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1. THE BOUNDARY OF THE p -RANK STRATUM OF THE MODULI SPACE OF CYCLIC COVERS OF THE PROJECTIVE LINE

   https://doi.org/10.1017/nmj.2022.12  

   OZMAN, EKIN; PRIES, RACHEL; WEIR, COLIN (December 2022, Nagoya Mathematical Journal)

   Abstract. We study the p-rank stratification of the moduli space of cyclic degree ! covers of the projective line in characteristic p for distinct primes p and !. The main result is about the intersection of the p-rank 0 stratum with the boundary of the moduli space of curves. When ! = 3 and p ≡ 2 mod 3 is an odd prime, we prove that there exists a smooth trielliptic curve in characteristic p, for every genus g, signature type (r,s), and p-rank f satisfying the clear necessary conditions. 

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2. Rational homotopy type of projectivization of the tangent bundle of certain spaces

   https://doi.org/10.1108/AJMS-02-2024-0029  

   Gastinzi, Jean Baptiste; Ndlovu, Meshach (August 2024, Arab Journal of Mathematical Sciences)

   PurposeThe paper aims to determine the rational homotopy type of the total space of projectivized bundles over complex projective spaces using Sullivan minimal models, providing insights into the algebraic structure of these spaces. Design/methodology/approachThe paper utilises techniques from Sullivan’s theory of minimal models to analyse the differential graded algebraic structure of projectivized bundles. It employs algebraic methods to compute the Sullivan minimal model of $P(E)$ and establish relationships with the base space. FindingsThe paper determines the rational homotopy type of projectivized bundles over complex projective spaces. Of great interest is how the Chern classes of the fibre space and base space, play a critical role in determining the Sullivan model ofP(E). We also provide the homogeneous space ofP(E)whenn = 2. Finally, we prove the formality ofP(E)over a homogeneous space of equal rank. Research limitations/implicationsLimitations may include the complexity of computing minimal models for higher-dimensional bundles. Practical implicationsUnderstanding the rational homotopy type of projectivized bundles facilitates computations in algebraic topology and differential geometry, potentially aiding in applications such as topological data analysis and geometric modelling. Social implicationsWhile the direct social impact may be indirect, advancements in algebraic topology contribute to broader mathematical knowledge, which can underpin developments in science, engineering, and technology with societal benefits. Originality/valueThe paper’s originality lies in its application of Sullivan minimal models to determine the rational homotopy type of projectivized bundles over complex projective spaces, offering valuable insights into the algebraic structure of these spaces and their associated complex vector bundles. 

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3. An update of the development of motor behavior

   https://doi.org/10.1002/wcs.1682  

   Franchak, John M; Adolph, Karen E (November 2024, WIREs Cognitive Science)

   Abstract This primer describes research on the development of motor behavior. We focus on infancy when basic action systems are acquired—posture, locomotion, manual actions, and facial actions—and we adopt a developmental systems perspective to understand the causes and consequences of developmental change. Experience facilitates improvements in motor behavior and infants accumulate immense amounts of varied everyday experience with all the basic action systems. At every point in development, perception guides behavior by providing feedback about the results of just prior movements and information about what to do next. Across development, new motor behaviors provide new inputs for perception. Thus, motor development opens up new opportunities for acquiring knowledge and acting on the world, instigating cascades of developmental changes in perceptual, cognitive, and social domains. This article is categorized under:Cognitive Biology > Cognitive DevelopmentPsychology > Motor Skill and PerformanceNeuroscience > Development 

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4. Experimental Characterization of Spatial Randomness of Elastic Properties of Heterogeneous Materials

   https://doi.org/10.1007/s11340-025-01218-6  

   Vievering, J; Ong, S; Fok, A; Labuz, J F; Le, J-L (October 2025, Experimental Mechanics)

   Abstract BackgroundUnderstanding the stochastic nature of elastic constants is crucial for the probabilistic analysis of structural response. Although significant progress has been made in experimentally characterizing deformation fields, few studies have addressed the spatial variability of material properties. ObjectiveThis study aims to develop a robust numerical-experimental method for characterizing the statistics of the elastic constants of heterogeneous materials. MethodsThe proposed method integrates digital image correlation (DIC) with finite element (FE) analysis. Through an iterative matching process between DIC-measured strain fields and FE simulations, the random spatial distributions of elastic constants are identified. This information is then used to determine the probability distributions, spatial autocorrelation functions, and cross-correlation functions of the elastic constants. ResultsThe method is applied to microcrystalline cellulose tablets subjected to diametral compression. The experimental results highlight the influence of compaction pressure on the statistical characteristics of the elastic constants. The analysis also uncovers key methodological considerations, including the DIC measurement noise, applied load level, matching region selection, and DIC resolution. ConclusionsThe study demonstrates that the spatial distribution of elastic constants of heterogenous materials can be determined by optimal fitting of DIC-measured strain fields with those from elastic FE analysis. The resulting probability distribution and spatial correlation can be directly employed to generate the random fields of elastic properties for stochastic FE simulations. 

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5. On the Concentration of the Chromatic Number of Random Graphs

   https://doi.org/10.37236/11638  

   Surya, Erlang; Warnke, Lutz (January 2024, The Electronic Journal of Combinatorics)

   Shamir and Spencer proved in the 1980s that the chromatic number of the binomial random graph $$G_{n,p}$$ is concentrated in an interval of length at most $$\omega\sqrt{n}$$, and in the 1990s Alon showed that an interval of length $$\omega\sqrt{n}/\log n$$ suffices for constant edge-probabilities $$p\in (0,1)$$. We prove a similar logarithmic improvement of the Shamir-Spencer concentration results for the sparse case $${p=p(n) \to 0}$$, and uncover a surprising concentration `jump' of the chromatic number in the very dense case $${p=p(n) \to 1}$$. 

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