We construct a simple two-dimensional holographic model of a closed "baby" universe. The baby universe spacetime originates from the black hole interior in Jackiw-Teitelboim (JT) gravity. The holographic description is a low-temperature thermal pure state of two Sachdev-Ye-Kitaev (SYK) models. The construction of the state relies on the insertion of a heavy matter operator, which supports the baby universe, together with a first-order thermal phase transition between a black hole phase and an empty Anti de Sitter (AdS) phase. For the transition, we employ a version of the Maldacena-Qi phase transition of two coupled SYK systems. The bulk entanglement between the AdS region and the baby universe remains O(N) below the transition, owing to the large number of light bulk fields. This entanglement admits a definition through coarse-graining over SYK couplings.

We study nonparametric Bayesian binary classification, in the case where the unknown probability response function is possibly spatially inhomogeneous, for example, being generally flat across the domain but presenting localized sharp variations. We consider a hierarchical procedure based on the Besov-Laplace priors from the inverse problems and imaging literature, with a carefully tuned hyper-prior on the regularity parameter. We show that the resulting posterior distribution concentrates towards the ground truth at optimal rate, automatically adapting to the unknown regularity. To implement posterior inference in practice, we devise an efficient Markov chain Monte Carlo (MCMC) algorithm based on recent ad-hoc dimension-robust methods for Besov-Laplace priors. We then test the considered approach in extensive numerical simulations, where we obtain a solid corroboration of the theoretical results.

In this work, we propose a modified Hybrid Parallel Kolmogorov--Arnold Network and Multilayer Perceptron Physics-Informed Neural Network to overcome the high-frequency and multiscale challenges inherent in Physics-Informed Neural Networks. This proposed model features a trainable weighting parameter to optimize the convex combination of outputs from the Kolmogorov--Arnold Network and the Multilayer Perceptron, thus maximizing the networks' capabilities to capture different frequency components. Furthermore, we adopt an overlapping domain decomposition technique to decompose complex problems into subproblems, which alleviates the challenge of global optimization. Benchmark results demonstrate that our method reduces training costs and improves computational efficiency compared with manual hyperparameter tuning in solving high-frequency multiscale problems.

This review paper uses renormalization group techniques for signal detection in nearly-continuous positive spectra. We highlight universal aspects of the analogue field-theory approach. The first aim is to present an extended self-consistent construction of the analogue effective field-theory framework for data, which can be viewed as a maximum entropy model. In particular and exploiting universality arguments, we justify the $\mathbb{Z}_2$-symmetry of the classical action and we stress the existence of a large-scale (local) regime and of a small-scale (nonlocal) regime. Secondly and related to noise models, we observe the universal relation between phase transition and symmetry breaking in the vicinity of the detection threshold. Finally, we discuss the issue of defining the covariance matrix for tensorial-like data. Based on the cutting graph prescription, we note the superiority of definitions based on complete graphs of large size for data analysis.

Quantum field theory exhibits rich spatial correlation structures even in the vacuum, where entanglement entropy between regions scales with the area of their shared boundary. While this vacuum structure has been extensively studied, far less is understood about how localized wave packets influence correlations between field values in different spatial regions. In this work, we use the Schrödinger representation to study the Rényi mutual information between complementary spatial regions for a localized wave packet of a free massless scalar field in $(d+1)$ dimensions. We find that the mutual information in this excited state includes both a vacuum term and an excitation-induced contribution. To obtain quantitative results, we specialize to $1+1$ dimensions and evaluate the Rényi-2 mutual information between the negative and positive halves of the real line. We find that the excitation generates finite, positive correlations that are maximized when the wave packet sits at the boundary and decrease with its distance from it, at a rate determined by the wave packet's width.Our findings constitute a contribution toward a more comprehensive understanding of quantum correlations in multiparticle states with nontrivial spatial localization, analyzed within a quantum field-theoretical framework.

In this paper, we develop a regularization theory for neural network approximations of general ill-posed operator equations with noisy data. Within the framework of iterative regularization, we introduce two expanding neural network methods (ENNs) under different a priori assumptions on the exact solution. Instead of prescribing a fixed architecture, ENNs adaptively select the number of neurons through an a posteriori stopping rule, so that the selected network size serves as a regularization parameter balancing approximation accuracy and stability with respect to data noise. We prove the regularization properties of the proposed ENNs and establish quantitative relationships between the selected network size and the noise level. Within the framework of variational regularization, we propose a neural network-based Tikhonov scheme and derive both convergence and convergence-rate results under mild assumptions. The resulting estimates account for the noise level, the network size, and the underlying smoothness expressed through general variational source conditions, thereby allowing greater flexibility than existing results. Numerical experiments demonstrate the effectiveness and robustness of the proposed algorithms. In particular, they show that, for highly noisy data, relatively small network architectures can already produce stable reconstructions, whereas excessively large architectures may degrade stability due to overfitting.

Due to their different nucleosynthetic origin, a stellar population produces oxygen (O) and iron (Fe) on different timescales and their relative abundance can deviate strongly from solar. Galaxy formation models should treat these elements separately, as they play a distinct role in shaping physical phenomena. For example, oxygen mainly sets the gas cooling rate, while the iron abundance sets stellar atmosphere opacities impacting stellar evolution, spectra and feedback. Observations of star-forming galaxies usually only constrain gas-phase oxygen abundance, vastly limiting our capabilities of separating the cosmic evolution of oxygen and iron. Here, we present an observationally-motivated framework to scale the cosmic evolution of O and Fe abundances. We apply the relation between the alpha-enhancement and galaxies' specific star formation rate ([O/Fe]-sSFR; Chruslinska et al. 2024) to derive the Fe and O-dependent cosmic star formation history (cSFH). We find that star formation with near-solar O/Fe is rare: at least 70% of the integrated cosmic stellar mass forms at non-solar O/Fe. The cosmic average metallicity is generally lower in [Fe/H] than in [O/H] (by up to a factor 3), with the offset increasing from redshifts z=0 to z~3 and then approaching the core-collapse O/Fe ratio. We validate our results against samples that probe the Fe-dependent cSFH in different regimes such as absorption-derived <[Fe/H]> from long gamma-ray bursts. Our results impact the interpretations of stellar and galaxy spectra and the predicted rates of transients, especially those linked to metal-poor progenitors (e.g., black hole mergers).

Glaucoma treatment relies on effective delivery of therapeutics to the anterior chamber; however, conventional approaches such as topical administration and intracameral injection are limited by rapid clearance and low intraocular bioavailability. In this study, a Computational Fluid Dynamics (CFD) framework was developed to comparatively evaluate drug transport, retention, and spatial distribution across three delivery strategies: intracameral injection, drug-eluting implants, and topical delivery via contact lens.

This paper studies the modal logical aspects of provability predicates and consistency statements for theories of arithmetic. First, we provide an overview of previous works on the correspondence between various derivability conditions for provability predicates and different modal logics. The main technical contribution of the present paper is to establish the arithmetical completeness of the logics $\mathsf{NP}$, $\mathsf{ND}$, $\mathsf{NP4}$, and $\mathsf{ND4}$ by extending Solovay's method and refining Arai's construction of Rosser provability predicates.

In this paper, we introduce a unified framework for nonlinear Krylov subspace methods (\textit{nlKrylov}) to solve systems of nonlinear equations. Building on classical GCR-like/type linear Krylov solvers such as GMRESR, we generalize these approaches to nonlinear problems via nested algorithmic structures. We present rigorous convergence results for problems, relying on relaxed assumptions that avoid the need for exact line searches. The framework is further extended to matrix-valued root finding problems using global nonlinear Krylov approaches. Extensive numerical experiments validate the theoretical insights and demonstrate the robustness and efficiency of our proposed algorithms.

We construct two quantum error correction codes for pure SU(2) lattice gauge theory in the electric basis truncated at the electric flux $j_{\rm max}=1/2$, which are applicable on quasi-1D plaquette chains, 2D honeycomb and 3D triamond and hyperhoneycomb lattices. The first code converts Gauss's law at each vertex into a stabilizer while the second only uses half of the vertices and is locally the carbon code. Both codes are able to correct single-qubit errors. The electric and magnetic terms in the SU(2) Hamiltonian are expressed in terms of logical gates in both codes. The logical-gate Hamiltonian in the first code exactly matches the spin Hamiltonian for gauge singlet states found in previous work.

In this paper, we introduce the concept of graded extension dimension for a group graded ring R, denoted by gr.ext.dim(R). We prove that when R is strongly graded, its graded extension dimension coincides with the non-graded extension dimension of both R itself and its degree-zero subring Re. Furthermore, we demonstrate that graded equivalence and graded separable equivalence preserve the extension dimension under appropriate conditions.

Generative AI (GenAI) models, particularly large language models (LLMs), have transformed multiple domains, including natural language processing, software analysis, and code understanding. Their ability to analyze and generate code has enabled applications such as source code summarization, behavior analysis, and malware detection. In this study, we systematically evaluate the capabilities of both small and large GenAI language models in understanding application behavior, with a particular focus on malware detection as a representative task. While larger models generally achieve higher overall accuracy, our experiments show that small GenAI models maintain competitive precision and recall, offering substantial advantages in computational efficiency, faster inference, and deployment in resource-constrained environments. We provide a detailed comparison across metrics such as accuracy, precision, recall, and F1-score, highlighting each model's strengths, limitations, and operational feasibility. Our findings demonstrate that small GenAI models can effectively complement large ones, providing a practical balance between performance and resource efficiency in real-world application behavior analysis.

We present a suite of packages in R, Python, Julia, and C++ that efficiently solve the Sorted L-One Penalized Estimation (SLOPE) problem. The packages feature a highly efficient hybrid coordinate descent algorithm that fits generalized linear models (GLMs) and supports a variety of loss functions, including Gaussian, binomial, Poisson, and multinomial logistic regression. Our implementation is designed to be fast, memory-efficient, and flexible. The packages support a variety of data structures (dense, sparse, and out-of-memory matrices) and are designed to efficiently fit the full SLOPE path as well as handle cross-validation of SLOPE models, including the relaxed SLOPE. We present examples of how to use the packages and benchmarks that demonstrate the performance of the packages on both real and simulated data and show that our packages outperform existing implementations of SLOPE in terms of speed.

The approximation of invariant measures for nonlinear ergodic stochastic differential equations (SDEs) is a central problem in scientific computing, with important applications in stochastic sampling, physics, and ecology. We first propose an easily applicable explicit Truncated Euler-Maruyama (TEM) scheme and prove its numerical ergodicity in the $L^p$-Wasserstein distance ($p\geqslant 1$). Furthermore, by combining truncation techniques with the coupling method, we establish a uniform-in-time $1/2$-order convergence rate in moments for the TEM scheme. Additionally, leveraging the exponential ergodicity of both the numerical and exact solutions, we derive a $1/2$-order convergence rate for the invariant measures of the TEM scheme and the exact solution in the $L^1$-Wasserstein distance. Finally, two numerical experiments are conducted to validate our theoretical results.

We study how Standard Model vacuum stability depends on the Higgs quartic coupling at the electroweak matching scale, parameterized through a dimensionless enhancement factor $k = λ_{\rm enhanced}(M_t)/λ_{\rm SM}(M_t)$, with the observed Higgs mass held fixed at $M_h = 125$~GeV. This is a scan of the coupling itself, treated as a free parameter set by physics beyond the Standard Model, and is distinct from the Higgs-mass scan that underlies the conventional stability bound. Using the complete three-loop renormalization group equations including all gauge and Yukawa couplings, we find a critical threshold $k_{\rm crit} \approx 1.076$ separating the metastable Standard Model trajectory from absolutely stable trajectories. At this threshold the matching-scale coupling is $λ(M_t) \approx 0.135$, which reproduces the established three-loop absolute-stability boundary, providing an internal consistency check of the framework. The instability scale is highly sensitive to $k$ near the threshold, with a logarithmic susceptibility $d\lnΛ_I/d\ln k$ of order $10^3$ as $k \to k_{\rm crit}^-$, larger by two to three orders of magnitude than the analogous susceptibility of $Λ_{\rm QCD}$ to $α_s(M_Z)$. For $k > k_{\rm crit}$ the vacuum is absolutely stable and $λ$ develops an ultraviolet Landau pole whose scale falls rapidly with increasing $k$: for moderate enhancement the pole lies near the Planck scale, while for the large enhancement $k \approx 7.2$ associated with radiative electroweak symmetry breaking the matching-scale coupling is $λ(M_t) \approx 0.9$ and perturbative validity is lost by $\sim 10^5$~GeV.

The search for new sources of CP violation is a cornerstone of the beyond the Standard Model phenomenology programme at the LHC and beyond. We provide a comprehensive analysis of such searches at a range of future facilities with the aim of informing the currently unfolding future collider roadmap. Focussing on new sources of CP violation specifically in the gauge-Higgs sector, we demonstrate the outstanding potential held by future electron-positron and proton-proton colliders to reveal and identify BSM physics with direct relevance for the observed matter-antimatter asymmetry. In particular, the future colliders will provide an order of magnitude improvement in sensitivity to anomalous CP-violating interactions induced by dimension-six effective field theory operators when compared to the high-luminosity LHC programme.

We construct the first examples of chamber-regular lattices on $\tilde C_2$-buildings. Assuming a conjecture of Kantor, our list of examples becomes a classification for type-preserving, chamber-regular $\tilde C_2$-lattices on locally finite $\tilde C_2$-buildings. The links of special vertices in the buildings we construct, are all isomorphic to the unique generalized quadrangle Q of order (3,5). In particular, our constructions involve chamber-regular actions on Q. These actions on Q are the first and if Kantor's conjecture holds the only chamber-regular actions on a finite generalized quadrangle and therefore interesting in their own right. Moreover Q is not Moufang and therefore none of our examples are Bruhat-Tits buildings and all our lattices are exotic building lattices.

The Cox proportional hazards model is the most widely used regression model in univariate survival analysis, yet extensions to bivariate survival data remain scarce. We propose two novel extensions based on a Lehmann-type representation of the survival function. The first, the simple Lehmann model, is a direct extension that retains a straightforward structure. The second, the generalized Lehmann model, allows greater flexibility by incorporating three distinct regression parameters and includes the simple Lehmann model as a special case. The models admit a direct interpretation in terms of survival probabilities, providing a transparent, fully semiparametric framework for assessing covariate effects on both marginal survival probabilities and their dependence, without requiring specification of a copula or frailty distribution. To estimate the regression parameters, we build on a pseudo-observation-based approach for bivariate survival data and extend it to the generalized model via a two-step procedure. We establish consistency and asymptotic normality of the resulting estimators. The proposed approach is illustrated through simulation studies and an application to data from the Global Retinoblastoma Outcome Study.

The interplay between unitary dynamics and quantum measurements induces diverse phenomena in open quantum systems with no counterparts in closed quantum systems at equilibrium. Here, we generally classify Kraus operators and their effective non-Hermitian dynamical generators, thereby establishing the tenfold classification for symmetry and topology of monitored free fermions. Our classification elucidates the role of topology in measurement-induced phase transitions and identifies potential topological terms in the corresponding nonlinear sigma models. Furthermore, we establish the bulk-boundary correspondence in monitored quantum dynamics: nontrivial topology in spacetime manifests itself as topologically nontrivial steady states and gapless boundary states in Lyapunov spectra, such as Lyapunov zero modes and chiral edge modes, leading to the topologically protected slowdown of dynamical purification.

Efficient verification of quantum computational resources is crucial as experiments advance toward fault-tolerance. Universal quantum computation can be achieved by consuming resource states through simple Pauli measurements, yet a significant gap remains between states that are easy to certify and those required for universality. We focus on \emph{Clifford-enhanced Product States}, a class of resource states obtained by applying Clifford circuits to a product of single-qubit, potentially magic, states. While essential for universal computation, the certification of such states has previously relied on query oracles that are \#P-hard to implement, leaving their efficient, oracle-free verification an open challenge. In this work, we demonstrate that such classically intractable resource states can be efficiently verified using only Pauli measurements. Our protocol achieves sample- and time-efficiency in both i.i.d.\ and adversarial settings. This work fills a gap in Pauli-based certification, providing a new practical pathway to verify resource states that drive universal Pauli-based quantum computation.

Wireless networks are undergoing a paradigm shift toward massive connectivity with energy-efficient operation, driving the integration of satellite-terrestrial architectures with simultaneous wireless information and power transfer (SWIPT). Optimizing transmit beamforming and power splitting in such systems faces formidable challenges, e.g., time-varying channels and multi-tier interference, which create a complex decision landscape where conventional model-free multi-agent reinforcement learning (MARL) suffers from sample inefficiency due to rarely-encountered state transitions and poor coordination as decentralized agents act independently. This paper proposes the Decentralized World Model with Reasoning Offloading (DWM-RO) framework to address these fundamental limitations. Specifically, each agent employs a world model to learn compact predictive representations of environment dynamics, enabling imagination-based policy training that dramatically reduces required environment interactions. An uncertainty-aware offloading gate monitors local interference levels and model reconstruction errors to trigger selective edge coordination. When activated, a lightweight latent decorrelation mechanism at the edge refines agents' strategic representations, guiding them toward orthogonal actions that minimize resource conflicts. Extensive simulations demonstrate that DWM-RO converges 5 times faster than state-of-the-art baselines while achieving 34.7% higher spectral efficiency and reducing constraint violations by 40%. In dense network scenarios with 10 users, DWM-RO maintains violation rates below 20% while baselines exceed 70%, validating superior robustness.

We study the operator algebra of a rank-one boundary defect in a semi-infinite tight-binding chain, $T=U+\varepsilon E$ on $\ell^2(\mathbb{Z}_{\ge 0})$, with $U$ the forward unilateral shift and $E=\langle e_0,\cdot\rangle e_0$. The Lie algebra $\mathcal{A}=\mathrm{span}\{U^aE(U^*)^b,\,U^n\}$ has finitely supported, trace-zero commutators, the noncommutativity confined to the boundary and vanishing on the bulk. To each site we attach a $2$-cochain $ω_j(X,Y)=\langle e_j,[X,Y]e_j\rangle$; each is a Chevalley--Eilenberg coboundary, yet $H^2(\mathcal{A},\mathbb{C})$ is infinite-dimensional, carried by the abelian bulk and classifying the central extensions. On the polynomial Toeplitz algebra obtained by adjoining $U^*$, the total cochain $\sum_{j}ω_j(T_f,T_g)$ equals the symbol pairing $\frac{1}{2πi}\oint f\,dg$, which for conjugate symbols $g=1/f$ is the Fredholm index; the $ω_j$ thus form a site-resolved index density, $ω_j(U^n,(U^*)^n)=-\mathbf{1}_{\{j<n\}}$, localized at the edge. For modulated couplings with $\varepsilon_j\to c$, the index is fixed by the bulk limit and undergoes a topological transition as $|c|$ crosses~$1$, independently of the boundary profile.

We present a theoretical investigation of two-neutrino double electron capture ($2ν$ECEC) in $^{132}$Ba and $^{78}$Kr based on large-scale shell-model calculations. The nuclear matrix elements (NMEs) for the $2ν$ECEC process in $^{132}$Ba and $^{78}$Kr are calculated using the SN100PN and GWBXG effective interactions, respectively. The reliability of the employed interactions is first examined through a comparison of the calculated and experimental spectroscopic properties of the parent, intermediate, and granddaughter nuclei involved in the decay. We also examine the cumulative contribution of the $2ν$ECEC NME with respect to the $1^+$ state energies in the intermediate nuclei. The present results provide an updated and improved shell-model estimate of the $2ν$ECEC NME and half-life for $^{78}$Kr relative to earlier studies, and a baseline theoretical prediction for $^{132}$Ba that may assist future experimental efforts in constraining this rare decay mode.

Fix a positive prime power $q$, and let $\mathbb{F}_q[t]$ be the ring of polynomials over the finite field $\mathbb{F}_q$ with $\text{char}(\mathbb{F}_q)>2$. Suppose $A \subseteq \{f \in mathbb{F}_q[t]: °f \leq N\}$ contains no pair of elements whose difference is of the form $P-1$ with $P$ irreducible. Adapting Green's approach to Sárközy's theorem for shifted primes in $\mathbb{Z}$ using the van der Corput property, we show that \[ |A| \ll q^{(N+1)(11/12+o(1))}, \] improving upon the bound $O\big(q^{(1-c/\log N)(N+1)}\big)$ due to Lê and Spencer. An important distinction between Green's argument and ours lies in the properties of exponential sums over function fields, which differ in several interesting ways from their number-field counterparts.

Comparing networks is essential for a number of downstream tasks, from clustering to anomaly detection. Despite higher-order interactions being critical for understanding the dynamics of complex systems, traditional approaches for network comparison are limited to pairwise interactions only. Here we construct a general information theoretic framework for hypergraph similarity, capturing meaningful correspondence among higher-order interactions while correcting for spurious correlations. Our method operationalizes any notion of structural overlap among hypergraphs as a principled normalized mutual information measure, allowing us to derive a hierarchy of increasingly granular formulations of similarity among hypergraphs within and across orders of interactions, and at multiple scales. We validate these measures through extensive experiments on synthetic hypergraphs and apply the framework to reveal meaningful patterns in a variety of empirical higher-order networks. Our work provides foundational tools for the principled comparison of higher-order networks, shedding light on the structural organization of networked systems with non-dyadic interactions.

Chiral molecules are known to preferentially select electrons with a particular spin state, an effect termed chirality-induced spin selectivity (CISS). In this work, the transient CISS dynamics in a chiral molecule are investigated through time-dependent quantum-transport simulations, an important step toward further understanding CISS and its application in devices such as magnetoresistive random access memories and spin-based quantum computers. We show that the spin-dependent group velocity of electrons is a possible contributor to a nonzero occupancy-based spin polarization throughout the chiral molecule. Contrary to the case which a chiral molecule is connected to a single lead, this spin polarization persists into the steady state when two leads are connected. We show that the simulated spin polarization qualitatively agrees with a reference experiment, as evidenced by the distinct magnetic-field signatures calculated from the spin polarization within a monolayer of chiral molecules.

The excess growth rate, defined as the gap in Jensen's inequality for the logarithm, is a fundamental functional in portfolio theory. In this paper, we present a mathematical study motivated by information theory. We begin by establishing its properties and showing that it has rich connections with information theoretic concepts such as the Helmholtz free energy, L. Campbell's measure of average code length and large deviations. Our main results consist of three axiomatic characterization theorems of the excess growth rate, in terms of (i) the relative entropy, (ii) the gap in Jensen's inequality, and (iii) the logarithmic divergence that generalizes the Bregman divergence. Furthermore, we study maximization of the excess growth rate and compare it with the growth optimal portfolio. Our results not only provide theoretical justifications of the significance of the excess growth rate, but also establish new connections between information theory and quantitative finance.

About ten years ago, Katz, Klemm and Huang conjectured that topological string amplitudes on compact, elliptically fibered Calabi-Yau threefolds at fixed base degree could be expressed in terms of meromorphic Jacobi forms for $SL(2,\mathbb{Z})$, giving access to Gromov-Witten invariants at arbitrary genus. This was later generalized to torus-fibered CY threefolds with $N$-sections, where topological string amplitudes are conjecturally governed by meromorphic Jacobi forms under the congruence subgroup $Γ_1(N)$. In this work, we show that these modularity properties follow from (and are equivalent to) the wave-function property of the topological string partition function $Z_{\rm top}$ under a relative conifold monodromy, implementing a particular Fourier-Mukai transformation on the derived category of coherent sheaves. In particular, we introduce a variant of $Z_{\rm top}$ which is both holomorphic and modular covariant. Under the same relative conifold monodromy, the generating series of genus 0 Gopakumar-Vafa invariants at fixed base degree is mapped to the generating series of rank 0 Donaldson-Thomas indices counting D4-D2-D0-brane bound states wrapped on the torus fiber. We show that the quasimodularity of the generating series of GV invariants matches the expected mock-modular behavior of the generating series of D4-D2-D0 indices, despite having different multi-cover contributions. We analyze and tabulate a large number of CY threefolds fibered over del Pezzo surfaces, with an $N$-section for $N\leq 5$, including several new examples beyond the realm of toric geometry.

We implement Genetic Algorithms for triangulations of four-dimensional reflexive polytopes which induce Calabi-Yau threefold hypersurfaces via Batyrev's construction. We demonstrate that such algorithms efficiently optimize physical observables such as axion decay constants or axion-photon couplings in string theory compactifications. For our implementation, we choose a parameterization of triangulations that yields homotopy inequivalent Calabi-Yau threefolds by extending fine, regular triangulations of two-faces, thereby eliminating exponentially large redundancy factors in the map from polytope triangulations to Calabi-Yau hypersurfaces. In particular, we discuss how this encoding renders the entire Kreuzer-Skarke list amenable to a variety of optimization strategies, including but not limited to Genetic Algorithms. To achieve optimal performance, we tune the hyperparameters of our Genetic Algorithm using Bayesian optimization. We find that our implementation vastly outperforms other sampling and optimization strategies like Markov Chain Monte Carlo or Simulated Annealing. Finally, we showcase that our Genetic Algorithm efficiently performs optimization even for the maximal polytope with Hodge numbers $h^{1,1} = 491$, where we use it to maximize axion-photon couplings. Our methods for sampling and optimization are implemented in a Python package cyopt.