Papers

Markovian open quantum systems are well modeled by the Lindblad Master Equation (ME) $\frac{\mathrm{d}}{\mathrm{d} t} \rho_t = \mathcal{L} \rho_t$, where $\mathcal{L}$ is a linear (super-)operator and $\rho_t$ is the system state, a positive matrix. When designing or characterizing a quantum system, one is usually interested in the steady state $\rho_\infty$ (such that $\mathcal{L} \rho_\infty = 0$), the first few excited states, and trajectories $t\mapsto \rho_t$. In finite dimension, $\rho_t$ is an $n\times n$ matrix, $\mathcal{L}$ thus typically costs $n^4$ to store explicitly as a dense matrix, and $O(n^6)$ to diagonalize or invert exactly, making standard linear algebraic techniques expensive for large systems. However, $\mathcal{L}$ usually costs only $O(n^3)$ to apply. This makes iterative methods appealing, but they do not work without a good preconditioner. In this article, our main observation is that a part of the Lindblad equation, corresponding to the so-called no-jump evolution $\mathcal{S}$, can be inverted efficiently. Using this inverse map, we introduce an auxiliary completely positive trace-preserving (CPTP) map $\Phi$ whose fixed point is directly related to $\rho_\infty$, all the other eigenvalues having smaller magnitude. The map $\Phi$ is thus well suited to iterative methods, and $\rho_\infty$ can be found in a few Arnoldi iterations. Using the same inverse map $\mathcal{S}^{-1}$ as preconditioner, we compute the low-lying spectrum efficiently via shift-invert Arnoldi, and, as a proof of concept, build an implicit time integrator that is competitive on stiff systems in the low-precision regime. For the steady-state and low excited states problems, our methods scale like $O(n^3)$ per iteration and offer state-of-the-art performance on CPU and GPU.

We study holographic subregion complexity (HSC) across a fully backreacted insulator/superconductor transition in an AdS-soliton background and compare it with holographic entanglement entropy (HEE) and holographic complexity based on the complexity=volume (CV) proposal. Both HSC and HEE signal the second-order transition. For a strip subsystem, competing connected and disconnected Ryu-Takayanagi surfaces give rise to a confinement/deconfinement transition. At fixed chemical potential in the superconducting phase, HSC exhibits a finite jump at the critical width, whereas HEE remains continuous. Beyond this width, HSC grows linearly with the strip width, while HEE is constant. At fixed strip width, HSC first decreases and then increases with chemical potential for $\ell<\ell_c$, opposite to HEE, but increases monotonically for $\ell>\ell_c$. After consistent normalization and subtraction of the respective insulating references, the half-space HSC and CV complexity densities are analytically identical. These results show that HSC can diagnose the insulator/superconductor transition, but its qualitative response remains sensitive to the subsystem scale and entanglement-wedge topology.

Practical robust self-testing of multipartite entanglement has so far been restricted to small-scale systems due to error bounds that degrade severely with system size. In this work, we establish multipartite self-testing with robustness independent of the size of the quantum network. We derive a fully analytic, device-independent self-testing bound for $n$-qubit Greenberger-Horne-Zeilinger (GHZ) states. The bound scales linearly with the observed violation error and lies universally within a constant factor of two from a theoretical upper bound. Furthermore, the operator-inequality framework reduces the verification of the conjectured optimal bound to a highly efficient numerical check, which we perform up to $n=100$. Consequently, GHZ entanglement can be certified under a fixed noise level in arbitrarily large systems, enabling scalable device-independent verification.

Purely leptonic bound states provide precision probes of QED. Positronium $(e^+e^-)$ and muonium $(\mu^+e^-)$ have long been observed, whereas dimuonium $(\mu^+\mu^-)$ and tauonium $(\tau^+\tau^-)$ remain undiscovered. We study exclusive vector-leptonium electroproduction in $ep$ collisions within nonrelativistic QED. We include the Bethe–Heitler and double deeply virtual Compton scattering contributions and their interference, and calculate the NLO QCD hard-scattering kernels entering the dominant Compton form factor $\Hcal$ within collinear GPD factorization. The NLO QCD correction to the DDVCS contribution changes from a strong suppression at low photon virtuality to a sizable enhancement as the lower virtuality cut is raised, with the gluon channel providing the dominant contribution. Bethe–Heitler production dominates the exclusive rate, supporting dedicated dimuonium searches at the EIC and JLab, with larger samples expected at higher-energy electron–proton colliders. The much larger positronium samples provide a high-statistics environment for precision QED studies, whereas tauonium production remains strongly suppressed.

We investigate information-flow generation in a nonequilibrium two-bead system coupled to two heat baths. We show that the system acts as an information-flow generator in both overdamped and underdamped regimes, with the underdamped dynamics revealing a divergence of the scaled information flow along specific paths in the thermal asymmetry–inertia parameter space that is hidden in the overdamped limit. This information generation suggests a possible route toward information engines and demon-like mechanisms in nanomachines. A symmetry-perturbation analysis of the response landscape of information flow reveals a geometric structure reminiscent of a Ginzburg–Landau framework: the symmetric reference state can correspond to a minimum or maximum depending on the perturbation direction, while the flat overdamped landscape develops a finite curvature under inertia. Mass asymmetry shifts the resulting maxima, and Hessian eigenvalue and eigenvector analysis reveals level touching of principal modes and bimodality along a constant-diffusion path. These results establish a minimal framework for understanding how inertia and microscopic heterogeneity shape information landscapes in nonequilibrium systems, with potential extensions to more complex heterogeneous networks.

The statistical description and acoustic diagnostics of anisotropic turbulence remain challenging. Real Schur flows (RSFs), prototype models of component-wise dimensionally reduced flows (CWDRFs), provide effective platforms for studying such problems. We combine absolute statistical equilibrium with the acoustic analogy to investigate helicity effects on the far-field directivity of sound radiated from three types of CWDRFs: two different RSFs, and a further reduction of them (liberated Schur flow). We evaluate the directivity from the vortex-sound source spectrum which is calculated with the Wick theorem from the absolute equilibirum Gaussian ensemble. Helicity amplifies the dimensional reduction induced anisotropy of the directivity functions across all CWDRFs, with distinct patterns.

We consider the difference between ensemble and volume average in cosmology. It is known that for sufficiently weak long-range correlations the root mean square of the difference, which we call ergodicity bias, decays like $R^{-3/2}$ in the limit of large volume $R^3$. We calculate the condition this imposes on the power spectrum of a Gaussian random field. We quantify the bias for finite $R$, and show that the $R\to\infty$ limit is of little relevance for cosmological observations when the measured scales and correlations extend to the size of the observable universe. We consider curvature, density, and velocity perturbations. On large scales the bias is important in all three cases. For the density perturbations, which are observationally the most relevant, the relative bias first exceeds 100% at the separation $r=177$ Mpc, and is larger than 100% for all $r>560$ Mpc. It should be taken into account when comparing ensemble and volume averages for large-scale structure. The bias is also large for the cosmic microwave background temperature perturbations on large angular scales, but this is not relevant for observations, as their analysis does not involve volume averaging.

Localization-delocalization transitions have recently been proposed for building a class of efficient quantum many-body critical sensors. This work scrutinizes metrological performances of such devices by focusing on the Aubry-André-Harper model that supports a localization-delocalization transition at finite strength of the onsite potential. We identify a metrological quantum-to-classical crossover driven by the interplay between noise and system size, whereby quantum-enhanced scaling of the quantum Fisher information persists only up to a finite, noise-dependent characteristic system-size. We first consider thermal noise and show that, at and near the localization-delocalization transition, the quantum Fisher information exhibits quantum-enhanced scaling for small systems but the system is stripped of this advantage beyond the characteristic crossover length. The crossover length decreases with increasing temperature. We then consider imperfections in the lattice hopping strengths and find a qualitatively similar crossover. There, the quantum-enhanced regime, identified with super-extensive scaling, gives way to an extensive scaling-a classical-limited weaker form-at sufficiently large system sizes. Thus, distinct noise mechanisms lead to a common limitation on the scalability of quantum-enhanced sensing: increasing the probe size beyond a noise-dependent limit can destroy the metrological quantum advantage.

The extension of coherent lattice contrast into the energy loss region in high-resolution transmission electron microscopy (HRTEM) is described by a pulse-like electron-sample interaction in the energy/time uncertainty limit. It generates a wave packet by electron self-interference in any coherent-inelastic scattering event with energy loss. The width of this wave packet is characterized by a self-coherence length ls({\Delta}E) that is predictable because an intrinsic decoherence phase around one radian is set by the expectation value for phase fluctuations. In this case the visibility of interference contrast from a crystalline sample with lattice parameter a is limited by a Rayleigh-like transfer factor P(ls, a) in the self-coherently illuminated sample area. The model is verified by energy-filtered HRTEM images of hexagonal BN and identifies energy-loss-induced phase noise as a single-electron visibility limit distinct from resolution limitations caused by ensemble-coherence or counting-statistical noise.

Near-infrared (NIR) emitters in hexagonal boron nitride (hBN) have recently emerged as bright and spectrally stable light sources, but they have so far been found at locations set by the local defect environment rather than by design. Here we show that NIR emitters can be activated at predefined sites by combining single-shot femtosecond laser writing with annealing in an oxygen-rich environment. To our knowledge, this is the first demonstration of site-selective activation of NIR emitters in hBN. The written matrices are recovered in post-anneal photoluminescence maps, including in collection bands centred at 800 and 900 nm. Site-resolved spectra under 532, 635 and 785 nm excitation show narrow lines extending to 1 um; 83% of the spectra acquired at written sites under 785 nm excitation and 71% under 635 nm excitation contain at least one resolved peak above 810 nm. The integrated emission increases with writing-pulse energy over the range studied, and many sites host more than one emitter, which identifies lower writing energies as the route to single-emitter occupancy. Photon-correlation measurements on selected sites show antibunching, with a raw, uncorrected second-order correlation value g(2)(0) of 0.31 in a band centred at 850 nm. Spectral time series reveal bands that persist over the recorded intervals together with intermittent emission beyond 900 nm. Comparison with identically written, argon-annealed samples indicates that the annealing atmosphere controls the spectral range of the activated emitters, while the laser defines where they form.

High-accuracy measurement systems operating in complex operational environments, such as airborne and seaborne gravimetry, are severely affected by interacting external influences (disturbances) including temperature variations, inertial accelerations, and platform rotations. This work aims to develop and prove a general method for compensating such disturbances beyond the limits of conventional approaches. We present a general framework based on three pillars: a multi-sensor system, supervised machine learning, and a dedicated laboratory -training platform-. This measurement technique was investigated through two experimental case studies relevant to airborne and seaborne gravimetry: (i) temperature and thermal-gradient rejection in a high-sensitivity tri-axial accelerometer, and (ii) pitch and roll rejection for vertical acceleration estimation. The experiments highlighted that, although the general framework provides a useful guideline, its application to airborne and seaborne gravimetry is challenging and not straightforward, requiring the development of dedicated and innovative experimental solutions. This difficulty arises from the specific nature of the measurand-gravity-which cannot be easily varied under controlled conditions. In this work, we present a dedicated approach to addressing these challenges.

We investigate lattice relaxation and band structures of helical and alternating twisted trilayer WSe$_2$ and MoTe$_2$ using machine-learning force fields and large-scale ab initio calculations. Interference between the two bilayer moiré lattices generates a supermoiré lattice that, upon relaxation, reconstructs into a few dominant domain types with locally commensurate bilayer moiré lattices. Because the systems lack $C_{2z}$ symmetry, domains otherwise related by this symmetry become energetically and topologically distinct, unlike in twisted trilayer graphene. Band structure calculations show that the topmost valence bands originate from the $K$ ($K'$) valleys and carry domain-dependent valley Chern numbers. The resulting supermoiré lattice hosts a mosaic of topologically inequivalent domains, offering a platform for exploring correlated and topological physics.

We studied the evolution of a butterfly-shaped coronal hole (CH) observed from 2025 September 8 to 14 using SDO/AIA 193~Å\ images and SDO/HMI line-of-sight magnetograms. The CH boundary was identified using a fixed 100~DN intensity threshold, and its area, mean EUV intensity, and total unsigned magnetic flux were tracked across the solar disk. As the CH approached the central meridian, its area increased from approximately $7.70\times10^{16}$ to $1.63\times10^{17}$~m$^{2}$ and its unsigned magnetic flux from $8.68\times10^{21}$ to $1.91\times10^{22}$~Mx, while the mean 193~Å\ intensity decreased from about 61 to 45~DN. The area and unsigned flux showed similar temporal trends, whereas the intensity varied oppositely. Near central-meridian passage, these quantities remained relatively stable for several days. A high-speed solar-wind stream was detected at 1~AU about 2–4 days later, reaching 600–750~km~s$^{-1}$, consistent with the CH being its likely solar source. These results link the morphological, radiative, and magnetic evolution of the CH with the subsequent high-speed solar-wind stream.

We investigate a nonequilibrium steady-state model consisting of two coupled beads with arbitrary masses in contact with two thermal baths at different temperatures. Using a covariance-matrix approach together with numerical simulations of the underdamped Langevin dynamics, we characterize steady-state probability distributions, heat transport, and entropy production. We show that irreversibility measures such as entropy production and heat current are invariant under an exchange of the bead masses, whereas energy-storage observables depend explicitly on the mass arrangement in a symmetrical set up. This reveals a fundamental distinction: energy observables exhibit path dependence in singular mass limits, while transport and irreversibility remain well defined. We show that kinetic temperatures provide the natural variables governing the thermodynamics of the system: their difference controls transport and entropy production, while their sum determines the mean energy via a model specific generalized equipartition relation. In the infinite-mass limit, only constitutive relations expressed in terms of kinetic temperatures remain meaningful. Thus, energy, transport, and irreversibility are unified through kinetic temperatures as the organizing variables. We also derive an effective temperature that defines an equilibrium-like canonical distribution. Finally, we analyze the notion of ergodicity and show that the time-averaged observables converge significantly faster than the ensemble averages.

The frequency and properties of stellar streams around dwarf galaxies remain observationally under-explored. Building a statistically significant sample is challenging because dwarf galaxies are smaller, fainter, and far more numerous than massive galaxies. We present the first results from a systematic survey for stellar streams around dwarf galaxies. We first introduce a classification metric for satellite accretion features (streams, shells, and asymmetric stellar haloes) using DECam imaging from the DES and DECaLS surveys. Applying this metric to the DES footprint, we find a low observed frequency of accretion features (5.1$\%$) and no bona fide stellar streams (with only one identified in DECaLS). We consider whether the apparent excess of shells relative to streams can be explained by observational biases. Our results indicate that stellar streams are observationally rare in the local Universe, motivating further theoretical work to determine whether this reflects genuine differences in merger rates across galaxy mass regimes.

Local constraints govern the low-energy physics of frustrated matter, but familiar ice-type rules constrain flux-like quantities and are insensitive to handedness. Here we show that handedness itself can be imposed as an exact local quantum constraint without selecting an axis in spin space. We construct positive-semidefinite, SU(2)-invariant parent Hamiltonians whose complete zero-energy space on a tetrahedron has a prescribed chirality sign, rather than selecting a particular chiral wave function. For spin-1/2 the local term is a rank-one projector onto a chiral tetrahedral singlet, while for arbitrary spin it factorizes as $B^\dagger B$ through a singlet-annihilation operator, with a completely characterized kernel given by the span of the globally rotated chiral color-ice states. For coherent states, the same zero-energy condition becomes an $S$-independent nonlinear constraint in which three spin directions determine the fourth through a Möbius transformation; compositions of these maps define constraint holonomies on extended lattices. Connecting the same local constraint in different ways produces qualitatively different collective regimes: corner-sharing lattices retain exponentially large quantum ground-state kernels, with rigorous lower bounds exceeding conventional ice benchmarks; edge-sharing lattices support subdimensional plane or line zero modes; while triangular constructions suppress nonuniform coherent deformations and contain the complete Anderson tower of tetrahedral magnetic order at exactly zero energy. Two inequivalent triangular coverings further show that harmonic zero-mode counting does not determine the size of the quantum kernel. These results establish a tractable setting in which local handedness, nonlinear constraint geometry, and quantum degeneracy can be disentangled and related directly to the connectivity of the constraint network.

In this article, we extend learning rules from real binary to complex-valued spins. This formulation allows for a robust and natural representation of grayscale patterns, where spins behave as multi-state neurons and can be stored in a complex-valued weight matrix. We describe a rule that performs better than standard methods, such as Hebbian learning, to encode information in a suitable form for pattern retrieval with networks of oscillators. Since in neural networks it is of interest to have local and incremental learning rules, we prove the extension of a result by Diederich and Opper with our complex-valued spin formulation. We then test the behavior of the associative memory for the system of oscillators under different circumstances for both real-valued, as well as complex-valued correlated and random patterns.

End-to-end weather forecasting systems produce skillful global gridded and station forecasts directly from raw Earth observations, replacing the numerical weather prediction pipeline, including data assimilation, at a fraction of its cost. These systems are deterministic and issue no uncertainty. Here we render the Aardvark Weather model probabilistic by attaching one stochastic mechanism to each component: learned, input-dependent noise at the observation encoder, capturing aleatoric uncertainty inherited from the observing system, and Monte Carlo dropout in the processor, capturing epistemic uncertainty in the learned dynamics. The resulting nested ensemble attributes forecast spread to the two sources through a law-of-total-variance decomposition, cross-checked by withholding observation streams. Probabilistic finetuning significantly improves the mean forecast, by 4.2% on average across variables and lead times. The ensemble is calibrated against ERA5 through the medium range (spread-skill ratio 0.98), keeps station RMSE within 2.4% of the deterministic model while beating it in CRPS at every lead time, and trails the operational ECMWF ensemble. The encoder branch behaves as observation-driven uncertainty. Component-attributed uncertainty makes end-to-end forecasts more transparent, a step toward observation-driven digital twins of the atmosphere.

Color centers in silicon offer great possibilities for scalable quantum technologies. The M-center, proposed to originate from a carbon-hydrogen complex, offers telecommunications-band emission and a paramagnetic ground state similar to the T-center. Here, we report on photoluminescence lines in the vicinity of the M-center and investigate their properties, including their dependence on temperature, implantation fluence, implantation isotope, and annealing temperature. Three emission lines are observed that are blue-shifted by 1.1, 2.8 and 3.6 meV relative to the 761 meV zero phonon line of the M center, where the 2.8 meV line exhibits negative thermal quenching and is therefore proposed to originate from a second excited state of the M-center. The remaining blue-shifted emission lines, together with two additional red-shifted (4.7 and 6.4 meV) emission lines display normal thermal quenching, and are unaffected by an isotope shift of the implanted carbon atom ($^{12}$C versus $^{13}$C implantation) and implantation fluence. Thus, they likely arise either from other defects with similar emission energies or from a perturbed configuration of the M-center.

Linear quantum repeater chains based on Werner-state purification (the BBPSSW protocol) and entanglement swapping (the BDCZ scheme) are fundamental to entanglement distribution in quantum networks. However, they operate under a stringent operation reliability threshold and rely on resource-intensive recurrence purification rounds, each consuming two entangled pairs to probabilistically produce one. In the literature, hyperentanglement has been proposed to exploit multiple degrees of freedom (DOF), such as polarisation and spatial modes, to encode independent entangled states within a single photon pair. This has led to the definition of DAEPP (DOF-Assisted Entanglement Purification Protocol), which we propose to integrate with the BDCZ scheme, resulting in a chain protocol that we call DAHR (DOF-Assisted Hyperentanglement Repeater). The DAEPP step distils the fidelity of a DOF by consuming other(s). In this work, we propose and analyse a DAHR variant which integrates DAEPP at every segment of an end-to-end path combined with BDCZ. We derive a closed-form end-to-end fidelity recursion that embeds single-segment DAEPP into the BDCZ scheme and give a strict resource lower bound for any BDCZ baseline utilising BBPSSW purification to match DAHR's per-segment effective fidelity. At a representative asymmetric operating point informed by prior experiment, we show numerically that matching DAHR's single-photon-pair performance requires two to three rounds of BBPSSW purification. Additionally, below a critical operation reliability, no amount of BBPSSW rounds matches DAHR's one DAEPP round performance.

Layering is a ubiquitous feature of astrophysical objects. Motivated by the fact that physical black holes retain the layered structure of their progenitor stars when viewed in the time concepts synchronizable with the clock of an outside fixed-position probe, we investigate linear perturbations and gravitational-wave (GW) echoes from a compact object composed of two concentric thin shells. Compared with the single-shell case, the double-shell structure introduces an extra barrier in the effective potential and partitions the wave propagation space into four coupled effective cavities. As the mass ratio of the inner shell increases, new spectral peaks enter from the high-frequency side of the echo spectrum; the second and later peaks shift toward higher frequencies; and the lowest-frequency peak first shifts toward lower frequencies and then returns to its $q=0$ position. We call this variation pattern spectral-peak queueing (SQ). Its existence suggests that GW echoes can be used as probes for the internal structure of compact objects under consideration.

Neutral atom qubits are one of the leading approaches for implementation of a large scale quantum computer. The original proposals for neutral atom qubits were formulated more than 25 years ago, with first demonstrations of a universal gate set following 10 years later. In the last few years the performance and scale of neutral atom qubit arrays has developed at a rapid pace leading to demonstrations of quantum algorithms, and logical qubits for fault tolerant error correction. This contribution reviews the physics of the neutral atom approach, surveys current capabilities, and provides an outlook for future progress.

The design of the IceCube-Gen2 observatory, proposed as a next-generation extension of IceCube, includes a surface array consisting of scintillators and radio antennas. In addition to several such detectors already deployed at IceCube's surface array at the South Pole, a complete prototype station including three SKALA antennas has been operating at the Pierre Auger Observatory for several years. This setup has been used to successfully observe radio signals from air showers, demonstrated through coincident observations with the Auger Surface Detector. In this contribution, we present an updated analysis of these radio signals, and compare them to CoREAS simulations using the reconstruction from the Auger Surface Detector as input.

Physical learning lets a trainable material or network use its own physical response to carry error signals, reducing the need for a separately programmed backward computation. We ask what determines whether such a system follows conventional gradient descent or evolves along a genuinely different learning trajectory. Our canonical model is a directed layered transport network in which every node redistributes a fixed amount of flow, so learning preserves positivity and total mass. In this model, conservation constrains only the allowable learning directions. Within the matched response class studied here, adjoint matching gives the physical output response a symmetric form. Non-negative mode-wise feedback then produces a reciprocal closed-loop response and a reweighted gradient flow. Adding an antisymmetric boundary component makes the closed-loop response rotational: the learning path can turn while the error driving that update still decreases at that moment. Turning is not automatically beneficial. Its finite-step effect is set by local curvature, and its accumulated effect also depends on step selection and on the new states visited along the path. Numerical consistency checks reproduce the exact response structure, predict the sign of the local effect across new network families, and show how trajectory drift can negate a local advantage. These results separate the roles of conservation, reciprocity, and nonreciprocity in physical learning.

In the early nineties, the introduction of turbo codes revolutionized classical error correction. The idea was mainly applied on two types of codes: convolutional turbo codes and turbo product codes. The first type of codes was adapted to quantum error correction which initiated the theory of quantum serial turbo codes. In this paper, we present a theory for quantum block turbo codes, the quantum analog of the second type of turbo codes. We describe their iterative decoding algorithm and simulate their performances on a depolarizing channel for different constituent codes.

We provide a comprehensive study of anomalies and discrete torsion in the worldsheet theories of Type II and Type I string theories on a general ten-dimensional target space. In the modern understanding, the anomaly of a worldsheet theory is characterized by an invertible field theory in three dimensions, and invertible field theories are classified by the Anderson dual of a suitable bordism theory. To study the anomaly cancellation condition, we employ the explicit model of the Anderson dual constructed by Yamashita and Yonekura. We find that, for both Type II and Type I string theories, the anomaly of the worldsheet theory is cancelled if and only if the target space is orientable and admits a spin structure. We also determine the discrete torsion and clarify its physical meaning. It includes the distinctions between Type IIA and Type IIB string theories and between ordinary Type I and Sugimoto string theories.

Magnetic nanoparticles (MNP) can be used in magnetic immunoassays (MIA) by functionalizing them with antibodies. In homogeneous assays that follow a "mix-and-measure" approach, it is then sufficient to add the sample in question and evaluate the response of the MNPs using a magnetic measurement method. Magnetic Particle Spectroscopy (MPS) is a fast and sensitive method for this purpose, capable of determining the binding state by measuring changes in Brownian relaxation. For further analysis, alternating current susceptometry (ACS) is considered, although it is significantly more time-consuming and therefore no option for applications interested in point of care detection. In this study, we aim to further improve the approach of MIA evaluated by MPS. To this end, we use self-synthesized scFv fragments instead of whole IgG antibodies during functionalization in order to keep the size of the BNF-Dextran MNP with 80 nm nominal diameter as small as possible, which allows for greater relative size changes upon binding to an analyte. Virus-like particles (VLP) and the N protein of SARS-CoV-2, which were also produced in-house, are used as analytes. Due to multiple binding sites, these form cluster structures, which, in the case of VLP, were investigated in greater depth ACS to assess their field dependence. In addition, the sensitivity of the assays was analyzed as a function of MNP concentration, and the detection limit for both analytes was estimated. We found that, using scFv-functionalized MNPs, we were able to detect low concentrations of just 490 fM of SARS-CoV-2 VLP and 1.7 nM of the N protein. However, the slightly above-proportional increase in sensitivity as the MNP concentration decreases does not automatically imply a better detection limit.

The dynamical Lie algebra (DLA) governs the controllability, expressibility, and simulation complexity of a quantum system. Explicitly computing it has been a major computational bottleneck: brute-force Lie closure scales exponentially in the number of qubits $n$. Many applications, however, consult only the isomorphism type of the DLA. We introduce PauLie, an open-source framework that decides this isomorphism type for DLAs generated by arbitrary Pauli strings, building on the anticommutation-graph reduction of Aguilar et al. PauLie runs in $O(n|\mathcal{G}|\max(n,|\mathcal{G}|))$ time, where $|\mathcal{G}|$ is the number of generators, turning DLA classification into a routine preprocessing step. We demonstrate its use as a structural oracle for routing Lie-algebraic simulation and Cartan decomposition, diagnosing barren plateaus in variational quantum algorithms, and engineering universal Pauli string generator sets with optimal generation rate.

The Epoch of Reionisation imprints its history and morphology on the Cosmic Microwave Background temperature and polarisation anisotropies through two effects: The kinetic Sunyaev Zel'dovich (kSZ) effect and Thomson scattering. To perform joint analyses of these observables and put tight constraints on the reionisation history and morphology, a common reionisation model is necessary. We present a quick, physically-accurate analytical approach to derive consistently the angular power spectra of the three main resulting imprints that are the spatial fluctuations of the Thomson optical depth, the patchy kSZ effect, and the scattering and screening B-modes. The approach differs from existing analytical models, as it is calibrated on high-resolution hydrodynamical simulations and depends on physical parameters of reionisation. Our predicted power spectra are consistent with the ones derived from cosmological simulations, whilst including more physical information – such as the typical size of ionised bubbles and the duration of reionisation. We provide an updated detectability assessment and show that both $C_\ell^{\tau\tau}$ and $C_\ell^{BB}$ could be measured by experiments similar to CMB Stage 4 and CMB-HD, respectively. We show the complementarity of the three observables in constraining reionisation history and morphology, and illustrate the potential of their joint analysis to get a global picture of reionisation. This analytical model will be a powerful tool in the analysis of upcoming CMB data, either alone or in combination with independent datasets such as measurements of the high-redshift 21cm signal. The code to derive these spectra is publicly available online as the preion Python package.

Breakpoint graphs originate in comparative genomics, where their alternating cycles encode relationships between genomes. We study a constrained class of three-colored breakpoint graphs associated with permutations and develop cycle-refined generating functions for two extremal families. These families have a natural topological interpretation: their canonical surfaces are, respectively, the sphere and the projective plane. The spherical family is characterized by noncrossing configurations, while the projective-plane family admits a different decomposition involving a distinguished family of Möbius ladders. The resulting generating-function equations retain the full cycle structure but nevertheless admit substantial reductions. This leads to explicit Catalan-weighted evaluations, polynomiality results for refined cycle statistics, and a connection between a natural diagonal specialization and noncrossing trees. The two topological families exhibit markedly different combinatorial mechanisms, providing complementary examples of how local transformations of breakpoint graphs can control refined permutation enumerations. As a further application, the same Catalan-weighted sums arise in asymptotic unitary-Weingarten expansions for entanglement of random Gaussian states in linear optics. The combinatorial results determine the leading and constant-order moment polynomials entering the Rényi entropy expansion, with the projective-plane contribution giving the finite-size constant correction.