Listeners discretize the speech signal by assigning sounds to phonetic categories, though there is variability in how individuals accomplish categorization. Having more consistent categorization of sounds may be advantageous for understanding speech-in-noise (SIN). Though, it is unclear how different levels of neural processing in the auditory system reflect these perceptual differences. We recorded brainstem frequency-following responses (FFRs) and cortical event-related potentials (ERPs) while listeners actively labeled vowels along an acoustic-phonetic continuum using a visual analog scale. We computed intertrial consistency of neural responses to index the stability of listeners' neural speech representations across stimulus presentations. We also assessed how faithfully midbrain and cortical responses represented stimulus acoustics using representational dissimilarity matrices (RDMs) computed across all token pairs. Neural RDMs were then compared with acoustic and phonetic category RDMs to assess whether FFRs and ERPs carried gradient vs. categorical information of the speech signal. We found greater behavioral consistency during phoneme labeling was correlated with improved SIN scores. Neurally, we found greater cortical or subcortical consistency predicted greater behavioral consistency. RDMs revealed subcortical responses retained more acoustic details, while cortical responses more closely reflected abstract phoneme categories. Our findings reveal important benefits of perceptual consistency to other domains of speech perception. We find perceptual consistency is driven by more consistent encoding of speech at either a cortical or subcortical level. More consistent sensory processing could provide a more stable readout of the speech signal to higher cortical brain areas which could confer advantages to later perceptual processes downstream.

In this work, we analyze the structure of higher-order reduced density matrices (RDMs) from the perspective of correlated electron transition processes. We introduce the orbital overlap degree (OOD) as a quantitative measure of the overlap between creation and annihilation orbital indices in individual RDM elements. Systematic analysis of representative strongly correlated systems reveals a strong correlation between the OOD and the magnitude of RDM elements. Motivated by this observation, we develop an orbital-aware (OA) approximation for calculating higher-order RDMs, i.e., oa4-RDMs, that selectively approximates the evaluation of fourth order RDM elements. The oa4-RDMs can be integrated with RDM-based multi-reference approaches, e.g., the density-matrix renormalized group n-electron valence second-order perturbation theory with oa4-RDMs (DMRG-oa4-NEVPT2). Numerical results for Cr2 and 1,2-dioxetanone show that the OA approximation significantly reduces computational cost while preserving the dominant contributions in strongly correlated calculations, and orbital-type analysis of trans-polyacetylene oligomers demonstrates the general applicability of OOD as a descriptor across different orbital representations.

We introduce a data-driven framework for approximating the convex set of N-representable two-electron reduced density matrices (2-RDMs). Traditional approaches characterize this set through linear matrix inequalities that define its supporting hyperplanes. Here, we instead learn a vertex-based approximation to its boundary from molecular data and use this information to improve the set defined by low-order positivity constraints, without explicitly constructing higher order conditions. The resulting semidefinite machine learning approach, combining an input convex neural network with semidefinite programming, drives a direct variational calculation of the 2-RDM with enhanced accuracy at a computational cost comparable to two-positivity calculations. Applications to the potential energy curves of C22-, N2, O22+, CO, NO+, and CN- demonstrate these systematic improvements as well as close agreement with complete active space configuration interaction results. Overall, semidefinite machine learning interweaves data-driven boundary information with semidefinite positivity constraints to yield more accurate energies and 2-RDMs without explicit higher order positivity conditions.

Representability determines when a two-particle reduced density matrix (2-RDM) corresponds to a physical quantum state, enabling many-particle quantum calculations with 2-RDMs rather than the wave function. In this Letter, we present a solution of the representability problem for quantum systems without particle-number conservation. The physically allowed set of 2-RDMs can be characterized from a geometrically "orthogonal" set, the polar cone. We derive explicit linear equations for the two-body operators in the polar cone-the intersection of the p-positive cone with the two-body operator space-to obtain a systematic hierarchy of representability conditions that do not depend on higher RDMs or the wave function. Moreover, by augmenting these conditions with the particle-number variance, we obtain a unified framework for treating both particle-number-conserving and nonconserving systems. We illustrate with a spin system and molecular H_{4}.

The digitalisation of research requires data management systems capable of supporting a broad spectrum of usage scenarios, ranging from document-oriented repositories to fully factographic environments. This paper introduces a methodological approach for the stepwise development of such systems, illustrated by the MatInf Research Data Management System (RDMS). The proposed framework combines a graph-based STAR paradigm-emphasising Statefulness, Traceability, Aim, and Result-with the SET methodology, which enables systematic Standardisation, Extraction, and Testing of research data. Together, these principles provide a pathway towards FAIR-compliant data infrastructures, facilitating reproducibility, re-use, and integration of heterogeneous materials science data. By demonstrating the gradual consolidation of research outputs into unified datasets, this study highlights how adaptive RDMS design can support accelerated scientific discovery and enhance collaborative research in large-scale projects.Scientific Contribution: This work develops a methodological framework for the progressive evolution of research data management systems in materials science, moving from document-oriented to graph-based and ultimately factographic approaches.

Reduced density matrices are central to describing observables in many-body quantum systems. In electronic structure theory, the two-particle reduced density matrix (2-RDM) suffices to determine the energy and other key properties. Recent work has used matrix completion, leveraging the low-rank structure of RDMs and approximate theoretical models, to reconstruct the 2-RDM from partial data and thus reduce the computational cost. However, matrix completion is, in general, an under-determined problem. Revisiting Rosina's theorem (Rosina, M. Queen's Papers on Pure and Applied Mathematics, 1968, No. 11, 369), we here show that the matrix completion is unique under certain conditions, identifying the subset of 2-RDM elements that enables its exact reconstruction from incomplete information. Building on this, we introduce a hybrid quantum-stochastic algorithm that achieves exact matrix completion, demonstrated through applications to the Fermi-Hubbard model.

Linear response (LR) is an important tool in the computational chemist's toolbox. It is therefore unsurprising that the emergence of quantum computers has led to a quantum counterpart known as quantum LR (qLR). However, the current quantum era of near-term intermediate-scale quantum (NISQ) computers is dominated by noise, short decoherence times, and slow measurement speeds. It is therefore of interest to find approximations that can greatly reduce the quantum workload while only slightly impacting the quality of a method. In an effort to achieve this, we approximate the naive qLR with the singles and doubles (qLRSD) method, by either directly approximating the reduced density matrices (RDMs) or indirectly through their respective reduced density cumulants (RDCs). We present an analysis of the measurement costs associated with qLR using RDMs and report qLR results for model hydrogen ladder systems; for varying active space sizes in OCS, SeH2, and H2S; and for symmetrically stretched H2O and BeH2. Discouragingly, while approximations to the 4-body RDMs and RDCs seem to produce good results for systems at the equilibrium geometry and for some types of core excitations, they both tend to fail when the system exhibits strong correlation. All approximations to the 3-body RDMs and/or RDCs severely affect the results and cannot be applied.

In this paper, an efficient implementation of the renormalized internally contracted multireference coupled cluster with singles and doubles (RIC-MRCCSD) into the ORCA quantum chemistry program suite is reported. To this end, Evangelista's Wick&d equation generator was combined with ORCA's native AGE code generator in order to implement the many-body residuals required for the RIC-MRCCSD method. Substantial efficiency gains are realized by deriving a spin-free formulation instead of the previously reported spin-orbital version developed by some of us. Since AGE produces parallelized code, the resulting implementation can directly be run in parallel with substantial speedups when executed on multiple cores. In terms of runtime, the cost of RIC-MRCCSD is shown to be between single-reference RHF-CCSD and UHF-CCSD, even when active space spaces as large as CAS(14,14) are considered. This achievement is largely due to the fact that no reduced density matrices or cumulants higher than three-body enter the formalism. The scalability of the method to large systems is furthermore demonstrated by computing the ground-state of a vitamin B12 model comprised of an active space of CAS(12,12) and 809 orbitals. In terms of accuracy, RIC-MRCCSD is carefully compared to second- and approximate fourth-order n-electron valence state perturbation theories (NEVPT2, NEVPT4(SD)), to the multireference zeroth-order coupled-electron pair approximation (CEPA(0)), as well as to the IC-MRCCSD from Köhn. In contrast to RIC-MRCCSD, the IC-MRCCSD equations are entirely derived by AGE using the conventional projection-based approach, which, however, leads to much higher algorithmic complexity than the former as well as the necessity to calculate up to the five-body RDMs. Remaining challenges such as the variation of the results with the flow, a free parameter that enters the RIC-MRCCSD theory, are discussed.

Machine learning of the one-electron reduced density matrix (1-RDM) provides a computationally efficient surrogate to conventional electronic structure methods. In this work, we train models that map the electron-nuclear interaction potential to the 1-RDM with such an accuracy that predicted 1-RDMs deviate from fully converged ones by no more than a standard self-consistent field (SCF) threshold. Through targeted model optimization strategies, we demonstrate that training set sizes substantially smaller than those required in our previous work [Shao, X. Nat. Commun. 14, 6281 (2023)] are sufficient to reach this accuracy. Furthermore, we introduce a force-correction algorithm that enables stable ab initio molecular dynamics powered by the machine learned 1-RDMs, extending the applicability of the surrogate electronic structure methods to molecules as large as biphenyl.

In spoken language, iconicity, referring to the resemblance between the sound structure of words and their meaning, is often studied using pseudowords. Previously, we showed that representational dissimilarity matrices (RDMs) of the shape ratings of pseudowords correlated significantly with RDMs of acoustic parameters reflecting spectro-temporal variations; the ratings also correlated significantly with voice quality parameters. Here, we examined how perceptual ratings relate to these parameters of pseudowords across eight meaning domains. We largely replicated our previous findings for shape, while observing different patterns for other domains. Using a k-nearest-neighbor (KNN) machine-learning algorithm, we compared 4095 combinations of 12 acoustic parameters (three spectro-temporal and nine characterizing vocal quality) to determine the optimal combination associated with iconicity ratings in each domain. We found that iconic mappings were linked to domain-specific combinations of acoustic parameters. One spectro-temporal parameter, the fast Fourier transform, contributed to all domains, indicating the importance of time-varying spectral properties for iconicity judgments. We applied the KNN approach to generate shape ratings for 160 real words. These generated ratings strongly correlated with perceptual ratings of real words, indicating the value of the KNN approach to assess iconic mapping in natural languages. Our findings support the relevance of iconicity to language.

The Ki67 proliferation index (PI) serves as a crucial prognostic indicator in clinical settings, widely utilized for evaluating breast cancer progression and forecasting chemotherapy efficacy. Nonetheless, conventional manual PI estimation methods are plagued by high subjectivity, time inefficiency, and limited reproducibility. Despite notable advancements in deep learning for Ki67 PI computation, current approaches face challenges in concurrently capturing local cellular morphological features and global tumor proliferation data, particularly when addressing issues like complex backgrounds, staining variability, tumor heterogeneity, and noise in low-resolution images. In response, we introduce Kpi-Net, a multi scale deep learning framework built on U-Net, designed to precisely quantify the Ki67 index in breast cancer pathology images. Initially, we develop a Residual Dilated Multi Scale Module (RDMS Module) that utilizes multi-branch dilated convolutions and residual connections to capture both local and global information, while integrating a Transformer Block to bolster global modeling, effectively mitigating missed and erroneous detections arising from irregular cell distribution. Next, we introduce the High-level Screening-Convolutional Block Attention Module Feature Pyramid Networks (HS-CBAM-FPN), incorporating channel and spatial attention mechanisms alongside the Selective Feature Fusion with CBAM (SFF-CBAM) to facilitate effective integration of multi-level features. Lastly, we apply the watershed algorithm to feature maps, refining cell cluster segmentation via distance transformation and local maximum detection, which improves the precision of Ki67 index computation. Comprehensive experimental results indicate that Kpi-Net surpasses current leading methods in metrics like F1 score and root mean square error (RMSE), highlighting its potential for accurate Ki67 index computation and precise cell detection, thereby offering a dependable tool for accurate breast cancer diagnosis and therapeutic decision-making.