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Heat stress is a major abiotic stress factor reducing crop productivity and climate change models predict increasing temperatures in many production regions. Common bean ( Phaseolus vulgaris L .) is an important crop for food security in the tropics and heat stress is expected to cause increasing yield losses. To study physiological responses and to characterize the genetics of heat stress tolerance, we evaluated the recombinant inbred line (RIL) population IJR (Indeterminate Jamaica Red) x AFR298 of the Andean gene pool. Heat stress (HS) conditions in the field affected many traits across the reproductive phase. High nighttime temperatures appeared to have larger effects than maximum daytime temperatures. Yield was reduced compared to non-stress conditions by 37% and 26% in 2016 and 2017 seasons, respectively. The image analysis tool HYRBEAN was developed to evaluate pollen viability (PolVia). A significant reduction of PolVia was observed in HS and higher viability was correlated with yield only under stress conditions. In susceptible lines the reproductive phase was extended and defects in the initiation of seed, seed fill and seed formation were identified reducing grain quality. Higher yields under HS were correlated with early flowering, high pollen viability and effective seed filling. Quantitative trait loci (QTL) analysis revealed a QTL for both pod harvest index and PolVia on chromosome Pv05, for which the more heat tolerant parent IJR contributed the positive allele. Also, on chromosome Pv08 a QTL from IJR improved PolVia and the yield component pods per plant. HS affected several traits during the whole reproductive development, from floral induction to grain quality traits, indicating a general heat perception affecting many reproductive processes. Identification of tolerant germplasm, indicator traits for heat tolerance and molecular tools will help to breed heat tolerant varieties to face future climate change effects.

Recent advances in quantum technology have led to the development and manufacturing of experimental programmable quantum annealing optimizers that contain hundreds of quantum bits. These optimizers, commonly referred to as ‘D-Wave’ chips, promise to solve practical optimization problems potentially faster than conventional ‘classical’ computers. Attempts to quantify the quantum nature of these chips have been met with both excitement and skepticism but have also brought up numerous fundamental questions pertaining to the distinguishability of experimental quantum annealers from their classical thermal counterparts. Inspired by recent results in spin-glass theory that recognize ‘temperature chaos’ as the underlying mechanism responsible for the computational intractability of hard optimization problems, we devise a general method to quantify the performance of quantum annealers on optimization problems suffering from varying degrees of temperature chaos: A superior performance of quantum annealers over classical algorithms on these may allude to the role that quantum effects play in providing speedup. We utilize our method to experimentally study the D-Wave Two chip on different temperature-chaotic problems and find, surprisingly, that its performance scales unfavorably as compared to several analogous classical algorithms. We detect, quantify and discuss several purely classical effects that possibly mask the quantum behavior of the chip.

Background Common bean is an important staple crop in the tropics of Africa, Asia and the Americas. Particularly smallholder farmers rely on bean as a source for calories, protein and micronutrients. Drought is a major production constraint for common bean, a situation that will be aggravated with current climate change scenarios. In this context, new tools designed to understand the genetic basis governing the phenotypic responses to abiotic stress are required to improve transfer of desirable traits into cultivated beans. Results A multiparent advanced generation intercross (MAGIC) population of common bean was generated from eight Mesoamerican breeding lines representing the phenotypic and genotypic diversity of the CIAT Mesoamerican breeding program. This population was assessed under drought conditions in two field trials for yield, 100 seed weight, iron and zinc accumulation, phenology and pod harvest index. Transgressive segregation was observed for most of these traits. Yield was positively correlated with yield components and pod harvest index (PHI), and negative correlations were found with phenology traits and micromineral contents. Founder haplotypes in the population were identified using Genotyping by Sequencing (GBS). No major population structure was observed in the population. Whole Genome Sequencing (WGS) data from the founder lines was used to impute genotyping data for GWAS. Genetic mapping was carried out with two methods, using association mapping with GWAS, and linkage mapping with haplotype-based interval screening. Thirteen high confidence QTL were identified using both methods and several QTL hotspots were found controlling multiple traits. A major QTL hotspot located on chromosome Pv01 for phenology traits and yield was identified. Further hotspots affecting several traits were observed on chromosomes Pv03 and Pv08. A major QTL for seed Fe content was contributed by MIB778, the founder line with highest micromineral accumulation. Based on imputed WGS data, candidate genes are reported for the identified major QTL, and sequence changes were identified that could cause the phenotypic variation. Conclusions This work demonstrates the importance of this common bean MAGIC population for genetic mapping of agronomic traits, to identify trait associations for molecular breeding tool design and as a new genetic resource for the bean research community.

The Mpemba effect occurs when a hot system cools faster than an initially colder one, when both are refrigerated in the same thermal reservoir. Using the custom-built supercomputer Janus II, we study the Mpemba effect in spin glasses and show that it is a nonequilibrium process, governed by the coherence length ξ of the system. The effect occurs when the bath temperature lies in the glassy phase, but it is not necessary for the thermal protocol to cross the critical temperature. In fact, the Mpemba effect follows from a strong relationship between the internal energy and ξ that turns out to be a sure-tell sign of being in the glassy phase. Thus, the Mpemba effect presents itself as an intriguing avenue for the experimental study of the coherence length in supercooled liquids and other glass formers.

The debate around the potential superiority of quantum annealers over their classical counterparts has been ongoing since the inception of the field. Recent technological breakthroughs, which have led to the manufacture of experimental prototypes of quantum annealing optimizers with sizes approaching the practical regime, have reignited this discussion. However, the demonstration of quantum annealing speedups remains to this day an elusive albeit coveted goal. We examine the power of quantum annealers to provide a different type of quantum enhancement of practical relevance, namely, their ability to serve as useful samplers from the ground-state manifolds of combinatorial optimization problems. We study, both numerically by simulating stoquastic and non-stoquastic quantum annealing processes, and experimentally, using a prototypical quantum annealing processor, the ability of quantum annealers to sample the ground-states of spin glasses differently than thermal samplers. We demonstrate that (i) quantum annealers sample the ground-state manifolds of spin glasses very differently than thermal optimizers (ii) the nature of the quantum fluctuations driving the annealing process has a decisive effect on the final distribution, and (iii) the experimental quantum annealer samples ground-state manifolds significantly differently than thermal and ideal quantum annealers. We illustrate how quantum annealers may serve as powerful tools when complementing standard sampling algorithms.

In plant and animal breeding, genomic prediction models are established to select new lines based on genomic data, without the need for laborious phenotyping. Prediction models can be trained on recent or historic phenotypic data and increasingly available genotypic data. This enables the adoption of genomic selection also in under-used legume crops such as common bean. Beans are an important staple food in the tropics and mainly grown by smallholders under limiting environmental conditions such as drought or low soil fertility. Therefore, genotype-by-environment interactions (G × E) are an important consideration when developing new bean varieties. However, G × E are often not considered in genomic prediction models nor are these models implemented in current bean breeding programs. Here we show the prediction abilities of four agronomic traits in common bean under various environmental stresses based on twelve field trials. The dataset includes 481 elite breeding lines characterized by 5,820 SNP markers. Prediction abilities over all twelve trials ranged between 0.6 and 0.8 for yield and days to maturity, respectively, predicting new lines into new seasons. In all four evaluated traits, the prediction abilities reached about 50-80% of the maximum accuracies given by phenotypic correlations and heritability. Predictions under drought and low phosphorus stress were up to 10 and 20% improved when G × E were included in the model, respectively. Our results demonstrate the potential of genomic selection to increase the genetic gain in common bean breeding. Prediction abilities improved when more phenotypic data was available and G × E could be accounted for. Furthermore, the developed models allowed us to predict genotypic performance under different environmental stresses. This will be a key factor in the development of common bean varieties adapted to future challenging conditions.

Common bean (Phaseolus vulgaris) is grown in two growth types, bush and climbing beans. The latter are preferred in several regions in East and Southern African as well as in Latin America (dominant in Rwanda and Colombia), due to higher yields and resilience compared with bush type. Common bean productivity is reduced by several pests and diseases between them. Bean common mosaic virus (BCMV), which is the most common and destructive poty‐virus affecting bean production worldwide, and anthracnose, caused by the fungus Colletotrichum lindemuthianum, can cause yield losses as high as 95% in susceptible cultivars. Further important traits in common bean are high micro mineral contents to alleviate malnutrition and grain quality traits such as the canning quality of bean varieties, which is important for farmers to access the processing market. In this study, new climbing bean populations were generated (coded ENF/CGA) to combine high seed iron (SdFe) and multiple diseases resistance. Double and triple crosses between parents with virus and anthracnose resistance, high SdFe, and good agronomic traits were employed. In trials in Darien and Popayan, lines were identified that combine BCMNV/BCMV and anthracnose resistance with seed yields above 4000 kg/ha. Phenotypic evaluations validated the usefulness of SNP markers tagging the genes bc‐3 and I for BCMN and Co‐3 for anthracnose as a selection tool for field resistance. These results show the genetic potential of the lines that are now being tested in target regions to be delivered to smallholder farmers.

Experiments featuring non-equilibrium glassy dynamics under temperature changes still await interpretation. There is a widespread feeling that temperature chaos (an extreme sensitivity of the glass to temperature changes) should play a major role but, up to now, this phenomenon has been investigated solely under equilibrium conditions. In fact, the very existence of a chaotic effect in the non-equilibrium dynamics is yet to be established. In this article, we tackle this problem through a large simulation of the 3D Edwards-Anderson model, carried out on the Janus II supercomputer. We find a dynamic effect that closely parallels equilibrium temperature chaos. This dynamic temperature-chaos effect is spatially heterogeneous to a large degree and turns out to be controlled by the spin-glass coherence length ξ . Indeed, an emerging length-scale ξ * rules the crossover from weak (at ξ  ≪  ξ * ) to strong chaos ( ξ  ≫  ξ * ). Extrapolations of ξ * to relevant experimental conditions are provided. While temperature chaos is an equilibrium notion that denotes the extreme fragility of the glassy phase with respect to temperature changes, it remains unclear whether it is present in non-equilibrium dynamics. Here the authors use the Janus II supercomputer to prove the existence of dynamic temperature chaos, a nonequilibrium phenomenon that closely mimics equilibrium temperature chaos.

Quantum annealers are commercial devices that aim to solve very hard computational problems 1 , typically those involving spin glasses 2 , 3 . Just as in metallurgic annealing, in which a ferrous metal is slowly cooled 4 , quantum annealers seek good solutions by slowly removing the transverse magnetic field at the lowest possible temperature. Removing the field diminishes the quantum fluctuations but forces the system to traverse the critical point that separates the disordered phase (at large fields) from the spin-glass phase (at small fields). A full understanding of this phase transition is still missing. A debated, crucial question regards the closing of the energy gap separating the ground state from the first excited state. All hopes of achieving an exponential speed-up, compared to classical computers, rest on the assumption that the gap will close algebraically with the number of spins 5 – 9 . However, renormalization group calculations predict instead that there is an infinite-randomness fixed point 10 . Here we solve this debate through extreme-scale numerical simulations, finding that both parties have grasped parts of the truth. Although the closing of the gap at the critical point is indeed super-algebraic, it remains algebraic if one restricts the symmetry of possible excitations. As this symmetry restriction is experimentally achievable (at least nominally), there is still hope for the quantum annealing paradigm 11 – 13 . We find that, in the quantum transition of Ising spin glass, the closing of the gap at the critical point can remain algebraic by restricting the symmetry of possible excitations, which is crucial for quantum annealing.

Spin glasses are a longstanding model for the sluggish dynamics that appear at the glass transition. However, spin glasses differ from structural glasses in a crucial feature: they enjoy a time reversal symmetry. This symmetry can be broken by applying an external magnetic field, but embarrassingly little is known about the critical behavior of a spin glass in a field. In this context, the space dimension is crucial. Simulations are easier to interpret in a large number of dimensions, but one must work below the upper critical dimension (i.e., in d < 6) in order for results to have relevance for experiments. Here we show conclusive evidence for the presence of a phase transition in a four-dimensional spin glass in a field. Two ingredients were crucial for this achievement: massive numerical simulations were carried out on the Janus special-purpose computer, and a new and powerful finite-size scaling method.