Modern package designs make use of technologies such as backside power delivery (BSPD) and 3D stacked chiplets that require accounting for the heterogeneity in back end of the line (BEOL) structures in hot-spot prediction. Multiscale homogenization strategies have been demonstrated to be effective for steady-state simulations, however accurate 3D transient simulations that include BEOL structures remain an open challenge. In this work, we demonstrate a transient thermal workflow that accounts for the 3D heterogeneous structures in the BEOL for problems with strong- and weak- temporal scale separation under the assumption of temperature independent constitutive properties. Our workflow, based on Bloomfield et. al. 2025, automatically extracts, meshes, and homogenizes thermal properties from GDSII and OASIS files to construct thermal property maps. Property maps (heat capacity and conductivity) have been generated for a 1 mm by 1 mm SoC-style model die that was constructed with LibreLane for 100 by 100 grids with 5 micron by 5 micron representative volume elements (RVEs), and 50 by 50 grids with 10 micron by 10 micron RVEs. The expressions for a transient effective conductivity are provided and a demonstration of the impact of the transient effects are provided for a single RVE. Finally, transient conductivity maps have been provided for a time integration timestep of dt=0.001.

In Riemannian optimization, it is well known that the condition number of the Riemannian Hessian at an optimum strongly influences the asymptotic convergence behavior of optimization algorithms. On the manifold of symmetric positive definite (SPD) matrices, several commonly used metrics for optimization, such as the Affine-Invariant (AI) and Bures--Wasserstein (BW) metrics, tend to become ill-conditioned as the underlying SPD matrix becomes ill-conditioned. As a result, even when the Euclidean Hessian remains uniformly well-conditioned on the SPD manifold, optimization may still become difficult near an optimum associated with an ill-conditioned SPD matrix. In this paper, we address this issue through the Alpha-Procrustes (AP) geometry on the SPD manifold. This geometry generalizes several well-known metrics, including the Log-Euclidean (LE) metric for \(α=0\) and the BW metric for \(α=1/2\). We first show that, when \(α=1\), all eigenvalues of the Riemannian metric operator induced by the AP geometry are uniformly bounded independently of the underlying SPD matrix. Therefore, under the assumption that the Euclidean Hessian satisfies the uniform spectral bounds, all the eigenvalues of the corresponding Riemannian Hessian are uniformly bounded independently of the underlying SPD matrix. Consequently, the case \(α=1\) provides a robust geometric framework for several Riemannian optimization problems involving ill-conditioned SPD matrices. Finally, we validate our theoretical findings through extensive numerical experiments across a range of applications.

Classical flocking models demonstrate how local interactions generate emergent order, but real-world multi-agent deployments are bound by severe constraints: limited actuator availability, heterogeneous communication latencies, and environmental noise. In this talk, we present a unified finite-N framework that tackles the interplay of these exact mechanisms. We study a delayed stochastic leader-follower particle system featuring topological communication, singular repulsion, and bounded sparse leader actuation. A central challenge in such systems is mathematical well-posedness, as discontinuous communication laws and singular repulsions clash with standard strong Ito frameworks. We resolve this by introducing an augmented Lyapunov functional that simultaneously enforces a strict collision barrier and closes a uniform Gronwall estimate. Building on this rigorous foundation, we formulate a free-terminal-time, chance-constrained optimal control problem. We show that temporally sparse, bang-off-bang leader actuation not only drastically reduces control effort compared to continuous baselines, but also reveals non-monotone sensitivities to leader density. Ultimately, we demonstrate that in delayed stochastic swarms, adding more direct actuation is not strictly optimal -- highlighting a highly non-trivial resource allocation paradox in cooperative control.

The physics governing the boundary between the most massive neutron stars (NSs) and the least massive black holes (BHs) is currently uncertain, but could potentially be constrained with new observations. While NSs have been observed with masses up to $\sim2~M_{\odot}$, there is a dearth of electromagnetic observations of compact objects in the $\sim2-5~M_{\odot}$ range, known as the lower mass gap. Recent observations of gravitational-wave (GW) signals from binary mergers detected by the LIGO-Virgo-KAGRA (LVK) collaboration indicate that this gap is likely not empty. Rapidly distinguishing whether a candidate GW event has components in this purported mass gap can indicate the likelihood of a detectable electromagnetic counterpart, and thus inform decisions for follow-up observations. In this work we train a neural network model, GWSkyNet-MassGap, that simultaneously predicts the probability that a candidate merger has a component in the lower mass gap ($P_{\mathrm{MassGap}}$) and the probability that it involves a NS ($P_{\mathrm{NS}}$). We find that the model is able to infer information about the source chirp mass to predict $P_{\mathrm{MassGap}}$ and $P_{\mathrm{NS}}$, leading to correct predictions for high-mass mergers with $\mathcal{M}_c\gtrsim15~M_{\odot}$, but less accurate predictions for lower-mass systems which require knowledge of the binary mass ratio to break the mass degeneracy. For candidate events in the first part of LVK's fourth observing run (O4a), the model has a mean prediction error of 9% for $P_{\mathrm{MassGap}}$ and 6% for $P_{\mathrm{NS}}$. The model could be further developed to rapidly predict the source chirp mass for candidate events in future observing runs.

We present a systematic introduction to first-order optimality conditions for mathematical programs with equilibrium constraints (MPECs), emphasizing the limitations of classical nonlinear programming techniques. The goal is twofold. First, we explain why a direct application of standard optimality conditions -- based on reformulating MPECs via KKT systems or differentiable exact penalty functions -- is often inadequate, as such approaches typically require strong and restrictive assumptions, including nondegeneracy and smoothness conditions. Second, we develop a first-principles framework for analyzing MPECs by focusing on the geometric structure of the feasible region. In particular, we study stationarity concepts and provide a detailed characterization of the tangent cone at feasible points, which leads to appropriate constraint qualifications tailored to MPECs. These results form the foundation for rigorous first-order analysis and clarify the relationship between the original MPEC formulation and its KKT-based representation, offering practical guidance for handling these inherently challenging optimization problems.

We present a focused introduction to exact penalty methods for nonlinear programs and mathematical programs with equilibrium constraints (MPECs), emphasizing their connection to modern error bound theory. The goal is twofold. First, we explain how classical optimality conditions can be interpreted through exact penalization, and why such results typically rely on constraint regularity conditions that can be understood as error bounds on perturbations of feasible sets. We then highlight how recent developments based on subanalytic geometry and Lojasiewicz-type inequalities extend this framework beyond classical regularity assumptions, enabling exact penalization under broader analytic conditions. Second, we demonstrate how this theory can be applied in practice to MPECs by reformulating them via KKT systems and constructing exact penalty functions based on residual mappings. Particular attention is given to fractional-order penalties arising from Lojasiewicz error bounds, as well as to improved formulations for special problem classes where sharper exponents can be obtained. These developments provide both theoretical insight and practical guidance for analyzing and solving challenging constrained optimization problems.

Our aim is to explain mathematical programs with equilibrium constraints (MPECs), motivate them through applications, present the main equivalent formulations of equilibrium constraints, and summarize the basic existence theory for optimal solutions. The central message is that an MPEC is an optimization problem whose feasible set is partly defined by another optimization, variational inequality, complementarity system, or equilibrium model.

The study of black hole thermodynamics becomes a central topic in gravitational physics, where the first law and the Smarr relation establish a deep connection between spacetime geometry and thermodynamic laws. As we know, these relations depend on the entropy; any modification to the entropy arising from quantum gravity or generalized statistical mechanics may impact the basic thermodynamic framework of black holes. In this work, we develop a general framework for deriving the first law of black hole thermodynamics and the associated Smarr relation for generic spherically symmetric spacetime under a wide class of generalized entropy models. In addition, a generalized Ruppeiner thermodynamic geometry is developed to utilize the generalized entropy model, from which the curvature scalar is determined in a general form. To demonstrate this framework, we assume the Resinser-Nordström black hole and investigate the corresponding extremal and non-extremal phase transition. Interestingly, our analysis reveals that entropy models consistent with the Abè-type composition rule result in a vanishing thermodynamic curvature, whereas violations of this rule exhibit curvature divergences, suggesting a geometric test for the consistency of generalized entropy models.

The hybrid approach to experimental design aims to control frequentist operating characteristics of Bayesian decision procedures. These operating characteristics are assessed by simulating sampling distributions of posterior summaries under assumed data-generation processes that also define posterior distributions. Model misspecification can distort effect estimation and compromise control over operating characteristics. Generalized posterior distributions are defined using generalized likelihoods that characterize data generation under fewer assumptions, enhancing the robustness of Bayesian analysis and study design. However, widely applicable and computationally efficient design methodology with generalized posteriors is lacking. We propose an economical method to determine suitable sample sizes and decision criteria associated with generalized posteriors under the hybrid approach. Using theoretical results to model posterior summaries as functions of the sample size, we efficiently assess operating characteristics throughout the sample size space given simulations conducted at only two sample sizes. While the benefits of the proposed methodology are emphasized by redesigning an adaptive clinical trial with time-to-event outcomes, we overview our framework's broader applicability to experiments involving Bayesian analogues to M-estimation.

Level 3 automated vehicles (AVs) issue a request to intervene (RtI) when the automated driving system approaches its system limitations. Although this takeover transition is safety-critical, it is usually invisible to surrounding manually driven vehicle (MV) drivers. This study proposes an external human-machine interface (eHMI) called eHMI C+O that externalizes the RtI-related takeover status of a Level~3 AV using cyan and orange light bars. A driving-simulator experiment with 40 participants examined whether the proposed eHMI supports surrounding MV drivers during AV takeover scenarios. The results showed that, compared with the ADS-status-only eHMI condition, which is similar to ``Automated Driving Marker Lights,'' and the no-eHMI condition, the proposed eHMI C+O significantly improved participants' understanding of the AV's driving intention, their prediction of its behavior, and their perceived sufficiency of the information presented by the AV. It also reduced hesitation, increased confidence, and promoted earlier and larger increases in time headway after the RtI was issued. In the AV accident scenario, eHMI C+O significantly reduced the odds of accident involvement for the following MV compared with the no-eHMI condition, corresponding to a 76.8% reduction in accident odds. Exploratory path analysis suggested that the safety benefit of the proposed eHMI C+O may be associated with improved situation awareness and earlier defensive driving responses. These findings indicate that externalizing RtI-related takeover status can help surrounding drivers better understand Level 3 AVs and respond more safely during safety-critical takeover transitions.

Maximum distance separable (MDS) array codes constitute an important class of error-correcting codes due to their optimal distance properties and their relevance in distributed storage systems. In this paper, we investigate the construction and decoding of MDS array codes over $\mathbb{F}_q^b$ based on superregular matrices, with emphasis on superregular Vandermonde and Cauchy matrices. We propose decoding algorithms for [n,k,d] MDS array codes, where n=m+k and d=m+1, capable of correcting symbol errors without prior knowledge of their locations. Unlike existing approaches restricted to specific parameter settings, the proposed algorithms apply to general configurations and rely on algebraic relations that do not follow from straightforward extensions of previous methods. Specifically, these algorithms correct one symbol error for $m \geq 2$ and two symbol errors for $m \geq 4$. For the two-error case, the decoding procedure admits a simplified form when Vandermonde superregular matrices are employed, reducing computational complexity. We analyze the algebraic structure of the three-symbol-error case, focusing on the most involved configuration in which all errors occur in information symbols, and we discuss how the method may be extended to the general case. These algorithms are computationally efficient for moderate parameter sizes, as they rely on structured algebraic operations over $\mathbb{F}_q^b$ and the solution of small linear systems, making them suitable for distributed storage applications. From an application perspective, the proposed approach provides a flexible alternative to RAID~6 schemes. Unlike RAID~6, which is limited to two parity disks and often requires prior knowledge of error locations, our construction supports general configurations and enables the correction of multiple symbol errors without location information, at the cost of increased algebraic complexity

Fast radio bursts (FRBs), highly polarized, mostly have a nearly constant polarization position angle (PA) during each burst. Their PAs are observed to vary from burst to burst, with the statistical properties remaining stable across different observation sessions. We found that the intrinsic PAs of repeating FRBs are approximately Gaussian distributed, suggesting that the emission likely originates from a localized region within the neutron star's magnetosphere. A periodicity search of the PA time series using the Lomb-Scargle periodogram reveals no credible periodic signal in the period range from 10 ms to $10^7$ ms, and similar analyses of several active observations also yield null detections. We interpret these properties by extending the rotating vector model to include a dynamically evolving magnetosphere, in which the effective magnetic axis varies from burst to burst due to stochastic perturbations. In this framework, the observed PA distributions can naturally arise from geometric projection effects, and the absence of periodicity reflects the random wandering of the magnetic axis within a confined region. This scenario provides a natural explanation for both repeating and apparently non-repeating FRBs.

Australia's social media ban is now in force. It requires platforms to take reasonable steps to stop users under 16 from holding accounts. Drawing on five focus groups with fifteen young people aged 12--16, this paper examines how children understood the ban's effectiveness, impact, and legitimacy as they encountered the platforms charged with enforcing it. Participants widely saw the ban as unfair and ineffective. Through platform access controls, they learned how the ban worked, where it failed, and how they and their peers could evade it. We also asked participants to imagine better approaches to age verification and youth digital governance. This paper develops sneaking as a theoretical lens for these practices. The concept names more than evasion: it captures the social encounter between children, platforms, techno-regulation, and the access controls that mediate digital participation. Our findings show that children are not passive subjects of platform regulation. They interpret, test, and negotiate digital infrastructure. They also expose a central weakness in age-based platform regulation: technological controls struggle to solve the social and governance problems they are asked to contain.

We study likelihood-based inference for the anisotropic hyperbolic wrapped normal distribution on standard hyperbolic space. The model has a manifold-valued location parameter and a full positive definite covariance matrix in tangent coordinates. For independent observations from this family, we analyze the profile maximum likelihood estimator obtained by optimizing the likelihood over the location after profiling out the covariance. To guarantee finite-sample existence, we formulate the estimator on a covariance shell that bounds eigenvalues away from zero and infinity. We prove that this constrained likelihood is well posed, that the anisotropic wrapped normal family is identifiable, and that the estimator is strongly consistent when the true covariance lies in the interior of the shell. In global normal coordinates for the location and log-covariance coordinates for the nuisance parameter, we establish joint asymptotic normality and derive efficient profile inference for the location parameter through the Schur-complement information. We further prove local asymptotic normality of the experiment and obtain the Hájek--Le Cam local asymptotic minimax lower bound under squared geodesic loss. The profile estimator attains this bound for truncated squared loss, and for ordinary squared loss under a uniform-integrability condition. We also give an explicit computational form of the estimator based on spectral clipping of the empirical tangent covariance, and present a Monte Carlo calibration study showing that the finite-sample scaled location risk and Wald coverage agree with the asymptotic theory.

We investigate nonlocal transport in single-layer Ti Hall bars to explore signatures of orbital-current transport driven by the orbital Hall effect. Despite the negligible spin Hall effect in Ti, we observe a finite nonlocal resistance in the single-layer Ti Hall bar and study its dependence on the central channel width. Finite-element simulations show that the measured signal contains a sizable Ohmic bypass contribution. However, the bypass contribution is strongly suppressed at small channel widths and cannot fully account for the observed nonlocal resistance even when variations in the Ti resistivity are taken into account. Our results therefore suggest an additional nonlocal contribution distinct from the Ohmic bypass background, which may be associated with orbital transport driven by the orbital Hall effect in Ti.

Attitudes about artificial intelligence and machine learning are recent victims of endemic misunderstanding; given our increasing reliance on these technologies, the need for widespread understanding and confidence in their use is paramount. To this end, our work seeks to increase understanding in these typically inaccessible topics through interactive visualizations, thereby garnering curiosity in the hopes of kickstarting a cycle of understanding leading to further pursuit of knowledge. We hope this will cyclically shift global attitudes away from the intimidation of the unknown currently plaguing ML. This work explores best practices for supporting curiosity in new technologies, to inspire attitudinal paradigm-shifts. Over three, distinct visualizations of machine learning data, we created prototypes with carefully selected, highly-transparent datasets, to examine the success factors of engagement required for more informed attitudes on ML less dictated by the fear of the unknown. By employing interactive visualizations, we can captivate the interest of teenagers and individuals from diverse fields, encouraging them to explore the fascinating world of machine learning.

For a normal surface singularity, the discrepancy between the ordinary and dual middle-perversity intersection complexes over \(\mathbb Z\) is measured by a finite group \(E\). In previous work, \(E\) was identified with link torsion, the exceptional-lattice discriminant group \(Λ^\vee/Λ\), a resolution-neighborhood boundary quotient, and, in the hypersurface case, \(\operatorname{coker}(T-\mathrm{id})_{\mathrm{tors}}\). This paper tracks the trajectory of this torsion from local singularity data to global obstruction theory. We follow the discriminant package \((E,q)\) through support cohomology, excision, global torsion, Brauer comparison, Bloch--Ogus residues, and rationalization. The method is example-driven: trajectory tables are computed for \(A_1\), \(A_k\), \(D_4\), \(E_8\), a non-ADE Brieskorn singularity, the threefold ordinary double point, nodal threefolds, nodal quintics, and the Benoist--Ottem benchmark. The computations reveal a sharp distinction: a surface \(A_1\) singularity has local \(\mathbb Z/2\)-torsion, whereas a threefold ordinary double point has torsion-free link \(S^2\times S^3\) and contributes free vanishing-cycle data instead. Thus finite discriminant torsion is naturally a codimension-two phenomenon, not a generic feature of nodes. The resulting pattern motivates a specialization problem: whether the Enriques \(2\)-torsion in Benoist--Ottem integral Hodge counterexamples is genuinely global, or can arise after degeneration from transverse \(A_1\)-type discriminant data along codimension-two strata.

Contrastive learning is a core component of modern retrieval systems, but its effectiveness heavily relies on the quality of negative examples used during training. In this work, we present a systematic approach to improving dense retrieval for IKEA product search through structured negative sampling strategies and scalable LLM-as-a-judge relevance evaluation. Building on IKEA Search Engine's late-interaction retrieval architectures, we introduce two key contributions: (1) structured negative sampling strategies that leverage product hierarchical taxonomy and product attributes to generate semantically challenging negatives, and (2) a comprehensive LLM-based evaluation methodology for generating training data. Rather than relying on sparse human annotations or random sampling, our LLM-based evaluation system allocates a score for all candidate products against each query. Our methodology achieves +2.6\% average category accuracy on offline real user query experiments on the Canada market. However, our A/B test on long-tail queries showed no statistically significant differences in user engagement metrics between the improved and baseline models ($p > 0.05$). We trace this gap to user search behavior: 67\% of popular searches exhibit zero-click rates above 50\%, indicating that a substantial proportion of search sessions result in no product engagement regardless of result ranking. These findings underscore the importance of hard negative mining but also the need for grounding training data and offline evals in real user search behavior -- including query intent distribution and zero-click patterns -- to bridge the gap between offline retrieval quality and online user engagement.

Modern organizations increasingly rely on log data and monitoring signals to protect products against account takeovers and abuse, yet integrating security analytics into fast-moving Agile workflows remains challenging. While it is important to understand how security practices are developed and sustained within Agile, real-world case studies of such integrations remain scarce. This experience report provides insights on developer perceptions of an effort to integrate log-based fraud detection within an organization, known as the "Red Flag Project". A cross-functional team of eight members (including one author) iterated weekly to implement a proof-of-concept log-based system that alerts stakeholders when accounts exhibit suspicious activity patterns. Through semi-structured interviews, we investigate developer perceptions of log-based fraud detection integration-exploring their willingness to adopt the system, challenges encountered, and the overall impact on day-to-day development activities and security perceptions. Our findings highlight key lessons, mitigation techniques, and best practices for embedding security analytics into Agile workflows. We provide insights for practitioners and researchers seeking to incorporate security practices into modern development processes while maintaining both speed and resilience in software delivery.

Precession is a very common phenomenon for small-scale astronomical objects. However, the precession of galactic disks, occurring on a scale larger than kilo-parsec, has barely been studied in the literature. Quantifying this precession in observations remains challenging due to the lack of high-resolution dynamical data. Cosmological simulations, where gravitational interactions are self-consistently modeled, offer a unique avenue for investigating disk precession. Leveraging the IllustrisTNG simulations, we trace the evolution of spin orientation in Milky Way-like galaxies over cosmic time. We find that disk precession is ubiquitous in galaxies and significantly affects galaxy evolution. The precession is driven by the external tidal torque originating from the anisotropic matter distribution within $30\ \mathrm{kpc}$, and is violent at $\mathrm{z} > 1$ and becomes gentler but significant at $\mathrm{z} \sim 0$, when the disks are considered dynamically settled. Disk precession can induce significant cold gas warp, which is often observed in the Milky Way and nearby galaxies. We predict that the Milky Way is precessing at a rate of $\simeq3-10$ degrees per billion years at current epoch based on its observed warp. Violent precession can heat the orbits of stars, which may eventually produce prolate elliptical galaxies. The tidal torque from central galaxies can cause the precession of nearby satellite galaxies and causes their disks to point towards the centrals, which explains the observational radial alignment. We also find that the precession of accreted cold gas stream, regulated by the galaxies' torque, is crucial for the evolution of disk galaxies.

We extend two results known for aspherical 3-manifolds to $PD_3$-pairs $(P,\partial{P})$ with aspherical ambient space $P$. Every such $PD_3$-pair may be assembled by attaching 1-handles to $PD_3$-pairs with aspherical; ambient space and $π_1$-injective boundary. (Thus the study of such pairs reduces to the study of $PD_3$-pairs of groups.) If $π$ is a group of type $FP$ whose indecomposable factors $G$ each have $χ(G_i)=0$ then there are only finitely many such $PD_3$-pairs with $π_1(P)\congπ$.

We investigate the properties of known RR Lyrae in the Vera C. Rubin Observatory Data Preview 1 (DP1) fields and compare those with the predictions based on stellar pulsation models tailored to the Legacy Survey of Space and Time (LSST) filters. The cross-match of the DP1 data with two public variable star catalogs resulted in $\sim 600$ RR Lyrae with adequate light curve sampling in five (out of seven) DP1 fields. The majority of RR Lyrae are in the 47 Tucanae and Fornax fields. We estimated photometric metallicities for these RR Lyrae using the theoretical metallicity-color relation based on $gri$-band data, and find a good agreement with literature values where the light curve sampling is sufficient for fitting template light curves accurately. The distance modulus to all RR Lyrae in DP1 fields were determined using the theoretical period-luminosity-metallicity (PLZ) relations and the $W_{gr}$ period-Wesenheit-metallicity (PWZ) relation which has the smallest metallicity term. The distances based on PWZ relations are in good agreement with the literature values with a mean offset of $0.01\pm0.36$~mag. However, the PLZ-based distance moduli are systematically large which could be due to the theoretical calibration uncertainties that include evolved horizontal branch models. The predicted period-amplitude relations based on evolved models are also inconsistent with the amplitudes based on DP1 light curves. We conclude that the metallicity and distance estimates are sensitive to the template fitting to sparsely sampled light curves in DP1 data and future data release will significantly improve these determinations for RR Lyrae stars.

We introduce a hierarchical algorithm for identifying the largest Pauli coefficients of an unknown $n$-qubit quantum state. The algorithm traverses a prefix-based tree whose nodes represent partial sums of squared Pauli coefficients, always expanding branches with the largest estimated weight and discarding the rest. Node weights are estimated using Bell sampling on two copies of the state, or alternatively via SWAP tests on subsystems. We analyze the sample complexity of each node estimation and derive bounds on the total number of nodes expanded as a function of the desired number of coefficients and the state's purity. For states admitting a sparse representation in the Pauli basis, the algorithm achieves a good reconstruction of the dominant components without requiring full state tomography. We validate the method with numerical simulations on Pauli-singleton states and random stabilizer states, showing that the algorithm's performance is competitive with other methods for structured states. Our work addresses an open problem in Pauli sampling and provides a practical tool for the targeted characterization of structured quantum states.

The medium of exchange of the traditional economy is mainly the fiat currency of each country or region, and when cross-border transactions occur, they need to be settled according to the exchange rate. In the AI world, however, the medium of exchange tends to be a globally recognized currency. Especially when AI acts as an agent for cross-border capital pool and cross cyclical asset allocation, it needs a sound money that can resist the depreciation of fiat currency and store long-term value. Therefore, we propose a globally consensus and universally accepted monetary rule framework for the AI era. The devaluation of money runs through almost the whole process of history, from the weight reduction and purity decrease of metallic coin to the unanchored over-issuance of paper currency. Whether it is the periodic compulsory recoinage in medieval Europe or Gesell's stamp scrip, both are essentially mechanisms for taxing money holdings. Unlike Gesell's stamp scrip, Redeemable Self-Decaying/Devaluing Money (RSDM) is a tokenized commodity money. Its essential innovation is to fill the hole in the storage fee of metal coins through the self-devaluing of metal weight recorded on the deposit certificate (warehouse receipt) of metal coins. In a sense, RSDM is an innovative version of Jiaozi (a deposit receipt for base metal coin that emerged in Sichuan, China, about a thousand years ago). In this paper, we propose five forms of online and offline issuance of RSDM, providing a prototype for creating a globally recognized modern honest money.

The strong interaction is the fundamental force that holds quarks and the gluon force carriers together to form protons and neutrons and also binds the atomic nucleus. The theory governing quark-gluon interactions is Quantum Chromodynamics (QCD). A wide variety of experimental data teaches us that quarks and gluons cannot be observed in isolation, a phenomenon known as confinement that is unique to QCD. But no one has used QCD to mathematically prove confinement. Here we show how to define and measure the force on quarks in the proton using available experimental data. Direct evidence for confinement is obtained because the force is found to be attractive and constant for a wide range of quark positions. This work guides future experimental efforts at future Electron-Ion Colliders aimed at obtaining a rigorous quantitative understanding of confinement and the origin of nuclear mass.

Owing to the radiation-force-induced nonlinearity, cavity optomechanical systems (COMS) exhibit dynamical phenomena such as back-action induced oscillation, chaos, mechanical amplitude locking, and anomalous stabilization, which occur under different driving conditions and different system parameters. We here identify a previously unknown dynamical pattern of staircase evolution for the energy of mechanical resonator, when a COMS with neither very large nor very small built-in mechanical frequency is driven by a two-tone field, which satisfies a condition that the frequency difference of the two tones matches the built-in mechanical frequency. The properties of this phenomenon are analyzed for the different system parameters due to fabrication such as mechanical frequencies and quality factors, as well as under the varied driving conditions such as unequal drive tone powers and mismatched drive tone difference from the mechanical frequency. Some special features, such as an emergent bifurcation due to the tone power difference, together with the totally different responses of the system to the drive tone mismatches of opposite signs, are discovered to exist only in this type of COMS with median mechanical frequencies. This work fills a gap in the study of the dynamics of COMS under two-tone drives. In the aspect of applications, the rapid increase of mechanical energy exhibited in the phenomenon promises phonon laser generation, and the sensitive dynamical response to the drive tone mismatches offers a potential approach to high-precision sensing.

Finger-type convection in double-diffusive instability (DDI) controls mixing and scalar transport in many stratified flows, yet a quantitative, finger-resolved description of the transient growth, transport, and saturation pathways has been limited. Here, finger-type DDI is analyzed in a sealed-surface laboratory facility using synchronized planar laser-induced fluorescence (PLIF) and particle image velocimetry (PIV) at fixed thermal contrast $ΔT=5^\circ$C and three salinity contrasts, $ΔS=350$, 450, and 550 ppm, complemented by a matched high-resolution three-dimensional DNS. A systematic fingertip detection and tracking framework generates ensemble growth curves. Fingertip growth follows a sequence of three stages (acceleration, quasi-steady propagation, and decay). The peak growth rates increase monotonically with $ΔS$, and nondimensional fingertip-height histories collapse onto a common trend. The peak growth rates are reproduced by DNS and agree with linear stability analysis, establishing experiment--DNS--theory consistency in the intermediate regime. The mixed-material area increases with time, initially following a common nondimensional trend before transitioning to $ΔS$-dependent interaction and breakdown. Finger-scale measurements reveal the formation of a symmetric vortex ring at the fingertips for $ΔS=450$ ppm, inducing vertical-aligned transport. At $ΔS=550$ ppm the roll-up becomes asymmetric: stronger buoyancy amplifies shear, destabilizes the vortex ring, and produces a zig-zag/lateral-drift mode that enhances the lateral transport. Finally, the evolution of the buoyancy anomaly links the growth-rate phases to a time-dependent force balance in which increasing buoyancy drives acceleration, shear-induced resistance regulates quasi-steady propagation, and dilution with top-boundary influence yields late-stage fingertip deceleration.

We consider joint inversion for two or more unknown parameters from observational data in the Bayesian framework. Standard approaches often either treat the parameters as independent or impose structural similarity through regularisation terms that can be difficult to interpret statistically. We instead construct jointly Gaussian prior models with prescribed Gaussian marginals, so that correlation between the parameters can be incorporated without altering the marginal prior distributions. We propose a joint covariance construction that preserves the marginals, allows spatially varying cross-correlation, and supports uncertainty and inference in the correlation itself. The construction is valid for any strict contraction encoding the desired cross-correlation and is optimal in a canonical correlation sense under the principal square root factorisation. We demonstrate the method using prior sampling and several inference examples: a low-dimensional illustrative example and two higher-dimensional examples, including a PDE-constrained problem. The examples highlight both the potential pitfalls of ignoring or neglecting uncertainty in the correlation as well as reinforcing a key principle of the Bayesian paradigm: unknown quantities included in a model should be treated as random variables.

The canonical Mach-Zehnder interferometer fed with a coherent state and a squeezed-vacuum state of equal intensities is theoretically predicted to achieve Heisenberg scaling in phase sensitivity. However, this ultimate performance is unattainable using direct photon-number-difference detection due to a divergence arising precisely at the optimal equal-intensity regime. In this work, we introduce a dual-squeezing approach that overcomes this fundamental limitation. Our scheme employs an additional single-mode squeezer before detection, forming a paired configuration with the input squeezer used to generate the squeezed-vacuum state. We analytically demonstrate that the resulting dual-squeezing Mach-Zehnder interferometer enables Heisenberg-limited phase sensitivity with di rect photon-number-difference detection, while remaining robust against detection noise. Our work provides a feasible and robust route toward quantum-limited interferometric phase measurements

Polarization ellipticity $β$ and the relative angle $Δ$ between electron momentum and driving field act as independent control parameters for coherent dynamics in periodically driven Dirac systems. In this work, we analyze the dynamics of resonantly driven Dirac electrons in graphene under elliptically polarized electromagnetic radiation using the Floquet-Magnus expansion. Working in the interaction picture and applying a rotating-wave-type transformation, we derive an effective two-level Hamiltonian that governs the macromotion at resonance ($ω= Ω/2$). The resulting quasienergy splitting depends nontrivially on $β$ and $Δ$ through interference between the Bessel harmonics $J_0(ζ)$ and $J_2(ζ)$. Circular polarization ($β= \pm 1$) restores rotational symmetry and yields a $Δ$-independent effective Rabi frequency, whereas elliptical and linear polarizations produce anisotropic responses with a $π$-periodic angular modulation. Beyond spectral properties, we identify a polarization-induced phase that acts as an effective initial Floquet kick, shifting the effective initial conditions and producing measurable shifts in the timing of occupation oscillations, whose sign depends on both helicity and relative orientation. Through an explicit Fourier decomposition of the time-evolution operator, we separate macromotion from micromotion contributions and validate the zeroth-order Magnus approximation via numerical simulations, achieving root-mean-square errors of $\sim 1\%$ over 100 driving periods in the weak-field regime. These results establish polarization ellipticity and relative orientation as tunable and experimentally accessible knobs for quantum control in two-dimensional Dirac materials, with direct implications for time-resolved spectroscopy.