We give a damped inexact Newton method for entropy-regularized least-squares on the nonnegative orthant that converges globally at a linear rate with $O(\logε^{-1})$ iteration complexity, locally at a superlinear-to-quadratic rate, and is immune to the finite-precision overflow that limits classical dual solvers. A scale-shape decomposition of the primal -- separating its scale from its direction -- produces a dual with a nonsingular Jacobian. Objectives and Jacobians are evaluated through stable log-sum-exp and softmax primitives. Lambert W bounds on the scale uniformly control the Jacobian's spectrum, from which both rates follow. The solution map is jointly Lipschitz in the data, regularization parameter, and reference measure, and extends continuously to the vanishing-regularization limit. Experiments on a problem from analytic continuation of quantum Monte Carlo data confirm the predicted overflow resilience and convergence behavior.

While current network intrusion detection systems achieve satisfactory accuracy, they often lack explainability. Subgroup Discovery (SD) addresses this by building interpretable rules that characterize feature interactions associated with attack traffic. With large datasets, classical heuristic beam search methods struggle with exponentially scaling search spaces and can prune critical multi-feature interactions. This paper introduces a quantum-enhanced pipeline for SD applied to network intrusion detection using NSL-KDD, formulating SD as quantum optimization for the first time. By encoding feature selection as a Quadratic Unconstrained Binary Optimization (QUBO) and solving it via the Quantum Approximate Optimization Algorithm (QAOA) on IBM Quantum hardware (ibm_pittsburgh), the pipeline identifies subgroups of network features that discriminate normal from attack traffic. A least-squares regression QUBO formulation fits the Weighted Relative Accuracy (WRAcc) landscape over feature subsets, with surrogate sampling for larger QUBOs. Results are benchmarked against exhaustive enumeration and Beam Search using ratios for Hamiltonian quality and WRAcc. Hardware scaling experiments on ibm_pittsburgh (10-30 qubits) reveal that QAOA at depth p = 1 shows WRAcc ratios of 0.983 at 10 qubits, 0.971 at 15 qubits, 0.855 at 20 qubits, and 0.624 at 25 qubits, degrading to 0.039 at 30 qubits as circuit noise dominates, establishing an empirical NISQ scaling boundary. Results demonstrate that QAOA discovers subgroups competitive with classical heuristics and finds multi-feature interaction patterns that greedy Beam Search prunes, with QAOA-unique subgroups achieving up to 99.6% test precision. This work establishes a framework for quantum combinatorial optimization in cybersecurity and characterizes hardware scaling for NISQ devices.

Wave-driven desalination systems are an innovative solution to the global freshwater crisis, leveraging the complementary characteristics of seawater reverse osmosis and wave energy converters. However, the high costs of this system pose a significant barrier to widespread adoption. Optimization can help these systems reach a more competitive levelized cost of water, but the highly coupled nature of the system necessitates a multidisciplinary design optimization approach. This paper presents a holistic, multidisciplinary design optimization framework for wave-driven desalination system design, integrating models for wave energy converter hydrodynamics, power take-off transmission, seawater reverse osmosis constraints, and economic analysis. This study demonstrates the impact of multidisciplinary design optimization for wave-driven desalination systems, resulting in a 69.5% reduction in levelized cost of water compared to a nominal design. We demonstrate that multidisciplinary design optimization outperforms sequential design approaches, yielding lower levelized costs of water and substantially different optimal designs. The multidisciplinary design optimization results suggest major design changes compared to designs found in the literature. Notably, smaller wave energy converters and larger pistons, along with smaller accumulators and larger seawater reverse osmosis plant installations, are preferred. These design trends are consistent across a range of sea states, suggesting potential generalizability beyond a single location. This study demonstrates the importance of holistic modeling and co-design for wave-driven desalination systems and establishes an effective optimization framework for future studies to build upon.

Continuous Integration (CI) enforces repository-level correctness through multi-stage workflows and is central to modern software development, yet diagnosing and repairing CI failures remains challenging. Unlike traditional program repair, CI failures frequently involve non-code artifacts, environment and dependency issues, noisy execution logs, and workflow-level constraints. Existing program repair benchmarks fall short in this setting: they are largely test-centric, restrict repairs to source code, assume fixed execution environments, and evaluate under simplified CI workflows that do not reflect real repository-level validation. We introduce CI-Repair-Bench, a benchmark for CI-verified, repository-level program repair constructed from real GitHub Actions executions. It contains 567 CI failure instances from 103 repositories and evaluates repair correctness exclusively through full CI re-execution under original workflows. Failures are categorized into 12 CI error types, enabling fine-grained, error-type-aware evaluation. To demonstrate benchmark usage, we include a reference CI repair workflow that analyzes CI logs to localize faults and generate candidate patches. Empirical results show that automated repair is most effective for localized, tool-enforced failures such as formatting and linting, while environment, dependency, and configuration-related failures remain challenging; the best-performing LLM achieves an 18.9% repair success rate. CI-Repair-Bench provides a realistic evaluation foundation for advancing research on CI-native automated program repair.

A recent construction of linear complementary pairs (LCPs) of algebraic geometry codes is intimately linked to the identification of non-special divisors of small degree within a function field over a finite field. Let $\mathbb{F}_q$ be the finite field of cardinality $q$. In this work, we consider a function field $F/\mathbb{F}_q$ of genus $g$ defined by a Kummer extension of type $y^m = f(x)$, where $f(x)$ is a polynomial in $\mathbb{F}_q[x]$. Based on the theory of generalized Weierstrass semigroups at several places, we provide an arithmetic criterion to identify all non-special divisors of degree $g-1$ and $g$ whose support is contained in a subset of the totally ramified places of the extension $F/\mathbb{F}_q(x)$. Furthermore, we explicitly determine all non-special divisors of degree $g-1$ in certain cases. Finally, we apply these results to provide explicit new families of LCPs algebraic geometry codes.

Isotopic fission-fragment distributions of $^{240}$Pu have been measured, for the first time, as a function of the initial excitation energy, and the prompt neutron multiplicity has been derived from these data. The $^{240}$Pu fissioning system was produced through the two-proton transfer reaction between $^{238}$U and $^{12}$C, a surrogate reaction for the neutron-capture-induced fission $^{239}$Pu(n,f). The reaction was measured in inverse kinematics, allowing the fission fragments to be fully identified with the VAMOS Spectrometer. When compared to neutron-capture-induced reactions, the observed prompt neutron multiplicity shows a clear reduction in the surrogate two-proton transfer, revealing an unexpected influence of the entrance channel in the fission output. At the same time, fission-fragment yield distributions obtained in neutron-capture-induced reactions show a relative fission-fragment production in the symmetry region similar to that measured in this work. The discrepancy in neutron multiplicity is attributed to the additional angular momentum induced in the multi-nucleon transfer reactions, which excites the fissioning system to higher-spin states, increasing the probability of gamma emission that competes with neutron evaporation, in particular from the fission barrier to the scission point. This observation underlines the limitations in the utilisation of properties derived from surrogate reactions in nuclear technology and other applications of nuclear fission.

We present quantitative evidence that high-quality internucleon forces derived from $χ$EFT exhibit a striking dominance of Wigner's supermultiplet symmetry, without invoking the large-$N_c$ limit of QCD or assumptions about specific nuclei. We trace the manifestation of this symmetry in nuclear structure using the \textit{ab initio} Symmetry Adapted Model (SAM) and identify suppressed spin-isospin polarizability. Our calculations show that a majority of $\rm ^4He$, $\rm ^6Li$, and $\rm ^6He$ wave functions is concentrated in a few $\rm U(4)$ irreducible representations, without imposing any \textit{a priori} constraints on the model space. This emergent feature points to a strategy for reducing explosive many-body bases of the NCSM while retaining physically important configurations needed to compute observables.

Computing the diameter of a graph is a problem of great interest both in general algorithms research and specifically within fine-grained complexity, where it is a cornerstone hard problem. Recent work has achieved a full conditional lower bound tradeoff curve for both directed and undirected graphs. However, the best known upper bounds do not match the lower bounds. In particular, the best known approximation scheme for undirected graph diameter has not been improved. Moreover, this scheme is randomized and no similar deterministic scheme is known. Another fundamental field of research in shortest paths computation is the construction of approximate distance oracles. Thorup and Zwick [JACM'05] provided the first such distance oracle with constant query time and (conditionally) optimal space, and in the years since many advances have led to a vast toolbox of techniques and data structures. These two areas of research seem natural to combine since they both concern approximating shortest paths. However, the known diameter approximation algorithms only use a small subset of the techniques used in distance oracles research. In this work we show that in fact approximate diameter and distance oracles are intricately connected. We first demonstrate a strong connection between the current best known diameter approximation scheme of Cairo, Grossi and Rizzi ("CGR") and the $(2k-1)$-approximate distance oracle of Thorup and Zwick. This allows us to derandomize the CGR algorithm and obtain the first deterministic diameter approximation tradeoff. We further derandomize other central techniques in the field of distance oracles and use them to achieve new deterministic diameter approximation algorithms. Finally, we show how these new techniques can be used to derandomize many current best known results in various fields of shortest paths approximations.

We study the Maximum Balanced Biclique (MBB) problem: Given a bipartite graph $G$ with $n$ vertices on each side, find a balanced biclique in $G$ with maximum size. We give a polynomial-time $\left(\frac{n}{\widetildeΩ\left((\log n)^3\right)}\right)$-approximation algorithm for the problem, which improves upon an $\left(\frac{n}{Ω\left((\log n)^2\right)}\right)$-approximation by Chalermsook et al. (2020) and answers their open question. Furthermore, our approximation ratio matches that of the maximum clique problem by Feige (2004) up to an $O(\log \log n)$ factor.

We prove that the directed five-dimensional torus $D_5(m) = \operatorname{Cay}((\mathbb{Z}_m)^5, \{e_0, e_1, e_2, e_3, e_4\})$ has a Hamilton decomposition for every odd integer $m \geq 3$. This is the first higher-dimensional case in which the return-map method requires a genuine zero-set selector rather than an odometer-type correction. The construction assigns the five outgoing generators by a cyclic layer schedule with one non-constant layer determined by a zero-set Latin table; an explicit finite exact-cover certificate proves that this layer is a matching. By cyclic symmetry, Hamiltonicity of all color classes reduces to a single normalized return map. For $m \geq 5$, an explicit first-return calculation on the section $p = 2$ gives one induced cycle whose excursion lengths sum to $m^4$. The remaining modulus $m = 3$ is settled by a printed finite cycle certificate. A companion Lean 4 formalization provides an independent machine verification of the Cayley statement and the finite certificates; source, audit scripts, and ancillary search code are available at https://github.com/aria1th/Torus-Hamilton-Decomposition-Program.

For the first time, this paper presents three very-near-Earth reconnection (VNERX) events observed within the same 12-hour-long storm main phase. The THEMIS inner probes observed the hallmarks of three episodes of tailward retreating x-lines positioned between magnetic local time (MLT) 23-24 and radial distance 12-13 Earth radii (RE). The events occurred within a thin current sheet, < 1 RE thick. Simultaneously, dispersionless energetic particle injections above 10s of keV and magnetic field dipolarizations were observed near and earthward of geosynchronous altitude by the KOMPSAT and Arase satellites. Arase observed earthward flow bursts at or below geosynchronous altitude via ExB enhancements, suggesting VNERX ejecta proceed below geosynchronous orbit. These observations demonstrate that VNERX events, which predominantly occur during the storm main phase, can be frequent and essential for driving injections that can effectively power the ring current. However, they can be observed only at the pre-midnight sector, close to the neutral sheet.

This paper proposes RCMAES, a novel variant of the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) for CEC benchmark optimization. RCMAES integrates a dimension-dependent nonlinear population-size reduction strategy with an adaptive restart mechanism within a pure CMA-ES framework. RCMAES is evaluated on three benchmark suites (CEC2017, CEC2020, and CEC2022) and compared with state-of-the-art DE algorithms as well as its closely related counterpart, BIPOP-aCMAES. Experimental results show that RCMAES achieves competitive and robust performance across all benchmarks.

Several recent methods have shown that it is possible to compute rate constants of very slow biomolecular processes using simulations where a time-dependent bias is added along one or several collective variables (CVs). We previously reported the exponential average time-dependent rate (EATR) method, which can improve upon these approaches by accounting for how efficiently the external biasing potential modifies the observed rate using a learned CV-quality factor $γ$. This results in more accurate rate estimates using the same data when biasing a suboptimal coordinate. However, as formulated EATR depended on the biasing potential varying over time to properly determine the biasing efficiency, which limits the method's applicability to quasi-static biasing schemes such as ``flooding'' or on-the-fly probability enhanced sampling (OPES). Here, we present the EATR-flooding approach, which generalizes our method by replacing the need for a time dependent bias by instead varying (stepping up) the strength of the biasing potential across multiple sets of simulations. We implement this approach as an open-source Python library, and demonstrate that this approach is accurate without substantial loss of efficiency compared to standard EATR for a coarse-grained protein system, and also show good performance on a fully atomistic cavity-ligand model. Two additional appealing features of EATR-flooding are an internal check for over-biasing and the fact that only a single $γ$ parameter is predicted for a given choice of CVs, as compared to our earlier results where $γ$ empirically depended on biasing rate. Finally, we believe EATR-flooding applies not only to OPES simulations but more generally to CV biasing enhanced sampling approaches, making it broadly useful.

Quantum state tomography provides a fundamental framework for reconstructing quantum states. When the measurement data are not informationally complete, the observed statistics admit multiple compatible density matrices, making the reconstruction problem inherently underdetermined and calling for the selection of a meaningful estimator. Two well-established approaches to address this ambiguity are Maximum Entropy (MaxEnt) and Variational Quantum Tomography (VQT). A variant of VQT, named VQT$_\infty$, has been introduced to reproduce MaxEnt-like solutions. In this work, we generalize this approach by introducing a parametrized cost function that interpolates between the 1-norm and the infinity norm, thereby unifying VQT and VQT$_\infty$ within a single framework. By tuning the associated hyperparameters, the proposed method enables controlled exploration of the set of compatible density matrices. We show that this interplay yields reconstructed states with higher fidelity to the MaxEnt solution than those obtained via VQT$_\infty$ while preserving computational tractability.

Recent observations of protostars with the James Webb Space Telescope have revealed unprecedented chemical complexity from their ice absorption features. However, these spectra are likely influenced by radiative transfer effects, and there is little understanding of how this impacts our ability to identify, quantify, and interpret the observed ice features. We have developed a new modeling framework to investigate the radiative transfer through icy protostellar envelopes, and apply this to the IRAS 15398-3359 protostar observed by the JWST CORINOS program. The modeled H$_2$O and CO column densities are similar to previous empirical studies, but we require a high CO$_2$/H$_2$O ratio of 76% to match the optical depth of the 15 $μ$m band. We use our modeled continuum to calculate a 6-10 $μ$m optical depth spectrum, and see considerable differences compared to a simple polynomial continuum model, underscoring the challenges with quantifying trace ice species in this range. For this source, we find that the observed absorption predominantly originates along the viewing line of sight between 1000 - 2000 au, peaking at the transition from the outflow cavity to the envelope; the spectra are largely insensitive to absorption from ices in the outer envelope, which extends out to 20,000 au. Lastly, we show that depending on how the line of sight intersects the cavity, the apparent CO$_2$/H$_2$O and CO/H$_2$O column density ratios can be underestimated compared to the underlying ice abundance ratios. Together this provides important context for interpreting the ice constraints derived from JWST observations of protostars.

Automatic detection of topical trends at scale is both challenging and essential for maintaining a dynamic content ecosystem on social media platforms. In this work, we present a large-scale system for identifying emerging topical trends on Snapchat, one of the world's largest short-video social platforms. Our system integrates multimodal topic extraction, time-series burst detection, and LLM-based consolidation and enrichment to enable accurate and timely trend discovery. To the best of our knowledge, this is the first published end-to-end system for topical trend detection on short-video platforms at production scale. Continuous offline human evaluation over six months demonstrates high precision in identifying meaningful trends. The system has been deployed in production at global scale and applied to downstream surfaces including content ranking and search, driving measurable improvements in content freshness and user experience.

Entanglement, a fundamental phenomenon of quantum theory, has recently been observed in processes in high-energy physics. This opens new avenues for probing quantum effects in relativistic regimes, but also poses conceptual and technical challenges. We develop a general framework based on shadow tomography techniques for characterising spin-spin correlations in collider experiments. This improves the analysis of spin-spin entanglement, where relativistic motion couples spin and momentum and the momenta of the investigated particles are not under experimental control. As a proof of concept we illustrate the application of our formalism to top quark pair production at the Large Hadron Collider at CERN. The framework, however, is general and flexible and can be readily applied to more complex final states and systems with more particles.

The growing capability of artificial intelligence (AI) leads to its increasing adoption in writing, spurring discussions around whether writers should disclose their AI use in writing. What influences the perceived necessity of disclosure? We look into this question from three dimensions: perspective (reader or writer of the text), purpose (the goal of reading or writing), and procedural factors (how AI was used in the writing process in terms of replaceability, effortfulness, intentionality, and directness). In a vignette study (N = 727), we find that readers consider disclosure to be more necessary than writers, and disclosure is regarded as more necessary when AI's contribution in writing is irreplaceable, directly incorporated, and when the writer does not intentionally steer AI generation. To our surprise, the writers' intentionality of AI use produces contrasting effects on readers' and writers' perceived necessity of disclosure. Moreover, the effort of writing shows no significant effect on the perceived necessity. This study contributes to the conversation on transparent AI use by revealing readers' and writers' grassroots judgments, providing a unique angle to reflect on existing regulations, and offering insights into how AI disclosure guidance and tools could be designed to better align with readers' and writers' perceptions.

The explainable artificial intelligence is used to analyze the stochastic Fredholm integral equations (SFIEs) and stochastic deep neural networks (SDNNs). The neural operator-based stochastic fixed point framework is used to develop SDNNs. The solution of an SFIE is obtained through successive applications of an integral operator, and this iterative structure naturally resembles the layered architecture of a neural network. The associated nonlinear versions of SFIE and SDNN are discussed. The SFIE and SDNN are used to solve the Black-Scholes equation, contagion dynamics of financial networks, and the Merten jump diffusion equation. It is observed that the results obtained through SFIE and SDNN for all the applications agree well.

The variational method is used to study the energy levels of muonic helium $(μ^{-} \, e^{-} \, He)$ with an electron in the ground state and a muon in an excited state with principal and orbital quantum numbers $n \sim l+1 \sim 14$. The variational wave functions are chosen in the Gaussian form. The matrix elements of the Hamiltonian in the nonrelativistic approximation, as well as corrections for the vacuum polarization and relativism, are calculated analytically. A series of energies of the Rydberg muon states is obtained, which can be studied experimentally.

Chalcogenide phase-change materials (PCMs) are important for nonvolatile memory and reconfigurable photonic technologies. The GeTe-Sb2Te3 mixture system, commonly referred to as GST, is the most well-known PCM family, but new PCMs are needed to broaden the accessible property space while retaining fast switching. Here, we propose a thermodynamic framework, motivated by Ostwald's rule, for understanding and identifying PCM materials. Since direct modeling of phase-transition dynamics is computationally expensive, Using first-principles calculations, we systematically evaluate the energetics of ternary chalcogenide mixtures along binary-binary tie lines and their polymorphs. By comparing ground-state and metastable structures, we assess phase stability, miscibility, and the likelihood of GST-like polymorph-mediated crystallization pathways across a broad composition space. The calculations reproduce known behavior in GST and related systems and identify several promising candidate mixtures with similar features. These results provide insight into why some PCM systems are more favorable than others and establish thermodynamic polymorph screening as a practical route for future PCM discovery.

Random matrices now play a role in many parts of computational mathematics. To advance these applications, it is desirable to have tools that are flexible, easy to use, and powerful. Over the last 25 years, researchers have developed a remarkable family of results, called matrix concentration inequalities, that meet the criteria. This paper offers an invitation to the field of matrix concentration and its multifarious applications.

We investigate the survival of dust trapped in magnetically confined cool gas clouds (or {\it prominences}) around rapidly rotating M-dwarfs exhibiting the ``scallop-shell'' light-curve morphology. Using a two-dimensional magnetohydrodynamic simulation, we extend previous coronal prominence models to include a passive tracer field to allow for a single injection of collisionally charged dust grains. The tracer evolution reveals how recurrent centrifugal breakouts--the slingshot process--remove dust and gas from the prominence while chromospheric evaporation replenishes gas from below. For our simulated star, which has $R_{\ast} = 0.6 R_{\odot}$, $M_{\ast} = 0.3 M_{\odot}$, and $P_{\ast} = 0.32$ days, the resulting dust content decays exponentially with a minimum half-life of approximately 6 stellar rotations, representing a lower limit set by our assumption of fully coupled dust and gas dynamics. Synthetic velocity-phase diagnostics show a single, phase-locked feature that fades steadily, reproducing the behaviour of dips seen in TESS and K2 light curves. Comparison with observed river plots suggests a natural classification: (i) persistent, non-decaying features formed by quiescent prominences below co-rotation; (ii) gradually fading features produced by slingshot prominences near co-rotation; and (iii) abrupt disappearances linked to magnetic reconnection and flare-driven ejections. These results demonstrate that dust-bearing prominences--undergoing repeated slingshots--can persist for tens of rotations, linking the observed longevity of the scallop-shell photometric features with the dynamic cycle of prominence slingshot ejections.

Developing scalable and environmentally benign anticorrosion coatings is critical for protecting steel infrastructure in chloride-rich environments. Here, a nacre-inspired multilayer epoxy coating reinforced with four MXene systems is investigated. This architecture forms a dense lamellar network that increases diffusion tortuosity and introduces electroactive surfaces for ion interactions. Electrochemical impedance spectroscopy (EIS) confirms that the multilayer design increases coating resistance from ~103 to ~108 Ohm/cm2. A clear performance hierarchy was observed: P-(TiVCrMo)C3 > O-Ti3C2Tx > O-(TiVCrMo)C3 > P-Ti3C2Tx. Density functional theory (DFT) calculations reveal that P-Ti3C2 strongly adsorbs O2, indicating higher surface reactivity, while oxygen termination stabilizes the surface by partially passivating Ti sites. In contrast, P-(TiVCrMo)C3 exhibits strong adsorption of oxygen-containing species due to its multi-metal electronic structure, promoting the formation of protective oxides. These results highlight the delicate balance of surface chemistry, electronic structure, and compositional entropy in designing next-generation MXene-based anticorrosion coatings for marine and industrial environments.

Vector-borne diseases often infect multiple host species, increasing the likelihood of disease persistence due to the presence of multiple reservoirs. Vector biting patterns and feeding preferences can shift in response to selective pressures introduced by disease control interventions, altering the dynamics of transmission. In this paper, we develop a mathematical model that couples host diversity and adaptive vector behavior with vector-borne disease transmission dynamics, focusing on a system with two hosts and a vector population exhibiting preference for one host. We derive the basic reproduction number, $R_0$, a threshold that determines the existence of two equilibria in our model, and obtain conditions that can lead to the long-term persistence of the disease. Our analysis suggests that shortening the infectious period of the vector's preferred host is an effective control strategy. We also identified a threshold that determines whether shifting vector preference toward a non-preferred host amplifies or reduces the disease burden on the primary preferred host. Our results show that protective measures for the preferred host can trigger adaptive shifts in vector preferences, reducing disease prevalence in that host. However, this shift may lead to an increase in overall host prevalence.

This paper explores the effectiveness of modular randomized testing for object oriented programs in Java. Modular testing involves testing individual components of a program in isolation. Often times, for effective test generation, a series of non-target setup calls must be included to obtain high coverage of the target component. In this work, we evaluate and improve modular testing with the EvoSuite test generator. We find that due to strict restrictions that disallow calls to non-target setup methods, EvoSuite's modular testing mode is ineffective and often results in low branch coverage. We propose \textsc{emote} (Effective Modular Testing with EvoSuite): an enhancement to EvoSuite that relaxes this restriction, allowing non-target methods to be included in the test prefixes. This modification draws inspiration from developer-written fuzz drivers, which often invoke setup methods to properly initialize the state before testing the target method. To ensure meaningful test generation, we modify EvoSuite's fitness function to focus branch coverage contributions on the call chain originating from the target method. \textsc{emote} is evaluated on a subset of the SF100 benchmark, showing a 15.15\% improvement in coverage of the target methods.

Let $K$ be a finite $p$-adic field with uniformiser $π$. In this paper we study the image of the logarithm attached to a Lubin-Tate series $[π](X)$ on the maximal ideal of so-called $π$-regular extensions of $K$; for such an extension $L|K$ we compute a basis for the additive group $\log_{[π]}(\mathcal{F}(\mathfrak{m}_L))$ as an $O_K$-module, where $\mathcal{F}(\mathfrak{m}_L)$ denotes the maximal ideal $\mathfrak{m}_L$ equipped with the $O_K$-module structure coming from the formal group associated to $[π](X)$, and determine the minimal valuation of the elements in $\log_{[π]}(\mathcal{F}(\mathfrak{m}_L))$. In the final section of this paper we discuss how some of these results extend to arbitrary finite extensions of $K$ and conclude by determining a basis of the $O_K$-module $\log_{[π]}(\mathcal{F}(\mathfrak{m}_{K_{π^n}}))$, where $K_{π^n}$ is the Lubin-Tate extension of level $n\geq 1$.

Project-based learning is recognized as an effective approach for improving engagement and applied understanding in STEM education. In quantum engineering courses, however, the question is no longer only whether students benefit from projects but how those projects should culminate if the goal is authentic disciplinary preparation. This paper examines the educational role of a conference-style paper requirement embedded within a project-based learning implementation for an introductory quantum mechanics course for engineers. We use post-course survey responses from students in a pilot run of the course. We evaluate perceived effects on conceptual understanding, scientific communication, research readiness, and attitudes toward the writing requirement itself. The results suggest that students viewed the project as beneficial for engagement, confidence, and technical skill development, while the conference-style paper emerged as a demanding but meaningful component of the experience. We argue that once PBL has been established in quantum mechanics education, conference-style writing can serve as an extension of that model, especially for graduate students. The findings support retaining the conference-paper requirement with improved scaffolding.

The evolutionary state of the 198 day eclipsing binary BM Cas is examined using spectra that cover five orbital cycles. Radial velocities measured from SiII 6347 and SiII 6371 track the motion of the primary, and a mass function is found that is similar to that obtained by Popper(1977) from MgII 4481. Absorption from a circumsystem shell complicates efforts to measure stellar velocities from FeII lines. Many of the characteristics of Halpha emission and absorption that are associated with the shell vary in sync with the motion of the primary, and it is suggested that the shell may form from material that exits the system from L2. The infrared spectral-energy distribution departs from that of an A supergiant only at wavelengths > 5um, and models are examined in which the secondary is obscured by an opaque envelope. Archived V band photometry is compared with model light curves, and it is concluded that the A supergiant is close to filling, or is filling, its Roche lobe, and that the as-yet undetected secondary may be more massive than the primary. Based on the overall properties of BM Cas and its environment, we suggest that it is an Algol or post-Algol system, in which the A supergiant was originally the more massive component. If this is the case then the stars in BM Cas had intermediate initial masses. Some of the photometric characteristics of the primary are indicative of alpha Cyg-type variability.

We study properties of the following four classes of operators on the Fock space in $\mathbb C^n:$ 1) weakly localized operators; 2) sufficiently localized operators in the sense of Xia and Zheng; 3) sufficiently localized operators; 4) strongly localized operators. In this respect, we examine composition operators, Toeplitz operators with a measure symbol whose total variation measure is a Fock-Carleson measure, and singular operators of convolution type introduced by Zhu, among others. We also provide a bounded operator which is not weakly localized and does not even belong to the Toeplitz algebra. Class 1) contains class 2), class 2) contains class 3), which clearly contains class 4). We prove that the first two inclusions are strict. Our proofs are in terms of singular operators of convolution type introduced by Zhu. The third inclusion was already known to be strict, as Wang, Cao and Zhu exhibited examples of composition operators which are sufficiently localized, but are not strongly localized. %As our main result, we show the existence of a singular operator of convolution type which is weakly localized, but is not sufficiently localized in the sense of Xia and Zheng. %The underlying question is whether the first two classes of operators coincide or not.