Large magnetic fields exist in magnetars and are produced in off-central heavy-ion collisions. For the latter, field strengths are estimated to be comparable to strong interaction scales. This fact has motivated many studies of QCD physics in large magnetic fields, ranging from various model studies to lattice QCD computations. We provide a selective overview of results stemming from chiral perturbation theory. These results are based solely on the pattern of spontaneous and explicit symmetry breaking of QCD in a magnetic field; accordingly, they constitute low-energy theorems that must be satisfied in any approach. A few discrepancies with models and tension with lattice data are highlighted.

Magnetic fields are ubiquitous across different physical systems of current interest; from the early Universe, compact astrophysical objects and heavy-ion collisions to condensed matter systems. A proper treatment of the effects produced by magnetic fields during the dynamical evolution of these systems, can help to understand observables that otherwise show a puzzling behavior. Furthermore, when these fields are comparable to or stronger than \Lambda_QCD, they serve as excellent probes to help elucidate the physics of strongly interacting matter under extreme conditions of temperature and density. In this work we provide a comprehensive review of recent developments on the description of QED and QCD systems where magnetic field driven effects are important. These include the modification of meson static properties such as masses and form factors, the chiral magnetic effect, the description of anomalous transport coefficients, superconductivity in extreme magnetic fields, the properties of neutron stars, the evolution of heavy-ion collisions, as well as effects on the QCD phase diagram. We describe recent theory and phenomenological developments using effective models as well as LQCD methods. The work represents a state-of-the-art review of the field, motivated by presentations and discussions during the "Workshop on Strongly Interacting Matter in Strong Electromagnetic Fields" that took place in the European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT*) in the city of Trento, Italy, September 25-29, 2023.

The goal of this work is to extend the standard persistent homology pipeline for exploratory data analysis to the 2-D persistence setting, in a practical, computationally efficient way. To this end, we introduce RIVET, a software tool for the visualization of 2-D persistence modules, and present mathematical foundations for this tool. RIVET provides an interactive visualization of the barcodes of 1-D affine slices of a 2-D persistence module $M$. It also computes and visualizes the dimension of each vector space in $M$ and the bigraded Betti numbers of $M$. At the heart of our computational approach is a novel data structure based on planar line arrangements, on which we can perform fast queries to find the barcode of any slice of $M$. We present an efficient algorithm for constructing this data structure and establish bounds on its complexity.

The pattern of chiral symmetry breaking is exploited to compute vector and axial-vector pion matrix elements in a uniform magnetic field. Our results are model independent, and thereby constitute low-energy theorems that must be obeyed by QCD in external magnetic fields. Chiral perturbation theory and lattice QCD results are compared, for which there is some tension. As an application, the matrix elements are utilized to compute pion decay rates in a magnetic field.

A growing number of students are completing undergraduate degrees in statistics and entering the workforce as data analysts. In these positions, they are expected to understand how to utilize databases and other data warehouses, scrape data from Internet sources, program solutions to complex problems in multiple languages, and think algorithmically as well as statistically. These data science topics have not traditionally been a major component of undergraduate programs in statistics. Consequently, a curricular shift is needed to address additional learning outcomes. The goal of this paper is to motivate the importance of data science proficiency and to provide examples and resources for instructors to implement data science in their own statistics curricula. We provide case studies from seven institutions. These varied approaches to teaching data science demonstrate curricular innovations to address new needs. Also included here are examples of assignments designed for courses that foster engagement of undergraduates with data and data science.

Monitoring the money supply is an important prerequisite for conducting sound monetary policy, yet monetary indicators are conventionally estimated in aggregate. This paper proposes a new methodology that is able to leverage micro-level transaction data from real-world payment systems. We apply a novel computational technique to measure the durations for which money is held in individual accounts, and compute the transfer velocity of money from its inverse. Our new definition reduces to existing definitions under conventional assumptions. However, inverse estimation remains suitable for payment systems where the total balance fluctuates and spending patterns change in time. Our method is applied to study Sarafu, a small digital community currency in Kenya, where transaction data is available from 25 January 2020 to 15 June 2021. We find that the transfer velocity of Sarafu was higher than it would seem, in aggregate, because not all units of Sarafu remained in active circulation. Moreover, inverse estimation reveals strong heterogineities and enables comparisons across subgroups of spenders. Some units of Sarafu were held for minutes, others for months, and spending patterns differed across communities using Sarafu. The rate of circulation and the effective balance of Sarafu changed substantially over time, as these communities experienced economic disruptions related to the COVID-19 pandemic and seasonal food insecurity. These findings contribute to a growing body of literature documenting the heterogeneous patterns underlying headline macroeconomic indicators and their relevance for policy. Inverse estimation may be especially useful in studying the response of spenders to targeted monetary operations.

We revisit two-color, two-flavor chiral perturbation theory at finite isospin and baryon density. We investigate the phase diagram obtained varying the isospin and the baryon chemical potentials, focusing on the phase transition occurring when the two chemical potentials are equal and exceed the pion mass (which is degenerate with the diquark mass). In this case, there is a change in the order parameter of the theory that does not lend itself to the standard picture of first order transitions. We explore this phase transition both within a Ginzburg-Landau framework valid in a limited parameter space and then by inspecting the full chiral Lagrangian in all the accessible parameter space. Across the phase transition between the two broken phases the order parameter becomes an $SU(2)$ doublet, with the ground state fixing the expectation value of the sum of the magnitude squared of the pion and the diquark fields. Furthermore, we find that the Lagrangian at equal chemical potentials is invariant under global $SU(2)$ transformations and construct the effective Lagrangian of the three Goldstone degrees of freedom by integrating out the radial fluctuations.

Materials discovery via high-throughput methods relies on the availability of structural prototypes, which are generally decorated with varying combinations of elements to produce potential new materials. To facilitate the automatic generation of these materials, we developed $\textit{The AFLOW Library of Crystallographic Prototypes}$$\unicode{x2014}$ a collection of crystal prototypes that can be rapidly decorated using the AFLOW software. Part 2 of this work introduces an additional 302 crystal structure prototypes, including at least one from each of the 138 space groups not included in Part 1. Combined with Part 1, the entire library consists of 590 unique crystallographic prototypes covering all 230 space groups. We also present discussions of enantiomorphic space groups, Wigner-Seitz cells, the two-dimensional plane groups, and the various different space group notations used throughout crystallography. All structures $\unicode{x2014}$ from both Part 1 and Part 2 $\unicode{x2014}$ are listed in the web version of the library available at aflow.org/CrystalDatabase.

On the Fr\'{e}chet space of entire functions $H(\mathbb{C})$, we show that every nonscalar continuous linear operator $L:H(\mathbb{C})\to H(\mathbb{C})$ which commutes with differentiation has a hypercyclic vector $f(z)$ in the form of the infinite product of linear polynomials: \[ f(z) = \prod_{j=1}^\infty \, \left( 1-\frac{z}{a_j}\right), \] where each $a_j$ is a nonzero complex number.

The ability to control the frequency of an external-cavity diode laser (ECDL) is an essential component for undergraduate laboratories and atomic physics research. Typically the housing for the ECDL's diffraction grating and piezoelectric transducer is either purchased commercially or machined from metal. Here, we present an alternative to these commonly used options that utilizes 3D printing, a tool available in many physics departments. We characterize the performance of our ECDL system using atomic spectroscopy and self-heterodyne interferometry and show that it is sufficient for use in undergraduate spectroscopy experiments and a number of research applications where extremely narrow laser linewidths are not necessary. The performance and affordability of 3D-printed designs make them an appealing option for future use.

An easily available resource of common crystal structures is essential for researchers, teachers, and students. For many years this was provided by the U.S. Naval Research Laboratory's $Crystal\ Lattice\ Structures$ web page, which contained nearly 300 crystal structures, including a majority of those which were given $Strukturbericht$ designations. This article presents the updated version of the database, now including 288 standardized structures in 92 space groups. Similar to what was available on the web page before, we present a complete description of each structure, including the formulas for the primitive vectors, all of the basis vectors, and the AFLOW commands to generate the standardied cells. We also present a brief discussion of crystal systems, space groups, primitive and conventional lattices, Wyckoff positions, Pearson symbols and $Strukturbericht$ designations.

Suppose $\Lambda$ is a discrete infinite set of nonnegative real numbers. We say that ${\Lambda}$ is type $2$ if the series $s(x)=\sum_{\lambda\in\Lambda}f(x+\lambda)$ does not satisfy a zero-one law. This means that we can find a non-negative measurable "witness function" $f: {\mathbb R}\to [0,+ {\infty})$ such that both the convergence set C(f, {\Lambda})=\{x: s(x)<+ {\infty} \} and its complement the divergence set $D(f, {\Lambda})=\{x: s(x)=+ {\infty} \}$ are of positive Lebesgue measure. If ${\Lambda}$ is not type $2$ we say that ${\Lambda}$ is type $1$. The main result of our paper answers a question raised by Z. Buczolich, J-P. Kahane, and D. Mauldin. By a random construction we show that one can always choose a witness function which is the characteristic function of a measurable set. We also consider the effect on the type of a set ${\Lambda}$ if we randomly delete its elements. Motivated by results concerning weighted sums $\sum c_n f(nx)$ and the Khinchin conjecture, we also discuss some results about weighted sums $\sum_{n=1}^{\infty}c_n f(x+\lambda_n)$.

We study the topological susceptibility and fourth cumulant of the QCD vacuum in a background magnetic field using three-flavor chiral perturbation theory ($\chi$PT) for arbitrary quark masses and $n$-flavor $\chi$PT with degenerate quark masses. We find that the enhancement of the topological susceptibility is larger in the three-flavor $\chi$PT compared to two-flavor $\chi$PT. Additionally, in comparing the fourth cumulant, we find that its suppression is comparable for magnetic fields, $eH\lesssim 0.8m_{\pi}^{2}$, and weaker for larger magnetic fields in three-flavor $\chi$PT with its enhancement beginning at a significantly lower critical magnetic field compared to two-flavor $\chi$PT. We also find that the enhancement of the topological susceptibility in $n$-flavor $\chi$PT with degenerate quarks is significantly larger and the suppression of the topological cumulant significantly greater at weak fields with the critical magnetic field pushed out to larger magnetic fields compared to both two and three-flavor $\chi$PT.

The degenerate affine and affine BMW algebras arise naturally in the context of Schur-Weyl duality for orthogonal and symplectic Lie algebras and quantum groups, respectively. Cyclotomic BMW algebras, affine Hecke algebras, cyclotomic Hecke algebras, and their degenerate versions are quotients. In this paper the theory is unified by treating the orthogonal and symplectic cases simultaneously; we make an exact parallel between the degenerate affine and affine cases via a new algebra which takes the role of the affine braid group for the degenerate setting. A main result of this paper is an identification of the centers of the affine and degenerate affine BMW algebras in terms of rings of symmetric functions which satisfy a "cancellation property" or "wheel condition" (in the degenerate case, a reformulation of a result of Nazarov). Miraculously, these same rings also arise in Schubert calculus, as the cohomology and K-theory of isotropic Grassmanians and symplectic loop Grassmanians. We also establish new intertwiner-like identities which, when projected to the center, produce the recursions for central elements given previously by Nazarov for degenerate affine BMW algebras, and by Beliakova-Blanchet for affine BMW algebras.

Classical theory predicts that for two competing populations subject to a constant downstream drift, the faster disperser will competitively exclude the slower disperser. In the current work, we consider a novel model of a "much faster" dispersing species, modeled via a $p$-Laplacian operator, competing with a slower disperser. We prove global existence of weak solutions to this model for any positive initial condition, in the regime \frac{3}{2} < p <2. Counterintuitively, we show that while the faster disperser always wins - the "much faster" disperser could actually lose, for certain initial data. Several numerical simulations are conducted to confirm our analytical findings. Our results have implications for biodiversity, refuge design, and improved biological control, driven by habitat fragmentation and climate change.

The Cryogenic Dark Matter Search (CDMS) utilizes large mass, 3" diameter x 1" thick target masses as particle detectors. The target is instrumented with both phonon and ionization sensors, the later providing a $\sim$1 V cm$^{-1}$ electric field in the detector bulk. Cumulative radiation exposure which creates $\sim 200\times 10^6$ electron-hole pairs is sufficient to produce a comparable reverse field in the detector thereby degrading the ionization channel performance. To study this, the existing CDMS detector Monte Carlo has been modified to allow for an event by event evolution of the bulk electric field, in three spatial dimensions. Our most resent results and interpretation are discussed.

We introduce a graph partitioning problem motivated by computational topology and propose two algorithms that produce approximate solutions. Specifically, given a weighted, undirected graph $G$ and a positive integer $k$, we desire to find $k$ disjoint trees within $G$ such that each vertex of $G$ is contained in one of the trees and the weight of the largest tree is as small as possible. We are unable to find this problem in the graph partitioning literature, but we show that the problem is NP-complete. We then propose two approximation algorithms, one that uses a spectral clustering approach and another that employs a dynamic programming strategy, which produce near-optimal partitions on a family of test graphs. We describe these algorithms and analyze their empirical performance.

We use the Polyakov-loop extended two-flavor quark-meson model as a low-energy effective model for QCD to study the phase diagram in the $\mu_I$--$T$ plane where $\mu_I$ is the isospin chemical potential. In particular, we focus on the Bose condensation of charged pions. At $T=0$, the onset of pion condensation is at $\mu_I={1\over2}m_{\pi}$ in accordance with exact results. The phase transition to a Bose-condensed phase is of second order for all values of $\mu_I$ and in the $O(2)$ universality class. The chiral critical line joins the critical line for pion condensation at a point whose position depends on the Polyakov-loop potential and the sigma mass. For larger values of $\mu_I$ these curves are on top of each other. The deconfinement line enters smoothly the phase with the broken $O(2)$ symmetry. We compare our results with recent lattice simulations and find overall good agreement.