Daily Papers

When an LLM agent reads a confidential file, then writes a summary, then emails it externally, no single step is unsafe, but the sequence is a data leak. We call this safety drift: individually safe actions compounding into violations. Prior work has measured this problem; we predict it. SafetyDrift models agent safety trajectories as absorbing Markov chains, computing the probability that a trajectory will reach a violation within a given number of steps via closed form absorption analysis. A consequence of the monotonic state design is that every agent will eventually violate safety if left unsupervised (absorption probability 1.0 from all states), making the practical question not if but when, and motivating our focus on finite horizon prediction. Across 357 traces spanning 40 realistic tasks in four categories, we discover that "points of no return" are sharply task dependent: in communication tasks, agents that reach even a mild risk state have an 85% chance of violating safety within five steps, while in technical tasks the probability stays below 5% from any state. A lightweight monitor built on these models detects 94.7% of violations with 3.7 steps of advance warning at negligible computational cost, outperforming both keyword matching (44.7% detection, 55.9% false positive rate) and per step LLM judges (52.6% detection, 38.2% false positive rate) while running over 60,000x faster.

Implantable wireless bioelectronic devices enable communication and/or power transfer through RF wireless connections with external nodes. These devices encounter notable design challenges due to the lossy nature of the host body, which significantly diminishes the radiation efficiency of the implanted antenna and tightens the wireless link budget. Prior research has yielded closed-form approximate expressions for estimating losses occurring within the lossy host body, known as the in-body path loss. To assess the total path loss between the implanted transmitter and external receiver, this paper focuses on the free-space path loss of the implanted antenna, from the body-air interface to the external node. This is not trivial, as in addition to the inherent radial spreading of spherical electromagnetic waves common to all antennas, implanted antennas confront additional losses arising from electromagnetic scattering at the interface between the host body and air. Employing analytical modeling, we propose closed-form approximate expressions for estimating this free-space path loss. The approximation is formulated as a function of the free-space distance, the curvature radius of the body-air interface, the depth of the implanted antenna, and the permittivity of the lossy medium. This proposed method undergoes thorough validation through numerical calculations, simulations, and measurements for different implanted antenna scenarios. This study contributes to a comprehensive understanding of the path loss in implanted antennas and provides a reliable analytical framework for their efficient design and performance evaluation.

Zipf's law appears in many application areas but does not have a closed form expression, which may make its use cumbersome. Since it coincides with the truncated version of the Zeta distribution, in this paper we propose three approximate closed form expressions for the truncated Zeta distribution, which may be employed for Zipf's law as well. The three approximations are based on the replacement of the sum occurring in Zipf's law with an integral, and are named respectively the integral approximation, the average integral approximation, and the trapezoidal approximation. While the first one is shown to be of little use, the trapezoidal approximation exhibits an error which is typically lower than 1\%, but is as low as 0.1\% for the range of values of the Zipf parameter below 1.

We numerically study excitation transfer in an artificial LH1-RC complex -- an N-site donor ring coupled to a central acceptor -- driven by a narrowband optical mode and evolved under a Lindblad master equation with loss and dephasing. In the absence of disorder, the light-driven system exhibits a tall, narrow on-resonance efficiency peak (near unity for our parameters); dephasing lowers and narrows this peak without shifting its position. Off resonance, the efficiency shows environmentally assisted transport with a clear non-monotonic dependence on dephasing and a finite optimum. Under static disorder, two regimes emerge: photon-ring coupling and diagonal energetic disorder mix the drive into dark ring modes, activate dissipative channels, and depress efficiency over a detuning window, whereas intra-ring coupling disorder has a much smaller impact in the tested range; increasing the intra-ring coupling g moves dark-mode crossings away from the operating detuning and restores near-peak performance. In the ordered, symmetric, single-excitation, narrowband limit we analytically derive closed-form transfer efficiencies by projecting onto the k{=}0 bright mode and solving the photon--bright mode--acceptor trimer via a Laplace/linear-algebra (determinant) formula; these expressions include a probability-conservation identity eta + sum_k L_k = 1 that benchmarks the simulations and quantitatively predicts the resonant line shape and its dephasing-induced narrowing. A minimal ring toy model further reproduces coherent trapping and its relief by moderate dephasing (ENAQT). These analytics are exact in the ordered limit and serve as mechanistic guides outside this limit, yielding practical design rules for robust, bio-inspired light-harvesting devices.

To meet the challenges of high-resolution molecular spectroscopy, increasingly sophisticated spectroscopic techniques were developed. For a long time FTIR and laser-based spectroscopies were used for these studies. The recent development of dual-comb spectroscopy at high-resolution makes this technique a powerful tool for gas phase studies. We report on the use and characterization of the IRis-F1, a tabletop mid-infrared dual-comb spectrometer, in the newly developed step-sweep mode. The resolution of the wavenumber axis is increased by step-wise tuning (interleaving) and accurate measurement of the laser center wavelength and repetition frequency. Doppler limited measurements of N2O and CH4 reveal a wavenumber accuracy of 1E-4 cm-1 on the covered range of > 50 cm-1. Measured half-widths of absorption lines show no systematic broadening, indicating a negligible instrument response function. Finally, measurements of nitrogen pressure broadening coefficients in the v4 band of methane show that quantum cascade laser dual-comb spectroscopy in step-sweep mode is well adapted for measurements of precision spectroscopic data, in particular line shape parameters.

The study demonstrates the capabilities of a vector-based approach for calculating stoichiometric coefficients in chemical equations, using black powder as an illustrative example. A method is proposed for selecting and constraining intermediate interactions between reactants, as well as for identifying final products. It is shown that even a small number of components can lead to a large number of final and intermediate products. Through concrete calculations, a correlation is established between the number of possible chemical equations and the number of reactants. A methodology is proposed for computing all possible chemical equations within a reaction system for arbitrary component ratios, enabling the derivation of all feasible chemical reactions. Additionally, a method is developed for calculating the chemical composition for a fixed set of reactants, allowing for the evaluation of the set of products resulting from all possible chemical interactions given a specified initial composition.

In this paper, a mathematical model is developed to describe the evolution of the concentration of compounds through a gas chromatography column. The model couples mass balances and kinetic equations for all components. Both single and multiple-component cases are considered with constant or variable velocity. Non-dimensionalisation indicates the small effect of diffusion. The system where diffusion is neglected is analysed using Laplace transforms. In the multiple-component case, it is demonstrated that the competition between the compounds is negligible and the equations may be decoupled. This reduces the problem to solving a single integral equation to determine the concentration profile for all components (since they are scaled versions of each other). For a given analyte, we then only two parameters need to be fitted to the data. To verify this approach, the full governing equations are also solved numerically using the finite difference method and a global adaptive quadrature method to integrate the Laplace transformation. Comparison with the Laplace solution verifies the high degree of accuracy of the simpler Laplace form. The Laplace solution is then verified against experimental data from BTEX chromatography. This novel method, which involves solving a single equation and fitting parameters in pairs for individual components, is highly efficient. It is significantly faster and simpler than the full numerical solution and avoids the computationally expensive methods that would normally be used to fit all curves at the same time.

Blueshifted absorption is the classic spectroscopic signature of an accretion disc wind in X-ray binaries and cataclysmic variables (CVs). However, outflows can also create pure emission lines, especially at optical wavelengths. Therefore, developing other outflow diagnostics for these types of lines is worthwhile. With this in mind, we construct a systematic grid of 3645 synthetic wind-formed H-alpha line profiles for CVs with the radiative transfer code SIROCCO. Our grid yields a variety of line shapes: symmetric, asymmetric, single- to quadruple-peaked, and even P-Cygni profiles. About 20% of these lines -- our `Gold' sample -- have strengths and widths consistent with observations. We use this grid to test a recently proposed method for identifying wind-formed emission lines based on deviations in the wing profile shape: the `excess equivalent width diagnostic diagram'. We find that our `Gold' sample can preferentially populate the suggested `wind regions' of this diagram. However, the method is highly sensitive to the adopted definition of the line profile `wing'. Hence, we propose a refined definition based on the full-width at half maximum to improve the interpretability of the diagnostic diagram. Furthermore, we define an approximate scaling relation for the strengths of wind-formed CV emission lines in terms of the outflow parameters. This relation provides a fast way to assess whether -- and what kind of -- outflow can produce an observed emission line. All our wind-based models are open-source and we provide an easy-to-use web-based tool to browse our full set of H-alpha spectral profiles.

The interdiffusion coefficients are estimated either following the Wagner's method expressed with respect to the composition (mol or atomic fraction) normalized variable after considering the molar volume variation or the den Broeder's method expressed with respect to the concentration (composition divided by the molar volume) normalized variable. On the other hand, the relations for estimation of the intrinsic diffusion coefficients of components as established by van Loo and integrated diffusion coefficients in a phase with narrow homogeneity range as established by Wagner are currently available with respect to the composition normalized variable only. In this study, we have first derived the relation proposed by den Broeder following the line of treatment proposed by Wagner. Further, the relations for estimation of the intrinsic diffusion coefficients of the components and integrated interdiffusion coefficient are established with respect to the concentration normalized variable, which were not available earlier. The veracity of these methods is examined based on the estimation of data in Ni-Pd, Ni-Al and Cu-Sn systems. Our analysis indicates that both the approaches are logically correct and there is small difference in the estimated data in these systems although a higher difference could be found in other systems. The integrated interdiffusion coefficients with respect to the concentration (or concentration normalized variable) can only be estimated considering the ideal molar volume variation. This might be drawback in certain practical systems.

In this paper we study quasinormal modes and absorption cross sections for the (1+3)-dimensional Bardeen black hole surrounded by perfect fluid dark matter. Studies of the massless scalar field is already done in Sun:2023slzl. Hence, in this paper we will focus on the massive scalar field perturbations and massless Dirac field perturbations. To compute the quasinormal modes we use the semi-analytical 3rd-order WKB method, which has been shown to be one of the best approaches when the effective potential is adequate and when n < ell and n < lambda. We have also utilized the P\"oschl-Teller method to compare the valus obtained using the WKB approach. We have computed quasinormal frequencies by varying various parameters of the theory such as the mass of the scalar field mu, dark matter parameter alpha and the magnetic charge g. We have summarized our solutions in tables and figures for clarity. As for the absorption cross section, we used third order WKB approach to compute reflection, transmission coefficients and partial absorption cross sections. Graphs are presented to demonstrate the behavior of the above quantities when the dark matter parameter and mass of the massive scalar field are varied.

In this paper, a novel machine learning derived control performance assessment (CPA) classification system is proposed. It is dedicated for a wide class of PID-based control industrial loops with processes exhibiting dynamical properties close to second order plus delay time (SOPDT). The proposed concept is very general and easy to configure to distinguish between acceptable and poor closed loop performance. This approach allows for determining the best (but also robust and practically achievable) closed loop performance based on very popular and intuitive closed loop quality factors. Training set can be automatically derived off-line using a number of different, diverse control performance indices (CPIs) used as discriminative features of the assessed control system. The proposed extended set of CPIs is discussed with comprehensive performance assessment of different machine learning based classification methods and practical application of the suggested solution. As a result, a general-purpose CPA system is derived that can be immediately applied in practice without any preliminary or additional learning stage during normal closed loop operation. It is verified by practical application to assess the control system for a laboratory heat exchange and distribution setup.

Hyperspectral pansharpening consists of fusing a high-resolution panchromatic band and a low-resolution hyperspectral image to obtain a new image with high resolution in both the spatial and spectral domains. These remote sensing products are valuable for a wide range of applications, driving ever growing research efforts. Nonetheless, results still do not meet application demands. In part, this comes from the technical complexity of the task: compared to multispectral pansharpening, many more bands are involved, in a spectral range only partially covered by the panchromatic component and with overwhelming noise. However, another major limiting factor is the absence of a comprehensive framework for the rapid development and accurate evaluation of new methods. This paper attempts to address this issue. We started by designing a dataset large and diverse enough to allow reliable training (for data-driven methods) and testing of new methods. Then, we selected a set of state-of-the-art methods, following different approaches, characterized by promising performance, and reimplemented them in a single PyTorch framework. Finally, we carried out a critical comparative analysis of all methods, using the most accredited quality indicators. The analysis highlights the main limitations of current solutions in terms of spectral/spatial quality and computational efficiency, and suggests promising research directions. To ensure full reproducibility of the results and support future research, the framework (including codes, evaluation procedures and links to the dataset) is shared on https://github.com/matciotola/hyperspectral_pansharpening_toolbox, as a single Python-based reference benchmark toolbox.

We present a new method for generating emission spectra from polycyclic aromatic hydrocarbons (PAHs) in arbitrary radiation fields. We utilize the single-photon limit for PAH heating and emission to treat individual photon absorptions as independent events. This allows the construction of a set of single-photon emission "basis spectra" that can be scaled to produce an output emission spectrum given any input heating spectrum. We find that this method produces agreement with PAH emission spectra computed accounting for multi-photon effects to within simeq10% in the 3-20~{rm mu m} wavelength range for radiation fields with intensity U<100. We use this framework to explore the dependence of PAH band ratios on the radiation field spectrum across grain sizes, finding in particular a strong dependence of the 3.3 to 11.2~mum band ratio on radiation field hardness. A Python-based tool and a set of basis spectra that can be used to generate these emission spectra are made publicly available.

Recent advances in photonic optimization have enabled calculation of performance bounds for a wide range of electromagnetic objectives, albeit restricted to single-material systems. Motivated by growing theoretical interest and fabrication advances, we present a framework to bound the performance of photonic heterostructures and apply it to investigate maximum absorption characteristics of multilayer films and compact, free-form multi-material scatterers. Limits predict trends seen in topology-optimized geometries -- often coming within factors of two of specific designs -- and may be exploited in conjunction with inverse designs to predict when heterostructures are expected to outperform their optimal single-material counterparts.

We present an extragalactic HI 21-cm absorption lines catalog from a blind search at z leqslant 0.35, using drift-scan data collected in 1325.6 hours by the ongoing Commensal Radio Astronomy FasT Survey (CRAFTS) and FAST All Sky HI Survey (FASHI), which spans a sky area of 6072.0 deg^{2} and covers 84533 radio sources with a flux density greater than 12 mJy. 14 previously identified HI absorbers and 20 newly discovered HI absorbers were detected, comprising 15 associated systems, 10 intervening systems, and 9 systems with undetermined classifications. Through spectral stacking, the mean peak optical path, mean velocity-integrated optical path, mean FWHM and mean HI column density are measured to be 0.47 and 0.30; 27.19 and 4.36 km s^{-1}; 42.61 and 9.33 km s^{-1}; 0.49 and 0.08 T_{s} times 10^{20}cm^{-2}K^{-1}, for the associated and intervening samples, respectively. Statistical analysis also reveals that associated systems tend to be hosted by red (g-r>0.7) galaxies at lower redshifts, whereas galaxies hosting intervening HI absorption are typically found at higher redshifts and are of a bluer (g-rleqslant0.7) type. A noticeable difference is observed in the positions of foregrounds, backgrounds of intervening systems, and high-redshift and low-redshift associated systems on the WISE color-color diagram. All identified foreground sources in our sample have W1-W2 magnitudes below 0.8, suggesting no Active Galactic Nuclei (AGN). In contrast, backgrounds of intervening systems tend to have W1-W2 magnitudes above 0.8, indicating AGN presence. For associated absorption, most low-redshift (zleqslant0.5) systems show W1-W2 values below 0.8, while higher-redshift associated absorption (z>0.5) displays a broader range of W1-W2 values.

Superconducting nanowire single-photon detectors are widely used in various fields of physics and technology, due to their high efficiency and timing precision. Although, in principle, their detection mechanism offers broadband operation, their wavelength range has to be optimized by the optical cavity parameters for a specific task. We present a study of the optical absorption of a superconducting nanowire single photon detector (SNSPD) with an optical cavity. The optical properties of the niobium nitride films, measured by spectroscopic ellipsometry, were modelled using the Drude-Lorentz model with quantum corrections. The numerical simulations of the optical response of the detectors show that the wavelength range of the detector is not solely determined by its geometry, but the optical conductivity of the disordered thin metallic films contributes considerably. This contribution can be conveniently expressed by the ratio of imaginary and real parts of the optical conductivity. This knowledge can be utilized in detector design.

Recent space-borne and ground-based observations provide photometric measurements as time series. The effect of interstellar dust extinction in the near-infrared range is only 10% of that measured in the V band. However, the sensitivity of the light curve shape to the physical parameters in the near-infrared is much lower. So, interpreting these types of data sets requires new approaches like the different large-scale surveys, which create similar problems with big data. Using a selected data set, we provide a method for applying routines implemented in R to extract most information of measurements to determine physical parameters, which can also be used in automatic classification schemes and pipeline processing. We made a multivariate classification of 131 Cepheid light curves (LC) in J, H, and K colors, where all the LCs were represented in 20D parameter space in these colors separately. Performing a Principal Component Analysis (PCA), we got an orthogonal coordinate system and squared Euclidean distances between LCs, with 6 significant eigenvalues, reducing the 20-dimension to 6. We also estimated the optimal number of partitions of similar objects and found it to be equal to 7 in each color; their dependence on the period, absolute magnitude, amplitude, and metallicity are also discussed. We computed the Spearman rank correlations, showing that periods and absolute magnitudes correlate with the first three PCs significantly. The first two PC are also found to have a relationship with the amplitude, but the metallicity effects are only marginal. The method shown can be generalized and implemented in unsupervised classification schemes and analysis of mixed and biased samples. The analysis of our Classical Cepheid near-infrared LC sample showed that the J, H, K curves are insufficient for determination of stellar metallicity, with mass being the key factor shaping them.

Materials combining both a high refractive index and a wide band gap are of great interest for optoelectronic and sensor applications. However, these two properties are typically described by an inverse correlation with high refractive index appearing in small gap materials and vice-versa. Here, we conduct a first-principles high-throughput study on more than 4000 semiconductors (with a special focus on oxides). Our data confirm the general inverse trend between refractive index and band gap but interesting outliers are also identified. The data are then analyzed through a simple model involving two main descriptors: the average optical gap and the effective frequency. The former can be determined directly from the electronic structure of the compounds, but the latter cannot. This calls for further analysis in order to obtain a predictive model. Nonetheless, it turns out that the negative effect of a large band gap on the refractive index can counterbalanced in two ways: (i) by limiting the difference between the direct band gap and the average optical gap which can be realized by a narrow distribution in energy of the optical transitions and (ii) by increasing the effective frequency which can be achieved through either a high number of transitions from the top of the valence band to the bottom of the conduction or a high average probability for these transitions. Focusing on oxides, we use our data to investigate how the chemistry influences this inverse relationship and rationalize why certain classes of materials would perform better. Our findings can be used to search for new compounds in many optical applications both in the linear and non-linear regime (waveguides, optical modulators, laser, frequency converter, etc.).

In recent years, the demand for hyperspectral imaging devices has grown significantly, driven by their ability of capturing high-resolution spectral information. Among the several possible optical designs for acquiring hyperspectral images, there is a growing interest in interferometric spectral imaging systems based on division of aperture. These systems have the advantage of capturing snapshot acquisitions while maintaining a compact design. However, they require a careful calibration to operate properly. In this work, we present the interferometer response characterization algorithm (IRCA), a robust three-step procedure designed to characterize the transmittance response of multi-aperture imaging spectrometers based on the interferometry of Fabry-Perot. Additionally, we propose a formulation of the image formation model for such devices suitable to estimate the parameters of interest by considering the model under various regimes of finesse. The proposed algorithm processes the image output obtained from a set of monochromatic light sources and refines the results using nonlinear regression after an ad-hoc initialization. Through experimental analysis conducted on four different prototypes from the Image SPectrometer On Chip (ImSPOC) family, we validate the performance of our approach for characterization. The associated source code for this paper is available at https://github.com/danaroth83/irca.

Using the supersymmetric method of random matrix theory within the Heidelberg approach framework we provide statistical description of stationary intensity sampled in locations inside an open wave-chaotic cavity, assuming that the time-reversal invariance inside the cavity is fully broken. In particular, we show that when incoming waves are fed via a finite number M of open channels the probability density {cal P}(I) for the single-point intensity I decays as a power law for large intensities: {cal P}(I)sim I^{-(M+2)}, provided there is no internal losses. This behaviour is in marked difference with the Rayleigh law {cal P}(I)sim exp(-I/I) which turns out to be valid only in the limit Mto infty. We also find the joint probability density of intensities I_1, ldots, I_L in L>1 observation points, and then extract the corresponding statistics for the maximal intensity in the observation pattern. For Lto infty the resulting limiting extreme value statistics (EVS) turns out to be different from the classical EVS distributions.

Wavefront shaping is a technique for directing light through turbid media. The theoretical aspects of wavefront shaping are well understood, and under near-ideal experimental conditions, accurate predictions for the expected signal enhancement can be given. In practice, however, there are many experimental factors that negatively affect the outcome of the experiment. Here, we present a comprehensive overview of these experimental factors, including the effect of sample scattering properties, noise, and response of the spatial light modulator. We present simple means to identify experimental imperfections and to minimize their negative effect on the outcome of the experiment. This paper is accompanied by Python code for automatically quantifying experimental problems using the OpenWFS framework for running and simulating wavefront shaping experiments.

We present 1d-qt-ideal-solver, an open-source Python library for simulating one-dimensional quantum tunneling dynamics under idealized coherent conditions. The solver implements the split-operator method with second-order Trotter-Suzuki factorization, utilizing FFT-based spectral differentiation for the kinetic operator and complex absorbing potentials to eliminate boundary reflections. Numba just-in-time compilation achieves performance comparable to compiled languages while maintaining code accessibility. We validate the implementation through two canonical test cases: rectangular barriers modeling field emission through oxide layers and Gaussian barriers approximating scanning tunneling microscopy interactions. Both simulations achieve exceptional numerical fidelity with machine-precision energy conservation over femtosecond-scale propagation. Comparative analysis employing information-theoretic measures and nonparametric hypothesis tests reveals that rectangular barriers exhibit moderately higher transmission coefficients than Gaussian barriers in the over-barrier regime, though Jensen-Shannon divergence analysis indicates modest practical differences between geometries. Phase space analysis confirms complete decoherence when averaged over spatial-temporal domains. The library name reflects its scope: idealized signifies deliberate exclusion of dissipation, environmental coupling, and many-body interactions, limiting applicability to qualitative insights and pedagogical purposes rather than quantitative experimental predictions. Distributed under the MIT License, the library provides a deployable tool for teaching quantum mechanics and preliminary exploration of tunneling dynamics.

This paper provides a non-asymptotic analysis of linear stochastic approximation (LSA) algorithms with fixed stepsize. This family of methods arises in many machine learning tasks and is used to obtain approximate solutions of a linear system Atheta = b for which A and b can only be accessed through random estimates {({bf A}_n, {bf b}_n): n in N^*}. Our analysis is based on new results regarding moments and high probability bounds for products of matrices which are shown to be tight. We derive high probability bounds on the performance of LSA under weaker conditions on the sequence {({bf A}_n, {bf b}_n): n in N^*} than previous works. However, in contrast, we establish polynomial concentration bounds with order depending on the stepsize. We show that our conclusions cannot be improved without additional assumptions on the sequence of random matrices {{bf A}_n: n in N^*}, and in particular that no Gaussian or exponential high probability bounds can hold. Finally, we pay a particular attention to establishing bounds with sharp order with respect to the number of iterations and the stepsize and whose leading terms contain the covariance matrices appearing in the central limit theorems.

The reduced basis method is a model reduction technique yielding substantial savings of computational time when a solution to a parametrized equation has to be computed for many values of the parameter. Certification of the approximation is possible by means of an a posteriori error bound. Under appropriate assumptions, this error bound is computed with an algorithm of complexity independent of the size of the full problem. In practice, the evaluation of the error bound can become very sensitive to round-off errors. We propose herein an explanation of this fact. A first remedy has been proposed in [F. Casenave, Accurate a posteriori error evaluation in the reduced basis method. C. R. Math. Acad. Sci. Paris 350 (2012) 539--542.]. Herein, we improve this remedy by proposing a new approximation of the error bound using the Empirical Interpolation Method (EIM). This method achieves higher levels of accuracy and requires potentially less precomputations than the usual formula. A version of the EIM stabilized with respect to round-off errors is also derived. The method is illustrated on a simple one-dimensional diffusion problem and a three-dimensional acoustic scattering problem solved by a boundary element method.

The Kramers-Kronig relations are a pivotal foundation of linear optics and atomic physics, embedding a physical connection between the real and imaginary components of any causal response function. A mathematically equivalent, but simpler, approach instead utilises the Hilbert transform. In a previous study, the Hilbert transform was applied to absorption spectra in order to infer the sole refractive index of an atomic medium in the absence of an external magnetic field. The presence of a magnetic field causes the medium to become birefringent and dichroic, and therefore it is instead characterised by two refractive indices. In this study, we apply the same Hilbert transform technique to independently measure both refractive indices of a birefringent atomic medium, leading to an indirect measurement of atomic magneto-optical rotation. Key to this measurement is the insight that inputting specific light polarisations into an atomic medium induces absorption associated with only one of the refractive indices. We show this is true in two configurations, commonly referred to in literature as the Faraday and Voigt geometries, which differ by the magnetic field orientation with respect to the light wavevector. For both cases, we measure the two refractive indices independently for a Rb thermal vapour in a 0.6 T magnetic field, finding excellent agreement with theory. This study further emphasises the application of the Hilbert transform to the field of quantum and atomic optics in the linear regime.

We introduce a general formulation for automatic differentiation through direct form filters, yielding a closed-form backpropagation that includes initial condition gradients. The result is a single expression that can represent both the filter and its gradients computation while supporting parallelism. C++/CUDA implementations in PyTorch achieve at least 1000x speedup over naive Python implementations and consistently run fastest on the GPU. For the low-order filters commonly used in practice, exact time-domain filtering with analytical gradients outperforms the frequency-domain method in terms of speed. The source code is available at https://github.com/yoyolicoris/philtorch.

Forthcoming space-based gravitational-wave (GW) detectors will employ second-generation time-delay interferometry (TDI) to suppress laser frequency noise and achieve the sensitivity required for GW detection. We introduce an inverse light-path operator P_{i_{1}i_{2}i_{3}ldots i_{n-1}i_{n}}, which enables simple representation of second-generation TDI combinations and a concise description of light propagation. Analytical expressions and high-accuracy approximate formulas are derived for the sky- and polarization-averaged response functions, noise power spectral densities (PSDs), and sensitivity curves of TDI Michelson, (alpha,beta,gamma), Monitor, Beacon, Relay, and Sagnac combinations, as well as their orthogonal A, E, T channels. Our results show that: (i) second-generation TDIs have the same sensitivities as their first-generation counterparts; (ii) the A, E, T sensitivities and the optimal sensitivity are independent of the TDI generation and specific combination; (iii) the A and E channels have equal averaged responses, noise PSDs, and sensitivities, while the T channel has much weaker response and sensitivity at low frequencies (2pi fL/clesssim3); (iv) except for the (alpha,beta,gamma) and zeta combinations and the T channel, all sensitivity curves exhibit a flat section in the range f_{n}<flesssim 1.5/(2pi L/c), where the noise-balance frequency f_{n} separates the proof-mass- and optical-path-dominated regimes, while the response-transition frequency sim 1.5/(2pi L/c) separates the response function's low- and high-frequency behaviors; (v) the averaged response, noise PSD, and sensitivity of zeta scales with those of the T channel. These analytical and approximate formulations provide useful benchmarks for instrument optimization and data-analysis studies for future space-based GW detectors.

Hyperspectral unmixing is one of the crucial steps for many hyperspectral applications. The problem of hyperspectral unmixing has proven to be a difficult task in unsupervised work settings where the endmembers and abundances are both unknown. What is more, this task becomes more challenging in the case that the spectral bands are degraded with noise. This paper presents a robust model for unsupervised hyperspectral unmixing. Specifically, our model is developed with the correntropy based metric where the non-negative constraints on both endmembers and abundances are imposed to keep physical significance. In addition, a sparsity prior is explicitly formulated to constrain the distribution of the abundances of each endmember. To solve our model, a half-quadratic optimization technique is developed to convert the original complex optimization problem into an iteratively re-weighted NMF with sparsity constraints. As a result, the optimization of our model can adaptively assign small weights to noisy bands and give more emphasis on noise-free bands. In addition, with sparsity constraints, our model can naturally generate sparse abundances. Experiments on synthetic and real data demonstrate the effectiveness of our model in comparison to the related state-of-the-art unmixing models.

Common moment-based radiative transfer methods, such as flux-limited diffusion (FLD) and the M1 closure, suffer from artificial interactions between crossing beams. In protoplanetary disks, this leads to an overestimation of the midplane temperature due to the merging of inward and outward vertical fluxes. Methods that avoid these artifacts typically require angular discretization, which can be computationally expensive. In the spirit of the two-stream approximation, we introduced a half-moment (HM) closure that integrates the radiative intensity over hemispheres, thereby suppressing beam interactions along a fixed spatial direction. We derived a multidimensional HM closure via entropy maximization and replaced this closure with an approximate expression that closely matches it, coinciding with it in the diffusion and free-streaming regimes while remaining expressible through simple operations. We implemented HM and M1 closures via implicit-explicit schemes, including multiple frequency groups. We tested these methods in numerical benchmarks such as computing the temperature in an irradiated disk around a T Tauri star, comparing our results with Monte Carlo (MC) radiative transfer simulations. The HM closure correctly reproduces the diffusion limit and prevents crossing flux interactions in a chosen spatial direction. In disk simulations, our multigroup HM method closely matches midplane temperature distributions obtained with classical MC methods. While the M1 closure produces midplane temperatures 44% higher than MC with one frequency group and 21% higher with 22 groups, HM reduces this discrepancy to 6% with 22 groups. Even with just three groups, HM significantly outperforms M1, with maximum departures of 8% compared to M1's 23%. Our results show that combining HM with a multigroup treatment yields more realistic disk temperatures than M1, particularly in optically thick regions.

Linear structural equation models are multivariate statistical models encoded by mixed graphs. In particular, the set of covariance matrices for distributions belonging to a linear structural equation model for a fixed mixed graph G=(V, D,B) is parameterized by a rational function with parameters for each vertex and edge in G. This rational parametrization naturally allows for the study of these models from an algebraic and combinatorial point of view. Indeed, this point of view has led to a collection of results in the literature, mainly focusing on questions related to identifiability and determining relationships between covariances (i.e., finding polynomials in the Gaussian vanishing ideal). So far, a large proportion of these results has focused on the case when D, the directed part of the mixed graph G, is acyclic. This is due to the fact that in the acyclic case, the parametrization becomes polynomial and there is a description of the entries of the covariance matrices in terms of a finite sum. We move beyond the acyclic case and give a closed form expression for the entries of the covariance matrices in terms of the one-connections in a graph obtained from D through some small operations. This closed form expression then allows us to show that if G is simple, then the parametrization map is generically finite-to-one. Finally, having a closed form expression for the covariance matrices allows for the development of an algorithm for systematically exploring possible polynomials in the Gaussian vanishing ideal.

Large-scale land enclosure for speculative mega-development constitutes a non-equilibrium spatial process whose velocity, topology, and irreversibility remain poorly quantified. We study the Pantai Indah Kapuk 2 (PIK2) coastal mega-development north of Jakarta, Indonesia, using eight years (2017--2024) of Sentinel-2 land-use/land-cover (LULC) data at 10-meter resolution. The landscape is projected onto a Marxian probability simplex partitioning terrestrial pixels into Commons, Agrarian, and Capital fractions. Fisher-Rao (FR) geodesic distances on this simplex identify a transformation pulse of 0.405~rad/yr during 2019--2020, coinciding with major construction activity. Absorbing Markov chain analysis yields expected absorption times into the built environment of 46.0~years for cropland and 38.1~years for tree cover, with a pooled built-area self-retention rate of 96.4%. Percolation analysis reveals that a giant connected component containing 89--95% of all built pixels persists at occupation probabilities p in [0.096, 0.162], far below the random percolation threshold p_c approx 0.593, indicating planned rather than stochastic spatial growth. The box-counting fractal dimension of the urban boundary increases from d_f = 1.316 to 1.397, consistent with increasingly irregular frontier expansion. These results suggest that information-geometric and statistical-mechanical tools can characterize the kinematic and topological signatures of capitalist spatial accumulation with quantitative precision.

Tunnelling reactions of molecules embedded on cryogenic noble-gas matrices are being used in fundamental studies of how reactivity varies with the nature of the supposedly inert matrix as well as pointers to the chemistry occurring in the interstellar medium on ice-grains. To these ends we present chemical kinetic rate constants for the cis to trans isomerisation of seleno-, thio- and monomeric formic acids and that of their three dimeric species, based on multidimensional calculations in the gas-phase, from 10~K to 300~K as a guide to the matrix reactions.

In this work, we introduce a novel approach for predicting thermodynamic properties of binary mixtures, which we call the similarity-based method (SBM). The method is based on quantifying the pairwise similarity of components, which we achieve by comparing quantum-chemical descriptors of the components, namely σ-profiles. The basic idea behind the approach is that mixtures with similar pairs of components will have similar thermodynamic properties. The SBM is trained on a matrix that contains some data for a given property for different binary mixtures; the missing entries are then predicted by the SBM. As an example, we consider the prediction of isothermal activity coefficients at infinite dilution (γ^infty_{ij}) and show that the SBM outperforms the well-established physical methods modified UNIFAC (Dortmund) and COSMO-SAC-dsp. In this case, the matrix is only sparsely occupied, and it is shown that the SBM works also if only a limited number of data for similar mixtures is available. The SBM idea can be transferred to any mixture property and is a powerful tool for generating essential data for many applications.

Identifying a small molecule from its mass spectrum is the primary open problem in computational metabolomics. This is typically cast as information retrieval: an unknown spectrum is matched against spectra predicted computationally from a large database of chemical structures. However, current approaches to spectrum prediction model the output space in ways that force a tradeoff between capturing high resolution mass information and tractable learning. We resolve this tradeoff by casting spectrum prediction as a mapping from an input molecular graph to a probability distribution over molecular formulas. We discover that a large corpus of mass spectra can be closely approximated using a fixed vocabulary constituting only 2% of all observed formulas. This enables efficient spectrum prediction using an architecture similar to graph classification - GrAFF-MS - achieving significantly lower prediction error and orders-of-magnitude faster runtime than state-of-the-art methods.

Modern-day time-domain photometric surveys collect a lot of observations of various astronomical objects and the coming era of large-scale surveys will provide even more information on their properties. Spectroscopic follow-ups are especially crucial for transients such as supernovae and most of these objects have not been subject to such studies. }{Flux time series are actively used as an affordable alternative for photometric classification and characterization, for instance, peak identifications and luminosity decline estimations. However, the collected time series are multidimensional and irregularly sampled, while also containing outliers and without any well-defined systematic uncertainties. This paper presents a search for the best-performing methods to approximate the observed light curves over time and wavelength for the purpose of generating time series with regular time steps in each passband.}{We examined several light curve approximation methods based on neural networks such as multilayer perceptrons, Bayesian neural networks, and normalizing flows to approximate observations of a single light curve. Test datasets include simulated PLAsTiCC and real Zwicky Transient Facility Bright Transient Survey light curves of transients.}{The tests demonstrate that even just a few observations are enough to fit the networks and improve the quality of approximation, compared to state-of-the-art models. The methods described in this work have a low computational complexity and are significantly faster than Gaussian processes. Additionally, we analyzed the performance of the approximation techniques from the perspective of further peak identification and transients classification. The study results have been released in an open and user-friendly Fulu Python library available on GitHub for the scientific community.

Current Large Language Models (LLMs) benchmarks are often based on open-ended or close-ended QA evaluations, avoiding the requirement of human labor. Close-ended measurements evaluate the factuality of responses but lack expressiveness. Open-ended capture the model's capacity to produce discourse responses but are harder to assess for correctness. These two approaches are commonly used, either independently or together, though their relationship remains poorly understood. This work is focused on the healthcare domain, where both factuality and discourse matter greatly. It introduces a comprehensive, multi-axis suite for healthcare LLM evaluation, exploring correlations between open and close benchmarks and metrics. Findings include blind spots and overlaps in current methodologies. As an updated sanity check, we release a new medical benchmark--CareQA--, with both open and closed variants. Finally, we propose a novel metric for open-ended evaluations --Relaxed Perplexity-- to mitigate the identified limitations.

Equality saturation is a technique for program optimization based on non-destructive rewriting and a form of program analysis called e-class analysis. The current form of e-class analysis is pessimistic and therefore ineffective at analyzing cyclic programs, such as those in SSA form. We propose an abstract interpretation algorithm that can precisely analyze cycles during equality saturation. This results in a unified algorithm for optimistic analysis and non-destructive rewriting. We instantiate this approach on a prototype abstract interpreter for SSA programs using a new semantics of SSA. Our prototype can analyze simple example programs more precisely than clang and gcc.

We present a generative framework for inverse design of five-layer transmissive Huygens' metasurfaces (HMSs), addressing a longstanding challenge in achieving full-phase, high-efficiency unit cell designs with minimal full-wave simulations. The key to achieving this is our reliance on the field-based semianalytical (SA) scheme developed in Part I of this paper, which allows rapid and highly effective synthesis of such multilayer composites, however with limited accuracy. To overcome the prohibitive data demands of traditional pipelines, we employ Mamba, a selective state space model well suited for long-range sequence modeling as the backbone of our learning framework. A bidirectional Mamba (Bi-Mamba) forward surrogate is first trained on SA-generated data and subsequently fine-tuned with full-wave CST samples. An ablation over a 1080-sample CST pool shows that as few as 270 full-wave calibration samples suffice to reach near-CST-level agreement at a fraction of the simulation cost. An autoregressive Mamba inverse generator is subsequently trained on surrogate-augmented data, treating unit-cell synthesis as a sequential generation task. The resulting one-to-many generative model produces diverse unit cell geometries conditioned on target scattering responses. It achieves CST-validated designs with field transmission magnitude 0.9 across the full 0-2π phase range at 20 GHz. Moreover, a CST-calibrated surrogate trained to accurately predict frequency responses (18-22 GHz) enables functional post-selection of inverse generated designs. Together, the hybrid SA-generative methodology in this two-part compilation establishes a scalable and data-efficient solution for multilayer HMS synthesis, with natural extensions toward broadband, oblique-incidence, and higher-dimensional electromagnetic inverse-design problems.