We prove that $\mathrm{SL}_3(\mathbb{Z})$ contains a non-split sharply 2-transitive subgroup, answering a question of Glasner and Gulko. We also prove that $\mathrm{SL}_4(\mathbb{Z})$ contains a non-split sharply 3-transitive subgroup, but that $\mathrm{SL}_3(\mathbb{Z})$ does not contain an infinite sharply 3-transitive subgroup.

A graph $G$ is $k$-vertex-critical if $χ(G)=k$ but $χ(G-v)<k$ for all $v\in V(G)$. In this paper we make progress on the open problem of the finiteness of $k$-vertex-critical $(P_4+\ell P_1)$-free graphs by showing that there are only finitely many $k$-vertex-critical graphs in the following subfamilies of $(P_4+\ell P_1)$-free graphs for all $k\ge 1$ and $\ell\ge 0$: $\bullet$ $(P_4+\ell P_1,\text{chair})$-free graphs, $\bullet$ $(P_4+\ell P_1,P_5,\text{bull})$-free graphs, and $\bullet$ $(P_4+\ell P_1,P_5,\text{cricket})$-free graphs. In fact, all but the first of these are special cases of our general result that there are only finitely many $k$-vertex-critical $(P_4+\ell P_1,B_{4}(m),B_{3}(m)^{+})$-free graphs for all $k\ge 1$ and $\ell,m\ge 0$. Here $B_{n}(m)$ is the graph obtained from a path of order $n$ by identifying one of its leaves with the centre vertex of $K_{1,m}$ and $B_{n}(m)^{+}$ is the graph obtained by identifying an edge of $K_3$ with the edge of $B_{n}(m)$ with endpoints of degrees $2$ and $m$, respectively. Our results imply the existence of simple polynomial-time certifying algorithms to decide the $k$-colourability of all graphs in these subfamilies for every fixed $k$. We also show that $χ(G)\le \ell+2$ for all $(P_4+\ell P_1,K_3)$-free graphs and all $\ell\ge 0$, improving the previously known upper bound of $2\ell+2$ that followed from Randerath and Schiermeyer's 2004 result on $(P_t,K_3)$-free graphs. More generally, we provide a $χ$-bound in $O(\ell^{ω-1})$ for $(P_4+\ell P_1)$-free graphs which improves the bound of $(2\ell+2)^{ω-1}$ which followed from Gravier, Hoàng and Maffray in 2003 for $P_{t}$-free graphs.

We design and experimentally characterize a balanced homodyne detector optimized for high-repetition-rate (100 MHz) pulsed optical sources. Unlike conventional transimpedance-amplifier architectures, which suffer from nonlinearities and dynamic instabilities with ultrashort pulses, our approach allows to directly amplify the photocurrent extracted at the common photodiode node without feedback loops. A theoretical model describing the detector response, noise, and pulse-to-pulse correlations is developed, providing quantitative predictions for the signal variance, signal-to-noise ratio (SNR), and inter-pulse correlations. Implemented with two matched InGaAs photodiodes illuminated by a 1030 nm mode-locked laser at 100 MHz, the detector exhibits excellent linearity and shot-noise-limited scaling of the signal variance with optical power. Optimizing the temporal integration window yields a maximum SNR of about 14 dB, while correlation measurements confirm negligible inter-pulse correlations. These results demonstrate that the proposed architecture offers a robust and simple solution for high-speed pulsed homodyne detection, suitable for quantum optics and continuous-variable quantum information applications.

It is proved that the C*-algebra of a graph is residually finite dimensional (RFD) if and only if the graph has no infinite receiver, no cycle with an exit, no infinite ackward chain and from each vertex, there is a finite path to a sink or a cycle or an infinite emitter.

Cost-effective wireless electrocardiograms (ECGs) enable long-term and scalable monitoring of cardiac patients in their home and work environments. Because they offer greater freedom of movement, they are also suitable for investigating the relationship between cardiac workload and underlying physical exertion. However, this requires that the quality of the generated data meets the standards of clinical devices. The aim of this study is to examine this closely. We therefore analyze data from 54 healthy subjects who performed five physical activities using wireless ECGs outside of clinical settings and without medical supervision. The results are compared with clinically collected data from standard 12-lead ECGs (2493 subjects) and Holter ECGs (29 subjects), with particular attention to the RR interval time series (tachogram) and heart rate variability (HRV). Our study shows significant statistical agreement between the different datasets. We calculated the 95% confidence intervals for the mean RR interval and HRV assuming that (1) the statistics of the 12-lead ECGs could serve as reliable reference, and (2) the statistics of the 12-lead ECGs cannot be taken as reliable reference. The p-values for both conditions (for the RR interval: 0.23 and 0.26 respectively; for HRV: 0.10 and 0.11 respectively) suggest that there is insufficient evidence to reject the hypothesis that significant statistical agreement exists between the different datasets.

Chip integration of quantum emitters is a crucial milestone for scalable quantum photonic information processing. Among optically active defect centers for quantum photonics, diamond color centers are promising because of their long spin coherence times and high photon emission rates. However, for a coherent-photon emission, they typically require a cryogenic environment to protect optical coherence from thermal phonons, which makes chip integration challenging. In this paper, we develop a chip-integrated diamond photonic crystal cavity embedding an ensemble of nitrogen-vacancy (NV) centers. We confirm cryogenic operation by observing Purcell enhancement of NV-center emission via an edge-coupled optical fiber. This result demonstrates successful integration of diamond color centers, a photonic crystal cavity, and an optical waveguide-fiber package, representing a key step toward scalable diamond-based quantum communication platforms.

Extinction maps are essential for tracing interstellar dust and enabling accurate stellar population studies in galaxies. Here, a high-resolution extinction distribution of nearby galaxy M33 is constructed by fitting multiband color indexes of the individually resolved red giant branch (RGB) stars from the Panchromatic Hubble Andromeda Treasury: Triangulum Extended Region (PHATTER) survey. Achieving an angular resolution of approximately 6$^{\prime\prime}$ ($\sim$ 24.4 pc), the extinction map reveals the intricate and heterogeneous distribution of dust throughout the entire disk of M33, with distinct delineation of spiral arms, inter-arm regions, and compact dust clouds. In addition, it exhibits strong spatial correspondence with the distributions of total hydrogen, H I, and CO, underscoring the reliability of the extinction map for tracing both diffuse and dense components of the interstellar medium. The derived $V$-band extinction reaches up to 2.5 mag per pixel, with a mean value of about 1.05 mag. Beyond providing new insights into the dust structure of M33, the extinction map offers a robust foundation for accurate extinction corrections and will support future studies, including upcoming observations with the Chinese Space Station Telescope.

We show that the global unique continuation principle holds for the parabolic fractional $p-$Laplace equation with very rough potentials $V(x,t) \in L^{p'}_tW^{-s,p'}_x$. Whereas the result is new even for the fractional $p-$Laplace operator, the corresponding local problem remains open even with zero potential. The short proof eschews extension techniques and Carleman estimates.

This paper concerns the adaptive control problem for a class of nonlinear stochastic systems in which the state update is given by a nonlinear function of linear dynamics plus additive stochastic noise. Such systems arise in a wide range of applications, including recurrent neural networks, social dynamics, and signal processing. Despite their importance, adaptive control for these systems remains relatively unexplored in the literature. This gap is primarily due to the inherently nonconvex dependence of the system dynamics on unknown parameters, which significantly complicates both controller design and analysis. To address these challenges, we propose an online nonlinear weighted least-squares (WLS)-based parameter estimation algorithm and establish the global strong consistency of the resulting parameter estimates. In contrast to most existing results, our consistency analysis does not rely on restrictive assumptions such as persistent excitation conditions of the trajectory data, making it applicable to stochastic adaptive control settings. Building on the proposed estimator, we further develop an adaptive control algorithm with an attenuating excitation signal that can effectively combine adaptive estimation and feedback control. Finally, we are able to show that the resulting closed-loop system is globally stable and that the system trajectory can track, in a long-run average sense, the reference trajectory generated with the true system parameters. The proposed methods and theoretical results are finally validated through simulations in two nonlinear interaction network applications.

A real Lie algebra defines by extension of scalars a complex Lie algebra that is isomorphic to its Galois conjugate. In this paper, we are interested in the converse property: given a complex Lie algebra that is isomorphic to its conjugate, is it defined over the real numbers? We prove the existence of a $10$-dimensional nilpotent complex Lie algebra for which the answer is negative, disproving a recent conjecture by Deré. In addition, we compute the generic obstruction to this descent problem in terms of Brauer groups.

We examine the relationship between the mass of present-day central supermassive black holes (SMBHs, $M_{\rm BH}$), and the stellar mass ($M_{\star}$) and halo mass ($M_{200}$) of their host galaxies in the EAGLE simulation, and find that scatter about these relations correlates with both halo structure and galaxy morphology. EAGLE reproduces the observed $M_{\rm BH}$-$M_{\star}$ relation, including (qualitatively) its dependence on morphology: at fixed $M_{\star}$, disc-dominated galaxies host less massive SMBHs than ellipticals. We show that $M_{\rm BH}$ correlates with $M_{200}$, as expected if SMBHs are regulated by processes acting on the scale of the host dark matter halo, but exhibits a tighter correlation with the halo binding energy ($E_{\rm bind}$), signalling that this quantity, which encodes information about both halo mass and halo structure, is more fundamental to $M_{\rm BH}$. As with $M_{\rm BH}$-$M_{\star}$, scatter about the $M_{\rm BH}$-$E_{\rm bind}$ relation is strongly correlated with morphology. Gas in the central few parsecs of galaxies with present-day discs retains strong rotational support as the galaxy grows, inhibiting inward transport and precluding periods of rapid SMBH growth by gas accretion. In galaxies destined to be present-day ellipticals, however, this rotational support is disrupted, enabling gas to be funnelled onto the central SMBH, triggering rapid growth. Evolution of the mass fraction of stars formed ex-situ indicates that this disruption is caused by galaxy-galaxy interactions and mergers. Our findings corroborate the conclusion of recent studies, based on controlled simulations of an ~$L^{\star}$ galaxy, that prolonged secular galaxy evolution inhibits central SMBH growth.

While most theoretical run time analyses of discrete randomized search heuristics provide bounds on the expected number of evaluations to find the global optimum, we consider the anytime performance of evolutionary and estimation-of-distribution algorithms. For this purpose, we analyze the fixed-target run time of various algorithms using BinVal as fitness function and bound the run time to optimize the most significant $k \in o(n)$ bits of a bit string with length $n$. We analyze the run times such that they hold not only for a fixed $k$, but simultaneously for all $k \in o(n)$. For the standard (1+1) EA with fixed mutation rate $1/n$, we show that the fixed-target run time for all $k \in o(n)$ is in $Θ(n \log k)$. Using an EDA instead, we get an expected number of evaluations of $Θ(k \log n)$ for the sig-cGA. Replacing in the standard (1+1) EA the fixed mutation rate with a self-adjusting rate, we show that the fixed-target run time for $k \in o(n)$ and a constant $\varepsilon >0$ arbitrarily close to zero is in $\mathcal{O}\left(k^{1+\varepsilon}\right)$ for this algorithm. In particular, this run time is independent of $n$, holds simultaneously for all $k \in o(n)$, and is close to the run time of $Θ(k \log k)$ for the (1+1) EA with the best fixed mutation rate if $k$ is known.

This lecture note addresses the common misconception that the Gaussian distribution always yields the largest Cramér-Rao Bound (CRB). We show that this property only holds under restrictive conditions: specifically, when the mean and covariance parameters are decoupled in the Fisher Information Matrix (FIM), when the parameter of interest lies in the mean vector and when there are no additive nuisance parameters. Beyond this framework, we provide counterexamples demonstrating that non-Gaussian distributions can produce larger CRB.

We present a novel approach for constructing discrete optimization benchmarks that enables fine-grained control over problem properties, and such benchmarks can facilitate analyzing discrete algorithm behaviors. We build benchmark problems based on a set of block functions, where each block function maps a subset of variables to a real value. Problems are instantiated through a set of block functions, weight factors, and an adjacency graph representing the dependency among the block functions. Through analyzing intermediate block values, our framework allows to analyze algorithm behavior not only in the objective space but also at the level of variable representations in the obtained solutions. This capacity is particularly useful for analyzing discrete heuristics in large-scale multi-modal problems, thereby enhancing the practical relevance of benchmark studies. We demonstrate how the proposed approach can inspire the related work in self-adaptation and diversity control in evolutionary algorithms. Moreover, we explain that the proposed benchmark design enables explicit control over problem properties, supporting research in broader domains such as dynamic algorithm configuration and multi-objective optimization.

With 6G evolving towards intelligent network autonomy, artificial intelligence (AI)-native operations are becoming pivotal. Wireless networks continuously generate rich and heterogeneous data, which inherently exhibits spatio-temporal graph structure. However, limited radio resources result in incomplete and noisy network measurements. This challenge is further intensified when a target variable and its strongest correlates are missing over contiguous intervals, forming systemic blind spots. To tackle this issue, we propose RieIF (Knowledge-driven Riemannian Information Flow), a geometry-consistent framework that incorporates knowledge graphs (KGs) for robust spatio-temporal graph signal prediction. For analytical tractability within the Fisher-Rao geometry, we project the input from a Riemannian manifold onto a positive unit hypersphere, where angular similarity is computationally efficient. This projection is implemented via a graph transformer, using the KG as a structural prior to constrain attention and generate a micro stream. Simultaneously, a Long Short-Term Memory (LSTM) model captures temporal dynamics to produce a macro stream. Finally, the micro stream (highlighting geometric shape) and the macro stream (emphasizing signal strength) are adaptively fused through a geometric gating mechanism for signal recovery. Experiments on three wireless datasets show consistent improvements under systemic blind spots, including up to 31% reduction in root mean squared error and up to 3.2 dB gain in recovery signal-to-noise ratio, while maintaining robustness to graph sparsity and measurement noise.

When output token counts can be predicted at submission time (Gan et al., 2026), client-side scheduling against a black-box LLM API becomes semi-clairvoyant: decisions condition on coarse token priors even though the provider's internals remain hidden. We decompose this boundary problem into three separable concerns: allocation (inter-class share via adaptive DRR), ordering (intra-class sequencing with feasible-set scoring), and overload control (explicit admit/defer/reject on a cost ladder). An information ladder experiment shows that coarse magnitude priors -- not class labels alone -- are the practical threshold for useful client control; removing magnitude inflates short-request P95 by up to $5.8\times$ and degrades deadline satisfaction. Under balanced / high congestion the full stack achieves 100% completion, 100% deadline satisfaction, and useful goodput of $4.2 \pm 1.6$ SLO-meeting requests/s with short P95 within tens of milliseconds of quota-tiered isolation. A predictor-noise sweep confirms graceful degradation under up to 60% multiplicative error. Heavy-dominated regimes separate policies on completion, tail, and interpretable shedding. We further compare short-priority allocation (biased toward interactive traffic) with Fair Queuing (round-robin across classes): Fair Queuing achieves +32% short-request P90 improvement over FIFO with only +17% long-request overhead, versus Short-Priority's +27% / +116% trade-off -- demonstrating that the allocation layer accommodates different fairness objectives without changing the remaining stack. We contribute the three-layer client-side decomposition, controlled evaluation of joint metrics across regimes, allocation-policy alternatives, and overload-policy evidence linking cost-ladder shedding to the stated service objective.

We give a necessary and sufficient condition on a matrix for its centralizer in $\sf{GL}(n,\mathbb{Z})$ to be polycyclic, or equivalently in this case, not to contain a non-abelian free subgroup. We give a simple condition on the matrix ensuring that it is abelian. This can be thought of as an effective Tits alternative on centralizers in $\sf{GL}(n,\mathbb{Z})$. We apply these criteria to the conjugacy problem in certain arithmetic groups preserving a non-degenerate $\mathbb{Q}$-bilinear form, such as integral symplectic groups. We derive an effective solution to the conjugacy problem in such groups when given matrices satisfy the above criterion. This solution is based on effective solutions to the conjugacy problem in $\sf{GL}(n,\mathbb{Z})$ by Eick-Hofmann-O'Brien and to an orbit problem for polycyclic groups, by Eick and Ostheimer.

The soliton-like coherent structure (SCS), which has been verified to exist in both transitional and turbulent boundary layers1-4, still poses a challenge in the understanding of its formation and behavior. In our previous study (Niu et al.5), the SCS was also found to exist in the transitional wake flow behind a sphere. In present study, the formation and evolution of the SCS is further investigated at four Reynolds numbers by numerical simulation. The results show that at the early stage of the turbulence transition, the SCS appears as a form of wave packet during the Tollmien-Schlichting (T-S) wave stage. With the increase of the Reynolds number, the SCS reaches its maximum amplitude downstream where the velocity discontinuity occurs. This position is located after the breakdown of the T-S wave and the three-dimensional structure is formed. Then, the SCS conserves its shape and amplitude over a long distance downstream. The relationships among the SCS, the spikes, the vortex structures, and the high-shear layers are further analyzed. It is found that the SCS in the wake flow has similarities to the phenomena observed in boundary layer flows during the turbulent transition. The vortex structures and high-shear layers mostly wrap around the border of the SCS. The vortex structure is considered to be as a consequence of the development of the SCS rather than its cause.

Given a porous set $E\in \mathbb{R}^d$ and a dyadic lattice $\mathcal{D}$, we refine the Carleson packing condition and the sparseness property for the dyadic cover $\mathcal{D}_E=\{Q \in \mathcal{D}: \: Q \cap E \neq \varnothing\}$. We study the inverse problem, when a Carleson family $\mathcal{S} \subset \mathcal{D}$ generates the porous set $E$ such that $\mathcal{S} \subset \mathcal{D}_E$.

Let $p$ be a prime number, and let $Δ_1,Δ_2 < 0$ be two coprime fundamental discriminants. When $p$ splits in $\mathbb{Q}(\sqrt{Δ_1})$ and $\mathbb{Q}(\sqrt{Δ_2})$ the height pairings of the corresponding CM divisors on $X_{\mathrm{spl}}^+(p)$ were determined by Gross--Kohnen--Zagier [GKZ87]. When $p$ is inert, we determine the arithmetic intersection numbers of the corresponding divisors on $X_{\mathrm{ns}}^+(p)$ at all finite primes. The key point of our analysis is at the prime of bad reduction $p$: to determine the intersection numbers at $p$, we provide a moduli interpretation for the smooth locus in the regular model of $X_{\mathrm{ns}}^+(p)$ over $\mathrm{Spec}(\mathbb{Z})$ constructed by Edixhoven--Parent [EP24].

We investigate the sliding strength of thin filaments in frictional contact with a translating cylinder, perpendicular to the filaments' axes, in knotted (clove hitch) and unknotted (capstan) configurations. Recent work reported superlinear scaling for surgical knots with elasto-plastic filaments [1]. Testing the clove hitch with various materials (elastomeric rods, metallic wires, braided ropes) reveals similar nonlinear behavior, ruling out plasticity. To explore the source of the previously reported nonlinear behavior, we perform three-dimensional FEM simulations (resolving full 3D mechanics) and reduced-order DER simulations (isolating geometric effects by neglecting cross-sectional deformation). Both FEM and DER simulations reproduce the experimental scaling. Simplifying the knot topology by studying capstan angles from $π/4$ to $4π$ yields comparable superlinear behavior, transitioning to linearity at smaller angles. We rationalize the results by developing an analytical model based on planar elastica theory for the capstan configuration (which exhibits behavior similar to the clove hitch but with a simpler topology). The model reproduces the observed superlinear behavior and rationalizes it by coupling the evolution of normal forces and contact arclength during tightening. The analysis further predicts transition to linearity when full contact between the filament and the cylinder is established, providing a mechanical framework applicable across materials, geometries, and topologies.

A widely tunable free spectral range (FSR) is essential for many optical microresonator applications, but achieving it remains a significant challenge. Recently, it has been experimentally demonstrated that side-coupling between two optical fibers can induce a high-Q whispering-gallery-mode (WGM) microresonator. In contrast to broadly explored monolithic optical microresonators, this configuration enables extensive tuning of the microresonator FSR through fiber bending, tilting, and twisting. Beyond fundamental interest, this class of microresonators is particularly important for a range of critical applications, including tunable delay lines, frequency comb generators, and reconfigurable optical sensors. Here, we develop the theory of such microresonators, which has remained largely unexplored. We consider weakly twisted fibers, whose geometry can be decomposed into tilting and bending. We show that an extremely small curvature of fibers critically affects the shape and spectrum of the induced microresonators. We discuss the physical origin of this curvature and show that taking it into account leads to excellent agreement between the developed theory and the experimental results.

In type II multiferroics, noncollinear spin textures are expected to induce electric polarization directly, leading to strong magnetoelectric coupling. Realizing such spin driven multiferroicity in two-dimensional systems, and elucidating the interplay between local spins and electric polarization, are of both fundamental and technological importance. Here, using vectorial spin polarized scanning tunneling microscopy, we investigated the spin-driven multiferroicity in monolayer NiI2 at atomic scale. We identify a canted spin-spiral state with fully determined spin rotation plane, accompanied by a 2Q charge modulation. At spin spiral domain walls, we discover topological spin textures that composed of meron/antimeron pairs. These textures are associated with distinct charge pattern and notable band shifts, indicating local bound charges induced by variations of ferroelectricity at domain wall. Our observations are well captured by a realistic spin model incorporating Kitaev interactions and generalized spin-current model of type II multiferroicity. The findings provide microscopic evidence of spin-driven multiferroicity in an extreme 2D system and establish a platform for low-dissipation, electric-field control of topological spin textures.

Transformer neural networks achieve state-of-the-art accuracy across language and vision tasks, but their deployment on embedded hardware is hindered by stringent area, latency, and energy constraints. During inference, performance and efficiency are increasingly dominated by the Key--Value (KV) cache, whose memory footprint grows with sequence length, straining on-chip memory utilization. Although existing mechanisms such as Grouped-Query Attention (GQA) reduce KV cache requirements compared to Multi-Head Attention (MHA), effectively exploiting this reduction requires understanding how on-chip memory demand evolves over time. This work presents TRAPTI, a two-stage methodology that combines cycle-level inference simulation with time-resolved analysis of on-chip memory occupancy to guide design decisions. In the first stage, the framework obtains memory occupancy traces and memory access statistics from simulation. In the second stage, the framework leverages the traces to explore banked memory organizations and power-gating configurations in an offline optimization flow. We apply this methodology to GPT-2 XL and DeepSeek-R1-Distill-Qwen-1.5B under the same accelerator configuration, enabling a direct comparison of MHA and GQA memory profiles. The analysis shows that DeepSeek-R1-Distill-Qwen-1.5B exhibits a 2.72x reduction in peak on-chip memory utilization in this setting compared to GPT-2 XL, unlocking further opportunities for power-gating optimization.

This paper explores the electrification of mezcal distilling in Oaxaca, Mexico, as a sustainable alternative to traditional firewood methods. We investigate the mezcal process, including cooking, grinding, fermentation, and distillation, and propose a photovoltaic system for distillation. The research also includes scientific outreach activities in the producing communities. We, in collaboration with the communities, proposed novel uses of renewable energies. The results of chemical analysis (chromatography and FTIR) and sensory data for distillation using firewood and electricity are presented to compare the mezcal produced with solar energy and traditional mezcal. Our studies conclude that electrical distillation can reduce environmental impact and improve energy efficiency without compromising product quality.

We study Hamiltonian systems near a compact symplectic Morse-Bott minimum. Our first result shows that if the flow is Zoll (that is, it induces a free circle action) along a sequence of energy levels converging to the minimum, then the Hessian of the Hamiltonian in the symplectic normal directions must be compatible with the restriction of the symplectic structure to the normal bundle (that is, its representing endomorphism is a complex structure of the symplectic normal bundle). For our second result, we specialize to magnetic systems on closed manifolds with symplectic magnetic form. In this setting, if the system is Zoll along a sequence of energy levels converging to the minimum, then the metric is compatible with the magnetic form and therefore defines an almost Kähler structure. We show that a natural curvature quantity, consisting of the holomorphic sectional curvature corrected by a term measuring the non-integrability of the almost complex structure, must be constant. In particular, we obtain a dynamical characterization of complex space forms among Kähler manifolds. Together, these results establish strong rigidity of systems which are Zoll at energies close to a Morse-Bott minimum, in the symplectic and in the magnetic settings.

Wavelet phase is a critical parameter in seismic processing, where zero-phase wavelets are essential for maximizing temporal resolution and ensuring accurate interpretation of subsurface structures. In practice, however, the seismic wavelet is often nonstationary, exhibiting a phase that varies in space and time due to physical factors such as attenuation, dispersion, and thin-bed tuning effects. Higher-order statistical measures-specifically kurtosis and skewness-are traditionally maximized to drive the signal toward a maximally non-Gaussian or maximally asymmetric zero-phase state. This paper addresses the computational and stability challenges inherent in nonstationary estimation by casting the problem as a regularized non-convex optimization task. We propose a robust framework based on the Alternating Direction Method of Multipliers (ADMM) that eliminates the instability and artifacts associated with traditional piecewise-stationary windowed approaches. The core of our contribution is the derivation of the first closed-form proximity operators for the scale-invariant inverse kurtosis and inverse skewness functionals. By exploiting the signed permutation invariance of these statistical measures, we reduce the high-dimensional proximal subproblems to efficient one-dimensional root-finding tasks. We provide a detailed geometric interpretation of the optimality conditions, demonstrating that the global minimizer is governed by a branch-separation property. Furthermore, we derive an explicit critical threshold parameter which provides a theoretical rule for identifying the global minimum among multiple stationary points. Numerical validations on synthetic and real seismic data demonstrate that the proposed proximal algorithms achieve linear computational complexity and superior stability compared to traditional methods, effectively enabling nonstationary phase correction.

Transport through correlated nanoscale systems underpins the operation of quantum-dot and molecular-scale devices, yet accurate simulations of large open quantum systems remain computationally challenging as system size increases. Tensor-network methods offer a promising route past this scaling barrier by efficiently compressing quantum states. Here we extend a tensor-based solver with a jump-counting estimator that enables direct computation of steady-state electron currents from lead-induced tunneling events. We benchmark the resulting currents against the state-of-the-art master-equation solver QmeQ across a range of lead-dot and inter-dot coupling parameters and find quantitative agreement in the tractable regime. Compared with classical approaches, TJM reduces memory requirements and wall-clock time by orders of magnitude, enabling simulations of interacting quantum-dot arrays far beyond the range accessible to density-matrix-based transport solvers and systematic studies of size-dependent nonequilibrium transport in larger arrays. Our approach allow us to model quantum transport in an array of up to fifty (50) quantum dots.

We perform a comprehensive observational test of a canonical quintessence model driven by an exponential potential, motivated by its emergence in higher-dimensional theories, string-inspired scenarios, and modified gravity. Using a Markov Chain Monte Carlo framework, we constrain the model with the latest high-precision observational datasets including Cosmic Chronometers, Baryon Acoustic Oscillation, Pantheon+, and DES-SN5YR Type Ia Supernovae. The combined data significantly tighten the parameter bounds on (H0, Omega_m0, eta0, gamma) and yield predictions for the Hubble parameter H(z), the distance modulus mu(z), and the scaled comoving angular diameter distance that remain in excellent agreement with observations and closely follow the LCDM baseline. An information-theoretic model comparison using the Akaike Information Criterion shows that the exponential quintessence model remains statistically comparable with LCDM despite having additional parameters. The model successfully reproduces the transition from matter domination to late-time acceleration, maintains w_tot > -1, and provides an age of the universe consistent with Planck 2018. Statefinder diagnostics indicate trajectories approaching the LCDM fixed point with small deviations, and energy condition analysis confirms physical viability, with only the Strong Energy Condition violated at late times as required for acceleration.

The optical response of a suspension microdroplet is governed not only by the properties of the dispersed phase, but also by the finite size and optical structure of the droplet itself. As a result, the interpretation of scattered-light patterns from such systems constitutes a non-trivial inverse problem. In this work, we examine whether laser speckle images recorded from single levitating microdroplets of suspension can be used for data-driven recognition of selected droplet and suspension parameters. Experiments were performed on slowly evaporating microdroplets of monodisperse TiO$_2$ nanoparticle suspensions in diethylene glycol confined in a linear electrodynamic quadrupole trap. Speckle images were analyzed with a convolutional neural network trained to classify droplet diameter, nanoparticle concentration, and nanoparticle diameter, first in separate tasks and then in combined two-parameter and three-parameter classifications. Under the present experimental conditions, droplet diameter was identified with good reliability, with an estimated accuracy better than approximately 6% for the tested dataset. Nanoparticle concentration was more difficult to resolve, but useful discrimination was obtained when concentration classes were sufficiently separated. Nanoparticle diameter was also classified unambiguously for the selected cases. In addition, simultaneous classification of up to three parameters across 27 classes was achieved. These results suggest that CNN-based analysis of speckle images may provide a viable route toward multi-parameter optical diagnostics of free suspension microdroplets and, potentially, more complex aerosol-like systems.