Short video streaming platforms have gained immense popularity in recent years, transforming the way users consume video content. A critical aspect of user interaction with these platforms is the swipe gesture, which allows users to navigate through videos seamlessly. However, the delay between a user's swipe action and the subsequent video playback can significantly impact the overall user experience. This paper presents the first systematic study investigating the effects of swipe delay on user Quality of Experience (QoE) in short video streaming. In particular, we conduct a subjective quality assessment containing 132 swipe delay patterns. The obtained results show that user experience is affected not only by the swipe delay duration, but also by the number of delays and their temporal positions. A single delay of eight seconds or longer is likely to lead to user dissatisfaction. Moreover, early-session delays are less harmful to user QoE than late-session delays. Based on the findings, we propose a novel QoE model that accurately predicts user experience based on swipe delay characteristics. The proposed model demonstrates high correlation with subjective ratings, outperforming existing models in short video streaming.

We prove a geometric local constancy theorem for affine Springer fibers in families of close local fields. Consequently, stable orbital integrals are locally constant in these families, and both the base change fundamental lemma and the standard endoscopic fundamental lemma transfer from characteristic zero to arbitrary positive characteristic.

This paper proposes a robust damage identification method using noisy frequency response functions (FRFs) and topology optimization. We formulate the damage identification problem as an inverse problem of generating the damage topology of the structure from measured dynamic responses of the structure to given external dynamic loading. The method is based on the minimization of the objective function representing errors between measured FRFs of the structure obtained by experimental modal analysis, and those obtained by harmonic response analysis using finite element analysis. In the minimization process, material distribution, or the topology of the structure is varied and the optimal damage topology is identified as regions with no material assigned as a result of the minimization using the solid isotropic material with penalization (SIMP). In order to overcome the problems caused by the ill-posedness of the inverse problem, it is proposed that the least absolute shrinkage and selection operator (Lasso) regularization, or the penalization to the L1 norm of the design variable be applied to the original objective function. By applying Lasso regularization, the method is expected not only to eliminate spurious damaged regions but also to minimize the effect of measurement noises. This paper first presents the mathematical background and its numerical implementation of the proposed methodology. The method is then applied to the identification of a damage of cantilevered plates. The FRFs were experimentally obtained and the proposed method is applied. It is shown that the method successfully identifies the damage.

Mixed (asymmetric) orthogonal arrays (MOAs) generalize classical orthogonal arrays by allowing columns over different alphabets. However, their study requires very different structural tools than those used for symmetric orthogonal arrays (OAs), since several key features of the symmetric setting are no longer available in the mixed case, including Euclidean duality, a unique global index, and certain classical bounds. In this paper, we establish three structural results for mixed orthogonal arrays. First, we prove a Singleton-type upper bound and obtain a characterization of MDS and almost-MDS mixed orthogonal arrays. Second, we introduce a trace duality for $\mathbb{F}_q$-linear MOAs over $\prod_{i=1}^{s} \mathbb{F}_{q^{n_i}}$ and establish a correspondence with $\mathbb{F}_q$-linear error-block codes that determines the strength of the MOA via the dual distance of the associated error-block code. Finally, we develop a structural theory of irredundant mixed orthogonal arrays (IrMOAs), motivated by their role in the construction of $t$-uniform and absolutely maximally entangled (AME) quantum states. In the extremal case $t=\lfloor s/2\rfloor$, we prove that $\mathbb{F}_q$-linear IrMOAs with minimum index $1$ (yielding AME states of minimal support) are equivalent to $\mathbb{F}_q$-linear error-block MDS codes.

We investigate the spontaneous scalarization of charged Taub-NUT black holes within the framework of Einstein-Maxwell-scalar-Gauss-Bonnet gravity. By selecting a suitable coupling function, the theory admits the analytic charged Taub-NUT geometry as a solution. We demonstrate that this scalar-free background becomes unstable within specific parameter regimes, leading to the bifurcation of a new branch of hairy charged Taub-NUT black holes. These solutions are characterized by a two-dimensional parameter space spanned by the electric charge and the NUT parameter. We conduct a systematic study of their properties, specifically the scalar charge, temperature, and entropy. Our analysis reveals that the entropy of the scalarized solutions exhibits particularly compelling features. Two universal characteristics emerge: first, the entropy of the hairy black hole is strictly greater than that of its scalar-free counterpart; second, the entropy reaches a local maximum precisely at the bifurcation point. Notably, when the electric charge is fixed, this maximum entropy value remains universal across a specific range of the mass parameter.

We present applications of quantum quadratic residue codes in magic state distillation. This includes showing that existing codes which are known to distill magic states, like the $5$-qubit perfect code, the $7$-qubit Steane code, and the $11$-qutrit and $23$-qubit Golay codes, are equivalent to certain quantum quadratic residue codes. We also present new examples of quantum quadratic residue codes that distill qubit $T$ states and qutrit Strange states with high thresholds, and we show that there are infinitely many quantum quadratic residue codes that distill $T$ states with a non-trivial threshold. All of these codes, including the codes with the highest currently known thresholds for $T$ state and Strange state distillation, are unified under the umbrella of quantum quadratic residue codes.

Traditional recommendation methods, which typically focus on modeling a single user behavior (e.g., purchase), often face severe data sparsity issues. Multi-behavior recommendation methods offer a promising solution by leveraging user data from diverse behaviors. However, most existing approaches entangle multiple behavioral factors, learning holistic but imprecise representations that fail to capture specific user intents. To address this issue, we propose a multi-behavior method by modeling latent factors with an expert network (MBLFE). In our approach, we design a gating expert network, where the expert network models all latent factors within the entire recommendation scenario, with each expert specializing in a specific latent factor. The gating network dynamically selects the optimal combination of experts for each user, enabling a more accurate representation of user preferences. To ensure independence among experts and factor consistency of a particular expert, we incorporate self-supervised learning during the training process. Furthermore, we enrich embeddings with multi-behavior data to provide the expert network with more comprehensive collaborative information for factor extraction. Extensive experiments on three real-world datasets demonstrate that our method significantly outperforms state-of-the-art baselines, validating its effectiveness.

We prove a conjecture of Kühn, Osthus, Townsend and Zhao \cite{kuhn2017structure} stating that almost every $C_k$-free oriented graph on $n$ vertices has $Θ(n)$ backwards edges in a transitive-optimal ordering. The same holds for $C_k$-free digraphs when $k$ is even. Our proof combines the hypergraph container method with a stability analysis and an inductive counting argument. As a byproduct, we also determine the typical structure of oriented graphs and digraphs that avoid the blow-up $C_{k}^t$, extending the main result of \cite{kuhn2017structure} to the blown-up setting.

Non-Arrhenius grain growth has been observed in a range of polycrystalline materials; however, its fundamental mechanisms, particularly whether the process is thermally activated or exhibits anti-thermally activation, remain controversial. In this study, SrTiO3 was employed as a model system to systematically investigate non-Arrhenius grain growth behavior through combined experimental and theoretical approaches, utilizing a newly developed grain growth model. The results reveal that non-Arrhenius grain growth is a thermally activated process without a definitive characteristic temperature, which is primarily controlled by the interplay between temperature-dependent factors and the temperature-independent parameters such as grain size and its distribution. Moreover, during abnormal grain growth (AGG), the non-Arrhenius behavior of grain growth primarily occurs at lower temperatures and gradually transitions to Arrhenius-type behavior as the temperature increases.

Dynamic Random Access Memory (DRAM) is pervasive in computer systems. Cell vulnerabilities caused by unintended phenomena (forced retention failure, latency alteration, rowhammer and rowpress) lead to unintended bit flips in memory. These phenomena have been explored as attacks to violate data integrity and confidentiality during normal operation, but also exploited as a benefit in security systems as a method to generate random secret keys and unique device fingerprints (e.g. Physically Unclonable Functions). In both cases, attackers may wish to exploit knowledge of individual cell flip vulnerability to predict the current/future data contents of a set of cells, which can be utilised to break security systems. In this work, we develop a quantitative, cell-level circuit framework that models DRAM vulnerability directly from its physical charge leakage and disturbance pathways. By linking these device-layer behaviours to system-level security properties, our framework enables systematic evaluation of DRAM with respect to volatility (retention), integrity (disturbance-induced modification), and confidentiality (pattern-dependent leakage). We further demonstrate how the framework can be applied to well-known failure modes, revealing non-uniform and context-dependent vulnerability patterns. This work provides both theoretical foundations and practical evaluation tools for evaluating the suitability of DRAM use within security applications.

This study evaluates the radiation tolerance of a 4H-SiC PIN detector under X-ray irradiation up to \SI{2}{MGy} (Si) at \SI{160}{keV}. The detector features a fully epitaxial vertical PIN structure with mesa terminations and field plates. Comprehensive pre- and post-irradiation characterization includes I-V/C-V measurements, charge collection efficiency (CCE) and timing resolution tests using $β$-particles ($^{90}$Sr). After \SI{2}{MGy} irradiation, the reverse leakage current remains at an ultralow level of $\sim 10^{-11}$ \si{A/cm^2} at \SI{-300}{V} with negligible degradation. C-V characteristics are basically consistent, with full depletion at \SI{~130}{V}. CCE for $β$-particles decreases by less than 5\%. The detector maintains good timing resolution: \SI{21}{ps} before and \SI{31}{ps} after irradiation, with jitter increasing moderately. These results demonstrate stable performance under extreme X-ray exposure, highlighting the detector's potential for radiation-hard applications in high-energy physics, space missions, and nuclear reactor monitoring.

Environmental, Social and Governance (ESG) rating is a way for investors to prioritise investments in companies with good corporate behaviour. However, ESG ratings are vulnerable to greenwashing in a number of ways. In this paper we study the effect that trade with badly rated companies has on a target company's own rating. To do this we introduce a measurement framework, generalising PageRank and Alpha Centrality, which allows tuning of aggregation and path counting approaches to resist greenwashing and reflect the rater's opinions and preferences for harm accumulation. These metrics allow updating of the target's ESG rating, identification of influential neighbours and assessment of vulnerability of the target to bad behaviour in their supply network. We study these metrics on synthetic ESG interaction networks as well as a real inter-company network and the international trade network.

The interplay between local and itinerant electrons underpins many correlated and topological quantum states. Kagome lattices provide an ideal platform by hosting both flat (localized states) and dispersive bands (itinerant states), yet direct spectroscopic evidence of their dynamical coupling has remained elusive. Here we report the long-sought flat band resonance in the quasi-two-dimensional kagome bilayer material CsCr6Sb6. Using angle-resolved photoemission spectroscopy, transport measurements, and combined density functional theory and dynamical mean-field theory, we identify coexisting flat band doublets and dispersive bands near the Fermi energy. Upon cooling, the flat and dispersive bands exhibit a pronounced enhancement of spectral weight and hybridization, directly evidencing flat band resonance. Crucially, this emergence coincides with the onset of short-range antiferromagnetic correlations, contrasting sharply with conventional Kondo lattice behavior. Our findings demonstrate not only the long-sought flat band resonance in kagome materials, but also its unconventional correlation with magnetism.

In 1959, Erdős and Gallai showed that every $2$-connected graph $G$ contains a cycle of length at least $\frac{2|E(G)|}{|V(G)|-1}$. This result was subsequently extended to weighted graphs by Bondy and Fan in 1991. A natural local variant of this problem arises by considering, for each edge $e\in E(G)$, the quantity $c(e)$, defined as the length of the longest cycle in $G$ containing $e$ (with $c(e)=2$ if $e$ is a bridge). Zhao and Zhang recently proved that for every graph $G$ on $n$ vertices satisfies $\sum_{e\in E(G)}\frac{1}{c(e)}\le \frac{n-1}{2}.$ In this note, we establish a weighted generalization of this inequality. For a weighted graph $(G,w)$ with positive edge weights, let $C_w(e)$ denote the maximum weight of a cycle containing $e$ (setting $C_w(e)=2w(e)$ if $e$ is a bridge). We prove that $$ \sum_{e\in E(G)}\frac{w(e)}{C_w(e)}\le \frac{n-1}{2}. $$ Our result can be viewed as a weighted local analogue of the Bondy-Fan theorem, thereby establishing a correspondence between the global and local perspectives. Furthermore, we present a broad class of graphs attaining equality and derive necessary conditions for equality.

As extended reality (XR) technologies rapidly become as ubiquitous as today's mobile devices, supporting one-handed interaction becomes essential for XR. However, the prevalent Gaze + Pinch interaction model partially supports unimanual interaction, where users select, move, and rotate objects with one hand, but scaling typically requires both hands. In this work, we leverage the spatial alignment between gaze and hand as a mode switch to enable single-handed pinch-to-scale. We design and evaluate several techniques geared for one-handed scaling and assess their usability in a compound translate-scale task. Our findings show that all proposed methods effectively enable one-handed scaling, but each method offers distinct advantages and trade-offs. To this end, we derive design guidelines to support futuristic 3D interfaces with unimanual interaction. Our work helps make eye-hand 3D interaction in XR more mobile, flexible, and accessible.

In this paper, we first establish Landau-Bloch-type theorems for poly $(K,K')$-elliptic harmonic mappings, which are sharp in some given cases. Thereafter, we provide several coefficient bounds for $(K,K')$-elliptic and $K$-quasiregular polyharmonic mappings with bounded minimum distortion. Furthermore, using these coefficient bounds, we establish Landau-Bloch-type theorems for these mappings.

This paper explores generalized slice monogenic functions by introducing their operator symbols, representation formula, and integral formula. The study extends the Teodorescu transform to a broader class of theorems and inferences, providing new analytical tools for function theory in this setting. Additionally, the Hodge decomposition is established, providing a foundation for further research.

Low Earth Orbit (LEO) satellite networks such as Starlink and Project Kuiper are increasingly integrated with cloud infrastructures, forming an important internet backbone for global web services. By extending connectivity to remote regions, oceans, and disaster zones, these networks enable reliable access to applications ranging from real-time WebRTC communication to emergency response portals. Yet the resilience of these web services is threatened by space radiation: it degrades hardware, drains batteries, and disrupts continuity, even if the space-cloud integrated providers use machine learning to analyze space weather and radiation data. Specifically, conventional fixes like altitude adjustments and thermal annealing consume energy; neglecting this energy use results in deep discharge and faster battery aging, whereas sleep modes risk abrupt web session interruptions. Efficient network-layer mitigation remains a critical gap. We propose RALT (Radiation-Aware LEO Transmission), a control-plane solution that dynamically reroutes traffic during radiation events, accounting for energy constraints to minimize battery degradation and sustain service performance. Our work shows that unlocking space-based web services' full potential for global reliable connectivity requires rethinking resilience through the lens of the space environment itself.

As stars evolve, they undergo significant changes in their physical properties, which can have a profound impact on the planets orbiting them. In particular, the mass lost through stellar wind may be partially accreted by orbiting planets. We present the results of 18 simulations of one-planet systems with planetary masses of 0.5, 1, 2.5, 5, 10, and 13~$\mathrm{M}_\mathrm{J}$, each at initial orbital distances of 5, 10, and 20~AU, orbiting a 2~M$_\odot$ star through its red giant branch and thermally pulsating asymptotic giant branch phases. Our results show that planets with smaller orbits and higher masses accrete more stellar wind material than their wider-orbit and lower-mass counterparts, although the total mass accreted across all simulations remains small compared to their initial planetary mass. Even for the most massive planet, 13 $\mathrm{M}_\mathrm{J}$ at 5 AU, the total mass accreted was $\sim0.56$\% of the planet's initial mass; nevertheless, we find that the accretion luminosities of the simulated planets, with the exception of one planet, exceed their expected equilibrium luminosities, suggesting that such emission could be potentially detected. This result is key for the detection of planets around AGB stars, which have no confirmed detections as of yet. We also estimated the accretion and luminosities of two detected two-planet systems over a few orbits, obtaining results consistent with the one-planet simulated systems. Additional tests without wind accretion and with stellar wind drag force showed that, while both have a negligible effect on the orbital evolution, wind accretion remains relevant for the planetary luminosity.

We investigate the stochastic dynamics of a quasiparticle within a gas of hard rods, focusing on the evolution of its mean, variance, and autocorrelation for two choices of initial states: (i) one with long-range (LR) correlations and (ii) the other without it. We derive analytical results for the phase space density correlations in the former case to complement the known results for the latter case. These results enable us to obtain expressions for the mean, variance, and autocorrelation of a quasiparticle, which are applicable to both initial states. The LR correlations introduce a diffusive-scale correction to the mean Euler generalized hydrodynamic (GHD) equations, modifying the standard local equilibrium form, and our findings reveal that the form of the correction term depends on the LR correlations present in the initial state.

We report the first observation of the decay $D_s^+ \to π^+π^0π^0η$ in a data set corresponding to an integrated luminosity of 7.33 fb$^{-1}$, collected in $e^+e^-$ collisions by the BESIII detector at center-of-mass energies between 4.128 and 4.226 GeV. An unexpectedly large branching fraction $\mathcal{B}( D_s^+ \to a_0(980)^+ f_0(500), a_0(980)^+ \to π^+η, f_0(500)\to π^0π^0) = (0.98 \pm 0.16_{\rm{stat.}} \pm 0.22_{\rm{syst.}})\%$ is measured with a significance exceeding $10σ$, offering new constraints on the internal structure of light scalar mesons. The dominant intermediate process is $D_s^+ \to a_1(1260)^+η, a_1(1260)^+\to ρ(770)^+π^0$ with a branching fraction of $(1.77 \pm 0.21_{\rm stat.} \pm 0.12_{\rm syst.})\%$. The isospin symmetry has been validated to the decays of $a_1(1260)^+\to ρ(770)^0π^+$ and $a_1(1260)^+\to ρ(770)^+π^0$. Moreover, the measured $\mathcal{B}(D_s^+\to π^+π^0π^0η|_{\rm{non}-η^\prime})=(2.97 \pm 0.23_{\rm stat.} \pm 0.14_{\rm sys.})$ reduces the undetected $D_s^+ \to ηX$ decay branching fractions to (0.1 $\pm$ 3.1)\%.

We present the first statistical census of emission-line variable active galactic nuclei (EVA) at cosmic noon by combining untargeted and deep HETDEX spectroscopy with multi-epoch spectra from SDSS, DESI, and LAMOST. Anchoring all candidates to a HETDEX spectroscopic epoch and requiring AGN classification in either the HETDEX or the external epoch(s), we identify a homogeneous sample of 100 EVA at z~1.5, including 98 newly identified. Emission-line variability is selected primarily through statistically significant line-flux changes, supplemented by extensive visual inspections using contemporaneous photometric light curves. The resulting incidence fraction is $f_{\rm EVA} \approx 0.9\%$. The rest-frame intervals between spectroscopic epochs span $\sim$1--10 yr, with brightening and dimming events exhibiting statistically indistinguishable characteristic timescales ($ΔT\sim2.2$ and $\sim2.6$ yr, respectively). A key result is the characterization of the Baldwin effect in the time domain: while many EVA follow the ensemble Baldwin effect (eBeff) between two epochs, a substantial fraction exhibit apparent anti-eBeff responses. Time-resolved spectroscopy of an individual source reveals that the intrinsic EW--luminosity relation is non-stationary, with the line-to-continuum responsivity systematically evolving from stronger to weaker across successive variability cycles; sparse two-epoch sampling of this evolving intrinsic Baldwin evolution (iBeff) naturally produces both eBeff-like and anti-eBeff behaviors. Finally, EVA show no strong preference for extreme Eddington ratios but exhibit a mild tendency toward lower $λ_{\rm Edd}$ values relative to matched control samples, driven primarily by sources observed in their dim states. Together, these results establish a coherent framework for interpreting emission-line variability in AGN at the peak epoch of cosmic black hole growth.

Randomness in optical systems emerges as a powerful resource for generating complex, non-deterministic light-matter interactions. In particular, random plasmonic metasurfaces harness nanoscale disorder to produce unique and irreproducible optical responses, positioning them as an ideal platform for physical unclonable function in secure optical authentication. However, realizing such random metasurfaces in a rapid, scalable, and chemical-free manner for optical PUFs remains challenging. Here, we introduce a nanosecond pulsed laser scribing method for one-step fabrication of a robust random plasmonic metasurface physical unclonable function. By delivering spatially localized, ultrafast energy bursts, this technique harnesses naturally occurring instability to generate stochastic plasmonic nanostructures in nanoseconds. The unique plasmonic metasurfaces are effectively transformed into a macroscopic, non-replicable optical fingerprint via morphology-dependent resonance at the nanoscale, enabling low-cost and fast readout. Leveraging the wavelength-selective plasmonic response, we present a multidimensional multiplexing strategy that expands the challenge response pairs space and encoding capacity by 5-fold via topography and RGB multiplexing. The resulting plasmonic keys exhibit good bit uniformity (average: 0.500), high uniqueness (inter-Hamming distance: 0.499), and large capacity (~28000 bits per PUF), with strong environmental stability and resistance to reverse nanofabrication. This work demonstrates how fast laser induced stochasticity can be rationally harnessed and engineered for optical PUFs, opening pathways toward disorder-enabled photonic devices.

Let $\mathcal{G}=\{G_1, G_2, \ldots , G_{kn}\}$ be a family of balanced bipartite graphs on the same vertex set $[2n]$. A rainbow $k$-factor of $\mathcal{G}$ is defined as a $k$-factor such that any two distinct edges come from different graphs in $\mathcal{G}.$ In this paper, we provide a tight sufficient condition in terms of the spectral radius for a family of balanced bipartite graphs $\mathcal{G}$ to contain a rainbow $k$-factor. Furthermore, we completely characterize the corresponding spectral extremal graph.

Deep research agents have emerged as LLM-based systems designed to perform multi-step information seeking and reasoning over large, open-domain sources to answer complex questions by synthesizing information from multiple information sources. Given the complexity of the task and despite various recent efforts, evaluation of deep research agents remains fundamentally challenging. This paper identifies a list of requirements and optional properties for evaluating deep research agents. We observe that existing benchmarks do not satisfy all identified requirements. Inspired by prior research on TREC Total Recall Tracks, we introduce the task of Total Recall Question Answering and develop a framework for deep research agents evaluation that satisfies the identified criteria. Our framework constructs single-answer, total recall queries with precise evaluation and relevance judgments derived from a structured knowledge base paired with a text corpus, enabling large-scale data construction. Using this framework, we build TRQA, a deep research benchmark constructed from Wikidata-Wikipedia as a real-world source and a synthetically generated e-commerce knowledge base and corpus to mitigate the effects of data contamination. We benchmark the collection with representative retriever and deep research models and establish baseline retrieval and end-to-end results for future comparative evaluation.

In discrete models describing growing rough interfaces of the Kardar-Parisi-Zhang universality class, we examine height fluctuations at a fixed site as a function of time in the monolayer unit. For small systems, we show that it is possible to reach the stationary state. We compute the two-time autocorrelation and power spectra independently. The correlation function remains non-exponential and vanishes after a correlation time that diverges with system size. As a result, the power spectra display a lower cutoff that maintains constant power. In the nontrivial frequency regime, we observe $1/f^α$-type scaling with the spectral exponent 5/3. Finite-size scaling reveals that the temporal correlation function follows a dynamic scaling. Our findings, supported by scaling-theoretical arguments, establish that the fluctuations are wide-sense stationary, implying applicability of the Wiener-Khinchin theorem.

In this paper, we explore the implications of the so-called slingshot effect. It represents a rather general phenomenon occurring when a localized source, such as a monopole, quark, or a $D$-brane, crosses a domain wall separating the confined (Higgsed) and unconfined (Coulomb) phases of the crossing source. The crossover is accompanied by a stretched ``string'' of proper co-dimensionality that confines the source to the domain wall. The effect takes place for different setups, such as phase transitions leading to confinement, both electric and magnetic, as well as in string theoretic inflation with $D$-branes. We discuss the role of the phenomenon in sourcing gravitational waves and dark matter in the form of Kaluza-Klein gravitons. We also show that the slingshot effect can lead to the formation of primordial black holes in observationally interesting mass ranges for dark matter and high-energy cosmic rays.

Traversable wormhole teleportation in the Sachdev-Ye-Kitaev (SYK) model links quantum channel integrity to black hole interior dynamics, using teleportation fidelity to probe holographic scrambling. We subject the SYK boundary to a gravitational-wave (GW)-inspired periodic Floquet deformation, mimicking a leading-order metric-strain perturbation from the JT-gravity dictionary. We characterize the channel response via exact numerical time evolution with disorder averaging at $βJ = 2$. The drive produces a coherent, frequency-selective fidelity suppression, yielding four main results: (i) two amplitude regimes separated near $\varepsilon \sim J$ (perturbative sensing vs.\ strong-drive); (ii) the channel acts as a low-pass filter, most sensitive at $ω\lesssim β^{-1}$ with monotone recovery above the thermal scale; (iii) an inspiral chirp drive delays the fidelity peak by $Δt_{\rm scr}^{(\rm fid)} = +0.11\, J^{-1}$, corroborated by an out-of-time-order correlator (OTOC) diagnostic ($Δt_{\rm scr}^{(\rm OTOC)} = +0.20\, J^{-1}$), establishing a genuine scrambling delay; and (iv) the effects persist across $N \in \{10, 12, 14, 16\}$ Majorana modes, indicating no systematic finite-size suppression. These results establish that holographic teleportation channels degrade gracefully under GW-inspired boundary deformations, with direct implications for near-term quantum processor implementations of traversable wormholes.

We prove that finite multivariate Erlang mixture densities with a common rate parameter are dense in the class of probability densities on $\mathbb{R}_{+}^{d}$ that belong to $L^{p}$, for every dimension $d\in\mathbb{N}$ and every $1\le p<\infty$. The argument is constructive: the one-dimensional Szász--Mirakjan--Kantorovich operator yields Erlang mixture approximations, and its tensor product yields multivariate approximants with a common scale. We then obtain several quantitative consequences. These include compact-set uniform approximation bounds and, under local Hölder conditions of order $α\in(0,1]$, rates of order $n^{-α/2}$ as the common scale $1/n$ tends to zero, whole-domain convergence in weighted sup norms, weighted and unweighted $L^{p}$ rates, and explicit rates for finite mixtures indexed by the number of mixture components. In particular, if the approximating density is required to have at most $K$ mixture components, then on fixed compact cubes we obtain an algebraic rate of order $K^{-α/(2d)}$; in global weighted sup norms we obtain the explicit algebraic component-count rate $K^{-α/[2d(2d+α)]}$; and for $1<p<\infty$ we obtain corresponding weighted $L^{p}$ component-count rates. The results strengthen the weak-approximation theory for multivariate Erlang mixture distributions and yield immediate corollaries for broader classes such as product-gamma mixtures. \noindent\textbf{Keywords:} multivariate Erlang mixtures; Erlang distributions; Szász--Mirakjan--Kantorovich operator; density approximation; weighted $L^{p}$ approximation; approximation rates.

We study the gradient flow of the length functional on the space of planar immersed closed curves, where the gradient is taken with respect to a family of homogeneous Sobolev $H^1$-type Riemannian metrics depending on parameters $λ>0$ and $a\in\mathbb{R}$. The gradient can be written explicitly in terms of arc-length convolution with the periodic Green's function for the second-order operator associated with the $H^1$ metric, and then the gradient flow is a reparametrisation-invariant nonlocal ODE. Working in the optimal low-regularity setting $W^{1,1}(\mathbb{S},\mathbb{R}^2)$, we show that the gradient is locally Lipschitz to obtain local well-posedness via the Picard--Lindelöf theorem in Banach spaces. A time-reparametrisation reduces the analysis for general $a$ to the model case ${a=2}$, for which we obtain exponential decay of the length and global existence with uniform convergence in $W^{1,1}$ to a constant map. For $C^1$ immersed initial data we show that immersion is preserved for all time, and we further prove that if the initial curve bounds a convex set then convexity is also preserved by the flow.