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| | <br><br>The Prime Chef Duels competition is truly about to heat up, as Antonia Lofaso is returning to the Major Chef kitchen tonight. Do not worry it will not occupy too significantly space and it will be incredibly simple to use. A starter set of kitchen knives usually does not price that much. Persons replace their hand towels and sponges quite generally, but good quality kitchen knives that are constructed to last can do so for many years just before they develop into as well weak to use. You can save on your kitchen knives by getting a comprehensive set from the starting. Only use your kitchen knives for food and other meal preparation requirements.<br><br>Wrap the clean knives properly in old newspaper, location them in a box labeled "Sharp Kitchen Knives" and provide them to a thrift shop in your area. Use curbside bins only for aluminum metal like beer or soda magnets employed at waste processing plants do not detect aluminum so aluminum requires separate recycling procedures. There are numerous distinct "recipes" that are applied when creating knives. 1 of the most important utensils in a kitchen is a skilled-grade kitchen knife set.<br><br>Even so, these style markers appear to be blurring in favor of Asian knives: All the knives we tested are deemed Western-style, however when we asked the suppliers, it turned out that half of the models sported 15-degree (or narrower) blades, which includes our best three favorites. These final results suggested that the 420 alloy made blades that weren't as hard as these produced from the other two metals.<br><br>The set is developed to let any individual to opt for your fantastic set of knives by delivering a set Best Chef Knife Big Hands that only contains a wood storage block, sharpening steel and a come apart kitchen shear. There's the Wusthof Asian Edge used for the Asian style knives. Whichever Wusthof Classic knife set you decide on for your kitchen, rest assured that you have produced the proper selection and that is an superb location to get them. A greatest kitchen knives with life time guarantees.<br><br>These are maybe a tiny lighter than some kitchen knives but for me that is a bonus - they are [http://answers.Yahoo.com/search/search_result?p=considerably&submit-go=Search+Y!+Answers considerably] significantly less tiring to use when you are undertaking heavy chopping - I often struggle a bit with butternut squash for example, my hand tends to cramp but not with these. If you are only going to obtain one set of kitchen knives - this is the set to go for. Weight: You'll require to try many knives to locate your perfect knife weight. See beneath for a lot more facts on ceramic knives.<br><br>Most important is a chef's knife that's the 1 you genuinely want to concentrate on.” (See the Sweethome's best option in Chef Knives) After that, a serrated knife—but not a bread knife. While America's Test Kitchen doesn't advocate shopping for knife sets, their editors do have opinions on what to look for in a set. Likewise, a wood block can preserve your knives tidy just do not ding the knives' edges against the wood.<br><br>Use our purchasing advice to sharpen your knowledge of knives and then refer to our Ratings to obtain the best models for your price range. This manual knife sharpener is exclusively built for offering you hassles-no cost and painless practical experience to sharp knives in the quickest way doable. It has predefined angles which are specially placed to offer sharpness and honing to Asian, European, American, Serrated, Santoku and Pocket knives.<br><br>So Globals are good for rough use but need to have frequent sharpening. As a chef if you want to hold sharp knives then becoming superior at sharpening is ultra significant. It is worth investing in a Tormek or some all-natural volcanic whetstones (even most highly-priced synthetic whetstones are not as good as them) and a dmt for flattening the whetstone but never use the dmt directly on your valuable knife! Especially for a qualified chef who demands to use it for work each day.<br><br>Well, the safest way is to order your fancied type of knives...kitchen knives or military knives, whatever. When you beloved this information along with you wish to obtain more details concerning [http://www.thebestkitchenknivesreviews.com/best-chef-knives-reviews/ Professional Chef Knives Reviews] i implore you to check out our own web page. I was capable to expand my knoweledge of knives right after reading your Hub. The blades employed in ceramic knives are made creating use of a process identified as sintering. Diamonds are hardest substance known to man, so creating use of diamonds to sharpen ceramic knives tells us a lot about the good quality of the knife. |
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| In [[computer networks]], [[self-similarity]] is a feature of network data transfer dynamics. When modeling network data dynamics the traditional time series models, such as an [[autoregressive moving average model]] (ARMA(p, q)), are not appropriate. This is because these models only provide a finite number of parameters in the model and thus interaction in a finite time window, but the network data usually have a [[Long-range dependency|long-range dependent]] temporal structure. A self-similar process is one way of modeling network data dynamics with such a long range correlation. This article defines and describes network data transfer dynamics in the context of a self-similar process. Properties of the process are shown and methods are given for [[Conceptual graph|graphing]] and estimating parameters modeling the self-similarity of network data.
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| == Definition ==
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| Suppose <math>X</math> be a [[Stationary process#Weaker forms of stationarity|weakly stationary (2nd-order stationary) process]]
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| with mean <math>\mu</math>, variance <math>\sigma^2</math>, and [[autocorrelation]] function <math>\gamma(t)</math>.
| |
| Assume that the autocorrelation function <math>\gamma(t)</math> has the form
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| <math>\gamma(t)\rightarrow t^{-\beta}L(t)</math> as <math>t\to\infty</math>, where <math>0<\beta<1</math>
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| and <math>L(t)</math> is a [[slowly varying function]] at [[infinity]], that is <math>\lim_{t\to\infty}\frac{L(tx)}{L(t)}=1</math> for all <math>x>0</math>. | |
| For example, <math>L(t)=const</math> and <math>L(t)=\log (t)</math> are slowly varying functions.<br>
| |
| Let <math>X_k^{(m)}=\frac{1}{m^H}(X_{km-m+1}+\cdot\cdot\cdot+X_{km})</math>,
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| where <math>k=1,2,3,\ldots</math>, denote an aggregated point series over non-overlapping blocks of size <math>m</math>, for each <math>m</math> is a [[positive integer]].
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| === Exactly self-similar process ===
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| * <math>X</math> is called an exactly self-similar process if there exists a self-similar parameter <math>H</math> such that <math>X_k^{(m)}</math> has the same distribution as <math>X</math>. An example of exactly self-similar process with <math>H</math> is [[Fractional Brownian motion|Fractional Gaussian Noise]] (FGN) with <math>\frac{1}{2}<H<1</math>.
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| '''Definition:Fractional Gaussian Noise (FGN)''' {{-}}
| |
| <math>X(t)=B_H(t+1)-B_H(t),~\forall t\geq 1</math> is called the Fractional Gaussian Noise, where <math>B_H(\cdot)</math> is a [[Fractional Brownian motion]].<ref>W. E. Leland, W. Willinger, M. S. Taqqu, D. V. Wilson, "On the self-similar nature of Ethernet traffic",ACM SIGCOMM Computer Communication Review 25,202-213,1995.</ref>
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| | |
| === exactly second order self-similar process ===
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| | |
| * <math>X</math> is called an exactly second order self-similar process if there exists a self-similar parameter <math>H</math> such that <math>X_k^{(m)}</math> has the same variance and autocorrelation as <math>X</math>.
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| | |
| === asymptotic second order self-similar process ===
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| * <math>X</math> is called an [[asymptotic]] second order self-similar process with self-similar parameter <math>H</math> if <math>\gamma^{(m)}(t)\to \frac{1}{2}[(t+1)^{2H}-2t^{2H}+(t-1)^{2H}]</math> as <math>m\to\infty</math>, <math>~\forall t=1,2,3,\ldots</math>
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| == Some relative situations of Self-Similar Processes ==
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| === Long-Range-Dependence(LRD) ===
| |
| Suppose <math>X(t)</math> be a weakly stationary (2nd-order stationary) process with mean <math>\mu</math> and variance <math>\sigma^2</math>. The Autocorrelation Function (ACF) of lag <math>t</math> is given by <math>\gamma(t)={ \mathrm{cov}(X(h),X(h+t))\over \sigma^2} ={ E[(X(h)-\mu)(X(h+t)-\mu)]\over \sigma^2}</math>{{-}}
| |
| '''Definition:'''{{-}} | |
| A weakly stationary process is said to be "Long-Range-Dependence" if <math> \sum_{t=0}^\infty |\gamma(t)|=\infty</math>
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| A process which satisfies <math>\gamma (t) \rightarrow t^{-\beta}L(t)</math> as <math>t\to \infty</math> is said to have long-range dependence. The [[spectral density]] function of long-range dependence follows a [[power law]] near the origin. Equivalently to <math>\gamma (t) \rightarrow t^{-\beta}L(t)</math>, <math>X</math> has long-range dependence if the spectral density function of autocorrelation function, <math>f_t(w)=\sum_{t=0}^\infty \gamma(t)e^{iwt}</math>, has the form of <math>w^{-\gamma}L(w)</math> as <math>w\to 0</math> where <math>0<\gamma<1</math>, <math>L</math> is slowly varying at 0.
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| [[Long-range dependency|also see]]
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| === Slowly decaying variances ===
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| <math>X^{(m)}=\frac{1}{m}(X_1+\cdot\cdot\cdot+X_m)</math><br> | |
| When an autocorrelation function of a self-similar process satisfies <math>\gamma (t) \rightarrow t^{-\beta}L(t)</math> as <math>t\to \infty</math>, that means it also satisfies <math>Var(X^{(m)})\to am^{-\beta}</math> as <math>m\to \infty</math>, where <math>a</math> is a finite positive constant independent of m, and 0<β<1.
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| == Estimating the self-similarity parameter "H" ==
| |
| | |
| === R/S analysis ===
| |
| Assume that the underlying process <math>X</math> is Fractional Gaussian Noise. Consider the series <math>X_{(1)},\ldots,X_{(n)}</math>, and let <math>Y_{(n)}= \sum_{i=1}^n X_{(i)}</math>.<br>
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| The sample variance of <math>X_{(i)}</math> is <math>S^2(n)=\frac{1}{n}\sum_{i=1}^n X^2_{(i)}-(\frac{1}{n})^2Y^2_n</math>{{-}}
| |
| '''Definition:R/S statistic'''
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| | |
| <math>\frac{R}{S}(n)=\frac{1}{S(n)}
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| [\max_{0\leq t\leq n}(Y_t -\frac{t}{n}Y_n)-\min_{0\leq t\leq n}(Y_t -\frac{t}{n}Y_n)]</math><br>{{-}}
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| If <math>X_{(i)}</math> is FGN, then <math>E(\frac{R}{S}(n))\to C_H \times n^H</math><br>
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| Consider fitting a regression model :
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| <math>log\frac{R}{S}(n)=log(C_H)+Hlog(n)+\epsilon_n</math>, where
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| <math>\epsilon_n \thicksim N(0,\sigma^2)</math><br>
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| In particular for a time series of length <math>N</math> divide the time series data into <math>k</math> groups each of size <math>\frac{N}{k}</math>, compute <math>\frac{R}{S}(n)</math> for each group.<br>
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| Thus for each n we have <math>k</math> pairs of data (<math>log(n),log\frac{R}{S}(n)</math>).There are <math>k</math> points for each <math>n</math>, so we can fit a [[regression model]] to estimate <math>H</math> more accurately. If the solpe of the [[regression line]] is between 0.5~1, it is a self-similar process.
| |
| | |
| === Variance-time plot ===
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| Variance of the sample mean is given by <math>Var(\bar{X}_n)\to cn^{2H-2},~\forall c>0</math>.<br>
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| For estimating H, calculate [[sample means]] <math>\bar{X}_1,\bar{X}_2,\cdots,\bar{X}_{m_k}</math> for <math>m_k</math> sub-series of length <math>k</math> .<br>
| |
| Overall mean can be given by <math>\bar{X}(k)=\frac{1}{k} \sum_{i=1}^{m_k} \bar{X}_i(k)</math>, sample variance <math>S^2(k)=\frac{1}{m_k-1}\sum_{i=1}^{m_k} (\bar{X}_i(k)-\bar{X}(k))^2</math>.<br>
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| The variance-time plots are obtained by plotting <math>\log S^2(k)</math> against
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| <math>\log k</math> and we can fit a simple least square line through the resulting points in the plane ignoring the small values of k.
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| For large values of <math>k</math>, the points in the plot are expected to be scattered around a straight line with a negative slope <math>2H-2</math>.For short-range dependence or independence among the observations, the slope of the straight line is equal to -1.<br>
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| Self-similarity can be inferred from the values of the estimated slope which is asymptotically between –1 and 0, and an estimate for the degree of self-similarity is given by <math>\hat{H}=1+\frac{1}{2}(slope).</math>
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| | |
| === Periodogram-based analysis ===
| |
| | |
| Whittle's approximate maximum likelihood estimator ([[Maximum likelihood|MLE]]) is applied to solve the Hurst's parameter via the [[spectral density]] of <math>X</math>. It is not only a tool for visualizing the Hurst's parameter, but also a method to do some statistical inference about the parameters via the asymptotic properties of the MLE. In particular, <math>X</math> follows a [[Gaussian process]]. Let the spectral density of <math>X</math>,
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| <math>f_x(w;\theta)=\sigma_\epsilon^2 f_x(w;(1,\eta))</math>, where
| |
| <math>\theta=(\sigma_\epsilon^2,\eta)=(\sigma_\epsilon^2,H,\theta_3,\ldots,\theta_k),H=\frac{\gamma+1}{2}</math>, and <math>\theta_3,\ldots,\theta_k</math> construct a short-range time series autoregression (AR) model, that is <math>X_j=\sum_{i=1}^k \alpha_i X_{j-i}+\epsilon_j</math>,
| |
| with <math>Var(\epsilon_j)=\sigma_\epsilon^2</math>.
| |
| | |
| Thus, the Whittle's estimator <math>\hat{\eta}</math> of <math>\eta</math> minimizes
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| the function <math>Q(\eta)=\int_{-\pi}^{\pi} \frac{I(w)}{f(w;(1,\eta))}\, dw</math>
| |
| , where I(w) denotes the periodogram of X as <math>(2\pi n)^{-1}|\sum_{j=1}^n X_je^{iwj}|^2</math> and <math>\hat{\sigma}^2=\int_{-\pi}^{\pi} \frac{I(w)}{f(w;(1,\hat{\eta}))}\, dw</math>. These integrations can be assessed by Riemann sum.<br> | |
| {{-}}
| |
| Then <math>n^{1/2}(\hat{\theta}-\theta)</math> asymptotically follows a normal distribution if <math>X_j</math> can be expressed as a form of an infinite moving average model.{{-}}
| |
| {{-}}
| |
| To estimate <math>H</math>, first, one has to calculate this periodogram. Since
| |
| <math>I_n(w)</math> is an estimator of the spectral density, a series with long-range dependence should have a periodogram, which is proportional to <math>|\lambda|^{1-2H}</math> close to the origin. The periodogram plot is obtained by ploting
| |
| <math>\log(I_n(w))</math> against <math>\log(w)</math>.<br>
| |
| Then fitting a regression model of the <math>\log(I_n(w))</math> on the <math>\log(w)</math> should give a slope of <math>\hat{\beta}</math>. The slope of the fitted straight line is also the estimation of <math>1-2H</math>. Thus, the estimation <math>\hat{H}</math> is obtained.
| |
| | |
| Note:<br>
| |
| There are two common problems when we apply the periodogram method. First, if the data does not follow a Gaussian distribution, transformation of the data can solve this kind of problems. Second, the sample spectrum which deviates from the assumed spectral density is another one. An aggregation method is suggested to solve this problem. If <math>X</math> is a Gaussian process and the spectral density function of <math>X</math> satisfies <math>w^{-\gamma}L(w)</math> as <math>w\to \infty</math>, the function,
| |
| <math>m^{-H}L^{-\frac{1}{2}}(m)\sum_{i=(j-1)m+1}^mk (X_i-E(|X_i|)),~j=1,2,\ldots,[\tfrac{n}{m}]</math>, converges in distribution to FGN as <math>m\to \infty</math>.
| |
| | |
| == References ==
| |
| * P. Whittle, "Estimation and information in stationary time series", Art. Mat. 2, 423-434, 1953.
| |
| * K. PARK,W. WILLINGER, Self-Similar Network Traffic and Performance Evaluation, WILEY,2000.
| |
| * W. E. Leland, W. Willinger, M. S. Taqqu, D. V. Wilson, "On the self-similar nature of Ethernet traffic",ACM SIGCOMM Computer Communication Review 25,202-213,1995.
| |
| * W. Willinger, M. S. Taqqu, W. E. Leland, D. V. Wilson, "Self-Similarity in High-Speed Packet Traffic: Analysis and Modeling of Ethernet Traffic Measurements",Statistical Science 10,67-85,1995.
| |
| | |
| {{Reflist}}
| |
| | |
| {{DEFAULTSORT:Self-Similarity Of Network Data Analysis}}
| |
| [[Category:Computer network analysis]]
| |
The Prime Chef Duels competition is truly about to heat up, as Antonia Lofaso is returning to the Major Chef kitchen tonight. Do not worry it will not occupy too significantly space and it will be incredibly simple to use. A starter set of kitchen knives usually does not price that much. Persons replace their hand towels and sponges quite generally, but good quality kitchen knives that are constructed to last can do so for many years just before they develop into as well weak to use. You can save on your kitchen knives by getting a comprehensive set from the starting. Only use your kitchen knives for food and other meal preparation requirements.
Wrap the clean knives properly in old newspaper, location them in a box labeled "Sharp Kitchen Knives" and provide them to a thrift shop in your area. Use curbside bins only for aluminum metal like beer or soda magnets employed at waste processing plants do not detect aluminum so aluminum requires separate recycling procedures. There are numerous distinct "recipes" that are applied when creating knives. 1 of the most important utensils in a kitchen is a skilled-grade kitchen knife set.
Even so, these style markers appear to be blurring in favor of Asian knives: All the knives we tested are deemed Western-style, however when we asked the suppliers, it turned out that half of the models sported 15-degree (or narrower) blades, which includes our best three favorites. These final results suggested that the 420 alloy made blades that weren't as hard as these produced from the other two metals.
The set is developed to let any individual to opt for your fantastic set of knives by delivering a set Best Chef Knife Big Hands that only contains a wood storage block, sharpening steel and a come apart kitchen shear. There's the Wusthof Asian Edge used for the Asian style knives. Whichever Wusthof Classic knife set you decide on for your kitchen, rest assured that you have produced the proper selection and that is an superb location to get them. A greatest kitchen knives with life time guarantees.
These are maybe a tiny lighter than some kitchen knives but for me that is a bonus - they are considerably significantly less tiring to use when you are undertaking heavy chopping - I often struggle a bit with butternut squash for example, my hand tends to cramp but not with these. If you are only going to obtain one set of kitchen knives - this is the set to go for. Weight: You'll require to try many knives to locate your perfect knife weight. See beneath for a lot more facts on ceramic knives.
Most important is a chef's knife that's the 1 you genuinely want to concentrate on.” (See the Sweethome's best option in Chef Knives) After that, a serrated knife—but not a bread knife. While America's Test Kitchen doesn't advocate shopping for knife sets, their editors do have opinions on what to look for in a set. Likewise, a wood block can preserve your knives tidy just do not ding the knives' edges against the wood.
Use our purchasing advice to sharpen your knowledge of knives and then refer to our Ratings to obtain the best models for your price range. This manual knife sharpener is exclusively built for offering you hassles-no cost and painless practical experience to sharp knives in the quickest way doable. It has predefined angles which are specially placed to offer sharpness and honing to Asian, European, American, Serrated, Santoku and Pocket knives.
So Globals are good for rough use but need to have frequent sharpening. As a chef if you want to hold sharp knives then becoming superior at sharpening is ultra significant. It is worth investing in a Tormek or some all-natural volcanic whetstones (even most highly-priced synthetic whetstones are not as good as them) and a dmt for flattening the whetstone but never use the dmt directly on your valuable knife! Especially for a qualified chef who demands to use it for work each day.
Well, the safest way is to order your fancied type of knives...kitchen knives or military knives, whatever. When you beloved this information along with you wish to obtain more details concerning Professional Chef Knives Reviews i implore you to check out our own web page. I was capable to expand my knoweledge of knives right after reading your Hub. The blades employed in ceramic knives are made creating use of a process identified as sintering. Diamonds are hardest substance known to man, so creating use of diamonds to sharpen ceramic knives tells us a lot about the good quality of the knife.