Modern applications have made ubiquitous high-dimensional data, especially time-dependent data, with more and more complicated structures, and it also has become more frequent to encounter the scenario of hierarchical relationships among variables. However, there is still a lack of supervised learning tool in the literature for them. To fill this gap, we introduce a new model-designing framework, and it then combines with unsupervised factor modeling tools to form an efficient and interpretable autoregressive model for high-dimensional time series with hierarchical structures. An ordinary least squares estimation is considered, and its non-asymptotic properties are established. Moreover, we propose an algorithm to search for estimates, and a boosting method is also suggested for hyperparameter selection. Simulation experiments are conducted to evaluate finite-sample performance of the proposed methodology, and its usefulness is demonstrated by an application to the Personality-120 dataset.

In a practical multi-antenna receiver, each element of the receive antenna array has a directive antenna pattern, which is still not fully explored and investigated in academia and industry until now. When the emitter is deviated greatly from the normal direction of antenna element or is close to the null-point direction, the sensing energy by array will be seriously attenuated such that the direction-sensing performance is degraded significantly. To address such an issue, a rotatable array system is established with the directive antenna pattern of each element taken into account, where each element has the same antenna pattern. Then, the corresponding the Cramer-Rao lower bound (CRLB) is derived. Finally, a recursive rotation Root-MUSIC (RR-Root-MUSIC) direction-sensing method is proposed and its root-mean-squared-error (RMSE) performance is evaluated by the derived CRLB. Simulation results show that the proposed rotation method converges rapidly with about ten iterations, and make a significant enhancement on the direction-sensing accuracy in terms of RMSE when the target direction departs seriously far away from the normal vector of array. Compared with conventional Root-MUSIC, the sensing performance of the proposed RR-Root-MUSIC method is much closer to the CRLB.

The mixed fractional Brownian motion - the sum of independent fractional and standard Brownian motions - is known to be a semimartingale if the Hurst exponent $H$ of its fractional component satisfies $H > 3/4$. The question posed in the title is motivated by recent findings in quantitative finance. In this note, we show that the drift in its Doob-Meyer decomposition has a derivative that is $γ$-Hölder continuous for any $γ< 2H - 3/2$.

Model selection in penalized regression critically depends on an accurate assessment of model complexity, commonly quantified through the effective degrees of freedom. While the Lasso admits a simple and unbiased characterization, given by the size of the active set, this property does not extend to adaptive penalization methods, despite the widespread use of this approximation in practice. To solve this issue, in this paper we derive a novel unbiased estimator of the effective degrees of freedom for the Adaptive Lasso within Stein's unbiased risk estimation framework. Our analysis reveals additional terms induced by data-dependent penalization, reflecting the role of adaptive weights and regularization in determining model complexity. We further revisit the Group Lasso, providing an alternative derivation of its degrees of freedom, and extend these results to the Adaptive Group Lasso. Importantly, we characterize the behavior of the degrees of freedom along the regularization path beyond the orthonormal design setting commonly assumed in the literature, providing a new theoretical description of this behavior under general design matrices. By correcting the common misuse of active set size as a proxy for degrees of freedom, our results enable more reliable risk estimation and inference, offering a rigorous foundation for understanding model complexity in adaptive penalized regression.

This work presents conjectures about eigenvalues of matrices associated with $k$-path graphs, the algebraic connectivity, defined as the second smallest eigenvalue of the Laplacian matrix, and the $α$-index, as the largest eigenvalue of the $A_α$-matrix. For this purpose, a process based in Pereira et al., is presented to generate lists of $k$-path graphs containing all non-isomorphic 2-paths, 3-paths, and 4-paths of order $n$, for $6 \leq n \leq 26, 8 \leq n \leq 19$, and $10 \leq n \leq 18$, respectively. Using these lists, exhaustive searches for extremal graphs of fixed order for the mentioned eigenvalues were performed. Based on the empirical results, conjectures are suggested about the structure of extremal $k$-path graphs for these eigenvalues.

In conventional quantum mechanics, all unitary evolution takes place within the space-time Hilbert space $\mathcal H_{xt}=L^2(\mathcal M_{xt})$, with time as the sole evolution parameter. The momentum-energy representation $ϕ(k,E)$ is treated merely as a Fourier re-expression of the same state-kinematically equivalent but dynamically inert. Here we restore the fundamental symmetry between the conjugate pairs $(x,t)$ and $(k,E)$ by extending the quantum theory to an enlarged Hilbert space $\mathcal H_{\text{total}} = \mathcal H_{xt} \oplus \mathcal H_{kE}$, within which the momentum-energy sector $\mathcal H_{kE}=L^2(\mathcal M_{kE})$ carries its own autonomous unitary evolution generated by a self-adjoint operator $\hat{\mathcal T}$. The resulting structure establishes a meta-symmetry: a symmetry between two conjugate dynamical projections of a single global quantum state. It produces a dual-manifold geometry in which each domain is locally complete yet globally open, with divergent limits in one mapping onto extended regions in the other. Remarkably, the dual-manifold symmetry alone reproduces both the uniform dark-energy background and the exponential boundary mapping near black-hole horizons that underlies Hawking radiation. This framework thus opens a quantum-theoretic route to cosmological phenomena that are ordinarily treated within general relativity.

Tests of general relativity (GR) with gravitational waves (GWs) introduce additional deviation parameters in the waveform model. The enlarged parameter space makes inference computationally costly, which has so far limited systematic, large-scale studies that are essential to quantify parameter degeneracies, check the effect of waveform systematics, and assess robustness across non-stationary and non-Gaussian noise effects. The need is even sharper for next-generation observatories where signals are longer, signal-to-noise ratios (SNRs) are higher, and likelihood evaluations increase substantially. We address this by applying relative binning to the TIGER framework for parameterized tests of GR. Relative binning replaces dense frequency waveform evaluations with evaluations on adaptively chosen frequency bins, reducing the cost per likelihood call while preserving posterior accuracy. Using simulated binary black hole signals, we demonstrate unbiased recovery for GR-consistent cases and targeted non-GR deviations, and we map how bin resolution controls accuracy, with finer binning primarily required for the $-1$ post-Newtonian term. A high-SNR simulated signal at next-generation sensitivity further shows accurate recovery with tight posteriors. Applied to GW150914 and GW250114, both single and multi-parameter TIGER analyses finish within a day, yielding bounds consistent with GR at 90\% credibility and in agreement with previous results. Across analyses, the method reduces wall time by factors of $\mathcal{O}(10)$ to $\mathcal{O}(100)$, depending on frequency range and binning scheme, without degrading parameter estimation accuracy.

Muon tomography is a non-destructive imaging technique that uses cosmic-ray muons to probe dense materials. Bar scintillator and scintillating fiber detectors equipped with one-dimensional SiPM arrays offer compact, high-resolution solutions, but large-area implementations require effective reduction of readout channels while preserving detector performance. To address this challenge, we present a novel multiplexing scheme based on a diode-based symmetric charge division circuit combined with a position-encoding algorithm, enabling up to $N_{\textrm{SiPM}}^{\textrm{max}}=C^{2}_{N_{\textrm{ele}}}$ SiPM channels to be read out using only ${N_{\textrm{ele}}}$ electronic channels. Circuit simulations confirm the feasibility of the multiplexing design and guide the choice of appropriate diodes to preserve SiPM signal integrity. The approach was validated using a SciFi detector module comprising 21 SiPM channels multiplexed into 7 electronic channels. Electronic tests show that this multiplexing circuit exhibits low crosstalk between electronic channels, and preserves linearity over a dynamic range from $\sim$10 to 122 photoelectrons. Cosmic-ray measurements further show that the multiplexed SciFi detector achieves a detection efficiency above 95\% and a spatial resolution of about 0.65~mm, with only minor degradation compared to the direct (per SiPM channel) readout. These results verify that the proposed method provides a scalable and cost-effective readout solution for large-area muon tomography systems and is applicable to other scintillator-based detectors employing similar one-dimensional SiPM array readout.

We study the problem of online graph coloring for $k$-colorable graphs. The best previously known deterministic algorithm uses $\widetilde{O}(n^{1-\frac{1}{k!}})$ colors for general $k$ and $\widetilde{O}(n^{5/6})$ colors for $k = 4$, both given by Kierstead in 1998. In this paper, we finally break this barrier, achieving the first major improvement in nearly three decades. Our results are summarized as follows: (1) $k \geq 5$ case. We provide a deterministic online algorithm to color $k$-colorable graphs with $\widetilde{O}(n^{1-\frac{1}{k(k-1)/2}})$ colors, significantly improving the current upper bound of $\widetilde{O}(n^{1-\frac{1}{k!}})$ colors. Our algorithm also matches the best-known bound for $k = 4$ ($\widetilde{O}(n^{5/6})$ colors). (2) $k = 4$ case. We provide a deterministic online algorithm to color $4$-colorable graphs with $\widetilde{O}(n^{14/17})$ colors, improving the current upper bound of $\widetilde{O}(n^{5/6})$ colors. (3) $k = 2$ case. We show that for randomized algorithms, the upper bound is $1.034 \log_2 n + O(1)$ colors and the lower bound is $\frac{91}{96} \log_2 n - O(1)$ colors. This means that we close the gap to a factor of $1.09$. With our algorithm for the $k \geq 5$ case, we also obtain a deterministic online algorithm for graph coloring that achieves a competitive ratio of $O(\frac{n}{\log \log n})$, which improves the best-known result of $O(\frac{n \log \log \log n}{\log \log n})$ by Kierstead. For the bipartite graph case ($k = 2$), the limit of online deterministic algorithms is known: any deterministic algorithm requires $2 \log_2 n - O(1)$ colors. Our results imply that randomized algorithms can perform slightly better but still have a limit.

In recent studies \cite{ZZ24, FY24}, the Interior Penalty Virtual Element Method (IPVEM) has been developed for solving a fourth-order singular perturbation problem, with uniform convergence established in the lowest-order case concerning the perturbation parameter. However, the resulting uniform convergence rate is only of half-order, which is suboptimal. In this work, we demonstrate that the proposed IPVEM in fact achieves optimal and uniform error estimates, even in the presence of boundary layers. The theoretical results are substantiated through extensive numerical experiments, which confirm the validity of the error estimates and highlight the method's effectiveness for singularly perturbed problems.

Let $A$ be a Nakayama algebra. Using Ringel's resolution quiver, we give a criterion to decide whether $A$ is minimal Auslander-Gorenstein. The criterion strongly relies on the parity of the selfinjective dimension of $A$.

Under high cylindrical confinement, segments of ring polymers can be localized along the long axis of the cylinder by introducing internal loops within the ring polymer. The emergent organization of the polymer segments occurs because of the entropic repulsion between internal loops. These principles were used to identify the underlying mechanism of bacterial chromosome organization. Here, we outline functional principles associated with entropic interactions, leading to specific orientations of the ring polymers relative to their neighbors in the cylindrical confinement. We achieve this by modifying the ring polymer topology by creating internal loops of two different sizes within the polymer, and thus create an asymmetry. This allows us to strategically manipulate polymer topology such that segments of a polymer face certain other segments of a neighboring polymer. The polymers therefore behave as if they are subjected to an `effective' entropic interaction reminiscent of interactions between Ising spins. But this emergent spatial and orientational organization is not enthalpy-driven. We consider a bead spring model of flexible polymers with only repulsive excluded volume interactions between the monomers. The polymers entropically repel each other and occupy different halves of the cylinder, and moreover, the adjacent polymers preferentially re-orient themselves along the axis of the cylinder. We further substantiate our observations by free energy calculations. To the best of our knowledge, this is the first study of the emergence of effective orientational interactions by harnessing entropic interactions in flexible polymers. The principles elucidated here could be relevant to understand the interactions between different sized loops within a large chromosome.

In this article, the behavior of a straight cosmic string is studied for the linearized version of Horndeski theory in cases where the scalar field is massless or massive. Several physical properties of such solutions are discussed in detail regarding the effects of the scalar field of this theory. The mass of the scalar field induces a screening effect such that, in the massive theory, the string solution approaches to the general relativistic one. We also consider wiggly cosmic strings, obtain the solutions for both massless and massive cases, discuss their properties and observe similar screening effects.

In this work, we provide an overview of various control strategies aimed at steering plasma toward desired configurations using an external magnetic field. From a modeling perspective, we focus on the Vlasov equation in a two-dimensional bounded domain, accounting for both a self-induced electric field and a strong external magnetic field. The results are presented in a polar coordinate framework, which is particularly well-suited for simulating toroidal devices such as Tokamaks and Stellarators. A key feature of the proposed control strategies is their feedback mechanism, which is based on an instantaneous prediction of the discretized system. Finally, different numerical experiments in the two-dimensional polar coordinate setting demonstrate the effectiveness of the approaches.

With a recent revival, novel features of the FLPR model have been reported in the literature. A connection between those features to QCD involving the Gribov problem is explored. We investigate the FLPR model in a recently proposed framework of BRST-related symmetries and perform its full functional quantization as a gauge invariant system taking into account the Gribov ambiguities. We obtain a family of BRST-related transformations generated by the discrete group of symmetries of the action. We show that gauges possessing Gribov ambiguities lead to a violation of the initial discrete group of symmetries of the gauge-fixed action. The obtained results shed light into similar issues in QCD by the corresponding association of variables and fields between the two systems.

Entanglement classification of pure multipartite quantum states is a challenging problem in quantum information theory that can be mathematically stated as orbit classification for some given group action on the ambient Hilbert space. The group action depends on the grained classification one expects, the finer-grained one being the classification up to local unitary transformation (LU). In this article, we show how a variational quantum circuit approach can be used to learn entanglement orbits, and we apply our findings to build a classifier for four-qubit states.

Pulsar timing arrays probe isotropic stochastic gravitational wave (GW) backgrounds in the nanohertz band but are insensitive to its parity-violating component. Motivated by recent progress in pulsar polarization arrays, we study the response of pulsar polarimetry to GWs and evaluate its potential to detect circular polarization in isotropic stochastic GW backgrounds, which characterizes parity violation. Based on geometric optics, we derive the rotation of the polarization of electromagnetic waves induced by propagation through a GW background. We show that the cross-correlation between pulsar timing and polarimetry signals isolates the circular polarization component from the GW intensity, sharing the same Hellings-Downs angular pattern. With future facilities such as the SKA, timing-polarimetry correlations could reach sensitivities to the circular polarization of GWs comparable to those of the current astrometric methods.

We set the scale of SU($N$) Yang--Mills theories for $N=3,5,8$ and in the large-$N$ limit via gradient flow, as a first step towards the computation of the large-$N$ $Λ$-parameter using step scaling. We adopt twisted boundary conditions to achieve large-$N$ volume reduction and the Parallel Tempering on Boundary Conditions algorithm to tame topological freezing. This setup allows accurate determinations of the gradient-flow scales down to lattice spacings as fine as $\sim 0.025$ fm for all the explored values of $N$, a regime that has never been reached with ergodic algorithms. Moreover, we are able to precisely estimate the finite-size systematics related to topological freezing, and to show the suppression of finite-volume effects expected by virtue of large-$N$ twisted volume reduction.

We provide a framework and explicit construction for the regularized measurement of a large class of spacetime-localized observables in bosonic quantum field theory. The measurements fully satisfy relativistic causality and causal transparency, i.e., avoid unphysical superluminal signaling. We show explicitly how the measurement of time-extended observables back-reacts on itself and induces correlations between other measurements in its causal future. Our framework is fully compositional in spacetime and extends previous results on the measurement of instantaneous observables.

The emergence of sixth-generation networks heralds an intelligent communication ecosystem driven by the rapid proliferation of intelligent services and increasingly complex communication scenarios. However, current physical-layer designs-typically following modular and isolated optimization paradigms-fail to achieve global end-to-end optimality due to neglected inter-module dependencies. Although large language models (LLMs) have recently been applied to communication tasks such as beam prediction and resource allocation, existing studies remain limited to single-task or single-modality scenarios and lack the ability to jointly reason over communication states and user intents for personalized strategy adaptation. To address these limitations, this paper proposes a novel multimodal communication decision-making model for link construction leveraging reinforcement learning on pretrained LLMs. The proposed model semantically aligns channel state information (CSI) and textual user instructions, enabling comprehensive understanding of both physical-layer conditions and communication intents. It then generates physically realizable, user-customized link construction that dynamically adapts to changing environments and preference tendencies. A two-stage reinforcement learning framework is employed: the first stage expands the experience pool via heuristic exploration and behavior cloning to obtain a near-optimal initialization, while the second stage fine-tunes the model through multi-objective reinforcement learning considering BER, throughput, and power consumption. Experimental results demonstrate that the proposed model significantly outperforms conventional planning-based algorithms under challenging channel conditions, achieving robust, efficient, and personalized end-to-end communication strategies.

In this work, we experimentally study the fluorescence decay of Acridine Orange at late times, in order to test whether a late-time power-law behaviour emerges, a feature expected to be very small but consistent with quantum mechanical and quantum field theoretical predictions. Using two distinct photon detectors, we find that the data are well described by a sum of two exponential functions with lifetimes $τ_1 = 1.7331 \pm 0.001$ ns and $τ_2 = 5.948 \pm 0.012$ ns, in agreement with values reported in the literature. While no deviation from the exponential decay law is observed, this study serves as a reliable test for the experimental setup and enables a precise determination of the sample lifetimes.

Solar Cycle 24 data are used to determine how often the Sun emerges sunspots in `activity nests', i.e., regions where sunspots and active regions (ARs) repeatedly emerge. We use the Solar Photospheric Ephemeral Active Region (SPEAR) catalog created from Helioseismic and Magnetic Imager (HMI) data as well as the HMI Carrington Rotation maps of radial magnetic field, $B_r$. The Sun shows moderate nesting behavior with 41\% (48\%) of AR magnetic flux found in Northern (Southern) hemispheric nests that are short-lived (average lifetimes $\sim$3.3 - 4.0 months). Different rotation rates are used to search for nests that may not be evident `by eye'. The maximum number of nests are found with slightly prograde rotational velocities, with significant nest flux also found at synodic 451--452 nHz prograde and 409--411 nHz retrograde frequencies. Nest patterns show strong hemispheric asymmetry, indicating that the physical origin of nests identified herein must also be asymmetric or antisymmetric across the equator.

The static spherical vacuum solution in a bumblebee gravity model where the bumblebee field $B_μ$ has a two-component space-like, light-like, and time-like vacuum expectation value $b_μ$ is studied. Based on the results, we present a comprehensive classification of the static spherical vacuum solutions in bumblebee gravity with general vacuum expectation values. We find that the model becomes degenerate for a specific set of parameter combinations, where the solution can be characterized by an arbitrary function, which indicates that the non-minimally coupled massless vector tensor theory is ill-defined when $ξ=κ/2$. We also find that contrary to the situation in general relativity, the bumblebee gravity admits the exact Schwarzschild solution with non-zero matter distributions of certain forms. The implications of this result are discussed, suggesting that the experimental constraints within the solar system would be invalid.

The magnetic ground state of RuO$_2$ has been under intense debate. Using first-principles calculations, we show that compressive strain along [001] direction stabilizes an altermagnetic phase in RuO$_2$ thin films grown on (100) and (110) TiO$_2$ substrates. We further identify that compressive strain enhances the density of states near the Fermi level, resulting in a Fermi surface instability and the emergence of altermagnetism. The magnitude of strain and the associated increase in the density of states can be tuned by varying the film thickness, as systematically confirmed by x-ray diffraction and photoemission spectroscopy measurements. Symmetry analysis further reveals that (100) RuO$_2$ hosts an ideal altermagnetic order, whereas broken symmetry in (110) films leads to an uncompensated ferrimagnetic state. Finally, we discuss the effects of Hubbard $U$ parameters and evaluate the realistic tunneling magnetoresistance of (100) RuO$_2$.

A liquid drop impacting a non-wetting rigid substrate laterally spreads, then retracts, and finally jumps off again. An elastic solid, by contrast, undergoes a slight deformation, contacts briefly, and bounces. The impact force on the substrate - crucial for engineering and natural processes - is classically described by Wagner's (liquids) and Hertz's (solids) theories. This work bridges these limits by considering a generic viscoelastic medium. Using direct numerical simulations, we study a viscoelastic sphere impacting a rigid, non-contacting surface and quantify how the elasticity number ($El$, dimensionless elastic modulus) and the Weissenberg number ($Wi$, dimensionless relaxation time) dictate the impact force. We recover the Newtonian liquid response as either $El \to 0$ or $Wi \to 0$, and obtain elastic-solid behavior in the limit $Wi \to \infty$ and $El \ne 0$. In this elastic-memory limit, three regimes emerge - capillary-dominated, Wagner scaling, and Hertz scaling - with a smooth transition from the Wagner to the Hertz regime. Sweeping $Wi$ from 0 to $\infty$ reveals a continuous shift from materials with no memory to materials with permanent memory of deformation, providing an alternate, controlled route from liquid drops to elastic beads. The study unifies liquid and solid impact processes and offers a general framework for the liquid-to-elastic transition relevant across systems and applications.

We study frustration-free control, a measurement-feedback protocol for quantum state preparation that extends the concept of frustration-free Hamiltonians to stochastic dynamics. The protocol drives many-body systems into highly entangled target states, common dark states of all measurement projectors, through minimal local unitary corrections that realize an absorbing-state dynamics without post-selection. We show that relaxation to the target state is governed by emergent transport of nonlocal charges, such as singlet excitations in SU$(2)$-symmetric dynamics. While measurement-feedback annihilates compatible charge configurations, both measurement and scrambling unitaries induce charge transport and thus determine the convergence time. Mapping a baseline model of SU$(N)$ SWAP measurements with local corrections to a solvable absorbing random walk yields a runtime scaling $t \sim L^z$ with transport exponent $z=2$. Simulations of Motzkin and Fredkin chains reveal subdiffusive scaling $z \ge \tfrac{8}{3}$, confirming the transport picture and suggesting strategies for controlled entangled-state preparation and charge-transport probing in monitored quantum dynamics.

It is common knowledge that black holes necessarily contain a region where general relativity breaks down, due to the inevitable formation of either a curvature singularity or a Cauchy horizon. In this work we challenge this view by analyzing a charged spherically symmetric black hole formed through gravitational collapse and evaporating via Hawking radiation. We show that the electromagnetic repulsion and the violation of energy conditions due to the presence of Hawking radiation are be sufficient to avoid the formation of both a singularity and a Cauchy horizon. We argue that a similar mechanism may apply to astrophysical black holes in which the role of the electric charge is replaced by the angular momentum.

A range of of unusual emergent behaviors have been reported in the charge-density wave (CDW) state of the $A$V$_3$Sb$_5$ ($A=~$K, Rb, Cs) kagome metals, including a CDW formation process without soft phonons, which points to an unconventional CDW mechanism. Here, we use inelastic x-ray scattering to show that the CDW in KV$_3$Sb$_5$ forms via phonons that soften to zero energy at the CDW ordering vector ($L$-point) around $T_{\rm CDW}=78$~K. The intensity of soft phonons exhibit a remarkable in-plane anisotropy, extending over a much larger momentum range along $L$-$A$ relative to $L$-$H$, which leads to diffuse scattering common among $A$V$_3$Sb$_5$. Using first-principles calculations, we find that the momentum-dependent electron-phonon coupling (EPC) is peaked at $L$ and exhibits the same in-plane anisotropy as the phonon softening. Conversely, the electronic susceptibility is not peaked at $L$ and shows the opposite in-plane anisotropy. Our findings favor momentum-dependent EPC as the driving mechanism of the CDW in KV$_3$Sb$_5$, with a CDW formation process similar to that of transition metal dichalcogenides.

We present a Bayesian latent model to describe the scaling relation between globular cluster populations and their host galaxies, updating the framework proposed in de Souza 2015. GC counts are drawn from a negative-binomial (NB) process linked to host stellar mass, augmented with a newly introduced Gaussian observation layer that enables efficient propagation of measurement errors. The revised formulation preserves the underlying NB process while improving computational tractability. The code snippets, implemented in Nimble and PyMC are released under the MIT license at https://github.com/COINtoolbox/Generalized-Linear-Models-Tutorial/blob/master/Count/readme.md

In this work, quantum Stirling engines based on monolayer, AB-stacked bilayer, and ABC-stacked trilayer graphene under perpendicular magnetic fields are analyzed. Performance maps of the useful work \((ηW)\) reveal a robust optimum at low magnetic fields and moderately low temperatures, with all stackings capable of reaching Carnot efficiency under suitable configurations. The AB bilayer achieves this across the broadest parameter window while sustaining finite work, the monolayer exhibits highly constrained regimes, and the trilayer shows smoother trends with sizable \(ηW\). These results identify multilayer graphene, particularly the AB bilayer, as a promising platform for efficient Stirling engines, while also highlighting the versatility of the monolayer in realizing all four operational regimes of the Stirling cycle.