Roman domination and its higher-order extensions have attracted considerable attention due to their natural interpretation in terms of defensive resource allocation on networks. The recently introduced $[k]$-Roman domination framework unifies classical Roman, double, triple, and higher-strength protection schemes by allowing each fortified vertex to provide up to $k$ levels of support. In this paper, we investigate the $[k]$-Roman domination number $γ_{[k]R}(G)$ on cylindrical grids $C_m \Box P_n$. We relate $[k]$-Roman domination to efficient domination and show that for efficient graphs one has $γ_{[k]R}(G)=(k+1)γ(G)$; as a consequence, we obtain explicit values for broad families of toroidal grids and determine exactly when the cylindrical graphs $C_m\Box P_n$ admit an efficient dominating set. Building on these structural insights, we derive several upper bounds for $γ_{[k]R}(C_m \Box P_n)$ for small fixed values of $m$, accompanied by explicit labeling patterns that attain these bounds. All obtained bounds are systematically compared, revealing parameter ranges in which different constructions dominate depending on the value of $k$ and the length of the path. In addition, we present exact packing numbers for selected cylindrical graphs, which complement the domination results and enable further refinements via local weight reductions. Our results extend and unify known domination-type parameters on grid-like structures and highlight new regularities that emerge as the reinforcement strength increases.

In this paper, we constrain the diffusive dark fluid cosmological model, which is the interacting dark energy framework, wherein energy is transferred between the two dark components through a diffusion process. We extended the work by S. Sahlu et al. (2026) by employing Cosmic Microwave Background (CMB) data from the Planck 2018 measurements in combination with Baryon Acoustic Oscillation (BAO) data from the Dark Energy Spectroscopic Instrument (DESI) DR2 (2024).From the results, we found that the discrepancies in $H_0$ measurements are $0.0105σ$ and $1.29σ$ between the Planck 2018 value $(H_0 = 67.4\pm0.5\ \mathrm{km,s^{-1},Mpc^{-1}})$ and our diffusive model values, $H_0 = 67.3876^{+1.0765}_{-1.0709}$ and $68.3804^{+0.5639}_{-0.5852}$, respectively. We also the we observe that the effects of the interaction on cosmic evolution and structure formation; we emphasize this by computing the scale-dependent density contrast and the matter power spectrum, compared with the $Λ$CDM model.

In a {\em grounded string representation} of a graph there is a horizontal line $\ell$ and each vertex is represented as a simple curve below $\ell$ with one end point on $\ell$ such that two curves intersect if and only if the respective vertices are adjacent. A grounded string representation is a {\em grounded L-reverseL-representation} if each vertex is represented by a 1-bend orthogonal polyline. It is a {\em grounded L-representation} if in addition all curves are L-shaped. We show that every biconnected series-parallel graph without edges between the two vertices of a separation pair (i.e., {\em transitive edges}) admits a grounded L-reverseL-representation if and only if it admits a grounded string representation. Moreover, we can test in linear time whether such a representation exists. We also construct a biconnected series-parallel graph without transitive edges that admits a grounded L-reverseL-representation, but no grounded L-representation.

This work presents a comprehensive phase-field framework for modeling anisotropic viscoelastic-viscoplastic fracture in short fiber-reinforced polymer (SFRP) composites under hygrothermal environments at finite deformation. The constitutive model employs a multiplicative decomposition of the deformation gradient into viscoelastic and viscoplastic components. An anisotropic phase-field formulation is developed using structural tensors to capture orientation-dependent fracture energy induced by multiple fiber families. Hygrothermal effects are incorporated through moisture-dependent swelling, thermal expansion, and temperature- and moisture-sensitive material parameters within the coupled framework. Numerical investigations demonstrate the framework's capability to capture complex fracture phenomena in SFRPs. Results reveal that fiber orientation fundamentally governs the spatial distribution of crack driving force, with maximum energy accumulation along fiber directions persisting throughout viscous relaxation. The anisotropy parameter controlling directional fracture resistance significantly influences crack path deflection. Hygrothermal degradation substantially reduces both peak load and fracture energy, with moisture absorption and elevated temperature each contributing to decreased mechanical performance. The framework captures the influence of fiber mechanical properties on global load-bearing capacity and crack propagation resistance. This unified computational framework advances the predictive modeling of damage evolution in SFRPs subjected to realistic environmental and mechanical loading conditions.

We study the Directed Steiner Tree (DST) problem in layered graphs through a simple path-based linear programming relaxation. This relaxation achieves an integrality gap of O(l log k), where k is the number of terminals and l is the number of layers, which matches the best known bounds for DST previously obtained via lift-and-project hierarchies. Our formulation bypasses hierarchy machinery, offering a more transparent route to the state-of-the-art bound, and it can be exploited to provide an alternative simpler proof that O(l) rounds of the Sherali-Adams hierarchy suffice for reducing the integrality gap on layered instances of DST.

We study the problem of global extremum seeking in the presence of local extrema. We investigate two different perturbation-based methods: 1) a well-known classical extremum seeking scheme for steady-state output optimization, and 2) a source seeking scheme for a two-dimensional point mass. In each of these two scenarios, the closed-loop system involves a damped double integrator subject to an oscillatory force. An averaging analysis reveals that the respective averaged system is again a damped double integrator, but now subject to a potential force. The potential force is given by the gradient of a locally averaged objective function. Such a function is less prone to have undesired local extrema and is therefore better suited for global optimization. We provide sufficient conditions for semi-global practical uniform asymptotic stability of the closed-loop systems. The sufficient conditions only involve assumptions on the averaged objective function but not the original one.

We introduce and study doubly twisted near-isometries. A doubly twisted near-isometry is a tuple of near-isometries satisfying certain relations determined by a prescribed family of unitaries, thereby generalizing the notion of doubly commuting near-isometries. We establish necessary and sufficient conditions for a tuple of near-isometries to admit a Wold-type decomposition and prove that the existence of such a decomposition automatically ensures its uniqueness by providing an explicit description of the summands. Furthermore, we show that every doubly twisted near-isometry admits a Wold-type decomposition. We also characterize unitary equivalence within the class of doubly twisted near-isometries and construct an analytic model for them. Several examples are included to highlight the distinctions between our results and the corresponding results in the setting of doubly twisted isometries.

Annotated English translation of Duleau's "Notice sur A. Fresnel" in Revue encyclopédique, vol.39, pp.558-67 (September 1828), and of the shorter obituary for Fresnel in id., vol.37, pp.316-7.

Exploiting many-body interaction and critical phenomena to improve the performance of quantum batteries is an emerging and promising line of research. A central question in this direction is whether quantum phase transitions can enhance the charging energy or the power. While preliminary works have addressed this problem in fine-tuned integrable models, its characterization in non-integrable systems remains limited due to the demanding numerical requirements. Here, we investigate a one-dimensional Axial Next-Nearest-Neighbor Ising model as an example of non-integrable quantum battery charged via a quantum-quench protocol. In contrast to integrable cases, we find that criticality in this setting can lead to a pronounced enhancement of the charging power. Our findings inform quantum-battery design of many-qubit systems and are amenable to experimental verification on current quantum-simulation platforms, including neutral-atom arrays.

Strong electron correlation drives 1T-TaS2 from a half-filled metallic state into a Mott insulating phase, coexisting with a charge density wave at low temperatures. Under external stimuli such as pressure or ionic gating, superconductivity emerges in 1T-TaS2, exhibiting an intricate relationship of competition and coexistence with the charge density wave order. In the two-dimensional (2D) limit, enhanced quantum fluctuations can stabilize a quantum spin liquid (QSL) state in the Mott insulator. This review summarizes recent advances in understanding these quantum states in 2D 1T-TaS2 from the perspective of angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM), with a focus on the dimensionality effect on its electronic structure. We outline the signatures of QSL state in electronic spectra and discuss how this state can be revealed in the family of this material through experimental approaches beyond conventional probes such as neutron scattering. The role of Kondo effect in detecting spinon excitations is further discussed. Finally, we suggest future experimental directions and highlight how external perturbations such as gating and light excitation offer versatile pathways to control and exploit these intertwined quantum states.

We prove global convergence in function space for the steepest descent method in shape optimisation with semilinear elliptic partial differential equations. Steepest descent is realized in the Lipschitz topology. In addition, we prove a conditional convergence result for the resulting shapes in two space dimensions.

We present a finite element formulation for incompressible viscous flow based on the principle of minimum pressure gradient (PMPG). This variational principle, recently established by Taha, Gonzalez & Shorbagy (Phys. Fluids, vol. 35, 2023), states that the Navier-Stokes equations are equivalent to determining the rate of change of velocity at each instant by minimizing the L2 norm of the implied pressure gradient, subject to incompressibility and boundary conditions. We discretize the PMPG functional directly using Q9 biquadratic finite elements and minimize over the nodal velocity rates (Rayleigh-Ritz). No pressure degrees of freedom appear; incompressibility and boundary conditions are enforced as linear equality constraints through a monolithic saddle-point system, whose Lagrange multipliers provide wall forces without pressure reconstruction. We verify the formulation against exact Poiseuille flow (machine-precision recovery) and the Kovasznay solution (convergence rate ~3.3), and validate it against published benchmarks for the lid-driven cavity, the backward-facing step, and flow past a circular cylinder. The formulation produces smooth, oscillation-free solutions on coarse meshes in the convection-dominated regime without stabilization. We further show that the element-wise PMPG functional density serves as a built-in error indicator for adaptive mesh refinement, and that the stationarity condition can be read backwards to estimate the kinematic viscosity directly from velocity field measurements.

The multiscale picture of hydrogen embrittlement (HE) mechanisms has been under controversy for a long time. Here I report a thermomechanically-consistent HERB framework driven by the Rice-Beltz concept meanwhile incorporating the hydrogen transport near the crack-tip and void growth within the plastic zone. Triggered solely by dislocation emission from the crack tip, the HERB theory unifies multiple HE mechanisms, such as HEDE, HELP, NVC and HESIV within a single framework. Specifically, a generalized model for predicting the hydrogen-informed dislocation emission is established by incorporating the Rice-Beltz model with the transition state theory. Accounting for the dynamic variation of the trapping energy of spherical inclusions, hydrogen transport is modeled in the dislocation free zone in front of the crack tip. Semi-analytical expressions of the density of geometrically necessary dislocations are obtained by incorporating the Hutchinson-Rice-Rosengren solution with the conventional theory of mechanism-based strain gradient plasticity model. By exploring the feasibility of stochastic analysis, the present theory demonstrates that the hydrogen-informed void dynamics is dominated by the dislocation density between the limits of Lifshitz-Allen-Cahn and Lifshitz-Slyozov-Wagner laws, even though individual events remain unpredictable. These insights fundamentally reshape hydrogen/dislocation interactions across multiple scales, including the core width, short-range and long-range levels.

Quantum Federated Learning (QFL) enables distributed training of Quantum Machine Learning (QML) models by sharing model gradients instead of raw data. However, these gradients can still expose sensitive user information. To enhance privacy, homomorphic encryption of parameters has been proposed as a solution in QFL and related frameworks. In this work, we evaluate the overhead introduced by Fully Homomorphic Encryption (FHE) in QFL setups and assess its feasibility for real-world applications. We implemented various QML models including a Quantum Convolutional Neural Network (QCNN) trained in a federated environment with parameters encrypted using the CKKS scheme. This work marks the first QCNN trained in a federated setting with CKKS-encrypted parameters. Models of varying architectures were trained to predict brain tumors from MRI scans. The experiments reveal that memory and communication overhead remain substantial, making FHE challenging to deploy. Minimizing overhead requires reducing the number of model parameters, which, however, leads to a decline in classification performance, introducing a trade-off between privacy and model complexity.

We offer a measure-theoretic extension of the concept and theory of $k$-contraction, including their generalization on fractional dimensions $d$. The respective contraction property is defined through the exponential decay of the $d$-dimensional volume of compact sets transported by a nonlinear flow. For autonomous systems on positively invariant compact sets, we derive comprehensive, i.e., necessary and sufficient, conditions for $d$-contractivity in two complementary forms. The first is expressed in terms of the finite-time Lyapunov characteristic exponents and is akin in spirit to the first Lyapunov method. The second one is consonant with the second Lyapunov method and relies on existence of a Riemannian metric ensuring exponential decay of the metric-induced $d$-dimensional Hausdorff measure. To acquire monotone measure-theoretic-based Lyapunov functions, we introduce a family of \emph{Hausdorff-Riemann measures}, which are elliptic, metric-dependent $d$-measures that strictly decrease along the trajectories and thus may serve as Lyapunov functions. These measures enable an anytime characterization of the rate of contraction and provide constructive tools for stability analysis and feedback design. To illustrate the applicability of the approach, we derive tractable criteria for orbital stability of periodic solutions of autonomous ODE's and employ several prototypical particular examples, including a rigid body with dissipation and constant torque, the Rössler system, and the Langford system.

Motivated by targeted drug delivery, we investigate the gathering of particles in the full tilt model of externally controlled motion planning: A set of particles is located at the tiles of a polyomino with all particles reacting uniformly to an external force by moving as far as possible in one of the four axis-parallel directions until they hit the boundary. The goal is to choose a sequence of directions that moves all particles to a common position. Our results include a polynomial-time algorithm for gathering in a completely filled polyomino as well as hardness reductions for approximating shortest gathering sequences and for determining whether the particles in a partially filled polyomino can be gathered. We pay special attention to the impact of restricted geometry, particularly polyominoes without holes. As corollaries, we make progress on an open question from [Balanza-Martinez et al., SODA 2020] by showing that deciding whether a given position can be occupied remains NP-hard in polyominoes without holes and provide initial results on the parameterized complexity of tilt problems. Our results build on a connection we establish between tilt models and the theory of synchronizing automata.

We study a one-dimensional McKean-Vlasov stochastic differential equation (SDE) with a drift equal to a product of a distribution depending on the state of the process and a non-linear function depending pointwise on the law density of the solution. Building on recent well-posedness results, we propose the first implementable numerical scheme for this class of SDEs. Our approach combines mollification of the distributional drift with the Euler-Maruyama scheme and a PDE-based approximation of the law via the associated Fokker-Planck equation. We prove strong convergence of the scheme and derive an explicit rate, showing how to balance the smoothing parameter with the time discretisation. Numerical experiments confirm the applicability of our scheme and demonstrate the significant influence of the McKean interaction term on the law of the solution.

Let $\mathcal{F}=\{A_1,A_2,\ldots,A_k\}$ be a collection of finite arithmetic progressions, where each $A_d$ is an initial segment of the set $D_d=\{d,2d,3d,\ldots\}$ of consecutive multiples of a positive integer $d$. Let $m(\mathcal{F})$ denote the minimum length of an interval containing pairwise disjoint \emph{shifted} copies of all members of the family $\mathcal{F}$. We study this parameter in the following two cases: for a fixed positive integer $n$, (1) each progression in $\mathcal{F}$ has the form $A_d=D_d\cap\{1,2,\ldots,n\}$, and (2) all progressions $A_d$ of $\mathcal{F}$ have the same size $n$, that is, $A_d=D_d\cap \{1,2,\ldots, nd\}$. We in particular derive the following asymptotic estimates. In case (1), when $k=n$, we get $m(\mathcal{F})=Θ(n^{3/2}/\ln n)$. In case (2), when $k=n$, we get $m(\mathcal{F})=Θ(n^3/\ln n)$, while if $k>k_0(n)$, then $m(\mathcal{F}) < 3kn$. In both cases we additionally determine $m(\mathcal{F})$ asymptotically or settle its order of magnitude for all $k<n$.

This paper proposes a point-to-point passive optical network (P2P-PON) architecture as an energy-efficient and low-latency backhaul solution for visible light communication (VLC)-enabled indoor fog computing systems. The proposed architecture passively interconnects VLC access points and distributed in-building fog servers through dedicated optical links, enabling flexible peer-to-peer connectivity and efficient traffic aggregation. A mixed integer linear programming (MILP) framework is developed to jointly optimize processing resource allocation, traffic routing, power consumption, and end-to-end queuing delay across a multi-layer fog computing infrastructure. The model explicitly captures the power consumption of both networking and processing elements and incorporates a piecewise linear approximation of an M/M/1 queuing model to represent delay-sensitive applications. The performance of the proposed P2P-PON architecture is evaluated and compared against an arrayed waveguide grating router (AWGR)-based PON architecture under multiple indoor traffic scenarios. The results show that the proposed P2P-PON architecture reduces total power consumption by up to 64\% under power-aware optimization and by 15\% under delay-aware optimization, while reducing average end-to-end queuing delay by up to 76\% compared to the AWGR-PON architecture, due to the improved in-building connectivity and more effective utilization of distributed fog resources.

Optimization algorithms are unlikely to converge to strict saddle points. Proofs to that effect rely on the Center-Stable Manifold Theorem (CSMT), casting algorithms as dynamical systems: $x_{k+1} = g_k(x_k)$. In its standard form, the CSMT is limited to autonomous systems (the maps $g_k$ are all the same). To study algorithms such as gradient descent with non-constant step-size schedules, we need a non-autonomous CSMT. There are a few, but they are unable to handle, for example, vanishing step sizes. To cover such scenarios, we establish a new Center-Stable Set Theorem (CSST) for non-autonomous systems. We use it to prove saddle avoidance for gradient descent (Euclidean and Riemannian) and for the proximal point method, without assuming Lipschitz gradients or isolated saddles, and allowing vanishing step sizes.

We present a detailed polarimetric analysis of Cen X-3 using \ixpe observations during its high state, revealing complex energy-dependent polarization behavior. While phase-averaged polarization shows marginal energy dependence, phase-resolved analysis reveals that the energy dependence of the polarization angle (PA) is strongly phase-dependent, with dramatic variations visible in a few specific phase intervals. We model this behavior using a two-component polarization framework consisting of a pulsed component governed by the Rotating Vector Model (RVM) and an additional phase-dependent component. By allowing the additional component's polarized flux to vary with pulse phase while fixing its PA, the observed complex behavior can be reconciled with a single set of RVM parameters across all energies. Spectroscopic analysis using \ixpe, \nicer and \nustar during the high state reveals phase-modulated intrinsic hydrogen column density and covering fraction, suggesting that the wind properties are modulated with pulse phase. Our findings indicate that phase-dependent scattering in the disk wind may significantly alter the observed polarization properties of X-ray pulsars.

Laminar drag reduction is a critical technology for enhancing the endurance and station-keeping capabilities of airship platforms. However, existing transport-based transition models fail to account for the premature transition induced by wall heating, a limitation that significantly hinders the robust engineering application of laminar-flow technology in realistic thermal environments.To address this deficiency, this study first develops stability-based correction for transition modeling that explicitly incorporates wall-to-freestream temperature ratios. Leveraging the Falkner--Skan--Cooke (FSC) equations and linear stability theory (LST) with the $e^N$ method, we derive physics-based correlations for the transition criteria as functions of the temperature ratio, pressure gradient, and turbulence intensity. These corrections are integrated into a simplified stability-based transition transport model proposed by \citet{franccois2023simplified} and validated against the classic Schubauer and Klebanoff flat-plate experiments, demonstrating accurate prediction of transition locations under adiabatic, heated, and cooled conditions. Crucially, wind-tunnel experiments on a heated airship model show that wall-heating sensitivity is strongly influenced by local pressure-gradient variations, which is due to Reynolds-number-driven transition-location shifts. The proposed model successfully reproduces the experimentally observed transition advancement caused by wall heating. This framework, covering both heating and cooling regimes, provides a capability to support future laminar-flow control technologies based on wall-temperature modulation.

Reliable simultaneous optical sensing of pressure and temperature under extreme and dynamically fluctuating conditions remains a major challenge due to intrinsic cross-sensitivity between these two thermodynamic parameters. Multimodal systems enabling simultaneous yet fully decoupled monitoring of both parameters are therefore highly sought after. Here, we demonstrate that the synergistic interplay between Cr3+ and Ni2+ luminescence provides a platform for bifunctional temperature-pressure sensing with independent readout channels. Two complementary detection strategies were systematically investigated: ratiometric approach based on luminescence intensity ratio and kinetic approaches exploiting emission decay dynamics. Among the kinetic strategies, a time-gated dual-ion lifetime concept - introduced here for the first time for luminescence manometry - enables pressure readout with record-high relative sensitivity reaching 148.33% GPa-1 while exhibiting complete immunity to temperature fluctuations. Conversely, temperature sensing is achieved via time-gated single-ion Ni2+ luminescence, ensuring high thermometric performance with negligible pressure-induced interference. Importantly, this work study, for the first time, the potential of Ni2+ ions for application in near-infrared luminescence manometry. The unique combination of ultrahigh sensitivity, multimodal readout capability, and possibility of near-infrared operation positions the Ni2+-Cr3+ luminescence synergy as a benchmark platform for next-generation bifunctional optical sensors, enabling reliable operation in complex, dynamically evolving, and optically demanding environments.

Directed transport is a characteristic feature of numerous biological systems in response to signals such as nutrient and chemical gradients. These signals often depend on time owing to the high complexity of interactions in these systems. In this study, we focus on the steady-state behavior of polymeric systems responding to such time-dependent signals. We model them as ideal Rouse polymers submerged in a nonequilibrium bath, which is described by a spatially and temporally varying self-propulsion wave field. Through a coarse-graining analysis, we show that these polymers display rich emergent response to the temporal stimuli as a function of their length and topology. In particular, long polymers and structures with ring and star topologies ride the wave, displaying a positive drift in the direction of the wave. Whereas, shorter polymers and fully connected structures drift against the wave signal. We confirm these analytical predictions with robust numerical simulations, showing that the response of polymeric systems to temporal stimuli can be controlled by the topology or the length of the polymer.

Liquid is a fundamental requirement for life as we understand it, but whether that liquid has to be water is not known. We propose the hypothesis that ionic liquids (ILs) and deep eutectic solvents (DES) constitute a class of non-aqueous planetary liquids capable of persisting on a wide range of bodies where stable liquid water cannot exist. This hypothesis is motivated by key physical properties of ILs and DES. Many exhibit vapor pressures orders of magnitude lower than that of water and remain liquid across exceptionally wide temperature ranges, from cryogenic to well above terrestrial temperatures. These properties permit stable liquids to exist where liquid water would rapidly evaporate or freeze and outside of bulk phases as persistent microscale reservoirs-such as thin films and pore-filling droplets. In other words, ILs and DES can persist in environments without requiring oceans, thick atmospheres, or narrowly regulated climate conditions. We further hypothesize that ILs and DES could act as solvents for non-Earth-like life. Our hypothesis ex-tends to the idea that ILs and DES could enable prebiotic chemistry by providing long-lived, protective liquid environments for complex organic molecules on bodies such as comets and asteroids, where liquid water is absent. Based on the occurrence of DES-like mixtures as protective intracellular liquids in desiccation-tolerant plants, we propose that ILs and DES might be solvents that life elsewhere purposefully evolves. We review protein and other biomolecule studies in ILs and DES and outline planetary environments in which ILs and DES might occur by discussing available anions and cations. We present strategies to advance the IL/DES solvent hypothesis using laboratory studies, computational chemistry, planetary missions, analysis of existing spectroscopic datasets, and modeling of liquid microniches and chemical survival on small bodies.

By constructing a suitable coupling by change of measures, the asymptotic log- Harnack inequality is established for a class of degenerate SPDEs with reflection. This inequality implies the asymptotic heat kernel estimate, the uniqueness of the invariant probability measure, the asymptotic gradient estimate (hence, asymptotically strong Feller property), and the asymptotic irreducibility. As application, the main result is illustrated by d-dimensional degenerate stochastic Navie-Stokes equations with reflection, where the dissipative operator is the Dirichlet Laplacian with a power θ\geq 1 \vee \frac{d+2}{4}, which includes the Laplacian when d \geq 2.

The Ising model, originally proposed a century ago, has become a cornerstone of combinatorial optimization in recent decades. However, Ising machines remain constrained by a fundamental hardware-speed trade-off. We introduce the Bounce-Bind Ising Machine (BBIM), a mechanism with a single tunable parameter that modulates spin dynamics without altering the energy landscape, building upon the classic golf-ball analogy but replacing it with a dynamic tennis ball/shot put system. The Bounce mode (accelerating escapes from local minima) and Bind mode (enabling rapid convergence) dynamically balance speed and quality. Benchmarked on dense MAX-CUT (edge density=0.5), BBIM achieves a peak speedup of 6.15 times at n=200. For sparse 3-Regular 3-XORSAT (second-order), the peak speedup reaches 27.3 times at n=160. Both results incur negligible additional hardware resource consumption. This work demonstrates a critical pathway to circumventing the hardware-speed bottleneck and its practical applicability to large-scale optimization hardware, validated on structurally distinct benchmarks.

Autocatalytic cores are minimal units in reaction networks (RNs) responsible for the emergence of autocatalysis. In the absence of explicit catalysis, i.e., when an entity appears both as reactant and product in the same reaction, they are known to be encoded by square submatrices of the stoichiometric matrix whose columns can be reordered as an irreducible child-selection (CS) matrix with negative diagonal and nonnegative off-diagonal (Metzler matrix). In the bipartite Koenig graph representing the RN, these CS matrices can be identified by fluffles, i.e., strong blocks with an identical number of entity and reaction vertices that have out- and in-degree 1, respectively. Here, we adapt the concepts derived for autocatalytic cores to RNs with explicitly catalyzed reactions, which emerge as digons, i.e., elementary circuits in the Koenig graph of length 2. In this setting, we confirm that an inspection of the stoichiometric matrix alone is inconclusive concerning the presence and number of autocatalytic cores, requiring a more delicate algebraic analysis. Nevertheless, this generalization preserves both the graph and the matrix representation as fluffles and irreducible Metzler CS matrices, respectively, although the diagonal is no longer necessarily strictly negative. We introduce the notion of hard autocatalytic cores, i.e. those that do not yield other autocatalytic cores upon inclusion of all reverse reactions. Finally, we consider the case of unit stoichiometries and show that each autocatalytic core can be constructed as the superposition of at most 2 elementary circuits. In particular, autocatalytic cores involving explicitly catalyzed reactions always contain a spanning subgraph consisting of a single elementary circuit together with a simple entity-to-reaction chord. Moreover, we identify the essentially unique example for which at least two circuits are required.

In this paper, we consider a synthetic aperture secure beamforming approach for a virtual multiple-input multiple output (MIMO) broadcast channel in the presence of hybrid wiretapping environments. Our goal is to design the flight node deployment constructed by a single-antenna mobile autonomous aerial vehicle (AAV), corresponding transmission symbol strategy, transmit precoding, and received beamforming to maximize the system channel capacity. Leveraging the synthetic aperture beamforming, we aim to provide spatial gain along a predefined angle in free space while reducing it in others and thus enhance physical layer (PHY) security. To this end, we analyze the expression of the asymptotic channel eigenvalues to optimize the AAV flight node deployment. For the optimal precoding design, an energy-efficient method that minimizes the transmit power consumption is studied based on the given virtual MIMO channel, while meeting the quality of service (QoS) for the base station (BS), leakage tolerance of eavesdroppers (Eves), and per-node power constraints. The power minimization problem is a non convex program, which is then reformulated as a tractable form after some mathematical manipulations. Moreover, we design the received beamforming by applying the linearly constrained minimum variance (LCMV) method such that the jamming can be effectively suppressed. Numerical results demonstrate the superiority of the proposed method in promoting capacity.

We present updated inclusive cross sections for electroweak Higgs boson pair production for energies of relevance to the LHC and High-Luminosity phase of the LHC. The cross sections are presented at N$^3$LO QCD+NLO EW for vector-boson fusion and NNLO QCD for associate production with a vector boson. We compute the cross sections using the most up-to-date theory inputs, both in the Standard Model and for a few anomalous values of the trilinear Higgs self-coupling.