On the Second-order Frechet Derivatives of Eigenvalues of Sturm-Liouville Problems in Potentials

The works of V. A. Vinokurov have shown that eigenvalues and normalized eigenfunctions of Sturm-Liouville problems are analytic in potentials, considered as mappings from the Lebesgue space to the space of real numbers and the Banach space of continuous functions respectively. Moreover, the first-order Frechet derivatives are known and paly an important role in many problems. In this paper, we will find the second-order Frechet derivatives of eigenvalues in potentials, which are also proved to be negative definite quadratic forms for some cases.Comment: 10 page

An environment-driven hybrid evolutionary algorithm for dynamic multi-objective optimization problems

open access articleIn dynamic multi-objective optimization problems, the environmental parameters may change over time, which makes the Pareto fronts shifting. To address the issue, a common idea is to track the moving Pareto front once an environmental change occurs. However, it might be hard to obtain the Pareto optimal solutions if the environment changes rapidly. Moreover, it may be costly to implement a new solution. By contrast, robust Pareto optimization over time provides a novel framework to find the robust solutions whose performance is acceptable for more than one environment, which not only saves the computational costs for tracking solutions, but also minimizes the cost for switching solutions. However, neither of the above two approaches can balance between the quality of the obtained non-dominated solutions and the computation cost. To address this issue, environment-driven hybrid dynamic multi-objective evolutionary optimization method is proposed, aiming to fully use strengths of TMO and RPOOT under various characteristics of environmental changes. Two indexes, i.e., the frequency and intensity of environmental changes, are first defined. Then, a criterion is presented based on the characteristics of dynamic environments and the switching cost of solutions, to select an appropriate optimization method in a given environment. The experimental results on a set of dynamic benchmark functions indicate that the proposed hybrid dynamic multi-objective evolutionary optimization method can choose the most rational method that meets the requirements of decision makers, and balance the convergence and robustness of the obtained non-dominated solutions

Selection of optimal escape routes in a flood-prone area based on 2D hydrodynamic modelling

Optimizing escape routes during an extreme flood event is an effective way to mitigate casualties. In this study, a model for selecting optimal escape routes in a flood-prone area has been proposed, which includes a module for predicting the two-dimensional hydrodynamics and modules for assessing the hazard degree for evacuees, calculation of evacuation times and determination of different escape routes. In the module for determining escape routes, two evacuation schemes were used: Scheme A to find optimal escape routes based on established road networks, and Scheme B to design a new optimal evacuation route. Extreme overbank floods occurred in the Lower Yellow River (LYR) in July 1958 (‘58.7’) and August 1982 (‘82.8’) and the proposed model was applied to select the optimal escape routes on a typical floodplain area of the LYR for these two floods. Model predictions indicated that: (i) the optimal escape routes for these two floods were the same for all three starting locations, and the optimized routes provided 3 h more time for evacuees to escape; and (ii) the time of evacuation would need to be earlier for the ‘58.7’ flood because of its larger amount of water volume and higher peak discharge

A Significantly High Abundance of “Candidatus Liberibacter asiaticus” in Citrus Fruit Pith: in planta Transcriptome and Anatomical Analyses

Huanglongbing, a highly destructive disease of citrus, is associated with the non-culturable phloem-limited α-proteobacterium “Candidatus Liberibacter asiaticus” (CLas). The distribution patterns of CLas in infected plant are variable and not consistent, which make the CLas detection and characterization more challenging. Here, we performed a systemic analysis of CLas distribution in citrus branches and fruits of 14 cultivars. A significantly high concentration of CLas was detected in fruit pith (dorsal vascular bundle) of 14 citrus cultivars collected at fruit maturity season. A 2-year monitoring assay of CLas population in citrus branches of “Shatangju” mandarin (Citrus reticulata Blanco “Shatangju”) revealed that CLas population already exhibited a high level even before the appearance of visual symptoms in the fruit rind. Quantitative analyses of CLas in serial 1.5-cm segments of fruit piths showed the CLas was unevenly distributed within fruit pith and tended to colonize in the middle or distal (stylar end) regions of pith. The use of CLas-abundant fruit pith for dual RNA-seq generated higher-resolution CLas transcriptome data compared with the leaf samples. CLas genes involved in transport system, flagellar assembly, lipopolysaccharide biosynthesis, virulence, stress response, and cell surface structure, as well as host genes involved in biosynthesis of antimicrobial-associated secondary metabolites, was up-regulated in leaf midribs compared with fruit pith. In addition, CLas infection caused the severe collapse in phloem and callose deposition in the plasmodesmata of fruit pith. The ability of fruit pith to support multiplication of CLas to high levels makes it an ideal host tissue for morphological studies and in planta transcriptome analyses of CLas–host interactions

Cell type-specific over-expression of chromosome 21 genes in fibroblasts and fetal hearts with trisomy 21

BACKGROUND: Down syndrome (DS) is caused by trisomy 21 (+21), but the aberrations in gene expression resulting from this chromosomal aneuploidy are not yet completely understood. METHODS: We used oligonucleotide microarrays to survey mRNA expression in early- and late-passage control and +21 fibroblasts and mid-gestation fetal hearts. We supplemented this analysis with northern blotting, western blotting, real-time RT-PCR, and immunohistochemistry. RESULTS: We found chromosome 21 genes consistently over-represented among the genes over-expressed in the +21 samples. However, these sets of over-expressed genes differed across the three cell/tissue types. The chromosome 21 gene MX1 was strongly over-expressed (mean 16-fold) in senescent +21 fibroblasts, a result verified by northern and western blotting. MX1 is an interferon target gene, and its mRNA was induced by interferons present in +21 fibroblast conditioned medium, suggesting an autocrine loop for its over-expression. By immunohistochemistry the p78(MX1 )protein was induced in lesional tissue of alopecia areata, an autoimmune disorder associated with DS. We found strong over-expression of the purine biosynthesis gene GART (mean 3-fold) in fetal hearts with +21 and verified this result by northern blotting and real-time RT-PCR. CONCLUSION: Different subsets of chromosome 21 genes are over-expressed in different cell types with +21, and for some genes this over-expression is non-linear (>1.5X). Hyperactive interferon signaling is a candidate pathway for cell senescence and autoimmune disorders in DS, and abnormal purine metabolism should be investigated for a potential role in cardiac defects

The Evolutionary Algorithm to Find Robust Pareto-Optimal Solutions over Time

In dynamic multiobjective optimization problems, the environmental parameters change over time, which makes the true pareto fronts shifted. So far, most works of research on dynamic multiobjective optimization methods have concentrated on detecting the changed environment and triggering the population based optimization methods so as to track the moving pareto fronts over time. Yet, in many real-world applications, it is not necessary to find the optimal nondominant solutions in each dynamic environment. To solve this weakness, a novel method called robust pareto-optimal solution over time is proposed. It is in fact to replace the optimal pareto front at each time-varying moment with the series of robust pareto-optimal solutions. This means that each robust solution can fit for more than one time-varying moment. Two metrics, including the average survival time and average robust generational distance, are present to measure the robustness of the robust pareto solution set. Another contribution is to construct the algorithm framework searching for robust pareto-optimal solutions over time based on the survival time. Experimental results indicate that this definition is a more practical and time-saving method of addressing dynamic multiobjective optimization problems changing over time