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Abstract We construct a thermodynamic potential that can guide training of a generative model defined on a set of binary degrees of freedom. We argue that upon reduction in description, so as to make the generative model computationally manageable, the potential develops multiple minima. This is mirrored by the emergence of multiple minima in the free energy proper of the generative model itself. The variety of training samples that employ N binary degrees of freedom is ordinarily much lower than the size 2N of the full phase space. The nonrepresented configurations, we argue, should be thought of as comprising a high-temperature phase separated by an extensive energy gap from the configurations composing the training set. Thus, training amounts to sampling a free energy surface in the form of a library of distinct bound states, each of which breaks ergodicity. The ergodicity breaking prevents escape into the near continuum of states comprising the high-temperature phase; thus, it is necessary for proper functionality. It may, however, have the side effect of limiting access to patterns that were underrepresented in the training set. At the same time, the ergodicity breaking within the library complicates both learning and retrieval. As a remedy, one may concurrently employ multiple generative models—up to one model per free energy minimum. 

The task of SQL query equivalence checking is important in various real-world applications (including query rewriting and automated grading) that involve complex queries with integrity constraints; yet, state-of-the-art techniques are very limited in their capability of reasoning about complex features (e.g., those that involve sorting, case statement, rich integrity constraints, etc.) in real-life queries. To the best of our knowledge, we propose the first SMT-based approach and its implementation, VeriEQL, capable of proving and disproving bounded equivalence of complex SQL queries. VeriEQL is based on a new logical encoding that models query semantics over symbolic tuples using the theory of integers with uninterpreted functions. It is simple yet highly practical -- our comprehensive evaluation on over 20,000 benchmarks shows that VeriEQL outperforms all state-of-the-art techniques by more than one order of magnitude in terms of the number of benchmarks that can be proved or disproved. VeriEQL can also generate counterexamples that facilitate many downstream tasks (such as finding serious bugs in systems like MySQL and Apache Calcite). 

Abstract Twinning, on par with dislocations, is critically required in plastic deformation of hexagonal close-packed crystals at low temperatures. In contrast to that in cubic-structured crystals, twinning in hexagonal close-packed crystals requires atomic shuffles in addition to shear. Though the twinning shear that is carried by twinning dislocations has been captured for decades, direct experimental observation of the atomic shuffles, especially when the shuffling mode is not unique and does not confine to the plane of shear, remains a formidable challenge to date. Here, by using in-situ transmission electron microscopy, we directly capture the atomic mechanism of the$$\left\{11\bar{2}1\right\}$$ $\left(11\overline{2}1\right)$twinning in hexagonal close packed rhenium nanocrystals. Results show that the$$\left\{11\bar{2}1\right\}$$ $\left(11\overline{2}1\right)$twinning is dominated by the (b_1/2, h_1/2) twinning disconnections. In contrast to conventional expectations, the atomic shuffles accompanying the twinning disconnections proceed on alternative basal planes along 1/6$$\left\langle 1\bar{1}00\right\rangle$$ $\left(1\overline{1}00\right)$, which may be attributed to the free surface in nanocrystal samples, leading to a lack of mirror symmetry across the$$\left\{11\bar{2}1\right\}$$ $\left(11\overline{2}1\right)$twin boundary. 

We argue that one can associate a pseudo-time with sequences of configurations generated in the course of classical Monte Carlo simulations for a single-minimum bound state if the sampling is optimal. Hereby, the sampling rates can be, under special circumstances, calibrated against the relaxation rate and frequency of motion of an actual physical system. The latter possibility is linked to the optimal sampling regime being a universal crossover separating two distinct suboptimal sampling regimes analogous to the physical phenomena of diffusion and effusion, respectively. Bound states break symmetry; one may thus regard the pseudo-time as a quantity emerging together with the bound state. Conversely, when transport among distinct bound states takes place—thus restoring symmetry—a pseudo-time can no longer be defined. One can still quantify activation barriers if the latter barriers are smooth, but simulation becomes impractically slow and pertains to overdamped transport only. Specially designed Monte Carlo moves that bypass activation barriers—so as to accelerate sampling of the thermodynamics—amount to effusive transport and lead to severe under-sampling of transition-state configurations that separate distinct bound states while destroying the said universality. Implications of the present findings for simulations of glassy liquids are discussed. 

Abstract Translational reprogramming allows organisms to adapt to changing conditions. Upstream start codons (uAUGs), which are prevalently present in mRNAs, have crucial roles in regulating translation by providing alternative translation start sites^1–4. However, what determines this selective initiation of translation between conditions remains unclear. Here, by integrating transcriptome-wide translational and structural analyses during pattern-triggered immunity inArabidopsis, we found that transcripts with immune-induced translation are enriched with upstream open reading frames (uORFs). Without infection, these uORFs are selectively translated owing to hairpins immediately downstream of uAUGs, presumably by slowing and engaging the scanning preinitiation complex. Modelling using deep learning provides unbiased support for these recognizable double-stranded RNA structures downstream of uAUGs (which we term uAUG-ds) being responsible for the selective translation of uAUGs, and allows the prediction and rational design of translating uAUG-ds. We found that uAUG-ds-mediated regulation can be generalized to human cells. Moreover, uAUG-ds-mediated start-codon selection is dynamically regulated. After immune challenge in plants, induced RNA helicases that are homologous to Ded1p in yeast and DDX3X in humans resolve these structures, allowing ribosomes to bypass uAUGs to translate downstream defence proteins. This study shows that mRNA structures dynamically regulate start-codon selection. The prevalence of this RNA structural feature and the conservation of RNA helicases across kingdoms suggest that mRNA structural remodelling is a general feature of translational reprogramming. 

Abstract Soliton microcombs are a promising new approach for photonic-based microwave signal synthesis. To date, however, the tuning rate has been limited in microcombs. Here, we demonstrate the first microwave-rate soliton microcomb whose repetition rate can be tuned at a high speed. By integrating an electro-optic modulation element into a lithium niobate comb microresonator, a modulation bandwidth up to 75 MHz and a continuous frequency modulation rate up to 5.0 × 10¹⁴Hz/s are achieved, several orders-of-magnitude faster than existing microcomb technology. The device offers a significant bandwidth of up to tens of gigahertz for locking the repetition rate to an external microwave reference, enabling both direct injection locking and feedback locking to the comb resonator itself without involving external modulation. These features are especially useful for disciplining an optical voltage-controlled oscillator to a long-term reference and the demonstrated fast repetition rate control is expected to have a profound impact on all applications of frequency combs. 

Access to well-defined, model-like, non-noble metal intermetallic compound nanomaterials (<10 nm) with phase pure bulk, bulk-like 1st-atomic-layer surface composition, and unique electronic and surface chemical properties is critical for the fields of catalysis, electronics, and sensor development. Non-noble metal intermetallic compounds are compositionally ordered solid compounds composed of transition metals and semimetals or post-transition metals. Their synthesis as model-like high-surface-area supported nanoparticles is challenging due to the elevated reactivity of the constituent elements and their interaction with the support material. In this study, we have developed a systematic understanding of the fundamental phenomena that control the synthesis of these materials such that phase pure bulk nanoparticles (<10 nm) may be produced with bulk-like surface terminations. The effects of the precursor and support choice, chemical potential of H 2 , reduction temperature, and annealing procedures were investigated to understand the fundamental kinetics of particle formation and interactions that dictate phase purity and stability and 1st-atomic-layer surface composition. The understanding developed may serve as a foundation for further developing advanced synthesis procedures for well-defined nanoparticles with increasing compositional complexity.