Journal articles: 'Tau class'

1

Ozansoy, M., and A. Başak. "Tauopathies: A Distinct Class of Neurodegenerative Diseases." Balkan Journal of Medical Genetics 10, no. 2 (January 1, 2007): 3–14. http://dx.doi.org/10.2478/v10034-008-0001-5.

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Tauopathies: A Distinct Class of Neurodegenerative DiseasesNeurodegenerative diseases are characterized by neuronal loss and intraneuronal accumulation of fibrillary materials, of which, neurofibrillary tangles (NFT) are the most common. Neurofibrillary tangles also occur in normal aging and contain the hyperphosphorylated microtubule-associated protein tau. A detailed presentation is made of the molecular bases of Alzheimer's disease (AD), postencephalitic parkinsonism, amyotrophic lateral sclerosis/parkinsonism-dementia complex (ALS/PDC) of Guam, progressive supranuclear palsy (PSP), corticobasal degeneration (CBD), Pick's disease, frontotemporal dementia (FTD), Down's syndrome, myotonic dystrophy (DM) and Niemann-Pick Type C (NPC) disease, which are considered to be common tauopathies. The unique human tau gene extends over 100 kb of the long arm of chromosome 17 and contains 16 exons. The human brain contains six tau isoforms that contain from 352 to 441 amino acids. To date, 34 pathogenic tau mutations have been described among 101 families affected by FTD with parkinsonism linked to chromosome 17 (FTDP-17). These mutations may involve alternative splicing of exon 10 that lead to changes in the proportion of 4-repeat- and 3-repeat-tau isoforms, or may modify tau interactions with microtubules. Tau aggregates differ in degree of phosphorylation and in content of tau isoforms. Five classes of tauopathies have been defined depending on the type of tau aggregates. The key event in tauopathies is the disorganization of the cytoskeleton, which is based on mutations/polymorphisms in the tau gene and lead to nerve cell degeneration. In this review, tauopathies as a distinct class of neurodegenerative diseases are discussed with emphasis on their molecular pathology and genetics.

2

Fajfer, S., and R. J. Oakes. "Second class current effects in Tau-Lepton decay." Physics Letters B 213, no. 3 (October 1988): 376–78. http://dx.doi.org/10.1016/0370-2693(88)91779-0.

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Demock, Melissa, and Steven Kornguth. "A Mechanism for the Development of Chronic Traumatic Encephalopathy From Persistent Traumatic Brain Injury." Journal of Experimental Neuroscience 13 (January 2019): 117906951984993. http://dx.doi.org/10.1177/1179069519849935.

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A mechanism that describes the progression of traumatic brain injury (TBI) to end-stage chronic traumatic encephalopathy (CTE) is offered in this article. This mechanism is based upon the observed increase in the concentration of both tau protein and of human leukocyte antigen (HLA) class I proteins; the HLA increase is expressed on the cell membrane of neural cells. These events follow the inflammatory responses caused by the repetitive TBI. Associated inflammatory changes include macrophage entry into the brain parenchyma from increased permeability of the blood-brain barrier (BBB) and microglial activation at the base of the sulci. The release of interferon gamma from the microglia and macrophages induces the marked increased expression of HLA class I proteins by the neural cells and subsequent redistribution of the tau proteins to the glial and neuronal surface. In those individuals with highly expressed HLA class I C, the high level of HLA binds tau protein electrostatically. The ionic region of HLA class I C (amino acid positions 50-90) binds to the oppositely charged ionic region of tau (amino acid positions 93-133). These interactions thereby shift the cellular localization of the tau and orient the tau spatially so that the cross-linking sites of tau (275-280 and 306-311) are aligned. This alignment facilitates the cross-linking of tau to form the intracellular and extracellular microfibrils of tau, the primary physiological characteristic of tauopathy. Following endocytosis of the membrane HLA/tau complex, these microfibrils accumulate and produce a tau-storage-like disease. Therefore, tauopathy is the secondary collateral process of brain injury, resulting from the substantial increase in tau and HLA expression on neural cells. This proposed mechanism suggests several potential targets for mitigating the clinical progression of TBI to CTE.

4

Novak, Michal. "First-in-man and First-in-class Tau Vaccine." Neurobiology of Aging 35 (March 2014): S18. http://dx.doi.org/10.1016/j.neurobiolaging.2014.01.100.

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Ruben, G. C., K. Iqbal, I. Grundke-Iqbal, H. Wisniewski, T. L. Ciardelli, and J. H. Johnson. "The microtubule associated protein (MAP) tau forms a new class of triple-stranded left-hand helical fibrous protein polymer." Proceedings, annual meeting, Electron Microscopy Society of America 50, no. 1 (August 1992): 540–41. http://dx.doi.org/10.1017/s0424820100123106.

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In neurons, the microtubule associated protein, tau, is found in the axons. Tau stabilizes the microtubules required for neurotransmitter transport to the axonal terminal. Since tau has been found in both Alzheimer neurofibrillary tangles (NFT) and in paired helical filaments (PHF), the study of tau's normal structure had to preceed TEM studies of NFT and PHF. The structure of tau was first studied by ultracentrifugation. This work suggested that it was a rod shaped molecule with an axial ratio of 20:1. More recently, paraciystals of phosphorylated and nonphosphoiylated tau have been reported. Phosphorylated tau was 90-95 nm in length and 3-6 nm in diameter where as nonphosphorylated tau was 69-75 nm in length. A shorter length of 30 nm was reported for undamaged tau indicating that it is an extremely flexible molecule. Tau was also studied in relation to microtubules, and its length was found to be 56.1±14.1 nm.

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Kilili, Kimiti G., Neli Atanassova, Alla Vardanyan, Nicolas Clatot, Khaled Al-Sabarna, Panagiotis N. Kanellopoulos, Antonios M. Makris, and Sotirios C. Kampranis. "Differential Roles of Tau Class GlutathioneS-Transferases in Oxidative Stress." Journal of Biological Chemistry 279, no. 23 (March 22, 2004): 24540–51. http://dx.doi.org/10.1074/jbc.m309882200.

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7

EL-MONSEF, M. E. ABD, A. M. KOZAE, and A. A. ABO KHADRA. "CO-RS-COMPACT TOPOLOGIES." Tamkang Journal of Mathematics 24, no. 3 (September 1, 1993): 323–32. http://dx.doi.org/10.5556/j.tkjm.24.1993.4504.

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A topology $R(\tau)$ is contructed from a given topolgy $\tau$ on a set $X$ . $R(\tau)$ is coarser than $\tau$, and the following are some results based on this topology: 1. Continuity and RS-continuity are equivalent if the codomain is re topologized by $R(\tau)$. 2. The class of semi-open sets with respect to $R(\tau)$ is a topology. 3. $T_2$ and semi-$T_2$ properties are equivalent on a space whose topology is $R(\tau)$. 4. Minimal $R_0$-spaces are RS-compact:

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Kahlson, Martha A., and Kenneth J. Colodner. "Glial Tau Pathology in Tauopathies: Functional Consequences." Journal of Experimental Neuroscience 9s2 (January 2015): JEN.S25515. http://dx.doi.org/10.4137/jen.s25515.

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Tauopathies are a class of neurodegenerative diseases characterized by the presence of hyperphosphorylated and aggregated tau pathology in neuronal and glial cells. Though the ratio of neuronal and glial tau aggregates varies across diseases, glial tau aggregates can populate the same degenerating brain regions as neuronal tau aggregates. While much is known about the deleterious consequences of tau pathology in neurons, the relative contribution of glial tau pathology to these diseases is less clear. Recent studies using a number of model systems implicate glial tau pathology in contributing to tauopathy pathogenesis. This review aims to highlight the functional consequences of tau overexpression in glial cells and explore the potential contribution of glial tau pathology in the pathogenesis of neurodegenerative tauopathies.

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Benfatah, Youssef, Amine El Bhih, Mostafa Rachik, and Marouane Lafif. "An Output Sensitivity Problem for a Class of Fractional Order Discrete-Time Linear Systems." Acta Mechanica et Automatica 15, no. 4 (November 29, 2021): 227–35. http://dx.doi.org/10.2478/ama-2021-0029.

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Abstract Consider the linear discrete-time fractional order systems with uncertainty on the initial state { Δ α x i + 1 = A x i + B u i , i ≥ 0 x 0 = τ 0 + τ ⌢ 0 ∈ ℝ n , τ ⌢ 0 ∈ Ω , y i = C x i , i ≥ 0 \left\{ {\matrix{{{\Delta ^\alpha }{x_{i + 1}} = A{x_i} + B{u_i},} \hfill & {i \ge 0} \hfill \cr {{x_0} = {\tau _0} + {{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over \tau } }_0} \in {\mathbb{R}^n},} \hfill & {{{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over \tau } }_0} \in \Omega ,} \hfill \cr {{y_i} = C{x_{i,}}\,\,\,i \ge 0} \hfill & {} \hfill \cr } } \right. where A, B and C are appropriate matrices, x0 is the initial state, yi is the signal output, α the order of the derivative, τ0 and τ ⌢ 0 {\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over \tau } _0} are the known and unknown part of x0, respectively, ui = Kxi is feedback control and Ω ⊂ ℝn is a polytope convex of vertices w1, w2, . . . , wp. According to the Krein–Milman theorem, we suppose that τ ⌢ 0 = ∑ j = 1 p α j w j {\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over \tau } _0} = \sum\limits_{j = 1}^p {{\alpha _j}{w_j}} for some unknown coefficients α1 ≥ 0, . . . , αp ≥ 0 such that ∑ j = 1 p α j = 1 \sum\limits_{j = 1}^p {{\alpha _j} = 1} . In this paper, the fractional derivative is defined in the Grünwald–Letnikov sense. We investigate the characterisation of the set χ( τ ⌢ 0 {\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over \tau } _0} , ϵ) of all possible gain matrix K that makes the system insensitive to the unknown part τ ⌢ 0 {\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over \tau } _0} , which means χ ( τ ⌢ 0 , ∈ ) = { K ∈ ℝ m × n / ‖ ∂ y i ∂ α j ‖ ≤ ∈ , ∀ j = 1 , … , p , ∀ i ≥ 0 } \chi \left( {{{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over \tau } }_0}, \in } \right) = \left\{ {K \in {\mathbb{R}^{m \times n}}/\left\| {{{\partial {y_i}} \over {\partial {\alpha _j}}}} \right\| \le \in ,\forall j = 1, \ldots ,p,\,\forall i \ge 0} \right\} , where the inequality ‖ ∂ y i ∂ α j ‖ ≤ ∈ \left\| {{{\partial {y_i}} \over {\partial {\alpha _j}}}} \right\| \le \in showing the sensitivity of yi relatively to uncertainties { α j } j = 1 p \left\{ {{\alpha _j}} \right\}_{j = 1}^p will not achieve the specified threshold ϵ > 0. We establish, under certain hypothesis, the finite determination of χ( τ ⌢ 0 {\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over \tau } _0} , ϵ) and we propose an algorithmic approach to made explicit characterisation of such set.

10

Hart, Sarah B., and Peter J. Rowley. "Maximal length elements of excess zero in finite Coxeter groups." Journal of Group Theory 21, no. 5 (September 1, 2018): 817–37. http://dx.doi.org/10.1515/jgth-2018-0016.

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Abstract In this paper we prove that for W a finite Coxeter group and C a conjugacy class of W, there is always an element of C of maximal length in C which has excess zero. An element {w\in W} has excess zero if there exist elements {\sigma,\tau\in W} such that {\sigma^{2}=\tau^{2}=1,w=\sigma\tau} and {\ell(w)=\ell(\sigma)+\ell(\tau)} , {\ell} being the length function on W.

11

Kanai, Y., R. Takemura, T. Oshima, H. Mori, Y. Ihara, M. Yanagisawa, T. Masaki, and N. Hirokawa. "Expression of multiple tau isoforms and microtubule bundle formation in fibroblasts transfected with a single tau cDNA." Journal of Cell Biology 109, no. 3 (September 1, 1989): 1173–84. http://dx.doi.org/10.1083/jcb.109.3.1173.

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Tau proteins are a class of low molecular mass microtubule-associated proteins that are specifically expressed in the nervous system. A cDNA clone of adult rat tau was isolated and sequenced. To analyze functions of tau proteins in vivo, we carried out transfection experiments. A fibroblast cell line, which was transfected with the cDNA, expressed three bands of tau, while six bands were expressed in rat brain. After dephosphorylation, one of the three bands disappeared, demonstrating directly that phosphorylation was involved in the multiplicity of tau. Morphologically, we observed a thick bundle formation of microtubules in the transiently and stably tau-gene-transfected cells. In addition, we found that the production of tubulin was prominently enhanced in the stably transfected cells. Thus, we suppose that tau proteins promote polymerization of tubulin, form bundles of microtubules in vivo, and play important roles in growing and maintaining nerve cell processes.

12

Shea, Thomas B., Eva P. Klinger, and Corinne M. Cressman. "Calcium influx recruits an additional class of kinases to hyperphosphorylate tau." NeuroReport 6, no. 10 (July 1995): 1437–40. http://dx.doi.org/10.1097/00001756-199507100-00019.

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13

El-Daou, Mohamed K., and Nadia R. Al-Matar. "An improved Tau method for a class of Sturm–Liouville problems." Applied Mathematics and Computation 216, no. 7 (June 2010): 1923–37. http://dx.doi.org/10.1016/j.amc.2010.03.022.

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14

Robert, Aiko, Michael Schöll, and Thomas Vogels. "Tau Seeding Mouse Models with Patient Brain-Derived Aggregates." International Journal of Molecular Sciences 22, no. 11 (June 7, 2021): 6132. http://dx.doi.org/10.3390/ijms22116132.

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Tauopathies are a heterogeneous class of neurodegenerative diseases characterized by intracellular inclusions of aggregated tau proteins. Tau aggregates in different tauopathies have distinct structural features and can be found in different cell types. Transgenic animal models overexpressing human tau have been used for over two decades in the research of tau pathology. However, these models poorly recapitulate the heterogeneity of tauopathies found in human brains. Recent findings demonstrate that injection of purified tau aggregates from the brains of human tauopathy patients recapitulates both the structural features and cell-type specificity of the tau pathology of the donor tauopathy. These models may therefore have unique translational value in the study of functional consequences of tau pathology, tau-based diagnostics, and tau targeting therapeutics. This review provides an update of the literature relating to seeding-based tauopathy and their potential applications.

15

Liu, Yuji. "Asymptotic behavior for a class of delay differential equations with a forcing term." Tamkang Journal of Mathematics 34, no. 4 (December 31, 2003): 309–16. http://dx.doi.org/10.5556/j.tkjm.34.2003.233.

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We study the asymptotic behavior of solutions of the following forced delay differential equation $$ x'(t)=-p(t)f(x(t-\tau))+r(t),\quad t\ge 0. \eqno{(*)}$$ It is show that if $ f$ is increasing and $ |f(x)|\le |x|$ for all $ x\in R$, $ \lim_{t\to +\infty} {r(t)\over p(t)}=0$, $ \int_0^{+\infty} p(s)ds=+\infty$ and $ \limsup_{t\to+\infty} \int_{t-\tau}^t p(s)ds

16

ARGYROS, SPIROS A., JESÚS F. CASTILLO, ANTONIO S. GRANERO, MAR JIMÉNEZ, and JOSÉ P. MORENO. "COMPLEMENTATION AND EMBEDDINGS OF c0(I) IN BANACH SPACES." Proceedings of the London Mathematical Society 85, no. 3 (October 14, 2002): 742–68. http://dx.doi.org/10.1112/s0024611502013618.

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We investigate in this paper the complementation of copies of $c_0(I)$ in some classes of Banach spaces (in the class of weakly compactly generated (WCG) Banach spaces, in the larger class $\mathcal{V}$ of Banach spaces which are subspaces of some $C(K)$ space with $K$ a Valdivia compact, and in the Banach spaces $C([1, \alpha ])$, where $\alpha$ is an ordinal) and the embedding of $c_0(I)$ in the elements of the class $\mathcal{C}$ of complemented subspaces of $C(K)$ spaces. Two of our results are as follows:(i) in a Banach space $X \in \mathcal{V}$ every copy of $c_0(I)$ with $\# I < \aleph _{\omega}$ is complemented;(ii) if $\alpha _0 = \aleph _0$, $\alpha _{n+1} = 2^{\alpha _n}$, $n \geq 0$, and $\alpha = \sup \{\alpha _n : n \geq 0\}$ there exists a WCG Banach space with an uncomplemented copy of $c_0(\alpha )$.So, under the generalized continuum hypothesis (GCH), $\aleph _{\omega}$ is the greatest cardinal $\tau$ such that every copy of $c_0(I)$ with $\# I < \tau$ is complemented in the class $\mathcal{V}$. If $T : c_0(I) \to C([1,\alpha ])$ is an isomorphism into its image, we prove that:(i) $c_0(I)$ is complemented, whenever $\| T \| ,\| T^{-1} \| < (3/2)^{\frac 12}$;(ii) there is a finite partition $\{I_1, \dots , I_k\}$ of $I$ such that each copy $T(c_0(I_k))$ is complemented.Concerning the class $\mathcal{C}$, we prove that an already known property of $C(K)$ spaces is still true for this class, namely, if $X \in \mathcal{C}$, the following are equivalent:(i) there is a weakly compact subset $W \subset X$ with ${\rm Dens}(W) = \tau$;(ii) $c_0(\tau )$ is isomorphically embedded into $X$.This yields a new characterization of a class of injective Banach spaces.2000 Mathematical Subject Classification: 46B20, 46B26.

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Zhu, Yanan, Lauren Gandy, Fuming Zhang, Jian Liu, Chunyu Wang, Laura J. Blair, Robert J. Linhardt, and Lianchun Wang. "Heparan Sulfate Proteoglycans in Tauopathy." Biomolecules 12, no. 12 (November 30, 2022): 1792. http://dx.doi.org/10.3390/biom12121792.

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Tauopathies are a class of neurodegenerative diseases, including Alzheimer’s disease, and are characterized by intraneuronal tau inclusion in the brain and the patient’s cognitive decline with obscure pathogenesis. Heparan sulfate proteoglycans, a major type of extracellular matrix, have been believed to involve in tauopathies. The heparan sulfate proteoglycans co-deposit with tau in Alzheimer’s patient brain, directly bind to tau and modulate tau secretion, internalization, and aggregation. This review summarizes the current understanding of the functions and the modulated molecular pathways of heparan sulfate proteoglycans in tauopathies, as well as the implication of dysregulated heparan sulfate proteoglycan expression in tau pathology and the potential of targeting heparan sulfate proteoglycan-tau interaction as a novel therapeutic option.

18

Batko, Joanna, Katarzyna Antosz, Weronika Miśków, Magdalena Pszczołowska, Kamil Walczak, and Jerzy Leszek. "Chaperones—A New Class of Potential Therapeutic Targets in Alzheimer’s Disease." International Journal of Molecular Sciences 25, no. 6 (March 17, 2024): 3401. http://dx.doi.org/10.3390/ijms25063401.

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The review describes correlations between impaired functioning of chaperones and co-chaperones in Alzheimer’s disease (AD) pathogenesis. The study aims to highlight significant lines of research in this field. Chaperones like Hsp90 or Hsp70 are critical agents in regulating cell homeostasis. Due to some conditions, like aging, their activity is damaged, resulting in β-amyloid and tau aggregation. This leads to the development of neurocognitive impairment. Dysregulation of co-chaperones is one of the causes of this condition. Disorders in the functioning of molecules like PP5, Cdc37, CacyBP/SIPTRAP1, CHIP protein, FKBP52, or STIP1 play a key role in AD pathogenesis. PP5, Cdc37, CacyBP/SIPTRAP1, and FKBP52 are Hsp90 co-chaperones. CHIP protein is a co-chaperone that switches Hsp70/Hsp90 complexes, and STIP1 binds to Hsp70. Recognition of precise processes allows for the invention of effective treatment methods. Potential drugs may either reduce tau levels or inhibit tau accumulation and aggregation. Some substances neuroprotect from Aβ toxicity. Further studies on chaperones and co-chaperones are required to understand the fundamental tenets of this topic more entirely and improve the prevention and treatment of AD.

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Shulman, Joshua M., and Mel B. Feany. "Genetic Modifiers of Tauopathy in Drosophila." Genetics 165, no. 3 (November 1, 2003): 1233–42. http://dx.doi.org/10.1093/genetics/165.3.1233.

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Abstract In Alzheimer's disease and related disorders, the microtubule-associated protein Tau is abnormally hyperphosphorylated and aggregated into neurofibrillary tangles. Mutations in the tau gene cause familial frontotemporal dementia. To investigate the molecular mechanisms responsible for Tau-induced neurodegeneration, we conducted a genetic modifier screen in a Drosophila model of tauopathy. Kinases and phosphatases comprised the major class of modifiers recovered, and several candidate Tau kinases were similarly shown to enhance Tau toxicity in vivo. Despite some clinical and pathological similarities among neurodegenerative disorders, a direct comparison of modifiers between different Drosophila disease models revealed that the genetic pathways controlling Tau and polyglutamine toxicity are largely distinct. Our results demonstrate that kinases and phosphatases control Tau-induced neurodegeneration and have important implications for the development of therapies in Alzheimer's disease and related disorders.

20

Chen, Xiaojing, and Wenchang Chu. "On a generalized class of bi-univalent functions defined by subordination and $q$-derivative operator." Open Journal of Mathematical Analysis 6, no. 1 (June 21, 2022): 7–14. http://dx.doi.org/10.30538/psrp-oma2022.0100.

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In this paper, the $q$-derivative operator and the principle of subordination were employed to define a subclass $\mathcal{B}_q(\tau,\lambda,\phi)$ of analytic and bi-univalent functions in the open unit disk $\mathcal{U}$. For functions $f(z)\in\mathcal{B}_q(\tau,\lambda,\phi)$, we obtained early coefficient bounds and some Fekete-Szegö estimates for real and complex parameters.

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Lasode, Ayotunde O., and Timothy O. Opoola. "On a generalized class of bi-univalent functions defined by subordination and $q$-derivative operator." Open Journal of Mathematical Analysis 5, no. 2 (September 6, 2021): 46–52. http://dx.doi.org/10.30538/psrp-oma2021.0092.

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In this paper, the $q$-derivative operator and the principle of subordination were employed to define a subclass $\mathcal{B}_q(\tau,\lambda,\phi)$ of analytic and bi-univalent functions in the open unit disk $\mathcal{U}$. For functions $f(z)\in\mathcal{B}_q(\tau,\lambda,\phi)$, we obtained early coefficient bounds and some Fekete-Szegö estimates for real and complex parameters.

22

Tan, Choon Peng. "Lower bounds for tau coefficients and operator norms using composite matrix norms." Bulletin of the Australian Mathematical Society 35, no. 1 (February 1987): 49–57. http://dx.doi.org/10.1017/s0004972700013034.

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Lower bounds for the tau coefficients and operator norms are derived by using composite matrix norms. For a special class of matrices B, our bounds on ‖B‖p (the operator norm of B induced by the ℓp norm) improve upon a general class of Maitre (1967) bounds for p ≥ 2.

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Basantani, Mahesh, and Alka Srivastava. "Plant glutathione transferases — a decade falls short." Canadian Journal of Botany 85, no. 5 (May 2007): 443–56. http://dx.doi.org/10.1139/b07-033.

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The glutathione transferase (GST) superfamily in plants has been subdivided into eight classes, seven of which (phi, tau, zeta, theta, lambda, dehydroascorbate reductase, and tetrachlorohydroquinone dehalogenase) are soluble and one is microsomal. Since their identification in plants in 1970, these enzymes have been well established as phase II detoxification enzymes that perform several other essential functions in plant growth and development. These enzymes catalyze nucleophilic conjugation of the reduced form of the tripeptide glutathione to a wide variety of hydrophobic, electrophilic, and usually cytotoxic substrates. In plants, the conjugated product is either sequestered in the vacuole or transferred to the apoplast. The GSTs of phi and tau classes, which are plant-specific and the most abundant, are chiefly involved in xenobiotic metabolism. Zeta- and theta-class GSTs have very restricted activities towards xenobiotics. Theta-class GSTs are glutathione peroxidases and are involved in oxidative-stress metabolism, whereas zeta-class GSTs act as glutathione-dependent isomerases and catalyze the glutathione-dependent conversion of maleylacetoacetate to fumarylacetoacetate. Zeta-class GSTs participate in tyrosine catabolism. Dehydroascorbate reductase- and lambda-class GSTs function as thioltransferases. Microsomal-class GSTs are members of the MAPEG (membrane-associated proteins in eicosanoid and glutathione metabolism) superfamily. A plethora of studies utilizing both proteomics and genomics approaches have greatly helped in revealing the functional diversity exhibited by these enzymes. The three-dimensional structure of some of the members of the family has been described and this has helped in elucidating the mechanism of action and active-site amino-acid residues of these enzymes. Although a large amount of information is available on this complex enzyme superfamily, more research is necessary to answer additional questions such as, why are phi- and tau-class GSTs more abundant than GSTs from other classes? What functions do phi- and tau-class GSTs perform in plant taxa other than angiosperms? Do more GST classes exist? Future studies on GSTs should focus on these aspects.

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JAVANSHIRI, HOSSEIN, and RASOUL NASR-ISFAHANI. "THE STRONG DUAL OF MEASURE ALGEBRAS WITH CERTAIN LOCALLY CONVEX TOPOLOGIES." Bulletin of the Australian Mathematical Society 87, no. 3 (April 8, 2013): 353–65. http://dx.doi.org/10.1017/s0004972713000142.

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AbstractFor a locally compact group $ \mathcal{G} $, we introduce and study a class of locally convex topologies $\tau $ on the measure algebra $M( \mathcal{G} )$ of $ \mathcal{G} $. In particular, we show that the strong dual of $(M( \mathcal{G} ), \tau )$ can be identified with a closed subspace of the Banach space $M\mathop{( \mathcal{G} )}\nolimits ^{\ast } $; we also investigate some properties of the locally convex space $(M( \mathcal{G} ), \tau )$.

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Huang, Jane, Christian Ginski, Myriam Benisty, Bin Ren, Alexander J. Bohn, Élodie Choquet, Karin I. Öberg, et al. "Disk Evolution Study through Imaging of Nearby Young Stars (DESTINYS): A Panchromatic View of DO Tau’s Complex Kilo-astronomical-unit Environment." Astrophysical Journal 930, no. 2 (May 1, 2022): 171. http://dx.doi.org/10.3847/1538-4357/ac63ba.

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Abstract While protoplanetary disks are often treated as isolated systems in planet formation models, observations increasingly suggest that vigorous interactions between Class II disks and their environments are not rare. DO Tau is a T Tauri star that has previously been hypothesized to have undergone a close encounter with the HV Tau system. As part of the DESTINYS ESO Large Programme, we present new Very Large Telescope (VLT)/SPHERE polarimetric observations of DO Tau and combine them with archival Hubble Space Telescope (HST) scattered-light images and Atacama Large Millimeter/submillimeter Array (ALMA) observations of CO isotopologues and CS to map a network of complex structures. The SPHERE and ALMA observations show that the circumstellar disk is connected to arms extending out to several hundred astronomical units. HST and ALMA also reveal stream-like structures northeast of DO Tau, some of which are at least several thousand astronomical units long. These streams appear not to be gravitationally bound to DO Tau, and comparisons with previous Herschel far-IR observations suggest that the streams are part of a bridge-like structure connecting DO Tau and HV Tau. We also detect a fainter redshifted counterpart to a previously known blueshifted CO outflow. While some of DO Tau’s complex structures could be attributed to a recent disk–disk encounter, they might be explained alternatively by interactions with remnant material from the star formation process. These panchromatic observations of DO Tau highlight the need to contextualize the evolution of Class II disks by examining processes occurring over a wide range of size scales.

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Meeter, Lieke H. H., Everard G. Vijverberg, Marta Del Campo, Annemieke J. M. Rozemuller, Laura Donker Kaat, Frank Jan de Jong, Wiesje M. van der Flier, Charlotte E. Teunissen, John C. van Swieten, and Yolande A. L. Pijnenburg. "Clinical value of neurofilament and phospho-tau/tau ratio in the frontotemporal dementia spectrum." Neurology 90, no. 14 (March 7, 2018): e1231-e1239. http://dx.doi.org/10.1212/wnl.0000000000005261.

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ObjectiveTo examine the clinical value of neurofilament light chain (NfL) and the phospho-tau/total tau ratio (p/t-tau) across the entire frontotemporal dementia (FTD) spectrum in a large, well-defined cohort.MethodsCSF NfL and p/t-tau levels were studied in 361 patients with FTD: 179 behavioral variant FTD, 17 FTD with motor neuron disease (FTD-MND), 36 semantic variant primary progressive aphasia (PPA), 19 nonfluent variant PPA, 4 logopenic variant PPA (lvPPA), 42 corticobasal syndrome, and 64 progressive supranuclear palsy. Forty-five cognitively healthy controls were also included. Definite pathology was known in 68 patients (49 frontotemporal lobar degeneration [FTLD]-TDP, 18 FTLD-tau, 1 FTLD-FUS).ResultsNfL was higher in all diagnoses, except lvPPA (n = 4), than in controls, equally elevated in behavioral variant FTD, semantic variant PPA, nonfluent variant PPA, and corticobasal syndrome, and highest in FTD-MND. The p/t-tau was lower in all clinical groups, except lvPPA, than in controls and lowest in FTD-MND. NfL did not discriminate between TDP and tau pathology, while the p/t-tau ratio had a good specificity (76%) and moderate sensitivity (67%). Both high NfL and low p/t-tau were associated with poor survival (hazard ratio on tertiles 1.7 for NfL, 0.7 for p/t-tau).ConclusionNfL and p/t-tau similarly discriminated FTD from controls, but not between clinical subtypes, apart from FTD-MND. Both markers predicted survival and are promising monitoring biomarkers for clinical trials. Of note, p/t-tau, but not NfL, was specific to discriminate TDP from tau pathology in vivo.Classification of evidenceThis study provides Class III evidence that for patients with cognitive issues, CSF NfL and p/t-tau levels discriminate between those with and without FTD spectrum disorders.

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Mattsson, Niklas, Ruben Smith, Olof Strandberg, Sebastian Palmqvist, Michael Schöll, Philip S. Insel, Douglas Hägerström, et al. "Comparing 18F-AV-1451 with CSF t-tau and p-tau for diagnosis of Alzheimer disease." Neurology 90, no. 5 (January 10, 2018): e388-e395. http://dx.doi.org/10.1212/wnl.0000000000004887.

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ObjectiveTo compare PET imaging of tau pathology with CSF measurements (total tau [t-tau] and phosphorylated tau [p-tau]) in terms of diagnostic performance for Alzheimer disease (AD).MethodsWe compared t-tau and p-tau and 18F-AV-1451 in 30 controls, 14 patients with prodromal AD, and 39 patients with Alzheimer dementia, recruited from the Swedish BioFINDER study. All patients with AD (prodromal and dementia) were screened for amyloid positivity using CSF β-amyloid 42. Retention of 18F-AV-1451 was measured in a priori specified regions, selected for known associations with tau pathology in AD.ResultsRetention of 18F-AV-1451 was markedly elevated in Alzheimer dementia and moderately elevated in prodromal AD. CSF t-tau and p-tau was increased to similar levels in both AD dementia and prodromal AD. 18F-AV-1451 had very good diagnostic performance for Alzheimer dementia (area under the receiver operating characteristic curve [AUROC] ∼1.000), and was significantly better than t-tau (0.876), p-tau (0.890), hippocampal volume (0.824), and temporal cortical thickness (0.860). For prodromal AD, there were no significant AUROC differences between CSF tau and 18F-AV-1451 measures (0.836–0.939), but MRI measures had lower AUROCs (0.652–0.769).ConclusionsCSF tau and 18F-AV-1451 have equal performance in early clinical stages of AD, but 18F-AV-1451 is superior in the dementia stage, and exhibits close to perfect diagnostic performance for mild to moderate AD.Classification of evidenceThis study provides Class III evidence that CSF tau and 18F-AV-1451 PET have similar performance in identifying early AD, and that 18F-AV-1451 PET is superior to CSF tau in identifying mild to moderate AD.

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Levi, Inessa, and Steve Seif. "COMBINATORIAL TECHNIQUES FOR DETERMINING RANK AND IDEMPOTENT RANK OF CERTAIN FINITE SEMIGROUPS." Proceedings of the Edinburgh Mathematical Society 45, no. 3 (October 2002): 617–30. http://dx.doi.org/10.1017/s0013091501000530.

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AbstractLet $\tau$ be a partition of the positive integer $n$. A partition of the set $\{1,2,\dots,n\}$ is said to be of type $\tau$ if the sizes of its classes form the partition $\tau$ of $n$. It is known that the semigroup $S(\tau)$, generated by all the transformations with kernels of type $\tau$, is idempotent generated. When $\tau$ has a unique non-singleton class of size $d$, the difficult Middle Levels Conjecture of combinatorics obstructs the application of known techniques for determining the rank and idempotent rank of $S(\tau)$. We further develop existing techniques, associating with a subset $U$ of the set of all idempotents of $S(\tau)$ with kernels of type $\tau$ a directed graph $D(U)$; the directed graph $D(U)$ is strongly connected if and only if $U$ is a generating set for $S(\tau)$, a result which leads to a proof if the fact that the rank and the idempotent rank of $S(\tau)$ are both equal to$$ \max\biggl\{\binom{n}{d},\binom{n}{d+1}\biggr\}. $$AMS 2000 Mathematics subject classification: Primary 20M20; 05A18; 05A17; 05C20

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Engstrom, Amanda K., Alicia C. Walker, Rohitha A. Moudgal, Dexter A. Myrick, Stephanie M. Kyle, Yu Bai, M. Jordan Rowley, and David J. Katz. "The inhibition of LSD1 via sequestration contributes to tau-mediated neurodegeneration." Proceedings of the National Academy of Sciences 117, no. 46 (November 2, 2020): 29133–43. http://dx.doi.org/10.1073/pnas.2013552117.

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Tauopathies are a class of neurodegenerative diseases associated with pathological tau. Despite many advances in our understanding of these diseases, the direct mechanism through which tau contributes to neurodegeneration remains poorly understood. Previously, our laboratory implicated the histone demethylase LSD1 in tau-induced neurodegeneration by showing that LSD1 localizes to pathological tau aggregates in Alzheimer's disease cases, and that it is continuously required for the survival of hippocampal and cortical neurons in mice. Here, we utilize the P301S tauopathy mouse model to demonstrate that pathological tau can exclude LSD1 from the nucleus in neurons. In addition, we show that reducing LSD1 in these mice is sufficient to highly exacerbate tau-mediated neurodegeneration and tau-induced gene expression changes. Finally, we find that overexpressing LSD1 in the hippocampus of tauopathy mice, even after pathology has formed, is sufficient to significantly delay neurodegeneration and counteract tau-induced expression changes. These results suggest that inhibiting LSD1 via sequestration contributes to tau-mediated neurodegeneration. Thus, LSD1 is a promising therapeutic target for tauopathies such as Alzheimer's disease.

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Nachman, Eliana, Anne S. Wentink, Karine Madiona, Luc Bousset, Taxiarchis Katsinelos, Kieren Allinson, Harm Kampinga, et al. "Disassembly of Tau fibrils by the human Hsp70 disaggregation machinery generates small seeding-competent species." Journal of Biological Chemistry 295, no. 28 (May 28, 2020): 9676–90. http://dx.doi.org/10.1074/jbc.ra120.013478.

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The accumulation of amyloid Tau aggregates is implicated in Alzheimer's disease (AD) and other tauopathies. Molecular chaperones are known to maintain protein homeostasis. Here, we show that an ATP-dependent human chaperone system disassembles Tau fibrils in vitro. We found that this function is mediated by the core chaperone HSC70, assisted by specific cochaperones, in particular class B J-domain proteins and a heat shock protein 110 (Hsp110)-type nucleotide exchange factor (NEF). The Hsp70 disaggregation machinery processed recombinant fibrils assembled from all six Tau isoforms as well as Sarkosyl-resistant Tau aggregates extracted from cell cultures and human AD brain tissues, demonstrating the ability of the Hsp70 machinery to recognize a broad range of Tau aggregates. However, the chaperone activity released monomeric and small oligomeric Tau species, which induced the aggregation of self-propagating Tau conformers in a Tau cell culture model. We conclude that the activity of the Hsp70 disaggregation machinery is a double-edged sword, as it eliminates Tau amyloids at the cost of generating new seeds.

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Sheehan, Patrick D., and Josh A. Eisner. "CONSTRAINING THE DISK MASSES OF THE CLASS I BINARY PROTOSTAR GV Tau." Astrophysical Journal 791, no. 1 (July 22, 2014): 19. http://dx.doi.org/10.1088/0004-637x/791/1/19.

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Novak, Michal. "F2-04-04: FIRST-IN-MAN AND FIRST-IN-CLASS TAU VACCINE." Alzheimer's & Dementia 10 (July 2014): P162. http://dx.doi.org/10.1016/j.jalz.2014.04.149.

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Vanani, S. Karimi, and A. Aminataei. "Operational Tau approximation for a general class of fractional integro-differential equations." Computational & Applied Mathematics 30, no. 3 (2011): 655–74. http://dx.doi.org/10.1590/s1807-03022011000300010.

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Fischer, Itzhak. "Big Tau: What We Know, and We Need to Know." eneuro 10, no. 5 (May 2023): ENEURO.0052–23.2023. http://dx.doi.org/10.1523/eneuro.0052-23.2023.

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Tau is a microtubule-associated protein (MAP) that has multiple isoforms generated by alternative splicing of the MAPT gene at a range of 45–60 kDa [low-molecular-weight (LMW) tau] as well as a unique isoform termed Big tau containing an additional exon 4a encoding a large projecting domain of ∼250 aa to form a protein of 110 kDa. Big tau is expressed in adult PNS neurons such as DRG neurons and specific regions of CNS such as the cerebellum in a developmental transition from LMW tau to Big tau during the postnatal period. Despite a conserved size of the 4a exons across the vertebrate phylogeny, there is no sequence homology among different species outside the Mammalia class, which underscores the focus on structural preservation of Big tau. Despite the original discovery of Big tau in the early 1990s, there has been little progress elucidating its physiological properties and pathologic implications. We propose that Big tau may be able to improve axonal transport in projecting axons and speculate on the potential protective properties in preventing tau aggregation in pathologic conditions. This perspective highlights the importance and benefits of understanding of the role of Big tau in neuronal health and disease.

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Lee, Yoonjin, and Yoon Kyung Park. "Ramanujan’s function k(τ)=r(τ)r 2(2τ) and its modularity." Open Mathematics 18, no. 1 (January 1, 2020): 1727–41. http://dx.doi.org/10.1515/math-2020-0105.

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Abstract We study the modularity of Ramanujan’s function k ( τ ) = r ( τ ) r 2 ( 2 τ ) k(\tau )=r(\tau ){r}^{2}(2\tau ) , where r ( τ ) r(\tau ) is the Rogers-Ramanujan continued fraction. We first find the modular equation of k ( τ ) k(\tau ) of “an” level, and we obtain some symmetry relations and some congruence relations which are satisfied by the modular equations; these relations are quite useful for reduction of the computation cost for finding the modular equations. We also show that for some τ \tau in an imaginary quadratic field, the value k ( τ ) k(\tau ) generates the ray class field over an imaginary quadratic field modulo 10; this is because the function k is a generator of the field of the modular function on Γ 1 ( 10 ) {{\mathrm{\Gamma}}}_{1}(10) . Furthermore, we suggest a rather optimal way of evaluating the singular values of k ( τ ) k(\tau ) using the modular equations in the following two ways: one is that if j ( τ ) j(\tau ) is the elliptic modular function, then one can explicitly evaluate the value k ( τ ) k(\tau ) , and the other is that once the value k ( τ ) k(\tau ) is given, we can obtain the value k ( r τ ) k(r\tau ) for any positive rational number r immediately.

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Gandini, Annachiara, Manuela Bartolini, Daniele Tedesco, Loreto Martinez-Gonzalez, Carlos Roca, Nuria E. Campillo, Josefa Zaldivar-Diez, et al. "Tau-Centric Multitarget Approach for Alzheimer’s Disease: Development of First-in-Class Dual Glycogen Synthase Kinase 3β and Tau-Aggregation Inhibitors." Journal of Medicinal Chemistry 61, no. 17 (August 4, 2018): 7640–56. http://dx.doi.org/10.1021/acs.jmedchem.8b00610.

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La Joie, Renaud, Alexandre Bejanin, Anne M. Fagan, Nagehan Ayakta, Suzanne L. Baker, Viktoriya Bourakova, Adam L. Boxer, et al. "Associations between [18F]AV1451 tau PET and CSF measures of tau pathology in a clinical sample." Neurology 90, no. 4 (December 27, 2017): e282-e290. http://dx.doi.org/10.1212/wnl.0000000000004860.

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ObjectiveTo assess the relationships between fluid and imaging biomarkers of tau pathology and compare their diagnostic utility in a clinically heterogeneous sample.MethodsFifty-three patients (28 with clinical Alzheimer disease [AD] and 25 with non-AD clinical neurodegenerative diagnoses) underwent β-amyloid (Aβ) and tau ([18F]AV1451) PET and lumbar puncture. CSF biomarkers (Aβ42, total tau [t-tau], and phosphorylated tau [p-tau]) were measured by multianalyte immunoassay (AlzBio3). Receiver operator characteristic analyses were performed to compare discrimination of Aβ-positive AD from non-AD conditions across biomarkers. Correlations between CSF biomarkers and PET standardized uptake value ratios (SUVR) were assessed using skipped Pearson correlation coefficients. Voxelwise analyses were run to assess regional CSF–PET associations.Results[18F]AV1451-PET cortical SUVR and p-tau showed excellent discrimination between Aβ-positive AD and non-AD conditions (area under the curve 0.92–0.94; ≤0.83 for other CSF measures), and reached 83% classification agreement. In the full sample, cortical [18F]AV1451 was associated with all CSF biomarkers, most strongly with p-tau (r = 0.75 vs 0.57 for t-tau and −0.49 for Aβ42). When restricted to Aβ-positive patients with AD, [18F]AV1451 SUVR correlated modestly with p-tau and t-tau (both r = 0.46) but not Aβ42 (r = 0.02). On voxelwise analysis, [18F]AV1451 correlated with CSF p-tau in temporoparietal cortices and with t-tau in medial prefrontal regions. Within AD, Mini-Mental State Examination scores were associated with [18F]AV1451-PET, but not CSF biomarkers.Conclusion[18F]AV1451-PET and CSF p-tau had comparable value for differential diagnosis. Correlations were robust in a heterogeneous clinical group but attenuated (although significant) in AD, suggesting that fluid and imaging biomarkers capture different aspects of tau pathology.Classification of evidenceThis study provides Class III evidence that, in a clinical sample of patients with a variety of suspected neurodegenerative diseases, both CSF p-tau and [18F]AV1451 distinguish AD from non-AD conditions.

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Himmler, A. "Structure of the bovine tau gene: alternatively spliced transcripts generate a protein family." Molecular and Cellular Biology 9, no. 4 (April 1989): 1389–96. http://dx.doi.org/10.1128/mcb.9.4.1389-1396.1989.

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Tau, a major class of microtubule-associated proteins, consists of a family of proteins that are heterogeneous in molecular weight. The presence of internal deletions in previously described cDNA clones for murine and bovine tau suggested that alternative splicing of transcripts could account for the protein size heterogeneity. Analysis of the exon-intron structure of the bovine tau gene provided sequence information necessary to detect new variants of tau transcripts by in vitro amplification techniques. The variant transcripts found corresponded to mRNA species missing one or more exons, which suggested that by skipping various exons during mRNA splicing, a family of proteins is generated. Four major tau protein isoforms isolated from bovine brain were identified by comparison with translation products of cDNA constructs and the use of antisera raised against synthetic peptides. These studies provide reagents and a basis for analyzing potentially altered forms of tau proteins in brains of patients with Alzheimer's disease.

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Himmler, A. "Structure of the bovine tau gene: alternatively spliced transcripts generate a protein family." Molecular and Cellular Biology 9, no. 4 (April 1989): 1389–96. http://dx.doi.org/10.1128/mcb.9.4.1389.

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Tau, a major class of microtubule-associated proteins, consists of a family of proteins that are heterogeneous in molecular weight. The presence of internal deletions in previously described cDNA clones for murine and bovine tau suggested that alternative splicing of transcripts could account for the protein size heterogeneity. Analysis of the exon-intron structure of the bovine tau gene provided sequence information necessary to detect new variants of tau transcripts by in vitro amplification techniques. The variant transcripts found corresponded to mRNA species missing one or more exons, which suggested that by skipping various exons during mRNA splicing, a family of proteins is generated. Four major tau protein isoforms isolated from bovine brain were identified by comparison with translation products of cDNA constructs and the use of antisera raised against synthetic peptides. These studies provide reagents and a basis for analyzing potentially altered forms of tau proteins in brains of patients with Alzheimer's disease.

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Hanes, Jozef, Andrej Kovac, Hlin Kvartsberg, Eva Kontsekova, Lubica Fialova, Stanislav Katina, Branislav Kovacech, et al. "Evaluation of a novel immunoassay to detect p-tau Thr217 in the CSF to distinguish Alzheimer disease from other dementias." Neurology 95, no. 22 (September 24, 2020): e3026-e3035. http://dx.doi.org/10.1212/wnl.0000000000010814.

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ObjectiveTo investigate whether tau phosphorylated at Thr217 (p-tau T217) assay in CSF can distinguish patients with Alzheimer disease (AD) from patients with other dementias and healthy controls.MethodsWe developed and validated a novel Simoa immunoassay to detect p-tau T217 in CSF. There was a total of 190 participants from 3 cohorts with AD (n = 77) and other neurodegenerative diseases (n = 69) as well as healthy participants (n = 44).ResultsThe p-tau T217 assay (cutoff 242 pg/mL) identified patients with AD with accuracy of 90%, with 78% positive predictive value (PPV), 97% negative predictive value (NPV), 93% sensitivity, and 88% specificity, compared favorably with p-tau T181 ELISA (52 pg/mL), showing 78% accuracy, 58% PPV, 98% NPV, 71% specificity, and 97% sensitivity. The assay distinguished patients with AD from age-matched healthy controls (cutoff 163 pg/mL, 98% sensitivity, 93% specificity), similarly to p-tau T181 ELISA (cutoff 60 pg/mL, 96% sensitivity, 86% specificity). In patients with AD, we found a strong correlation between p-tau T217 and p-tau T181, total tau and β-amyloid 40, but not β-amyloid 42.ConclusionsThis study demonstrates that p-tau T217 displayed better diagnostic accuracy than p-tau T181. The data suggest that the new p-tau T217 assay has potential as an AD diagnostic test in clinical evaluation.Classification of evidenceThis study provides Class III evidence that a CSF immunoassay for p-tau T217 distinguishes patients with AD from patients with other dementias and healthy controls.

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Tripathi, Ankita, Yuvraj Indoliya, Madhu Tiwari, Poonam Tiwari, Dipali Srivastava, Pankaj kumar Verma, Shikha Verma, Neelam Gautam, and Debasis Chakrabarty. "Transformed yeast (Schizosaccharomyces pombe) overexpressing rice Tau class glutathione S-transferase (OsGSTU30 and OsGSTU41) shows enhanced resistance to hexavalent chromium." Metallomics 6, no. 8 (2014): 1549–57. http://dx.doi.org/10.1039/c4mt00083h.

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Suslina, Tatiana Aleksandrovna. "Operator-theoretic approach to the homogenization of Schrödinger-type equations with periodic coefficients." Russian Mathematical Surveys 78, no. 6 (2023): 1023–154. http://dx.doi.org/10.4213/rm10143e.

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In $L_2(\mathbb{R}^d;\mathbb{C}^n)$, we consider a selfadjoint strongly elliptic second-order differential operator ${\mathcal A}_\varepsilon$. It is assumed that the coefficients of ${\mathcal A}_\varepsilon$ are periodic and depend on ${\mathbf x}/\varepsilon$, where $\varepsilon>0$. We study the behaviour of the operator exponential $e^{-i{\mathcal A}_\varepsilon\tau}$ for small $\varepsilon$ and $\tau \in \mathbb{R}$. The results are applied to the homogenization of solutions of the Cauchy problem for the Schrödinger-type equation $i\partial_\tau{\mathbf u}_\varepsilon({\mathbf x},\tau)=({\mathcal A}_\varepsilon{\mathbf u}_\varepsilon)({\mathbf x},\tau)$ with initial data from a special class. For fixed $\tau$, as $\varepsilon \to 0$, the solution converges in $L_2(\mathbb{R}^d;\mathbb{C}^n)$ to the solution of the homogenized problem; the error is of the order $O(\varepsilon)$. For fixed $\tau$ we obtain an approximation of the solution ${\mathbf u}_\varepsilon( \cdot ,\tau)$ in the $L_2(\mathbb{R}^d;\mathbb{C}^n)$-norm with error $O(\varepsilon^2)$, and also an approximation of the solution in the $H^1(\mathbb{R}^d;\mathbb{C}^n)$-norm with error $O(\varepsilon)$. In these approximations correctors are taken into account. The dependence of errors on the parameter $\tau$ is traced. Bibliography: 113 items.

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KUZMIN, KONSTANTIN S., VLADIMIR V. LYUBUSHKIN, and VADIM A. NAUMOV. "POLARIZATION OF TAU LEPTONS PRODUCED IN QUASIELASTIC NEUTRINO–NUCLEON SCATTERING." Modern Physics Letters A 19, no. 39 (December 21, 2004): 2919–28. http://dx.doi.org/10.1142/s0217732304016184.

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A numerical analysis of the polarization vector of τ's produced through quasielastic ντ and [Formula: see text] interactions with nucleons is given with two models for vector electromagnetic form factors of proton and neutron. The impact of G parity violating axial and vector second-class currents is investigated by applying a simple heuristic model for the induced scalar and tensor form factors.

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LAFFERTY, G. D. "TAU LEPTON HADRONIC DECAYS AT BABAR AND BELLE." Modern Physics Letters A 28, no. 24 (August 7, 2013): 1360007. http://dx.doi.org/10.1142/s0217732313600079.

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The BaBar and Belle experiments together recorded a total sample of some 3 ×109 tau lepton decays between the years 2000 and 2010. This enabled many new and improved measurements of tau hadronic decays to be made, and resulted in lower limits for branching fractions to rare and forbidden hadronic modes, such as those mediated by second-class weak currents which are sensitive to the u–d quark mass difference. Better measurements of strange decays have contributed to more precise data on the CKM matrix element, |Vus|. However, only limited progress has been made in measurements that feed into knowledge of the value of the strong coupling constant, αs, and the strange quark mass. This is largely due to the dominance of systematic uncertainties on branching fractions and shapes of mass spectra (spectral functions) for some of the important hadronic tau decay modes.

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Mattsson-Carlgren, Niklas, Lea T. Grinberg, Adam Boxer, Rik Ossenkoppele, Magnus Jonsson, William Seeley, Alexander Ehrenberg, et al. "Cerebrospinal Fluid Biomarkers in Autopsy-Confirmed Alzheimer Disease and Frontotemporal Lobar Degeneration." Neurology 98, no. 11 (February 16, 2022): e1137-e1150. http://dx.doi.org/10.1212/wnl.0000000000200040.

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Background and ObjectivesTo determine how fully automated Elecsys CSF immunoassays for β-amyloid (Aβ) and tau biomarkers and an ultrasensitive Simoa assay for neurofilament light chain (NFL) correlate with neuropathologic changes of Alzheimer disease (AD) and frontotemporal lobar degeneration (FTLD).MethodsWe studied 101 patients with antemortem CSF and neuropathology data. CSF samples were collected a mean of 2.9 years before death (range 0.2–7.5 years). CSF was analyzed for Aβ40, Aβ42, total tau (T-tau), tau phosphorylated at amino acid residue 181 (P-tau), P-tau/Aβ42 and Aβ42/Aβ40 ratios, and NFL. Neuropathology measures included Thal phases, Braak stages, Consortium to Establish a Registry for Alzheimer's Disease (CERAD) scores, AD neuropathologic change (ADNC), and primary and contributory pathologic diagnoses. Associations between CSF biomarkers and neuropathologic features were tested in regression models adjusted for age, sex, and time from sampling to death.ResultsCSF biomarkers were associated with neuropathologic measures of Aβ (Thal, CERAD score), tau (Braak stage), and overall ADNC. The CSF P-tau/Aβ42 and Aβ42/Aβ40 ratios had high sensitivity, specificity, and overall diagnostic performance for intermediate-high ADNC (area under the curve range 0.95–0.96). Distinct biomarker patterns were seen in different FTLD subtypes, with increased NFL and reduced P-tau/T-tau in FTLD–TAR DNA-binding protein 43 and reduced T-tau in progressive supranuclear palsy compared to other FTLD variants.DiscussionCSF biomarkers, including P-tau, T-tau, Aβ42, Aβ40, and NFL, support in vivo identification of AD neuropathology and correlate with FTLD neuropathology.Classification of EvidenceThis study provides Class II evidence that distinct CSF biomarker patterns, including for P-tau, T-tau, Aβ42, Aβ40, and NFL, are associated with AD and FTLD neuropathology.

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Satar, Serdar, Adnan Tusun, Miraç Yayla, and Gülsevim Tiring. "Amblyseius swirskii Athias-Henriot ve Euseius scutalis Athias-Henriot (Acari:Phytoseiidae)’e Tau-Fluvalinatin Etkisi." Turkish Journal of Agriculture - Food Science and Technology 7, no. 12 (December 15, 2019): 2190. http://dx.doi.org/10.24925/turjaf.v7i12.2190-2197.2949.

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Amblyseius swirskii Athias-Henriot (Acari:Phytoseiidae) and Euseius scutalis Athias-Henriot (Acari: Phytoseiidae) are important predatory mites for citrus orchards in Turkey. The side effects of insecticides on these predatory mites have been rarely studied. In this study was investigated to the effect of tau-fluvalinate on A. swirskii and E. scutalis. The studies have conducted both laboratory and field. Field studies were carried out detecting of the side effects of tau-fluvalinate on the mixed stages of A.swirskii. and E scutalis. at Seyhan and Kozan districts in Adana, while laboratory studies were evaluated the side effects of tau-fluvalinate on the nymph stages of A. swirskii The studies were carried out following the standard guidelines which were adopted and issued by the IOBC-WPRS Working group ‘Pesticedes and Benefical Organism’. In the field studies, the effects of the pesticides were calculated according to the Henderson-Tilton formula. As a result of study, tau-fluvalinate was determined as toxic on predatory mites in the laboratory studies. Side effects of abamectin, one of the standard toxic acaricides, on predatory mites were found to be “T” (Toxic) according to IOBC class value. Side effects of tau-fluvalinate were found to be ’M’’ (Moderately Harmful) on 7th days while were detected to be “N” (Harmless) on 28th days according to IOBC class value in field condition. The fields studies at Kozan and Seyhan districts showed similar results.

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Rainnie, D. G., E. K. Asprodini, and P. Shinnick-Gallagher. "Intracellular recordings from morphologically identified neurons of the basolateral amygdala." Journal of Neurophysiology 69, no. 4 (April 1, 1993): 1350–62. http://dx.doi.org/10.1152/jn.1993.69.4.1350.

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1. Intracellular current-clamp recordings were made from neurons of the basolateral nucleus of the amygdala (BLA) of the rat in the in vitro slice preparation. Neurons were identified morphologically after intracellular injection of biocytin, and the electrophysiological properties and morphological characteristics were correlated. 2. Three distinct morphological subtypes were identified: Class I pyramidal neurons, Class I stellate neurons, and Class II neurons. Each morphological subtype could also be distinguished according to its characteristic electrophysiological properties. 3. Class I pyramidal neurons typically had pyramidal perikarya (cross-sectional area = 245 microns2) with spine-laden apical and basal dendrites. The axon originated from the largest basal dendrite and produced several collaterals that ramified throughout the dendritic arborization of the parent cell. These neurons were characterized electrophysiologically by their higher input resistance (65.6 M omega), long time constant of membrane charging tau 0 (27.8 ms), long duration action potential (half-width = 0.85 ms), and regular firing pattern [1st interspike interval ISI) = 91 ms]. 4. Class I stellate neurons differed morphologically from Class I pyramidal neurons only in the size (cross sectional area = 330 microns 2) and stellate appearance of their perikarya. These neurons had characteristic lower input resistance (40.1 M omega), shorter time constant of membrane charging tau 0 (14.5 ms), shorter duration action potential (half-width = 0.7 ms), and a burst firing pattern (1st ISI = 6.0 ms), all of which were statistically different from Class I pyramidal neurons. 5. Class II neurons were multipolar (cross sectional area = 235 microns 2) and were distinguishable from Class I neurons by the almost complete absence of dendritic spines. Class II neurons were characterized electrophysiologically by a midrange input resistance (58 M omega), intermediate time constant of membrane charging tau 0 (19 ms), intermediate action-potential duration (half-width = 0.77 ms), and a burst firing pattern (1st ISI = 6.0 ms). In contrast to Class I neurons, action-potential firing of Class II neurons did not accommodate in response to prolonged depolarizing current injection. 6. In conclusion, BLA neurons may be characterized by their specific electrophysiological properties as well as by their morphological traits. Therefore, permitting assessment of signal transduction in identified populations of neurons within this nucleus.

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Thom, Russell, Ian Cummins, David P. Dixon, Robert Edwards, David J. Cole, and Adrian J. Lapthorn. "Structure of a Tau Class GlutathioneS-Transferase from Wheat Active in Herbicide Detoxification†,‡." Biochemistry 41, no. 22 (June 2002): 7008–20. http://dx.doi.org/10.1021/bi015964x.

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Dutrey, A., S. Guilloteau, and M. Simon. "The BP Tau disk: A missing link between Class II and III objects?" Astronomy & Astrophysics 402, no. 3 (April 23, 2003): 1003–11. http://dx.doi.org/10.1051/0004-6361:20030317.

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El Baraka, Azzeddine, and Mohammed Masrour. "A-priori Estimates Near the Boundary for Solutions of a class of Degenerate Elliptic Problems in Besov-type Spaces." Moroccan Journal of Pure and Applied Analysis 3, no. 2 (December 1, 2017): 149–72. http://dx.doi.org/10.1515/mjpaa-2017-0013.

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Abstract:

AbstractIn this paper, we give a priori estimates near the boundary for solutions of a degenerate elliptic problems in the general Besov-type spaces $B_{p,q}^{s,\tau }$, containing as special cases: Goldberg space bmo, local Morrey-Campanato spaces l2,λ and the classical Hölder and Besov spaces $B_{p,q}^s $. This work extends the results of [13, 2, 15] from Hölder and Besov spaces to the general frame of $B_{p,q}^{s,\tau }$ spaces.

Journal articles on the topic 'Tau class'

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