SMBGhost

SMBGhost (or SMBleedingGhost or CoronaBlue) is a type of security vulnerability, with wormlike features, that affects Windows 10 computers and was first reported publicly on 10 March 2020. == Security vulnerability == A proof of concept (PoC) exploit code was published 1 June 2020 on GitHub by a security researcher. The code could possibly spread to millions of unpatched computers, resulting in as much as tens of billions of dollars in losses. Microsoft recommends all users of Windows 10 versions 1903 and 1909 and Windows Server versions 1903 and 1909 to install patches, and states, "We recommend customers install updates as soon as possible as publicly disclosed vulnerabilities have the potential to be leveraged by bad actors ... An update for this vulnerability was released in March [2020], and customers who have installed the updates, or have automatic updates enabled, are already protected." Workarounds, according to Microsoft, such as disabling SMB compression and blocking port 445, may help but may not be sufficient. According to the advisory division of Homeland Security, "Malicious cyber actors are targeting unpatched systems with the new [threat], ... [and] strongly recommends using a firewall to block server message block ports from the internet and to apply patches to critical- and high-severity vulnerabilities as soon as possible."

Super-resolution optical fluctuation imaging

Super-resolution optical fluctuation imaging (SOFI) is a post-processing method for the calculation of super-resolved images from recorded image time series that is based on the temporal correlations of independently fluctuating fluorescent emitters. SOFI has been developed for super-resolution of biological specimen that are labelled with independently fluctuating fluorescent emitters (organic dyes, fluorescent proteins). In comparison to other super-resolution microscopy techniques such as STORM or PALM that rely on single-molecule localization and hence only allow one active molecule per diffraction-limited area (DLA) and timepoint, SOFI does not necessitate a controlled photoswitching and/ or photoactivation as well as long imaging times. Nevertheless, it still requires fluorophores that are cycling through two distinguishable states, either real on-/off-states or states with different fluorescence intensities. In mathematical terms SOFI-imaging relies on the calculation of cumulants, for what two distinguishable ways exist. For one thing an image can be calculated via auto-cumulants that by definition only rely on the information of each pixel itself, and for another thing an improved method utilizes the information of different pixels via the calculation of cross-cumulants. Both methods can increase the final image resolution significantly although the cumulant calculation has its limitations. Actually SOFI is able to increase the resolution in all three dimensions. == Principle == Likewise to other super-resolution methods SOFI is based on recording an image time series on a CCD- or CMOS camera. In contrary to other methods the recorded time series can be substantially shorter, since a precise localization of emitters is not required and therefore a larger quantity of activated fluorophores per diffraction-limited area is allowed. The pixel values of a SOFI-image of the n-th order are calculated from the values of the pixel time series in the form of a n-th order cumulant, whereas the final value assigned to a pixel can be imagined as the integral over a correlation function. The finally assigned pixel value intensities are a measure of the brightness and correlation of the fluorescence signal. Mathematically, the n-th order cumulant is related to the n-th order correlation function, but exhibits some advantages concerning the resulting resolution of the image. Since in SOFI several emitters per DLA are allowed, the photon count at each pixel results from the superposition of the signals of all activated nearby emitters. The cumulant calculation now filters the signal and leaves only highly correlated fluctuations. This provides a contrast enhancement and therefore a background reduction for good measure. As it is implied in the figure on the left the fluorescence source distribution: ∑ k = 1 N δ ( r → − r → k ) ⋅ ε k ⋅ s k ( t ) {\displaystyle \sum _{k=1}^{N}\delta ({\vec {r}}-{\vec {r}}_{k})\cdot \varepsilon _{k}\cdot s_{k}(t)} is convolved with the system's point spread function (PSF) U(r). Hence the fluorescence signal at time t and position r → {\displaystyle {\vec {r}}} is given by F ( r → , t ) = ∑ k = 1 N U ( r → − r → k ) ⋅ ε k ⋅ s k ( t ) . {\displaystyle F({\vec {r}},t)=\sum _{k=1}^{N}U({\vec {r}}-{\vec {r}}_{k})\cdot \varepsilon _{k}\cdot s_{k}(t).} Within the above equations N is the amount of emitters, located at the positions r → k {\displaystyle {\vec {r}}_{k}} with a time-dependent molecular brightness ε k ⋅ s k {\displaystyle \varepsilon _{k}\cdot s_{k}} where ε k {\displaystyle \varepsilon _{k}} is a variable for the constant molecular brightness and s k ( t ) {\displaystyle s_{k}(t)} is a time-dependent fluctuation function. The molecular brightness is just the average fluorescence count-rate divided by the number of molecules within a specific region. For simplification it has to be assumed that the sample is in a stationary equilibrium and therefore the fluorescence signal can be expressed as a zero-mean fluctuation: δ F ( r → , t ) = F ( r → , t ) − ⟨ F ( r → , t ) ⟩ t {\displaystyle \delta F({\vec {r}},t)=F({\vec {r}},t)-\langle F({\vec {r}},t)\rangle _{t}} where ⟨ ⋯ ⟩ t {\displaystyle \langle \cdots \rangle _{t}} denotes time-averaging. The auto-correlation here e.g. the second-order can then be described deductively as follows for a certain time-lag τ {\displaystyle \tau } : δ F ( r → , t ) = ⟨ δ F ( r → , t + τ ) ⋅ δ F ( r → , t ) ⟩ t {\displaystyle \delta F({\vec {r}},t)=\langle \delta F({\vec {r}},t+\tau )\cdot \delta F({\vec {r}},t)\rangle _{t}} From these equations it follows that the PSF of the optical system has to be taken to the power of the order of the correlation. Thus in a second-order correlation the PSF would be reduced along all dimensions by a factor of 2 {\displaystyle {\sqrt {2}}} . As a result, the resolution of the SOFI-images increases according to this factor. === Cumulants versus correlations === Using only the simple correlation function for a reassignment of pixel values, would ascribe to the independency of fluctuations of the emitters in time in a way that no cross-correlation terms would contribute to the new pixel value. Calculations of higher-order correlation functions would suffer from lower-order correlations for what reason it is superior to calculate cumulants, since all lower-order correlation terms vanish. == Cumulant-calculation == === Auto-cumulants === For computational reasons it is convenient to set all time-lags in higher-order cumulants to zero so that a general expression for the n-th order auto-cumulant can be found: A C n ( r → , τ 1 … n − 1 = 0 ) = ∑ k = 1 N U n ( r → − r → k ) ε k n w k ( 0 ) {\displaystyle AC_{n}({\vec {r}},\tau _{1\ldots n-1}=0)=\sum _{k=1}^{N}U^{n}({\vec {r}}-{\vec {r}}_{k})\varepsilon _{k}^{n}w_{k}(0)} w k {\displaystyle w_{k}} is a specific correlation based weighting function influenced by the order of the cumulant and mainly depending on the fluctuation properties of the emitters. Albeit there is no fundamental limitation in calculating very high orders of cumulants and thereby shrinking the FWHM of the PSF there are practical limitations according to the weighting of the values assigned to the final image. Emitters with a higher molecular brightness will show a strong increase in terms of the pixel cumulant value assigned at higher-orders as well as this performance can be expected from a diverse appearance of fluctuations of different emitters. A wide intensity range of the resulting image can therefore be expected and as a result dim emitters can get masked by bright emitters in higher-order images:. The calculation of auto-cumulants can be realized in a very attractive way in a mathematical sense. The n-th order cumulant can be calculated with a basic recursion from moments K n ( r → ) = μ n ( r → ) − ∑ i = 1 n − 1 ( n − 1 i ) K n − i ( r → ) μ i ( r → ) {\displaystyle K_{n}({\vec {r}})=\mu _{n}({\vec {r}})-\sum _{i=1}^{n-1}{\begin{pmatrix}n-1\\i\end{pmatrix}}K_{n-i}({\vec {r}})\mu _{i}({\vec {r}})} where K is a cumulant of the index's order, likewise μ {\displaystyle \mu } represents the moments. The term within the brackets indicates a binomial coefficient. This way of computation is straightforward in comparison with calculating cumulants with standard formulas. It allows for the calculation of cumulants with only little time of computing and is, as it is well implemented, even suitable for the calculation of high-order cumulants on large images. === Cross-cumulants === In a more advanced approach cross-cumulants are calculated by taking the information of several pixels into account. Cross-cumulants can be described as follows: C C n ( r → , τ 1 … n − 1 = 0 ) = ∏ j < l n U ( r → j − r → l n ) ⋅ ∑ i = 1 N U n ( r → i − ∑ k n r → k n ) ε i n w i ( 0 ) {\displaystyle CC_{n}({\vec {r}},\tau _{1\ldots n-1}=0)=\prod _{j

Asynchronous module definition

Asynchronous module definition (AMD) is a specification for the programming language JavaScript. It defines an application programming interface (API) that defines code modules and their dependencies, and loads them asynchronously if desired. Implementations of AMD provide the following benefits: Website performance improvements. AMD implementations load smaller JavaScript files, and then only when they are needed. Fewer page errors. AMD implementations allow developers to define dependencies that must load before a module is executed, so the module does not try to use outside code that is not available yet.... In addition to loading multiple JavaScript files at runtime, AMD implementations allow developers to encapsulate code in smaller, more logically-organized files, in a way similar to other programming languages such as Java. For production and deployment, developers can concatenate and minify JavaScript modules based on an AMD API into one file, the same as traditional JavaScript. AMD provides some CommonJS interoperability. It allows for using a similar exports and require() interface in the code, although its own define() interface is more basal and preferred. The AMD specification is implemented by Dojo Toolkit, RequireJS, and other libraries.

History of RISC OS

RISC OS, the computer operating system developed by Acorn Computers for their ARM-based Acorn Archimedes range, was originally released in 1987 as Arthur 0.20, and soon followed by Arthur 0.30, and Arthur 1.20. The next version, Arthur 2, became RISC OS 2 and was completed in September 1988 and made available in April 1989. RISC OS 3 was released with the very earliest version of the A5000 in 1991 and contained a series of new features. By 1996 RISC OS had been shipped on over 500,000 systems. RISC OS 4 was released by RISCOS Ltd (ROL) in July 1999, based on the continued development of OS 3.8. ROL had in March 1999 licensed the rights to RISC OS from Element 14 (the renamed Acorn) and eventually from the new owner, Pace Micro Technology. According to the company, over 6,400 copies of OS 4.02 on ROM were sold up until production was ceased in mid-2005. RISC OS Select was launched in May 2001 by ROL. This is a subscription scheme allowing users access to the latest OS updates. These upgrades are released as soft-loadable ROM images, separate to the ROM where the boot OS is stored, and are loaded at boot time. Select 1 was shipped in May 2002, with Select 2 following in November 2002 and the final release of Select 3 in June 2004. ROL released the ROM based OS 4.39 the same month, dubbed RISC OS Adjust as a play on the RISC OS GUI convention of calling the three mouse buttons 'Select', 'Menu' and 'Adjust'. ROL sold its 500th Adjust ROM in early 2006. RISC OS 5 was released in October 2002 on Castle Technology's Acorn clone Iyonix PC. OS 5 is a separate evolution based upon the NCOS work done by Pace for set-top boxes. In October 2006, Castle announced a source sharing license plan for elements of OS 5. This Shared Source Initiative (SSI) is managed by RISC OS Open Ltd (ROOL). RISC OS 5 has since been released under a fully free and open source Apache 2.0 license, while the older no longer maintained RISC OS 6 has not. RISC OS Six was also announced in October 2006 by ROL. This is the next generation of their stream of the operating system. The first product to be launched under the name was the continuation of the Select scheme, Select 4. A beta-version of OS 6, Preview 1 (Select 4i1), was available in 2007 as a free download to all subscribers to the Select scheme, while in April 2009 the final release of Select 5 was shipped. The latest release of RISC OS from ROL is Select 6i1, shipped in December 2009. == Arthur == The OS was designed in the United Kingdom by Acorn for the 32-bit ARM based Acorn Archimedes, and released in its first version in 1987, as the Arthur operating system. The first public release of the OS was Arthur 1.20 in June 1987. It was bundled with a desktop graphical user interface (GUI), which mostly comprises assembly language software modules, and the Desktop module itself being written in BBC BASIC. It features a colour-scheme typically described as "technicolor". The graphical desktop runs on top of a command-line driven operating system which owes much to Acorn's earlier MOS operating system for its BBC Micro range of 8-bit microcomputers. Arthur, as originally conceived, was intended to deliver similar functionality to the operating system for the BBC Master series of computers, MOS, as a reaction to the fact that a more advanced operating system research project (ARX) would not be ready in time for the Archimedes. The Arthur project team, led by Paul Fellows, was given just five months to develop it entirely from the ground up—with the directive "just make it like the BBC micro". It was intended as a stop-gap until the operating system which Acorn had under development (ARX) could be completed. However, the latter was delayed time and again, and was eventually dropped when it became apparent that the Arthur development could be extended to have a window manager and full desktop environment. Also, it was small enough to run on the first 512K machines with only a floppy disc, whereas ARX required 4 megabytes and a hard drive. The OS development was carried out using a prototype ARM-based system connected to a BBC computer, before moving onto the prototype Acorn Archimedes the A500. Arthur was not a multitasking operating system, but offered support for adding application-level cooperative multitasking. No other version of the operating system was released externally, but internally the development of the desktop and window management continued, with the addition of a cooperative multitasking system, implemented by Neil Raine, which used the memory management hardware to swap-out one task, and bring in another between call-and-return from the Wimp_Poll call that applications were obliged to make to get messages under the desktop. Reminiscent of a similar technique employed by MultiFinder on the Apple Macintosh, this transformed a single-application-at-a-time system into one that could operate a full multi-tasking desktop. This transformation took place at version 1.6 though it was not made public until released, with the name change from Arthur to RISC OS, as version 2.0. Most software made for Arthur 1.2 can be run under RISC OS 2 and later because, underneath the desktop, the original Arthur OS core, API interfaces and modular structures remain as the heart of all versions. (A few titles will not work, however, because they used undocumented features, side effects or in a few cases APIs that became deprecated). In 2011, Business Insider listed Arthur as one of ten "operating systems that time forgot". == RISC OS 2 == RISC OS was a rapid development of Arthur 1.2 after the failure of the ARX project. Given growing dissatisfaction with various bugs and limitations with Arthur, testing of what was then known as Arthur 2 was apparently ongoing during 1988 with selected software houses. At this stage, Computer Concepts, who had been prolific developers for the BBC Micro and who had begun software development for the Archimedes, had already initiated a rival operating system project, Impulse, to support their own applications (including the desktop publishing application that would eventually become Impression), stating that Arthur did not meet the "hundreds of requirements" involved including "true multi-tasking". Such an operating system was to be offered free of charge with the planned application packages, but with the release of RISC OS and Computer Concepts acknowledging that RISC OS "overcomes the old problems with Arthur", the applications were to be able to run under either RISC OS or Impulse. Impression was eventually released as a RISC OS application. Ultimately, Arthur 2 was renamed to RISC OS, and was first sold as RISC OS 2.00 in April 1989. The operating system implements co-operative multitasking with some limitations but is not multi-threaded. It uses the ADFS file system for both floppy and hard disc access. It ran from a 512 KB set of ROMs. The WIMP interface offers all the standard features and fixes many of the bugs that had hindered Arthur. It lacks virtual memory and extensive memory protection (applications are protected from each other, but many functions have to be implemented as 'modules' which have full access to the memory). At the time of release, the main advantage of the OS was its ROM; it booted very quickly and while it was easy to crash, it was impossible to permanently break the OS from software. Its high performance was due to much of the system being written in ARM assembly language. The OS was designed with users in mind, rather than OS designers. It is organised as a relatively small kernel which defines a standard software interface to which extension modules are required to conform. Much of the system's functionality is implemented in modules coded in the ROM, though these can be supplanted by more evolved versions loaded into RAM. Among the kernel facilities are a general mechanism, named the callback handler, which allows a supervisor module to perform process multiplexing. This facility is used by a module forming part of the standard editor program to provide a terminal emulator window for console applications. The same approach made it possible for advanced users to implement modules giving RISC OS the ability to do pre-emptive multitasking. A slightly updated version, RISC OS 2.01, was released later to support the ARM3 processor, larger memory capacities, and the VGA and SVGA modes provided by the Acorn Archimedes 540 and Acorn R225/R260. == RISC OS 3 == RISC OS 3 introduced a number of new features, including multitasking Filer operations, applications and fonts in ROM, no limit on number of open windows, ability to move windows off screen, safe shutdown, the Pinboard, grouping of icon bar icons, up to 128 tasks, native ability to read MS-DOS format discs and use named hard discs. Improved configuration was also included, by way of multiple windows to change the settings. RISC OS 3.00 was released with the very earliest version of the A5000 in 1991; it is almo

Pridgen v University of Calgary

Pridgen v University of Calgary was freedom of speech case which took place in Alberta, Canada, in 2010. The case deals with two university students, Keith and Steven Pridgen, who were found guilty and punished by the University of Calgary in 2008, on grounds of "non-academic misconduct". The University of Calgary defines "non-academic misconduct" as:(a) conduct which causes injury to a person and/or damage to University property and/or the property of any member of the University community; (b) unauthorized removal and/or unauthorized possession of University property; and (c) conduct which seriously disrupts the lawful educational and related activities of other students and/or University staff.The Court of the Queen's Bench of Alberta found the University of Calgary to be wrong in prosecuting ten students, including the Pridgen brothers, in regards to comments made about a professor on Facebook. The key ruling in this case was that the universities are not exempt from, and that these students were in fact protected under, section 2(b) of the Charter of Rights and Freedoms. This case is notable as it highlights the jurisdiction of the Charter in terms of both new media technologies and university institutions in Canada. == Background == Keith and Steven Pridgen were undergraduate students at the University of Calgary in 2008. The twin brothers shared a Law and Society class being taught by Aruna Mitra. Professor Mitra was teaching this class for the first time in her career, and many of the students were very critical of her knowledge of the course. A Facebook page entitled “I NO Longer Fear Hell, I Took a Course with Aruna Mitra” was created, and many students began posting comments. In particular, Steven Pridgen's comment on November 13, 2007, read: “Somehow I think she just got lazy and gave everybody a 65....that's what I got. Does anybody know how to apply to have it remarked?” Many students had similar concerns to Pridgen's and after having their work re-marked, a number of them did in fact receive higher grades. Keith Pridgen also commented on August 26, 2008: “Hey fellow LWSO. Homees.. So I am quite sure Mitra is NO LONGER TEACHING ANY COURSES WITH THE U OF C !!!!! Remember when she told us she was a long-term professor? Well, Actually she was only sessional and picked up our class at the last moment because another prof wasn't able to do it ...lucky us. Well, anyways I think we should all congratulate ourselves for leaving a Mitra-free legacy for future students!” On September 4, 2008, Aruna Mitra complained about the Facebook page to the Interim Dean of the Faculty of Communication and Culture at the University of Calgary. Dean Tettey called a meeting for the ten students who posted material about Mitra on the Facebook page. The meeting took place on September 18, 2008, and included four professors from the department as well as the Dean. At this meeting, all ten students, including the Pridgen brothers, were found guilty of non-academic misconduct. On November 20, 2008, the Appellant's received a letter from Dean Tettey advising them that their comments “clearly caused unwarranted professional and personal injury to Prof. Mitra and clearly meets the criteria for non-academic misconduct as outlined in the University of Calgary Calendar”. Keith Pridgen was put on probation for 24 months, and both brothers were required to write a letter of apology to Prof. Mitra and refrain from posting or circulating defamatory material regarding any faculty members of the University of Calgary. The Pridgen brothers appealed the decision to the University of Calgary Review Committee and later to the Board of Governors of the University of Calgary however neither of these attempts succeeded in having the decision overturned. == Opinion of the Court == Eight main issues to be determined were laid out by the Honourable Madam Justice J. Strekaf: (a) Does the Charter apply to the disciplinary proceedings taken by the Respondent; (b) If, so were the Applicants' Charter rights infringed; (c) Were the actions taken by the University ultra vires the jurisdiction of the Province of Alberta; (d) Did the Board of Governors err in refusing to hear the Applicants appeals; (e) Were the Applicants' denied a fair hearing; (f) Did the Review Committee provide adequate reasons for its decisions; (g) Did the Review Committee err in concluding that the activities of the Applicants constituted non-academic misconduct; and (h) What, if any, remedy should be granted to the Applicants. The Court determined from previous cases that "a non-government entity may still be subject to the Charter of Rights and freedoms when implementing a specific government policy or program". Justice Strekaf distinguished that the University was acting as agent of the provincial government in providing accessible post-secondary education services to students in Alberta pursuant to the provisions of the PSL Act. Justice Strekaf felt there was sufficient evidence to show that universities in Alberta have some level of reliance on government funds and therefore they are not a "Charter free zone". Justice Strekaf concluded that comments made by Keith and Steven Pridgen, regarding Professor Mitra, on Facebook did not constitute academic misconduct and the Pridgen brothers' right to freedom of expression, under section 2(b) of the Charter, was infringed by the University of Calgary Review Committee.

LiveChat

LiveChat is an AI customer service software with chatbot, online chat, help desk software, and web analytics capabilities. LiveChat is used by over 76,000 companies. It was first launched in 2002 and is offered via a SaaS (software as a service) business model by Text. Organizations use LiveChat as a single point of contact to manage customer service and online sales activities with a single program. == Product == LiveChat is proprietary software. LiveChat's website chat widget can be embedded on customers' websites as a small chat box, often displayed in the bottom right corner of the web browser. It can be used to conduct chats, share files and save transcripts. The agent application is used by company employees to respond to questions asked by the customers. This is available through both web-based application, desktop applications, and mobile apps. Web chat sessions can be initiated by the visiting customer, or by the agent, either manually or automatically by the LiveChat system when the visitor meets the predefined criteria (i.e. searched keyword, time on website, encountered error, etc.). LiveChat's system attempts to identify the best prospects visiting a website based on data gathered from past purchasing decisions. Other features include real-time website traffic monitoring, built-in ticketing system and agents' efficiency analytics. LiveChat is available in 48 languages. == Research and reception == Reviewing LiveChat's usefulness for online learning in 2020, psychologist Jaclyn Broadbent said "LiveChat occurs as a real-time conversation, it can be time-consuming for staff and disruptive to other tasks." However, using it has resulted in reduced communication traffic from other channels, such as the discussion boards or email. As a teacher, the best time to be available on LiveChat is when you are doing other administrative jobs." Since 2014 LiveChat has been publishing Customer Service Report - an annual study of customer satisfaction and analysis of online business communication trends. It includes research of thousands of companies and millions of customer service email and live support interactions.

Randomized benchmarking

Randomized benchmarking is an experimental method for measuring the average error rates of quantum computing hardware platforms. The protocol estimates the average error rates by implementing long sequences of randomly sampled quantum gate operations. Randomized benchmarking is the industry-standard protocol used by quantum hardware developers such as IBM and Google to test the performance of the quantum operations. The original theory of randomized benchmarking, proposed by Joseph Emerson and collaborators, considered the implementation of sequences of Haar-random operations, but this had several practical limitations. The now-standard protocol for randomized benchmarking (RB) relies on uniformly random Clifford operations, as proposed in 2006 by Dankert et al. as an application of the theory of unitary t-designs. In current usage randomized benchmarking sometimes refers to the broader family of generalizations of the 2005 protocol involving different random gate sets that can identify various features of the strength and type of errors affecting the elementary quantum gate operations. Randomized benchmarking protocols are an important means of verifying and validating quantum operations and are also routinely used for the optimization of quantum control procedures. == Overview == Randomized benchmarking offers several key advantages over alternative approaches to error characterization. For example, the number of experimental procedures required for full characterization of errors (called tomography) grows exponentially with the number of quantum bits (called qubits). This makes tomographic methods impractical for even small systems of just 3 or 4 qubits. In contrast, randomized benchmarking protocols are the only known approaches to error characterization that scale efficiently as number of qubits in the system increases. Thus RB can be applied in practice to characterize errors in arbitrarily large quantum processors. Additionally, in experimental quantum computing, procedures for state preparation and measurement (SPAM) are also error-prone, and thus quantum process tomography is unable to distinguish errors associated with gate operations from errors associated with SPAM. In contrast, RB protocols are robust to state-preparation and measurement errors Randomized benchmarking protocols estimate key features of the errors that affect a set of quantum operations by examining how the observed fidelity of the final quantum state decreases as the length of the random sequence increases. If the set of operations satisfies certain mathematical properties, such as comprising a sequence of twirls with unitary two-designs, then the measured decay can be shown to be an invariant exponential with a rate fixed uniquely by features of the error model. == History == Randomized benchmarking was proposed in Scalable noise estimation with random unitary operators, where it was shown that long sequences of quantum gates sampled uniformly at random from the Haar measure on the group SU(d) would lead to an exponential decay at a rate that was uniquely fixed by the error model. Emerson, Alicki and Zyczkowski also showed, under the assumption of gate-independent errors, that the measured decay rate is directly related to an important figure of merit, the average gate fidelity and independent of the choice of initial state and any errors in the initial state, as well as the specific random sequences of quantum gates. This protocol applied for arbitrary dimension d and an arbitrary number n of qubits, where d=2n. The SU(d) RB protocol had two important limitations that were overcome in a modified protocol proposed by Dankert et al., who proposed sampling the gate operations uniformly at random from any unitary two-design, such as the Clifford group. They proved that this would produce the same exponential decay rate as the random SU(d) version of the protocol proposed in Emerson et al.. This follows from the observation that a random sequence of gates is equivalent to an independent sequence of twirls under that group, as conjectured in and later proven in. This Clifford-group approach to Randomized Benchmarking is the now standard method for assessing error rates in quantum computers. A variation of this protocol was proposed by NIST in 2008 for the first experimental implementation of an RB-type for single qubit gates. However, the sampling of random gates in the NIST protocol was later proven not to reproduce any unitary two-design. The NIST RB protocol was later shown to also produce an exponential fidelity decay, albeit with a rate that depends on non-invariant features of the error model In recent years a rigorous theoretical framework has been developed for Clifford-group RB protocols to show that they work reliably under very broad experimental conditions. In 2011 and 2012, Magesan et al. proved that the exponential decay rate is fully robust to arbitrary state preparation and measurement errors (SPAM). They also proved a connection between the average gate fidelity and diamond norm metric of error that is relevant to the fault-tolerant threshold. They also provided evidence that the observed decay was exponential and related to the average gate fidelity even if the error model varied across the gate operations, so-called gate-dependent errors, which is the experimentally realistic situation. In 2018, Wallman and Dugas et al., showed that, despite concerns raised in, even under very strong gate-dependence errors the standard RB protocols produces an exponential decay at a rate that precisely measures the average gate-fidelity of the experimentally relevant errors. The results of Wallman. in particular proved that the RB error rate is so robust to gate-dependent errors models that it provides an extremely sensitive tool for detecting non-Markovian errors. This follows because under a standard RB experiment only non-Markovian errors (including time-dependent Markovian errors) can produce a statistically significant deviation from an exponential decay The standard RB protocol was first implemented for single qubit gate operations in 2012 at Yale on a superconducting qubit. A variation of this standard protocol that is only defined for single qubit operations was implemented by NIST in 2008 on a trapped ion. The first implementation of the standard RB protocol for two-qubit gates was performed in 2012 at NIST for a system of two trapped ions