Quadratic Model

14,000,000 Leading Edge Experts on the ideXlab platform

Scan Science and Technology

Contact Leading Edge Experts & Companies

Scan Science and Technology

Contact Leading Edge Experts & Companies

The Experts below are selected from a list of 124467 Experts worldwide ranked by ideXlab platform

Jinjun Xiong - One of the best experts on this subject based on the ideXlab platform.

  • non gaussian statistical timing analysis using second order polynomial fitting
    IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2009
    Co-Authors: Lerong Cheng, Jinjun Xiong
    Abstract:

    For nanometer manufacturing, process variation causes significant uncertainty for circuit performance verification. Statistical static timing analysis (SSTA) is thus developed to estimate timing distribution under process variation. Most existing SSTA techniques have difficulty in handling the non-Gaussian variation distribution and nonlinear dependence of delay on variation sources. To address this problem, we first propose a new method to approximate the max operation of two non-Gaussian random variables through second-order polynomial fitting. With such approximation, we then present new non-Gaussian SSTA algorithms for three delay Models: Quadratic Model, Quadratic Model without crossing terms (semiQuadratic Model), and linear Model. All the atomic operations (max and sum) of our algorithms are performed by closed-form formulas; hence, they scale well for large designs. Experimental results show that compared to the Monte Carlo simulation, our approach predicts the mean, standard deviation, skewness, and 95% percentile point within 1%, 1%, 6%, and 1% error, respectively.

  • non gaussian statistical timing analysis using second order polynomial fitting
    Asia and South Pacific Design Automation Conference, 2008
    Co-Authors: Lerong Cheng, Jinjun Xiong
    Abstract:

    In the nanometer manufacturing region, process variation causes significant uncertainty for circuit performance verification. Statistical static timing analysis (SSTA) is thus developed to estimate timing distribution under process variation. However, most of the existing SSTA techniques have difficulty in handling the non-Gaussian variation distribution and non-linear dependency of delay on variation sources. To solve such a problem, in this paper, we first propose a new method to approximate the max operation of two non- Gaussian random variables through second-order polynomial fitting. We then present new non-Gaussian SSTA algorithms under two types of variational delay Models: Quadratic Model and semi-Quadratic Model (i.e., Quadratic Model without crossing terms). All atomic operations (such as max and sum) of our algorithms are performed by closed-form formulas, hence they scale well for large designs. Experimental results show that compared to the Monte-Carlo simulation, our approach predicts the mean, standard deviation, and skewness within 1%, 1%, and 5% error, respectively. Our approach is more accurate and also 20times faster than the most recent method for non-Gaussian and nonlinear SSTA.

Shadi Kheirandish - One of the best experts on this subject based on the ideXlab platform.

  • chitosan extraction from lobster shells and its grafted with functionalized mwcnt for simultaneous removal of pb2 ions and eriochrome cyanine r dye after their complexation
    International Journal of Biological Macromolecules, 2017
    Co-Authors: Shadi Kheirandish, Mehrorang Ghaedi, Kheibar Dashtian, Fatemeh Heidari, Faezeh Pourebrahim, Shaobin Wang
    Abstract:

    Abstract Chitosan (CS) extracted from lobster shells (Persian Gulf, Iran), was grafted with amino functionalized multiwalled carbon nanotube (MWCNT). This novel material was characterized by FE-SEM and FT-IR and used for the ultrasound-assisted removal of Pb2+ ions and eriochrome cyanine R (ECR) dye. A central composite design (SCCD) under response surface methodology was used for studying the influences of important variables in removal process such as initial ECR and Pb2+ ions concentrations, adsorbent mass and sonication time on the removal efficiency. Linear, 2FI, Quadratic and cubic Models were performed and a Quadratic Model was selected for analysis of each response. ANOVA for the Quadratic Model shows the F-value parameter (820.44 and 537.12 for ECR and Pb2+ ions removal, respectively) and very low p-value (

  • simultaneous removing of pb2 ions and alizarin red s dye after their complexation by ultrasonic waves coupled adsorption process spectrophotometry detection and optimization study
    Ultrasonics Sonochemistry, 2017
    Co-Authors: Faezeh Pourebrahim, Kheibar Dashtian, Mehrorang Ghaedi, Fatemeh Heidari, Shadi Kheirandish
    Abstract:

    Abstract Funthenalized chitosan (CS) was composited with mesoprous SBA-15 and characterized via. different techniques such as FT-IR and FE-SEM. Subsequently, this new material was applied for simulations ultrasound-assisted adsorption of Pb 2+ ion and alizarin red S (ARS) dye after their complexation. Efficient conventional variables in adsorption process such as initial ARS and Pb 2+ concentration, adsorbent mass and sonication time were studied by small central composite design (CCD) and optimized with desirability function approach. Lack of fit testes and Model summary statistics for linear, 2FI, Quadratic and cubic Models were investigated and according to the insignificant lack of fit and maximizing the R-squared (R 2 ), adjusted R-squared and the predicted R-squared Quadratic Model was selected for other step analysis for removal of ARS dye, while, for Pb 2+ ions 2FI Model was selected as best Model. Quadratic Model ANOVA for ARS dye removal shows the F-value parameter (683.91), very low p-value Model ( 2+ ions removal shows the F-value parameter (282.51), very low p-value Model ( 2+ ions (83.54%) was shown at optimum of condition that were set as at: 25 and 25 mg L −1 , 0.028 g and 11.8 min for initial ARS and Pb 2+ ions concentration, adsorbent mass and sonication time, respectively. Finally, it was found that the equilibrium and kinetic of adsorption process follow the Langmuir isotherm and pseudo-second-order kinetic Model, respectively. From the Langmuir isotherm, maximum monolayer capacity (q max ) was obtained 50.25 and 57.14 mg g −1 for ARS and Pb 2+ ions removal, respectively.

Seymour H Levitt - One of the best experts on this subject based on the ideXlab platform.

  • radiobiology of stereotactic body radiation therapy stereotactic radiosurgery and the linear Quadratic Model
    International Journal of Radiation Oncology Biology Physics, 2013
    Co-Authors: Chang W Song, Chinsoo L Cho, Jianling Yuan, Kathryn E Dusenbery, Robert J Griffin, Seymour H Levitt
    Abstract:

    Received Feb 26, 2013, and in revised form Mar 11, 2013. Accepted for publication Mar 12, 2013The validity of the linear-Quadratic (LQ) Model for calculatingisoeffect doses in radiation therapy has been intensivelydebated in recent issues of the International Journal of Radi-ation Oncology, Biology, Physics (1-3).TheLQModelissimple and convenient, and by far it has been the most usefulmeans for isodose calculation in treating tumors with conven-tional fractionated radiation therapy (2-4). The LQ Modelsolely depends on the expected incidence of direct interactionsof radiation with specific cellular targets (ie, DNA strands).Because the LQ survival curve continuously bends downwardwith increasing radiation dose, many assume that the LQcalculation will inherently overestimate cell death caused byhigh-dose-per-fraction radiation therapy. Interestingly, however,clinical results have shown that the LQ Model actually under-estimates tumor control by stereotactic body radiation therapy(SBRT) or stereotactic radiosurgery (SRS) (5), indicating thatmechanism(s) in addition to DNA strand breaks and/or chro-mosome aberrations may be involved in response of tumors toSBRT or SRS. Therefore, it has been hypothesized that SBRTor SRS may cause significant vascular damage in tumors,leading to indirect cell death (5, 6). We have recently reviewedprevious studies on the radiation-induced vascular damage intumors and pointed out the potentially important role of indi-rect/necrotic cell death due to the vascular damage in tumorcontrol with SBRT and SRS (7). We further discussed theradiobiological principles of SBRT and SRS in relation toradiation-induced vascular damage and resultant indirect celldeath (8). Interestingly, some 35 years ago we (C.W.S. andS.H.L.) realized that irradiation of rodent tumors with 10-20Gy in a single dose caused severe vascular injury, leading tonecrotic cell death in significant fractions of tumor cells 2 to 3days after the treatment (9, 10). Figure 1 summarizes theobservations we made on the effects of 10 Gy (1000 rads) ofx-rays in a single dose on the clonogenic surviving cells inWalker 256 rat tumors (10). The surviving cell fraction, asmeasured with an in vivoein vitro excision method, wasapproximately 2.6 10

David Djajaputra - One of the best experts on this subject based on the ideXlab platform.

  • on relating the generalized equivalent uniform dose formalism to the linear Quadratic Model
    Medical Physics, 2006
    Co-Authors: David Djajaputra
    Abstract:

    Two main approaches are commonly used in the literature for computing the equivalent uniform dose (EUD) in radiotherapy. The first approach is based on the cell-survival curve as defined in the linear-Quadratic Model. The second approach assumes that EUD can be computed as the generalized mean of the dose distribution with an appropriate fitting parameter. We have analyzed the connection between these two formalisms by deriving explicit formulas for the EUD which are applicable to normal distributions. From these formulas we have established an explicit connection between the two formalisms. We found that the EUD parameter has strong dependence on the parameters that characterize the distribution, namely the mean dose and the standard deviation around the mean. By computing the corresponding parameters for clinical dose distributions, which in general do not follow the normal distribution, we have shown that our results are also applicable to actual dose distributions. Our analysis suggests that caution should be used in using generalized EUD approach for reporting and analyzing dose distributions.

Shaobin Wang - One of the best experts on this subject based on the ideXlab platform.

  • chitosan extraction from lobster shells and its grafted with functionalized mwcnt for simultaneous removal of pb2 ions and eriochrome cyanine r dye after their complexation
    International Journal of Biological Macromolecules, 2017
    Co-Authors: Shadi Kheirandish, Mehrorang Ghaedi, Kheibar Dashtian, Fatemeh Heidari, Faezeh Pourebrahim, Shaobin Wang
    Abstract:

    Abstract Chitosan (CS) extracted from lobster shells (Persian Gulf, Iran), was grafted with amino functionalized multiwalled carbon nanotube (MWCNT). This novel material was characterized by FE-SEM and FT-IR and used for the ultrasound-assisted removal of Pb2+ ions and eriochrome cyanine R (ECR) dye. A central composite design (SCCD) under response surface methodology was used for studying the influences of important variables in removal process such as initial ECR and Pb2+ ions concentrations, adsorbent mass and sonication time on the removal efficiency. Linear, 2FI, Quadratic and cubic Models were performed and a Quadratic Model was selected for analysis of each response. ANOVA for the Quadratic Model shows the F-value parameter (820.44 and 537.12 for ECR and Pb2+ ions removal, respectively) and very low p-value (