We show that the realization theorem of Fernández de Bobadilla, which identifies the Milnor fiber of a weighted-homogeneous polynomial with the complement of a germ of analytic set, can be combined with the systematic Massey product constructions of Grbić-Linton for moment-angle complexes $\mathcal{Z}_K = \mathcal{Z}_K(D^2, S^1)$ to produce weighted-homogeneous polynomials whose Milnor fibers are arbitrarily highly connected and non-formal. The original application of this strategy, due to Fernández de Bobadilla, used the Denham-Suciu classification of lowest-degree triple Massey products and yielded only 2-connected non-formal Milnor fibers. The Grbić-Linton framework, which constructs non-trivial $n$-fold Massey products in $H^*(\mathcal{Z}_K;\mathbb{Z})$ for arbitrary $n$ and in arbitrary cohomological degrees, removes this connectivity restriction entirely.

When exact magnetic surfaces are assumed to exist, the gyrokinetic theory of microturbulence gives the same radial transport for ions and electrons. But, exact magnetic surfaces do not exist in the presence of what is called electrostatic microturbulence. When the plasma pressure is non-zero, a turbulent electric potential is accompanied by a turbulent magnetic field, which splits the rational magnetic surfaces with which it resonates. If the magnetic field is assumed to have an ideal topology-conserving evolution, delta function current densities arise on resonant surfaces. The singularity of the current density allows islands to open quickly, but there is no singularity that allows a rapid closure. Islands remain and do not flutter into and out of existence. A relative rotation of the electron fluid in neighboring island chains produces a non-dissipative force that can lock the islands together and produce a non-ambipolar transport. At sufficient plasma pressure, the islands associated with different resonant rational surfaces can overlap. When this occurs some magnetic field lines will cross the entire radial region occupied by overlapping islands. The effect on the electron fluid is to create a viscosity-like force, which is dissipative and tends to remove gradients in the electron rotation. This also produces a non-ambipolar transport. Under many assumptions, the island locking force is larger than the viscosity-like force.

Let $\mathbb{F}$ be an algebraically closed field of characteristic $0$. Given a square matrix $A \in \mathbb{F}^{n \times n}$ and a polynomial $f \in \mathbb{F}[w]$, we determine the Jordan canonical form of the formal Fréchet derivative of $f(A)$, in terms of that of $A$ and of $f$. When $\mathbb{F}\subseteq \mathbb{C}$, via Hermite interpolation, our result provides a solution to [N.J. Higham, \emph{Functions of Matrices: Theory and Computation}, Research Problem 3.11]. A generalization consists of finding the Jordan canonical form of linear combinations of Kronecker products of powers of two square matrices, i.e., $\sum_{i,j} a_{ij} (X^i \otimes Y^j)$. For this generalization, we provide some new partial results, including a partial solution under certain assumptions and general bounds on the number and the sizes of Jordan blocks.

This manuscript introduces a novel method to assess tissue oxygen concentration via the quantum entanglement (QE) of photons originating from positronium which is produced within the patient's body during positron emission tomography. We also investigate the possibility of assessing hypoxia by simultaneously detecting positronium lifetime and the positronium decay rate ratio. We introduce two distinct quantum sensing approaches. Method 1 utilizes the correlation between oxygen concentration and ortho-positronium (o-Ps) decay rates, relying on the simultaneous measurement of the mean o-Ps lifetime ($τ_{\mathrm{oPs}}$) and the $3γ$-to-$2γ$ annihilation rate ratio of o-Ps ($R_{\mathrm{oPs-3γ/2γ}}$). Method 2 introduces a novel hypothesis: that the degree of QE is sensitive to the relative contribution of annihilation mechanisms (pick-off vs. conversion), which in turn depends on oxygen concentration. We derive a formula for partial pressure of oxygen ($p\mathrm{O}_2$) as a function of $R_{\mathrm{oPs-3γ/2γ}}$ and $τ_{\mathrm{oPs}}$ and estimate the measurement accuracy required for these parameters - and for the degree of QE - to sense in-vivo oxygen pressure in the range between hypoxic and physoxic conditions. Theoretical models and quantitative estimates for $R_{\mathrm{oPs-3γ/2γ}}$, $τ_{\mathrm{oPs}}$ and for the degree of QE ($C_{\mathrm{QE}}$ ) as a function of $p\mathrm{O}_2$ are provided for water, isopropanol, cyclohexane, isooctane, and adipose tissue. In particular, applying the formulas derived under the working hypothesis that in pick-off process the photons are not entangled, we estimated that for $p\mathrm{O}_2 = 0$, the degree of quantum entanglement $C_{\mathrm{QE}}$ is equal to 0.890 for adipose, 0.886 for isopropanol, 0.867 for water, 0.818 for cyclohexane, and 0.784 for isooctane.

Access to genomic data is highly regulated due to its sensitive nature. While safeguards are essential, cumbersome data access processes pose a significant barrier to the development of AI methods for genomics. Synthetic data generation can mitigate this tension by enabling broader data sharing without exposing sensitive information. Synthetic genomic data are produced by training generative models on real data and subsequently sampling artificial data that preserves relevant statistics while limiting disclosures about the underlying individuals. In some settings, a single data holder may have sufficient data to train such generative models; however, in many applications data must be combined across multiple sites to achieve adequate scale. This need arises, e.g., in rare disease studies, where individual hospitals typically hold data for only a small number of patients. The solution we present in this paper enables multiple data holders to jointly train a synthetic data generator without revealing their raw data. Our approach combines secure multiparty computation (MPC) to ensure input privacy, so that no party ever discloses its data in unencrypted form, with differential privacy (DP) to provide output privacy by mitigating information leakage from the released synthetic data. We empirically demonstrate the effectiveness of the proposed method by generating high-utility synthetic datasets from multiple real RNA-seq cohorts in federated settings, showing that our approach enables privacy-preserving data synthesis even when data are distributed across institutions.

We study the problem of computing a competitive equilibrium with approximately optimal bundles in Fisher markets with separable piecewise-linear concave (SPLC) utility functions, meaning that every buyer receives a $(1-δ)$-optimal bundle, instead of a perfectly optimal one. We establish the first intractability result for the problem by showing that it is PPAD-hard for some constant $δ> 0$, assuming the PCP-for-PPAD conjecture. This hardness result holds even if all buyers have identical budgets (competitive equilibrium with equal incomes), linear capped utilities, and even if we also allow $\varepsilon$-approximate clearing instead of perfect clearing, for any constant $\varepsilon < 1/9$. Importantly, we show that the PCP-for-PPAD conjecture is in fact required to show hardness for constant $δ$: showing PPAD-hardness for finding such approximate market equilibria in a broad class of markets encompassing those generated by our hardness result would prove the conjecture. This is the first natural problem where the conjecture is provably required to establish hardness for it.

A variant of the flatness problem from integer programming is studied, in which one considers convex bodies in $\mathbb{R}^d$ with at most $k$ interior lattice points. The maximum lattice width of such a body is denoted by Flt(d,k) and it is related to the classical flatness constant as well as a conjectural dual version of Minkowski's convex body theorem due to Makai. Moreover, it is shown that Flt(2, 1) = 3, i.e., any planar convex body with at most one interior point has lattice width at most three. This leads to an isominwidth inequality for the lattice point enumerator of planar convex bodies.

We study phase transitions on dynamic triadic hypergraphs, in which a continuous formation field evolves under stochastic Ginzburg--Landau dynamics with a cubic three-body coupling $g_τϕ_iϕ_jϕ_k$, while a discrete opinion variable $s_i\in\{-1,+1\}$ undergoes Kawasaki exchange under a Hamiltonian with pairwise alignment and an irreducible three-body energy $-λ_τ\prod_{a\inτ}s_a$. Near the formation critical point the cubic coupling is subleading and the transition remains continuous, controlled at leading order by a pairwise Ising baseline with renormalized coupling $J_{\rm eff}=J+γw$. The dominant observable is the triadic formation correlator $Ψ_{\rm form}\equiv\langleϕ_iϕ_jϕ_k\rangle$, a $k=3$ composite operator built over the underlying $\mathbb{Z}_2$-symmetric order parameter. Composite-operator scaling yields the effective exponents $β_{\rm TF}=3/2$ and $γ_{\rm TF}=-1$. The susceptibility conjugate to $Ψ_{\rm form}$ vanishes at the critical temperature $T_c$ rather than diverging, in contrast to the divergence characterizing scalar (pairwise) order parameters. The exact partition function of the minimal triad on $\{-1,+1\}^3$ identifies a crossover scale $T^*=4J_{\rm eff}/\ln 3$. A field-theoretic two-point function argument reproduces the same vanishing susceptibility. Restoring the three-body coupling ($λ\neq0$) makes the transition first-order, with a critical endpoint at $λ=0$. The exponent relations $β_{\rm TF}=3β_{\rm Ising}$ and $γ_{\rm TF}=γ_{\rm Ising}-4β_{\rm Ising}$ hold exactly on dense hypergraphs via cluster decomposition, and the vanishing-susceptibility signature persists for $d\geq3$ but fails in $d=2$. A Mori--Zwanzig memory kernel yields a continuously tunable dynamical exponent $z_{\rm TF}$, completing the composite-operator scaling regime.

We propose a hybrid quantum system in which a magnet supporting non-reciprocal magnons, chiral magnons, or both mediates the dissipative and unidirectional coupling of spin qubits. By driving the qubits, the steady state of this qubit-qubit coupling scheme becomes the maximally entangled Bell state. We devise a protocol where the system converges to this entangled state and benchmark it including qubit decay and dephasing. The protocol is numerically tested on a hybrid system consisting of nitrogen-vacancy (NV) centers coupled to magnon surface modes of an yttrium iron garnet (YIG) film. We show that the dephasing time of the NV centers forms the bottleneck for achieving the entanglement of NV centers separated by a distance within the magnon coherence length. Our findings identify the key technological requirements and demonstrate a viable route toward steady-state entanglement of solid-state spins over distances of several microns using magnonic quantum networks, expanding the toolbox of magnonics for quantum information purposes.

We develop a geometric procedure for finding the Apéry set of any numerical semigroup with embedding dimension four. Previous methods of comparable strength worked only for embedding dimension three or under very specific conditions. We illustrate our method by finding the Frobenius numbers, genera, Betti elements, minimal presentations, and catenary degrees of numerical semigroups generated by four consecutive squares and by four consecutive triangular numbers.

The Lie algebra $\bar{S}_2$ of polynomial vector fields on $\mathbb{C}^2$ with constant divergence is an important Cartan type Lie algebra. In this paper, we study Whittaker $\bar{S}_2$-modules that are locally finite over $\text{span}\{\frac{\partial}{\partial t_1}, \frac{\partial}{\partial t_2}\}$. We first show that each block $Ω^{\widetilde{S}_2}_{\mathbf{a}}$ of the category of $(A_2, \bar{S}_2)$-Whittaker modules with finite-dimensional Whittaker vector spaces is equivalent to the category of finite-dimensional modules over the parabolic subalgebra $\bar{S}_2^{\geq 0}$. Then we classify all simple Whittaker $\bar{S}_2$-modules in every block $Ω^{\bar{S}_2}_{\mathbf{a}}$ . Finally, we establish an equivalence between $Ω^{\bar{S}_2}_{\mathbf{1}}$ and the category $H_{\mathbf{1}}$-fmod of finite-dimensional modules over an associative algebra $H_{\mathbf{1}}$, whose generators are also determined.

We construct the Higgs and Yukawa sectors as a structural completion of an algebraic three-generation model based on the complex Clifford algebra $\mathbb{C}\ell(10)$ with an intrinsic $S_3$ family symmetry. This addresses a common limitation of algebraic frameworks, in which Standard Model fermion multiplets and gauge symmetries may be described naturally, while the Higgs and Yukawa sectors remain less developed or absent. In the present framework, three algebraically distinguished fermion sectors are permuted by $S_3$, while the Standard Model gauge generators remain generation-independent. Higgs components are realised as right-action operators mapping weak-doublet fermion sectors into the corresponding weak-singlet sectors, and Yukawa coefficients are extracted using a Hilbert--Schmidt trace pairing. This yields two first-generation Higgs doublets with electroweak quantum numbers $(1,2,-1)$ and $(1,2,+1)$ under $SU(3)_C \times SU(2)_L \times U(1)_Y$, together with a Type-II-like separation between down-type and up-type Yukawa channels. Acting with the order-three family generator then generates a family-resolved Higgs sector organised into cyclic $S_3$ orbits. In the cyclically averaged Higgs limit, the Type-II-like Yukawa selection rule is preserved, while the generation-space Yukawa matrix is fixed algebraically and is non-diagonal in the algebraic generation basis. Under the usual implementation of electroweak symmetry breaking, the neutral Higgs couplings are aligned with the corresponding mass matrices, so tree-level flavour-changing neutral currents are not expected in this limit. The result is a constrained algebraic starting point for future $S_3$-breaking flavour phenomenology.

We predict a field-free transverse Josephson diode effect in altermagnets (AMs) with Rashba spin--orbit coupling, achieving diode efficiencies exceeding $3000\%$ and unidirectional transverse supercurrents in four-terminal junctions. In this geometry, a longitudinal phase bias generates transverse supercurrents that exhibit nonreciprocity and a finite anomalous phase shift, while the longitudinal current itself displays a Josephson diode effect. Both responses are tunable via the Néel vector orientation. We further show that the effect remains robust against moderate disorder and imperfect interfaces. These results establish AMs as a promising platform for nonreciprocal superconducting transport, with clear routes toward experimental realization.

In this work, we investigate the non-equilibrium dynamics in a one-dimensional two-component anyon-Hubbard model, which can be mapped to an extended Bose-Hubbard ladder with density-dependent hopping phase and synthetic gauge flux. Through numerical simulations of two-particle dynamics and the symmetry analysis, we reveal the asymmetric transport with broken inversion symmetry and two dynamical symmetries in the expansion dynamics. The expansion of two-component anyons is dynamically symmetric under spatial inversion and component flip, when the sign of anyonic statistics phase or the signs of gauge flux and interaction are changed. In the non-interacting case, we show the dynamical suppression induced by both the statistics phase and gauge flux. In the interacting case, we demonstrate that both chiral and antichiral dynamics can be exhibited and tuned by the statistics phase and gauge flux. The dynamical phase regimes with respect to the chiral-antichiral dynamics are obtained. These findings highlight the rich dynamical phenomena arising from the interplay of anyonic exchange statistics, synthetic gauge fields, and interactions in multi-component anyons.

We analyze the stability properties of a family of anti-de Sitter flux compactifications of the tachyon-free non-supersymmetric heterotic string in ten dimensions. In contrast with simpler such solutions, the solutions include two independent unbounded fluxes, leading to richer instability phenomena. In particular, when the two fluxes are sufficiently close in magnitude, the perturbative spectrum develops tachyonic modes, which can be projected out by an orbifold action. When the fluxes are far apart, tachyonic modes are absent, and the geometry displays inverse scale separation, where a factor of the internal manifold becomes parametrically larger than the anti-de Sitter factor. Still, non-perturbative instabilities in the form of brane nucleation are always available decay channels, and tend to drive the two fluxes closer together, eventually triggering the tachyonic instability when present.

A primary goal of the Habitable Worlds Observatory (HWO) is to detect and measure the abundance of biosignature molecules, such as water (H2O) and oxygen (O2), in the atmosphere of Earth analogs. This is expected to require deep spectroscopic observations lasting hundreds of hours per planet. In this context, it is essential to optimize the spectral resolution of the spectrograph to both maximize the number of planets that can be studied over the lifetime of the mission, and also to reduce the risks of false detections. The purpose of this work is to provide a framework to explore the spectral resolution design trade-space for HWO. This framework must be valid and comparable across all spectral resolutions from low (R<100) to high resolutions (R>10,000), and account for the spectral correlation of the residual starlight (i.e., speckle noise chromaticity). Leveraging the concept of "template matching", we develop a simulation toolkit based on the Python package EXOSIMS to compute the detection significance of planets and molecules. We then simulate observations of Earth analogs around 164 stars using representative mission parameters to explore the effects of the detector noise and the correlated speckle noise floor. Our findings suggest that a moderate or high resolution spectrograph (R>1,000) will provide higher sensitivity to critical molecules compared to a low resolution spectroscopy mode (e.g., R~140). The correlated speckle noise may also entirely suppress our ability to detect bio-signatures at low spectral resolutions. We conclude that a more comprehensive study combined with detailed models of its stability, and other sources of correlated noise, is necessary to fully explore the trade space of spectral resolution and detectability of key species.

Tetraphenylpyrazine (TPP) and 2,3,4,5-tetraphenyl-1H-pyrrole (TePP) are closely related heterocycles bearing four phenyl substituents, whose structural similarity makes them a useful pair for comparing how intramolecular flexibility influences excited-state relaxation and emission in the gas phase and in the solid state. TPP is a prototypical solid-state luminescence enhancement (SLE) emitter, exhibiting a markedly increased quantum yield upon molecular aggregation. In contrast, TePP displays similar quantum yields in solution and solid state, characteristic of dual-state emission (DSE). This behaviour indicates that intramolecular rotations are already significantly hindered in the isolated-molecule regime, consistent with our previous observations for TPP and other solid-state emitters (Hernández-Rodríguez et al., ChemPhysChem, 2024, 25, e202400563). To unravel the excited-state dynamics underlying this contrasting behaviour, we performed mixed quantum-classical trajectory simulations on a single molecule of TPP and TePP employing the surface-hopping method. Twelve singlet states were included at the TD-B3LYP-D3/def2-SVP level, which were previously benchmarked against coupled cluster methods. Simulated observables such as gas phase ultrafast electron diffraction (GUED) and time-resolved fluorescence (TR-FL) signals allow us to dissect the distinct deactivation pathways operating in both systems in the gas phase, while also providing mechanistic insight into how these pathways are expected to evolve in solution and solid-state environments.

We report the discovery of an exceptionally eccentric binary system, BE Lyncis (BE Lyn), which might host a compact companion with mass $\gtrsim 2.5~M_{\odot}$. By combining TESS photometry with an extensive set of times of maximum light spanning 39 years, we identify BE Lyn as a high-amplitude $δ$ Scuti star in a binary with an orbital period of $\approx15.9$ years and an extraordinary eccentricity of $e=0.9989^{+0.0008}_{-0.0021}$ ($>0.9968$ at 95% confidence) -- the most extreme eccentricity reliably measured for any binary system. Dynamical constraints limit the orbital inclination to $i \lesssim 10^{\circ}.1$, implying a companion mass $M_2 \gtrsim 2.5~M_{\odot}$, which identifies the companion as a compact object. This mass points to it most likely being a black hole; if instead it is a rapidly rotating neutron star, it would be the most massive known. If the black hole interpretation holds, it would be the closest such object to Earth. This system provides a unique laboratory for studying asteroseismology in strong gravitational fields, as well as the formation and evolution of extremely eccentric binaries. Our work demonstrates the use of the light-travel time effect in a pulsating star to reveal a compact companion, offering a novel method for detecting black holes in noninteracting binaries.

We present a summary of gravitational-wave (GW) follow-up using the Las Cumbres Observatory global network of telescopes during the third (O3) and fourth (O4) observing runs of the GW detectors. As in O2, we implemented the Gehrels et al. 2016 galaxy-targeted strategy. Here we test its efficacy in O3 and O4 and analyze the Las Cumbres Observatory response time and depth for nine GW alerts that showed a possibility of having an electromagnetic counterpart (GW190425, GW190426_152155, S190510g, GW190728_064510, GW190814, S190822c, GW191216_213338, S240422ed and S250206dm). We find that Las Cumbres Observatory is able to begin observations in response to GW alerts within minutes of the alert, with the observations being deep enough to detect possible GW170817-like kilonovae out to a median distance of 250 Mpc. In this sense a global rapid-response network of telescopes like Las Cumbres is an excellent GW follow-up facility. However, the galaxy-targeted follow-up strategy was much less efficient in O3 and O4 than originally predicted, given the larger than assumed GW localizations. We conclude that coordination between various facilities to include both wide-field and rapid-response capabilities is required to achieve efficient and comprehensive follow-up of GW events.

We introduce large $p$ asymptotic geometric quantities associated with $p$-capacity, the first $p$-eigenvalue, and the Maz'ya constant on complete noncompact Riemannian manifolds. We prove the hierarchy $$ \mathcal{V}(M)\geq \mathcal C(Ω)\geq Λ(M)=\mathcal M(M)\geq0, $$ and show that, under a centered-ball isoperimetric condition or a rotational symmetry condition, these quantities coincide with the volume entropy or the dimension. In the Hadamard nonpositively curved case it also agrees with the topological entropy of the geodesic flow. As an application, combining with the entropy rigidity theorem, we obtain a characterization of hyperbolic manifolds. We also prove a second-order refinement. For a Hadamard manifold with compact quotient, under certain condition, the first-order large $p$ capacitary limit detects volume entropy, whereas the logarithmic second-order correction detects the rank.

We revisit size controllability results in Pötscher and Preinerstorfer (2025) concerning heteroskedasticity robust test statistics in regression models. For the special, but important, case of testing a single restriction (e.g., a zero restriction on a single coefficient), we povide a necessary and sufficient condition for size controllability, whereas the condition in Pötscher and Preinerstorfer (2025) is, in general, only sufficient (even in the case of testing a single restriction).

Neutrons are important final-state particles in neutrino interactions, yet they are not considered or reconstructed in most current neutrino LArTPC physics analyses. In this paper, we present a simulation-based proof-of-concept study of neutron reconstruction in a generic LArTPC detector. Leveraging isolated, MeV-scale energy deposits, or blips, from neutron inelastic scattering, and using realistic blip response from published experimental results, we demonstrate the capability to identify neutrons and to reconstruct the direction and energy of the final-state neutron system in sub-GeV neutrino interactions. We then explore how neutron-related blip attributes can be used to improve physics studies of neutrino interactions, such as enhancing neutrino-antineutrino separation in atmospheric neutrinos and reverse-horn-current beam neutrinos. This simple study provides an initial quantification of LArTPC neutron reconstruction capabilities, which we expect to improve with future advancements in blip reconstruction, identification, and classification algorithms, as well as the modeling of neutrons.

We extend the algebraic diversity (AD) framework from classical signal processing to quantum measurement theory. The Quantum Algebraic Diversity (QAD) Theorem establishes that a group-structured positive operator-valued measure (POVM) applied to a single copy of a quantum state produces a full-rank, group-averaged density matrix estimator whose eigenbasis and eigenvalue ordering track those of the true density matrix, with a bias toward the symmetrized state, analogous to the classical recovery of covariance eigenstructure from a single observation. We establish a Classical-Quantum Duality Map connecting classical covariance estimation to quantum state tomography, and an Optimality Inheritance Theorem showing that classical group optimality transfers to quantum settings via the Born map within the group-averaged family. SIC-POVMs are identified as AD with the Heisenberg-Weyl group and mutually unbiased bases as AD with the Clifford group, revealing the hierarchy $\mathrm{HW}(d) \subseteq \mathcal{C}(d) \subseteq S_d$ that mirrors the classical $\mathbb{Z}_M \subseteq G_{\min} \subseteq S_M$. The double-commutator eigenvalue theorem gives polynomial-time adaptive POVM selection. A worked qubit example shows the group-averaged estimator from a single computational-basis measurement, averaged over a matched $\mathbb{Z}_2$ group, reaching fidelity 0.99 where standard single-basis tomography gives a rank-1 estimate of fidelity 0.80. Monte Carlo simulations for $d = 2$ to $13$ confirm fidelity above 0.90 from a single outcome while standard fidelity degrades as $\sim 1/d$. The growing ratio reflects collapse of the rank-1 standard estimator, not fewer copies per parameter: the biased single-copy estimator reduces the number of distinct measurement settings, not the per-parameter sampling cost, and a genuine copy reduction holds only under exact symmetry.

Let $β$ be a non-unit real algebraic integer greater than one and $\{a_{n}\}_{n \geq 0}$ be a sequence satisfying a linear recurrence relation $a_{n+3}=aa_{n+2}+ba_{n+1}+ca_{n}$. Under certain conditions, we prove that the number of $a_{n}$ which are palindromic concatenations of two repdigits in base $β$ is finite.

The Majoron is a hypothetical (pseudo) Nambu-Goldstone boson arising from the spontaneous breaking of a global lepton number symmetry, and is known as a candidate for dark matter in our Universe. In this paper, we investigate the possibility of probing the Majoron dark matter with a linear optical cavity used in the interferometric gravitational wave detectors. We consider a scenario in which the Majoron dark matter couples to photons through a QED anomaly, leading to an oscillatory photon birefringence induced by the coherent dark matter background. The anomaly coefficient is fixed by requiring the model to simultaneously reproduce the electroweak Higgs scale and a typical right-handed Majorana neutrino mass scale, and the resulting dark matter-photon coupling naturally falls within the sensitivity range of optical interferometers. By incorporating additional optics to extract the birefringence signal, we find that ground-based laser interferometers such as Advanced LIGO, KAGRA, as well as future detectors, can probe a region of the parameter space of Majoron dark matter.

The calculus of relations was introduced by De Morgan and Peirce during the second half of the 19th century, as an extension of Boole's algebra of classes. Later developments on quantification theory by Frege and Peirce himself, paved the way to what is known today as first-order logic, causing the calculus of relations to be long forgotten. This was until 1941, when Tarski raised the question on the existence of a complete axiomatisation for it. This question found only negative answers: there is no finite axiomatisation for the calculus of relations and many of its fragments, as shown later by several no-go theorems. In this paper we show that -- by moving from traditional syntax (cartesian) to a diagrammatic one (monoidal) -- it is possible to have complete axiomatisations for the full calculus. The no-go theorems are circumvented by the fact that our calculus, named the calculus of neo-Peircean relations, is more expressive than the calculus of relations and, actually, as expressive as first-order logic. The axioms are obtained by combining two well known categorical structures: cartesian and linear bicategories.

We present the results of Green Bank Telescope (GBT) observations of two pulsars discovered with the Five-hundred-meter Aperture Spherical Radio Telescope (FAST) during the 19-beam Commensal Radio Astronomy FasT Survey (CRAFTS). We highlight the first timing solutions, pulse profiles, flux densities, and polarization measurements at 820 MHz for PSR J0535-0231, with a spin period of 415 ms, and PSR J1816-0518, with a spin period of 1.93 s, from a year-long follow-up campaign. PSR J0535-0231 appears to be partially recycled, but isolated, and likely belongs to the class of disrupted recycled pulsars (DRPs). We find that the two widely used electron density models, NE2001 and YMW16, both fall short of accurately modeling the line-of-sight to PSR J0535-0231, as the maximum dispersion measure (DM) predicted by both models is lower than the pulsar's DM of 118.1 pc cm$^{-3}$. Finally, we place both pulsar discoveries in the context of other FAST pulsars discovered in the CRAFTS survey and of the currently known pulsar population, in general, and discuss ways in which future FAST discoveries of faint, distant pulsars might facilitate the development of improved versions of the aforementioned electron density models in certain regions of our Galaxy.

Space weathering of lunar minerals, due to bombardment from solar wind (SW) particles and micrometeoroid impacts, modifies the mineralogy within tens of nanometers of the surface, i.e., the rim. Spectroscopic signatures of these modifications, observed via remote sensing, have long been used to gauge surface exposure times on the Moon. However, the relative contributions of SW and micrometeoroids in the creation of rim features are still debated, particularly for the nanometer-scale clusters known as nanophase iron (npFe0), which commonly form in ferrous minerals. We address this issue in the laboratory, using deuterium ions and low-energy electrons as a synthetic solar wind plasma to irradiate ilmenite (FeTiO3), a common lunar mineral. Characterization by high-resolution scanning transmission electron microscopy and electron energy-loss spectroscopy shows that the SW alone creates rims with all the main characteristics of lunar samples. We conclusively identify npFe0 and quantify its distribution as a function of depth and fluence, allowing us to estimate the SW exposure of Apollo soil 71501. Our results confirm that small npFe0 particles (<10 nm in diameter) form from SW irradiation. Such experiments provide microscopic details of space weathering, improving the link between surface modification processes and macroscopic remote-sensing data.

This paper is the second and final part of a two-part study. We construct positive-energy relativistic spatial localization observables in Minkowski spacetime within standard quantum field theory, using the stress--energy--momentum tensor smeared with suitable test functions. For each fixed timelike direction, the construction gives positive operator-valued measures (POVMs) on spacelike hypersurfaces, well defined on every $n$-particle sector and satisfying a relativistic causality condition excluding superluminal propagation of detection probabilities. The observables are built from local or quasi-local field-theoretic quantities, thus providing a rigorous version of earlier heuristic proposals. In the one-particle sector, the construction reduces to the observable previously introduced by the author, and its first moment gives the Newton--Wigner position operator under appropriate normalization and centering assumptions. Because the Reeh--Schlieder theorem prevents the normally ordered stress--energy--momentum tensor from being positive on the full Fock space, we use quantum energy inequalities to obtain lower bounds controlling deviations from positivity. This leads to regularized operator families, bounded from below, which approximate the localization effects. Finally, we define conditional localization observables for finite laboratories through modified local energy operators. By Haag duality, the corresponding conditional POVMs belong to local von Neumann algebras and commute for causally separated regions, in accordance with the Araki--Haag--Kastler framework. The results show how commutativity of localization observables is recovered for conditional measurements in finite spacetime regions.

Radiation reaction cooling plays an important role in describing the extreme plasma conditions found in the magnetospheres of astrophysical compact objects. Strong electromagnetic fields, characteristic of these environments, can trigger the development of anisotropic ring-shaped plasma distributions with inverted Landau populations in momentum space. In this work, we present the first systematic investigation of this mechanism in realistic astrophysical configurations, by accounting for how non-uniform electromagnetic field geometries and general-relativistic effects modify the phase-space dynamics of radiatively cooled plasmas. We demonstrate analytically that drift velocities favour the formation of spiral-shaped momentum distributions that still display inverted Landau populations, and estimate the minimum and maximum plasma injection distances required for inverted momentum distributions to be able to power the emission of coherent radiation through kinetic instabilities. From numerical simulations, we conclude that curved spacetime increases the gradient of the distribution function responsible for the development of kinetic instabilities, and prolongs the persistence of the inverted momentum structure relative to flat spacetime, confirming that realistic astrophysical conditions preserve and enhance the conditions necessary for synchrotron-powered emission of coherent radiation to occur.