We establish a quantitative homogenization result for an interface moving through a field of sufficiently sparse but possibly impenetrable random obstacles. From a physical viewpoint, such problems arise e.g. in the context of the motion of dislocations or magnetic domain walls in a material with impurities. More precisely, given an interface moving by forced mean curvature flow -- with a positive global driving force plus a spatially fluctuating (negative) driving force modeling the obstacles -- , we prove that the effective large-scale behavior of the forward front is governed by a constant-speed effective motion. For typical values of the global forcing, on large scales of the order $\varepsilon^{-1}$ we obtain a (relative) error estimate for arrival times of the front of the order $\varepsilon^{1/9-}$. Previous stochastic homogenization results for forced mean curvature motion in the literature have required a positive pointwise lower bound on the combined forcing, which implies the absence of any actual obstacles capable of locally blocking the interface motion. In contrast, our results are valid even in the presence of islands with locally negative forcing, potentially allowing for locally pinned interfaces and eventually enclosures left behind the main front. Thus, our homogenization result applies to settings closer to (but still strictly away from) the pinning-depinning transition.

We establish polynomially improved $L^\infty$ bounds for eigenfunctions of magnetic Laplacians on hyperbolic surfaces in the critical energy regime. We also show that, below the critical energy, the Hörmander bound is saturated by explicit eigenstates, which we call \emph{magnetic zonal states}. These states resemble zonal harmonics on the sphere and equidistribute on Lagrangian tori in phase space.

De Morgan bisemilattices are expansions of distributive bisemilattices by an involution satisfying De Morgan properties. They have attracted interest both as algebraic models of analytic containment logics, and as a case study for a certain generalisation of the Płonka sum construction (De Morgan- Płonka sums). In this paper, we provide a complete description of the lattice of subvarieties of the variety DMBL of De Morgan bisemilattices. For each subvariety in the lattice, we identify a finite set of finite generators, a characterisation of the De Morgan-Płonka representations of its members, and a syntactic description of its valid identities. In many cases, we also give an axiomatisation relative to DMBL.

In this work, we report coherent perfect absorption (CPA) of anti-modes in an indirectly coupled magnon--polariton system. By examining both single and indirectly coupled cases, we experimentally distinguish the modal decay rate $γ$ from the effective decay rate $γ_{\rm{eff}}$. At CPA, $γ_{\rm{eff}} = 0$, leading to a vanishing output and a visually narrow spectrum in the dB-scale, while the intrinsic linewidth set by $2γ$ remains unchanged, demonstrating that the effective decay rate dictates the spectral amplitude rather than the physical loss. Furthermore, in the indirectly coupled system, CPA persists over a broad, magnetically tunable detuning range, in contrast to the single-detuning CPA observed in the directly coupled case, thereby enabling magnetically reconfigurable and frequency-selective microwave absorbers.

We aim to study star-forming regions and the spectral energy distribution of two possibly interacting galaxies, PGC 56121 and PGC 56125, in the Hickson Compact Group 77. We utilized the far-ultraviolet (FUV) channel of the Ultra Violet Imaging Telescope (UVIT) on board AstroSat to observe and produce FUV images of the galaxies. Our FUV images are at a much higher resolution in comparison to those obtained from previous galaxy surveys by GALEX in the near-UV and those from PS-1, DSS. We have identified several star-forming regions in the two possibly interacting galaxies, PGC 56121 and PGC 56125. These two galaxies form a pair widely separated in redshift and are seen in projection. We also report the presence of a candidate tidal dwarf galaxy at the end of one of the tidal tails located to the east of the pair, and we identified three major star-forming regions in the tidal dwarf. The spectral energy distribution of three galaxies in the system is presented and analyzed to investigate the key physical properties, such as stellar mass, dust mass, total luminosity, and star formation history, of the three galaxies. Based on these observations and on a comparison with observations in radio, these three galaxies are probably part of a small group of interacting galaxies.

This paper investigates the problem of covert communications in a heterogeneous wireless network where multiple communication modalities are used simultaneously. In this setup, a legitimate transmitter sends confidential data to its receiver by selecting multiple modalities with the goal of maximizing communication covertness against a passive adversary (Willie) while satisfying a transmission rate requirement. We analyze two distinct scenarios for a given observation time by Willie. The two scenarios are: (i) Willie knows the modalities selected by the friendly transmitter, and (ii) Willie is unaware of the selected modalities. We first derive the optimal detector for Willie that minimizes the detection error probability (DEP) in both cases. For the first scenario, we derive an exact expression for the DEP and provide a computationally efficient approximation. For the second scenario, we introduce the DEP expressions in the low-signal-to-noise ratio (SNR) regime at Willie. Building on this analysis, we propose a novel low-complexity modality set selection technique designed to maximize the DEP subject to a rate constraint. Numerical simulations validate the derived analytical expressions and demonstrate that the proposed modality set selection technique achieves near-optimal performance, outperforming benchmark schemes.

We study which classic modal definability and preservation results survive when attention is restricted to finite structures, where many first-order transfer theorems are known to break down. Several semantic characterizations for modal formula classes survive the passage to the finite, while a number of first-order preservation theorems for basic frame operations fail. Our main positive result is that the Bisimulation Safety Theorem does transfer to finite structures. We also discuss computability aspects, and analogues in the finite for the Goldblatt-Thomason theorem and for modal correspondence theory.

Driven nonlinear oscillators constitute a universal paradigm for understanding synchronization, frequency pulling, and frequency comb formation in nonequilibrium systems. Here, we realize such an emergent nonlinear oscillator in strongly interacting cesium Rydberg vapor, where coherent optical excitation, dissipation, and long-range interactions give rise to a driven-dissipative time crystal phase with intrinsic oscillation frequencies. Applying a radio-frequency (RF) field allows controlled tuning of the intrinsic oscillation frequency. Under RF heterodyne conditions, we observe intermodulation, frequency pulling, and, at strong drive, the emergence of a comb-like spectrum in the atomic coherence. We quantitatively capture these observations using a four-level mean-field model and demonstrate a classical analogue with a driven Van der Pol oscillator. Our results establish interacting Rydberg ensembles as a tunable platform for exploring nonequilibrium time-crystalline order, nonlinear synchronization, and frequency comb generation in many-body atomic systems.

Chalcogenides-rich transition metal compounds host a rich landscape of emergent quantum phenomena that are intimately governed by their quasi-one-dimensional chemical-bonding frameworks and their response to external perturbations such as pressure. Here, we report a pressure-induced iso-symmetric structural transition in the quasi-one-dimensional compound CrNbSe$_5$, in which the electronic ground state is controlled not by symmetry breaking but by a continuous reorganization of local bonding interactions. Applied pressure reversibly tunes CrNbSe$_5$ between semiconducting and semimetallic states, enabling access to low- and high-carrier electronic regimes through direct modulation of metal-chalcogen bonding. High-pressure single-crystal X-ray diffraction directly resolves the evolution of Cr-Se and Nb-Se bond distances, coordination polyhedra, and connectivity, revealing a fully reversible semimetal-semiconductor-semimetal transition driven by gradual yet cooperative bond rearrangements within a preserved crystallographic symmetry. In contrast to chemical substitution, which irreversibly alters composition and introduces disorder, pressure acts as a clean, continuous control parameter that reshapes the bonding landscape without disrupting structural symmetry. These results establish CrNbSe$_5$ as a model system for electronically driven phase switching via tunable chemical bonding, highlighting iso-symmetric bond reorganization as a powerful design principle for pressure-controlled electronic and spintronic functionalities.

The sky localisation of about $10$ to $100~\text{deg}^2$, which is expected to be achieved in all-sky blind searches for gravitational waves from supermassive black hole binaries (SMBHBs) with Pulsar Timing Array (PTA) experiments, has long been posed as a prohibitive factor in utilising these sources as standard sirens for precision cosmology. We propose a solution to this problem, which makes use of targeted searches rather than all-sky blind searches for SMBHBs. Using our simulated data informed by current PTA observations, we show that the Chinese Pulsar Timing Array (CPTA) alone could infer the Hubble constant with a precision of 2~km/s/Mpc. Such precision in an independent cosmological probe could provide decisive support in the resolution of the Hubble tension. We demonstrate the application of our method to several simultaneously observed SMBHBs, as well as the method's robustness against confusion between the host galaxies of SMBHB sources in realistic observing scenarios.

High-fidelity quantum operations are the cornerstone of fault-tolerant quantum computation. In open quantum systems, traditional optimal control only passively resists decoherence, leaving environment-induced uncertainty as a fundamental performance bottleneck. To overcome this, we propose a new optimal control framework with flag ancillas and the Flag-GRAPE algorithm, which can actively tailor the system's noise structure. Through embedding post-selection directly into the objective function, Flag-GRAPE correlates decoherence errors with the ancilla's unexpected state. Subsequent measurement and post-selection effectively expel this uncertainty, circumventing the fidelity bounds of traditional control. Numerical simulations in a superconducting quantum circuit demonstrate a $51\%$ reduction in infidelity compared to traditional closed-system pulses and also show that such enhancement is robust across broad noise regimes. Furthermore, by actively converting unstructured decoherence into heralded erasure errors, Flag-GRAPE is inherently compatible with quantum error correction. We demonstrate this by initializing a logical cat-code state, showing that the combination between Flag-GRAPE and QEC yields immediate state preparation enhancements. This new framework can reduce hardware overhead for fault-tolerant architectures and open up a practical path toward logical state preparation gain in near-term experiments.

Developing quantum algorithms to simulate fluid dynamics has become an active area of research, as accelerating fluid simulations could have significant impact in both industry and fundamental science. While many approaches have been proposed for simulating fluid dynamics on quantum computers, it is largely unclear whether these algorithms will provide speedup over existing classical approaches. In this paper we give evidence that quantum computers cannot significantly outperform classical simulations of fluid dynamics in general. We study two models of fluids: the Korteweg-de Vries (KdV) equation, which models shallow water waves, and the incompressible Euler equations, which model ideal, inviscid fluids. We show that any quantum algorithm simulating the KdV equation or the Euler equations for time $T$ requires $Ω(T^2)$ and $e^{Ω(T)}$ copies of the initial state in the worst case, respectively. These lower bounds hold for the task of preparing the final state, and similar bounds hold for history state preparation. We prove the lower bound for the KdV equation by investigating divergence of solitons. For the Euler equations, we show that instabilities enable fast state discrimination.

The coordination complexes of Yb(III) exhibit some of the longest spin coherence times among 4f compounds, making them a promising platform for molecular quantum technologies. While spin-phonon relaxation remains a limiting factor for coherence times even at low temperature, its control through chemical design has the potential to push these spin qubits prototypes beyond current limits. With the aim of providing insights on how to chemically control spin-phonon relaxation, we here present a full ab initio study of spin-phonon dynamics for three Yb(III) molecules exhibiting minimal chemical differences, yet quantitatively different spin relaxation times. Results show that low-temperature relaxation is governed by Raman processes triggered by a small group of largely delocalized low-energy phonons. The analysis of these contributions highlights that the modulation of spin-phonon coupling by molecular structure modifications beyond the first coordination shell are highly non-trivial in nature and hard to rationalize in simple chemical terms. These findings call for a conceptual step change from the attempt to use simple magneto-structural correlations to interpret the effect of molecular structural modifications on spin-phonon relaxation, and present predictive first-principles frameworks as a potential driving force of future chemical design strategies

In this paper, we investigate the distribution of values of the complete exponential sum $S_{p,χ}(θ)=\sum_{n=1}^p χ(n)e(nθ)$, where $p$ is a large prime, $χ$ is a Dirichlet character (mod $p$) of order $d\geq 2$, and $θ$ varies over certain subsets of $[0,1]$. When $d=2$, these sums correspond to the values of the Fekete polynomial associated with $p$ on the unit circle. Our first result gives precise estimates for the tail of the distribution of $|S_{p,χ}(θ)|$ in a large uniform range, when $θ$ varies over the set $\{(k+1/2)/p\}_{1\leq k\leq p}$. This improves upon a result of Conrey, Granville, Poonen, and Soundararajan. We also consider the distribution of the maximum of $|S_{p,χ}(θ)|$ for $θ\in I_k=[k/p,(k+1)/p]$, and obtain upper and lower bounds for the distribution of large values of this maximum, valid in a uniform range that is nearly optimal: we make this precise in the paper. Our results provide strong support for a conjecture of Montgomery on the maximum of Fekete polynomials on the unit circle. In particular, we show that the distribution function exhibits double-exponential decay, with a surprising difference in behavior between the cases of even and odd order $d$.

Computational physics is a key part of what it means to do physics in the twenty-first century. However, upper division computational physics remains a largely understudied area. We set out to understand the experiences of students in an upper division computational physics lab course. To that end we conducted semi-structured interviews with five students at the end of their second of three terms in the course sequence. We then analyzed these interviews utilizing the emerging framework of Physics Computational Literacy. We found that the way students express how they learn computational physics implies they are making tradeoffs between their development of the different aspects of computational literacy. Additionally, we found that how students approach developing social computational literacy varies across individuals, and is driven by unspoken assumptions.

We study compactness and noncompactness phenomena for the CR Yamabe equation on compact strictly pseudoconvex CR manifolds. First, in dimension five we establish uniform \emph{a priori} estimates for families of positive solutions of subcritical equations for the conformal CR sub-Laplacian \[ L_{J}u = u^{p}, \] with $p$ bounded away from the critical exponent, assuming positivity of the CR Yamabe constant and positivity of the $p$-mass at every point. As a consequence, the corresponding set of solutions is precompact in Hölder topologies. Secondly, we consider the equivariant CR Yamabe problem for a compact subgroup $G$ of pseudo-Hermitian transformations. We construct a $G$-invariant CR structure on $S^{3}$, not equivalent to the standard one, for which the associated CR Yamabe equation admits a sequence of $G$-invariant solutions whose maxima diverge, thereby proving noncompactness in the equivariant setting. The arguments combine a Pohozaev-type identity in pseudohermitian normal coordinates with a blow-up analysis and Liouville-type classification results on the Heisenberg group.

Memory-(in)efficiency is a crucial consideration that oftentimes prevents deployment of state-of-the-art distributed algorithms in real-life modern networks. In the context of the MST problem, roughly speaking, there are three types of algorithms. The algorithm of Gallager-Humblet-Spira and its versions are memory- and message- efficient, but their running time is at least linear in the number of vertices $n$, even when the unweighted diameter $D$ is much smaller than $n$. The algorithm of Garay-Kutten-Peleg and its versions are time-efficient, but not message- or memory-efficient. The more recent algorithms of are time- and message-efficient, but are not memory-efficient. As a result, GHS-type algorithms are much more prominent in real-life applications than time-efficient ones. In this paper we develop a deterministic time-, message- and memory-efficient algorithm for the MST problem. It is also applicable to the more general partwise aggregation problem. We believe that our techniques will be useful for devising memory-efficient versions for many other distributed problems.

Generative Artificial Intelligence (gen-AI) is rapidly becoming more integrated into today's classrooms in all ranges of education. In higher education, Gen-AI is often seen as a resource for students, aiding them in drafting outlines, solving simple mathematical problems, or even decoding or constructing code. In this paper, we analyze essay-based interviews (N=6) from an upper-division computational physics course, in which physics majors addressed their views and attitudes towards Gen-AI and how it affects their learning. We analyzed the concepts of creativity and gen-AI using the Four C Model, a framework encompassing four types of creativity. Our analysis of the data involved coding and characterizing students' definitions of creativity and generative AI. Our findings revealed two main observations: first, students conceptualized their creativity primarily within mini-c and little-c; second, students perceived gen-AI as a resource and learning tool but expressed skepticism regarding its accuracy and creativity.

Heterointerfaces are ubiquitous in modern devices, found in technologies ranging from microelectronics to structural components for energy applications. Many of these emerging technologies are found in applications such as satellites, batteries, and next generation nuclear reactors, that are subject to harsh environments. In some scenarios, multiple extreme conditions, such as irradiation and corrosion, act on the material simultaneously. Extending the lifetime of these technologies is dependent on a detailed understanding of how their component materials platforms and interfaces respond in extreme environments, where irradiation and corrosion may couple in unique ways, distinct from corrosion under ambient conditions. Oxides, which form readily over metal underlayers, can act as protective coatings; enhancing the robustness of oxide overlayers to protect underlying metal alloys is a potential avenue towards corrosion mitigation. Here we study the impact of irradiation-induced non-equilibrium defects on charge segregation and electric fields at and near multi-phase oxide heterointerfaces. We perform a detailed study of irradiated Fe2O3-Cr2O3 thin film heterostructures using first-principles DFT electronic structure modeling paired with 4D-STEM DPC and EELS techniques to measure nanoscale changes in electric fields. Our results show clear evidence that irradiation drives substantial modulation of interfacial electric fields that can be tailored by controlling the atomistic chemical structure of the oxide interface. We show that irradiation can selectively induce built-in electric fields, thereby altering their direction; this suggests a pathway to engineering protective oxide heterostructure overlayers that can electrically control the spatial distribution of defects, with significant implications for the design of corrosion-resistant materials for extreme environments.

In quantum theory, equilibrium statistical mechanics is usually formulated through the canonical ensemble, whose privileged status is tied to the Euclidean continuation of time evolution. The microcanonical ensemble, by contrast, is commonly introduced as a separate spectral construction. In this work we show that this asymmetry is representational rather than structural. We formulate the system in an extended Hilbert space in which time is promoted to an auxiliary clock degree of freedom and physical states are selected by a reparametrization-invariant constraint operator $\hat C = \hat P_T + \hat H$. The corresponding projector $δ(\hat C)$ provides a single unified object from which both canonical and microcanonical ensembles emerge as complementary projections in the clock sector. In the clock-time representation, a purely imaginary clock separation yields the Euclidean kernel and the canonical partition function. In the conjugate clock-energy representation, the same projector reduces to the spectral operator $δ(\hat H-E)$ and hence to the microcanonical density of states. The main consequence is structural: canonical and microcanonical statistics need not be introduced as independent constructions, since both are already encoded in the same constrained quantum dynamics.

Binary fluid turbulence distinguishes itself from ordinary fluid turbulence by virtue of interfacial dynamics. Whether Kolmogorov-like scaling laws also exist for binary fluid turbulence is a fundamental question to explore. Starting from tensor formalism à la von Kármán and Howarth, here we derive exact scaling laws for isotropic Cahn-Hilliard-Navier-Stokes (CHNS) turbulence both in terms of two point correlators and increments. In particular, we derive the CHNS analogs for $1/3$, $4/3$, $2/15$ and $4/5$ laws known for isotropic hydrodynamic turbulence and show that the new scaling laws contain contributions both from the bulk flow and interface. The $2/15$ and $4/5$ laws of CHNS turbulence are found to be expressed purely in terms of two-point correlators and structure functions and their derivatives, respectively. However, unlike their hydrodynamic counterparts, these relations involve additional contributions from non-longitudinal directions. By means of direct numerical simulations with up to $1024^3$ grid points, all the derived exact laws are numerically verified and the scale dependence of the cascade rates obtained from different exact laws are thoroughly compared. As one moves from the homogeneous (but not necessarily isotropic) divergence form to the isotropic $4/5$ form, the inertial range is found to shift towards larger scales with a comparatively flatter cascade rate profile as a result of successive integrations over the small scales.

Differential Privacy (DP) is widely adopted in data management systems to enable data sharing with formal disclosure guarantees. A central systems challenge is understanding how DP noise translates into effective protection against inference attacks, since this directly determines achievable utility. Most existing analyses focus only on membership inference -- capturing only a threat -- or rely on reconstruction robustness (ReRo). However, under realistic assumptions, we show that ReRo can yield misleading risk estimates and violate claimed bounds, limiting their usefulness for principled DP calibration and auditing. This paper introduces reconstruction advantage, a unified risk metric that consistently captures risk across membership inference, attribute inference, and data reconstruction. We derive tight bounds that relate DP noise to adversarial advantage and characterize optimal adversarial strategies for arbitrary DP mechanisms and attacker knowledge. These results enable risk-driven noise calibration and provide a foundation for systematic DP auditing. We show that reconstruction advantage improves the accuracy and scope of DP auditing and enables more effective utility-privacy trade-offs in DP-enabled data management systems.

MC networks are envisioned to enable synthetic information exchange between nanoscale biological entities. For many algorithm proposals in the MC research field, the question of implementation at nanoscales and in biological environments remains open. Chemical reaction networks (CRNs) provide a natural framework to model computing processes in biological systems, while detailed simulations capture realistic stochastic effects. In this work, we present ChemSICal-Net, a comprehensive CRN simulation model of a chemical receiver implementing successive interference cancellation (SIC) to differentiate messages from multiple transmitters. We present the structure of the SIC algorithm in the form of basic chemical building blocks and incorporate clocked timing control by a chemical oscillator. We propose an adaptive Bayesian optimization (BO) scheme with a Gaussian process surrogate to find appropriate values for the reaction rate constants and the initial concentrations and show that it outperforms baseline methods from related work based on a fair computational cost metric. Then, the performance of the ChemSICal-Net framework is evaluated stochastically across a range of clock speeds and in different configurations focusing on communication system metrics such as detection accuracy and decision time. Our results highlight that the timing via a chemical clock can improve the detection accuracy by a factor of 2 in scenarios with shorter decision times, which underlines how the trade-off between decision time and detection probability can shape CRN design choices. The BO scheme is shown to reliably optimize parameters for different configurations by approximately one order of magnitude compared to the non-optimized case. Our system reveals the need for a multi-scale approach with external BO and stochastic simulation of molecular reaction dynamics for communication-metric-focused system design.

We present a method for optimizing stellarator configurations that combine omnigenity and piecewise omnigenity (pwO). Within the \texttt{OOPS} optimization framework [Liu \textit{et al.}, arXiv:2502.09350 (2025)], we introduce a mapping technique that can ``squeeze'' general omnigenous fields to approximate pwO in the high-field side. Using this approach, we obtain a range of optimized configurations that combine poloidal omnigenity (PO) and pwO, spanning different field periods and aspect ratios. We further show that these configurations are compatible with a magnetic well. The resulting configurations exhibit favorable neoclassical transport and bootstrap current properties while partially relaxing the strict constraints of omnigenity. These results suggest that such configurations are promising candidates for future stellarator reactors.

We propose and analyze a unified framework that interleaves peer-to-peer opinion dynamics with performative effects of learning systems. While network theory studies how opinions evolve via social connections, and performative prediction examines how learning systems interplay with individuals' opinions, neither captures the emergent dynamics when these forces co-evolve. We model this interplay as a recursive feedback loop: a platform's predictions influence individual opinions, which then evolve through social interactions before forming the training data for the next platform model update. We demonstrate that this co-evolution induces a novel equilibrium that qualitatively differs from standard network equilibria. Specifically, we show that standard predictive objectives act as a ``homogenizing force" driving networks toward consensus even under conditions where classical opinion-dynamics models lead to disagreement. Further, we demonstrate how learning under partial observations creates spillover effects among individuals, even if individuals are not susceptible to peer-influence. Finally, we study a platform that systematically deviates from standard predictive objectives, and demonstrate how classical opinion-dynamics models underestimate the equilibrium response to node-level interventions. We complement our theoretical findings with semi-synthetic simulations on social network data. Combined, our results illuminate performativity as an important, so far neglected, qualifying factor in social networks.

For mixed-integer linear programming and linear programming it is well known that symmetries can have a negative impact on the performance of branch-and-bound and linear optimization algorithms. A common strategy to handle symmetries in linear programs is to reduce the dimension of the linear program by aggregating symmetric variables and solving a linear program of reduced dimension. In their work ``Dimension Reduction via Color Refinement'' (DRCR), Grohe, Kersting, Mladenov and Selman show that it is sufficient to run a fast color refinement algorithm to detect permutation symmetries and reduce the dimension of the linear program. We extend DRCR in two directions. First, we show that DRCR can be extended to reflection symmetries, which generalize permutation symmetries. Second, we show the folklore result that DRCR can be applied to the continuous columns of mixed-integer linear programs. In order to derive additional reductions on the integer variables we use affine totally unimodular decompositions to reformulate mixed-integer linear programs into mixed-integer linear programs with fewer integer variables. Computational experiments on MIPLIB 2017 collection set using SCIP 10 show that DRCR is an effective tool for handling symmetries. For the linear programming relaxations, DRCR with reflection symmetries yields a modest reduction in running time compared to the original DRCR procedure. For mixed-integer linear programming models, DRCR is very effective at reducing the solution time compared to the default configuration of SCIP. Moreover, the developed DRCR detection algorithms are fast and scale well to large problem instances.

The detection of single particles or molecules represents a critical milestone in the development of biosensing technologies. Recently developed optical sensors based on quasi-bound states in the continuum (qBICs) have primarily focused on detecting global refractive index changes, aiming to simultaneously enhance both refractive index sensitivity and quality ($Q$) factors. However, sensors capable of resolving local refractive index perturbations, such as the binding of a nanometer-sized molecule on a surface, remain elusive and have not yet been demonstrated in BIC geometries due to the limited $Q$ factors and relatively large mode volumes. Here, we demonstrate low-contrast BIC metasurfaces that can perform sensing with a virus-sized single-nanoparticle resolution. The qBIC resonance operating at the critical coupling condition exhibits an experimental $Q$ factor of 4.5 x 10$^4$ in heavy water. The strong interaction between the localized electric field and polystyrene nanoparticles with a diameter of 100 nm enable the experimental observation of step-like resonance wavelength shifts, serving as signatures of individual particle binding events. Furthermore, binding-induced modifications to the qBIC resonance alter the optical confinement and asymmetry factor, inducing changes not only in the resonance wavelength but also in the linewidth and amplitude with single-particle sensitivity. Combined with position-insensitive response and free-space accessible features, low-contrast BIC metasurfaces provide a user-friendly platform for next-generation single-molecule sensing integrated with microfluidic systems.

Magnetic relaxation drives plasma toward lower-energy equilibria under helicity constraints. In ideal magnetohydrodynamics (MHD), helicity is locally conserved, while resistive theories such as Taylor relaxation preserve only global helicity. This distinction has important implications for structure-preserving numerical methods. We compare three finite element formulations: an unconstrained scheme that does not conserve helicity, a mixed method based on finite element exterior calculus that preserves all local helicities, and a Lagrange multiplier approach that enforces only global helicity conservation. Numerical experiments on braided and knotted magnetic fields show that local helicity preservation prevents spurious reconnection and maintains nontrivial topology in ideal MHD or magneto-friction, whereas enforcing only global helicity allows further relaxation through local reconnection. Numerical results on magnetic knots and braids are provided. These results clarify how different levels of discrete helicity constraints influence magnetic relaxation and equilibrium structure in numerical computation.

We present a method for analyzing general time series by employing the history state formalism of quantum mechanics. This formalism allows us to describe a complete evolution based on a single quantum state, the history state, which simultaneously includes -also as a quantum system- the reference clock. It naturally leads to the concept of system-time entanglement, with the ensuing entanglement entropy constituting a measure of the effective number of distinguishable states visited in the history. Through a quantum coherent state embedding of the time series data, it is then possible to associate a quantum history state to the series. The gaussian overlap between these coherent states provides thus a smooth measure of distinguishability between the series data. The eigenvalues of the corresponding overlap matrix determine in fact the entanglement spectrum and entropy of the history state, which provide a rigorous characterization of the evolution. As illustration, the formalism is applied to typical financial time-series data. Through the entanglement entropy and spectrum, different evolution regimes can be identified. Entanglement based volatility indicators are also derived, and compared with standard volatility measures.

Quantum channel discrimination is a fundamental task in quantum information processing. In the one-shot regime, discrimination between two candidate channels is characterized by the diamond norm. Beyond this basic setting, however, many scenarios in distributed quantum information processing remain unresolved, motivating notions of distinguishability that capture the power of the available resources. In this work, we formulate a theory of testers for bipartite channel discrimination, leading to the concept of the entanglement cost of bipartite channel discrimination: the minimum Schmidt rank $k$ of a shared maximally entangled state required for local protocols to achieve the globally optimal success probability. We introduce $k$-injectable testers as a tester-based description of entanglement-assisted local discrimination and, in particular, study the class of $k$-injectable positive-partial-transpose (PPT) testers, which constitutes a numerically tractable relaxation of the practically relevant class of LOCC testers. For every $k$, we derive a semidefinite program (SDP) for the optimal success probability, which in turn yields an efficiently computable one-shot PPT entanglement cost. To render these optimization problems numerically feasible, we prove a symmetry-reduction principle for covariant channel pairs, thereby reducing the effective dimension of the associated SDPs. Finally, by dualizing the SDP, we derive bounds on the composite channel-discrimination problem and illustrate our framework with proof-of-principle examples based on the depolarizing channel, the depolarized SWAP channel, and the Werner--Holevo channels.