Observations of Cosmic Microwave Background (CMB) B-mode polarization provide a way to probe primordial gravitational waves and test inflationary predictions. Extragalactic point sources become a major source of contamination after foreground cleaning and can bias estimates of the tensor-to-scalar ratio $r$ at the $10^{-3}$ level. We introduce Generalized Point Spread Function Fitting (GPSF), a method for removing point-source contamination in polarization maps. GPSF uses the full pixel-domain covariance, including off-diagonal terms, and models overlapping sources. This allows accurate flux estimation under realistic conditions, particularly for small-aperture telescopes with large beams that are more susceptible to source blending. We test GPSF on simulated sky maps, apply foreground cleaning using the Needlet Internal Linear Combination (NILC) method, and compare its performance with standard masking and inpainting. The results show GPSF reduces point-source contamination without significantly affecting the background signal, as seen in both the maps and their power spectra. For the constraint on $r$, GPSF reduces the bias from $1.67 \times 10^{-3}$ to $2.9 \times 10^{-4}$, with only a 2% increase in standard deviation. Compared to inpainting and masking, GPSF yields lower bias while maintaining comparable variance. This suggests that it may serve as a promising method for future CMB experiments targeting measurements of $r \sim 10^{-3}$.

We study the holonomy of the Obata connection on 2-step hypercomplex nilmanifolds. By explicitly computing the curvature tensor, we determine the conditions under which the Obata connection is flat, showing that this depends on the nilpotency step of each complex structure. In particular, we show that for 2-step hypercomplex nilmanifolds the holonomy algebra of the Obata connection is always an abelian subalgebra of $\mathfrak{sl}(n, \mathbb{H})$ and we prove that the $\mathbb{H}$-solvable conjecture holds in this case. Furthermore, we provide new examples of $k$-step nilpotent hypercomplex nilmanifolds, with arbitrary $k$, which are not Obata flat.

Memory consistency models define the order in which accesses to shared memory in a concurrent system may be observed to occur. Such models are a necessity since program order is not a reliable indicator of execution order, due to microarchitectural features or compiler transformations. Concurrent programming, already a challenging task, is thus made even harder when weak memory effects must be addressed. A rigorous specification of weak memory models is therefore essential to make this problem tractable for developers of safety- and security-critical, low-level software. In this paper we survey the field of formalisations of weak memory models, including their specification, their effects on execution, and tools and inference systems for reasoning about code. To assist the discussion we also provide an introduction to two styles of formal representation found commonly in the literature (using a much simplified version of Intel's x86 as the example): a step-by-step construction of traces of the system (operational semantics); and with respect to relations between memory events (axiomatic semantics). The survey covers some long-standing hardware features that lead to observable weak behaviours, a description of historical developments in practice and in theory, an overview of computability and complexity results, and outlines current and future directions in the field.

The axion is a well-motivated and generic extension of the Standard Model. If produced in the early universe, axions may still be relativistic today, forming a Cosmic Axion Background (C$a$B) potentially detectable in direct detection experiments. Although C$a$B is expected to be broadband, which makes it challenging to be detected, a high-quality-factor microwave cavity acts as a narrowband filter with response peaked at its resonant frequency. We propose a new strategy using multi-cavity arrays to distinguish signal from background noise by exploiting spatial correlations of the axion-induced electric field which are set by the cavity quality factor. We compute the two-point correlation function for electric fields in spatially separated cavities sourced by an isotropic C$a$B. Analyzing various cavity geometries, we find that stacked, wide-base cavity arrays offer coherent enhancement of the axion signal. We apply our formalism to prospective upgrades of the ADMX experiment, including configurations with four and eighteen coupled cavities. Although these arrays do not achieve a coherent enhancement, optimizing the geometry could potentially yield an $\mathcal{O}(1)$ improvement in the sensitivity to the C$a$B.

Exceptional points (EPs) are non-Hermitian spectral degeneracies marking a simultaneous coalescence of eigenvalues and eigenvectors. Despite the fact that multiband $n$-fold EPs (EP$n$s) generically emerge as special points on manifolds of EP$m$s, where $m<n$, EP$n$s as well as their topological properties have hitherto been studied as isolated objects. In this work we address this issue and carefully map out the emerging properties of multifold exceptional structures in three and four dimensions under the influence of one or multiple generalized similarities, revealing diverse combinations of EP$m$s in direct connection to EP$n$s. We find that simply counting the number of constraints defining the EP$n$s is not sufficient in the presence of similarities; the constraints can also be satisfied by the EP$m$-manifolds obeying certain spectral symmetries in the complex eigenvalue plane, reducing their dimension beyond what is expected from counting the number of constraints. Furthermore, the induced spectral symmetries not always allow for any EP$m$-manifold to emerge in $n$-band systems, making the plethora of exceptional structures deviate further from naive expectations. We illustrate our findings in simple periodic toy models. By relying on similarity relations instead of the less general symmetries, we simultaneously cover several physically relevant scenarios, ranging from optics and topolectrical circuits, to open quantum systems. This makes our predictions highly relevant and broadly applicable in modern research, as well as experimentally viable within various branches of physics.

Accurately characterizing higher-order interactions of brain regions and extracting interpretable organizational patterns from Functional Magnetic Resonance Imaging data is crucial for brain disease diagnosis. Current graph-based deep learning models primarily focus on pairwise or triadic patterns while neglecting signed higher-order interactions, limiting comprehensive understanding of brain-wide communication. We propose HOI-Brain, a novel computational framework leveraging signed higher-order interactions and organizational patterns in fMRI data for brain disease diagnosis. First, we introduce a co-fluctuation measure based on Multiplication of Temporal Derivatives to detect higher-order interactions with temporal resolution. We then distinguish positive and negative synergistic interactions, encoding them in signed weighted simplicial complexes to reveal brain communication insights. Using Persistent Homology theory, we apply two filtration processes to these complexes to extract signed higher-dimensional neural organizations spatiotemporally. Finally, we propose a multi-channel brain Transformer to integrate heterogeneous topological features. Experiments on Alzheimer' s disease, Parkinson' s syndrome, and autism spectrum disorder datasets demonstrate our framework' s superiority, effectiveness, and interpretability. The identified key brain regions and higher-order patterns align with neuroscience literature, providing meaningful biological insights.

We report the electronic structure of the thermoelectric semimetal Ta$_2$PdSe$_6$ with a large thermoelectric power factor and giant Peltier conductivity by means of angle-resolved photoemission spectroscopy (ARPES). The ARPES spectra reveal the coexistence of a sharp hole band with a light electron mass and a broad electron band with a relatively heavy electron mass, which originate from different quasi-one-dimensional (Q1D) chains in Ta$_2$PdSe$_6$. Moreover, the electron band around the Brillouin-zone (BZ) boundary shows a replica structure with respect to the energy originating from plasmonic polarons due to electron-plasmon interactions. The different scattering effects and interactions in each atomic chain lead to asymmetric transport lifetimes of carriers: a large Seebeck coefficient can be realized even in a semimetal. Our findings pave the way for exploring the thermoelectric materials in previously overlooked semimetals and provide a new platform for low-temperature thermoelectric physics, which has been challenging with semiconductors.

Voting is an important social activity for expressing public opinions. By conceptually considering a group of voting agents to be intelligent matter, the impact of real-time information on voting results is quantitatively studied by an intelligent Ising model, which is formed by adding nonlinear instantaneous feedback of the overall magnetization to the conventional Ising model. In the new model, the interaction strength becomes a variable depending on the total magnetization rather than a constant, which mimics the scenario that the decision of an individual during vote influenced by the dynamically changing polling result during the election process. Our analytical derivations along with Mote Carlo simulations reveal that, with a positive feedback, the intelligent Ising model exhibits phase transitions at any finite temperatures, a feature lacked in the conventional one-dimensional Ising model. In all dimensions, by varying the feedback strength, the system changes from going through a second-order phase transition to going through a first-order phase transition with increasing temperature, and the two types of phase transitions are connected by a tricritical point. This study on the one hand demonstrates that the intelligent matter with a nonlinear adaptive interaction can exhibit qualitatively different phase behaviors from conventional matter, and on the other hand shows that, during voting, even unbiased feedback may possibly induce spontaneous symmetry breaking, leading to a biased outcome where one side of the vote becomes favored.

Predicting whether a molecule can cross the blood-brain barrier (BBB) is a key step in early-stage neuro-pharmaceutical design, directly influencing the efficiency and success rate of drug development. Traditional methods based on physicochemical properties are prone to systematic misjudgements due to their reliance on previous empirical evidence. Early machine learning (ML) models, although data-driven, often suffer from limited capacity, poor generalization, and insufficient interpretability. In recent years, more advanced models have become essential tools for predicting BBB permeability and guiding related drug design, owing to their ability to simulate molecular structures and capture complex biological mechanisms. This article systematically reviews the evolution of this field-from deep neural networks to graph-based structural modelling-highlighting the advantages of multi-task and multimodal learning strategies in identifying mechanism-related features. We further explore the emerging potential of generative models and causal inference methods for integrating permeability prediction with mechanism-aware drug design. Nowadays, ML-based BBB crossing prediction is in the critical transition from mere discriminative classification toward structure-function modelling from a mechanistic perspective. This paradigm shift provides a methodological progression and future roadmap for the integration of AI into neuropharmacological development.

Fluid filled pipes are ubiquitous in both man-made constructions and living organisms. In the latter, biological pipes, such as arteries, have unique properties as their walls are made of soft, incompressible, highly deformable materials. In this article, we experimentally investigate wave propagation in a model artery: an elastomer strip coupled to a rigid water channel. We measure out-of-plane waves using synthetic Schlieren imaging, and evidence a single dispersive mode which resembles the pulse wave excited by the heartbeat. By imposing an hydrostatic pressure difference, we reveal the strong influence of pre-stress on the dispersion of this wave. Using a model based on the acoustoelastic theory accounting for the material rheology and for the large static deformation of the strip, we demonstrate that the imposed pressure affects wave propagation through an interplay between stretching, orthogonal to the propagation direction, and curvature-induced rigidity. We finally highlight the relevance of our results in the biological setting, by discussing the determination of the arterial wall's material properties from pulse wave velocity measurements in the presence of pre-stress.

Viscous drag arises from the fluid at a surface having zero relative velocity, a phenomenon known as the no-slip condition. Superhydrophobic surfaces, when submerged in water, trap a layer of air in their surface texture, partially replacing the liquid-solid interface with a liquid-gas interface. This air layer, called the plastron, results in partial slip at the surface, thereby reducing the viscous drag. In turbulent flows, large fluctuations in pressure and velocity can deplete or completely remove the plastron from the surface. This makes evaluating the effects of superhydrophobic surface treatments on flow dynamics particularly challenging. This study examines the impact of a sustained plastron on the dynamics in the shear layer of a sphere, achieved by supplying air at low pressure through pores in the sphere's surface. Instantaneous planar velocities in the wakes of spheres, both with and without superhydrophobic surface treatment, are measured within a plane passing through the spheres' centre. Dynamic mode decomposition (DMD) is applied to the velocity fluctuations in the shear layer to evaluate how superhydrophobic surface treatment affects the instabilities there. It is shown that the addition of the pores has a relatively small effect on the instabilities in the shear layer, while they are significantly changed by the addition of superhydrophobic surface treatment when the plastron is sustained.

We investigate the microscopic mechanisms behind the stabilization of three-dimensional (3D) charge order by Pr doping in YBa$_2$Cu$_3$O$_7$ (YBCO7). Density-functional-theory calculations locate the lowest-energy Pr superlattices for both Ba- and Y-site substitution. In the Ba-site case, the smaller Pr ion pulls the surrounding atoms inward. This breathing-mode distortion pins charge-stripe walls to the Pr columns and forces them to align along the $c$ axis. Y-site Pr is larger than the host ion, produces an outward distortion, and fails to pin the stripes. Coarse-grained Monte-Carlo simulations show that the stripe correlation length rises in step with the structural correlation length of the Pr dopant as observed in prior experiments. We thus identify Ba-site substitution and dopant-induced lattice pinning as the key mechanism behind 3D charge order in Pr-doped YBCO7. This approach provides quantitative guidelines for engineering electronic orders through targeted ionic substitution.

We study theories breaking diffeomorphism (Diff) invariance down to the subgroup of transverse diffeomorphisms (TDiff), consisting of multiple scalar fields in a cosmological background. In particular, we focus on models involving a field dominated by its kinetic term and a field dominated by its potential, coupled to gravity through power-law functions of the metric determinant. The Diff symmetry breaking results in the individual energy-momentum tensors not being conserved, although the total conservation-law is satisfied. Consequently, an energy exchange takes place between the fields, acting as an effective interaction between them. With this in mind, we consider the covariantized approach to describe the theory in a Diff invariant way but with an additional field, and discuss the phenomenological consequences of these models when it comes to the study of the dark sector.

We consider the sensor network localization problem, which is closely related to multidimensional scaling and Euclidean distance matrix completion. Given a ground truth configuration of $n$ points in $\mathbb{R}^\ell$, we observe a subset of the pairwise distances and aim to recover the underlying configuration (up to rigid transformations). We show with a simple counterexample that the associated optimization problem is nonconvex and may admit spurious local minimizers, even when all distances are known. Yet, inspired by numerical experiments, we argue that all second-order critical points become global minimizers when the problem is relaxed by optimizing over configurations in dimension $k > \ell$. Specifically, we show this for two settings, both when all pairwise distances are known: (1) for arbitrary ground truth points, and $k= O(\sqrt{\ell n})$, and: (2) for isotropic random ground truth points, and $k = O(\ell + \log n)$. To prove these results, we identify and exploit key properties of the linear map which sends inner products to squared distances.

L. Kauffman (2024) introduced multi-virtual and symmetric multi-virtual braid groups, which are generalizations of the virtual braid group. We introduce multi-virtual pure and multi-virtual semi-pure braid groups, which are normal subgroups of index $n!$. We give a set of generators and defining relations for these groups, show that multi-virtual (symmetric multi-virtual) braid group is a semi-direct products of multi-virtual pure (symmetric multi-virtual pure) braid group and symmetric group. Also, we introduce multi-welded and multi-unrestricted braid groups and examines structure of three-strand 2-virtual braid group and some its subgroups and quotients. The paper concludes by outlining open problems and suggesting avenues for future research in this area.

Orbital effects, despite their fundamental significance and potential to engender novel physical phenomena and enable new applications, have long been underexplored compared to their spin counterparts. Recently, surging interest in the orbital degree of freedom has led to the discovery of a plethora of orbital-related effects, underscoring the need for a deeper understanding of their roles in quantum materials. Here, we report systematic experimental evidence consistent with orbital magnetization and spontaneous rotational symmetry breaking in trigonal Tellurium, an elemental semiconductor with a unique helical crystal structure that serves as a natural platform for investigating orbital effects. Detailed angular dependent linear and nonlinear magnetotransport measurements, supported by symmetry-guided Boltzmann transport analysis, support the interpretation of coexistence of current-induced spin polarization and orbital magnetization. With the goal of disentangling the interplay between spin and orbital degrees of freedom through electrostatic gating, this work establishes a general framework for understanding orbital magnetization in chiral crystals and beyond, paving the way for its utilization in orbitronics and spintronics.

In this paper, we initiate the study of lepton flavor violating (LFV) dark matter (DM) interactions, expanding our focus beyond the flavor-conserving DM interactions typically considered in conventional direct and indirect detections. We work in an effective field theory (EFT) framework, focusing on the leading-order local operators of the form, $\bar \ell_j Γ\ell_i\,{\tt DM}^2$, where $(ij)=(eμ, eτ, μτ)$ and the DM includes the three well-known scenarios: a scalar, a fermion, and a vector. We derive the invariant-mass distribution for the three-body decay $\ell_i \to \ell_j +{\tt DM+DM}$ and demonstrate that it can be used to distinguish between different operator structures and to determine the DM mass. By utilizing current experimental bounds on the charged muon LFV decay involving neutrinos and the ratio of tau leptonic decay widths, we establish stringent limits on the effective scale associated with each operator. Additionally, for the $eμ$ flavor combination, we investigate the muon four-body radiative decay ($μ\to e +{\tt DM+DM}+γ$) to complement our probe of such interactions. Finally, we examine muonium invisible decays based on the derived bounds on the effective operators and find that the branching ratios can be significantly enhanced compared to the predictions of the standard model. In particular, any future observation of the para-muonium invisible decay serves as a compelling signature for these flavored DM interactions.

At SuperKEKB, sudden beam loss (SBL) events pose a significant challenge to stable accelerator operation. To investigate and better understand SBL, we have developed a new Bunch Oscillation Recorder (BOR), as reported by R. Nomaru et al. (JINST 19 P12026, 2024). Using this newly developed BOR, we successfully observed SBL events and conducted a detailed analysis of the recorded data. By analyzing the patterns of bunch position oscillations and charge loss, we found a strong correlation between SBL events and pressure burst phenomena occurring inside the vacuum chamber. These pressure bursts are known to accompany almost all SBL events, and our analysis shows that the bunch position oscillation patterns vary depending on the location of the pressure burst. Our observations suggest that bunch positions begin oscillation under some influence at the location of the pressure burst. These observations and analyses have significantly advanced our understanding of the causes and mechanisms behind SBL.

Dicke states are permutation-invariant superpositions of qubit computational basis states, which play a prominent role in quantum information science. We consider here two higher-dimensional generalizations of these states: $SU(2)$ spin-$s$ Dicke states and $SU(d)$ Dicke states. We present various ways of preparing both types of qudit Dicke states on a qudit quantum computer, using two main approaches: a deterministic approach, based on exact canonical matrix product state representations; and a probabilistic approach, based on quantum phase estimation. The quantum circuits are explicit and straightforward, and are arguably simpler than those previously reported.

A wideband Gaussian Noise Model of the nonlinear noise power spectral density is developed for a single semiconductor optical amplifier as described by the Agrawal model. A simple, interpretable closed-form expression is obtained for the nonlinear noise-to-signal ratio of broadband wavelength-division multiplexed signals as a function of the Agrawal model parameters, the amplifier output power and the transmission bandwidth. The accuracy of the closed-form expression and its region of validity are assessed in numerical simulations. The error is smaller than 0.1 dB when the product of bandwidth and gain recovery time $B\timesτ_c$ exceeds 100. A complete treatment of gain compression is shown to enhance nonlinear noise by a factor $1+P_\text{out}/P_\text{sat}$ compared to the first-order perturbation theory result.

This paper investigates downlink transmission in 5G Integrated Satellite-Terrestrial Networks (ISTNs) supporting automotive users (UEs) in urban environments, where base stations (BSs) and Low Earth Orbit (LEO) satellites (LSats) cooperate to serve moving UEs over shared C-band frequency carriers. Urban settings, characterized by dense obstructions, together with UE mobility, and the dynamic movement and coverage of LSats pose significant challenges to user association and resource allocation. To address these challenges, we formulate a multi-objective optimization problem designed to improve both throughput and seamless handover (HO). Particularly, the formulated problem balances sum-rate (SR) maximization and connection change (CC) minimization through a weighted trade-off by jointly optimizing power allocation and BS-UE/LSat-UE associations over a given time window. This is a mixed-integer and non-convex problem which is inherently difficult to solve. To solve this problem efficiently, we propose an iterative algorithm based on the Successive Convex Approximation (SCA) technique. Furthermore, we introduce a practical prediction-based algorithm capable of providing efficient solutions in real-world implementations. Especially, the simulations use a realistic 3D map of London and UE routes obtained from the Google Navigator application to ensure practical examination. Thanks to these realistic data, the simulation results can show valuable insights into the link budget assessment in urban areas due to the impact of buildings on transmission links under the blockage, reflection, and diffraction effects. Furthermore, the numerical results demonstrate the effectiveness of our proposed algorithms in terms of SR and the CC-number compared to the greedy and benchmark algorithms.

This paper develops a spatially resolved perturbation theory for singular vectors under high-dimensional separable noise and applies it to data-driven matrix recovery. In the asymptotic regime where the matrix dimensions are proportional and significantly larger than the signal rank, we derive exact leading-order variance formulas for the singular vector perturbation projected onto any spatial patch. The variance decomposes into a spatially non-uniform component governed by the local noise covariance and a spatially uniform component governed by the global noise level. These formulas provide the foundation for the \emph{extended optimal shrinkage and wavelet shrinkage} (e$\mathcal{OWS}$) algorithm, which recovers low-rank matrices satisfying a mixed Hölder condition. The pipeline begins with optimal shrinkage of singular values, then constructs coupled multiscale partition trees on the row and column spaces from the denoised estimate, generating a tensor Haar-Walsh wavelet basis. Spatially adaptive wavelet shrinkage is applied using data-driven, coefficient-level thresholds derived from the perturbation theory. We establish convergence rates that strictly improve upon both optimal shrinkage and wavelet shrinkage applied in isolation. Numerical simulations demonstrate reliable matrix recovery and accurate reconstruction of the underlying singular subspaces, including an application to fetal ECG extraction.

A strategy to construct physics-based local surrogate models for parametric Stokes flows and coupled Stokes-Darcy systems is presented. The methodology relies on the proper generalized decomposition (PGD) method to reduce the dimensionality of the parametric flow fields and on an overlapping domain decomposition (DD) paradigm to reduce the number of globally coupled degrees of freedom in space. The DD-PGD approach provides a non-intrusive framework in which end-users only need access to the matrices arising from the (finite element) discretization of the full-order problems in the subdomains. The traces of the finite element functions used for the discretization within the subdomains are employed to impose arbitrary Dirichlet boundary conditions at the interface, without introducing auxiliary basis functions. The methodology is seamless to the choice of the discretization schemes in space, being compatible with both LBB-compliant finite element pairs and stabilized formulations, and the DD-PGD paradigm is transparent to the employed overlapping DD approach. The local surrogate models are glued together in the online phase by solving a parametric interface system to impose continuity of the subdomain solutions at the interfaces, without introducing Lagrange multipliers to enforce the continuity in the entire overlap and without solving any additional physical problem in the reduced space. Numerical results are presented for parametric single-physics (Stokes-Stokes) and multi-physics (Stokes-Darcy) systems, showcasing the accuracy, robustness, and computational efficiency of DD-PGD, and its capability to outperform DD methods based on high-fidelity finite element solvers in terms of computing times.

Non-Hermitian systems possess exotic localization phenomena beyond their Hermitian counterparts, exhibiting massive accumulation of eigenstates at the system boundaries with different scaling behaviors. In this study, we investigate two weakly coupled non-Hermitian Hatano-Nelson chains under Möbius boundary conditions (MBCs), and reveal the coexistence of two distinct localization behaviors for eigenstates. Namely, eigenstates exhibit non-Hermitian skin effect in one chain and scale-free localization in the other. Notably, the localization characteristics of eigenstates can exchange between the two chains depending on their eigenenergies. This phenomenon is found to emerge from the critical behaviors induced by the weak interchain coupling, which can even be enhanced by MBCs in comparison \red{to} the system under other boundary conditions. Our findings deepen the understanding of non-Hermitian localization and criticality, and offer new insights into engineering tunable edge-localized states in synthetic quantum systems.

Assortment optimization is a critical tool for online retailers aiming to maximize revenue. However, optimizing purely for revenue can lead to unbalanced sales across products, potentially causing a long tail of low-selling products and products with excessively large market shares, both of which could be harmful to the seller. To address these issues, we introduce a market share balancing constraint that limits the disparity in expected sales between any two offered products to a factor of a given parameter $α$. We study both static and dynamic assortment optimization under the multinomial logit (MNL) model with this fairness constraint. In the static setting, the seller selects a distribution over assortments that satisfies the market share balancing constraint while maximizing expected revenue. We show that this problem can be solved in polynomial time, and we characterize the structure of the optimal solution: a product is included if and only if its revenue and preference weight exceed certain thresholds. We further extend our analysis to settings with additional feasibility constraints on the assortment and demonstrate that, given a $β$-approximation oracle for the constrained problem, we can construct a $β$-approximation algorithm under the fairness constraint. In the dynamic setting, each product has a finite initial inventory, and the seller implements a dynamic policy to maximize total expected revenue while respecting both inventory limits and the market share balancing constraint in expectation. We design a policy that is asymptotically optimal, with its approximation ratio converging to one as inventories grow large.

Zero-helicity vortices, such as Hill's vortex and field-reversed configurations (FRCs), have long been assumed to be toroidal in topology. This paper proves this assumption false: under arbitrarily small odd-parity (with respect to the symmetry axis) transverse field perturbations, interior flux surfaces become simply connected. The previous topological categorization--open and closed field lines separated by an ellipsoid separatrix--is updated to three distinct categories: open field lines in the outermost region, closed field lines on torus flux surfaces in an intermediate region, and closed field lines on simply connected flux surfaces in the innermost region. In addition to a shifted ellipsoid outer separatrix separating closed and open field lines, a new crescent-shaped inner separatrix separates the torus and simply connected surfaces. The simply connected region is significant even for small perturbations; e.g., in a spherical vortex with a perturbation 10% of the background field strength, it occupies 40% of the outer separatrix. The analysis also proves the conjecture regarding field line closure under odd-parity perturbation in the full three-dimensional context. Preliminary numerical simulations of charged particle trajectories in FRC magnetic confinement under odd-parity perturbation were also conducted; crescent-like simply connected volumes were observed even when gyro-radii were small compared to the system size. Since FRCs are sustained by a rotating magnetic field with odd parity, these results motivate a revision of FRC-related fusion confinement physics. Given the mathematical equivalence to Hill's vortex, this also updates our topological understanding of fluid flow in a wide array of phenomena.

Using the theoretical basis developed by Yao and Zeilberger, we consider certain graph families whose structure results in a rational generating function for sequences related to spanning tree enumeration. Said families are Powers of Cycles and Powers of Path; later, we briefly discuss Torus graphs and Grid graphs. In each case we know, a priori, that the set of spanning trees of the family of graphs can be described in terms of a finite-state-machine, and hence there is a finite transfer-matrix that guarantees the generating function is rational. Finding this ``grammar'', and hence the transfer-matrix is very tedious, so a much more efficient approach is to use experimental mathematics. Since computing numerical determinants is so fast, one can use the matrix tree theorem to generate sufficiently many terms, then fit the data to a rational function. The whole procedure can be done rigorously a posteriori.

In a ferroelectric nematic liquid crystal, the electrostatic interaction can induce a spontaneous cholesteric helix, even if the material is not chiral. If the liquid-crystal cell is infinitely thick, then the predicted pitch depends continuously on material parameters. Here, we consider how the prediction must be modified in a cell of finite thickness. If the Debye screening length is large enough, we find that the free energy has multiple minima. In these minima, the cholesteric pitch is locked to the cell thickness, so that the cell contains an integer number of pitches. However, if the screening length is smaller, then the cholesteric pitch can vary continuously.

The XRISM Resolve X-ray spectrometer allows to gain detailed insight into gas motions of the intra cluster medium (ICM) of galaxy clusters. Current simulation studies focus mainly on statistical comparisons, making the comparison to the currently still small number of clusters difficult due to unknown selection effects. This study aims to bridge this gap, using simulated counterparts of Coma, Virgo, and Perseus from the SLOW constrained simulations. These clusters show excellent agreement in their properties and dynamical state with observations, thus providing an ideal testbed to understand the processes shaping the properties of the ICM. We find that the simulations match the order of the amount of turbulence for the three considered clusters, Coma being the most active, followed by Perseus, while Virgo is very relaxed. Typical turbulent velocities are a few $\approx100$ km s$^{-1}$, very close to observed values. The resulting turbulent pressure support is $\approx1\%$ for Virgo, $\approx 6\%$ for Perseus, and $\approx 8\%$ for Coma within the central $1-2\%$ of $R_{200}$. Compared to previous simulations and observations, measured velocities and turbulent pressure support are on average lower, in line with XRISM findings, thus indicating the importance of selection effects.

In this work we introduce a field theory capable of describing the critical properties of nonideal systems undergoing continuous phase transitions beyond the leading order radiative corrections or in the number of loops (effective field theories limited only to leading order were recently defined in literature). These systems present defects, inhomogeneities and impurities as opposed to ideal ones which are perfect, homogeneous and pure. We compute the values of the critical exponents of the theory beyond leading order and compare with their corresponding experimental measured results. The results show some interplay between nonideal effects and fluctuations.