Coherence x
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Coherence X 4.6 builds on top of Coherence X 4.5 by rebuilding the Coherence Extension and introducing significant performance enhancements. As a reminder of our DOWNLOAD DJVU. Coherent semiconductor optics. Read more. Coherent X-Ray Optics. Read more. Coherent x-ray optics. Read more. (Lasers and Golography: An Introduction to Coherent Optics, 2025) Read more. Coherent States in Quantum Physics. Read more. Recommend Documents. Coherent semiconductor optics
Coherence X 4.6 - TidBITS
Bandpass filter that selects only certain time series components. Thus, a continuous wavelet transform looks like the following:$${W}_{x}\left(u, s\right)=\underset{-\infty }{\overset{\infty }{\int }}x\left(t\right)\frac{1}{\sqrt{s}}{\uppsi }^{*}\left(\frac{t-u}{s}\right)dt$$ (1) where the variable ψ* is the complex conjugate of ψ.The wavelet coherence between time series X and Y is:$${R}_{xy}=\frac{S\left({W}_{xy}\left(s,t\right)\right)}{\sqrt{S\left({\left|{W}_{x}\left(s,t\right)\right|}^{2}\right) S\left({\left|{W}_{y}\left(s,t\right)\right|}^{2}\right)}}$$ (2) where S() is an appropriate smoothing function. \({W}_{z}\left(s,t\right)\) is the Morlet wavelet transform of time series x, and \({W}_{xy}\left(s,t\right)\) is the cross-wavelet transform between time series x and y. The Morlet wavelet is a complex exponential (the mother wavelet) scaled by a Gaussian (father wavelet):$${{\psi }_{0}\left(t\right)=\frac{1}{\sqrt[4]{\pi }}}e^{i{\omega }_{0}t}{e}^{-{t}^{2}/2}$$ (3) where \({\omega }_{0}\) is the angular frequency of the complex exponential, t is a translated time parameter, and i is the imaginary unit (Morlet et al. 1982).To arrive at conclusions regarding causal relationships, we must use the coherence phase difference:$${\phi }_{XY}=Arctan\frac{Im\left({W}_{XY}\left(s,t\right)\right)}{Re\left({W}_{XY}\left(s,t\right)\right)}$$ (4) which is the complex argument of the scalar value, \(\phi\), with Im being the imaginary part and Re the real part of a complex number.PWC is the extension of wavelet coherence in a multivariate specification. Similar to the Pearson-type partial autocorrelation, PWC eliminates the influence of all other variables on the coherence between \({X}_{i}\) and \({X}_{j}\). At the same time, it induces the possibility of controlling for nonlinearity. PWC can be computed using equation (5):$${PWC}_{{X}_{i}{X}_{j}}=-\frac{{R}_{ij}}{\sqrt{{R}_{ii}{R}_{jj}}}$$ (5) Where \({R}_{ij}\)is the corresponding cofactor in the determinant of the matrix of all the smoothed cross-wavelet coherences R=∥rij∥ (i.e., the cross-wavelet analog of the correlation matrix).Like the Pearson-type multiple correlation coefficient, multiple wavelet coherence (MWC) aims to quantify The experiment. The coherence order is dependent on the transitions possible within the spin system, and to the lowest order (non-interacting spin \( 1/2 \)) one may define the coherence order \( p = 0 \) in the direction of the external field and \( p = \pm 1 \) transverse to it. A single spin initially at thermal equilibrium with the external field, will after the application of a 90° RF-pulse change the coherence level to \( + 1 \) (rotating clockwise in the plane transverse to the external field), \( - 1 \) (rotating counterclockwise), or it may be unaffected by the RF-pulse (i.e. coherence order 0). The \( \pm 1 \) coherence levels are the two solutions for the transverse magnetization in the Bloch-Torrey equations. For the phase of the RF-pulses there are four possibilities; 0, \( \frac{\pi }{2} \), \( \pi \) and \( \frac{3\pi }{2} \). In the rotating coordinate system this implies that the RF-pulse is applied in the \( \pm x \) or \( \pm y \) direction.As an example, the coherence transfer pathway from the spin echo sequence is to be considered. A phase sequence is to be constructed, such that the only surviving signal is the one following the coherence order pathway \( p \to 0 \to - 1 \to + 1 \), shown in Fig. 1.19 as the solid line.Fig. 1.19Coherence order pathway for spin echo sequence (also equivalent to the read interval in the 13-interval PFGSTE sequence)Full size image For the first scan, let the phases of the RF-pulses equal 0. Then the resulting phases for the different pathways are written as follows$$ \varphi = - 1 \cdot 0 + 2 \cdot 0 = 0\quad and\quad \varphi^{\prime} = + 1 \cdot 0 + 0 \cdot 0 = 0 $$ (1.54) For the second scan let the phase of the 90° RF-pulse be shifted by \( \frac{\pi }{2} \) while keeping the phase of the 180° RF-pulse unchanged. Then the resulting phases for the different pathways are written as follows$$ \varphi = - 1 \cdot \frac{\pi }{2} + 2 \cdot 0 = - \frac{\pi }{2}\quad and\quad \varphi^{\prime} = + 1 \cdot \frac{\pi }{2} + 0 \cdot 0 = \frac{\pi }{2} $$ (1.55) If the receiver phase is set to 0 and \( - \frac{\pi }{2} \), and the two scans are added, the proposed phase sequence will result in aCoherence concurrence for X states
Native operating system.Whilst Apple's Bootcamp app creates a bootable copy of Windows. Parallels is different in that it runs Windows within an environment on OS X.If you need it, Windows can be run in its own window, in full screen mode, or in an integrated view called Coherence. Coherence allows Mac and Windows apps to be used side by side.Key features include:Ultimate flexibility.Retina display support.Connect devices.One-click performance tuning.Office 365 integration.Save disc space.Travel mode.Works with Boot Camp.Parallels can modify the standard Mac OS X interface, and adds a new window control button for any VMs. Along with the existing buttons that close and minimise windows, Parallels has a new button, which allows you to switch a VM into Coherence mode, thereby hiding the Windows desktop. This then allows any Windows apps to seamlessly sit right on the Mac OS desktop.A great feature of Parallels that is worth noting, is when you run Windows 10 in Coherence mode, the Windows Action Centre is able to be viewed as a panel, which slides in from the right-hand side of the screen, next to the Notification panel in Mac OS X.Overall, Parallels is not the only virtualization option that is available for Mac OS X users who need to run Windows apps. It is, however, more of a polished product than the other products. The close integration of both Windows OS and Mac OS provides users the best of both worlds. You can switch easily between apps, regardless of which operating system they were written for, especially using Coherence.Apple ConfiguratorStreamline Device Management with Apple ConfiguratorApple GarageBandApple GarageBand is a great music production studio for those who are looking for a software utility to help take their music production to the next level. The application helps users record their instruments and/or vocals. You can then use these to make audio tracks, mixing in other sources of music. Beginners will also find the ‘Learn to Play’ feature handy. It is available for piano as well as guitar.GarageBand has a number of built-in effects that can be used on the 24-bit audio interface. The Smart Controls, the Drummers, the Sound Library etc., are great for mixing your songs. Along with this, the Pedal board and Amp Designer is also a great pick. You can also save the GarageBand projects in your iCloud account, making sure they are always safe and accessible. Key features include:Record instrumentals and vocals.Mix. Coherence X 4.6 builds on top of Coherence X 4.5 by rebuilding the Coherence Extension and introducing significant performance enhancements. As a reminder of our DOWNLOAD DJVU. Coherent semiconductor optics. Read more. Coherent X-Ray Optics. Read more. Coherent x-ray optics. Read more. (Lasers and Golography: An Introduction to Coherent Optics, 2025) Read more. Coherent States in Quantum Physics. Read more. Recommend Documents. Coherent semiconductor opticsCoherent X-Ray - an overview
Signal where the only contribution (ideally) is from the desired coherence transfer pathway \( p \to 0 \to - 1 \to + 1 \).Finally, the concept of effective gradients is closely connected to the coherence transfer pathway. Karlicek et al. [1] showed using the Bloch-Torrey equations that the application of a 180° RF-pulse is equivalent to changing the polarity of the magnetic field gradient acting on the spin system. This can be seen using the concept of the density matrix: Consider the PFGSE in Fig. 1.3. The sequence yields an echo at \( t = 2\tau \) with two positive, apparently dephasing magnetic field gradients. How is it then possible to acquire an echo at \( t = 2\tau \)? The mechanism for echo formation can be understood by examining the action of the 180° RF pulse on the transverse magnetization. The effect of this pulse is to change the coherence order from +1 to −1 (and vice versa), and (1.48) shows the resulting density matrix at \( t = 2\tau \). When evaluating the resulting density matrix, it can be seen that the application of the 180° RF-pulse is equivalent to a change in the polarity of the effective magnetic field gradient . Thus, in the evaluation of the echo attenuation for more complicated PFGSTE sequences the 180° RF-pulse may be replaced by a change in sign of the magnetic field gradient following the RF-pulse.1.1.6 Mathematica Program for Solving the Echo Attenuation from the Ordinary Monopolar PFGSTE Sequence with Rectangular Shaped Gradients Mathematica 5.1 program for evaluation of attenuation from ordinary PFGSTE (Fig. 1.5); h[x = −G*x i[x] = −G*x+g*(x−a) j[x] = −G*x+g*(b−a) n[x] = g*(b−a)−G*c o[x] = G*(x−(2*c+d))+g*(b−a) p[x] = G*(x−(2*c+d))+g*(b−a)−g*(x−(c+d+a)) q[x] = G*(x−(2*c+d)) h1[x] = h[x]^2 i1[x] = i[x]^2 j1[x] = j[x]^2 n1[x] = n[x]^2 o1[x] = o[x]^2 p1[x] = p[x]^2 q1[x] = q[x]^2 h2[x] = Integrate[h1[x],] i2[x] = Integrate[i1[x],] j2[x] = Integrate[j1[x],] n2[x] = Integrate[n1[x],{x,c,c+d}] o2[x] = Integrate[o1[x],{x,c+d,c+d+a}] p2[x] = Integrate[p1[x],{x,c+d+a,c+d+b}] q2[x] = Integrate[q1[x],{x,c+d+b,2*c+d}] sum1[x] = h2[x]+i2[x]+j2[x] sum2[x] = n2[x]+o2[x]+p2[x]+q2[x] sum5[x] = sum1[x]+sum2[x] sum5[x] = Simplify[sum5[x]] X1[x] = Coefficient[sum5[x],g^2]*g^2 sum5[x] = sum5[x]−X1[x] sum5[x] = Simplify[sum5[x]] X3[x] = Coefficient[sum5[x],G^2]*G^2 sum5[x] = sum5[x]−X3[x] sum5[x] = Simplify[sum5[x]] X1[x] = Simplify[X1[x]] X3[x] = Simplify[X3[x]] X4[x] = Coefficient[sum5[x],G,1]*G Result[x] = X1[x]+X3[x]+X4[x] 1.1.7 Mathematica Programs for Solving the Echo Attenuation from the 13-Interval PFGSTE Sequence with Sinusoidal Gradients Mathematica 5.1 program for evaluation of attenuation from the 13-PFGSTE (Fig. 1.20) using f=g; Not move in the direction of the magnetic field gradient during the gradient pulse. The well known δ/3 correction to the diffusion time τ, the duration between the gradient pulses, is then neglected. Again, using the commutator relations and the high temperature approximation, ρ R can be written$$ \rho_{R} (2\tau ) = Constant - \frac{{\gamma \hbar H_{0} }}{(2I + 1)kT}(I_{x} \cos (\gamma \delta g(z(\tau ) - z_{0} )) + I_{y} \sin (\gamma \delta g(z(\tau ) - z_{0} )) $$ (1.49) Letting the x-component of the magnetization be the real part and the y-component the imaginary part, the expectation value for the magnetization of moving spins at t = 2τ is then written$$ \left\langle {M(2\tau )} \right\rangle = M_{0} \int {\int {p(z_{0} )P(z,z_{0} ,\tau ){\text{e}}^{{i\gamma \delta g(z(\tau ) - z_{0} )}} } } dzdz_{0} $$ (1.50) where$$ M_{0} = - \gamma^{2} \hbar^{2} H_{0} \frac{NI(I + 1)}{3kT} $$ (1.51) To solve the integrals in (1.50) knowledge about how the spins move must be used. That is, the solution of the differential equation called Fick’s law must be found. For a homogeneous system it is shown in Chap. 2 that \( p(z_{0} )P(z,z_{0} ,\tau ) \) is Gaussian and (1.50) then yields the second order moment with respect to the magnetic field gradient$$ \left\langle {M(2\tau )} \right\rangle = M_{0} {\text{e}}^{{ - \gamma^{2} \delta^{2} g^{2} D\tau }} $$ (1.52) D is the diffusion coefficient for the nuclear spins, and τ is the duration between the gradient pulses.1.1.5 Coherence Transfer Pathways and Effective GradientsWhen applying more than two RF-pulses in any pulse sequence, several echoes may be generated [18]. For example, in the ordinary pulsed field gradient stimulated echo experiment where three 90° RF-pulses are applied, five echoes will appear together with the FID’s following each RF-pulse [34]. As the stimulated echo is the echo required in this sequence, the remaining echoes should be suppressed. A way to do this is to employ the concept of coherence transfer pathways aiming at constructing a phase sequence where the only surviving signal is the stimulated echo [49]. The coherence transfer pathway is given by$$ \varphi = \sum\limits_{j = 1}^{n} {\Delta p_{j} \varphi_{j} } $$ (1.53) where \( \varphi \) is the accumulated phase change determined by the product of the change in coherence order \( \Delta p_{j} \) and the phase \( \varphi_{j} \) of the RF-pulse number j. n equals the number of RF-pulses applied inCoherence X Alternatives for Windows
Table of ContentsCohesion and coherenceWhat is the difference between coherence and cohesion?1. What Is Coherence?2. What is cohesion?Examples of Lexical and Grammatical cohesion1. Lexical Cohesion2. Grammatical CohesionStructuring Discourse1. Cohesive Devices and Discourse MarkersSummary1. Key Takeaways2. Table: Difference Between Coherence and CohesionRelated PagesWhat Is the Difference Between Coherence and Cohesion?Broadly speaking, coherence and cohesion refer to the way a text is organized so that it holds together. In a coherent text, ideas flow meaningfully and logically, often through the use of grammatical and lexical cohesive devices.The following sections define and provide examples of coherence and cohesion. We will also explore how productive skills involve structuring discourse so that speakers or writers can convey meaningful messages.What is the difference between coherence and cohesion?What is the Difference Between Coherence and Cohesion?To understand the difference between coherence and cohesion, let’s start by defining each term:1. What Is Coherence?Coherence is what makes a text semantically meaningful. In a coherent text, ideas are logically connected to produce meaning. It ensures that the ideas in a discourse are logical and consistent. Coherence is closely related to cohesion, as cohesive elements contribute to the overall coherence of a text.The linguistic features that make a text coherent are classified under the concept of cohesion.2. What is cohesion?According to LEXICO, cohesion literally means::The action or fact of forming a united whole, as in “The work at present lacks cohesion.”In physics, cohesion refers to:The sticking together of particles of the same substance.In applied linguistics, cohesion refers to the formal and semantic features of a text. In other words, it is the grammatical and lexical linking that holds a text together and gives it meaning. Cohesion is a crucial aspect of the broader concept of coherence.There are two types of cohesion: lexical and grammatical.Examples of Lexical and Grammatical cohesionMastering Coherent and Cohesive WritingHere are examples of lexical and grammatical cohesion:1. Lexical CohesionThis type of cohesion refers to the meaningful relationships between sentence elements. It involves the repetition of words or the use of synonyms, hyponyms, meronyms, or antonyms. Here are some examples:Repetition: “Birds are beautiful. Everybody likes birds.”Synonymy: “Paul saw a snakeDownload Coherence X for Mac - MacUpdate
100 Positive / 2 Ratings | Version: 1.0.0Go to shopDownload Coherence on PC With GameLoop EmulatorCoherence, is a popular steam game developed by Coherence. You can download Coherence and top steam games with GameLoop to play on PC. Click the 'Get' button then you could get the latest best deals at GameDeal.Get Coherence steam gameCoherence, is a popular steam game developed by Coherence. You can download Coherence and top steam games with GameLoop to play on PC. Click the 'Get' button then you could get the latest best deals at GameDeal.Coherence FeaturesSteam VideoThis content is only available in an online streaming format. More information about streaming videos can be found in the Streaming Videos on Steam FAQ.About the VideoOn the night of an astronomical anomaly, eight friends at a dinner party experience a troubling chain of reality bending events. Part cerebral sci-fi and part relationship drama, COHERENCE is a tightly focused, intimately shot film that quickly ratchets up with tension and mysteryShow MoreDownload Coherence on PC With GameLoop EmulatorGet Coherence steam gameCoherence, is a popular steam game developed by Coherence. You can download Coherence and top steam games with GameLoop to play on PC. Click the 'Get' button then you could get the latest best deals at GameDeal.Coherence FeaturesSteam VideoThis content is only available in an online streaming format. More information about streaming videos can be found in the Streaming Videos on Steam FAQ.About the VideoOn the night of an astronomical anomaly, eight friends at a dinner party experience a troubling chain of reality bending events. Part cerebral sci-fi and part relationship drama, COHERENCE is a tightly focused, intimately shot film that quickly ratchets up with tension and mysteryShow MorePreviewInformationDeveloperLatest Version1.0.0Last Updated2016-03-02CategorySteam-gameShow MoreFAQsPC Games Cheaper On Gamedeal | Find The Best Deals of Games Here!Finding the right place to get the best game deals can prove to be quite a hassle when comparing game prices on multiple sites. However, you can skip through all the trouble by letting Gamedeal handle the price comparisons and grab only the best deal prices for you!We compare game prices on all the trusted storefronts and list game deals starting with the lowest price possible at the moment. Looking for something more specific? Search it on Gamedeal and find all the best deals and cd keys discount codes to make the most out of your bucks. Not sure what you looking for? Browse through our massive library of games from different genres to find epic deals for your favorite games from the biggest retailers in the market. Can’t afford the game you are looking for? Make sure to wishlist it and stay up-to-date with all the price changes in the future.Say Bye to Hefty Game. Coherence X 4.6 builds on top of Coherence X 4.5 by rebuilding the Coherence Extension and introducing significant performance enhancements. As a reminder of our DOWNLOAD DJVU. Coherent semiconductor optics. Read more. Coherent X-Ray Optics. Read more. Coherent x-ray optics. Read more. (Lasers and Golography: An Introduction to Coherent Optics, 2025) Read more. Coherent States in Quantum Physics. Read more. Recommend Documents. Coherent semiconductor opticsCoherence with OS X (Server) guests
Introduction # Released 2018-06-02 ·Daniel Kermany, Kang Zhang, Michael GoldbaumThe Large Dataset of Labeled Optical Coherence Tomography (OCT) and Chest X-Ray Images encountered challenges related to reliability and interpretability in implementing clinical-decision support algorithms for medical imaging. They embarked on developing a diagnostic tool utilizing a deep-learning framework specifically designed for screening patients with common treatable blinding retinal diseases. The final OCT dataset contains 109,309 images.The full dataset consists of the following parts:ZhangLabData: OCT (current)ZhangLabData: Chest X-Ray (available on DatasetNinja)Spectral-Domain OCT ImagingThe primary application was in the diagnosis of retinal OCT images. Spectral-domain OCT captures high-resolution optical cross sections of the retina, assembling them into three-dimensional-volume images. It has become a widely performed medical imaging procedure, particularly in diagnosing age-related macular degeneration (DRUSEN, choroidal neovascularization CNV) and diabetic macular edema (DME).OCT imaging has become a standard of care in guiding the diagnosis and treatment of leading causes of blindness, including AMD and diabetic macular edema. The prevalence of these diseases is significant, with millions affected, and the utilization of anti-vascular endothelial growth factor (anti-VEGF) medications has revolutionized treatment.Dataset Details and Training OutcomeThe authors obtained 207,130 OCT images initially, with 108,312 images passing quality review for training the AI system. Testing involved 1,000 images from 633 patients. After 100 epochs, training was halted due to the absence of further improvement in both accuracy and cross-entropy loss.An independent test set of 1,000 images was used to compare the AI network’s referral decisions with those of human experts. The AI system’s performance was comparable to human experts in distinguishing patients needing urgent referral.The authors conducted an occlusion test on 491 images to identify areas contributing most to the neural network’s assignment of the predicted diagnosis. The testing successfully identified regions of interest, demonstrating high accuracy in recognizing clinically significant areas of pathology.ExpandHomepageResearch PaperSummary #Large Dataset of Labeled Optical Coherence Tomography (OCT) and Chest X-Ray Images is a dataset for a classification task. It is used in the medical industry.The dataset consists of 109309 images with 0 labeled objects. There are 2 splits in the dataset: train (108309 images) and test (1000 images). Alternatively, the dataset could be split into 4 classification splits: NORMAL (51390 images), CNV (37455 images), DME (11598 images), and DRUSEN (8866 images). The dataset was released in 2018 by the Zhang Lab, Univercity of San Diego, USA.Here are the visualized examples for the classes: Explore #ZhangLabData: OCT dataset has 109309 images. Click on one of the examples below or open "Explore" tool anytime you need to view dataset images with annotations. This tool has extended visualization capabilities like zoom, translation, objects table, custom filters and more. Hover the mouse over the images to hide or show annotations. 👀 Have a look at 109309 images View images along with annotations and tags, search and filter by various parametersLicense #Large Dataset of Labeled Optical Coherence Tomography (OCT) and Chest X-Ray Images is under CC BY 4.0 license.SourceCitation #If you make use of the ZhangLabData: OCT data, please cite the following reference:Kermany, Daniel;Comments
Bandpass filter that selects only certain time series components. Thus, a continuous wavelet transform looks like the following:$${W}_{x}\left(u, s\right)=\underset{-\infty }{\overset{\infty }{\int }}x\left(t\right)\frac{1}{\sqrt{s}}{\uppsi }^{*}\left(\frac{t-u}{s}\right)dt$$ (1) where the variable ψ* is the complex conjugate of ψ.The wavelet coherence between time series X and Y is:$${R}_{xy}=\frac{S\left({W}_{xy}\left(s,t\right)\right)}{\sqrt{S\left({\left|{W}_{x}\left(s,t\right)\right|}^{2}\right) S\left({\left|{W}_{y}\left(s,t\right)\right|}^{2}\right)}}$$ (2) where S() is an appropriate smoothing function. \({W}_{z}\left(s,t\right)\) is the Morlet wavelet transform of time series x, and \({W}_{xy}\left(s,t\right)\) is the cross-wavelet transform between time series x and y. The Morlet wavelet is a complex exponential (the mother wavelet) scaled by a Gaussian (father wavelet):$${{\psi }_{0}\left(t\right)=\frac{1}{\sqrt[4]{\pi }}}e^{i{\omega }_{0}t}{e}^{-{t}^{2}/2}$$ (3) where \({\omega }_{0}\) is the angular frequency of the complex exponential, t is a translated time parameter, and i is the imaginary unit (Morlet et al. 1982).To arrive at conclusions regarding causal relationships, we must use the coherence phase difference:$${\phi }_{XY}=Arctan\frac{Im\left({W}_{XY}\left(s,t\right)\right)}{Re\left({W}_{XY}\left(s,t\right)\right)}$$ (4) which is the complex argument of the scalar value, \(\phi\), with Im being the imaginary part and Re the real part of a complex number.PWC is the extension of wavelet coherence in a multivariate specification. Similar to the Pearson-type partial autocorrelation, PWC eliminates the influence of all other variables on the coherence between \({X}_{i}\) and \({X}_{j}\). At the same time, it induces the possibility of controlling for nonlinearity. PWC can be computed using equation (5):$${PWC}_{{X}_{i}{X}_{j}}=-\frac{{R}_{ij}}{\sqrt{{R}_{ii}{R}_{jj}}}$$ (5) Where \({R}_{ij}\)is the corresponding cofactor in the determinant of the matrix of all the smoothed cross-wavelet coherences R=∥rij∥ (i.e., the cross-wavelet analog of the correlation matrix).Like the Pearson-type multiple correlation coefficient, multiple wavelet coherence (MWC) aims to quantify
2025-03-28The experiment. The coherence order is dependent on the transitions possible within the spin system, and to the lowest order (non-interacting spin \( 1/2 \)) one may define the coherence order \( p = 0 \) in the direction of the external field and \( p = \pm 1 \) transverse to it. A single spin initially at thermal equilibrium with the external field, will after the application of a 90° RF-pulse change the coherence level to \( + 1 \) (rotating clockwise in the plane transverse to the external field), \( - 1 \) (rotating counterclockwise), or it may be unaffected by the RF-pulse (i.e. coherence order 0). The \( \pm 1 \) coherence levels are the two solutions for the transverse magnetization in the Bloch-Torrey equations. For the phase of the RF-pulses there are four possibilities; 0, \( \frac{\pi }{2} \), \( \pi \) and \( \frac{3\pi }{2} \). In the rotating coordinate system this implies that the RF-pulse is applied in the \( \pm x \) or \( \pm y \) direction.As an example, the coherence transfer pathway from the spin echo sequence is to be considered. A phase sequence is to be constructed, such that the only surviving signal is the one following the coherence order pathway \( p \to 0 \to - 1 \to + 1 \), shown in Fig. 1.19 as the solid line.Fig. 1.19Coherence order pathway for spin echo sequence (also equivalent to the read interval in the 13-interval PFGSTE sequence)Full size image For the first scan, let the phases of the RF-pulses equal 0. Then the resulting phases for the different pathways are written as follows$$ \varphi = - 1 \cdot 0 + 2 \cdot 0 = 0\quad and\quad \varphi^{\prime} = + 1 \cdot 0 + 0 \cdot 0 = 0 $$ (1.54) For the second scan let the phase of the 90° RF-pulse be shifted by \( \frac{\pi }{2} \) while keeping the phase of the 180° RF-pulse unchanged. Then the resulting phases for the different pathways are written as follows$$ \varphi = - 1 \cdot \frac{\pi }{2} + 2 \cdot 0 = - \frac{\pi }{2}\quad and\quad \varphi^{\prime} = + 1 \cdot \frac{\pi }{2} + 0 \cdot 0 = \frac{\pi }{2} $$ (1.55) If the receiver phase is set to 0 and \( - \frac{\pi }{2} \), and the two scans are added, the proposed phase sequence will result in a
2025-04-17Native operating system.Whilst Apple's Bootcamp app creates a bootable copy of Windows. Parallels is different in that it runs Windows within an environment on OS X.If you need it, Windows can be run in its own window, in full screen mode, or in an integrated view called Coherence. Coherence allows Mac and Windows apps to be used side by side.Key features include:Ultimate flexibility.Retina display support.Connect devices.One-click performance tuning.Office 365 integration.Save disc space.Travel mode.Works with Boot Camp.Parallels can modify the standard Mac OS X interface, and adds a new window control button for any VMs. Along with the existing buttons that close and minimise windows, Parallels has a new button, which allows you to switch a VM into Coherence mode, thereby hiding the Windows desktop. This then allows any Windows apps to seamlessly sit right on the Mac OS desktop.A great feature of Parallels that is worth noting, is when you run Windows 10 in Coherence mode, the Windows Action Centre is able to be viewed as a panel, which slides in from the right-hand side of the screen, next to the Notification panel in Mac OS X.Overall, Parallels is not the only virtualization option that is available for Mac OS X users who need to run Windows apps. It is, however, more of a polished product than the other products. The close integration of both Windows OS and Mac OS provides users the best of both worlds. You can switch easily between apps, regardless of which operating system they were written for, especially using Coherence.Apple ConfiguratorStreamline Device Management with Apple ConfiguratorApple GarageBandApple GarageBand is a great music production studio for those who are looking for a software utility to help take their music production to the next level. The application helps users record their instruments and/or vocals. You can then use these to make audio tracks, mixing in other sources of music. Beginners will also find the ‘Learn to Play’ feature handy. It is available for piano as well as guitar.GarageBand has a number of built-in effects that can be used on the 24-bit audio interface. The Smart Controls, the Drummers, the Sound Library etc., are great for mixing your songs. Along with this, the Pedal board and Amp Designer is also a great pick. You can also save the GarageBand projects in your iCloud account, making sure they are always safe and accessible. Key features include:Record instrumentals and vocals.Mix
2025-04-14Signal where the only contribution (ideally) is from the desired coherence transfer pathway \( p \to 0 \to - 1 \to + 1 \).Finally, the concept of effective gradients is closely connected to the coherence transfer pathway. Karlicek et al. [1] showed using the Bloch-Torrey equations that the application of a 180° RF-pulse is equivalent to changing the polarity of the magnetic field gradient acting on the spin system. This can be seen using the concept of the density matrix: Consider the PFGSE in Fig. 1.3. The sequence yields an echo at \( t = 2\tau \) with two positive, apparently dephasing magnetic field gradients. How is it then possible to acquire an echo at \( t = 2\tau \)? The mechanism for echo formation can be understood by examining the action of the 180° RF pulse on the transverse magnetization. The effect of this pulse is to change the coherence order from +1 to −1 (and vice versa), and (1.48) shows the resulting density matrix at \( t = 2\tau \). When evaluating the resulting density matrix, it can be seen that the application of the 180° RF-pulse is equivalent to a change in the polarity of the effective magnetic field gradient . Thus, in the evaluation of the echo attenuation for more complicated PFGSTE sequences the 180° RF-pulse may be replaced by a change in sign of the magnetic field gradient following the RF-pulse.1.1.6 Mathematica Program for Solving the Echo Attenuation from the Ordinary Monopolar PFGSTE Sequence with Rectangular Shaped Gradients Mathematica 5.1 program for evaluation of attenuation from ordinary PFGSTE (Fig. 1.5); h[x = −G*x i[x] = −G*x+g*(x−a) j[x] = −G*x+g*(b−a) n[x] = g*(b−a)−G*c o[x] = G*(x−(2*c+d))+g*(b−a) p[x] = G*(x−(2*c+d))+g*(b−a)−g*(x−(c+d+a)) q[x] = G*(x−(2*c+d)) h1[x] = h[x]^2 i1[x] = i[x]^2 j1[x] = j[x]^2 n1[x] = n[x]^2 o1[x] = o[x]^2 p1[x] = p[x]^2 q1[x] = q[x]^2 h2[x] = Integrate[h1[x],] i2[x] = Integrate[i1[x],] j2[x] = Integrate[j1[x],] n2[x] = Integrate[n1[x],{x,c,c+d}] o2[x] = Integrate[o1[x],{x,c+d,c+d+a}] p2[x] = Integrate[p1[x],{x,c+d+a,c+d+b}] q2[x] = Integrate[q1[x],{x,c+d+b,2*c+d}] sum1[x] = h2[x]+i2[x]+j2[x] sum2[x] = n2[x]+o2[x]+p2[x]+q2[x] sum5[x] = sum1[x]+sum2[x] sum5[x] = Simplify[sum5[x]] X1[x] = Coefficient[sum5[x],g^2]*g^2 sum5[x] = sum5[x]−X1[x] sum5[x] = Simplify[sum5[x]] X3[x] = Coefficient[sum5[x],G^2]*G^2 sum5[x] = sum5[x]−X3[x] sum5[x] = Simplify[sum5[x]] X1[x] = Simplify[X1[x]] X3[x] = Simplify[X3[x]] X4[x] = Coefficient[sum5[x],G,1]*G Result[x] = X1[x]+X3[x]+X4[x] 1.1.7 Mathematica Programs for Solving the Echo Attenuation from the 13-Interval PFGSTE Sequence with Sinusoidal Gradients Mathematica 5.1 program for evaluation of attenuation from the 13-PFGSTE (Fig. 1.20) using f=g;
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