Individual Brain Metabolic Connectome Indicator Based on Jensen-Shannon Divergence Similarity Estimation Predicts Seizure Outcomes of Temporal Lobe Epilepsy

Objective: We aimed to use an individual metabolic connectome method, the Jensen-Shannon Divergence Similarity Estimation (JSSE), to characterize the aberrant connectivity patterns and topological alterations of the individual-level brain metabolic connectome and predict the long-term surgical outcomes in temporal lobe epilepsy (TLE).Methods: A total of 128 patients with TLE (63 females, 65 males; 25.07 ± 12.01 years) who underwent Positron emission tomography (PET) with 18F-fluorodeoxyglucose (FDG) imaging were enrolled. Patients were classified either as experiencing seizure recurrence (SZR) or seizure free (SZF) at least 1 year after surgery. Each individual’s metabolic brain network was ascertained using the proposed JSSE method. We compared the similarity and difference in the JSSE network and its topological measurements between the two groups. The two groups were then classified by combining the information from connection and topological metrics, which was conducted by the multiple kernel support vector machine. The validation was performed using the nested leave-one-out cross-validation strategy to confirm the performance of the methods.Results: With a median follow-up of 33 months, 50% of patients achieved SZF. No relevant differences in clinical features were found between the two groups except age at onset. The proposed JSSE method showed marked degree reductions in IFGoperc.R, ROL. R, IPL. R, and SMG. R; and betweenness reductions in ORBsup.R and IOG. R; meanwhile, it found increases in the degree analysis of CAL. L and PCL. L, and in the betweenness analysis of PreCG.R, IOG. R, PoCG.R, PCL. L and PCL.R. Exploring consensus significant metabolic connections, we observed that the most involved metabolic motor networks were the INS-TPOmid.L, MTG. R-SMG. R, and MTG. R-IPL.R pathways between the two groups, and yielded another detailed individual pathological connectivity in the PHG. R-CAU.L, PHG. R-HIP.L, TPOmid.L-LING.R, TPOmid.L-DCG.R, MOG. R-MTG.R, MOG. R-ANG.R, and IPL. R-IFGoperc.L pathways. These aberrant functional network measures exhibited ideal classification performance in predicting SZF individuals from SZR ones at a sensitivity of 75.00%, a specificity of 92.79%, and an accuracy of 83.59%.Conclusion: The JSSE method indicator can identify abnormal brain networks in predicting an individual’s long-term surgical outcome of TLE, thus potentially constituting a clinically applicable imaging biomarker. The results highlight the biological meaning of the estimated individual brain metabolic connectome.

A new divergence measure of interval-valued pythagorean fuzzy sets and its application

As the extension of the Fuzzy sets (FSs) theory, the Interval-valued Pythagorean Fuzzy Sets (IVPFS) was introduced which play an important role in handling the uncertainty. The Pythagorean fuzzy sets (PFSs) proposed by Yager in 2013 can deal with more uncertain situations than intuitionistic fuzzy sets because of its larger range of describing the membership grades. How to measure the distance of Interval-valued Pythagorean fuzzy sets is still an open issue. Jensen–Shannon divergence is a useful distance measure in the probability distribution space. In order to efficiently deal with uncertainty in practical applications, this paper proposes a new divergence measure of Interval-valued Pythagorean fuzzy sets,which is based on the belief function in Dempster–Shafer evidence theory, and is called IVPFSDM distance. It describes the Interval-Valued Pythagorean fuzzy sets in the form of basic probability assignments (BPAs) and calculates the divergence of BPAs to get the divergence of IVPFSs, which is the step in establishing a link between the IVPFSs and BPAs. Since the proposed method combines the characters of belief function and divergence, it has a more powerful resolution than other existing methods.

Skewed Jensen—Fisher Divergence and Its Bounds

A non-uniform (skewed) mixture of probability density functions occurs in various disciplines. One needs a measure of similarity to the respective constituents and its bounds. We introduce a skewed Jensen–Fisher divergence based on relative Fisher information, and provide some bounds in terms of the skewed Jensen–Shannon divergence and of the variational distance. The defined measure coincides with the definition from the skewed Jensen–Shannon divergence via the de Bruijn identity. Our results follow from applying the logarithmic Sobolev inequality and Poincaré inequality.

Novel Pythagorean fuzzy entropy and Pythagorean fuzzy cross-entropy measures and their applications1

Entropy and cross-entropy are very vital for information discrimination under complicated Pythagorean fuzzy environment. Firstly, the novel score factors and indeterminacy factors of intuitionistic fuzzy sets (IFSs) are proposed, which are linear transformations of membership functions and non-membership functions. Based on them, the novel entropy measures and cross-entropy measures of an IFS are introduced using Jensen Shannon-divergence (J-divergence). They are more in line with actual fuzzy situations. Then the cases of Pythagorean fuzzy sets (PFSs) are extended. Pythagorean fuzzy entropy, parameterized Pythagorean fuzzy entropy, Pythagorean fuzzy cross-entropy, and weighted Pythagorean fuzzy cross-entropy measures are introduced consecutively based on the novel score factors, indeterminacy factors and J-divergence. Then some comparative experiments prove the rationality and effectiveness of the novel entropy measures and cross-entropy measures. Additionally, the Pythagorean fuzzy entropy and cross-entropy measures are designed to solve pattern recognition and multiple criteria decision making (MCDM) problems. The numerical examples, by comparing with the existing ones, demonstrate the applicability and efficiency of the newly proposed models.

A Study on the Genetics of Primary Ciliary Dyskinesia

Primary ciliary dyskinesia (PCD) is a poorly understood disorder. It is primarily autosomal recessive and is prevalent in tribal communities of the United Arab Emirates due to consanguineous marriages. This retrospective study aimed to assess the pathogenicity of the genetic variants of PCD in indigenous patients with significant clinical respiratory problems. Pathogenicity scores of variants obtained from the chart review were consolidated using the Ensembl Variant Effect Predictor. The multidimensional dataset of scores was clustered into three groups based on their pathogenicity. Sequence alignment and the Jensen–Shannon Divergence (JSD) were generated to evaluate the amino acid conservation at the site of the variation. One-hundred and twelve variants of 28 genes linked to PCD were identified in 66 patients. Twenty-two variants were double heterozygous, two triple heterozygous, and seven homozygous. Of the thirteen novel variants, two, c.11839 + 1G > A in dynein, axonemal, heavy chain 11 (DNAH11) and p.Lys92Trpfs in dynein, axonemal, intermediate chain 1 (DNAI1) were associated with dextrocardia with situs inversus, and one, p.Gly21Val in coiled-coil domain-containing protein 40 (CCDC40), with absent inner dynein arms. Homozygous C1orf127:p.Arg113Ter (rs558323413) was also associated with laterality defects in two related patients. The majority of variants were missense involving conserved residues with a median JSD score of 0.747. Homology models of two deleterious variants in the stalk of DNAH11, p.Gly3102Asp and p.Leu3127Arg, revealed structural importance of the conserved glycine and leucine. These results define potentially damaging PCD variants in the region. Future studies, however, are needed to fully comprehend the genetic underpinnings of PCD.

Epitope scaffolding using α-synuclein cyclic peptides to generate oligomer-selective antibodies for Parkinson’s disease

Effectively scaffolding epitopes on immunogens, in order to raise conformationally selective antibodies through active immunization, is a central problem in treating protein misfolding diseases, particularly neurodegenerative diseases such as Alzheimer’s disease or Parkinson’s disease. We seek to selectively target conformations enriched in toxic, oligomeric propagating species while sparing the healthy forms of the protein that are often more abundant. To this end, we scaffolded epitopes in cyclic peptides by varying the number of flanking glycines, to best mimic a misfolding-specific conformation of an epitope of α-synuclein enriched in the oligomer ensemble, as characterized by a region most readily disordered and solvent-exposed in a stressed, partially denatured protofibril. We screen and rank the cyclic peptide scaffolds of α-synuclein in silico based on their ensemble overlap properties with the fibril, oligomer-model, and isolated monomer ensembles. We introduce a method for screening against structured off-pathway targets in the human proteome, by selecting scaffolds with minimal conformational similarity between their epitope and the same solvent-exposed primary sequence in structured human proteins. Different cyclic peptide scaffolds with variable numbers of glycines can have markedly different conformational ensembles. Ensemble comparison and overlap was quantified by the Jensen-Shannon Divergence, and a new measure introduced here—the embedding depth, which determines the extent to which a given ensemble is subsumed by another ensemble, and which may be a more useful measure in sculpting the conformational-selectivity of an antibody.

Some applications of the Hermit-Hadamard inequality for log-convex functions in quantum divergence

One of the beautiful and very simple inequalities for a convex function is the Hermit-Hadamard inequality [S. Mehmood, et. al. Math. Methods Appl. Sci., 44 (2021) 3746], [S. Dragomir, et. al., Math. Methods Appl. Sci., in press]. The concept of log-convexity is a stronger property of convexity. Recently, the refined Hermit-Hadamard’s inequalities for log-convex functions were introduced by researchers [C. P. Niculescu, Nonlinear Anal. Theor., 75 (2012) 662]. In this paper, by the Hermit-Hadamard inequality, we introduce two parametric Tsallis quantum relative entropy, two parametric Tsallis-Lin quantum relative entropy and two parametric quantum Jensen-Shannon divergence in quantum information theory. Then some properties of quantum Tsallis-Jensen-Shannon divergence for two density matrices are investigated by this inequality. \newline \textbf{Keywords:} \textit{ Hermit-Hadamard’s inequality; log-convexity; Density matrices; Quantum relative entropy; Tsallis quantum relative entropy; quantum Jensen-Shannon divergence divergence.

Statistical Distance-Based Travel-Time Reliability Measurement for Freeway Bottleneck Identification and Ranking

Freeway bottleneck identification is an essential component in the process of deploying mitigation strategies to reduce congestion at freeway bottlenecks. Most previous studies on bottleneck identification focus on recurrent bottlenecks, and limited work has been conducted to identify the locations of non-recurrent bottlenecks. Therefore, in this study, we propose a new travel time reliability (TTR) measurement and develop a freeway bottleneck identification method based on this measurement, which can identify with high probability not only recurrent bottlenecks but also the locations of non-recurrent bottlenecks. The TTR measurement is developed based on statistical distance between travel time distributions. Three statistical distance measurements, Jensen–Shannon divergence, Wasserstein distance, and Hellinger distance, are applied in the TTR measurement. The bottleneck identification method is evaluated in a case study on I-15 freeway corridor in Salt Lake City, Utah. The three statistical distance measurements show good consistency in ranking locations by the impacts of recurrent and non-recurrent congestion, especially for extreme cases with very high or low variation between travel time distributions. The recurrent bottlenecks identified in this study show their clustering characteristics, which is similar to the generating and dismissing process of recurrent congestion. The locations with high probability of non-recurrent bottlenecks scatter both spatially and temporally, which agrees with the random characteristic of non-recurrent congestion.