Researchers analyze coauthorship networks, but author name ambiguity in their network data remains a significant challenge as it can change the number of vertices, distorting network properties. Although many scholars use straightforward heuristics for author name disambiguation using author's forename initials, these techniques can skew our understanding of network properties by merging or splitting vertices, raising concerns about the reliability and validity of these methods. This study investigates how different levels of vertex merging and splitting errors that are induced by name ambiguity impact network measures, using three large coauthorship networks with highly accurate algorithmic author name disambiguation. As a counterfactual scenario, two initial-based disambiguation methods widely used in coauthorship network research were applied to these datasets. Nine coauthorship network metrics were computed while varying randomly the numbers of merged or split vertices. Results show that initial-based disambiguation generates coauthorship networks with specific network properties underestimated, leading to the discovery of coauthorship networks that are smaller and more closely connected than they genuinely are. In contrast, other network metric values increase, making authors appear more collaborative and embedded within less fragmented research communities than they are. The study emphasizes the importance of careful disambiguation of vertex names in analyzing coauthorship networks for rigorous and valid findings.

In this paper, we present an archival search for short gamma-ray bursts (sGRBs) over 13 years (2013-2025) of Fermi/GBM data using a Poisson matched-filter pipeline that performs a fully coherent analysis across all detectors and energy channels, significantly improving sensitivity relative to the onboard triggering algorithms. A central component of the analysis is the empirical estimation of trigger significance using 'timeslided' data, allowing each candidate to be assigned a probability of astrophysical origin. We also developed a new parameter-estimation framework based on the Poisson matched filter, which uses the global structure of the detected event across spectral, temporal, and spatial parameter spaces. This enables us to systematically classify bursts and distinguish between GRBs, soft gamma repeaters, terrestrial gamma-ray flashes, and solar flares. We identify 568 new GRB candidates with $p_{\text{astro}}\geq0.9$ and thousands of magnetar bursts, significantly expanding the known short-transient population in GBM data. To further strengthen the significance of the GRB candidates, we performed a targeted follow-up search in Swift/BAT rate data. Applying the followup to all of our triggers - including triggers below the detection threshold yielded 1736 temporally coincident events with association probability above $90\%$. The resulting probabilistically ranked catalog substantially expands the population of short GRBs and magnetar flares detected in GBM data and provides a statistically robust framework for multimessenger searches.

We present a general framework for the high-precision numerical evaluation of multivariate hypergeometric functions defined as solutions of holonomic systems of partial differential equations. Our approach adapts and extends methods originally developed for multi-loop Feynman integrals to the setting of hypergeometric functions of many variables. In particular, we construct Pfaffian systems for arbitrary multivariate hypergeometric functions by applying the Laporta reduction algorithm to suitable systems of differential relations. Next, we construct a numerical scheme based on the Frobenius method, which allows us to compute local power-series solutions with controlled precision and to transport them along prescribed paths in the space of variables. A central part of the paper is devoted to a systematic analysis of multivaluedness and branch structure: we show how the Frobenius method can be used to access different Riemann sheets in a controlled way and to track changes of the solution under analytic continuation around singular loci.

GenEO (`Generalised Eigenvalue problems on the Overlap') is a method for constructing coarse spaces used in the preconditioning of iterative solvers for discrete PDEs. This method combines a (small) number of modes of local PDE eigenproblems to obtain a global coarse space. A coarse solve is then combined with local solves of the global PDE to obtain the preconditioner. A substantial theory for GenEO has been developed for the case when the local elgenproblems are positive semi-definite. This has been applied mostly to positive definite global PDEs, but also recently extended to the case of convection--diffusion--reaction problems, which may be neither self-adjoint, nor positive definite. However, when the global problem is highly indefinite, coarse spaces built from positive semi-definite local eigenproblems fail to be robust in practice. In this paper we consider highly indefinite global PDE problems, characterised by a large parameter $k$ (allowing also highly variable coefficients), and we develop a new spectral coarse space built from solving eigenvalue problems based on \textit{local copies of the global problem}. We put no constraint on the diameters of the local domains, thus allowing the local eigenvalue problems to be indefinite. The new method (which we call $H_k$-GenEO) is seen to be much more robust as $k$ increases than methods based on positive semi-definite eigenproblems. We provide sufficient conditions for robustness of the preconditioned GMRES iterative method, in terms of the tolerance of the local eigenproblems and the size of the subdomains for the local PDE solves. In practice the method is observed to be robust with respect to $k$ under even weaker conditions on the local eigenproblem tolerance. The experiments also suggest the method can be resilient to high variation in PDE coefficients.

Microwave linear analog computers (MiLACs) have recently emerged to enable high-performance and efficient beamforming in the analog domain. In this paper, we introduce a dual-functionality framework for MiLAC-aided transceivers. Beyond analog-domain precoding/combining (active beamforming), a MiLAC and its antenna array can simultaneously act as a reconfigurable intelligent surface (RIS) (passive beamforming). This allows the MiLAC to execute beamforming for transmission/reception while reflecting external incident signals. We provide an optimal reconfiguration strategy for this dual-functional MiLAC, and characterize the fundamental limits on the trade-off between active and passive rate, namely the capacity region bounds and the sum-rate capacity.

The Fundamental Plane (FP) of Early-Type Galaxies (ETGs) encapsulates a tight correlation among their structural and dynamical properties and provides an important benchmark for galaxy formation models. However, cosmological hydrodynamical simulations have historically struggled to reproduce the observed FP tilt, with discrepancies often attributed to to flawed feedback physics or insufficient resolution. Using the IllustrisTNG100-1 simulation, we show that adopting observationally motivated measurements, including Sérsic-derived photometric parameters and dynamically inferred velocity dispersions designed to minimise softening-length effects, substantially reduces the discrepancy between simulated and observed FPs. We further explore the impact of non-universal, mass-dependent Initial Mass Function (IMF) variations through forward modelling of their effects on galaxy structural and dynamical quantities. In particular, bottom-heavy IMF variations produce FP coefficients fully consistent with observational constraints for both direct and orthogonal fits. Our results suggest that a significant fraction of the long-standing FP tension arises from how galaxy observables are extracted and interpreted in simulations, although residual discrepancies may still reflect limitations in the underlying baryonic physics. These findings highlight the importance of observational realism and IMF variations for interpreting galaxy scaling relations and for improving the predictive power of hydrodynamical simulations of ETG formation.

We introduce weak and strong poset Ramsey-Turán numbers for $t$-chains in host poset families, focusing on the Boolean lattice family $\mathcal{B}=\{B_n:n\ge 1\}$. For any poset $P$, we show $\operatorname{RT}(\mathcal{B};n,P,l,t)\le \operatorname{RT}^{\sharp}(\mathcal{B};n,P,l,t)$, with equality when $P$ is a chain. In particular, for $t=1$, $\operatorname{RT}(\mathcal{B};n,C_k,l)=\operatorname{RT}^{\sharp}(\mathcal{B};n,C_k,l)=(k-1)(l-1)$. We also give universal upper bounds for both versions. For fixed $k,l,t$ with $\min\{l-1,k-1\}\ge 1$, we prove $\operatorname{RT}^{\sharp}(\mathcal{B};n,A_k,l,t)=Θ(n^t)$. More generally, for every non-chain poset $P$, the strong number is $Θ(n^t)$ for fixed $l,t$. Finally, if $h(P)=r>t$ and $l(n)=\lfloor M_n^β\rfloor$ with $0<β\le α<1$, then both weak and strong versions admit lower bounds of order $Ω\!\left(2^{βn}n^{-β/2}\right)$.

Orbital transfers in multi-body systems are often studied as isolated trajectory design problems, making it difficult to identify the larger transport structure connecting families of periodic orbits, including which families act as hubs, gateways, relays, or persistently difficult-to-access regions. This work introduces a reachable-set-based framework for constructing orbital networks in the circular restricted three-body problem. Finite-$ΔV$ and finite-time-of-flight reachable-set overlaps are used to infer accessibility relationships between representative periodic orbit families on a common Jacobi energy manifold and to assemble these relationships into a weighted orbital network. Applied to the Earth-Moon system, the resulting network reveals distinct accessibility regimes in which direct reachability, graph connectedness, and feasible multileg closure emerge separately. The analysis identifies multi-orbiter cycler orbits as the dominant hub, gateway, and relay families, with the (3,2)-cycler dominating across much of the sampled budget plane and the short-period (1,1)-cycler dominating in the low-time-of-flight regime, while the stable 2:1 resonant orbit remains persistently difficult to access. Although the maximum-budget network is nearly complete in a binary sense, its weighted accessibility remains strongly non-uniform. Selected proxy-supported connections are refined into concrete trajectories through differential correction, with corrected transfer costs remaining below the proxy estimates in all tested cases. Together, the results demonstrate how reachable-set overlap geometry can expose large-scale transport structure in nonlinear gravitational systems without requiring exhaustive pairwise trajectory optimization.

We study the conditions for a three-phase contact line to return to a previous position. We drive a water-air-glass contact line between two horizontal plates, by slowly adding and removing water with a constant volume amplitude. For the first several cycles, the contact line ends each cycle with a different shape, in contrast with previously published work. Eventually the shapes begin to repeat, and the system has memory: a cycle with a smaller amplitude ends in a different shape, but even one cycle at the original amplitude recovers the steady-state shape. After a cycle at a larger amplitude, the steady-state shape is erased. We find that our tight control of the enclosed volume creates a global interaction, wherein only the least stable part of the contact line can move. Using theory and minimal models, we show that this interaction gives rise to the transient behaviors. Our study sheds light on the origins of reversibility and memory in a system where neither is guaranteed, and shows that the physics of contact line motion changes in a confined environment.

It has been conjectured that generic smooth solutions of the two-dimensional Euler equation exhibit linear growth of vorticity gradients. We prove an elementary arbitrary-background perturbation principle in the odd symmetric setting. More precisely, for any compactly supported nonnegative function in the half-plane, one can find an arbitrarily small smooth nonnegative perturbation whose associated solution undergoes linear-in-time filamentation in the quadrant. The main ingredients are the lower bound of the center of mass given by Iftimie-Sideris-Gamblin, and the velocity estimate for the sparse part to capture those slowly moving particles.

This note addresses a number of subtle issues pertaining to the long-standing problem of strong phonon-like fermion-boson coupling. Among the central topics are the customary Migdal-Eliashberg approximation in the pertinent Schwinger-Dyson gap equation and its solutions. The previously gained insight is assessed by contrasting it against the various (non-)supersymmetric variants of the Yukawa-Sachdev-Ye-Kitaev model. Also, some previously discussed (pseudo-)holographic aspects of fermion pairing in such models are commented upon.

A hyperbolic structure on a group $G$ is a (not necessarily properly discontinuous) cobounded action of $G$ on a Gromov hyperbolic space, considered up to coarsely $G$-equivariant quasi-isometry. We show that for groups $G$ acting geometrically and positively on a horocyclic product $X\bowtie Y$, all hyperbolic structures on $G$ come from the two actions on the factors. The ingredients of the proof include Malcev rigidity and a new ("vertical") boundary of horocyclic products. We also give the first example of a group acting geometrically on a horocyclic product of two mixed millefeuille spaces.

Haldane pseudopotentials $V_{|m|}$ provide the effective interaction parameters governing correlated states in the fractional quantum Hall regime. In conventional formulations, these quantities are obtained by projecting the Coulomb interaction onto relative-angular-momentum states within the lowest Landau level, thereby neglecting virtual transitions to higher Landau levels. Here, we formulate a nonperturbative description of effective interactions directly from the exact two-electron spectrum in a magnetic field. By solving the relative-motion problem beyond the lowest-Landau-level approximation, we define renormalized pseudopotentials $V^*_{|m|}$ from the exact eigenenergies and introduce dynamical corrections $Δ_{|m|}=V^*_{|m|}-V_{|m|}$. The corrections remain systematically negative and depend strongly on both interaction strength and relative angular momentum, reflecting dynamical correlation effects associated with higher-state virtual admixture. The exact results reproduce the perturbative Landau-level-mixing limit at weak coupling while exhibiting substantial deviations in the strong-mixing regime, signaling the breakdown of low-order perturbative expansions. In particular, the short-range interaction channels relevant to Laughlin-type correlations undergo strong renormalization, leading to substantial modification of the effective interaction hierarchy in strongly interacting systems such as ZnO/MgZnO heterostructures. The present formulation establishes a microscopic framework for incorporating nonperturbative Landau-level-mixing effects into effective interaction theories of quantum Hall systems.

The polar-angle marginal of a centred bivariate Gaussian distribution, obtained after integrating out the radial coordinate, gives the two-dimensional angular central Gaussian (ACG) distribution of Tyler. While its trigonometric and vector-valued moments have been studied in detail, to our knowledge there are no explicit closed-form expressions for the \emph{linear} moments $\mathbf{E}[θ]$ and $\mathbf{E}[θ^{2}]$ on the natural domain $θ\in\left]-π/2,π/2\right[$. Here \textit{linear} refers to the ordinary moments $\intθ^{k}f(θ)\,dθ$ of the angle regarded as a real-valued variable, in contrast to the circular (trigonometric) moments $\mathbf{E}[e^{ikθ}]$ customary in directional statistics. We provide such expressions: the mean is a simple arctangent of the parameters, while the second moment is given by the real part of a dilogarithm. The derivation, based on a contour integration around the branch cut of $\arctan z$, is elementary. These quantities naturally arise in physics, where $θ$ is interpreted as a real-valued phase rather than a circular variable.

Maritime weather routing must optimize route geometry under dynamic wind-wave conditions, obstacle constraints, and fixed-arrival requirements. We present Bézier Evolve and Refine Strategy (\name{}), a two-stage framework that combines global evolutionary search (CMA-ES) with local variational refinement (FMS). Routes are parametrized as Bézier curves and evaluated with dense along-path sampling, enabling smooth trajectories while preserving practical feasibility constraints and accounting for mid-segment effects. We evaluate \name{} on synthetic benchmarks designed to stress seven operational criteria: continuity, obstacle avoidance, dynamic adaptation, flexible objective design, constant-load feasibility, just-in-time arrival, and local optimality. Across these tests, \name{} matches or improves published baselines while maintaining robust convergence under challenging flow fields and land geometries. We then validate the method on real ocean data using hourly ERA5 forcing over 366 daily departures in 2024 for two trans-oceanic corridors (Atlantic and Pacific), with a physics-based model of an 88~m cargo vessel with optional rigid wingsails. In real-ocean experiments, route optimization alone reduces mean propulsive energy by 23--59\% versus great-circle baselines of the same propulsion mode. Combined with wind-assisted propulsion, total savings reach up to 75\%. These results show that \name{} provides a practical and scalable foundation for just-in-time, energy-efficient weather routing in maritime decarbonization workflows.

Direct real-space probes of altermagnetic order remain scarce. Here we introduce multiplet-selective photoelectron diffraction (PED), a methodology in which different regions of a transition-metal core-level multiplet act as distinct photoemission source waves. Using multiple-scattering calculations for the metallic altermagnet candidate CrSb, we show that selected Cr $3p$ multiplet features with predominantly $Y_1^{+1}$ and $Y_1^{-1}$ character generate robust diffraction asymmetries sensitive to altermagnetic domains. We demonstrate that both circularly and linearly polarized light provide access to the effect, while suitable combinations of domains, light polarizations, and multiplet-energy windows suppress nonmagnetic diffraction backgrounds. The proposed approach can be implemented using standard momentum-resolved photoemission instrumentation and establishes core-level PED as a practical route toward domain-resolved studies of altermagnets.

The two-particle correlation function measured in femtoscopic analyses provides access to the interaction potentials between emitted particles. This offers a unique opportunity to investigate interactions among charmed mesons and to explore the nature of possible exotic hadronic states. In this Letter, we study femtoscopic correlations of various charmed-meson pairs in relativistic heavy-ion collisions. The dynamical evolution of the system and charm hadron production are described within the Parton-Hadron-String Dynamics (PHSD) transport approach, while the correlation functions are computed using the Correlation Analysis Tool using the Schrödinger equation (CATS). We demonstrate that heavy-ion collisions provide a significantly more favorable environment than $pp$ collisions for accessing charmed meson femtoscopic correlations. This arises from enhanced charm-quark production, reduced relative momenta due to in-medium energy loss, and a strong suppression of initial-state correlations. Our results indicate that femtoscopic measurements in heavy-ion collisions offer a sensitive probe of charmed meson interactions and possible hadronic molecular states.

Satellite communications are envisioned as a key enabler for ubiquitous coverage in future 6G networks, yet the broadcast nature renders them vulnerable to eavesdropping, especially given the long-distance transmissions and associated high uncertainties. In this paper, we propose the physical layer security enhancement for multi-beam satellite communications with the assistance of an aerial reconfigurable intelligent surface (ARIS). Considering the high dynamics and uncertainties of channels, we characterize the channel distribution with moment-based ambiguity sets. Accordingly, a distributionally robust secrecy rate optimization is formulated through joint design of transmit and reflection beamforming. We then introduce a conditional value-at-risk-based reformulation to convert the probabilistic constraints into deterministic forms. An alternating optimization framework is subsequently employed to iteratively update the transmit and reflective beamforming vectors until convergence. Simulation results demonstrate that the proposed distributionally robust scheme significantly enhances secrecy performance, and maintains reliable performance across various channel error distributions.

Device-independent (DI) quantum cryptography provides secure cryptography with minimal trust in, or characterisation of, the used quantum devices. An essential component of DI protocols is the use of randomness extractors for privacy amplification, but these typically require an initial seed of randomness that introduces a potential vulnerability. To solve this problem, the security of seedless extractors was proven in Quantum 9, 1654 (2025). The core idea was to use the Bell violation of the raw data, rather than its min-entropy, as the extractor promise. However, the large fluctuations in the Bell inequality used required many rounds to precisely estimate the Bell violation, consuming substantial randomness and making the protocol very inefficient. In this work, we present a new proof technique based on a truncation method that allows the user to estimate the protocol parameters with an asymptotically vanishing fraction of rounds and, as a consequence, achieves the optimal rate of one key bit per singlet. Notably, we prove this result using seedless extractors that can be implemented efficiently.

Exoplanet demographic studies rely on large and homogeneous catalogs, yet stellar multiplicity remains incompletely characterised in many planet samples. Misidentified stellar companions can bias both stellar and planetary parameters, leading to ambiguous and incomplete conclusions about planet formation and evolution. We aim to construct a robust and reliable reference catalog of S-type exoplanets for future investigations of planet formation and evolution in multiple-star environments, and to reassess exoplanet demographics by comparing planets hosted by single-stars and binary systems in a statistically consistent framework. We update the PlanetS catalog of transiting exoplanets by systematically identifying gravitationally bound stellar companions using Gaia DR3. Adopting a deliberately conservative classification, we distinguish binary and single-star systems and constructed a matched control sample of single hosts to mitigate selection and observational biases. Using this curated dataset of 860 transiting exoplanets including 133 S-type planets, we performed a comparative demographic analysis of planetary properties as a function of host multiplicity, stellar mass, and binary separation. We find a binary fraction of 19.4% relative to the control sample (15.5% relative to the full single-star sample), consistent with previous estimates but derived from a larger and more homogeneous dataset. Significant demographic differences emerge in the giant planet regime, less affected by observational biases. We find that giant planets in binaries tend to be more massive than their single-star counterparts and to orbit closer to their host stars, making their radius more inflated. In particular, we identify a tentative excess of giant planets orbiting M-dwarfs in binaries with separations < 1000 AU, suggesting a potentially informative regime for future demographic studies.

Entanglement is known to be a powerful resource that improves performance in various quantum information and computational tasks. A standard example of such a phenomenon is the possibility of perfectly discriminating all four Pauli operations in a single shot via the superdense coding protocol. While entanglement is often a powerful resource for quantum channel discrimination, this is not necessarily the case. In this work, we identify scenarios in which the maximally entangled state is a bad choice of input state and, more generally, show that excessive entanglement can reduce channel discriminability dramatically. To do so, we present an explicit pair of unitary channels which are perfectly discriminable without entanglement, but for which any strategy with maximally entangled input states is $ε$-close to a blind uniform guessing strategy. To develop a systematic approach, we introduce the concepts of Maximal Entanglement Worst Case (MEWC) and Maximal Entanglement Best Case (MEBC) pairs of channels, and present conditions for a pair of channels to be MEWC or MEBC. With these conditions, we show that the optimal input states for discriminating MEWC pairs of channels are necessarily separable, and provide non-trivial examples of measurement channels for which entanglement necessarily reduces the maximum probability of discrimination.

Algebraic steppers help students learn functional programming by displaying evaluation as a sequence of small-step reductions, but even simple programs produce long traces in which key ideas are buried under mundane reductions. This paper presents the filtered stepper calculus, a formal framework that gives users scoped, pattern-based control over which reduction steps are shown or hidden. Users annotate programs with lightweight filter expressions that match on the structure of redexes. Filters compose via lexical scoping so that inner filters override outer ones. We prove preservation, progress, and a simulation theorem establishing that the filtered stepper agrees with the underlying unfiltered semantics, and mechanize all proofs in Agda. We implement the calculus in the Hazel live programming environment, including its support for stepping programs with holes and type errors. To do so, we reconcile Hazel's internal environment-based evaluator with the substitution-based presentation expected in the classroom. We deploy the system in a university programming languages course. Our evaluation shows that students adopt the stepper organically, though more advanced uses of filters may require further instruction, and that instructors can use filters to craft focused traces for use in lectures.

When considering the complexity of communication protocols, the aim is to perform a certain task with the minimum amount of communication resources, such as time and transmitted information. The use of quantum states may lead to an exponential advantage in the use of such resources. Here, we are interested in the task of calculating the Euclidean distance between two vectors representing real data sets. It has been previously shown that it is possible to obtain an advantage for this task based on quantum fingerprinting. This protocol is defined in the simultaneous message passing model of communication complexity, where the two parties do not communicate with each other but send data to a third party, and exploits practical fingerprints generated using trains of coherent state pulses instead of highly entangled qubit states that are hard to generate for large input sizes needed to demonstrate an exponential advantage. We perform a proof-of-principle experimental demonstration of the Euclidean distance protocol using amplitude modulation techniques for encoding non-binary data sets and high-performance superconducting nanowire single-photon detectors required to increase the accessible input size. We show a quantum advantage in transmitted information surpassing the best classical protocol for an input size of $10^8$, for diverse types of data sets, including those corresponding to real grayscale images, and with reasonable precision and error bounds. Our results highlight the potential of quantum communication complexity for use in a broad set of applications.

This paper was triggered by recent results on the maximal `average distance between consecutive points' of uniformly distributed sequences (u.f.d.s.). Here we address a generalized version of this question, consider pairwise maximal/minimal/total distances in blocks/segments of $ d \geq 2 $ consecutive points of u.f.d.s., and derive sharp upper bounds for all three aggregations. Our main idea of proof consists in, firstly, adding degrees of freedom, secondly, translating the resulting problem to a solvable optimization problem over the compact family of $ d $-stochastic measures, and, thirdly, showing that the obtained bounds are also sharp bounds for the original problem.

Medical decision-making increasingly requires rapid and reliable assignment of patients to disease subtypes, as many diseases are no longer treated as single entities. For example, cancer patients may be stratified into aggressive and non-aggressive subtypes, with different treatment strategies for each group. We propose a Bayesian nonparametric approach based on a Dirichlet process mixture model for clustering individuals into disease subtypes. We implement a coordinate ascent variational inference algorithm, yielding an effective and computationally efficient alternative to Markov chain Monte Carlo (MCMC), to support medical decision-making. In synthetic experiments, we demonstrate that the proposed approach accurately assigns observations to their ground-truth clusters, achieving strong performance across evaluation metrics, such as homogeneity and completeness. Additionally, we illustrate the proposed approach achieves a substantial improvement in computational cost compared to MCMC, without sacrificing accuracy that would lead to the increased risk of misdiagnosis.

Cell-free massive multi-input-multi-output (CFmMIMO) communication networks aim to provide uniform quality of service by distributing access points (APs) across a coverage area. In user-centric variants, each user equipment (UE) can choose a cluster of APs with the best channel conditions (e.g., the closest APs) for accessing service. This approach eliminates the notion of cells with dedicated regions and APs, as found in cellular mMIMO communication networks. Estimating uplink channels between UEs and APs is a crucial step in CFmMIMO communication networks; however, existing channel estimation (CE) approaches typically originate from mMIMO systems without considering the unique properties of CFmMIMO communication networks. For instance, shorter AP-UE distances in CFmMIMO systems result in Rician channel models with prominent line of sight (LoS) components between APs and UEs, motivating cooperation between APs for improved performance. In this paper, we propose a cooperative minimum-mean-squared-error (MMSE)-based uplink CE approach where APs share their linearly compressed signals as fused signals with other APs in the same cluster. The proposed approach is optimal, i.e., its performance is equivalent to that of the centralized CE approach, where APs share their uncompressed raw signals. Notably, this optimality is achieved in one shot; that is, given the required correlation matrices, the optimal fusion filters and estimators are derived non-iteratively. Consequently, the proposed approach guarantees lower communication overhead for cooperative CE compared to the centralized approach. Numerical experiments corroborate the superior performance of the proposed cooperative CE approaches in terms of CE accuracy and convergence rate.

In the finite-dimensional setting, it is known that STFT phase retrieval is always possible when the window's ambiguity function does not vanish. However, it is not known how many zeros are allowed in the ambiguity function for the window still to allow phase retrieval. In order to tackle this problem, we first consider a two-window approach where the second window equals the Fourier transform of the first window. This allows us to apply the uncertainty principle in order to obtain sufficient conditions for phase retrieval. Using the relation between STFT phase retrieval and ambiguity sampling, we can prove sufficient conditions for the single-window phase retrieval problem, showing that only approximately eight ninths of the entries of the window's ambiguity function (and only three quarters in prime dimensions) are required to be nonzero.

We propose the \emph{sketched landing method}, a randomized variant of the landing method for optimization under orthogonality constraints. Each landing step consists of the sum of a \emph{normal} component, which reduces infeasibility, and a \emph{tangent} component, which decreases the objective function. Our main contribution is the introduction of low-dimensional random \emph{sketch matrices} to reduce the computational cost of these directions. We consider both dense (Gaussian) and sparse (subsampling) sketch matrices, and show how they reduce the per-iteration cost while preserving convergence guarantees in expectation.

We study the Hausdorff dimension spectrum of asymptotic approximation rates of complex Diophantine approximation and that of the asymptotic average excursion time of cusp excursions on the Bianchi orbifold $\mathbb{H}^3/\operatorname{PSL}(2,\mathbb {Z}[i])$ via a unified approach using the Hurwitz map. In particular, we construct a conformal graph directed system (CGDS) for the Hurwitz map and show that the Lyapunov exponent of the Hurwitz CGDS simultaneously captures the asymptotic approximation rate and the the asymptotic average excursion time. Applying the multifractal analysis of Lyapunov exponents for this system, we obtain a formula and real-analyticity for the Hausdorff dimension spectrum functions.

Recent experimental observations in the noncentrosymmetric Weyl semimetal PtBi$_2$ indicate unconventional superconductivity hosted by topological surface states -- Weyl Fermi arcs -- with a node at the center of each arc. Focusing on these Fermi arcs, we calculate the electronically mediated pairing interaction using a Kohn-Luttinger approach and find that, in a large region of the phase diagram, the leading superconducting instability has an $i$-wave symmetry featuring precisely such an intra-arc node. We study the dependence of the leading superconducting instabilities on electronic interaction parameters and chemical potential and show that the $i$-wave state is robust to changes in the model parameters. Our results provide a possible mechanism for the observation of topological $i$-wave superconductivity on the surface of PtBi$_2$ and may have implications for the broader landscape of superconducting instabilities arising from repulsive interactions on the surfaces of Weyl semimetals.