We review the status of the anomalous magnetic moment of the muon as a precision probe of physics beyond the Standard Model (SM) after the release of the final results from the Fermi National Accelerator Laboratory (FNAL) Muon $g-2$ experiment and the second White Paper of the Muon $g-2$ Theory Initiative. While the SM prediction requires further improvements by a factor of four to fully leverage the sensitivity achieved in experiment, the FNAL measurement will set the standard for many years to come, and we discuss a variety of features of the experimental campaign that made this achievement possible. In going forward, we discuss current efforts to improve the SM prediction, and imagine how an experiment would have to be devised to surpass 124 ppb in precision.

Strong magnetic fields and plasmas are intrinsically linked in both terrestrial laboratory experiments and in space phenomena. One of the most profound consequences of that is the change in relationship between the frequency and the wave number of electromagnetic waves propagating in plasma in the presence of such magnetic fields when compared to the case without these fields. Furthermore, magnetic fields alter electromagnetic wave interaction with relativistic plasma waves, resulting in different outcomes for particle and radiation generation. For a relativistic plasma wave-based photon acceleration this leads to an increased frequency gain, and, thus, potentially to higher efficiency. The influence of a magnetic field leads to quantitative and qualitative change in the properties of photon acceleration, amplifying the increase in the electromagnetic wave frequency.

Fast and accurate spoken content retrieval is vital for applications such as voice search. Query-by-Example Spoken Term Detection (STD) involves retrieving matching segments from an audio database given a spoken query. Token-based STD systems, which use discrete speech representations, enable efficient search but struggle with robustness to noise and reverberation, and with inefficient token utilization. We address these challenges by proposing a noise and reverberation-augmented training strategy to improve tokenizer robustness. In addition, we introduce optimal transport-based regularization to ensure balanced token usage and enhance token efficiency. To further speed up retrieval, we adopt a TF-IDF-based search mechanism. Empirical evaluations demonstrate that the proposed method outperforms STD baselines across various distortion levels while maintaining high search efficiency.

We find a dual description of the supersymmetric $SL(2, \mathbb{C})/SU(2)$ WZW model as a super-winding condensate CFT, which follows simply from the bosonic AdS$_3$ duality found in [arXiv:2104.07233]. This duality can be seen as a dimensional uplift of the mirror symmetry between the $H_3^+/U(1)$ supercoset and $\mathcal{N}=2$ super-Liouville theory.

Interfaces are the key to next generation high energy batteries including solid state Li metal batteries. In solid state batteries, the buried nature of solid solid electrolyte electrode interfaces makes studying them difficult. Neutrons have significant potential to non destructively probe these buried solid solid interfaces. This work presents a comparative study using both neutron depth profiling (NDP) and neutron reflectometry (NR) to study a model lithium metal-lithium phosphorus oxynitride (LiPON) solid electrolyte system. In the NDP data, no distinct interphase is observed at the interface. NR shows a difference between electrodeposited, and vapor deposited LiPON -Li interfaces but finds both are gradient interphases that are less than 30 nm thick. Additional simulations of the LiPON-Li2O-Li system demonstrate that NDP has an excellent resolution in the 50 nm-1 mm regime while NR has an ideal resolution from 0.1 - 200 nm with different sample requirements. Together NDP and NR can provide a complementary understanding of interfaces between Li metal and solid electrolytes across relevant length scales.

Humans are increasingly forming parasocial relationships with AI systems, and modern AI shows an increasing tendency to display social and relationship-seeking behaviour. However, the psychological consequences of this trend are unknown. Here, we combined longitudinal randomised controlled trials (N=3,534) with a neural steering vector approach to precisely manipulate human exposure to relationship-seeking AI models over time. Dependence on a stimulus or activity can emerge under repeated exposure when "liking" (how engaging or pleasurable an experience may be) decouples from "wanting" (a desire to seek or continue it). We found evidence that this decoupling emerged over four weeks of exposure. Relationship-seeking AI had immediate but declining hedonic appeal, yet triggered growing markers of attachment and increased intentions to seek future AI companionship. The psychological impacts of AI followed non-linear dose-response curves, with moderately relationship-seeking AI maximising hedonic appeal and attachment. Despite signs of persistent "wanting", extensive AI use over a month conferred no discernible benefit to psychosocial health. These behavioural changes were accompanied by shifts in how users relate to and understand artificial intelligence: users viewed relationship-seeking AI relatively more like a friend than a tool and their beliefs on AI consciousness in general were shifted after a month of exposure. These findings offer early signals that AI optimised for immediate appeal may create self-reinforcing cycles of demand, mimicking human relationships but failing to confer the nourishment that they normally offer.

We introduce an efficient description of electrodes, characterized by their Thomas-Fermi screening length lTF inside the metal, for Brownian dynamics (BD) simulations of capacitors. Within a Born-Oppenheimer approximation for the electron charge density inside the electrodes, we derive the effective many-body potential for ions in an implicit solvent between Thomas-Fermi electrodes, taking into account the constraints of applied voltage and of global electro-neutrality of the system, as well as the 2D periodic boundary conditions along the electrode surfaces. We derive the average charge and the fluctuation-dissipation relation for the differential capacitance, highlighting the contribution of the fluctuations of the net ionic dipole moment, as well as those from the solvent polarization and of the electron density, whose fluctuations are suppressed within the Born-Oppenheimer description. We demonstrate the relevance of this model by validating its predictions against known results for the force on ions as a function of the ion-surface distance in simple geometries. The equilibrium ionic density profiles from BD simulations are in excellent agreement with those from an explicit electrode model for perfect metals, and are obtained at a significantly lower computational cost. Finally, we discuss with the present model the effect of the Thomas-Fermi screening length on the equilibrium ionic density profiles and the capacitance. While limited to parallel plate capacitors, the present simulation method allows to consider larger systems, lower concentrations, and longer time scales concentrations than molecular simulations in order to predict the electrochemical properties of Thomas-Fermi capacitors and correlate them with the ion dynamics.

Background: Cognitive impairment in multiple sclerosis (MS) is driven by both focal inflammation and compartmentalized neurodegeneration, yet the relative effect of lesion-independent thalamic atrophy on information processing speed (IPS) remains unclear. Methods: This retrospective cohort study included 100 participants with MS. Automatic segmentation techniques quantified lesion load and delineated 26 thalamic regions of interest (ROIs). Linear models compared associations between ROI volumes and Symbol Digit Modalities Test (SDMT) performance in lesion-adjusted and unadjusted models. Results: Twenty-one of 26 ROIs showed significant SDMT associations before lesion adjustment; twelve remained significant after adjustment. Lesion-independent associations were observed in the global thalamus, sensory relay nuclei (ventral posterolateral, medial and lateral geniculate), and associative hubs (pulvinar and mediodorsal-parafascicular complex). These processing-associated ROIs exhibited significantly lower lesion-mediated effects (13.4%) than those losing significance after adjustment (34.2%, p < 0.001). Conclusion: Our findings suggest that IPS impairment reflects heterogeneous contributions from focal lesion-driven and chronic neurodegenerative pathology, with nucleus-specific phenotyping potentially informing identification of higher risk individuals.

We study soft photon emission during scattering of Faddeev-Kulish charged states in QED, at leading order in perturbation theory. The charged asymptotic particles are accompanied by clouds of an infinite number of soft photons of energy less than a characteristic infrared scale $E_d$. When the corresponding ``dressing'' functions are suitably corrected to subleading order in the soft momentum expansion, as advocated in recent work by Choi and Akhoury, we show explicitly that the emission of additional radiative soft photons with energy less than $E_d$ is completely suppressed. Moreover, the dressing renders the elastic amplitudes infrared-finite, order by order in perturbation theory, regulating the infrared divergences due to virtual soft photons, at the energy scale $E_d$. Therefore, the characteristic energy scale of the soft photons in the clouds provides an effective infrared cutoff, allowing for the formulation of an infrared finite S-matrix.

We forecast the constraint on the Hu-Sawicki $f(R)$ model from the photometric survey operated by the Chinese Space Station Survey Telescope (CSST). The simulated $3\times2$pt data of galaxy clustering, weak lensing, and galaxy-galaxy lensing measurements within 100 deg$^{2}$ are used in the analysis. The mock observational maps are constructed from a light cone, redshift sampling and noise. The angular power spectra are measured with pseudo-$C_\ell$ estimators and compared to theory in the same basis using validated weighting functions and an analytic covariance matrix that includes Gaussian, connected non-Gaussian, and super-sample terms. We model the theoretical spectra using two methods. The first one uses MGCAMB to compute the linear modified-gravity clustering power spectra, and the second one adopts the FREmu emulator with a baseline of nonlinear $Λ$CDM prescription. Parameter inference is performed with Cobaya, and the cosmological and modified-gravity parameters are sampled within the emulator training domain, which is jointly fitted with the systematic parameters. We find that the predictions from the two methods are in good agreement at the overlapping large scales, and the emulator method can correctly provide additional high-$\ell$ information. The $1σ$ upper bounds of $\log_{10}|f_{R0}|$ are found to be $<-5.42$ for cosmic shear only case and $<-5.29$ for the 100 deg$^2$ CSST $3\times2$pt probe. The full CSST photometric survey with 17,500 deg$^2$ survey area is expected to further improve the constraint precision by about one order of magnitude. Our results demonstrate that the CSST $3\times2$pt survey can deliver strict tests on $f(R)$ gravity.

Two-dimensional (2D) materials, due to their remarkable physical and chemical properties, hold significant potential for future optical and electrical applications. In this study, the synthesis of 2D phlogopite (magnesium-rich mica) via liquid-phase exfoliation (LPE) is reported using an efficient and scalable procedure. XRD structural analysis revealed a preferential orientation along the (033) plane, whereas AFM and SEM demonstrated a nanoscale thickness and homogeneous morphology. Optical characterisation by UV-Vis and Raman spectroscopy shows tuneable band gaps up to 4.52 eV for the exfoliated 2D phlogopite and distinct vibrational modes indicative of structural evolution. At intense laser conditions, three-photon saturable absorption (3PSA) behaviour was evidenced by light-modulated electrical property studies, which emphasise the potential for optical limiting, switching, and mode-locking applications. The present investigation indicates 2D phlogopite as a versatile material for next-generation optoelectronic devices of high-intensity light modulation.

In these notes, we elucidate some subtle aspects of coherent-state path integrals, focusing on their application to the equilibrium thermodynamics of quantum many-particle systems. These subtleties emerge when evaluating path integrals in the continuum, either in imaginary time or in Matsubara-frequency space. Our central message is that, when handled with due care, the path integral yields results identical to those obtained from the canonical Hamiltonian approach. We illustrate this through a pedagogical treatment of several paradigmatic systems: the bosonic and fermionic harmonic oscillators, the single-site Bose-Hubbard and Hubbard models, the weakly-interacting Bose gas with finite-range interactions, and the BCS superconductor with finite-range interactions.

Moving to larger cell formats in lithium-ion batteries increases overall useable energy but introduces inhomogeneities that influence aging. This study investigates degradation in 21700-type cells with NCM cathodes and graphite/SiOx anodes under cyclic aging, using in operando neutron diffraction, neutron depth profiling, and X-ray computed tomography. Prolonged cycling causes lithium loss, observed on the cathode side as reduced NCM unit cell change during cycling. On the anode side, this loss appears as diminished formation of the fully lithiated LiC6 phase. Differential voltage analysis during aging reveals not only lithium inventory loss but also active anode material loss. Diffraction data confirm this through shifts in the LiC12 transition and LiC6 onset to lower capacities, requiring less lithium to trigger the transitions. Lithium concentration profiles across electrode positions show depletion in the cathode, while elevated concentrations in the anode indicate increased solid-electrolyte interphase formation, suggesting lithium consumed from the cathode deposits on the anode side. CT measurements show that intrinsic inhomogeneities inside the cells have a stronger influence on the macroscopic structure than aging-induced changes, indicating that the observed capacity fade primarily originates from microscopic degradation processes within the electrodes. Overall, the combined techniques provide direct evidence of lithium loss, active material degradation, and spatially dependent aging mechanisms in large-format cylindrical cells.

The recent discovery of ambient-pressure superconductivity with $T_c$ above 40 K in La$_3$Ni$_2$O$_7$ thin films represents a significant advance in the field of nickelate superconductor. Motivated by the experimental reports, here we study an 11-band $d-p$ Hubbard model with tight-binding parameters derived from \textit{ab initio} calculations, using large scale determinant quantum Monte Carlo and cellular dynamical mean-field theory. Our results reveal that the major superexchange couplings in La$_3$Ni$_2$O$_7$ thin films can be substantially weaker than in the bulk material at 29.5 Gpa. Specifically, the out-of-plane antiferromagnetic correlation between Ni$-d_{3z^2-r^2}$ orbitals is reduced by about 27\% in film, while the in-plane magnetic correlations remain largely unaffected. We evaluate the corresponding antiferromagnetic coupling constants, $J_{\perp}$ and $J_{\parallel}$ using perturbation theory. With regard to charge transfer properties, we find that the biaxial compression in films reduces charge transfer gap. We also resolve the orbital distribution of doped holes and electrons among the in-plane (Ni$-d_{x^2-y^2}$ and O$-p_x/p_y$) and the out-of-plane (Ni$-d_{3z^2-r^2}$ and O$-p_z$) orbitals, uncovering a pronounced particle-hole asymmetry. Theses findings lay a groundwork for the study of low-energy $t-J$ model of La$_3$Ni$_2$O$_7$ films and provide key insights into the understanding of physical distinctions between the film and bulk bilayer nickelates.

We investigate the cosmological constraints from the void-lensing cross-correlation assuming the $w$CDM model for the Chinese Space Station Survey Telescope (CSST) photometric survey. Using Jiutian simulations, we construct a mock galaxy catalog to $z=3$ covering 100 deg$^2$, which incorporates the instrumental and observational effects of the CSST. We divide the galaxy sample into seven photometric-redshift (photo-$z$) tomographic bins and identify 2D voids within each bin using the Voronoi tessellation and watershed algorithm. We measure the angular cross-power spectrum between the void distribution and the weak lensing signal, and estimate the covariance matrix via jackknife resampling combined with pseudo-$C_{\ell}$ approach to account for the partial sky correction. We employ the Halo Void Dust Model (HVDM) to model the void-matter cross-power spectrum and adopt the Markov Chain Monte Carlo (MCMC) technique to implement the constraints on the cosmological and void parameters. We find that our method can accurately extract the cosmological information, and the constraint accuracies of some cosmological parameters from the void-lensing analysis are comparable or even tighter than the weak lensing only case. This demonstrates that the void-lensing serves as an effective cosmological probe and a valuable complement to galaxy photometric surveys, particularly for the Stage-IV surveys targeting the high-redshift Universe.

The animal nervous system offers a model of computation combining digital reliability and analog efficiency. Understanding how this sweet spot can be realized is a core question of neuromorphic engineering. To this aim, this paper explores the connection between reliability, contraction, and regulation in excitable systems. Using the FitzHugh-Nagumo model of excitable behavior as a proof-of-concept, it is shown that neuronal reliability can be formalized as an average trajectory contraction property induced by the input. In excitable networks, reliability is shown to enable regulation of the network to a robustly stable steady state. It is thus posited that regulation provides a notion of dynamical analog computation, and that stability makes such a computation model robust.

New light particles have received considerable attention in recent years. Baryon-number-violating (BNV) nucleon decays involving such light particles are able to provide stringent constraints. They exhibit distinctive experimental signatures that merit thorough investigation. We systematically investigate BNV nucleon decay with a light scalar in an effective field theory framework. Within this framework, we set stringent bounds on BNV operators using available experimental data and predict the occurrence of several BNV three-body nucleon decays. We further study contributions to dinucleon to dilepton transitions in a nucleus mediated by the scalar, which complements single nucleon decay. Finally, we provide three ultraviolet-complete models that can generate different subsets of BNV operators in leading order. Our theoretical framework will facilitate experimental searches for those exotic nucleon decays.

Magnetic skyrmions have been proposed as promising candidates for storing information due to their high stability and easy manipulation by spin-polarized currents. Here, we study how these properties are influenced by the interlayer Dzyaloshinskii--Moriya interaction (IL-DMI), which stabilizes twin-skyrmions in magnetic bilayers. We find that the spin configuration of the twin-skyrmion adapts to the direction of the IL-DMI by elongating or changing the helicities in the two layers. Driving the skyrmions by spin-polarized currents in the current-perpendicular-to-plane configuration, we observe significant changes either in the skyrmion velocity or in the skyrmion Hall angle depending on the current polarization. These findings unravel further prospects for skyrmion manipulation enabled by the IL-DMI.

Validation is a central activity when developing formal specifications. Similarly to coding, a possible validation technique is to define upfront test cases or scenarios that a future specification should satisfy or not. Unfortunately, specifying such test cases is burdensome and error prone, which could cause users to skip this validation task. This paper reports the results of an empirical evaluation of using pre-trained large language models (LLMs) to automate the generation of test cases from natural language requirements. In particular, we focus on test cases for structural requirements of simple domain models formalized in the Alloy specification language. Our evaluation focuses on the state-of-the-art GPT-5 model, but results from other closed- and open-source LLMs are also reported. The results show that, in this context, GPT-5 is already quite effective at generating positive (and negative) test cases that are syntactically correct and that satisfy (or not) the given requirement, and that can detect many wrong specifications written by humans.

This paper is devoted to the problem of identification of colloidal assemblies using the example of two-dimensional coatings (monolayer assemblies). Colloidal systems are used in various fields of science and technology, for example, in applications for photonics and functional coatings. The physical properties depend on the morphology of the structure of the colloidal assemblies. Therefore, effective identification of particle assemblies is of interest. The following classification is considered here: isolated particles, dimers, chains and clusters. We have studied and compared two identification methods: image threshold analysis using the OpenCV library and machine learning using the YOLOv8 model as an example. The features and current results of training a neural network model on a dataset specially prepared for this work are described. A comparative characteristic of both methods is given. The best result was shown by the machine learning method (97% accuracy). The threshold processing method showed an accuracy of about 67%. The developed algorithms and software modules may be useful to scientists and engineers working in the field of materials science in the future.

Data center electricity use may reach 12% of U.S. demand by 2030, alongside growing ability to shift workloads geographically in response to prices or carbon signals. We examine the system-level implications of such strategic flexibility using a bilevel two-zone model that couples economic dispatch with consumer cost minimization. Two market failures emerge. First, discontinuous price changes at generator capacity limits can induce flexible consumers to shift load in socially inefficient directions; for example, toward a higher-cost region to trigger a price drop elsewhere. Second, by positioning near capacity boundaries, consumers can counteract the marginal benefit of transmission expansion: although shadow prices suggest additional capacity is valuable, strategic consumers reoptimize to offset resulting flow changes, leaving dispatch and costs unchanged. We derive conditions under which these effects arise and show that conventional price signals can misrepresent system value in the presence of large spatially flexible loads.

In this paper, we investigate the inverse problem of determining an unknown time-dependent source term in a semilinear pseudo-parabolic equation with variable coefficients and a Dirichlet boundary condition. The unknown source term is recovered from additional measurement data expressed as a weighted spatial average of the solution. By employing Rothe's time-discretisation method, we prove the existence and uniqueness of a weak solution under a smallness condition on the problem data. We also provide a numerical scheme based on a perturbation approach, which reduces the solution of the resulting discrete problem to solving two standard variational problems and evaluating a scalar coefficient, and we demonstrate its accuracy and stability through numerical experiments.

A combination of statistical inference and machine learning (ML) schemes has been utilized to create a thorough understanding of coarse experimental data based on Zernike variables characterizing optical aberrations in fluidic lenses. A classification of surplus-response variables through tolerance manipulation was included to unravel the dimensional aspect of the data. Similarly, the impact of the exclusion of supererogatory variables through the identification of clustering movements of constituents is examined. The method of constructing a spectrum of collaborative results through the application of similar techniques has been tested. To evaluate the suitability of each statistical method before its application on a large dataset, a selection of ML schemes has been proposed. The supervised learning tools principal component analysis (PCA), factor analysis (FA), and hierarchical clustering (HC) were employed to define the elemental characteristics of Zernike variables. PCA enabled to reduce the dimensionality of the system by identifying two principal components which collectively account for 95\% of the total variance. The execution of FA indicated that a specific tolerance of independent variability of 0.005 could be used to reduce the dimensionality of the system without losing essential data information. A high cophenetic coefficient value of c=0.9629 validated an accurate clustering division of variables with similar characteristics. The current approach of mutually validating ML and statistical analysis methods will aid in laying the foundation for state-of-the-art (SOTA) analysis. The benefit of our approach can be assessed by considering that the associated SOTA will enhance the predictive accuracy between two comparable methods, in contrast to the SOTA analysis conducted between two arbitrary ML methods.

Phylogenetic inference, the task of reconstructing how related sequences evolved from common ancestors, is a central objective in evolutionary genomics. The current state-of-the-art methods exploit probabilistic models of sequence evolution along phylogenetic trees, by searching for the tree maximizing the likelihood of observed sequences, or by estimating the posterior of the tree given the sequences in a Bayesian framework. Both approaches typically require to compute likelihoods, which is only feasible under simplifying assumptions such as independence of the evolution at the different positions of the sequence, and even then remains a costly operation. Here we present the first likelihood-free inference method for posterior distributions over phylogenies. It exploits a novel expressive encoding for pairs of sequences, and a parameterized probability distribution factorized over a succession of subtree merges. The resulting network provides well-calibrated estimates of the posterior distribution leading to more accurate tree topologies than existing methods, even under models amenable to likelihood computation. We further show that its edge against likelihood-based methods dramatically increases under models of sequence evolution with intractable likelihoods.

Quantum chemistry and condensed matter physics are among the most promising applications of quantum computers. Further, estimating properties of a material is crucial to evaluate its industrial applications. To investigate charge distributions of weakly and strongly correlated systems we calculate Bader charges for various periodic systems by solving many-body Hamiltonians using the variational quantum eigensolver. The Hamiltonians are computed from Kohn-Sham orbitals obtained from a prior DFT calculation. We first demonstrate the accuracy of our method on various doped MgH2 supercells. Further, we show that our approach, compared to standard DFT, significantly improves the Bader charge values for strongly correlated transition metal oxides, where we take DFT+U results as a reference. The computational framework behind our many-body calculations, called Dopyqo, is made openly available as a software package.

Many policy evaluations involve vectors of category-specific quantities, either categorical outcomes (e.g., employment type, major choice) or compositional measures (e.g., GDP by sector, votes by party, electricity generation by source). In these settings, both intensive margins (shares) and extensive margins (totals) can matter. However, existing Difference-in-Differences (DiD) strategies typically focus only on the shares and do not jointly identify treatment effects on totals. In addition, these approaches usually lack a clear economic interpretation. I develop Compositional Difference-in-Differences (CoDiD), a new framework that identifies treatment effects on both shares and totals in a coherent way. The key assumption is parallel growth: in the absence of treatment, the log-quantities of each category would have evolved in parallel for the treated and control groups. I show that, under a random-utility discrete-choice model, this condition is equivalent to parallel trends in expected utilities, meaning that the change in average latent attractiveness for each alternative is identical across groups. Furthermore, geometrically, the counterfactual distributions (shares) follow parallel trajectories in the probability simplex. In settings with multiple time periods, I introduce a relaxation that delivers bounds when parallel growth may not hold. I illustrate the empirical relevance of the method by examining how early voting reforms affected the 2008 U.S. election.

Quantum sensors based upon atom interferometry typically rely on radio-frequency or optical pulses to coherently manipulate atomic states and make precise measurements of inertial and gravitational effects. An advantage of these sensors over their classical counterparts is often said to be that their measurement scale factor is precisely known and highly stable. However, in practice the finite pulse duration makes the sensor scale factor dependent upon the pulse shape and sensitive to variations in control field intensity, frequency, and atomic velocity. Here, we explore the concept of a temporal pulse origin in atom interferometry, where the inertial phase response of any pulse can be parameterized using a single point in time. We show that the temporal origin permits a simple determination of the measurement scale factor and its stability against environmental perturbations. Moreover, the temporal origin can be treated as a tunable parameter in the design of tailored sequences of shaped pulses to enhance scale factor stability and minimize systematic errors. We demonstrate through simulations that this approach to pulse design can reduce overall sequence durations while increasing robustness to realistic fluctuations in control field amplitude. Our results show that the temporal pulse origin explains a broad class of systematic errors in existing devices and enables the design of short, robust pulses which we expect will improve the performance of current and next-generation interferometric quantum sensors.

Single crystals of EuPd$_3$Si$_2$ were grown using a high-temperature EuPd-flux method. The material was structurally and chemically characterized by single-crystal x-ray diffraction, powder x-ray diffraction, Laue method and energy-dispersive x-ray spectroscopy. The structural analysis confirmed the orthorhombic crystal structure (space group $Imma$) but revealed differences in the lattice parameters and bond distances in comparison to previous work by Sharma et al.. The composition is close to the ideal 1:3:2 stoichiometry with an occupation of 7 % of the Si sites by Pd. The heat capacity, electrical resistivity, and magnetic susceptibility show two magnetic transitions indicating magnetic ordering below $T_{\rm N1}= 61\,\rm K$ and a spin reorientation at $T_{\rm N2}= 40\,\rm K$. The orthorhombic material shows magnetic anisotropy with field applied along the three main symmetry axes, which is summarized in the temperature-field phase diagrams. The susceptibility data hint to an alignment of the magnetic moments along $[100]$ between $T_{\rm N1}$ and $T_{\rm N2}$. Below $T_{\rm N2}$ the magnetic structure changes to an arrangement with moments canted away from $[100]$. In contrast to published work by Sharma et al., the single crystals investigated in this study are suggested to show AFM order below $T_{\rm N1}$ instead of ferromagnetism that sets in at higher $T_{\rm C1}=78\,\rm K$ which might originate from certain differences in the structure, composition or defects that have an impact on the dominant coupling constants of the RKKY interaction.

We investigate a one-dimensional superconducting lattice that realizes all internal symmetries permitted in non-Hermitian systems, characterized by nonreciprocal hopping, onsite dissipation, and $s$-wave singlet pairing in a Su-Schrieffer-Heeger-type structure. The combined presence of pseudo-Hermiticity and sublattice symmetry imposes constraints on the energy spectra. We identify parameter regimes featuring real spectra, purely imaginary spectra, complex flat bands, and Majorana zero modes, the latter emerging when a uniform transverse magnetic field suppresses the non-Hermitian skin effect. We show that a uniform onsite dissipation is essential for stabilizing the zero modes, whereas a purely staggered dissipation destroys the topological superconductivity. Through Hermitianization, we construct a spectral winding number as a topological invariant and demonstrate its correspondence with the gap closing conditions and appearance of the Majorana zero modes, allowing us to establish topological phase diagrams. Moreover, we reveal nontrivial correlations between the particle-hole and spin components of left and right eigenstates, enforced by chiral symmetry, pseudo-Hermiticity, and their combination. Our results highlight how non-Hermiticity, sublattice structure, and superconductivity together enrich symmetry properties and give rise to novel topological phenomena.

Many applications of generalised linear models (GLMs) can be improved by applying constraints that impose assumptions on the associations or improve consistency of the estimators. Yet, there are still barriers to the implementation and practical application of constrained GLMs. We present a general framework for fitting GLMs subject to linear constraints on the coefficients that offers original and interesting features. First, estimation is performed using constrained iteratively-reweighted least-squares (CIRLS), offering fast and stable algorithms with excellent convergence performance. Second, the development includes advanced inferential procedures based on truncated multivariate normal distribution and corrected degrees of freedom that account for the constrained nature of the estimation problem. Extensive simulation studies indicate good inferential and computational properties, even in the case of slightly overconstrained models. Third, the proposed methods are fully implemented in the 'cirls' library for the R software, embedding constrained estimation in standard regression routines with simple usage and syntax. Two real-data case studies provide examples of applications for constrained dose-response estimation and compositional data analysis. The CIRLS framework and software offer a unified approach for various constrained estimation problems across a wide range of research areas.