Papers

In this paper, we develop methods for constructing $\mathbb{Z}/2$-harmonic 1-forms in dimension three by varying the background metric. On $\mathbb{R}^3$, we construct an example for which the complement of the smooth locus in the singular set is a Cantor set. We realize every finite graph with positive even valence at each vertex as the monodromy locus of a $\mathbb{Z}/2$-harmonic 1-form on $B^3$. We also construct desingularization models for every critical $\mathbb{Z}/2$-eigensection, agreeing exactly with the associated homogeneous model outside a compact set. Finally, we construct a nondegenerate $\mathbb{Z}/2$-harmonic 1-form on every closed connected oriented three-manifold for a suitable smooth metric.

The Matrix Spencer conjecture asks whether any $n$ real symmetric matrices A_1,...,A_n \in \mathbb{R}^{m \times m} of operator norm at most one admit a signing $x\in\{-1,1\}^n$ such that the operator norm of the signed sum is at most O(\sqrt{n \log(2m/n)}) We give a randomized algorithm establishing this bound with polynomial runtime in the real-arithmetic model. We first prove the $O(\sqrt n)$ bound for $m\le n$, resolving the square case, and then obtain the rectangular bound by changing the regularizer. As in earlier algorithmic discrepancy methods \cite{lovettmeka2012,bansalLaddhaVempala2022,pesentivladu2026}, we run a covariance-controlled random walk from the origin of the hypercube, rounding coordinates near its faces and keeping them fixed. Our potential measures a soft spectral edge of the evolving discrepancy matrix perturbed by an operator-valued free semicircular element. Inspired by the free interpolation approach of \cite{bbvh2023}, we combine Lehner's variational formula for the free edge \cite{lehner1999} with spectral Tsallis regularization \cite{allenZhuLiaoOrecchia2015,pesentivladu2026}. This puts the discrepancy and remaining covariance in a single smooth optimization problem. The potential has a finite-dimensional semidefinite formulation. Stability of its optimizer, governed by equations related to the matrix Dyson equation \cite{erdos2019}, lets us find a large subspace in which to move while controlling discrepancy. The square case uses the Tsallis–$1/2$ regularizer; the rectangular case uses a suitable generalized Tsallis power regularizer. Our companion paper \cite{kathuria2026ks} applies these ideas to give an algorithmic proof of Weaver's discrepancy theorem, whose existence proof by [MSS15] resolved the Kadison–Singer conjecture \cite{mss2015}.Lean formalizations of our main discrepancy theorems have been completed and will be released shortly.

\cite{mss2015} proved Weaver's discrepancy result existentially, resolving the Kadison–Singer conjecture . Finding such signs efficiently for general inputs remained an open algorithmic question. In the real-arithmetic model, we give a deterministic algorithm running in polynomial time with discrepancy at most $35\sqrt\varepsilon$. The algorithm walks from the origin of the hypercube to a vertex, fixing coordinates as they hit a face. Its potential measures a soft spectral edge of the discrepancy matrix perturbed by an operator-valued free semicircular element. The perturbation's covariance vanishes as the coefficients reach their endpoints. Inspired by the free interpolation approach of Bandeira, Boedihardjo, and van Handel \cite{bbvh2023}, we combine Lehner's variational formula \cite{lehner1999} with spectral Tsallis–$1/2$ regularization used in \cite{allenZhuLiaoOrecchia2015} and \cite{pesentivladu2026}. The resulting potential has a finite-dimensional SDP formulation, allowing the discrepancy and remaining covariance to be analyzed together. We analyze the optimizer's stability through the linearized Karush–Kuhn–Tucker (KKT) system of a regularized min–max problem, whose stationarity equations are related to the matrix Dyson equation \cite{erdos2019}. This gives the movement rule: either a coordinate can move toward its nearer endpoint at small spectral cost, or a low-curvature direction orthogonal to the current coefficient vector allows further progress. Choosing the better sign of this direction controls discrepancy while increasing the squared distance from the origin. Upcoming work \cite{kathuria2026higherRank} will address higher-rank Kadison-Singer and spectrally thin trees. Lean formalizations of our main discrepancy theorems have been completed and will be released shortly.

The Type I superluminous supernova (SLSN-I) SN 2025wny, multiply imaged by two foreground galaxies at $z_l = 0.375$, is the first confirmed strongly lensed SLSN and the highest-redshift ($z_s = 2.015$) multiply imaged supernova in a galaxy-scale configuration. We ask whether one discovery in seven years of Zwicky Transient Facility (ZTF) operations is consistent with expectations, and whether SN 2025wny is typical of the detectable population. We develop a forward simulation of strongly lensed SLSNe-I in ZTF, combining an empirically calibrated volumetric rate and luminosity function with a galaxy-scale deflector population, unresolved lensed light curves, and the actual ZTF observing history. We predict $0.037^{+0.022}_{-0.020}\,{\rm yr}^{-1}$, consistent with the rate of $0.14^{+0.31}_{-0.11}\,{\rm yr}^{-1}$ inferred from a single discovery in seven years of ZTF operations. Conditioning the simulation on discovery by ZTF corrects the magnifications and intrinsic luminosity of SN 2025wny for Malmquist- and magnification biases: the debiased peak bolometric luminosity, $\log_{10}(L_{\rm bol,int}/{\rm erg\,s^{-1}}) = 44.60^{+0.05}_{-0.10}$, places it at the $\sim$97th percentile of the assumed SLSNe-I luminosity function. SN 2025wny is typical of the detectable population in redshift, luminosity, and magnification, but its $4.9''$ image separation exceeds single-galaxy deflector expectations, implying our rates are conservative for wide-separation systems.

We develop a geometric framework for Hamiltonian engineering in finite-dimensional quantum systems using ideal control pulses. Starting from a bilinear Schrödinger equation with unbounded control amplitudes, we construct the closed pulse group and use extensions of control systems and Filippov's relaxation theorem to obtain a family of effective Hamiltonians given by the convex hull of the drift's adjoint orbit plus the Lie algebra of the pulse group. The geometry of this orbitope describes possibilities beyond group averaging. Using the isotypic decomposition of the adjoint representation, we characterize its affine hull and show that the group average lies in its interior. This yields locally accessible families of effective Hamiltonians around the invariant part of the drift. We apply the framework to recover the necessary and sufficient condition for dynamical decoupling from arbitrary interactions with a finite-dimensional bath. For connected abelian pulse groups, we describe the relevant representation decomposition through restricted roots. Finally, for qubit networks with identical pairwise couplings, we give a qualitative characterization and quantitative estimation of effective Hamiltonians that can be generated using our framework.

Conventional motion planning treats collision as a binary constraint, although contact with different objects can have drastically different consequences. A robot may safely brush against a cardboard box while even minor contact with a glass, laptop, or unstable object may be undesirable. Moreover, a direct robot–object collision can move the contacted object and trigger secondary object–object collisions, making the risk of a motion depend on the physical evolution of the scene rather than only on the robot's geometric path. We present CaSCo, a cascade-aware soft-collision motion planning framework in which a vision-language or language model assigns semantic risk to objects and a physics simulator predicts the consequences of candidate robot motions. CaSCo searches for a path that minimizes the total semantic risk of the unique objects displaced either directly by the robot or indirectly through cascaded collisions. Because collisions change the environment, we augment roadmap states with the predicted object arrangement and the set of objects whose risk has already been incurred. We develop an optimal graph-search algorithm with an admissible and consistent cascade-relaxed heuristic and caching and pruning mechanisms for efficient search. Experiments in cluttered manipulation environments evaluate semantic risk, cascade reasoning, planning efficiency, and real-robot operation.

Agent benchmarks are substantially more costly to evaluate than conventional LLM benchmarks. Benchmark compression is therefore a natural solution, yet existing methods primarily model redundancy in task–model final-score distributions, which is important in agentic evaluation. To address this limitation, we analyze large-scale trajectories and identify six complementary process signals that are systematically associated with final agent performance. To disentangle agent performance redundancy from a complete perspective, we propose DualViewEval, an agent benchmark compression method that jointly exploits outcome and process relations to learn an exact-size miniset and predict the full-benchmark scores. Across five agent benchmarks and five representative baselines, DualViewEval achieves the best results in all datasets. With only 20 tasks, it achieves $24\times$–$40\times$ compression on APEX-Agents and BFCL, reducing mean absolute error (MAE) by $14.5\%$–$28.2\%$ over the strongest competitors while improving Kendall's $\tau$ by up to $7.2\%$ relative to EssenceBench on SWE-bench Verified. The selected minisets further reveal capability differences among different agents, providing compact and diagnostic feedback for efficient agentic model development.

Existing legal benchmarks cover diverse tasks, while continuous monetary remedies remain comparatively underexplored. We introduce ECtHR-NPD, to the best of our knowledge, the first benchmark for predicting non-pecuniary damage (NPD) awards at the European Court of Human Rights (ECtHR) from case information when no statutory formula or explicit calculation rule determines the amount. ECtHR-NPD contains 14,575 cases with case-level awards in nominal euros, chronological splits, and a protocol separating target construction from model input. We evaluate a battery of methods, including constant predictors, gradient-boosted trees, retrieval methods, fine-tuned encoder language models (LMs), prompted decoder LMs, and knowledge-augmented agents. Our results show that more sophisticated LM and agentic approaches do not consistently outperform the strongest feature-based baseline. All model families struggle to identify zero awards and to calibrate high-award predictions, with further degradation on the Challenging test view, making ECtHR-NPD a challenging testbed for current state-of-the-art open-weight and proprietary LMs.

We show that boson sampling with an arbitrary $m$-mode interferometer and $n\le m$ single-photon inputs can be simulated to inverse-polynomial total-variation error by a logarithmic-depth qubit circuit with polynomially many qubits. The circuit uses Clifford+$T$ gates, arbitrary qubit connectivity, and a single final measurement, and its family is logspace uniform. The key idea is to enlarge the optical system, decompose the resulting transformation into six quadratic shears, and distribute each mode over many submodes. This redistribution permits a fixed local occupation cutoff, after which local basis changes and parallel phase gates give the qubit circuit. Consequently, our result places boson sampling within shallow quantum computation.

Motivated by the recent CMS data on a family of $2^{++}$ states from $J/\psi J/\psi$ mass spectrum, we determine the masses of the $2^{++}$ $J/\psi J/\psi$ molecule and $cc\bar c\bar c$ states, by using (for the first time) the two lowest QCD Laplace Sum Rules (LSR) moment-ratios within the standard optimization criteria with respect to the LSR variable $\tau$ and to the QCD continuum threshold $t_c$ implemented by the $R_{P/C}$ requirement that the lowest ground state (Pole) contribution to the LSR is larger than the QCD continuum one. Including factorized NLO perturbative and LO $G^4$ gluon condensates in the OPE, we obtain the the lowest ground state masses: $M^{2^{++}}_{J/\psi J/\psi}=6521(69)$ MeV and $M^{2^{++}}_{cc\bar c \bar c}=6347(99)$ MeV with the couplings\,: $f^{2^{++}}_{J/\psi J/\psi}=96(14)$ keV and $f^{2^{++}}_{cc\bar c \bar c}= 151(29)$ keV normalized as $f_\pi=93$ MeV. The masses of the first radial excitations are :$M^{2^{++}{rad}}_{J/\psi J/\psi}=7987(251 )$ MeV and $M^{2^{++}{rad}}_{cc\bar c \bar c}=7739(221)$ MeV indicating a mass-splitting about $2.5 (M_{\psi(2S)}-M_{J/\psi})$. The decay constants are $f^{2^{++}{rad}}_{J/\psi J/\psi}=248(70)$ keV and: $f^{2^{++}{\rm rad}}_{cc\bar c\bar c}=453(96) $ keV which are (unexpectedly) larger than the lowest ground state ones. These features may indicate some new dynamics compared to ordinary $\bar cc$ states. We extend the analysis to the $0^{++}$ states and to the $\Upsilon\Upsilon$ family where the results are compiled in Tables 2 and 3. We critically review some other QCD spectral sum rules (QSSR) results. We suggest that the X(6600) might be a molecule ground state. Using a two-component mass mixing scheme, the X(6900) and X(7100) might be interpreted as a mixture of the $cc\bar c\bar c$ lowest ground state with its 1st radial excitation via an angle $\theta=5^0$.

Health discourse in social media videos often contains densely entangled claims spanning multiple thematic aspects, stances, evidential frames, and rhetorical functions within short conversational spans. Existing approaches largely rely on coarse topic-level, sentiment-based, or stance-oriented representations that do not adequately capture this structure. Our analysis identifies an average of 13.22 atomic claims per minute, motivating richer claim-level discourse representations. We introduce a structured framework for claim-level discourse analysis in dense health narratives. Our framework models discourse through tuples linking atomic claims with thematic aspects, stance, and multidimensional pragmatic discourse attributes. To support this setting, we construct a benchmark spanning four health domains with 1,191 manually annotated claims from 60 videos. Using this framework, we evaluate automated structured discourse analysis under different discourse context settings. Results show that current LLMs achieve strong performance on thematic categorization and stance prediction, but struggle with high-dimensional pragmatic profiling. We also find that different discourse tasks benefit from different forms of contextual reasoning, suggesting that future systems may require task decomposition and specialized inference strategies.

A compactification of the discrete space $\omega$ of all integers is called symmetric if it is the quotient space obtained by gluing together the remainders of two copies of some other compactification of $\omega$. This is a generalization of both a convergent sequence, which is in a way the minimal symmetric compactification of $\omega$, and the Arkhangel'skiĭ–Bereznitskiĭ–Schachermayer space studied in $C_p$-theory, which is in a sense the maximal symmetric compactification of $\omega$. We investigate symmetric compactifications of $\omega$ and their relations to the Separable Quotient Problem for spaces $C_p(X)$ and to the existence of Josefson–Nissenzweig sequences of finitely supported Borel measures on spaces $X$, in particular with supports of bounded size. Further, we reduce the Separable Quotient Problem for spaces $C_p(K)$, $K$ compact, to the case when $K$ is a totally asymmetric compactification of $\omega$. Our results shed some new light on the Grothendieck property of Banach spaces $C(K)$.

Discovering interpretable subgroups whose complier effects deviate from the average is a central goal of instrumental variable analysis under imperfect compliance, yet existing tree-based methods degrade when most covariates are irrelevant to the effect. We propose Shrinkage Bayesian Causal Forest with Instrumental Variable (SBCF-IV) for discovering and estimating subgroups with heterogeneous Complier Average Causal Effects (CACE) in sparse high-dimensional settings. SBCF-IV places a sparsity-inducing Dirichlet prior on the splitting probabilities of the Bayesian Additive Regression Trees that estimate the conditional intention-to-treat and the complier share, concentrating posterior mass on the few covariates that moderate the complier effect and thereby regularizing effect estimation. The posterior split frequencies additionally enter a downstream CART as variable-level costs that steer the partition toward relevant moderators, providing an interpretable division of the covariate space. Monte Carlo experiments show that, as the share of irrelevant covariates grows, SBCF-IV recovers the true partition more reliably than its non-sparse predecessor BCF-IV at the tree and unit level, and retains nominal coverage where BCF-IV's intervals deteriorate. We apply the method to the Oregon Health Insurance Experiment and the 401(k) eligibility data.

We construct skein theory for 3-manifolds with embedded line defects, starting from the data of a ribbon tensor category and its balanced braided module category. We focus on line defects arising from quantum symmetric pairs, and prove finiteness properties for their defect skein modules. As an application, we consider $\mathbf{Z}_2$-equivariant skein theory and establish an equivalence with defect skein theory in certain settings, leading to a skein theoretical construction of a family of $\mathrm{C}^\vee\mathrm{C}$ DAHA-modules in the Type AIII case.

In physics-informed machine learning, a target function $u^*$ is learned from noisy value observations $y_i=u^*(x_i)+ \varepsilon_i$, together with differential information, given either by noisy observations $d_j=(Du^*)(z_j)+\xi_j$ or by a known physical constraint $Du^*=v$. We consider the setting where $D$ is a linear differential operator and analyze a physics-informed kernel estimator $\hat u$ combining $n$ value observations and $m$ differential observations. In this context, we ask how much can differential information improve predictions, and how does this improvement depend quantitatively on $n$, $m$, and $D$. We prove finite-sample bounds, supported by numerical simulations, revealing a two-regime structure for the prediction error. When $m$ is limited, the rate depends jointly on $n$ and $m$; when $m$ exceeds a problem-dependent threshold, the rate saturates and matches the oracle rate obtained when the perfect constraint $D \hat u = Du^*$ is imposed. Examples are discussed for Sobolev spaces which are reproducing kernel Hilbert spaces and include partial Laplacian constraints on the torus and gradient observations on bounded domains. These examples illustrate the range of possible learning rate improvements — from the standard nonparametric $n^{-1/4}$ to the parametric rate $n^{-1/2}$. Finally, we derive physically consistent rates in a stronger norm that jointly controls the errors in $\hat u$ and $D\hat u$.

Prototyping and evaluating human-robot teaming (HRT) scenarios in the real-world is costly. Virtual simulation of HRT scenarios has been adopted as an alternative to conducting user studies in the real-world to investigate user perceptions, behaviors, and performance during human-robot interactions. The consistency of human behavior between the real and virtual-worlds is integral to the validity of utilizing such virtual experimentation. This paper presents a user study examining the difference in human behavior between an HRT scenario conducted in a virtual vs real environment. We employed mixed-methods to examine team performance and human factors during the HRT. Our quantitative results showed a significant difference in workload between the two modalities. Our qualitative analysis expanded on the quantitative results and found differences in participants' strategy, their mental model of robots, and the type of trust they had for robots between modalities.

Quantum networks are resources for scaling quantum computers and distributed sensing technologies while offering post-quantum security benefits. Teleporting non-classical resources like entanglement, via so called entanglement swapping, is essential for networks in particular overcoming rate-loss limits via quantum repeaters. Deploying these systems on real infrastructure will likely require multiplexing photonic qubits into fibers carrying 'classical' light encoding standard Internet communications and control plane signals for multi-node quantum protocols. Here, we report the first demonstration of entanglement swapping and conventional communications operating over the same fibers. Entanglement is swapped across a five-node quantum relay topology connected by four long-distance fibers, each populated with classical data signals. Time-bin entangled photons in the C-band are multiplexed alongside C-band classical signals using dense-wavelength division multiplexing, introducing noise photons generated by high-power classical light. We experimentally and theoretically characterize the trade-off between quantum fidelity and Raman noise photons. Entanglement swapping is demonstrated over a maximum fiber length of 40 km (four 10-km fibers) while simultaneously transmitting 10-Gbps classical data through all fibers. These results represent a significant advancement in the demonstrated complexity of coexisting quantum and classical networks and provide a roadmap for achieving the widespread deployment of advanced quantum technologies.

Training-free weighted aggregation is widely used to lift 2D semantic features onto 3D Gaussians for open-vocabulary scene understanding, yet its theoretical role remains insufficiently understood. Existing analyses typically justify this operation from the rendering side, treating Gaussian features as linearly composable Euclidean variables for reconstructing 2D feature maps. However, this view does not match downstream 3D usage, where each Gaussian is often queried independently in a cosine-based embedding space. We revisit feature lifting from the 3D side and formulate per-Gaussian assignment as a cosine alignment problem on the CLIP unit sphere. Under this objective, the $\ell_2$-normalized semantic back-projected feature emerges as the closed-form solution, providing a complementary interpretation of the standard lifting rule from the perspective of per-Gaussian semantic assignment. This solution is still a convex combination of the observed directions, so every lifted feature is inherently a mixture. Such mixing is unavoidable for any per-Gaussian estimator, and the question is whether it can be measured. The same formulation answers this: the norm of the back-projected feature decomposes into intra-view and inter-view consistency, so the feature magnitude quantifies how mixed the observations are and serves as a semantic reliability signal. Calibrated by effective multi-view support, this reliability score identifies the Gaussians whose lifted direction has drifted and guides a mode-voting refinement that corrects them by copying a single observed CLIP direction instead of averaging. Experiments on open-vocabulary 3D semantic segmentation show that NormLift is an efficient, training-free framework that achieves strong performance across evaluation protocols. Our code is available at https://github.com/kaust-violab/NormLift_release

Difference sets, external difference families and near-factorizations of groups are much-studied structures satisfying certain uniformity conditions on the differences or sums within or between elements of sets in groups. Research has centred on abelian groups, though there are classic results (such as Dillon's Dihedral Trick for difference sets and the work of Pêcher on near-factorizations) connecting abelian and non-abelian structures, which have recently regained attention. We present a new explicit framework enabling transfer of difference structures between groups using a semidirect product approach, establishing new tools and constructions, encompassing various previous results and addressing an open problem of Swartz et al. Motivated by the classic dihedral results, we focus on semidirect products $G \rtimes \mathbb{Z}_2$. Transfer from abelian to non-abelian groups, and between distinct non-abelian groups, are both possible, and our framework can handle $\lambda$-fold near-factorizations, difference sets and external difference structures with arbitrarily many sets. We obtain new near-factorizations and difference structures in a range of groups, and can transfer various examples not transferrable by previous approaches. We showcase our approach by establishing a new infinite family of three-set abelian circular external difference families, then producing from this the first infinite family of non-abelian circular external difference families.

This study focuses on propanethiol (or propyl mercaptan, C3H7SH), a sulfur analogue of propanol and a key target for investigating interstellar sulfur chemistry. We report the laboratory rotational spectroscopic characterization of its two structural isomers, propane-1-thiol (1PT) and propane-2-thiol (2PT). For 1PT, experimental analysis led to the observation of three almost isoenergetic conformers, Aa,Ag and Gg, marking the first-time report of the latter. For 2PT, both the anti and gauche conformers were identified. We also assigned, for the first time, several monosubstituted isotopologues in natural abundance: the 34S, 13C1, and 13C2 species for the anti-2PT conformer, as well as the 34S species for the gauche-2PT conformer.Resolvable tunneling splitting, caused by the large-amplitude motion of the sulfhydryl (SH) group, was observed for both the Ag-1PT and gauche-2PT conformers. Global fittings, integrating previous measurements, allowed for the accurate determination of rotational constants, quartic centrifugal distortion constants, and vibrational coupling parameters. The newly derived spectroscopic parameters were utilized to conduct an astronomical search toward the chemically rich Galactic Center molecular cloud G+0.693-0.027. While no evidence for propanethiol was found, we established rigorous upper limits for their column densities. These results indicate that 1PT and 2PT are approximately 13 and 5 times less abundant than ethanethiol in this source, respectively. Furthermore, the derived lower limit for the O/S ratio (29) for the 1-propanol/1-propanethiol pair is consistent with the solar value (37), proviiding a valuable benchmark for understanding the depletion of sulfur in the ISM.

We report the detection of a remarkable shell around the red hypergiant VY CMa using data from the Spectro-Photometer for the History of the Universe, Epoch of Reionization, and Ices Explorer (SPHEREx). The shell, which in projection on the plane of the sky appears as a ring, is almost circular in appearance. It has an external diameter of $\sim14'$ to $15'$, and is seen most clearly in the SPHEREx 7827A spectro-photometric image. Filaments, radially aligned with VY CMa, are seen to cut across the shell in several places. We discuss the possibility that the shell is matter swept out from the neighboring star forming region Sh 2-310, by the wind from VY CMa. Resonant atomic scattering, a light echo, or Extended Red Emission are explored as the source of the observed SPHEREx emission. However, no interpretation is without difficulty and further observations are most desirable.

Constructing Lyapunov functions for nonlinear dynamical systems is a central problem in stability analysis, yet remains challenging. Lyapunov functions are commonly characterized as solutions to first-order partial differential equations (PDEs), but these solutions are typically obtained for single systems, limiting their reuse across systems. In this paper, we study the Lyapunov solution operator that maps a vector field to the corresponding Lyapunov function defined by a dissipation-based Lyapunov PDE. We establish that, on compact subsets of the domain of attraction and under exponential stability assumptions, this operator is well-defined, unique, and continuous with respect to perturbations of both the vector field and the dissipation function. These results provide a theoretical foundation for approximating Lyapunov functions uniformly over families of nonlinear systems. Building on these theoretical foundations, we employ Fourier Neural Operators (FNOs) as a data-driven approximation of the Lyapunov solution operator. Numerical experiments demonstrate that a single trained operator can accurately approximate the numerical Lyapunov functions across parameterized families of dynamics. This illustrates the potential of neural operators for approximating Lyapunov functions.

Autonomous underwater navigation typically relies on complex and expensive multi-modal sensor suites designed to prioritize global Simultaneous Localization and Mapping (SLAM) accuracy. However, local reactive behaviors such as coarse navigation and obstacle avoidance require only local consistency—a capability that should be feasible using only a Forward-Looking Sonar (FLS), yet remains largely unaddressed, leaving a critical gap in FLS-only local SLAM. Moreover, existing acoustic SLAM frameworks predominantly rely on sparse feature extraction methods that discard substantial portions of the already information-sparse acoustic returns. To overcome these limitations, this work introduces a dense direct registration approach that aligns full acoustic intensity scans to a recursively updated local map. Real-time execution is achieved via an Inverse Compositional Gauss-Newton optimization strategy that minimizes computational overhead. Experimental evaluations show that this dense method yields significant improvements on translation error compared to sparse keypoint baselines, maintaining stable sub-meter tracking precision over wide displacement gaps. Moreover, this approach delivers odometry performance comparable to multi-sensor fusion pipelines (FLS, DVL, and IMU), bypassing expensive payload dependencies in feature-rich environments. We validate real-world applicability through AUV field trials, running the full local SLAM approach onboard an embedded, resource-constrained computer.

Tau spin correlations at the $Z$ pole probe CP violation with a sensitivity that depends strongly on the spin projection. For a fixed $Z$ sample, transverse moments avoid the chirality suppression of longitudinal and triple-product observables, enhancing the response by a factor $m_Z/2m_\tau=26$. Two transverse moments also select the axial tau charge, gaining $|a_\tau/v_\tau|=13.5$; the sign-weighted normal moment has a response $521$ times that of the triple product. These two transverse moments give single-parameter uncertainties no more than $14\%$ above our calculated Cramer-Rao bound for independent single-pion measurements, approaching the best precision within this analysis. A five-moment fit with $5\%$ off-peak luminosity yields statistical uncertainties of $4.5 (5.5)\times10^{-7}$ and $2.7 (3.2)\times10^{-6}$ on $\operatorname{Re}\widetilde{d}_\tau^W$ and $\operatorname{Im}\widetilde{d}_\tau^W$, respectively, at FCC-ee (CEPC), improving on ALEPH by three orders of magnitude. The electromagnetic-dipole uncertainty is $9.6 (12)\times10^{-6}$ on $\operatorname{Re}\widetilde{d}_\tau^\gamma$, two orders beyond Belle. These projections assume ideal angular reconstruction and constant form factors across the scan.

The $f_0(1500)$ is a quite special resonance in the light scalar spectrum. Compared with other nearby resonance, it has an unexpectedly narrow decay width. Since its mass region overlaps strongly with $f_0(1370)$ and $f_0(980)$, physicists have long debated its internal structure. To explore this issue, this work adopted the conventional quark-antiquark $q\bar{q}$ picture and investigated the behavior of the $f_0(1500)$-resonance in quasi-four-body decay channels. Based on this, we constructed a twist-2 light-cone distribution amplitude(LCDA) schemes based on the light-cone harmonic oscillator model, and presented their moments $\langle \xi ^n _{2;f_0(1500)} \rangle |_\mu$ and Gegenbauer moments $a_{n;f_0(1500)}(\mu)$ at $\mu_0=1~\mathrm{GeV}$ and $\mu_k= 3~\mathrm{GeV}$ for $n=1,3,5$. Meanwhile, the $B_s\to f_0(1500)$ transition form factors (TFFs) are calculated by using the QCD light-cone sum rule. Then, we obtained the three TFFs at large recoil point, i.e., $f_ + ^{B_s f_0(1500)}(0)= 0.390_{-0.046}^{ + 0.047}$, $f_-^{B_s f_0(1500)}(0)= -0.460_{-0.055}^{ + 0.051}$, and $f_{\rm T}^{B_s f_0(1500)}(0)= 0.568^{ + 0.069}_{-0.065}$. In addition, we extrapolated TFFs to the whole physical $q^2$-region by using the simplified $z(q^2)$-series expansion. Then we computed the branching fractions of the quasi-four-body rare decays $B_s \to f_0(1500)(\to \pi^ + \pi^-)\ell^ + \ell^-$ and $B_s \to f_0(1500)(\to \pi^ + \pi^-)\nu\bar{\nu}$. For comparison, we also present the results of the corresponding three-body decays obtained under the narrow-width approximation. Finally, we show the distribution of the double-differential decay width $d^2\Gamma/ds dq^2$ for the quasi-four-body decay $B_s\to f_0(1500)(\to\pi^ + \pi^-)\mu^ + \mu^-$. We hope that our predictions can provide a useful theoretical reference for future experimental measurements and phenomenological research.

We prove the existence of admissible subsolutions to the Dirichlet problem for symmetric augmented $k$-Hessian type equations. An important sufficient condition is the uniform $(k-1)$-$A$-convexity of the domain $\Omega,$ where $A(x, z, p)$ is the augmented symmetric matrix appearing in the equation. This condition was originally introduced by F. Jiang, N. S. Trudinger, and X.-P. Yang and we have chosen a special their case. The structural conditions on the matrix $A(x, z, p)$ include its growth with respect to the variables $z$ and $p,$ particularly requiring that some of its first and second derivatives are sufficiently small in a sufficiently small neighborhood of the boundary. Under certain structural conditions on $A(x, z, p),$ the uniform $(k-1)$-$A$-convexity of $\Omega$ is also a necessary condition for the existence of admissible subsolutions of the equation in a neighborhood of the boundary. Our results extend the classic result by L. Caffarelli, L. Nirenberg, and J. Spruck from the case $A \equiv 0$ to the general case $A \neq 0.$ Our same theorems are valid also for augmented quotient Hessian type equations.

As data center (DC) loads increasingly penetrate the power grid, there is an urgent need for grid operators to provide clear dynamic specifications to DC owners to ensure safe grid operation. To this end, we study two salient behaviors of large language model (LLM) training loads: abrupt ramps at job initiation and termination, which induce transient frequency excursions, and sustained periodic oscillations during training, which result in oscillatory steady-state behavior. For ramping loads, we show that nodal rotor frequencies can be accurately approximated by the center-of-inertia (COI) frequency and derive analytical expressions for its nadir and rate of change of frequency (RoCoF). These expressions determine allowable combinations of ramp times and steady-state load demands satisfying prescribed frequency limits. For oscillatory loads, we derive spectral specifications on their Fourier coefficients and show that the admissible coefficient set can be approximated by a polytope. We further obtain a compact representation via its maximum-volume inscribed ellipsoid, which we show is axis-aligned. Numerical tests on the WECC 179-bus system demonstrate that the resulting specifications remain valid for higher-order nonlinear dynamics. The proposed framework provides actionable specifications for regulating the dynamic behavior of large DC loads and informing load-shaping mechanisms within the data center ecosystem.

Nitrogen-vacancy (NV) centers in diamond are a leading platform for vector magnetometry, offering intrinsic sensitivity to both the magnitude and direction of magnetic fields. NV magnetometers typically rely on an external bias field to lift the degeneracy of the ground-state spin sublevels, enabling spectral discrimination of different NV orientations and spin transitions. At high accuracy, however, such a bias field systematically introduces errors through thermal, mechanical, and hysteretic drifts, thus hindering the accurate measurement of the magnetic field of interest. Several strategies have been proposed to address this limitation, including optical polarization-based orientation labeling, optical anisotropy, strong coupling to nearby nuclear spins, circular microwave polarization, and tailored pulse sequences. In this work, we introduce an optimization-based pulse-shaping control framework that enables selective and robust manipulation of NV ensembles without relying on a static bias field. Our method achieves both orientation-selective and subspace-selective control through optimal temporal modulation of the driving fields, providing a route to resolving spectral overlaps in degenerate NV systems.

Traditional blockchain-based document notarization follows a snapshot-oriented model in which each document revision is represented as an independent state anchored on-chain through a cryptographic reference. While effective for immutable artifacts, this approach becomes inadequate when documents evolve through collaborative editing. Concurrent modifications create divergent document versions that must be reconciled outside the notarization layer, while even minor changes require generating and distributing new document snapshots. Conversely, collaborative replication frameworks such as CRDTs provide deterministic reconciliation of concurrent updates, but do not inherently provide independently verifiable evidence of when contributions were published. This paper introduces Fluid Notarization, a notarization paradigm in which document evolution itself becomes the object of notarization. Rather than certifying isolated states, Fluid Notarization certifies a graph of causally related evolution artifacts generated by a JSON-native delta-CRDT. The proposed model builds upon Melda, which represents document changes as compact, content-addressed deltas linked through causal dependencies. Blockchain notarization is reduced to recording identifiers of these evolution artifacts, while synchronization, reconstruction, and conflict resolution remain entirely off-chain. The resulting architecture combines two complementary guarantees: deterministic convergence provided by the CRDT and independently auditable proof-of-existence, provenance, and publication evidence provided by the blockchain. A prototype implementation and validation scenario based on collaboratively edited electronic health records demonstrate the feasibility of the approach and highlight the advantages of notarizing document evolution rather than successive document snapshots.

In this article, we study the facilitated exclusion process (FEP) on the $d$-dimensional discrete torus of side length $N$, with $d\ge2$. For Bernoulli initial data with a fixed density $\rho\in(0,1)$, we first prove that, with high probability, the particle-number sector selected by the initial configuration has a unique active recurrent class if $\rho>1-2^{-d}$ and multiple recurrent classes if $\rho<1-2^{-d}$. We then show that, for sufficiently small $\rho$, the process reaches an absorbing state (a singleton recurrent class) within a poly-logarithmic time in $N$ with high probability. In contrast, for $\rho\in(1/2,3/4)$ and even $N$, we establish a polynomial lower bound on the time required to reach the recurrent set. These results provide strong evidence for a double phase transition, analogous to absorbing-state phase transitions in the contact process, activated random walks, and stochastic sandpiles. To our knowledge, these are the first rigorous estimates for absorption and transient times for the FEP in dimensions two and higher.