Nested counter systems (NCS) are a generalization of counter systems to higher-order counters. Here, a higher-order counter is allowed to have other (lower-order) counters as elements, instead of just a number. Such systems can be viewed as working on trees, where the height of the tree naturally corresponds to the highest order counter that the system is working with. It is known that the coverability problem for NCS, which asks if a given final tree can be covered from a given initial tree, is $\mathbf{F}_{ε_0}$-complete. Here $\mathbf{F}_{ε_0}$ is a class in the fast-growing hierarchy of complexity classes. In this paper, we consider an extension of NCS called nested reset counter systems (NRCS) that extends NCS with resets. We show that coverability for NRCS over order-$k$ counters is $\mathbf{F}_{Ω_k}$-complete where $Ω_k$ is the tower of height $k$ of the $ω$ ordinal. This gives the first natural hierarchy of complete problems for all of these classes. Furthermore, to prove our upper bounds, we also develop length function theorems for any fixed amount of applications of the multiset operation on finite sets. As an application of our results, we improve existing upper bounds for various problems from XML processing, graph transformation systems, $π$-calculus, logic and parameterized verification. Furthermore, using our completeness results for $k$-NRCS, we also prove $\mathbf{F}_{Ω_k}$-completeness of the considered problems from the realms of parameterized verification and logic, for all $k$.

LLM-driven conversational AI is beginning to disappear into the background, shifting from something used directly towards something increasingly integrated into existing workflows. In the process, markers of origin and training are smoothed away as LLMs become commodified in the eyes of users. We explore how people approach using a web browser with conversational AI built in, focusing on how they develop their understanding and determine whether to trust its outputs. We conducted a study where 20 participants used the Copilot AI features in Microsoft Edge to conduct information retrieval and planning tasks. Participants relied on a combination of existing perceptions of LLMs and internet search, tracing the effect of beliefs about how Copilot generated answers on prompting strategies. The inclusion of citations increased the trustworthiness of answers without participants feeling the need to be check them, with participants often reaching for the same information sources as the CAI when fact-checking.

We propose a data-driven Model Predictive Control (MPC) framework that employs a transformer encoder to generate multi-step predictions. To handle the nonconvex attention mechanism, we derive difference of convex (DC) representations of the transformer encoder components and embed them in a successive convex programming (SCP) iteration. Recursive feasibility and convergence of the SCP iterates are guaranteed, and each iterate yields a solution estimate satisfying the problem constraints. Under mild assumptions, the SCP iteration converges to a locally optimal solution of the MPC problem. The approach is illustrated on a benchmark nonlinear control problem.

Affine frequency division multiplexing (AFDM) has recently emerged as a promising waveform for high-mobility communications due to its resilience to Doppler effects and its advantages for integrated sensing and communication (ISAC). AFDM modulates transmit data symbols using chirp subcarriers with two adjustable parameters. One is used for dealing with the Doppler effect and the second parameter can be used for physical layer security (PLS). In this paper, we focus on designing the second chirp parameter in the form of a generic phase function to enhance the robustness of the waveform against brute-force demodulation by the eavesdropper. In particular, we first derive a design criterion that reveals the brute-force demodulation complexity depends on the first derivative of the phase function. Then, we introduce a family of phase functions that can increase the brute-force demodulation complexity in an unbounded and controllable manner, while preserving chirp structure of AFDM. Our simulation results demonstrate that the proposed phase function design enhances the PLS performance of AFDM by several orders of magnitude compared with the conventional AFDM in terms of brute-force demodulation complexity.

Problems defined on binary decision spaces have been intensively studied in the theory of multi-objective evolutionary algorithms (MOEAs). In contrast, no mathematical runtime analyses exist so far for MOEAs dealing with decision variables that take a finite number $r > 2$ of values, despite the prevalence of such problems in practice. In this work, we begin to fill this research gap. We analyze how the classic SEMO algorithm with unit-strength local mutation computes the Pareto front of an $r$-valued counterpart of the classic \oneminmax benchmark. For the expected number of function evaluations until the Pareto front is covered by the population of this MOEA, we prove an upper bound of $O(n^2 r^2 \log n)$ and a near-tight lower bound of $Ω(n^2 r (r + \log n))$. We can close the small remaining gap between these two bounds by considering a variant of the algorithm that accepts only strictly better solutions; for this variant, we show an upper bound of $O(n^2 r (r + \log n))$, matching our lower bound (which also holds for this variant). Our results suggest that classic MOEAs encounter no significant additional difficulties when dealing with multi-valued decision variables. However, significantly more advanced tools may be required to obtain tight bounds for algorithms with more complex population dynamics.

Computer graphics algorithms for generating photorealistic imagery are widely perceived to be universal, and capable of conjuring anything that a filmmaker or game designer can imagine. However, recent works have suggested that 3D algorithms for depicting synthetic humans are far from generic, and instead favor historically hegemonic characteristics. We present the first systematic review of human depiction in the top computer graphics conference and the journal of record (SIGGRAPH and ACM Transactions on Graphics) that confirms previous hypotheses. Algorithms that claim to be generically rendering "human skin'' are in fact imagined and formulated for translucent, "high albedo" materials such as white skin. Algorithms claiming to apply generically to "human hair" are formulated for "rods", "wires" and "threads" which are analogous to straight hair. Our analysis reveals conceptual binarization, where algorithms for white skin are treated as computational substrate for "all" skin, imposing a hierarchical assumption that all skin descends from the math and physics of white skin. Hair algorithms follow a similar historical pattern, with the first examples of computer-generated Type 4 hair only appearing after the murder of George Floyd in 2020. We offer a new conceptual label, McDaniels Methods, for characterizing and critiquing computer graphics algorithms that reinforce racial hierarchy under a false cover of diversity. We also offer an inverse label, Durald Methods, for algorithms that were closely co-designed with the people being depicted. Our analysis points the way towards several neglected avenues for future research.

Single-photon detection possibility is a fundamental requirement for quantum technologies, including communication, computing and sensing. To achieve scalability and practical deployment, increasing attention is being directed toward integration of detectors with photonic integrated circuits, which offer compactness and compatibility with mass production. Superconducting nanowire single-photon detectors have emerged as the leading solution, combining near-unity efficiency, high temporal performance and the ability to be embedded across a wide range of photonic material platforms. In this review we trace the development of integrated superconducting nanowire single-photon detectors from early demonstrations to recent advances, outlining the progress in device architectures, material engineering and integration strategies. We also discuss performance benchmarks, emerging alternative designs, the future opportunities and challenges for this rapidly evolving field.

Matter under irradiation may enter unusual transient states, outside of its equilibrium phase diagram. One of such states is a superionic-like state, in which one sublattice of a compound liquifies, whereas another one remains solid. Here, we study theoretically post-transition metal oxides under ultrafast excitation of its electronic system, identifying which compounds produce such a superionic state. It is shown that oxides with sufficiently sparce metallic sublattices (e.g. corundum structure) generally form transient superionic states via nonthermal phase transition. More closely packed lattices (such as the zinc-blend structure in ZnO and CdO) do not exhibit superionicity. Tl and Pb oxides only enter thermally-produced superionic states (induced by the atomic heating via electron-phonon coupling), but not nonthermal ones. Sn and Bi oxides demonstrate states that cannot be clearly classified, in which oxygen subsystem diffuses significantly more and faster than the metallic one, but the metallic one is not stable as it would be in a truly superionic state.

Solid mineral-based particles have been proposed as alternatives to sulfates for climate intervention by stratospheric aerosol injection, as a means for improving optical or chemical characteristics and thereby minimize risks and uncertainties. However, the heterogeneous reactivity of solid particles with stratospheric trace gases, and possible implications to the ozone layer, is currently not fully constrained, particularly at stratospheric concentrations. We present a systematic comparative study of the uptake of HNO3, HCl, and NO2 on calcite, alumina, crystalline silica (quartz), and amorphous silica, using complementary Knudsen cell and flow reactor techniques. We find that NO2 uptake is weak on all surfaces, with estimated removal timescales indicating negligible impact on stratospheric nitrogen chemistry. Conversely, HCl uptake is substantial, with a pronounced concentration dependence consistent with surface site limited Langmuir adsorption. Extracting adsorption isotherms, we find that HCl surface coverage at stratospheric concentrations differs by four orders of magnitude between the surfaces, with calcite adsorbing the most and amorphous silica the least, suggesting a dominant role of surface acid-base character. Using HCl surface coverage as a proxy for ClONO2 reactive uptake, we estimate that amorphous silica could deplete substantially less ozone than calcite or alumina under equivalent injection scenarios. We find a marked difference between crystalline and amorphous silica, underscoring the sensitivity of heterogeneous chemistry to surface microstructure and the importance of selecting particles with low-reactivity surfaces in addition to considering bulk characteristics. Our findings motivate the development of particles with surfaces tailored for minimizing SAI risks and uncertainties, including minimal reactivity with stratospheric gases and background sulfate aerosols.

Statistical properties of light produced in spontaneous Raman scattering on an ensemble of molecules indicate the quantum nature of this phenomenon. The scattered light is non-classical and has high non-classical intensity correlations between Stokes and anti-Stokes components. The temporal coherence of this light is well investigated, while many questions related to spatial coherence remain open. Recent experiments reveal two peculiar features of the spatial coherence of the Stokes and anti-Stokes light. First, the intensity correlations between Stokes and anti-Stokes light remain non-classical even for macroscopic samples containing many molecules. Second, these correlations decrease when signal propagates through a multi-mode optical fiber: the more propagating fiber modes at Stokes and anti-Stokes frequencies the less the correlations. Moreover, the second-order autocorrelation function of Stokes and anti-Stokes light also decreases with the number of propagating modes in multi-mode fiber. In this paper, we build a model of spontaneous Raman scattering correlations of light produced by an ensemble of molecules and propagating through weakly guiding optical fiber that quantitatively explains all these observations. We show that spacial orthogonality of the fiber modes makes the light propagating through these modes uncorrelated in the standard detection scheme. This leads to suppression of non-classical intensity correlations of the total field in the multi-mode fiber. We find the degree of non-classical correlations on fiber parameters. The obtained results pave the way for engineering of non-classical Stokes -- anti-Stokes correlations.

In this paper, a class of linear authentication codes with secrecy are constructed, which have simple encoding rules and are easy to implement. Based on the special Weil sum, the maximum success probabilities of substitution attack and impersonation attack are calculated, and these codes are proven to be asymptotically optimal with respect to certain bounds.

We consider an extended model of quantum computation where a scalable fault-tolerant quantum computer is coupled to one or more ancilla qubits that evolve according to a nonlinear Schrödinger equation. Following the approach of Abrams and Lloyd, an efficient quantum circuit evaluating an $n$-bit Boolean function in conjunctive normal form is used to prepare an ancilla encoding its number $s$ of satisfying assignments ($0 \le s \le 2^n$). This is followed by a nonlinear quantum state discrimination gate on the ancilla qubit that is used to learn properties of $s$. Here we consider three types of state discriminators generated by different nonlinear Hamiltonians. First, given a restricted Boolean satisfiability problem with the promise of at most one satisfying assignment ($ 0 \le s \le 1$), we show that a qubit with $\langle σ^z \rangle σ^z$ nonlinearity can be used to efficiently determine whether $s = 0$ or $s = 1$, solving the UNIQUE SAT problem. Here $\langle A \rangle := \langle ψ| A |ψ\rangle $ denotes expectation in the current state. UNIQUE SAT is NP-hard under a randomized polynomial-time reduction (of course any discussion of complexity assumes a scalable, fault-tolerant implementation). Second, for unrestricted satisfiability problems with $ 0 \le s \le 2^n$, a Hamiltonian with $ \langle σ^x \rangle σ^y - \langle σ^y \rangle σ^x$ nonlinearity can be used to efficiently determine whether $s=0$ or $s>0$, thereby solving 3SAT, which is NP-complete. Finally, we show that $ \langle σ^y \rangle \langle σ^z \rangle σ^x - \langle σ^x \rangle \langle σ^z \rangle σ^y $ nonlinearity can be used to efficiently measure $s$ and solve #SAT, which is #P-complete. The nonlinear models are of mean field type and might be simulated with ultracold atoms.

The Heisenberg-Weyl group $HW(d)$ related to a $d$-dimensional Hilbert space $H(d)$, is enlarged into the Heisenberg-Weyl-parity group $HWP(d)$ that incorporates parity transformations. It consists of $2d^3$ elements, of which $d^3$ elements belong to the $HW(d)$ subgroup, and extra $d^3$ elements which are related through a Fourier transform with the former ones. It is shown that $HWP(d)$ is a generalised version of the dihedral group. The properties of operators that combine displacements and parity, are discussed. $HWP(d)$ is shown to be a solvable group, and commutators of its elements perform displacement and parity transformations of quantum states, along loops in the discrete phase space.$2d^2$ coherent states related to the $HWP(d)$ group are introduced, which consist of $d^2$ coherent states related to the $HW(d)$ subgroup, and extra $d^2$ coherent states which are related through a Fourier transform with the former ones. In noisy cases, expansion of an arbitrary state in terms of the $2d^2$ coherent states with Bargmann coefficients, is advantageous in comparison to expansion in terms of the $d^2$ coherent states related to $HW(d)$. One of the consequences of the $HWP(d)$ group, is a natural unification of the Wigner and Weyl functions. The properties of the unified Wigner-Weyl function are discussed.

Numerical methods for modeling thin-film magnetization are primarily focused on computing the current density distribution. The highly nonlinear current-voltage characteristic of type-II superconductors significantly complicates the accurate computation of the electric field. The T-E formulation-based mixed finite element method, previously derived for flat superconducting films, enables the simultaneous, accurate determination of both variables. Another advantage of this method is that the computational domain is limited to the film itself: no meshing of the surrounding space is required. The thin-shell approximation reduces the problem to a two-dimensional one. This work extends the T-E formulation and numerical method to non-flat superconducting shells with a metal substrate. We validate the method with several test examples, including modeling the magnetization of a sphere. The method is then applied to a realistic model of a cylindrical magnetic dynamo pump, and the generated open-circuit voltage is computed.

We consider finite pencils of Jacobi matrices \[ J_n(w)=A+wB, \] where $A$ is diagonal and $B$ is tridiagonal with zero diagonal. The spectral curve is the affine plane curve \[ χ_n(λ,w)=\det(λI+J_n(w))=0 . \] The main question is to describe when this curve is reducible. We prove generic irreducibility for fixed pairwise distinct diagonal entries and discuss several elementary reducibility mechanisms. Besides disconnected Jacobi chains, constant eigenvalue branches, and reflection-symmetric components, one must also take into account reducibility caused by scalar diagonal blocks. We formulate a reducibility conjecture and record low-dimensional evidence and counterexamples to several overly optimistic classifications. A central point of the picture is a codimension-growth principle: apart from the cutting divisors $b_i=0$, genuinely connected primitive reducibility should move to higher and higher codimension as the size of the chain grows.

The dynamical evolution of binary asteroid systems is deeply influenced by spin-orbit resonances. However, their domains of influence and mutual interactions remain elusive, in particular in the space where multiple resonant modes coexist. In such regimes, the standard single-resonance approach is intrinsically limited and fails to capture the true coupled dynamics. To overcome this, we develop a global Hamiltonian framework based on elliptic expansions of the spin-orbit coupling model, enabling the numerical construction of comprehensive resonant networks. Concentrating on a representative synchronous region that encompasses synchronous spin-orbit, spin-spin, spin-orbit-spin, and doubly synchronous resonances, we study the dynamical boundaries of different resonant modes in a systematical manner. Crucially, we identify a secondary resonance structure arising from the strong nonlinear coupling between the synchronous resonances of the primary and secondary asteroids. Ultimately, this study provides a reliable parameter-space atlas, which is helpful for predicting the long-term evolutionary pathways of binary asteroid systems.

Genome-scale metabolic models (GEMs) are essential tools for systems biology and rational chassis design, but conventional top-down reconstruction depends heavily on sequence homology and often leaves unknown enzymes and metabolic dark matter unresolved. Direct reconstruction from metabolomics is also difficult because mapping observed metabolites to reactions is an ill-posed inverse problem with combinatorial ambiguity and possible spurious networks. Here we present MetaGEM, a bottom-up framework that uses enzymes as physical anchors to convert system-level network inference into enzyme-metabolite interaction prediction. MetaGEM uses a multimodal dual-tower architecture that combines protein evolutionary semantics from a protein language model with three-dimensional metabolite representations. It further introduces contrastive learning with hard negative mining to separate structurally similar metabolites and reduce false positive interactions. On a de-homologized benchmark, MetaGEM achieves state-of-the-art enzyme-metabolite prediction performance, with AUROC of 0.9701 and MCC of 0.8033, and remains robust under low sequence identity splits. In downstream reconstruction, MetaGEM generates functional genome-scale metabolic models for Escherichia coli, Bacillus subtilis, and Pseudomonas aeruginosa. The reconstructed models improve network connectivity, capture promiscuous enzymes, and show strong agreement with experimental phenotype microarray and gene essentiality data. These results indicate that MetaGEM provides a practical route from metabolomic evidence to computable metabolic networks and offers a foundation for automated AI-driven virtual cell reconstruction.

Circumbinary planets (CBPs) currently identified are in nearly coplanar configurations relative to their host binaries, yet the dynamical origin of this preference remains unclear. We investigate this question by simulating the secular spin-orbit evolution of CBP systems with tidal decay. A representative case shows that the system evolves through three stages (coplanarization, spin-orbit synchronization, and spin-orbit alignment) through the angular momentum exchange between stellar spin and orbital motion. The evolution of mutual inclination is strongly coupled to stellar obliquity. Phase-space analysis and examination of stellar Cassini states reveal that arbitrary initial inclinations are gradually damped to coplanarity by tides, while stellar obliquity is adiabatically captured into Cassini states with diminishing oscillation amplitudes. This study provides a self-consistent analytical and numerical framework for determining stellar Cassini states and understanding coupled spin-orbit evolution in CBP systems. It shows that tidal dissipation, combined with adiabatic capture into Cassini states, drives the observed dynamical behavior.

One of the most common approaches for coupling optical single-photon sources and photonic integrated circuits is to use a cavity. The cavity acts as a spectral filter that distorts the light spectrum and changes its statistical properties. But in the general case one should take into account not only spectral filtering of light but also the spectral filter influence on the single-photon source dynamics. We build an effective analytical model for description of the cavity influence on the photon statistics of light emitted by the single-photon source as spectral filtering only. We show that this model correctly describes the photon statistics even in a strong-coupling regime between the single-photon source and the spectral filter. Our results can be useful for analytical modeling of photon statistics of quantum emitters strongly coupled to various electromagnetic interfaces.

Ruddlesden-Popper bilayer nickelates provide an emerging platform for studying high-temperature superconductivity, yet the superconducting pairing symmetry remains under debate. Here, we use atomic-resolution scanning tunnelling microscopy and spectroscopy to investigate superconducting 1.5-unit-cell (La,Pr)3Ni2O7 films grown on SrLaAlO4. A cryogenic ultrahigh-vacuum (UHV) sample transfer preserves an ordered sqrt(2) * sqrt(2) surface and yields reproducible U-shaped spectra with two gap scales of ~14 and ~20 meV and extended flat zero-conductance bottoms. By contrast, samples exposed for a longer time in UHV without cooling during transfer show V-shaped spectra despite retaining the surface reconstruction and a transport superconducting transition onset above 40 K. Wide-energy-range spectra indicate that oxygen loss can mix density-wave-related spectral weight. Our measurements provide an atomic-scale observation of the intrinsic nodeless superconducting gap in bilayer nickelate ultrathin films.

A cycle system of order $n$ is a decomposition of the edges of the complete graph $K_n$ into cycles of a fixed length. A cycle system is said to be $k$-colourable if we can assign $k$ colours to its vertices so that no cycle is monochromatic. A $k$-colourable cycle system is uniquely $k$-colourable if its colouring is unique up to the permutation of colour classes. In this paper, we construct uniquely $2$-colourable $4$-cycle systems of order $n$ for all admissible $n\geq 49$, and also uniquely $2$-colourable $4$-cycle decompositions of $K_n - I$, for all admissible $n \geq 50$. These constructions contribute to the broader study of uniquely colourable cycle systems and open new directions for future research.

Roger Penrose introduced the concept of the trapped surface: a spacelike hypersurface where the two null normals have negative expansion. The trapped surface along with the null convergence condition leads to null geodesic incompleteness. If an event horizon forms, the trapped surface is also always behind it, providing evidence for the weak cosmic censorship conjecture. When the null convergence condition is violated, as in the case of semiclassical gravity, trapped surfaces lose these guarantees. A generalized notion, the sufficiently trapped surface, accommodates weaker energy conditions consistent with quantum fields. This concept restores key roles in singularity and area theorems and continues to support the weak cosmic censorship conjecture.

Existing integer-valued autoregressive (INAR) models for count random fields suffer from difficulties in characterizing the stationary marginal distribution and in computing conditional probabilities (as required for likelihood inference). To overcome these drawbacks, the novel class of combined INAR (CINAR) models is proposed, which both exhibits the classical autoregressive dependence structure and allows to specify the marginal distribution within the wide class of discrete self-decomposable distributions. In particular, CINAR random fields can be equipped with a Poisson or negative-binomial marginal distribution. The CINAR's key stochastic properties are derived (including a simple expression for conditional probabilities), and special cases as well as possible extensions are discussed. Approaches for parameter estimation are developed and investigated, and the practical relevance of the novel CINAR family is demonstrated by an agricultural data application.

The AMPS firewall argument relies on treating early radiation, late outgoing Hawking modes, and interior partner modes as approximately independent quantum subsystems. In diffeomorphism-invariant quantum gravity, however, gravitational dressing and asymptotic constraints obstruct such a tensor-product factorization of physical observables. In this essay, we sharpen this obstruction by formulating subsystem independence directly in operator-algebraic terms. Using modular theory, half-sided modular inclusions along null directions, and the sector-wise maximality of the dressed radiation algebra at future null infinity, we show that -- within a fixed asymptotic charge sector -- the algebra associated with the interior Hawking partner cannot form an independent commuting subalgebra, but must be contained as a (non-commuting) subalgebra of the radiation algebra itself. The subsystem-independence assumption underlying the AMPS paradox therefore fails, and the entanglement-monogamy step never becomes applicable. As a result, unitary black hole evaporation and semiclassical horizon smoothness are compatible in asymptotically flat quantum gravity, without invoking entanglement islands, replica wormholes, or modifications of semiclassical horizon physics.

We investigate the melting behavior of calcium oxide (CaO) under extreme conditions, a problem that remains poorly constrained due to experimental limitations despite its relevance for geophysical and technological applications. We develop a Machine Learning Interatomic Potential (MLIP) for CaO with PANNA 2.0 and the LATTE descriptor, training it on a dataset of $\sim$12,000 configurations including solid, liquid, interfacial, and void-containing structures, extracted from ab-initio molecular dynamics data employing PBEsol exchange-correlation functional. We perform large-scale molecular dynamics simulations to compute the melting temperature at ambient pressure using both the void-nucleated melting (VNM) and two-phase coexistence (TPC) methods, obtaining $T_m=3055\pm11$ K and $T_m=2847\pm15$ K, respectively.\\ We calculate an enthalpy of fusion of $ΔH_f\sim73$ kJ/mol, in agreement with thermodynamic assessments and ab initio calculations. We also reproduce the thermal expansion and obtain a volume increase of $\sim$29% at Tm, consistent with the corresponding decrease in density extracted from spatially resolved number density profiles. Finally, we calculate the high-pressure melting curve of CaO up to 20 GPa, providing one of the very few computational determinations of this quantity to date. The results confirm that the overheating ratio $η$ is not constant under pressure, increasing from 17% at ambient pressure to 24% at 20 GPa, confirming previous findings and ruling out the assumption of a fixed overheating ratio. Our results establish MLIP-based simulations as a robust and efficient framework for investigating phase stability in ionic oxides and provide new insight into the melting behavior of CaO under extreme conditions.

The thermal expansion of natural FeWO$_4$ (ferberite) and synthetic FeWO$_4$:Fe$_2$WO$_6$ (7:1) was investigated over the 2-1123 K temperature range combining single-crystal and powder X-ray diffraction together with neutron powder diffraction. High-precision lattice parameters were obtained for both samples. The temperature dependence of the unit-cell volume was analysed using physically based thermodynamic models, including the Kroll and Berman approaches as implemented in EoSFit7. All datasets are well reproduced within their respective temperature intervals. However, significant differences are observed between the behavior of ferberite and FeWO$_4$:Fe$_2$WO$_6$, which has a \~40% smaller thermal expansion coefficient and a reduced reference volume. Possible origins, including microstructural and phase-coexistence effects, are discussed. The results provide a comprehensive description of the thermal expansion behavior of FeWO$_4$ across a wide temperature range.

Fully compressible numerical simulations of two-dimensional laminar lean hydrogen-air premixed flames have been performed, with the flame front subjected to acoustic forcing through the specification of a monopole-type sound source at the inflow. Simulations have been performed for acoustic frequencies ranging from 35~kHz to 500~kHz at two equivalence ratios, $ϕ= 0.4$ and $ϕ= 0.7$. During the flame-acoustic interaction, the flame evolves from an initially weakly stretched state to exponential perturbation growth, wrinkle interaction, and the formation of non-linear cellular structures, with distinct linear and non-linear stages identified from Fourier mode analysis. The instability dynamics depend strongly on both forcing frequency and equivalence ratio. In the case of $ϕ=0.4$, the flame behaviour is strongly influenced by thermodiffusive instability, with a characteristic sequence of uniform cells, cell splitting, and cell merging. For $ϕ=0.7$, weaker thermodiffusive effects result in a response more strongly governed by hydrodynamic instability and large-scale wrinkle growth. At low forcing frequencies, flame corrugations remain relatively uniform, whereas at high frequencies the flame front becomes increasingly modulated and develops envelope-like structures, which can be interpreted as the interaction between an intrinsic standing cellular mode and the imposed acoustic disturbance. In the linear growth regime, the density-weighted displacement speed, $S_d^*$, shows a linear correlation with total stretch rate, $K$, for all forcing frequencies. While in the non-linear growth regime, two distinct branches appear, corresponding to weakly stretched flame segments and strongly negatively curved segments associated with flame pinch-off.

Large-scale chemical plants rely on distributed process control systems (PCS) comprising numerous processing units, communication modules, and I/O devices interconnected via industrial networks. The design of a cost-efficient and reliable hardware architecture under partial uncertainty in plant parameters remains a challenging combinatorial optimization problem. This paper proposes a formal model for distributed control system hardware architecture synthesis. A hybrid ant colony-based metaheuristic framework is developed to construct feasible hierarchical architectures. The proposed approach is validated on a large-scale sulfuric acid plant control system case study. Plant parameters are identified from operational data, system stability is analyzed, and a controller synthesis is performed based on the optimized architecture. The results demonstrate the feasibility of the approach and confirm that the obtained architecture satisfies structural and dynamic performance requirements.

Optimal observables provide statistically powerful probes of small deformations from a reference theory, but in realistic collider measurements they are rarely available in compact analytic form. We show that interpretable event-level observables can be discovered by AI-driven symbolic evolution using score information from matrix-element reweighting as the statistical target. Focusing on the CP-sensitive interaction $HZ_{μν}\tilde Z^{μν}$, we study two complementary realizations of the same coupling structure: associated production $e^+e^-\to Z(\to μ^-μ^+)H$ and the decay channel $pp\to H\to ZZ^*\to e^-e^+μ^-μ^+$. The learned observables retain substantially more local Fisher information than standard angular baselines while remaining compact analytic functions. In both cases, the discovered expressions recover characteristic helicity-interference harmonics. In associated production these harmonics are supplemented by laboratory-frame asymmetry mappings, while in four-lepton decay the robust component is the angular kernel, with the mass-ratio factor serving as a bounded representative prefactor. These results recast optimal-observable design as a symbolic discovery problem and provide a transparent route to information-efficient, interpretable probes of collider interference.

In this paper, we extend the notion of directed clique complex to quivers and introduce an associated homology theory. By applying this construction to biquandle coloring quivers, we obtain new invariants of links. We then introduce a quiver filtration-valued invariant of links induced by filtrations of biquandle endomorphism sets. We construct persistent homological invariants of links by applying persistence techniques to these quiver filtrations through the introduced homology theory.