We propose regularized dynamical systems for finding zeros of generalized monotone operators in both continuous- and discrete-time settings. We establish strong convergence of the trajectories generated by such systems. Our results not only refine and extend the existing results, but also highlight examples where our results are applicable where current theory does not. Examples indicate that our methods exhibit varying convergence behaviors, with speeds that can be either faster or slower than the existing methods, depending on particular problems.
Understanding how crystallographic strain orientation governs coupled structural, electronic, and thermoelectric responses of low-symmetry two-dimensional materials remains an open challenge. In particular, the strain-structure-property relationships in pentagonal transition-metal dichalcogenides have not been systematically clarified. In this work, we employ first-principles density functional theory combined with semiclassical Boltzmann transport analysis to investigate the effects of uniaxial strain applied along the in-plane x-and y-directions on PdS2 and PtS2 monolayers. Owing to their non-equivalent X-S bonding topology, strain applied along different directions activates distinct microscopic deformation pathways, with epsilon xxaccommodated predominantly through bond-length variation, whereas epsilon yy involves a greater contribution from bond-angle rearrangement and out-of-plane structural relaxation. At equilibrium, PdS2 and PtS2 exhibit band gaps of 2.13 eV and 3.00 eV, respectively, which decrease significantly under tensile strain, with reductions of up to 66.63% and 52.0%. Strain-dependent projected density-of-states analysis further reveals orientation-dependent changes in the energetic distribution and overlap of Pd/Pt-d and S-p states near the band edges, providing an orbital-level link between directional lattice deformation and electronic reconstruction. These electronic changes are reflected in the thermoelectric response, with the Seebeck coefficient and power exhibiting pronounced dependence on both strain magnitude and loading orientation for both p-type and n-type carriers. Comparative analysis reveals that PtS2 displays a more favorable thermoelectric response, while PdS2 shows enhanced sensitivity to strain orientation demonstrating complementary thermoelectric performance and strain tunability. The dynamical and thermal stability of representative highly strained configurations were further examined by phonon and ab initio molecular dynamics simulations. Overall, the results establish crystallographic strain orientation as an additional degree of freedom, beyond strain magnitude alone, for controlling coupled structural, electronic, and thermoelectric properties in low-symmetry two-dimensional materials.
This study examines whether hydrogen peroxide (H2O2) addition extends lean rotating-detonation operation while preserving pressure-front coherence. Two-dimensional transient reacting-flow simulations were performed for 38 lean conditions in a premixed nitrogen-diluted H2-O2 rotating detonation engine, spanning equivalence ratios of 0.550-0.700 with case-dependent H2O2 addition. Propagated states were assessed using wave velocity relative to the case-specific Chapman-Jouguet (CJ) value, dominant high-pressure-component fraction, front-disruption events, upper-tail pressure intensity relative to the case-specific Zel'dovich-von Neumann-Doring (ZND) pressure, mean OH mass fraction, and pressure-OH spatial coupling. Within the sampled matrix, H2O2 addition extended observed lean propagation from cent = 0.700 to phi = 0.560. All propagated cases retained detonation-like velocities, with U-x/U-CJ = 0.892-0.930, but velocity alone did not distinguish coherent-front from transverse-wave or front-disrupted propagation. Coherent-front cases exhibited a more dominant pressure structure, fewer disruption events, near-reference upper-tail pressure intensity, and near-unity pressure-OH coupling. Mean OH increased monotonically with H2O2 addition within each equivalence-ratio series, whereas pressure-OH coupling provided the clearest separation among the diagnostics evaluated within this two-dimensional matrix. Sensitised lean operability should therefore be assessed using coupled propagation, pressure-topology, and OH-field diagnostics rather than wave survival or velocity alone.
Cancer drug response prediction (DRP) remains a challenging problem due to the intrinsic heterogeneity of tu mors and the dependence of structure-activity relationships on cellular context. Most existing approaches rely on single-omics data and global molecular representations, limiting their ability to capture how specific chemical substructures, known as motifs, interact with complex cellular states. We present Cell-Conditioned Motif Graph (CCMG), a graph-based framework that explicitly models interactions between molecular motifs and multi-omics cellular context for accurate and interpretable DRP. CCMG augments molecular graphs with motif-level represen tations and integrates them with cell-specific multi-omics embeddings through a unified graph structure, enabling context-aware learning of structure-activity relationships. This design allows the model to capture fine-grained substructure-cell interactions while enabling interpretability at the atom, motif, and gene levels. We evaluate CCMG on the Genomics of Drug Sensitivity in Cancer (GDSC) under several data-splitting schemes and conduct ablations to quantify each component's contribution. Results demonstrate that explicit motif-cell coupling im proves generalization over late-fusion baselines, particularly under challenging splits, while offering mechanistic insights that support downstream biological interpretation and clinical hypothesis generation.
This paper revisits the recently introduced stepsize in the gradient descent scheme called NGD, proposed by Hoai et al. We first investigate the NGD stepsize in conjunction with two well-known acceleration techniques: the Heavy Ball method and Nesterov's method. In the convex setting of unconstrained nonlinear optimization problems, we establish the ergodic convergence of the iterates generated by the accelerated versions of NGD at a sublinear rate. We introduce stochastic versions of the proposed accelerated algorithms and analyze their convergence in nonconvex settings. Although our proposed algorithms require global Lipschitz continuity of the gradient, we do not utilize the global Lipschitz constant during computations. Instead, we leverage information about local Lipschitz constants derived from previous iterations. Numerical experiments on various practical machine learning and deep learning problems demonstrate the efficiency of our proposed methods compared to the recent ones.
