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Context: Dual-task (simultaneous cognitive–motor activities) assessments have been adapted into reliable and valid clinical concussion measures. However, abundant motor and cognitive variations leave researchers and clinicians uncertain about which combinations elicit the intended dual-task effect. Our objective was to examine differences between commonly employed dual-task motor and cognitive combinations among healthy, college-aged individuals. Design: Cross-sectional laboratory study. Methods: Twenty participants (age: 21.3 [2.4] y; height: 176.0 [9.1] cm; mass: 76.0 [16.4] kg; 20% with concussion history) completed 4 motor tasks (gait, tandem gait, single-leg balance, and tandem balance) under 5 cognitive conditions (single task, subtraction, month reversal, spelling backward, and visual Stroop) in a research laboratory. The motor performance outcomes were spatiotemporal variables for gait and tandem gait and center of pressure path length (in centimeters) for single-leg and tandem balance. Cognitive outcomes were response rate (responses/second) and cognitive accuracy. We used separate repeated-measures analyses of variance for each motor and cognitive outcome with post hoc Tukey t tests. Results: Gait velocity, gait stride length, and tandem gait velocity demonstrated significant cognitive–motor interactions (P's <.001) such that all dual-task conditions resulted in varyingly slower or shorter movement than single task. Conversely, single-leg balance (P =.627) and tandem balance (P =.434) center of pressure path length did not significantly differ among the dual-task cognitive conditions or relative to single task. Statistically significant cognitive–motor interactions were observed only for spelling backward accuracy (P =.004) and response rates for spelling backward, month reversal, and visual Stroop (P's <.001) such that worse accuracy, but faster response rates, occurred during motor tasks. Conclusions: Gait and tandem gait motor tasks accompanied with spelling backward or subtraction cognitive tasks demonstrated consistently strong dual-task effects and, therefore, may be the best suited for clinical and research use following concussion. [ABSTRACT FROM AUTHOR]

This survey introduces 101 new publications on applications of Clifford's geometric algebras (GAs) newly published during 2022 (until mid‐January 2023). The selection of papers is based on a comprehensive search with Dimensions.ai, followed by detailed screening and clustering. Readers will learn about the use of GA for mathematics, computation, surface representations, geometry, image, and signal processing, computing and software, quantum computing, data processing, neural networks, medical science, physics, electric engineering, control and robotics. [ABSTRACT FROM AUTHOR]

In this paper, we first investigate the regularity of finite energy solutions to the following Wolff type integral system: { u (x) = R 1 (x) W β , γ (v p u r) (x) , u (x) > 0 , x ∈ R N , v (x) = R 2 (x) W β , γ (u q v s) (x) , v (x) > 0 , x ∈ R N , where γ > 1 , β > 0 , β γ < N , W β , γ is the Wolff potential, R 1 , R 2 are double bounded functions in R N and p , q > max ⁡ { 1 , γ − 1 } , r , s ≥ 0 with p − s ≥ q − r > − γ + 1. We exploit the regularity lifting lemma to obtain the optimal integrability, boundedness and decaying property of finite energy solutions to the system. Secondly, we establish sharp pointwise estimates of positive finite energy solutions to the p -Laplacian and k -Hessian systems related to the above integral system, by using the previous regularity results, the interior Hölder estimates of solutions for the corresponding differential systems and a doubling lemma of Poláčik, Quittner and Souplet (Duke Math. J.,2007). These extend Vétois's decay results (Indiana Univ. Math. J.,2019) on the positive solutions of Laplacian systems to the p -Laplacian and k -Hessian cases. We remark that our methods do not need Harnack type inequalities and it can be applied to deal with the solutions without radial structures. As far as we know, this is the first attempt to derive sharp decay estimates for possibly non-radial solutions involving k -Hessian operators. We also obtain some decay estimates of the gradients at infinity. [ABSTRACT FROM AUTHOR]

In this paper, the dynamical behavior in a delayed Aron–May model for malaria transmission is investigated. The basic reproduction number is defined. The global stability of the malaria-free equilibrium (MFE) is established. By using the Bendixson theorem, a sufficient condition for the global stability of the delay-free equilibrium (DFE) is also established. Furthermore, to deal with the local stability of endemic equilibrium (EE), by means of the stability switches analysis method proposed in [E. Beretta and Y. Kuang, Geometric stability switch criteria in delay differential systems with delay dependent parameters, SIAM J. Math. Anal. 33(5) (2002) 1144–1165.] the related characteristic equation at EE is investigated, and the occurrence of Hopf bifurcation is discussed by using the incubation period in mosquito as a bifurcation parameter. Last, the simulation analysis is also performed to verify the dynamical behavior of the model. [ABSTRACT FROM AUTHOR]

This paper answers a question of Usuba [Extendible cardinals and the mantle, Arch. Math. Logic 58(1–2) (2019) 71–75], establishing the optimality of the large cardinal assumption of his remarkable theorem that if there is an extendible cardinal, there is a minimum inner model from which the universe of sets can be obtained as a forcing extension. [ABSTRACT FROM AUTHOR]

In this research, structural equation modeling and TIMSS data were employed to examine the impact of school belonging on math achievement among secondary students in Japan, Korea, and the United States, with a focus on the roles of math attitude and disorderly behavior. Utilizing SmartPLS 4.0, the study delved into the reliability and validity of the measurement model, the direct and indirect effects within the structural model, and gender differences in these dynamics. The findings indicated that while school belonging directly affected math achievement in the United States, it did not in Japan and Korea. Math attitude, encompassing aspects like enjoyment of math (liking math), math self‐concept, and the value placed on math (math value), along with disorderly behavior, emerged as key mediators in this relationship. The study also revealed that the associations between school belonging, math attitude, disorderly behavior, and math achievement were more pronounced in boys than in girls. Implications for educators are discussed. [ABSTRACT FROM AUTHOR]

AbstractMathematics is often thought to have a unique association with certainty. The present study investigated a possible consequence of this association, namely that general conditionals are interpreted more deterministically in math than in other domains. To test this hypothesis, in two studies (Ns = 146 and 117), adults were presented general conditionals involving fictional categories in math and science and were asked to judge whether the conditionals were compatible with various frequencies of exceptions to them. Participants indicated that even rare exceptions (e.g., 1 exception per 99 confirming cases) would falsify a conditional (Studies 1 and 2), that a conditional could not be true and rare exceptions to it at the same time exist (Study 1), and that the truth of a conditional precluded the existence of even rare exceptions (Study 2), more when the conditionals involved math than science. The findings are consistent with the hypothesis that mathematical context is particularly likely to elicit deterministic interpretations of general conditionals. Implications of the findings for theories of conditional reasoning, and for individual differences in conditional reasoning, are discussed. [ABSTRACT FROM AUTHOR]

We show that a compact representation of either a semisimple Lie group or a totally disconnected group has a filtration with irreducible subquotients of finite multiplicity. In the Lie group case we show the stronger assertion, that it has an orthogonal decomposition into summands of finite lengths. This generalises and simplifies a number of more special spectral theorems in Deitmar and Monheim (Math Z 284(3–4):1199–1210, 2016, https://doi.org/10.1007/s00209-016-1695-9), Müller (Int Math Res Not 9(2):2068–2109, 2011), Venkov (in: Proceedings of the Steklov Institute of Mathematics, no. 4(153), ix+163 pp. (1983), 1982). We apply it to the case of cusp forms, thus settling the spectral theory for the space of non-unitary twisted cusp forms. We finally show that the space of cusp forms is complemented by the space of Eisenstein series. [ABSTRACT FROM AUTHOR]

In this paper, we generalize the notion of rational singularities for any reflexive sheaf of rank 1, link our notion of rational singularities with the notion of rational singularities in, [S. Kovacs, Irrational centers, Pure Appl. Math. Q. 7(4) (2011) 1495–1515], and prove generalizations of standard facts about rational singularities. Moreover, by using a definition of non-rational locus, we introduce the notion of (Bq+1) as a dual notion of well-known Serre’s notion of (Sq+1), and prove a theorem about q-birational morphisms. [ABSTRACT FROM AUTHOR]

On the one hand, I show that the later Wittgenstein's practice‐based approach to meaning, including the idea that the meaningfulness of mathematics ultimately is rooted in the everyday ‘applications’ it emerged from, as well as his insistence on the variability in and contingency of mathematical and mathematics‐like practices, foreshadows more recent work in Philosophy of Mathematical Practice (PMP), although Wittgenstein's approach was more radically practice‐based than what is prevalent in present‐day PMP. On the other hand, I also show that Wittgenstein's work on mathematics is driven by a pervasive critical attitude towards some key characteristics (monism, foundationalism and exceptionalism) of mainstream philosophical discourse about mathematics (then and now), which is mostly absent from present‐day PMP, and I argue that this aspect of Wittgenstein's work on mathematics could inspire present‐day practitioners of PMP to rethink the identity of their discipline. [ABSTRACT FROM AUTHOR]

School mathematics is not universal. It produces and is produced by social norms. What is considered as normatively appropriate school mathematics may vary when immigrant students (re)produce school mathematics in transitions between school mathematical practices at home and at school. In this study, one group of primary school students and two groups of secondary school students were interviewed to investigate their experiences with school mathematics in transitions. In contrast to some previous studies, the present study reveals instances where students positioned their parents as mathematically knowledgeable. To some students, it was important to know mathematical concepts in the mother tongue to be positioned as knowledgeable in mathematical conversations at home. This suggests that pedagogical practices should not only facilitate the transition of students’ everyday experiences into mathematics classrooms but also explore how school mathematics can be transitioned out of school, particularly considering transnationalities where ways of knowing transcend national boundaries. [ABSTRACT FROM AUTHOR]

Recently, W. Berndt and S. Sra (Hlawka-Popoviciu inequalities on positive definite tensors. Linear Algebra Appl. 2015;486:317–327) proved a Popoviciu type inequality for any arbitrary finite number of positive definite matrices. In this paper, we proved a quantitative Popoviciu type inequality for four positive semi-definite matrices, which is stronger than Berndt-Sra's corresponding result and also a generalization of Hong-Qi's (Refinements of two determinantal inequalities for positive semidefinite matrices. Math Inequal Appl. 2022;25(3):673–678) result. As applications, we partially recovered our early result in F. Wang (A quantitative Popoviciu type inequality, submitted.] and obtained a quantitative Hartfiel inequality. [ABSTRACT FROM AUTHOR]

In this paper, the existence and the uniqueness of an evolutionary anisotropic $ p_i(x) $ p i (x) -Laplacian equation with a damping term are studied. If the damping term is with a subcritical index, by the Di Giorgi iteration technique, the $ L^{\infty } $ L ∞ -estimate of the weak solutions can be obtained. The existence of weak solution is proved by the renormalized solution method, and how the anisotropic characteristic of the considered equation affect the $ L^{\infty } $ L ∞ -estimate of the weak solutions is revealed. The uniqueness is true strongly depending on subcritical index of the damping term, and this result goes beyond previous efforts in the literature (Bertsch M, Dal Passo R, Ughi M: Discontinuous viscosity solutions of a degenerate parabolic equation. Trans Amer Math Soc. 1990;320:779–798; Li Z, Yan B, Gao W. Existence of solutions to a parabolic $ p(x)- $ p (x) − Laplace equation with convection term via $ L^{\infty }- $ L ∞ − Estimates. Electron J Differ Equ. 2015;46:1–21; Zhang Q, Shi P. Global solutions and self-similar solutions of semilinear parabolic equations with nonlinear gradient terms. Nonlinear Anal. 2010;72:2744–2752; Zhou W, Cai S. The continuity of the viscosity of the Cauchy problem of a degenerate parabolic equation not in divergence form. J Jilin University (Natural Sci.). 2004;42:341–345), etc. [ABSTRACT FROM AUTHOR]

In what way does a mathematical proof depend on the notation used in its presentation? This paper examines this question by analysing the computational differences, in the sense of Larkin and Simon's ‘Why a diagram is (sometimes) worth 10,000 words’, between diagrammatic and sentential notations as a means for presenting geometric proofs. Wittgenstein takes up the question of mathematical notation and proof in Section III of Remarks on the Foundations of Mathematics. After discussing his observations on a proof's ‘characteristic visual shape’ in Section III with respect to arithmetical proofs, the paper shows how the notion of a characteristic visual shape illuminates the special effectiveness of diagrammatic notation in geometry. [ABSTRACT FROM AUTHOR]

Let (G/\Gamma,R_a) be an ergodic k-step nilsystem for k\geq 2. We adapt an argument of Parry [Topology 9 (1970), pp. 217–224] to show that L^2(G/\Gamma) decomposes as a sum of a subspace with discrete spectrum and a subspace of Lebesgue spectrum with infinite multiplicity. In particular, we generalize a result previously established by Host–Kra–Maass [J. Anal. Math. 124 (2014), pp. 261–295] for 2-step nilsystems and a result by Stepin [Uspehi Mat. Nauk 24 (1969), pp. 241–242] for nilsystems G/\Gamma with connected, simply connected G. [ABSTRACT FROM AUTHOR]

Motivated by the many roles that hook lengths play in mathematics, we study the distribution of the number of t-hooks in the partitions of n. We prove that the limiting distribution is normal with mean \[ \mu _t(n)\sim \frac {\sqrt {6n}}{\pi }-\frac {t}{2} \] and variance \[ \sigma _t^2(n)\sim \frac {(\pi ^2-6)\sqrt {6n}}{2\pi ^3}. \] Furthermore, we prove that the distribution of the number of hook lengths that are multiples of a fixed t\geq 4 in partitions of n converge to a shifted Gamma distribution with parameter k=(t-1)/2 and scale \theta =\sqrt {2/(t-1)}. [ABSTRACT FROM AUTHOR]

In the literature, besides the assumption of strict complementarity, superlinear convergence of implementable polynomial-time interior point algorithms using known search directions, namely, the HKM direction, its dual or the NT direction, to solve semi-definite programs (SDPs) is shown by (i) assuming that the given SDP is nondegenerate and making modifications to these algorithms [Kojima et al. Local convergence of predictor–corrector infeasible-interior-point algorithms for SDPs and SDLCPs, Math. Program. Ser. A 80 (1998), pp. 129–160], or (ii) considering special classes of SDPs, such as the class of linear semi-definite feasibility problems (LSDFPs) and requiring the initial iterate to the algorithm to satisfy certain conditions [Sim, Superlinear convergence of an infeasible predictor–corrector path-following interior point algorithm for a semidefinite linear complementarity problem using the Helmberg–Kojima–Monteiro direction, SIAM J. Optim. 21 (2011), pp. 102–126], [Sim, Interior point method on semi-definite linear complementarity problems using the Nesterov-Todd (NT) search direction: Polynomial complexity and local convergence, Comput. Optim. Appl. 74 (2019), pp. 583–621]. Otherwise, these algorithms are not easy to implement even though they are shown to have polynomial iteration complexities and superlinear convergence [Luo et al. Superlinear convergence of a symmetric primal–dual path following algorithm for semidefinite programming, SIAM J. Optim. 8 (1998), pp. 59–81]. The conditions in [Sim, Superlinear convergence of an infeasible predictor–corrector path-following interior point algorithm for a semidefinite linear complementarity problem using the Helmberg–Kojima–Monteiro direction, SIAM J. Optim. 21 (2011), pp. 102–126], [Sim, Interior point method on semi-definite linear complementarity problems using the Nesterov-Todd (NT) search direction: Polynomial complexity and local convergence, Comput. Optim. Appl. 74 (2019), pp. 583–621] that the initial iterate to the algorithm is required to satisfy to have superlinear convergence when solving LSDFPs however are not practical. In this paper, we propose a practical initial iterate to an implementable infeasible interior point algorithm that guarantees superlinear convergence when the algorithm is used to solve the homogeneous feasibility model of an LSDFP. [ABSTRACT FROM AUTHOR]

Being inspired by the biological eye, event camera is a novel asynchronous technology that poses a paradigm shift in acquisition of visual information. This paradigm enables event cameras to capture pixel-size fast motions much more naturally compared to classical cameras.In this paper, we present a new asynchronous event-driven algorithm for detection of high-frequency pixel-size periodic signals using an event camera. Development of such new algorithms to efficiently process the asynchronous information of event cameras is essential to utilize its special properties and potential, and being a main challenge in the research community.It turns out that this algorithm, which was developed in order to satisfy the new paradigm, is related to an untreated theoretical problem in probability: Let 0 ≤ τ1 ≤ τ2 ≤⋯ ≤ τm ≤ 1 originated from an unknown distribution. Let also 휖,δ ∈ ℝ, and d ∈ ℕ. What can be said about the probability Φ(m,d) of having more than d adjacent τi-s pairs that the distance between them is δ, up to an error 휖? This problem, which reminds the area of order statistic, shows how the new visualization paradigm is also an opportunity to develop new areas and problems in mathematics. [ABSTRACT FROM AUTHOR]

In [D. Rees, Hilbert functions and pseudo-rational local rings of dimension two, J. London Math. Soc. (2) 24 (1981) 467–479], Rees gave a characterization for the normal joint reduction number zero of two 픪-primary ideals in an analytically unramified Cohen–Macaulay local ring of dimension two. Rees’ result is a generalization of Zariski’s product theorem for complete ideals in a regular local ring of dimension two. The aim of this paper is to extend Rees’ theorem for the ordinary powers of 픪-primary ideals I and J in a Cohen–Macaulay local ring of dimension two. Following Rees’ approach, we define the modified Koszul homology modules Mr,s1(ak,bk) for a joint reduction (a,b) of I and J. Under the additional assumption that the associated graded rings of I and J have positive depth, we obtain a characterization of the joint reduction number zero of I and J in terms of the vanishing of the module M0,01(a,b), as well as in terms of the Hilbert coefficients and the bigraded Hilbert coefficients. More generally, we introduce the joint reduction lattice and study the vanishing of Mr,s1(a,b) for any r,s ≥ 0. This gives a characterization for a vector (r,s) to be in the joint reduction lattice of I and J. We also give a cohomological interpretation of these theorems by investigating the local cohomology modules of the bigraded extended Rees algebra. This gives another characterization for a vector (r,s) to be in the joint reduction lattice and also extends a recent result of Masuti and Verma in [Local cohomology of bigraded Rees algebras and normal Hilbert coefficients, J. Pure Appl. Algebra 218(5) (2014) 904–918] for ordinary powers of ideals. [ABSTRACT FROM AUTHOR]

We prove the local Lipschitz continuity of sub-elliptic harmonic maps between certain singular spaces, more specifically from the 푛-dimensional Heisenberg group into CAT ⁡ ( 0 ) \operatorname{CAT}(0) spaces. Our main theorem establishes that these maps have the desired Lipschitz regularity, extending the Hölder regularity in this setting proven in [Y. Gui, J. Jost and X. Li-Jost, Subelliptic harmonic maps with values in metric spaces of nonpositive curvature, Commun. Math. Res. 38 (2022), 4, 516–534] and obtaining same regularity as in [H.-C. Zhang and X.-P. Zhu, Lipschitz continuity of harmonic maps between Alexandrov spaces, Invent. Math. 211 (2018), 3, 863–934] for certain sub-Riemannian geometries; see also [N. Gigli, On the regularity of harmonic maps from RCD ⁢ ( K , N ) \mathrm{RCD}(K,N) to CAT ⁢ ( 0 ) \mathrm{CAT}(0) spaces and related results, preprint (2022), https://arxiv.org/abs/2204.04317; and A. Mondino and D. Semola, Lipschitz continuity and Bochner–Eells–Sampson inequality for harmonic maps from RCD ⁡ ( k , n ) \operatorname{RCD}(k,n) spaces to CAT ⁡ ( 0 ) \operatorname{CAT}(0) spaces, preprint (2022), https://arxiv.org/abs/2202.01590] for the generalisation to RCD spaces. The present result paves the way for a general regularity theory of sub-elliptic harmonic maps, providing a versatile approach applicable beyond the Heisenberg group. [ABSTRACT FROM AUTHOR]

The aim of this paper is to transfer the restrictedness theory to Hom-Lie algebras. The concept of restricted Hom-Lie algebras, which is introduced in [S. Bouarroudj and A. Makhlouf, Hom-lie superalgebras in characteristic 2, Mathematics 11 2023, 24, Paper No. 4955], will be used in this paper. First, the existence and uniqueness of p-structures on a Hom-Lie algebra is studied. Then the definition of a restrictable Hom-Lie algebra is given and the equivalence relation between restrictable Hom-Lie algebras and restricted Hom-Lie algebras is constructed. Finally, the p-envelopes of a Hom-Lie algebra are defined and studied. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce the new class of left and right B-Weyl operators, which naturally extends the conventional concepts of left and right Weyl operators. Our contributions encompass demonstrating the stability of the left (and right) B-Weyl operators under small perturbations. We further characterize the left (and right) B-Weyl operators as the direct sum of a closed left (and right) Drazin invertible operator and a finite rank operator. Additionally, we present some characterizations of the left and right B-Weyl spectra, utilizing the left and right Drazin spectra as essential components. Furthermore, our obtained results play a pivotal role in exploring the interrelations between the left and right B-Weyl spectra and other spectra integral to the realm of B-Fredholm theory. This paper seeks to enhance and extend the recent research explored in [F. Abdmouleh and T. Ben Lakhal, Left and right B-Fredholm operators, Ukrainian Math. J. 74 2023, 10, 1479–1489] to a larger class in the unbounded B-Fredholm operators theory. [ABSTRACT FROM AUTHOR]

Effort tolerance refers to a repertoire of selecting a larger reinforcer requiring a higher‐effort response over a smaller reinforcer requiring a lower‐effort response. The current study investigated the effects of an online group‐based effort‐tolerance training on students' effort tolerance. The study adds to the literature because no studies have investigated the effects of a progressive ratio schedule of reinforcement as an intervention that targets effort tolerance for a whole class in an online platform and in general education settings. During the intervention, researchers gradually increased the response requirements (i.e., number of math problems) to access a larger reinforcer and incorporated choice‐making opportunities to promote second‐grade students' selection of a higher‐effort/larger‐reinforcer response. The findings yielded mixed results – the intervention was relatively effective at increasing effort tolerance for students performing on and below grade level for math, but the same effects were not shown in students performing above grade level. Future applications in education and research are discussed. [ABSTRACT FROM AUTHOR]

Introduction Advancements in information technology have facilitated information exchange practices within the Military Health System (MHS), enabling "systems of systems" approaches that broaden and coordinate the set of capabilities available to enhance patient outcomes. This is applicable for MHS modeling and simulation (M&S) applications as well. Learning from successful approaches applied in current interoperability solutions used in the military helps to ensure interoperability practices yield trusted compositions of simulations. Materials and Methods The use of formal methods provides the rigor necessary to unambiguously communicate these approaches across the MHS community. Here, 3 formal methods are proposed to ensure the harmonization of models and alignment of M&S data needed for simulation interoperability for MHS applications. Results To clarify considerations relevant for establishing simulation interoperability, the proposed formal methods are examined within a notional example of an injury sustained because of blast exposure. The first method applies the principles of semiotics, addressing the coding of information via syntax and semantics, to understand how to align and transform data across simulations within a composition. The second method applies the concepts of well-specified co-simulations, and the use of different techniques, tools, and algorithms to address the composition and synchronization of M&S components. The third method applies the mathematical branch of model theory to codify expert knowledge about concepts, assumptions, and constraints to ensure conceptual alignment within the simulation composition. Conclusions Biomedical research must contend with complexity inherent to computational human body modeling, enlisting expert knowledge from multiple domains supporting the development of cross-disciplinary research tools that resolve research foci and associated differences in underlying theories, methods, and applied tools. This is closely related to the broader context of digital engineering for military systems engineering. [ABSTRACT FROM AUTHOR]

The theory of complex dynamics is an area of pure mathematics. Even though the theory of dynamical systems belongs to analysis, it is studied in relation to various fields of mathematics, including algebra and geometry. I study it using the theory of non-archimedean numbers from number theory, which seems distant from dynamics. In this article, we discuss how attractive these theories are. [ABSTRACT FROM AUTHOR]

Significant attention has been paid to the use of ICT by teachers, especially during the COVID-19 health crisis. This usage has mostly been captured through self-reported survey measurements. Learning analytics can complement such findings, by using log data to document precisely how long teachers use ICT, and what ICT behaviors they perform online. Using log data of 800 teachers, the present study documents their use of ICT in mathematics on a digital learning platform used across Luxembourg during COVID-19 remote education. Our findings confirm the large differences between teachers' use of ICT found in previous research, measured here through the time spent active on the platform. The types of ICT behaviors teachers engage with online, measured via the SAMR model, explain most of this variation. Specifically, more time on the platform is associated with activities that create a meaningful learning experience, and redefined tasks that could engage students as active learners. Experience with the technology, and participation in incentive events and teacher training, explain another significant part of this variation. [ABSTRACT FROM AUTHOR]

Targeted resistance training stimulates hamstring muscle hypertrophy, but its effect on tendon‐aponeurosis geometry is unknown. This study examined changes in hamstring muscle, free tendon, and aponeurosis geometry following a 10 week Nordic or hip extension exercise intervention. Thirty recreationally active males were randomly allocated (n = 10 per group) to a Nordic, hip extension, or control group. Magnetic resonance imaging of both thighs was acquired pre‐ and post‐intervention. Changes in free tendon and aponeurosis volume for each hamstring muscle, biceps femoris long head (BFlh) aponeurosis interface area and muscle volume‐to‐interface area ratio were compared between groups. Regional changes in muscle CSA were examined via statistical parametric mapping. The change in semimembranosus free tendon volume was greater for the Nordic than control group (mean difference = 0.06 cm3, 95% CI = 0.02–0.11 cm3). No significant between‐group differences existed for other hamstring free tendons or aponeuroses. There were no between‐group differences in change in BFlh interface area. Change in BFlh muscle volume‐to‐interface area ratio was greater in the hip extension than Nordic (mean difference = 0.10, 95% CI = 0.007–0.19, p = 0.03) and control (mean difference = 0.12, 95% CI = 0.03–0.22, p = 0.009) groups. Change in muscle CSA following training was greatest in the mid‐portion of semitendinosus for both intervention groups, and the mid‐portion of BFlh for the hip extension group. There was limited evidence for tendon‐aponeurosis hypertrophy after 10 weeks of training with the Nordic or hip extension exercises. For the BFlh, neither intervention altered the interface area although hip extension training stimulated an increase in the muscle volume‐to‐interface area ratio, which may have implications for localized tissue strains. Alternative muscle‐tendon loading strategies appear necessary to stimulate hamstring tendon adaptations. [ABSTRACT FROM AUTHOR]

Background: In recent years, the exploration of innovative interventions for addressing problems of children and adolescents with specific learning disabilities (SLD) has garnered significant attention within the realm of neurocognitive research. Transcranial electrical stimulation (TES) has emerged as a promising tool for enhancing cognitive skills in children, offering a non‐invasive and safe method that may particularly benefit those with learning difficulties. We aimed to appraise the extent and the quality of studies about impact of TES on cognitive skills including academic skills in children and adolescents with SLD. Methods: A literature search was performed according to the Preferred Reporting Items for Systematic Reviews and Meta‐Analyses (PRISMA) guidelines. Articles published between January 2000 and January 2024 were searched in PubMed, Embase, Scopus, Web of Science and Google Scholar. The study eligibility criteria were previously established according to the PICO model. The Physiotherapy Evidence Database (PEDro) scale and Cochrane Collaboration tool (ROB2) were used to assess the methodological quality and the risk of bias of the included studies, respectively. Results: The initial search yielded 1571 studies among which 30 studies were systematically reviewed. The total number of participants was 224 individuals (intervention: 114; control: 110). Findings showed significant improvements in reading skills such as text reading, high‐frequency word reading speed and efficiency and mathematical skills. Conversely, other cognitive skills such as working memory were not improved in people with dyslexia and dyscalculia. Discussion: TES interventions can positively affect cognitive skills in children and adolescents with SLD; However, due to the small number of studies, medium methodological quality and high risk of bias, caution should be taken when interpreting the results. [ABSTRACT FROM AUTHOR]

Behavior and academic outcomes in school are interrelated; students who struggle with academics are likelier to exhibit troublesome behavior and students who struggle with behavior tend to fall behind academically. Multitiered systems of support (MTSS) offer frameworks for providing increasingly intensive support for students with academic and behavioral difficulties, but it can be challenging to efficiently integrate academic and behavioral supports rather than implementing separate resource-intensive systems. This article describes how behavior support can be integrated within Tier-2 interventions for reading and mathematics. A strategy that included four evidence-based elements—teaching expectations, self-monitoring, self-evaluation, and mystery match—was embedded within academic intervention lessons to target students' academic engagement, respectful behavior, and effort. In this article, we describe our approach as one way that academic and behavioral supports might be integrated within a tiered intervention system. [ABSTRACT FROM AUTHOR]

We design succinct encodings of series-parallel, block-cactus and 3-leaf power graphs while supporting the basic navigational queries such as degree, adjacency and neighborhood optimally in the RAM model with logarithmic word size. One salient feature of our representation is that it can achieve optimal space even though the exact space lower bound for these graph classes is not known. For these graph classes, we provide succinct data structures with optimal query support for the first time in the literature. For series-parallel multigraphs, our work also extends the works of Uno et al. (Disc. Math. Alg. and Appl., 2013) and Blelloch and Farzan (CPM, 2010) to produce optimal bounds. [ABSTRACT FROM AUTHOR]

Prior research in Western contexts has tested the hypothesis that stereotype threat induces a prevention focus and that in contexts where both prevention focus and stereotype threat are simultaneously activated, members of stereotyped groups experience a performance boost due to the fit between one's goal orientation and the task demands (i.e. regulatory fit or stereotype fit). The present Study tested this hypothesis with high school students in Uganda, East Africa. Study findings revealed that in this cultural context where high-stakes testing fosters a predominantly promotion-focused testing culture, individual differences in regulatory focus interacted with the broader cultural, regulatory focus test culture to impact student performance. [ABSTRACT FROM AUTHOR]

Theoretical, methodological, and empirical contributions regarding networks within the context of graph theory constitute a valuable interface between geography and mathematics. Seeking to assess mathematical network geography's past, present, and future, this article addresses such research and literature by discussing new knowledge produced from networked geographic phenomena—especially Erdös collaboration graphs depicting mentorships or authorships among scholars; outlining a brief history of networks in geographical analysis; and couching spatial autocorrelation within its geographic network links. General commentary transitions into examples of Erdös graphs and their implications for collaborations. The narrative also speaks to networked space challenges of established geographic thought (e.g., Tobler's first law of geography), with special reference to contributions by Boots and his coauthors. This article concludes with a treatment of graph theory, networks, and spatial autocorrelation. [ABSTRACT FROM AUTHOR]

Let |$f:[0,1]^{d}\to{\mathbb{R}}$| be a completely monotone integrand as defined by Aistleitner and Dick (2015, Acta Arithmetica, 167, 143–171) and let points |$\boldsymbol{x}_{0},\dots ,\boldsymbol{x}_{n-1}\in [0,1]^{d}$| have a non-negative local discrepancy (NNLD) everywhere in |$[0,1]^{d}$|⁠. We show how to use these properties to get a non-asymptotic and computable upper bound for the integral of |$f$| over |$[0,1]^{d}$|⁠. An analogous non-positive local discrepancy property provides a computable lower bound. It has been known since Gabai (1967, Illinois J. Math. 11, 1–12) that the two-dimensional Hammersley points in any base |$b\geqslant 2$| have NNLD. Using the probabilistic notion of associated random variables, we generalize Gabai's finding to digital nets in any base |$b\geqslant 2$| and any dimension |$d\geqslant 1$| when the generator matrices are permutation matrices. We show that permutation matrices cannot attain the best values of the digital net quality parameter when |$d\geqslant 3$|⁠. As a consequence the computable absolutely sure bounds we provide come with less accurate estimates than the usual digital net estimates do in high dimensions. We are also able to construct high-dimensional rank one lattice rules that are NNLD. We show that those lattices do not have good discrepancy properties: any lattice rule with the NNLD property in dimension |$d\geqslant 2$| either fails to be projection regular or has all its points on the main diagonal. Complete monotonicity is a very strict requirement that for some integrands can be mitigated via a control variate. [ABSTRACT FROM AUTHOR]

Financial forecasting involves predicting the future financial states and performance of companies and investors. Recent technological advancements have demonstrated that machine learning-based models can outperform traditional financial forecasting techniques. In particular, hybrid approaches that integrate diverse methods to leverage their strengths have yielded superior results in financial prediction. This study introduces a novel hybrid model, entitled EMD-TI-LSTM, consisting of empirical mode decomposition (EMD), technical indicators (TI), and long short-term memory (LSTM). The proposed model delivered more accurate predictions than those generated by the conventional LSTM approach on the same well-known financial datasets, achieving average enhancements of 39.56%, 36.86%, and 39.90% based on the MAPE, RMSE, and MAE metrics, respectively. Furthermore, the results show that the proposed model has a lower average MAPE rate of 42.91% compared to its state-of-the-art counterparts. These findings highlight the potential of hybrid models and mathematical innovations to advance the field of financial forecasting. [ABSTRACT FROM AUTHOR]

The Fibonacci sequence has broad applications in mathematics, where its inherent patterns and properties are utilized to solve various problems. The sequence often emerges in areas involving growth patterns, series, and recursive relationships. It is known for its connection to the golden ratio, which appears in numerous natural phenomena and mathematical constructs. In this research paper, we introduce new concepts of convergence and summability for sequences of real and complex numbers by using Fibonacci sequences, called Δ -Fibonacci statistical convergence, strong Δ -Fibonacci summability, and Δ -Fibonacci statistical summability. And, these new concepts are supported by several significant theorems, properties, and relations in the study. Furthermore, for this type of convergence, we introduce one-sided Tauberian conditions for sequences of real numbers and two-sided Tauberian conditions for sequences of complex numbers. [ABSTRACT FROM AUTHOR]

The home math environment is vital for early math development. Yet, there is limited understanding of how parents translated their attitudes towards helping children learn math (HCLM) into actions to influence their young children's math-related outcomes. Thus, the present study examined whether parents' perceived competence, value, and pressure about HCLM contributed to young children's math competence through parents' interest in HCLM, home math activities, and children's interest in math. One hundred forty-seven parents were surveyed about their attitudes, practices, and their children's math interest. Meanwhile, their children were individually tested on applied math problem solving. Results showed that parents' perceived competence and value about HCLM predicted their interest in HCLM, while parents' pressure about HCLM predicted children's math interest. Parents' interest in HCLM is positively linked to children's applied math problem solving via children's math interest. This study shed light on the importance of promoting parents' positive attitudes towards HCLM. [ABSTRACT FROM AUTHOR]

Understanding math and the ability to use math in various situations can greatly contribute to a successful life. Different math skills are of importance for understanding and supporting math ability. In addition, math interest may influence math ability. We investigated the relationship between math conceptual and procedural skills, their development over time, and the relation to math interest in Grades three and five. Participants in the study were Estonian students (N = 855), who were in Grade three (2019/2020) during the first testing and in Grade five (2021/2022) during the second testing. Students completed math competence testing which consisted of procedural and conceptual skill tasks and a questionnaire about math interest. Both person- and variable-oriented approaches were used in the analyses. Students' math conceptual and procedural skills in Grades three and five were moderately related to each other. Furthermore, based on latent profile analysis, three profiles of skills were identified in both grades, distinguishing between students with low, average, and high levels of skills in both skills, with the exception of an approximately average-skill group in Grade five that had low conceptual skills but average procedural skills. Students were likely to remain in similar-skill groups for both Grades three and five. Lastly, there was a significant difference in math interest in Grade three among the groups with stable low, stable average, and stable high skills from Grades three to five. Fostering interest in math may be beneficial for achieving a high level of math proficiency. Future research should prioritize the integration of person-oriented methods into studies aimed at enhancing understanding of math skill development. [ABSTRACT FROM AUTHOR]

The present study investigated multilevel models posited to predict student approaches to homework. Participants were 1,072 middle school students in China. Results revealed that deep and surface approaches were positively associated with performance-approach. Furthermore, deep approach to homework was associated negatively with homework cost, yet positively with mastery-approach, homework expectancy, and prior knowledge. Surface approach to homework was associated positively with homework cost and parent education, yet negatively with homework expectancy and mastery-approach. Females were less likely to use surface approach to homework than males. At the class level, surface approach to homework was negatively associated with parent education. Implications for homework practice and future investigation are discussed in terms of these results. [ABSTRACT FROM AUTHOR]

This study aimed to ascertain the contribution of children's effortful control (EC) to math achievement by testing the mediational involvement of math anxiety. Participants were 704 children (367 girls) aged between 7 and 12 years (M = 9.43, SD = 1.23). Children's EC was measured by parent's report, math anxiety was assessed through self-report, whereas math achievement was evaluated by performance on standard math tests. The models tested involved EC higher-order factor or specific EC components (activation control, attentional focusing, and inhibitory control). The results showed that activation control, attentional focusing, and EC higher-order factor contributed to math performance directly and through the mediation of math anxiety. Inhibitory control did not yield a significant effect on math performance. The findings suggest that children with higher dispositional effortful self-regulation tend to experience lower levels of math anxiety, with positive effects on math performance. [ABSTRACT FROM AUTHOR]

Early detection of and relevant information on children's mathematical difficulties is important to initiate targeted teaching and intervention. This study investigated the extent to which strategy use in single-digit addition provides additional predictive information about 61 grade one children's (6-year-old) mathematical achievement 3 years later that is not available from a standardised mathematics achievement test. Four predictors available in year one (arithmetic strategy use, mathematical achievement, non-verbal reasoning skills and sex) explained 54% of the variation in grade four mathematics achievement. Arithmetic strategy use was the most important single predictor of year four mathematics achievement (R2 = 30%) and explained an additional 12% variation if added to a model comprised by the three other year one predictors. This result suggests that systematically obtained measures of how young children solve single-digit arithmetic problems might provide useful information about their foundational number knowledge, which in turn may reveal how well they achieve later in school. [ABSTRACT FROM AUTHOR]

A research project involving 16 children with Down syndrome aged 4–14 approaching mathematics at home was developed during the COVID‐19‐lockdown in Spain. In the research project a series of 14 short mathematical challenges were designed and delivered in a WhatsApp group used as a communication and documentation tool with the participating families. Videos recorded by them were subsequently analyzed with the purpose of describing and analyzing: (a) the experience children live in contact with informal situations underlying the concepts of number and shape and (b) the engagement of families. The choice of these informal situations is based upon recent research that shows the need to consider the wide range of occasional experiences with mathematical ideas children have in their family prior to schooling. In order to design productive mathematical activities we drew on our past research for the choosing of crucial mathematical issues (whole numbers, plane geometry, and solids). We discuss the evolution in parents from practical help to deep engagement, and the fact that notwithstanding diversity in family contexts, engagement and an especially joyful approach to mathematics emerged. The use of videos opens up a path to the possibility to online learning for children with Down syndrome. [ABSTRACT FROM AUTHOR]

This paper concerns the bubbling phenomena for the L2$L^2$‐critical half‐wave equation in dimension one. Given arbitrarily finitely many distinct singularities, we construct blow‐up solutions concentrating exactly at these singularities. This provides the first examples of multi‐bubble solutions for the half‐wave equation. In particular, the solutions exhibit the mass quantization property. Our proof strategy draws upon the modulation method in Krieger, Lenzmann and Raphaël [Arch. Ration. Mech. Anal. 209 (2013), no. 1, 61–129] for the single‐bubble case, and explores the localization techniques in Cao, Su and Zhang [Arch. Ration. Mech. Anal. 247 (2023), no. 1, Paper No. 4] and Röckner, Su and Zhang [Trans. Amer. Math. Soc., 377 (2024), no. 1, 517–588] for bubbling solutions to non‐linear Schrödinger equations (NLS). However, unlike the single‐bubble or NLS cases, different bubbles exhibit the strongest interactions in dimension one. In order to get sharp estimates to control these interactions, as well as non‐local effects on localization functions, we utilize the Carlderón estimate and the integration representation formula of the half‐wave operator, and find that there exists a narrow room between the orders |t|2+$|t|^{2+}$ and |t|3−$|t|^{3-}$ for the remainder in the geometrical decomposition. Based on this, a novel bootstrap scheme is introduced to address the multi‐bubble non‐local structure. [ABSTRACT FROM AUTHOR]

This paper presents a modular approach to motion planning with provable stability guarantees for robots that move through changing environments via periodic locomotion behaviors. We focus on dynamic walkers as a paradigm for such systems, although the tools developed in this paper can be used to support general compositional approaches to robot motion planning with dynamic movement primitives (DMPs). By formulating the planning process as a switching system with multiple equilibria (SSME), we prove that the system's evolution remains within explicitly characterized trapping regions in the state space under suitable constraints on the frequency of switching among the DMPs. These conditions encapsulate the low-level stability limitations in a form that can be easily communicated to the planner. Furthermore, we show how the available primitives can be safely composed online in a receding horizon manner to enable the robot to react to moving obstacles. The proposed framework can be applied in a wide class of 3D bipedal walking models, and offers a modular approach for integrating readily available low-level locomotion control and high-level planning methods. [ABSTRACT FROM AUTHOR]