In this paper we study the least squares (LS) estimator in a linear panel regression model with unknown number of factors appearing as interactive fixed effects. Assuming that the number of factors used in estimation is larger than the true number of factors in the data, we establish the limiting distribution of the LS estimator for the regression coefficients as the number of time periods and the number of cross-sectional units jointly go to infinity. The main result of the paper is that under certain assumptions the limiting distribution of the LS estimator is independent of the number of factors used in the estimation, as long as this number is not underestimated. The important practical implication of this result is that for inference on the regression coefficients one does not necessarily need to estimate the number of interactive fixed effects consistently.

Trusted Execution Environments (TEEs) have emerged as a cornerstone for securing sensitive computations by providing isolated enclaves protected from untrusted software. However, their security guarantees are undermined by vulnerabilities in both the enclave code and the underlying hardware design, which can allow sensitive data to leak despite strong isolation guarantees. This paper presents KINGSGUARD, a novel TEE design that systematically monitors and controls the propagation of sensitive data within an enclave. By enforcing fine-grained data flow tracking and checks in hardware, our approach ensures that sensitive data does not leave the enclave boundary, thus bridging the gap between the idealized threat models of TEEs and their practical realizations. Additionally, to balance security with practical functionality, we introduce controlled declassification at enclave boundaries, allowing intentional release of data to the outside world. Our implementation of KINGSGUARD on a RISC-V processor has a 10.8% hardware area overhead when synthesized on FPGA and a 5.69% performance overhead.

We analyze linear panel regression models with interactive fixed effects and predetermined regressors, for example lagged-dependent variables. The first-order asymptotic theory of the least squares (LS) estimator of the regression coefficients is worked out in the limit where both the cross-sectional dimension and the number of time periods become large. We find two sources of asymptotic bias of the LS estimator: bias due to correlation or heteroscedasticity of the idiosyncratic error term, and bias due to predetermined (as opposed to strictly exogenous) regressors. We provide a bias-corrected LS estimator. We also present bias-corrected versions of the three classical test statistics (Wald, LR, and LM test) and show their asymptotic distribution is a chi-squared distribution. Monte Carlo simulations show the bias correction of the LS estimator and of the test statistics also work well for finite sample sizes.

Reliable long-range qubit shuttling is a powerful tool for scalable quantum computing architectures. We investigate strategies to improve the coherence of moving spin qubits by performing continuous dynamical decoupling by modulating their confinement potential. Specifically, we introduce temporal and spatial breathing shuttling protocols that leverage spin-orbit interactions in hole-spin systems to electrically drive the qubit while moving. This enables efficient dressed-state shuttling, where the spin is continuously rotated during transport, suppressing the effect of low-frequency noise. Using the filter function formalism, we identify driving regimes that efficiently mitigate both global and local magnetic and electric noise sources. We find that confinement-modulated shuttling can significantly enhance coherence during transport, while revealing distinct limitations depending on the correlation length of the noise. Applying our framework to germanium hole-spin qubits, we show that these protocols provide a practical route toward noise-resilient long-range coherent quantum links.

The rational design of bifunctional electrocatalysts for the hydrogen evolution reaction (HER) and oxygen evolution reaction (OER) is essential for achieving efficient and cost-effective overall water splitting. Atomically dispersed transition-metal catalysts, including single-atom catalysts and dual-atom catalysts (DACs), have emerged as a prominent class of heterogeneous catalysts, in which coordination engineering plays a decisive role in tuning catalytic performance. Herein, we explore coordination-engineered bifunctional overall water splitting electrocatalysts using graphene-supported DACs (TM1TM2-C6-xNx) as model systems. By tuning C/N coordination and dual-metal combinations (Fe, Co, Ni, and Cu), a library of 228 structures was constructed. A three-step screening strategy, combining constant-charge and constant-potential density functional theory with kinetic analysis of proton-coupled electron transfer (PCET), identifies 24 highly active candidates (TM1TM2 = CoNi, CoCu and Co2) with mixed C/N coordination for OER. These catalysts exhibit overpotentials comparable to that of IrO2 and low PCET barriers (lower than 0.40 eV), among which 22 also show high HER activity. Machine learning reveals clear coordination-dependent structure-performance relationships. Such bifunctionality arises from coordination engineering that enables the simultaneous optimization of OER intermediate adsorption and the hydrogen binding strength for HER. This work establishes coordination engineering as an effective strategy for designing high-performance bifunctional dual-atom electrocatalysts for overall water splitting.

Using ''color cut'' method we obtained from SDSS DR16 catalog 733 red quasar candidates which amounted to approximately 4% of the objects from the initial sample. Then we estimated the radiative efficiency, spins, inclination angles, and corresponding new SMBH masses for all 733 objects using three theoretical models. Obtained spin distributions contain a large percentage of objects with retrograde rotation. It may indicate that these are either very young objects or objects that formed as a result of mergers. The dependencies of the estimated spin values on SMBH masses show strong correlation with linear fit slope 0.9-1.0 which allows us to assume that red quasars are likely to contain both Seyferts and NLS1, and that the main mechanism of SMBH mass growth in these objects is disk accretion.

We present a non-supersymmetric mechanism for baryogenesis driven by the nonlinear dynamics of a complex scalar field with generalized self-interaction potentials that explicitly break the global $U(1)$ symmetry. Specifically, three representative forms of the interaction potential are considered, which give rise to intricate nonlinear source terms in the evolution of the field components. In all cases, we show that these nonlinear source terms dynamically generate a nonzero Noether charge density from symmetric initial conditions, providing a purely dynamical origin of charge asymmetry. At late times, the charge density scales as $\sim t^{-3/2}$, leading to a constant baryon-to-photon ratio through dynamical freeze-in. While the qualitative behavior is robust across models, the quantitative features depend sensitively on the interaction structure. We find that one class of potentials yields a viable parameter space over a wide range of scalar masses, whereas another requires unrealistically suppressed mass scales. A third scenario stands out in that the final asymmetry is independent of the scalar mass and depends only on the coupling parameter, enhancing predictivity and allowing compatibility across a broad range of energy scales. Assuming efficient transfer of the generated asymmetry to the Standard Model sector and negligible washout effects, the mechanism can account for the observed baryon asymmetry.

We consider upward-planar layered drawings of directed graphs, i.e., crossing-free drawings in which each edge is drawn as a y-monotone curve going upward from its tail to its head, and the y-coordinates of the vertices are integers. The span of an edge in such a drawing is the absolute difference between the y-coordinates of its endpoints, and the span of the drawing is the maximum span of any edge. The span of an upward-planar graph is the minimum span over all its upward-planar drawings. We study the problem of determining the span of upward-planar graphs and provide both combinatorial and algorithmic results. On the combinatorial side, we present upper and lower bounds for the span of directed trees. On the algorithmic side, we show that the problem of determining the span of an upward-planar graph is NP-complete already for directed trees and for biconnected single-source graphs. Moreover, we give efficient algorithms for several graph families with a bounded number of sources, including st-planar graphs and graphs where the planar or upward-planar embedding is prescribed. Furthermore, we show that the problem is fixed-parameter tractable with respect to the vertex cover number and the treedepth plus the span.

We extend the Berry, Levinsohn and Pakes (BLP, 1995) random coefficients discrete-choice demand model, which underlies much recent empirical work in IO. We add interactive fixed effects in the form of a factor structure on the unobserved product characteristics. The interactive fixed effects can be arbitrarily correlated with the observed product characteristics (including price), which accommodates endogeneity and, at the same time, captures strong persistence in market shares across products and markets. We propose a two-step least squares-minimum distance (LS-MD) procedure to calculate the estimator. Our estimator is easy to compute, and Monte Carlo simulations show that it performs well. We consider an empirical illustration to US automobile demand.

The superconducting diode effect (SDE), characterized by a nonreciprocal critical current in superconductors, has recently been observed in strongly correlated electron systems and near quantum criticality, pointing to unconventional mechanisms beyond weak-coupling theories. Here we investigate the SDE in the Rashba-Zeeman-Hubbard model, which captures $d$-wave superconductivity in an antiferromagnetic quantum critical regime, using the Dyson-Gor'kov equation with the fluctuation exchange approximation. We show that electron correlations suppress the conventional intrinsic SDE arising from depairing currents. More importantly, a supercurrent nonreciprocally induces antiferromagnetic order, which fundamentally governs the critical current and enables perfect diode efficiency. Our results reveal a previously unrecognized correlation-driven mechanism of the SDE and establish strongly correlated superconductors as a platform for superconducting diode physics.

Organic--inorganic complexes are promising materials for light-emitting applications. Here, we report a new organometallic complex, cis-[Cd(Tz)$_2$(py)$_2$], featuring a distorted octahedral Cd(II) coordination environment. IR and Raman spectroscopy reveal pronounced coordination-induced changes, particularly in the Raman response of the triazene moiety, indicating electronic and structural perturbation upon Cd(II) complexation. Hirshfeld surface analysis shows that the crystal packing is mainly governed by H$\cdots$H, O$\cdots$H/H$\cdots$O, and C$\cdots$H/H$\cdots$C contacts, whereas $π$--$π$ stacking interactions contribute modestly. Solid-state UV--Vis spectroscopy reveals broad absorption from $\sim$700 to 200 nm and a direct optical band gap of 1.83 eV, indicating semiconductor-like behavior. Photoluminescence measurements show a broad emission band at 500--850 nm with enhanced red contribution upon coordination. The emission is mainly assigned to ligand-centered transitions ($π\rightarrow π^*$ and $n \rightarrow π^*$), consistent with the $d^{10}$ configuration of Cd(II), which suppresses metal-centered and charge-transfer processes. The CIE chromaticity coordinates confirm warm emission, highlighting the potential of cis-[Cd(Tz)$_2$(py)$_2$] for red-emitting optoelectronic applications.

We propose a robust clustering framework for high-dimensional data with heavy tails and a large fraction of irrelevant variables. The method replaces the mean updates of Lloyd's $K$-means with \emph{spatial medians} to enhance robustness. For the assignment step, it admits either a Euclidean rule for computational simplicity or a robust Mahalanobis-type metric constructed from the spatial sign covariance matrix to account for heterogeneous scales and feature dependence. To handle the $p \gg n$ regime, we further introduce a simple \emph{hard feature-exclusion} mechanism that removes weakly separating dimensions based on across-center dispersion, with the exclusion threshold selected automatically via a permutation-based Gap criterion. Simulation studies under correlated Gaussian and multivariate $t$ models demonstrate that the proposed approach provides competitive clustering accuracy and improved stability relative to $K$-means and sparse $K$-means baselines.

Keyphrase extraction aims to automatically identify concise phrases that effectively represent the content of a document. While recent methods leveraging pre-trained language models (PLMs) have significantly improved the extraction of keyphrases with strong global semantic relevance, they often fall short in capturing the local contextual importance of keyphrases tied to specific subtopics dispersed in a document. In this paper, we propose a novel context-centric framework, MUDY, that effectively captures multi-granular contextual salience of candidate keyphrases. MUDY employs two complementary components: (1) a prompt-based scoring that estimates the generation likelihood of each candidate keyphrase, augmented with candidate-aware weighting to better reflect its local contextual importance, and (2) a self-attention-based scoring that utilizes multi-granular attention patterns from PLMs to assess candidate significance at both the document-wide and segment-specific levels. Evaluations on four real-world datasets demonstrate that MUDY outperforms state-of-the-art baselines in top-k accuracy at various cutoff thresholds. In-depth quantitative and qualitative analyses further highlight the efficacy of context-centric keyphrase extraction with multi-granular saliency. For reproducibility, the source code of MUDY is available at https://github.com/HgKang1/MUDY.

We propose and analyze a quantum interferometry scheme based on a Raman-dressed Bose gas with spin-orbit coupling. In this system, the atom-light coupling mixes spin and momentum degrees of freedom, giving rise, in the low-energy regime, to an effective spinor condensate whose spin-mixing interaction can be tuned independently of the atomic density. This controllability enables a separation between state preparation and phase imprinting, and provides a natural route to echo-type protocols based on effective time reversal. Within this framework, critical regimes of the effective spinor Hamiltonian can be used to generate entanglement and enhance interferometric sensitivity beyond the standard quantum limit. In addition, the spin-momentum locking of the dressed modes gives access to spatial density modulations that provide an alternative readout of the interferometric phase. In particular, phase information can be extracted from the displacement of spin-orbit-induced density stripes even when conventional spin observables are insensitive within the effective spinor description. Our results identify Raman-dressed spinor gases as a flexible platform for nonlinear atomic interferometry, combining controllable spin-mixing dynamics with spatially resolved phase readout.

We analyze the sum-of-squares rank of unweighted instances of the Minimum Knapsack (MK) problem, i.e., minimization of $\sum_{i=1}^n x_i$ for 0/1 variables under the constraint $\sum_{i=1}^n x_i \geq q$, with $q \in \mathbb{R}$. Such instances have long served as a testbed for understanding the limitations of lift-and-project methods in Boolean optimization. For example, both the Lovász-Schrijver and Sherali-Adams hierarchies require (maximal) rank $n$ to solve them, already when $q=1/2$ is constant. The SOS hierarchy requires only \emph{sublinear} rank $O(\sqrt{n})$ to solve unweighted MK when $q=1/2$. On the other hand, when $q$ is allowed to vary with~$n$, the SOS rank of the problem may become linear. Interestingly, this is known to happen both when $q$ is large, and when $q$ is very small ($0<q \leq 2^{-n}$). This raises the question of whether we should think of hard instances of unweighted MK as being typical for the SOS hierarchy, or as a consequence of very specific choices of the threshold parameter $q$. In this paper, we address this question by showing new upper and lower bounds on the SOS rank of unweighted MK in the whole regime of the parameter $q$. For $n-q \leq O(1)$, we show that the SOS rank is constant. In contrast, when $q \leq O(1)$, a linear rank is needed if $q$ is exponentially close to an integer. As our main positive result, we show that linear rank is very rare for $q \leq O(1)$. This can be expressed in the language of smoothed analysis: after perturbing $q$ by a Gaussian with mean $0$ and variance $σ^2$, the expected SOS rank of MK is $O(\sqrt{n} \log (n/σ))$.

We study reflection symmetry and Atiyah-Patodi-Singer (APS) boundary conditions for twisted Dirac operators on a finite warped cylinder. For a complex line twist with holonomy parameter $A$, we show that the reflection lifts to a unitary symmetry of the twisted Dirac setting if and only if $2A\in\mathbb Z$. In the resulting reflection-compatible fixed-holonomy case, reflection pairs opposite shifted angular modes, and the paired APS blocks are unitarily equivalent. The reflection trace on the APS harmonic space localizes to the unique self-paired zero-mode sector. We then turn to parameter-dependent versions of the model. For fixed gauge-trivial holonomy, the family remains pointwise \(O(2)\)-equivariant, and its spectral flow admits an \(RO(O(2))\)-valued decomposition. For genuinely varying holonomy, pointwise \(O(2)\)-equivariance is lost along the path. The representation-ring-valued invariant is then replaced by a residual sign-level invariant: the mod-two parity of the APS crossing events.

Demand-side management (DSM) enables distribution system operators (DSOs) to steer electricity consumption through dynamic price signals or incentive mechanisms, thereby leveraging end-users' flexibility potential for delivering grid services. The resulting hierarchical interaction between the DSO and the end-users can be formulated as a Stackelberg game, where the operator dynamically sets the prices and the end-users optimally respond to them. Efficiently designing these price signals is challenging, as the users' response models are unknown or difficult to estimate. In this paper, we propose a learning-based zeroth-order algorithm for incentive design, in which the iterative update of the incentive signals is efficiently assisted by a data-driven online estimation of the users' responses. The proposed method is then proven to converge to an equilibrium tariff while allowing the DSO to estimate the decision-making problems at the user level. Moreover, the method preserves users' privacy, as the update rule of the DSO is solely based on observations of communicated end-user actions. Numerical simulations employing real-world data illustrate the efficient convergence of our learning-based proposed method, while significantly reducing the number of required interactions between the DSO and the end-users with respect to the state-of-the-art approach.

Optical heating of plasmonic nanostructures is a critical challenge in nanoscale systems. Although plasmonic effects enable enhanced optical functionalities, the associated temperature rise can degrade performance in heat-sensitive applications such as biosensing, nanophotonics, and microelectronics. Conventional cooling strategies fail at these scales due to limited heat transport and high interfacial thermal resistance, motivating the integration of advanced materials for thermal management. Here, we investigate hexagonal boron nitride (hBN) thin flakes as heat spreaders to mitigate plasmonic heating of gold nanospheres immobilized on hBN deposited on glass and surrounded by water. Using finite-element simulations, we quantify the influence of hBN thickness, in-plane thermal conductivity, and interfacial thermal conductance on cooling efficiency. Complementary experiments employ cross-grating wavefront microscopy (CGM) for nanothermometry to map the temperature around optically heated gold nanoparticles and quantify the cooling effect of hBN. We extend the application of CGM for rapid, non-invasive, and all-optical characterization of non-absorbing 2D materials. Our results reveal a strong thickness dependence, where heat dissipation in thin flakes is limited by the heat capacity of hBN and in thick flakes by interfacial thermal conductance. Including hBN, we obtain a reduction in temperature rise by up to 60% compared to glass. In addition, the presence of two main heat dissipation pathways emerges: a direct one from the nanoparticle to the hBN and an indirect one from the particle via water to the hBN. This combined simulation-experiment framework offers a versatile approach to improve thermal management in plasmonic systems and beyond, establishing design guidelines for integrating 2D materials into thermally sensitive platforms such as biosensors and integrated circuits.

We present a comparative study of Langevin dynamics and a Metropolis random walk model applied to thermal neutron-induced fission of $^{229}$Th, $^{235}$U, $^{239}$Pu, $^{245}$Cm, $^{249}$Cf, and $^{255}$Fm. Both methods are implemented within an identical four-dimensional Fourier-over-Spheroid framework, using potential energy surfaces derived from the macroscopic-microscopic model. We show that the Metropolis walk corresponds to the overdamped limit of the Langevin equations and confirm this correspondence numerically by Langevin calculations performed in the strongly damped regime and with quantum corrections to the random force switched off. Under these conditions, the two approaches produce essentially identical mass distributions for the lighter actinides. Systematic deviations develop for the heavier actinides, where the Langevin dynamics yields a non-negligible symmetric fission component absent in the random walk results. We trace this difference to the kinematic structure of the Metropolis sampling and to the residual inertial dynamics retained in the Langevin framework. A parallel comparison of Langevin calculations with and without the quantum-corrected effective temperature $T^*$ isolates the contribution of zero-point fluctuations and suggests that their standard phenomenological treatment may overestimate their impact in certain cases. Both approaches qualitatively reproduce the asymmetric peak positions and their systematic evolution across the actinide chain, while a common quantitative limitation -- the narrowness of the predicted distributions -- points to the role of higher-dimensional deformation modes not included in the present parametrization.

Modeling signals as linear combinations of atoms from a dictionary is ubiquitous in modern signal processing. In the finite-dimensional setting, whenever atoms depend nonlinearly upon unknown parameters, the signal model is said to be separable. In this work, we study least-squares reconstruction of separable signals and establish a unified theoretical framework for their analysis. We introduce the unmixing metric, a distance that captures the distinct roles and sensitivities of linear and nonlinear parameters, and establish local convergence and stability guarantees under its topology. We then analyze variable projection from a geometric perspective, showing that it corresponds to restricting the optimization to the manifold of optimal linear parameters. This viewpoint provides a principled explanation for the improved algorithmic behavior of variable projection observed in practice, and produces sharp theoretical guarantees. The generic theory for separable problems is specialized to the case of point spread function (PSF) unmixing. We introduce a parametric notion of coherence and show that support separation directly controls both the size of the convergence region and the stability of recovery. Numerical experiments corroborate the theoretical predictions and demonstrate the practical relevance of the proposed framework.

We investigate the scalar emission from binary neutron stars in shift-symmetric scalar-tensor theories with kinetic screening ($K$-essence), using 3+1 numerical simulations in the decoupling limit. To construct static binary initial data in the regime where the screening radius $r_*$ greatly exceeds the orbital separation, we introduce a hyperbolization of the static field equations that bypasses the Keldysh-type breakdown affecting direct time evolutions. For equal-mass binaries, where the scalar emission is dominated by the $\ell=m=2$ mode, kinetic screening acts non-monotonically on the scalar radiation, suppressing or enhancing the quadrupolar amplitude depending on the relative size of $r_*$ and $λ_{22}$ (with $λ_{22}$ the wavelength): for $λ_{22}\ll r_*$ it is suppressed relative to the Fierz-Jordan-Brans-Dicke (FJBD) case, while for $λ_{22}\gtrsim r_*$ it is amplified above FJBD. For unequal-mass binaries a scalar dipole re-emerges, growing linearly with the mass asymmetry, while the quadrupolar screening remains close to the equal-mass case down to mass ratios $\sim 0.6$. The non-monotonic behavior of kinetic screening that we uncover has potential implications for gravitational-wave-based tests of gravity. The relativistic double pulsar, in particular, requires $r_*\gg 10^9$~km to efficiently suppress the scalar quadrupole; for cosmologically-motivated $Λ$, $r_*\sim 10^{11}$~km (for a solar-mass source), giving only moderate suppression.

Range coders and ANS replace empirical probabilities with integer frequencies summing to a fixed $M$; the resulting per-symbol code-length redundancy is exactly the KL divergence of the empirical distribution from the quantized one. Existing normalizers (Giesen, Bloom, Collet) are heuristic or only partially marginal-optimal. We give three provably KL-optimal algorithms: a bottom-up archetype, a bidirectional exchange repair of Bloom's heap correction, and a top-down window method that runs in $\mathcal{O}(r)$, asymptotically optimal in $r$, where $r$ is the number of positive-count symbols.

Over the last decade, there has been steady research on superconducting junctions with a ferromagnet as the weak link, and where triplet correlations can transport supercurrents over a substantial distances. Of particular interest are halfmetallic ferromagnets, in which only one spin band is present, so that, presumably, the induced supercurrent is fully spin-polarized. We have earlier reported on a study of triplet transport in planar La0.7Sr0.3MnO3(LSMO) nanostrip Josephson junctions with NbTi superconducting contacts, where we found high values for the supercurrents, and large junction lengths (up to 1.3 μm). Here, we extend that work by studying the dependence of the critical current Ic on the length of the nanostrip between the contacts and the width of the strip. All junctions show strong supercurrents, but we do not observe simple systematics. Apparently, the fabrication process does not allow sufficient control over some of its parameters. To gain more insight in the mechanism for triplet generation at the LSMO/NbTi interface, we also studied the effect of Pt as an interlayer between the LSMO and the NbTi. For this, we etched a NbTi/Pt electrode structure on a full film of LSMO. The results are highly promising, showing sharp superconducting transitions and zero-resistance states being reached at an electrode distance of 2 μm, with indications that larger distances should be feasible.

Diamond quantum sensors offer high precision and spatial resolution as magnetic probes, making them promising for a wide range of applications. While diamond anvil cells (DACs) can generate extremely high pressures, techniques for magnetometry under such conditions remain limited. By fabricating an ensemble of NV centers directly on the anvil diamond surface, we enable precise magnetic measurements under high pressure. In this work, we employ this NV ensemble to image the stray magnetic field of iron up to 30 GPa, enabling the observation of the magnetic transition ($α$-$\varepsilon$ transition) in iron.

Second-harmonic generation microscopy is a powerful technique capable of probing local crystal symmetries and electric fields at interfaces. However, it often suffers from weak signal strength and is difficult to understand in multilayer systems where many materials can give competing signal contributions. In this work we present direct observation of delocalized, surface plasmon polariton-mediated second-harmonic generation on gold monocrystalline surfaces and structures. We generate second-harmonic light up to 35 um from the excitation spot and, excitingly, we obtain signal from atomically flat surfaces without a fundamental excitation beam present in the same region. We reveal that this process arises from the interaction of two counter-propagating surface plasmon polaritons, which we believe to be the first observation of this process at the microscale. This signal has the same polarisation dependence as localised second-harmonic generation and is emitted in a collimated beam travelling perpendicular to the sample surface. In part due to local electric field enhancements, we were able to observe these signals on a CMOS camera with 1 s exposure and no gain using an industrial-grade pulsed laser. Our results enable wide area multilayer samples to be probed using a single excitation beam, with applications including in energy, catalysis and single particle surface sensing.

Choosing suitable psychometric scales is an essential and difficult step in psychological consultation, which requires clinicians to integrate patient information, behaviors, and dynamic contextual information. Existing systems mainly use static pipelines to choose scale, or directly predict symptoms according to user inputs, limiting their ability to support dynamic assessment, risk management, and transparent decision-making. To address these limitations, we propose DySRec, a multi-agent conversational system for dynamic psychometric scale recommendation. DySRec operates as an interactive chatbot that engages users in multi-turn dialogue, models scale selection as a continuous conversational decision process, and coordinates specialized agents to maintain user context, recommend assessment scales, monitor psychological risk, and log decision trajectories. In this way, DySRec can integrate and capture heterogeneous signals, including semantic, interaction behaviors, assessment history, and content state, to dynamically update user representations and calculate scale-context compatibility score for recommending most matched scales. Moreover, DySRec incorporates a closed-loop refinement mechanism. Recommendation agent will feedback the missing or uncertain attributes and guide the conversation to elicit the targeted information. In this paper, we showcase the prototype design and architecture of DySRec, and this system has been verified in a real-world application.

A body cuboid is a rectangular parallelepiped with integer edges and integer face diagonals; if its space diagonal is also integer, it is a perfect cuboid, whose existence is a long-standing open problem. We make two contributions to the study of body cuboids parametrised by two coprime Pythagorean pairs $(a,b)$ and $(m,n)$ in Euclid form (Master-Hits). The first is a verified exponent-one blocker phenomenon: for every Master-Hit, the space-diagonal norm $f_1 := (W_1 U_2)^2 + (U_1 V_2)^2$ admits a prime divisor $\ell$ of exponent exactly one which is coprime to a fixed list of $29$ canonical expressions in the parameters. This is strictly stronger than the existence of any odd-exponent prime divisor: a prime of exponent $3, 5, \ldots$ would obstruct $f_1$ from being a square but carry an extra square factor; the observed obstruction is always primitive. The phenomenon is verified on all $151{,}575$ Master-Hits whose $f_1$ has been fully factorised. Two natural strengthenings fail: the largest outside-parameter prime need not be a blocker, and the smallest outside-parameter blocker need not have exponent one. The second contribution uses the elliptic fibration of the Master-Hit variety over the $(m,n)$-plane. For coprime $(m,n)$ the Master-Hit equation defines a genus-one quartic $H_{m,n}$; a quartic-to-Weierstrass normalisation gives an elliptic model $E_{m,n}$ with a rational function $τ$ returning $t^2$. Our generator enumerates bounded Mordell-Weil combinations on $E_{m,n}(\mathbb{Q})$, lifts the points satisfying $τ(P) \in \mathbb{Q}_{>0}^{\square}$ to admissible Euclid pairs $(a,b)$, and certifies each via exact integer arithmetic. From $61{,}829$ classical Master-Hits we generate $1{,}222{,}841$ further ones über $411$ fibres. None of the resulting $1{,}284{,}670$ Master-Hits is a perfect cuboid; all fully factored records satisfy the exponent-one blocker phenomenon.

We investigate quantum corrections to the Josephson dynamics of two weakly coupled Bose-Einstein condensates using the population imbalance as the sole dynamical variable. Starting from the two-variable action, we derive the imbalance-only Lagrangian with a position-dependent mass and quantize it via symmetric operator ordering. The leading quantum corrections to the classical potential and mass are computed via the one-loop quantum effective action, using a covariant background-field method that fully accounts for the coordinate dependence of the mass. This yields explicit expressions for the effective potential and the effective mass, from which we derive the quantum-corrected Josephson frequency. Numerical comparison with exact diagonalization of the two-site Bose-Hubbard model shows that the imbalance-only formulation outperforms the complementary phase-only approach in the regime of strong interactions, which is the natural domain of validity of the population-imbalance description.

Beyond-5G (B5G) and 6G networks are expected to enable more complex industrial services, which often operate according to multi-phase workflows with phase-specific communication requirements. However, current interaction between applications and networks remains predominantly request-driven: Quality of Service (QoS) is requested at each workflow phase transition and evaluated independently, without explicit consideration of upcoming demand or network's near-term capability. This mismatch limits the ability of both sides to plan ahead, often resulting in foreseeable incompatibilities, even service disruptions. This article presents a capability-aware coordination framework for workflow-based industrial services. Within a bounded planning window, the network exposes the QoS profiles it can sustainably support, while the industrial side maps upcoming workflow phases to these disclosed capabilities and submits the resulting demand trajectory for joint assessment. The framework also supports coordinated updates when network conditions change during execution. An industrial video inspection case study on a real B5G system, complemented by large-scale simulation, illustrates that such coordination can improve service continuity, reduce disruptive rejections, and increase workflow completion under heavy load. The results suggest that future industrial networking should move beyond reactive per-request QoS handling toward forward-looking, capability-aware, workflow-level coordination.

The magnetotropic susceptibility $k(ω)$ probes ultra-low-frequency uniform fluctuations. For a crystal mounted on an oscillating cantilever in a magnetic field, it is defined as the ratio of torque to angular-displacement amplitude. Its real and imaginary parts determine the oscillation-frequency shift and crystal-induced damping. It is a low-energy probe of uniform $q=0$ spin and charge degrees of freedom. We demonstrate this by deriving $k(ω)$ within linear response theory for a generic correlated-electron Hamiltonian with charge and spin degrees of freedom. Although it covers metallic and insulating magnets, correlated paramagnets, and exotic quantum critical points, we focus on limiting cases. For insulating spin systems $k(0)$ is sensitive to magnetic anisotropy whereas its finite-frequency imaginary part probes uniform dynamical spin susceptibility even in spin-symmetric models. For metallic systems we identify when eddy currents cause low-frequency damping. Our numerical results focus on Kitaev-material magnetotropic response. Using auxiliary-field quantum Monte Carlo with machine-learning-based sign-problem optimization we compute $k(ω)$ for several models proposed for $α$-RuCl$_3$. The observed low-temperature scaling of $k(0)/T$ with $B/T$ results from dominant Kitaev couplings: parameter sets without dominant Kitaev coupling do not exhibit this scaling. It remains robust upon inclusion of optical phonons. Beyond the static response, $k''(ω)$ for the $α$-RuCl$_3$ parameter set reproducing the experimental $k(0)$ data shows local-moment features at high and low $T$, with a single peak at the Larmor frequency. Beyond Kitaev systems we highlight broader applications. Probing ultra-low-energy uniform charge fluctuations is pertinent to Kondo destruction quantum criticality, of broad interest in strange metallicity and unconventional superconductivity.