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Abstract: We obtained several structural features of an NK fitness landscape by analytical approach. Particularly, we focused on spatial distributions of “ascending slopes”, “highlands”, “nearly neutral networks”, and “local optima” along the fitness coordinate , from the viewpoint of adaptive walks with step-width d , where d is the number of mutated sites (Hamming distance) after a generation. The parameter k governs the degree of the ruggedness on the NK landscape, and we handled cases where k is moderate against the sequence length. From the foot up to the middle region on the landscape, many ascending slopes exist (high evolvability) and these slopes extend up near the “highland”, which is mathematically defined as the specific region where the expectation of the fitness increment becomes zero. Denoting the standard deviation of the fitness change at by , we considered the existence of “nearly neutral networks”, which percolate in the fitness band between and . Our results suggest that the highland corresponds to a phase-transition threshold of the formation of the nearly neutral networks. Near or over the highland, “local optima at the dth order” appear drastically (low evolvability), where d means the radius of their basins. The value of increases with d increasing. Then, as the fitness becomes higher, the basin size of the local optima increases. This leads to a conclusion that it is very hard or impossible for walkers with step-width d to reach near the global peak when d is a realistic large value: –6, and suggests that the region over the middle in real landscapes may be considerably smooth with small k-values to maintain high evolvability. [Copyright &y& Elsevier]

Abstract: In this paper we present a combinatorial model of sequence to shape maps. Our particular construction arises in the context of representing nucleotide interactions beyond Watson–Crick base pairs and its key feature is to replace biophysical steric by combinatorial constraints. We show that these combinatory maps produce exponentially many shapes and induce sets of sequences which contain extended connected subgraphs of diameter n, where n denotes the length of the sequence. Our main result is to prove the existence of exponentially many shapes that have neutral networks. [Copyright &y& Elsevier]

Abstract: It is known (Reidys et al., 1997b. Bull. Math. Biol. 59(2), 339–397) that for any two secondary structures there exists an RNA sequence compatible with both, and that this result does not extend to more than two secondary structures. Indeed, a simple formula for the number of RNA sequences compatible with secondary structures plays a role in the algorithms of Flamm et al. (2001. RNA 7, 254–265) and of Abfalter et al. (2003. Proceedings of the German Conference on Bioinformatics, http://www.tbi.univie.ac.at/papers/Abstracts/03-018.pdf) to design an RNA switch. Here we show that a natural extension of this problem is NP-complete. Unless , there is no polynomial time algorithm, which when given secondary structures , for , determines the least number of positions, such that after removal of all base pairs incident to these positions there exists an RNA nucleotide sequence compatible with the given secondary structures. We also consider a restricted version of this problem with a “fixed maximum” number of possible stars and show that it has a simple polynomial time solution. [Copyright &y& Elsevier]

Abstract: We investigate the evolutionary dynamics of a finite population of RNA sequences replicating on a neutral network. Despite the lack of differential fitness between viable sequences, we observe typical properties of adaptive evolution, such as increase of mean fitness over time and punctuated-equilibrium transitions, after initial mutation–selection balance has been reached. We find that a product of population size and mutation rate of approximately 30 or larger is sufficient to generate selection pressure for mutational robustness, even if the population size is orders of magnitude smaller than the neutral network on which the population resides. Our results show that quasispecies effects and neutral drift can occur concurrently, and that the relative importance of each is determined by the product of population size and mutation rate. [Copyright &y& Elsevier]

Motivation Motoo Kimura's neutral theory stipulates that evolution is predominantly driven by neutral mutations. RNA, realizing both genotype (its linear sequence of nucleotides) as well as phenotype (its folded secondary structure) represents a particularly well suited test bed for studying neutrality. This leads to neutral networks of RNA secondary structures, i.e. sets of sequences all of which folding into a fixed phenotype and whose organization plays a crucial role for neutral evolution. In this paper we bring a new perspective to the neutral theory by studying the consequences of the mostly ignored fact that the genotype-to-phenotype map for RNA is often one-to-many. In fact 29.5% of random RNA sequences realize more than one phenotype (minimum free energy structure). We call two genotypes to be quasineutral if their sets of associated phenotypes have non-empty intersection. Results We show that even though the energy profile of quasineutral mutations is almost identical to the neutral ones, a walk in the genotype space whose consecutive steps are quasineutral, can percolate phenotype space and so such walks bridge between neutral and random walks. This provides further evidence that evolution is continuous. We also study how these drift walks transition between neutral networks. [ABSTRACT FROM AUTHOR]

Abstract: Robustness, the insensitivity of some of a biological system''s functionalities to a set of distinct conditions, is intimately linked to fitness. Recent studies suggest that it may also play a vital role in enabling the evolution of species. Increasing robustness, so is proposed, can lead to the emergence of evolvability if evolution proceeds over a neutral network that extends far throughout the fitness landscape. Here, we show that the design principles used to achieve robustness dramatically influence whether robustness leads to evolvability. In simulation experiments, we find that purely redundant systems have remarkably low evolvability while degenerate, i.e. partially redundant, systems tend to be orders of magnitude more evolvable. Surprisingly, the magnitude of observed variation in evolvability can neither be explained by differences in the size nor the topology of the neutral networks. This suggests that degeneracy, a ubiquitous characteristic in biological systems, may be an important enabler of natural evolution. More generally, our study provides valuable new clues about the origin of innovations in complex adaptive systems. [Copyright &y& Elsevier]

Abstract: and have studied a simple model of the evolution of a network of N genes, in order to explain the observed phenomenon that systems evolve to be robust. These authors primarily considered the case and used simulations to reach their conclusions. Here we investigate this model in more detail, considering systems of different sizes with and without recombination, and with selection for convergence instead of to a specified limit. For the simpler evolutionary model lacking recombination, we analyze the system as a neutral network. This allows us to describe the equilibrium distribution networks within genotype space. Our results show that, given a sufficiently large population size, the qualitative observation that systems evolve to be robust, is itself robust, as it does not depend on the details of the model. In simple terms, robust systems have more viable offspring, so the evolution of robustness is merely selection for increased fecundity, an observation that is well known in the theory of neutral networks. [Copyright &y& Elsevier]

Designating amino-acid sequences that fold into a common main-chain structure as “neutral sequences” for the structure, regardless of their function or stability, we investigated the distribution of neutral sequences in protein sequence space. For four distinct target structures (α, β,α/β and α+β types) with the same chain length of 108, we generated the respective neutral sequences by using the inverse folding technique with a knowledge-based potential function. We assumed that neutral sequences for a protein structure have Z scores higher than or equal to fixed thresholds, where thresholds are defined as the Z score for the corresponding native sequence (case 1) or much greater Z score (case 2). An exploring walk simulation suggested that the neutral sequences mapped into the sequence space were connected with each other through straight neutral paths and formed an inherent neutral network over the sequence space. Through another exploring walk simulation, we investigated contiguous regions between or among the neutral networks for the distinct protein structures and obtained the following results. The closest approach distance between the two neutral networks ranged from 5 to 29 on the Hamming distance scale, showing a linear increase against the threshold values. The sequences located at the “interchange” regions between the two neutral networks have intermediate sequence-profile-scores for both corresponding structures. Introducing a “ball” in the sequence space that contains at least one neutral sequence for each of the four structures, we found that the minimal radius of the ball that is centered at an arbitrary position ranged from 35 to 50, while the minimal radius of the ball that is centered at a certain special position ranged from 20 to 30, in the Hamming distance scale. The relatively small Hamming distances (5–30) may support an evolution mechanism by transferring from a network for a structure to another network for a more beneficial structure via the interchange regions. [Copyright &y& Elsevier]

Evolvability and robustness are crucial for the origin and maintenance of complex organisms, but may not be simultaneously achievable as robust traits are also hard to change. Andreas Wagner has proposed a solution to this paradox by arguing that the many-to-few aspect of genotype–phenotype maps creates neutral networks of genotypes coding for the same phenotype. Phenotypes with large networks are genetically robust, but they may also have more neighboring phenotypes and thus higher evolvability. In this paper, we explore the generality of this idea by sampling large numbers of random genotype–phenotype maps for Boolean genotypes and phenotypes. We show that there is indeed a preponderance of positive correlations between the evolvability and robustness of phenotypes within a genotype–phenotype map, but also that there are negative correlations between average evolvability and robustness across maps. We interpret this as predicting a positive correlation across the phenotypic states of a character, but a negative correlation across characters. We also argue that evolvability and robustness tend to be negatively correlated when phenotypes are measured on ordinal or higher scale types. We conclude that Wagner's conjecture of a positive relation between robustness and evolvability is based on strict and somewhat unrealistic biological assumptions. [ABSTRACT FROM AUTHOR]

Abstract: Neutral dynamics occur in evolution if all types are ‘effectively equal’ in their reproductive success, where the definition of ‘effectively equal’ depends on the population size and the details of mutations. Empirically observed neutral genetic evolution in extremely large clonal populations can only be explained under current models if selection is completely absent. Such models typically consider the case where population dynamics occurs on a different timescale to evolution. However, this assumption is invalid when mutations are not rare in a whole population. We show that this has important consequences for the occurrence of neutral evolution in clonal populations. In highly connected type spaces, neutral dynamics can occur for all population sizes despite significant selective differences, via the forming of effectively neutral networks connecting rare neutral types. Biological implications include an explanation for the high diversity of rare types that survive in large clonal populations, and a theoretical justification for the use of neutral null models. [Copyright &y& Elsevier]

Abstract: In this paper we enumerate k-noncrossing RNA pseudoknot structures with given minimum stack-length, σ. One main result of the paper is the asymptotic formula for their number: , where is explicitly known. Our results show that the number of k-noncrossing structures without isolated base pairs is significantly smaller than the number of all k-noncrossing structures. In particular we prove that, for large n, the number of 3- and 4-noncrossing RNA structures with stack-length ⩾2 is given by and , respectively. Our results are of importance for prediction algorithms and provide evidence for the existence of neutral networks of RNA pseudoknot structures. [Copyright &y& Elsevier]

• An ensemble CNN is established to fuse multiple features from different architectures. • Multi-scale capability is equipped with the network by using various-perspective features. • Improved CNN model reliability by feature visualization and expert selection. For patients with glioblastoma multiform (GBM), differentiating pseudoprogression (PsP) from true tumor progression (TTP) is a challenging and time-consuming task for radiologists. Although deep neural networks can automatically diagnose PsP and TTP, lacking of interpretability has always been its major drawback. To overcome these shortcomings and produce more reliable outcomes, we propose a transparency-guided ensemble convolutional neural network (CNN) to automatically discriminate PsP and TTP in magnetic resonance imaging (MRI). A total of 84 patients with GBM were enrolled in the study. First, three typical convolutional neutral networks, namely VGG, ResNet and DenseNet, were trained to distinguish PsP and TTP. Subsequently, we used class-specific gradient information from convolutional layers to highlight the important regions in MRI scans. And radiologists selected the most lesion-relevant layer for each CNN. Finally, the selected layers are utilized to guide the construction of a multi-scale ensemble CNN whose classification accuracy reached 90.20%, and whose specificity is promoted 20% than that of a single CNN. The results demonstrate the presented network can enhance the reliability and accuracy of CNNs. [ABSTRACT FROM AUTHOR]

Air pollution in many countries is worsening with industrialization and urbanization, resulting in climate change and affecting people's health, thus, making the work of policymakers more difficult. It is therefore both urgent and necessary to establish amore scientific air quality monitoring and early warning system to evaluate the degree of air pollution objectively, and predict pollutant concentrations accurately. However, the integration of air quality assessment and air pollutant concentration prediction to establish an air quality system is not common. In this paper, we propose a new air quality monitoring and early warning system, including an assessment module and forecasting module. In the air quality assessment module, fuzzy comprehensive evaluation is used to determine the main pollutants and evaluate the degree of air pollution more scientifically. In the air pollutant concentration prediction module, a novel hybridization model combining complementary ensemble empirical mode decomposition, a modified cuckoo search and differential evolution algorithm, and an Elman neural network, is proposed to improve the forecasting accuracy of six main air pollutant concentrations. To verify the effectiveness of this system, pollutant data for two cities in China are used. The result of the fuzzy comprehensive evaluation shows that the major air pollutants in Xi'an and Jinan are PM 10 and PM 2.5 respectively, and that the air quality of Xi'an is better than that of Jinan. The forecasting results indicate that the proposed hybrid model is remarkably superior to all benchmark models on account of its higher prediction accuracy and stability. [ABSTRACT FROM AUTHOR]

Abstract: Although the basic mechanics of evolution have been understood since Darwin, debate continues over whether macroevolutionary phenomena are driven by the fitness structure of genotype space or by ecological interaction. In this paper we propose a simple model capturing key features of fitness-landscape and ecological models of evolution. Our model describes evolutionary dynamics in a high-dimensional, structured genotype space with interspecies interaction. We find promising qualitative similarity with the empirical facts about macroevolution, including broadly distributed extinction sizes and realistic exploration of the genotype space. The abstraction of our model permits numerous applications beyond macroevolution, including protein and RNA evolution. [Copyright &y& Elsevier]

Abstract: We analyze here the evolutionary consequences of selection with delay in a population genetics context. In the classical works on evolutionary dynamics, an individual produces off-springs in direct proportion to its fitness, a process in which mutations may occur. In the present scenario of delayed selection, individuals that acquire deleterious mutations can still reproduce unharmed for several generations. During this time delay, the damage passed on to off-springs can potentially be repaired by subsequent compensatory mutations. In the absence of such a repair, the individual becomes sterile. Here we study the population-genetic effects of such a time delay by means of both numerical simulations and theoretical modeling. The results show that delayed selection lowers the extinction threshold, endangering the survival of the population. Surprisingly, however, no traces of this delay effect are encountered in the sequence diversity of the population. These conclusions suggest that delayed selection is hard to detect in genetic data and thus could be a wide-spread but rarely detected phenomenon. [Copyright &y& Elsevier]

Abstract: We study how correlations in the random fitness assignment may affect the structure of fitness landscapes, in three classes of fitness models. The first is a phenotype space in which individuals are characterized by a large number n of continuously varying traits. In a simple model of random fitness assignment, viable phenotypes are likely to form a giant connected cluster percolating throughout the phenotype space provided the viability probability is larger than . The second model explicitly describes genotype-to-phenotype and phenotype-to-fitness maps, allows for neutrality at both phenotype and fitness levels, and results in a fitness landscape with tunable correlation length. Here, phenotypic neutrality and correlation between fitnesses can reduce the percolation threshold, and correlations at the point of phase transition between local and global are most conducive to the formation of the giant cluster. In the third class of models, particular combinations of alleles or values of phenotypic characters are “incompatible” in the sense that the resulting genotypes or phenotypes have zero fitness. This setting can be viewed as a generalization of the canonical Bateson–Dobzhansky–Muller model of speciation and is related to K-SAT problems, prominent in computer science. We analyze the conditions for the existence of viable genotypes, their number, as well as the structure and the number of connected clusters of viable genotypes. We show that analysis based on expected values can easily lead to wrong conclusions, especially when fitness correlations are strong. We focus on pairwise incompatibilities between diallelic loci, but we also address multiple alleles, complex incompatibilities, and continuous phenotype spaces. In the case of diallelic loci, the number of clusters is stochastically bounded and each cluster contains a very large sub-cube. Finally, we demonstrate that the discrete NK model shares some signature properties of models with high correlations. [Copyright &y& Elsevier]

We examine the applicability of Principal Component Analysis (PCA) and Artificial Neural Network (ANN) methods of data analysis to biosignature detection. These techniques show promise in classifying and simplifying the representation of patterns of amino acids resulting from biological and non-biological syntheses. PCA correctly identifies glycine and alanine as the amino acids contributing the most information to the task of discriminating biotic and abiotic samples. Trained ANNs correctly classify between 86.1 and 99.5% of a large set of amino acid samples as biotic or abiotic. These and similar techniques are important in the design of automated data analysis systems for robotic missions to distant planetary bodies. Both techniques are robust with respect to noisy and incomplete data. Analysis of the performance of PCA and ANNs also lends insight into the localization of useful information within a particular data set, a feature that may be exploited in the selection of experiments for efficient mission design. [Copyright &y& Elsevier]