Among the recognized sources of decoherence in superconducting qubits, the spatial inhomogeneity of the superconducting state and the possible presence of magnetic-flux vortices remain comparatively underexplored. Niobium is commonly used as a structural material in transmon qubits that host Josephson junctions, and excess dissipation anywhere in the transmon can become a bottleneck that limits overall quantum performance. The metal/substrate interfacial layer may simultaneously host pair-breaking loss channels (e.g., two-level systems, TLS) and control thermal transport, thereby affecting dissipation and temperature stability. Here, we use quantitative magneto-optical imaging of the magnetic-flux distribution to characterize the homogeneity of the superconducting state and the critical current density, $j_{c}$, in niobium films fabricated under different sputtering conditions. The imaging reveals distinct flux-penetration regimes, ranging from a nearly ideal Bean critical state to strongly nonuniform thermo-magnetic dendritic avalanches. By fitting the measured magnetic-induction profiles, we extract $j_{c}$ and correlate it with film physical properties and with measured qubit internal quality factors. Our results indicate that the Nb/Si interlayer can be a significant contributor to decoherence and should be considered an important factor that must be optimized.

Simulating low-temperature properties of three-dimensional frustrated quantum magnets is challenging due to the sign problem and the system sizes required to mitigate substantial finite-size effects. However, there are many experimental examples of three-dimensional crystals that could host exotic low-temperature states of matter, such as quantum spin liquids. We calculate the ground-state phase diagrams of frustrated quantum spin models on the body-centered cubic lattice using neural quantum states. First, we study the antiferromagnetic $J_1-J_2$ model where we find a direct first-order phase transition between Néel and collinear long-range-ordered phases at $(J_2/J_1)_c = 0.705$, consistent with previous studies. Then, in a tetragonally-distorted variant, proposed as a minimal model of NaCa$_2$Cu$_2$(VO$_4$)$_3$, we find no evidence of a quantum paramagnetic ground state, with a first-order phase transition between Néel and chain phases at $(J_{2ab}/J_1)_c = 1.0375$. Therefore, the ground state of the tetragonally-distorted model does not reproduce the low-temperature magnetic properties of NaCa$_2$Cu$_2$(VO$_4$)$_3$, and the inclusion of other effects is necessary to rationalize experimental observations.

This paper introduces and studies split two-sided 2-fibrations and locally discrete split two-sided 2-fibrations, using a formal categorical approach. We generalise Street's notion of split two-sided fibration internal to a 2-category to one internal to a sesquicategory. Given a sesquicategory we construct a virtual double category whose horizontal (loose) morphisms are its internal split two-sided fibrations. Specialising to the sesquicategory of lax natural transformations we obtain the virtual double category of split two-sided 2-fibrations, which we study in detail. We then restrict to the sub-virtual double category of locally discrete split two-sided 2-fibrations and show that therein the usual Yoneda 2-functors satisfy a double-categorical formal notion of Yoneda morphism, which formally captures universal properties similar to those satisfied by the morphisms comprising a Yoneda structure on a 2-category. As a consequence we obtain a 'two-sided Grothendieck correspondence' of locally discrete split two-sided 2-fibrations $A \nrightarrow B$ and 2-functors $B \to Cat^{A^{op}}$. Restricting to $A = 1$, the terminal 2-category, we improve Buckley and Lambert's 'Grothendieck correspondence' for locally discrete split op-2-fibrations by extending the sense in which it is functorial.

Using a new approach involving embedding spaces in II$_1$ factors with plenty of freely independent Haar unitaries, we prove that $C^\ast_r(\mathbb{F}_n)\ncong C^\ast_r(\mathbb{F}_m)$ for $n \neq m$. This recovers the seminal result of Pimsner and Voiculescu with a short new proof.

In the era of 6G Air-Ground Integrated Networks (AGINs), Unmanned Aerial Vehicles (UAVs) are pivotal for providing on-demand wireless coverage in mission-critical environments, such as post-disaster rescue operations. However, traditional Deep Reinforcement Learning (DRL) approaches for multi-UAV orchestration often face critical challenges: instability due to the non-stationarity of multi-agent environments and the difficulty of balancing energy efficiency with service equity. To address these issues, this paper proposes ORCHID (Orchestration of Resilient Coverage via Hybrid Intelligent Deployment), a novel stability-enhanced two-stage learning framework. First, ORCHID leverages a GBS-aware topology partitioning strategy to mitigate the exploration cold-start problem. Second, we introduce a Reset-and-Finetune (R\&F) mechanism within the MAPPO architecture that stabilizes the learning process via synchronized learning rate decay and optimizer state resetting. This mechanism effectively suppresses gradient variance to prevent policy degradation, thereby ensuring algorithmic resilience in dynamic environments. Furthermore, we uncover a counter-intuitive efficiency-fairness synergy: contrary to the conventional trade-off, our results demonstrate that the proposed Max-Min Fairness (MMF) design not only guarantees service for cell-edge users but also achieves superior energy efficiency compared to Proportional Fairness (PF), which tends to converge to suboptimal greedy equilibria. Extensive experiments confirm that ORCHID occupies a superior Pareto-dominant position compared to state-of-the-art baselines, ensuring robust convergence and resilient connectivity in mission-critical scenarios.

By examining recently published images in different wavelengths, I identify a point-symmetric morphology in the Large Magellanic Cloud core-collapse supernova (CCSN) remnant (CCSNR) J0450.4-7050 (SNR 0450-70.9; nicknamed Veliki), which I attribute to at least three pairs of energetic jets that participated in the explosion of the progenitor in the framework of the jittering jets explosion mechanism (JJEM). Two pairs of ears, a pair of blowouts in the north and south along the long axis of this SNR, and a pair of dents compose the point symmetric morphology. The fact that the symmetry axes of two pairs include pairs of opposite structural features in the inner ejecta implies that the shaping is by jets and not due to an interaction with an ambient material. While the JJEM predicts such morphologies, the competing neutrino-driven mechanism cannot account for point-symmetric morphologies. This study provides strong support for the claim that the JJEM is the primary CCSN explosion mechanism.

We develop an information-theoretic reconstruction of quantum dynamics based on inference over action space. The fundamental object is a density of action states encoding the multiplicity of dynamical alternatives between configurations. Maximum-entropy inference introduces a finite resolution scale in action, implying that sufficiently close action contributions are operationally indistinguishable. We show that this indistinguishability, together with probability normalization and action additivity, selects complex amplitudes and unitary evolution as the minimal continuous representation compatible with action additivity, probability normalization, and inference under finite resolution. Quantum interference and unitarity therefore emerge as consequences of these assumptions rather than independent postulates. From the resulting propagator, the Lagrangian, Hilbert-space structure, and Schrödinger equation follow as derived consequences. In the infinitesimal-time limit, action differences universally fall below the resolution scale, making coherent summation the minimal consistent description at every step. The numerical value of the action scale is fixed empirically and identified with $\hbar$.

This paper proposes a new way of evaluating the accuracy and validity of probabilistic forecasts that change over time (such as an in-game win probability model, or an election forecast). Under this approach, each model to be evaluated is treated as a canonical Kelly bettor, and the models are pitted against each other in an iterative betting contest. The growth or decline of each model's bankroll serves as the evaluation metric. Under this approach, market consensus probabilities and implied model credibilities can be updated real time as each model updates, and do not require one to wait for the final outcome. Using a simulation model, it will be shown that this method is in general more accurate than traditional average log-loss and Brier score methods at distinguishing a correct model from an incorrect model. This Kelly approach is shown to have a direct mathematical and conceptual analogue to Bayesian inference, with bankroll serving as a proxy for Bayesian credibility.

A graph is geometric 1-planar if it admits a straight-line drawing where each edge is crossed at most once. We provide the first systematic study of the parameterized complexity of recognizing geometric 1-planar graphs. By substantially extending a technique of Bannister, Cabello, and Eppstein, combined with Thomassen's characterization of 1-planar embeddings that can be straightened, we show that the problem is fixed-parameter tractable when parameterized by treedepth. Furthermore, we obtain a kernel for Geometric 1-Planarity parameterized by the feedback edge number $\ell$. As a by-product, we improve the best known kernel size of $O((3\ell)!)$ for 1-Planarity and $k$-Planarity under the same parameterization to $O(\ell \cdot 8^{\ell})$. Our approach naturally extends to Geometric $k$-Planarity, yielding a kernelization under the same parameterization, albeit with a larger kernel. Complementing these results, we provide matching lower bounds: Geometric 1-Planarity remains \NP-complete even for graphs of bounded pathwidth, bounded feedback vertex number, and bounded bandwidth.

We combine spectral- and split representations to factorize multi-loop momentum space diagrams, in the Schwinger-Keldysh formulation for cosmological correlators, with massive scalars in the loop. This allows us to extend the resummation of loop contributions from flat to de Sitter space. Furthermore, in our split representation the signal part of the correlators can be identified directly on the integrand level from the spectral function. We apply this to describe the non-perturbative flow of the EFT background and the cosmological collider signals in a large-N model.

A homogeneous bivariate $d$-form defines an $(i+1)$-rowed Toeplitz matrix for each $i$ between $0$ and $d$. We use Hodge theory and Schur polynomials to prove that if the $(i+1)$-rowed Toeplitz matrix of a form is totally nonnegative, then so is the $i$-rowed one. This fixes a gap in the main result of paper above.

Chemical substitution in crystalline quantum materials is a powerful way to explore the consequences of strong spin-orbit coupling on their structural and electronic properties. In this work, we present an investigation of thin films of the La$\textit{Pn}_2$ ($\textit{Pn}$~=~Sb, Bi) class of layered square-net intermetallics. We report the growth of LaBi$_2$ with a pristine layer-by-layer growth mode, classifying it as a good metal displaying superconductivity at $\sim$0.55~K. Compared to LaSb$_2$, we attribute the enhanced metallic behavior and improved growth dynamics of LaBi$_2$ to significant relativistic corrections to its electronic band structure and the resulting impact on both surface energy and intrinsic phonon scattering.

We prove that the category of profinite cosheaves valued in a pro-regular category (satisfying mild assumptions) is itself a pro-regular category. As a corollary, we extend Wilkes's cosheaf-bundle equivalence from profinite modules to profinite groups.

Let $k$ and $\ell$ be positive integers. The multiset star transposition graph ST$_k^\ell$ has as vertices the $k\ell$-strings $v_0\cdots v_{k\ell-1}$ on $k$ symbols, each symbol repeated $\ell$ times, and edges given by the transpositions $(v_0\;v_i)$ with $v_i\ne v_0$ ($0<i<k\ell$). It is shown for $k>1$ and $\ell>2$ that ST$_k^\ell$ is $(\ell-1)$-choosable and that, as a result, admits total colorings. In order to prove such assertions, the notion of efficient domination set (or E-set) of a graph is generalized for $\ell>1$ to that of an efficient dominating$\,^\ell$-set and applied to the graphs ST$_k^\ell$\,, showing they admit vertex partitions that generalize the Dejter-Serra partitions of ST$_k^1$ into E-sets, but not efficiently in the sense that the distance of each E$^\ell$-set be 3. Efficiently in such sense however, $ST^2_k$ and the related 2-set pancake permutation graph PC$^2_k$, among other intermediate permutation graphs, are shown to admit total colorings with $2k-1$ colors that determine partitions into $2k-1$ E-sets, each with distance 3. Furthermore, associated E-chains are examined.

We revisit an anomaly-free extension of the Standard Model (SM) $viz.$ gauged ${L_μ-L_τ}$ model in the Dirac framework, where the local $U(1)_{L_μ-L_τ}$ symmetry breaks and gives rise to a new gauge boson $Z'$ and corresponding gauge coupling $g_{μτ}$. Three additional heavy vector-like fermions, three light right-handed neutrinos and two heavy singlet scalars are added to complete the model framework for Dirac neutrinos. Another singlet vector-like fermion is added with a new gauge charge, which serves as a viable DM candidate, and the correct relic abundance is obtained via the resonance effect. The parameter space is considered after satisfying the current bounds on $M_{Z'}$ and the gauge coupling $g_{μτ}$. The influence of dark radiations coming from the additional light degrees of freedoms are studied in connection with the dark matter. After imposing all relevant theoretical and experimental constraints, the allowed parameter space is found to be highly restricted yet still accessible to ongoing and near-future experiments, rendering the scenario strongly predictive. Moreover, clear correlations among the relevant observables emerge throughout this study, making the model testable in current and future experimental searches.

Future 6G non-terrestrial networks aim to deliver ubiquitous connectivity to remote and undeserved regions, but unmanned aerial vehicle (UAV) base stations face fundamental challenges such as limited numbers and power budgets. To overcome these obstacles, high-altitude platform station (HAPS) equipped with a reconfigurable intelligent surface (RIS), so-called HAPS-RIS, is a promising candidate. We propose a novel unified joint multi-objective framework where UAVs and HAPS-RIS are fully integrated to extend coverage and enhance network performance. This joint multi-objective design maximizes the number of users served by the HAPS-RIS, minimizes the number of UAVs deployed and minimizes the total average UAV path loss subject to quality-of-service (QoS) and resource constraints. We propose a novel low-complexity solution strategy by proving the equivalence between minimizing the total average UAV path loss upper bound and k-means clustering, deriving a practical closed-form RIS phase-shift design, and introducing a mapping technique that collapses the combinatorial assignments into a zone radius and a bandwidth-portioning factor. Then, we propose a dynamic Pareto optimization technique to solve the transformed optimization problem. Extensive simulation results demonstrate that the proposed framework adapts seamlessly across operating regimes. A HAPS-RIS-only setup achieves full coverage at low data rates, but UAV assistance becomes indispensable as rate demands increase. By tuning a single bandwidth portioning factor, the model recovers UAV-only, HAPS-RIS-only and equal bandwidth portioning baselines within one formulation and consistently surpasses them across diverse rate requirements. The simulations also quantify a tangible trade-off between RIS scale and UAV deployment, enabling designers to trade increased RIS elements for fewer UAVs as service demands evolve.

In calculus, l'Hopital's rule provides a simple way to evaluate the limits of quotient functions when both the numerator and denominator vanish. But what happens when we move beyond real functions on a real interval? In this article, we study when the quotient of two complex-valued functions in higher dimension can be defined continuously at the points where both functions vanish. Surprisingly, the answer is far subtler than in the real-valued setting. We provide a complete characterization for the continuity of the quotient function. We also point out why extending this result to smoother quotients remains an intriguing challenge.

We present an algorithm for the numerical evaluation of elliptic multiple polylogarithms for arbitrary arguments and to arbitrary precision. The cornerstone of our approach is a procedure to obtain a convergent $q$-series representation of elliptic multiple polylogarithms. Its coefficients are expressed in terms of ordinary multiple polylogarithms, which can be evaluated efficiently using existing libraries. In a series of preparation steps the elliptic polylogarithms are mapped into a region where the $q$-series converges rapidly. We also present an implementation of our algorithm into the \texttt{GiNaC} framework. This release constitutes the first public package capable of evaluating elliptic multiple polylogarithms to high precision and for arbitrary values of the arguments.

This chapter is motivated by the need for a rigorous and comprehensive analysis of the Doppler effects encountered by electromagnetic and acoustic signals across a diverse spectrum of modern applications. These include land mobile communications, various Internet of Things (IoT) networks, machine-type communications (MTC), and various radar and satellite-based systems for navigation and sensing, as well as the emerging regime of integrated sensing and communications (ISAC). A wide array of kinematic profiles is investigated, ranging from uniform motion and constant acceleration to more complex general motion. Consequently, the multi-faceted factors influencing the Doppler shift are addressed in detail, encompassing classical kinematics, special and general relativity, atmospheric dynamics, and the properties of the propagation medium. This work is intended to establish a definitive theoretical foundation for both the general enthusiast and the specialized researcher seeking to master the complexities of signal frequency shifts in modern wireless sensing and communications systems.

The circumnuclear star-forming ring of the barred spiral galaxy NGC 1097 provides a unique laboratory to study star formation under extreme conditions. This work aims to derive the physical properties of the circumnuclear star-forming regions (CNSFRs) using MUSE integral field spectroscopy observations. A total of 24 individual ionised HII are identified and analysed within its ring, which spans from $\sim$385 pc to $\sim$1.3 kpc. Despite the complex nuclear activity, all HII regions are found to be purely photoionised. Directly derived abundances reveal supersolar metallicities, with the highest one exceeding five times the solar value (12+log(S/H) = 7.875 $\pm$ 0.353, T$_e$([SIII]) = 3912 $\pm$ 567 K), and representing the highest abundance reported to date. In this high-metallicity regime, we find a break in the ionisation parameter-[SII]/[SIII] relation, which can be explained by changes in the ionisation structure and line emissivities, as confirmed by photoionisation models that successfully reproduce the observed emission-line ratios. Our results also indicate that the local gas supply regulates the star formation activity within the ring, with the young stars ionising 8 % of the total gas in the ring. Furthermore, our findings support a propagating starburst scenario, originating in the galaxy nucleus and extending towards the ends of the bar and into the circumnuclear ring through bar-driven shocks, this being consistent with the results of previous multi-wavelength studies. Finally, we likely detect optical signatures associated with one of the two known jets in this galaxy. This finding, together with the radio core emission previously found at sub-parsec scales, reflects the presence of feedback processes operating even on small galactic disc scales.

We show that any uniformly escaping and wandering dynamics of a holomorphic function on a compact subset of the plane can be realised by a transcendental meromorphic function on $\mathbb{C}$. More precisely, let $φ$ be a holomorphic function on an open subset of the complex plane, and suppose that $K$ is a compact set such that $φ$ and all its iterates $φ^n$ are defined on $K$, and $φ^n(K)\to\infty$ as $n\to\infty$. We prove that there exist a transcendental meromorphic function $f\colon\mathbb{C}\to\widehat{\mathbb{C}}$ and a compact set $\widetilde{K}$ such that the dynamics of $f$ on the orbit of $\widetilde{K}$ is conjugate, via a smooth change of coordinate close to the identity, to that of $φ$ on the orbit of $K$. If $K$ does not separate the plane, the function $f$ may be chosen to be entire. If all iterates of $φ$ are univalent on $K$, we can take $\widetilde{K}=K$. We also prove a similar theorem for oscillating dynamics. Finally, we use our results to answer a number of questions of Benini et al. concerning wandering domains of entire functions.

In this paper, we prove a localisation of a slightly supercritical (Orlicz) regularity criterion for the 3D incompressible Navier-Stokes equations. This is a refinement to the recent partial positive answer to Tao's conjecture [Tao21] as given in [BP21b]. The proof requires new quantitative estimates for critically bounded solutions of the forced Navier-Stokes equations, where the forcing is induced by the localisation. A by-product of these new estimates is an application to the Boussinesq equations, where we prove a quantitative blow-up rate for the critical $L^3$ norm of the velocity. We prove these quantitative estimates using Carleman inequalities as in [Tao21], and subsequently in [BP21a], with an additional forcing term. An obstacle to doing this is that, in the Carleman inequalities, the forcing term is amplified on large scales. Additionally, the low regularity of the forcing requires the addition of Caccioppoli-type estimates to deal with the Carleman inequalities appropriately.

Motivated by recent results on the dual formulation of optimal stopping problems, we investigate in this short paper how the knowledge of an approximating dual martingale can improve the efficiency of primal methods. In particular, we show on numerical examples that accurate approximations of a dual martingale efficiently reduce the variance for the primal optimal stopping problem.

Current agentic AI architectures are fundamentally incompatible with the security and epistemological requirements of high-stakes scientific workflows. The problem is not inadequate alignment or insufficient guardrails, it is architectural: autoregressive language models process all tokens uniformly, making deterministic command--data separation unattainable through training alone. We argue that deterministic, architectural enforcement, not probabilistic learned behavior, is a necessary condition for trustworthy AI-assisted science. We introduce the Trinity Defense Architecture, which enforces security through three mechanisms: action governance via a finite action calculus with reference-monitor enforcement, information-flow control via mandatory access labels preventing cross-scope leakage, and privilege separation isolating perception from execution. We show that without unforgeable provenance and deterministic mediation, the ``Lethal Trifecta'' (untrusted inputs, privileged data access, external action capability) turns authorization security into an exploit-discovery problem: training-based defenses may reduce empirical attack rates but cannot provide deterministic guarantees. The ML community must recognize that alignment is insufficient for authorization security, and that architectural mediation is required before agentic AI can be safely deployed in consequential scientific domains.

In this work we introduce a viscosity-based notion of solution for general approximation schemes associated with partial differential equations, such as dynamic programming principles~(DPPs). A key feature of our approach is that it bypasses any measurability requirement on solutions of the DPP, an assumption that is often difficult to verify and may even fail in relevant examples. We establish a comparison principle between classical strict supersolutions and viscosity subsolutions of the DPP, which yields stability results under minimal and natural hypotheses. As a consequence, we prove existence of viscosity solutions of the DPP and their convergence to viscosity solutions of a PDE that is consistent with the underlying approximation scheme. Moreover, we show that solutions of the limiting PDE admit an asymptotic expansion encoded by the approximation operator. Finally, we demonstrate that a broad class of local, nonlocal, and nonlinear partial differential equations fits into our framework, recovering known examples in the literature and completing gaps in the existing literature.

Modern software systems continuously undergo code upgrades to enhance functionality, security, and performance, and Large Language Models (LLMs) have demonstrated remarkable capabilities in code migration tasks. However, while research on automated code migration which including refactoring, API adaptation, and dependency updates has advanced rapidly, the exploration of the automated environment interaction that must accompany it remains relatively scarce. In practice, code and its environment are intricately intertwined. Relying solely on static analysis of the environment leads to an inadequate understanding of the target setting, prolongs feedback cycles, and consequently causes significant rework and project delays, thereby reducing overall efficiency. We contend that successful software evolution demands a holistic perspective that integrates both code and environment migration. To understand the current landscape and challenges, we first provide an overview of the status of automated environment construction. We then propose a novel framework paradigm that tightly integrates automated environment setup with the code migration workflow. Finally, we explore the challenges and future directions for automated environment interaction within the code migration domain. Our findings emphasize that without automated environment interaction, the automation of code migration is only half complete.

Solar pores are strongly magnetized regions lacking a photospheric penumbra and characterized by predominantly vertical magnetic fields. We present a multi-line study of flashes in a solar pore using high-resolution observations from the Swedish 1-m Solar Telescope in Fe~\textsc{i}~6302~Å, Ca~\textsc{ii}~8542~Å and K, and H-$β$, complemented by (E)UV data from \textit{IRIS} and \textit{SDO}/AIA. Bisector analysis and spectral inversions with \textsc{SIR} and \textsc{NICOLE} were used to infer stratifications of temperature, line-of-sight velocity, and magnetic field. Flashes, confined to one half of the pore, exhibit cooler photospheric temperatures ($ΔT \approx 400$~K), stronger magnetic fields ($ΔB \approx 250$~G), larger inclinations ($\sim25^{\circ}$ versus $\sim18^{\circ}$), and persistent upflows ($\sim0.5$~km~s$^{-1}$) compared to the quiescent pore. They are co-spatial with enhanced 3- and 5-minute power in the photosphere, while only 3-minute power persists in the chromosphere. Flashes are detected down to $\sim50\%$ line depth in Ca~\textsc{ii}~8542~Å intensity and show central chromospheric upflows ($\sim1$~km~s$^{-1}$) flanked by strong downflows ($\sim8$~km~s$^{-1}$). Temperature enhancements reach $\sim500$~K at $\logτ\approx -5$ and $\sim2500$~K at $\logτ\approx -6$, with a bimodal velocity distribution. Flashes correspond one-to-one with radially outward running waves near the pore boundary (5--15~km~s$^{-1}$). Strong Ca~\textsc{ii} core emission, occasional Stokes~$V$ reversals, and H-$β$ enhancements indicate that pore flashes are confined to the lower and mid-chromosphere, with little influence on higher atmospheric layers.

As quantum algorithms and hardware continue to evolve, ensuring the correctness of the quantum software stack (QSS) has become increasingly important. However, testing QSSes remains challenging due to the oracle problem, i.e., the lack of a reliable ground truth for expected program behavior. Existing metamorphic testing approaches often rely on equivalent circuit transformations, backend modifications, or parameter tuning to address this issue. In this work, inspired by Equivalence Modulo Inputs (EMI), we propose Quantum EMI (QEMI), a new testing approach for QSSes. Our key contributions include: (1) a random quantum program generator that produces code with dead code based on quantum control-flow structures, and (2) an adaptation of the EMI technique from classical compiler testing to generate variants by removing dead code. By comparing the behavior of these variants, we can detect potential bugs in QSS implementations. We applied QEMI to Qiskit, Q#, and Cirq, and successfully identified 11 crash bugs and 1 behavioral inconsistency. QEMI expands the limited set of testing techniques available for quantum software stacks by going beyond structural transformations and incorporating semantics-preserving ones into quantum program analysis.

Vortex dynamics are intriguing and challenging across multiple physics fields. In optics, customized spatiotemporally structured optical fields, especially spatiotemporal optical vortices (STOV), offer the potential to tailor light via coupled space-time degrees of freedom. However, the interaction mechanisms between multiple transverse orbital angular momentum singularities within a single wave packet remain elusive. This study explores the intrinsic dynamics of a STOV with three phase singularities, observing a pronounced vortex singularity oscillation phenomena by tuning the temporal dispersion. We show that these phenomena originate from the counterintuitive spatiotemporal attractive effect between vortices, which is closely related to the singularity distance. Furthermore, the stretching into filaments and annihilation behaviors is observed by introducing antivortex in the center of the wavepacket. Experimentally, we propose a Full Interferometric Retrieval of Spatiotemporal Tomography (FIRST) method that enables the complete, single-shot capture of wave packets, with excellent agreement between theoretical predictions and experimental results. To the best of our knowledge, the dynamics of transverse spatiotemporal singularities within a single wave packet are reported here for the first time. These findings confirm the existence of interesting interactions between STOV singularities, deepen our understanding of photonics and open a new direction for investigating the complex dynamics of vortex singularities in the spatiotemporal domain.

We study the almost complete intersection ring $R$ defined by $n+1$ general quadrics in a polynomial ring in $n$ variables over a field $\sf{k}$ and a corresponding linked Gorenstein ring $A$. The overarching theme is that, while not Koszul (except for some small values of $n$), these rings have homological properties that extend those of Koszul rings. We establish that finitely generated modules over these rings have rational Poincaré series and we give concrete formulas for the Poincaré series of $\sf{k}$ over both $A$ and $R$. We also show that $A$ has minimal rate and its Yoneda algebra $\text{Ext}_A(\sf{k},\sf{k})$ is generated by its elements of degrees $1$ and $2$. While the graded Betti numbers of $R$ and $A$ over the polynomial ring are not known when $n$ is odd, our approach provides bounds and yields values for two of these Betti numbers, showing in particular that $R$ is level.