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Background: Consumers' preferences for food crops are guided by quality attributes. This study aimed at deciphering the genetic basis of quality traits, especially tuber flesh color (FC) and oxidative browning (OB) in Dioscorea alata, based on the genome-wide association studies (GWAS) approach. The D. alata panel was planted at two locations in Guadeloupe. At harvest, the FC was scored visually as white, cream, or purple on longitudinally sliced mature tubers. The OB was scored visually as the presence or absence of browning after 15 minutes of exposure of the sliced samples to ambient air. Results: Phenotypic characterization for FC and OB of a diverse panel of D. alata genotypes highlighted significant variation within the panel and across two locations. The genotypes within the panel displayed a weak structure and could be classified into 3 subpopulations. GWAS identified 14 and 4 significant associations for tuber FC and OB, respectively, with phenotypic variance, explained values ranging from 7.18 to 18.04%. Allele segregation analysis at the significantly associated loci highlighted the favorable alleles for the desired traits, i.e., white FC and no OB. A total of 24 putative candidate genes were identified around the significant signals. A comparative analysis with previously reported quantitative trait loci indicated that numerous genomic regions control these traits in D. alata. Conclusion: Our study provides important insights into the genetic control of tuber FC and OB in D. alata. The major and stable loci can be further utilized to improve selection in breeding programs for developing new cultivars with enhanced tuber quality.

We investigate the numerical approximation of integrals over $\mathbb{R}^d$ equipped with the standard Gaussian measure $\gamma$ for integrands belonging to the Gaussian-weighted Sobolev spaces $W^\alpha_p(\mathbb{R}^d, \gamma)$ of mixed smoothness $\alpha \in \mathbb{N}$ for $1 < p < \infty$. We prove the asymptotic order of the convergence of optimal quadratures based on $n$ integration nodes and propose a novel method for constructing asymptotically optimal quadratures. As for related problems, we establish by a similar technique the asymptotic order of the linear, Kolmogorov and sampling $n$-widths in the Gaussian-weighted space $L_q(\mathbb{R}^d, \gamma)$ of the unit ball of $W^\alpha_p(\mathbb{R}^d, \gamma)$ for $1 \leq q < p < \infty$ and $q=p=2$., Comment: 23 pages

In the present paper, we study the analyticity of the leftmost eigenvalue of the linear elliptic partial differential operator with random coefficient and analyze the convergence rate of the quasi-Monte Carlo method for approximation of the expectation of this quantity. The random coefficient is assumed to be represented by an affine expansion $a_0(\boldsymbol{x})+\sum_{j\in \mathbb{N}}y_ja_j(\boldsymbol{x})$, where elements of the parameter vector $\boldsymbol{y}=(y_j)_{j\in \mathbb{N}}\in U^\infty$ are independent and identically uniformly distributed on $U:=[-\frac{1}{2},\frac{1}{2}]$. Under the assumption $ \|\sum_{j\in \mathbb{N}}\rho_j|a_j|\|_{L_\infty(D)} <\infty$ with some positive sequence $(\rho_j)_{j\in \mathbb{N}}\in \ell_p(\mathbb{N})$ for $p\in (0,1]$ we show that for any $\boldsymbol{y}\in U^\infty$, the elliptic partial differential operator has a countably infinite number of eigenvalues $(\lambda_j(\boldsymbol{y}))_{j\in \mathbb{N}}$ which can be ordered non-decreasingly. Moreover, the spectral gap $\lambda_2(\boldsymbol{y})-\lambda_1(\boldsymbol{y})$ is uniformly positive in $U^\infty$. From this, we prove the holomorphic extension property of $\lambda_1(\boldsymbol{y})$ to a complex domain in $\mathbb{C}^\infty$ and estimate mixed derivatives of $\lambda_1(\boldsymbol{y})$ with respect to the parameters $\boldsymbol{y}$ by using Cauchy's formula for analytic functions. Based on these bounds we prove the dimension-independent convergence rate of the quasi-Monte Carlo method to approximate the expectation of $\lambda_1(\boldsymbol{y})$., Comment: 18 pages

We establish sparsity and summability results for coefficient sequences of Wiener-Hermite polynomial chaos expansions of countably-parametric solutions of linear elliptic and parabolic divergence-form partial differential equations with Gaussian random field inputs. The novel proof technique developed here is based on analytic continuation of parametric solutions into the complex domain. It differs from previous works that used bootstrap arguments and induction on the differentiation order of solution derivatives with respect to the parameters. The present holomorphy-based argument allows a unified, ``differentiation-free'' proof of sparsity (expressed in terms of $\ell^p$-summability or weighted $\ell^2$-summability) of sequences of Wiener-Hermite coefficients in polynomial chaos expansions in various scales of function spaces. The analysis also implies corresponding analyticity and sparsity results for posterior densities in Bayesian inverse problems subject to Gaussian priors on uncertain inputs from function spaces. Our results furthermore yield dimension-independent convergence rates of various \emph{constructive} high-dimensional deterministic numerical approximation schemes such as single-level and multi-level versions of Hermite-Smolyak anisotropic sparse-grid interpolation and quadrature in both forward and inverse computational uncertainty quantification., Comment: 165 pages

We investigate non-adaptive methods of deep ReLU neural network approximation in Bochner spaces $L_2({\mathbb U}^\infty, X, \mu)$ of functions on ${\mathbb U}^\infty$ taking values in a separable Hilbert space $X$, where ${\mathbb U}^\infty$ is either ${\mathbb R}^\infty$ equipped with the standard Gaussian probability measure, or ${\mathbb I}^\infty:= [-1,1]^\infty$ equipped with the Jacobi probability measure. Functions to be approximated are assumed to satisfy a certain weighted $\ell_2$-summability of the generalized chaos polynomial expansion coefficients with respect to the measure $\mu$. We prove the convergence rate of this approximation in terms of the size of approximating deep ReLU neural networks. These results then are applied to approximation of the solution to parametric elliptic PDEs with random inputs for the lognormal and affine cases., Comment: arXiv admin note: substantial text overlap with arXiv:2111.05504

The purpose of the present paper is to study the computation complexity of deep ReLU neural networks to approximate functions in H\"older-Nikol'skii spaces of mixed smoothness $H_\infty^\alpha(\mathbb{I}^d)$ on the unit cube $\mathbb{I}^d:=[0,1]^d$. In this context, for any function $f\in H_\infty^\alpha(\mathbb{I}^d)$, we explicitly construct nonadaptive and adaptive deep ReLU neural networks having an output that approximates $f$ with a prescribed accuracy $\varepsilon$, and prove dimension-dependent bounds for the computation complexity of this approximation, characterized by the size and the depth of this deep ReLU neural network, explicitly in $d$ and $\varepsilon$. Our results show the advantage of the adaptive method of approximation by deep ReLU neural networks over nonadaptive one., Comment: 30 pages. arXiv admin note: text overlap with arXiv:2007.08729

We study high-dimensional nonlinear approximation of functions in H\"older-Nikol'skii spaces $H^\alpha_\infty(\mathbb{I}^d)$ on the unit cube $\mathbb{I}^d:=[0,1]^d$ having mixed smoothness, by parametric manifolds. The approximation error is measured in the $L_\infty$-norm. In this context, we explicitly constructed methods of nonlinear approximation, and give dimension-dependent estimates of the approximation error explicitly in dimension $d$ and number $N$ measuring computation complexity of the parametric manifold of approximants. For $d=2$, we derived a novel right asymptotic order of noncontinuous manifold $N$-widths of the unit ball of $H^\alpha_\infty(\mathbb{I}^2)$ in the space $L_\infty(\mathbb{I}^2)$. In constructing approximation methods, the function decomposition by the tensor product Faber series and special representations of its truncations on sparse grids play a central role., Comment: 25 pages

Background and Aims: Inferring the diffusion history of many human-dispersed species is still not straightforward due to unsolved past human migrations. The centre of diversification and routes of migration of the autopolyploid and clonally propagated greater yam, Dioscorea alata, one of the oldest edible tubers is still unsolved. Here, we address yam demographic and dispersal history using a worldwide sample. Methods: We characterized genome-wide patterns of genetic variation by genotyping by sequencing 643 greater yam accessions spanning four continents. First, we disentangled the polyploid and clonal components of yam diversity using alleles frequency distribution and identity by descent approaches. Then, we addressed yam geographical origin and diffusion history with a model-based coalescent inferential approach. Key Results: Diploid genotypes were more frequent than triploids and tetraploids in all the continents. Genetic diversity was generally low and clonality appeared to be a main factor of diversification. The most likely evolutionary scenario supported an early divergence of mainland Southeast Asian and Pacific gene pools with continuous migration between them. Triploids and tetraploids genetic make-up suggests that they have originated from these two regions before westward yam migration. The Indian Peninsula gene pool gave origin to the African gene pool, which was later introduced in the Caribbean region. Conclusions: Our results are congruent with the hypothesis of independent domestication origins of the two main Asian and Pacific gene pools. The low genetic diversity and high clonality observed suggest a strong domestication bottleneck followed by thousands of years of widespread vegetative propagation and polyploidisation. Both processes reduced the extent of diversity available for breeding, which most likely threaten future adaptation.

Background and Aims: Inferring the diffusion history of many human-dispersed species is still not straightforward due to unsolved past human migrations. The centre of diversification and routes of migration of the autopolyploid and clonally propagated greater yam, Dioscorea alata, one of the oldest edible tubers is still unsolved. Here, we address yam demographic and dispersal history using a worldwide sample. Methods: We characterized genome-wide patterns of genetic variation by genotyping by sequencing 643 greater yam accessions spanning four continents. First, we disentangled the polyploid and clonal components of yam diversity using alleles frequency distribution and identity by descent approaches. Then, we addressed yam geographical origin and diffusion history with a model-based coalescent inferential approach. Key Results: Diploid genotypes were more frequent than triploids and tetraploids in all the continents. Genetic diversity was generally low and clonality appeared to be a main factor of diversification. The most likely evolutionary scenario supported an early divergence of mainland Southeast Asian and Pacific gene pools with continuous migration between them. Triploids and tetraploids genetic make-up suggests that they have originated from these two regions before westward yam migration. The Indian Peninsula gene pool gave origin to the African gene pool, which was later introduced in the Caribbean region. Conclusions: Our results are congruent with the hypothesis of independent domestication origins of the two main Asian and Pacific gene pools. The low genetic diversity and high clonality observed suggest a strong domestication bottleneck followed by thousands of years of widespread vegetative propagation and polyploidisation. Both processes reduced the extent of diversity available for breeding, which most likely threaten future adaptation.

We study the computation complexity of deep ReLU (Rectified Linear Unit) neural networks for the approximation of functions from the H\"older-Zygmund space of mixed smoothness defined on the $d$-dimensional unit cube when the dimension $d$ may be very large. The approximation error is measured in the norm of isotropic Sobolev space. For every function $f$ from the H\"older-Zygmund space of mixed smoothness, we explicitly construct a deep ReLU neural network having an output that approximates $f$ with a prescribed accuracy $\varepsilon$, and prove tight dimension-dependent upper and lower bounds of the computation complexity of this approximation, characterized as the size and the depth of this deep ReLU neural network, explicitly in $d$ and $\varepsilon$. The proof of these results are in particular, relied on the approximation by sparse-grid sampling recovery based on the Faber series., Comment: 5 figures

Rice and fish are preferred foods, critical for healthy and nutritious diets, and provide the foundations of local and national economies across Asia. Although transformations, or “revolutions,” in agriculture and aquaculture over the past half-century have primarily relied upon intensified monoculture to increase rice and fish production, agroecological approaches that support biodiversity and utilize natural processes are particularly relevant for achieving a transformation toward food systems with more inclusive, nutrition-sensitive, and ecologically sound outcomes. Rice and fish production are frequently integrated within the same physical, temporal, and social spaces, with substantial variation amongst the types of production practice and their extent. In Cambodia, rice field fisheries that strongly rely upon natural processes persist in up to 80% of rice farmland, whereas more input and infrastructure dependent rice-shrimp culture is expanding within the rice farmland of Vietnam. We demonstrate how a diverse suite of integrated production practices contribute to sustainable and nutrition-sensitive food systems policy, research, and practice. We first develop a typology of integrated production practices illustrating the nature and degree of: (a) fish stocking, (b) water management, (c) use of synthetic inputs, and (d) institutions that control access to fish. Second, we summarize recent research and innovations that have improved the performance of each type of practice. Third, we synthesize data on the prevalence, outcomes, and trajectories of these practices in four South and Southeast Asian countries that rely heavily on fish and rice for food and nutrition security. Focusing on changes since the food systems transformation brought about by the Green Revolution, we illustrate how integrated production practices continue to serve a variety of objectives to varying degrees: food and nutrition security, rural livelihood diversification and income improvement

The periodization of a stationary Gaussian random field on a sufficiently large torus comprising the spatial domain of interest is the basis of various efficient computational methods, such as the classical circulant embedding technique using the fast Fourier transform for generating samples on uniform grids. For the family of Mat\'ern covariances with smoothness index $\nu$ and correlation length $\lambda$, we analyse the nonsmooth periodization (corresponding to classical circulant embedding) and an alternative procedure using a smooth truncation of the covariance function. We solve two open problems: the first concerning the $\nu$-dependent asymptotic decay of eigenvalues of the resulting circulant in the nonsmooth case, the second concerning the required size in terms of $\nu$, $\lambda$ of the torus when using a smooth periodization. In doing this we arrive at a complete characterisation of the performance of these two approaches. Both our theoretical estimates and the numerical tests provided here show substantial advantages of smooth truncation., Comment: 24 pages, 3 figures

Regions around the globe with a monsoon climate experience large inter- seasonal variations of river flows (FAO, 2009). One of the world’s largest river basins, the Mekong River, is a shared water resource of great social, economic and environmental importance to the six countries (Myanmar, China, Laos, Thailand, Cambodia and Vietnam) through which it flows (Moglia et al., 2008). Optimizing the sustainable use of the basin’s water is considered the best approach to improving welfare and realizing the Millen- nium Development Goals of poverty alleviation (ibid.). Inhabitants of the Mekong River Basin (MRB) are mostly rural farmers/fishers and are among the poorest in the world with a third of the population living on less than US$2 per day (FAO, 2011; MRC, 2012). In the Mekong River Basin, rapidly increasing population and urbaniza- tion are placing pressure on food, water and energy needs (MRC, 2012; Huong and Pathirana, 2013). In this region, the impacts of climate change and climate variability increasingly occur. Stern (2006, 2007) and Garnaut (2008) predict that global climate change impacts will lead to sea level rise, coastal erosion, spreading vector borne diseases and more frequent and intense extreme events, i.e. cyclones, heat waves, storm surges and flooding events. This chapter focuses on the impact of more frequent and extreme flooding events in the Mekong River Delta (MRD). Such floods have direct implica- tions for Vietnam’s rice crop, which relies heavily on the waters of the MRD to sustain annual production. While flood events occur annually from July to November in the MRD, increasing flood variability can be seen as a reflec- tion of changing precipitation and land use patterns (Moglia et al., 2008, 2012; WMO, 2009). Flood events have inherently localized impacts, yet are interdependent and almost fully reliant on the interaction between social systems and their technical and ecological contexts (Alexander et al., 2010;Alexander and West, 2011).

Regions around the globe with a monsoon climate experience large inter- seasonal variations of river flows (FAO, 2009). One of the world’s largest river basins, the Mekong River, is a shared water resource of great social, economic and environmental importance to the six countries (Myanmar, China, Laos, Thailand, Cambodia and Vietnam) through which it flows (Moglia et al., 2008). Optimizing the sustainable use of the basin’s water is considered the best approach to improving welfare and realizing the Millen- nium Development Goals of poverty alleviation (ibid.). Inhabitants of the Mekong River Basin (MRB) are mostly rural farmers/fishers and are among the poorest in the world with a third of the population living on less than US$2 per day (FAO, 2011; MRC, 2012). In the Mekong River Basin, rapidly increasing population and urbaniza- tion are placing pressure on food, water and energy needs (MRC, 2012; Huong and Pathirana, 2013). In this region, the impacts of climate change and climate variability increasingly occur. Stern (2006, 2007) and Garnaut (2008) predict that global climate change impacts will lead to sea level rise, coastal erosion, spreading vector borne diseases and more frequent and intense extreme events, i.e. cyclones, heat waves, storm surges and flooding events. This chapter focuses on the impact of more frequent and extreme flooding events in the Mekong River Delta (MRD). Such floods have direct implica- tions for Vietnam’s rice crop, which relies heavily on the waters of the MRD to sustain annual production. While flood events occur annually from July to November in the MRD, increasing flood variability can be seen as a reflec- tion of changing precipitation and land use patterns (Moglia et al., 2008, 2012; WMO, 2009). Flood events have inherently localized impacts, yet are interdependent and almost fully reliant on the interaction between social systems and their technical and ecological contexts (Alexander et al., 2010;Alexander and West, 2011).

Regions around the globe with a monsoon climate experience large inter- seasonal variations of river flows (FAO, 2009). One of the world’s largest river basins, the Mekong River, is a shared water resource of great social, economic and environmental importance to the six countries (Myanmar, China, Laos, Thailand, Cambodia and Vietnam) through which it flows (Moglia et al., 2008). Optimizing the sustainable use of the basin’s water is considered the best approach to improving welfare and realizing the Millen- nium Development Goals of poverty alleviation (ibid.). Inhabitants of the Mekong River Basin (MRB) are mostly rural farmers/fishers and are among the poorest in the world with a third of the population living on less than US$2 per day (FAO, 2011; MRC, 2012). In the Mekong River Basin, rapidly increasing population and urbaniza- tion are placing pressure on food, water and energy needs (MRC, 2012; Huong and Pathirana, 2013). In this region, the impacts of climate change and climate variability increasingly occur. Stern (2006, 2007) and Garnaut (2008) predict that global climate change impacts will lead to sea level rise, coastal erosion, spreading vector borne diseases and more frequent and intense extreme events, i.e. cyclones, heat waves, storm surges and flooding events. This chapter focuses on the impact of more frequent and extreme flooding events in the Mekong River Delta (MRD). Such floods have direct implica- tions for Vietnam’s rice crop, which relies heavily on the waters of the MRD to sustain annual production. While flood events occur annually from July to November in the MRD, increasing flood variability can be seen as a reflec- tion of changing precipitation and land use patterns (Moglia et al., 2008, 2012; WMO, 2009). Flood events have inherently localized impacts, yet are interdependent and almost fully reliant on the interaction between social systems and their technical and ecological contexts (Alexander et al., 2010;Alexander and West, 2011).

Regions around the globe with a monsoon climate experience large inter- seasonal variations of river flows (FAO, 2009). One of the world’s largest river basins, the Mekong River, is a shared water resource of great social, economic and environmental importance to the six countries (Myanmar, China, Laos, Thailand, Cambodia and Vietnam) through which it flows (Moglia et al., 2008). Optimizing the sustainable use of the basin’s water is considered the best approach to improving welfare and realizing the Millen- nium Development Goals of poverty alleviation (ibid.). Inhabitants of the Mekong River Basin (MRB) are mostly rural farmers/fishers and are among the poorest in the world with a third of the population living on less than US$2 per day (FAO, 2011; MRC, 2012). In the Mekong River Basin, rapidly increasing population and urbaniza- tion are placing pressure on food, water and energy needs (MRC, 2012; Huong and Pathirana, 2013). In this region, the impacts of climate change and climate variability increasingly occur. Stern (2006, 2007) and Garnaut (2008) predict that global climate change impacts will lead to sea level rise, coastal erosion, spreading vector borne diseases and more frequent and intense extreme events, i.e. cyclones, heat waves, storm surges and flooding events. This chapter focuses on the impact of more frequent and extreme flooding events in the Mekong River Delta (MRD). Such floods have direct implica- tions for Vietnam’s rice crop, which relies heavily on the waters of the MRD to sustain annual production. While flood events occur annually from July to November in the MRD, increasing flood variability can be seen as a reflec- tion of changing precipitation and land use patterns (Moglia et al., 2008, 2012; WMO, 2009). Flood events have inherently localized impacts, yet are interdependent and almost fully reliant on the interaction between social systems and their technical and ecological contexts (Alexander et al., 2010;Alexander and West, 2011).