Journal articles: 'Tau Theory'

1

Pich, A. "Tau Physics: Theory Overview." Nuclear Physics B - Proceedings Supplements 181-182 (September 2008): 300–305. http://dx.doi.org/10.1016/j.nuclphysbps.2008.09.054.

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Pich, A. "Tau lepton physics: theory overview." Nuclear Physics B - Proceedings Supplements 55, no. 3 (May 1997): 3–22. http://dx.doi.org/10.1016/s0920-5632(97)00195-3.

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Yokoya, Hiroshi. "Theory of Higgs to tau tau signatures at the LHC." Nuclear Physics B - Proceedings Supplements 253-255 (August 2014): 167–70. http://dx.doi.org/10.1016/j.nuclphysbps.2014.09.041.

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4

Carroll, Robert. "Symmetries, sato theory, and tau functions." Applicable Analysis 56, no. 1-2 (February 1995): 147–64. http://dx.doi.org/10.1080/00036819508840316.

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Li, Li, Xiqun Chen, and Zhiheng Li. "Asymmetric stochastic Tau Theory in car-following." Transportation Research Part F: Traffic Psychology and Behaviour 18 (May 2013): 21–33. http://dx.doi.org/10.1016/j.trf.2012.12.002.

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6

Heuer, Ben. "Rigid \tau -crystals." Journal de Théorie des Nombres de Bordeaux 29, no. 3 (2017): 1059–82. http://dx.doi.org/10.5802/jtnb.1012.

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7

Powers, Elizabeth, and Galsan Tschinag. "Tau und Gras." World Literature Today 77, no. 2 (2003): 79. http://dx.doi.org/10.2307/40158008.

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Adachi, Takahide, Osamu Iyama, and Idun Reiten. "-tilting theory." Compositio Mathematica 150, no. 3 (December 3, 2013): 415–52. http://dx.doi.org/10.1112/s0010437x13007422.

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AbstractThe aim of this paper is to introduce $\tau $-tilting theory, which ‘completes’ (classical) tilting theory from the viewpoint of mutation. It is well known in tilting theory that an almost complete tilting module for any finite-dimensional algebra over a field $k$ is a direct summand of exactly one or two tilting modules. An important property in cluster-tilting theory is that an almost complete cluster-tilting object in a 2-CY triangulated category is a direct summand of exactly two cluster-tilting objects. Reformulated for path algebras $kQ$, this says that an almost complete support tilting module has exactly two complements. We generalize (support) tilting modules to what we call (support) $\tau $-tilting modules, and show that an almost complete support $\tau $-tilting module has exactly two complements for any finite-dimensional algebra. For a finite-dimensional $k$-algebra $\Lambda $, we establish bijections between functorially finite torsion classes in $ \mathsf{mod} \hspace{0.167em} \Lambda $, support $\tau $-tilting modules and two-term silting complexes in ${ \mathsf{K} }^{\mathrm{b} } ( \mathsf{proj} \hspace{0.167em} \Lambda )$. Moreover, these objects correspond bijectively to cluster-tilting objects in $ \mathcal{C} $ if $\Lambda $ is a 2-CY tilted algebra associated with a 2-CY triangulated category $ \mathcal{C} $. As an application, we show that the property of having two complements holds also for two-term silting complexes in ${ \mathsf{K} }^{\mathrm{b} } ( \mathsf{proj} \hspace{0.167em} \Lambda )$.

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MAKGAMATHA, M. P., and M. L. Bopape. "TAU MODULATHOKO." South African Journal of African Languages 13, sup3 (January 1993): 4–13. http://dx.doi.org/10.1080/02572117.1993.10586992.

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10

Charles, Denis Xavier. "Computing the Ramanujan tau function." Ramanujan Journal 11, no. 2 (April 2006): 221–24. http://dx.doi.org/10.1007/s11139-006-6509-y.

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11

Mason, L. J., M. A. Singer, and N. M. J. Woodhouse. "Tau functions and the twistor theory of integrable systems." Journal of Geometry and Physics 32, no. 4 (February 2000): 397–430. http://dx.doi.org/10.1016/s0393-0440(99)00038-8.

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12

Wann, John P. "Anticipating arrival: Is the tau margin a specious theory?" Journal of Experimental Psychology: Human Perception and Performance 22, no. 4 (1996): 1031–48. http://dx.doi.org/10.1037/0096-1523.22.4.1031.

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13

Alkhalifah, Tariq. "Tau migration and velocity analysis: Theory and synthetic examples." GEOPHYSICS 68, no. 4 (July 2003): 1331–39. http://dx.doi.org/10.1190/1.1598126.

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Prestack migration velocity analysis in the time domain reduces the velocity‐depth ambiguity usually hampering the performance of prestack depth‐migration velocity analysis. In prestack τ migration velocity analysis, we keep the interval velocity model and the output images in vertical time. This allows us to avoid placing reflectors at erroneous depths during the velocity analysis process and, thus, avoid slowing down its convergence to the true velocity model. Using a 1D velocity update scheme, the prestack τ migration velocity analysis performed well on synthetic data from a model with a complex near‐surface velocity. Accurate velocity information and images were obtained using this time‐domain method. Problems occurred only in resolving a thin layer where the low resolution and fold of the synthetic data made it practically impossible to estimate velocity accurately in this layer. This 1D approach also provided us reasonable results for synthetic data from the Marmousi model. Despite the complexity of this model, the τ domain implementation of the prestack migration velocity analysis converged to a generally reasonable result, which includes properly imaging the elusive top‐of‐the‐reservoir layer.

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Tran, Truong Nguyen, and Le Viet Dung. "Equivalence Between Vector Meson Dominance and Unitarised Chiral Perturbation Theory." Communications in Physics 24, no. 4 (March 9, 2015): 289. http://dx.doi.org/10.15625/0868-3166/24/4/5504.

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It is explicitly shown that either the approximate solution of the integral equation for the inverse of the pion form facto,r or the result of the Pad$\text{\'e}$ approximant method of resumming the one loop Chiral Perturbation Theory (CPTH) are equivalent to the standard vector meson dominance (VMD) models, using the vector meson coupling to two pseudoscalars given by the KSRF relation. Inconsistencies between the one loop CPTH and its unitarised version (or the VMD model) are pointed out. The situation is better for the CPTH calculation of the scalar form factor and the related S-wave $\pi \pi$ scattering. The branching ratios of $\tau \to \pi^+ \pi^0 \nu $, $\tau \to K \pi \nu $, $\tau \to K^+ \eta \nu$ and $\tau \to K^+ \bar{K^0} \nu\) using only two inputs as the $\rho$ and $K^*$ masses, or the two corresponding rms radii, agree with the experimental data. Using the same number of parameters, the corresponding one loop CPTH calculation cannot explain the $\tau$ data.

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15

Padfield, G. D. "The tau of flight control." Aeronautical Journal 115, no. 1171 (September 2011): 521–56. http://dx.doi.org/10.1017/s0001924000006187.

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AbstractWith this survey paper, the author proposes a new ‘tao’ – a new way of understanding – of how pilots do what they do. Research into the control of purposeful action in the natural world suggests that very rapid, efficient and ‘instinctive’ techniques have evolved based on the time to close on a goal, or close a gap, τ(t), and its derivatives. Purposeful actions involve the closure of one or more physical gaps, each with its own time to close, varying with time. Maintaining a constant rate of change of τ(t) with time (< 1) during an approach will ensure a successful arresting when the gap is closed, but an animal’s strategy can be adapted to the circumstances to achieve either a hard stop (aggressive action with ṫ > 0·5), or a soft stop (gentle action with ṫ < 0·5). Synchronous coupling of two motions,x(t) andy(t), such that the times to close are coupled, τx=kτy, results in the motion gapsx(t) andy(t) being related through a power law,x=Cy1/k, and closing smoothly together; examples of such coupling in the form of pursuit tracking in the natural world abound. Research has also shown that gaps can be closed by following ‘intrinsic’ guides, or self-generated mental models of desired motion, that have particular forms; for example, constant deceleration or constant acceleration. The gathering evidence from research into animal behaviour in the natural-world forms a background for the exploration of flight control in the man-made world. The implications for control theory, flight control developments and flight handling qualities, are considered to be profound. τ-theory suggests that natural control has a particular non-linear, albeit very simple, time varying form and that pilots learn control strategy skills by developing mental models, or internalised schemata, in the form of what are described as ‘τ guides’. In this context the author presents his perspective on flight control, briefly reviewing τ-theory and providing examples from research conducted at The University of Liverpool during the period 1999-2011, including the work of several PhD students. Concepts for guidance algorithms suitable for augmented manual or autonomous control are discussed and the implications for handling qualities developments, particularly relating to flight in degraded visual conditions, are presented. Some outstanding questions pointing directions for future research are raised.

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16

Vance, Katherine. "Tau invariants for balanced spatial graphs." Journal of Knot Theory and Its Ramifications 29, no. 09 (August 2020): 2050066. http://dx.doi.org/10.1142/s0218216520500662.

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In 2003, Ozsváth and Szabó defined the concordance invariant [Formula: see text] for knots in oriented 3-manifolds as part of the Heegaard Floer homology package. In 2011, Sarkar gave a combinatorial definition of [Formula: see text] for knots in [Formula: see text] and a combinatorial proof that [Formula: see text] gives a lower bound for the slice genus of a knot. Recently, Harvey and O’Donnol defined a relatively bigraded combinatorial Heegaard Floer homology theory for transverse spatial graphs in [Formula: see text], extending HFK for knots. We define a [Formula: see text]-filtered chain complex for balanced spatial graphs whose associated graded chain complex has homology determined by Harvey and O’Donnol’s graph Floer homology. We use this to show that there is a well-defined [Formula: see text] invariant for balanced spatial graphs generalizing the [Formula: see text] knot concordance invariant. In particular, this defines a [Formula: see text] invariant for links in [Formula: see text]. Using techniques similar to those of Sarkar, we show that our [Formula: see text] invariant is an obstruction to a link being slice.

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Its, A. R., and A. Prokhorov. "On Some Hamiltonian Properties of the Isomonodromic Tau Functions." Reviews in Mathematical Physics 30, no. 07 (July 25, 2018): 1840008. http://dx.doi.org/10.1142/s0129055x18400081.

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We discuss some new aspects of the theory of the Jimbo–Miwa–Ueno tau function which have come to light within the recent developments in the global asymptotic analysis of the tau functions related to the Painlevé equations. Specifically, we show that up to the total differentials the logarithmic derivatives of the Painlevé tau functions coincide with the corresponding classical action differential. This fact simplifies considerably the evaluation of the constant factors in the asymptotics of tau functions, which has been a long-standing problem of the asymptotic theory of Painlevé equations. Furthermore, we believe that this observation is yet another manifestation of L. D. Faddeev’s emphasis of the key role which the Hamiltonian aspects play in the theory of integrable system.

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18

Ceccherini-Silberstein, Tullio, Fabio Scarabotti, and Filippo Tolli. "Mackey’s theory of $${\tau}$$ τ -conjugate representations for finite groups." Japanese Journal of Mathematics 10, no. 1 (December 18, 2014): 43–96. http://dx.doi.org/10.1007/s11537-014-1390-8.

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19

Graham, Kevin. "Precision Tau and Electron Neutral Current Asymmetry Measurements from the Tau Polarization at OPAL." International Journal of Modern Physics A 16, supp01b (September 2001): 555–57. http://dx.doi.org/10.1142/s0217751x01007480.

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A measurement of the τ lepton polarization and forward-backward asymmetry near the Z0 resonance using the OPAL detector is described. The measurement is based on analysis of [Formula: see text], [Formula: see text], τ → π (K) ντ, τ → ρ ντ and τ → a1 ντ decays from a sample of 144, 810 e + e - → τ+ τ- candidates corresponding to an integrated luminosity of 151 pb-1. Assuming that the τ lepton decays according to V - A theory, we measure the average τ polarization near [Formula: see text] to be <Pτ> = (-14.11 ± 0.73 ± 0.56)% and the τ polarization forward-backward asymmetry to be [Formula: see text], where the first error is statistical and the second systematic. These results are consistent with the hypothesis of lepton universality and, within the context of the Standard Model, combine to produce [Formula: see text].

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20

Magder, S. "Venous mechanics of contracting gastrocnemius muscle and the muscle pump theory." Journal of Applied Physiology 79, no. 6 (December 1, 1995): 1930–35. http://dx.doi.org/10.1152/jappl.1995.79.6.1930.

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The time constant of venous drainage (tau v) is an important determinant of the return of blood to the heart. The lower the tau v, the higher the flow for a given volume. To determine whether the tau v of muscle decreases during muscle contraction, we anesthetized dogs with pentobarbital sodium and mechanically ventilated them. We isolated the vasculature of the gastrocnemius muscle and attached the muscle to a force transducer. The muscle was pump perfused, and flows were measured with electromagnetic flow probes on the artery and vein. Pressure in the venous compliant region (Pel) was obtained by simultaneously occluding the artery and vein. Changes in volume (delta V) were produced by changing inflow and obtaining the integral of the difference between inflow and outflow. The tau v was obtained from delta V divided by change in flow. Compliance was calculated from delta V divided by change in Pel from before to after a change in flow. The venous resistance was calculated from tau v divided by venous compliance. The muscle was set at the optimal length, and contractions were produced by stimulating the nerve to the muscle with supramaximal voltage at either 1- or 5-Hz trains with stimulations at 20 Hz, 0.2-ms duration, and duty cycle of 0.25. The tau v at rest was 4.06 +/- 2.16 s and decreased to 2.44 +/- 1.07 s (P < 0.05) at 1 Hz and to 1.81 +/- 0.4 s at 5 Hz. There were no significant changes in venous compliance or venous resistance. In conclusion, muscle contractions can reduce the time constant of venous drainage of muscle and could thereby contribute to the increased venous return and cardiac output during exercise.

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21

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.

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Antonini, Paolo, Sara Azzali, and Georges Skandalis. "The Baum–Connes conjecture localised at the unit element of a discrete group." Compositio Mathematica 156, no. 12 (December 2020): 2536–59. http://dx.doi.org/10.1112/s0010437x20007502.

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AbstractWe construct a Baum–Connes assembly map localised at the unit element of a discrete group $\Gamma$. This morphism, called $\mu _\tau$, is defined in $KK$-theory with coefficients in $\mathbb {R}$ by means of the action of the idempotent $[\tau ]\in KK_{\mathbin {{\mathbb {R}}}}^\Gamma (\mathbb {C},\mathbb {C})$ canonically associated to the group trace of $\Gamma$. We show that the corresponding $\tau$-Baum–Connes conjecture is weaker than the classical version, but still implies the strong Novikov conjecture. The right-hand side of $\mu _\tau$ is functorial with respect to the group $\Gamma$.

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Cowan, Catherine M., Francis Chee, David Shepherd, and Amritpal Mudher. "Disruption of neuronal function by soluble hyperphosphorylated tau in a Drosophila model of tauopathy." Biochemical Society Transactions 38, no. 2 (March 22, 2010): 564–70. http://dx.doi.org/10.1042/bst0380564.

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Axonal microtubules are essential for transport of materials to the synapse. Compromised microtubules and synaptic loss have been demonstrated in AD (Alzheimer's disease), which is believed to contribute to cognitive dysfunction before neuronal death in the early stages of the disease. The mechanism by which hyperphosphorylated tau, the building block of neurofibrillary tangles, one of the pathological hallmarks of AD, disrupts neuronal and synaptic function is unclear. There is a theory that hyperphosphorylated tau does not bind effectively to microtubules and is no longer able to function in stabilizing them, thus axonal transport can no longer proceed efficiently. This leads to synaptic dysfunction. We have tested this theory in a Drosophila model of tauopathies in which we expressed human tau (h-tau). Using this model, we have tested all aspects of this hypothesis and have demonstrated that axonal transport does become compromised in the presence of hyperphosphorylated h-tau and this leads to synaptic and behavioural defects. We are currently investigating the mechanism by which hyperphosphorylated h-tau mediates this effect and are preliminary data indicate that this entails phospho-tau-mediated effects that are predicted by the tau–microtubule hypothesis, as well as novel effects. These deleterious effects of h-tau occur in the absence of tau filaments and before neuronal death. This sequence of pathogenic events may constitute the mechanism by which abnormal tau disrupts neuronal and synaptic function and contributes to cognitive impairment before neuronal death in the early stages of tauopathies such as AD.

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Lygeros, Nik, and Olivier Rozier. "Odd prime values of the Ramanujan tau function." Ramanujan Journal 32, no. 2 (March 15, 2013): 269–80. http://dx.doi.org/10.1007/s11139-012-9420-8.

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Gonzàlez-Solís, Sergi. "Tau decays into two mesons: an overview." EPJ Web of Conferences 212 (2019): 08003. http://dx.doi.org/10.1051/epjconf/201921208003.

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We review the state-of-the-art theoretical analyses of tau decays into a pair of mesons and a neutrino. The participant vector and scalar form factors, f+ (s) and f0(s), are described in the frame of Chiral Perturbation Theory with resonances supplemented by dispersion relations, and the physical parameters of the intermediate resonances produced in the decay are extracted through the pole position of f+,0(s) in the complex plane. As a side result, we also determine the low-energy observables associated to the form factors. We hope our study to be of interest for present and future experimental analyses of these decays.

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MILTON, KIMBALL A., and OLGA P. SOLOVTSOVA. "PERTURBATIVE EXPANSIONS IN THE INCLUSIVE DECAY OF THE TAU-LEPTON." International Journal of Modern Physics A 17, no. 26 (October 20, 2002): 3789–808. http://dx.doi.org/10.1142/s0217751x02010935.

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A comparative analysis is performed for various forms of perturbative expansions in spacelike and timelike regions. As applied to the inclusive decay of the τ-lepton, comparison is given for the results derived within the framework of the standard perturbation theory and the analytic approach that modernizes perturbative expansions so that the new approximations reflect basic principles of the theory: renormalization invariance, spectrality, and causality. Advantages and self-consistency of the analytic approach in describing τ-lepton decay are demonstrated.

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Liang, Chaozhao. "AB001. Prostate-pelvic syndrome: new theory and new practice." Translational Andrology and Urology 7, S5 (September 2018): AB001. http://dx.doi.org/10.21037/tau.2018.ab001.

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ZHANG, Shutao. "Bio-inspired Trajectory Planning for Robot Catching Movements Based on Tau Theory." Journal of Mechanical Engineering 50, no. 13 (2014): 42. http://dx.doi.org/10.3901/jme.2014.13.042.

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Zhang, Zhen, Pu Xie, and Ou Ma. "Bio-Inspired Trajectory Generation for UAV Perching Movement Based on Tau Theory." International Journal of Advanced Robotic Systems 11, no. 9 (January 2014): 141. http://dx.doi.org/10.5772/58898.

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30

Brouwer, Anne-Marie, Eli Brenner, and Jeroen B. J. Smeets. "When Is Behavioral Data Evidence for a Control Theory? Tau-Coupling Revisited." Motor Control 7, no. 2 (April 2003): 103–10. http://dx.doi.org/10.1123/mcj.7.2.103.

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Zhang, Shutao, Jinwu Qian, Zhen Zhang, Linyong Shen, Xi Wu, and Xiaowu Hu. "Age- and Parkinson’s disease-related evaluation of gait by General Tau Theory." Experimental Brain Research 234, no. 10 (June 6, 2016): 2829–40. http://dx.doi.org/10.1007/s00221-016-4685-6.

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Mezzadri, F., and N. J. Simm. "Tau-Function Theory of Chaotic Quantum Transport with β = 1, 2, 4." Communications in Mathematical Physics 324, no. 2 (October 13, 2013): 465–513. http://dx.doi.org/10.1007/s00220-013-1813-z.

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Lee, D. N., M. N. O. Davies, P. R. Green, and F. R. (Ruud). Van Der Weel. "VISUAL CONTROL OF VELOCITY OF APPROACH BY PIGEONS WHEN LANDING." Journal of Experimental Biology 180, no. 1 (July 1, 1993): 85–104. http://dx.doi.org/10.1242/jeb.180.1.85.

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Films of pigeons flying to a perch were analysed to test a theory of how speed of approach and timing of foot extension in preparation for landing are visually controlled. Rapid neural computation of distance to perch and of speed and deceleration would seem to be required. However, according to the theory, none of this is necessary. Simpler control is possible based solely on the value of the tau function of certain optic variables x, where the tau function of × is × divided by its rate of change; i.e. tau(x)=x/x˙˙ tau(x) is a first-order approximation of time to contact with the perch and so could be used for timing foot extension. Controlled braking is possible by simply keeping tau(x), the rate of change of tau(x), constant. The results indicated that pigeons did regulate their braking when approaching the perch by keeping tau(x) constant and initiated foot extension when tau(x) reached a threshold value of approximately 150 ms. They followed this procedure even when they had one eye covered, and so binocular vision was not necessary for regulating braking or timing foot extension. It is shown that an optic variable that the pigeons could be using is the width of the optic projection of the gap between foot and perch. It is further shown that they could be using the same optic variable for controlling the trajectory of their feet to contact the perch.

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de Azevedo Pribitkin, Wladimir. "A generalization of Knopp’s Observation on Ramanujan’s tau-function." Ramanujan Journal 41, no. 1-3 (January 27, 2016): 519–42. http://dx.doi.org/10.1007/s11139-015-9756-y.

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ALKAN, EMRE, and ALEXANDRU ZAHARESCU. "NONVANISHING OF THE RAMANUJAN TAU FUNCTION IN SHORT INTERVALS." International Journal of Number Theory 01, no. 01 (March 2005): 45–51. http://dx.doi.org/10.1142/s1793042105000029.

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Trindade, M., J. Matos, and P. B. Vasconcelos. "Dealing with Functional Coefficients Within Tau Method." Mathematics in Computer Science 12, no. 2 (March 17, 2018): 183–95. http://dx.doi.org/10.1007/s11786-018-0331-y.

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Wei, Shuhuan, Huijun Feng, Lingen Chen, and Yanlin Ge. "Constructal Equivalent Thermal Resistance Minimization for Tau-Shaped Fin." Entropy 22, no. 11 (October 25, 2020): 1206. http://dx.doi.org/10.3390/e22111206.

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With the aid of constructal theory and entransy theory, a Tau-shaped fin (TAUSF) is investigated in this paper, and the widths of the bend end and elemental fins are assumed to be different. The construct of the TAUSF is optimized by the minimum equivalent thermal resistance (ETR) obtained by entransy dissipation rate. The constraints of total enveloping volume and fin material volume are considered. The results show that in the specified range of width ratio, the twice minimum ETR of the TAUSF can be yielded by an optimal width ratio and an optimal length ratio. In addition, comparing the optimal performance of the TAUSF with the counterpart of a T-shaped fin, the former sacrifices a small amount of heat transfer performance and its stiffness increases due to its structure with the bend end. The optimal structure of the TAUSF yielded from ETR minimization is conspicuously different with the counterpart yielded from maximum thermal resistance minimization. Comparing the thermal performances of the two optimal constructs, the ETR of the former optimal construct is declined by 10.58%, whereas the maximum thermal resistance is augmented by 5.22%. The former optimal construct can lead to the uniformity of temperature gradient and the reduction in thermal stress, and can guide the engineering designs of practical fins.

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ÇELİK, CANAN, and GÖKÇEN ÇEKİÇ. "BIFURCATION ANALYSIS OF A LOGISTIC PREDATOR–PREY SYSTEM WITH DELAY." ANZIAM Journal 57, no. 4 (April 2016): 445–60. http://dx.doi.org/10.1017/s1446181116000055.

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We consider a coupled, logistic predator–prey system with delay. Mainly, by choosing the delay time${\it\tau}$as a bifurcation parameter, we show that Hopf bifurcation can occur as the delay time${\it\tau}$passes some critical values. Based on the normal-form theory and the centre manifold theorem, we also derive formulae to obtain the direction, stability and the period of the bifurcating periodic solution at critical values of ${\it\tau}$. Finally, numerical simulations are investigated to support our theoretical results.

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Koiran, Pascal, Natacha Portier, Sébastien Tavenas, and Stéphan Thomassé. "A $$\tau $$ τ -Conjecture for Newton Polygons." Foundations of Computational Mathematics 15, no. 1 (October 23, 2014): 185–97. http://dx.doi.org/10.1007/s10208-014-9216-x.

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CAPRINI, I. "STRONG COUPLING FROM THE TAU HADRONIC WIDTH BY NON-POWER QCD PERTURBATION THEORY." Modern Physics Letters A 28, no. 24 (August 7, 2013): 1360003. http://dx.doi.org/10.1142/s0217732313600031.

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Starting from the divergent character of the perturbative expansions in QCD and using the technique of series acceleration by the conformal mappings of the Borel plane, I define a novel, non-power perturbative expansion for the Adler function, which simultaneously implements renormalisation-group summation and has a tamed large-order behaviour. The new expansion functions, which replace the standard powers of the coupling, are singular at the origin of the coupling plane and have divergent perturbative expansions, resembling the expanded function itself. Confronting the new perturbative expansions with the standard ones on specific models investigated recently in the literature, I show that they approximate in an impressive way the exact Adler function and the spectral function moments. Applied to the τ hadronic width, the contour-improved and the renormalisation-group summed non-power expansions in the [Formula: see text] scheme lead to the prediction [Formula: see text], which translates to [Formula: see text].

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Henneghan, Ashley, Andreana P. Haley, and Shelli Kesler. "Exploring Relationships Among Peripheral Amyloid Beta, Tau, Cytokines, Cognitive Function, and Psychosomatic Symptoms in Breast Cancer Survivors." Biological Research For Nursing 22, no. 1 (November 10, 2019): 126–38. http://dx.doi.org/10.1177/1099800419887230.

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Objective: Accelerated brain aging has been proposed to explain cancer-related cognitive impairment, but empirical evidence for this relationship is lacking. The purpose of this study was to evaluate amyloid beta (Aβ) and tau, biomarkers of neurodegeneration, in relation to cognition in breast cancer survivors (BCSs). We explored relationships among peripheral concentrations of Aβ42, Aβ-40, tau, and cytokines; cognitive function; and psychosomatic symptoms in a cohort of BCSs post-chemotherapy. Methods: This secondary analysis of a cross-sectional study was conducted with 65 BCSs. Serum total Aβ-42, Aβ-40, and tau levels were measured with single molecule array technology. Cytokines (interleukin [IL]-6, tumor necrosis factor [TNF]-α, granulocyte-macrophage colony-stimulating factor [GM-CSF], interferon [IFN]-g, IL-10, IL-12, IL-13, IL1-b, IL-2, IL-4, IL-5, IL-7, and IL-8) were simultaneously measured in serum using multiplex assays. Cognitive function was measured with five standardized neuropsychological tests and psychosomatic symptoms (stress, loneliness, anxiety, depressive symptoms, fatigue, sleep quality, and daytime sleepiness) with self-report questionnaires. Data analyses included correlations and random forest regression (RFR). Results: Significant correlations were identified among hip-to-waste ratio, number of treatment modalities, Aβ-42, Aβ-40, and tau levels ( rs = .27–.35, ps < .05). RFR modeling including Aβ-42, Aβ-40, tau, and cytokines as features explained significant variance in cognitive function ( R 2 = .71, F = 9.01, p < .0001) and psychosomatic symptoms ( R 2 = .74, F = 10.22, p < .0001). Conclusions: This study suggests that neurodegenerative biomarkers interact with cytokines to influence cognitive functioning and psychosomatic symptoms in BCSs following chemotherapy, but additional research is needed.

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Yuraszeck, Theresa M., Pierre Neveu, Maria Rodriguez-Fernandez, Anne Robinson, Kenneth S. Kosik, and Francis J. Doyle. "Vulnerabilities in the Tau Network and the Role of Ultrasensitive Points in Tau Pathophysiology." PLoS Computational Biology 6, no. 11 (November 11, 2010): e1000997. http://dx.doi.org/10.1371/journal.pcbi.1000997.

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Domagalski, Rachel, and Sivaram Narayan. "Tree Cover Number and Maximum Semidefinite Nullity of Some Graph Classes." Electronic Journal of Linear Algebra 36, no. 36 (September 30, 2020): 678–93. http://dx.doi.org/10.13001/ela.2020.5319.

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Let $G$ be a graph with a vertex set $V$ and an edge set $E$ consisting of unordered pairs of vertices. The tree cover number of $G$, denoted $\tau(G)$, is the minimum number of vertex disjoint simple trees occurring as induced subgraphs of $G$ that cover all the vertices of $G$. In this paper, the tree cover number of a line graph $\tau(L(G))$ is shown to be equal to the path number $\pi(G)$ of $G$. Also, the tree cover numbers of shadow graphs, corona and Cartesian product of two graphs are found. The graph parameter $\tau(G)$ is related to another graph parameter $M_+(G)$, called the maximum semidefinite nullity of $G$. Suppose $S_+(G,\mathbb{R})$ denotes the collection of positive semidefinite real symmetric matrices associated with a given graph $G$. Then $M_+(G)$ is the maximum nullity among all matrices in $S_+(G,\mathbb{R})$. It has been conjectured that $\tau(G)\leq M_+(G)$. The conjecture is shown to be true for graph classes considered in this work.

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Asai, Sota. "Semibricks." International Mathematics Research Notices 2020, no. 16 (July 5, 2018): 4993–5054. http://dx.doi.org/10.1093/imrn/rny150.

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Abstract In representation theory of finite-dimensional algebras, (semi)bricks are a generalization of (semi)simple modules, and they have long been studied. The aim of this paper is to study semibricks from the point of view of $\tau $-tilting theory. We construct canonical bijections between the set of support $\tau $-tilting modules, the set of semibricks satisfying a certain finiteness condition, and the set of 2-term simple-minded collections. In particular, we unify Koenig–Yang bijections and Ingalls–Thomas bijections generalized by Marks–Št’ovíček, which involve several important notions in the derived categories and the module categories. We also investigate connections between our results and two kinds of reduction theorems of $\tau $-rigid modules by Jasso and Eisele–Janssens–Raedschelders. Moreover, we study semibricks over Nakayama algebras and tilted algebras in detail as examples.

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Leuzy, Antoine, Tharick A. Pascoal, Olof Strandberg, Philip Insel, Ruben Smith, Niklas Mattsson-Carlgren, Andréa L. Benedet, et al. "A multicenter comparison of [18F]flortaucipir, [18F]RO948, and [18F]MK6240 tau PET tracers to detect a common target ROI for differential diagnosis." European Journal of Nuclear Medicine and Molecular Imaging 48, no. 7 (May 27, 2021): 2295–305. http://dx.doi.org/10.1007/s00259-021-05401-4.

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Abstract Purpose This study aims to determine whether comparable target regions of interest (ROIs) and cut-offs can be used across [18F]flortaucipir, [18F]RO948, and [18F]MK6240 tau positron emission tomography (PET) tracers for differential diagnosis of Alzheimer’s disease (AD) dementia vs either cognitively unimpaired (CU) individuals or non-AD neurodegenerative diseases. Methods A total of 1755 participants underwent tau PET using either [18F]flortaucipir (n = 975), [18F]RO948 (n = 493), or [18F]MK6240 (n = 287). SUVR values were calculated across four theory-driven ROIs and several tracer-specific data-driven (hierarchical clustering) regions of interest (ROIs). Diagnostic performance and cut-offs for ROIs were determined using receiver operating characteristic analyses and the Youden index, respectively. Results Comparable diagnostic performance (area under the receiver operating characteristic curve [AUC]) was observed between theory- and data-driven ROIs. The theory-defined temporal meta-ROI generally performed very well for all three tracers (AUCs: 0.926–0.996). An SUVR value of approximately 1.35 was a common threshold when using this ROI. Conclusion The temporal meta-ROI can be used for differential diagnosis of dementia patients with [18F]flortaucipir, [18F]RO948, and [18F]MK6240 tau PET with high accuracy, and that using very similar cut-offs of around 1.35 SUVR. This ROI/SUVR cut-off can also be applied across tracers to define tau positivity.

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Muvva, Charuvaka, Natarajan Arul Murugan, and Venkatesan Subramanian. "Assessment of Amyloid Forming Tendency of Peptide Sequences from Amyloid Beta and Tau Proteins Using Force-Field, Semi-Empirical, and Density Functional Theory Calculations." International Journal of Molecular Sciences 22, no. 6 (March 23, 2021): 3244. http://dx.doi.org/10.3390/ijms22063244.

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A wide variety of neurodegenerative diseases are characterized by the accumulation of protein aggregates in intraneuronal or extraneuronal brain regions. In Alzheimer’s disease (AD), the extracellular aggregates originate from amyloid-β proteins, while the intracellular aggregates are formed from microtubule-binding tau proteins. The amyloid forming peptide sequences in the amyloid-β peptides and tau proteins are responsible for aggregate formation. Experimental studies have until the date reported many of such amyloid forming peptide sequences in different proteins, however, there is still limited molecular level understanding about their tendency to form aggregates. In this study, we employed umbrella sampling simulations and subsequent electronic structure theory calculations in order to estimate the energy profiles for interconversion of the helix to β-sheet like secondary structures of sequences from amyloid-β protein (KLVFFA) and tau protein (QVEVKSEKLD and VQIVYKPVD). The study also included a poly-alanine sequence as a reference system. The calculated force-field based free energy profiles predicted a flat minimum for monomers of sequences from amyloid and tau proteins corresponding to an α-helix like secondary structure. For the parallel and anti-parallel dimer of KLVFFA, double well potentials were obtained with the minima corresponding to α-helix and β-sheet like secondary structures. A similar double well-like potential has been found for dimeric forms for the sequences from tau fibril. Complementary semi-empirical and density functional theory calculations displayed similar trends, validating the force-field based free energy profiles obtained for these systems.

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Hsieh, Jin-Jian. "Estimation of Kendall’s tau from censored data." Computational Statistics & Data Analysis 54, no. 6 (June 2010): 1613–21. http://dx.doi.org/10.1016/j.csda.2010.01.015.

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de Pagter, Ben, and Fyodor Sukochev. "COMMUTATOR ESTIMATES AND $\RR$-FLOWS IN NON-COMMUTATIVE OPERATOR SPACES." Proceedings of the Edinburgh Mathematical Society 50, no. 2 (May 17, 2007): 293–324. http://dx.doi.org/10.1017/s0013091505000957.

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AbstractThe principal results in this paper are concerned with the description of domains of infinitesimal generators of strongly continuous groups of isometries in non-commutative operator spaces $E(\mathcal{M},\tau)$, which are induced by $\mathbb{R}$-flows on $\mathcal{M}$. In particular, we are concerned with the description of operator functions which leave the domain of such generators invariant in all symmetric operator spaces, associated with a semi-finite von Neumann algebra $\mathcal{M}$ and a separable function space $E$ on $(0,\infty)$. Furthermore, we apply our results to the study of operator functions for which $[D,x]\in E(\mathcal{M},\tau)$ implies that $[D,f(x)]\in E(\mathcal{M},\tau)$, where $D$ is an unbounded self-adjoint operator. Our methods are partly based on the recently developed theory of double operator integrals in symmetric operator spaces and the theory of adjoint $C_{0}$-semigroups.

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Karimi Vanani, S., and A. Aminataei. "Tau approximate solution of fractional partial differential equations." Computers & Mathematics with Applications 62, no. 3 (August 2011): 1075–83. http://dx.doi.org/10.1016/j.camwa.2011.03.013.

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Bunchaft, M. E. Froes. "Some extensions of the Lanczos-Ortiz theory of canonical polynomials in the Tau Method." Mathematics of Computation 66, no. 218 (April 1, 1997): 609–22. http://dx.doi.org/10.1090/s0025-5718-97-00816-8.

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Journal articles on the topic 'Tau Theory'

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