We report structural, magnetic, and Raman studies of the disordered double perovskite GdSrCoMnO$_{6}$~(GSCM). DC magnetization shows a ferromagnetic transition at $T_{C} \approx 153$~K. The inverse susceptibility exhibits a downturn above $T_{C}$ and is consistent with a Griffiths-like regime extending up to $T_{G} \approx 172$~K. Raman measurements show a deviation of the phonon frequency from the anharmonic background near the magnetic-ordering region, consistent with spin-phonon coupling. AC susceptibility indicates slow magnetic dynamics below the freezing temperature $T_{f} \approx 30$~K. These results point to magnetic inhomogeneity generated by the random distribution of mixed-valence Co and Mn ions and by the resulting competition between ferromagnetic and antiferromagnetic interactions. In the low-temperature regime, an exchange-bias effect is observed up to 50~K, with an exchange-bias magnitude $|H_{EB}| = 379$~Oe at 5~K. Structural disorder therefore plays an important role in the magnetic correlations, spin dynamics, and spin-lattice response of GSCM.

Guaranteeing the safety of controllers is vital for real-world applications, but is markedly difficult when the states are not perfectly known and when the control inputs are bounded. Backup control barrier functions (bCBFs) use predictions of the flow under a prescribed controller to achieve safety in the presence of bounded inputs and perfect state information. However, when only an estimate of the true state is known, this flow may not be precisely computed, as the initial condition is unknown. Furthermore, the true flow evolves using feedback from the estimated state, thus introducing coupling between known and unknown flows. To address these challenges, we propose a technique that leverages an uncertainty envelope centered around the estimated flow and show that ensuring the safety of this envelope guarantees that the true state satisfies the safety constraints. Additionally, we show that in the presence of state uncertainty, using the resulting Output Feedback Backup Control Barrier Functions (O-bCBFs), there always exists a feasible control input that can guarantee the safety of the true state, even in the presence of input constraints.

Federated Learning (FL) is an emerging solution to the data scarcity problem for training deep learning models in hardware assurance. While FL is designed to enhance privacy by not sharing raw data, it remains vulnerable to Membership Inference Attacks (MIAs) that can leak sensitive intellectual property (IP). Traditional MIAs are often impractical in this domain because they require access to auxiliary datasets that can match the unique statistical properties of private data. This paper introduces a novel, data-free MIA targeting image segmentation models in FL for hardware assurance. Our methodology leverages Standard Cell Library Layouts (SCLLs) as priors to guide a gradient inversion attack, allowing an adversary to reconstruct images from a client's intercepted model update without needing any private data. We demonstrate that, by analyzing the reconstruction fidelity, an adversary can infer sensitive hardware characteristics, successfully distinguishing between circuit layers (e.g., metal vs. diffusion) and technology nodes (e.g., 32nm vs. 90nm). Our findings reveal that a novel loss term can conditionally amplify the attack's effectiveness by overcoming evaluation bottlenecks for structurally complex data. This work underscores a significant IP risk, challenging the assumption that FL provides inherent privacy guarantees and proving that severe information leakage can occur even without access to domain-specific datasets.

Fully homomorphic encryption (FHE) enables computation on encrypted data without decryption, making it central to privacy-preserving applications. However, no existing scheme efficiently supports both arithmetic and comparison operations in a unified framework. Prior approaches such as scheme switching and polynomial approximation face serious limitations: switching incurs prohibitive overhead for large inputs, while approximation methods introduce errors near critical points, restricting use in accuracy-sensitive tasks. We propose space switching method to integrate arithmetic and comparison computation seamlessly within FV-style schemes. Our approach identifies that the two types of operations require different plaintext spaces and introduces two procedures: a reduction step to transition from the number space $\mathbb{Z}_{p^r}$ to the digit space $\mathbb{Z}_{p}$, and a modulus-raising step to map results back to $\mathbb{Z}_{p^r}$. This design enables continuous evaluation of arithmetic and comparison within the same scheme. Experiments show that our method achieves up to $17\times$ faster performance than scheme switching and $15\times$ faster than direct comparison on database workloads, demonstrating its practicality for real-world privacy-preserving computation. Code and artifacts are available at https://github.com/UCF-Lou-Lab-PET/Universal-BGV.

We develop a recently introduced representation of quantum dynamics based on sampling negative Markov chain processes. By introducing particles and antiparticles, this formalism maps generic quantum dynamics onto a Markov process defined over an exponentially large configuration space. Within this framework, quantum complexity arises from the proliferation of stochastic particles, which ultimately renders classical simulation and sampling intractable beyond a certain timescale. In the presence of noise, we demonstrate that for any unitary evolution generated by a linear combination of local or pairwise interactions, there exists at least one noise channel that effectively classicalizes the system by suppressing particle growth and making Monte Carlo sampling efficient. As a corollary, we show that for this class of unitaries, the dynamics of an open quantum spin chain subject to depolarizing noise undergoes an exact transition to classical simulability once the noise strength exceeds a critical threshold which can be efficiently determined for any model.

Spanning trees are fundamental for efficient communication in networks. For fault-tolerant communication, it is desirable to have multiple spanning trees to ensure resilience against failures of nodes and edges. To this end, various notions of disjoint or independent spanning trees have been studied, including edge-disjoint, node/edge-independent, and completely independent spanning trees. Alongside these, several Steiner variants have also been investigated, where the trees are required to span a designated subset of vertices called terminals. For instance, the study of edge-disjoint spanning trees has been extended to edge-disjoint Steiner trees; a stronger variant is the problem of internally disjoint Steiner trees, where any two Steiner trees intersect exactly in the terminals. In this paper, we investigate the Steiner analogue of completely independent spanning trees, which we call \emph{completely independent Steiner trees}. A set of Steiner trees is completely independent if, for every pair of terminals $u,v$, the $(u,v)$-paths in all the Steiner trees are internally vertex-disjoint and edge-disjoint. This notion generalizes both completely independent spanning trees and internally disjoint Steiner trees. We provide a systematic study of completely independent Steiner trees from structural, algorithmic, and complexity-theoretic perspectives. In particular, we present several characterisations, connectivity bounds, algorithms, hardness results, and applications to special graph classes such as planar graphs and graphs of bounded treewidth. Along the way, we also introduce a directed variant of completely independent spanning trees via an equivalence with completely independent Steiner trees.

The study of quasi-period microstructures in pulsars offers valuable insights into the underlying emission mechanism. However, identifying these features through manual inspection of the intensity time series, often containing thousands to millions of pulses, is both laborious and time-consuming. To address this challenge, we have developed a Python-based software, Quasi-periodic MIcrostructure Search Tool (QMIST), to automate the search for quasi-periodic microstructures in radio pulsar time-series data. We provide a detailed description of the algorithms used in QMIST, demonstrate its efficacy using data on pulsars known to exhibit microstructures, and discuss potential future improvements. Using QMIST, we have performed a multi-epoch survey of quasi-periodic microstructures in a sample of 27 pulsars, using observations from the Giant Metrewave Radio Telescope and the Green Bank Telescope, as well as the archival data from the Parkes telescope. In addition to recovering previously reported microstructures from several pulsars, we report, for the first time, detection of quasi-periodic microstructures in three pulsars, B1451-68, B1706-16 and B1845-19. We also estimate the typical period of microstructures in another pulsar, B0540+23, that was known to exhibit microstructures earlier but the periodicity was unknown. Using the periodicity measurements from our survey, and earlier such measurements from the literature, we confirm the near linear relationship between the microstructure periodicity and the rotation period of pulsars, and discuss our results in the context of the emission mechanism of microstructures.

We present a comprehensive study of radial basis function (RBF) approximations for elliptic and obstacle-type boundary value problems under a variational formulation. Our focus is on practical accuracy, robustness and efficiency. To address ill-conditioning in dense systems, we apply truncated singular value decomposition (TSVD) and investigate its effect on stability and accuracy trade-offs. Numerical experiments report benchmarks on accuracy and show fast error decay. We investigate the trade-off between approximation and truncation errors for practical settings for the number of basis functions, the oversampling ratio and the truncation threshold. In comparison with other methods, RBF variational solvers deliver high accuracy at similar or lower cost for boundary value problems.

We determine the type-A Weyl anomaly coefficient $b$, associated with the intrinsic scalar curvature of the defect, for the class of holographically realised co-dimension two defect CFTs (dCFTs) introduced in arXiv: 2506.14505 and arXiv: 2512.14853. At strong coupling, we employ the dual D5-brane solutions in Euclidean signature, where the defect is supported on an $S^2$ submanifold of the Euclidean $AdS_3\times S^1$ boundary. At weak coupling, we use the classical solutions of the ${\cal N}=4$ SYM equations of motion, previously conjectured to describe the defects dual to the D5-brane configurations. Notably, the coefficient $b$ is found to be negative in a finite region of parameter space. To our knowledge, this constitutes the first explicit example of an {\it interacting} unitary dCFT with $b<0$. We also compute the type-B Weyl anomaly coefficients associated with the extrinsic curvature of the defects, first at strong coupling and subsequently at weak coupling. In a certain limit, we find agreement between the weak- and strong-coupling results for both the type-A and type-B anomaly coefficients.

Neutrino telescopes have detected astrophysical neutrinos with energies up to ${O}(100)$ PeV. Several current and proposed experiments aim to observe neutrinos at even higher energies, with the goal of detecting cosmogenic neutrinos. This increase in neutrino energy makes tests of Lorentz invariance violation (LIV) particularly appealing, since the effects of higher-dimension LIV operators on neutrino propagation grow rapidly with energy. In this work, we investigate the potential of the upcoming experiments GRAND and POEMMA to probe LIV in the neutrino sector through the detection of ultra-high-energy tau neutrinos. We generate the cosmogenic neutrino flux using SimProp and interface it with a calculation of neutrino flavor transition probabilities in the presence of LIV effects. Deviations from standard flavor transition probabilities manifest as changes in the expected tau neutrino event rates at GRAND and POEMMA. We first consider the case with a single nonzero LIV operator of various dimensions, and find that the projected sensitivities exceed existing limits from lower-energy probes by orders of magnitude. We then explore scenarios with multiple nonzero LIV parameters and show that their interplay can significantly modify the sensitivities compared to the single-parameter case. Overall, we find that upcoming observations of ultra-high-energy tau neutrinos will place some of the most stringent constraints on LIV.

The fragmentation properties of parsec-scales clumps play a fundamental role in shaping the dense gas condensations known as cores, the immediate progenitor of stars. The distribution of core masses, the so-called core mass function, is the precursor of the stellar initial mass function, which governs the distribution of stellar masses and, consequently, the evolution of galaxies. The stellar initial mass function is often described by a typical Salpeter-like slope, although deviations toward more top-heavy distributions have been reported in extreme environments, raising questions about its universality and about the physical connection between the two mass functions. To date, there are no observational constraints on the core mass function and its link to the initial mass function beyond the Milky Way. Here we present a study of the fragmentation properties and the measurement of the core mass function in an external galaxy, focusing on the 30Dor-10 region in the Large Magellanic Cloud, using high resolution observations that probe spatial scales down to 2000 au. Robust statistical analysis demonstrates that the core mass function is consistent with a Salpeter-like slope and suggests that variations in the stellar mass distribution arise from evolutionary processes rather than from initial fragmentation.

We employ the Multiscale Entanglement Renormalization Ansatz (MERA) tensor network to investigate a critical line of continuous quantum phase transitions of the $\mathbb{Z}_3$ chiral clock model. This critical line is believed to be described by a slow renormalization group flow from the 3-state Potts fixed point to another fixed point that features anisotropic scaling of space and time. We use the variational principle to construct a MERA representation of the model's ground state, from which we obtain the ground state energy and the set of scaling operators and their scaling dimensions. These scaling dimensions determine the critical exponents of the model, and we study these critical exponents and other scaling data as a function of the model's chiral parameter. We find a set of effective scaling data that smoothly varies starting from the Potts data as the chiral parameter is increased. Within the context of our approach, we discuss how this result may nevertheless be consistent with the two fixed point hypothesis provided the renormalization group flow is sufficiently slow. Our findings demonstrate MERA's effectiveness in capturing the complex low-energy physics of the chiral clock model and in extracting field theory data for an anisotropic continuum theory.

Electromagnetic invisibility, defined as reflectionless transmission with zero phase delay, imposes strict constraints on metasurface designs that go beyond conventional reflection suppression based on the Kerker effect. This condition can be viewed as a metasurface analogue of radiationless states such as anapole excitations. Here, we show that invisibility in metasurfaces embedded in identical media can only be achieved by introducing degrees of freedom, such as non-zero angle of incidence or higher-order multipolar responses. We demonstrate that, in dissimilar substrate and superstrate, achieving invisibility within a dipolar framework fundamentally requires pure bianisotropic coupling, while purely electric and magnetic responses are insufficient for lossless, passive and reciprocal systems. Using effective surface susceptibilities that account for the surrounding media and transverse wave vector, we derive closed-form conditions for both co- and cross-polarized invisibility. Importantly, we also demonstrate that the required bianisotropy does not need to be intrinsic, as an effective bianisotropic response may be achieved with anisotropic metasurface in dissimilar media leading to magnetoelectric coupling. Full-wave simulations of a metasurface at an air-dielectric interface confirm invisibility under oblique incidence. This work establishes a universal dipolar framework for invisible meta-optics in practically realistic scenarios.

In classical dynamical systems, stochastic feedback can stabilize otherwise unstable periodic orbits, giving rise to distinct controlled and uncontrolled phases as the rate of control application is varied. In this work, we apply these control protocols in classical, semiclassical, and quantum regimes to the kicked top, a paradigmatic model of quantum chaos. The quantum kicked top, modeled as the dynamics of a spin-S object, naturally interpolates between these regimes with the spin size S acting as an effective Planck constant. We show that the dynamics of the kicked top in classical, semiclassical, and fully quantum limits can all be controlled using stochastic feedback protocols. Comparing the full quantum dynamics to a truncated Wigner approximation that captures quantum noise but neglects interference beyond the Ehrenfest time, we find that low-moment observables are largely accounted for semiclassically, while the remaining discrepancy in higher moments is consistent with contributions from interference and possibly nonlinearities in rare trajectories that explore the compact phase space. We also find rapid purification in the numerics studied for all rates of control considered, suggesting that control quenches the top's ability to encode a qubit of quantum information even in the uncontrolled phase.

A dark matter sector composed of magnetic monopoles of a dark U(1) symmetry having a small kinetic mixing with the Standard Model photon has a rich and interesting phenomenology. The model in itself is also of theoretical interest. Based on the temperature of the dark sector and scale of spontaneous symmetry breaking for this U(1), three phenomenologically distinct cases for this model of dark matter are discussed. In all cases, constraints on dark matter self-interactions are translated into constraints on the model parameters. As the magnetic monopoles acquire a small visible magnetic charge, the survival of galactic magnetic fields, known as the Parker effect, places further constraints on the mixing between the dark and visible sectors.

We determine the border subrank of higher order structure tensors of several families of algebras, and in particular obtain the following results. (1) We determine tight bounds on the border subrank of $k$-fold matrix multiplication and $k$-fold upper triangular matrix multiplication for all $k$. (2) We determine the border subrank of the higher order structure tensors of truncated polynomial algebras, null algebras, and apolar algebras of a quadric. (3) We determine the border subrank of the higher order structure tensors of the Lie algebra $\mathfrak{sl}_2$ for all orders. (4) We prove that degeneration of structure tensors of algebras propagates from higher to lower order. Along the way, we investigate which upper bound methods (geometric rank, $G$-stable rank, socle degree) are effective in which settings, and how they relate. Our work extends the results of Strassen (J.~Reine Angew.~Math., 1987, 1991), who determined the asymptotic subrank of these algebras for tensors of order three, in two directions: we determine the border subrank itself rather than its asymptotic version, and we consider higher order structure tensors.

Near-term quantum workloads demand error management, yet the two lightest-weight techniques, Quantum Error Detection (QED) and Probabilistic Error Cancellation (PEC), have complementary cost profiles whose joint architectural design space remains unexplored. QED encodes logical qubits and discards error-flagged runs, filtering noise with low qubit overhead but leaving residual errors; PEC can correct these in software, but at exponential cost in noise strength. If QED efficiently reduces per-gate noise, PEC's cost savings can outweigh QED's discard overhead; realizing this, however, requires solving two system-level design challenges. First, the \textit{QED interval} -- how often detection cycles are inserted -- is a tunable architectural parameter governing the cost-accuracy tradeoff. We derive an efficiency condition and show that the canonical one-cycle-per-gate frequency does not achieve break-even in any code we evaluate, while optimized intervals on high-rate Iceberg codes do. Second, we discover that naive PEC+QED integration \textit{degrades} accuracy below the QED-only baseline. The root cause is a transient error profile in the first detection cycle that corrupts PEC's noise model. We develop \textit{steady-state extraction}, a co-designed characterization protocol that isolates steady-state error behavior, reducing estimation bias by up to $10.2\times$. On a $[[6,4,2]]$ Iceberg code running QAOA ($p{=}4$--$8$) with a fixed shot budget, PEC+QED achieves $2$--$11\times$ lower absolute error and up to $31\times$ lower MSE versus PEC on physical qubits, with per-interval savings compounding over interval depth.

It is generally believed that quantum fluctuations collaborate with thermal fluctuations, effectively reducing transition temperatures (e.g. for melting of charge order). We show that this is not always the case and that the interplay between quantum and thermal fluctuations can be competitive. We find excellent motivation for addressing this thanks to the discovery of correlated insulating "generalized Wigner crystal" (GWC) states in hetero-bilayer transition metal dichalcogenide (WS$_2$/WSe$_2$) moiré systems [Y. Xu, et al., Nature 587, 214-218 (2020)]. We account for the impact of quantum effects on the melting temperature of GWCs, carrying out finite temperature Lanczos calculations on an extended Hubbard model on the triangular lattice (both with a double-gate screened potential, and the nearest neighbor model) for multiple electron densities. We show that quantum effects capture the shift relative to the classical estimates, which in some cases are more than 50 percent off from the experimental values. Then building on these numerical findings, we provide a qualitative picture that clarifies that while quantum melting of GWC (by increasing the bandwidth) naturally softens the ground state order parameter, it does not always decrease the melting temperature; conversely it can increase it. To do so we employ a finite temperature perturbation theory, treating the kinetic energy perturbatively on top of a classical Wigner crystal. Our predictions should be observable in future experiments where the bandwidth can be tuned.

Quantum computers are moving into HPC centers, and the main challenge is now integration rather than pure hardware access. Many current software paths still depend on vendor-specific adapter chains between user SDKs, schedulers, and backend APIs. This pattern makes operations more complex than necessary and slows the transition from pilots to production workflows. We present a practical integration path centered on the Quantum Device Management Interface (QDMI). Using IQM superconducting systems as a hardware case study, we implement an IQM-backed QDMI layer and connect it to two software layers that HPC centers working with quantum computers already care about: Slurm-based job execution and Qiskit-facing user workflows. The implementation is publicly available at https://github.com/iqm-finland/QDMI-on-IQM. The key message is simple: integrating quantum hardware into HPC does not have to be a bespoke engineering effort for each backend. Once the software-hardware boundary is standardized, large parts of the stack become reusable across providers and deployment styles. Our results do not claim that standardization eliminates all HPCQC challenges. They show that this specific boundary can already be standardized today in a way that is practical for users, operators, and vendors.

It has been shown that there are an infinite set of asymptotic symmetries in quantum gravity and QED, and this has been extended to dressed states in some cases. Here we rederive these statements in terms of detectors in order to clarify, confirm, and generalize these results to include external hard gravitons. Using detectors and including the full t dependence in Faddeev-Kulish dressings allows us to correct discrepancies in the literature and make new statements. We show that Faddeev-Kulish dressings correctly encode the memory effect in the 'in' and 'out' scattering Fock spaces. We find a physical contribution to the memory eigenvalues arising from the dressings in both cases.

Feedback from radio AGN jets is regularly implemented into contemporary models of galaxy evolution to offset radiative cooling in the large-scale environments in which they typically reside. While previous studies suggest that the total kinetic power output from radio AGN is sufficient for this purpose, many have relied on jet-power estimation from radio luminosities using generalised scaling relations that neglect additional information such as source size and environment. We here infer the cosmic evolution of radio AGN kinetic jet powers using a physically motivated semi-analytic model for the first time. Initial analysis on a sample of 619 radio AGN at $z < 2.5$ from LoTSS Deep Field and International LOFAR Telescope images of the Lockman Hole implies a population dominated by short-lived sources typically of lower jet power. After incorporating weighting towards shorter lifetimes in the inference models, we utilise ELAIS-N1 and Boötes LoTSS Deep Field data to expand our analysis to a much larger sample of 5,187 objects, deriving jet kinetic luminosity functions and integrated kinetic luminosity densities for the radio AGN population out to $z = 2.5$. In broad agreement with previous results in the literature, we find the total power output per comoving volume to be $\sim$10$^{32}-$10$^{33}$ W Mpc$^{-3}$ across the full redshift range, with some suggestions of moderate positive evolution from $z$ = 0$-$1 and little evolution from $z$ = 1$-$2. These values are compatible with expectations from some cosmological models, providing strong evidence for the viability of feedback from radio AGN jets across cosmic time.

We propose a search at the LHC for GeV-scale particles coupling predominantly to light quarks based on low-multiplicity jets. The search targets production in association with a hard photon and uses the feature that a light gauge-singlet can only decay into a small number of hadronic channels, yielding jets with anomalously low charged-track multiplicity and mass compared to QCD jets at the same transverse momentum. We determine the sensitivity to scalar and pseudoscalar couplings to up-quarks, and suggest a data-driven estimate that reduces the sensitivity to jet modeling uncertainties. This search extends the reach to hadronically-coupled particles into a previously inaccessible regime.

The shapes of fluid planets bear the signatures of rotational flattening and atmospheric flows. Precise knowledge of their shapes and wind profiles may therefore reveal their interior rotation rates. We re-examine this idea for the ice giants, where missions like the Uranus Orbiter and Probe could use radio occultations to measure atmospheric heights near 1 bar at multiple latitudes, complementing Voyager 2's near-equatorial constraint for Uranus. Applying geodetic calculations and considering zonal wind uncertainties, we find that only a narrow range for Uranus's 1-bar polar radius, $R_{\rm pol}=24,968.6\pm4.7$ km, is consistent with Uranus's winds, occultations, and gravity field, even treating Uranus's interior spin as a free parameter. This is because the isobaric shape depends on the total rotation of the isobaric surface, which is already well constrained by observations, irrespective of what portion is attributed to bulk rotation versus winds. Occultations will, however, be valuable for testing our underlying assumption that the winds manifest the full differential rotation that sets the shape. The apparent north-south asymmetry in Uranus's winds, if permanent, produces a 5-km difference between the northern and southern polar radii, measurable with suitable radio occultations. Neptune's much more uncertain winds yield ~100 km variations in polar and equatorial radii. We confirm that Uranus and Neptune's magnetic rotation periods yield nonzero mean dynamical heights for their atmospheres. Accurate results for Uranus and Neptune require that the full latitude-dependent rotation be incorporated when fitting radii from occultations. Only significantly faster interior rotation -- periods close to 15 h in both Uranus and Neptune -- would minimize their dynamical heights.

We demonstrate that combining the positivity of density matrices with steady-state conditions yields a systematic bootstrap method for studying open quantum many-body systems governed by Lindblad master equations on infinite lattices, which exhibit absorbing phase transitions. As a concrete example, we apply this method to the quantum contact process with an absorbing state. We obtain bootstrap bounds on steady-state expectation values, the critical coupling, certain ratios of expectation values in the nontrivial steady state in the supercritical phase, and the Liouvillian spectral gap in the subcritical phase.

In quantum field theory, it is not always possible to excite one state out of another using only local operators. This paper establishes abstract algebraic criteria for (local) excitability in general quantum theories, and computes these criteria explicitly for zero-mean Gaussian states in (generalized) free field theories. We find that in this context, due to the special nature of Gaussian states, one-way excitability always implies two-way excitability, and our results generalize the "quasiequivalence theorems" of Powers, Stormer, van Daele, Araki, and Yamagami. A key role in our proof is played by the information-theoretic tool of canonical purification. In appendices, we provide a pedagogical introduction to the algebraic formulation of (generalized) free field theory.

The vacuum mutual information (MI) of subregion algebras provides a universal window into the data of general conformal field theories (CFTs). Exploiting the geometric nature of the modular flow associated to ball-shaped regions and the operator product expansion of twist operators implementing the replica symmetry in an $n$-fold version of a CFT, it is possible to construct a hierarchy of increasingly refined approximations to the full MI. In this letter, we use the two-point functions of primaries of arbitrary spin in the replicated theory to constrain the twist operators, and find their contribution to the MI of arbitrarily boosted balls in any $d$-dimensional CFT. When the two-point functions involve the primary with the lowest scaling dimension, our result provides the most precise approximation for the long-distance behavior of the MI, superseding all previous expansions. Building upon this result and certain universal properties of the short- and long-distance regimes, we put forward a new high-precision analytic approximation to the MI for arbitrary separations. The accuracy of our approach is validated against exact $d=2$ and lattice $d=3$ results. We further apply it to characterize the MI of a $d=4$ Maxwell field, a case for which no prior results are available.

In this article, we prove that the quantum $f$-divergence between two normal states on a semifinite von~Neumann algebra is equal to the classical $f$-divergence between two corresponding classical states, which are called Nussbaum-Szkoła distributions. This result has been proved by the second named author and T.C.~John for normal states on the von~Neumann algebra $\mathbb{B}(\mathscr{H})$ of all bounded operators on a Hilbert space $\mathscr{H}$. We extend their result for normal states on any semifinite von~Neumann algebra, not only $\mathbb{B}(\mathscr{H})$.

Cell proliferation and cell movement are fundamentally stochastic processes which lead to variability in the growth and spatial structure of cell populations in many biological settings, such as cell invasion, wound healing, and tumour growth. We develop stochastic, on-lattice agent-based models (ABMs) which incorporate volume exclusion, random movement, and multi-stage representations of the cell cycle. The multi-stage framework enables a more realistic representation of true cell cycle time distributions. We also introduce a novel form of myopic behaviour, in which cells sense their local environment when attempting to proliferate. For each ABM, we derive a corresponding continuum partial differential equation (PDE) description under the mean-field approximation. Using numerical simulations, we investigate how different proliferation mechanisms influence population-level dynamics in both the discrete and continuum models. In particular, we consider biologically relevant contexts of growth-to-confluence assays (using uniform initial conditions) and travelling wave behaviour associated with cell invasion. We examine how the PDE solutions compare with the behaviour of the corresponding ABMs averaged over many realisations.

In this work, we have analyzed the cosmology of the Tsallis holographic dark energy (THDE), a particular case of Nojiri-Odintsov HDE proposed in [S. Nojiri and S. D. Odintsov, \textit{Gen. Relativ. Gravit.} \textbf{38} (2006), 1285; \textit{Eur. Phys. J. C} \textbf{77} (2017) 528], using Hubble's horizon cutoff in $f(R,T)=μR+νT$ model considering pressureless dark matter. We have examined the equation of state (EoS) parameters in this scenario. The deceleration parameter has been evaluated for this interacting model to justify the late-time acceleration of the expanding universe. We have also studied the cosmological consequences of Statefinder pair, $O_{m}(z)$ diagnostics, $r-q$ plane, and $w_{DE}-w^{'}_{DE}$ pair for interacting THDE in $f(R,T)=μR+νT$ model. We have also illustrated the cosmology of the interacting THDE using Hubble's horizon cutoff in $f(R,T)=R+γR^2+ξT$ model. The EoS parameter, deceleration parameter and Statefinder pair are studied in this interacting scenario. Attainment of $Λ$CDM fixed point has been observed for both models. We have also constrained model parameters based on observational data sets through the formalism of $χ^{2}$ minimum test.

This work focuses on the structure, wettability and corrosion behaviors of Ti-6Al-4V alloy after roughening treatments in different concentrations of NaOH aqueous solutions followed by low surface energy hexadecyltrimethoxysilane (HDTMS) coating. In this regard, scanning electron microscopy, contact angle measurements, potentiodynamic polarization and electrochemical impedance spectroscopy were used to characterize the samples. In contrast to hydrophilicity caused by the hydrothermal alkaline treatments, the subsequent HDTMS coating donated considerable hydrophobicity. Typically, the highest sessile water contact angle (about 147 deg) was obtained for the sample treated in 3 molar NaOH solution followed by the HDTMS coating. In addition, the alkaline treatment reduced the corrosion resistance of the surface in a NaCl aqueous solution; however, the HDTMS hydrophobization process improved it significantly. It is eventually concluded that the coupled use of alkaline treatment and HDTMS functionalization can be further considered for moisture-exposed applications of Ti-based alloys.