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If you’re using Gmail or G Suite for your email, I recommend MailKing. It’s a free Chrome browser extension available from the Chrome Web store, and it turns your existing inbox into an email marketing command center.Here’s how it works:Choose a customizable template from the library (or import your favorites from MailChimp)Upload your list from Microsoft Excel or a CSV file.Send up to 2,000 emails per day per Google send limits, or use the tool to schedule up to 10,000 emails over a few days.Track open rates and link click-throughs from a convenient dashboard, where you can download results.Follow up to any unopened or unreplied emails using 48-hour reminders.It’s also 100% free. There’s also a premium version that automatically removes the cloudHQ signature at the bottom of the email, and it includes email and phone support.Check out this brief video to see more:I hope this is helpful! Please feel free to contact me directly with any questions or if you need help!Cheers,-NaomiDisclosure: I have a vested interest in cloudHQ.

The exact frequencies we use are arbitrary: our scales are based around A 440 Hz, but they could just have easily have been based around A 442 Hz or 428 Hz. For a long time, continental European concert pitch was different from British concert pitch.In terms of why we have a twelve note chromatic scale and not, say, a 24 note, this has more to do with history and convenience.The basis of the octave is that when you halve or double the frequency, the note sounds as if it is ‘the same’, but at a higher or lower place. This is because, intrinsic in a moving column of air or a string (both of which are active in the human voice), the principal harmonic overtone is the octave. The next harmonic is the fifth, and further harmonics include the major third. As harmonics go up, they tend to get more and more out of tune.If you start with A, and take its second overtone, the 5th, you get E. From E you get to B, from B you get to F#, and thus you will go all the way round until you come to Gx (G double-sharp). This will give you all of the chromatic tones.However, doing it this way does not bring you back to A. Gx will be differently tuned. If you construct a piano or an organ on this basis, you will find the keys around where you started from are pretty much in tune, but as you go further, they will get further and further out of tune.To solve this, instrument makers created ‘tempered’ tuning, which is very slightly flat of ‘true’ fifths-based tuning, though not enough for most people to notice. Bach’s ‘Well-Tempered Clavier’ suite of pieces exploited the new tempered tuning, allowing him to write something in every single chromatic key.With tempered tuning, Gx is the same as A, and Ab is the same as G#.Tempered tuning is in use for the great majority of contemporary Western music, except for barbershop, which exploits the ‘ring and lock’ sound of ‘true’ tuning.Why 12 notes, and not 24?The Greeks came up with three scales. The diatonic was the ancestor of our eight note scale of the ‘natural’ notes. The chromatic was the ancestor of our 12 note scale of chromatic notes. The enharmonic (not linked to the modern use of the word) made use of what we would call quarter-tones. Arabic music and some others use quarter tones, giving, in some cases, a 24-note palette, although the enharmonic was still an eight note scale. Any kind of 24 note scale is harder to work with, and you move away quickly from notes which are harmonically related at all to the tonic note, which is why quarter-tone music is less popular.Why eight notes, and not 12?The original diatonic scale had several shades, and its exact composition only settled down gradually, but it essentially has no interval larger than a major 2nd. Clearly, if you only use major 2nds, you end up with fewer notes: a major 2nd scale is the whole-tone scale, which goes C-D-E-F#-G#-A#-C, but this means that you miss out the two most powerful harmonics—the 5th, which is the second harmonic of the tonic, and the 4th, of which the tonic is the second harmonic. Therefore, to get in a G and an F, but only to use notes that would be generated by the circle of 5th or circle of 4ths (which is the harmonic series we talked about at the beginning), you have to include a couple of half-steps. In terms of the notes you get to most quickly going forwards or backwards on a circle of 5ths or 4ths, you would have F-C-G-D-A-E-B as one potential arrangement, and Ab-Eb-Bb-F-C-G-D as another potential arrangement.In fact, all of these arrangements came to be used, which are known as the Modes. However, the Ionian and Aeolian modes became the most popular. The Ionian is identical to our major scale, and the Aeolian is identical to our natural minor scale, though, usually, you would use the harmonic minor, which sharpens the 7th to give a stronger leading note.Why eight notes instead of five?Much folk music uses not eight notes, but five, being the pentatonic scale. The pentatonic builds exclusively on the circle of fifths going forwards, so you have C-G-D-A-E, and it stops at the fifth of these, not going on to the B.During the middle-ages, much church music was based on quartal harmony (which is to say, the harmony of going backwards to the 4th, rather than forwards to the 5th). Secular folk music, based on quintal harmony, going forwards, established its own distinct flavour. The hymn Amazing Grace owes its popularity partly from distinctively breaking away from ‘spiritual’ sounding church music, which often involved the plagal cadence of IV-I instead of the more compelling V-I, and is written entirely in the pentatonic, which helps with its folky, authentic feel.It’s popularly believed that guitar solos are played in the pentatonic, and that many well-known songs are pentatonic, but, if you analyse them, you often find that they are based around a pentatonic feel, but occasionally include non-pentatonic notes. The famous solo on Stairway to Heaven, for example, makes powerful use of the non-pentatonic F (in the key of Am—Am pentatonic is A, C, D, E, G, analogous to C pentatonic C, D, E, G, A).▲ The circle of fifths. Each note (and key) going clockwise goes up a 5th, each note (and key) going anticlockwise goes down a 5th, which is the same as going up a 4th. For keys based on those notes, the key signature changes so that the notes always stay in the same relationship of tone-tone-semitone-tone-tone-tone-semitone for the major. The relative minor keys, inside the circle, have the same key signature as their majors, but they generally have a sharpened 7th written as an accidental (harmonic minor), or a sharpened 6th and 7th when ascending (melodic minor). To avoid writing out huge strings of sharps, flats and double-sharps and double-flats, we make an ‘enharmonic change’ (not the same meaning as the Greek scale) where we call C# Db, and Gb F#. However, this only works with tempered tuning.What about other non-diatonic and non-chromatic notes?The blue note in jazz and blues is a ‘bent’ note (achieved by bending the string on a guitar). Originally this would be a flattened fifth or sharpened 4th, but a bend around the 7th is also heard. This is an ‘out of tune’ note, but it is not a constant note. The character of the blue notes is that they are changing over time, so you might start with the 4th and bend up to a flattened 5th (in minor blues), or start with a minor 7th and bend up toward a major 7th. Although you can play blues to an extent on a keyboard that does not allow for bending, it never has quite the same feel as a saxophone or guitar bending the note.

I once read somewhere that piano is the easiest instrument to play in the beginning but the hardest to master in the end; and truth be told, I really agree with this. I started taking piano lessons at the age of 7 when my mom got sick of hearing me slamming random keys all the time. At first, I made quite a lot progress. I practiced around 15 minutes a day, and in less than a month or so I was already playing familiar melodies. However, as years went by, it started to get more and more challenging and 15 minutes a day wasn’t enough anymore. At that time, I had several friends playing at my level who quit, thinking it was too much work, but I didn't. In fact I started practicing more deligently, really dedicating myself. Long story short, I eventually completed grade 8 (Conservatory Canada) with honors, as well as the theory part. But all of this didn't happen overnight. My advice to you if you want to learn piano and be good at it (like actually good, not just “Chopsticks good”) is first and foremost, start taking piano lessons with a teacher and practice what you've learned EVERYDAY. I can't stress this enough; Piano is like a language, if you don't practice, you'll likely forget it just as quickly as you learned it. So that’s why it's so important to make time everyday for piano, even when you’re tired and you don't feel like it. Furthermore, when you get to the part where it gets more complicated, don't quit! Just hang in there, once you pass this crucial step, you’ll find that playing gets way more fun and effortless. Another tip: don't rely on your ear too much at the beginning, as it will interfere with your sight reading skills. You need a good foundation on which you can build upon.In conclusion, learning the piano can be a short or a long process, depending on how skilled you desire to be. All in all, the key (pun intended, ha!) when learning the piano is to be tenacious, persevering and to practice everyday!Good luck my friend!

These are Probabilistic Graphical Models. They are arguably our most complete and promising toolkit for inferring truth from complexity. They're born from a single set of principles that endow our machines to dominate chess, diagnose disease, translate language, decipher sound, recognize images and drive cars. 'Neural Networks' and 'Probabilistic Programming' are famous signatures of the Machine Learning community simply because they are effective tool sets for applying these devices.My aim here is to reveal the machinery behind this magic. I intend to show what they are, why we use them and how we actually use them. To do that, I’ve answered seven questions on this subject:What are Probabilistic Graphical Models and why are they useful?What is 'exact inference' in the context of Probabilistic Graphical Models?What is Variance Inference in the context of Probabilistic Graphical Models?How are Monte Carlo methods used to perform inference in Probabilistic Graphical Models?How are the parameters of a Bayesian Network learned?How are the parameters of a Markov Network learned?How is the graph structure of Probabilistic Graphical Models learned?I realize this is a ton to digest, especially for internet browsing, but allow me to sell you. This information is typically delivered with a worthwhile 1000+ page textbook to graduate computer scientists. We can 80/20 these ideas with just a few answers! It'll take discipline, but you'll gain a surprisingly good understanding of an absolutely foundational theory of Machine Learning.As a compromise, I've structured things such that you need only read a subset of these answers to get a full picture. Here's a map of that structure:For example, if you read [math]1 \rightarrow 2 \rightarrow 6 \rightarrow 7[/math], you'll get a complete taste. Also, I'll include refreshers at the beginning of each answer - this should make things more self contained. (If you read these answers in sequence, I'd skip those refreshers, as they will sound redundant.)If this sounds like a good deal to you, please follow those questions!Now, let's start walking.Notation GuideAs a first stop, we'll review notation, an admittedly boring place. But, it's my unconventional belief that most confusion is due to notation. So if we wish to survive, we'll need a few tips:An upper case non-bold letter indicates a single random variable ('RV'). The same letter lower cased with a super script indicates a specific value that RV may take. For example, [math]X=x^1[/math] is the event the RV [math]X[/math] took on the value [math]x^1[/math]. We call this event an assignment. The set of unique values an RV may take is [math]Val(X)[/math]. So we might have [math]Val(X)=\{x^0,x^1\}[/math] in this case.A bold upper case letter indicates a set of RVs (like [math]\mathbf{X}[/math]) and a bold lower case letter indicates a set of values they may take. For example, we may have [math]\mathbf{X}=\{A,B\}[/math] and [math]\mathbf{x}=\{a^3,b^1\}[/math]. Then the event [math]\mathbf{X}=\mathbf{x}[/math] is the event that [math]A=a^3[/math] happens and [math]B=b^1[/math] happens. Naturally, [math]Val(\mathbf{X})[/math] is the set of all possible unique joint assignments to the RVs in [math]\mathbf{X}[/math].If you see [math]\mathbf{x}[/math] (or [math]\mathbf{y}[/math] or [math]\mathbf{z}[/math] etc...) within a probability expression, like [math]P(\mathbf{x}|\cdots)[/math] or [math]P(\cdots|\mathbf{x})[/math], that's always an abbreviation of the event '[math]\mathbf{X}=\mathbf{x}[/math]'.Perhaps confusingly, we also abbreviate the event '[math]\mathbf{X}=\mathbf{x}[/math]' as '[math]\mathbf{X}[/math]', though this isn't a clean abbreviation. Omission of [math]\mathbf{x}[/math] means one of two things: either we mean this for any given [math]\mathbf{x}[/math] or for all possible [math]\mathbf{x}[/math]'s. As an example for the latter case, 'calculate [math]P(\mathbf{X})[/math]' would mean calculate the set of probabilities [math]P(\mathbf{X}=\mathbf{x})[/math] for all [math]\mathbf{x}\in Val(\mathbf{X})[/math].[math]\sum_\mathbf{X}f(\mathbf{X})[/math] is shorthand for [math]\sum_{\mathbf{x}\in Val(\mathbf{X})}f(\mathbf{X}=\mathbf{x})[/math]. This is similarly true for [math]\prod_\mathbf{X}(\cdot)[/math] and [math]\textrm{argmin}_\mathbf{X}(\cdot)[/math]. Look out for this one - it can sneak in there and change things considerably.You may see equations like [math]f(A,B,C)=g(\mathbf{X})h(\mathbf{Y})[/math]. They look strange - the RVs on the left aren't on the right! Well, in such cases, you also have something like [math]\mathbf{X} = \{A,B\}[/math] and [math]\mathbf{Y} = \{B,C\}[/math]. So the equation really is [math]f(A,B,C)=g(A,B)h(B,C)[/math].Probability distributions are references with a [math]P[/math], [math]\textrm{Q}[/math], [math]q[/math] or [math]\pi[/math]. Keep in mind that distributions are a special kind of function. Remember that!Everything is in reference to the discrete case. Unfortunately, the continuous case is not a simple generalization from the discrete case. The minor exception is in the visuals. The discrete case is less friendly to graphs, so I might use some continuous distributions. As it relates to the discussion, pretend these are in fact discrete distributions with a fine granularity.Almost all of this notation comes from the text Probabilistic Graphical Models - one of those 1000 page monsters. That book is extremely thorough, and should be considered stop number 8.Still here? You must have discipline! Onto the fun stuff - we ask:What generic problem do PGMs address?Our goal is to understand a complex system. We assume the complex system manifests as [math]n[/math] RVs, which we may write as [math]\mathcal{X} = \{X_1,X_2,\cdots,X_n\}[/math] [1][2]. We take it that 'a good understanding' means we can answer two types of questions accurately and efficiently for these RVs. If we say [math]\mathbf{Y}[/math] and [math]\mathbf{E}[/math] are two given subsets of [math]\mathcal{X}[/math], then those questions are:Probability Queries: Compute the probabilities [math]P(\mathbf{Y}|\mathbf{E}=\mathbf{e})[/math]. That is, what is the distribution of the RV's of [math]\mathbf{Y}[/math] given we have some observation of the RVs of [math]\mathbf{E}[/math]?MAP Queries: Determine [math]\textrm{argmax}_\mathbf{Y}P(\mathbf{Y}|\mathbf{E}=\mathbf{e})[/math]. That is, determine the most likely assignments of RVs given an assignment of other RVs.Before continuing, we should point a few things out:Since [math]\mathbf{Y}[/math] and [math]\mathbf{E}[/math] are any two subsets of [math]\mathcal{X}[/math], there is potentially a remaining set (call it [math]\mathbf{Z}[/math]) that's in [math]\mathcal{X}[/math]. In other words, [math]\mathbf{Z} = \mathcal{X} - \{\mathbf{Y},\mathbf{E}\}[/math]. This set appears left out of our questions, but is very much at play. We have to sum these RVs out, which can considerably complicate our calculations. For example, [math]P(\mathbf{y}|\mathbf{e})[/math] is actually [math]\sum_\mathbf{Z}P(\mathbf{y},\mathbf{Z}|\mathbf{e})[/math].We haven't mentioned any model yet. This set up is asking generically for probabilities and values that accurately track reality.To this end, we are assisted by the fact that we have some, at least partial, joint observations of [math]\mathcal{X}[/math]. However, some of our [math]n[/math] RVs may never be observed. These are called 'hidden' variables and they will complicate our lives later on.This set up is extremely general, and as such, this problem is extremely hard.The problem with joint distributions.Our starting point, perhaps surprisingly, will be to consider the joint distribution of our RVs [math]\mathcal{X}[/math], which we aren't given in real application (but we'll get there). We'll call that joint distribution [math]P[/math]. Conceptually, we can think of this as a table that lists out all possible joint assignments of [math]\mathcal{X}[/math] and their associated probabilities. So if [math]\mathcal{X}[/math] is made up of 10 RVs, each of which can take 1 of 100 values, this table has [math]100^{10}[/math] rows, each indicating a particular assignment of [math]\mathcal{X}[/math] and it's probability.The issue is, for a complex system, this table is too big. Even if we had the crystal ball luxury of having [math]P[/math], we can't handle it. So now what?The Conditional Independence statementWe need a compact representation of [math]P[/math] - something that gives us all the information of that table, but doesn’t involve writing it down. To this end, our saving grace is the Conditional Independence (CI) statement:Given subsets of RVs [math]\mathbf{X}[/math], [math]\mathbf{Y}[/math] and [math]\mathbf{Z}[/math] from [math]\mathcal{X}[/math], we say [math]\mathbf{X}[/math] is conditionally independent of [math]\mathbf{Y}[/math] given [math]\mathbf{Z}[/math] if[math]P(\mathbf{x},\mathbf{y}|\mathbf{z})=P(\mathbf{x}|\mathbf{z})P(\mathbf{y}|\mathbf{z})\tag*{}[/math]for all [math]\mathbf{x}\in Val(\mathbf{X})[/math], [math]\mathbf{y}\in Val(\mathbf{Y})[/math] and [math]\mathbf{z}\in Val(\mathbf{Z})[/math]. This is stated as '[math]P[/math] satisfies [math](\mathbf{X}\perp \mathbf{Y}|\mathbf{Z})[/math][3]'Now, if we had sufficient calculation abilities, we could calculate the left side and the right side for a distribution [math]P[/math]. If the equations hold for all values, then, by definition, the CI statement holds. Intuitively, though not obviously, this means that if you are given the assignment of [math]\mathbf{Z}[/math], then knowing the assignment of [math]\mathbf{X}[/math] will never help you guess [math]\mathbf{Y}[/math] (and vice versa). In other words, [math]\mathbf{X}[/math] provides no information for predicting [math]\mathbf{Y}[/math] beyond what [math]\mathbf{Z}[/math] has. Similarly, you can't predict [math]\mathbf{X}[/math] from [math]\mathbf{Y}[/math] any better.Knowing such statements turns out to be massively useful - they give us that compact representation we need. To see this, let's say [math](X_i \perp X_j)[/math] for all [math]i \in \{1,\cdots,10\}[/math] and [math]j \in \{1,\cdots,10\}[/math] where [math]i\neq j[/math]. This is to say, all RVs are independent of all other RVs. It turns out that with these statements, we only need to know the marginal probabilities of each value for each RV (which is a total of [math]10\cdot 100=1000[/math] values) and may reproduce all the probabilities of [math]P[/math]. So if we are considering the case where [math]\mathbf{X}=\mathcal{X}[/math] and would like to know the probability [math]P(\mathbf{X}=\mathbf{x})[/math], we simply return [math]\prod_{i=1}^{10}P(X_i=x_i)[/math], where [math]x_i[/math] is the [math]i[/math]-th element of [math]\mathbf{x}[/math].Though this isn't just a save on storage. This is a simplification on [math]P[/math] that will ease virtually any interaction with [math]P[/math], including summing over many assignments and finding the most likely assignment. So at this point, I'd like you to think that CI statements regarding [math]P[/math] are a requirement for wielding it.Now put a pin in this and let's switch gears.The Bayesian NetworkIt's time to introduce the first type of PGM - the Bayesian Network ('BN'). A BN refers to two things, both in relation to some [math]\mathcal{X}[/math]: a BN graph (called [math]\mathcal{G}[/math]) and an associated probability distribution [math]P_B[/math]. [math]\mathcal{G}[/math] is a set of nodes, one for each RV of [math]\mathcal{X}[/math], and a set of directed edges, such that there are no directed cycles. Said differently, it's a DAG. [math]P_B[/math] is a distribution with probabilities for assignments of [math]\mathcal{X}[/math] using a certain rule and Conditional Probability Tables ('CPTs' and 'CPDs'), which augment [math]\mathcal{G}[/math]. That rule, called the 'Chain Rule for BNs', for determining probabilities can be written:[math]P_B(X_1,\cdots,X_n)=\prod_{i=1}^n P_B(X_i|\textrm{Pa}_{X_i}^\mathcal{G})\tag*{}[/math]where [math]\textrm{Pa}_{X_i}^\mathcal{G}[/math] indicates the set of parent nodes/RVs of [math]X_i[/math] according to [math]\mathcal{G}[/math]. The CPDs tell us what the [math]P_B(X_i|\textrm{Pa}_{X_i}^\mathcal{G})[/math] probabilities are. That is, a CPD lists out the probabilities of all assignments of [math]X_i[/math] given any joint assignment of [math]\textrm{Pa}_{X_i}^\mathcal{G}[/math][4]. These CPDs are the parameters of our model. Their form is to list out actual conditional probabilities from [math]P_B[/math].To help, let's consider a well utilized example from that monstrous text: the 'Student Bayesian Network'. Here, we're concerned with a system of five RVs: a student's intelligence ([math]I[/math]), their class's difficulty ([math]D[/math]), their grade in that class ([math]G[/math]), their letter of recommendation ([math]L[/math]) and their SAT score ([math]S[/math]). So [math]\mathcal{X}=\{I,D,G,L,S\}[/math]. The BN graph along with the CPDs can be represented as:According to our rule, we have that any joint assignment of [math]\mathcal{X}[/math] factors as:So we would calculate a given assignment as:Not too bad, right? All this is to show is that a BN along with CPDs gives us a way to calculate probabilities for assignments of [math]\mathcal{X}[/math].Now we're ready for:The big idea.It's so big, it gets its own quote block:The BN graph, just those nodes and edges, implies a set of CI statements regarding it's accompanying [math]P_B[/math].It's a consequence of the Chain Rule for calculating probabilities. As a not-at-all-obvious result, a BN graph represents all [math]P[/math]'s that satisfy these CI statements and each of those [math]P[/math]'s could be attained with an appropriate choice of CPDs.For a BN, one form of those CI statements are:[math](X_i \perp\textrm{NonDescendants}_{X_i}|\textrm{Pa}_{X_i}^\mathcal{G})[/math] for [math]X_i \in \mathcal{X}[/math]So in the student example, we'd have this set:The third statement tells us that if you already know the student's intelligence and their class's difficulty, then knowing their SAT score won't help you guess their grade. This is because the SAT score is correlated with their grade only via their intelligence, and you already know that.These are referred to as the local semantics of the BN graph. To complicate matters, there are almost always many other true CI statements associated with a BN graph outside of the local semantics. To determine those by inspecting the graph, we use a scary 'D-separation' algorithm that I will shamelessly not explain.There is a reason this is so important. Since a BN graph is a way of representing CI statements and such statements are a requirement for handling a complex system's joint distribution (if you had it), then this is a good reason to use a BN to represent such systems. If we can accurately represent a system with a BN, we will be able to calculate our probability and MAP queries. Therefore, BNs will solve our problems when we're dealing with a certain class of [math]P[/math]'s. This choice, unsurprisingly, is called our representation.But there's an issue - I said a 'class' of [math]P[/math]'s. It's not hard to invent [math]P[/math]'s that come with CI statements a BN cannot represent.So now what? Well, we have other tools, the biggest of which is...The Markov NetworkA Markov Network ('MN') is likewise composed of a graph ([math]\mathcal{H}[/math]) and a probability distribution ([math]P_M[/math]). Though this time, the graph's edges are undirected and it may have cycles. The consequence is that a MN can represent a different set of CI statements. But, the lack of directionality means we can no longer use CPDs. Instead, that information is delivered with a factor, which is a function (function! remember it) that maps from an assignment of some subset of [math]\mathcal{X}[/math] to some nonnegative number. These factors are used to calculate probabilities with the 'Gibbs Rule'[5].To understand the Gibbs Rule, we must define a complete subgraph. A ‘subgraph’ is exactly what it sounds like - we make a subgraph by picking a set of nodes from [math]\mathcal{H}[/math] and including all edges from [math]\mathcal{H}[/math] that are between nodes from this set. A 'complete' graph is one which has every edge it can - each node has an edge to every other node.Now, let's say [math]\mathcal{H}[/math] breaks up into a set of [math]m[/math] complete subgraphs. By 'break up', I mean that the union of all nodes and edges across these subgraphs gives us all the nodes and edges from [math]\mathcal{H}[/math]. Let's write the RVs associated with the nodes of these subgraphs as [math]\{\mathbf{D}_i\}_{i=1}^m[/math]. Let's also say we have one factor (call it [math]\phi_i(\cdot)[/math]) for each of these. We refer to these factors together with [math]\Phi[/math], so [math]\Phi=\{\phi_i(\cdot)\}_{i=1}^m[/math]. For terminology's sake, we say that the 'scope' of the factor [math]\phi_i(\cdot)[/math] is [math]\mathbf{D}_i[/math] because [math]\phi_i(\cdot)[/math] takes an assignment of [math]\mathbf{D}_i[/math] as input.Finally, the Gibbs Rule says we calculate a probability as:where(It's hidden from this notation, but we're assuming it's clear how to match up the assignment of [math]X_1,\cdots,X_n[/math] with the assignments of the [math]\mathbf{D}_i[/math]'s.)Wait - the MN was introduced because it represents a different set of CI statement. So, which ones? It's considerably simpler in the case of a MN. A MN implies the CI statement [math](\mathbf{X} \perp \mathbf{Y}|\mathbf{Z})[/math] if all paths between [math]\mathbf{X}[/math] and [math]\mathbf{Y}[/math] go through [math]\mathbf{Z}[/math]. Easy!Now let's get specific. Below is an MN for the system [math]\mathcal{X}=\{A,B,C,D\}[/math] and the CI statements it represents:As you may notice, it's not hard to write those CI statements by viewing the graph.While we're here, let's write out the Gibbs Rule. By looking at this, we could identify our complete subgraphs as: [math]\{\{A,B\},\{B,C\},\{C,D\},\{D,A\}\}[/math]. With that, we calculate a probability as:whereTo repeat, each [math]\phi_i(\cdot,\cdot)[/math] is just a function that maps from it's given joint assignment to some nonnegative. So if [math]A[/math] and [math]B[/math] could only take on two values each, [math]\phi_1(\cdot,\cdot)[/math] would relate the four possible assignments to four nonnegative numbers. These functions serve as our parameters just as the CPDs did. Determining these functions brings us from a class of [math]P[/math]'s to a specific [math]P[/math] within it, defined with probabilities.But, ahem, uhh… there's an issue. In the BN case, I said:As a not-at-all-obvious result, a BN graph represents all [math]P[/math]'s that satisfy its CI statements and each of those [math]P[/math]'s could be attained with an appropriate choice of CPDs.The analogous is not true in the case of MNs. There may exist a [math]P[/math] that satisfies the CI statements of a MN graph, but we can't calculate it's probabilities with the Gibbs rule. Damn!Fortunately, these squirrely [math]P[/math]'s falls into a simple, though large, category: those which assign a zero probability to at least one assignment. This leads us to the Hammersley-Clifford theorem:If [math]P[/math] is a positive distribution ([math]P(\mathbf{X}=\mathbf{x})>0[/math] for all [math]\mathbf{x} \in Val(\mathcal{X})[/math]) which satisfies the CI statements of [math]\mathcal{H}[/math], then we may use the Gibbs Rule, along with a choice of complete subgraphs and associated factors, to yield the probabilities of [math]P[/math]. [6]And that about does it for the basics of MNs. They are just another way of representing another class of [math]P[/math]'s.How do BNs and MNs compare?At this point, we're not evolved enough for a full comparison, so let's do a partial one.First, it's clearly easier to determine CI statements in a MN - no fancy D-separation algorithm required. This follows from their simple symmetric undirected edges, which make them a natural candidate for certain problems. Broadly, MNs do better when we have decidedly associative observations - like pixels on a screen or concurrent sounds. BNs are better suited when we suspect the RVs attests to distinct components of some causal structure. Timestamps and an outside expectation of what's producing the data are helpful for that.Also, there's a certain overlap between a MN and a BN that'll unify our discussion in later answers. That is, the probabilities produced by the Chain Rule of any given BN can be exactly reproduced by the Gibbs Rule of a specially defined MN. To see this, look at the Chain Rule - [math]P_B(X_i|\textrm{Pa}_{X_i}^\mathcal{G})[/math] is just the conditional probability of some (unspecified) [math]X_i[/math] value given some assignment of the parent RVs. Well, to translate this to the Gibbs Rule, let [math]\mathbf{D}_i=\{X_i\}\cup\textrm{Pa}_{X_i}^\mathcal{G}[/math]. Next, define [math]\phi_i(\mathbf{D}_i)[/math] to produce the same output you'd get from looking up the BN conditional probability in the CPD (which is [math]P_B(X_i|\textrm{Pa}_{X_i}^\mathcal{G})[/math]). Awesome - now the Gibbs Rule is the same expression as the Chain Rule. This is useful because we can speak solely in terms of the Gibbs Rule and whatever we discover, we know will also work for the Chain Rule (and hence BNs). What this doesn't mean is that MNs are a substitute for BNs. If you were to look at this invented MN, it would likely imply way more edges in its graph and therefore, fewer CI statements and therefore, a wider and more unwieldy class of [math]P[/math]'s. In other words, BNs are still useful representations.But there's more to learn.Let's say we determined our graphical model along with its parameters. How do we actually answer those queries? Well, I have three suggestions:2. What is 'exact inference' in the context of Probabilistic Graphical Models?3. What is Variance Inference in the context of Probabilistic Graphical Models?4. How are Monte Carlo methods used to perform inference in Probabilistic Graphical Models?Footnotes[1] This is the one exception where we don't refer to a set of RVs with a bold uppercase letter.[2] This actually isn't the fully general problem specification. In complete generality, the set of RVs should be allowed to grow/shrink over time. That, however, is outside what I expect to accomplish in these posts.[3] There is a subtlety of language here. Often we'll say '[math]P[/math] satisfies these CI statements'. That means those CI statements are true for [math]P[/math], but others may be true as well. So it means 'these CI statements' are a subset of all [math]P[/math]'s true CI statements. This technicality matters, so keep an eye out for it.[4] If [math]X_i[/math] doesn't have any parents, then the CPD is the unconditional probability distribution of [math]X_i[/math].[5] This isn't a real name I'm aware of, but the form of that distribution makes it a Gibbs distribution and I'd like to maintain an analogy to BNs, which had the Chain Rule.[6] The implication goes the other way as well: If the probabilities of [math]P[/math] can be calculated with the Gibbs Rule, then it's a positive distribution which satisfies CI statements implied by a graph which has complete subgraphs of RVs that correspond to the RVs of each factor. This direction, however, doesn't fit into the story I'm telling, so it sits as a lonely footnote.Sources[1] Koller, Daphne; Friedman, Nir. Probabilistic Graphical Models: Principles and Techniques (Adaptive Computation and Machine Learning series). The MIT Press. Kindle Edition. This is the source of the notation, the graphics in this answers (with permission) and my appreciation for this subject.

There's plenty of discussion on here with several explanations-- just figured I'd drop by and "place my ballot" in the "It's Bb with a #11"-box. Also, I second the thoughts in Scott Sakurai's post. ESPECIALLY this part:""">I still say that you can only work with what's given and you're not allowed to change A# to Bb.This is where I must say "that's nice in theory, but in practice it doesn't work that way". In real-world, commercial situations, notation is generally balanced toward maximum legibility at the expense of theoretical correctness."""To the OP: I cannot recommend this *highly* enough-- do yourself a favor (if you haven't already) and MASTER the music theory subjects of Key((s)/ (Signatures)), Scale Degrees, Referring to chords inside of each key by roman numerals, and understand the purpose of the modes. Learning how to spell any type of chord is also *invaluable*. If I give you a triad and press ANY note on the piano, you should be able to tell me what chord tone that note is in relation to the triad (ex. If I play a C major triad and play an Ab note, you should tell me that it's a "b6" to the C chord. If I play a D minor triad and play an F#, you should be able to tell me that it's a "3" to the D minor chord).Good luck in your musical journey, and if you have any questions about resources for these topics, leave me a comment and I'd be glad to hook you up with some materials to learn from.[***UPDATE]I was asked to provide materials to study Music Theory in the comments section of my response. I spent a signNow amount of time on my response and would like it to be more accessible for others to read by copying it here, into my original response.DIY Music Theory Study - Content/Materials:Welcome! I really enjoy teaching music theory, so I'm super glad to be able to help you out! That being said, I know that sometimes I don't explain things quite clearly enough, so feel free to ask any questions you may have about anything I share below.As one last comment before we begin, I wanted to suggest the idea that the resources I'm about to share with you are to teach you certain subjects in music that I personally consider to be the *most important*. I consider these learning objectives to be a "practical" approach to music theory. Basically, completing the learning objectives that I share below will enable you to play any song of what I consider to be a "commercial genre" (pop, rock, metal, blues, jazz, Christian worship, etc.). If playing any song with relative ease and "by ear" from these genres is your goal, then my learning objectives suit you with IMMENSE accuracy. If your goal is to play Classical music where pretty much everything is written down on sheet music for you to play, these learning objectives will help you deconstruct what's happening in a piece and give you a "conceptual" approach to understanding what's going on. Here goes!Learning Objectives:Master: Keys (Key Signatures) via the Nashville Number System (NNS)Scale DegreesNNS ChordsMaster: Playing every major and minor triad in all inversionsMajor TriadsMinor TriadsBecause this is a post on the internet, I'm going to have to limit how much information I can give you all at once. Nobody wants to read 15 pages of explanation so I will try my best to be thorough but concise. If you need to ask (a) question(s) to have me clarify something that you don't understand, go for it.Learning Objective 1: Master the 12 Keys via NNSGoal 1: Scale DegreesTo master scale degrees, you essentially need to memorize this chart.(Note: Make it a long term goal to memorize the scale degrees of the keys: C, G, F, A, and D. If you never memorize another one, that's probably fine as these are pretty much the most common keys in "commercial genres". If I had to recommend learning one more, it would probably be Bb.)Goal 1 - Success Looks Like This:What is the 5th scale degree in the key of C? You quickly answer: "G". What is the 3rd scale degree in the key of G? You quickly answer: "B". What is the 6th scale degree in the key of D? "B". What is the 4th scale degree in the key of A? "D". Make flash cards or look for games online to help with memorizing these.I hate rote-memorization and can't stand having a teacher tell me to "memorize a bunch of information" when I don't know *WHY* I need to know it. I'm going to try my best to explain why throughout this post.Goal 1 - While Learning, Do This Too:Practice learning them while learning the *shapes* of each key on the piano as well. Below this paragraph will be a chart to show you the *shape* of each key. You can get the same effect on a *real* piano by pressing all of the notes in the key down at once and looking at the shape you're making by doing so.If you are learning the scale degrees key of G, Press different notes within that "shape" on the piano at a medium/slow tempo. Internalize the sound of each note in that key and identify those sounds as "this is the 3rd scale degree, this is the 5th scale degree, this is the 2nd scale degree, etc". You don't want to listen and try to associate any sound with the "letter name" of a note in each key [Key: G, note: B], you want to associate the sound of each note with the "scale degree" of a note in each key [Key: G, note: 3 (3rd scale degree)]. It may help to play a G in the bass somewhere with your left hand every 4 or 5 seconds while noodling around within the "shape" of the key of G major. The most important part is memorizing the sound of each scale degree, and the note name of each scale degree. Try to sing each scale degree for some time too to help internalize the sound of each scale degree.Goal 2: NNS ChordsTo master the NNS System of identifying chords, you pretty much need to memorize this new chart (it's very similar to the first one, it just introduces a "pattern" to the keys that you have already learned):Goal 2 - Success Looks Like This:What is the 4th chord in the key of C? You quickly answer: "F". What is the 5th chord in the key of G? You quickly answer "D". What is the 3rd chord in the key of A? "C# Minor". What is the 6th chord in the key of D? "B Minor".Learning Objective 1 - Success Looks Like This:What is a 1-5-6-4 chord progression in the key of C? You quickly respond: "C, G, Am, F". What is a 6-4-1-5 chord progression in the key of G? You quickly respond: "Em, C, G, D" What is a 1-4-6-5 progression in the key of D? "D, G, Bm, A". What is a 1-6-5-4 progression in the key of A? "A, F#m, E, D".This song is in the key of C and the progression is Am, F, C, G. What are the NNS numbers? You quickly respond:"6minor, 4, 1, 5". How would I play this in the key of D? You quickly respond: "Bm, G, D, A". What about the key of A? You quickly respond: "F#m, D, A, E". /// This song is in the key of G. The progression is G, C, Em, D. If I wanted to play this song in the key of C, what chords would I play? You quickly respond: "C, F, Am, G".This song uses the chords: A, D, and G. What key is this song in? "D". This song uses the chords C, G and F. What key is this song in? "C". This song uses the chords, C, G and D. What key is this song in? "G". This song uses F#m, E, A and D. What key is the song in? "A". This song uses Em, D, G and C. What key is the song in? "G".Learning Objective 2: Master the Maj/Min TriadsThe first Learning Objective teaches you which notes belong in each key as well as what each scale degree "sounds like". It also teaches you which chords belong in each key and which "scale degree they correspond to" as well as whether or not they are maj/min from the NNS. So basically, you now can memorize pretty much any pop song in existence in a flash. Example: Im Yours. Click that link and examine the chords (ignore the "guitar tab" written at the top-- that's for people who don't understand music). The chords are G, D, Em, C. You know that's 1-5-6m-4. You can play that song in any freaking key right this second ;) And if you can't, the only thing standing in your way is "how to play each chord type".Goal 1: Major TriadsYou pretty much have to sit at the piano and memorize these "shapes". Press all 3 notes down at once, and see how it looks. Play each note individually at random, etc. Next, play a major chord such as a C major in both hands in two neighboring octaves. Your hands should be spelling "C E G --- C E G". This is called the "root position" of the chord. Keep holding down those two triads because I'm going to demonstrate how the concept called "inversions" works. See that shape that the E-G-C Makes? That is the C major chord in the 1st inversion. See that shape that the G-C-E makes? That is the C major chord in the 2nd inversion. The identity of a C major triad is made up of the C, E and G notes in any order. Memorize the root, 1st inversion and 2nd inversion triad shapes for every note.Goal 1 - Success Looks Like This:Play a D major in the 1st inversion. You quickly play the F#, A, D shape.Play an A major in root position: You quickly play the A, C#, E shape.Play a G major in 2nd position: You quickly play the D, G, B shape.Play a C major in 2nd position: You quickly play the G, C, E shape.Goal 2: Minor TriadsTo learn these minor triads, you basically have to do the same thing as before. You can practice all the minor chords together, or you can do a major chord then the parallel minor chord (C major, C minor. G major, G minor etc).You can learn the major and minor chords together if you wish and at any point, you can practice playing simple chords to songs like "I'm Yours". You can practice your G Major, D, Major, E minor, and C Major triads by playing that song in the key of G. You could play the same song in the key of C to practice C, G, Am, F. You could also play that same song in the keys of D or A to practice different chords (D, A, Bm, G / A, E, F#m, D).Goal 2 - Success Looks Like This:Play a D minor in the 1st inversion. You quickly play the F, A, D shape.Play an A minor in root position: You quickly play the A, C, E shape.Play a G minor in 2nd position: You quickly play the D, G, Bb shape.Play a C minor in 2nd position: You quickly play the G, C, Eb shape.Learning Objective 2 - Success Looks like This:You can now learn any song really quickly from Learning Objective 1. You look at a song, you see that each section of a song uses a certain progression over and over. The success of Learning Objective 2 is that you now can fluently play all of the major and minor chords and switch between them to play the chords to pretty much any "commercial genre" song. Here are some examples of looking at a song and breaking down the chord progressions of each section of the song.[Ex.1] For a song like Im Yours by Jason Mraz, the key is G and WHOLE SONG uses the 1, 5, 6m, 4 progression.[Ex. 2] For a song like Love Yourself by Justin Beiber, the key is C. The Verse progression is [1-5-6m/2m-1-5]. The PreChorus progression is [6m-4-1/6m-4-1/6m-4-1-5/6m-4-5]. Then the Chorus progression is [1-5-6m-4/1-5-1][Ex. 3] For a song like, Someone Like You by Adele, the key is A. The Verse is [1-1-6m-4] (that Gbm is incorrectly "spelled". Gbm and F#m are the same chord, but there is no Gbm in the key of A, so you use the F#m chord, because that IS in the key of A). The Bridge is [5-6m-4]. The Chorus is [1-5-6m-4]. The part labled "Break" is [5-6m-4] again. Then the outtro is [1-5-6m-4] again.This concludes my "Practical Music Theory" lesson. Master this stuff, play and sing every song you've ever wanted. Join a band. Play any song in any key effortlessly because you understand the NNS and Scale Degrees. Memorize a song in like 5 minutes because practically every song is just some variation of [1-5-6m-4]. Is this song in the key of A but the singer thinks it's a little too high? Drop it down to G. You know how to do it! Because you know that the song doesn't go "A-F#m-D-E", it ACTUALLY goes "1-6m-4-5" which means that, in the key of A, it is "A-F#m-D-E". Because you know your keys and you know the song goes "1-6m-4-5", it's easy to think in the key of G and identify that the song goes: "G-Em-C-D" in the key of G.I hope I've help you and anybody else who wants to learn how to play music~Edit: Fixed each link so the images would display. I didn’t want them taking up so much space initially, but I think it helps the continuity of this post.

Submarine warfare is relatively unique in its specific requirements and conditions. Stealth is the key factor, but so are patience and the knowledge of who or what you are looking for can make a difference. Vessels of different classes and role each have a unique sound signature, and even vessels within a class can be identified by the minor variations in noise they produce in the water.The advantage of stealth would seem to go to the Type 212 in many regards, as it uses a diesel-fuel cell propulsion system. When the fuel cell is in use, it is very, very quiet as it requires very few moving parts to operate to generate movement, which is largely limited to slow revolutions of the screws (the propellers that make subs move).One of the Type 212s at sea.A quick aside about propulsion on a submarine and silence and why subs don’t dart about without good reason.The slower movement of the screws prevents them from cavitating, that is, making tiny air bubbles (cavities) in the vortex on the trailing edge of the propeller, which makes noise in the water. Hulls can also cavitate during rapid movement or course changes. These are all important to remember. Sound means you get detected on passive sonar. Detection means you’re dead, perhaps even before you’re aware of the fact that you’ve been detected. Passive sonars are extremely sensitive these days and submarine crews are trained to utilize sound discipline if they are running silent. My understanding is that submarines prowl in a predetermined area, monitoring surface vessels and keeping a close eye out for any other submarines that might also be operating in the area. They might move to their patrol area at high speed, but once there, they’ll go to silent running, use evasive maneuvers to shake any possible ‘tails’ they might have picked up, and then prowl about for the duration of their mission/tasking/what have you. Rapid movement might be undertaken if they’ve been alerted to something they want to have a closer look at, an imminent threat, etc.Okay, with some of that out of the way, I hope you, my dear reader(s) now have a basic grasp of some of the basic considerations for submarine warfare when it comes to stealth, so I can continue.A Type 212, U32, at dock. It’s a surprisingly small boat (about 57m long), but that doesn’t mean it should be underestimated.The Type 212 is probably a very, very quiet boat. Its designed to operate in a variety of conditions, including close to shore and has a pretty decent theoretical range and operational time, under optimal conditions, somewhere around 12 weeks at sea with snorkeling (required for using the diesel engine). Without snorkeling, it can remain underwater for about three weeks, according to Wikipedia. It carries a small but effective armament seems well suited to working the coastlines of Europe on patrol missions with little to no chance of detection from most vessels. The compact nature of the boat gives it the ability to move in areas a longer vessel could not, but it is not nearly as quick as the Seawolf class, moving at a stately 20knots as opposed to the sprightly 32 knots of the Seawolf.Ah, but as I said, submarines tend to move around quietly and slowly to minimize potential problems that faster movement might create. Well, yes. That is true, especially for a more traditional submarine design like the Type 212. For all its advances in design, it still runs on a traditional propeller based propulsion system and has to move slowly to prevent the aforementioned cavitating.The Seawolf class does not have this problem. Something with its design, and don’t ask me what (because I really don’t know, maybe something with the way its screws are designed), lets it have a high silent running speed, something like 20 knots. In other words, even if the Type 212 is moving as fast as it possibly can, submerged, the Seawolf could trail behind it, at the same speed, and not be easily detectable. At all. That is considering that the Seawolf uses a nuclear reactor, widely considered to be louder than most other modern propulsion systems. The Seawolf’s design apparently minimizes the noise produced by a signNow margin (again, don’t ask me how, I have no idea), giving it a massive step up on the Type 212 in terms of range and endurance, allowing it to operate practically anywhere it wants to go without concern for fuel, and apparently quieter than the legendary Los Angeles class by a big margin.The USS Connecticut (SSN 22) being moved into dock. The Seawolf Class is about twice as large (108m long) as the Type 212, but is it quieter? Maybe.A Seawolf can also operate in battle conditions far deeper in the ocean than the Type 212, with a test depth believed to be around 700 meters. If the US Navy’s test depth (1/3rd of operating depth) scaling is correct, this means its maximum depth is 1830m, which is rather impressive. The German Navy’s test depth rating is one half of its operating depth, leaving the Type 212 with a maximum of 1400m, though I have no idea what either submarine’s “Do Not Exceed” is, much less their Collapse depths are. My guess is that the Seawolf is probably still holding the edge here, with advanced sensors allowing it to more accurately detect a thermal layer (thermocline) in the ocean, helping it avoid detection. To quote an article I saw:“Submarines use the ocean's thermal layers to hide from surface ships and other submarines. The thermal layers in the operational area of any submarine is a key tactical consideration at all times for Sonar operations. Sound travels at different speeds based on water temperature, pressure and salinity.”The Seawolf and the Type 212 would both make extensive use of these, but the Seawolf probably make more effective use of it due to its greater depth capabilities and very advanced sensors. That’s not to say the Type 212 is a slouch, but it’s not at all unreasonable to expect that the Seawolf still has a signNow advantage in its sensor suite over the Germans and Italians, though it may not be a huge edge.Mk 48 torpedoes in a torpedo room.The armament these ships have are both very advanced, with the Type 212 using the DM2A4 (German) or Black Shark (Italian) heavy torpedos, which have a lot of very advanced features such as fiber-optic guidance and designs to reduce their acoustic signature. The Seawolf would be using the Mark 48 Mod 7 CBASS, which is also very advanced, but details about some of its systems are a lot more vague. What I can gather is that both torpedoes have roughly the same range, with the Mark 48 having a larger warhead, but slower speed and the DM2A4 having a higher speed, but smaller warhead. It’s pretty hard, really, to compare their performance without a whole lot of specifics, but it seems like both are designed to deliver a killing punch, both are designed to be fairly quiet, and both are not to be trifled with as far as weapons go.I’m honestly uncertain who might hold the edge here, so far. I’m inclined towards the Seawolf due to overall speed, range, and depth, but determining things like the exact acoustic signature levels of both the Type 212 and Seawolf, the sensitivity of their sonar systems, the effectiveness of their countermeasures, all tend to be very highly classified and mere speculation alone seems insufficient to really provide a deep answer that I’m comfortable with.I think it’s fair to say both are advanced, capable designs, both serve their respective nations well in their capacities. I think they also have well trained, dedicated crews, though I, being an American would be inclined to lean towards the greater degree of overall experience in modern submarine warfare the US Navy has and its general support and logistical structure to maintain the advantage in any naval advantage. I think mental exercises of “Is Y better than X?” and all the variations on this theme can be fun, but still miss the bigger picture involved in modern warfare, naval or otherwise. In a conflict, it’s almost never Y fighting X alone. It’s more like Y fighting X with A, B, C, D, E, G, K, L, and other systems and weapons backing up Y or X or both. Warfare is complex, with overlapping areas that create redundancies and reinforce any advantages a single system has while trying to cover for its weaknesses. Admittedly, in submarine warfare, you’re more likely than in almost any other scenario, to have only two vehicles facing off against one another without enormous, extensive support, but that’s still going to be a rare occurrence and the best we can do is speculate, due to how highly classified and closely guarded the exact numbers and characteristics of submarine systems in play are.Because of all these considerations, I again feel I would lean towards the Seawolf having the upper hand in most engagements over the Type 212 in most scenarios, but not having anything like an absolute dominance over the vessel. We’re comparing two very good apples here to one another. The difference is much more stark with older Russian, Chinese, or… hahahaha. Hahaha… North Korean submarines. But even these vessels still cannot be simply ignored, as they can still pose a signNow threat under the right circumstances and scenarios to any surface vessel or even other submarines.TL;DR - I’m inclined to go with the Seawolf, but only just barely. Both are excellent, well-designed submarines, and both fulfill their respective roles admirably.

As technology is increasingly intertwined with every business aspects, Google’s G Suite can help you to simplify all your work in real time. G Suite is a well established professional online tool that is used by major businesses. It is simply a collaborative productivity apps suite that offers everything a business needs viz professional emails, online documentation editing, data storage, video chat, spreadsheets and lots more.As G Suite combines all of the productivity and collaboration tools in an all-in-one suite, it provides many benefits that businesses can enjoy in the long run. One of the main benefits of G Suite is an ability to enhance the business branding by adding the company domain name and also adding a custom email address.Additional benefits of G Suite are as follows:Google Cloud Search: This is one of the most convenient options offered by the G Suite. The Google Cloud Search allows you to search the business files that are stored in the G Suite. In simple terms, a person can review and have access to the vital business data doesn't matter which employee has created or stored the data. This option enables easy accessibility and data is saved by multiple users.Unlimited Storage Space: Another advantage of G Suite is unlimited data storage. G Suite Business, as well as Enterprise Plans, offer unlimited data storage. This includes unlimited space storage for Google Photos, Gmail, Google Drive for file uploading as well as sharing among the team members.For instance, if a business has 4 or fewer users, each G Suite Business user will receive 1 TB (terabyte) of data storage space where one can roughly store probably 3,10,000 images, 17,000 hours of music files and long video files too.File ownership: With G Suite, all the Google Docs, Sheets and Slides created by the team members are owned by the business. One can also create a business policy that requires team members to back up their laptop or MAC folders and data files to Google Drive. Hence, this will allows one to have full access to all business files.CRM Integrations: A business may decide to invest in a well-established CRM system to revamp customer prospects, track better leads, customers, jobs and much more. G Suite is reconcilable and can be well synced with the CRM solutions. This will enable impeccable communication as well as reporting from both the ends.Company Branding UI: Now, add your valuable logo within all G Suite apps. One will be able to see their logos on top of the screens.All-in-one integration: G Suite is a complete business suite which consists of various integrated tools where team members can work together. For instance, a person receives an invitation mail can easily convert the same into a calendar event. A person can also edit the doc. All the changes will be notified to all the team members collaboratively.G Suite has Docs, Hangouts, Google Drive, Gmail all in one suite. So, this helps a person to work easily anywhere, anytime and with the help of any device.G Suite helps a business to create productivity and efficiency in the overall work process. Thus, it eliminates every concern of the business, be it file storing or data security or transparency in work.Hope it helps you!

This is a great question! Google has a tremendous opportunity to make an impact in the Microsoft Office world, and a lot of legacy systems as well.In my opinion, the biggest thing that Google is not doing properly with G Suite is they’re not leveraging their partners properly.When you look at the Google ISV page and their recommended partners, they have amazing partners that enable you to take the G Suite to the next level for the enterprise.For customer support, you have companies like Fresh Desk, for simple Sign on you have Octa, for document management and enterprising control you have AODocs - full disclosure, I work for AoDocs which basically is a Sharepoint on top of Google G Suite. Any clients that we get are traditionally moving from the Sharepoint environment to G Suite and they put AoDocs on top of it to make that possible. There are other partners, big ones like signNow for e-signatures, Dial Pad for VPN services, Xero for invoice etc.The point is that Google has got to do a better job of understanding what these partners do, and getting them in conversations with clients because right now the process is largely separate - they’re not exactly bringing those partners into the conversations to make the best use of G Suite.For instance, the perfect comparison is Facebook. Facebook has Global Account Managers that are responsible for knowing, in general, about all Facebook products. They will go to a client like BMW North America (making it up) and say “Okay, here’s the entire list of Facebook products, here is how we can help you internally, and these are the Facebook reps and external partners that we’ll introduce you to.”That’s not how Google is currently doing it, at least not to outsiders. When you look at the way Facebook does it, they are successful because they realized that they can’t do everything nor be specialists in everything, they just have to know a little bit about everything that can be done, and then prove that the relationships make a win-win-win situation for everybody that’s involved in the eco system.Basically, for G Suite to become more popular in business world, there is one huge player and that’s Office 365. The fact is that G Suite has a better product - the only product that really lacks currently is versus Microsoft Excel, and that’s actually changing very quickly. Google Sheets is about to have a major release.There are companies that pay millions of dollars a year just because they want to keep Microsoft Excel - they actually hate the rest of the Microsoft Office (so I’ve been told by Microsoft clients). They don’t switch because Google is not giving them a competent solution with their partners to figure it out. For them to tackle this beast, it’s going to take a partnership effort.Microsoft does a great job of leveraging their partners to promote their products, and make sure there is a win-win-win situation for everyone.As soon as Google can figure out how to do this more effectively with G Suite, they will become more popular in the business world.

How do I compose a song using the piano?Alright, I may not be the best person to ask this question to, but I’ll try to offer the little advice I have.In creating the melody, you can choose to start by… making up a random melody in your mind and finding the right keys for the notes. That seems like the simplest way to start. On the other hand, it may be kinda tricky if you don’t know where to start.I suggest starting with the chord progressions.For example, try a C-major chord, followed by an A-minor chord, then an F-major chord, and a G-major chord. Keep playing it and see if it can inspire you to think of a melody based on the progression. You can also change the key signature and/or find different chords.I’d say those sets of chords are like the foundation of the song. Often, it’s the base of the melody of the chorus. For example, the pattern mentioned earlier is repetitively used in the song “Can’t Help Falling In Love” by (someone please help I forgot who made the song)“(C-major) Wise men (A-minor) say only (F-major) fools rush (G-major) in…”“(C-major) Take my (A-minor) hand; take my (F-major) whole life (G-major) too…”And while it’s a nice part of the melody that suits the chords, it’s not the only one that can. You can come up with different melodies based on a single chord progression.You can also switch up the order of the chords in different parts of the song. The aforementioned song also does this in the other parts. I just recommend sticking with a single key signature all throughout until you’re comfortable trying out key changes.Now, if you don’t feel like making or checking out those structured patterns, you can try a simpler pattern by using descending notes. For example, “This Is Gospel” by Panic! At The Disco seems to rely on a pattern of descending notes on the D-major scale.“(D) This is gospel (C-sharp) for the fallen ones (B) locked away in a (A) permanent slumber…(D) Assembling (C-sharp) their philosophies (B) from pieces of (A) broken memories…”“…’Cause these (D) words are (C-sharp) knives and (B) often leave (A) scars! (G) The (F-sharp) fear of (E-major) falling (E-minor) apart.”“…And (D) truth be (C-sharp) told I (B) never was (A) yours! (G) The (F-sharp) fear, the (E-major) fear of (E-minor) falling apart”(You can also play it with the chords. I just forgot the names of those chords. But basically the notes I mentioned are the base notes. Furthermore, you can play the piece with broken chords. It can sound cool.)Technically, I guess it still counts as a progression. It just seems like a way simpler one. As always, you can try it with different key signatures and come up with different melodies.Lastly, maybe try to learn about music theory. To be honest, I don’t know much about it, but I heard it helps. Just saying.When playing, don’t pressure yourself too much. Relax, and let your mind flow and wander freely. It’s trickier to come up with music stuff if you’re too tense. Play what comes to mind and refine it over time.Good luck and have fun! Have an awesome day!