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FAQs
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What are the best electronic signature (e-signature) solutions on the market, in your opinion?
[full disclosure: I’m VP Digital Transformation at Solutions Notarius Inc., a company that supplies electronic and digital signature solutions]It completely depends on the requirements. I do not believe there is a uniquely better e-signature solution for all scenarios. For example, if the type of documents to be signed require low to medium reliability only, most modern e-signature platforms could be ok, subject to meeting legal requirements in the applicable jurisdiction, but if the document must meet stringent regulatory and statutory requirements that include high reliability of identity of signers, those platforms do not typically meet that threshold.Ideally, you would analyze, define and obtain agreement as to what constitutes the minimal acceptable legal reliability threshold you are willing to accept - or that readers of that document will accept. Next, define the technology requirements that correspond to that threshold. Finally, research e-signature options that meet these requirements and provide the best combination of price, features, scalability, etc..Finally, it should be noted that higher legal reliability e-signature platforms and solutions can always accommodate lower reliability documents while the converse is not true…
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What are the career options after graduating with a Bachelor's in physics?
There are actually Three things you can do after you ‘earn’ your Bachelor degree in Physics :Continue your studiesGet a Job , orGive a JobAllow me to explain each in detail -Continue your studies :-> Here you have several Options:a) Pursue Masters from IIT by cracking IITJAM or from any other university on Physics and earn a PHd later on. You can also do Integrated PHd by applying and getting a good rank in JEST , TIFR , IISER etc.b) Pursue your Masters from any IIT (or from any other University) and then pursue MTech by cracking GATE. After MTech you can get placed in some PSUs or some reputed MNCs. Many prefer higher studies though (like PHd after Mtech). (P.S - IIT Kharagpur provides Integrated Mtech-PHd for Computer Science and Data Analytics after qualifying in GATE)c) Give an entrance test conducted by few universities for Btech and get into some good Engineering Colleges. (Ex : Jadavpur University in Kolkata conducts an entrance test for students of BSc(Hons) Physics. Qualified Candidates enter into 2nd year of BTech. Likewise Calcutta University provides Btech in Radiophysics.)d) Do Bachelors in Education(BEd) for a Teaching Job.e) MSc on other subjects like Biophysics, RadioPhysics, Geophysics, Instrumentation etc. Ex - MScTech in Geophysics from ISM Dhanbad (Note : the degree mention MScTech not MTech; Both are different).f) Other Masters programme in other disciplines if you want to do it like MCA, MBA, MA, LLB etc. (Being interested in Defence Services, personally I would have preferred Masters from Institute of Defence Studies in Pune and PHd later on— a path very few know or like to tread .)g) If you have a Gap in years after your BSc Physics and possess the thought that you will be unable to share the class with the younger generation, feel free to pursue distance learning through IGNOU. You can pursue your masters on other subjects via IGNOU or sit for an entrance examination for MSc. Physics (distance learning) which by the way IGNOU conducts in collaboration with Indian Institute of Astrophysics (forms available in the month of september).h) You can also pursue higher studies from Foreign universities. Of course you have to crack the competitive exams related for that purpose.2. Get a Job :→ You can Apply for Various entrance examinations for Banks(RBI Grade B, SBI PO, IBPS etc), Railways( ASM, Goods Guard, JE, RPF SI etc) , PSUs or State Units(AAI ATC, Electricity Executives, Forest Guard etc), Armed Forces(AFCAT, CDSE, Coast Guard(only interview) ), Civil Services(UPSC CSE, State CSE, IFoS) and Central/State Police Services( SSC CAPF, UPSC CAPF, SSC CGL etc). Crack these Examinations and earn a respectable service with the Central or State Governments or Banking Sector or PSUs.(PS : If you have completed MSc Physics then you can apply in Indian Navy as an Officer or else not. Indian Navy does not recruit candidates having just BSc in Physics. You either should have BTech or do MSc Physics- the condition valid even in UPSC CDSE recruitment)→ If you want a job in your core field(subject), there are exams like ISRO Scientific Assistant, SSC IMD Scientific Assistant, BHAVINI Scientific Assistant, NCPOR Scientific Assistant(which do not conduct any exam but only Personal Interview), NPCIL Scientific Assistant etc. which too are Govt Organisations that requires Bachelor’s in Physics as a qualification.(PS- If you complete MSc in Physics however you can apply for a relatively higher position in similar organisations for the post of Scientific Officer - Some institutes like BARC donot recruit candidates having a degree less than that of MSc.)You know the craze for Government Jobs, Don’t you? Some Jobs are indeed Earned. :)→ However You can always find a Job in the Corporate Sector. Ex: TCS, WIPRO etc.So, All the very Best if getting a Job is your sole Aim.P.S - Build and Develop Skills via sites(also Android App) like Udemy, Coursera, edX, Skillshare, Codecademy etc. Trust me sometimes recruiters will be much interested if they learn that you have invested some quality time in having knowledge which can give you an edge over other candidates. Also makes your Resume look quite attractive. Moreover guess what, most courses are totally free of Cost. After Completing the Course if you wish to have the valid Certificate with a signature and stamp from reputed universities, you can pay them a certain fee. Totally ok if you dont pay as those digital certificates will not hold much value over regular courses;but do keep in mind the skill you learn can make you top notch over others.Personally I prefer to pay as a token of appreciation. Doesn’t seem much(approx 3k INR & sometimes even only 600 INR) if you consider the fact that the knowledge you receive is immense and magnificent.3. Give a Job :→ Well you know what I am going to say. The Word that became the centre of attention lately in India- ‘Entrepreneurship’.Take risks, try out new ways, give people a source of Income, earn Fortunes and build your own Empire. And the thing is you don’t even need a Bsc or Physics to be a great entrepreneur. You don’t need to work for anyone, You can always work for yourself.But yes to be brutally honest- as lovely as the situation might seem- you will most likely Fail in this venture. Dont get me wrong but what I am saying here is the ‘Reality’. However I haven’t seen or met Entrepreneurs who didnot fail and yet achieved big.Who knows You might become the next Zuckerburg or the next Elon Musk - which by the way if you dont know, Mr. Musk has done his Bachelors in Physics. ;)These are the three things which I feel you can do. The Interest and the Will rests on you and you alone. I hope I was able to remove all your doubts. Still if you have one, feel free to comment.By the way, Upvotes are Welcome. Thank you for the 177 upvotes. Means a lot.All the Best for your future.(>_<) ♡Edit- Thank you Quorans for my first 500 upvotes.
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What are probabilistic graphical models, and why are they useful?
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.
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How do I register a startup in India? How much money and time does it take? If am currently only 17, what issues will I face dur
Algorithm for starting a Private Limited Company: Engineer's View Personally I believe, If someone is starting a company with long term perspective or to bring some change through their unique Product/Services, one must go for Private limited firm. Prime reason for this is easy to raise funds from Angels/VC in case you go for investment. Step 1. Registration of Company 1. Name Selection: Check whether your desired company name is available or not at MCA website [ http://www.mca.gov.in/ ]. Name must be unique & must resemble with business you intend to do (highlighted one). EX: Arihant Labs Retail Services Pvt. Ltd 2. Registration of Name at ROC: Name approval usually takes maximum of 14 days. This is done online through MCA website. Moreover, you need to apply with at least 4 names for approval with a writeup about significance of names with main business of the company. 3. 1. Documents Required: 2. 1. Options for names for the proposed Company (on the basis of preference) 2. Amount of Share Capital; proposed shareholding ratio 3. A paragraph on the proposed major line of business of the company (main objects) 4. City of Registered Office. 5. Copy of ownership deed/sale deed(if property is owned) 6. Copy of rent agreement with NOC (if property is rented) 7. Copy of latest electricity bill/telephone bill/mobile bill for both directors 8. Copy of latest electric bill/telephone bill for the registered office proof. 4. Obtaining DIN & DSC: 5. 1. Documents Required 2. 1. PAN Card copies for directors and shareholders. 2. Voter ID/Passport/Driving License for directors and shareholders. 3. Occupation of the Directors for directors and shareholders. 4. E-Mail IDs of all directors and shareholders. 5. Phone Numbers for all directors and shareholders. 6. Photos for directors and shareholders 6. Company Incorporation: After above mentioned formalities have been completed, we need to file following forms/docs in Rs 100 stamp paper: 7. 1. Affidavits for non- acceptance 2. INC 9, INC 10 3. DIR 2 4. NOC : This is required to be filed by the owner of the property on which your company will be situated. 5. Subscriber Sheets of MOA & AOA 6. Documents required for filling MOA & AOA 7. 1. Must be filled on OWN handwriting 2. Passport size photos 3. Sheets needs to be witnessed by CA/CS/Advocate Step 2. Obtaining PAN/TAN: After company gets incorporated, you may apply for PAN/TAN. Step 3. Trade Licence in case you are selling PRODUCTS: This is required in some places for carrying out sales. You can obtain this from local Municipality. Step 4. VAT/CST registration for selling Products: For selling intra-state, you need VAT registration & for selling inter-state, you need to register for CST. 1. Documents Required: 2. 1. Trade Licence 2. Company Incorporation Certificate 3. PAN card of company as well as of all the directors 4. Proof of residence of Directors 5. Proof of occupancy of place of business (Rent agreement/ ownership deed, Rent Bills etc) 6. MOA & AOA of company 7. Current Account in the name of company in any national bank Step 5. Service tax registration for Service Industry: In India, you need to pay service tax of 14.5% on every services you have charged customer for. 1. Documents Required: 2. 1. Company Incorporation Certificate 2. PAN card of company as well as of all the directors 3. Proof of residence of Directors 4. Proof of occupancy of place of business (Rent agreement/ ownership deed, Rent Bills etc) 5. MOA & AOA of company 6. Current Account in the name of company in any national bank That's All folks! Your STARTUP is up to Conquer the World. UPVOTE & SHARE your views/issues We at labkafe [ http://labkafe.com/ ], prefer taxmantra [ http://taxmantra.com/ ] for our legal requirements.
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What are the biggest lessons you have learned in the corporate world?
Arriving early and doing nothing is viewed more favorably than staying late and working assiduously. It’s unfair, but it’s only the first boot of real life to kick you in the ass.HR and the ethics hotline don’t exist as a resource to you; they exist to cover management’s ass. I’ve worked for bosses who have used racial slurs, homophobic epithets, threatened and intimidated staff, used drugs in the office, and misappropriated their expense credits, but they were never so much as suspended. I almost lost my job for marking a sale as closed when I got verbal confirmation from my client (with my manager on the phone), only to get the actual signed documents a few days later.Always, always, ALWAYS document and organize files of communication between you and your superiors and you and problem clients. Did I say always? Discrepancies (read lies) in accounts of your interactions from either of these parties is a fast track to being escorted out of the building. Nothing shuts up a lying SOB like a time-stamped email with the intro, “Per my email on July 15, I mentioned….”Always keep a pulse on the job market. At least twice a year apply for jobs in your industry to get a sense on what your skills trade for in the open market and to sharpen your interviewing skills. It’s also a great habit to be in the orbit of recruiters because they operate within a tight-knit ecosystem, network with, and know one another. If you’re not a great fit for one role, and they like you, they’ll refer you to a friend or colleague looking to fill another role as a courtesy.Even if you’re not interested in a role that they may signNow you for, always try to recommend or refer qualified candidates to recruiters. This pays dividends down the road.Be wise as a serpent, yet as humble as a dove. Many people advise against making friends, but I would advise that you make them believe that you’re a friend. Being too cold and stoic in the office will make your colleagues withhold gossip, news, and politics from you that may be actionable. You can be friendly without being friends. Whatever your line is, find it and stick to it.Never get comfortable. I had a former colleague who never placed photos of his family or accomplishments in his cube and I asked him why. He said he is always prepared to walk out of the building with the items on his person at a moment’s notice. Speaking from experience, there’s nothing more humiliating or anxiety-inducing than taking the security assisted walk of shame with all of your belongings in a box and colleagues peeking above their cubes like prairie dogs to watch you walk the green mile. Work is a place where you should be as productive as possible; your family, spouse, hobbies, religion, proclivities, and creature comforts shouldn’t occupy the work space.Your manager is NOT to be trusted with personal information. Whether your mom has cancer, wife left you, your kids are suspended from school, or you’re late on the rent, these aren’t the people to share your most vulnerable moments with for two reasons; 1. They don’t have the power to do anything about them, and 2. They are more likely to report this things up the chain of command to use against you should it ever become convenient as a manipulation tactic. I know this oversimplifies things for the truly empathic, and supportive managers out there, but for the sake of generalities, let’s leave those 8 people out of this and err on the side of caution.Use your lunch hour as an opportunity to network with people within different departments to grow your customer base. Every employee has internal and external customers, and it will behoove you to learn how to cater to them. If you’re in sales, take someone in Dev Ops, Professional Services, R&D, or Customer Experience to lunch. You’ll learn all the horrible things sales people do that make their job a living hell, so you won’t perpetuate that. You’ll also forge some great individual relationships for emergencies when you need to phone a friend.Stay away from the office complainer. Every office has at least one, and he/she is a cancer on your outlook and productivity. Regardless of how valid their complaints are about the quality of the snacks, the scheduled All Hands meetings, the increased co-pays on the new insurance for annual enrollment, the way management is trying to screw us with the new Comp Plan, etc., the best thing to do is to keep your exposure to this individual AT. A. MINIMUM.Become a Subject Matter Expert in at least one or more topics within your department. This makes you indispensable among your peers and management, because they don’t want to(or can’t do) do the job of training the whole staff or answering all their questions.Volunteer to headline new products or services, and you’ll become more visible with leadership and ahead of the curve when those products/services become mandatory.Make your career decisions for the people who will attend your funeral one day; not the people in that office. Days, or even hours after your death, someone will be posting a requisition for your position, and your duties will fall on the shoulders of another. Make sure you spend your strategic decisions improving the quality of time with the people who will be crying at your funeral. This puts a whole lot of unnecessary office bullshit into perspective.If you’re in the US, talk to your colleagues about your salary. Corporations benefit from dwindling unions and individual, rather than collective bargaining by negotiating salary and compensation on an individual basis. Men, this is our opportunity to gain solidarity with women who work equally to ensure that they’re paid equally. White folks, this is an opportunity to ensure Black folks, Hispanics, and Natives are paid equally. This isn’t a zero-sum equation; corporations make enough money to pay us all equally. They have the luxury of not doing so. Hold their feet to the fire, or have them risk losing the war of retention.Be kind. Especially to the people who least deserve it. 9 times out of 10, they’re fighting prodigious personal battles, and the only place they can funnel their energy is at work. Be gentle, but don’t be a doormat either.Bring your authentic self to work. I’ve seen introverts, extroverts, flashy dressers, frumpy dressers, those gifted with supreme elocution, and those with the longest, strongest Southern drawl succeed in business, which proves one thing. Success doesn’t care how you show up; just that you show up. I wish you the best of luck on your journey!
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What is the deal with scale modes? If I’m playing in the key of C major, what difference does it make if I play in D Dorian, F L
Hahaaa I totally can identify with that question, because that very exact same thing you are asking about, confused the hell out of me too in my first years in music school.Fact of that matter is, that even many really great teachers, more often than not fall short in adequately explaining how and why these really are 7 completely different scales (AND keys), even though yes, these 7 scales all do exist of the same 7 notes. I’ve experienced this first hand myself, having studied with many fantastic teachers, yet no one really fully could make me understand this thing you are asking about.I ended up figuring it out myself over years of studying music and later also teaching music.So here we go:When you play a C major scale, you are playing all the white keys of the piano, starting from C to C, right? That scale has a certain particular sound, and that sound is called “the major scale”.It is the scale that you use in songs that start on a C chord, keep coming back to a C chord over and again, and that eventually end on a C chord. Because of that constantly coming back to a C chord, that song is in the key of C, and your 7 white keys are going to sound like a C major scale over that song, BECAUSE you are playing the scale of a song that is centered around a C chord. (which is another way of saying that it is in the key of C)All the rest of the chords in the song, need to be chords that consist of white key notes (naturals) only. Those chords are: C Dm Em F G Am Bdim. (All the chords of a C scale)However…When you play exactly the same 7 naturals (which is another name for “white keys of the piano”, or in other words: no sharp and no flat notes), over a song that starts on a Dm chord, keeps coming back to a Dm chord over and again, and eventually ends on a Dm chord, with whatever other chords that are happening, all being chords that consist of naturals only (Dm Em F G Am Bdim C Dm), you are now playing a D Dorian scale.Why?Because you are not USING those 7 naturals/notes the same way as you did over the previous (C major) song. You are actually (and you might not even have noticed this or might not even realize this), ending more of your melody lines on the notes D, F and A (notes of a Dm chord), whereas over the C major song, you were ending more of your phrases in your solo with the notes C, E and G, which are the notes of a C chord.Why would you end more of your melody lines on the notes D, F or A when soloing over a song in the key of D minor or in this case, D Dorian?Well… Human nature is such that for the most part, nobody likes unresolved tension, meaning: everybody always tends to use/play the notes more that sound “more pleasing”, or “sound better” in the scale over a song or chord. Those notes (that “sound better”) are the notes that make up the chord the song keeps resolving to, which is the I chord, which in D Dorian is a Dm chord.By the same token, when you solo with those same 7 notes over a song that starts on an F chord, keeps coming back to an F chord over and again, and eventually ends on an F chord, with all the other chords being chords that consist of naturals only ( the chords F G Am Bdim C Dm Em F), you are now playing an F Lydian scale. The scale no longer sounds like a C major scale, because it is used over chord progressions that keep coming back/resolving/revolving around an F chord. Your key center no longer is C, but F. As such, you will outline more F, A and C notes in your solo, (notes of an F chord), than you did over the C major or D Dorian etc song.So conclusion: they are 7 entirely different scales (and keys), and their sound is defined by the chord you solo over.To test this out, go on YouTube, and in the search field type“C Ionian backing track”, or “C Ionian 1-chord groove”.“D Dorian backing track”, or “C Dorian 1-chord groove”.“E Phrygian backing track”, or “E Phrygian 1-chord groove”.“F Lydian backing track”, or “F Lydian 1-chord groove”.etc…And solo for a couple of minutes with all the naturals over each one of these backing tracks.You will notice howYour same 7 notes are going to sound different over every track. It’s going to sound like a different scale for each track. (Though each track is composed of chords that consist of all the same notes for teach track). It’s the chord each track starts on and keeps coming back to that makes that each of these tracks sounds like they are in a different key.When you know your fret board well enough to know what the notes are you are actually playing, you will realize that you are not using the 7 notes the same way for each backing track: you will for the most part play certain specific notes more often than others for each of the backing tracks you solo over. You will find yourself playing more C E and G notes over the C major song, and more D F and A notes over the D Dorian song, and more E G and B notes over the E Phrygian song, etc. etc. You will (intuitively) feel that the other notes don’t sound “as pleasing”.The other notes in the scale are important too though, because they add the spice, pepper, vinegar, character etc to your solo. But it IS THE CHORD TONES, that make each one of your scales sound like it’s own scale. Meaning: When you play all the white keys of the piano and you play more A C and E notes, you are playing an A minor scale, when you play all naturals but you are ending all your phrases on the notes G B and D, you are now soloing in a G Mixolydian scale, and you are sounding like you’re in the key of G Mixo, and so on.Another way of explaining all the above: the chord you solo over, will dictate what your 7 notes are going to sound like. When you use all the naturals (the notes C D E F G A B) over a Bdim chord, you will sound like a B Locrian scale, when you play all those notes over an Am chord, you will sound like an Am scale, etc… The chord you solo over, will also dictate which of the 7 notes you are going to use more and which ones you’ll use less, which will lead to you sounding like your scale connects to that chord.Some fun common chord progressions for each mode:C major chord progression: C F G CD Dorian chord progression: Dm G Am DmE Phrygian chord progression: Em F G F Em (very Spanish, Flamenco in feel)F Lydian chord progression: F G C FG Mixolydian chord progression: G C Dm GA Aeolian (minor scale) chord progression: Am Dm Em AmB Locrian chord progression. Because of the structure (and the sound, which is the result of that structure) of the Locrian scale, this scale is not really “useful” for songwriting. It’s very seldom used and there is hence not really a “typical Locrian type of chord progression”. You could still solo with it of course, over a Bdim 1 chord groove for example.I wrote a blog in the past about this here: The Modes ExplainedIf you would like to take this a step further and learn how to figure out the key signature to each mode in each key, you can learn this here Easy System To Memorize The Key Signatures To All Modes in All KeysHope that makes sense and helps. If not, definitely hit me up anytime. :)
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As a defense attorney, how would you handle having to “break” someone on the witness stand that you may believe is a victim of y
Shades of Nero Wolfe! I am not and never have been a criminal defense attorney, but in my articles I have occasionally been assigned issues of criminal law or procedure, so have isolated bits of knowledge. I do believe, however, that criminal defense lawyers are in the front lines of those who defend democracy since their constant job is to see that every defendant receives a fair trial before an impartial adjudicator and that the result is supported by the trial evidence properly admitted. Plus they seem to always have the best stories.I once did have a witness, not mine, who more or less “broke” during a trial. This was a state court matter. My client owned a business selling cell phones and leasing service for them. The future defendant came in and purchased a cell phone and service, and for some reason signed the related documents over the course of two days instead of all at once. I don’t remember why and it didn’t matter to the trial. He paid the phone fee on the second day, but refused to pay for service over the course of nearly three months. His reason for not paying, he said, was that he was “testing” the service. My client had records of the numbers he called and the length of time for each call. I had taken his deposition, and he had admitted he signed each document I showed him concerning the purchase. The only real issue was whether his claim of testing the phone service was going to stand up.For our trial judge, we drew an older man who probably presided at God’s case against Cain, but was one of my favorites because he was experienced, didn’t like having his time wasted but would listen politely, and knew contract law. It was an excellent draw for us since I wouldn’t have to spend time explaining how contracts worked.The defendant showed up for trial with another fellow he introduced as his cousin and said he had been with him on the second day when he signed the rest of the documents and picked up his phone. I assumed the cousin was there to try to bolster the defendant’s claim of testing. But if they hadn’t already discussed the case, I was going to deny them the opportunity to coordinate further, so I invoked the “Rule” at the start, meaning the exclusionary rule that said anyone not a party had to wait outside in the hall until called.I started with the defendant. I put him on the stand and we began the basic stuff - the contract and its terms. I asked him the same stuff I had in the defendant’s deposition - “do you recognize this exhibit? what is it? is that your signature on page #?” Usually these are pretty routine, but the defense hadn’t wanted to stipulate admissibility, so I was just laying the groundwork. Needless to say, there was nothing in the documents about a period for testing, but there were warranties. So I am just loping along doing something I had done lots of times before and then …For some reason never made clear, the defendant decided to deny he had signed the second day’s paperwork. This really was the less important stuff, but it had warranty language in it, so one would think he would want it in. I suspect he just lost track or panicked. I am standing there with the transcript of his deposition in plain sight in front of me. It even had little paper tabs in it. I was careful not to react in any way to his denials - just a bit about being sure he looked in the right place and knew he’d seen them before. I took him through the rest of the paperwork and he insisted he hadn’t signed anything on day 2. No one seemed to catch it except my client. But what I did next got the judge’s attention because it was unusual.I asked the judge if I could suspend the defendant’s testimony for a bit, subject to recalling him later, while I called another witness out of order to “clarify” a point. Still no penny dropped with the defendant or, as far as I could tell, with his attorney, although I noticed the trial judge changed his posture so I figured he knew something was up and it had to do with the signatures. The judge let me call the cousin in from the hall, and now looked alert, waiting to see what was going on.The defendant went back to his seat beside his attorney and there was a lot of whispering until the judge shushed them. I called the cousin in from the hall, telling him only that we were going to be there for a while yet, and were taking him early so he wouldn’t have to stand around in the hall any longer than necessary. Now he is not my witness, so I designated him as hostile before I called him in so I could lead him some, but there really wasn’t much need.He obligingly recognized his cousin’s signatures on all of the documents, even correcting me when he thought I missed one, and explaining that he was present when the paperwork was all signed. He was pleasant, cheerful, and completely oblivious to the implications, so I knew they hadn’t discussed denying the signature beforehand - plus I still had the deposition statements to whack the defendant with if necessary. But it wasn’t.After the cousin finished and was excused, subject to later recall by the other side, the judge invited counsel up to the bench. And here is where experience mattered. The judge caught on that I wouldn’t have done what I did if the defendant hadn’t lied about signing some of the documents.I don’t use profanity, so I will use *** instead. The judge was annoyed by the defendant’s obvious lies. In whispers, the judge asked me if I had any further evidence regarding the question of the defendant’s signatures on the documents we’d been discussing and this was when the defendant’s lawyer woke up. He tried to object to the question, but the judge burnt him with a look that was better than a ruling. I just said I had a transcript of his deposition during which his memory was different, and that was all I said. The judge gestured to the defendant’s lawyer to come a bit closer (he’d backed up some during the burning) to the bench and the judge said words to the effect that his “G**D*** client had better settle with me before he was judicially determined to be a ***** perjurer and maybe recommended for prosecution for wasting the court’s time on a ****show like this case, and he was giving us a recess to resolve it without his [the judge] having to listen to any more **** from the *********** defendant.So we went outside, the defendant’s attorney “conferred” with his client, and we did just what the judge ordered. I never did find out why the defendant thought three months of free testing was appropriate.
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What made David Bowie’s music unique?
It is all very listenable, appealing, and virtually, all his early albums, through 1967 to 1983, are all good songs. Every album, is playable, through. Most of the time. This rarely happens with all other musicians. Or, you skip, or contemplate, only certain songs. Bowie, typically, transformed the process, to make almost every song, count. Credible. He produced, a massive body of work, in those years, and following. Few artists can compare, in terms, productivity, longevity, and still remain as good, or even better, after a decade and more. Yet, he remained, much longer in the music industry, always maintaining his status. Bowie, though, was truly very adaptable, always able to reinvent himself, or search for instant new ideas, or conjure up basically, anything, out of the blue. Yet, naturally, he also took a lot of inspiration, influence, not just in his formative years. Yet, still remained highly individualistic, and almost incomparable, since no-one quite had his sound, music-theory, and in turn, a greater influence on everyone else, or music, culture, in general:[/] Bowie “See Emily Play” (1973). From the album Pin Ups. All songs were based on covers/remakes. He chose an interesting selection, and transformed every song.[/] Pink Floyd “See Emily Play” (1967). Original track. ^^[/] ^^ 1973.[/] ^^ The Model Twiggy.[/] Bowie “Queen Bitch” (Live Old Grey Whistle Test 1972). This highlights, just how good he could be. Not to mention, foreshadowing punk, by many years. The song itself, is originally from his 1971 album, Hunky Dory.[/] Bowie “Rubber Band” (based on his 1966 single release, in mono). the song again appears on his 1967 debut album release, re-recorded in stereo. The video, is from 1969, which also featured segments of mime, among other songs, entitled “Love You Till Tuesday”. It served as a promotional video album.[/][/] Bowie “Space Oddity” (1969). Original version. This version, appears on his video album,from that year, yet only officially released in 1984.[/] His second solo album, released in 1969, featuring the official release, Space Oddity. So too the official single release.[/][/] ^^ 1969 single release.[/] ^^ 1972 reissue of the 1969 album. Entitled, Space Oddity, with the title track.[/] Bowie “Space Oddity” Official video, of the official 1969 version, taken from his second solo album. The video was produced December 1972. New York.[/] ^^ Early years. Between 1967 - 1975.[/][/] Bowie “The Width of a Circle” (recorded live, 1973, Motion Picture). The song here is some 14 mins long, extended version, with great guitar antics from Mick Ronson. Great backing band. The song was originally released on his 1970 album, The Man Who Sold The World.[/] ^^ Mick Ronson.[/] Bowie “Golden Years” (1976). The song was originally released as a single in Nov 1975. The album version, is slightly longer, by about half a minute.[/] Bowie “Moonage Daydream” (1972). Classic album.[/] Bowie “TVC 15” (1976). The song warms up, then basically, an amazing sound. Great production.[/][/][/] Bowie “Scary Monsters (And Super Creeps)” (1980).
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