New Fractional Derivative Expression of the Shifted Third-Kind Chebyshev Polynomials: Application to a Type of Nonlinear Fractional Pantograph Differential Equations by Y. H. Youssri, W. M. Abd-Elhameed, H. M. Ahmed

“…To solve a nonlinear fractional pantograph differential equation with quadratic nonlinearity, the fractional derivative formula is used in conjunction with the tau technique. The role of the tau method is to convert the pantograph differential equation with its governing initial/boundary conditions into a nonlinear system of algebraic equations that can be treated with the aid of Newton’s iterative scheme. …”
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Generalization of Okamoto's Equation to Arbitrary 2×2 Schlesinger System by Dmitry Korotkin, Henning Samtleben

“…The Painlevé VI equation can in turn be rewritten in the symmetric form of Okamoto's equation; the dependent variable in Okamoto's form of the PVI equation is the (slightly transformed) logarithmic derivative of the Jimbo-Miwa tau-function of the Schlesinger system. The goal of this note is twofold. …”
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Research Progress on the Interaction between Taurine Metabolism and the Gut Microbiota by YANG Xinyu, WU Qingjie, MI Shengquan, ZHANG Yanzhen, GUO Junxia

“…Taurine can combine with bile acids to form taurine-conjugated bile acids (Tau-Bas), which can be dissociated to release taurine by the gut microbiota. …”
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Information Entropy Based on Propagation Feature of Node for Identifying the Influential Nodes by Linfeng Zhong, Yu Bai, Yan Tian, Chen Luo, Jin Huang, Weijun Pan

“…Especially in the Facebook network, Kendall’s Tau can grow by 120% as compared with the original IE method. …”
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Dimuon and ditau production in photon-photon collisions at next-to-leading order in QED by Hua-Sheng Shao, David d’Enterria

“…Abstract Next-to-leading-order (NLO) quantum electrodynamics (QED) corrections to the production of muon and tau pairs in photon-photon collisions, γγ → μ + μ − , τ + τ − , are calculated in the equivalent photon approximation. …”
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On Concordance Measures for Discrete Data and Dependence Properties of Poisson Model by Taoufik Bouezmarni, Mhamed Mesfioui, Abdelouahid Tajar

“…We study Kendall's tau and Spearman's rho concordance measures for discrete variables. …”
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Doubling constructions and tensor product L-functions: coverings of the symplectic group by Eyal Kaplan

“…In this work, we develop an integral representation for the partial L-function of a pair $\pi \times \tau $ of genuine irreducible cuspidal automorphic representations, $\pi $ of the m-fold covering of Matsumoto of the symplectic group $\operatorname {\mathrm {Sp}}_{2n}$ and $\tau $ of a certain covering group of $\operatorname {\mathrm {GL}}_k$ , with arbitrary m, n and k. …”
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Prognostic Value of Left Ventricular Diastolic Dysfunction in Patients Undergoing Cardiac Catheterization for Coronary Artery Disease by Hidekatsu Fukuta, Nobuyuki Ohte, Kazuaki Wakami, Toshihiko Goto, Tomomitsu Tani, Genjiro Kimura

“…Among LV diastolic function indices, Tau > 48 ms and 𝑒<5.8 cm/s were each significantly associated with lower rate of survival free of cardiovascular hospitalization. …”
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Multicenter Randomized Clinical Trial of Brief Psychotherapy versus Usual Treatment for Common Mental Disorders in Adults by Marco A. Luengo-Castro, Javier Fernández-Méndez, José M. García-Montes, Pedro J. Caunedo-Riesco, Juan M. García-Haro, Begoña Braña-Menéndez, Dolores González-Díaz, Andrés Cabero-Álvarez, Marcelino Cuesta-Izquierdo

“…Background: This paper addresses the evaluation of the effectiveness of brief psychological treatment (BPT) for common mental disorders (CMD) in mental health centers (MHC), comparing it to treatment as usual (TAU). Method: 144 patients were randomly assigned to either the experimental treatment group (EG), receiving BPT, or the control group (CG), receiving TAU. …”
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Leptonic dipole operator with $$\Gamma _2$$ Γ 2 modular invariance in light of Muon $$(g-2)_\mu $$ ( g - 2 ) μ by Takaaki Nomura, Morimitsu Tanimoto, Xing-Yu Wang

“…The branching ratios of $$\tau \rightarrow e\gamma $$ τ → e γ and $$\tau \rightarrow \mu \gamma $$ τ → μ γ are also discussed.…”
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When specific exercise is more effective than medication - Sensorimotor training is currently the most promising option to treat and prevent chemotherapy-induced peripheral neuropa... by Fiona Streckmann, Maryam Balke, Céline Hammadou, Bianca Schmidli, Oliver Faude, Sarah Koch

“…Results A total 158 patients (mean [SD] age, 49.1 [18.0-82.0] years; 93 [58.9%] male) were randomized into 1 of 3 groups: 55 (34.8%) in SMT, 53 (33.5%) in WBV, and 50 (31.6%) in treatment as usual (TAU). The incidence of CIPN in participants was significantly lower in both intervention groups compared to the control group (TAU): (SMT, 12 of 40 [30.0%; 95% CI, 17.9%-42.1%] and WBV, 14 of 34 [41.2%; 95% CI, 27.9%-54.5%] vs TAU, 24 of 34 [70.6%; 95% CI, 58.0%-83.2%]; P = .002 for intention to treat–MH). …”
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Flavor symmetries from modular subgroups in magnetized compactifications by Tatsuo Kobayashi, Kaito Nasu, Ryusei Nishida, Hajime Otsuka, Shohei Takada

“…The modular symmetry of T 1 2 × T 2 2 $$ {T}_1^2\times {T}_2^2 $$ is SL 2 ℤ τ 1 × SL 2 ℤ τ 2 ⊂ Sp 4 ℤ $$ \textrm{SL}{\left(2,\mathbb{Z}\right)}_{\tau_1}\times \textrm{SL}{\left(2,\mathbb{Z}\right)}_{\tau_2}\subset \textrm{Sp}\left(4,\mathbb{Z}\right) $$ and it is broken to Γ0(N) × Γ0(N) by the moduli constraint. …”
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Some fixed point results with the vector degree of nondensifiability in generalized Banach spaces and application on coupled Caputo fractional delay differential equations by Laksaci Noura, Hasan Fady, Boudaoui Ahmed, Mustafa Zead, Shatanawi Wasfi

“…An existence result for coupled Caputo fractional delay differential equations in the GBSC([−τ,T],R)×C([−τ,T],R){\mathfrak{G}}{\mathfrak{B}}{\mathfrak{S}}\hspace{0.33em}{\mathcal{C}}\left(\left[-\tau ,T],{\mathbb{R}})\times {\mathcal{C}}\left(\left[-\tau ,T],{\mathbb{R}}) is given to show the significance and the applicability of our theoretical results.…”
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Axion dark matter, proton decay and unification by Pavel Fileviez Pérez, Clara Murgui, Alexis D. Plascencia

“…In this context, we predict an upper bound for the proton decay channels with antineutrinos, τ p → K + ν ¯ ≲ 4 × 10 37 $$ \tau \left(p\to {K}^{+}\overline{\nu}\right)\lesssim 4\times {10}^{37} $$ yr and τ p → π + ν ¯ ≲ 2 × 10 36 $$ \tau \left(p\to {\pi}^{+}\overline{\nu}\right)\lesssim 2\times {10}^{36} $$ yr. …”
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Ultrastable and ultra-accurate clock transitions in open-shell highly charged ions by Chunhai Lyu, Christoph H. Keitel, Zoltán Harman

“…Their projected instabilities and accuracies are $${\sigma }_{\tau } \sim 1{0}^{-17}/\sqrt{\tau }$$ σ τ ~ 1 0 − 17 / τ and δ ν/ν < 10−20, respectively, surpassing state-of-the-art optical clocks by several orders of magnitude. …”
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Therapeutic Actions of the Thiazolidinediones in Alzheimer’s Disease by María José Pérez, Rodrigo A. Quintanilla

“…In the AD brain is common to observe the accumulation of senile plaques formed by amyloid-beta (Aβ) peptide and the neurofibrillary tangles composed of modified tau protein, which both lead to cellular damage and progressive neurodegeneration. …”
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Spines, Plasticity, and Cognition in Alzheimer's Model Mice by Tara Spires-Jones, Shira Knafo

“…Together, these data support a model of AD pathogenesis in which soluble Aβ initiates synaptic dysfunction and loss, as well as pathological changes in tau, which contribute to both synaptic and neuronal loss. …”
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Association of plasma biomarkers of Alzheimer’s pathology and neurodegeneration with gait performance in older adults by Farwa Ali, Jeremy A. Syrjanen, Dan J. Figdore, Walter K. Kremers, Michelle M. Mielke, Clifford R. Jack, David S. Knopman, Prashanthi Vemuri, Jonathan Graff-Radford, B. Gwen Windham, Leland R. Barnard, Ronald C. Petersen, Alicia Algeciras-Schimnich

“…Results In this study multiple statistically significant relationships are observed for GFAP, NfL, and P-Tau181 with gait parameters. Each standard deviation increase in GFAP, NfL, and P-Tau181 is associated with a reduction in velocity of 2.100 (95% CI: −3.004, −1.196; p = 5.4 × 10−6), 4.400 (−5.292, -3.507; p = 9.5 × 10−22), and 2.617 (−3.414, −1.819; p = 1.5 × 10−10) cm/sec, respectively. …”
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Blood-based biomarkers suggest prolonged axonal Injury following pediatric mild traumatic brain injury by Andrew R. Mayer, Tracey V. Wick, Jessica R. McQuaid, Masen L. Boucher, Andrew B. Dodd, Cidney R. Robertson-Benta, Harm J. van der Horn, Erik B. Erhardt, Robert E. Sapien, Rawan Tarawneh, Rebekah Mannix

“…Samples were analyzed for GFAP, NFL, Tau, pTau181 and UCH-L1 protein concentrations in conjunction with a clinical battery. …”
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Efficacy of unified protocol for transdiagnostic treatment of emotional disorders in adolescents (UP-A) in China: protocol for a randomised controlled trial by Xue Gao, Lu Liu, Mei-Rong Pan, Hai-Mei Li, Yu-Feng Wang, Xue-Ying Liu, Zhong-Fang Fu, Qiujin Qian

“…Forty-eight participants will be randomly assigned to either the treatment as usual (TAU) group or the TAU combined with UP-A (UP-A+TAU) group. …”
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