This paper targets e-commerce search relevance. While Large Language Models (LLMs) have demonstrated significant potential in this field, they often encounter performance bottlenecks in persistent 'corner cases' within complex industrial scenarios. Existing research primarily focuses on optimizing reasoning trajectories via Reinforcement Learning. However, real-world observations suggest that the primary bottleneck stems from knowledge boundaries, where the absence of domain-specific intelligence in the model's parametric memory creates a contextual void. This void persists when interpreting idiosyncratic queries or niche products and cannot be resolved solely through reasoning-path optimization. To bridge this gap, we propose K-CARE, a framework that extends the model's cognitive reach by grounding reasoning in external knowledge. K-CARE comprises two synergistic components: (1) Symmetrical Contextual Anchoring (SCA), which fills the contextual void by anchoring queries and products with behavior-derived implicit knowledge; and (2) Analogical Prototype Reasoning (APR), which leverages expert-curated prototypical knowledge to calibrate decision boundaries through in-context analogy. Extensive offline evaluations and online A/B tests on a leading e-commerce platform demonstrate that K-CARE significantly outperforms state-of-the-art baselines, delivering substantial commercial impact by resolving knowledge-intensive relevance challenges.

Priority queues are data structures that maintain a dynamic collection of elements and allow inserting new elements and removing the smallest element. The most widely known and used priority queue is likely the implicit binary heap, even though it is has frequent cache misses and is hard to optimize using e.g. SIMD instructions. We introduce the SimdQuickHeap, a variant of the QuickHeap that was introduced by Navarro and Paredes in 2010. As suggested by the name, the data structure bears some similarity to QuickSort. We modify the data layout of the original QuickHeap to have all \emph{pivots} adjacent in memory, with elements between consecutive pivots stored in dedicated \emph{buckets}. This allows efficient SIMD implementations for both partitioning of buckets and scanning the list of pivots to find the bucket to append newly inserted elements to. The SimdQuickHeap has amortized expected complexity $O(\log n)$ per operation, which improves to $O(\frac 1W\log n)$ in non-degenerate cases, where $W$ is the number of words in a SIMD register. In this case, the I/O-complexity is amortized $O(\frac 1B)$ per push and $O(\frac 1B \log_2 \frac nM)$ per pop. In synthetic benchmarks, the SimdQuickHeap is up to twice as fast as the next-best competitor, including the non-comparison radix heap, and needs around $1.5\log_2 n$ comparisons and $\log_2 n$ nanoseconds per pair of push and pop operations. On graph benchmarks with Dijkstra's shortest path algorithm and Jarnik-Prim's minimum spanning tree algorithm, the SimdQuickHeap is consistently the fastest.

A measurement of the eight angular polarization coefficients, $A_0$ to $A_7$, in the cross section for the Drell$-$Yan production of two muons is presented. The analysis is based on proton-proton (pp) collision data recorded with the CMS detector at the LHC at a center-of-mass energy of $\sqrt{s}$ = 13 TeV, corresponding to an integrated luminosity of 140 fb$^{-1}$. The coefficients are determined double differentially in eight intervals of transverse momentum and two intervals of rapidity of the muon pair $μ^+μ^-$. The results are presented for the $μ^+μ^-$ invariant mass range 81$-$101 GeV and are compared with theoretical predictions calculated at next-to-next-to-leading order in perturbative quantum chromodynamics. The measurement provides relevant information about the underlying partonic dynamics and the Z boson production mechanisms.

We investigate the stability of a segmented deformable mirror (DM) on high-contrast testbeds and its impact on the images produced with coronagraphs. Segmented apertures are promising to obtain large primary mirrors for future missions with starlight suppression capabilities. Cophased at the sub-nanometer level, segments can be slightly misaligned by small drifts, proving harmful for exoplanet observations. We study the impact of misalignments on contrast using the High-contrast Imager for Complex Aperture Telescopes (HiCAT), a testbed which includes a 37-segment DM and produces coronagraphic images with 2.5e-8 contrast in narrowband light. Temporal wavefront errors due to the segmented DM are estimated with a Zernike wavefront sensor. Our in-lab results show aberrations at the sub-nanometer level, proving encouraging for contrast stability studies. We then use a digital twin of HiCAT to simulate coronagraphic images with an initial 0.5e-8 contrast and the segments in flat position. By injecting known perturbations on the segments, we observe a contrast degradation by a factor of 2.5, nearly corresponding to the typical contrast observed on HiCAT. These results highlight the importance of segment cophasing sensing and control strategies to ensure the required contrasts for exo-Earth imaging with a large segmented aperture for the Habitable Worlds Observatory mission.

In this work we explore the semileptonic $τ$ decays into the axion-like particle ($a$)-meson final states within chiral effective field theory. The next-to-leading-order mixing matrix for the $π^0$-$η$-$η'$-$a$ system with the linear isospin-breaking effects, is exploited and then implemented to calculate the hadronic form factors relevant to the $τ$ decays. The resonance parameters entering the form factors are determined from fits to the experimental spectra of $τ^- \to π^- π^0 ν_τ$, $τ^- \to K_S π^- ν_τ$, and $τ^- \to K^- ην_τ$. We then focus on the predictions to the branching ratios, invariant-mass distributions, and forward-backward asymmetries from the $τ^-\to P a ν_τ$ processes, with $P=π^-$ and $K^-$. Our results provide a quantitative basis for future searches of the axion-like particle signals in semileptonic $τ$ decays.

In this paper, we investigate arithmetical structures on Cartesian product graphs, particularly, ladder graph of the form P2\square Pm and grid graph of the form Pn \square Pm. An arithmetical structure on a finite and connected graph G is a pair (d, r) of positive integer vectors such that r is primitive (the gcd of its entries is 1) and (diag(d) - A)r = 0, where A is the adjacency matrix of G. Arithmetical structures have been widely studied for basic graph families such as paths and cycles. Extending these ideas to graph products, we first analyze the ladder graph P2 \square Pm, deriving structural properties and identifying patterns in the corresponding arithmetical configurations. We then generalize these results to the grid graph Pn \square Pm, where increased complexity arises due to higher-dimensional interactions. Our work provides new insights into the behavior, characterization, and enumeration of arithmetical structures on grid-like graphs, contributing to the broader understanding of Laplacian based invariants and their combinatorial properties.

We show that finite-energy weak solutions to the incompressible Navier--Stokes equations on a three-dimensional bounded smooth domain are regular up to the boundary, provided that the $L^4_tL^4_x$-norm of the solution is smaller than a constant depending only on the domain. This answers a problem raised in [D. Albritton, T. Barker, and C. Prange, J. Math. Fluid Mech. 25 (2023), Paper No. 49]. Our proof relies on a new slicing construction near the boundary of the domain.

Based on discrete observations, we develop a test to infer if the volatility function $σ(\cdot)$ within the nonparametric Gaussian white noise model $dY_t = σ(t)dW_t$ is constant. The testing procedure is shown to be minimax-optimal and adaptive for infill asymptotics and these results entail that a deviation from the null hypothesis of constancy is best measured in terms of the ratio of $σ(t)$ and its $L^2$-average. The derivation of optimal constants requires the construction of hypotheses with height $h(b)$, where the parameter $b$ solves $F_n(b)=0$ for given functions $F_n$. Proving this equation to be solvable for each $n\in\mathbb{N}$ and establishing quantitative bounds of the solutions is built upon the implicit function theorem.

Parallel scan primitives compute element-wise inclusive or exclusive prefix sums of input vectors contributed by $p$ consecutively ranked processors under an associative, possibly expensive, binary operator $\oplus$. In message-passing systems with bounded, one-ported communication capabilities, at least $\lceil\log_2 p\rceil$ or $\lceil\log_2 (p-1)\rceil$ send-receive communication rounds are required to perform the scans. While there are well-known, simple algorithms for the inclusive scan that solve the problem in $\lceil\log_2 p\rceil$ send-receive communication rounds with $\lceil\log_2 p\rceil$ applications of the $\oplus$ operator, the exclusive scan is different and has been much less addressed. By considering natural invariants for the exclusive prefix sums problem, we present two different algorithms that are efficient in the number of communication rounds and in the number of applications of the $\oplus$ operator. The first algorithm consists of an inclusive scan phase and an exclusive scan phase and trades the number of communication rounds against the number of applications of the $\oplus$ operator. The smallest number of inclusive scan rounds with $q=\lceil\log_2 p\rceil$ rounds in total is $q'\geq q-\log_2(2^q-p+1)$. The other algorithm is a modification of a round-optimal all-reduce algorithm, and the number of additional applications of the $\oplus$ operator is dependent on the number of bits set (popcount of) in $p-1$. Both algorithms are relevant for small(er) input vectors where performance is dominated by the number of communication rounds. For large input vectors, other (pipelined, fixed-degree tree) algorithms must be used.

Single-photon light detection and ranging (LiDAR) extends active three-dimensional sensing at the fundamental level and has found applications in extreme environments involving long-range operation, low-reflectance targets, and adverse visibility. However, the acquired measurements often give rise to single-photon point clouds that are sparse, spatially non-uniform, and corrupted by outliers and depth distortions, making multi-view registration challenging especially when sensor poses are not accurately known. In this work, we present a geometry-intensity coupled registration framework (GIC-Reg) of pose-free multi-view fusion for single-photon sensing. It is established by combining physical-aware preprocessing, joint geometry-intensity grid feature aggregation, global matching, and local ambiguity disambiguation to estimate inter-view rigid transformations and hence to construct a globally consistent reconstruction. On the synthetic benchmark, it admits the lowest relative rotation error (RRE), relative translation error, and root mean square error across all background-noise and dropout rates, in comparison to baselines. Notably, under the most degraded dropout, it reduces the RRE from $13.167^\circ$ to $8.459^\circ$ compared with the learning-based baseline. Furthermore, experimental results on real multi-view data acquired at about 80~m show that it achieves more reliable global orientation and local alignment. Our results show that photon intensity provides an effective physical cue for stabilizing multiview registration in single-photon point cloud, and thus our work aids significant progress in exploring practical utility of single-photon sensing.

Entropic uncertainty relations are universal quantifiers of fundamental uncertainties of quantum measurements and are widely discussed in the quantum metrology literature. Quantum memory is a phenomenon related to the specific type of quantum correlations that allows for reducing fundamental uncertainties of quantum measurements. In the present work, the modified concept of quantum memory for time-dependent problems is proposed. We compare the time-dependent formulation of quantum memory with the out-of-time-ordered correlator (OTOC). Quantum memory is a rigorous mathematical concept that requires demanding calculations. Thus, until now, quantum memory has been discussed mainly for simple model systems and stationary problems. In the present work, we demonstrate that quantum memory can also be studied for realistic and physically relevant systems, e.g., the atomic helical spin chain, as well as the emergence and propagation of quantum correlations in time. We found that quantum memory manifests faster oscillations in time than OTOC and does not equilibrate. Furthermore, an artificial neural network is trained and asked to predict results for OTOC and quantum memory. These results show that quantum memory is more sensitive than OTOC in terms of broken inversion symmetry and the nonreciprocal effect.

We continue studies on phase retrieval for continuous and discrete Fourier transforms in multidimensions. Using finite difference operators, we give a large class of unexpected examples of non-uniqueness for this problem, including examples with the sparsity condition. A prototype of this construction in the continuous case is given in the work Novikov, Xu (JFAA, 2026), using linear differential operators. The construction of the present work also yields a large class of non-trivial Pauli partners, i.e., different functions with the same intensities in both configuration and Fourier domains. Besides, our construction yields examples that solve an old open question in phase retrieval with background information arising in many areas including Fourier holography.

Electrical control of spin and magnetic sublattice degrees of freedom is essential for multifunctional and low-power spintronic devices. Bipolar altermagnetic semiconductors (BAMSs)-characterized by opposite spin polarizations at the valence and conduction band edges-offer such control, yet known systems require external strain and sizable valley polarization for gate-tunable switching. Here, we propose a universal spin-axis-layer locking (SALL) paradigm to overcome these limitations. By stacking two quasi-1D ferromagnetic monolayers with a 90 degrees twist, the bilayer reconstructs altermagnetic symmetry, yielding an intrinsic BAMS state where carrier spin is locked to specific layers and transport directions. Using synthesized CuBr2 monolayers as proof-of-concept, we demonstrate via first-principles calculations a robust BAMS state. Electrostatic gating enables simultaneous, reversible switching of carrier type, spin, and active layer, generating fully spin-polarized axial charge currents and directionally controllable pure spin currents with near-unity charge-to-spin conversion efficiency. This SALL model establishes a versatile, strain-independent strategy for advanced all-electrical altermagnetic devices.

Chinese ceramic-making involves complex and interdependent steps, making it technically demanding. Digital fabrication methods attempt to make the process more accessible, but for craft-creators, technical challenges such as CAD and CAM skills remain major obstacles. To address this, we designed a hybrid workflow that integrates Generative AI with clay 3D printing to support new creative possibilities. We evaluated the workflow through ClayScape, a design tool that operationalizes this approach, with four ceramic creators. Our findings show that the workflow supports accessible ceramic creation while revealing both expanded opportunities for creative exploration and challenges in balancing agency and control. This work demonstrates how hybrid workflows can lower barriers to digital fabrication while supporting creative possibilities in culturally grounded ceramic practices.

The Euclid Ecliptic Survey was conducted during the calibration phase of the mission, 23-31 December 2023, as a campaign to study Solar System objects. We used data from this survey to analyse more than 23 000 appeareances of 2321 known asteroids. Due to their high apparent angular motion relative to the background stars (5-$60^{\prime\prime}\,\mathrm{h}^{-1}$), these objects appear as streaks in VIS long-exposure images. We set out to estimate their spin periods, since only $7\%$ of them have periods published in the literature. We used multiple apertures along each streak to increase the time resolution of our light curves. Our method combines a Lomb-Scargle approach with a Markov chain Monte Carlo (MCMC) algorithm to characterise the posterior distributions. Some asteroids show multimodality in the MCMC search, indicating period aliases; in these cases, we report all aliases and their likelihoods. We validate our pipeline by comparing our fitted periods with 48 published periods, including period harmonics. We find that $44\%$ of our periods are within $1\%$ of those published and $98\%$ are within $15\%$, and we establish that with $98\%$ confidence the best solution can be found among the first three aliases. All reliable periods reported agree with our current understanding of the spin-period distribution for asteroids. We find 16 periods below the spin barrier of 2.2 h with absolute magnitudes below 19, and thus 16 candidate super-fast rotators. We provide light curves for all 2321 objects observed and 889 high-quality periods in an open-access catalogue. The asteroids with reported periods include five Mars crossers, four Cybeles, four Hildas, three Hungarias, and 877 asteroids in other regions of the main belt. Our results represent the first batch of spin periods extracted from Euclid light curves and include the first-ever period measurements for $93\%$ of the objects.

We study the problem of estimating locations in time at which the level of technology in an economy changes when given a sequence of time ordered inputs and outputs. We approach the problem through the lens of nonparametric frontier analysis with frontiers that expand sharply and globally over time, and develop an offline change point detection procedure which achieves the minimax localization rates for the problem at hand up to logarithmic factors. We additionally give a simple method for constructing confidence intervals for the unobserved change point locations. Finally, we explain how the procedure can be modified to accommodate local changes in technology, meaning that efficiency gains are only realized for certain combinations of inputs. Simulation studies and real data examples are also presented to illustrate the practical value of our methods.

We propose a human in the loop approach for black-box testing of Functional Mock-up Units (FMUs) using Large Language Models (LLMs). The goal is to reduce the manual effort in defining test scenarios for dynamic simulation models and to improve the interpretability of results. The approach takes the functional and interface specifications of an FMU as input, and prompts an LLM to generate structured scenario goals in Given-When-Then format that define the initial input conditions of the simulation, a possible change in those conditions, and the expected output behaviour of the system against those changes. The corresponding scenario plans specify input patterns and add assertion oracles that describe expected output patterns defined in scenario goals. The approach generates a complete input time series for the scenario plans, runs the FMU simulation, and evaluates assertions on the recorded outputs. It produces human-readable logs and plots that show statistics for each scenario with overlays, aggregate pass rates, and per-goal outcomes. The generated scenarios and results are stored for evaluation and later re-execution. We evaluate the approach on a Lube Oil Cooling system and discuss design choices that make the approach practical for everyday use. Results suggest that LLM-assisted scenario generation can facilitate automatic test design and verification of dynamic simulation models.

This chapter examines the relationship between curiosity and metacognition as critical drivers of autonomous and self-regulated learning. We synthesize recent research to propose a unified framework integrating behavioral, computational, and psychoeducational dimensions, arguing that curiosity, i.e. the intrinsic drive to acquire new knowledge, relies fundamentally on metacognitive monitoring and control. From an educational perspective, we evaluate interventions designed to enhance curiosity in classroom settings. While promising, our review indicates that these interventions yield mixed results, often proving differentially effective for struggling learners, thereby underscoring the necessity for approaches tailored to individual profiles. Finally, we address the paradigm shift introduced by Generative AI. While Large Language Models (LLMs) offer unprecedented scalability for personalized inquiry, we argue that their default interaction modes pose significant risks to the dynamics of curiosity-driven learning. To mitigate these challenges, we review strategies to transform AI from a potential cognitive shortcut into a powerful partner for sustained epistemic development.

Defined as the magnetic field permeating cosmic voids, the Intergalactic Magnetic Field (IGMF) is thought to be a relic of the Big Bang, tracing a primordial magnetic seed at the origin of all astrophysical fields. Yet, it has thus far escaped detection. Lower limits on the IGMF strength can be established by observing very high-energy (VHE) photons from extragalactic sources. Specifically, this can be achieved by characterising the time-delayed secondary emission induced by highly energetic transient sources, such as gamma-ray bursts (GRBs). Most studies exclude values of the IGMF below $10^{-17}\;\mathrm{G}$ by comparing the expected effect to the sensitivity curves of various instruments in the $\mathrm{GeV}$ range or above. In this work, we simulate CTAO observation data under realistic observation conditions and perform spectral-temporal fits to estimate the constraints CTAO will bring on the IGMF once fully deployed. We apply the methodology to simulated sources with properties comparable to the few GRBs detected at VHE. In particular, we show that CTAO will probe strengths up to $\sim 10^{-15}\;\mathrm{G}$ when detecting sources similar to GRBs 221009A and 190114C. We also show that existing observations of GRB 221009A by the first CTAO Large Sized Telescope LST-1 favour a strength of $3\times 10^{-17}\;\mathrm{G}$.

Let $G=PSL(n,\mathbb{C})$. Let $T$ be a maximal torus of $G$. Let $ω_{r}$ denote the $r^{th}$ fundamental weight. Let $\mathcal{L}(nω_{r})$ denote the line bundle on the Grassmannian $G_{r,n}$ associated to the character $nω_{r}$ of $T$. In an earlier work of Kannan and Sardar, it is proved that there is a unique minimal dimensional Schubert variety $X(w_{r,n})$ in $G_{r,n}$ admitting semistable points for the $T$-linearized ample line bundle $\mathcal{L}(nω_{r})$. Assume that $n=rq+1$, where $r,q\in\mathbb{N}$ and $q\geq 2$. In this paper, we study the GIT quotient of $X(w_{r,n})$ modulo a subtorus $T_{J_{r}}$ of $T$ generated by the one parameter subgroups of $T$ corresponding to the peaks of $w_{r,n}$. We prove that the GIT quotient of $X(w_{r,n})$ modulo $T_{J_{r}}$ is isomorphic to the total space of the $r^{th}$ stage of an iterated projective space bundle over $\mathbb{P}^{q-1}$.

Efficient quantum state preparation is a critical component in quantum algorithms that process large classical data, and it is fundamental to realizing quantum advantage in domains such as machine learning, quantum linear algebra, and quantum finance. Building on the framework of~\cite{berti2025efficient}, which integrates Bucket Brigade QRAM (BBQRAM) with a segment tree to achieve amplitude encoding in polylogarithmic query time, we present two improvements within the same architecture-aware framework. First, we remove the $U_{2\mathrm{CR}}$ subroutine by classically precomputing the rotation angles determined by the segment tree and storing these angles directly in the BBQRAM cells. The tradeoff is that the classically loaded QRAM stores precomputed fixed-point angles rather than raw subtree weights. Second, we extend the construction to complex-valued matrices $A \in \mathbb{C}^{M \times N}$ by storing a leaf phase alongside each precomputed rotation angle and using a two-step magnitude-then-phase procedure; the real signed case is naturally subsumed as a one-bit phase specialization. At unchanged $\mathcal{O}(\log_2^2(MN))$ BBQRAM query complexity, the QPU procedure reduces to BBQRAM retrievals and controlled-rotation cascades, with $\mathcal{O}(MN)$ memory cells per matrix and no reversible arithmetic on the QPU.

A polynomial approximation of the minimum energy estimator, also called Mortensen observer, is discussed. The method relies on successive differentiations of an underlying value function and the Hamilton-Jacobi-Bellman equation, respectively. By means of neglecting higher order derivatives of the value function along the unknown observer trajectory, a coupled set of nonlinear tensor structured differential equations is derived. In its simplest form, the approach boils down to the well-known extended Kalman filter. Numerical experiments with polynomials up to the order eight illustrate the potential of the new approach and indicate local convergence to the Mortensen observer.

5G backscatter communication presents an emerging energy-efficient IoT connectivity solution with enhanced availability and data rate advantages over traditional wireless networks. For 5G backscatter, synchronization is crucial as it ensures high-quality transmission. Popular synchronization methods employ autocorrelation and cross-correlation for accurate timing, yet they are constrained by resources. Traditional cross-correlation-based methods for resource utilization optimization also fail in 5G backscatter due to the presence of multiple templates for 5G. A synchronization strategy that supports high accuracy and low power would be highly attractive for wireless backscatter communication. We propose Symmetric Differential (SD)-based Sync, an accurate and resource-efficient synchronization method for 5G backscatter. We have observed that the envelope of the 5G Primary Synchronization Signal (PSS) exhibits a unique mirror symmetry, which enables us to employ differential techniques for low-power PSS detection. We extensively evaluated our design using a testbed of backscatter hardware, SDR gNodeB, and User Equipment (UE). Results show that our SD consumes 3,175 D flip-flops, which is 87x lower than NR fine timing (NFT), 181x lower than symmetry-based semi-template sync (SST), and 30x lower than symmetric autocorrelation (SA)-based sync.

We study a random unitary quantum circuit with only reset channels, which has high feasibility for real quantum devices. In particular, we investigate the many-body statistical physics properties, "reset-induced" entanglement phase transitions comparing the classical statistical picture in the large "$d$" limit of qudits. In the property of the reset-induced phase transition the parameter of qudit $d$ is essential. That is, the transition properties induced by the reset channel significantly depend on $d$. We numerically elucidate this statement employing efficient stabilizer circuit simulations for $d=2$. Specifically, large fluctuations are observed near the critical point, indicating that the reset-induced phase transition is continuous. We obtain clear data collapses, consistent with a second-order mixed phase transition. This behavior differs from expectations based on the classical statistical mapping in the large-$d$ limit.

Deciphering the complicated interplay between collective and separate behaviors lies at the heart of first-order metal-insulator transition (MIT) in correlated electron systems, enabling the rational design of exotic electronic states and functionalities. The critical balance between collective and separate behaviors defines a fundamental collective length scale, typically shorter than 5 nm, that governs emergent quantum orders, yet active control over this dichotomy remains elusive. Here, we realize on-demand manipulation of the collective and separate MIT within the correlated VO2 system in a reversible fashion. Artificially designing the oxygen deficiency in VO2/VO2-x homojunction fosters a collective MIT with an extended collective length scale, whereas the introduction of a TiO2 interlayer drives a crossover from this collective to a two-step separate MIT via decoupling of the electronic order parameter. Incorporating mobile hydrogens into the VO2/TiO2/VO2-x trilayer enables reversible control over electronic phase modulations, transitioning a two-step MIT towards either a one-step MIT or collective electron localization. This ionic control over the electronic band structure of VO2 flexibly triggers multi-state MIT, a process governed by hydrogen-related band filling. Our findings transform the collective length scale from a passive threshold into a dynamic design parameter, establishing a viable handle for engineering collective and separate MIT for adaptive correlated electronics.

We consider a Ziegler pair of plane arrangements, that is two plane arrangements $\mathcal{A}:f=0$ and $\mathcal{A}':f'=0$ in the projective space $\mathbb{P}^3$, such that the intersection lattices $L(\mathcal{A})$ and $L(\mathcal{A}')$ are isomorphic, but the Betti numbers of the minimal resolutions of their Jacobian algebras are not the same. We introduce several properties for such pairs and relate them to cones over Ziegler pairs of line arrangements in $\mathbb{P}^2$.

Topological edge states are an attractive starting point for post-CMOS device concepts, but turning them into elementary logic still requires simple architectures with a clear physical mechanism. Here we investigate binary logic in Kane-Mele nanostructures with spatially localized control regions. Logical inputs are encoded through local electrostatic, exchange-like, and Rashba-type perturbations, while the output is read out from terminal transmission within a coherent Landauer-Büttiker framework. We demonstrate working NOT and AND gates in multiterminal honeycomb geometries and show, with the help of current maps, that their operation is governed by controlled rerouting of edge currents rather than by fine-tuned interference. Robustness tests further indicate a stable operating window within the tested parameter range for the NOT gate and a somewhat narrower but still reliable one for the AND gate. These results identify Kane-Mele nanostructures as a transparent platform for primitive topological binary logic.

We study how environment affects the mass-metallicity relation (MZR) at $z=4$-$10$ using deep imaging and spectroscopy from the James Webb Space Telescope (JWST). Combining CEERS and JADES, we compile a sample of 225 galaxies with stellar masses, star-formation rates, and gas-phase metallicities. We characterize environment using the projected fifth-nearest-neighbour surface density, $Σ_{5}$, within $Δz=\pm0.25$. At $4.5<z<7$, we find that galaxies in dense regions are more metal-rich at fixed $M_\star$ by $\sim0.1$-0.2 dex, while the slopes of the MZR remain similar across environments. Including SFR increases the separation, suggesting more efficient chemical enrichment in overdense regions. Compared to the local $T_e$-based FMR, our full sample lies $\simeq0.2$-0.3 dex below the $z\sim0$ relation, with a smaller deficit in overdense environments. We also examine how metallicity relates to galaxy size using NIRCam-based effective radii. Metallicity increases weakly with size up to $R_e\sim1$ kpc and then flattens, with only a modest residual trend at fixed $M_\star$ and little environmental dependence. Using mass-weighted stellar ages at $5<z<10$, we find a positive age-metallicity relation in both environments, steeper in the field. Finally, we find that the star-formation rate density is higher in overdense regions at $z\simeq6$-9 by a factor of $\sim2$-3. Overall, our results suggest that environment accelerates both star formation and chemical enrichment during the epoch of reionization. Future wide-area JWST spectroscopy, combined with ALMA and Euclid, will better constrain the role of environment in early galaxy evolution.

A key bottleneck in quantum machine learning is the computational cost of repeated quantum circuit evaluations during the inference phase. To address this, we present a framework for constructing fast, cheap, provably accurate classical tensor-train surrogates of fully trained quantum machine learning models within local patches of their input data space. The approach combines Taylor polynomial approximation with a tensor-train (TT) representation and embeds it in a statistical learning paradigm via empirical risk minimization. In our analysis, the Taylor-TT construction serves as a deterministic error certificate proving that the TT hypothesis class contains a good approximation; empirical risk minimization then provably recovers a surrogate with controlled generalization error and explicit bounds. This translates into three independently controllable error sources: (i) Taylor truncation error controlled by the patch radius $r$ and polynomial degree $p$, (ii) TT approximation error controlled by the bond dimension $χ$, and (iii) statistical estimation error. While the parameter count scales polynomially in the number of data dimensions $N$, i.e., $d_{\mathrm{eff}} = N(p+1)χ^2$ rather than the naive $(p+1)^N$, the worst-case constants inherit an exponential factor through the tensor-product feature norm during Taylor polynomial embedding onto TT. This cleanly separates representation complexity from feature-induced constants. Our risk bounds and sample complexity depend explicitly on the local patch radius $r$.

We investigate the thermodynamics, criticality, and selected radiative and optical properties of an Euler-Heisenberg AdS black hole surrounded by quintessence, perfect fluid dark matter, and a cloud of strings. Within the extended phase-space formalism, we derive the thermodynamic quantities, verify the modified first law and Smarr relation, and analyze the corresponding equation of state and critical behavior. We show that the Euler--Heisenberg coupling and the surrounding matter fields substantially modify the temperature profile, the stability structure, and the location of the critical point. We also examine the sparsity of Hawking radiation, together with the photon sphere, black hole shadow, and the associated geometric-optics emission rate.