Let $X$ be a metric space and $μ$ an $s$-regular Ahlfors measure. Let $Y$ be a metric space. We prove that for Besov functions $u \in B^r_{q,\infty}(X,μ;Y)$, every point is a {\it general average Lebesgue point} of $u$ outside a $σ$-finite set with respect to the Hausdorff measure $\mathcal{H}^{s - rq}$. The proof is based on density-type estimates involving Hausdorff measure. In addition, we prove that for functions $u$ in the fractional Sobolev space $W^{r,q}(X,μ;Y)$, almost every point with respect to $\mathcal{H}^{s - rq}$ is an {\it average Lebesgue point} of $u$. Finally, if $Y$ is also complete, we prove that for $u \in B^r_{q,\infty}(X,μ;Y)$, almost every point is a {\it Lebesgue point} outside a set of Hausdorff dimension at most $s - rq$.

We prove global bifurcation results for prescribed mean curvature equations. These equations are defined on R3 and the radial solutions belonging in these branches are smooth and positive.

Our study seeks to address the debate over the spin of MAXI J1820+070 through broadband spectral modeling of NuSTAR observations obtained during the soft state. We further compare our results with previous spin estimates and examine the source variability across the soft state. In addition, we investigate the origin of the soft X-ray excess, which we argue does not originate from the plunge region as previously suggested. To further investigate the origin of this excess, we calculate spin-dependent radial disk temperature profiles across all epochs. Our results indicate that the black hole in MAXI J1820+070 is rapidly spinning, with spin $a$ > 0.75, potentially powering the relativistic jets. Our analysis reveals a significant decline in the inner disk temperature midway through the soft state, accompanied by a modest increase in the inferred inner disk radius up to 3.5Rg. This behavior is consistent with slight disk truncation, possibly associated with a reduction in gas ionization and nonthermal processes. Furthermore, the soft excess emission below 10 keV is well described by a blackbody component with kT=0.5 keV, approximately 38% cooler than the inner disk. This suggests that the emission may originate from a warm corona layer located beyond 10Rg, analogous to warm Comptonization models proposed to explain the soft X-ray excess in active galactic nuclei.

Robust invisible watermarks are widely used to support copyright protection, content provenance, and accountability by embedding hidden signals designed to survive common post-processing operations. However, diffusion-based image editing introduces a fundamentally different class of transformations: it injects noise and reconstructs images through a powerful generative prior, often altering semantic content while preserving photorealism. In this paper, we provide a unified theoretical and empirical analysis showing that non-adversarial diffusion editing can unintentionally degrade or remove robust watermarks. We model diffusion editing as a stochastic transformation that progressively contracts off-manifold perturbations, causing the low-amplitude signals used by many watermarking schemes to decay. Our analysis derives bounds on watermark signal-to-noise ratio and mutual information along diffusion trajectories, yielding conditions under which reliable recovery becomes information-theoretically impossible. We further evaluate representative watermarking systems under a range of diffusion-based editing scenarios and strengths. The results indicate that even routine semantic edits can significantly reduce watermark recoverability. Finally, we discuss the implications for content provenance and outline principles for designing watermarking approaches that remain robust under generative image editing.

Large-scale power quality (PQ) measurement campaigns generate vast amounts of multivariate data, in which systematic dependencies are difficult to identify using conventional analysis techniques. This paper presents a methodology for the automated analysis and visualization of correlation structures in large PQ datasets. Building on an existing framework, the approach is adapted for shorter observation periods and enhanced with aggregation and distance-based visualization techniques. Daily Spearman correlation coefficients are averaged via Fishers z-transformation and aggregated across phases, parameters, and sites. The resulting correlation structures are visualized using hierarchical clustering and multidimensional scaling to reveal consistent and recurring relationships. The methodology is demonstrated using data from 85 measurement sites within the German transmission system.

In this note, we study the geometry of the unit ball of the Banach space generated by the adequate family of all subsets of branches of the infinite binary tree, and answer several open questions related to slicely countably determined Banach spaces. Our main result is that the binary tree space is an example of a Banach space with an unconditional basis which fails to be slicely countably determined. In particular, it provides an example of a non slicely countably determined separable Banach space which contains no isomorphic copy of a space with the Daugavet property. We also exhibit some other geometric features of this space: we prove that its unit ball is dentable, that it has numerical index~1, and that the points of continuity of its unit ball form a weakly dense set. Finally, we show that the binary tree space contains a non-convex subset which is slicely countably determined, but does not admit a countable $π$-base for its relative weak topology, and that there is a 2-equivalent renorming of this space whose unit ball fails to be slicely countably determined.

Privacy-Preserving Machine Learning as a Service (PP-MLaaS) enables secure neural network inference by integrating cryptographic primitives such as homomorphic encryption (HE) and multi-party computation (MPC), protecting both client data and server models. Recent mixed-primitive frameworks have significantly improved inference efficiency, yet they process batched inputs sequentially, offering little flexibility for prioritizing urgent requests. Naïve queue jumping introduces considerable computational and communication overhead, increasing non-negligible latency for in-queue inputs. We initiate the study of privacy-preserving queue jumping in batched inference and propose PrivQJ, a novel framework that enables efficient priority handling without degrading overall system performance. PrivQJ exploits shared computation across inputs via in-processing slot recycling, allowing prior inputs to be piggybacked onto ongoing batch computation with almost no additional cryptographic cost. Both theoretical analysis and experimental results demonstrate over an order-of-magnitude reduction in overhead compared to state-of-the-art PP-MLaaS systems.

Supermassive black hole (SMBH) masses can be measured using molecular gas kinematics. Here we present high angular resolution ($0.12$ arcsec or $\approx11$ pc) Atacama Large Millimeter/submillimeter Array observations of the $^{12}$CO(2-1) line emission of the early-type galaxy NGC 1387. The observations reveal a face-on, regularly-rotating central molecular gas disc with a diameter of $\approx18$ arcsec ($\approx1.7$ kpc) and a central depression slightly larger than the SMBH sphere of influence. We forward model the CO data cube in a Bayesian framework with the \textsc{Kinematic Molecular Simulation} code, and use \textit{Hubble Space Telescope} data to constrain the stellar gravitational potential contribution to the molecular gas kinematics. We infer a SMBH mass of $1.10^{+1.71}_{-0.95}[\text{stat},3σ]^{+2.45}_{-1.09}[\text{sys}]\times10^8$ M$_\odot$ and a F160W-filter stellar mass-to-light ratio of $0.90^{+0.44}_{-0.35}[\text{stat}, 3σ]^{+0.46}_{-0.36}[\text{sys}]$ M$_\odot$/L$_{\odot,\text{F160W}}$. This SMBH mass is consistent with the SMBH mass -- stellar velocity dispersion relation.

This paper is devoted to the study of an age-structured SIRS epidemic model, in which a population affected by a disease is divided into susceptible, infected, and removed individuals. We assume that the force of infection may be nonlinear and time-dependent. The model, originally introduced and studied by Iannelli and his co-authors, can be naturally formulated in an abstract setting and has traditionally been analyzed using fixed point techniques, most often the Banach contraction principle. Following the approaches of Inaba and Banasiak, our investigation is based on the semigroup theory, through which we study the existence of mild (integral) solutions. The main novelty of our work lies in the use of the topological degree for condensing maps instead of classical fixed-point arguments. We prove the existence of a unique, global, nonnegative solution to the model that satisfies the prescribed initial and nonlocal conditions and takes values in the space $L^1$ with respect to the age variable. Moreover, this solution depends continuously on the initial data.

The resistance of hydrogen-bond networks to ambient flow in water produces viscoelectric stresses and contributes to electrostrictive pressure. Within Onsager's nonequilibrium thermodynamic framework, a lattice-gas description of aqueous electrolytes is combined with a coarse-grained hydrodynamic representation of hydrogen-bonded molecular networks, where viscous dissipation is modeled through energetically equivalent Brownian entities. This formulation connects molecular structural information from experiments and molecular dynamics to a unified dipolar Poisson-Nernst-Planck-Stokes (dPNP-S) continuum theory, quantitatively reproducing the measured viscoelectric coefficient of Jin et al. (PNAS 2022) and contributions to electrostrictive pressure. These results identify a microscopic mechanism by which hydrogen-bond dynamics influence electrohydrodynamic flow.

Large Language Models (LLMs) can infer sensitive attributes such as gender or age from indirect cues like names and pronouns, potentially biasing recommendations. While several debiasing methods exist, they require access to the LLMs' weights, are computationally costly, and cannot be used by lay users. To address this gap, we investigate implicit biases in LLM Recommenders (LLMRecs) and explore whether prompt-based strategies can serve as a lightweight and easy-to-use debiasing approach. We contribute three bias-aware prompting strategies for LLMRecs. To our knowledge, this is the first study on prompt-based debiasing approaches in LLMRecs that focuses on group fairness for users. Our experiments with 3 LLMs, 4 prompt templates, 9 sensitive attribute values, and 2 datasets show that our proposed debiasing approach, which instructs an LLM to be fair, can improve fairness by up to 74% while retaining comparable effectiveness, but might overpromote specific demographic groups in some cases.

In this paper we study a general class of nonlinear elliptic problems in divergence form. First, we prove that the solutions to these problems satisfy a convexity property when the given domain is strictly convex. Then, making use of this convexity property, we develop some minimum principles for an appropriate $P$-function, in the sense of L.~E.~Payne. Finally, this new minimum principle is applied to find a priori estimates for the solutions, in terms of the mean curvature of the boundary of the underlying domain.

Reaction-rate calculations relevant to r-process nucleosynthesis depend sensitively on the nuclear $γ$-strength function ($γ$SF). Here we investigate the impact of low-lying pygmy dipole strength (PDS) in $(n,γ)$ and $(γ,n)$ reactions using $γ$SF based on relativistic nuclear energy density functional theory and propagate these strengths into Hauser--Feshbach statistical model calculations of the reaction rates. We show that considerable reaction-rate enhancements at temperatures relevant for r-process nucleosynthesis are governed by the alignment of the pygmy dipole strength energy with the neutron separation threshold $S_n$ rather than by the total low-energy strength. Consequently, nuclei such as $^{68}$Ni and $^{132}$Sn, where the PDS energy-$S_n$ alignment occurs, exhibit the strongest effects on reaction-rate enhancements. These results demonstrate that modeling reliable reaction rates in r-process nucleosynthesis necessitates accurate microscopic descriptions of low-energy dipole strength, in close synergy with experimental investigations in the vicinity of neutron threshold.

We consider highly inaccurate measurements made on classical stochastic and quantum systems. In the quantum case such a \e{weak} measurement preserves coherence between the system's alternatives. We demonstrate that in both cases the information about the scenario realised in each individual trial is lost. However, ensemble parameters such as classical path probabilities, and quantum quasi-probabilities can be extracted from the obtained statistics. In both cases causality ensures that additional post-selection only redistributes individual outcomes between the system's final states. Quantum quasi-probabilities may change sign, which allows for anomalously large meter's (pointer's) reading for some final states. These, we show, result from mere \e{reshaping} of a broad distribution obtained earlier, and provide no \e{experimental evidence} of quantum variables taking, on rare occasions, exceptionally large values.

Context: The active involvement of users and customers in agile software development remains a persistent challenge in practice. For this reason, it is important that students in higher education become familiar with good practices in Agile Requirements Engineering during their studies. Objective: Our objective is to enable students to learn how to interact with Generative Artificial Intelligence (GenAI) through the use of a stakeholder simulation with AI Personas, while also developing an understanding of the limitations of AI tools in practical contexts. Method: In our courses, we employ a stakeholder simulation using GenAI, in which students conduct interviews with AI Personas through a provided meta-prompt. Based on the outcomes of these interviews, students apply agile practices (e.g., story mapping or impact mapping) to document requirements. The use of GenAI is subsequently reflected upon in a structured group discussion. Results: Through this approach, students gain practical experience by applying state-of-the art agile practices for requirements elicitation and documentation while simultaneously developing an understanding of the technical and ethical limitations associated with the use of generative AI. Conclusion: We have applied this approach over several terms and found that using a meta-prompt provides flexibility, allowing us to remain independent of specific large language model providers.

First-order structural phase transition is a common phenomenon in materials that qualitatively alters their physical properties. Yet, the abrupt first-order nature is usually unexplained by realistic computations, implying an omission of important physics in describing the electronic structure of the nearby stable phases. Using the recently discovered nickelate superconductors La$_3$Ni$_2$O$_7$ as a prototypical example, we demonstrate that such first-order nature is typically beyond intra-atomic correlation considered in state-of-the-art material computations. Instead, a full many-body treatment of low-energy active orbitals reveals a generic inter-atomic "orbital dimerization" mechanism of first-order structural phase transition, corresponding to abrupt energy reduction upon a spin-singlet bond formation. Such an inter-atomic correlation qualitatively changes not only the essential lattice bonding but also the characteristics of low-energy electronic properties across the transition. This strong mechanism and the developed computational framework are generally applicable to a wide variety of ionic materials, to produce valuable insights into atomic and electronic structures essential for their physical properties and functionalities.

High-frequency electromagnetic fields (EMFs) are increasingly recognized either as environmental risk factors or as tools for electromagnetic attacks, which are difficult to detect in situ. Existing high-frequency EMF sensors face significant limitations related to structural simplicity, integration with mobile technology, and low energy consumption. To address these challenges, we propose a novel sensor concept based on a magnetically hybridized liquid crystal (LC) microdevice. The hybrid LC chip is designed to exhibit an optical response to external radio-frequency fields without the need for electronic components or an external power supply, relying solely on ambient light. Both sides of the chip are covered with polymer-based crossed polarizer films. The chip is filled with flexible matrices containing thermotropic LCs, such as the rod-like 4-cyano-4'-pentylbiphenyl, into which a network of thin ferromagnetic wires is embedded. The resulting field-responsive LC microdisplay operates via a simple magnetothermal mechanism, and its optical response is sufficiently strong to be visible to the naked eye.

For a metric compact space $L$ and a Banach space $E$, we provide a characterization of the complementability of the Banach space $\mathcal{C}(L)$ of continuous functions on $L$ inside $E$ in terms of the existence of a certain tree in the product $E \times E^*$, based on new descriptions of the Banach spaces $\mathcal{C}([1, ω^α])$ for countable ordinal numbers $α$ and $\mathcal{C}(2^ω)$. Applying this general result in the case where $E=\mathcal{C}(K)$ for some compact space $K$, we further obtain a characterization of the existence of a positively $1$-complemented positively isometric copy of $\mathcal{C}(L)$ inside $\mathcal{C}(K)$ in terms of the topology of $K$ and the space of probability Radon measures on $K$. In the process, we also prove a variant of the classical Holsztyński theorem for isometric embeddings onto complemented subspaces.

In this work, we construct a perturbative black hole (BH) solution motivated by renormalization group (RG) improvement and investigate the quasinormal modes (QNMs) of the BH under scalar field perturbations in both Schwarzschild-de Sitter (SdS) and Schwarzschild-anti-de Sitter (SAdS) backgrounds. To compute the QNMs in the SdS spacetime, we employ the 6th-order Padé-averaged WKB approximation method, while for the SAdS background we utilize the direct shooting method. We examine the dependence of the QNM frequencies on the free parameter of the solution. Furthermore, we analyze the time evolution of a scalar field perturbation around the BH and present the corresponding time-domain profiles. The QNMs are also extracted from the time-domain data using the matrix pencil method. Using the extracted QNM frequencies, we reconstruct the waveform and compare it with the original time-domain profile, finding good agreement between the two. The QNM frequencies obtained from the 6th-order Padé-averaged WKB method and the time-domain analysis in the SdS background, as well as those obtained from the direct shooting method and time-domain analysis in the SAdS spacetime, show very good consistency.

We present quantum circuits for comparison and increment operations that achieve an asymptotically optimal gate count of $Θ(n)$ and depth of $Θ(\log n)$ over the Clifford+Toffoli gate set, while using a provably minimal number of qubits. We extend these results to classical-quantum comparators, yielding an improved classical-quantum adder with an optimal qubit count. Given the ubiquity of these operations as algorithmic building blocks, our constructions translate directly into reduced circuit complexity for many quantum algorithms. As a notable example, they can be used to improve a space-efficient circuit for Shor's factoring algorithm, reducing circuit depth from $\mathcal{O}(n^3)$ to $\mathcal{O}(n^2 \log^2 n)$ without increasing either the qubit count or the asymptotic gate complexity. Underpinning these results is a general theorem demonstrating how to trade ancilla qubits for control qubits with low overhead in both depth and gate count, providing a broadly applicable tool for quantum circuit design.

We consider a low Earth orbit downlink communication, where multiple satellites jointly serve multi-antenna ground users, transmitting multiple spatial streams per user. Using a line-of-sight-dominant satellite channel model with statistical channel state information, including angular information and large-scale fading, we study two distributed transmission modes with different fronthaul requirements. First, for joint transmission, where all satellites transmit all user streams, we formulate a sum spectral efficiency (SE) maximization problem under general convex power constraints and address the intractability of the exact ergodic SE expression by adopting a tractable approximation. Exploiting the equivalence between sum SE maximization and weighted sum mean square error minimization, we derive a novel iterative transceiver design. Second, to reduce fronthaul load, we propose streamwise transmission, where each stream is sent by a single satellite, and develop an eigenmode-based stream-satellite association using participation factors and a maximum-weight bipartite matching problem solved by the Hungarian algorithm. Numerical simulations evaluate the validity of the SE approximation, demonstrate conditions under which streamwise transmission performs nearly optimally or trades SE for lower overhead, highlight the impact of stream/user loading, and show substantial performance gains over conventional benchmarks.

Range-filtered approximate nearest neighbor (RFANN) search is a fundamental operation in modern data systems. Given a set of objects, each with a vector and a numerical attribute, an RFANN query retrieves the nearest neighbors to a query vector among those objects whose numerical attributes fall within the range specified by the query. Existing state-of-the-art methods for RFANN search often require constructing multiple range-specific graph indexes to achieve high query performance, which incurs significant indexing overhead. To address this, we first establish a novel graph indexing theory, the range-aware relative neighborhood graph (RRNG), which jointly considers spatial and attribute proximity. We prove that the RRNG satisfies two crucial properties: (1) monotonic search-ability, which ensures correct nearest neighbor retrieval via beam search; and (2) structural heredity, which guarantees that any range-induced subgraph remains a valid RRNG, thus enabling efficient search with a single graph index. Based on this theoretical foundation, we propose a new graph index called RNSG as a practical solution that efficiently approximates RRNG. We develop fast algorithms for both constructing the RNSG index and processing RFANN queries with it. Extensive experiments on five real-world datasets show that RNSG achieves significantly higher query performance with a more compact index and lower construction cost than existing state-of-the-art methods.

We investigate the restoration patterns of chiral and $U(1)$ axial symmetries at finite temperature using a soft-wall holographic QCD model. The study employs two distinct parameter sets (Case I and Case II), both calibrated to reproduce a pseudocritical temperature $T_{\rm pc} \sim 155$ MeV and the physical pion mass. The temperature dependence of the light and strange quark condensates confirms a smooth chiral crossover transition, with pseudocritical temperatures of $T_{\rm pc}=0.157$ GeV and $T_{\rm pc}=0.154$ GeV for Cases I and II, respectively. The screening masses of chiral partner mesons ($π$-$σ$ and $η$-$a_0$) become degenerate near $T_{\rm pc}$, providing a clear signature of chiral symmetry restoration. Analysis of the corresponding meson susceptibilities further supports this conclusion. However, the indicator for $U(1)$ axial symmetry restoration, $χ_π- χ_{a_0}$, vanishes at a temperature $T \sim 0.190 $ GeV, which indicates a distinct restoration scale with chiral symmetry restoration scale within the present holographic framework. The temperature-dependent topological susceptibility $χ_{\rm top}^{1/4}$ is also computed, showing a sharp drop near $T_{\rm pc}$ and a subsequent slight decrease. While the model qualitatively captures established features of the chiral transition, the results highlight a limitation in the qualitative description of the $U(1)$ axial anomaly compared to LQCD in our work.

We exhibit a local residual set of surface $C^1$ diffeomorphisms that are continuum-wise expansive but are not expansive. We also exhibit an open and dense set of surface $C^1$ diffeomorphisms where expansiveness implies being Anosov.

This thesis explores several facets of Carroll symmetries through their applications to field theories and gravity. The geometric description of curved Carroll manifolds is developed from a Cartan-geometric viewpoint, reviewed at the outset. On these backgrounds, we study various field theories, including scalar and vector Carroll swiftons. Imposing causality and locality, we derive a universal sector of the commutators between Carroll stress-energy tensor components valid for any Carroll quantum field theory. In two dimensions, we confirm the connection to holography by showing that a Carroll boost anomaly gives rise to additional Schwinger-like terms in these brackets, sourcing the familiar central extensions of the asymptotic symmetries of three-dimensional asymptotically flat Einstein gravity. Afterwards, we come to theories of Carroll gravity which, as we argue, provide a valuable playground for understanding quantum gravity in a specific scaling limit which we refer to as the tantum gravity limit. At first, we review Carroll gravity in general dimensions and subsequently restrict to two spacetime dimensions where we introduce Carroll dilaton gravity. We define Carroll black holes as massive vacuum solutions to these theories that admit well-defined thermodynamic properties but have a Carroll extremal surface instead of an event horizon. After investigating several models and their solutions we finally add quantum matter to these backgrounds and study how the thermodynamic properties of a Carroll black hole reflect in its vacuum states. For the Carroll-Schwarzschild black hole we find a non-vanishing asymptotic energy density. We refer to this phenomenon as the Carroll-Hawking effect.

Dispersively coupled distant qubits in a shared cavity can become entangled through virtual photon exchange with energy-conserving phase evolution of their quantum states. This interaction can potentially be accelerated by operating on resonance, allowing for the exchange of real photons. In this theoretical study, we examine photon-mediated entanglement between two distant spins of electrons confined in double quantum dots formed in a Si/SiGe heterostructure. We calculate the dynamics of the combined system comprised of both spin qubits and the cavity, assuming that both spin qubits can be tuned into and out of resonance with the host cavity. We demonstrate that the exchange of real photons between the two spin qubits can result in rapid entanglement that is robust against decoherence. These results pave the way for the development of quantum gates on resonantly coupled distant semiconductor spin qubits.

This paper presents a systematic characterization of wearable galvanic coupling (GC) channels under narrowband and wideband operation. A physics-consistent digital human twin maps anatomical properties, propagation geometry, and electrode-skin interfaces into complex transfer functions directly usable for communication analysis. Attenuation, phase delay, and group delay are evaluated for longitudinal and radial configurations, and dispersion-induced variability is quantified through attenuation ripple and delay standard deviation metrics versus bandwidth. Results confirm electro-quasistatic, weakly dispersive behavior over 10 kHz-1 MHz. Attenuation is primarily geometry-driven, whereas amplitude ripple and delay variability increase with bandwidth, tightening equalization and synchronization constraints. Interface conditioning (gel and foam) significantly improves amplitude and phase stability, while propagation geometry governs link budget and baseline delay. Overall, the framework quantitatively links tissue electromagnetics to waveform distortion, enabling informed trade-offs among bandwidth, interface design, and transceiver complexity in wearable GC systems.

Polycrystalline solid-state ionic conductors (PolySSICs) are key energy materials for all-solid-state Li-ion batteries (LIBs). However, achieving room-temperature ionic conductivity comparable to that of liquid electrolytes ($σ\sim 10^{-2}-10\,\mathrm{S\cdot cm^{-1}}$) remains a major challenge. Here, we experimentally demonstrate that thermal neutron irradiation provides an effective strategy for engineering ion transport in a model PolySSIC, LiBO$_2$, a promising electrode coating material for LIBs. High-flux ($\sim 10^{9}$ neutrons$\cdot$cm$^{-2}\cdot$s$^{-1}$) thermal neutrons ($\sim 25$ meV), delivered at Beam Port E of the University of Missouri Research Reactor (MURR), selectively transmute the strong neutron absorbers $^{10}\mathrm{B}$ and $^{6}\mathrm{Li}$ at their natural abundances ($\sim19.9\%$ and $\sim7.5\%$). This process generates lattice vacancies within polycrystalline grains while preserving long-range crystallographic order. In addition, $γ$ photons produced during $^{10}$B transmutation release electrons that suppress atomic displacement and partially neutralize the space charge associated with positively charged oxygen vacancies at grain boundaries. As a result, the ionic conductivity increases by nearly $20\%$ in grains and more than $80\%$ at grain boundaries. These results validate theoretical predictions and demonstrate a controllable strategy for enhancing ion transport in PolySSICs for solid ionic devices, including LIBs.

We analyze the pairing instability of an altermagnetic metal on a square lattice driven by an attractive nearest-neighbor interaction. This interaction enables multiple pairing channels, including even-parity extended $s$-wave and $d$-wave states, as well as two odd-parity $p$-wave channels. We verify that altermagnetic spin-splitting in the single-particle dispersion gives rise to finite-momentum pairing between electrons with unlike spins, in agreement with earlier predictions. Quite unexpectedly, this pairing typically emerges across multiple channels with mixed parity. Consequently, the resulting finite-momentum Fulde--Ferrell--Larkin--Ovchinnikov (FFLO) superconducting phase is expected to exhibit a multi-component order parameter featuring singlet-triplet mixing. We examine several forms of altermagnetism, specifically $d_{xy}$-wave and $d_{x^{2}-y^{2}}$-wave altermagnetic couplings, and present the corresponding phase diagrams. Additionally, we investigate the triplet pairing between electrons with identical spins, and find that it consistently occurs at zero center-of-mass momentum and is unfavorable at weak altermagnetic coupling and low electron filling. The influence of on-site attractive interactions on mixed-parity pairing is also explored.

This paper proposes an environment-aware near-field (NF) user equipment (UE) tracking method for extremely large aperture arrays. By integrating known surface geometries and tracking the line-of-sight (LOS) and non-line-of-sight (NLOS) indicators per antenna element, the method captures partial blockages and reflections specific to the NF spherical-wavefront regime, which are unavailable under the conventional far-field (FF) assumption. The UE positions are tracked by maximizing the cosine similarity between the predicted and received channels, enabling tracking even under complete LOS obstruction. Simulation results confirm that increasing environment-awareness improves accuracy, and that NF consistently outperforms FF baselines, achieving a $0.22\,\mathrm{m}$ root-mean-square error with full environment-awareness.