Dense retrieval services increasingly underpin semantic search, recommendation, and retrieval-augmented generation, yet clients typically receive only a top-$k$ list with no auditable evidence of how it was produced. We present V3DB, a verifiable, versioned vector-search service that enables audit-on-demand correctness checks for approximate nearest-neighbour (ANN) retrieval executed by a potentially untrusted service provider. V3DB commits to each corpus snapshot and standardises an IVF-PQ search pipeline into a fixed-shape, five-step query semantics. Given a public snapshot commitment and a query embedding, the service returns the top-$k$ payloads and, when challenged, produces a succinct zero-knowledge proof that the output is exactly the result of executing the published semantics on the committed snapshot -- without revealing the embedding corpus or private index contents. To make proving practical, V3DB avoids costly in-circuit sorting and random access by combining multiset equality/inclusion checks with lightweight boundary conditions. Our prototype implementation based on Plonky2 achieves up to $22\times$ faster proving and up to $40\%$ lower peak memory consumption than the circuit-only baseline, with millisecond-level verification time. Github Repo at https://github.com/TabibitoQZP/zk-IVF-PQ.

The Rice-Mele (RM) model, as a paradigmatic extension of the Su-Schrieffer-Heeger (SSH) chain, plays a pivotal role in understanding topological phases and quantized adiabatic transport in one-dimensional systems. Its realization in acoustic systems, however, has been hindered by the need for simultaneous precise modulation of on-site potentials and couplings. In this work, we demonstrate a method to linearly tune on-site potentials and couplings, thus realizing an acoustic Rice-Mele model. During parameter evolution, the system exhibits a Thouless pump, with the acoustic field distribution adiabatically shifting from the left edge through the bulk to the right edge, fully consistent with tight-binding model predictions. Moreover, the strategy of leveraging geometric parameters to linearly and precisely control on-site potentials and couplings is highly effective and universal for designing acoustic metamaterials, and it can be extended to other classical wave systems.

We investigate the orbital-to-charge current conversion in CoFeB|CuO bilayers as a function of CuO thickness, employing orbital pumping via ferromagnetic resonance. The dynamic injection of orbital angular momentum into the CuO layer generates a transverse voltage through the Inverse Orbital Hall Effect (IOHE). By systematically varying the CuO thickness from 2 nm to 30 nm, we observe a pronounced dependence of the IOHE-induced voltage on the CuO layer thickness, indicating efficient orbital-to-charge conversion. These results highlight the key role of the orbital degree of freedom in orbitronics and provide insights into the potential of transition-metal oxides for next-generation orbitronic devices.

We present new mechanisms that produce either a future Big Crunch turnaround or a past non-singular bounce in flat FLRW cosmologies within general relativity at the background level, driven solely by non-gravitational interactions between dark matter (DM) and dark energy (DE). We study phenomenological interacting dark energy (IDE) models based on linear kernels of the form $Q = 3H(δ_{\rm dm}ρ_{\rm dm} + δ_{\rm de}ρ_{\rm de})$, focusing on parameter regimes with strong energy transfer from dark energy to dark matter. In this strong interacting regime, the interaction does not vanish when one component crosses zero density, allowing one of the dark-sector densities to become negative. The resulting sign changes can violate the energy conditions required for cosmological turnarounds in a flat universe, thereby enabling either (i) a maximum scale factor followed by recollapse into a big crunch, or (ii) a minimum non-zero scale factor corresponding to a bounce. We derive analytic conditions for these turnarounds and obtain closed-form expressions for the associated maximum or minimum scale factor. We also show that, in a closed universe, a special case of the same IDE framework can be tuned to yield a cyclic scenario. Although these strong interaction scenarios are unlikely to describe the observed Universe, they provide a concrete demonstration that exotic cosmological behaviour can arise naturally in underexplored regions of the parameter space of familiar IDE models.

Modern societal challenges, such as climate change, urbanization, and water resource management, demand integrated, multi-discipline, multi-problem approaches to frame and address their complexity. Unfortunately, current methodologies often operate within disciplinary silos, leading to fragmented insights and missed opportunities for convergence. A critical barrier to cross-disciplinary integration lies in the disparate ontologies that shape how different fields conceptualize and communicate knowledge. To address these limitations, this paper proposes a system-of-systems (SoS) convergence paradigm grounded in a meta-cognition map, a framework that integrates five complementary domains: real-world observations, systems thinking, visual modeling, mathematics, and computing. The paradigm is based on the Systems Modeling Language (SysML), offering a standardized, domain-neutral approach for representing and analyzing complex systems. The proposed methodology is demonstrated through a case study of the Chesapeake Bay Watershed, a socio-environmental system requiring coordination across land use, hydrology, economic and policy domains. By modeling this system with SysML, the study illustrates practical strategies for navigating interdisciplinary challenges and highlights the potential of agile SoS modeling to support large-scale, multi-dimensional decision-making.

Determining the work statistics of quantum engines is challenging due to measurement backaction. We here show that a dynamic Bayesian network-based measurement scheme, which preserves quantum coherence within an engine cycle, is minimally invasive, in the sense that the averaged measured state over one cycle exactly coincides with the unmeasured state. It therefore provides a general framework to investigate energy exchange statistics in quantum machines. This stands in contrast to the standard two-point measurement protocol, whose backaction can be so strong that it generally fails to reproduce the average work output of a coherent motor. It may even alter its mode of operation, causing it to cease functioning as an engine under observation. We further demonstrate that recently proposed universal fluctuation bounds do not necessarily apply to coherent machines.

We prove the quantum unique ergodicity (QUE) conjecture of Rudnick and Sarnak for the sequence of Pitale lifts, which are Hecke-Maass forms on a congruence quotient of $\mathbb{H}^4$ constructed as lifts from half-integral weight forms (i.e. non-holomorphic analogues of the Saito-Kurokawa lifts). The result is unconditional, unlike other mass equidistribution results for similar lifts. Our main innovation is the delicate construction of an amplifier with favorable geometric properties (while we do use the non-temperedness of the lifts, it alone is not enough). To the best of our knowledge, this is the first successful use of the amplification method for escaping a non-tempered subgroup.

We construct infinite time bubble tower solutions to the critical wave maps equation taking values in the two-sphere. More precisely, for any integers $k\geq3$ and $J\geq1$, we construct a solution that is global in one time direction, has $k$-corotational symmetry, and asymptotically decomposes into $J$-many concentric bubbles of alternating signs with asymptotically vanishing radiation. The scales of each bubble are of order $t^{-α_{j}}$ with $α_{j}=(\frac{k}{k-2})^{j-1}-1$. This shows the existence of multi-bubble solutions with an arbitrary number of bubbles in soliton resolution, provided that $k\geq3$, global existence in one time direction, and alternating signs are considered. Our proof is based on modulation analysis with the method of backward construction. The key new ingredient is a Morawetz-type functional that provides suitable monotonicity estimates for solutions around multi-bubble configurations.

The precise measurement of the $e^+e^-\toπ^+π^-π^0$ cross section is performed in the center-of-mass energy range $E = 560$--1100 MeV using a data sample of 66 pb$^{-1}$ collected in the experiment with the SND detector at the VEPP-2000 $e^+e^-$ collider. The systematic uncertainty of the cross section measurement is 0.9\% at the maximum of the $ω$ resonance and 1.2\% at the maximum of the $ϕ$ resonance. The leading-order hadronic contribution to the muon magnetic anomaly calculated using the $e^+e^-\toπ^+π^-π^0$ cross section measured by SND from 0.62 to 1.975 GeV is $(45.95\pm0.06\pm 0.46)\times 10^{-10}$. From the fit to the cross section data with the vector meson dominance model, the parameters of the $ω$, $ρ$, and $ϕ$ resonances are obtained. The obtained values of ${\cal B}(ω\to e^+e^-) {\cal B}(ω\to 3π)$, mass and width of the $ω$ meson, and ${\cal B}(ρ\to 3π)$ have accuracy better than the current world average values.

In the Vasicek credit portfolio model, tail risk is driven primarily by the asset-correlation parameter, yet empirically is subject to correlation risk. We propose a stochastic correlation extension of the Vasicek framework in which the correlation state evolves as a diffusion on the circle. This representation accommodates both non-mean-reverting and mean-reverting dependence regimes via circular Brownian motion and von Mises process, while retaining tractable transition densities. Conditionally on a fixed correlation state, we derive closed or semi-closed form expressions for the joint distribution of two assets, the joint first-passage (default) time distribution, and the joint survival probability. A simulation study quantifies how correlation volatility and persistence reshape joint default-at-horizon, survival, and joint barrier-crossing probabilities beyond marginal volatility effects. An empirical illustration using U.S. bank charge-off rates demonstrates economically interpretable time-variation in a dependence index and shows how inferred stochastic dependence translates into materially different joint tail-event probabilities. Overall, circular diffusion models provide a parsimonious and operationally tractable route to incorporating correlation risk into Vasicek structural credit calculations.

Kanade explored the construction of modular companions to $q$-series identities, using the asymptotics of Nahm sums, and Mizuno [Ramanujan J.\ {\bf 66} (2025), Paper No.\ 62, 31] recently obtained a generalization of Kanade's asymptotic formula for symmetrizable Nahm sums. A related conjecture from Kanade concerning the dilogarithm function and related to the work of Kur\c sungöz on Andrews--{G}ordon-type series [Ann.\ Comb.\ {\bf 23} (2019), 835--888] has remained open. In this paper, we prove Kanade's conjecture, through an application of dilogarithm identities due to Kirillov together with a dilogarithm ladder due to Lewin and Loxton. Inspired by Kanade's result, we extend this to conjecture two new dilogarithm identities and associated rank-2 matrices.

In this paper, we prove a generalized reverse Hölder inequality of harmonic functions on cable systems induced by post-critically finite (p.c.f.) self-similar sets. Furthermore, we also establish the Hölder regularity of harmonic functions on both bounded and unbounded p.c.f. self-similar sets, which does not involve heat kernel estimates and resistance estimates.

In this work, we explore physical systems which support not only multipartite interparticle entanglement, but also intraparticle entanglement between different degrees of freedom of the constituent particles and entanglement between different degrees of freedom of different particles, i.e., algebraic entanglement. We derive a simple method for calculating the algebraic entanglement entropy between two of the particles' degrees of freedom from collective states of the whole ensemble. Our procedure makes use of underlying symmetries in these systems, in particular permutation symmetry of the particle indices, and shows a connection between the algebraic entanglement entropy in these systems and the irreducible representations of Lie groups which describe the particles' degrees of freedom. Namely, we use the direct sum over irreducible representations to diagonalize the reduced density matrices in a block-by-block manner, then utilize the multiplicity of these irreducible representations to reproduce the results from an exponentially-scaled Hilbert space in only polynomial complexity. We use this to explore a variety of systems where the constituent particles support two degrees of freedom each with two levels, such as atoms with two electronic states and two momentum states. Notably, these systems may be exactly simulated in a polynomial-scaled Hilbert space, yet they support an algebraic entanglement entropy that grows linearly with the particle number which typically requires an exponentially-scaled Hilbert space.

We present a cross-cavity system in which steady-state superradiance is achieved using solely collective dissipative dynamics. Two cavities symmetrically couple an ensemble of four-level atoms by driving transitions between two electronic states and two motional states along perpendicular cavity axes. Both cavities operate in the bad-cavity regime: one cavity mediates collective atomic decay, while the other cavity, together with a coherent drive, mediates collective pumping via an off-resonant Raman transition. With this, we find steady-state superradiant states that possess nonclassical properties, such as super-Poissonian photon statistics. The system thus requires a beyond mean-field description, and so we develop an exact master equation simulation technique utilizing strong symmetries of the system's jump operators. Because superradiant decay is accompanied by a momentum impulse along the corresponding cavity axis, the system exhibits substantial hybrid entanglement between the atoms' spin and motional degrees of freedom at steady state. We also demonstrate that heralded measurements of the two cavity outputs prepare a state with significant particle-particle entanglement with prospects for quantum-enhanced acceleration sensing.

We study a 3-Higgs Doublet Model (3HDM) with an imposed Z3 symmetry, allowing for two Inert scalar doublets and one active Higgs doublet. The WIMP dark matter candidates correspond to two mass-degenerate states, H1 and A1, which possess opposite CP quantum numbers and can reproduce the correct relic density simultaneously with all theoretical and experimental constraints. We use state-of-the-art machine learning algorithms to probe the parameter space of the model by employing an Evolutionary Strategy augmented with Novelty Reward. We consider two situations: a limit for the dark matter mixing angle θ that closes a gauge annihilation channel that would deplete the DM relic density, and the general case without imposing this limit. For both scenarios, we find viable dark matter candidates within two separate mass regimes, ranging from 50 GeV < mDM < mW and 380 < mDM < 1000 GeV. Moreover, we find it is possible to fulfill all the existing constraints while still obtaining values for the dark matter-higgs coupling of order O(0.1). Exploring the model outside the θ = π/4 limit proved to be an extremely challenging task, as there are regions which seem easy to explore when projected on a 2D plane, yet may be completely disconnected on the hypersurface supporting the valid points, given its non-convex and multi-dimensional nature. We consider new methods of prototype selection to seed new exploration runs, which allow for efficient global scans over the parameter space.

Recent observations revealed that distant galaxies have bursty star formation histories, regulated by stellar or active galactic nuclei (AGN) feedback and gas inflows. According to theoretical models, feedback preferentially removes metal-rich gas, while subsequent starbursts are triggered by mergers and newly-accreted gas that is generally less enriched than the galaxy interstellar medium (ISM). Therefore, gas-phase metallicity holds key insights into the baryonic processes shaping early galaxies. We present the first NIRSpec/IFU study of spatially resolved ISM properties in the MACS0647-JD system ($z=10.17$). The system consists of two stellar components detected in NIRSpec/IFU and NIRCam photometry. The main component ($\log (M_{\ast}/M_{\odot}) =7.77 \pm 0.09$; $12+ \log(O/H)=7.89 \pm 0.11$) is more massive and significantly more metal-rich compared to its companion ($\log (M_{\ast}/M_{\odot}) =7.42 \pm 0.07$; $12+ \log(O/H)=7.47 \pm 0.14$), suggesting an older stellar population and a prolonged chemical enrichment history. We find that the H$γ$ line emission centroid is offset by $0.1^{\prime \prime}$ (150 pc in the source plane) from the stellar continuum centroid; the latter coincides with the location of the main stellar component. This offset provides possible evidence of a merger-driven starburst in this system. By comparing the spatial distribution of the metallicity, velocity dispersion, and the burstiness of star formation history, we infer the presence of turbulent, metal-poor gas outside the stellar components. This metal-poor, dynamically unstable gas is likely responsible for the increase in the recent star formation in the north-east region of the system.

Let X be an irreducible complex affine algebraic variety defined over $\mathbb{R}$, equipped with a faithful action of a finite group G, and let Y = X // G denote the categorical quotient with projection $π$. We study the geometry of the real image $L = π(X(\mathbb{R})) \subset Y(\mathbb{R})$ and its consequences for G-invariant optimization. Equipping $Y(\mathbb{R})$ with the measure induced by a G-invariant metric on X, we prove that the relative volume of L in $Y(\mathbb{R})$ equals $(\#\mathrm{Inv}(G))^{-1}$, where $\mathrm{Inv}(G)$ is the set of involutions of G. For the symmetric group $S_n$ acting on $\mathbb{R}^n$, this ratio decays super-exponentially in n. In particular, L is metrically rare within the ambient real quotient. We apply this result to two phenomena observed in G-invariant optimization problems: Regime I (Rarity of asymmetric critical points). The super-exponential decay of the volume of L renders the interior $L^\circ$ statistically negligible as a locus for critical points. This geometric rarity provides a rationale for the observed prevalence of symmetry: generic critical points are constrained to the boundary strata of L, corresponding to orbits with non-trivial stabilizers. Regime II (Energetic ordering by symmetry). We formulate the Active Constraint hypothesis: due to the metric rarity of the real image L, the landscape is dominated by a global gradient that drives the deepest descent trajectories toward the boundary of L. This global gradient directs the global minimum into the high-codimension strata of the boundary -- corresponding to large stabilizers -- thereby establishing a structural link between low energy and non-trivial stabilizers. This mechanism rationalizes the funnel topography of Lennard-Jones clusters, where the system is funneled into a crystallized ground state.

The Betke-Henk-Wills conjecture provides an upper bound for the lattice point enumerator $G(K, Λ)$ of a convex body in terms of its successive minima. While the conjecture is established for orthogonal parallelotopes, its validity for general convex bodies in dimensions $d \ge 5$ remains open. In this paper, we examine the stability of the conjecture under metric perturbations. Specifically, we demonstrate that the inequality is strictly maintained for integer boxes subjected to rotations within a calculated radius, a consequence of the discrete nature of the lattice point enumerator. We derive explicit, geometry-invariant quantitative bounds on the perturbation radius using the operator norm. Furthermore, we extend the analysis to $L_p$-balls for sufficiently large $p$, identifying a sharp threshold $p_0$ for the invariance of the integer hull.

Atomically confined spins are emerging as active components in quantum optoelectronic devices such as quantum bits and sensors. However, interrogating single spins at atomic length-scales remains a sizeable challenge, limited by diffraction in conventional optics. Here we show that the highly-local excitation provided by injecting energetic charge carriers from the atomically sharp probe of a scanning tunneling microscope can trigger single-photon emission from individual atomic vacancy centers in a layered semiconductor. With an effective spatial resolution of <1 nm, we show that the captured light closely mirrors the orbital symmetry of the bound-state wavefunction of the vacancy center while photon correlation measurements confirm single-photon emission, as reflected in clear photon anti-bunching signatures. Our results constitute an important step toward the realization of an electrically addressable single-atom quantum light source and solid-state spinphoton interface, addressed at the atomic-scale.

Measurement-only models offer an ideal platform for exploring entanglement dynamics in the absence of unitary evolution. Despite extensive numerical evidence for entanglement phase transitions in measurement-only dynamics, the underlying mechanism attributed to non-commutativity among multi-site projective measurements has remained qualitative and coarse-grained. In this work, we identify a quantitative non-commutative index. By applying this index into three representative measurement-only models, we elucidate the role of non-commutativity in measurement-only dynamics: the emergence of a volume-law phase is governed by the non-commutative structure of the measurement ensemble, while the transition point is quantitatively determined by the amount of critical non-commutativity. More strikingly, the critical non-commutativity exhibits a universal linear scaling with the measurement range, independent of the microscopic details of the measurement ensembles. Our findings deepen the understanding of the fundamental mechanism behind the measurement-only entanglement phase transition.

Seismic wavefields recorded on land are strongly distorted by near-surface heterogeneity, introducing trace-specific, frequency-dependent phase perturbations that persist even after advanced time processing. Conventional surface-consistent deconvolution targets long- to mid-wavelength phase variability through overdetermination, but cannot correct localized, non-surface-consistent distortions, and its effectiveness degrades when such effects dominate, as is often the case for point-receiver data. Additionally, conventional workflows provide no direct, quantitative measure of phase reliability; phase quality is assessed only indirectly through amplitude behavior or visual inspection, leaving residual phase disorder largely undiagnosed. We introduce phase variance as a seismic quality-control attribute by treating seismic phases as circular random variables and analyzing local trace ensembles using circular statistics. This data-driven measure quantifies localized phase dispersion without phase unwrapping, enabling analysis of local phase trends without global assumptions or wavelet models. Phase variance is computed automatically and provides frequency-by-frequency classification from coherent signal to fully randomized, noise-dominated phase. Synthetic tests confirm that phase variance reliably captures imposed phase perturbations and their frequency dependence. Application to field prestack land data shows that conventional processing reduces phase variability primarily in the low-to-intermediate frequency range and struggles within the noise cone, while the highest and lowest frequencies show little improvement. Phase variance operates automatically over the full prestack volume, frequency by frequency, providing a consistent, human-independent metric for defining effective bandwidth and supporting phase-sensitive workflows such as AVO, migration, and full-waveform inversion.

In this paper, we develop a mean-field game model for SEIR epidemics on heterogeneous contact networks, where individuals choose state-dependent contact effort to balance infection losses against the social and economic costs of isolation. The Nash equilibrium is characterized by a coupled Hamilton--Jacobi--Bellman/Kolmogorov system across degree classes. An important feature of the SEIR setting is the exposed compartment: the incubation period separates infection from infectiousness and changes incentives after infection occurs. In the baseline formulation, exposed agents optimally maintain full contact, while susceptible agents reduce contact according to an explicit best-response rule driven by infection pressure and the value gap. We also discuss extensions that yield nontrivial exposed precaution by introducing responsibility or compliance incentives. We establish existence of equilibrium via a fixed-point argument and prove the uniqueness under a suitable monotonicity condition. The analysis identifies a delay in the onset of precaution under longer incubation, which can lead to weaker behavioral responses and larger outbreaks. Numerical experiments illustrate how network degree and the cost exponent shape equilibrium policies and epidemic outcomes.

We develop structure-preserving discontinuous Galerkin methods for the Cahn-Hilliard-Navier-Stokes equations with degenerate mobility. The proposed SWIPD-L and SIPGD-L methods incorporate parametrized mobility fluxes with edge-wise mobility treatments for enhanced coercivity-stability control. We prove coercivity for the generalized trilinear form and demonstrate optimal convergence rates while preserving mass conservation, energy dissipation, and the discrete maximum principle. Comparisons with existing SIPG-L and SWIP-L methods confirm similar stability. Validation on $hp$-adaptive meshes for both standalone Cahn-Hilliard and coupled systems shows significant computational savings without accuracy loss.

We demonstrate a compact, non-toxic, low-cost neutron-yield diagnostic for pulsed D--T fusion systems using an undoped fused-silica (SiO$2$) rod as both activation target and Cherenkov radiator. D--T neutrons (14.1 MeV) activate $^{28}$Si and $^{16}$O to produce short-lived $^{28}$Al ($T{1/2}=134,\mathrm{s}$) and $^{16}$N ($T_{1/2}=7.13,\mathrm{s}$). The resulting $β^-$ particles exceed the Cherenkov threshold and generate UV--visible light detected by a fast photomultiplier tube. A SiO$_2$ rod of dimensions $6,\mathrm{in}\times1,\mathrm{in}$ (length $\times$ diameter) is optically coupled and read out with a CAEN DT5730 digitizer operating in list mode with digital pulse processing. The post-pulse count rate is fit using fixed $^{16}$N and $^{28}$Al half-lives together with background terms to infer neutron fluence. Testing at the ZEUS D--T Dense Plasma Focus established a reference calibration and agreement with a praseodymium-calibrated silver activation detector. Measurements near a D--D Dense Plasma Focus show no activation signal, confirming D--T selectivity. The diagnostic enables pulse-to-pulse yield measurements within minutes following a pulse and is being deployed on Helion Energy's seventh fusion prototype, Polaris.

Under the hypothesis that the $f_0(1370)$ is a $κ\barκ$ molecular state, we calculate the partial widths of its various decay channels, including the two-body decay $K \bar{K}$, $ππ$, $ηη$ and the four-body decay $ρρ/ σσ\to 4 π$ and $K \bar{K} ππ$. The coupling of $g_{f_0(1370) κ\barκ}\approx 13$ GeV estimated from the Weinberg criterion yields a width of $f_0(1370)$ significantly smaller than the experimental data. By adjusting this coupling to $25 \sim 40$ GeV, the total width of $f_0(1370)$ can be fitted to the measured value $200\sim 500$ MeV. At the center-of-mass energy $\sqrt{s}=1.37$ GeV, the channels that mainly contribute to the total width are $K \bar{K}$, $ππ$ and $4 π$ ranked as $Γ(K \bar{K }) > Γ(4 π) \approx Γ(ππ) $ with $g_{f_0(1370) κ\barκ}= 35$ GeV. Around $1.37$ GeV, the decay widths of the two-body channels $K \bar{K}$, $ππ$ and $ηη$ remain stable with variation in $\sqrt{s}$, whereas the decay widths of the four-body channels $4 π$ and $K \bar{K }ππ$ increase continuously with $\sqrt{s}$. Most current data are model-dependent and conflicting, particularly regarding the conclusion of $4 π$ dominance and the ratio of $K\bar{K}$ to $ππ$ decay widths. The current data can not rule out the $κ\barκ$ assignment for $f_0(1370)$. Further reliable theoretical and experimental analyses of $f_0(1370)$ are required to reveal its nature.

In this paper, we investigate the optimal real-time fusion of data collected by multiple sensors. In our set-up, the sensor measurements are considered to be private and are jointly correlated with an underlying process. A fusion center combines the private sensor measurements and releases its output to an honest-but-curious party, which is responsible for estimating the state of the underlying process based on the fusion center's output. The privacy leakage incurred by the fusion policy is quantified using Rényi differential privacy. We formulate the privacy-aware fusion design as a constrained finite-horizon optimization problem, in which the fusion policy and the state estimation are jointly optimized to minimize the state estimation error subject to a total privacy budget constraint. We derive the constrained optimality conditions for the proposed optimization problem and use them to characterize the structural properties of the optimal fusion policy. Unlike classical differential privacy mechanisms, the optimal fusion policy is shown to adaptively allocates the privacy budget and regulates the adversary's belief in a closed-loop manner. To reduce the computational burden of solving the resulting constrained optimality equations, we parameterize the fusion policy using a structured Gaussian distribution and show that the parameterized fusion policy satisfies the privacy constraint. We further develop a numerical algorithm to jointly optimize the fusion policy and state estimator. Finally, we demonstrate the effectiveness of the proposed fusion framework through a traffic density estimation case study.

Weak-interaction-mediated chiral imbalance generation in idealized massless electrons during core-collapse supernovae was once proposed to be the source of strong magnetic fields found in neutron stars. The effect goes by the name of chiral plasma instability (CPI). However, it was found that a finite electron mass damps out this process, inactivating the instability and preventing magnetic field growth. In this work we show that the instability can survive in the presence of abrupt density and temperature perturbation that drives the system sufficiently far out of weak equilibrium. As an example, we work with such perturbations generated by shockwaves which are common during both core collapse as well as neutron star mergers. We find that the chiral imbalance resulting from shock waves, under the right conditions of density and temperature, can sustain the chiral plasma instability despite the damping from the electron mass. Additionally, in an already magnetized medium, the chiral magnetic effect resulting from shock wave density and temperature perturbation can generate substantial ohmic heating. Our results imply that shockwaves during core-collapse supernovae and merging neutron stars can act as a source of strong heating in a magnetized medium as well as CPI.

Affine frequency division multiplexing (AFDM) has recently emerged as a resilient waveform candidate for high-mobility next-generation wireless systems. However, current literature mostly focuses on discrete time (DT) models, often overlooking effects and hardware non-idealities of actual continuous time (CT) signal generation. In this paper, we bridge this gap by developing a CT-analytical framework based on the affine Fourier series (AFS) representation, which allows us to demonstrate that strictly bandlimited pulses and subcarrier suppression strategies are essential to maintain the multicarrier structure of the transmitted signal. In addition, we derive the analytical power spectral density of AFDM and compare its spectral characteristics in comparison with those of other multicarrier schemes, taking into account the impact of realistic truncated pulse-shaping. Furthermore, we analyze the sensitivity of the CT model to phase noise, carrier frequency offset, and sampling jitter, providing a theoretical analysis of communication performance. Finally, we derive closed-form Cramér-Rao bounds for channel parameter estimation, showing that the chirped modulation peculiar of AFDM increases estimation variance but enables the resolution of Doppler ambiguities. Our findings lay the necessary theoretical and practical foundations for the implementation of AFDM in realistic wireless transceivers.

We revisit Jacobson's thermodynamic derivation of gravitational dynamics in the presence of generalized, non-extensive horizon entropies. Working within a local Rindler-wedge framework, we formulate the Clausius relation as the stationarity condition of a Massieu functional at fixed Unruh temperature, which identifies the entropy slope as the parameter controlling the effective gravitational coupling. For area-type entropies with constant slope, the construction reproduces Einstein's equations with $G_{eff} = 1/(4s_0)$, while curvature-dependent entropy densities supplemented by an internal entropy-production term yield the field equations of $f(R)$ gravity. Motivated by group-entropic considerations and long-range correlations, we model the entropy of horizon cross sections by a power law $S(A) = η(A/4G)^δ$ and analyze its local and global implications. To fix the otherwise arbitrary coarse-graining scale entering the entropy slope, we introduce a Topological Calibration Principle that ties the reference area to intrinsic geometric data through the Gauss-Bonnet theorem. For compact two-dimensional sections, this selects a canonical calibration area and leads to a topology-dependent effective coupling $G_{eff}(χ) \propto |χ|^{1-δ}$ where $χ$ represents the Euler characteristic. Consistency across scales and topologies yields logarithmic bounds on $|1-δ|$, while the associated scale dependence induces a characteristic modulation of the gravitational coupling in cosmology. The framework thus provides a controlled route to confront non-extensive horizon thermodynamics with both theoretical consistency requirements and observational constraints.

Plastic waste, being one of the most important problems for humankind, poses severe threats to ecosystems, wildlife, and human health. Tracing, quantifying, and identifying types of plastic waste is of crucial importance to understand its environmental pathways and develop targeted strategies for reduction, recycling, and remediation. To contribute to addressing this global issue, we investigated the spin-labeling capabilities of aqueous chlorine dioxide (ClO$_2$) radicals upon introduction into poly(ethylene terephthalate) and utilized electron spin resonance spectroscopy for detection. The technique is capable of identifying plastic species as the unpaired electron of the radical molecule is strongly sensitive to its local environment through its coupling parameters. Temperature-dependent measurements revealed that the molecules are immobilized at low temperatures and exhibit well-resolved anisotropic and hyperfine spectra that are quantitatively described by a model spin Hamiltonian. Even above the melting point of water, some degrees of freedom remain blocked as a result of the polymer matrix. Furthermore, employing a time-series measurement at room temperature enabled us to determine the diffusion coefficient of the molecule in the polymer.