An ANN is a model based on a collection of connected units or nodes called "artificial neurons", which loosely model the neurons in a biological brain. Each connection, like the synapses in a biological brain, can transmit information, a "signal", from one artificial neuron to another. An artificial neuron that receives a signal can process it and then signal additional artificial neurons connected to it. In common ANN implementations, the signal at a connection between artificial neurons is a real number, and the output of each artificial neuron is computed by some non-linear function of the sum of its inputs. The connections between artificial neurons are called "edges". Artificial neurons and edges typically have a weight that adjusts as learning proceeds. The weight increases or decreases the strength of the signal at a connection. Artificial neurons may have a threshold such that the signal is only sent if the aggregate signal crosses that threshold. Typically, artificial neurons are aggregated into layers. Different layers may perform different kinds of transformations on their inputs. Signals travel from the first layer (the input layer) to the last layer (the output layer), possibly after traversing the layers multiple times. The original goal of the ANN approach was to solve problems in the same way that a human brain would. However, over time, attention moved to performing specific tasks, leading to deviations from biology. Artificial neural networks have been used on a variety of tasks, including computer vision, speech recognition, machine translation, social network filtering, playing board and video games and medical diagnosis. Deep learning consists of multiple hidden layers in an artificial neural network. This approach tries to model the way the human brain processes light and sound into vision and hearing. Some successful applications of deep learning are computer vision and speech recognition.[68] Decision trees Main article: Decision tree learning Decision tree learning uses a decision tree as a predictive model to go from observations about an item (represented in the branches) to conclusions about the item's target value (represented in the leaves). It is one of the predictive modeling approaches used in statistics, data mining, and machine learning. Tree models where the target variable can take a discrete set of values are called classification trees; in these tree structures, leaves represent class labels and branches represent conjunctions of features that lead to those class labels. Decision trees where the target variable can take continuous values (typically real numbers) are called regression trees. In decision analysis, a decision tree can be used to visually and explicitly represent decisions and decision making. In data mining, a decision tree describes data, but the resulting classification tree can be an input for decision making. Support vector machines Main article: Support vector machines Support vector machines (SVMs), also known as support vector networks, are a set of related supervised learning methods used for classification and regression. Given a set of training examples, each marked as belonging to one of two categories, an SVM training algorithm builds a model that predicts whether a new example falls into one category or the other.[69] An SVM training algorithm is a non-probabilistic, binary, linear classifier, although methods such as Platt scaling exist to use SVM in a probabilistic classification setting. In addition to performing linear classification, SVMs can efficiently perform a non-linear classification using what is called the kernel trick, implicitly mapping their inputs into high-dimensional feature spaces. Illustration of linear regression on a data set. Regression analysis Main article: Regression analysis Regression analysis encompasses a large variety of statistical methods to estimate the relationship between input variables and their associated features. Its most common form is linear regression, where a single line is drawn to best fit the given data according to a mathematical criterion such as ordinary least squares. The latter is often extended by regularization (mathematics) methods to mitigate overfitting and bias, as in ridge regression. When dealing with non-linear problems, go-to models include polynomial regression (for example, used for trendline fitting in Microsoft Excel[70]), logistic regression (often used in statistical classification) or even kernel regression, which introduces non-linearity by taking advantage of the kernel trick to implicitly map input variables to higher-dimensional space. Bayesian networks Main article: Bayesian network A simple Bayesian network. Rain influences whether the sprinkler is activated, and both rain and the sprinkler influence whether the grass is wet. A Bayesian network, belief network, or directed acyclic graphical model is a probabilistic graphical model that represents a set of random variables and their conditional independence with a directed acyclic graph (DAG). For example, a Bayesian network could represent the probabilistic relationships between diseases and symptoms. Given symptoms, the network can be used to compute the probabilities of the presence of various diseases. Efficient algorithms exist that perform inference and learning. Bayesian networks that model sequences of variables, like speech signals or protein sequences, are called dynamic Bayesian networks. Generalizations of Bayesian networks that can represent and solve decision problems under uncertainty are called influence diagrams. Genetic algorithms Main article: Genetic algorithm A genetic algorithm (GA) is a search algorithm and heuristic technique that mimics the process of natural selection, using methods such as mutation and crossover to generate new genotypes in the hope of finding good solutions to a given problem. In machine learning, genetic algorithms were used in the 1980s and 1990s.[71][72] Conversely, machine learning techniques have been used to improve the performance of genetic and evolutionary algorithms.[73] Training models Usually, machine learning models require a lot of data in order for them to perform well. Usually, when training a machine learning model, one needs to collect a large, representative sample of data from a training set. Data from the training set can be as varied as a corpus of text, a collection of images, and data collected from individual users of a service. Overfitting is something to watch out for when training a machine learning model. Federated learning Main article: Federated learning Federated learning is an adapted form of distributed artificial intelligence to training machine learning models that decentralizes the training process, allowing for users' privacy to be maintained by not needing to send their data to a centralized server. This also increases efficiency by decentralizing the training process to many devices. For example, Gboard uses federated machine learning to train search query prediction models on users' mobile phones without having to send individual searches back to Google.[74] Applications There are many applications for machine learning, including: Agriculture Anatomy Adaptive websites Affective computing Banking Bioinformatics Brain–machine interfaces Cheminformatics Citizen science Computer networks Computer vision Credit-card fraud detection Data quality DNA sequence classification Economics Financial market analysis[75] General game playing Handwriting recognition Information retrieval Insurance Internet fraud detection Linguistics Machine learning control Machine perception Machine translation Marketing Medical diagnosis Natural language processing Natural language understanding Online advertising Optimization Recommender systems Robot locomotion Search engines Sentiment analysis Sequence mining Software engineering Speech recognition Structural health monitoring Syntactic pattern recognition Telecommunication Theorem proving Time series forecasting User behavior analytics In 2006, the media-services provider Netflix held the first "Netflix Prize" competition to find a program to better predict user preferences and improve the accuracy of its existing Cinematch movie recommendation algorithm by at least 10%. A joint team made up of researchers from AT&T Labs-Research in collaboration with the teams Big Chaos and Pragmatic Theory built an ensemble model to win the Grand Prize in 2009 for $1 million.[76] Shortly after the prize was awarded, Netflix realized that viewers' ratings were not the best indicators of their viewing patterns ("everything is a recommendation") and they changed their recommendation engine accordingly.[77] In 2010 The Wall Street Journal wrote about the firm Rebellion Research and their use of machine learning to predict the financial crisis.[78] In 2012, co-founder of Sun Microsystems, Vinod Khosla, predicted that 80% of medical doctors' jobs would be lost in the next two decades to automated machine learning medical diagnostic software.[79] In 2014, it was reported that a machine learning algorithm had been applied in the field of art history to study fine art paintings and that it may have revealed previously unrecognized influences among artists.[80] In 2019 Springer Nature published the first research book created using machine learning.[81] Limitations Although machine learning has been transformative in some fields, machine-learning programs often fail to deliver expected results.[82][83][84] Reasons for this are numerous: lack of (suitable) data, lack of access to the data, data bias, privacy problems, badly chosen tasks and algorithms, wrong tools and people, lack of resources, and evaluation problems.[85] In 2018, a self-driving car from Uber failed to detect a pedestrian, who was killed after a collision.[86] Attempts to use machine learning in healthcare with the IBM Watson system failed to deliver even after years of time and billions of dollars invested.[87][88] Bias Main article: Algorithmic bias Machine learning approaches in particular can suffer from different data biases. A machine learning system trained on current customers only may not be able to predict the needs of new customer groups that are not represented in the training data. When trained on man-made data, machine learning is likely to pick up the same constitutional and unconscious biases already present in society.[89] Language models learned from data have been shown to contain human-like biases.[90][91] Machine learning systems used for criminal risk assessment have been found to be biased against black people.[92][93] In 2015, Google photos would often tag black people as gorillas,[94] and in 2018 this still was not well resolved, but Google reportedly was still using the workaround to remove all gorillas from the training data, and thus was not able to recognize real gorillas at all.[95] Similar issues with recognizing non-white people have been found in many other systems.[96] In 2016, Microsoft tested a chatbot that learned from Twitter, and it quickly picked up racist and sexist language.[97] Because of such challenges, the effective use of machine learning may take longer to be adopted in other domains.[98] Concern for fairness in machine learning, that is, reducing bias in machine learning and propelling its use for human good is increasingly expressed by artificial intelligence scientists, including Fei-Fei Li, who reminds engineers that "There’s nothing artificial about AI...It’s inspired by people, it’s created by people, and—most importantly—it impacts people. It is a powerful tool we are only just beginning to understand, and that is a profound responsibility.”[99] Model assessments Classification of machine learning models can be validated by accuracy estimation techniques like the holdout method, which splits the data in a training and test set (conventionally 2/3 training set and 1/3 test set designation) and evaluates the performance of the training model on the test set. In comparison, the K-fold-cross-validation method randomly partitions the data into K subsets and then K experiments are performed each respectively considering 1 subset for evaluation and the remaining K-1 subsets for training the model. In addition to the holdout and cross-validation methods, bootstrap, which samples n instances with replacement from the dataset, can be used to assess model accuracy.[100] In addition to overall accuracy, investigators frequently report sensitivity and specificity meaning True Positive Rate (TPR) and True Negative Rate (TNR) respectively. Similarly, investigators sometimes report the false positive rate (FPR) as well as the false negative rate (FNR). However, these rates are ratios that fail to reveal their numerators and denominators. The total operating characteristic (TOC) is an effective method to express a model's diagnostic ability. TOC shows the numerators and denominators of the previously mentioned rates, thus TOC provides more information than the commonly used receiver operating characteristic (ROC) and ROC's associated area under the curve (AUC).[101] Ethics Machine learning poses a host of ethical questions. Systems which are trained on datasets collected with biases may exhibit these biases upon use (algorithmic bias), thus digitizing cultural prejudices.[102] For example, using job hiring data from a firm with racist hiring policies may lead to a machine learning system duplicating the bias by scoring job applicants against similarity to previous successful applicants.[103][104] Responsible collection of data and documentation of algorithmic rules used by a system thus is a critical part of machine learning. Because human languages contain biases, machines trained on language corpora will necessarily also learn these biases.[105][106] Other forms of ethical challenges, not related to personal biases, are more seen in health care. There are concerns among health care professionals that these systems might not be designed in the public's interest but as income-generating machines. This is especially true in the United States where there is a long-standing ethical dilemma of improving health care, but also increasing profits. For example, the algorithms could be designed to provide patients with unnecessary tests or medication in which the algorithm's proprietary owners hold stakes. There is huge potential for machine learning in health care to provide professionals a great tool to diagnose, medicate, and even plan recovery paths for patients, but this will not happen until the personal biases mentioned previously, and these "greed" biases are addressed.[107] Hardware Since the 2010s, advances in both machine learning algorithms and computer hardware have led to more efficient methods for training deep neural networks (a particular narrow subdomain of machine learning) that contain many layers of non-linear hidden units.[108] By 2019, graphic processing units (GPUs), often with AI-specific enhancements, had displaced CPUs as the dominant method of training large-scale commercial cloud AI.[109] OpenAI estimated the hardware compute used in the largest deep learning projects from AlexNet (2012) to AlphaZero (2017), and found a 300,000-fold increase in the amount of compute required, with a doubling-time trendline of 3.4 months.[110][111] Software Software suites containing a variety of machine learning algorithms include the following: Free and open-source so

[Advanced] Data Science Fundamentals and Practical Applications for Financial Engineering

Bitcoin: A Peer-to-Peer Electronic Cash System Satoshi Nakamoto satoshin@gmx.com www.bitcoin.org Abstract. A purely peer-to-peer version of electronic cash would allow online payments to be sent directly from one party to another without going through a financial institution. Digital signatures provide part of the solution, but the main benefits are lost if a trusted third party is still required to prevent double-spending. We propose a solution to the double-spending problem using a peer-to-peer network. The network timestamps transactions by hashing them into an ongoing chain of hash-based proof-of-work, forming a record that cannot be changed without redoing the proof-of-work. The longest chain not only serves as proof of the sequence of events witnessed, but proof that it came from the largest pool of CPU power. As long as a majority of CPU power is controlled by nodes that are not cooperating to attack the network, they'll generate the longest chain and outpace attackers. The network itself requires minimal structure. Messages are broadcast on a best effort basis, and nodes can leave and rejoin the network at will, accepting the longest proof-of-work chain as proof of what happened while they were gone. 1. Introduction Commerce on the Internet has come to rely almost exclusively on financial institutions serving as trusted third parties to process electronic payments. While the system works well enough for most transactions, it still suffers from the inherent weaknesses of the trust based model. Completely non-reversible transactions are not really possible, since financial institutions cannot avoid mediating disputes. The cost of mediation increases transaction costs, limiting the minimum practical transaction size and cutting off the possibility for small casual transactions, and there is a broader cost in the loss of ability to make non-reversible payments for non- reversible services. With the possibility of reversal, the need for trust spreads. Merchants must be wary of their customers, hassling them for more information than they would otherwise need. A certain percentage of fraud is accepted as unavoidable. These costs and payment uncertainties can be avoided in person by using physical currency, but no mechanism exists to make payments over a communications channel without a trusted party. What is needed is an electronic payment system based on cryptographic proof instead of trust, allowing any two willing parties to transact directly with each other without the need for a trusted third party. Transactions that are computationally impractical to reverse would protect sellers from fraud, and routine escrow mechanisms could easily be implemented to protect buyers. In this paper, we propose a solution to the double-spending problem using a peer-to-peer distributed timestamp server to generate computational proof of the chronological order of transactions. The system is secure as long as honest nodes collectively control more CPU power than any cooperating group of attacker nodes. 1 2. Transactions We define an electronic coin as a chain of digital signatures. Each owner transfers the coin to the next by digitally signing a hash of the previous transaction and the public key of the next owner and adding these to the end of the coin. A payee can verify the signatures to verify the chain of ownership. Transaction Hash Transaction Hash Transaction Hash Owner 1's Public Key Owner 2's Public Key Owner 3's Public Key Owner 0's Signature Owner 1's Signature The problem of course is the payee can't verify that one of the owners did not double-spend the coin. A common solution is to introduce a trusted central authority, or mint, that checks every transaction for double spending. After each transaction, the coin must be returned to the mint to issue a new coin, and only coins issued directly from the mint are trusted not to be double-spent. The problem with this solution is that the fate of the entire money system depends on the company running the mint, with every transaction having to go through them, just like a bank. We need a way for the payee to know that the previous owners did not sign any earlier transactions. For our purposes, the earliest transaction is the one that counts, so we don't care about later attempts to double-spend. The only way to confirm the absence of a transaction is to be aware of all transactions. In the mint based model, the mint was aware of all transactions and decided which arrived first. To accomplish this without a trusted party, transactions must be publicly announced [1], and we need a system for participants to agree on a single history of the order in which they were received. The payee needs proof that at the time of each transaction, the majority of nodes agreed it was the first received. 3. Timestamp Server The solution we propose begins with a timestamp server. A timestamp server works by taking a hash of a block of items to be timestamped and widely publishing the hash, such as in a newspaper or Usenet post [2-5]. The timestamp proves that the data must have existed at the time, obviously, in order to get into the hash. Each timestamp includes the previous timestamp in its hash, forming a chain, with each additional timestamp reinforcing the ones before it. Hash Hash Owner 2's Signature Owner 1's Private Key Owner 2's Private Key Owner 3's Private Key Block Item Item ... 2 Block Item Item ... Verify Verify Sign Sign 4. Proof-of-Work To implement a distributed timestamp server on a peer-to-peer basis, we will need to use a proof- of-work system similar to Adam Back's Hashcash [6], rather than newspaper or Usenet posts. The proof-of-work involves scanning for a value that when hashed, such as with SHA-256, the hash begins with a number of zero bits. The average work required is exponential in the number of zero bits required and can be verified by executing a single hash. For our timestamp network, we implement the proof-of-work by incrementing a nonce in the block until a value is found that gives the block's hash the required zero bits. Once the CPU effort has been expended to make it satisfy the proof-of-work, the block cannot be changed without redoing the work. As later blocks are chained after it, the work to change the block would include redoing all the blocks after it. The proof-of-work also solves the problem of determining representation in majority decision making. If the majority were based on one-IP-address-one-vote, it could be subverted by anyone able to allocate many IPs. Proof-of-work is essentially one-CPU-one-vote. The majority decision is represented by the longest chain, which has the greatest proof-of-work effort invested in it. If a majority of CPU power is controlled by honest nodes, the honest chain will grow the fastest and outpace any competing chains. To modify a past block, an attacker would have to redo the proof-of-work of the block and all blocks after it and then catch up with and surpass the work of the honest nodes. We will show later that the probability of a slower attacker catching up diminishes exponentially as subsequent blocks are added. To compensate for increasing hardware speed and varying interest in running nodes over time, the proof-of-work difficulty is determined by a moving average targeting an average number of blocks per hour. If they're generated too fast, the difficulty increases. 5. Network The steps to run the network are as follows: 1) New transactions are broadcast to all nodes. 2) Each node collects new transactions into a block. 3) Each node works on finding a difficult proof-of-work for its block. 4) When a node finds a proof-of-work, it broadcasts the block to all nodes. 5) Nodes accept the block only if all transactions in it are valid and not already spent. 6) Nodes express their acceptance of the block by working on creating the next block in the chain, using the hash of the accepted block as the previous hash. Nodes always consider the longest chain to be the correct one and will keep working on extending it. If two nodes broadcast different versions of the next block simultaneously, some nodes may receive one or the other first. In that case, they work on the first one they received, but save the other branch in case it becomes longer. The tie will be broken when the next proof- of-work is found and one branch becomes longer; the nodes that were working on the other branch will then switch to the longer one. 3 Block Nonce Tx Tx ... Block Nonce Tx Tx ... Prev Hash Prev Hash New transaction broadcasts do not necessarily need to reach all nodes. As long as they reach many nodes, they will get into a block before long. Block broadcasts are also tolerant of dropped messages. If a node does not receive a block, it will request it when it receives the next block and realizes it missed one. 6. Incentive By convention, the first transaction in a block is a special transaction that starts a new coin owned by the creator of the block. This adds an incentive for nodes to support the network, and provides a way to initially distribute coins into circulation, since there is no central authority to issue them. The steady addition of a constant of amount of new coins is analogous to gold miners expending resources to add gold to circulation. In our case, it is CPU time and electricity that is expended. The incentive can also be funded with transaction fees. If the output value of a transaction is less than its input value, the difference is a transaction fee that is added to the incentive value of the block containing the transaction. Once a predetermined number of coins have entered circulation, the incentive can transition entirely to transaction fees and be completely inflation free. The incentive may help encourage nodes to stay honest. If a greedy attacker is able to assemble more CPU power than all the honest nodes, he would have to choose between using it to defraud people by stealing back his payments, or using it to generate new coins. He ought to find it more profitable to play by the rules, such rules that favour him with more new coins than everyone else combined, than to undermine the system and the validity of his own wealth. 7. Reclaiming Disk Space Once the latest transaction in a coin is buried under enough blocks, the spent transactions before it can be discarded to save disk space. To facilitate this without breaking the block's hash, transactions are hashed in a Merkle Tree [7][2][5], with only the root included in the block's hash. Old blocks can then be compacted by stubbing off branches of the tree. The interior hashes do not need to be stored. Block Hash0 Hash1 Hash2 Hash3 Tx0 Tx1 Tx2 Tx3 Block Header (Block Hash) Prev Hash Nonce Root Hash Hash01 Hash23 Block Block Header (Block Hash) Prev Hash Nonce Root Hash Hash01 Hash23 Hash2 Hash3 Tx3 Transactions Hashed in a Merkle Tree After Pruning Tx0-2 from the Block A block header with no transactions would be about 80 bytes. If we suppose blocks are generated every 10 minutes, 80 bytes * 6 * 24 * 365 = 4.2MB per year. With computer systems typically selling with 2GB of RAM as of 2008, and Moore's Law predicting current growth of 1.2GB per year, storage should not be a problem even if the block headers must be kept in memory. 4 8. Simplified Payment Verification It is possible to verify payments without running a full network node. A user only needs to keep a copy of the block headers of the longest proof-of-work chain, which he can get by querying network nodes until he's convinced he has the longest chain, and obtain the Merkle branch linking the transaction to the block it's timestamped in. He can't check the transaction for himself, but by linking it to a place in the chain, he can see that a network node has accepted it, and blocks added after it further confirm the network has accepted it. Longest Proof-of-Work Chain Block Header Block Header Block Header Prev Hash Nonce Prev Hash Nonce Prev Hash Nonce Merkle Root Merkle Root Merkle Root Hash01 Hash23 Merkle Branch for Tx3 Hash2 Hash3 Tx3 As such, the verification is reliable as long as honest nodes control the network, but is more vulnerable if the network is overpowered by an attacker. While network nodes can verify transactions for themselves, the simplified method can be fooled by an attacker's fabricated transactions for as long as the attacker can continue to overpower the network. One strategy to protect against this would be to accept alerts from network nodes when they detect an invalid block, prompting the user's software to download the full block and alerted transactions to confirm the inconsistency. Businesses that receive frequent payments will probably still want to run their own nodes for more independent security and quicker verification. 9. Combining and Splitting Value Although it would be possible to handle coins individually, it would be unwieldy to make a separate transaction for every cent in a transfer. To allow value to be split and combined, transactions contain multiple inputs and outputs. Normally there will be either a single input from a larger previous transaction or multiple inputs combining smaller amounts, and at most two outputs: one for the payment, and one returning the change, if any, back to the sender. It should be noted that fan-out, where a transaction depends on several transactions, and those transactions depend on many more, is not a problem here. There is never the need to extract a complete standalone copy of a transaction's history. 5 Transaction In Out In ... ... 10. Privacy The traditional banking model achieves a level of privacy by limiting access to information to the parties involved and the trusted third party. The necessity to announce all transactions publicly precludes this method, but privacy can still be maintained by breaking the flow of information in another place: by keeping public keys anonymous. The public can see that someone is sending an amount to someone else, but without information linking the transaction to anyone. This is similar to the level of information released by stock exchanges, where the time and size of individual trades, the "tape", is made public, but without telling who the parties were. Traditional Privacy Model Identities Transactions New Privacy Model Identities Transactions As an additional firewall, a new key pair should be used for each transaction to keep them from being linked to a common owner. Some linking is still unavoidable with multi-input transactions, which necessarily reveal that their inputs were owned by the same owner. The risk is that if the owner of a key is revealed, linking could reveal other transactions that belonged to the same owner. 11. Calculations We consider the scenario of an attacker trying to generate an alternate chain faster than the honest chain. Even if this is accomplished, it does not throw the system open to arbitrary changes, such as creating value out of thin air or taking money that never belonged to the attacker. Nodes are not going to accept an invalid transaction as payment, and honest nodes will never accept a block containing them. An attacker can only try to change one of his own transactions to take back money he recently spent. The race between the honest chain and an attacker chain can be characterized as a Binomial Random Walk. The success event is the honest chain being extended by one block, increasing its lead by +1, and the failure event is the attacker's chain being extended by one block, reducing the gap by -1. The probability of an attacker catching up from a given deficit is analogous to a Gambler's Ruin problem. Suppose a gambler with unlimited credit starts at a deficit and plays potentially an infinite number of trials to try to reach breakeven. We can calculate the probability he ever reaches breakeven, or that an attacker ever catches up with the honest chain, as follows [8]: p = probability an honest node finds the next block q = probability the attacker finds the next block qz = probability the attacker will ever catch up from z blocks behind Trusted Third Party q ={ 1 if p≤q} z q/pz if pq 6 Counterparty Public Public Given our assumption that p > q, the probability drops exponentially as the number of blocks the attacker has to catch up with increases. With the odds against him, if he doesn't make a lucky lunge forward early on, his chances become vanishingly small as he falls further behind. We now consider how long the recipient of a new transaction needs to wait before being sufficiently certain the sender can't change the transaction. We assume the sender is an attacker who wants to make the recipient believe he paid him for a while, then switch it to pay back to himself after some time has passed. The receiver will be alerted when that happens, but the sender hopes it will be too late. The receiver generates a new key pair and gives the public key to the sender shortly before signing. This prevents the sender from preparing a chain of blocks ahead of time by working on it continuously until he is lucky enough to get far enough ahead, then executing the transaction at that moment. Once the transaction is sent, the dishonest sender starts working in secret on a parallel chain containing an alternate version of his transaction. The recipient waits until the transaction has been added to a block and z blocks have been linked after it. He doesn't know the exact amount of progress the attacker has made, but assuming the honest blocks took the average expected time per block, the attacker's potential progress will be a Poisson distribution with expected value:  = z qp To get the probability the attacker could still catch up now, we multiply the Poisson density for each amount of progress he could have made by the probability he could catch up from that point: ∞ ke−{q/pz−k ifk≤z} ∑k=0 k!⋅ 1 ifkz Rearranging to avoid summing the infinite tail of the distribution... z ke− z−k 1−∑k=0 k! 1−q/p  Converting to C code... #include <math.h> double AttackerSuccessProbability(double q, int z) { double p = 1.0 - q; double lambda = z * (q / p); double sum = 1.0; int i, k; for (k = 0; k <= z; k++) { double poisson = exp(-lambda); for (i = 1; i <= k; i++) poisson *= lambda / i; sum -= poisson * (1 - pow(q / p, z - k)); } return sum; } 7 Running some results, we can see the probability drop off exponentially with z. q=0.1 z=0 P=1.0000000 z=1 P=0.2045873 z=2 P=0.0509779 z=3 P=0.0131722 z=4 P=0.0034552 z=5 P=0.0009137 z=6 P=0.0002428 z=7 P=0.0000647 z=8 P=0.0000173 z=9 P=0.0000046 z=10 P=0.0000012 q=0.3 z=0 P=1.0000000 z=5 P=0.1773523 z=10 P=0.0416605 z=15 P=0.0101008 z=20 P=0.0024804 z=25 P=0.0006132 z=30 P=0.0001522 z=35 P=0.0000379 z=40 P=0.0000095 z=45 P=0.0000024 z=50 P=0.0000006 Solving for P less than 0.1%... P < 0.001 q=0.10 z=5 q=0.15 z=8 q=0.20 z=11 q=0.25 z=15 q=0.30 z=24 q=0.35 z=41 q=0.40 z=89 q=0.45 z=340 12. Conclusion We have proposed a system for electronic transactions without relying on trust. We started with the usual framework of coins made from digital signatures, which provides strong control of ownership, but is incomplete without a way to prevent double-spending. To solve this, we proposed a peer-to-peer network using proof-of-work to record a public history of transactions that quickly becomes computationally impractical for an attacker to change if honest nodes control a majority of CPU power. The network is robust in its unstructured simplicity. Nodes work all at once with little coordination. They do not need to be identified, since messages are not routed to any particular place and only need to be delivered on a best effort basis. Nodes can leave and rejoin the network at will, accepting the proof-of-work chain as proof of what happened while they were gone. They vote with their CPU power, expressing their acceptance of valid blocks by working on extending them and rejecting invalid blocks by refusing to work on them. Any needed rules and incentives can be enforced with this consensus mechanism. 8 References [1] W. Dai, "b-money," http://www.weidai.com/bmoney.txt, 1998. [2] H. Massias, X.S. Avila, and J.-J. Quisquater, "Design of a secure timestamping service with minimal trust requirements," In 20th Symposium on Information Theory in the Benelux, May 1999. [3] S. Haber, W.S. Stornetta, "How to time-stamp a digital document," In Journal of Cryptology, vol 3, no 2, pages 99-111, 1991. [4] D. Bayer, S. Haber, W.S. Stornetta, "Improving the efficiency and reliability of digital time-stamping," In Sequences II: Methods in Communication, Security and Computer Science, pages 329-334, 1993. [5] S. Haber, W.S. Stornetta, "Secure names for bit-strings," In Proceedings of the 4th ACM Conference on Computer and Communications Security, pages 28-35, April 1997. [6] A. Back, "Hashcash - a denial of service counter-measure," http://www.hashcash.org/papers/hashcash.pdf, 2002. [7] R.C. Merkle, "Protocols for public key cryptosystems," In Proc. 1980 Symposium on Security and Privacy, IEEE Computer Society, pages 122-133, April 1980. [8] W. Feller, "An introduction to probability theory and its applications," 1957. 9

This repo is all about how Data Science can improve and facilitate financial analytics using python libraries.

Coursera Course Link: https://www.coursera.org/professional-certificates/ibm-data-science Instructions: Now that you have been equipped with the skills and the tools to use location data to explore a geographical location, over the course of two weeks, you will have the opportunity to be as creative as you want and come up with an idea to leverage the Foursquare location data to explore or compare neighborhoods or cities of your choice or to come up with a problem that you can use the Foursquare location data to solve. If you cannot think of an idea or a problem, here are some ideas to get you started: In Module 3 We explored New York City and the city of Toronto and segmented and clustered their neighborhoods. Both cities are very diverse and are the financial capitals of their respective countries. One interesting idea would be to compare the neighborhoods of the two cities and determine how similar or dissimilar they are. Is New York City more like Toronto or Paris or some other multicultural city? I will leave it to you to refine this idea. In a city of your choice, if someone is looking to open a restaurant, where would you recommend that they open it? Similarly, if a contractor is trying to start their own business, where would you recommend that they setup their office? These are just a couple of many ideas and problems that can be solved using location data in addition to other datasets. No matter what you decide to do, make sure to provide sufficient justification of why you think what you want to do or solve is important and why would a client or a group of people be interested in your project. Review criteria This capstone project will be graded by your peers. This capstone project is worth 70% of your total grade. The project will be completed over the course of 2 weeks. Week 1 submissions will be worth 30% whereas week 2 submissions will be worth 40% of your total grade. For this week, you will required to submit the following: A description of the problem and a discussion of the background. (15 marks) A description of the data and how it will be used to solve the problem. (15 marks) For the second week, the final deliverables of the project will be: A link to your Notebook on your Github repository, showing your code. (15 marks) A full report consisting of all of the following components (15 marks): Introduction where you discuss the business problem and who would be interested in this project. Data where you describe the data that will be used to solve the problem and the source of the data. Methodology section which represents the main component of the report where you discuss and describe any exploratory data analysis that you did, any inferential statistical testing that you performed, if any, and what machine learnings were used and why. Results section where you discuss the results. Discussion section where you discuss any observations you noted and any recommendations you can make based on the results. Conclusion section where you conclude the report. Your choice of a presentation or blogpost. (10 marks) My Submission Clearly define a problem or an idea of your choice, where you would need to leverage the Foursquare location data to solve or execute. Remember that data science problems always target an audience and are meant to help a group of stakeholders solve a problem, so make sure that you explicitly describe your audience and why they would care about your problem. This submission will eventually become your Introduction/Business Problem section in your final report. So I recommend that you push the report (having your Introduction/Business Problem section only for now) to your Github repository and submit a link to it. Text Box For Link: Describe the data that you will be using to solve the problem or execute your idea. Remember that you will need to use the Foursquare location data to solve the problem or execute your idea. You can absolutely use other datasets in combination with the Foursquare location data. So make sure that you provide adequate explanation and discussion, with examples, of the data that you will be using, even if it is only Foursquare location data. This submission will eventually become your Data section in your final report. So I recommend that you push the report (having your Data section) to your Github repository and submit a link to it. Text Box For Link:

A sequential business visionary, Prof. Alex has more than two many years of experience during which he has worked crosswise over different ventures with organizations, for example, Scout Electromedia, SOMA Networks, BroadSoft, and Singularity Networks, and even established three organizations. In the times past, a specialist would choose what ought to be constructed, a coder would code it, a client would utilize it(maybe), and after that an investigator would attempt to make sense of what occurred. Today, high-performing organizations sanction interdisciplinary groups to iteratively improve results in a specific territory utilizing light-footed. That is somewhat dynamic; so here’s a progressively substantial perspective on what it implies by and by: That is a testable depiction of deft and you’ll know it’s working if: a) The group is utilizing ceaseless plan to improve the level of highlights that see high commitment b) The group is utilizing dexterous to build their speed as far as highlight yield c) The group is utilizing DevOps to make an increasingly ceaseless pipeline and discharge to clients all the more as often as possible Where do investigation become an integral factor? Not toward the end, and not afterward. An advanced group is utilizing lithe investigation to carry center and cognizance to their work crosswise over structure, coding, and conveyance. How would you know whether you’re getting to coordinated examination? I’ve watched seven central focuses with groups that have an advanced practice: All Ideas are Testable: When I got some information about his organization’s routine with regards to nimble, a CTO companion of mine let me know: ‘You know; you can’t simply take a multi month thought, cut it into fourteen day emphasess, and get coordinated’. We’re terrible at making our thoughts testable. I’ve differently been an originator, CEO, guide, and financial specialist for quite a long time, and when I get another thought, despite everything I begin with ‘Would n’t it be cool if’. Furthermore, that is alright, yet not once you choose to build up that thought. By then, render your thought testable. I like if the plan ‘In the event that we accomplish something for some particular persona or fragment, at that point they will react in some particular, quantifiable way’. For instance, in the event that we ran an organization that fixes cooling frameworks and chose it is cool to make an application for our field experts, we may render something like ‘On the off chance that we manufacture an application for the field specialists, at that point they will utilize it and it will build their billable hours’. Enormous Ideas Get Tested: This is the embodiment of Lean Startup. So as to limit squander, thoughts get tried with item intermediaries (MVPs) before they’re contender for being constructed. What’s more, a ton of organizations have a group off some place accomplishing something Lean Startup-ish. Be that as it may, do the huge thoughts get tried? The ones that the organization is putting truckloads of money in and trusting will drive its natural development? That is the significant inquiry. “Past the conspicuous advantage of utilizing proof to locate the correct plan early, model testing likewise makes a progressively engaged and rational change to investigation in the product once it’s discharged” All User Stories are Readily Testable: The client story fills in as a highlight for iterative improvement. It has the organization ‘As a client persona, I need to accomplish something so I can accomplish some testable reward’. That last statement about the testable reward? That is very significant and a foundation of spry investigation. For each client story, it ought to be clear how you would model that story, place it before a guinea pig, brief them with an objective, and check whether they accomplish that objective or not. Key User Stories get Tested: And do key client stories get tried? I complete a great deal of work with groups and we invest energy recorded as a hard copy increasingly testable client stories. I’ve never met any individual who thought composing better client stories was a poorly conceived notion. In any case, the groups make a propensity for testing early and frequently, with intuitive models for example, that really stay with the act of making their accounts testable. Past the undeniable advantage of utilizing proof to locate the correct structure early, model testing additionally makes a progressively engaged and reasonable change to examination in the product once it’s discharged. Analyses are Instrumented into Code: Instrumenting examination into code is simple and reasonable, and most organizations do it. All things considered, the group’s conveying solid, client driven theories through their item pipeline that is going to pick the privilege central focuses for the investigations those perceptions are supporting. For instance, one anticipate our Masters of Science in Business Analytics understudies are chipping away at is the USFDA’s ‘MedWatch’ site. On it, clients submit data about antagonistic responses to drugs. Suppose we’re attempting to make it simpler for a bustling specialist to present these responses so as to expand the information we gather. What would it be a good idea for us to A/B test? There are a great deal of ‘fascinating’ conceivable outcomes, however without approved learning on what that specialist is thinking and needing when they visit the site, we’re probably not going to put resources into A/B tests that truly move the needle on execution. Examination are Part of Retrospectives: Successful groups don’t demo their product; they translate tests. Working in short 1-multi week dashes is a typical element of lithe. Groups talk about how things went, and why and how they need to change their routine with regards to deft. Fortunately, this is normal practice. What’s less basic is for groups to make a propensity for looking into their investigations during those reviews. Eventually, we’re animals of propensity, thus, a group that is not unequivocally making time to audit their examinations is likely not going to get to deft investigation. Choices are Implied by Analytics: Are choices suggested by the group’s examination, or is the arrangement just to ‘audit the numbers’? The group that is rehearsing spry examination definitely knows the ramifications of their perceptions, on the grounds that their perceptions are attached to tests and the analyses are attached to choices. For instance, would you say you are truly prepared to slaughter that element in the event that it sees low commitment? Imagine a scenario where a client grumbles and says they totally must have it. Dexterous investigation makes the activity of choosing simple. for more information click here : technology.siliconindia.com

Global "PTFE CCL Market" 2022 compromises many advantages that have accelerated the adoption of absorption among various industrial users. These elements make absorption an attractive option from the industrial sector and enable many industrial customers to meet their environmental and regulatory targets. The PTFE CCL industry is expected to remain innovation-led, with frequent achievements and strategic deals adopted as the key strategies by the players to increase their industry presence. The report covers the present scenario and the growth prospects of the PTFE CCL market for 2022-2026. Global PTFE CCL market size is estimated to grow at CAGR of almost 9.6% with USD 750.1 million during the forecast period 2022-2026. 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Key Stakeholders in the Global PTFE CCL Market: Raw material suppliers Distributors/traders/wholesalers/suppliers Regulatory bodies, including government agencies and NGO Commercial research and development (RandD) institutions Importers and exporters Government organizations, research organizations, and consulting firms Trade associations and industry bodies End-use industries Purchase this report (Price 2900 USD for a single user license) - https://www.businessresearchinsights.com/checkout-page/100051 Table of Content: 1 PTFE CCL Market Overview 1.1 Product Overview and Scope of PTFE CCL 1.2 PTFE CCL Segment by Type 1.2.1 Global PTFE CCL Market Size Growth Rate Analysis by Type 2021 VS 2027 1.2.2 PTFE/Fibreglass Type 1.2.3 PTFE/Filled Type 1.2.4 Others 1.3 PTFE CCL Segment by Application 1.3.1 Global PTFE CCL Consumption Comparison by Application: 2016 VS 2021 VS 2027 1.3.2 Communication Infrastructure 1.3.3 Electronics Product 1.3.4 Automotive 1.3.5 Defense 1.3.6 Others 1.4 Global Market Growth Prospects 1.4.1 Global PTFE CCL Revenue Estimates and Forecasts (2016-2027) 1.4.2 Global PTFE CCL Production Capacity Estimates and Forecasts (2016-2027) 1.4.3 Global PTFE CCL Production Estimates and Forecasts (2016-2027) 1.5 Global PTFE CCL Market by Region 1.5.1 Global PTFE CCL Market Size Estimates and Forecasts by Region: 2016 VS 2021 VS 2027 1.5.2 North America PTFE CCL Estimates and Forecasts (2016-2027) 1.5.3 Europe PTFE CCL Estimates and Forecasts (2016-2027) 1.5.5 China PTFE CCL Estimates and Forecasts (2016-2027) 1.5.5 Japan PTFE CCL Estimates and Forecasts (2016-2027) 1.5.6 South Korea PTFE CCL Estimates and Forecasts (2016-2027) 2 Market Competition by Manufacturers 2.1 Global PTFE CCL Production Capacity Market Share by Manufacturers (2016-2021) 2.2 Global PTFE CCL Revenue Market Share by Manufacturers (2016-2021) 2.3 PTFE CCL Market Share by Company Type (Tier 1, Tier 2 and Tier 3) 2.4 Global PTFE CCL Average Price by Manufacturers (2016-2021) 2.5 Manufacturers PTFE CCL Production Sites, Area Served, Product Types 2.6 PTFE CCL Market Competitive Situation and Trends 2.6.1 PTFE CCL Market Concentration Rate 2.6.2 Global 5 and 10 Largest PTFE CCL Players Market Share by Revenue 2.6.3 Mergers & Acquisitions, Expansion 3 Production and Capacity by Region 3.1 Global Production Capacity of PTFE CCL Market Share by Region (2016-2021) 3.2 Global PTFE CCL Revenue Market Share by Region (2016-2021) 3.3 Global PTFE CCL Production, Revenue, Price and Gross Margin (2016-2021) 3.4 North America PTFE CCL Production 3.4.1 North America PTFE CCL Production Growth Rate (2016-2021) 3.4.2 North America PTFE CCL Production Capacity, Revenue, Price and Gross Margin (2016-2021) 3.5 Europe PTFE CCL Production 3.5.1 Europe PTFE CCL Production Growth Rate (2016-2021) 3.5.2 Europe PTFE CCL Production Capacity, Revenue, Price and Gross Margin (2016-2021) 3.6 China PTFE CCL Production 3.6.1 China PTFE CCL Production Growth Rate (2016-2021) 3.6.2 China PTFE CCL Production Capacity, Revenue, Price and Gross Margin (2016-2021) 3.7 Japan PTFE CCL Production 3.7.1 Japan PTFE CCL Production Growth Rate (2016-2021) 3.7.2 Japan PTFE CCL Production Capacity, Revenue, Price and Gross Margin (2016-2021) 3.8 South Korea PTFE CCL Production 3.8.1 South Korea PTFE CCL Production Growth Rate (2016-2021) 3.8.2 South Korea PTFE CCL Production Capacity, Revenue, Price and Gross Margin (2016-2021) 4 Global PTFE CCL Consumption by Region 4.1 Global PTFE CCL Consumption by Region 4.1.1 Global PTFE CCL Consumption by Region 4.1.2 Global PTFE CCL Consumption Market Share by Region 4.2 North America 4.2.1 North America PTFE CCL Consumption by Country 4.2.2 U.S. 4.2.3 Canada 4.3 Europe 4.3.1 Europe PTFE CCL Consumption by Country 4.3.2 Germany 4.3.3 France 4.3.4 U.K. 4.3.5 Italy 4.3.6 Russia 4.4 Asia Pacific 4.4.1 Asia Pacific PTFE CCL Consumption by Region 4.4.2 China 4.4.3 Japan 4.4.4 South Korea 4.4.5 Taiwan 4.4.6 Southeast Asia 4.4.7 India 4.4.8 Australia 4.5 Latin America 4.5.1 Latin America PTFE CCL Consumption by Country 4.5.2 Mexico 4.5.3 Brazil 5 Production, Revenue, Price Trend by Type 5.1 Global PTFE CCL Production Market Share by Type (2016-2021) 5.2 Global PTFE CCL Revenue Market Share by Type (2016-2021) 5.3 Global PTFE CCL Price by Type (2016-2021) 6 Consumption Analysis by Application 6.1 Global PTFE CCL Consumption Market Share by Application (2016-2021) 6.2 Global PTFE CCL Consumption Growth Rate by Application (2016-2021) 7 Key Companies Profiled 7.1 Rogers Corporation 7.1.1 Rogers Corporation PTFE CCL Corporation Information 7.1.2 Rogers Corporation PTFE CCL Product Portfolio 7.1.3 Rogers Corporation PTFE CCL Production Capacity, Revenue, Price and Gross Margin (2016-2021) 7.1.4 Rogers Corporation Main Business and Markets Served 7.1.5 Rogers Corporation Recent Developments/Updates 7.2 Taconic 7.2.1 Taconic PTFE CCL Corporation Information 7.2.2 Taconic PTFE CCL Product Portfolio 7.2.3 Taconic PTFE CCL Production Capacity, Revenue, Price and Gross Margin (2016-2021) 7.2.4 Taconic Main Business and Markets Served 7.2.5 Taconic Recent Developments/Updates 7.3 AGC 7.3.1 AGC PTFE CCL Corporation Information 7.3.2 AGC PTFE CCL Product Portfolio 7.3.3 AGC PTFE CCL Production Capacity, Revenue, Price and Gross Margin (2016-2021) 7.3.4 AGC Main Business and Markets Served 7.3.5 AGC Recent Developments/Updates 7.4 Chukoh 7.4.1 Chukoh PTFE CCL Corporation Information 7.4.2 Chukoh PTFE CCL Product Portfolio 7.4.3 Chukoh PTFE CCL Production Capacity, Revenue, Price and Gross Margin (2016-2021) 7.4.4 Chukoh Main Business and Markets Served 7.4.5 Chukoh Recent Developments/Updates 7.5 Shengyi Technology 7.5.1 Shengyi Technology PTFE CCL Corporation Information 7.5.2 Shengyi Technology PTFE CCL Product Portfolio 7.5.3 Shengyi Technology PTFE CCL Production Capacity, Revenue, Price and Gross Margin (2016-2021) 7.5.4 Shengyi Technology Main Business and Markets Served 7.5.5 Shengyi Technology Recent Developments/Updates 7.6 Zhongying Science & Technology 7.6.1 Zhongying Science & Technology PTFE CCL Corporation Information 7.6.2 Zhongying Science & Technology PTFE CCL Product Portfolio 7.6.3 Zhongying Science & Technology PTFE CCL Production Capacity, Revenue, Price and Gross Margin (2016-2021) 7.6.4 Zhongying Science & Technology Main Business and Markets Served 7.6.5 Zhongying Science & Technology Recent Developments/Updates 8 PTFE CCL Manufacturing Cost Analysis 8.1 PTFE CCL Key Raw Materials Analysis 8.1.1 Key Raw Materials 8.1.2 Key Raw Materials Price Trend 8.1.3 Key Suppliers of Raw Materials 8.2 Proportion of Manufacturing Cost Structure 8.3 Manufacturing Process Analysis of PTFE CCL 8.4 PTFE CCL Industrial Chain Analysis 9 Marketing Channel, Distributors and Customers 9.1 Marketing Channel 9.2 PTFE CCL Distributors List 9.3 PTFE CCL Customers 10 Market Dynamics 10.1 PTFE CCL Industry Trends 10.2 PTFE CCL Growth Drivers 10.3 PTFE CCL Market Challenges 10.4 PTFE CCL Market Restraints 11 Production and Supply Forecast 11.1 Global Forecasted Production of PTFE CCL by Region (2022-2027) 11.2 North America PTFE CCL Production, Revenue Forecast (2022-2027) 11.3 Europe PTFE CCL Production, Revenue Forecast (2022-2027) 11.4 China PTFE CCL Production, Revenue Forecast (2022-2027) 11.5 Japan PTFE CCL Production, Revenue Forecast (2022-2027) 11.6 South Korea PTFE CCL Production, Revenue Forecast (2022-2027) 12 Consumption and Demand Forecast 12.1 Global Forecasted Demand Analysis of PTFE CCL 12.2 North America Forecasted Consumption of PTFE CCL by Country 12.3 Europe Market Forecasted Consumption of PTFE CCL by Country 12.4 Asia Pacific Market Forecasted Consumption of PTFE CCL by Region 12.5 Latin America Forecasted Consumption of PTFE CCL by Country 13 Forecast by Type and by Application (2022-2027) 13.1 Global Production, Revenue and Price Forecast by Type (2022-2027) 13.1.1 Global Forecasted Production of PTFE CCL by Type (2022-2027) 13.1.2 Global Forecasted Revenue of PTFE CCL by Type (2022-2027) 13.1.3 Global Forecasted Price of PTFE CCL by Type (2022-2027) 13.2 Global Forecasted Consumption of PTFE CCL by Application (2022-2027) 14 Research Finding and Conclusion 15 Methodology and Data Source 15.1 Methodology/Research Approach 15.1.1 Research Programs/Design 15.1.2 Market Size Estimation 15.1.3 Market Breakdown and Data Triangulation 15.2 Data Source 15.2.1 Secondary Sources 15.2.2 Primary Sources 15.3 Author List 15.4 Disclaimer Browse complete table of contents at - https://www.businessresearchinsights.com/market-reports/toc/100051 About Us: Business Research Insights is a unique organization that offers expert analysis and accurate data-based market intelligence, aiding companies of all shapes and sizes to make well-informed decisions. We tailor inventive solutions for our clients, helping them tackle any challenges that are likely to emerge from time to time and affect their businesses. Contact Us: Business Research Insights Phone: US: +1 424 253 0807 UK: +44 203 239 8187 Email: sales@businessresearchinsights.com Web: https://www.businessresearchinsights.com