A subset of the vertex set of a graph is geodetically convex if it contains every vertex on any shortest path between two elements of the subset. The convex hull of a set of vertices is the smallest convex set containing the set. We study two games in which two players take turns selecting vertices of a graph until the convex hull of the jointly unselected vertices is too small. The last player to move is the winner. The achievement game ends when the convex hull of the jointly unselected vertices is not the vertex set. In the avoidance game, the convex hull of the jointly unselected vertices must always be the vertex set. We study the nim-values for several graph families, including cycle graphs, hypercube graphs, complete multipartite graphs, wheel graphs, generalized wheel graphs, and graphs with a unique minimal generating set.

We investigate the periodic $L_2$-discrepancy of infinite sequences $§_d$ in $[0,1)^d$ and its analytic counterpart, the diaphony. We prove that infinite order-2 digital sequences over $\mathbb{F}_2$ attain the optimal order $L_{2,N}^{\rm per}(§_d) \le C_d (\log N)^{d/2}/N$ for all $N \in \mathbb{N}\setminus \{1\}$, matching known lower bounds for infinitely many $N \in \mathbb{N}$. This confirms the conjectured optimality of order-2 constructions. By this result, we improve upon previously known constructions using order-5 digital sequences, and reduce the underlying dimension for the interlacing construction from $5d$ to $2d$, significantly improving practicality. We establish our bounds within a broader framework of quasi-Monte Carlo integration for periodic Besov spaces $S_{p,q}^rB(\mathbb{T}^d)$ with dominating mixed smoothness $r \in (1/p,2)$, where $p,q\in [1,\infty]$. Rules based on infinite order-2 digital sequences yield worst-case errors of order $(\log N)^{(d-1)(1-1/q)} / N^{ \min(r,1)}$ for $r \not=1$, and $(\log N)^{d(1-1/q)}/N$ for $r=1$, for all $N \in \mathbb{N}\setminus\{1\}$, while preserving extensibility in $N$.

We propose the Control Algorithm Performance Evaluation (CAPE) framework, a systematic methodology for benchmarking racing controllers under our proposed learned enhanced physics model (EPM). The proposed framework enables cross-controller comparison by evaluating five closed-loop control architectures. We further compare our proposed EPM with two state-of-the-art learned vehicle dynamics models: Deep Pacejka Model (DPM) and Deep-learning Dynamics Model (DDM). Closed-loop experiments show that across all models and controllers, the proposed EPM achieves best average lap times. Specifically, the Adaptive NMPC with EPM achieves a time of 5.82 s, compared with 12.99 s for DPM and 8.80 s for DDM, while simultaneously producing substantially lower longitudinal and lateral tracking errors under identical controller configurations. We further evaluate all three models and five controllers using a disturbance-aware simulation framework incorporating measurement noise, process disturbances, actuator delay, and parametric uncertainty. Under moderate global disturbance scaling factor (η = 1), results averaged across the five controllers show that EPM reduces a) longitudinal tracking error by 29.0% and 17.2%; b) lateral tracking error by 24.6% and 12.3%; c) while increasing average velocity magnitude by 39.9% and 3.1% relative to DPM and DDM, respectively. Overall, CAPE establishes a systematic benchmark for evaluating the performance of learned vehicle dynamics models in a closed-loop control framework and demonstrates that our proposed EPM significantly improves controller robustness and performance under realistic uncertainties.

In this work we explore the ability of inhomogeneities to result in an apparent dynamical evolution of dark energy. The idea that inhomogeneities may alter the expansion history of the Universe is not a new one. However, with the current excitement surrounding the inferred time-evolution of the equation of state of dark energy by the Dark Energy Spectroscopic Instrument (DESI), combined with Cosmic Microwave Background (CMB) and supernovae observations, it is worth revisiting. We use numerical relativity simulations of large-scale structure formation combined with nonlinear general-relativistic ray tracing to infer dark energy parameters for synthetic observers. We adopt a simplified set-up to roughly mimic the observational properties of the DESI plus supernovae and CMB constraints. In our small sample of 20 observers, we find one who infers parameters consistent with the DESI values at 2-$σ$ significance. While it is rare in our limited sample size, we show that it is at least possible for observers to infer significant non-LCDM parameters when their universe is well-described by a cosmological constant on average.

We establish robust log-convex interpolation inequalities within the scale of Gagliardo seminorms. We achieve this by deriving some Chebyshev-type integral inequalities for general non-synchronous functions. Our primary motivation for establishing these robust interpolation inequalities stems from the study of the asymptotic nonlocal-to-local stability of weak solutions to the boundary Dirichlet problem associated with the regional fractional $p$-Laplacian. More precisely, if $u_s \in W^{s,p}(Ω)$ weakly satisfies $(-Δ)_{p, Ω}^s u_s = f_s $ in $Ω$ and $ γ^s_0(u_s) = g_s$ on $\partialΩ,$ with $\frac{1}{p} < s \leq 1$ and $Ω\subset \mathbb{R}^d$ is bounded Lipschitz, then, under appropriate convergence of the data $f_s$ and $g_s$ as $s \to 1^-$, we establish that $\| u_s - u_1 \|_{W^{η,p}(Ω)} \xrightarrow{s \to 1^-} 0 $ for all $0 \leq η< 1$.

Security misconfigurations remain a leading cause of OS-level compromise, and manually keeping systems compliant with standards like Defense Information Systems Agency (DISA) Security Technical Implementation Guides (STIGs) is a tedious and expensive process. Existing compliance automation tools can reduce some of this burden, but they depend on static, pre-written corrective actions. In this paper, we introduce SHIELDS, a multi-agent system that uses large language models (LLMs) to approach OS hardening as an iterative, feedback-driven process. Instead of applying fixed remediations, SHIELDS continuously proposes fixes and refines them based on feedback from target system execution and validation scans. We evaluate the system across multiple virtual machine configurations using six contemporary LLMs ranging from 20B to 400B parameters, and find that SHIELDS successfully remediates up to 73% of scan findings. Our results also suggest that success in this setting depends less on model size (parameter count) than on effective tool use and information gathering, paving a practical path toward reducing the burden of security compliance in environments where compute is limited or security and privacy needs drive local model use.

In the $D$-dimensional Vicsek graph, we prove that the Riesz-like inequality $ \|\nabla f\|_p \leq C \|Δ^γf\|_p $ holds for every $p\in(1,\infty)$ and every $ 0<γ<γ^*(p):=\frac{1}{D+1}+\frac{D-1}{D+1}\,\frac{1}{p}, $ while it fails whenever $p\in(1,\infty)$ and $γ^*(p)<γ<1$. Thus, the validity of the inequality remains open only at the critical exponent $γ=γ^*(p)$. This provides the first example of an $L^p$-bounded ``super-Riesz transform'', namely an operator of the form $\nabla Δ^{-γ}$ with $γ$ strictly larger than the Euclidean threshold $\frac12$. To achieve this, we establish a more general result linking the diffusion escape rate and a Poincaré inequality on balls to the validity of the reverse Riesz-like inequality $\|Δ^γf\|_p \leq C \|\nabla f\|_p.$

In a previous quantitative retrospective study we showed that different demographic groups of students leave different numbers of problems blank on physics exams, leading to inequities in course outcomes. In that work we argued that there were good reasons to treat these blanks as missing data, rather than indicators of a lack of understanding. In this paper, we refine this analysis and show more detailed breakdowns uncollected test item responses by race/ethnicity and first generation college student status, coming to the same conclusion: test item responses are uncollected for students with different ethnic and racial backgrounds at different rates, and these patterns exist even for high-performing students. We also correct an error from our previous work, finding here that there is no significant gender difference in uncollected test item responses. Finally, we provide a more robust analysis of course level data illustrating that blanks are a variable controlled at the course level rather than the student level, providing more evidence for the use of a course deficit model (rather than a student deficit model) when examining equity disparities, and also suggesting that there are plausible means for instructors to minimize uncollected test item responses, and therefore eliminate the bias associated with this missing data. We provide some suggestions for faculty who want to have more equitable course outcomes.

With the advance of generative artificial intelligence (AI) synthetic texts and images have become commonplace. These capabilities offer clear benefits, but have also raised a number of ethical concerns that often have to do with misrepresenting AI outputs as genuine material. A lesser known capability of generative AI is to perform the basic analysis, processing and even synthesis of numerical data. This raises the question of whether AI can be used to imitate experimental data that an expert would consider scientifically meaningful and on par with data in the figures of peer-reviewed manuscripts? In this paper, we focus on synthesizing data inspired by well-known experiments done frequently on quantum electronic devices. This field is related to information technologies such as spintronics and quantum computing, and is considered data-rich and data-driven. We demonstrate that it is possible to generate dramatic signals associated with iconic effects such as quantum bit control, Majorana fermions, Josephson effects, quantum dots and wires using widely available ChatGPT. We find that because some of the clearest data from quantum devices can be expressed in terms of relatively basic mathematical models, AI does not need to learn on the specialized body of data. Instead, knowledge of the physics equations and of the basic features of experimental signals can go a long way towards building a realistic dataset. We also demonstrate that real data can be augmented by AI, and that AI can mimic the noise of common scientific instruments. To help assure that published data come from experiments and are not synthesized by AI, we recommend sharing large volumes of the primary data. While it is straightforward for AI to mimic a few sets of data, consistently generating long measured sequences poses sufficient barriers to the proliferation of undisclosed synthetic data.

A grand Motzkin path with air pockets is a non-empty lattice path in the first and fourth quadrant of $\mathbb{Z}^2$, starting at the origin $(0,0)$, ending on the $x$-axis, and consisting of up-steps $(1, 1)$, horizontal steps $(1, 0)$, down-steps $(1, -k)$ where $k \geq 1$, and with no consecutive down-steps. A {grand Dyck path with air pockets} is a grand Motzkin path with air pockets that uses no horizontal steps. We present the first known 2-Gray codes for grand Motzkin paths with air pockets. Setting the number of horizontal steps to zero in our algorithm yields the first known 2-Gray codes for grand Dyck paths with air pockets. Our three-stage algorithm generates each path in constant amortized time per string, using $O(n^2)$ memory. We also provide enumeration formulae for grand Motzkin paths and grand Dyck paths with air pockets.

We calculate diffractive $D^{0}$ photoproduction in ultraperipheral lead--lead (Pb--Pb) collisions at the Large Hadron Collider (LHC) within the recently developed G$γ$A--FONLL framework, where photon--lead diffraction is modeled using nuclear diffractive parton distributions obtained in the leading twist shadowing approach and the photon fluxes include corrections for independent electromagnetic dissociation accompanying the hard photoproduction process. We then use the predicted diffractive cross section to quantify the coherent diffractive contribution rejected by the $Xn0n$ neutron-tagged event selection adopted in the first measurement of $D^0$ photoproduction in Pb-Pb collisions at the LHC, which requires neutron emission from only one of the two lead nuclei. In this work, we also extend the G$γ$A--FONLL framework to proton--lead ($p$--Pb) UPCs and present predictions for inclusive and diffractive $D^{0}$ photoproduction at the LHC. In this case, the dominant configuration is photon emission from the lead ion followed by photon--proton scattering, and the diffractive contribution is evaluated using proton diffractive parton distributions constrained by HERA data.

A long-running append-mostly sequence, such as an edit log, event store, or versioned working set, is usually tiered into a bounded hot stratum and colder folded summaries. This saves memory but breaks stable references: a handle minted while a record is hot may later be resolved after the record has moved into a digest, after it has been superseded, or while a fold is in flight. We define the resulting cross-tier anomalies--dangling, stale, corrupt, and snapshot-skewed resolution--and present the Cascade Log, a reference-stable tiered append structure. The structure keeps a single persistent coalescing interval map over handles as the sole authority on each live version; folding a contiguous run replaces many singleton entries by one digest-backed interval node, and immutable roots provide snapshot tokens. Its cost is characterized by the fragmentation $A$, the number of index pieces, namely live handles plus maximal same-digest runs. The index uses $Θ(A)$ space, resolves a point in $O(\log A)$, reports a $k$-handle range in $O(\log A+k)$, and performs $a$ appends and $s$ supersedes in $O((a/B+s)\log A)$ update work for fold block size $B$. Matching lower bounds show that $Ω(A)$ space and $Ω(\log A+k)$ ordered range cost are unavoidable, and an adversary can force $A=Θ(s)$. Thus the index is sublinear on append-dominated histories and grows linearly only under fragmenting edits. A reference implementation and reproducible experiments to $10^6$ records validate the anomaly-freedom and the fragmentation bounds.

Tagging of generic dynamic values is important in symbolic-computation and dynamic-language systems, but the trade-offs change as machine architectures and workloads evolve. In particular, old folklore about boxed values, immediate values, and type tags must be recalibrated from time to time. We revisit the performance of badged object headers, low-bit tagging, and two NaN-boxing layouts on a range of platforms in use today, including AArch64 and x86-64 architectures from different manufacturers. The experiments isolate two distinct effects: the cost avoided by not heap-allocating common scalar values, and the cost avoided by obtaining tag information from the value word rather than by performing a heap read. The results show that several local bit operations are often cheaper than opening a heap object to obtain a tag or small value. Low-bit tagging remains the simplest and usually fastest choice for mostly symbolic workloads, while NaN-boxing is close in access cost and avoids the time and space of heap allocation for ordinary floating-point values.

Calibrating thermomechanical material models from experiments is challenging because deformation, temperature, and force responses are strongly coupled, while measurements are usually restricted to specimen surfaces. We present a full-field calibration framework for coupled finite-strain thermomechanical material models using boundary displacement, reaction-force data, and temperature. The forward model is formulated as a near-incompressible thermo-hyperelastic problem with thermomechanical coupling derived from a Helmholtz free energy, and the inverse problem is posed as a PDE-constrained optimization problem with weighted observation terms for the available data streams. Reduced gradients are computed with adjoint sensitivities that are obtained by automatic differentiation, enabling gradient-based calibration of nonlinear transient thermomechanical systems. The formulation is first verified on synthetic examples involving uniform thermal preconditioning and localized transient rod contact, where the ground-truth parameters are recovered from full-field measurements and force observations. The same workflow is then applied to experimental thermomechanical data by first calibrating a hyperelastic mechanical baseline from cyclic equibiaxial loading and subsequently identifying thermal expansion and directional shrinkage parameters from surface-temperature and boundary-force histories. The results demonstrate that coupled thermomechanical parameters can be inferred from experimentally accessible surface data without requiring volumetric observations.

Many nonlinear iterative procedures generate high-dimensional trajectories whose early behavior is informative but difficult to compare directly. This paper studies a soft-computing representation problem: how to convert a short early trajectory segment into compact, interpretable, fixed-dimensional fuzzy coordinates that preserve information about subsequent convergence and trajectory geometry. The problem is investigated for iterated Pearson correlation matrices, a nonlinear matrix iteration historically connected with CONCOR-type blockmodeling and repeated-correlation methods. The proposed descriptor uses two logarithmic signals from the early post-transient regime: a step-size signal, measuring contraction magnitude, and a contraction-ratio signal, measuring local contraction evolution. Each signal is projected onto a three-node triangular fuzzy partition using zero-degree F-transform coefficients and one centered first-degree coefficient. This yields an eight-dimensional two-channel representation separating local level from local trend and contraction magnitude from contraction evolution. Across 22 matrix dimensions with 1000 trajectories per dimension, the descriptor is compared with raw trajectory samples, statistical summaries, and PCA-compressed raw features using Random Forest regression for convergence-length approximation. It achieves mean R^2 = 0.6480, close to raw trajectories (0.6518) and statistical summaries (0.6528), while improving over the step-size-only F-transform descriptor (0.5001). Repeated random-split and shifted-window experiments confirm stability. PCA and clustering further show reproducible low-dimensional organization, with the first two principal components explaining 84.26% of variance and k = 3 favored by the mean silhouette criterion.

The safety, security, and reliability of microelectronic systems depend on a trustworthy, secured supply chain and design flow. Globally distributed supply chains or unintentional design weaknesses leave the door open for attacks on the hardware level. These scenarios encompass counterfeiting, hardware trojans, or on-device attacks. For these, hardware reverse engineering (RE) results play a pivotal role. The ongoing publication of new RE-involved attacks motivated the development of the common RE scoring system (CRESS). The system enables a general classification of RE-involved scenarios for a common, consistent rating. In this work, the originally qualitative system is extended to a quantitative system. We performed an extensive interview study with experts in the field. The interview results allowed us to derive weights that measure the severity of different RE-involved attack categories. The weights form an equation that quantifies scenarios, resulting in the severity-indicating CRESS score. The score enables the coherent rating of novel scenarios, renders them comparable, and supports the development of effective countermeasures. To showcase the effectiveness of the quantitative CRESS Score, six selected case studies are rated qualitatively and quantitatively. The CRESS Score proves to be significantly more expressive than the industry-standard Common Vulnerability Scoring System (CVSS).

Ultrafast laser excitation of metals induces electronic nonequilibrium both in space and locally in the energy distribution. The subsequent dynamics are governed by the interplay between non-local transport and local scattering of hot electrons, yet combined microscopic descriptions of these processes remain sparse. Here, we disentangle the influence of these processes on thermalization using a reformulation of the Boltzmann transport equation in energy space that consistently describes both spatial equilibration and scattering through full collision integrals. Our results reveal that transport accelerates the apparent thermalization observed at the irradiated surface by removing athermal carriers, while the same spatial redistribution delays complete equilibration of the full electron system. We analyze the experimentally accessible energy-dependent dynamics at the front and back surface and find that the dominant process varies, depending on both position and on the energetic window. Overall, our work improves the understanding of the interplay of electronic nonequilibrium processes occurring in optically thick laser-driven systems with relevant implications for future electronic applications.

We show that the continuous functional calculus is computable. As consequences we obtain the computable compactness of the spectrum of any computable normal element of a computably presented $\mathrm{C}^*$-algebra, the existence of effective approximate units for computably presented $\mathrm{C}^*$-algebras, and an effective version of the Spectral Theorem for compact operators on separable Hilbert spaces.

In the sequence reconstruction problem, a codeword $\x$ is transmitted through several identical channels where each channel produces a noisy read of $\x$, and the problem is to analyze how to uniquely reconstruct $\x$ based on these noisy reads. Levenshtein has studied the minimum number of reads which guarantees unique reconstruction of $\x$, which is one sufficient condition for unique reconstruction. In this paper, we move on to a different perspective and propose a new framework for unique reconstruction. Our new sufficient condition for unique reconstruction takes both the number of reads and the distances among the reads into consideration. We offer both theoretical analysis and corresponding efficient reconstruction algorithms for our reconstruction framework.

We study the curvature conditions introduced in [Class. Quant. Grav. 27, 152002] to predict focal points for trapped spacelike submanifolds in spacetimes of arbitrary dimensions, with the purpose of generalizing Penrose's singularity theorem to compact trapped submanifolds (CTMs) of codimension higher than two. We find that these conditions do not apply in general but may apply for specific CTMs. As a result, higher codimension CTMs may still work as singularity predictors, although the possibility that they intersect the domain of outer communications cannot be ruled out using standard arguments.

The article addresses the construction and geography of negatively curved metrics on hyperbolic complex manifolds. We introduce a mechanism for constructing complete Kähler metrics with negative bisectional curvature. This applies to some product complex manifolds, thereby resolving a longstanding problem attributed to N. Mok. We then construct projective Kobayashi hyperbolic surfaces with negative holomorphic sectional curvature whose Chern slopes $c_1^2/c_2$ realize any $s \in \mathbf{Q} \cap \left( \frac{2}{7}, \frac{2}{3} \right)$. For slopes $s\in \mathbf{Q}\cap \left( \frac{2}{7},\frac{1}{3} \right)$, the corresponding surfaces admit a Hermitian metric with $\text{HSC}<0$, but their Kähler--Einstein metric cannot have $\text{HSC}<0$. We finally construct, for every $s \in \left( \frac{1}{2}, 3 \right)$, a sequence of projective Kobayashi hyperbolic surfaces that do not admit a Hermitian metric of nonpositive holomorphic sectional curvature, whose Chern slopes $c_1^2/c_2$ converge to $s$.

The ultraviolet (UV) spectrum of a host star strongly shapes the atmospheric composition and potential biosignatures of its planets. This relationship may be especially important for the planets orbiting TRAPPIST-1, an M8V star with substantially different published UV spectral energy distributions (SEDs). Using a one-dimensional photochemical model, we quantify how these SED uncertainties affect Archean Earth-like atmospheric analogs on TRAPPIST-1 e with and without biospheres. We emphasize Earth's Archean epoch because it represents a planet in transition from primarily abiotic to biotic controls on atmospheric composition. Different stellar spectra produce order-of-magnitude variations in the predicted abundances of CH4, CO, O2, and O3, thereby generating photochemical degeneracies that complicate the interpretation of potential biosignatures. For one TRAPPIST-1 UV reconstruction, a modeled atmosphere with abiotic deposition velocities and volcanic CH4 input can sustain simultaneous spectrally discernible CH4 and O3, yielding a potential false-positive disequilibrium biosignature. For all SEDs tested, surface deposition consistent with microbially-mediated CO consumption allows substantial O2 and O3 accumulation even without oxygenic photosynthesis, implying that oxygen-rich atmospheres around ultracool M dwarfs may not uniquely trace oxygenic ecosystems. Across our models, CO remains a powerful discriminator between abiotic and biotic surface boundary assumptions. Overall, we show that the abundances of co-occurring CH4, CO, and O3 can vary by orders of magnitude, depending on the assumed UV SED, creating ambiguities in interpreting atmospheric biosignatures, though observability may be challenging with current capabilities. Reducing UV spectral uncertainties is therefore essential for assessing surface-to-atmosphere interactions of temperate exoplanets around ultracool M dwarfs.

The power consumption of the analog-to-digital converters (ADCs) and digital-to-analog converters (DACs) in fully digital massive multiple-input multiple-output (MIMO) systems motivates the adoption of low-resolution architectures. In particular, 1-bit DACs reduce the power consumption and hardware complexity at the transmitter, but introduce severe transmit-side quantization distortion. In this paper, we investigate data detection for a point-to-point massive MIMO system with 1-bit DACs at the transmitter, where the linearly precoded signal is dithered prior to quantization, and either full-resolution or 1-bit ADCs at the receiver. Assuming that the dither vector applied at the transmitter is known at the receiver, we first develop softestimation-based data detection methods with symbol-independent dither removal for both full-resolution and 1-bit ADCs. We then introduce a new symbol-dependent linearization of the transmitted signal at the output of the 1-bit DACs and use it to derive maximum-likelihood (ML)-based data detection methods that directly recover the data symbol vector from the received signal. For full-resolution ADCs, this leads to an ML-based method with and without dither removal. For 1-bit ADCs, we develop an approximate ML-based method that exploits the derived statistics of the received signal without dither removal. We also propose low-complexity variants of the ML-based methods to mitigate the exponential complexity growth with the number of streams. Numerical results in terms of symbol error rate highlight the critical role of the dither power and demonstrate that the proposed ML-based methods (along with their low-complexity variants) achieve significant gains over a baseline based on binary ML detection via a homotopy algorithm.

We present the complete formulation of resistive wall boundary conditions in axisymmetric toroidal geometries as implemented in the PIXIE3D extended magnetohydrodynamics (MHD) code, along with a complete suite of analytical verification examples that demonstrate correctness in the implementation. The formulation centers around a thin wall approximation and a Boundary Integral Method to solve for the magnetic scalar potential in the immediately surrounding vacuum. This requires specialized quadrature rules derived from existing literature to handle the numerical integration of singular and hypersingular integrands (the Green's function of Laplace's equation and its derivatives), for which we provide the nodes and weights. Further, we describe an extension to the formalism to include the effect of a perfectly conducting second, outer wall exterior to the resistive (plasma-facing) wall and separated by vacuum, and exterior to the computational plasma mesh proper. Lastly, we describe an extension to include the effect of current-carrying coils also defined exterior to the plasma mesh in the resistive wall boundary condition treatment. For most aspects of the method, we present self-contained verification examples using analytic solutions in axisymmetric toroidal geometries (with both 2D and 3D plasmas) and show it to be accurate to second order. We demonstrate the algorithm with a vertical displacement event (VDE) using the ITER tokamak geometry.

For non-interacting fermions in a harmonic trap, the partition function at any discrete number of imaginary time slices (or beads) and for any choice of short-time propagator admits an exact recursion relation derived directly from the contracted determinant form of the path integral. This finite-bead recursion is distinct from earlier continuum-limit recursions, which do not apply to the discrete time partition functions. By identifying a direct correspondence between this recursion and Newton's identity, application of a closed-form result from the theory of partitions provides an exact expression for the one-dimensional $n$-fermion finite-bead partition function. From this, the Thermodynamic and Hamiltonian energies and specific heats are analytically calculated for any $n$, $N$, $τ$, and propagator choice.

Children's automatic speech recognition (ASR) remains challenging because child speech differs from adult speech and varies substantially across developmental stages. While adapter tuning provides a promising way to adapt large pretrained ASR models to children's speech, a single shared child adapter may not fully capture age-dependent variation. In this work, we present one of the first systematic studies of age-aware adapter tuning for child ASR, focusing on speech from children aged 3--12 and older years. We propose age-specialized adapters trained separately for different age groups and compare them with a unified age-conditioned FiLM adapter. With ground-truth age routing, age-specialized adapters improve over the standard shared child adapter baseline from 12.6% to 12.3% overall word error rate (WER) and from 18.4% to 17.6% macro WER, while consistently improving WER for all age groups. We further show that predicted-age routing remains close to ground-truth routing, achieving 12.3% overall WER and 17.8% macro WER without ground-truth age labels at inference. In contrast, unified FiLM conditioning provides smaller gains, indicating that a single unified adapter may be insufficient to capture developmental variation in child speech.

There are $2^{n-1}$ ways to tile a $1 \times n$ rectangle with rectangular tiles (of any length, of course they all must have width $1$), but in how many ways can you tile a $100 \times 100$ checkerboard with such tiles? Neither humankind, nor computer-kind, will (most probably) ever know the exact number. But it is possible to compute these numbers for $m \times n$ rectangular grids, if $m$ is not too big, while $n$ can be as big as one wishes. This was initially done in 1988 by David Klarner and Spyros Magliveras, and beautifully extended, around 2006, by, at-the-time, first-year LSU undergraduate Joshua Smith, in collaboration with his faculty mentor, Helena Verrill. Here we extend this to weighted-counting, also keeping track of the number of tiles (that ranges from $1$ to $mn$), and the number of participating grid-edges (that range from $2m+2n$ to $2mn+m+n$). This quickly leads to statistical analyses (mean, variance, and higher moments) of these quantities. While we admire the clever approaches of Klarner-Magliveras and Smith-Verrill, we use two alternative approaches to the original problem, that are more amenable for deriving these generalizations. At the same time, we illustrate the power and beauty of experimental-yet-rigorous enumerative combinatorics.

This paper considers Sobolev-Morrey and Besov-Morrey spaces. For Morrey spaces, multipliers are studied, and a theorem on multipliers from M_p^lambda(T) to M_p^lambda(T) is obtained for 1 < p < infinity and 0 <= lambda < 1/p. Based on this result, embeddings between Besov-Morrey and Sobolev-type spaces are established, namely B_1^alpha(M_p^lambda) embedded into W^alpha(M_p^lambda) embedded into B_infinity^alpha(M_p^lambda) for 0 < p <= infinity, 0 <= lambda <= 1/p, and alpha in R. In addition, an interpolation theorem for Besov-Morrey spaces is proved.

We study the optical properties of gravitating Abelian-Higgs cosmic strings and compare them with those of the idealized infinitely thin string. We analyze the structure of the corresponding vortex solutions, characterizing their width, curvature profile, and approach to the ideal string limit. By investigating photon propagation in the string spacetime, we show that the finite core of the vortex gives rise to distinctive observational signatures absent in the ideal string approximation, including a characteristic triple-imaging configuration, strong demagnification of the central image, and a nontrivial Shapiro time delay between external and internal images. We determine how these effects depend on the parameters of the Abelian-Higgs model and show that the sign of the time delay is controlled by the ratio of the gauge boson mass to the Higgs boson mass, causing the string core to behave as either a temporal shortcut or a temporal barrier. Our results demonstrate that lensing effects can reveal information about the vortex formation and internal structure.

We introduce the \emph{complex equivariant spectral flow} -- a virtual $G$-representation assembling the eigenvalue winding numbers of the linearization at an isolated two-parameter critical point for $G = S^1 \times Γ$ bifurcation problems -- and prove that, for maximal twisted orbit types, the coefficient of the local bifurcation invariant in $A_1^t(G)$ reduces to a closed-form dimension formula, bypassing the standard pipeline of basic degree factorization and Burnside ring multiplication entirely. When the eigenvalue dependence is holomorphic, topological cancellation among winding numbers is impossible, yielding unconditional local and global bifurcation guarantees. As applications, we establish the macroscopic escape of symmetric Hopf branches in $Γ$-equivariant systems and of patterned relative equilibria for the complex Ginzburg--Landau equation directly from spectral data.