Identifying phenotype-associated genes is a common first step in polygenic risk score construction, enrichment testing, target prioritisation and variant interpretation, but relevant evidence is distributed across heterogeneous databases with different interfaces, formats and evidence models. Here, we present PhenotypeToGeneDownloaderR, a phenotype-guided R/Python pipeline for automated gene retrieval, harmonisation, symbol validation and cross-source summary analysis. Given a phenotype term, the pipeline queries integrated biological databases, standardises per-source outputs, combines gene lists, validates retrieved symbols against the NCBI human gene reference and generates summary tables and visualisations. Across 13 clinically relevant phenotypes and 13 databases, PhenotypeToGeneDownloaderR generated 136,487 raw gene retrievals, with at least one source returning genes for every phenotype. Across all 13 phenotypes, 100,175 of 114,345 combined input symbols were retained after direct or synonym-based validation, corresponding to an 87.6\% validation rate. Cross-source overlap was low, supporting the complementarity of integrated evidence sources. Against an HPO/ClinVar/OMIM-derived gold standard, the pipeline recovered 1,039 of 1,056 known phenotype-associated genes, corresponding to 98.4\% recall. PhenotypeToGeneDownloaderR provides a lightweight, reproducible upstream framework for generating candidate gene sets for downstream prioritisation and interpretation. The pipeline is implemented in R and Python, released under the MIT licence, and available at https://github.com/MuhammadMuneeb007/PhenotypeToGeneDownloaderR.

We present an optimal control problem to guide the selection of morphology classes arising in organic solar cells. The study focuses on phase separation processes in polymer solvent mixtures, with particular attention to solvent evaporation as a mechanism to arrest morphology formation. We establish the existence of optimal controls and analyze the Frechet derivative of the control to state mapping. Finally, we derive the first order necessary optimality condition via the corresponding adjoint system.

Multipartite entanglement is the premier resource for quantum technologies. Yet, its exact quantification in the laboratory is notoriously challenging, typically requiring the full knowledge of high dimensional quantum states. Here, we construct observable bounds to multipartite entanglement for systems of arbitrary size, which are functions of the local and global state purities, and correlation functions. First, we derive experimentally accessible upper and lower limits to both the bipartite entanglement of formation and the squashed entanglement of bipartite systems, by leveraging cornerstone results of quantum information theory: the entropy strong subadditivity inequality and the Koashi-Winter monogamy relation. Then, we convert them into bounds to the entanglement up to degree k for arbitrary states, and to the genuine k-partite entanglement, by employing a recently proposed method. Finally, we analytically and numerically test these results, by bounding the multipartite entanglement of several relevant states and mixtures, including the important classes of GHZ, Dicke, W states, and random pure states.

In a strongly interacting Rydberg atom array, the dynamics are often constrained to the decoupled Hilbert subspaces, representing an intriguing paradigm for nonergodicity. By considering a variable detuning of the global Rydberg coupling, we show that, not only is the existence of these Hilbert subspaces dependent on the interplay of detuning and interaction, but they are also strongly fragmented, with the fragment dimensions exhibiting various scaling behaviors with increasing system size. The resulting constrained dynamics of the system are thus governed by the dimension and connectivity of these fragments. We then adopt an auxiliary fermion description to reveal the underlying emergent kinetic constraints for the subspace fragmentation and fragment-confined dynamics. Our results provide a systematic understanding of Hilbert-space fragmentation in Rydberg arrays, and shed light on engineering nonergodic many-body dynamics beyond the PXP model.

Grid-integrated building districts must provide energy flexibility while preserving occupant comfort and equitable distribution of control burden. We study how coordination architecture influences the ability of building clusters to track aggregated load profiles, comparing four paradigms: centralized model predictive control (MPC), decentralized independent reinforcement learning (SAC), centralized-training-decentralized-execution multi-agent RL (MAPPO), and a hybrid MPC--SAC controller that separates district-level battery optimization from building-level HVAC regulation. A rule-based controller serves as a baseline. We evaluate a 25-building residential district across three metrics: aggregate load tracking, thermal comfort, and spatial variability of control actions. We find that architecture choice determines the trade-off structure. Centralized MPC achieves low tracking bias (8.8% NMBE) but concentrates actuation on a subset of buildings, causing elevated comfort violations (24.8% exceedance) and spatial imbalance. Decentralized RL distributes control effort more evenly but fails to sustain accurate tracking. The hybrid architecture achieves the best balance: accurate tracking (4.8% NMBE), moderate comfort impact (16.8% exceedance), and the lowest spatial variability. These findings demonstrate that architecture choice determines the trade-off structure between tracking and comfort.

The reservoir computing based on the thin film embedded with magnetic impurities in the presence of the long-range (the dipole-dipole) interaction is numerically investigated. We simulated the magnetization dynamics by taking into account the dipole-dipole interaction and performed the handwritten-digit recognition task. Although the training data is prepared by taking spatial average in the sample, the high classification accuracy is achieved. Our result demonstrates that the long range interaction effectively encodes the complex spatial input pattern into the time domain, even when only a spatially averaged output is accessible. The proposed system paves the way for easily realizable magnetic reservoir computing.

We prove existence and convergence of sequences generated by the proximal point method and its two variants for monotone vector fields in Hadamard spaces. Before obtaining our results, we investigate some fundamental properties of tangent spaces, resolvents, and monotone vector fields in such spaces.

We present a forward-modeling framework to forecast the galaxies detected in the Chinese Space Station Survey Telescope (CSST) spectroscopic survey and the Square Kilometre Array (SKA) HI survey. Starting from the L-Galaxies 2020 semi-analytic model run on the Millennium-II N-body simulation (MS-II), the cold gas in galaxies is partitioned into atomic and molecular components self-consistently within the model. We further model the emission-lines (H $α$, H $β$, O III) relevant for the slitless spectrograph of the CSST in a post-processing step. We construct mock lightcones using the Mock Map Facility (MoMaF) approach, simulating the neutral hydrogen (HI) data cubes representing a 2000 hour SKA-Mid spectral line observation from redshifts 0.25--0.5, and employ the Source Finding Application 2(SOFIA-2) source-finding package to generate an HI galaxy catalog. In parallel, we apply the CSST selection function and noise model to obtain a realistic catalog of emission-line galaxies; the emission-line signal is proportional to the star formation rate. These products allow us to cross compare the galaxy samples and assess the synergy between CSST and SKA. We study the correlations of the HI and the emission-line signal with the halo mass, HI mass, and the stellar mass, and the baryonic Tully-Fisher relation (BTFR). We also perform stacking analysis of the HI signal from the CSST-selected sample, which probes the HI content in galaxies with low HI mass. Finally, we derive the optical-HI cross-correlation power spectrum of the galaxies, and measure the bias of these galaxies. These results can provide useful insight on the cold gas and stellar content of the galaxies.

This paper presents the rAIson platform, a high-level technological environment for the development of automated, reliable and explainable decision-making agents. The research underlying the platform and its technological progress has now reached a mature stage that allows the platform to be used for the development of complex real-life applications without writing a single line of code.

In this paper, we propose a consistent and asymptotically efficient estimation method for Box-Jenkins (BJ) models that is applicable under both open-loop and closed-loop data conditions, serving as a possible alternative to the weighted null-space fitting approach. The method comprises two stages: an initial sequentially decoupling (SD) estimator, followed by Gauss-Newton (GN) refinement step. The SD estimator is constructed from three sequential least squares (LS) estimators: (i) estimation of a high-order autoregressive model with exogenous inputs (ARX) model; (ii) estimation of the BJ model's dynamic model via an auxiliary output-error (OE) model; and (iii) estimation of the noise model of the BJ model using another auxiliary OE model. We establish the consistency of the SD estimator under standard regularity conditions, leveraging the consistency of the underlying LS estimators for both the ARX and OE models. Moreover, we show that one-step GN iteration starting from the SD estimator yields an estimator that is asymptotically equivalent to the prediction error method, provided the ARX model order satisfies a mild growth condition. Simulation studies confirm the theoretical properties of the proposed method.

This tutorial provides an overview of the generalized Lyapunov method (GLM) for analyzing input-to-state stability (ISS) of partial differential equations (PDEs). We begin by revisiting the classical Lyapunov method and the standard ISS-Lyapunov theorem, highlighting their limitations when applied to systems with complex boundary disturbances. In contrast, the GLM, based on the concept of generalized Lyapunov functionals (GLFs) that explicitly depend on the external input, offers greater flexibility and efficiency, particularly for PDEs with Dirichlet-type disturbances. The main objective of this tutorial is to demonstrate how to systematically construct GLFs to establish ISS estimates in $L^q$ spaces with any $q\in[2,\infty]$ for different PDEs. Specifically, we consider three representative classes of PDEs: (i) an $N$-dimensional nonlinear parabolic equation with mixed nonlinear boundary disturbances, (ii) a first order nonlinear hyperbolic equation with boundary disturbances, and (iii) a second order linear hyperbolic equation, i.e., a wave equation, with boundary damping and disturbances. For each case, we provide step-by-step constructions of appropriate GLFs and derive explicit ISS estimates, illustrating the general applicability of the GLM. Finally, we discuss open challenges and future directions, including the systematic construction of GLFs for broader classes of PDEs and their applications in controller design.

This manuscript examines viability and stability of anisotropic compact objects in the framework of $f(Q,L_m)$ gravity ($Q$ is the non-metricity and $L_m$ is the matter Lagrangian). We assume a particular functional form of this theory to get explicit expressions for the field equations which govern the behavior of matter and geometry in this context. The configuration of static spherically symmetric structures is evaluated using the two innovative non-singular solutions. We use smooth matching conditions to evaluate the values of unknown constants in the metric coefficients. The viability of considered compact stars is assessed using a graphic analysis of various important physical characteristics. We also investigate stability of the considered stellar objects through sound speed method. It is found that these stellar objects are viable and stable, as all the required conditions are satisfied.

OpenAlex has recently emerged as a leading alternative to proprietary bibliometric sources. However, concerns remain regarding the quality of its metadata, especially the institutional profiles which are crucial for evaluating organizations. This study assesses the quality of affiliation data in OpenAlex using German research institutions. Publications from top-tier journals were analyzed and institutional publication counts in OpenAlex were systematically compared with counts in Scopus. The results show that OpenAlex generally contains more publications at the journal level, reflecting its broader coverage. However, institutional publication counts in OpenAlex are consistently lower, indicating missing or incorrectly assigned affiliations. Nevertheless, the correlations between institutional outputs in both databases are very high, suggesting that relative institutional rankings remain stable. These findings suggest that OpenAlex is suitable for comparative institutional analyses in academic research but requires further improvement in affiliation metadata before it can be used for evaluation contexts that rely on absolute publication counts.

We give simple new proofs of two well-known results for the Schrödinger operator: first, the Brunn--Minkowski inequality for Dirichlet eigenvalues and, second, the log-concavity of the first Dirichlet eigenfunction. Our proof of the first applies to a class of domains including $C^{1,1}$ connected domains and convex potentials. In the special case of convex domains, the second result is a simple corollary.

In this article, we investigate the toric Schubert varieties in partial flag varieties $G/P$ for a connected semisimple algebraic group $G$. Using Deodhar's decomposition of Richardson varieties and the work of Pasquier, we give an explicit description of the fan of a toric Schubert variety, leading to a combinatorial model for its cones. As an application, we obtain necessary and sufficient conditions for smoothness of toric Schubert varieties in terms of the Cartan integers associated to a reduced expression. Furthermore, we prove that for a Coxeter-type element $w \in W^P$, the interval $[e,w]_{W^P}$ is a supersolvable join-distributive lattice. Finally, we apply these results to the study of spherical and horospherical Schubert varieties, providing a combinatorial method for checking the smoothness via the associated toric Schubert varieties.

Affine frequency division multiplexing (AFDM) is a recently proposed multicarrier waveform whose bit error rate (BER) performance in doubly selective channels is comparable to that of orthogonal time-frequency space (OTFS) and superior to that of orthogonal frequency division multiplexing (OFDM). In this paper, the impacts of joint transmitter (Tx) and receiver (Rx) in-phase and quadrature imbalance (IQI) on AFDM signals are investigated, where we show that AFDM suffers more severe IQI than OFDM and OTFS due to the inherent feature of complicated chirp-assisted modulation. We further derive analytical expressions for the pairwise and average bit error probability as a function of the IQI parameters. These indicate that such distortions significantly limit the achievable operating signal-to-noise ratio at the receiver side and data rates. To this end, we propose a cascade compensation scheme to mitigate these effects. Specifically, we first compensate for Rx IQI to convert the improper Gaussian noise into additive white Gaussian noise, and then apply a judicious design to eliminate the Tx IQI. Both analytical and simulation results reveal that joint Tx and Rx IQI introduce an error floor in the BER performance of AFDM systems, whereas the proposed approach effectively compensates such impairments.

The challenge in predicting sub-regional climate within the Indian monsoon region is exacerbated by its increasing variability in a warming world. While exploring the seasonal predictability of rainfall over the state of Tamil Nadu in southeast India, we identify an overall increase in the monthly rainfall and its variability in recent years due to an increase in surface temperature, water vapour and moisture convergence. We attribute the increasing excess rainfall to a long-term reduction in convective inhibition. We further find an increasing trend in the length of the rainy season due to an earlier onset and a delayed withdrawal of the large-scale monsoon over the southeastern and southwestern regions of southern peninsular India, respectively. Further, the simultaneous (0- month lead) predictability of the primary wet-season (October-December, OND) rainfall over Tamil Nadu is dominated by sea surface temperature (SST) anomalies in the North Indian Ocean. However, a global tropical SST climate network reveals a high potential predictability and potential to realize significant forecast skill at a lead time of up to 10 months. The long-lead predictability arises from SST and rainfall interactions across the tropical Indo-Pacific and equatorial Atlantic regions. Our findings provide a robust data-driven methodology for skillful seasonal rainfall prediction over Tamil Nadu, despite the increasing rainfall variability.

We apply exact WKB analysis to the spectral problem arising in black hole perturbation theory. The boundary conditions for quasinormal modes lead to exact quantization conditions for the complex frequencies. To solve these conditions, one needs to evaluate the so-called quantum periods, or Voros symbols. For scalar perturbations of extremal Reissner--Nordström and Kerr black holes, we compute these quantities up to very high orders in the WKB expansion and perform Borel--Padé resummation. The resulting resummed quantization conditions successfully reproduce the correct quasinormal mode frequencies with high precision.

We study the interplay between gravitational waves (GWs) from domain wall collapse and the electron electric dipole moment (EDM) in a complex singlet extension of the standard model with dimension-five Yukawa interactions. In this framework, the scalar potential admits CP-related degenerate vacua, leading to the formation of CP domain walls. While the resulting GW signal provides a probe of the vacuum structure of the singlet scalar sector, it does not by itself constitute a CP-violating observable. Once the singlet scalar is coupled to standard model fermions, CP-violating phases become observable through EDMs. We analyze whether current and future EDM experiments can probe the parameter region where the GW signal is detectable by SKA and THEIA. We find that the current electron EDM bound already constrains part of the parameter space, while future sensitivities at the level of $10^{-31}$--$10^{-32}\,e\,\mathrm{cm}$ can probe regions overlapping with the GW-detectable domain. Our results highlight the complementarity between GW and EDM observables in probing the singlet scalar sector, providing a coherent picture of its vacuum structure and CP properties.

Electronic and structural degrees of freedom are often intimately coupled in strongly correlated systems, which result in intriguing macroscopic and microscopic phenomena. Using the well-studied material VO$_2$ as a prototype, here we explore the domain distribution across the metal-insulator transition (MIT). We use macroscopic as well as microscopic techniques, such as first-order reversal curve (FORC) and infrared imaging, to probe the domain distributions across the MIT. This study compares MIT in thin films of VO$_2$ with different grain sizes grown by pulsed laser deposition and dc sputtering. We explore the relation between the nature of the FORC distribution and the corresponding thermal hysteresis due to interactions between the supercooled metallic domains and surrounding insulating matrix. Our multi-probe study with quantitative analysis provides a correlation between the growth, domain interaction, and domain nucleation process in MIT.

Semi-implicit semi-Lagrangian (SISL) methods are commonly used for the shallow water equations (SWE) because they allow for larger time steps than those permitted by the Courant-Friedrichs-Lewy (CFL) stability condition in Eulerian schemes. In these methods, the semi-Lagrangian treatment of advection is typically performed using lower-order interpolation, such as tensor-product Lagrange interpolation with cubic or quintic polynomials. However, operational SISL schemes routinely employ spectrally accurate spatial discretizations, such as spherical harmonics or the double Fourier sphere (DFS) method, for computing horizontal derivatives of the prognostic variables. This creates a mismatch in numerical accuracy, making the use of low-order interpolation less clearly justified. In this work, we present the first numerical investigation of spectrally accurate interpolation in SISL schemes for the SWE. Our approach builds upon the recently developed DFS-based SWE model, incorporating a spectral interpolation scheme that is accelerated using the nonuniform fast Fourier transform (NUFFT) to maintain the same overall computational complexity as the original model. Using several standard SWE test cases, we evaluate the accuracy, conservation, and numerical diffusion of the new model, particularly over long integration times. Compared to an equivalent SISL model with low-order interpolation, the new model achieves higher accuracy, improved mass and energy conservation, and reduced numerical diffusion, demonstrating the potential benefits of incorporating spectrally accurate interpolation into SISL schemes.

We propose and analyze the moving median absolute deviation (MMAD) as a robust depth construction based on the median absolute distance functional with particular emphasis on its local geometry and probabilistic structure. In the univariate setting, we derive the derivative of the MMAD scale and interpret it through boundary mass imbalance, thereby establishing a direct connection to a robust skewness measure. This idea extends naturally to a multivariate setting that describes how observations are arranged along the 50% central region using a directional derivative, a gradient representation, and a spherical boundary distribution. From a computational perspective, MMAD can be estimated efficiently using distance calculations without needing complex optimization or projection schemes. Multivariate applications based on depth correlations, contour visualizations, and central region overlap demonstrate that MMAD identifies essentially the same central observations as classical depth notions while delivering additional information and geometric insight about directional structure. These features make MMAD a practical and informative approach for robust multivariate data analysis.

Multireference density functional theory (MR-DFT) provides a pivotal microscopic framework for the description of the ground state properties, low-lying nuclear spectra and transition properties of atomic nuclei. Conventionally, practical implementations of MR-DFT rely on empirically chosen generator coordinates, which may omit relevant collective degrees of freedom and thus fail to capture sufficient collective correlations. Here we introduce the stochastic-basis multireference density functional theory (MR-SDFT). This is an extended scheme that augments the MR-DFT toolkit by (i) generating a diverse ensemble of mean-field reference configurations via a stochastic external field and (ii) selecting a compact subspace with Projection-Selection method. The chosen reference configurations are then linearly superposed within the MR-DFT framework to yield spectroscopic observables. Applying this framework to \nuclide[20]{Ne}, \nuclide[24]{Mg} and \nuclide[28]{Si} with the covariant density functional theory (CDFT), it is demonstrated that the MR-SCDFT leads to lower ground-state energies, smaller point-proton rms radius, and a softer ground-state band compared to the conventional MR-CDFT.

To address the initial singularity inherent in solutions to fractional partial differential equations (fPDEs), we propose an accelerated Alikhanov discretization formulation implemented on nonuniform time grids. Based on the physics-informed neural networks (PINNs) framework, we introduce an Alikhanov-extended fractional PINNs (XfPINNs) architecture that combines high-order temporal discretization and deep learning. The nonlocal memory term in fPDEs leads to high computational cost, while the weak singularity near $t\to 0^+$ can deteriorate accuracy on uniform meshes. To separate temporal discretization effects from optimization and sampling errors, we further develop an auxiliary time-marching configuration that enables auditable temporal-convergence studies under controlled training tolerances. This architecture can solve general nonlinear fPDEs. The XfPINNs approach is designed for forward and inverse problems, allowing for data-driven solution reconstruction and parameter estimation. First, the neural network approximates the solution of nonlinear fPDEs; then, an adaptive activation function accelerates convergence and enhances training efficiency. The optimization framework embeds a variational loss function constructed from the Alikhanov scheme, where the initial and boundary conditions are imposed using a combination of hard and soft constraints. Numerical experiments, including cases with known and unknown exact solutions which demonstrate the robustness, computational efficiency, and significant CPU time savings of the Alikhanov-XfPINNs method.

Collaborative perception allows connected and autonomous vehicles (CAVs) to improve perception by sharing sensory data, but it also introduces security risks from manipulated inputs. Prior work shows that attackers can spoof or remove objects by fabricating shared data, yet the practicality of such attacks in real-world driving remains unclear. Existing attacks are often detectable or evaluated in manually constructed scenarios, leaving open whether they can induce safety-critical outcomes in dynamic environments. To bridge this gap, we present a stealthy, scenario-realistic data fabrication attack that induces unsafe driving behaviors through end-to-end system effects. Instead of creating large, easily detectable anomalies, our attack subtly manipulates the poses of existing objects in shared perception results, keeping perturbations below detection thresholds. These small errors are then propagated through downstream modules, including object tracking and trajectory prediction, leading to significant deviations in predicted behaviors and ultimately unsafe driving decisions. We further design an online, scenario-aware attack framework that adapts to dynamic traffic conditions and optimizes attack strategies at runtime. Experiments on OPV2V and V2X-Real demonstrate that the attack achieves over 90% success in inducing detection errors and triggers safety-critical behaviors, such as unnecessary hard braking, in up to 50% of scenarios, while largely evading state-of-the-art defenses. We also propose a mitigation that focuses on detecting anomalies in localized, safety-critical regions, achieving an 80% detection rate on the small pose perturbation compared to 11% for the best existing methods.

Traditional technical analysis indicators, although widely used by market participants, are often not sufficiently effective. We propose the Visibility Graphs Relative Strength Index (VGRSI), based on backward visibility relations in the price of a financial instrument. Rescaled to the 0--100 range, it can generate profitable trading signals. The performance of the indicator was evaluated using an automated trading strategy based on a 30-day optimisation window and a 7-day test window for three instruments representing different asset classes: DJI30, EUR/USD and XAU/USD over the 2024--2025 period (503 trading days). The strategy based on VGRSI signals generated a profit of USD~146,000 for DJI30, USD~69,000 for EUR/USD, and USD~125,000 for XAU/USD. This gives a total result of USD$\sim$340,000, which corresponds to an average profit of USD$\sim$676 per trading day, with a fixed investment of USD~1,000 to open a single trade. For all three assets, the strategy generated substantial profits while maintaining a moderate drawdown (10--18\% relative to a portfolio value of USD~10,000), a relatively low trading intensity (3.3--4.8 trades per day) and high Sharpe ratio values (2.55--3.6). These results indicate that VGRSI constitutes a promising technical analysis tool that goes beyond the classical trend-following approach by exploiting the geometric properties of asset price fluctuations.

Atomic force microscopy (AFM) using qPlus sensors is a powerful tool for high-resolution analysis in various liquids, including high-viscosity or opaque environments. However, the relatively high displacement sensor noise density (n_{ds}), combined with the high spring constant and the low resonance frequency, limits force sensitivity and has hindered high-speed imaging. In this paper, we clarify the dominant factors governing n_{ds} and the minimum detectable force gradient (F'_{min}) through a comprehensive analysis of sensor geometry and circuit theory. Based on these findings, we developed a low-noise qPlus sensor that achieves an n_{ds} of 9.3 fm Hz^{-1/2}, which is approximately one-third that of conventional sensors, and reduces F'_{min} by half. Using this sensor, we demonstrated high-speed, atomic-resolution imaging of a molten gallium interface at a frame rate of 6.6 s frame^{-1} (39 lines s^{-1}), proving its advantage for analyzing fast interfacial dynamics in liquid environments.

Indoor lighting affects cognition, affect, and behavioural regulation, but these effects are often treated as isolated findings rather than as parts of a unified process. This paper proposes an active inference account of shared indoor lighting in multi-user environments such as offices, classrooms, and libraries. It argues that lighting shapes behaviour through three distinct channels: illuminance modulates perceptual precision, correlated colour temperature modulates arousal relative to circadian optimum, and spectral composition biases behavioural disposition toward engagement or rest. The paper formalises this hypothesis through a proof-of-concept POMDP model of agents performing sustained reading over five hours, using both reading performance and eye-tracking observations. The model generates six falsifiable predictions, all confirmed across 20 Monte Carlo simulations.

We consider time-periodic competitive systems of ordinary differential equations of Kolmogorov type. However, compared with standard assumptions, we relax the regularity of the time-dependent per-capita growth rates by imposing much weaker regularity, namely Carathéodory conditions. An important tool in investigating such systems is the concept of carrying simplex, that is, of an unordered invariant manifold of codimension one that attracts all nonzero orbits. We define the carrying simplex via the compact attractor of compact sets of an extended flow, and that attractor can be obtained as the limit of the actions of the solution operator on some set. Compared with previous papers, our approach has more dynamical flavour, and, further, provides a method of numerical approximation of the carrying simplex. Another feature of our paper is that we prove that the system restricted to the extended carrying simplex is topologically conjugate to a system of one dimension less. This property, appearing in the path-breaking paper by Morris W. Hirsch, has been almost universally neglected in the later papers.

Inverse design of inorganic crystals, in which structures are generated to satisfy a target property while preserving diversity and physical plausibility, remains more demanding than ab initio generation, as property conditioning can degrade the structural quality that current generative models otherwise achieve. We propose a diffusion framework that jointly denoises crystal-structure variables and site-resolved local electronic descriptors through a shared score network. As representative descriptors, we adopt Bader charge and atomic density of states (atomic DOS). Under both band-gap and formation energy conditioned generation, the joint models achieved higher success rates than the structure-only baseline in most target conditions, while simultaneously increasing the fraction of generated structures that satisfy uniqueness, novelty, thermodynamic stability, and physical validity (VSUN criteria). A dummy-variable control confirms that these gains originate from the electronic content of the descriptors rather than from auxiliary site-wise variables. The generated Bader charges agree with DFT references with an MAE of 5.5e-2 e on stable structures, and the generated atomic DOS captures the coarse spectral profile of the DFT reference around the modal accuracy range, although finer details and accuracy vary with elemental species. These results establish local electronic descriptors as effective generative variables that serve two complementary roles: broadening the explored materials space through increased structural diversity, and mitigating the trade-off between property targeting and structural quality by guiding the structural trajectory toward electronically plausible configurations during joint denoising.