Primecoin paper store
Showing of 76 extracted citations. Brooks 14th Annual Conference on Privacy, Security…. Be Selfish and Avoid Dilemmas: Repurposing bitcoin work for data preservation. Majority Is Not Enough: Alydian targets big ticket miners with terahash hosting.
Government shutdown closes Library of Congress — online too. Cryptocurrency with prime number proof-of-work. Kroll , Ian C. Davey , Edward W. However, news servers communicate with one another as peers to propagate Usenet news articles over the group of network servers.
In May , with more people on the Internet, Shawn Fanning introduced the music. A peer-to-peer network is designed around the notion of equal peer nodes simultaneously functioning as both clients and servers to the nodes on the network. This model of network arrangement differs from the model where communication is usually to. Overlays are used for indexing and peer discovery, and make the P2P system independent from the network topology. Based on how the nodes are linked to each other within the overlay network, unstructured peer-to-peer networks do not impose a particular structure on the overlay network by design, but rather are formed by nodes that randomly form connections to each other.
Communications protocol — These are the rules or standard that defines the syntax, semantics and synchronization of communication and possible error recovery methods. Protocols may be implemented by hardware, software, or a combination of both, Communicating systems use well-defined formats for exchanging various messages. Each message has a meaning intended to elicit a response from a range of possible responses pre-determined for that particular situation.
The specified behavior is independent of how it is to be implemented. Communications protocols have to be agreed upon by the parties involved, to reach agreement, a protocol may be developed into a technical standard. Multiple protocols often describe different aspects of a single communication, a group of protocols designed to work together are known as a protocol suite, when implemented in software they are a protocol stack.
As the PSTN and Internet converge, the two sets of standards are also being driven towards convergence, the nature of a communication, the actual data exchanged and any state-dependent behaviors, is defined by these specifications. In digital computing systems, the rules can be expressed by algorithms, expressing the algorithms in a portable programming language makes the protocol software operating-system independent.
Operating systems usually contain a set of cooperating processes that manipulate shared data to communicate each other. This communication is governed by protocols, which can be embedded in the process code itself. In contrast, because there is no memory, communicating systems have to communicate with each other using a shared transmission medium. Transmission is not necessarily reliable, and individual systems may use different hardware or operating systems, to implement a networking protocol, the protocol software modules are interfaced with a framework implemented on the machines operating system.
This framework implements the functionality of the operating system. Systems typically do not use a protocol to handle a transmission. Instead they use a set of cooperating protocols, sometimes called a family or protocol suite.
Open-source model — Open-source software may be developed in a collaborative public manner. In the early days of computing, programmers and developers shared software in order to learn from each other, eventually the open source notion moved to the way side of commercialization of software in the years Netscapes act prompted Raymond and others to look into how to bring the Free Software Foundations free software ideas, the new term they chose was open source, which was soon adopted by Bruce Perens, publisher Tim OReilly, Linus Torvalds, and others.
The Open Source Initiative was founded in February to encourage use of the new term, a Microsoft executive publicly stated in that open source is an intellectual property destroyer. I cant imagine something that could be worse than this for the software business, IBM, Oracle, Google and State Farm are just a few of the companies with a serious public stake in todays competitive open-source market.
There has been a significant shift in the corporate philosophy concerning the development of FOSS, the free software movement was launched in In , a group of individuals advocated that the free software should be replaced by open-source software as an expression which is less ambiguous.
Software developers may want to publish their software with an open-source license, the Open Source Definition, notably, presents an open-source philosophy, and further defines the terms of usage, modification and redistribution of open-source software. Software licenses grant rights to users which would otherwise be reserved by law to the copyright holder. Several open-source software licenses have qualified within the boundaries of the Open Source Definition, the open source label came out of a strategy session held on April 7, in Palo Alto in reaction to Netscapes January announcement of a source code release for Navigator.
They used the opportunity before the release of Navigators source code to clarify a potential confusion caused by the ambiguity of the free in English. Many people claimed that the birth of the Internet, since , started the open source movement, the Free Software Foundation, started in , intended the word free to mean freedom to distribute and not freedom from cost. Since a great deal of free software already was free of charge, such software became associated with zero cost.
The Open Source Initiative was formed in February by Eric Raymond and they sought to bring a higher profile to the practical benefits of freely available source code, and they wanted to bring major software businesses and other high-tech industries into open source.
Perens attempted to open source as a service mark for the OSI. The Open Source Initiatives definition is recognized by governments internationally as the standard or de facto definition, OSI uses The Open Source Definition to determine whether it considers a software license open source.
Proof-of-work system — The concept may have been first presented by Cynthia Dwork and Moni Naor in a journal article. The term Proof of Work or POW was first coined and formalized in a paper by Markus Jakobsson, a key feature of these schemes is their asymmetry, the work must be moderately hard on the requester side but easy to check for the service provider.
This idea is known as a CPU cost function, client puzzle. Proof of bandwidth approaches have been discussed in the context of cryptocurrency, Proof of ownership aims at proving that specific data are held by the prover. One popular system—used in bitcoin mining and Hashcash— uses partial hash inversions to prove that work was done, as a good-will token to send an e-mail. There are two classes of proof-of-work protocols, challenge-response protocols assume a direct interactive link between the requester and the provider.
The provider chooses a challenge, say an item in a set with a property, the requester finds the relevant response in the set, as the challenge is chosen on the spot by the provider, its difficulty can be adapted to its current load.
The work on the side may be bounded if the challenge-response protocol has a known solution. Most such schemes are unbounded probabilistic iterative procedures such as Hashcash, a generic technique for reducing variance is to use multiple independent sub-challenges, as the average of multiple samples will have lower variance. There are also fixed-cost functions such as the time-lock puzzle, memory-bound where the computation speed is bound by main memory accesses, the performance of which is expected to be less sensitive to hardware evolution.
Network-bound if the client must perform few computations, but must collect some tokens from remote servers before querying the final service provider, in this sense the work is not actually performed by the requester, but it incurs delays anyway because of the latency to get the required tokens.
Finally, some POW systems offer shortcut computations that allow participants who know a secret, typically a private key, the rationale is that mailing-list holders may generate stamps for every recipient without incurring a high cost.
Whether such a feature is desirable depends on the usage scenario, the idea of making proofs-of-work reusable for some practical purpose had already been established in Prime number — A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
A natural number greater than 1 that is not a number is called a composite number. For example,5 is prime because 1 and 5 are its only positive integer factors, the property of being prime is called primality. A simple but slow method of verifying the primality of a number n is known as trial division. It consists of testing whether n is a multiple of any integer between 2 and n, algorithms much more efficient than trial division have been devised to test the primality of large numbers.
Particularly fast methods are available for numbers of forms, such as Mersenne numbers. As of January , the largest known prime number has 22,, decimal digits, there are infinitely many primes, as demonstrated by Euclid around BC. There is no simple formula that separates prime numbers from composite numbers.
However, the distribution of primes, that is to say, many questions regarding prime numbers remain open, such as Goldbachs conjecture, and the twin prime conjecture. Such questions spurred the development of branches of number theory. Prime numbers give rise to various generalizations in other domains, mainly algebra, such as prime elements. A natural number is called a number if it has exactly two positive divisors,1 and the number itself. Natural numbers greater than 1 that are not prime are called composite, among the numbers 1 to 6, the numbers 2,3, and 5 are the prime numbers, while 1,4, and 6 are not prime.
Peercoin — Peercoin, also known as PPCoin or PPC, is a peer-to-peer cryptocurrency utilizing both proof-of-stake and proof-of-work systems. Peercoin is based on an August paper which listed the authors as Scott Nadal, Sunny King, who also created Primecoin, is a pseudonym. Nadals involvement had diminished by November , leaving King as Peercoins sole core developer, Peercoin was inspired by bitcoin, and it shares much of the source code and technical implementation of bitcoin.
Unlike bitcoin, Namecoin, and Litecoin, Peercoin does not have a limit on the number of possible coins. There is an aspect to Peercoin as the transaction fee of 0. This feature, along with increased efficiency, aim to allow for greater long-term scalability.
A peer-to-peer network handles Peercoins transactions, balances and issuance through SHA, Peercoins are currently traded for fiat currencies, bitcoins, and other cryptocurrencies, mostly on online exchanges. Reversible transactions are not normally used to buy Peercoins as Peercoin transactions are irreversible, payments in the Peercoin network are made to addresses, which are based on digital signatures.
They are strings of 34 numbers and letters which begin with the letter P. One can create as many addresses as needed without spending any Peercoins and it is quite common to use one address for one purpose only which makes it easy to see who actually sent the Peercoins.
New coins can be created in two different ways, mining and minting, mining uses the SHA algorithm to directly secure the network.
Minting rewards users in proportion to the coins that they hold, there are long term plans to reduce gradually the amount of mining and to rely more on minting. This is to create a distribution and could lead to an increase in the reward from minting. With bitcoin, for example, there is a risk of resulting from a monopoly on mining share. Massachusetts Institute of Technology — The Massachusetts Institute of Technology is a private research university in Cambridge, Massachusetts, often cited as one of the worlds most prestigious universities.
Researchers worked on computers, radar, and inertial guidance during World War II, post-war defense research contributed to the rapid expansion of the faculty and campus under James Killian. The current acre campus opened in and extends over 1 mile along the bank of the Charles River basin. The Institute is traditionally known for its research and education in the sciences and engineering, and more recently in biology, economics, linguistics. Air Force and 6 Fields Medalists have been affiliated with MIT, the school has a strong entrepreneurial culture, and the aggregated revenues of companies founded by MIT alumni would rank as the eleventh-largest economy in the world.
In , a proposal was submitted to the Massachusetts General Court to use newly filled lands in Back Bay, Boston for a Conservatory of Art and Science, but the proposal failed. A charter for the incorporation of the Massachusetts Institute of Technology, Rogers, a professor from the University of Virginia, wanted to establish an institution to address rapid scientific and technological advances.
The Rogers Plan reflected the German research university model, emphasizing an independent faculty engaged in research, as well as instruction oriented around seminars, two days after the charter was issued, the first battle of the Civil War broke out. After a long delay through the war years, MITs first classes were held in the Mercantile Building in Boston in , in under the same act, the Commonwealth of Massachusetts founded the Massachusetts Agricultural College, which developed as the University of Massachusetts Amherst.
In , the proceeds from sales went toward new buildings in the Back Bay. MIT was informally called Boston Tech, the institute adopted the European polytechnic university model and emphasized laboratory instruction from an early date. Despite chronic financial problems, the institute saw growth in the last two decades of the 19th century under President Francis Amasa Walker. Programs in electrical, chemical, marine, and sanitary engineering were introduced, new buildings were built, the curriculum drifted to a vocational emphasis, with less focus on theoretical science.
The fledgling school still suffered from chronic financial shortages which diverted the attention of the MIT leadership, during these Boston Tech years, MIT faculty and alumni rebuffed Harvard University president Charles W. There would be at least six attempts to absorb MIT into Harvard, in its cramped Back Bay location, MIT could not afford to expand its overcrowded facilities, driving a desperate search for a new campus and funding.
However, a decision by the Massachusetts Supreme Judicial Court effectively put an end to the merger scheme, the neoclassical New Technology campus was designed by William W. Bosworth and had been funded largely by anonymous donations from a mysterious Mr. Smith, starting in In January , the donor was revealed to be the industrialist George Eastman of Rochester, New York, who had invented methods of production and processing. X provides the framework for a GUI environment, drawing and moving windows on the display device and interacting with a mouse.
X does not mandate the user interface — this is handled by individual programs, as such, the visual styling of X-based environments varies greatly, different programs may present radically different interfaces.
X originated at the Massachusetts Institute of Technology in , the protocol has been version 11 since September Org Foundation leads the X project, with the current reference implementation, X. Org Server, available as free and open source software under the MIT License, X is an architecture-independent system for remote graphical user interfaces and input device capabilities.
Each person using a terminal has the ability to interact with the display with any type of user input device. X provides the framework, or primitives, for building such GUI environments, drawing and moving windows on the display and interacting with a mouse.
X does not mandate the user interface, individual client programs handle this, programs may use Xs graphical abilities with no user interface. As such, the styling of X-based environments varies greatly. Unlike most earlier display protocols, X was specifically designed to be used over network connections rather than on an integral or attached display device. X features network transparency, which means an X program running on a computer somewhere on a network can display its user interface on an X server running on other computer on the network.
The fact that the server is applied to the software in front of the user is often surprising to users accustomed to their programs being clients to services on remote computers. Xs network protocol is based on X command primitives and this approach allows both 2D and 3D operations by an X client application which might be running on a different computer to still be fully accelerated on the X servers display.
X provides no support for audio, several projects exist to fill this niche. X uses a model, an X server communicates with various client programs. The server accepts requests for graphical output and sends back user input, a client and server can even communicate securely over the Internet by tunneling the connection over an encrypted network session.
An X client itself may emulate an X server by providing services to other clients. This is known as X nesting, open-source clients such as Xnest and Xephyr support such X nesting. Bitcoin — Bitcoin is both a cryptocurrency and an electronic payment system,3 invented by an unidentified programmer, or group of programmers, under the name of Satoshi Nakamoto. Bitcoin was introduced on 31 October to a mailing list.
The identity of Nakamoto remains unknown, though many have claimed to know it, the system is peer-to-peer, and transactions take place between users directly, without an intermediary.
These transactions are verified by network nodes and recorded in a public distributed ledger called the blockchain, since the system works without a central repository or single administrator, the U. Treasury categorizes bitcoin as a decentralized virtual currency. Bitcoin is often called the first cryptocurrency, although prior systems existed, Bitcoin is the largest of its kind in terms of total market value.
Bitcoins are created as a reward in a competition in which users offer their computing power to verify and this activity is referred to as mining and successful miners are rewarded with transaction fees and newly created bitcoins. Besides being obtained by mining, bitcoins can be exchanged for other currencies, products, when sending bitcoins, users can pay an optional transaction fee to the miners.
This may expedite the transaction being confirmed, as of February , over , merchants and vendors accept bitcoin as payment. The European Banking Authority and other sources have warned that bitcoin users are not protected by refund rights or chargebacks, the use of bitcoin by criminals has attracted the attention of financial regulators, legislative bodies, law enforcement, and media.
Criminal activities are focused on darknet markets and theft, though officials in countries such as the United States also recognize that bitcoin can provide legitimate financial services. The word bitcoin occurred in the paper that defined bitcoin published in It is a compound of the bit and coin.
The white paper uses the shorter coin. There is no convention for bitcoin capitalization. Some sources use Bitcoin, capitalized, to refer to the technology and network and bitcoin, lowercase, the Wall Street Journal, The Chronicle of Higher Education, and the Oxford English Dictionary advocate use of lowercase bitcoin in all cases, which this article follows.
The blockchain is a ledger that records bitcoin transactions. A novel solution accomplishes this without any trusted central authority, maintenance of the blockchain is performed by a network of communicating nodes running bitcoin software, transactions of the form payer X sends Y bitcoins to payee Z are broadcast to this network using readily available software applications.
Source code — In computing, source code is any collection of computer instructions, possibly with comments, written using a human-readable programming language, usually as ordinary text.
The source code of a program is designed to facilitate the work of computer programmers. The source code is often transformed by an assembler or compiler into binary machine code understood by the computer, the machine code might then be stored for execution at a later time. Alternatively, source code may be interpreted and thus immediately executed, most application software is distributed in a form that includes only executable files.
If the source code were included it would be useful to a user, programmer or a system administrator, the Linux Information Project defines source code as, Source code is the version of software as it is originally written by a human in plain text. The notion of source code may also be more broadly, to include machine code and notations in graphical languages. It is therefore so construed as to include code, very high level languages.
Often there are several steps of program translation or minification between the source code typed by a human and an executable program. The earliest programs for stored-program computers were entered in binary through the front panel switches of the computer and this first-generation programming language had no distinction between source code and machine code.
When IBM first offered software to work with its machine, the code was provided at no additional charge. At that time, the cost of developing and supporting software was included in the price of the hardware, for decades, IBM distributed source code with its software product licenses, until Most early computer magazines published source code as type-in programs, Source code can also be stored in a database or elsewhere.
The source code for a piece of software may be contained in a single file or many files. Though the practice is uncommon, a source code can be written in different programming languages. For example, a program written primarily in the C programming language, in some languages, such as Java, this can be done at run time.
The code base of a programming project is the larger collection of all the source code of all the computer programs which make up the project. It has become practice to maintain code bases in version control systems. Moderately complex software customarily requires the compilation or assembly of several, sometimes dozens or even hundreds, in these cases, instructions for compilations, such as a Makefile, are included with the source code.
Moore's law — Moores law is the observation that the number of transistors in a dense integrated circuit doubles approximately every two years. In , looking forward to the decade, he revised the forecast to doubling every two years. The period is often quoted as 18 months because of Intel executive David House, Moores prediction proved accurate for several decades, and has been used in the semiconductor industry to guide long-term planning and to set targets for research and development.
Advancements in digital electronics are strongly linked to Moores law, quality-adjusted microprocessor prices, memory capacity, sensors and even the number, digital electronics has contributed to world economic growth in the late twentieth and early twenty-first centuries.
Moores law describes a force of technological and social change, productivity. Moores law is an observation or projection and not a physical or natural law, although the rate held steady from until around , the rate was faster during the first decade. In general, it is not logically sound to extrapolate from the growth rate into the indefinite future.
Intel stated in that the pace of advancement has slowed, starting at the 22 nm feature width around , Brian Krzanich, CEO of Intel, announced that our cadence today is closer to two and a half years than two.
This is scheduled to hold through the 10 nm width in late and he cited Moores revision as a precedent for the current deceleration, which results from technical challenges and is a natural part of the history of Moores law.
In January , he declared that Ive heard the death of Moores law more times than anything else in my career, and Im here today to really show you and tell you that Moores Law is alive and well and flourishing. Today hardware has to be designed in a manner to keep up with Moores law. In turn, this means that software has to be written in a multi-threaded manner to take full advantage of the hardware. In , Douglas Engelbart discussed the projected downscaling of integrated circuit size in the article Microelectronics, Engelbart presented his ideas at the International Solid-State Circuits Conference, where Moore was present in the audience.
For the thirty-fifth anniversary issue of Electronics magazine, which was published on April 19, and his response was a brief article entitled, Cramming more components onto integrated circuits. Within his editorial, he speculated that by it would be possible to contain as many as 65, components on a single quarter-inch semiconductor, the complexity for minimum component costs has increased at a rate of roughly a factor of two per year.
Certainly over the term this rate can be expected to continue. Mersenne prime — In mathematics, a Mersenne prime is a prime number that is one less than a power of two. They are named after Marin Mersenne, a French Minim friar, the first four Mersenne primes are 3,7,31, and It is not even whether the set of Mersenne primes is finite or infinite.
Though the above examples might suggest that Mp is prime for all p, this is not the case. The evidence at hand does suggest that a randomly selected Mersenne number is more likely to be prime than an arbitrary randomly selected odd integer of similar size.
Nonetheless, prime Mp appear to grow increasingly sparse as p increases, in fact, of the 2,, prime numbers p up to 37,,, Mp is prime for only 45 of them. The lack of any simple test to determine whether a given Mersenne number is prime makes the search for Mersenne primes a difficult task, the Lucas—Lehmer primality test is an efficient primality test that greatly aids this task. The search for the largest known prime has somewhat of a cult following, consequently, a lot of computer power has been expended searching for new Mersenne primes, much of which is now done using distributed computing.
Anarcho-capitalism — Anarcho-capitalism is a political philosophy that advocates the elimination of the state in favor of individual sovereignty, private property, and free markets. Anarcho-capitalists believe that, in the absence of statute, society would improve itself through the discipline of the free market, in an anarcho-capitalist society, law enforcement, courts, and all other security services would be operated by privately funded competitors rather than centrally through taxation.
Money, along all other goods and services, would be privately and competitively provided in an open market. Various theorists have espoused legal philosophies similar to anarcho-capitalism, a Rothbardian anarcho-capitalist society would operate under a mutually agreed-upon libertarian legal code which would be generally accepted, and which the courts would pledge themselves to follow.
This pact would recognize self-ownership and the principle, although methods of enforcement vary. Anarcho-capitalists argue for a society based on the trade of private property. However, they also recognize charity and communal arrangements as part of the same voluntary ethic, though anarcho-capitalists are known for asserting a right to private property, some propose that non-state public or community property can also exist in an anarcho-capitalist society.
For them, what is important is that it is acquired and transferred without help or hindrance from the compulsory state, anarcho-capitalists see free-market capitalism as the basis for a free and prosperous society. Many anarchists view capitalism as an authoritarian and hierarchical system. On the Nolan chart, anarcho-capitalists are located at the northernmost apex of the libertarian quadrant — since they reject state involvement in economic and personal affairs.
Many also argue that subsidized monopolies tend to be corrupt and inefficient, many anarchists also argue that private defense and court agencies would have to have a good reputation in order to stay in business. Rothbard bases his philosophy on natural law grounds and also provides economic explanations of why he thinks anarcho-capitalism is preferable on pragmatic grounds as well.
Friedman says he is not an absolutist rights theorist but is not a utilitarian, however. Peter Leeson argues that the case for anarchy derives its strength from empirical evidence, hans-Hermann Hoppe, meanwhile, uses argumentation ethics for his foundation of private property anarchism, which is closer to Rothbards natural law approach.
I define anarchist society as one where there is no possibility for coercive aggression against the person or property of any individual. In effect, this means no one else may justly invade, or aggress against. It follows then that each person justly owns whatever previously unowned resources he appropriates or mixes his labor with, from these twin axioms — self-ownership and homesteading — stem the justification for the entire system of property rights titles in a free-market society.
This system establishes the right of man to his own person, the right of donation, of bequest. Complementary currency — Many private currencies are complementary currencies issued by private businesses or organizations. Other terms include alternative currency, auxiliary currency, and microcurrency, advocates in the s, especially in Canada, promoted complementary currencies to supplement national currencies. Certain leaders of this movement were careful to use the term complementary and they used it to emphasize the importance of working in cooperation with governments and the tax system, businesses and other established organisations.
Since the s there has been an increase in the number of complementary currencies. In there was roughly , by there was over They can be useful for communities that do not have access to financial capital, aims may include, lifeboat currencies to increase financial stability. They can be valued and exchanged in relationship to national currencies, Complementary currencies lie outside the nationally defined legal realm of legal tender and are not used as such.
Rate of exchange, scope of circulation and use in combination with other currencies differs greatly between complementary currency systems, as is the case with national currency systems, some complementary currencies incorporate value scales based on time or the backing of real resources.
A time-based currency is valued by the required to perform a service in hours. Another type of monetary systems is the barter, an exchange of specific goods or services is performed without the use of any currency. In , the most widespread auxiliary currency system — the Local Exchange Trading Systems was created and it regulates the exchange of goods and services between the members of the cooperative.
The introductory fee paid by the new members is subsequently directed toward investments in a variety of commercial projects. Some complementary currencies take advantage of demurrage fees, a devaluation of the currency over time.
Some complementary currencies which are regional or global, such as the Community Exchange System, WIR and Friendly Favors, a community currency is a type of complementary currency that has the explicit aim to support and build more equal, connected and sustainable societies.
A community currency is designed to be used by a specific group, the Toronto dollar system is fully funded by Canadian dollars. Participating merchants are free to exchange the Toronto dollars for Canadian dollars, the Toronto dollar has been supported by activists, clergy and a number of political leaders, including, several mayors.
Money supply — In economics, the money supply is the total amount of monetary assets available in an economy at a specific time. There are several ways to define money, but standard measures usually include currency in circulation, Money supply data are recorded and published, usually by the government or the central bank of the country.
Public and private sector analysts have long monitored changes in money supply because of the belief that it affects the level, inflation, the exchange rate. That relation between money and prices is historically associated with the quantity theory of money, there is strong empirical evidence of a direct relation between money-supply growth and long-term price inflation, at least for rapid increases in the amount of money in the economy.
For example, a such as Zimbabwe which saw extremely rapid increases in its money supply also saw extremely rapid increases in prices. This is one reason for the reliance on monetary policy as a means of controlling inflation, the nature of this causal chain is the subject of contention. Some heterodox economists argue that the supply is endogenous and that the sources of inflation must be found in the distributional structure of the economy.
In addition, those economists seeing the central control over the money supply as feeble say that there are two weak links between the growth of the money supply and the inflation rate. First, in the aftermath of a recession, when resources are underutilized. Second, if the velocity of money changes, an increase in the supply could have either no effect. See also European Central Bank for other approaches and a global perspective.
Money is used as a medium of exchange, a unit of account and its different functions are associated with different empirical measures of the money supply. There is no single measure of the money supply. Instead, there are measures, classified along a spectrum or continuum between narrow and broad monetary aggregates.
Narrow measures include only the most liquid assets, the ones most easily used to spend, broader measures add less liquid types of assets. This continuum corresponds to the way that different types of money are more or less controlled by monetary policy, narrow measures include those more directly affected and controlled by monetary policy, whereas broader measures are less closely related to monetary-policy actions.
It is a matter of debate as to whether narrower or broader versions of the money supply have a more predictable link to nominal GDP. The different types of money are typically classified as Ms, the Ms usually range from M0 to M3 but which Ms are actually focused on in policy formulation depends on the countrys central bank.
Directed acyclic graph — In mathematics and computer science, a directed acyclic graph, is a finite directed graph with no directed cycles. Equivalently, a DAG is a graph that has a topological ordering. DAGs can model different kinds of information. Similarly, topological orderings of DAGs can be used to order the compilation operations in a makefile, the program evaluation and review technique uses DAGs to model the milestones and activities of large human projects, and schedule these projects to use as little total time as possible.
Combinational logic blocks in electronic design, and the operations in dataflow programming languages. More abstractly, the reachability relation in a DAG forms a partial order, the corresponding concept for undirected graphs is a forest, an undirected graph without cycles.