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The molecular clock provides a powerful way to estimate species divergence times. If information on some species divergence times is available from the fossil or geological record, it can be used to calibrate a phylogeny and estimate divergence times for all nodes in the tree. The Bayesian method provides a natural framework to incorporate different sources of information concerning divergence times, such as information in the fossil and molecular data. Current models of sequence evolution are intractable in a Bayesian setting, and Markov chain Monte Carlo (MCMC) is used to generate the posterior distribution of divergence times and evolutionary rates. This method is computationally expensive, as it involves the repeated calculation of the likelihood function. Here, we explore the use of Taylor expansion to approximate the likelihood during MCMC iteration. The approximation is much faster than conventional likelihood calculation. However, the approximation is expected to be poor when the proposed parameters are far from the likelihood peak. We explore the use of parameter transforms (square root, logarithm, and arcsine) to improve the approximation to the likelihood curve. We found that the new methods, particularly the arcsine-based transform, provided very good approximations under relaxed clock models and also under the global clock model when the global clock is not seriously violated. The approximation is poorer for analysis under the global clock when the global clock is seriously wrong and should thus not be used. The results suggest that the approximate method may be useful for Bayesian dating analysis using large data sets.

Castration-resistant prostate cancer (CRPC) poses a significant challenge in the medical field. The study developed a novel model, the branching bivariate Weibull distribution (BBWD), tailored to address CRPC and stems from the maximum likelihood estimation (MLE) function. It considers a medicinal biosystem aimed at transitioning androgen-dependent prostate cancer into an androgen-independent state. The BBWD model is designed to optimize the solution for bio variables pertinent to CRPC and evaluate various treatment techniques for androgen-dependent and androgen-independent behaviour. Through rigorous analysis, the kinetics of LINC01213 in androgen-deprived mediums are highlighted as promising, showing superior efficacy in castration compared to other techniques. The model utilizes the joint effect on the log-likelihood function (JELF) as a crucial analytical tool to assess the impact of LINC01213 in both normal and androgen-deprived medium. The results affirm the veracity of statements made within the medical field and support the notion that LINC01213 may serve as a novel therapeutic target for CRPC patients. The analysis underscores the pivotal role of exosomal LINC01213 in androgen-dependent prostate cancer, demonstrating its significance in treatment efficacy. The BBWD model highlighting the efficacy of LINC01213 in androgen-deprived mediums provides compelling evidence for its potential as a therapeutic target. This study corroborates existing medical hypotheses and offers detailed clarification and reports on treatment techniques for prostate cancer patients. Ultimately, it emphasizes the critical role of exosomal LINC01213 in addressing the challenges posed by androgen-dependent prostate cancer, offering a pathway toward more effective treatments.

The phylogenetic likelihood function (PLF) is the major computational bottleneck in several applications of evolutionary biology such as phylogenetic inference, species delimitation, model selection, and divergence times estimation. Given the alignment, a tree and the evolutionary model parameters, the likelihood function computes the conditional likelihood vectors for every node of the tree. Vector entries for which all input data are identical result in redundant likelihood operations which, in turn, yield identical conditional values. Such operations can be omitted for improving runtime and, using appropriate data structures, reducing memory usage. We present a fast, novel method for identifying and omitting such redundant operations in phylogenetic likelihood calculations, and assess the performance improvement and memory savings attained by our method. Using empirical and simulated data sets, we show that a prototype implementation of our method yields up to 12-fold speedups and uses up to 78% less memory than one of the fastest and most highly tuned implementations of the PLF currently available. Our method is generic and can seamlessly be integrated into any phylogenetic likelihood implementation.

Background In contrast to the Western Palearctic and Nearctic biogeographic regions, the phylogeography of Eastern-Palearctic terrestrial vertebrates has received relatively little attention. In East Asia, tectonic events, along with Pleistocene climatic conditions, likely affected species distribution and diversity, especially through their impact on sea levels and the consequent opening and closing of land-bridges between Eurasia and the Japanese Archipelago. To better understand these effects, we sequenced mitochondrial and nuclear markers to determine phylogeographic patterns in East-Asian tree frogs, with a particular focus on the widespread H. japonica . Results We document several cryptic lineages within the currently recognized H. japonica populations, including two main clades of Late Miocene divergence (~5 Mya). One occurs on the northeastern Japanese Archipelago (Honshu and Hokkaido) and the Russian Far-East islands (Kunashir and Sakhalin), and the second one inhabits the remaining range, comprising southwestern Japan, the Korean Peninsula, Transiberian China, Russia and Mongolia. Each clade further features strong allopatric Plio-Pleistocene subdivisions (~2-3 Mya), especially among continental and southwestern Japanese tree frog populations. Combined with paleo-climate-based distribution models, the molecular data allowed the identification of Pleistocene glacial refugia and continental routes of postglacial recolonization. Phylogenetic reconstructions further supported genetic homogeneity between the Korean H. suweonensis and Chinese H. immaculata , suggesting the former to be a relic population of the latter that arose when the Yellow Sea formed, at the end of the last glaciation. Conclusions Patterns of divergence and diversity were likely triggered by Miocene tectonic activities and Quaternary climatic fluctuations (including glaciations), causing the formation and disappearance of land-bridges between the Japanese islands and the continent. Overall, this resulted in a ring-like diversification of H. japonica around the Sea of Japan. Our findings urge for important taxonomic revisions in East-Asian tree frogs. First, they support the synonymy of H. suweonensis (Kuramoto, 1980) and H. immaculata (Boettger, 1888). Second, the nominal H. japonica (Günther, 1859) represents at least two species: an eastern (new taxon A) on the northern Japanese and Russian Far East islands, and a southwestern species (n. t. B) on southern Japanese islands and possibly also forming continental populations. Third, these continental tree frogs may also represent an additional entity, previously described as H. stepheni Boulenger, 1888 (senior synonym of H. ussuriensis Nikolskii, 1918). A complete revision of this group requires further taxonomic and nomenclatural analyses, especially since it remains unclear to which taxon the species-epitheton japonica corresponds to.

In today’s interconnected society, cyberattacks have become more frequent and sophisticated, and existing intrusion detection systems may not be adequate in the complex cyberthreat landscape. For instance, existing intrusion detection systems may have overfitting, low classification accuracy, and high false positive rate (FPR) when faced with significantly large volume and variety of network data. An intrusion detection approach based on improved deep belief network (DBN) is proposed in this paper to mitigate the above problems, where the dataset is processed by probabilistic mass function (PMF) encoding and Min-Max normalization method to simplify the data preprocessing. Furthermore, a combined sparsity penalty term based on Kullback-Leibler (KL) divergence and non-mean Gaussian distribution is introduced in the likelihood function of the unsupervised training phase of DBN, and sparse constraints retrieve the sparse distribution of the dataset, thus avoiding the problem of feature homogeneity and overfitting. Finally, simulation experiments are performed on the NSL-KDD and UNSW-NB15 public datasets. The proposed method achieves 96.17% and 86.49% accuracy, respectively. Experimental results show that compared with the state-of-the-art methods, the proposed method achieves significant improvement in classification accuracy and FPR.

Likelihood function has significant advantages in the fields of statistical inference. Based on this theory, Yager proposed a soft likelihood function to make it more widely used. However, Yager’s method can only deal with probabilities expressed by crisp values, and has strict restrictions on the form of data. Due to human subjectivity and lack of effective information, it is inevitable that data uncertainty will be involved. In order to deal with the uncertain data more flexibly and intuitively and solve the complex problems faced in real-world applications, a generalized soft likelihood function in combining multi-source belief distribution functions is proposed in this paper. Different from other existing methods, this paper uses a distribution function to represent uncertain information, which can retain more original information and improve the credibility of the results. The expectation and variance are used to rank the obtained evidences, and the evidence that contributes more to the results is ranked higher. Finally, the reliable likelihood results are obtained. The proposed method extends the method of Yager and can work well in more uncertain environment. Several numerical examples and comparative experimental simulation are used to illustrate the efficiency of the proposed soft likelihood function.

The article proposes a method of assessing information transmission reliability by using the output normalized logarithmic ratio of the likelihood function (LRLF) of the decoder. Based on the evaluation, the method allows adapting system parameters with turbo codes (TC) or LDPC code. This method can be used in combination with other methods of parametric and structural adaptation using turbo codes or LDPC codes.

The standard bootstrap (SBS), despite being computationally intensive, is widely used in maximum likelihood phylogenetic analyses. We recently proposed the ultrafast bootstrap approximation (UFBoot) to reduce computing time while achieving more unbiased branch supports than SBS under mild model violations. UFBoot has been steadily adopted as an efficient alternative to SBS and other bootstrap approaches. Here, we present UFBoot2, which substantially accelerates UFBoot and reduces the risk of overestimating branch supports due to polytomies or severe model violations. Additionally, UFBoot2 provides suitable bootstrap resampling strategies for phylogenomic data. UFBoot2 is 778 times (median) faster than SBS and 8.4 times (median) faster than RAxML rapid bootstrap on tested data sets. UFBoot2 is implemented in the IQ-TREE software package version 1.6 and freely available at http://www.iqtree.org.

Large phylogenomics data sets require fast tree inference methods, especially for maximum-likelihood (ML) phylogenies. Fast programs exist, but due to inherent heuristics to find optimal trees, it is not clear whether the best tree is found. Thus, there is need for additional approaches that employ different search strategies to find ML trees and that are at the same time as fast as currently available ML programs. We show that a combination of hill-climbing approaches and a stochastic perturbation method can be time-efficiently implemented. If we allow the same CPU time as RAxML and PhyML, then our software IQ-TREE found higher likelihoods between 62.2% and 87.1% of the studied alignments, thus efficiently exploring the tree-space. If we use the IQ-TREE stopping rule, RAxML and PhyML are faster in 75.7% and 47.1% of the DNA alignments and 42.2% and 100% of the protein alignments, respectively. However, the range of obtaining higher likelihoods with IQ-TREE improves to 73.3–97.1%. IQ-TREE is freely available at http://www.cibiv.at/software/iqtree.

Abstract We introduce the 12th version of the Molecular Evolutionary Genetics Analysis (MEGA12) software. This latest version brings many significant improvements by reducing the computational time needed for selecting optimal substitution models and conducting bootstrap tests on phylogenies using maximum likelihood (ML) methods. These improvements are achieved by implementing heuristics that minimize likely unnecessary computations. Analyses of empirical and simulated datasets show substantial time savings by using these heuristics without compromising the accuracy of results. MEGA12 also links-in an evolutionary sparse learning approach to identify fragile clades and associated sequences in evolutionary trees inferred through phylogenomic analyses. In addition, this version includes fine-grained parallelization for ML analyses, support for high-resolution monitors, and an enhanced Tree Explorer. MEGA12 can be downloaded from https://www.megasoftware.net.