This article introduces a novel cryptographic paradigm based on nonderived polyadic algebraic structures. Traditional cryptosystems rely on binary operations within groups, rings, or fields, whose well-understood properties can be exploited in cryptanalysis. To overcome these vulnerabilities, we propose a shift to polyadic rings, which generalize classical rings by allowing operations of higher arity: an $m$-ary addition and an $n$-ary multiplication. The foundation of our approach is the construction of polyadic integers -- congruence classes of ordinary integers endowed with such $m$-ary and $n$-ary operations. A key innovation is the parameter-to-arity mapping $Φ(a,b)=(m,n)$, which links the parameters $(a,b)$ defining a congruence class to the specific arities required for algebraic closure. This mapping is mathematically intricate: it is non-injective, non-surjective, and multivalued. This complex, non-unique relationship forms the core of the proposed cryptosystem's security. We present two concrete encryption procedures that leverage this structure by encoding plaintext within the parameters of polyadic rings and transmitting information via polyadically quantized analog signals. In one method, plaintext is linked to the additive arity $m_{i}$ and secured using the summation of such signals; in the other, it is linked to a ring parameter $a_{i}$ and secured using their multiplication. In both cases, the "quantized" nature of polyadic operations generates systems of equations that are straightforward for a legitimate recipient with the correct key but exceptionally difficult for an attacker without it. The resulting framework promises a substantial increase in cryptographic security. This work establishes the theoretical foundation for this new class of encryption schemes and highlights their potential for constructing robust, next-generation cryptographic protocols.

We argue that modular classes of Q-manifolds provide an efficient method for addressing the existence of supersymmetric Berezin volumes in the supergeometric representation theory of the $\mathcal{N}=2$ $d=1$ supertranslation algebra. We establish a cohomological coherence criterion for the existence of a Berezin volume that is invariant under both of the supercharges.

We show that certain 't Hooft anomalies not detected by standard closed four-dimensional probes can become visible when a quantum field theory is placed on asymptotically locally Euclidean (ALE) spaces. As a concrete example, we use the Eguchi-Hanson (EH) space, whose defining features are its nontrivial second cohomology generated by the self-intersecting two-sphere and its asymptotic boundary $\mathbb{RP}^3$, which carries torsion and thus furnishes additional cohomological data absent on conventional backgrounds. For a theory with symmetry $G_1\times G_2$, we turn on background flux for $G_1$ and probe potential anomalies by performing a global $G_2$ transformation; the resulting anomaly is captured by a five-dimensional mapping torus. The anomaly receives contributions from the four-dimensional characteristic classes on EH space as well as from the $η$-invariant associated with the $\mathbb{RP}^3$ boundary. The anomaly detected in this way imposes additional constraints on asymptotically free gauge theories with fixed trivial asymptotic boundary conditions. In particular, infrared composite spectra that match anomalies on standard closed manifolds may nevertheless fail to reproduce the EH anomaly, and thus cannot by themselves furnish a complete symmetry-preserving infrared realization.

Phase estimation, due to Kitaev [arXiv'95], is one of the most fundamental subroutines in quantum computing. In the basic scenario, one is given black-box access to a unitary $U$, and an eigenstate $\lvert ψ\rangle$ of $U$ with unknown eigenvalue $e^{iθ}$, and the task is to estimate the eigenphase $θ$ within $\pmδ$, with high probability. The cost of an algorithm for us is the number of applications of $U$ and $U^{-1}$. We tightly characterize the cost of several variants of phase estimation where we are no longer given an eigenstate, but are required to estimate the maximum eigenphase of $U$, aided by advice in the form of states (or a unitary preparing those states) which are promised to have at least a certain overlap $γ$ with the top eigenspace. We give algorithms and nearly matching lower bounds for all ranges of parameters. We show that a small number of copies of the advice state (or of an advice-preparing unitary) are not significantly better than having no advice at all. We also show that having lots of advice (applications of the advice-preparing unitary) does not significantly reduce cost, and neither does knowledge of the eigenbasis of $U$. We immediately obtain a lower bound on the complexity of the Unitary recurrence time problem, resolving an open question of She and Yuen~[ITCS'23]. Lastly, we study how efficiently one can reduce the error probability in the basic phase-estimation scenario. We show that a phase-estimation algorithm with precision $δ$ and error probability $ε$ has cost $Ω\left(\frac{1}δ\log\frac{1}ε\right)$, matching an easy upper bound. This contrasts with some other scenarios in quantum computing (e.g., search) where error-probability reduction costs only a factor $O(\sqrt{\log(1/ε)})$. Our lower bound uses a variant of the polynomial method with trigonometric polynomials.

In many new physics models with extended gauge symmetry, the new gauge boson $Z'$ could mediate the interactions between the dark matter and standard model particles. For the conventional $Z^\prime$ portal dark matter, the collider and the direct detection constraints typically pose a significant challenge. To address this pressing issue, we present in this paper a new benchmark model based on the gauged $U(1)_{B-L}$ symmetry, which introduces a Dirac dark fermion $\tildeχ_1$ and a heavier partner $\tildeχ_2$ with zero and nonzero $U(1)_{B-L}$ charge, respectively. Including the mass term $δm \bar{\tildeχ}_1\tildeχ_2$ results in the dark fermions $χ_1$ and $χ_2$ in the mass eigenstate, where the lighter one $χ_1$ is regarded as the dark matter candidate. Various intriguing processes for the relic density arise with the compressed mass spectrum $m_{χ_1}\simeq m_{χ_2}$, such as the coscattering $χ_2f\toχ_1f$, the conversion $χ_2χ_i\toχ_1χ_j$, and the coannihilation $χ_1χ_2\to f\bar{f}$ processes. Suppressed by the small mixing angle $θ$ between the dark fermions, the small effective gauge coupling of dark matter $χ_1$ to the gauge boson $Z'$ is one distinct feature of this model, rendering phenomenology in many aspects more promising. In this paper, we investigate the production of dark matter through new mechanisms within the frameworks of resonance and secluded scenarios. The impacts of phenomenological constraints from collider, dark matter, and cosmology are also taken into account. We report that the conversion mechanism is both favored by the resonance and secluded scenarios under current constraints.

The upcoming Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST) is expected to discover nearly a million Type Ia supernovae (SNeIa), offering an unprecedented opportunity to constrain dark energy. The vast majority of these events will lack spectroscopic classification and redshifts, necessitating a fully photometric approach to maximize cosmology constraining power. We present detailed simulations based on the Extended LSST Astronomical Time Series Classification Challenge (ELAsTiCC), and a cosmological analysis using photometrically classified SNeIa with host galaxy photometric redshifts. This dataset features realistic multi-band light curves, non-SNIa contamination, host mis-associations, and transient-host correlations across the high-redshift Deep Drilling Fields (DDF) (~ 50 deg^2). We also include a spectroscopically confirmed low-redshift sample based on the Wide Fast Deep (WFD) fields. We employ a joint SN+host photometric redshift fit, a neural network based photometric classifier (SCONE), and BEAMS with Bias Corrections (BBC) methodology to construct a bias-corrected Hubble diagram. We produce statistical + systematic covariance matrices, and perform cosmology fitting with a prior using Cosmic Microwave Background constraints. We fit and present results for the wCDM dark energy model, and the more general Chevallier-Polarski-Linder (CPL) w0wa model. With a simulated sample of ~6000 events, we achieve a Figure of Merit (FoM) value of about 150, which is significantly larger than the DESVYR FoM of 54. Averaging analysis results over 25 independent samples, we find small but significant biases indicating a need for further analysis testing and development.

The wide-angle Polarimetric Camera (PolCam) onboard South Korea's first lunar orbiter, Danuri, is a pioneering instrument designed to conduct the first global polarimetric and high-phase-angle survey of the Moon. Precise geometric calibration is critical for this mission, particularly due to PolCam's highly oblique viewing geometry, which introduces significant topographic distortion. We present a comprehensive on-orbit geometric calibration that relies on 160,256 tie points derived from matching features between PolCam images and the well-orthorectified global map of the Kaguya Multiband Imager (MI). This dataset allows us to address two fundamental challenges: (1) the accurate reconstruction of the observation time for each line of an observation strip via a simple linear model, and (2) the refinement of the precise camera model, geometric model for PolCam optics. Our optimization method for these two challenges transforms the 2D image coordinates of identified features into 3D lunar coordinates and minimizes the reprojection error against the reference coordinates provided by the Kaguya MI map. From the refined observation time and camera model, we compute the precise longitude, latitude, and elevation of each pixel of an observed image. These estimated 3D coordinates are then used to generate orthorectified images, the final product of the geometric calibration. The resulting calibration achieves a geometric precision comparable to that of previous lunar orbiters and establishes the foundational framework necessary to produce geometrically-corrected data products of PolCam.

We study the first-order electroweak phase transition (FO-EWPT) within the Standard Model Effective Field Theory (SMEFT) framework induced by dimension-6 operators. Such phenomena can be probed independently via \textit{di}-Higgs production at the collider experiments as well as via the detection of gravitational waves (GW). There are three (one) dimension-6 SMEFT operators that simultaneously modify the Higgs potential at tree (1-loop) level and contribute to the \textit{di}-Higgs production at the hadron colliders. With \textit{di}-Higgs production being suppressed at current LHC runs, we aim to probe this production at high luminosity (HL) and high energy (HE) runs of the LHC to achieve better sensitivity of dimension-6 SMEFT operators. The correlations among these operators are analyzed in the context of probing FO-EWPT, emphasizing the complementarity between future GW observations and upgraded LHC searches.

We give a comprehensive description of Wasserstein gradient flows of maximum mean discrepancy (MMD) functionals $\mathcal F_ν:= \text{MMD}_K^2(\cdot, ν)$ towards given target measures $ν$ on the real line, where we focus on the negative distance kernel $K(x,y) := -|x-y|$. In one dimension, the Wasserstein-2 space can be isometrically embedded into the cone $\mathcal C(0,1) \subset L_2(0,1)$ of quantile functions leading to a characterization of Wasserstein gradient flows via the solution of an associated Cauchy problem on $L_2(0,1)$. Based on the construction of an appropriate counterpart of $\mathcal F_ν$ on $L_2(0,1)$ and its subdifferential, we provide a solution of the Cauchy problem. For discrete target measures $ν$, this results in a piecewise linear solution formula. We prove invariance and smoothing properties of the flow on subsets of $\mathcal C(0,1)$. For certain $\mathcal F_ν$-flows this implies that initial point measures instantly become absolutely continuous, and stay so over time. Finally, we illustrate the behavior of the flow by various numerical examples using an implicit Euler scheme, which is easily computable by a bisection algorithm. For continuous targets $ν$, also the explicit Euler scheme can be employed, although with limited convergence guarantees.

Layered Zintl compounds exhibit significant tunability of thermoelectric (TE) parameters facilitated by their multiple elemental combinations and flexibility in stacking order within the layers. In this work, the effect of stacking order on TE properties of theoretically predicted layered Zintl compounds XZnBi (X = Rb, Cs) is studied using 1st-principles calculations and Boltzmann equations. The materials are semiconductors having moderate band gaps ranging from 0.44 to 0.52 eV. There exist six identical hole pockets for valence band maxima due to the crystal symmetry. This leads to high band degeneracy but simultaneously promotes intervalley scatterings. While as for conduction bands, the Fermi surface consists of a single but highly anisotropic, quasi-two dimensional electron pockets with cylindrical shape along z-axis. This kind of Fermi surface is a characteristic of a pudding mold band shape. It facilitates a unique combination of heavy and light electron masses, simultaneously optimizing Seebeck coefficient and electrical conductivity. At first, electronic transport coefficients are calculated using constant relaxation time approximation (CRTA) or electron-phonon coupling matrix elements (el-ph). The calculated relaxation times are then integrated with transport results to get the realistic values of TE parameters. The analysis of three-phonon scattering reveals low thermal conductivity ($k_{l}$) below 2 W/m/K in these compounds. The $k_{l}$ also depends on stacking order with the values of nearly half in AB stacking as compared to that of AA stacking. These combined factors lead to a high ZT at 900 K, reaching to a maximum of 2.42 using CRTA and 0.52 when el-ph are included. The study highlights the potential of XZnBi systems as promising TE materials as well as the critical roles of stacking and el-ph in accurately evaluating TE properties.

More than half of the 1.19 million annual traffic fatalities globally involve vulnerable road users, such as pedestrians, with a significant proportion attributable to human error. Level-5 automated driving systems (ADSs) have the potential to reduce these incidents; However, their effectiveness depends not only on automation performance but also on their ability to communicate intent and coordinate safely with pedestrians in the absence of traditional driver cues. This study aims to model pedestrian decision-making in road-crossing scenarios involving level-5 ADSs by extending the Theory of Planned Behavior (TPB) with safety, trust, compatibility, and understanding. An online survey (n = 212) found that perceived behavioral control, attitude, and social information significantly influence pedestrians' crossing intentions, with perceived safety and understanding having the strongest effects on the TPB constructs. The results offer guidance for designing eHMIs and cooperative V2X communication strategies that promote safe pedestrian-ADS interactions and advance human-centered design for autonomous vehicles.

Recently, proximity-induced spin-orbit coupling (SOC) has been observed in heterostructures consisting of monolayer graphene (ML-G) and transition metal dichalcogenides (TMDCs) such as WSe$_{2}$. Successful tuning of SOC in graphene/WSe$_{2}$ heterostructures by applying mechanical pressure and electric fields was also demonstrated in previous studies. In addition, theoretical calculations predicted a strong dependence of the proximity-induced SOC on the twist angle between graphene and TMDC. Here, we put these predictions to experimental test in ML-G/ML-WSe$_{2}$/hBN-heterostructures, where the twist angle is determined by aligning fractured edges, and by crystallographic etching of graphene. By performing weak anti-localization measurements, we determine the strength of the Rasbha-type SOC ($λ_\mathrm{R}$) and the valley-Zeeman-type SOC ($λ_\mathrm{VZ}$). Our experiments confirm a strong twist angle dependence of the proximity-induced SOC in agreement with theoretical predictions. Finally, we demonstrate the tunability of the SOC strength via mechanical pressure, which is in agreement with earlier findings.

We determine the universal part of pseudoentropy for small shape deformations of spherical entangling surfaces in the context of de Sitter/conformal field theory (dS/CFT) correspondence. The leading correction at quadratic order in the deformation parameter is controlled by the analytic continuation of the coefficient of the two-point stress-energy tensor correlator in AdS/CFT (i.e., $\left. L_{*} \right|_{\text{AdS}}\rightarrow -i \left. L_{*} \right|_{\text{dS}}$), thereby establishing the sphere as a local extremum. The same structure holds in higher-curvature theories, as we check explicitly for quadratic curvature gravity, suggesting a universal behavior across non-unitary holographic CFTs. Our findings extend the Mezei formula to the dS/CFT setting and indicate that the shape dependence of pseudoentropy in dS holography resembles that of entanglement entropy in AdS space. Thus, we conjecture this coefficient to be the $C_T$ for the non-unitary CFT dual.

Many complex physical systems naturally decompose into an exactly solvable component augmented by a perturbative correction. Rather than directly employing neural networks to analyze complex physical systems, we introduce Neural Network Perturbation Theory (NNPT)--a correction learning approach that predicts residual perturbations after analytically subtracting known exact solutions. Using the gravitational three-body problem as testbed, we vary Jovian mass from f=0.05 to 30 times its physical value while holding network architecture fixed. An equalized-accuracy protocol with 1% tolerance reveals an unexpected non-monotonic capacity profile: capacity peaks at f=5 in the late integrable regime (3x32, 2242 parameters), remains elevated through the transition region (f~15-17), then decreases in the fully chaotic regime (f>=17, requiring only 2x32 with 1186 parameters)--a 47% reduction from peak. With symplectic integrator energy conservation below 2x10^{-4}, this counterintuitive phenomenon reflects genuine physical structure rather than numerical artifacts. Sequential correction experiments show negligible refinement (||y2||/||y1||~0.997), confirming single-stage networks capture dominant perturbative features without hierarchical decomposition. The capacity transition at f_c=16.6+-2.8 aligns with Chirikov's resonance-overlap criterion. Intermediate-complexity regimes impose maximal capacity requirements, while fully chaotic dynamics undergo ergodic smoothing--trajectory-specific fluctuations become irreducible noise, leaving only statistically smooth corrections requiring fewer parameters.

We establish several independent results concerning extremal, left modular, congruence uniform, and semidistributive lattices. An equivalent characterization of left modular lattices is obtained in terms of edge-labellings, together with necessary and sufficient conditions on the doubling steps in the construction of congruence normal lattices that ensure left modularity or extremality. We prove that a congruence uniform lattice is shellable if and only if it is extremal. We answer a question of Barnard by constructing a counterexample showing that an induced subcomplex of a canonical join complex need not itself be such a complex. Finally, we show that the order dimension of a semidistributive extremal lattice equals the chromatic number of the complement of its Galois graph, generalizing a theorem of Dilworth for distributive lattices. As an application, we determine the dimensions of generalizations of the Hochschild lattice, of the parabolic Tamari lattice, and of some lattices of torsion classes.

Mid-infrared (mid-IR) spectroscopy offers unparalleled opportunities in sensing through chemically specific detection of molecular absorption fingerprints. Yet, its practical applications are limited by the weak light-matter interaction in the mid-IR range and low brightness of mid-IR light sources. Surface-enhanced infrared absorption (SEIRA) spectroscopy addresses the sensitivity limitations by leveraging resonant photonic structures, in particular, plasmonic and frequency-selective dielectric metasurfaces. However, current implementations of SEIRA approach mainly rely on complex instruments and scanning components such as Fourier-transform infrared spectroscopy and tunable external cavity quantum cascade lasers (EC QCLs). Here, we present a compact and high-throughput imaging-based SEIRA platform that combines broadband gradient metasurfaces with a radiofrequency-modulated QCL that generates remarkably broad instantaneous emission spectrum (250 cm$^{-1}$) covering absorption bands of multiple distinct molecular vibrational modes. By matching the resonance spectrum of the compact (1 mm$^2$) broadband gradient metasurface with the laser emission projected on its surface through a dispersive element, we ensure that every QCL spectral component is uniquely addressed for an efficient targeted enhancement of the electromagnetic field. This enables us to use a low-cost and room-temperature mid-IR camera, acquiring in a single frame the enhanced absorption signatures of analytes deposited on the metasurface as a barcode image, thus reducing the acquisition time by up to 3 orders of magnitude compared to the FTIR and EC QCL based measurements. Eliminating the need for tunable light sources, bulky spectrometers, and expensive low-temperature detectors, our approach enables high-throughput, miniaturized, and highly specific molecular diagnostics for diverse chemical and biological applications.

In this paper, we study the domain wall dynamics under electric current in the helimagnet MnAu$_2$. We have found that the threshold electric current of the transition from a multidomain state to a single-chiral domain state in a magnetic field is much lower than that of chirality reversal from a single-chiral domain within certain ranges of temperature and magnetic field. The chirality after the transition depends on whether the magnetic field and electric current were parallel or antiparallel. Numerical calculations based on the Landau-Lifshitz-Gilbert equation reproduced the experimental observations. These results indicate that the domain walls are highly mobile in the helimagnet.

In this work, we develop a convergence framework for iterative algorithms whose updates can be described by a one-parameter family of nonexpansive operators. Within the framework, each step involving one of the main algorithmic operators is followed by a second step which ''relocates'' fixed points of the current operator to the next. As a consequence, our analysis does not require the family of nonexpansive operators to have a common fixed point, as frequently assumed in the literature. Our analysis uses a parametric extension of the demiclosedness principle for nonexpansive operators. As an application of our convergence results, we develop a version of the graph-based extension of the Douglas--Rachford algorithm for finding a zero of the sum of $N\geq 2$ maximally monotone operators, which does not require the resolvent parameter to be constant across iterations.

In this paper, we study the long time behavior of solutions to the defocusing Calogero--Moser derivative nonlinear Schrödinger equation (CM-DNLS). Using the Gérard-type explicit formula, we prove the scattering result of solutions to this equation with initial data in $L_{+}^{2,α}(\mathbb R): = \{u \in L_{+}^2(\mathbb{R}): |x|^α u \in L^2(\mathbb{R})\}$ with some $α>0$. We also characterize the scattering term using the distorted Fourier transform associated with the Lax operator. This is one of the first works that apply the Gérard-type explicit formula to study the long-time behavior of an integrable equation for a broad class of initial data, beyond the previously studied rational cases.

We implement the constrained hyperbolic/parabolic divergence cleaning algorithm into the cosmological smoothed particle magnetohydrodynamics (SPMHD) code {\sc OpenGadget3}, modifying the governing equations so that the scheme can be applied consistently in an expanding cosmological framework. This ensures that divergence errors in the magnetic field are actively propagated away and damped, rather than advected with the flow and partially controlled by source terms as in the previously employed Powell eight-wave approach. We validate the implementation on a series of standard test problems -- the advection of an artificial divergence pulse, the Orszag--Tang vortex, the Brio--Wu shock tube, and a magnetised Zeldovich pancake -- which confirm that the scheme reduces divergence errors while preserving the correct physical evolution. We then apply the method to a fully cosmological simulation of a massive galaxy cluster with $M_\mathrm{200c} \approx 10^{15}~\mathrm{M}_{\odot}$, and compare directly to the Powell-only approach. The overall density structure of the cluster is largely unchanged by the choice of divergence cleaning, and the magnetic field geometry and strength in the cluster core remain similar. In the cluster outskirts ($r \approx 1$--$3~h^{-1}$~Mpc), however, the magnetic field is amplified by a factor of 5--10 compared to the Powell-only run, while the divergence error is reduced by 2--3 orders of magnitude throughout the cluster volume. Our results suggest that accurate divergence control is essential for capturing magnetic field amplification in the low-density, poorly resolved outskirts of galaxy clusters.

Let $\cA$ be a locally coherent Grothendieck category, $\fp\cA$ be the full subcategory of $\cA$ consisting of finitely presented objects and $\ASpec\cA$ be the atom spectrum of $\cA$. In this paper, we classify localizing subcategories of finite type of $\cA$ via open subsets of $\ASpec\cA$. We investigate $\ASpec\fp\cA$ and show that if $\ASpec\fp\cA=\ASpec\cA$, then $\cA$ is locally noetherian. As an application, we specialize our investigation to the case of commutative coherent rings.

Wind turbine vibration monitoring under variable speed operation requires separating nonstationary rotor-order components whose frequencies and operating intervals depend on operating state. These components can occupy local support regions in the short-time Fourier transform (STFT) plane rather than fixed spectral bands or continuous ridges. This study presents time-frequency mode decomposition (TFMD), a segmentation-based method that estimates connected STFT support regions and reconstructs one mode from each region. TFMD selects STFT coefficients with high magnitude, groups them by connected component labeling, filters small regions, expands retained support regions with mask dilation and conflict resolution, and reconstructs modes by inverse STFT. In a synthetic response with six operating states, TFMD separates the components of each state and produces low reconstruction error without specifying the number of components in advance. In a controlled wind turbine blade strain experiment, the first decomposition reconstructs nine modes whose peak frequencies lie near the nominal once per revolution frequencies and whose energies are concentrated in the corresponding operating intervals. Residual decomposition further reveals weaker harmonic structure. These results support TFMD as a practical candidate for vibration analysis under variable speed operation, while offshore field use requires validation under environmental loading and with measured operating references.

We present the scientific case for exploiting the capabilities of the PLATO mission to study bright pulsating white dwarfs across a wide spectral range, including hydrogen-deficient types (GW Vir and DBV stars) and hydrogen-rich classes (classical DAVs, pulsating extremely low-mass DA white dwarfs, and ultra-massive DA white dwarfs). PLATOs exceptional photometric precision, long-duration continuous monitoring, and extensive sky coverage promise transformative advances in white dwarf asteroseismology. Our key objectives include probing the internal structure and chemical stratification of white dwarfs, detecting secular changes in pulsation modes over extended timescales, and discovering rare or previously unknown classes of pulsators. To assess feasibility, we constructed a sample of 650 white dwarf candidates identified within PLATOs Southern LOPS2 field using the PLATO complementary science catalogue combined with Gaia DR3, and derived atmospheric parameters through photometric modeling. This sample comprises 118 DA white dwarfs (including 23 ZZ Ceti candidates), and 41 non-DAs (including 35 DBV candidates). Simulated observations using PlatoSim demonstrate that PLATO will be capable of detecting white dwarf pulsation modes with amplitudes as low as 0.1 mma depending on stellar magnitude, observation duration, pixel location, and the number of contributing cameras. We provide detailed detection limits and visibility forecasts for known pulsators across a representative range of these parameters. Furthermore, we emphasize strong synergies with Gaia astrometry, TESS photometry, and targeted spectroscopic campaigns, which together will enable robust mode identification and detailed stellar modeling. Collectively, these efforts will unlock unprecedented insights into white dwarf origins, evolution and internal physics, and the fate of their planetary systems.

Locally probing pairing in fermionic superfluids, ranging from micro- to macroscopic scales, has been a long-standing challenge. Here, we investigate a new approach that uses Rydberg impurities as a spectroscopic sensor of the surrounding strongly correlated state of ultracold paired fermions. The extended wavefunction of the Rydberg electron induces a finite-range potential that can bind atoms from the BCS medium, forming molecular states. As a consequence, the optical absorption spectrum of the impurity encodes key many-body properties. Using the functional determinant approach, we provide a direct measure of the superfluid gap through frequency shifts of dimer and trimer peaks. The spectra also reveal whether the Cooper pairs are broken or trapped intact. For static Rydberg atoms, we relate this signature of pairing to the suppression of the orthogonality catastrophe due to the superconducting gap resulting in the formation of well-defined polaron quasiparticles. Our work establishes Rydberg atom spectroscopy as a powerful local probe of strongly correlated matter.

The rapid growth of the Internet of Things (IoT) has created large-scale, heterogeneous ecosystems that are increasingly vulnerable to sophisticated, distributed cyber threats. However, many existing anomaly detection systems prioritize detection accuracy while overlooking system-level constraints, such as latency, computational overhead, and energy consumption, thereby limiting their practicality for resource-constrained edge gateways. This paper presents EcoDefender, an edge-oriented hybrid anomaly detection framework that combines Autoencoder (AE)-based latent representation learning with Isolation Forest (IF) anomaly scoring for IoT traffic analysis. The proposed architecture introduces several enhancements over conventional AE-IF pipelines, including anomaly-aware latent manifold regularization, variance-weighted isolation splits in the latent space, and a learnable fusion mechanism that adaptively combines reconstruction error and isolation-based anomaly scores in the presence of potential distributional drift. By compressing high-dimensional traffic features into compact latent representations and performing anomaly scoring in this reduced space, EcoDefender enables lightweight and fully unsupervised anomaly detection suitable for edge deployment. An experimental evaluation of realistic IoT traffic and a distributed Raspberry Pi edge testbed demonstrates that EcoDefender achieves up to 94% detection accuracy while maintaining low computational overhead, with an average CPU usage of 22% and an end-to-end inference latency of 27 ms. Furthermore, energy-aware measurements obtained through device-level power monitoring show an average energy consumption of 0.45 J per inference (0.28 g CO2 emissions), representing a 30% reduction in energy consumption compared with AE-only baselines while sustaining inference throughput of up to 5,000 samples per second.

We investigate the $h$-principle problem for fat distributions. These are maximally non-integrable distributions with natural symplectisations and contactisations, that generalize contact distributions to higher corank. We focus on the corank-$2$ case, where we study a natural class of submanifolds, which we call prelegendrians. Their key feature is that they admit a canonical Legendrian lift to the contactisation. Our main results state that the $h$-principle fails for these submanifolds in all dimensions. To the best of our knowledge, this is the first example of rigidity in the study of maximally non-integrable distributions, outside of contact topology. First, we find an infinite family of $(2n+1)$-tori in the standard fat $(\mathbb{C}^{2n+1},\mathcal{D}_{\mathrm{std}})$, with the following two properties: (1) They all represent the same formal prelegendrian class, (2) but they are not prelegendrian isotopic because they are distinguished by pseudoholomorphic curve invariants of their Legendrian lift. Secondly, we define the notion of prelegendrian stabilization in $(\mathbb{C}^{2n+1},\mathcal{D}_{\mathrm{std}})$. This allows us to take an arbitrary prelegendrian and produce another one, in the same formal class, whose Legendrian lift is loose. In order to prove these results we also develop the fundamentals of the theory of prelegendrians. This includes: (1) introducing the notion of front projection in $(\mathbb{C}^{2n+1},\mathcal{D}_{\mathrm{std}})$, (2) proving that pseudoholomorphic curve invariants are robust under perturbations of the fat structure, allowing us to transport our results to non-standard fat structures, (3) introducing a zooming argument showing that any fat structure in dimension $6$ admits prelegendrians.

We present a novel method for accurately measuring the absolute electric quadrupole moments of light transition elements $(23 \leq Z \leq 30 )$. Our approach is based on performing precision muonic x-ray spectroscopy of the $2s-2p$ manifold, which is also referred to as the Lamb shift. These transitions are too weak to be detected with dispersive methods and too overlapping to be resolved by solid-state detectors. Here, we propose the use of cryogenic microcalorimeters, which possess high efficiency and excellent energy resolution in the relevant energy regime, coupled with state-of-the-art theoretical calculations. We demonstrate the feasibility of this approach by performing extensive calculations and realistic simulations. In this way, we establish that the uncertainty in the absolute moment, which is transferred to the quadrupole moments of all isotopes in the chain, could be reduced by up to an order of magnitude within a day of measurement. These precise reference quadrupole moments serve as valuable inputs for nuclear structure studies and for benchmarking state-of-the-art quantum chemistry calculations in open-shell elements.

We study the spin dynamics in the quasi-2D spin-$1/2$ dimer compound Ba$_2$CuSi$_2$O$_6$Cl$_2$, which exhibits a magnetic field-induced Bose-Einstein condensate (BEC) of triplons. Using nuclear magnetic resonance spin-lattice relaxation rate ($T_1^{-1}$) measurements combined with large-scale quantum Monte Carlo (QMC) simulations, we investigate critical fluctuations across the field-temperature phase diagram. Bridging the behavior observed in 1D and 3D systems, the $T_1^{-1}$ relaxation rate shows a pronounced peak extending well above the Néel temperature $T_N$, indicating strong two-dimensional Berezinskii-Kosterlitz-Thouless (BKT)-type fluctuations. A quantitative match between experimental and theoretical BEC phase boundaries validates an effective XXZ model. The study determines the intrinsic BKT transition temperature $T_{\mathrm{BKT}}$ from QMC, revealing a nearly field-independent $T_{\mathrm{BKT}}/T_N \approx 0.74$. Scaling analysis of the relaxation rate shows critical exponents consistent with 2D universality, and a narrow temperature window is identified where 2D physics dominates. These findings establish Ba$_2$CuSi$_2$O$_6$Cl$_2$ as a model system for exploring BKT dynamics in quantum magnets.

It is well-known that general bilevel linear programs (BLPs) are strongly $NP$-hard, even when the leader's and the follower's objective functions are exact opposites. However, the complexity classification of BLPs remains incomplete when one of the decision-makers has a fixed number of variables or constraints. In this paper, we close the remaining gap in this complexity landscape. Thus, while optimistic BLPs are known to be polynomially solvable when the number of follower variables is fixed, we prove that the corresponding pessimistic problem is strongly $NP$-hard. To the best of our knowledge, this is the first result demonstrating that, under comparable assumptions, the pessimistic formulation can be computationally harder than its optimistic counterpart. In addition, we prove that BLPs remain polynomially solvable in both the optimistic and the pessimistic settings when the number of follower constraints is fixed. We further investigate whether these polynomial-time solvability results persist for bilevel convex quadratic programs. While the optimistic formulation remains polynomially solvable when the number of follower variables is fixed, we prove that the pessimistic formulation with a fixed number of follower constraints becomes $NP$-hard. In other words, unless $P = NP$, there is a strict complexity gap between bilevel programs with linear and convex quadratic objective functions. Finally, we show that replacing a convex quadratic follower objective with a nonconvex quadratic one renders the optimistic problem $NP$-hard, even when both follower dimensions are fixed.

In this paper, we give a unified treatment of the local well-posedness for the wave kinetic equation in almost critical weighted $L^r$ spaces with $2 \leq r \leq \infty.$ The proof builds on ideas from our earlier works \cite{AmLe24, AmLemain25}. Our approach is based solely on kinetic tools, with no appeal to Fourier theory.