We investigate the nonequilibrium dynamics and loss of coherence in a quantum impurity system using the spinless resonant level model subject to sudden quenches of the hybridization between the impurity and the metal. The survival probability (fidelity) and impurity occupation are analyzed as probes of the dephasing induced by particle-hole excitations. For finite systems, the loss of coherence loss is only apparent, as discrete spectra lead to quasi-periodic dynamics and revivals when phases realign. We show that a mixed linear-logarithmic discretization suppresses these finite-size artifacts by rendering excitation energies incommensurate, thereby reducing revivals. Starting from the exactly solvable two-level limit exhibiting coherent Rabi oscillations, we extend the analysis to large lattices, where damping and relaxation emerge. Combining analytical and numerical results, we provide a unified picture of the crossover from coherent oscillations to effectively irreversible decoherence.

Time series forecasting models often exhibit inconsistent performance across datasets with varying statistical and structural properties. Despite the wide range of available forecasting techniques, it remains unclear whether model selection can be reliably guided by simple data characteristics. This paper investigates why rule-based model selection fails in time series forecasting by analyzing the relationship between data-regime descriptors and model performance. A descriptor-based framework is introduced to characterize time series using measurable properties, including trend strength, seasonality, noise level, and temporal dependence. Based on these descriptors, a rule-based selection mechanism is formulated to map data regimes to candidate forecasting models. The approach is evaluated on multiple real-world datasets across different domains and forecasting horizons. The results show that rule-based model selection achieves low accuracy, with correct model identification occurring in only a small fraction of cases. Significant discrepancies are observed between recommended and empirically optimal models, particularly in noisy and mixed regimes. Further analysis reveals that model performance is highly sensitive to both dataset characteristics and forecasting horizon, resulting in substantial ranking instability across scenarios. These findings explain why simple heuristic rules fail to generalize and demonstrate that forecasting performance cannot be reliably predicted using static, descriptor-based approaches. This study provides empirical evidence that model selection in time series forecasting is inherently context-dependent and highlights the need for more adaptive, data-driven strategies.

We present the point-spread function (PSF) of the Extreme Ultraviolet High-Resolution Imager (HRIEUV) onboard Solar Orbiter, which observes the Sun at 174 Angstrom. This PSF provides a quantitative description of light diffracted by the mesh and mounting supporting the entrance filter, light diffracted by the mesh supporting the filter-wheel filter, as well as light that is diffusely scattered by the microroughness of the mirrors. Deconvolution with this PSF corrects the images for instrumental scattered light, substantially improving image quality and photometric accuracy. First, we determine the diffraction component of the PSF from mechanical drawings of the instrument. We find that 26% of the incoming light is diffracted, predominantly by the entrance-filter mounting and mesh. Second, we fit the diffuse scattered light using partial image occultations during the 2023-Jan-03 Mercury transit. We find that the diffuse scattered light is well described by a softened power law, which scatters 42% of light over the detector. Combined, 57% of the incoming light is redistributed over the detector by diffraction and scattering. Correcting for these effects markedly enhances the dynamic range and contrast of the observations. The intensity in bright structures intensifies by up to 40% and the intensity in dark structures decreases by up to 85 %. All images features become much clearer, facilitating a more precise scientific analysis of HRIEUV observations.

Quantile estimation is central when interest lies in thresholds or tail behavior rather than the mean. When exact measurement is costly but units can be ranked cheaply, ranked set sampling (RSS) provides an attractive alternative to simple random sampling (SRS). We develop two families of RSS-based L-estimators for population quantiles that extend Stigler-type and Harrell--Davis estimators to the RSS framework. The first applies weighted-order-statistic estimation directly to the pooled ordered RSS sample and serves primarily as an exact conceptual benchmark, since its computational burden increases rapidly with the set size. The second exploits a decomposition induced by the RSS design that constructs $k$ pooled transformed-scale component estimators indexed by rank stratum and leads to a computationally scalable procedure. We derive large-sample results for these component estimators under regularity conditions; these results provide a principled first-order motivation for the combined estimators employed in practice. Simulation results across several distributions, quantile levels, and ranking qualities show consistent efficiency gains over empirical quantile estimators under both SRS and RSS, with the RSS Harrell--Davis version performing especially well for moderate and upper quantiles. Beyond the simulation study, we demonstrate the practical relevance of the proposed estimators through an application to NHANES transient elastography data, highlighting their usefulness for estimating clinically meaningful quantiles in a biomedical setting

The dirichletprocess package provides software for creating flexible Dirichlet process objects. Users can perform nonparametric Bayesian analysis using Dirichlet processes without the need to program their own inference algorithms. Instead, the user can utilise our pre-built models or specify their own models whilst allowing the dirichletprocess package to handle the Markov chain Monte Carlo sampling. Our Dirichlet process objects can act as building blocks for a variety of statistical models including: density estimation, clustering and prior distributions in hierarchical models.

We investigate traversable wormhole solutions within a four-dimensional effective theory derived from a five-dimensional Einstein-Maxwell-Chern-Simons action with a non-minimally coupled scalar field. A warped Kaluza-Klein compactification yields an Einstein-frame theory containing a phantom dilaton, a canonical axion, a Maxwell field, and a Kaluza-Klein vector, with the couplings fixed by the higher-dimensional origin. Focusing on the Ellis-Bronnikov geometry, we construct solutions that incorporate both dyonic Maxwell and Kaluza-Klein fields. For exponential gauge couplings, the Einstein equations determine the scalar kinetic term and the combined potentials, while the remaining field equations reduce to algebraic relations fixing the individual potentials and the radial behaviour of the electric charges. We obtain a systematic classification of configurations, ranging from the pure phantom-supported wormhole to fully coupled dilaton-axion-gauge configurations. The Kaluza-Klein sector enriches the solution space with additional structure while preserving analytic tractability. These results show that regular, asymptotically flat traversable four-dimensional wormholes arise naturally from higher-dimensional scalar-tensor theories.

Blazars are promising sources of extragalactic high-energy astrophysical neutrinos, detected at energies $\gtrsim 10$ TeV by the IceCube neutrino observatory. Here, we report the first-ever broadband timing and spectral study of the flat-spectrum radio quasar PKS 1725+123, which has recently emerged as a compelling multimessenger target following its spatial association with the IceCube event IC-201021A. This triggered extensive follow-up observations from radio to VHE $γ$-rays, and a multi-episode flare was identified at a later time. During this period, the source exhibited high flux variability across all wavelengths. The {\it Fermi}-LAT analysis suggests rapid variability on timescales of less than 6 hours, implying a compact emission region with a radius of $\sim10^{16}$ cm. Our one-zone leptohadronic model shows that the high-energy $γ$-ray flux is produced by a combination of inverse-Compton scattering of external photons from the hot accretion disk and the broad-line region, while the X-ray emission is dominated by synchrotron self-Compton radiation from relativistic electrons. The secondary radiation from the hadronic cascade is found to be sub-dominant in the $γ$-ray regime, and the X-ray data constrain the maximum proton energy to $\sim 20$ PeV in the observer frame. Photopion production occurs predominantly with accretion-disk photons, resulting in an estimated muon-neutrino event rate of $\approx 0.3~\mathrm{yr}^{-1}$ during the flaring state with the flux peaking at $\sim1$ PeV. Future observations of TeV $γ$-rays by CTA and LHAASO will further constrain cosmic-ray production in this source.

Empirical process control, a way of managing work based on the observation of the successes or misfortunes of earlier activities, is a key process in Scrum and other agile development frameworks. In this experience report, we present a lightweight, scalable, free and customizable sprint simulation activity designed to teach students how to empirically control a Scrum project by engaging in the presentation and interpretation of work status information, task selection and resource allocations in a single teaching session. We reflect on our experience using the simulation as an active learning complement to direct instruction in two master level courses at two different universities and in the training of teaching assistants at a third institution, and abductively establish its effectiveness by mapping student comments to the teaching practices in the threshold concepts framework.

Data-driven weather models have made rapid advances in recent years, reaching and in some metrics surpassing the large-scale forecast skill of operational numerical weather prediction. This progress, however, has been built almost entirely on the reanalysis data that NWP produced, while the methodological knowledge that the NWP community distilled over decades of multi-scale atmospheric modelling remains largely unused. Here we present Cast3, a generative forecasting framework that systematically absorbs NWP meta-knowledge to close this gap. Cast3 operates on variable-resolution cubed-sphere grids for scale-aware representation and constructs structurally diverse super-ensembles that sample the complementary biases of different grid discretizations, delivering state-of-the-art ensemble prediction. It further introduces generative nudging, a posterior-sampling strategy that distils the collective information of the full ensemble into a single forecast possessing both the large-scale accuracy of the ensemble mean and the mesoscale realism of a high-resolution member. Evaluated across synoptic-scale skill, spectral fidelity, station-level surface verification, and tropical cyclone prediction, Cast3 outperforms established deterministic and generative baselines across various dimensions. More broadly, these results demonstrate that the design principles embedded in computational atmospheric science offer a rich and largely untapped foundation for the next generation of data-driven Earth system modelling.

We present a theoretical model of the ionization-recombination balance in the ultracold Rydberg gas-plasma mixture, which is caused by the collective processes rather than by individual interparticle interactions. This should be well relevant to the steady-state ultracold plasmas obtained in the recent experiment [B. Zelener, et al. Phys. Rev. Lett. 132, 115301 (2024)]. As follows from our calculations, there should be a sharp crossover from the insulating phase (Rydberg gas) to the conducting one (plasma) with increase in the particle density, which closely resembles Mott transition in the condensed-matter physics.

We investigate entanglement dynamics in bipartite systems governed by inhomogeneous Hamiltonians of the form $H = H_L + H_R$, where $H_{L/R}$ acts only on the left or right region and is homogeneous within each region. Focusing on the XX chain and the transverse-field Ising chain, we derive analytical formulas for the entanglement entropy between the two regions in the hydrodynamic limit of long times. In this regime, fermions incident on the interface undergo scattering, generating entanglement between reflected and transmitted modes. The resulting quasiparticle picture is controlled by the transmission coefficient, which we obtain analytically by solving the stationary lattice Schrödinger equation. Due to the bounded dispersion, strong inhomogeneity suppresses both transport and entanglement growth. We benchmark our analytical predictions against numerical simulations in paradigmatic setups. Finally, we extend the analysis to the interacting XXZ chain using tDMRG. The numerical data show qualitative agreement with the quadratic case: entanglement growth remains suppressed in the strongly inhomogeneous limit. Notably, however, entanglement continues to increase even when transport is suppressed, at least at intermediate times.

This study proposes a framework for estimating demand in differentiated product markets with high dimensional product characteristics, building upon the seminal Berry, Levinsohn, and Pakes (1995) model, using market level data. We allow for a very large set of potential product characteristics, where the number of characteristics may exceed the number of market observations. Our contributions are twofold. First, we establish a general estimation theory for BLP models featuring high-dimensional nuisance parameters. We propose a Neyman orthogonal estimator specifically adapted to this framework, utilizing machine learning techniques, such as Lasso, to construct nuisance parameter estimators that are plugged into the Neyman orthogonal estimator. This approach offers a significant advantage: it achieves $\sqrt{T}$-asymptotic normality for parameters of interest--such as the price coefficient and price heterogeneity--even when nuisance parameters are estimated at slower rates due to their high dimensionality. Second, we apply this theory to a specialized BLP model under approximate sparsity, developing an estimation strategy for the high-dimensional nuisance parameters. The approximate sparsity condition posits that nuisance parameters can be controlled, up to a small approximation error, by a small and unknown subset of variables. In an economic context, this implies that while products have a vast array of characteristics, consumers focus on only a small subset of these due to bounded rationality. This condition makes the recovery of parameters of interest feasible by enabling nuisance parameter estimators to converge at the required rates. The practical performance of the method is evaluated through comprehensive Monte Carlo simulations, which demonstrate its efficacy in finite samples.

We study the Witness Set problem, a natural dual to the classical Art Gallery problem. In the Witness Set problem, we are given a polygon $P$ and an integer $k$ as input, and the objective is to determine whether $P$ has a witness set of size at least $k$. A point set $X$ in $P$ is called a witness set if every point in $P$ is visible from at most one point in $X$. For simple polygons, we show that Witness Set lies in both $NP$ and $XP$. This stands in sharp contrast to its dual, the Art Gallery problem, which was recently shown to be $\exists \mathbb{R}$-complete by Abrahamsen et al. and is therefore neither in $NP$ nor admits a polynomial-size discretization unless $NP=\exists \mathbb{R}$. In contrast, we prove that Witness Set for simple polygons admits a finite discretization of size $n^{f(k)}$ for some function $f$. For comparison, even for simple polygons, Efrat and Har-Peled gave an algorithm for Art Gallery running in time $n^{O(k)}$ using tools from real algebraic geometry, and it appears difficult to obtain such algorithms without this machinery. On the other hand, our approach for Witness Set is purely combinatorial and relies on discretization, leading to an $n^{f(k)}$-time algorithm. Although Amit et al. claimed more than fifteen years ago that Witness Set is $NP$-hard, no proof or reference was provided. We show that the discrete version of the Witness Set problem - where the witness set must be chosen from a given finite point set $Q$ (instead of allowing witnesses to be chosen anywhere in the polygon), referred to as Discrete Witness Set - is $NP$-complete, even when the input is restricted to rectilinear polygons with holes. However, for simple polygons, Discrete Witness Set admits a polynomial-time algorithm by Das et al. Thus, it remains an open question whether the Witness Set problem is $NP$-hard.

For quadratic fields \(k=\mathbb{Q}(\sqrt{d})\) with discriminant \(d\), \(3\)-class group \(\mathrm{Cl}_3(k)\simeq (\mathbb{Z}/3\mathbb{Z})^2\), and four \textit{simple} \(3\)-principalization types \(\varkappa(k)\in\lbrace (1122),(3122),(1231),(2231)\rbrace\), we establish necessary and sufficient conditions for the Galois group \(S=\mathrm{Gal}(\mathrm{F}_3^\infty(k)/k)\) of the unramified Hilbert \(3\)-class field tower of \(k\) to coincide with the Galois group \(M=\mathrm{Gal}(\mathrm{F}_3^2(k)/k)\) of the maximal metabelian unramified \(3\)-extension of \(k\). In the case of non-coincidence, we study the path between \(M\) and \(S\) in the descendant tree of the elementary bicyclic \(3\)-group \((\mathbb{Z}/3\mathbb{Z})^2\). For two \textit{complex} \(3\)-principalization types \(\varkappa(k)\in\lbrace (2122),(4231)\rbrace\), we show that infinitely many non-metabelian possible Galois groups \(S=\mathrm{Gal}(\mathrm{F}_3^\infty(k)/k)\) with presumably unbounded derived length \(\mathrm{dl}(S)\) share a common metabelianization \(M=S/S^{\prime\prime}\), whence only partial criteria can be stated. Minimal discriminants \(d>0\) with assigned simple \(3\)-principalization type \(\varkappa(k)\) and fixed length \(\ell_3(k)\in\lbrace 2,3\rbrace\) of the \(3\)-class field tower are determined experimentally for nilpotency class \(\mathrm{cl}(M)\in\lbrace 5,7,9,11\rbrace\) under assumption of the generalized Riemann hypothesis.

Ultra-hot Jupiters present extreme atmospheric phenomena not found in the Solar System. These planets' daysides experience strong temperature inversions, molecular species (including H2) dissociate, and magnetism disrupts their atmospheric circulation. On their nightsides H2 can recombine and clouds may form. Spectroscopic phase curves let us measure these spatially inhomogeneous conditions, which can then be interpreted with three-dimensional (3-D) models. In this work we compare the JWST/NIRISS spectroscopic phase curve of the ultra-hot Jupiter WASP-121 b to state-of-the-art 3-D models with varying modeling assumptions, including the aforementioned physical phenomena. We demonstrate the importance of accurately accounting for the planet's radius in comparison between data and models, as it changes the implied overall planetary emission. We find that the 3-D models predict planet emission $\sim$12% higher than observed, contributing to a continued tension between measured and predicted hot Jupiter albedos. We identify multiple pieces of evidence that confirm a strong source of drag operating in this planet's atmosphere. In addition, the nightside emission spectrum is devoid of strong absorption features, which may be best explained by nightside clouds. One feature of the dataset that is not matched by the 3-D models is a trend of increasing eastward phase offset with decreasing wavelength, for wavelengths shorter than $\sim$1.4 \textmu m. This result is not consistent with reflection from dayside clouds, nor can it be explained by removing atmospheric opacity sources. Our analysis highlights the complexities in generating 3-D models and interpreting observations of ultra-hot Jupiters in the JWST era.

As wireless networks transition toward 6G, high mobility, clustered scattering, and hardware impairments increasingly challenge classical assumptions on channel sparsity, resolvability, and stationarity. In these regimes, performance assessments based on apparent sparsity or nominal delay and Doppler separation can be misleading, since finite observation, sampling granularity, windowing, and fractional delay or Doppler spreading introduce coupling and leakage that reshape the effective channel seen by the receiver. This article provides a signal processing centric framework that links sparsity, resolvability, and selectivity through receiver observable indicators, including the fraction of power captured by dominant coefficients, the level of coefficient correlation, the effective delay and Doppler resolving capability over the observation window, and processing induced leakage. Building on these observations, we propose an interchanged domain frame concept principle, where the representation and the degree of component separation are adapted according to the propagation regime, the effective SNR under impairments, and the application objective. Using the Extended Vehicular A channel profile as a running case study, we show how different representations lead to different equalization and detection behavior, with implications for communication, sensing, and physical layer security.

Waveform evaluation for sixth generation (6G) networks has largely relied on sparse and quasi-stationary channel models that enabled mathematical tractability, diversity gains, and Doppler robustness. However, such models obscure the propagation complexity of dense urban environments, high mobility scenarios, and heterogeneous network deployments. This paper sheds light on a generalized and scalable channel model that incorporates cluster birth-death dynamics, Doppler spectral spreading, time-varying delays, and piecewise local stationarity. Based on this model, the effective input-output relationships of the main 6G waveforms are derived, exposing waveform dependent interference structures that remain hidden under conventional sparse assumptions. Building on these effective channels, a channel-aware waveform prioritization framework is developed based on delay-Doppler resolvability, stationarity conditions, effective signal-to-interference-plus-noise ratio (SINR), and user equipment (UE) cell distribution. Simulation results under the proposed channel model using 3GPP CDL parameters confirm that affine frequency division multiplexing (AFDM) and orthogonal time frequency space (OTFS) retain their spectral efficiency advantage and path combining gains only under sparse, resolvable, stationarity conditions, whereas orthogonal frequency division multiplexing (OFDM) and discrete Fourier transform spread (DFT-s)-OFDM can be both tuned to achieve superior reliability and more stable performance under the proposed channel model.

We develop uniformly fast random variate generators for the Pearson IV distribution that can be used over the entire range of both shape parameters and highlight some applications in a Bayesian setting.

This textbook is drawn from notes for a two-semester graduate course in quantum mechanics. It begins with the most constrained quantum system, and recovers the rest of the subject by relaxing those constraints one at a time. The starting point is a single qubit, the smallest nontrivial Hilbert space with the strongest possible restriction on its dynamics, made concrete by a Bloch cube whose six faces are the cardinal states of a spin-1/2 system. Tensor products admit many qubits; lattices give them a place to live; time evolution sets them in motion; the continuum limit produces wavefunctions; three-dimensional angular momentum, the hydrogen atom, and perturbation theory follow; Lorentz invariance promotes the lattice of spinors to the Dirac equation; and the renormalization group asks how theories at different scales relate. Each chapter loosens one feature of the qubit while keeping the others fixed, so that the standard apparatus of graduate quantum mechanics arrives as a sequence of controlled generalizations rather than as separate topics. Discrete-to-continuous transitions recur at four scales: in Hilbert-space dimension, in real space, in time, and in coupling. The book closes by reimposing one of the original constraints, returning to a two-level system that is now a logical qubit protected by quantum error correction, with the fault-tolerance threshold appearing as an unstable RG fixed point and supplying the reason a logical qubit, independent of its underlying hardware, can exist at all.

Sophisticated Khovanov-Rozansky (KhR) description of knot invariants in the fundamental representation can be reformulated in terms of bicomplex with a simple physical meaning. Namely, the counterintuitive matrix factorization is substituted by simple operators $D$, locally constructed for every MOY resolution of a link diagram, which becomes nilpotent when the diagram has no external lines. Operators for different resolutions are related by equally simple conjugations $χ^{(\pm)}$. The KhR procedure then splits in two steps - defining ``vertical'' cohomologies of $D$, which are associated with particular resolutions and will be put at vertices of the hypercube, and conjugations $χ^{(\pm)}$, that define morphisms along its edges. As usual, standard combinations of morphisms are nilpotent, and one can define ``horizontal'' cohomologies - which are then combined into Poincaré polynomial, called KhR polynomial in application to links. This construction remains global in the sense that resulting cohomologies depend on the entire link diagram, but all its building blocks, including the operators and morphisms are local in the sense that they are defined for its particular vertices. Sometimes, this allows simple local reductions, allowing to eliminate or change particular vertices or sets of those. Along with the obvious case of Reidemeister equivalencies this happens also for antiparallel-lock tangles, what is responsible for simplification of bipartite calculus. In the $N=2$ and arbitrary $N$ bipartite cases, one can also provide global reductions transferring the local construction of the KhR double-complex to the global construction of the Khovanov(-like) single-complex.

Strong light-matter coupling gives rise to polaritons - hybrid excitations whose mixed photonic and matter character enables control over optical, electronic and chemical properties. This Feature Article surveys the main architectures supporting polariton formation, including photonic microcavities, plasmonic nanostructures, open cavities and metasurfaces, and outlines how inorganic semiconductors, organic aggregates and hybrid systems access strong and ultrastrong coupling. Key phenomena such as coherent dynamics, vibronic interactions, dark-state reservoirs and polariton-mediated energy and electron transport are discussed, together with the experimental and theoretical tools used to study them. We highlight examples where strong coupling modifies charge transport, energy flow and chemical reactivity, and we summarize emerging regimes, including intermediate and dark-strong coupling, that broaden the landscape of hybrid light-matter physics.

A vertex in a graph is called central if it minimizes its maximum distance to the other vertices. The radius of a graph $G$ is the largest distance between a central vertex and the other vertices, and it is denoted by $rad(G)$. In the center problem, we are asked to find a central vertex. We study the fine-grained complexity of the center problem on graphs with small Gromov hyperbolicity. Roughly, the Gromov hyperbolicity of a graph represents how close, locally, it is to a tree, from a metric point of view. It has applications in the design of approximation algorithms. In particular, there is a linear-time algorithm that for every $δ$-hyperbolic graph $G$ outputs some vertex at distance at most $rad(G) + 5δ$ to the other vertices [Chepoi et al, SoCG'08]. However, a linear-time algorithm for computing a central vertex is known only for $0$-hyperbolic graphs, whereas its existence was ruled out for $2$-hyperbolic graphs under the Hitting Set Conjecture of [Abboud et al, SODA'16]. Our main contribution in the paper is a linear-time algorithm for computing a central vertex in the class of $\frac 1 2$-hyperbolic graphs. Furthermore, we rule out the existence of such an algorithm for $1$-hyperbolic graphs, under the Hitting Set Conjecture, thus completely settling all the cases left open.

A celebrated theorem by Coven and Hedlund (1973) states that Sturmian words are characterized by their abelian complexity: they are precisely the infinite words with rationally independent letter frequencies and constant abelian complexity equal to 2. In this article, we prove a conjecture of Rauzy (1983), showing that there do not exist infinite ternary words with rationally independent letter frequencies and constant abelian complexity equal to 3.

We study the interior of the Schwarzschild black hole which is isometric to the Kantowski-Sachs cosmological model, using a fully relational and gauge-invariant quantization framework. The physical Hilbert space is constructed via refined algebraic quantization, and quantum dynamics is recovered through the Page-Wootters formalism with a covariant POVM clock built from one of the two configuration variables, whose Hamiltonian is proportional to the momentum of the said variable. Gauge-invariant relational observables for the area of 2-spheres, the Kretschmann scalar, and the expansion scalar of null geodesic are constructed via group averaging (G-twirl) and evaluated on physical states. We find that the Kretschmann and expansion scalars remain finite throughout the black hole, while the area of 2-spheres is bounded below by a minimum value proportional to the uncertainty in the system variable, which is the other configuration variable distinct from the clock variable. In particular, the expansion scalar vanishes and changes sign at the quantum bounce, establishing a black-hole-to-white-hole transition. These results hold for any general clock whose operator forms a canonical pair with the clock Hamiltonian, and require no specific quantization scheme other than the Schrodinger representation. The singularity resolution emerges directly from relationality, the Heisenberg uncertainty principle, and the structure of the physical Hilbert space.

The march toward developing relevant and robust CPU benchmarks continues with the introduction of SPEC CPU 2026, the next generation suite for measuring processor performance. This paper details the methodology behind its creation, showcasing a process centered on community collaboration and principled development. The suite is built upon a foundation of modern, open-source applications, selected and hardened through a process that emphasizes workload diversity, portability, and software longevity. A key contribution is Rolling-Round-Robin Rate, a novel and standardized approach to running heterogeneous, multiprogrammed workloads that addresses a long-standing gap in benchmarking practice. Additionally, the suite features an expanded set of multithreaded benchmarks and introduces workloads with distinct microarchitectural profiles, reflecting the demands of contemporary software. By detailing our principled approach to benchmark selection, adaptation, and validation, we demonstrate how the SPEC CPU 2026 suite sets the standard for performance evaluation in the next era of computer architecture research and development.

The atomic nucleus, viewed as a system of bound quarks, should, in principle, be described within an effective theory of low-energy quantum chromodynamics. This paper provides an overview of recently developed models that embody essential features of the desired effective theory. The Fermi gas model helps explain why the number of $d$ quarks is approximately equal to that of $u$ quarks in stable light nuclei up to ${\rm {}^{40}_{20}Ca}$. A modified bag model accounts for the deviation from this rule in heavier nuclei. With this model, the static properties of a wide range of stable nuclei can be described with reasonable accuracy. To make the most of the modified bag model, it is useful to invoke gauge/gravity duality. A refined version of duality states: ``The dynamics inside an extremal black hole in ${\rm AdS}_5$ is mapped onto the corresponding dynamics of a stable subnuclear system in ${\mathbb R}_{1,3}$''. This version of duality allows one to predict the primary decay channel of the lightest glueball. Another implication is that this framework explains why the periodic table contains a finite number of stable elements. Duality makes it possible to calculate the maximum allowed charge $Z_{\rm max}$ of stable heavy nuclei: $Z_{\rm max}\approx 82$, which is the charge of the ${\rm {}^{208}_{82}Pb}$ nucleus.

In this paper, we study polynomial chaoses of degree $d$ constructed from sequences of functions; that is, sets of all possible $d$-fold products of sequence elements, allowing repeated factors. The tetrahedral chaos of degree $d$ is defined as the subset consisting of products with pairwise distinct factors. We prove that polynomial $d$-chaoses (and, consequently, the tetrahedral chaoses) with respect to $d$-dissociated subsystems of characters on compact abelian groups are $q$-lacunary and $2d/(d+1)$-Sidon systems.

This study develops a functional Liu-type shrinkage estimator (fLiu) for scalar-on-function regression in the presence of strong multicollinearity and high-dimensional functional predictors. The approach extends the classical Liu estimator to the functional setting by combining directional shrinkage with smoothness regularization, providing flexible control over the bias-variance trade-off. Theoretical analysis is used to examine the behavior of the estimator and the associated parameter selection problem. In particular, an explicit mean squared error (MSE) decomposition is derived, characterizing the risk of the estimator in terms of variance reduction and shrinkage bias. This further yields an explicit optimal choice of the shrinkage parameter of the fLiu estimator through a one-dimensional convex risk minimization problem, leading to a practical plug-in tuning rule. Moreover, it is shown that in high-dimensional (underdetermined) settings, commonly used criterion such as GCV (and equivalently PRESS/LOO-CV) become constant with respect to the parameter d, thus uninformative for tuning. This provides a theoretical explanation for the predominant focus on the overdetermined regime in existing Liu-type methods. Numerical results demonstrate that the estimator achieves competitive predictive accuracy relative to existing methods. Implementation is carried out in R using the fda package, and in Python via the fLiu.py package developed for this study.

Faster-than-Nyquist (FTN) signalling has emerged as a compelling technique for enhancing spectral efficiency in bandwidth-constrained communication systems. By intentionally introducing controlled intersymbol interference (ISI), FTN allows transmission at rates exceeding the traditional Nyquist limit, unlocking new potential in high-speed data communication. However, its practical deployment remains challenged by the need for low-complexity detection strategies that can cope with the induced ISI while maintaining low latency and robust performance. We propose deep learning receivers that are resilient to non-idealities. In this paper, we present a deep learning-based framework for FTN signalling that addresses these challenges through several novel contributions. First, we propose a sliding window detection method that leverages temporal context while preserving computational efficiency. Second, we demonstrate the viability of FTN systems with very low packing factors, showing that reliable performance can be achieved even under aggressive spectral compression (up to 75\%). Our architecture is optimised for low latency and low complexity, making it suitable for real-time applications and scalable deployment. In addition, we assess the robustness of our models across varying channel conditions and noise profiles, providing insights into their generalisability and resilience.

Virtual Private Networks (VPNs) have become essential privacy tools for mobile users, yet current implementations face significant limitations in shared environments. Mainstream VPN providers impose device limits, while Android's native hotspot functionality lacks support for routing shared traffic through VPN connections. Existing solutions either require root access or lack comprehensive monitoring capabilities. This paper presents ShieldShare, a proxy-based Android application that enables secure VPN-backed hotspot sharing with per-user traffic accounting without requiring root access. Our system employs a modular architecture comprising VPN detection, hotspot management, proxy-based traffic forwarding supporting HTTP, HTTPS, and SOCKS5, and comprehensive traffic metering with quota management. Our evaluation shows that ShieldShare reliably routes client traffic through VPN tunnels while maintaining accurate per-client bandwidth allocation and accounting. This enables affordable, community-controlled secure access in censored or high-surveillance environments, benefiting activists, investigative journalists, and shared household networks. We release ShieldShare as open-source software to support further research and real-world deployment.