Tau truncation in the pathogenesis of Alzheimer's disease:a narrative review

Alzheimer's disease is characterized by two major neuropathological hallmarks—the extracellularβ-amyloid plaques and intracellular neurofibrillary tangles consisting of aggregated and hyperphosphorylated Tau protein.Recent studies suggest that dysregulation of the microtubuleassociated protein Tau,especially specific proteolysis,could be a driving force for Alzheimer's disease neurodegeneration.Tau physiologically promotes the assembly and stabilization of microtubules,whereas specific truncated fragments are sufficient to induce abnormal hyperphosphorylation and aggregate into toxic oligomers,resulting in them gaining prion-like characteristics.In addition,Tau truncations cause extensive impairments to neural and glial cell functions and animal cognition and behavior in a fragment-dependent manner.This review summarizes over 60 proteolytic cleavage sites and their corresponding truncated fragments,investigates the role of specific truncations in physiological and pathological states of Alzheimer's disease,and summarizes the latest applications of strategies targeting Tau fragments in the diagnosis and treatment of Alzheimer's disease.

Empirical Bayes Absolute Error Loss Estimation for Parameter of One-Side Truncation Distribution Families

In this paper we propose an absolute error loss EB estimator for parameter of one-side truncation distribution families. Under some conditions we have proved that the convergence rates of its Bayes risk is o, where 0<λ,r≤1,Mn≤lnln n (for large n),Mn→∞ as n→∞.

Hybrid Model Testing Technique for Deep-Sea Platforms Based on Equivalent Water Depth Truncation

In this paper, an inner turret moored FPSO which works in the water of 320 m depth, is selected to study the socalled ＂passively-truncated ＋ numerical-simulation＂ type of hybrid model testing technique while the tnmcated water depth is 160 m and the model scale ）, = 80. During the investigation, the optimization design of the equivalent-depth truncated system is performed by using the similarity of the static characteristics between the truncated system and the full depth one as the objective function. According to the truncated system, the corresponding physical test model is made. By adopting the coupling time domain simulation method, the tnmcated system model test is numerically reconstructed to carefully verify the computer simulation software and to adjust the corresponding hydrodynamic parameters. Based on the above work, the numerical extrapolation to the full depth system is performed by using the verified computer software and the adjusted hydrodyrmmic parameters. The full depth system model test is then performed in the basin and the results are compared with those from the numerical extrapolation. At last, the implementation procedure and the key technique of the hybrid model testing of the deep-sea platforms are summarized and printed. Through the above investigations, some beneficial conclusions are presented.

Mooring Truncation Design of a Deepwater SPAR

To solve the dimensional limitations of physical models in tests, an equivalent water depth truncated design for a classical SPAR working in 913 m water was investigated. The water depth was reduced to 736m and then to 552m. As this was done, the mooting line lengths, EA value, and mass per meter were adjusted. Truncation rules and formulas for parameters and truncation factors were proposed. SPAR static characteristics were made to be consistent with those at full water depth. Then further time-domain coupled analysis was carried out for the SPAR when the mooting system experienced waves. The mooring lines were simulated by quasi-static method. Global responses and mooring line forces were found to agree well with test results for a prototype at that water depth. The truncation method proved to be robust and reliable.

Discussion on the influence of truncation of ground motion residual distribution on probabilistic seismic hazard assessment

Recent studies on assessment of a very low annual probability of exceeding （APE） ground motions, 10-4 or less, have highlighted the importance of the upper bound of ground motions when very low probability results are acquired. The truncation level adopted in probabilistic seismic hazard analysis （PSHA） should be determined by an aleatory uncertainty model （i.e., distribution model） of ground motions and the possible maximum and minimum ground motion values of a specific earthquake. However, at the present time, it is impossible to establish the upper bound model for ground motions based on the source characteristics and/or ground motion propagation. McGuire suggested a truncation level be fixed at a number of = 6, or the distribution of residuals be truncated in such a manner that site intensity cannot be greater than the epicenter intensity. This study aims to find a reasonable and feasible truncation level to be used in PSHA when the physical mechanism is not available to find the extreme ground motion. A mathematical analysis of the influence of the truncation level on PSHA, case studies of sites in different seismotectonic settings, and a distribution analysis of ground motion residuals are conducted in this study. It is concluded that = 4 is the minimum acceptable value for engineering applications for APEs within 0.002 to 10-4, and for low APEs, such as 10-5 and 10-6, the value of should be no less than 5 in most regions of China.

Truncation and aliasing errors for Whittaker-Kotelnikov-Shannon sampling expansion

Let B^pΩ, 1 ≤ p 〈 ∞, be the space of all bounded functions from Lp（R） which can be extended to entire functions of exponential type Ω. The uniform error bounds for truncated Whittaker-Kotelnikov-Shannon series based on local sampling are derived for functions f ∈ B^pΩ without decay assumption at infinity. Then the optimal bounds of the aliasing error and truncation error of Whittaker-Kotelnikov-Shannon expansion for non-bandlimited functions from Sobolev classes L/（Wp（R）） are determined up to a logarithmic factor.

Iterative Methods for Solving the Nonlinear Balance Equation with Optimal Truncation

Two types of existing iterative methods for solving the nonlinear balance equation(NBE)are revisited.In the first type,the NBE is rearranged into a linearized equation for a presumably small correction to the initial guess or the subsequent updated solution.In the second type,the NBE is rearranged into a quadratic form of the absolute vorticity with the positive root of this quadratic form used in the form of a Poisson equation to solve NBE iteratively.The two methods are rederived by expanding the solution asymptotically upon a small Rossby number,and a criterion for optimally truncating the asymptotic expansion is proposed to obtain the super-asymptotic approximation of the solution.For each rederived method,two iterative procedures are designed using the integral-form Poisson solver versus the over-relaxation scheme to solve the boundary value problem in each iteration.Upon testing with analytically formulated wavering jet flows on the synoptic,sub-synoptic and meso-αscales,the iterative procedure designed for the first method with the Poisson solver,named M1a,is found to be the most accurate and efficient.For the synoptic wavering jet flow in which the NBE is entirely elliptic,M1a is extremely accurate.For the sub-synoptic wavering jet flow in which the NBE is mostly elliptic,M1a is sufficiently accurate.For the meso-αwavering jet flow in which the NBE is partially hyperbolic so its boundary value problem becomes seriously ill-posed,M1a can effectively reduce the solution error for the cyclonically curved part of the wavering jet flow,but not for the anti-cyclonically curved part.

Convergence of Invariant Measures of Truncation Approximations to Markov Processes

Let Q be the Q-matrix of an irreducible, positive recurrent Markov process on a countable state space. We show that, under a number of conditions, the stationary distributions of the n × n north-west corner augmentations of Q converge in total variation to the stationary distribution of the process. Two conditions guaranteeing such convergence include exponential ergodicity and stochastic monotonicity of the process. The same also holds for processes dominated by a stochastically monotone Markov process. In addition, we shall show that finite perturbations of stochastically monotone processes may be viewed as being dominated by a stochastically monotone process, thus extending the scope of these results to a larger class of processes. Consequently, the augmentation method provides an attractive, intuitive method for approximating the stationary distributions of a large class of Markov processes on countably infinite state spaces from a finite amount of known information.

Air-combat behavior data mining based on truncation method

This paper considers the problem of applying data mining techniques to aeronautical field.The truncation method,which is one of the techniques in the aeronautical data mining,can be used to efficiently handle the air-combat behavior data.The technique of air-combat behavior data mining based on the truncation method is proposed to discover the air-combat rules or patterns.The simulation platform of the air-combat behavior data mining that supports two fighters is implemented.The simulation experimental results show that the proposed air-combat behavior data mining technique based on the truncation method is feasible whether in efficiency or in effectiveness.

Preliminary analysis of mode truncation of single-layered reticulated domes under earthquakes

In anti-seismic calculation, the mode truncation is a significant problem to engineers if the mode-superposition response spectrum method is used, which has not been completely solved yet in some large and complex structures such as reticulated domes. In this case, some useful advices, concentrating on the problem above, are expected through a careful and comprehensive investigation of this paper. During the investigation, the authors first point out shortcomings of former researches. Then frequency-spectrum characteristics of single-layered reticulated domes were studied from the perspective of structural responses. During this process, some important results such as the existence of the main resonant section, and the fact that the relative sensitivity of these domes under horizontal and vertical impulse varies with the different R/S ratios were achieved. Furthermore, based on the study of frequency-spectrum characteristics, as well as that of earthquake input, reasonable numbers of mode truncation in single layered reticulated domes with different R/S ratio were presented. Results of case studies prove the mode truncation number proposed is valid.

ON TRUNCATION ERROR BOUND FOR MULTIDIMENSIONAL SAMPLING EXPANSION LAPLACE TRANSFORM

The truncation error associated with a given sampling representation is defined as the difference between the signal and on approximating sumutilizing a finite number of terms. In this paper we give uniform bound for truncation error of bandlimited functions in the n dimensional Lebesgue space Lp(Rn) associated with multidimensional Shannon sampling representation.

Controllable precision of the projective truncation approximation for Green's functions

Recently, we developed the projective truncation approximation for the equation of motion of two-time Green's functions(Fan et al., Phys. Rev. B 97, 165140(2018)). In that approximation, the precision of results depends on the selection of operator basis. Here, for three successively larger operator bases, we calculate the local static averages and the impurity density of states of the single-band Anderson impurity model. The results converge systematically towards those of numerical renormalization group as the basis size is enlarged. We also propose a quantitative gauge of the truncation error within this method and demonstrate its usefulness using the Hubbard-I basis. We thus confirm that the projective truncation approximation is a method of controllable precision for quantum many-body systems.

DDFS spurious signals due to amplitude quantization in absence of phase-accumulator truncation

Spurious signals in direct digital frequency synthesizers （DDFSs） are partly caused by amplitude quantization and phase truncation, which affect their application to many wireless telecommunication systems. These signals are deterministic and periodic in the time domain, so they appear as line spectra in the frequency domain. Two types of spurious signals due to amplitude quantization are exactly formulated and compared in the time and frequency domains respectively. Then the frequency spectra and power levels of the spurious signals due to amplitude quantization in the absence of phase-accumulator truncation are emphatically analyzed, and the effects of the DDFS parameter variations on the spurious signals are thoroughly studied by computer simulation. And several important conclusions are derived which can provide theoretical support for parameter choice and spurious performance evaluation in the application of DDFSs.

An Optimal Spatial Finite-Difference Operator which ReducesTruncation Error to a Minimum

Highly accurate spatial discretization is essentially required to perform numerical climate and weather prediction. The difference between the differential and the finite-difference operator is however a primitive error source in the numerics. This paper presents an optimization of centered finite-difference operator based on the principle of constrained cost function, which can reduce the truncation error to minimum. In the optimization point of view, such optimal operator is in fact an attempt to minimize spatial truncation er-rors in atmospheric modeling, in a simple way and indeed a quite innovative way to implement Variational Continuous Assimilation (VCA) technique. Furthermore, the optimizing difference operator is consciously designed to be meshing-independent, so that it can be used for most Arakawa-mesh configurations, such as un-staggered (Arakawa-A) or com-monly staggered (Arakawa-B, Arakawa-C, Arakawa-D) mesh. But for the calibration purpose, the pro-posed operator is implemented on an un-staggered mesh in which the truncation oscillation is mostly ex-cited, and it thus makes a severe and indeed a benchmark test for the proposed optimal scheme. Both theo-retical investigation and practical modeling indicate that the aforementioned numerical noise can be significantly eliminated.

Novel analysis method for the spurious spectrum of direct digitalfrequency synthesizer in the presence of phase truncation

Based on the analysis of the spurious introduced by phase accumulation truncation which was made by Nicholas, a new simplified algorithm for spurious spectrum in the presence of phase truncation is presented by using the mapping mathematics and number theoretic method, it is possible to precisely analyze the spurious location and the spurious amplitude introduced by phase truncation in practical applications by computer.

TRUNCATION ERROR REDUCTION METHOD FOR PLANAR CAVITY FLOW

A new so called truncation error reduction method (TERM) is developed in this work. This is an iterative process which uses a coarse grid (2 h ) to estimate the truncation error and then reduces the error on the original grid ( h ). The purpose is to use coarse grids to get more accurate results and to develop a new method which could do coarse grid direct numerical simulation (DNS) for more accurate and acceptable DNS solutions.

Improved modal truncation method for eigensensitivity analysis of asymmetric matrix with repeated eigenvalues

An improved modal truncation method with arbitrarily high order accuracy is developed for calculating the second- and third-order eigenvalue derivatives and the first- and second-order eigenvector derivatives of an asymmetric and non-defective matrix with repeated eigenvalues. If the different eigenvalues λ1, λ2,……, λs of the matrix satisfy ｜λ1｜ ≤... ≤｜λr｜ and ｜λs｜ 〈｜〈s＋1｜ （s ≤r-l）, then associated with any eigenvalue λi （i≤ s）, the errors of the eigenvalue and eigenvector derivatives obtained by the qth-order approximate method are proportional to ｜λi｜/λs＋1｜q＋l, where the approximate method only uses the eigenpairs corresponding to λ1, λ2,……,λs A numerical example shows the validity of the approximate method. The numerical example also shows that in order to get the approximate solutions with the same order accuracy, a higher order method should be used for higher order eigenvalue and eigenvector derivatives.

Truncation and Rounding-Based Scalable Approximate Multiplier Design for Computer Imaging Applications

Advanced technology used for arithmetic computing application,comprises greater number of approximatemultipliers and approximate adders.Truncation and Rounding-based Scalable ApproximateMultiplier(TRSAM)distinguish a variety of modes based on height(h)and truncation(t)as TRSAM(h,t)in the architecture.This TRSAM operation produces higher absolute error in Least Significant Bit(LSB)data shift unit.A new scalable approximate multiplier approach that uses truncation and rounding TRSAM(3,7)is proposed to increase themultiplier accuracy.With the help of foremost one bit architecture,the proposed scalable approximate multiplier approach reduces the partial products.The proposed approximate TRSAM multiplier architecture gives better results in terms of area,delay,and power.The accuracy of 95.2%and the energy utilization of 24.6 nJ is observed in the proposed multiplier design.The proposed approach shows 0.11%,0.23%,and 0.24%less Mean Absolute Relative Error(MARE)when compared with the existing approach for the input of 8-bit,16-bit,and 32-bit respectively.It also shows 0.13%,0.19%,and 0.2%less Variance of Absolute Relative Error(VARE)when compared with the existing approach for the input of 8-bit,16-bit,and 32-bit respectively.The proposed approach is implemented with Field-Programmable Gate Array(FPGA)and shows the delay of 3.640,6.481,12.505,22.572,and 36.893 ns for the input of 8-bit,16-bit,32-bit,64-bit,and 128-bit respectively.The proposed approach is applied in digital filters designwhich shows the Peak-Signal-to-NoiseRatio(PSNR)of 25.05 dB and Structural Similarity Index Measure(SSIM)of 0.98 with 393 pJ energy consumptions when used in image application.The proposed approach is simulated with Xilinx and MATLAB and implemented with FPGA.

Double sampling derivatives and truncation error estimates

This paper investigates double sampling series derivatives for bivariate functions defined on R2 that are in the Bernstein space. For this sampling series, we estimate some of the pointwise and uniform bounds when the function satisfies some decay conditions. The truncated series of this formula allow us to approximate any order of partial derivatives for function from Bernstein space using only a finite number of samples from the function itself. This sampling formula will be useful in the approximation theory and its applications, especially after having the truncation error well-established. Examples with tables and figures are given at the end of the paper to illustrate the advantages of this formula.