Department of Mathematics, UCI

A new mathematical theory is proposed to explain the population size oscillations described in the paper by P. Turchin. The model is based on Turchin's demographic-structural theory and includes the "inertia of war" phenomenon together with the tendency for retribution in military conflicts.

We compute the rational points on certain members of the following family of hyperelliptic curves C a : y 2 = x 8 + ( 4 − 4 a 4 ) x 6 + ( 8 a 4 + 6 ) x 4 + ( 4 − 4 a 4 ) x 2 + 1 via the method first developed by Dem'yanenko [Dem68] and then further generalized by Manin [Man69]. In particular, we show that the method of Chabauty–Coleman, while applicable to certain members of this family, is not the most efficient way of computing C a ( Q ) . We adapt the approach of [Kul99], incorporating root numbers to further restrict the possible ranks of the elliptic curves arising in the Jacobian decomposition.

This paper generalizes infinite games played with filters on algebras from the Welch Games to playing normal filters that concentrate on a fixed base set.

On symplectic manifolds, we introduce a Morse-type complex with elements generated by pairs of critical points of a Morse function. The differential of the complex consists of gradient flows and an integration of the symplectic structure over spaces of gradient flow lines. Using results from the Witten deformation method, we prove that the cohomology of this complex is independent of both the Riemannian metric and the Morse function used to define the complex and is in fact isomorphic to the cohomology of differential forms of Tsai, Tseng and Yau (TTY). We also obtain Morse-type inequalities that bound the dimensions of the TTY cohomologies by the number of Morse critical points and the interaction of symplectic structure with the critical points.

Latine parents from lower socioeconomic backgrounds in the United States (US) often face challenges when supporting their adolescents’ education in subjects like math. Guided by strengths-based, culturally grounded frameworks, this study explored the challenges Latine parents faced when supporting adolescents’ math learning and how they leveraged their community cultural wealth via specific strategies to address challenges. We conducted semi-structured qualitative interviews with 20 Latine-descent parents (19 mothers, one father; 12 with less than a high school education, five with a high school education, three with some college education) of adolescents (eight girls, 12 boys; eight 6th graders, seven 7th graders, and five 8th graders) attending four middle schools in southern California. Systematic coding and theming of the interview data were used to help identify challenges parents experienced at the individual level (e.g., gaps in content/curriculum knowledge, problems with technology, linguistic differences) and at the contextual level (e.g., conflicting obligations, nonideal circumstances). Parents used their community cultural wealth by employing five strategies: (a) working closely with adolescents, (b) seeking help from their social networks, (c) providing learning spaces and organized activities to help, (d) using digital tools, and (e) hoping to build their knowledge and skills in the future. Finally, analyses revealed emergent linkages between specific math support challenges and adaptive strategies. The findings underscore the utility of leveraging parents’ cultural funds of knowledge and community cultural wealth to understand not just the math-specific needs of Latine families but also how families already actively address challenges to math support.

Liquid argon time projection chambers (LArTPCs) rely on highly pure argon to ensure that ionization electrons produced by charged particles reach readout arrays. ProtoDUNE Single-Phase (ProtoDUNE-SP) was an approximately 700-ton liquid argon detector intended to prototype the Deep Underground Neutrino Experiment (DUNE) Far Detector Horizontal Drift module. It contains two drift volumes bisected by the cathode plane assembly, which is biased to create an almost uniform electric field in both volumes. The DUNE Far Detector modules must have robust cryogenic systems capable of filtering argon and supplying the TPC with clean liquid. This paper will explore comparisons of the argon purity measured by the purity monitors with those measured using muons in the TPC from October 2018 to November 2018. A new method is introduced to measure the liquid argon purity in the TPC using muons crossing both drift volumes of ProtoDUNE-SP. For extended periods on the timescale of weeks, the drift electron lifetime was measured to be above 30 ms using both systems. A particular focus will be placed on the measured purity of argon as a function of position in the detector.

The accurate computational prediction of mutant burden in spatially structured growing cell populations is a major goal both for basic evolutionary science, such as interpreting bacterial evolution studies, and for clinical applications, such as predicting the timing of drug resistance-induced cancer relapse for individual patients. Yet, this is currently not feasible for biologically realistic parameters, due to the inefficiency of computationally simulating stochastic mutant dynamics in large populations. Here, we fill this gap by deriving universal scaling laws that allow the straightforward prediction of the number of single-hit, double-hit, and multihit mutants as a function of wild-type population size in spatially expanding populations, in different spatial geometries, without the need to perform lengthy computer simulations. We demonstrate the applicability of this approach by reconciling different results from experimental evolution studies in bacteria that examine the role of gene amplifications for the rate of evolution.

The regulation of organ size is a fundamental biological question. This study investigates how feather length is regulated in chickens. We found that collar bulge stem cell zones vary in size: main sickle > lesser sickle > contour feathers. During growth, IGF and FGF9 signaling are highly expressed, while BMP, WIF1, and FGF18 increase toward growth termination. Functional assays show that insulin-like growth factor/fibroblast growth factor signaling promotes feather elongation via tyrosine kinase receptor signaling. Single-cell RNA sequencing analysis reveals accelerated differentiation of keratinocytes in short contour feathers compared to long sickle feathers. In Phoenix chickens, superlong main sickle feathers exhibit specialized stem cell zones with enhanced DLL1 expression and expanded intermediate-layer cell clusters with dynamic interactions involving NOTCH1/DLL1, YAP1, and WNT signaling in progenitor zones in the proximal follicle. Perturbation experiments induce short feather phenotypes arrested at various stages, shedding light on versatile regulatory mechanisms and paving the way for functional control of diverse feather lengths.

In order to diagnose the cause of some defects in the category of canonical hypergroups, we investigate several categories of hyperstructures that generalize hypergroups. By allowing hyperoperations with possibly empty products, one obtains categories with desirable features such as completeness and cocompleteness, free functors, regularity, and closed monoidal structures. We show by counterexamples that such constructions cannot be carried out within the category of canonical hypergroups. This suggests that (commutative) unital, reversible hypermagmas—which we call mosaics—form a worthwhile generalization of (canonical) hypergroups from the categorical perspective. Notably, mosaics contain pointed simple matroids as a subcategory, and projective geometries as a full subcategory.