In this paper, we study the class Σ_{H}^{k}(p) of sense-preserving univalent harmonic mappings in the unit disk \mathbb{D} that possess a simple pole at p\in[0,1) and admit a k-quasiconformal extension to the extended complex plane for k\in[0,1). In 2024, Bhowmik and Satpati established an area theorem and derived a sufficient condition for the k-quasiconformal extension of harmonic mappings belonging to Σ_{H}^{k}(p) without logarithmic terms. Motivated by their work, we investigate the corresponding problem when a logarithmic singularity is present. Our main contributions are two-fold: we first prove a generalized area theorem for all mappings in Σ_{H}^{k}(p); we then obtain a sufficient condition for sense-preserving univalent harmonic mappings in \mathbb{D} to admit explicit k-quasiconformal extensions. These results extend the aforementioned work to the setting where logarithmic singularities are allowed.

In this paper, we study the noncommutative fractional symmetric Sobolev spaces on noncommutative torus. We prove noncommutative distributional fractional Sobolev inequality and as its application, we obtain Sobolev embeddings. In order to obtain these results, we first prove a noncommutative version of the famous O'Neil inequality for the convolution. As a first application of our main results, we obtain a Cwikel-Solomyak-type estimate. As an another application, we show a $L_2$-time decay for the mild solution of the Cauchy problem for the diffusion equation in this noncommutative setting. When $θ=0,$ our results recover many known results on Sobolev embedding on the torus.

While the uncrowding algorithm on set-valued tableaux has long been instrumental in proving the Schur positivity of stable symmetric Grothendieck polynomials, lattice models have emerged as a modern framework for investigating symmetric functions, in particular symmetric Grothendieck polynomials. In this work, we synthesize these combinatorial and lattice-theoretic approaches by defining both the Robinson--Schensted--Knuth (RSK) correspondence and the uncrowding operation directly on a 5-vertex model of Motegi and Sakai and its subsequent reinterpretation by Buciumas, Scrimshaw, and Weber. Our lattice-based RSK formulation yields a powerful new result: the direct construction of the associated crystal structure on the states of the 5-vertex model.

Let $\mathbb Z_n$ be the cyclic group equipped with the uniform probability measure $π$, and let $A_{ψ_n}$ be the Laplacian with word length \[ ψ_n(k) = \min(k,n-k). \] We prove the sharp log-Sobolev inequality \[ \text{Ent}_π(f^2) \le 2π(f A_{ψ_n} f), \qquad f:\mathbb Z_n \to [0,\infty), \] for every $n \ge 4$. The proof is inspired by the recent work of Frank and Ivanisvili~\cite{FrankIvanisvili2026} on a sharp log-Sobolev inequality for nearest-neighbor simple random walk. We use their cubic-majorant reduction, which turns the problem into a 3rd moment estimate; the new point is a blockwise 3rd moment estimate adapted to the word-length multiplier. The same 3rd moment argument also recovers the log-Sobolev inequality for Poisson-semigroup on the circle, first proved by Weissler~\cite{Weissler1980}. The same sharp inequalities were also obtained recently by Yao~\cite{Yao2026} by a different method.

We reinvestigate the theory of spectral sequences by studying the $(\infty,1)$-category of filtered spectra through the cofiber-of-$τ$ formalism of Burklund-Isaksen-Pstragowski-Wang-Xu. In this framework, we define and analyze hidden extensions along arbitrary maps of filtered spectra, establishing computational principles that extend the generalized Leibniz rule and the generalized Mahowald trick of Lin-Wang-Xu, as well as Burklund's Leibniz rule for total differentials, from the Adams spectral sequence to this broader setup. Our formulation uses a more refined, layered notion of extension, which slightly sharpens these statements even for the Adams spectral sequence. As an application, we study equivariant slice spectral sequences and obtain new families of "exotic transfer" differentials in the $C_4$-slice spectral sequences for the Hill-Hopkins-Ravenel theories $\mathrm{BP}^{((C_4))}\langle m\rangle$ for every $m \ge 1$.

Machine-learning interatomic potentials now approach quantum-mechanical accuracy on standard benchmarks, but the training cost of the most expressive equivariant architectures has become a serious bottleneck. We introduce DPA4, an SE(3)-equivariant interatomic-potential architecture with an EMFA (Edge-conditioned, Multi-Focus, Attention) SO(2)-equivariant convolution that combines a low-rank edge-node SO(2)-equivariant product, a multi-focus design for message nonlinearity, and envelope-gated attention for message aggregation. A Lebedev-grid projection further preserves SO(3)-equivariance in the nonlinearity to machine precision. A compiler-friendly conservative energy-gradient training path provides up to $\sim$3 times wall-clock speedup under torch compile. On the compliant Matbench Discovery benchmark, DPA4-Pro attains the best Combined Performance Score (CPS) on the leaderboard, while the 2.76M-parameter DPA4-Air exceeds the accuracy of the 30.1M-parameter eSEN-30M-MP baseline with 10.9$\times$ fewer parameters and 42.9$\times$ less training compute. On SPICE-MACE-OFF, the 5.4M-parameter DPA4-Plus lowers the aggregate molecular energy and force errors of the 6.5M-parameter eSEN baseline by 29% and 30%, while the 2.7M-parameter DPA4-Air still surpasses that baseline with $\sim$2.4$\times$ fewer parameters. Together these results place DPA4 on a new accuracy-cost Pareto frontier on Matbench Discovery and position it as a strong candidate backbone for future multi-task large atomistic model (LAM) pretraining.

The ability to engineer and control quantum states of many-body systems is a central challenge in quantum information science. For a register of $N$ qubits, the full Hilbert space dimension grows exponentially as $2^N$, rendering generic state preparation and control infeasible without exploiting structure or symmetry. A particularly important and physically motivated restriction is to the fully symmetric subspace, spanned by the Dicke states, which are simultaneous eigenstates of collective spin $J=N/2$. Ensembles of Rydberg atoms interacting via electric dipoles in two-dimensional tweezer arrays form a promising platform for achieving such control. However, the finite range of dipole-dipole interactions poses a challenge to generating and controlling the Dicke manifold because the Hamiltonian incurs leakage from the computational subspace. To counteract this leakage, we perform quantum optimal control algorithms on a truncated Hilbert space according to our newly developed method of ``irrep distillation'' (IRD), which captures the process by which the symmetric subspace couples to leakage error-spaces, using only linear-scaling Hilbert dimension. We implement gradient ascent pulse engineering (GrAPE) on control schemes with little or no local addressing, to generate resourceful states like Greenberger-Horne-Zeilinger, Dicke, and extremal quantum states. We benchmark each scheme of IRD-GrAPE for its quantum speed limit (QSL), as well as exactly testing pulse fidelities on small system sizes and predicting fidelities using higher-order IRD on larger systems.

Self-supervised speech representation learning has made significant progress through Siamese networks, which leverage different views of the same input. However, existing methods often require frame-wise alignment between these views, overlooking the broader linguistic context invariance across different speaking styles. We introduce SiamCTC, a framework that integrates Siamese networks with Connectionist Temporal Classification (CTC) to learn speech representations without strict frame-level correspondence. By employing CTC loss to establish flexible, monotonic alignments between differing temporal realizations of the same content, SiamCTC accommodates speed perturbations and other temporal augmentations. This design relaxes frame-wise constraints while preserving temporal coherence and enhancing robustness to speaking-rate variations in downstream tasks. Our experiments demonstrate that SiamCTC leads to more adaptable speech representations, particularly at diverse speaking rates.

We report that the biaxial birefringence of $α$-MoO$_3$ can activate two spectrally distinct quasi-bound states in the continuum (quasi-BICs) within a single symmetric TiO$_2$ nanobar-pair metasurface, with each resonance governed by a different crystallographic axis pair of the van der Waals crystal. With a full 60\,nm $α$-MoO$_3$ gap fill, a TE resonance at 883.9\,nm ($Q=92$, Fano $q=0.090$) and a TM resonance at 923.2\,nm ($Q=31$, Fano $q=0.393$) are obtained. The Q ratio follows the inverse-square permittivity contrast, $Q\propto(Δ\varepsilon)^{-2}$, calibrated across both polarization channels. Oblique-incidence sweeps show that the TE channel acts as a dual-null spatial highpass filter with a broadband stopband ($|H|<0.13$ for $|k_x|\leq0.63\,μ$m$^{-1}$, $T_\mathrm{bg}=0.962$), while the TM channel transfers as $|H|\propto|k_x|$ ($R^2=0.94$), consistent with first-order spatial differentiation. Both operations are verified on a USAF~1951 resolution chart processed in a simulated 4$f$ framework. Channel selection is purely by input polarization angle with no structural modification.

We study local pure coordination games on finite social networks, continuing the framework of Hutchcroft, Rospuskova, and Tamuz. They showed that low inefficiency in local coordination forces the underlying graph to be amenable, with a square-root loss in the amenability parameter. We improve this loss in the binary unbiased setting. Using Shapley values of a mutual-information game associated with the players' local outputs, we prove that if the average disagreement is at most $\varepsilon$, then the graph is $(O(\varepsilon\log(1/\varepsilon)),r)$-amenable. This gives a sharper quantitative converse between local coordination and graph amenability.

This paper presents closed BH, a uniform improvement of the False Discovery Rate controlling method of Benjamini and Hochberg (BH). Closed BH is valid under the same assumption of Positive Regression Dependency on a Subset (PRDS) as BH, but also under an alternative and weaker minimal sufficient condition. As a uniform improvement, closed BH never rejects fewer hypotheses than BH, but it may reject quite a few more. An increase in power is observed especially when the number of false null hypotheses is large. The novel method is constructed using the e-Closure principle, a recently derived general principle for multiple testing. The method is implemented in the eClosure package in R.

We consider the problem of estimating the true Sharpe ratio of an asset selected for having the highest observed in-sample Sharpe ratio among many assets. We discuss estimators based on the polyhedral lemma, James Stein shrinkage, debiasing the expected maximum Sharpe ratio, thresholding and empirical Bayes. We test these estimators in simulations, computing bias and root mean square error across different values of sample size, number of assets, and spread and shape of population Sharpe ratios. We also compute rank correlation of the estimators against the underlying quantity, simulating how these estimators might be used to compare or rank the output of different teams which perform this selection process. We find that the James Stein estimator provides the best performance across many different realistic values of the relevant parameters, followed by the GMLEB estimator of Jiang and Zhang. These results are fairly robust to correlation of asset returns, with some caveats.

We investigate collective excitations in flat-band superfluids by incorporating the coupled dynamics of pairing (phase and amplitude) and density fluctuations. We demonstrate that for any time-reversal symmetric superfluid system with an isolated flat band, only a single low-energy collective mode emerges in the long-wavelength limit. In contrast to the linearly dispersive Goldstone mode in conventional superfluids, this hybridized mode is gapless at zero momentum but exhibits a quadratic dispersion ($ω\propto q^2$) at small momenta. We show that the dispersion coefficients of this collective mode are governed by the normal-state quantum metric of the flat band. These analytical predictions are in excellent agreement with numerical calculations. Our results are applicable to any generic $s$-wave flat-band superfluid, provided the flat band is energetically well separated from other dispersive bands.

A single CPU core sustains 32 million order messages per second at sub-microsecond median end-to-end host-path response latency, 4.7-11 times faster than the best available open-source matching engines on identical hardware. Scaled out, a single 96-core commodity server (~$1,630/month) sustains ~640 million messages per second across 10,000 symbols, over 20 times the provisioned capacity of the U.S. consolidated quote feed. We reach these numbers by attacking the storage layer that sets matching latency. The dominant order-book implementation, linked lists chained through a balanced tree, imposes two costs on every operation: pointer-chased traversal to the insertion point, and root-to-leaf search to locate the target price level. Under micro-bursts these costs produce tail-latency spikes that degrade market quality precisely when liquidity is most needed. We present two data-structure contributions that eliminate them. The first is the Priority-Indicated Node (PIN), a priority queue in which entries occupy fixed-capacity, contiguously addressable slots, with indicators encoding the entry's global priority status. Unlike heaps, which require O(log n) comparisons per operation, the PIN resolves insertion position directly from the indicators without comparing entries; indicator updates are O(1), independent of queue size. A depth-aware capacity model sizes each PIN so hot entries fit within L1 residency. The second targets a broader inefficiency: balanced search trees search from root to leaf on every insertion and deletion, even when the caller already knows the key's in-order neighbors, which in electronic trading are available at zero cost. Neighbor-aware insertion and deletion use known neighbor references to attach or remove a node with O(1) reference writes, followed by single-path rebalancing, across red-black, AVL, and B+-tree variants.

The $τ$ anomalous magnetic dipole moment (MDM) $a_τ= (g-2)_τ/2$ and electric dipole moment (EDM) $d_τ$, are precision probes of electroweak dynamics and possible new physics sources, yet both remain weakly constrained experimentally. Treated as generalized form factors, these quantities exhibit a generic $q^2$ dependence for an off-shell interacting photon. For timelike momentum transfer above the $τ^+τ^-$ threshold, $q^2 = s > 4m_τ^2$, the form factors can acquire absorptive imaginary parts. We investigate how such a $q^2$ dependence and the associated imaginary parts are generated from two complementary perspectives: the model-independent Standard Model Effective Field Theory (SMEFT) and a UV-complete Two-Higgs-Doublet Model (2HDM). The effective framework reveals the intimate correlation between $a_τ$ and $d_τ$. New CP-violating interactions which generate a non-zero $d_τ$, can also generically have non-zero contributions to $a_τ$, thereby deeply linking their phenomenological studies. Within the 2HDM, we demonstrate that sizable imaginary parts and significant $q^2$ running can be generated at levels accessible by $e^+e^-$ colliders. Motivated by these features, we propose experimental methods to extract both the real and imaginary components of the dipole form factors. Utilizing these techniques, we show that Belle II and the Super Tau-Charm Facility (STCF) can improve current bounds on $a_τ$ by more than one order of magnitude. Finally, we highlight that combining measurements across the distinct center-of-mass energies of Belle II and STCF provides a unique, previously unexplored avenue to explicitly obtain information about the $q^2$ evolution of these dipole form factors.

Coverage-guided kernel fuzzers such as syzkaller rely on edge coverage (trace-pc) as their sole feedback signal. This context-blind approach cannot distinguish execution paths that differ only in argument values -- for example, two invocations of copy_from_user() with different size parameters hit identical basic blocks yet have vastly different security implications. I present TOOLNAME, an LLVM-based instrumentation framework that extends Linux KCOV with data-flow extraction of function arguments and return values. A compiler pass emits lightweight callbacks capturing structured tuples of program counter, argument metadata, and field values at function entry and return. Composite types are automatically decomposed via DWARF DICompositeType metadata with zero source annotation. A lock-free per-task ring buffer delivers records to user space with no interference to existing KCOV or syzkaller infrastructure. I demonstrate dual utility: (1) fuzzers gain state-aware feedback for mutation guidance into value-dependent state transitions, and (2) security analysts obtain deterministic argument records for root-cause analysis without printk or kprobe overhead. Two Rust instrumentation paths are provided: a post-compilation pipeline requiring no rustc modification, and native instrumentation via rustc built against the custom LLVM -- both the only runtime methods for capturing Rust function arguments given that drgn/vmcore fails under -O2 DWARF elision.

We consider the periodic quintic nonlinear Schrödinger and prove small-mass global well-posedness in $H^s(\mathbb{T})$ for $s>0$. The proof relies on a new derivative-loss-free $L^6_{t,x}$ Strichartz estimate which is established using the high-low method, an asymmetric superlevel set estimate and a new refined broad-narrow argument. Although our $L^6_{t,x}$ Strichartz estimate is not sharp, being valid on slightly shorter time scales than the optimal logarithmic scale, combining it with the $I$-method enables the extension of local solutions to arbitrary times.

We present a constructive version of the Brøndsted-Rockafellar theorem in general geodesic metric spaces. Applications include a constructive form of the Caristi theorem and quantitative relations between metric slope error bounds and the global growth of functionals.

Fractional Gaussian noise and $\FARIMA(0,d,0)$ have the same long-memory pole $|θ|^{-2d}$ and hence the same leading PACF law $α(n)\sim d/n$. We show that this agreement breaks at the first non-universal order. For $0<d<1/2$, the pure fGn PACF satisfies $$ α_{\fGn}(n)=\frac d n+\frac{C_{\fGn}(d)}{n^2}+o(n^{-2}), \qquad C_{\fGn}(d)<d^2, $$ The proof uses the Bingham--Inoue--Kasahara representation, a phase-coefficient expansion for fGn, and a Hankel-operator perturbation argument. Thus the fGn spectral envelope is invisible at first order but visible in second-order finite prediction, explaining why short-memory order selection can differ when fGn data are fitted by FARIMA-type models.

The bulk motion of E-region radar aurora provides a sparsely distributed, direct measurement of the ionospheric electric field in intermittent bursts. We present a tracking procedure for \textsc{icebear} VHF measurements of Farley-Buneman waves. Each cluster is represented as an $α$-shape; frame-to-frame association is a Hungarian linear-assignment problem with a cost combining centroid distance and shape Intersection-over-Union; kinematic prediction amounts to a degenerate Kalman filter. Births, deaths, splits, and mergers are monitored; each tracked trajectory is reduced to per-segment velocities by piecewise-linear regression. We validate against \textit{in-situ} observations. During the G5 storm of 10 May 2024, on closed dayside field-lines, our method recovers a five-second cluster moving at $11{,}240\pm660$~m/s, implying an electric field strength of $\approx 560$~mV/m, a value that exceeds documented sub-auroral thermal emission speeds and the most extreme reported sub-auroral drifts. The detection is consistent with extreme E-field structures appearing as short-lived bursts, representing field variability, and we provide parameterizations of this variability for space weather modeling.

This paper presents a rigorous convergence analysis for the lightning plus polynomial approximation scheme, which employs rational approximations constructed with preassigned tapered, exponentially clustered poles. This pole placement strategy was originally introduced by Trefethen and his collaborators for the resolution of corner singularities. Ample numerical results indicate that this scheme achieves root-exponential convergence, and in particular attains the same optimal convergence rate as the best rational approximation to $x^α$ on $[0,1]$ established by Stahl.% which is conjectured in [SIAM J. Numer. Anal., 61:2580-2600, 2023]. In this work, we establish optimal root-exponential convergence for the class of prototype functions of the form $g(z)z^α$ or $g(z)z^α\log z$, where $g$ is analytic on a neighborhood of the sector domain. These results confirm the validity of Conjectures 3.1 and 5.3 stated in [SIAM J. Numer. Anal., 61:2580-2600, 2023], and demonstrate that the choice $σ_{\mathrm{opt}} =\frac{\sqrt{2(2 - β)}π}{\sqrtα}$ achieves the theoretically optimal convergence rate $\mathcal{O}\left(e^{-\sqrt{2(2 - β)Nα}π}\right)$. Notably, for the specific case of $β= 0$, the scheme recovers Stahl's optimal convergence rate for $x^α$. Furthermore, working within the decomposition framework for corner domains proposed by Gopal and Trefethen, this paper provides a rigorous proof of optimal root-exponential convergence for lightning plus polynomial approximation problems, and explicitly derives the optimal pole clustering parameter.

Let $\mathcal{T}$ be a finite nonempty set of $3$-element subsets of a totally ordered set $V$. We view $\mathcal{T}$ as the set of triangles in the support graph. Let $δ_{1,\mathcal{T}}$ be the signed edge-triangle incidence matrix, and $λ(\mathcal{T})$ the spectral gap of $δ_{1,\mathcal{T}}^Tδ_{1,\mathcal{T}}.$ Our main results show that large $λ(\mathcal{T})$ forces strong overlap and a large minimum degree in the support graph. In particular, every support edge lies in at least $\lceil λ(\mathcal{T})\rceil-2$ triangles in $\mathcal{T}$ and hence the graph has minimum degree at least $\lceil λ(\mathcal{T})\rceil-1$. We further prove that $\binom{n}{3}$ is the exact threshold for attaining level $n:$ if $|\mathcal{T}|< \binom{n}{3}$, then $λ(\mathcal{T}) \leq n-1,$ while if $|\mathcal{T}|=\binom{n}{3}$ and $λ(\mathcal{T}) > n-1,$ then $\mathcal{T}$ is exactly the full set of triangles on an $n$-vertex clique. Moreover, this clique peak is isolated in a strong interval-scale sense: letting $ϕ(t)=\max_{|\mathcal{T}|=t} λ(\mathcal{T})$, immediately above $\binom{n}{3}$ there is a forbidden interval on which $ϕ(t) \leq n-1$, and the first passage above the level $n-1$ is delayed by $Θ(n^2)$ additional triangles. Since $\binom{n+1}{3} - \binom{n}{3}=Θ(n^2),$ this implies that after the peak at $\binom{n}{3}$ one must traverse a nonzero proportion of the full gap until the next clique threshold before substantial recovery can occur. In particular, $ϕ$ is not monotone. However, $ϕ(t)=Θ(t^{\frac{1}{3}}).$ Finally, if $Λ(t):=\max_{1 \leq s \leq t}ϕ(s),$ then $Λ(t)=\max\{n \in \mathbb{N}:\binom{n}{3} \leq t\}.$ Thus complete triple systems are the unique minimal spectral extremizers, but their peaks are isolated on the natural scale between consecutive clique thresholds.

This paper tackles the optimization of the point spread function (PSF) of unmanned aerial vehicle (UAV)-borne multiple-input multiple-output (MIMO) synthetic aperture radar (SAR) tomography systems. A swarm of UAV-borne SAR systems is deployed to image an area to obtain its height profile. To achieve a high-quality three-dimensional (3D) image of the scene, the PSF has to exhibit low sidelobes. The heavy computations, required for image generation, are performed on the ground. To this end, the sensor data collected by the UAV-SARs is offloaded in real time via a frequency division multiple access (FDMA) air-to-ground backhaul link. In this work, the UAV formation and the power allocated for offloading are jointly optimized for the minimization of the PSF sidelobe levels. To this end, we propose a novel solution based on the particle swarm optimization (PSO) algorithm, which meets practical sensing and communication constraints. Our simulation results demonstrate that the proposed solution can significantly improve sidelobe suppression compared to several benchmark schemes.

Phononic crystals can confine elastic waves through localized defect states within bandgaps, offering promising opportunities for vibration control and energy localization. However, designing defect states at prescribed frequencies while maintaining adequate separation from other in-gap modes remains a significant challenge. Existing optimization approaches generally treat the target mode indirectly and provide limited control over competing localized modes. This study presents a gradient-based two-stage topology optimization framework for the frequency placement of localized defect modes in periodic elastic media. First, a host unit cell is optimized to create a bandgap around a prescribed frequency. Subsequently, only the defect cell is modified to attract a selected localized mode toward the target frequency while repelling non-target modes away from the central region of the bandgap. The formulation incorporates a smooth mode-selection function that combines mode attraction and repulsion within a unified objective, enabling automatic tracking of the relevant modes throughout the optimization process. Because the localized defect branches of interest are nearly flat, the optimization is performed using only the $Γ$-point eigenspectrum, while the corresponding dispersion relations over a reduced irreducible Brillouin zone are evaluated afterwards for verification. Numerical examples involving two material systems and two supercell sizes demonstrate accurate placement of localized resonances, clear separation from competing in-gap modes, and substantial preservation of the host bandgap. The resulting structures exhibit strong elastic-wave localization, highlighting the potential of the proposed approach for the design of phononic devices for vibration confinement and energy trapping.

The interplay between interactions and quantum geometry can drive weakly dispersive bosons into different exotic many-body phases. In this work we study a quasi flat-band model in one dimension that exhibits an extended pair-superfluid phase in the all-flat-band limit. Introducing single-particle hopping leads to an intriguing competition with a more conventional single-particle superfluid: we find that the pair superfluid remains stable for a finite range of the hopping strength until the system eventually transitions into the conventional superfluid phase. In our study, we make use of a variational Gaussian state approach that provides a unified description of the single-particle and pair superfluid phases, regarding both the ground state wavefunction and the collective excitation spectrum. In particular, we derive a general relation between the speed of sound and a ``quantum geometric kernel'', thereby extending earlier connections to the quantum metric, which relied on single-particle mean-field theory. This approach is combined with insights from the two-boson problem and exact diagonalization to map out the full phase diagram of the model. Our results show that the Gaussian approach is a versatile tool for studying a broad range of superfluid phases of interacting bosons in multi-orbital lattices.

Galaxy rotation curves exhibit systematic deviations from the Newtonian expectation inferred from visible matter alone. Existing phenomenological descriptions capture many aspects of these deviations, but a common residual structure across massive disks and dwarf irregular galaxies remains unclear. We investigate whether rotation-curve residuals organize into a simple empirical form across the SPARC and LITTLE THINGS samples. We analyze 175 SPARC galaxies and 22 LITTLE THINGS dwarf irregular galaxies in velocity-squared space after subtracting a leading Newtonian-like term. We fit a generalized residual family, v^2-A/r=B+Cr^{q+1}, and examine which radial scaling is selected by the data. The galaxy population systematically favors the limit \(q\simeq0\), corresponding to an approximately linear residual relation, \(v^2-A/r=B+Cr\). SPARC galaxies generally occupy a high-\(B\) branch, whereas LITTLE THINGS dwarf galaxies show suppressed residual intercepts, including several systems consistent with \(B=0\). For the SPARC sample, the high-\(B\) branch approximately follows \(B\propto M_{\rm bar}^{0.72}\). {Rotation-curve residuals are not featureless scatter beyond the leading Newtonian-like contribution, but instead show a simple population-dependent empirical organization across massive and dwarf galaxy systems.}

Molecular magneto-optical traps (MOTs) typically capture orders of magnitude fewer particles than their atomic counterparts due in part to their significantly lower capture velocities. Here, we employ a Stochastic Schrödinger Equation Monte Carlo approach to model a CaF DC MOT to understand the factors limiting capture velocity. We provide physical intuition into the mechanisms that affect capture velocity and identify important parameters and general strategies to improve it. In addition, we point out a loss mechanism intrinsic to molecular MOTs and determine parameter regimes that should be avoided experimentally. We benchmark our simulations against a CaF DC MOT and experimentally implement the improvements predicted by our model. In doing so, we demonstrate a molecular MOT with 1.5 million trapped molecules. This represents an eight-fold improvement and is an important step toward achieving quantum degeneracy with laser cooled molecules.

Stars form in molecular clouds under the influence of their local environments, yet the role of massive stellar feedback in either triggering or suppressing star formation remains a fundamental question in astrophysics. The Pillars of Creation in the Eagle Nebula, sculpted by ionizing radiation and stellar winds from massive stars in NGC 6611, offer a natural laboratory for investigating this question. Here we present high-resolution observations of the Pillars of Creation using the JWST Near Infrared Camera and Mid-Infrared Instrument, revealing 253 young stellar object (YSO) candidates. These YSO candidates show spatial correlations with the edges of feedback-driven structures, with overdensities along the boundaries. A weak trend of decreasing stellar age with increasing distance from the ionizing source was tentatively observed. There also appears to be an enhancement in the star formation rate within the past 1 Myr in this region. Such age and spatial associations suggest that while the bulk of the YSOs may have formed contemporaneously with the central cluster, a subset could be associated with triggered star formation. The JWST image of intricate structures, including a spiral-like disk and bi-reflection nebulae at the tips of Pillar I and Pillar II, further highlights the complexity of star formation processes.

In the present work, we propose an improved harmonic oscillator model to systematically evaluate the proton radioactivity half-lives in spherical nuclei, incorporating centrifugal potential effects. By fitting the experimental data, the centrifugal parameter $d = 0.143$ for the correction term $dl(l+1)$ and nuclear potential depth $V_0 = 62.4$ MeV are obtained. The model integrates the relativistic mean field (RMF) theory with the BCS method based on the DD-ME2 force to determine spectroscopic factors $S_p$. Moreover, by verifying the linear relationship between the logarithm of the normalized width $\log_{10}{γ^2}$ and fragmentation potential $V_{frag}$, the connection between nuclear structure and tunneling dynamics is confirmed, and an analytical expression for the adjustable parameter $d$ corresponding to the centrifugal potential is derived as $d^{\rm{Ae}}$ $\approx$ 0.167. Compared with $d^{\rm{Ae}}$, the modified model based on $d$ yields results in better agreement with experimental half-lives, and is able to control the error of the experimental data within a factor of 2.4. Furthermore, the extended improved model is used to predict the half-lives of some possible proton radioactivity candidates in NUBASE2020 that are energetically allowed or have been observed but not yet quantified. This work improves the accuracy of proton radioactivity studies and provides a robust theoretical framework for future nuclear structure research.

Tropical cyclone (TC) trajectories are governed by large-scale steering flows and exhibit sensitive dependence on atmospheric initial conditions. Using Hurricane Sandy (2012) in the Aurora AI weather model, we investigate whether targeted thermodynamic perturbations can induce meaningful track deviations. Two distinct perturbation regimes emerge. In the Caribbean, forward finite-time Lyapunov exponent (FTLE) diagnostics identify dynamically sensitive regions within Sandy's steering flow, where perturbations produce substantially larger responses than random placement. In the Pacific, a preferred corridor near 165W influences Sandy through Rossby wave teleconnections, confirmed using Takaya-Nakamura wave activity flux diagnostics. Despite their different physical pathways, both regimes share a common amplification mechanism: small initial perturbations generate modest trajectory offsets that are rapidly amplified when Sandy enters the highly sensitive recurvature region. The largest experiments produce track deviations exceeding 500 km after seven days. These results provide a proof-of-concept demonstration of the Weather Jiu-Jitsu framework, illustrating how targeted perturbations can be amplified through atmospheric dynamics in an AI weather model. Because the required perturbations exceed current operational cloud-seeding capabilities, the experiments should be interpreted as a theoretical sensitivity analysis rather than an operational weather modification strategy.