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An age-structured fish model with birth and harvesting pulses is established, where birth pulses are responsible for increasing the amount of fish due to the constant multiple placement of juveniles, and harvesting pulses describe the decrease of fish due to fishing activities. The principal eigenvalue as a threshold value depending on the harvesting and birth intensity is firstly investigated by three different ways. The asymptotic behavior of the population is fully investigated and sufficient conditions for the species to be extinct or persist are given. Numerical simulations suggest that interaction between negative harvesting intervention and positive birth perturbation decides extinction and persistence of the species. It is also shown that perturbation timing plays an important role., Comment: 19 pages,5 figures

This study deals with a piecewise $\phi^2$ scalar field theory in $(1+1)$ dimensions. The scalar field potential is designed with a triple-well shape, engendering kink solutions with asymmetric square-well linearized potentials. Thus, the localized and delocalized modes in this model can be obtained analytically in terms of transcendental equations. This allows us to explore kink-antikink and antikink-kink collisions with any desired number of localized and delocalized modes. We obtain new scenarios of resonance windows suppression, shedding light on the role of higher excited modes in kink scattering.

In order to understand how nonlocal diffusion and pulse intervention affect dynamics of species, we focus on an age-structured nonlocal diffusion model in moving and heterogeneous environment, where nonlocal diffusion describes the long range dispersal of species itself and time-periodic harvesting pulse exacting on the adult reflects human intervention. A generalized principal eigenvalue involving harvesting rate used to identify the spreading and vanishing outcomes is firstly defined and the existence of the principal eigenvalue is given under some conditions. Subsequently, properties of the generalized principal eigenvalue and the principal eigenvalue related to harvesting rate and length of habitat interval are analyzed, respectively. The criteria to governing spreading or vanishing of the species are finally investigated, with sufficient conditions for spreading-vanishing established. Our results indicate that complexities can be induced by the internal long rang dispersal and expanding capacities of species, as well as external harvesting intervention of human. Specifically, appropriate harvesting rate and expanding capacities can even change the reciprocal outcomes of species from co-existence to co-extinction., Comment: 31 pages, 1 figure

Chopsticks is a game played by two players where they start with one finger raised on each hand. On their turn, each player moves by pointing an attacking hand at one of their opponent's hands. The number of fingers on the pointed hand increases by the number of fingers on the attacking hand. If, after a move, a hand contains more than five fingers, it is removed from play. There are also other rules that allow players to move fingers from one hand to another, but we focus on this simple setup. We introduce a generalization of Chopsticks, called Simple Chopsticks, in which the players may have any number of $n$-fingered hands. We find that having more hands than your opponent is generally good, and use this fact to fully characterize the outcomes of \octopus/ in the case where the players have 2-fingered hands., Comment: 12 pages

To understand how impulsive intervention and regional evolution jointly influence the spread of faecal-oral diseases, this paper develops an impulsive faecal-oral model in a periodically evolving environment. The well-posedness of the model is first checked. Then, the existence of the principal eigenvalue dependent on impulse intensity and evolving rate is proved based on Krein-Rutman theorem. With the help of this value, the threshold dynamical behaviours of the model are explored. More importantly, this paper also derives the monotonicity of the principal eigenvalue with respect to initial region and impulse intensity and estimates the principal eigenvalue in some special cases. Finally, numerical simulations are used to verify the correctness of the theoretical results and to explore the impact of regional evolution rate on the spread of the diseases. Our research shows that large impulsive intensity $1-g'(0)$ and small evolving rate $\rho(t)$ play a positive role in the prevention and control of the diseases., Comment: 29 pages, 8 figures

Purpose: Multicriteria decision analysis (MCDA) has become increasingly essential for decision-making in complex environments. In response to this need, the pyDecision library, implemented in Python and available at https://bit.ly/3tLFGtH, has been developed to provide a comprehensive and accessible collection of MCDA methods. Methods: The pyDecision offers 70 MCDA methods, including AHP, TOPSIS, and the PROMETHEE and ELECTRE families. Beyond offering a vast range of techniques, the library provides visualization tools for more intuitive results interpretation. In addition to these features, pyDecision has integrated ChatGPT, an advanced Large Language Model, where decision-makers can use ChatGPT to discuss and compare the outcomes of different methods, providing a more interactive and intuitive understanding of the solutions. Findings: Large Language Models are undeniably potent but can sometimes be a double-edged sword. Its answers may be misleading without rigorous verification of its outputs, especially for researchers lacking deep domain expertise. It's imperative to approach its insights with a discerning eye and a solid foundation in the relevant field. Originality: With the integration of MCDA methods and ChatGPT, pyDecision is a significant contribution to the scientific community, as it is an invaluable resource for researchers, practitioners, and decision-makers navigating complex decision-making problems and seeking the most appropriate solutions based on MCDA methods., Comment: 23 pages, 2 figures

This paper deals with an impulsive degenerate logistic model, where pulses are introduced for modeling interventions or disturbances, and degenerate logistic term may describe refugees or protections zones for the species. Firstly, the principal eigenvalue depending on impulse rate, which is regarded as a threshold value, is introduced and characterized. Secondly, the asymptotic behavior of the population is fully investigated and sufficient conditions for the species to be extinct, persist or grow unlimitedly are given. Our results extend those of well-understood logistic and Malthusian models. Finally, numerical simulations emphanzise our theoretical results highlighting that medium impulse rate is more favorable for species to persist, small rate results in extinction and large rate leads the species to an unlimited growth., Comment: 21 pages,9 figures

There are many combinatorial games in which a move can terminate the game, such as a checkmate in chess. These moves give rise to diverse situations that fall outside the scope of the classical normal play structure. To analyze these games, an algebraic extension is necessary, including infinities as elements. In this work, affine normal play, the algebraic structure resulting from that extension, is analyzed. We prove that it is possible to compare two affine games using only their forms. Furthermore, affine games can still be reduced, although the reduced forms are not unique. We establish that the classical normal play is order-embedded in the extended structure, constituting its substructure of invertible elements. Additionally, as in classical theory, affine games born by day n form a lattice with respect to the partial order of games., Comment: 68 pages, 24 figures

The growth of distributed renewable energy in the electrical grid presents challenges to its stability and quality. To address this at the local level, flexibility energy strategies emerge as an innovative technique. However, managing these strategies in residential areas becomes complex due to the unique characteristics of each prosumer. A major challenge lies in managing communication among diverse devices with different protocols. To address these issues, a comprehensive framework is designed and implemented to facilitate prosumers' integration in flexibility strategies, addressing communication at various levels. The effectiveness of the proposed framework is demonstrated through its implementation in a real smart home environment with diverse devices. The framework enables seamless integration and communication between IoT devices and IEC 61,850-compliant power devices. This research presents a novel approach to address the challenges of managing flexibility strategies in residential areas, providing a practical solution for prosumers to actively participate in optimizing energy consumption and enhancing the stability and quality of the electricity system amidst the growing integration of distributed renewable energy.

The class of Poset Take-Away games includes many interesting and difficult games. Playing on an $n$-dimensional positive quadrant (the origin being the bottom of the poset) gives rise to nim, wythoff's nim and chomp. These are impartial games. We introduce a partisan game motivated by chomp and the recent chocolate-bar version. Our game is played on a chocolate bar with alternately flavored pieces (or a checkerboard). We solve this game by showing it is equivalent to blue-red hackenbush strings. This equivalence proves that the values of game are numbers and it gives an algorithm for optimal play when there is more than one chocolate bar. The checkerboard interpretation leads to many natural questions., Comment: 21 pages, 9 figures

In order to understand how impulsive interventions and environmental perturbations affect dynamics of competitors, we focus on a diffusive competition model with free boundaries and periodic pulses in a temporally heterogeneous environment with upward or downward advection. The dependence of the principal eigenvalue of corresponding periodic impulsive eigenvalue problem on advection rates, habitat sizes and pulses is investigated, which gives precise conditions that classify the dynamics into four types of competition outcomes including coexistence, co-extinction, two different competition exclusions for small or negative advection rates. Some sufficient conditions on pulses or initial habitats for species spreading or vanishing, and spreading speeds are then established. Our results not only extend the existing ones to the case with pulses, but also reveal the effects of human and natural factors, that is, impulsive interventions factors including positive or negative impulsive effect, pulse intensity and timing can significantly affect and alter the competition outcomes. The different performances of the superior and inferior affected by environmental perturbations are also reflected in the simulations., Comment: 43 pages, 6 figures

Large numbers of radiographic images are available in knee radiology practices which could be used for training of deep learning models for diagnosis of knee abnormalities. However, those images do not typically contain readily available labels due to limitations of human annotations. The purpose of our study was to develop an automated labeling approach that improves the image classification model to distinguish normal knee images from those with abnormalities or prior arthroplasty. The automated labeler was trained on a small set of labeled data to automatically label a much larger set of unlabeled data, further improving the image classification performance for knee radiographic diagnosis. We developed our approach using 7,382 patients and validated it on a separate set of 637 patients. The final image classification model, trained using both manually labeled and pseudo-labeled data, had the higher weighted average AUC (WAUC: 0.903) value and higher AUC-ROC values among all classes (normal AUC-ROC: 0.894; abnormal AUC-ROC: 0.896, arthroplasty AUC-ROC: 0.990) compared to the baseline model (WAUC=0.857; normal AUC-ROC: 0.842; abnormal AUC-ROC: 0.848, arthroplasty AUC-ROC: 0.987), trained using only manually labeled data. DeLong tests show that the improvement is significant on normal (p-value<0.002) and abnormal (p-value<0.001) images. Our findings demonstrated that the proposed automated labeling approach significantly improves the performance of image classification for radiographic knee diagnosis, allowing for facilitating patient care and curation of large knee datasets., Comment: This is the preprint version

In Combinatorial Game Theory, short game forms are defined recursively over all the positions the two players are allowed to move to. A form is decomposable if it can be expressed as a disjunctive sum of two forms with smaller birthday. If there are no such summands, then the form is indecomposable. The main contribution of this document is the characterization of the indecomposable nimbers and the characterization of the indecomposable numbers. More precisely, a nimber is indecomposable if and only if its size is a power of two, and a number is indecomposable if and only if its absolute value is less or equal than one., Comment: 23 pages

Bibliometric and Scientometric analyses offer invaluable perspectives on the complex research terrain and collaborative dynamics spanning diverse academic disciplines. This paper presents pyBibX, a python library devised to conduct comprehensive bibliometric and scientometric analyses on raw data files sourced from Scopus, Web of Science, and PubMed, seamlessly integrating state of the art AI capabilities into its core functionality. The library executes a comprehensive EDA, presenting outcomes via visually appealing graphical illustrations. Network capabilities have been deftly integrated, encompassing Citation, Collaboration, and Similarity Analysis. Furthermore, the library incorporates AI capabilities, including Embedding vectors, Topic Modeling, Text Summarization, and other general Natural Language Processing tasks, employing models such as Sentence-BERT, BerTopic, BERT, chatGPT, and PEGASUS. As a demonstration, we have analyzed 184 documents associated with multiple-criteria decision analysis published between 1984 and 2023. The EDA emphasized a growing fascination with decision-making and fuzzy logic methodologies. Next, Network Analysis further accentuated the significance of central authors and intra-continental collaboration, identifying Canada and China as crucial collaboration hubs. Finally, AI Analysis distinguished two primary topics and chatGPT preeminence in Text Summarization. It also proved to be an indispensable instrument for interpreting results, as our library enables researchers to pose inquiries to chatGPT regarding bibliometric outcomes. Even so, data homogeneity remains a daunting challenge due to database inconsistencies. PyBibX is the first application integrating cutting-edge AI capabilities for analyzing scientific publications, enabling researchers to examine and interpret these outcomes more effectively., Comment: 30 pages, 12 figures, 6 tables

Combinatorial Game Theory typically studies sequential rulesets with perfect information where two players alternate moves. There are rulesets with {\em entailing moves} that break the alternating play axiom and/or restrict the other player's options within the disjunctive sum components. Although some examples have been analyzed in the classical work Winning Ways, such rulesets usually fall outside the scope of the established normal play mathematical theory. At the first Combinatorial Games Workshop at MSRI, John H. Conway proposed that an effort should be made to devise some nontrivial ruleset with entailing moves that had a complete analysis. Recently, Larsson, Nowakowski, and Santos proposed a more general theory, {\em affine impartial}, which facilitates the mathematical analysis of impartial rulesets with entailing moves. Here, by using this theory, we present a complete solution for a nontrivial ruleset with entailing moves., Comment: 21 pages, 5 figures

In recent years, high-speed navigation and environment interaction in the context of aerial robotics has become a field of interest for several academic and industrial research studies. In particular, Search and Intercept (SaI) applications for aerial robots pose a compelling research area due to their potential usability in several environments. Nevertheless, SaI tasks involve a challenging development regarding sensory weight, on-board computation resources, actuation design and algorithms for perception and control, among others. In this work, a fully-autonomous aerial robot for high-speed object grasping has been proposed. As an additional sub-task, our system is able to autonomously pierce balloons located in poles close to the surface. Our first contribution is the design of the aerial robot at an actuation and sensory level consisting of a novel gripper design with additional sensors enabling the robot to grasp objects at high speeds. The second contribution is a complete software framework consisting of perception, state estimation, motion planning, motion control and mission control in order to rapid- and robustly perform the autonomous grasping mission. Our approach has been validated in a challenging international competition and has shown outstanding results, being able to autonomously search, follow and grasp a moving object at 6 m/s in an outdoor environment

We discuss the existence of multiple positive solutions leading to the occurrence of an S-shaped bifurcation curve to the equations of the form $$ -\Delta_p u= f(\mu,\lambda, u)~ \mbox{in} ~\Omega \subset \mathbb{R}^N $$ where $\Delta_p$ is a $p$-Laplacian, $p>1$, $N\geq 1$, $\mu, \lambda \in \mathbb{R}$. We deal with relatively unexplored cases when $f(\mu,\lambda, u)$ is non-Lipschitz at $u=0$, $f(\mu,\lambda, 0) = 0 $ and $ f(\mu,\lambda, u) <0$, $u \in (0,r)$, for some $r<+\infty$. We develop the nonlinear generalized Rayleigh quotients method to find a range of parameters where the equation may have distinct branches of positive solutions. As a consequence, applying the Nehari manifold method and the mountain pass theorem, we prove that the equation for some range of values $\mu, \lambda$, has at least three positive solutions with two linearly unstable solutions and one linearly stable. The results evidence that the bifurcation curve is S-shaped and exhibits the so-called dual cusp catastrophe which is characterized by the fact that the corresponding dynamic equation has stable states only within the cusp-shaped region in the control plane of parameters. Our results are new even in the one-dimensional case and $p=2$., Comment: 25 pages, 4 figures

In this paper we are concerned with existence of positive solutions for a Schr\"odinger-Maxwell system with singular or strongly-singular terms. We overcome the difficulty given by the singular terms through an approximation scheme and controlling the approximated sequences of solutions with suitable barriers from above and from below. Besides this, in some particular case, we show that the unique energy solution of the singular system is a saddle point of a suitable functional.