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Quantum-chemistry methods in the time domain with Gaussian basis sets are increasingly used to compute high-harmonic generation (HHG) spectra of atomic and molecular systems. The quality of these approaches is limited by the accuracy of Gaussian basis sets to describe continuum energy states. In the literature, optimal-continuum Gaussian basis sets have been proposed: Kaufmann et al. [J. Phys. B: At., Mol. Opt. Phys. 22, 2223 (1989)], Woźniak et al. [J. Chem. Phys. 154, 094111 (2021)], Nestmann and Peyerimhoff [J. Phys. B: At., Mol. Opt. Phys. 23, L773 (1990)], Faure et al. [Comput. Phys. Commun. 144, 224 (2002)], and Krause et al. [J. Chem. Phys. 140, 174113 (2014)]. In this work, we have compared the performances of these basis sets to simulate HHG spectra of H atom at different laser intensities. We have also investigated different strategies to balance basis sets with these continuum functions, together with the role of angular momentum. To quantify the performance of the different basis sets, we introduce local and global HHG descriptors. Comparisons with the grid and exact calculations are also provided. [ABSTRACT FROM AUTHOR]

Vector inversion generators or spiral generators are compact, high voltage pulse generators consisting of a pair of conducting foils wound in a spiral and a switch. We developed an improved analytical model predicting the time evolution of the output voltage of such spiral generators. Our model (i) takes into account that the current in the switch results from the current on active and passive waveguides and (ii) takes into account the losses of the conductor in equations describing the propagation of voltage and current pulses in both waveguides. The model is compared to experimental results involving different input switches and at different temperatures to investigate the influence of resistive losses on the output voltage. The model is further developed to obtain the time evolution of the current in the switch. Our model is then used to predict the amplitude of the first two peaks of the oscillatory response of spiral generators as a function of a set of dimensionless parameters. [ABSTRACT FROM AUTHOR]

We present a method to compute the photoionization spectra of atoms and molecules in linear-response, time-dependent density functional theory. The electronic orbital variations corresponding to ionized electrons are expanded on a basis set of delocalized functions, obtained as the solution of the inhomogeneous Helmholtz equation, with gaussian basis set functions as the right-hand side. The resulting scheme is able to reproduce the photoionization spectra without any need for artificial regularization or localization. We demonstrate that this Green's function-based approach is able to produce accurate spectra for semilocal exchange-correlation functionals, even using relatively small standard gaussian basis sets. [ABSTRACT FROM AUTHOR]

We investigate, in this paper, the Gaussian (G) function with odd powers of r, rxaybzc exp(−αr2), called the r-Gaussian or simply the rG function. The reason we investigate this function here is that it is generated as the elements of the complement functions (cf's) when we apply the free complement (FC) theory for solving the Schrödinger equation to the initial functions composed of the Gaussian functions. This means that without the rG functions, the Gaussian set of functions cannot produce the exact solutions of the Schrödinger equation, showing the absolute importance of the rG functions in quantum chemistry. Actually, the rG functions drastically improve the wave function near the cusp region. This was shown by the applications of the present theory to the hydrogen and helium atoms. When we use the FC-sij theory, in which the inter-electron function rij is replaced with its square s i j = r i j 2 that is integrable, we need only one- and two-electron integrals for the G and rG functions. The one-center one- and two-electron integrals of the rG functions are always available in a closed form. To calculate the integrals of the multi-centered rG functions, we proposed the rG-NG expansion method, in which an rG function is expanded by a linear combination of the G functions. The optimal exponents and coefficients of this expansion were given for N = 2, 3, 4, 5, 6, and 9. To show the accuracy and the usefulness of the rG-NG method, we applied the FC-sij theory to the hydrogen molecule. [ABSTRACT FROM AUTHOR]

In this paper we consider decision functions in which voters have three options and one of them is abstention or indifference and the output is a binary decision between two alternatives so that a tie is not possible. These resolute decision functions appear frequently in grading, in some sport competitions, in voting situations in which the status quo is put to the vote, etc. It is a more restricted case of the voting context considered in the seminal article by Kenneth May on decision functions, published in Econometrica in 1952, because the output set does not admit a tie. Among these resolute decision functions we focus on the study of majority functions, in which the number of favorable votes to an alternative must be strictly greater than the number of votes against it. This work provides an axiomatic characterization for the set of majority functions and for the relative majority function with status quo bias. Both characterizations are based on weaker versions of neutrality. Other complementary characterizations are also provided. [ABSTRACT FROM AUTHOR]

The study on how equilibria behave when perturbations occur in the data of a game is a fundamental theme, since actions and payoffs of the players may be affected by uncertainty or trembles. In this paper, we investigate the asymptotic behavior and the variational stability of the subgame perfect Nash equilibrium (SPNE) in one-leader one-follower Stackelberg games under perturbations both of the action sets and of the payoff functions. To pursue this aim, we consider a general sequence of perturbed Stackelberg games and a set of assumptions that fit the usual types of perturbations. We study if the limit of SPNEs of the perturbed games is an SPNE of the original game and if the limit of SPNE-outcomes of perturbed games is an SPNE-outcome of the original game. We fully positively answer when the follower's best reply correspondence is single-valued. When the follower's best reply correspondence is not single-valued, the answer is positive only for the SPNE-outcomes; whereas the answer for SPNEs may be negative, even if the perturbation does not affect the sets and affects only one payoff function. However, we show that under suitable non-restrictive assumptions it is possible to obtain an SPNE starting from the limit of SPNEs of perturbed games, possibly modifying the limit at just one point. [ABSTRACT FROM AUTHOR]

This paper deals with α -core of set payoffs games with finitely many players and finite coalition α -core of set payoffs games with infinitely many players. We present an existence theorem of α -core of set payoffs games with finitely many players. By virtue of finite intersection property, we also establish an existence theorem of finite coalition α -core of set payoffs games with infinitely many players. Besides, we obtain some stability results of solution mapping of α -core of set payoffs games, where set payoff functions and action sets of agents involve perturbed parameters. Moreover, as applications, we obtain the corresponding results for α -core of vector payoffs games. [ABSTRACT FROM AUTHOR]

A profile π = (x 1 , x 2 , ... , x k) of length k in a connected graph G is a sequence of vertices in G with possible repetitions of vertices. A median x of a profile π in G is a vertex that minimizes the remoteness value, that is, the sum of the distances from x to the elements x i in π is minimized. The median function output the set of medians (denoted as M e d (π)) of π , for every profile π in G. It is one of the basic models for the location of a desirable facility in a network. The median function on graphs is well studied. For instance, it has been characterized axiomatically by simple axioms on trees, hypercubes, median graphs, cocktail-party graphs, and complete graphs minus a matching. In this paper, we study the median sets and median function of block graphs, an immediate generalization of trees. We determine the median sets of all types of profiles and we obtain two sets of axiomatic characterizations of the median function on block graphs. [ABSTRACT FROM AUTHOR]

The axiomatic theory of ordinary differential equations, owing to its simplicity, can provide a useful framework to describe various generalizations of dynamical systems. In this study, we consider how dynamical properties can be generalized to this setting. First, we study the generalizations of dynamical properties, such as invariance and limit sets and show that compact weakly invariant sets can be characterized in terms of the corresponding shift-invariant sets in the function space. This result enables us to consider weakly invariant sets in terms of shift-invariant sets. Next, we compare the axiomatic theory of ODE with other formalisms of generalized dynamical systems, namely generalized semiflow and multivalued semigroup. Finally, we introduce the notion of invariant measures and show that we can generalize classical results, such as Poincaré recurrence theorem. [ABSTRACT FROM AUTHOR]

This study presents a methodology for designing the periodic unit cell (PUC) to optimize the sound absorption properties of rigid porous materials using Bayesian optimization (BO). BO is a machine learning algorithm proficient in identifying the global optimum of a 'black-box' objective function with a limited set of observations. This BO methodology was applied in the design of two distinct types of PUCs: a body-centered cubic structure and a Kelvin cell structure. To verify the efficiency and robustness of the proposed approach, the optimization process was executed multiple times, each with varying initial random samples. In the case of the body-centered cubic design, the optimal PUC was ascertained by examining a mere 2.08 % of the total candidate designs; for the Kelvin cell design, this value was 4.33 %. The effectiveness of the BO-driven approach was validated by comparing it with random sampling method. [ABSTRACT FROM AUTHOR]

Core homeostatic and activation signatures have been defined for mammalian microglia in new transcriptomic and functional studies. Microglia respond to changes in the homeostatic environment using similar signal modules during neurodevelopment as those seen for different types of neurodegenerative diseases. Danger signals present in neurodevelopment often mirror those encountered by microglia in neurodegenerative conditions. The mechanisms microglia utilize to sense their environment (sensome) are akin to those defined in other tissue-resident macrophage populations. Convergent versus divergent responses among microglia might reflect differences in expressed/engaged receptors, microenvironment, and immunological memory. Interest in microglia is surging with increased recognition that these cells significantly influence brain function and neurologic disease pathogenesis. When aiming to treat different neurologic diseases, a fine-tuned approach to enhance the protective abilities of microglia while dampening destructive off-target effects is an attractive and compelling one. Understanding the receptors, downstream signaling, and functional outputs that microglia employ throughout a healthy lifespan and in diverse disease states (their toolkit) is essential for harnessing their therapeutic potential. After decades of being overlooked, a recent wave of studies have explored the roles of microglia in brain health and disease. Microglia perform important physiological functions to set up and maintain proper neural network functions, as well as orchestrate responses to toxic stimuli to limit harm. Many microglial transcriptional programs, extracellular sensing molecules, and functional outputs are seen throughout life. A stark example is the similarity of microglial responses to stressors during neurodevelopment and neurodegeneration. The same themes often match that of other tissue-resident macrophages, presenting an opportunity to apply known concepts as therapeutics develop. We argue that microglial signaling during development and neurologic disease overlap with one another and with other tissue-resident macrophage pathways, in part due to similar sensed stimuli and a conserved sensome of receptors and signaling molecules, akin to a toolkit. [ABSTRACT FROM AUTHOR]

We investigate shift invariant subspaces within the realm of analytic functions in the unit disc, whose radial growth is determined by a majorant w$w$. Our main result offers a complete characterization of the shift invariant subspaces generated by Nevanlinna class functions within the aforementioned class of growth spaces. Our description is expressed in terms of a certain w$w$‐entropy condition, which naturally arises in connection with boundary zero sets for analytic functions in the unit disc, having modulus of continuity not exceeding w$w$ on the unit circle. Furthermore, we utilize our findings to establish a structural theorem on approximation in model spaces. [ABSTRACT FROM AUTHOR]

Bergweiler and Kotus gave sharp upper bounds for the Hausdorff dimension of the escaping set of a meromorphic function in the Eremenko–Lyubich class, in terms of the order of the function and the maximal multiplicity of the poles. We show that these bounds are also sharp in the Speiser class. We apply this method also to construct meromorphic functions in the Speiser class with preassigned dimensions of the Julia set and the escaping set. [ABSTRACT FROM AUTHOR]

The definitions provided by the authors of the current study are offered together with a discussion of the recent advances that they have contributed. We begin with an introduction to fn-Fr#bϱN, which includes the concepts of closed and open sets. We explore characteristics in fn-βd#bϱN and fn-℮bϱN(ϱN), and provide an idea of obtained results by adding the notion of FNbϱNOS and analyzing a few of their properties in fnts. We've researched the contrasts between the derived, exterior, and frontier notions that are provided. We also looked at the ideas of 〈TbϱN〉 C-functions and Γs-segregated functions and examined and determined the traits. [ABSTRACT FROM AUTHOR]

This work presents analyses of interfacial crack in piezoelectrics bimaterial plate under electromechanical loading environment by extended isogeometric analysis (XIGA) approach using Bézier extraction of NURBS. Asymptotic crack–tip branch functions and discontinuous Heaviside function are implemented for local enrichment in the approximation of isogeometric analysis for capturing singularity at cracktip and discontinuity across surfaces of a crack. Bézier extraction of NURBS–based basis functions are implemented in discretization of domain for approximating both unknown field solution and geometries. The Bézier extraction operation decomposes the NURBS basis functions into a set of linear combination of Bernstein polynomials and a set of C 0 –continuity Bézier elements. Domain–form interaction integral is implemented to obtain generalized fracture parameters. To assess the robustness and accuracy in results obtained from XIGA, numerical results are first validated from analytical ones and then additionally, few numerical problems are solved for calculating the fracture parameters in terms of normalized intensity factors with respect to shear loads, electrical loads, crack orientation angle and angle of polarization. [ABSTRACT FROM AUTHOR]

The combination of machine learning and topology optimization has preliminarily mitigated the enormous computational costs incurred during optimization processes. Its powerful design capabilities are warmly welcomed by many scholars, but this strategy still faces many problems, such as unclear structural boundaries and high dependence on big data. Here, we propose a new machine learning topology optimization paradigm that learns the mapping relationship between the initial and optimized Level set functions in the infinite-dimensional function space under the Fourier neural operator to truly parameterize the structural model and its mechanical information, thereby achieving purely data-driven topology optimization. A base model trained under the proposed approach could obtain a topological structure with clear and smooth structural boundaries within 0.4 seconds, making it faster than traditional methods by tens of times. In addition, a lightweight retraining strategy under the base model was proposed. Four additional numerical examples were used to demonstrate that this strategy requires only 100 or 200 new samples and 3-6 seconds of retraining time to attain prediction capabilities under different boundary conditions, different meshes (resolution), various initial level set functions, and multiple loads. In addition, we discussed all the experiments and found that most of the mechanical properties of the results were close to the ground truths, while some results were even better than those of the traditional method. Although we only used the maximum structural stiffness as an example, this method can be extended to different objective functions. • FNO-based topology optimization framework: faster and more powerful. • Purely data-driven TO of parameterized structures and their mechanical models. • A lightweight retraining strategy for attaining various predictive capabilities. • Instantly predicting topological structure with clear and smooth boundaries. • The predicted structure has high accuracy in terms of mechanical properties and volume. [ABSTRACT FROM AUTHOR]

This paper presents a multiple material-phase level-set approach for acoustic full-waveform inversion in the time domain. By using a single level set (LS) function, several level values are used to define virtual boundaries between material phases with different (and known) wave propagation velocities. The aim of the proposed approach is to provide a suitable framework to identify multiple/nested inclusions or a finite number of almost homogeneous sedimentary layers with sharp interfaces between them. The use of a single LS function provides a significant reduction in the number of variables to be identified, when compared with the usual multi-material phase approaches defined by multiple functions, especially for problems with a high number of degrees of freedom. Numerical experiments show satisfactory results in identifying simultaneously different interfaces. Cases with and without inverse crime are evaluated, showing that the approach is reasonably robust in dealing with such a condition. [ABSTRACT FROM AUTHOR]

Risk assessment lies at the core of decision making practices, relying on the likelihood of failure incidents and their consequential impacts integrated through a set of decision rules. The incorporation of fuzzy inference systems (FIS) into risk assessment has been proven to elevate the management and sustainability of infrastructures by reducing uncertainties in decision making and mimicking human decisions. Its parameters, primarily the fuzzy sets, are conventionally defined heuristically to align with the visions and objectives of decision makers or through clustering methods if data are available. However, utilizing these methods is insufficient for the comprehensive adoption or finetuning of input-output relationships, and it does not adequately address the incorporation of future changes in decision makers' opinions due to its inability to self train. To overcome this challenge, a Mamdani-based neurofuzzy system is proposed and modified for best practice in risk assessment, and a framework is developed for compiling the required training data set. Additionally, modifications in the training process include adding Lagrange equality constraints to the objective function and testing different optimizers to maintain the fuzzy logic and reduce the computational cost, respectively. The validation of the model's ability to learn the knowledge base and parameters of fuzzy set membership functions was conducted through training simulation on generic data developed from a predefined knowledge base, as explained in a case study. The data serve as an idealization or simulation of any risk data set that can be generated using the proposed framework. The model has confirmed its ability to learn the knowledge base from which the data are generated and the corresponding parameters of membership functions toward the comprehensive adoption of input-output relationships. This emphasizes the model's capability to learn the knowledge base from any risk data set developed using the proposed framework. Also, results have shown that the added constraints control the training process efficiently by maintaining proper interactions among fuzzy sets membership functions satisfying fuzzy logic; additionally, the Adam (adaptive momentum estimation) optimizer has reduced the training computational cost by more than 99%. Finally, to explain and validate the flexibility of the neurofuzzy model in risk assessment in adopting changes in the FIS hyperparameters and rules, the model was retrained after inducing three independent possible changes to the decision rules and the fuzzy sets. The model has proved its ability to grasp diverse decision maker requirements, giving more flexibility and broader implementation of FIS in risk assessment. [ABSTRACT FROM AUTHOR]

All parameters in structural vector autoregressive (SVAR) models are locally identified when the structural shocks are independent and follow non‐Gaussian distributions. Unfortunately, standard inference methods that exploit such features of the data for identification fail to yield correct coverage for structural functions of the model parameters when deviations from Gaussianity are small. To this extent, we propose a locally robust semiparametric approach to conduct hypothesis tests and construct confidence sets for structural functions in SVAR models. The methodology fully exploits non‐Gaussianity when it is present, but yields correct size/coverage for local‐to‐Gaussian densities. Empirically, we revisit two macroeconomic SVAR studies where we document mixed results. For the oil price model of Kilian and Murphy (2012), we find that non‐Gaussianity can robustly identify reasonable confidence sets, whereas for the labor supply–demand model of Baumeister and Hamilton (2015) this is not the case. Moreover, these exercises highlight the importance of using weak identification robust methods to assess estimation uncertainty when using non‐Gaussianity for identification. [ABSTRACT FROM AUTHOR]

This study investigates the pragmatic functions of the idiomatic expression Tamam (lit. 'complete') as used by university students who speak Jordanian Arabic (JA). To this end, the researchers developed an electronic questionnaire that contained 14 different situations/contexts, each illustrating one pragmatic function as identified and determined by the researchers. The questionnaire was distributed electronically via the WhatsApp application to 164 BA Jordanian students at The University of Jordan. The students were requested to pass intuitive judgements on the acceptability of these situations and related functions. The results showed that nine of the proposed functions were accepted by 70 per cent or more of the subjects, while five were accepted by 51-68 per cent. The former set of functions included expressing approval, seeking confirmation, showing understanding, expressing appreciation, showing joy and pleasure, showing tolerance, expressing sadness and submission, reassuring, and checking the attention of the addressee. The latter included expressing dissatisfaction, ending a conversation and expressing impatience, ridiculing/mocking, threatening, and expressing shock and disappointment. The study recommends that future research may examine the acceptability of such scenarios and functions among older generations (45+) with the aim of comparing the two aforementioned groups. Future research may also investigate the pragmatic functions of other idiomatic expressions in JA and other Arabic dialects. [ABSTRACT FROM AUTHOR]

There has been increasing interest in the effects of note taking in second language (L2) research. However, no meta-analysis has been conducted to examine the relationship between note taking and learning through exposure to L2 input. We retrieved 28 effect sizes from 21 studies (N = 1992) to explore the overall effects of note taking as well as to examine the extent to which the effectiveness of note taking is likely to vary as a function of a set of potential moderators (i.e., learner variables, treatment variables, note-taking features, learning target, and measurement type). Results revealed that note taking had a small to medium positive overall effect on learning through exposure to L2 input (g = 0.56, 95% CI: 0.24–0.88). Subsequent moderator analyses revealed that variability in the size of note-taking effects across studies was explained by learner variables (context, region, orthographic scripts, institutional level), treatment variables (mode of input, material type), note-taking features (note-taking behavior, number of note-taking sessions, provision and type of note-taking strategy instruction, total length of instruction, opportunity to review notes), learning target, and measurement type. Based on the obtained findings, teachers are recommended to incorporate note taking in L2 classrooms. Pedagogical suggestions and directions for future research are also provided. [ABSTRACT FROM AUTHOR]

We express the fundamental properties of commutative polygroups (also known as canonical hypergroups) in category-theoretic terms, over the category Set formed by sets and functions. For this, we employ regularity as well as the monoidal structure induced on the category Rel of sets and relations by cartesian products. We highlight how our approach can be generalised to any regular category. In addition, we consider the theory of partial multirings and find fully faithful functors between certain slice or coslice categories of the category of partial multirings and other categories formed by well-known mathematical structures and their morphisms. [ABSTRACT FROM AUTHOR]

This paper is dedicated to the rigorous numerical analysis of a Multiscale Finite Element Method (MsFEM) for the Stokes system, when dealing with highly heterogeneous media, as proposed in B.P. Muljadi et al., Non-conforming multiscale finite Element method for Stokes flows in heterogeneous media. Part Ⅰ: Methodologies and numerical experiments, SIAM MMS (2015), 13(4) 1146-–1172. The method is in the vein of the classical Crouzeix-Raviart approach. It is generalized here to arbitrary sets of weighting functions used to enforce continuity across the mesh edges. We provide error bounds for a particular set of weighting functions in a periodic setting, using an accurate estimate of the homogenization error. Numerical experiments demonstrate an improved accuracy of the present variant with respect to that of Part Ⅰ, both in the periodic case and in a broader setting. [ABSTRACT FROM AUTHOR]

In this paper we introduce a class of one dimensional non-centered minimal operator m ~ Φ associated to a function Φ , which covers the usual minimal operator. We establish the boundedness of m ~ Φ : BV (R) → BV (R) under a more restrictive condition on Φ . Here BV (R) is the set of functions of bounded variation defined on R . In the discrete setting, we prove the discrete minimal operator is bounded and continuous from BV (Z) to itself under a more restrictive condition on Φ . [ABSTRACT FROM AUTHOR]

Statistical analysis of samples of the orbits of celestial bodies is complicated by the fact that the Keplerian orbit is a multidimensional object, the coordinate representation of which non-linearly depends on the choice of orbital elements. In this work, using the construction of the Fréchet mean, concepts of mean orbit and dispersion of the orbit family are introduced, consistent with the distance function on the orbit set. The introduced statistical characteristics serve as analogues of sample mean and variance of a one-dimensional random variable. Exact formulas for calculating the elements of mean orbits and dispersion quantities with respect to two metrics on the orbit space are derived. For a large sample of meteoroid orbits from the Geminid stream, numerical simulations of orbit evolution over 20 000 yr in the past were conducted. By analysing the dependency of statistical characteristics on time, estimates for the age of the stream and the gas outflow velocity are obtained under the assumption of the birth of the Geminids due to the rapid destruction of the cometary nucleus. The estimate of the age of the stream lies in the interval from 1200 to 2400 yr, and the speed of gas outflow at perihelion should have been more than 1.2 km s−1. [ABSTRACT FROM AUTHOR]

Controlled cell death is essential for the regulation of the immune system and plays a role in pathogen defense. It is often altered in pathogenic conditions such as cancer, viral infections and autoimmune diseases. The Fas receptor and its corresponding membrane‐bound ligand (FasL) are part of the extrinsic apoptosis pathway activated in these cases. A soluble form of FasL (sFasL), produced by ectodomain shedding, displays a diverse but still elusive set of non‐apoptotic functions and sometimes even serves as a pro‐survival factor. To gather more knowledge about the characteristics of this protein and the impact N‐glycosylations may have, access to homogeneous posttranslationally modified variants of sFasL is needed. Therefore, we developed a flexible strategy to obtain such homogeneously N‐glycosylated variants of sFasL by applying chemical protein synthesis. This strategy can be flexibly combined with enzymatic methods to introduce more complex, site selective glycosylations. [ABSTRACT FROM AUTHOR]

The aim of this study is to examine certain open three-point Newton–Cotes-type inequalities for differentiable generalized s -convex functions on a fractal set. To begin, we introduce a novel parametrized identity involving the relevant formula, which yields various new findings as well as previously established ones. Finally, an example is given to demonstrate the accuracy of the new results and their graphical depiction. Moreover, we emphasize the applications of the results obtained. [ABSTRACT FROM AUTHOR]

Graphs are a powerful tool for solving various mathematical problems. One such task is the representation of discrete structures. Combinatorial generation methods make it possible to obtain algorithms that can create discrete structures with specified properties. This article is devoted to issues related to the construction of such combinatorial generation algorithms for a wide class of directed lattice paths. The main method used is based on the representation of a given combinatorial set in the form of an AND/OR tree structure. To apply this method, it is necessary to have an expression for the cardinality function of a combinatorial set that satisfies certain requirements. As the main result, we have found recurrence relations for enumerating simple directed lattice paths that satisfy the requirements of the applied method and have constructed the corresponding AND/OR tree structure. Applying the constructed AND/OR tree structure, we have developed new algorithms for ranking and unranking simple directed lattice paths. Additionally, the obtained results were generalized to the case of directed lattice paths. [ABSTRACT FROM AUTHOR]

Graph pebbling is a combinatorial game played on an undirected graph with an initial configuration of pebbles. A pebbling move consists of removing two pebbles from one vertex and placing one pebble on an adjacent vertex. The pebbling number of a graph is the smallest number of pebbles necessary such that, given any initial configuration of pebbles, at least one pebble can be moved to a specified root vertex. Recent lines of inquiry apply computational techniques to pebbling bound generation and improvement. Along these lines, we present a computational framework that produces a set of tree strategy weight functions that are capable of proving pebbling number upper bounds on a connected graph. Our mixed-integer linear programming approach automates the generation of large sets of such functions and provides verifiable certificates of pebbling number upper bounds. The framework is capable of producing verifiable pebbling bounds on any connected graph, regardless of its structure or pebbling properties. We apply the model to the 4th weak Bruhat to prove π (B 4) ≤ 66 and to the Lemke square graph to produce a set of certificates that verify π (L □ L) ≤ 96. [ABSTRACT FROM AUTHOR]

In this paper, we give an in-depth error analysis for surrogate models generated by a variant of the Sparse Identification of Nonlinear Dynamics (SINDy) method. We start with an overview of a variety of nonlinear system identification techniques, namely SINDy, weak-SINDy, and the occupation kernel method. Under the assumption that the dynamics are a finite linear combination of a set of basis functions, these methods establish a linear system to recover coefficients. We illuminate the structural similarities between these techniques and establish a projection property for the weak-SINDy technique. Following the overview, we analyze the error of surrogate models generated by a simplified version of weak-SINDy. In particular, under the assumption of boundedness of a composition operator given by the solution, we show that (i) the surrogate dynamics converges towards the true dynamics and (ii) the solution of the surrogate model is reasonably close to the true solution. Finally, as an application, we discuss the use of a combination of weak-SINDy surrogate modeling and proper orthogonal decomposition (POD) to build a surrogate model for partial differential equations (PDEs). [ABSTRACT FROM AUTHOR]

Employing traditional Galerkin method, a coupled-mode flutter is predicted in the supercritical region of simply-supported pipes which constitutes a paradox since the internal flow effect is conservative and there is no energy to sustain the oscillation. Although there is a consensus that the flutter does not exist, the intrinsic mechanism remains to be clarified. This study has found that the internal flow induced Coriolis force term cannot be decoupled in traditional Galerkin method which leads to the dissatisfaction of the convergence conditions required in weighted residual approach (WRA). Moreover, the disparities in the predicted complex frequencies have been witnessed at different base function numbers when the internal flow velocity is sufficiently large. A modified Galerkin method adopting a new set of weighting functions is proposed based on WRA, and the Coriolis force term disappears by use of the orthogonality relations (it is stated that the Coriolis force is not directly omitted). Thus, a convergent solution for the set of residual functions which are identically equal to zeros can be guaranteed. Employing the modified method, the convergence in simulations is confirmed and the flutter phenomenon does not occur. This study can be a workbench for the study on the unsolved or partly solved issues in simulations of fluid-conveying pipes. Moreover, it has demonstrated that the predictions in traditional Galerkin method overestimate the natural frequencies, and it becomes more profound in higher-order natural modes at larger internal flow velocities which are of practice significance for dynamic analysis of flexible pipeline systems. [ABSTRACT FROM AUTHOR]

Let Y be a nonempty subset of X and T(X, Y) the set of all functions from X into Y. Then T(X, Y) with composition is a subsemigroup of the full transformation semigroup T(X). Let E be a nontrivial equivalence on X. Define a subsemigroup T E (X , Y) of T(X, Y) by T E (X , Y) = { α ∈ T (X , Y) : ∀ (x , y) ∈ E , (x α , y α) ∈ E }. We study T E (X , Y) with the natural partial order and determine when two elements are related under this order. We also give a characterization of compatibility on T E (X , Y) and then describe the maximal and minimal elements. [ABSTRACT FROM AUTHOR]

Active contour model (ACM) is considered as one of the most frequently employed models in image segmentation due to its effectiveness and efficiency. However, the segmentation results of images with intensity non-uniformity processed by the majority of existing ACMs are possibly inaccurate or even wrong in the forms of edge leakage, long convergence time and poor robustness. In addition, they usually become unstable with the existence of different initial contours and unevenly distributed intensity. To better solve these problems and improve segmentation results, this paper puts forward an ACM approach using adaptive local pre-fitting energy (ALPF) for image segmentation with intensity non-uniformity. Firstly, the pre-fitting functions generate fitted images inside and outside contour line ahead of iteration, which significantly reduces convergence time of level set function. Next, an adaptive regularization function is designed to normalize the energy range of data-driven term, which improves robustness and stability to different initial contours and intensity non-uniformity. Lastly, an improved length constraint term is utilized to continuously smooth and shorten zero level set, which reduces the chance of edge leakage and filters out irrelevant background noise. In contrast with newly constructed ACMs, ALPF model not only improves segmentation accuracy (Intersection over union(IOU)), but also significantly reduces computation cost (CPU operating time T), while handling three types of images. Experiments also indicate that it is not only more robust to different initial contours as well as different noise, but also more competent to process images with intensity non-uniformity. [ABSTRACT FROM AUTHOR]

There are deep historical connections between symmetry, harmonic functions, and stratified sets. In this article, we prove an analog of the removable singularity theorem for bounded harmonic functions on stratified sets. The harmonic functions are understood in the sense of the soft Laplacian. The result can become one of the main technical components for extending the well-known Poincaré–Perron's method of proving the solvability of the Dirichlet problem for the soft Laplacian. [ABSTRACT FROM AUTHOR]

The adjoint function of connection number has unique advantages in solving uncertainty problems of water resource complex systems, and has become an important frontier and research hotspot in the uncertainty research of water resource complex problems. However, in the rapid evolution of the adjoint function, some problems greatly limit the application of the adjoint function in the research of water resources. Therefore, based on bibliometric analysis, development, practical application issues, and prospects of the hot directions are analyzed. It is found that the development of the connection number of water resource set pair analysis can be divided into three stages: (1) relatively sluggish development before 2005, (2) a period of rapid advancement in adjoint function research spanning from 2005 to 2017, and (3) a subsequent surge post-2018. The introduction of the adjoint function of connection number promotes the continuous development of set pair analysis of water resources. Set pair potential and partial connection number are the crucial research directions of the adjoint function. Subtractive set pair potential has rapidly developed into a relatively independent and important trajectory. The research on connection entropy is comparatively less, which needs to be further strengthened, while that on adjacent connection number is even less. The adjoint function of set pair potential can be divided into three major categories: division set pair potential, exponential set pair potential, and subtraction set pair potential. The subtraction set pair potential, which retains the original dimension and quantity variation range of the connection number, is widely used in water resources and other fields. Coupled with the partial connection number, a series of new connection number adjoint functions have been developed. The partial connection number can be mainly divided into two categories: total partial connection number, and semi-partial connection number. Among these, the calculation expression and connotation of total partial connection numbers have not yet reached a consensus, accompanied by the slow development of high-order partial connection numbers. Semi-partial connection number can describe the mutual migration movement between different components of the connection number, which develops rapidly. With the limitations and current situation described above, promoting the exploration and application of the adjoint function of connection number in the field of water resources and other fields of complex systems has become the focus of future research. [ABSTRACT FROM AUTHOR]

In this paper, we consider the augmented Lagrangian duality for optimization problems with sparsity and abstract set constraints and present second-order conditions for the existence of augmented Lagrange multipliers by calculating the second-order epi-derivative of the augmented Lagrangian. The ingredient of the augmented Lagrangian here includes the indicator function of a sparse set and a composition of the Moreau envelope of the indicator function of a second-order regular set and a twice continuously differentiable mapping. The main process depends heavily on the calculation of the second-order epi-derivative of the indicator function of sparse set which is shown to be second-order regular and also parabolically regular. The second-order sufficient conditions for the sparse nonlinear programming, the sparse inverse covariance selection problem, and the sparse second-order cone programming are obtained as special cases of our general results. We prove that the existence of augmented Lagrange multipliers ensures the exactness of penalty functions and the stability of augmented solutions under small perturbations of the corresponding augmented Lagrange multipliers. [ABSTRACT FROM AUTHOR]

An enhanced dung beetle optimization algorithm (EDBO) is proposed for nonlinear optimization problems with multiple constraints in manufacturing. Firstly, the dung beetle rolling phase is improved by removing the worst value interference and coupling the current solution with the optimal solution to each other, while retaining the advantages of the original formulation. Subsequently, to address the problem that the dung beetle dancing phase focuses only on the information of the current solution, which leads to the overly stochastic and inefficient exploration of the problem space, the globally optimal solution is introduced to steer the dung beetle, and a stochastic factor is added to the optimal solution. Finally, the dung beetle foraging phase introduces the Jacobi curve to further enhance the algorithm's ability to jump out of the local optimum and avoid the phenomenon of premature convergence. The performance of EDBO in optimization is tested using the CEC2017 function set, and the significance of the algorithm is verified by the Wilcoxon rank-sum test and the Friedman test. The experimental results show that EDBO has strong optimization-seeking accuracy and optimization-seeking stability. By solving four engineering optimization problems of varying degrees, EDBO has proven to have good adaptability and robustness. [ABSTRACT FROM AUTHOR]

In this paper, a short review of the calculus of exact finite-differences of integer order is proposed. The finite-difference operators are called the exact finite-differences of integer orders, if these operators satisfy the same characteristic algebraic relations as standard differential operators of the same order on some function space. In this paper, we prove theorem that this property of the exact finite-differences is satisfies for the space of simple entire functions on the real axis (i.e., functions that can be expanded into power series on the real axis). In addition, new results that describe the exact finite-differences beyond the set of entire functions are proposed. A generalized expression of exact finite-differences for non-entire functions is suggested. As an example, the exact finite-differences of the square root function is considered. The use of exact finite-differences for numerical and computer simulations is not discussed in this paper. Exact finite-differences are considered as an algebraic analog of standard derivatives of integer order. [ABSTRACT FROM AUTHOR]

We introduce a new basis of quasisymmetric functions, the row-strict dual immaculate functions. We construct a cyclic, indecomposable 0-Hecke algebra module for these functions. Our row-strict immaculate functions are related to the dual immaculate functions of Berg-Bergeron-Saliola-Serrano-Zabrocki (2014-15) by the involution \psi on the ring \operatorname {QSym} of quasisymmetric functions. We give an explicit description of the effect of \psi on the associated 0-Hecke modules, via the poset induced by the 0-Hecke action on standard immaculate tableaux. This remarkable poset reveals other 0-Hecke submodules and quotient modules, often cyclic and indecomposable, notably for a row-strict analogue of the extended Schur functions studied in Assaf-Searles (2019). Like the dual immaculate function, the row-strict dual immaculate function is the generating function of a suitable set of tableaux, corresponding to a specific descent set. We give a complete combinatorial and representation-theoretic picture by constructing 0-Hecke modules for the remaining variations on descent sets, and showing that all the possible variations for generating functions of tableaux occur as characteristics of the 0-Hecke modules determined by these descent sets. [ABSTRACT FROM AUTHOR]

The spatial exploration of richness, endemism, and evolutionary diversity patterns has become an important part of biogeographic research and conservation planning. As the volume and complexity of biogeographical and phylogenetic data increase, the need for efficient tools to manipulate and analyze these datasets becomes essential. The 'phyloraster' package addresses this need by facilitating the analysis of evolutionary diversity and endemism for rasters. Our package offers a set of functions to support the linkage of species distribution models (SDMs) with phylogenies, providing then an understanding of the spatial distribution of biodiversity. It covers three main stages: pre‐processing, processing, and post‐processing of macroecological and phylogenetic data. During the pre‐processing step, basic functions are provided to prepare the data. The processing step combines functions to calculate indices including species richness, Faith's phylogenetic diversity, phylogenetic endemism, weighted endemism, and evolutionary distinctiveness. Additionally, this step includes functions to compute the standardized effect size for each metric using spatial and phylogenetic randomization methods, ensuring proper control for richness effects. The post‐processing stage includes functions to calculate the change of metrics between different times (e.g. present and future). In relation to processing in our functions, we show that 'phyloraster' takes up considerably less RAM than the other packages when computing the same metrics (weighted endemism). Lower RAM usage minimizes the hardware requirements to work with high‐resolution datasets from local to global scales. This broadens user accessibility of the spatialized measures of endemism and evolutionary diversity. [ABSTRACT FROM AUTHOR]

The Lerch zeta-function L(λ, α, s), s = σ + it, depends on two real parameters P λ and 0 < α ⩽ 1, and, for σ > 1, is defined by the Dirichlet series ∞ m=0 e2πiλm(m + α)-s, and by analytic continuation elsewhere. In the paper, we consider the joint approximation of collections of analytic functions by discrete shifts (L(λ1, α1, s+ikh1), . . ., L(λr, αr, s+ikhr)), k = 0, 1, . . ., with arbitrary λj, 0 < αj ⩽ 1 and hj > 0, j = 1, . . ., r. We prove that there exists a non-empty closed set of analytic functions on the critical strip 1/2 < σ < 1 which is approximated by the above shifts. It is proved that the set of shifts approximating a given collection of analytic functions has a positive lower density. The case of positive density also is discussed. A generalization for some compositions is given. [ABSTRACT FROM AUTHOR]

We define a concept of truthmaker function, and prove the functional completeness, w.r.t. truthmaker functions in this sense, of a set of four-valued functions corresponding to standard connectives of the system of relevance logic known as First-Degree Entailment or Belnap–Dunn logic. [ABSTRACT FROM AUTHOR]

Cloud computing has become increasingly popular due to its scalability, cost-effectiveness, and ability to handle large volumes of data. However, entrusting (sensitive) data to a third party raises concerns about data security and privacy. Homomorphic encryption is one solution that allows users to store and process data in a public cloud without the cloud provider having access to it. Currently, homomorphic encryption libraries only support addition and multiplication; other mathematical functions must be implemented by the user. To this end, we discuss and implement the division, exponential, square root, logarithm, minimum, and maximum function, using the CKKS cryptosystem of the OpenFHE library. To demonstrate that complex applications can be realized with this extended function set, we have used it to homomorphically realize the Box–Cox transform, which is used in many real-world applications, e.g., time-series forecasts. Our results show how the number of iterations required to achieve a given accuracy varies depending on the function. In addition, the execution time for each function is independent of the input and is in the range of ten seconds on a reference machine. With this work, we provide users with insights on how to extend the original restricted function set of the CKKS cryptosystem of the OpenFHE library with basic mathematical functions. [ABSTRACT FROM AUTHOR]

Considering the context of functional data analysis, we developed and applied a new Bayesian approach via the Gibbs sampler to select basis functions for a finite representation of functional data. The proposed methodology uses Bernoulli latent variables to assign zero to some of the basis function coefficients with a positive probability. This procedure allows for an adaptive basis selection since it can determine the number of bases and which ones should be selected to represent functional data. Moreover, the proposed procedure measures the uncertainty of the selection process and can be applied to multiple curves simultaneously. The methodology developed can deal with observed curves that may differ due to experimental error and random individual differences between subjects, which one can observe in a real dataset application involving daily numbers of COVID-19 cases in Brazil. Simulation studies show the main properties of the proposed method, such as its accuracy in estimating the coefficients and the strength of the procedure to find the true set of basis functions. Despite having been developed in the context of functional data analysis, we also compared the proposed model via simulation with the well-established LASSO and Bayesian LASSO, which are methods developed for non-functional data. [ABSTRACT FROM AUTHOR]

Summary: Plants possess a large variety of nonacquisitive belowground organs, such as rhizomes, tubers, bulbs, and coarse roots. These organs determine a whole set of functions that are decisive in coping with climate, productivity, disturbance, and biotic interactions, and have been hypothesized to affect plant distribution along environmental gradients.We assembled data on belowground organ morphology for 1712 species from Central Europe and tested these hypotheses by quantifying relationships between belowground morphologies and species optima along ecological gradients related to productivity and disturbance. Furthermore, we linked these data with species co‐occurrence in 30 115 vegetation plots from the Czech Republic to determine relationships between belowground organ diversity and these gradients.The strongest gradients determining belowground organ distribution were disturbance severity and frequency, light, and moisture. Nonclonal perennials and annuals occupy much smaller parts of the total environmental space than major types of clonal plants. Forest habitats had the highest diversity of co‐occurring belowground morphologies; in other habitats, the diversity of belowground morphologies was generally lower than the random expectation.Our work shows that nonacquisitive belowground organs may be partly responsible for plant environmental niches. This adds a new dimension to the plant trait spectrum, currently based on acquisitive traits (leaves and fine roots) only. [ABSTRACT FROM AUTHOR]

A new swarm-based metaheuristic that is also enriched with the crossover technique called swarm flip-crossover algorithm (SFCA) is introduced in this work. SFCA uses swarm intelligence as its primary technique and the crossover as its secondary one. It consists of three searches in every iteration. The swarm member walks toward the best member as the first search. The central point of the swarm becomes the target in the second search. There are two walks in the second search. The first walk is getting closer to the target, while the second is avoiding the target. The better result between these two walks becomes the candidate for the replacement. In the third search, the swarm member performs balance arithmetic crossover with the central point of the space or jumps to the opposite location within the area (flipping). The assessment is taken by confronting SFCA with five new metaheuristics: slime mold algorithm (SMA), golden search optimization (GSO), osprey optimization algorithm (OOA), coati optimization algorithm (COA), and walrus optimization algorithm (WaOA) in handling the set of 23 functions. The result shows that SFCA performs consecutively better than SMA, GSO, OOA, COA, and WaOA in 20, 23, 17, 17, and 17 functions. [ABSTRACT FROM AUTHOR]

In this contribution, a novel optimization approach, derived from the behavioral patterns exhibited by Duroc pig herds, is proposed. In the developed metaheuristic, termed Artificial Duroc Pigs Optimization (ADPO), Ordered Fuzzy Numbers (OFN) have been applied to articulate and elucidate the behavioral dynamics of the pig herd. A series of experiments has been conducted, using eight standard benchmark functions, characterized by multiple extrema. To facilitate a comprehensive comparative analysis, experiments employing Particle Swarm Optimization (PSO), Bat Algorithm (BA), and Genetic Algorithm (GA), were executed on the same set of functions. It was found that, in the majority of cases, ADPO outperformed the alternative methods. [ABSTRACT FROM AUTHOR]