Granular materials are inherently out-of-equilibrium systems due to energy dissipation through inelastic collisions and friction. When driven by mechanical agitation such as vibration, they exhibit rich collective behaviors including segregation, clustering, and spontaneous oscillations. Here, we report directional stepwise migration of particle clusters from one compartment to the next in a vertically vibrated granular system composed of small and large particles. To clarify the underlying mechanism, we directly measured how the flux of both particle species depends on the instantaneous particle populations. The measurements reveal an asymmetric interaction between particle species: the flux of small particles is enhanced by the presence of large particles, whereas that of large particles is suppressed by small particles. A minimal flux model incorporating these measured fluxes reproduces the observed directional dynamics and provides an experimentally grounded framework for collective transport in vibrated granular systems.

In finance, portfolio management is a traditional yet difficult problem that has drawn attention from practitioners and researchers for many years. However, there are still difficult technological problems that need to be solved. In the world of finance, managing a portfolio has never been easy. Selecting portfolios in a volatile market is made easier with the help of portfolio management. The goal of this review study is to present the concept of physics-informed neural networks because they provide a novel approach to directly incorporating physics and finance principles into the neural network's learning process. By doing so, physics-informed neural networks ensure that their forecasts are in line with established financial regulations and processes in addition to offering precise forecasts. Furthermore, this article provides an overview of the current state of research in portfolio optimization with the support of mathematical models, deep learning models and physics-informed neural networks. In addition, the advantages and disadvantages of various deep learning and mathematical modelling are discussed. Researchers and business professionals alike should find the data useful for advancing the field of investment management and trying out new portfolio management strategies. For this purpose, in this review work, emphasis is given to these factors. Finally, a few challenging issues and potential future directions are discussed, encouraging readers to consider fresh ideas in this field of study.

The nature of eclipsing time variations (ETVs) in post-common-envelope binaries (PCEBs) is still unknown. Circumbinary planets routinely fail the test of time and the Applegate mechanism has energetic constraints and problems in reproducing observations. Based on recent analytic models of magnetically-induced ETVs and stellar dynamo simulations, we aim at explaining ETVs via non-axisymmetric magnetic fields that drift in the azimuthal direction of the star, know as azimuthal dynamo waves (ADWs). We implement a time-varying non-axisymmetric quadrupole moment ($Q$) in a binary system. We solve for the dynamics of the system, compute the resulting eclipsing times, and construct O-C, diagrams. We perform several simulations with different amplitudes of $Q$, periods, stellar masses and binary separations. ADWs naturally give rise to characteristic shapes in the O-C diagram that resemble observations. Depending on how fast $Q$ changes, the solutions can have a sharp decrease in O-C producing amplitudes such as the one obtained in QS Vir, or sinusoidal-like shapes such as in V471 Tau or NN Ser. We also find that the amplitude of the eclipsing times varies from tens to hundreds of seconds. ADWs offer a self-consistent explanation for ETVs as they are expected in dynamo theory. They can explain a variety of features in the observed O-C diagrams. As suggested by dynamo simulations, ADWs are easily excited in rapidly rotating stars, alleviating energetic constrains required in the context of the Applegate mechanism. They produce non-axis $Q$ that in turn produce ETVs that can account for the long-term variation of the O-C, diagrams. We expect in this case that the resulting O-C diagrams are not strictly periodic, unlike explanations based on a third body that would imply a strict periodicity unless additional mechanisms are being invoked.

We present a transient quantum sensing framework for cavity-magnon systems that circumvents the inevitable loss of initial-state quantum properties plaguing conventional steady-state protocols. Explicitly incorporating finite-time dynamics and adopting an engineered steady state as the initial condition, we derive the exact transient noise spectrum. We show that residual initial quantum correlations alone can drastically enhance the short-time signal-to-noise ratio (SNR) beyond that achievable with unsqueezed steady-state schemes. Through analysis of the transient spectral density and joint measurements of orthogonal cavity quadratures, we realize crosstalk-free reconstruction of all three magnetic field components, enabling orientation of magnetic signals. In the long-time limit, our theory yields a closed-form stationary noise spectrum and uncovers a resonance condition $g_{am}=\sqrt{κ_aκ_m}/2$, where cavity field quantum noise is fully canceled without requiring strong coherent coupling. Away from this resonance, injected squeezing further suppresses cavity induced noise and broadens the detection bandwidth. Extending the framework to an array of $N$ yttrium iron garnet (YIG) spheres generates a collective bright mode, with magnon-probe noise scaling as $1/N$. Our results establish a unified route to scalable, high precision, multidimensional quantum magnetometry using cavity-magnon platforms.

We propose a method to probe weakly bound s-wave neutron components near the neutron emission threshold in heavy nuclei using Coulomb-assisted neutron transfer reactions. Weakly bound s-wave neutrons have large asymptotic amplitudes, which are difficult to access directly with conventional methods. This work focuses on the $(d,p)$ reaction at low incident energies and backward angles, where the reaction is localized in the nuclear exterior due to the Coulomb barrier. Under these conditions, the transition amplitude becomes sensitive to the asymptotic part of the single-particle wave function. Finite-range DWBA calculations show that the cross section for weakly bound states exhibits a weak dependence on incident energy, while that for strongly bound states decreases rapidly with decreasing energy. Contributions from orbitals with $l \geq 1$ are suppressed by the centrifugal barrier, resulting in selectivity for s-wave components. This method provides a probe of the strength distribution of weakly bound s-wave components near threshold and the asymptotic structure of their wave functions.

In this paper we consider parameter estimation for discretely observed diffusion processes. In particular, we focus on data that are observed at low frequency and methodology that can estimate parameters with uncertainty quantification. Most statistical work in this domain develops advanced Markov chain Monte Carlo (MCMC) algorithms for sampling from the posterior of the parameters, a task which is often complicated by the fact that one seldom has access to the transition density of the diffusion process; one has to combine sophisticated MCMC methods which are robust to the required time discretization of the diffusion, which can yield expensive algorithms. We focus on developing the martingale posterior method for the context of interest, when one can only numerically approximate the transition density of the diffusion. Based on using types of diffusion bridges we introduce a new martingale posterior method for parameter estimation for discretely observed diffusion processes. We prove that this algorithm approximates, in some sense, the martingale posterior which has no time-discretization bias up-to $\mathcal{O}(Δ)$ if $Δ$ is the time discretization step. Our approach is illustrated on several examples, showing orders of magnitude speed up versus state-of-the-art MCMC algorithms.

Extended gamma-ray sources provide significant information about particle propagation. 4FGL J1626.0-4917 was labeled as an unassociated source in 4FGL catalog without known counterparts at other wavelengths. We report an analysis on 4FGL J1626.0-4917 with 17 years Fermi Large Area Telescope data and archival Chandra X-ray Observatory data. We find extended GeV emission around this source, which can be modelled by a Gaussian disk of 0.28 degree radius with a significance of the extension of 7.2 sigma. The gamma-ray spectrum of 4FGL J1626.0-4917 has a photon index of 2.73. The gas content, including molecular, neutral and ionized gas, was investigated and the potential hadronic origin is discussed. The diffuse GeV gamma-ray emission may likely originate from the interaction between accelerated protons in 4FGL J1626.0-4917 and the target proton in surrounding gas, although the leptonic process cannot be ruled out. The X-ray spectral analysis was performed, which reveal a point source inside 4FGL J1626.0-4917. We investigate potential counterparts, including the stellar cluster NGC 6134 and the supernova remnant G335.2+0.1. Our results highlight the complexity of unidentified extended gamma-ray sources and the need for further observations.

Multimodal Retrieval-Augmented Generation (MRAG) is widely adopted for Multimodal Large Language Models (MLLMs) with external evidence to reduce hallucinations. Despite its success, most existing MRAG frameworks treat retrieved evidence as indivisible documents, implicitly assuming that all content within a document is equally informative. In practice, however, sometimes only a small fraction of a document is relevant to a given query, while the remaining content introduces substantial noise that may lead to performance degradation. We address this fundamental limitation by reframing MRAG as a fine-grained evidence selection problem. We propose Fragment-level Evidence Selection for RAG (FES-RAG), a framework that selects atomic multimodal fragments rather than entire documents as grounding evidence. FES-RAG decomposes retrieved multimodal documents into sentence-level textual fragments and region-level visual fragments, enabling precise identification of evidence that directly supports generation. To guide fragment selection, we introduce Fragment Information Gain (FIG), a principled metric that measures the marginal contribution of each fragment to the MLLM's generation confidence. Based on FIG, we distill fragment-level utility judgments from a high-capacity MLLM into a lightweight selector, achieving accurate evidence selection with low inference overhead. Experiments on the M2RAG benchmark show that FES-RAG consistently outperforms state-of-the-art document-level MRAG methods, achieving up to 27 percent relative improvement in CIDEr. By selecting fewer yet more informative fragments, our approach substantially reduces context length while improving factual accuracy and generation coherence.

Field/circuit coupling is a common approach when a lumped representation of a certain electrotechnical device is not accurate enough. To exploit existing code and underlying properties of the coupled systems, cosimulation techniques such as waveform relaxation can be used. The coupled system is of differential-algebraic type, which can potentially lead to divergence. This paper presents a novel, sufficient topological convergence criterion for field/circuit coupled systems of higher index containing a generalized capacitance. Hereby, the criterion holds for a full range of field systems whose structure can be classified as a generalized capacitance. Finally, the theoretical results are supported by numerical simulations.

Tunable flat optics are essential for advancing compact photonic devices. Here we show a numerical study of a reflective magneto-optical metasurface with a dynamically tunable focal length. The structure comprises bismuth iron garnet nanodisks in a Gires-Tournois resonator configuration. The magneto-optical properties of the garnet modulate the reflected phase response via an external magnetic field, allowing focusing at different focal lengths. Full-wave simulations demonstrate that the metasurface exhibits distinct focusing characteristics depending on the applied magnetic field direction for a fixed right circularly polarized incident wave at 1.550 μm. Specifically, switching the external field from +0.2 T to -0.2 T changes the focal length by a factor of approximately two (from 7.16 mm to 13.76 mm). These findings demonstrate that magneto-optical metasurfaces offer a flexible, viable approach for non-mechanical, tunable focusing in compact reflective optical components.

Let $\mathcal A$ be an $\mathbb F$-algebra and $ω\in \mathcal A\langle x_1, \ldots, x_m \rangle$ which defines a map $\mathcal A^m \rightarrow \mathcal A$ by evaluation, called a polynomial map with constant. We consider $\mathcal {A} = M_n(\mathbb{F})$, the algebra of $n \times n$ matrices over an algebraically closed field $\mathbb{F}$ of characteristic $0$, and polynomial maps given by $ω(x_1, x_2) = A_1x_1^k + A_2x_2^k$, where $A_1,A_2\in M_n(\mathbb F)$. For $n=2$, the images of such a map is competely determined in an earlier work (Panja, S.; Saini, P.; Singh, A., Images of polynomial maps with constants, Mathematika 71 (2025), no. 3, Paper No. e70031). In this article, by assuming one of the coefficients, say $A_1$, is invertible, we relate the surjectivity of $ω$ to the nullity of $A_2$. When $n=3, 4$, we completely classify the surjectivity of $ω(x_1, x_2)$ by obtaining the necessary and sufficient condition in terms of $n$, $k$, and the nullity of $A_2$.

The convergence of 5G and IoT enables fully connected, intelligent environments, but it faces challenges from the fragmentation of public/private 5G networks and the heterogeneity of IoT networks. We propose a unified framework using CAMARA open gateways, which provide standardized, open APIs to expose network capabilities, reducing fragmentation and simplifying interoperability, supported by a federated SDN architecture that ensures scalable cross-domain control. We further demonstrate 5G-based remote control of KNX devices, extending industrial and building automation. These contributions lay the foundation for a secure, dynamic "network of networks" supporting next-generation applications.

We prove that the category of quasi-pseudometric modular spaces whose morphisms are the nonexpansive mappings is isomorphic to a quantale enriched category. To achieve this, we construct an appropriate quantale of isotone functions. We also show that, by means of this isomorphism, the topology associated with a quasi-pseudometric modular coincides with that generated by its corresponding quantale enriched category. Furthermore, we demonstrate that the class of quasi-pseudometrizable topological spaces coincides with the topological spaces whose topology is induced by a quasi-pseudometric modular.

This paper develops a sliding mode control based frame work for equality constrained optimization by reformulation the first order Karush Kuhn Tucker conditions as control affine dynamical system. The optimization variables are treated as states and the Lagrange multipliers as control input, with equality constraints defined as sliding manifold. The resulting design guarantees exact constraint enforcement with finite time convergence, independent of objective convexity, and exhibits robustness to matched disturbance, structural uncertainty and bounded measurement noise. To accelerate the convergence, a nonsingular terminal sliding mode based normed gradient flow is introduced, ensuring both finite time convergence to optimal solution and constraint satisfaction. Rigorous Lyapunov analysis establishes closed loop stability and convergence. Numerical studies across diverse benchmark problems demonstrate superior accuracy and robustness over classical continuous time optimization method, highlighting effectiveness under disturbance.

In non-Hermitian systems, spectra can be maximally boundary-sensitive, yet bulk physics need not be. Here we experimentally show that spectral moments provide boundary-robust bulk observables in finite non-Hermitian lattices, even when the spectra undergo dramatic geometry-dependent reshaping due to the skin effect. Using a unified acoustic platform with full spectral reconstruction and time-domain access, we probe one-, two- and three-dimensional lattices and demonstrate that spectral moments remain nearly invariant across distinct boundary geometries while the corresponding complex spectra differ strongly. To connect the thermodynamic theorem to realistic finite systems, we develop a loop-counting theory that identifies the physical origin of finite-size deviations in terms of missing boundary loops, quantitatively captures the corrections, and predicts a scaling law, which we verify experimentally. Beyond acoustic spectroscopy, we reveal a counterintuitive dynamical consequence of moment invariance: a dispersive-to-proliferative bulk transition governed by bulk moment structure rather than spectral boundary sensitivity. As a result, local bulk dynamics can remain stable (dispersive) even in a $\mathcal{PT}$-broken spectral regime, challenging the conventional expectation that $\mathcal{PT}$ breaking necessarily implies feedback-induced dynamical instability (proliferation) through exponentially amplifying spectral components. These results establish spectral moments as practical bulk descriptors for finite non-Hermitian matter and open a route to extracting and controlling intrinsic bulk behavior in realistic wave-based non-Hermitian devices.

We present a comprehensive analysis of dense cores and filamentary structures in the M16 Eagle Nebula using high-resolution ($11.7^{\prime\prime}$) surface density and temperature maps derived from \textit{Herschel} observations. Using the \textit{hires} algorithm for map construction and the \textit{getsf} method for source and filament extraction, we identified 233 cores and 111 filaments in this massive star-forming region. The filaments exhibit a median width of 0.4\,pc -- and a median linear density of 61\,$M_\odot$\,pc$^{-1}$, with 76\% being supercritical for gravitational fragmentation. Our radial analysis of the $\sim$60\,pc diameter shell driven by the central NGC 6611 cluster reveals strong enhancements in structure formation: filament formation efficiency (FFE) is 2.3 times higher within the shell (peaking at 22\%), while core density shows a concurrent 1.5-fold enhancement. The moderate correlation between core density and FFE ($r=0.67$) indicates coupled formation processes. Theoretical analysis demonstrates that observed surface densities exceed the critical threshold for fragmentation by a factor of $\sim$8, with a fragmentation timescale ($\sim$1.5--2.0\,Myr) comparable to the shell's dynamical age ($\sim$1.0--1.3\,Myr), indicating we are observing fragmentation in progress. These results reveal a hierarchical fragmentation sequence -- shell compression $\rightarrow$ filament formation $\rightarrow$ core formation -- providing clear observational evidence for positive feedback where massive star formation triggers secondary structure formation in the surrounding molecular cloud.

The inner regions of protoplanetary disks are promising formation sites of rocky planetesimals. Theoretical studies have proposed a scenario in which thermal ionization activates the magnetorotational instability (MRI) in the hot inner disk, and the resulting pressure maximum at the MRI activation boundary accumulates dust and promotes planetesimal formation. However, the inner disk may be thermally unstable, and the activation boundary can vary in time, potentially preventing the maintenance of a dust trap sustained by a steady pressure maximum. We propose an alternative scenario in which planetesimals form in a thermally unstable inner disk through dust self-accumulation driven by the coevolution of dust and disk temperature. To this end, we perform simulations that simultaneously calculate the non-equilibrium thermal evolution, the gas and dust surface density evolution, dust growth, and planetesimal formation. Our results show that thermal instability triggers cyclic MRI activation and deactivation, during which planetesimals are formed. The MRI is activated in the inner disk, and driven by thermal instability, the active region expands outward and then reverts to an inactive state. Triggered by a local enhancement in the dust surface density, dust undergoes self-accumulation while migrating inward in the MRI-inactive phase, causing planetesimal formation. Once the MRI is reactivated at a smaller radius, the cycle restarts. For a typical accretion rate of $10^{-8}M_{\odot}~{\rm yr^{-1}}$, a planetesimal belt forms near 1 au. This mechanism can produce sufficient planetesimal mass to form multiple super-Earths. This work provides a framework for a self-consistent model of planetesimal formation based on the coevolution of dust and disk temperature, serving as an initial condition for subsequent planet formation simulations.

In this paper, we propose an enhanced physical layer security approach, named joint secrecy and covert communication (JSACC), which aims to improve the performance of physical layer security (PLS). The JSACC system can dynamically switch between secrecy mode and covert mode according to the channel difference between legitimate and illegitimate receivers. We further leverage reconfigurable intelligent surface (RIS) to extend the communication range. For each scenario, we derive the closed-form expressions for the outage probability (OP) and ergodic rate (ER). To further understand system performance, we derive asymptotic approximations in the high signal-to-noise ratio (SNR) regime to obtain the diversity order and high-SNR slope. We demonstrate that the diversity order of the JSACC depends on Nakagami fading parameters and the RIS reflecting element number. Simulation results are consistent with our theoretical analysis and reveal the superiority of the JSACC system over the conventional secrecy communication (SC) system.

The classical cascading pipeline of retrieve--rerank suffers from a bounded recall problem, stemming from limitations of the first-stage retriever. Most current approaches address the bounded recall problem by improving the first-stage retriever, but this incurs substantial training and inference costs, especially to handle queries that require substantial reasoning. To circumvent the computational costs of reasoning-based retrievers, we replicate the findings of GAR, Graph-based Adaptive Reranking, on the BRIGHT reasoning-intensive retrieval benchmark. GAR addresses the bounded recall problem by modifying the reranking process itself through iterative exploration of a corpus graph, but it was previously only tested on models designed for topical and question-answering-style queries. Hence, reproduce GAR in reasoning-intensive settings with reasoning and non-reasoning reranking models. We observe that the quality of the reranker's signal plays an important role in identifying additional relevant documents within the corpus graph. Overall, we find that GAR boosts the effectiveness of reasoning-intensive retrieval across a variety of models while contributing minimally to computational overheads. Ultimately, this work enables more practical deployment of retrieval systems that can address reasoning-intensive queries.

Within the framework of the post-Newtonian $2\frac12$ approximation theory, a kinetic theory for relativistic gases in the presence of gravitational fields is developed. The Boltzmann equation and the equilibrium Maxwell-Jüttner distribution function are determined up to $1/c^7$--order, which are used to calculate the components of the particle four-flow and energy-momentum tensor and to find the Eulerian hydrodynamic equations for the mass, mass-energy, and momentum densities in the $2\frac12$--post-Newtonian approximation. The energy conservation law follows from the hydrodynamic equation for the total energy density, which is a combination of the hydrodynamic equations for the mass and the mass-energy densities.

Sand painting is a process-driven art where visual appearance emerges from granular accumulation. Given a single image, reconstructing a plausible sand painting process requires modeling coherent stroke structures and material-dependent effects. Existing methods, including stroke-based optimization and diffusion-based video synthesis, often lack structural coherence and material consistency, leading to unrealistic drawing sequences. We present SandSim, a framework that reconstructs a sand painting process from a single image. We introduce a curve-guided Gaussian representation that models strokes as sequences of anisotropic primitives along continuous trajectories, whose smooth kernels capture the soft boundaries of sand strokes and enable coherent stroke formation. We further adopt a subtractive compositing scheme to model light attenuation during sand accumulation. We incorporate a semantic-guided planning module for scene decomposition and drawing order inference. Our framework jointly optimizes stroke geometry and appearance and can be integrated with a physics-based simulator for interactive sand dynamics and editing. Experiments show that our method produces temporally coherent and visually realistic results, achieving improved reconstruction quality and perceptual fidelity compared to existing approaches.

This paper studies flexible non-uniform array design for monostatic integrated sensing and communication (ISAC) systems. An antenna pool is considered at the base station, where each candidate antenna can be dynamically assigned to transmit, receive, or inactive modes, such that a non-uniform effective array is jointly constructed with the ISAC precoding design. We formulate a sum communication rate maximization problem by jointly optimizing the ISAC beamforming schemes and antenna-mode assignment under sensing, power, and antenna mode constraints. We develop an alternating-optimization-based solution framework mainly with the aid of weighted minimum mean square error, continuous relaxation-based penalty, and successive convex approximation. Numerical results show that the proposed non-uniform array achieves higher sum-rates than the uniform-array baselines, with particularly large gains when the number of activated antennas is small. Moreover, the proposed non-uniform array can achieve, and in some cases exceed, the performance of uniform array baselines with substantially fewer activated antennas, highlighting geometry-aware non-uniform array design as a compelling alternative to brute-force antenna scaling-based array design.

Software stacks embedded on microcontroller-based hardware typically provide rudimentary APIs programmed in C/C++, basic connectivity and, sometimes, a firmware update mechanism. Such coarse mechanisms contrast with widely used APIs and more advanced networked interaction expected from software stacks deployed on less resource-constrained hardware (microprocessor-based). In this paper, we aim to bridge this gap by designing treVM, a generic scheme to host high-level WebAssembly code capsules, bolted on a general-purpose Rust embedded software platform, able to run on a large variety of 32-bit microcontrollers. Not only can treVM capsules host highly customizable business logic, but capsules can also be securely updated on demand over the network, on devices already deployed in the field. We implement treVM in Rust, on top of Ariel OS, a general-purpose RTOS, and we publish the code as open source. Based on our implementation, we validate the feasibility of treVM on commonly available boards, and we report on extensive benchmarks we performed on heterogeneous hardware including Arm Cortex-M, RISC-V, and Xtensa microcontroller architectures. As such, treVM provides a promising new framework to secure continuous deployment of embedded software on low-power networked devices.

The Paneitz operator is a dimension-4 conformally invariant fourth-order differential operator that has recently attracted attention for possible cancellations of the vacuum energy. We show that, in four dimensions, the Paneitz operator acting on a scalar field falls within the class of extended mimetic gravity theories. Thus, it exhibits the usual instabilities of mimetic gravity. Assuming such instabilities are cured by higher derivative terms, we derive constraints on the Paneitz operator from a modified propagation speed of gravitational waves, after including the Einstein-Hilbert action in the mimetic gravity formulation.

Quantum universal invariants of a Gaussian state's covariance matrix, which can be derived from intensity correlation moments, have been adopted to characterize the entanglement properties of Gaussian states via the positive partial transpose criterion, also known as the Peres-Horodecki separability criterion. Such intensity correlation moments enable the extraction of information about the covariance matrix without the need for a coherent local oscillator. Here, we experimentally detect the entanglement properties of multimode Gaussian states using high-order\,(up to sixth-order) intensity correlation moments. These multimode Gaussian states are prepared via spontaneous and cascaded parametric down-conversion pumped by a high-peak-energy pulsed laser. Their intensity correlation moments are measured using a pseudo-photon-number-resolving detector constructed through spatial multiplexing of 32 threshold superconducting nanowire single photon detectors. This method is successfully demonstrated for two-mode and three-mode Gaussian states and can be extended to $N$-mode Gaussian states with $N>3$.

We prove a conjecture of Paquette, Rock, and Yildirim by showing that, for every thread quiver, the abelian category of pointwise finite dimensional representations is hereditary. Since this category typically lacks enough projectives and injectives, standard homological methods do not apply directly. Our approach combines a Yoneda Ext criterion for hereditariness, established in this paper, with structural reductions to the subcategory of quasi noise free representations. We also indicate an alternative proof using a Keller's theorem on derived categories.

Bosonic quantum error correction encodes a logical qubit in an oscillator, avoiding the hardware overhead of large qubit arrays. Among such encodings, Gottesman-Kitaev-Preskill (GKP) states are paticularly powerful because their phase-space grid structure protects against small displacement errors simultaneously in both conjugate quadratures. Here we provide the first protocol for preparing magnonic GKP states, which involves an ellipsoidal magnetic crystal effectively coupled to a superconducting qubit via a microwave cavity. The geometric anisotropy intrinsically squeezes the magnon mode, while the cavity-mediated qubit control realizes an effective conditional-displacement interaction. We show that two rounds of a conditional-displacement interaction and a qubit projective measurement yield three- and four-component magnonic GKP-like states. We also show how to realize single logical qubit gate operations, such as Pauli, Hadamard and phase gates, completing the logical Pauli basis of the approximate GKP code. Our results establish hybrid magnon-qubit systems as a promising platform for preparing bosonic code states, with applications in magnonic fault-tolerant quantum computation and quantum sensing.

\indent In this paper, we study a class of parabolic-elliptic Keller-Segel systems with diffusion sensitivity dependent on spatial position, given by type \begin{equation} \left\{ \begin{array}{ll} u_{t} = \bigtriangledown\cdot(|x|^β \bigtriangledown u)-\bigtriangledown\cdot(u^α \bigtriangledown v), 0=\bigtriangleup v-μ+u, \qquad μ:=\frac{1}{|Ω|}\int_Ωudx,\end{array}\right. \end{equation} under homogeneous Neumann conditions in a ball $Ω=B_{R}(0)\subset \mathbb{R}^{n}$ with $α\ge 1$, $β>0$ and $n\ge 2$.\par \indent It is proved that any nonconstant nonnegative radial initial data $u_{0}\in C^θ(\overlineΩ)$, where $θ\in (0,1)$, there exists a radially symmetric classical solution of the system (0.1) in $(Ω\setminus \{ 0 \})\times (0,T)$ for some $T>0$; moreover, if the initial values $u_{0}\in C^{1+θ}(\overlineΩ)$ for some $θ\in (0,1)$ and satisfy a certain compatibility criterion and are radially decreasing, then this solution is bounded and unique in $(Ω\setminus \{ 0 \})\times (0,T^{*})$ with $T^{*}<T$.\par Finally, it is found that the initial mass corresponding to this parabolic-elliptic problem (0.1) is sufficiently concentrated to allow the solution to blow up in finite time.

Boolean circuits form the foundational computational substrate of symmetric cryptography, yet the exploration of their architectural design space has remained largely confined to a handful of canonical paradigms - SPN, Feistel networks, and their immediate variants. This paper takes a deliberately broader perspective by formalizing the design space of cryptographic Boolean systems through six independent binary structural constraints: Stratification, Acyclicity, Regularity, Interleaving, Homogeneity, and Locality. These constraints generate a hypercube of $2^6 = 64$ distinct architectural classes defined over Synchronous Boolean Networks, a general model that subsumes both acyclic combinational circuits and recurrent synchronous systems. We systematically evaluate all 64 classes against three generic cryptanalytic fitness objectives - differential, linear and algebraic resistance - using a five-stage methodology centered on Formal Concept Analysis. The results reveal that the best Boolean networks are governed by the identification of sparse, mutually compatible combinations of constraints - a fundamentally epistatic problem that classical cryptography has barely addressed.

Significance: Jacobians, or spatially resolved sensitivity profiles, are central to image reconstruction in model-based optical tomography of biological tissue. Although Monte Carlo (MC) simulations are the gold standard for modeling light transport in turbid media, methodology for frequency- and time-domain Jacobians remains incomplete. Aim: This work extends MC to directly compute absorption and scattering Jacobians for frequency-domain (amplitude and phase) and time-domain (intensity and mean time-of-flight) measurements and prism-terminated optical fiber detectors. Approach: Jacobians are derived in the perturbation MC framework and implemented in the high-performance, open-source Monte Carlo eXtreme (MCX) simulator. Results are validated against the diffusion approximation (DA) solved using the finite element method in neonatal head models. MC with split voxels on curved surfaces is extended to Jacobian computation. The detector model is implemented in post-processing and compared with isotropic reception at surface. Results: MC- and DA-derived Jacobians show excellent agreement only in high-scattering regimes, highlighting the importance of MC for low-scattering domains. The detector model reduces surface sensitivity and marginally increases sensitivity to deeper tissues at short (< 2 cm) source-detector separations. Conclusion: A complete theoretical framework and MC software for computing frequency- and time-domain Jacobians is provided. Realistic detector modeling is encouraged for short-separation channels.