the number of visitors in Water Forest was the largest, and the main activities were walking. In autumn, the number of visitors in Lawn Park was largest, and main activities were picnics.(4) The number of visitors showed negative correlation with air relative humidity, UV radiation intensity and light quantum in summer. And there was a significantly negative correlation with light quantum in autumn. In conclusion, the difference of microclimate in different seasons can affect the stay time of visitors, and the impact on the recreational content of visitors is not obvious. Therefore, space improvement should be made according to the different characteristics of the three sample sites. [ABSTRACT FROM AUTHOR]

Statistics in sports plays a key role in predicting winning strategies and providing objective performance indicators. Despite the growing interest in recent years in using statistical methodologies in this field, less emphasis has been given to the multivariate approach. This work aims at using the Bayesian networks to model the joint distribution of a set of indicators of players' performances in basketball in order to discover the set of their probabilistic relationships as well as the main determinants affecting the player's winning percentage. From a methodological point of view, the interest is to define a suitable model for non-Gaussian data, relaxing the strong assumption on normal distribution in favour of Gaussian copula. Through the estimated Bayesian network, we discovered many interesting dependence relationships, providing a scientific validation of some known results mainly based on experience. At last, some scenarios of interest have been simulated to understand the main determinants that contribute to rising in the number of won games by a player. [ABSTRACT FROM AUTHOR]

In recent years, sport analytics evolved in the massive collection of data, especially from Global Positioning System (GPS) sensors installed in sport facilities or worn by the athletes. The largest amount of data are used to track locations and trajectories of players during their performance. Data analysis of positioning information during the actions of a game allows a deep characterization of the performance of single players and the whole team. Basketball is one of the team sports where analytics are becoming a fundamental asset. However, during a game, actions are interleaved with inactive periods (e.g., pauses or breaks). For a proper knowledge extraction on the game features, the analysis of players movements must be restricted to active periods only. This paper proposes an algorithm to automatically identify active periods by using players' tracking data in basketball. The algorithm is based on thresholds that apply to players kinematic parameters. The values of thresholds are identified by setting-up a "ground truth" extracted from the video analysis of the games and by developing a performance evaluation method derived from "Receiver Operating Characteristic" (ROC) curves. When tested on a number of real games, the method shows good performance. This algorithm, along with the identified parameters, could be adopted by practitioners to identify game active periods without the need for video analysis. [ABSTRACT FROM AUTHOR]

Substantiality is an important but misunderstood part of the concept of genocide. One problem is that substantiality holds different meanings within law and sociology. Legally, substantiality is connected to the difficulty of proving there is "intention to destroy" in the absence of a specific plan. Substantiality in this sense is a marker of the level of death and destruction required to support an inference of intent. Sociologically, substantiality is connected to popular understandings of genocide that link the gravity of the crime to the volume of destruction. Substantiality in this latter sense has been problematized by scholars who point out that genocide does not necessarily entail a greater level of harm and destruction than other atrocities, which might fall under the label of war crimes or crimes against humanity. This article examines the concept of substantiality with a view to illuminating the tension that exists between legal and sociological understandings of genocide. The article uses the alleged genocide of the Rohingya in Myanmar as a case study to demonstrate the complexity and contradictions of legal and sociological applications of the concept of substantiality. The article concludes that problems with substantiality reflect deeper problems with the recognition and articulation of the particular wrong inherent in the crime of genocide. [ABSTRACT FROM AUTHOR]

(Kreisel) Let HT ht be Peano Arithmetic axiomatized with the successor induction schema and identity axioms. And at the same time, they establish that over HT ht the uniform Kruskal theorem does not imply HT ht . Must it be the case that HT ht ? It was previously known that the existence property fails for HT ht . [Extracted from the article]

Research Highlight: Woodman, J. P., Cole, E. F., Firth, J. A., Perrins, C. M., & Sheldon, B. C. (2022). Disentangling the causes of age‐assortative mating in bird populations with contrasting life‐history strategies. Journal of Animal Ecology, https://doi.org/10.1111/1365‐2656.13851. In their study of age‐assortative mating, Woodman and colleagues thoroughly and concisely detail its behavioural determinants using datasets, astonishing in themselves, amassed from their decades‐long studies of mute swans (Cygnus olor) and great tits (Parus major), species that are respectively longer‐ and shorter‐lived and occupying different segments of the slow/fast life‐history continuum. Here, they show that positive age‐assortative mating occurs through active, age‐based mate selection in mute swans which play the long game, whereas in the shorter‐lived great tit this is principally a passive byproduct of demographic processes. That great tits have relatively lower interannual survivorship means that newly recruited, young birds occupy a larger proportion of the breeding population in any given year than occurs in mute swans. The adaptive significance of age‐assortative mating is yet to be determined, but the current study provides an exciting possibility for the role of selection on assortative mating generally in either promoting or constraining active mate selection and sexual dimorphism within and across the tree of life. [ABSTRACT FROM AUTHOR]

Artificial reefs (ARs) have been advocated for and implemented as management tools for recreational fisheries, species conservation, and habitat replacement; however, the research that includes attracting marine species of floating ARs remains in its early stages. Here, two types of floating ARs were designed to evaluate the attractive effects using the occurrence rate and attracting index for six commercially important species (Lateolabrax maculatus, Liza haematocheila, Sebastes schlegelii, Acanthopagrus schlegelii, Litopenaeus vannamei, and Amphioctopus fangsiao) in the Bohai Bay of China; their combined ARs were meanwhile compared with two variants of artificial seagrass beds (SA and SB) and the traditional double-frame artificial reef (TD). All of the designed ARs were effective in attracting experimental species. The ARs with higher shelter areas (SB and TD) showed a better attracting effect. The efficiency of the ARs in attracting different species depended on their life histories. The bottom-mounted ARs were more efficient in attracting demersal species, while the floating ARs attracted epipelagic fish. In addition, the combined reefs had a better attractive effect than single ARs did. Overall, floating ARs and their combined ARs show the potential to deploy especially for attracting epipelagic fishes, although further study is needed. [ABSTRACT FROM AUTHOR]

In this paper the behavior of the game domination number γg(G) and the Staller start game domination number γg (G) by the contraction of an edge and the subdivision of an edge are investigated. Here we prove that contracting an edge can decrease γg (G) and γg (G) by at most two, whereas subdividing an edge can increase these parameters by at most two. In the case of no-minus graphs it is proved that subdividing an edge can increase both these parameters by at most one but on the other hand contracting an edge can decrease these by two. All possible values of these parameters are also analysed here. [ABSTRACT FROM AUTHOR]

The following examination focuses on the moral dilemmas surrounding the comparison of self-protective and utilitarian autonomous vehicles. These vehicles can be programmed to prioritize the safety of passengers in an accident or prioritize the greater good to save more lives. The essay will explore various ethical questions such as evaluating the numbers game approach, analyzing the principles of beneficence correlated with social inequality, and interpreting the principle of autonomy in the context of autonomous vehicles. Additionally, the examination will consider the harm–benefit ratio. In the sense of methods, this analysis uses the classical issues in a new way and provides recommendations for decision-makers to consider. [ABSTRACT FROM AUTHOR]

We study dynamic games with strategic complements where each player is modeled by a scalar flow dynamical system with a controlled input and an uncontrolled output. The model originates in inventory control problems with shared set-up costs and a large number of players. An activation cost is shared among active players, namely players who control their dynamics at a given time. As a main contribution, we prove that two-threshold strategies, like the (s, S) strategies used in inventory control, are mean-field equilibrium strategies in dynamic games with a large number of players. Furthermore, we provide conditions for the convergence of the nonstationary mean-field equilibrium to the stationary one in the limit. [ABSTRACT FROM AUTHOR]

• Examined the effects of two naturalistic, game-based preschool math interventions • A CRT design examined the added value of a family math component for Head Start • Results indicated that the family math component added value to classroom math • For preschoolers age 50+ months, both interventions had significant effects • Number of math games played was significantly associated with higher math scores Differences in children's mathematics knowledge are evident at kindergarten entry, favoring children who have greater access to economic resources. Fostering preschoolers' mathematics learning at home and in classroom settings, through games and other developmentally appropriate activities, is of great interest to educators, early childhood leaders, and policymakers. This cluster randomized trial examined the effects of a naturalistic, game-based mathematics intervention implemented in Head Start classrooms and examined whether including a family math component added value. A total of 573 children (64% Hispanic; 60% multilingual) were included from 66 classrooms which were randomly assigned to Classroom Math (CM), Classroom Math + Family Math (CM+FM), or business-as-usual (BAU). Results indicated that the family math component did add value to the classroom-based intervention as CM+FM resulted in a significant positive impact on children's mathematics knowledge relative to BAU, but CM alone did not. For preschoolers age 50+ months, both interventions had significant effects on children's mathematics knowledge relative to BAU, but CM+FM had a stronger effect (d =.36). The number of math games played was significantly associated with higher mathematics scores and the number of family math mini-books returned had a significant impact on children's spring scores, over and above the number of games played. The CM+FM intervention also had a significant effect on teachers' instructional practice (d =.79). Adding a family math component to a game-based classroom intervention resulted in positive impacts for preschoolers and seems to be an effective, ecologically valid intervention that fosters early mathematical competencies. [ABSTRACT FROM AUTHOR]

Objectives: Chatbots, conversational agents that walk medical students (MS) though a clinical case, are serious games that seem to be appreciated by MS. Their impact on MS's performance in exams however was not yet evaluated. Chatprogress is a chatbot-based game developed at Paris Descartes University. It contains 8 pulmonology cases with step-by-step answers delivered with pedagogical comments. The CHATPROGRESS study aimed to evaluate the impact of Chatprogress on students' success rate in their end-term exams. Methods: We conducted a post-test randomized controlled trial held on all fourth-year MS at Paris Descartes University. All MS were asked to follow the University's regular lectures, and half of them were randomly given access to Chatprogress. At the end of the term, medical students were evaluated on pulmonology, cardiology and critical care medicine. Main outcomes measures: The primary aim was to evaluate an increase in scores in the pulmonology sub-test for students who had access to Chatprogress, compared to those who didn't. Secondary aims were to evaluate an increase in scores in the overall test (Pulmonology, Cardiology and Critical care medicine test (PCC)) and to evaluate the correlation between access to Chatprogress and overall test score. Finally, students' satisfaction was assessed using a survey. Results: From 10/2018 to 06/2019, 171 students had access to Chatprogress (the Gamers) and among them, 104 ended up using it (the Users). Gamers and Users were compared to 255 Controls with no access to Chatprogress. Differences in scores on the pulmonology sub-test over the academic year were significantly higher among Gamers and Users vs Controls (mean score: 12.7/20 vs 12.0/20, p = 0.0104 and mean score: 12.7/20 vs 12.0/20, p = 0.0365 respectively). This significant difference was present as well in the overall PCC test scores: (mean score: 12.5/20 vs 12.1/20, p = 0.0285 and 12.6/20 vs 12.1/20, p = 0.0355 respectively). Although no significant correlation was found between the pulmonology sub-test's scores and MS's assiduity parameters (number of finished games among the 8 proposed to Users and number of times a User finished a game), there was a trend to a better correlation when users were evaluated on a subject covered by Chatprogress. MS were also found to be fans of this teaching tool, asking for more pedagogical comments even when they got the questions right. Conclusion: This randomised controlled trial is the first to demonstrate a significant improvement in students' results (in both the pulmonology subtest and the overall PCC exam) when they had access to Chatbots, and even more so when they actually used it. [ABSTRACT FROM AUTHOR]

We explore whether training parents' math skills or playing number games improves children's mathematical skills. Participants were 162 parent–child dyads; 88.3% were white and children (79 female) were 4 years (M = 46.88 months). Dyads were assigned to a number game, shape game, parent‐only approximate number system training, parent‐only general trivia, or a no‐training control condition and asked to play twice weekly for 8 weeks. Children in the number game condition gained over 15% SD on an assessment of mathematical skill than did those in the no‐training control. After 8 additional weeks without training, effects diminished; however, children of parents in the ANS condition underperformed those in the no‐treatment control, which was partially explained by changes in the home numeracy environment. [ABSTRACT FROM AUTHOR]

Recreational mathematics is having something of a moment just now. III As David Singmaster notes, recreational mathematics is generally understood to refer not just to problems that are fun - most mathematicians enjoy even their deepest research problems, after all - but also to problems that are easy to understand and have some pedagogical value. Two especially prominent defenders of the pedagogical value of recreational mathematics were Lewis Carroll and Raymond Smullyan. Singmaster's books can be enjoyed either as writings to dip into when you have some free time or as books that reward careful study by anyone interested in the history of recreational mathematics. [Extracted from the article]

Little is known about manta ray population size, structure and connectivity in the Philippines. In collaboration with dive operators, non‐governmental organizations and authorities, sightings of manta rays were collated into a single national database. Using in‐water photographs and videos gathered through citizen science and dedicated research efforts, this study compiled sightings between 2004 and 2020, showing 22 separate sites throughout the archipelago with manta rays present. A total of 392 individual reef manta rays (Mobula alfredi) and 107 oceanic manta rays (Mobula birostris) were identified from the collected footage. Four specific sites in the provinces of Masbate and Palawan together hosted 89% of all identified individuals and accounted for 95% of sightings, highlighting these areas are key aggregation sites. This study also reports the movements of M. birostris within the Philippines, based on photo‐identification of three individuals moving 150 km between Cebu and Masbate. Despite the growing number of recreational divers in Daanbantayan and San Jacinto, an 80% decline in M. birostris sightings was observed at these sites. To ensure effective future conservation, it is recommended that efforts focus on the identification and protection of manta ray hotspots and migratory corridors, the creation of a sustainable tourism framework and, most important, the implementation of mitigation strategies to reduce fisheries interactions. [ABSTRACT FROM AUTHOR]

In 2020, Costa et al. answered a long-standing open question, proposed by Bodlaender in 1991: the graph coloring game is PSPACE -complete. They also proved that the greedy coloring game, introduced by Havet and Zhu in 2013, is also PSPACE -complete. In 2019, Andres and Lock proposed five variants of the graph coloring game, which were proved PSPACE -complete by Lima et al. in 2022. In this paper, we extend these variants of the graph coloring game to the greedy coloring game and prove that all of them are PSPACE -complete, even if the number of colors is the chromatic number. Moreover, based on the connected variant of the graph coloring game proposed by Charpentier et al. in 2020, we introduce the connected greedy coloring game and prove that two natural variants of this game are PSPACE -complete. Despite this, we prove that in split graphs these two variants of the connected greedy coloring game are polynomial time solvable and we characterize the split graphs for which the associated connected game Grundy numbers are the minimum possible value (the chromatic number). Finally, we also characterize the split graphs which are bad, a notion introduced by Le and Trotignon in 2018 regarding connected greedy colorings. [ABSTRACT FROM AUTHOR]

The best allocation of limited resources to activities with the aim of accomplishing the desired goal, such as maximization of profit or minimization of cost, is the focus of linear programming. The relationships between activities in linear programming models satisfy the proportionality and additivity requirements since they are linear interactions. This feature of linear programming is extended to the tourism industry which is one of the major industries in the global economy with respect to invested capital and earnings of foreign currencies. In todays era of design thinking, automation, and met averse, there is a very close margin between solutions to similar real-world problems. This is where the need and demand for fuzzy and imprecise linear programming arises. The membership functions provide the model developer the freedom to grade the imprecision as per his/her preference, thereby enabling a unique solution for each problem. While considering the tourism problem a number of factors like natural resources, people, history, culture, security, accommodation, entertainment, political stability, cost of services, tour operator, tour information, and advertisement play an important role in enhancing the sector to a large extent. Combined and classified they come under the following categories like leisure tourism, therapeutic/spa tourism, conference tourism, political tourism, sports/recreational tourism, cultural tourism, social tourism, conference tourism, recreational tourism, sports tourism, religious tourism, health tourism, etc. Each of these sectors requires careful investment on the part of the Government and other stake holders for development purpose. i.e. only a proper marketing mix will ensure a better return for the state. Taking this aspect into consideration the authors decided to introduce a hypothetical LP maximization model for the tourism industry in North East. Cost and space allocation are the constraints in the model. Among the various categories, three tourism forms (heritage, eco-tourism, and pilgrimage tourism) are considered which are used to optimize the allocation of the States marketing budget in tourism in such a way that the appropriate sector provides the greatest likelihood of producing the strongest return on investment. The maximization of profit has been done using various methods, like Werner's, Verdegay's, and Zimmermans. The authors have concluded the results based on the sensitivity analysis that has been done in the process of maximizing profit along with a maximal satisfaction level. [ABSTRACT FROM AUTHOR]

Education with science and mathematics as its major components determines the level of welfare of people and a nation. Nowadays, great attention is given to technological advancements and mathematics education. Hence, this paper explicitly discusses the use of mathematics laboratories and their implication for teaching mathematics, finding out the practices and impact on teaching mathematics and teachers' frequency of using teaching aids (manipulatives) in high schools of Mekelle zone. Manipulatives are valuable aid to teachers that can be used by analyzing students' concrete representations of mathematical concepts. In addition to this, topics like geometry and measurement are topics that are frequently taught using tools. On the contrary, solving equations, relations, and functions is rarely taught using these manipulatives. This study indicates that there is no direct correlation between teachers' teaching experience years and the use of manipulatives in their classrooms. It is, therefore, recommended that mathematics teachers should get training and workshops on the use of teaching aids (manipulatives), useful software like (geogebra, sketchpad, and other timely used technologies) and other methods of teaching mathematics in mathematics laboratories. [ABSTRACT FROM AUTHOR]

Time-relaxed sports timetables use more time slots than strictly needed, and are particularly popular in amateur (indoor) leagues. However, due to unexpected events, a considerable number of games may not be played as initially planned before the start of the tournament, leading to a potentially very different realized timetable. This study focuses on dealing with these uncertain events in time-relaxed round-robin sports timetabling, and how to mitigate their effect on the quality of the timetable. We use three quality measures to evaluate the time-relaxed timetables, namely, the games played difference index, the rest difference index and the number of cancelled games. We present several combined proactive and reactive approaches taking into account venue and team availability. Proactive strategies determine the position of time slots that are used as a buffer, while reactive strategies reschedule matches to these buffers in terms of the quality measures. [ABSTRACT FROM AUTHOR]

This article examines the reasons that mathematical schools (mathschools) have become an important and very productive phenomenon in Russian education in recent decades. A brief description of the modern model of productive education is traced back to the established tradition of teaching in mathschools, which can lead to the construction of a reproducible model of productive education not only for specialized teaching of mathematics, but also for other areas of Russian general education. [ABSTRACT FROM AUTHOR]

Health economics has long been neglected as a subset of the larger discipline of Economics and Finance. However, this could not be further from the truth. There is a large body of researchers and professionals alike that are of the consensus that extensive studying and working upon Healthcare Economics can help us avert the situation that arose in the wake of the recent COVID-19 pandemic. Applying the core principles of Health Economics to a situation like that would help avert bad outcomes. In this article, the authors begin by defining and establishing the concepts of Health Economics and then building on them. We further explain the concepts in light of the Indian Economy and Healthcare Sector and how it has seen unprecedented growth in the last decade. Furthermore, we touch on the various diseases that put the most strain on the healthcare infrastructure and what we can do to make the situation better. We also shed light on how the COVID-19 pandemic affected the Health Economics in the Indian setting and go on to elaborate how India managed to tackle it. Finally, we elaborate on what steps we can take, as researchers and healthcare professionals, to make it easier for the common man to get access to better and more economical healthcare. We determine the importance and effectiveness of data collection and processing and also how to make better research attempts to study, evaluate and process that said data. The onus falls on the academic and the healthcare professional to ensure that the true meaning of Health Economics is not reduced to a mere numbers game, but is something which is truly subjective and for the benefit of the masses. [ABSTRACT FROM AUTHOR]

The discriminant equations with the minimum number for a symmetric game are derived. By using a new version of the semi‐tensor product method based on adjacent transpositions, the analysis of symmetric games is greatly simplified. Some new necessary and sufficient conditions for symmetric games are proposed, a basis of the symmetric game space is easily calculated, and the computing complexity is achieved. Finally, two examples are displayed to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This article presents analysis results from a long-term multi-site Global Navigation Satellite System (GNSS) Radio Frequency Interference (RFI) monitoring campaign in the context of Ground Based Augmentation System (GBAS) Dual Frequency Multi Constellation (DFMC) concept operation. GBAS resilience against unintentional RFI is an important area for investigation as the ground station receivers often must operate adjacent to high-traffic roads where chances of being affected by RFI are high. To be able to develop algorithms and reaction strategies necessary to ensure continuity and availability of service, knowledge of interference signal characteristics and frequency band/bands affected, as well as relative occurrence rates between the considered frequencies and frequency combinations, is necessary. The analysis presented in the article covers the prevalence and properties of the RFI events observed on the GPSs L1 and L5 and the Galileo E1 and E5a frequency bands that are considered by the on-going DFMC GBAS concept development initiatives. Due to being spectrally adjacent, the observed event analysis is also carried out for the Galileo E5b and GLONASS G1 frequency bands. The article also addresses the issue of spectral occupancy distribution of the observed events and presents new interesting RFI event types captured during the considered monitoring period. [ABSTRACT FROM AUTHOR]