Single-cell multi-omics clustering requires integrated representations that preserve shared biological states and modality-specific signals. Graph-based generative methods often couple clustering and reconstruction through a common latent pathway and a single neighborhood graph. We propose SP-LSNTA-GeDGC, which combines task-oriented shared–private (SP) routing and Latent Spectral Neighborhood–Transport Alignment (LSNTA) within a graph-embedded deep generative clustering (GeDGC) framework. Modality-specific residuals support reconstruction, while clustering uses the shared representation without introducing an independent private posterior. LSNTA integrates shared-latent spectral learning, feature-gated mutual nearest neighbors and unbalanced optimal transport to refine graph sample centers and cross-modal relations. The refined centers also serve as reconstruction targets during joint training. Consensus neighborhoods and averaged pairwise transport extend the framework to more than two inputs. Across five bimodal benchmarks, five-run comparisons on identical processed inputs yield a mean clustering accuracy (ACC) increase of 3.08 percentage points over GeDGC. Holm-adjusted paired t tests support ACC and adjusted Rand index (ARI) improvements on Pbmc10k, while gains on other datasets remain descriptive. Metric means decrease on the transcripts, epitopes and accessibility sequencing (TEA-seq) dataset, whereas the compatible four-input dyngen simulation shows small gains. Component ablations reveal dataset-dependent effects without establishing an additional SP–LSNTA interaction. These findings support conditional clustering benefits under known-K evaluation, while broader multimodal generalization and computational scalability remain open challenges.
This study examines the computational scaling of mixed-integer linear programming (MILP) for 12-bar blues guitar-solo generation. A Python/PuLP implementation uses CBC to select and order licks under duration, turnaround, repetition, pause, and connectivity constraints. Transitions receive deterministic rule-based scores. The 7 baseline configurations contain 100 sampled instances each, yielding 693 proven-optimal completions, 6 timeouts, and 1 error. Among completed runs, larger candidate sets have lower mean and median transition scores and higher optimization times. Standard errors, bootstrap confidence intervals, distributional diagnostics, and nonparametric comparisons characterize these results. A paired sensitivity study uses 100 candidate instances per pool to vary repetition and pause limits. Relaxing the repetition limit substantially reduces transition scores across all pools, while runtime decreases in Moderate and increases in Fast. Relaxing the pause limit produces smaller score improvements. The released implementation exports MusicXML outputs and records the information needed to reproduce sampled instance.
Lightweight single-image super-resolution (SISR) requires effective local structural representation and broader contextual modeling under a restricted computational budget. We propose DPALSR, a Dual Prior-Aware Lightweight Super-Resolution Network that conditions successive attention-query representations with complementary directional cues. Learnable Constrained Laplacian Attention (LCLA) derives local directions from the gradient of a learnable zero-sum structural response, whereas Fourier Neural Operator Attention (FNOA) derives coarser within-window contextual directions through compact spectral processing. These cues provide structured inductive biases for learned feature interaction. On five standard SISR benchmarks, DPALSR achieves a competitive reconstruction accuracy–complexity trade-off. At ×4, it obtains 27.01 dB/0.8128 on Urban100 and 31.52 dB/0.9203 on Manga109 using 887K parameters and 59.8G reported FLOPs. Relative to the published MambaIRv2-Light operating point, these PSNR values are higher by 0.19 and 0.28 dB, respectively, with approximately 20.9% fewer FLOPs.
Digital twins are expected to improve supply chain decisions by linking physical operations with models that simulate and optimize them. This literature review, guided by PRISMA 2020, analyzes 104 studies (2016 to 2026) on the enabling technologies of supply chain digital twins, the barriers to their adoption and the algorithmic evidence behind them. The studies were classified into evidence tiers by application domain; twelve supply chain studies and six algorithm studies from other sectors were coded by decision problem, algorithm family, integration level and validation, and the methodological quality of fifteen of them was appraised. The Internet of Things, artificial intelligence, cloud and edge computing, extended reality and blockchain are the main enablers, but in the analyzed set the supply chain evidence is largely conceptual: only two supply chain studies apply an algorithm, none implements a bidirectional digital twin, and only one reports performance measures from a model run. State estimation, reduced-order models and reinforcement learning, which would allow real-time operation, have been evaluated only in other sectors. Technical, organizational and economic barriers appear to reinforce each other. We propose a three-stage implementation pathway and an agenda of seven research gaps, including closed-loop integration, shared benchmarks and multi-company data governance.
Inspired by bio-medical applications, a new mathematical model of the equilibrium of a heterogeneous Timoshenko plate with two thin rigid inclusions connected by a hinge joint is studied. It is assumed that one inclusion is not delaminated from the plate’s elastic matrix, while the second inclusion is delaminated on both sides, thus generating two cracks. Nonlinear conditions of the non-penetration type are imposed on the delaminated cracks. The existence of a variational solution to the delamination problem is established based on the Weierstrass theorem. Optimality conditions characterizing the solution in the domain, as well as on the curves describing the cracks and the inclusion, are derived in the form of a primal-dual system. For its solution, a semi-smooth Newton algorithm is provided rigorously and tested numerically.
