A Google matrix is a particular stochastic matrix that is used by Google's PageRank algorithm. The matrix represents a graph with edges representing links between pages. The PageRank of each page can then be generated iteratively from the Google matrix using the power method. However, in order for the power method to converge, the matrix must be stochastic, irreducible and aperiodic. == Adjacency matrix A and Markov matrix S == In order to generate the Google matrix G, we must first generate an adjacency matrix A which represents the relations between pages or nodes. Assuming there are N pages, we can fill out A by doing the following: A matrix element A i , j {\displaystyle A_{i,j}} is filled with 1 if node j {\displaystyle j} has a link to node i {\displaystyle i} , and 0 otherwise; this is the adjacency matrix of links. A related matrix S corresponding to the transitions in a Markov chain of given network is constructed from A by dividing the elements of column "j" by a number of k j = Σ i = 1 N A i , j {\displaystyle k_{j}=\Sigma _{i=1}^{N}A_{i,j}} where k j {\displaystyle k_{j}} is the total number of outgoing links from node j to all other nodes. The columns having zero matrix elements, corresponding to dangling nodes, are replaced by a constant value 1/N. Such a procedure adds a link from every sink, dangling state a {\displaystyle a} to every other node. Now by the construction the sum of all elements in any column of matrix S is equal to unity. In this way the matrix S is mathematically well defined and it belongs to the class of Markov chains and the class of Perron-Frobenius operators. That makes S suitable for the PageRank algorithm. == Construction of Google matrix G == Then the final Google matrix G can be expressed via S as: G i j = α S i j + ( 1 − α ) 1 N ( 1 ) {\displaystyle G_{ij}=\alpha S_{ij}+(1-\alpha ){\frac {1}{N}}\;\;\;\;\;\;\;\;\;\;\;(1)} By the construction the sum of all non-negative elements inside each matrix column is equal to unity. The numerical coefficient α {\displaystyle \alpha } is known as a damping factor. Usually S is a sparse matrix and for modern directed networks it has only about ten nonzero elements in a line or column, thus only about 10N multiplications are needed to multiply a vector by matrix G. == Examples of Google matrix == An example of the matrix S {\displaystyle S} construction via Eq.(1) within a simple network is given in the article CheiRank. For the actual matrix, Google uses a damping factor α {\displaystyle \alpha } around 0.85. The term ( 1 − α ) {\displaystyle (1-\alpha )} gives a surfer probability to jump randomly on any page. The matrix G {\displaystyle G} belongs to the class of Perron-Frobenius operators of Markov chains. The examples of Google matrix structure are shown in Fig.1 for Wikipedia articles hyperlink network in 2009 at small scale and in Fig.2 for University of Cambridge network in 2006 at large scale. == Spectrum and eigenstates of G matrix == For 0 < α < 1 {\displaystyle 0<\alpha <1} there is only one maximal eigenvalue λ = 1 {\displaystyle \lambda =1} with the corresponding right eigenvector which has non-negative elements P i {\displaystyle P_{i}} which can be viewed as stationary probability distribution. These probabilities ordered by their decreasing values give the PageRank vector P i {\displaystyle P_{i}} with the PageRank K i {\displaystyle K_{i}} used by Google search to rank webpages. Usually one has for the World Wide Web that P ∝ 1 / K β {\displaystyle P\propto 1/K^{\beta }} with β ≈ 0.9 {\displaystyle \beta \approx 0.9} . The number of nodes with a given PageRank value scales as N P ∝ 1 / P ν {\displaystyle N_{P}\propto 1/P^{\nu }} with the exponent ν = 1 + 1 / β ≈ 2.1 {\displaystyle \nu =1+1/\beta \approx 2.1} . The left eigenvector at λ = 1 {\displaystyle \lambda =1} has constant matrix elements. With 0 < α {\displaystyle 0<\alpha } all eigenvalues move as λ i → α λ i {\displaystyle \lambda _{i}\rightarrow \alpha \lambda _{i}} except the maximal eigenvalue λ = 1 {\displaystyle \lambda =1} , which remains unchanged. The PageRank vector varies with α {\displaystyle \alpha } but other eigenvectors with λ i < 1 {\displaystyle \lambda _{i}<1} remain unchanged due to their orthogonality to the constant left vector at λ = 1 {\displaystyle \lambda =1} . The gap between λ = 1 {\displaystyle \lambda =1} and other eigenvalue being 1 − α ≈ 0.15 {\displaystyle 1-\alpha \approx 0.15} gives a rapid convergence of a random initial vector to the PageRank approximately after 50 multiplications on G {\displaystyle G} matrix. At α = 1 {\displaystyle \alpha =1} the matrix G {\displaystyle G} has generally many degenerate eigenvalues λ = 1 {\displaystyle \lambda =1} (see e.g. [6]). Examples of the eigenvalue spectrum of the Google matrix of various directed networks is shown in Fig.3 from and Fig.4 from. The Google matrix can be also constructed for the Ulam networks generated by the Ulam method [8] for dynamical maps. The spectral properties of such matrices are discussed in [9,10,11,12,13,15]. In a number of cases the spectrum is described by the fractal Weyl law [10,12]. The Google matrix can be constructed also for other directed networks, e.g. for the procedure call network of the Linux Kernel software introduced in [15]. In this case the spectrum of λ {\displaystyle \lambda } is described by the fractal Weyl law with the fractal dimension d ≈ 1.3 {\displaystyle d\approx 1.3} (see Fig.5 from ). Numerical analysis shows that the eigenstates of matrix G {\displaystyle G} are localized (see Fig.6 from ). Arnoldi iteration method allows to compute many eigenvalues and eigenvectors for matrices of rather large size [13]. Other examples of G {\displaystyle G} matrix include the Google matrix of brain [17] and business process management [18], see also. Applications of Google matrix analysis to DNA sequences is described in [20]. Such a Google matrix approach allows also to analyze entanglement of cultures via ranking of multilingual Wikipedia articles abouts persons [21] == Historical notes == The Google matrix with damping factor was described by Sergey Brin and Larry Page in 1998 [22], see also articles on PageRank history [23], [24].
Hierarchical Risk Parity
Hierarchical Risk Parity (HRP) is an advanced investment portfolio optimization framework developed in 2016 by Marcos López de Prado at Guggenheim Partners and Cornell University. HRP is a probabilistic graph-based alternative to the prevailing mean-variance optimization (MVO) framework developed by Harry Markowitz in 1952, and for which he received the Nobel Prize in economic sciences. HRP algorithms apply discrete mathematics and machine learning techniques to create diversified and robust investment portfolios that outperform MVO methods out-of-sample. HRP aims to address the limitations of traditional portfolio construction methods, particularly when dealing with highly correlated assets. Following its publication, HRP has been implemented in numerous open-source libraries, and received multiple extensions. == Key features == HRP portfolios have been proposed as a robust alternative to traditional quadratic optimization methods, including the Critical Line Algorithm (CLA) of Markowitz. HRP addresses three central issues commonly associated with quadratic optimizers: numerical instability, excessive concentration in a small number of assets, and poor out-of-sample performance. HRP leverages techniques from graph theory and machine learning to construct diversified portfolios using only the information embedded in the covariance matrix. Unlike quadratic programming methods, HRP does not require the covariance matrix to be invertible. Consequently, HRP remains applicable even in cases where the covariance matrix is ill-conditioned or singular—conditions under which standard optimizers fail. Monte Carlo simulations indicate that HRP achieves lower out-of-sample variance than CLA, despite the fact that minimizing variance is the explicit optimization objective of CLA. Furthermore, HRP portfolios exhibit lower realized risk compared to those generated by traditional risk parity methodologies. Empirical backtests have demonstrated that HRP would have historically outperformed conventional portfolio construction techniques. Algorithms within the HRP framework are characterized by the following features: Machine Learning Approach: HRP employs hierarchical clustering, a machine learning technique, to group similar assets based on their correlations. This allows the algorithm to identify the underlying hierarchical structure of the portfolio, and avoid that errors spread through the entire network. Risk-Based Allocation: The algorithm allocates capital based on risk, ensuring that assets only compete with similar assets for representation in the portfolio. This approach leads to better diversification across different risk sources, while avoiding the instability associated with noisy returns estimates. Covariance Matrix Handling: Unlike traditional methods like Mean-Variance Optimization, HRP does not require inverting the covariance matrix. This makes it more stable and applicable to portfolios with a large number of assets, particularly when the covariance matrix's condition number is high. == The problem: Markowitz's Curse == Portfolio construction is perhaps the most recurrent financial problem. On a daily basis, investment managers must build portfolios that incorporate their views and forecasts on risks and returns. Despite the theoretical elegance of Markowitz's mean-variance framework, its practical implementation is hindered by several limitations that undermine the reliability of solutions derived from the Critical Line Algorithm (CLA). A principal concern is the high sensitivity of optimal portfolios to small perturbations in expected returns: even minor forecasting errors can result in significantly different allocations (Michaud, 1998). Given the inherent difficulty of producing accurate return forecasts, numerous researchers have advocated for approaches that forgo expected returns entirely and instead rely solely on the covariance structure of asset returns. This has given rise to risk-based allocation methods, among which risk parity is a widely cited example (Jurczenko, 2015). While eliminating return forecasts mitigates some instability, it does not eliminate it. Quadratic programming techniques employed in portfolio optimization require the inversion of a positive-definite covariance matrix, meaning all eigenvalues must be strictly positive. When the matrix is numerically ill-conditioned—that is, when the ratio of its largest to smallest eigenvalue (its condition number) is large—matrix inversion becomes unreliable and prone to significant numerical errors (Bailey and López de Prado, 2012). The condition number of a covariance, correlation, or any symmetric (and thus diagonalizable) matrix is defined as the absolute value of the ratio between its largest and smallest eigenvalues in modulus. The figure on the right presents the sorted eigenvalues of several correlation matrices; the condition number is represented by the ratio of the first to last eigenvalues in each sequence. A diagonal correlation matrix, which is equal to its own inverse, exhibits the minimum possible condition number. As the number of correlated (or multicollinear) assets in a portfolio increases, the condition number rises. At high levels, this leads to severe numerical instability, whereby slight modifications in any matrix entry may result in drastically different inverses. This phenomenon, often referred to as Markowitz’s curse, encapsulates the paradox wherein increased correlation among assets heightens the theoretical need for diversification, yet simultaneously increases the likelihood of unstable optimization outcomes. Consequently, the potential benefits of diversification are frequently overshadowed by estimation errors. These problems are exacerbated as the dimensionality of the covariance matrix increases. The estimation of each covariance term consumes degrees of freedom, and in general, a minimum of 1 2 N ( N + 1 ) {\displaystyle {\frac {1}{2}}N(N+1)} independent and identically distributed (IID) observations is required to estimate a non-singular covariance matrix of dimension N {\displaystyle N} . For example, constructing an invertible covariance matrix of dimension 50 necessitates at least five years of daily IID observations. However, empirical evidence suggests that the correlation structure of financial assets is highly unstable over such extended periods. These difficulties are highlighted by the observation that even naïve allocation strategies—such as equally weighted portfolios—have frequently outperformed both mean-variance and risk-based optimizations in out-of-sample tests (De Miguel et al., 2009). == The solution: Hierarchical Risk Parity == The HRP algorithm addresses Markowitz's curse in three steps: Hierarchical Clustering: Assets are grouped into clusters based on their correlations, forming a hierarchical tree structure. Quasi-Diagonalization: The correlation matrix is reordered based on the clustering results, revealing a block diagonal structure. Recursive Bisection: Weights are assigned to assets through a top-down approach, splitting the portfolio into smaller sub-portfolios and allocating capital based on inverse variance. === Step 1: Hierarchical clustering === Given a T × N {\displaystyle T\times N} matrix of asset returns X {\displaystyle X} , where each column represents a time series of returns for one of N {\displaystyle N} assets over T {\displaystyle T} time periods, a hierarchical clustering process can be used to construct a tree-based representation of asset relationships. First, we compute the N × N {\displaystyle N\times N} correlation matrix ρ = ρ i , j i , j = 1 . . . N {\displaystyle \rho ={\rho _{i,j}}\;{i,j=1\;...\;N}} , where ρ i , j = c o r r ( X i , X j ) {\displaystyle \rho _{i,j}=\mathrm {corr} (X_{i},X_{j})} . From this, a pairwise distance matrix D = d i , j {\displaystyle D={d_{i,j}}} is defined using the transformation: d i , j = 1 2 ( 1 − ρ i , j ) {\displaystyle d_{i,j}={\sqrt {{\frac {1}{2}}(1-\rho _{i,j})}}} This distance function defines a proper metric space, satisfying non-negativity, identity of indiscernibles, symmetry, and the triangle inequality. Next, a secondary distance matrix D ~ = d ~ i , j {\displaystyle {\tilde {D}}={{\tilde {d}}_{i,j}}} is computed, where each entry measures the Euclidean distance between the distance profiles of two assets: d ~ i , j = ∑ n = 1 N ( d n , i − d n , j ) 2 {\displaystyle {\tilde {d}}_{i,j}={\sqrt {\sum _{n=1}^{N}(d_{n,i}-d_{n,j})^{2}}}} While d i , j {\displaystyle d_{i,j}} reflects correlation-based proximity between two assets, d ~ i , j {\displaystyle {\tilde {d}}_{i,j}} quantifies dissimilarity across the entire system, as it depends on all pairwise distances. Hierarchical clustering proceeds by identifying the pair ( i , j ) {\displaystyle (i,j)} with the smallest value of d ~ i , j {\displaystyle {\tilde {d}}_{i,j}} (for i ≠ j {\displaystyle i\neq j} ), and forming a new cluster u [ 1 ] = ( i , j ) {\displaystyle u[1]=(i,j)} .
Economía Feminista
Economía Feminista, in English: Feminist Economics, is an Argentine digital media, focused on disclosure and creation of economics information about the gender gap. The media is managed by Mercedes D`Alessandro, Magalí Brosio, Violeta Guitart and Agurtzane Urrutia. == Concept == Economía Femini(s)ta, is a portmanteau of feminista and minita. It attempts to end stereotypes about women. It was created in 2015 and its goal is to be a source of economic data to help to display economic differences by gender, especially in Argentina. == Awards == Economía Feminista was awarded the Lola Mora prize in 2016 for the best digital media by Dirección General de la Mujer, promoted by Buenos Aires city's Legislature.
Usage share of operating systems
The usage share of an operating system is the percentage of computers running that operating system (OS). These statistics are estimates as wide scale OS usage data is difficult to obtain and measure. Reliable primary sources are limited and data collection methodology is not formally agreed. Currently devices connected to the internet allow for web data collection to approximately measure OS usage. As of December 2025, Android, which uses the Linux kernel, is the world's most popular operating system with 38.94% of the global market, followed by Windows with 29.99%, iOS with 15.66%, macOS with 2.14%, and other operating systems with 10.78%. This is for all device types excluding embedded devices. For smartphones and other mobile devices, Android has 72% market share, and Apple's iOS has 28%. For desktop computers and laptops, Microsoft Windows has 60.8%, followed by unknown operating systems at 19.7%, Mac OS at 14.4%, desktop Linux at 3.2%, then Google's ChromeOS at 1.6%, as of March 2026. For tablets, Apple's iPadOS (a variant of iOS) has 52% share and Android has 48% worldwide. For the top 500 most powerful supercomputers, Linux distributions have had 100% of the market share since 2017. The global server operating system market share has Linux leading with a 63.1% marketshare, followed by Windows, Unix and other operating systems. Linux is also most used for web servers, and the most common Linux distribution is Ubuntu, followed by Debian. Linux has almost caught up with the second-most popular (desktop) OS, macOS, in some regions, such as in South America, and in Asia it's at 6.4% (7% with ChromeOS) vs 9.7% for macOS. In the US, ChromeOS is third at 5.5%, followed by (desktop) Linux at 4.3%. The most numerous type of device with an operating system are embedded systems. Not all embedded systems have operating systems, instead running their application code on the "bare metal"; of those that do have operating systems, a high percentage are standalone or do not have a web browser, which makes their usage share difficult to measure. Some operating systems used in embedded systems are more widely used than some of those mentioned above; for example, modern Intel microprocessors contain an embedded management processor running a version of the Minix operating system. == Worldwide device shipments == Shipments (to stores) do not necessarily translate to sales to consumers, therefore suggesting the numbers indicate popularity and/or usage could be misleading. Not only do smartphones sell in higher numbers than PCs, but also a lot more by dollar value, with the gap only projected to widen, to well over double. According to Gartner, the following is the worldwide device shipments (referring to wholesale) by operating system from 2012 to 2016, which includes smartphones, tablets, laptops and PCs together. On 27 January 2016, Paul Thurrott summarized the operating system market, the day after Apple announced "one billion devices": Apple's "active installed base" is now one billion devices. [..] Granted, some of those Apple devices were probably sold into the marketplace years ago. But that 1 billion figure can and should be compared to the numbers Microsoft touts for Windows 10 (200 million, most recently) or Windows more generally (1.5 billion active users, a number that hasn’t moved, magically, in years), and that Google touts for Android (over 1.4 billion, as of September). My understanding of iOS is that the user base was previously thought to be around 800 million strong, and when you factor out Macs and other non-iOS Apple devices, that's probably about right. But as you can see, there are three big personal computing platforms. And only one of them is actually declining. We’ll see how Windows 10 fares over the long term, but even if Microsoft hits the 1 billion figure in 1-2 years as promised, it will by then still be the smallest of those three platforms. In 2018, Apple stopped revealing unit sales in its reports. Since 2018, the company have been publishing only revenues per device models which, nonetheless, allowed the analysers to extrapolate the unit sales from the model revenues by applying the wholesale device prices. Other hardware manufacturers usually do not report unit sales. === PC shipments === For 2015 (and earlier), Gartner reports for "the year, worldwide PC shipments declined for the fourth consecutive year, which started in 2012 with the launch of tablets" with an 8% decline in PC sales for 2015 (not including cumulative decline in sales over the previous years). Microsoft backed away from their goal of one billion Windows 10 devices in three years (or "by the middle of 2018") and reported on 26 September 2016 that Windows 10 was running on over 400 million devices, and in March 2019, on more than 800 million. In May 2020, Gartner predicted further decline in all market segments for 2020 due to COVID-19, predicting a decline of 13.6% for all devices. while the "Work from Home Trend Saved PC Market from Collapse", with only a decline of 10.5% predicted for PCs. However, in the end, according to Gartner, PC shipments grew 10.7% in the fourth quarter of 2020 and reached 275 million units in 2020, a 4.8% increase from 2019 and the highest growth in ten years." Apple in 4th place for PCs had the largest growth in shipments for a company in Q4 of 31.3%, while "the fourth quarter of 2020 was another remarkable period of growth for Chromebooks, with shipments increasing around 200% year over year to reach 11.7 million units. In 2020, Chromebook shipments increased over 80% to total nearly 30 million units, largely due to demand from the North American education market." Chromebooks sold more (30 million) than Apple's Macs worldwide (22.5 million) in pandemic year 2020. According to the Catalyst group, the year 2021 had record high PC shipments with total shipments of 341 million units (including Chromebooks), 15% higher than 2020 and 27% higher than 2019, while being the largest shipment total since 2012. According to Gartner, worldwide PC shipments declined by 16.2% in 2022, the largest annual decrease since the mid-1990s, due to geopolitical, economic, and supply chain challenges. In 2024 and 2025, due to lower adoption of Windows 11 and Microsoft ending its support to Windows 10, the number of PCs shipped with pre-installed Windows OS dropped. Pundits attribute the low Windows 11 acceptance to its steep hardware requirements and especially the TPM 2.0 ready chipset requirement and the 2024 CrowdStrike-related IT outages. Meanwhile, the macOS device market share in PC device shipments increased to new heights, with improved numbers seen for Linux devices too. In Q3 2025, the macOS pre-installed device shipments increased by 14.9% year-over-year (YoY), while the overall PC-shipments increased only by 8.1%, in Q2 2025, it grew 21.4% YoY while the global PC-shipments increased only by 6.5%, and in Q1 2025, it grew 7% YoY while the global PC-shipments increased by 4.8%. === Tablet computers shipments === In 2015, eMarketer estimated at the beginning of the year that the tablet installed base would hit one billion for the first time (with China's use at 328 million, which Google Play doesn't serve or track, and the United States's use second at 156 million). At the end of the year, because of cheap tablets – not counted by all analysts – that goal was met (even excluding cumulative sales of previous years) as: Sales quintupled to an expected 1 billion units worldwide this year, from 216 million units in 2014, according to projections from the Envisioneering Group. While that number is far higher than the 200-plus million units globally projected by research firms IDC, Gartner and Forrester, Envisioneering analyst Richard Doherty says the rival estimates miss all the cheap Asian knockoff tablets that have been churning off assembly lines.[..] Forrester says its definition of tablets "is relatively narrow" while IDC says it includes some tablets by Amazon — but not all.[..] The top tech purchase of the year continued to be the smartphone, with an expected 1.5 billion sold worldwide, according to projections from researcher IDC. Last year saw some 1.2 billion sold.[..] Computers didn’t fare as well, despite the introduction of Microsoft's latest software upgrade, Windows 10, and the expected but not realized bump it would provide for consumers looking to skip the upgrade and just get a new computer instead. Some 281 million PCs were expected to be sold, according to IDC, down from 308 million in 2014. Folks tend to be happy with the older computers and keep them for longer, as more of our daily computing activities have moved to the smartphone.[..] While Windows 10 got good reviews from tech critics, only 11% of the 1-billion-plus Windows user base opted to do the upgrade, according to Microsoft. This suggests Microsoft has a ways to go before the software gets "hit" status. Apple's new operating system El Capitan has been
M-DISC
M-DISC (Millennial Disc) is a write-once optical disc technology introduced in 2009 by Millenniata, Inc. and available as DVD and Blu-ray discs. == Overview == M-DISC's design is intended to provide archival media longevity. M-Disc claims that properly stored M-DISC DVD recordings will last up to 1000 years. The M-DISC DVD looks like a standard disc, except it is almost transparent with later DVD and BD-R M-Disks having standard and inkjet printable labels. The patents protecting the M-DISC technology assert that the data layer is a glassy carbon material that is substantially inert to oxidation and has a melting point of 200–1000 °C (392–1832 °F). M-Discs are readable by most regular DVD players made after 2005 and Blu-Ray and BDXL disc drives and writable by most made after 2011. Available recording capacities conform to standard DVD/Blu-ray sizes: 4.7 GB DVD+R to 25 GB BD-R, 50 GB BD-R and 100 GB BDXL. == History == M-DISC developer Millenniata, Inc. was co-founded by Brigham Young University professors Barry Lunt, Matthew Linford, CEO Henry O'Connell and CTO Doug Hansen. The company was incorporated on May 13, 2010, in American Fork, Utah. Millenniata, Inc. officially went bankrupt in December 2016. Under the direction of CEO Paul Brockbank, Millenniata had issued convertible debt. When the obligation for conversion was not satisfied, the company defaulted on the debt payment and the debt holders took possession of all of the company's assets. The debt holders subsequently started a new company, Yours.co, to sell M-DISCs and related services. As of the 2020s, there are only 2 licensed manufacturers of M-Discs: Ritek, sold under the Ritek and RiDATA brands, and Verbatim with co-branded discs, marketed as the "Verbatim M-DISC". 128 GB BDXL never made it to market due to the 2016 bankruptcy. Early in 2022, Verbatim changed the formulation of their M-DISC branded Blu-rays. These new discs could be written at a faster rate than the previous ones – 6× speed instead of 4×. The new discs also had different colouration and markings compared with older version. Later in the year customers accused Verbatim of selling an inferior product and deceptive marketing. Verbatim responded that the new discs were a further development of the older discs and should have the same longevity, and that the technical changes therein were responsible for the altered appearance and higher write speeds. The updated M-DISC currently sold on the market uses the same metal ablative layer (MABL) metal oxide inorganic recording layer used in many of Verbatim's regular Blu-ray products. == Durability claims == The original M-DISC DVD+R was tested according to ISO/IEC 10995:2011 and ECMA-379 with a projected rated lifespan of several hundred years in archival use. The glassy carbon layers, in theory if preserved correctly in an environment like a salt mine, could store the data for over 10,000 years before going outside of readable specifications. However, the polycarbonate plastics, which are commonly used by almost all optical media and heavily in CBRN and ballistic protective equipment due to their optical, physical impact and chemical resistant properties, have a lifespan rating of only around 1000 years before degradation. Verbatim Japan claims that M-DISCs now use a titanium layer to prevent moisture ingression and to provide environmental stability. M-DISCs sold in Japan are advertised to have a projected lifespan of 100 years or more based on internal ISO/IEC 16963 testing, while other regional Verbatim websites claim that M-DISCs have a projected lifespan of "several hundred years" based on ISO/IEC 16963 testing. == Durability testing == In 2009, testing was done by the US Department of Defense (DoD) producing the China Lake Report testing Millenniata's M-Disk DVD to current market offerings from Delkin, MAM-A, Mitsubishi, Taiyo Yuden and Verbatim with all brands using organic dyes failing to pass the series of accelerated aging tests. From 2010 to 2012, the French National Laboratory of Metrology and Testing (LNE) used high-temperature accelerated aging testing, at 90 °C (194 °F) and 85% relative humidity inside a CLIMATS Excal 5423-U, for 250 to 1000 hours with a mix of inorganic DVD+R discs from MPO, Verbatim, Maxell, Syylex and DataTresor. The summary of the tests states that Syylex Glass Master Disc was rated for 1000+ hours, DataTresor Disc 250 hours+ and M-Disk under 250 hours. The Syylex disc was a custom-ordered product that could not be burned in a consumer player when they were still purchaseable from Syylex before their bankruptcy, so it was not truly in the same category as the others. In 2016, a consumer Mol Smith did real world stress testing on the 25 GB BD-R M-Disc alongside TDK's standard BD-R 25 GB disc using a copied movie, which demonstrated the reliability of M-Disc's molding compared to standard discs; after 60 days of outdoor direct exposure the M-Disk was played without error, while the TDK disc was physically destroyed. In 2022, the NIST Interagency Report NIST IR 8387 listed the M-Disc as an acceptable archival format rated for 100+ years, citing the aforementioned 2009 and 2012 tests by the US Department of Defense and French National Laboratory of Metrology and Testing as sources. == Commercial support == While recorded discs are readable in conventional DVD and BD drives, M-disc DVDs can only be burned by drives with firmware that supports the slightly higher power mode that M-Disk requires for burning its inorganic layers, as such writing speed is typically 2× speed. Blu-ray M-discs can be both written and read in most standard Blu-ray drives and are certified by the Blu-ray Disc Association to meet all current standard specifications as of 2019. Typically, the M-Discs cost 1.5–3× the price of standard Blu-Ray discs with DVD M-Discs now having sparse availability. With the first-generation DVD M-DISCs, it was difficult to determine which was the writable side of the disc due to being near fully translucent, until coloring and later labels similar to that on standard DVD discs was added to discs to help distinguish the sides preventing user error. Asus, LG Electronics, Lite-On, Pioneer, Buffalo Technology, and Hitachi-LG produce drives that can record M-DISC media while Verbatim and Ritek produce M-DISC discs. == Adoption == The regional government of the U.S. state of Utah has used M-Disc since 2011. Some consumers and avid datahoarders have adopted the format for cold digital data storage. == Alternative technologies == === Optical === Syylex Glass Master Disc: these discs use etched glass and are only typically degradable by physical or chemical damage, but not by normal ageing inside an archival environment. Current BD 25 GB, BD-R DL 50 GB & BDXL 100 GB (three layer) and Sony's BDXL 128 GB (four layer) discs are rated for up to 50 years (Standard inorganic HTL discs). Sony's Optical Disc Archive, is an optical competitor to the LTO tape-based data storage system, currently with up to 5.5 TB cartridges of dual-sided 120mm discs, with desktop readers and automated rackmount standard archival systems allowing for large scale archival and data retrieval rated for an estimated 100+ years. Pioneer DM for Archive is a disc media and drive combination developed by Pioneer to meet the requirements laid out by the Japanese government for preservation of financial data for a minimum of 100 years. The discs use a MABL type recording layer and are manufactured with tight tolerances. Although burnable in any BD Writer, when burned in Pioneers DM for Archive writers using the DM Archiver software the media and burn quality meet ISO/IEC 18630 which defines the testing methods needed for ensuring media and burn quality. === Magnetic === Linear Tape-Open (LTO) is rated for up to 30 years in a climate-controlled environment and is currently in use by most industries, including broadcast and corporate digital data systems. The latest generation released in 2026 is LTO-10, it defines two unique cartridge types which can hold 30 TB or 40 TB each Hard disk drives are currently available up to 30 TB (HDD) capacity in 3.5-inch format and 5 TB in 2.5-inch laptop format. However, unlike optical media, they are limited to 5–25 years of operation lifespan due to inevitable mechanical failure or magnetic instability. == Gallery ==
List of ARM Cortex-M development tools
This is a list of development tools for 32-bit ARM Cortex-M-based microcontrollers, which consists of Cortex-M0, Cortex-M0+, Cortex-M1, Cortex-M3, Cortex-M4, Cortex-M7, Cortex-M23, Cortex-M33, Cortex-M35P, Cortex-M52, Cortex-M55, and Cortex-M85 cores. == Development toolchains == IDE, compiler, linker, debugger, flashing (in alphabetical order): Ac6 System Workbench for STM32 (based on Eclipse and the GNU GCC toolchain with direct support for all ST-provided evaluation boards, Eval, Discovery and Nucleo, debug with ST-LINK) ARM Development Studio 5 by ARM Ltd. Atmel Studio by Atmel (based on Visual Studio and GNU GCC Toolchain) Code Composer Studio by Texas Instruments CoIDE by CooCox (note - website dead since 2018) Crossware Development Suite for ARM by Crossware CrossWorks for ARM by Rowley Dave by Infineon. For XMC processors only. Includes project wizard, detailed register decoding and a code library still under development. DRT by SOMNIUM Technologies. Based on GCC toolchain and proprietary linker technology. Available as a plugin for Atmel Studio and an Eclipse-based IDE. EmBitz (formerly Em::Blocks) – free, fast (non-eclipse) IDE for ST-LINK (live data updates), OpenOCD, including GNU Tools for ARM and project wizards for ST, Atmel, EnergyMicro etc. Embeetle IDE - free, fast (non-eclipse) IDE. Works both on Linux and Windows. emIDE by emide – free Visual Studio Style IDE including GNU Tools for ARM GNU ARM Eclipse – A family of Eclipse CDT extensions and tools for GNU ARM development GNU Tools (aka GCC) for ARM Embedded Processors by ARM Ltd – free GCC for bare metal IAR Embedded Workbench for ARM by IAR Systems ICC by ImageCraft Keil MDK-ARM by Keil LPCXpresso by NXP (formerly Red Suite by Code Red Technologies) MikroC by mikroe – mikroC MULTI by Green Hills Software, for all Arm 7, 9, Cortex-M, Cortex-R, Cortex-A Ride and RKit for ARM by Raisonance SEGGER Embedded Studio for ARM by Segger. SEGGER Ozone by Segger. STM32CubeIDE by STMicroelectronics - Combines STCubeMX with TrueSTUDIO into a single Eclipse style package Sourcery CodeBench by Mentor Graphics TASKING VX-Toolset by Altium TrueSTUDIO by Atollic Visual Studio by Microsoft as IDE, with GNU Tools as compiler/linker – e.g. supported by VisualGDB VXM Design's Buildroot toolchain for Cortex. It integrates GNU toolchain, Nuttx, filesystem and debugger/flasher in one build. winIDEA/winIDEAOpen by iSYSTEM YAGARTO – free GCC (no longer supported) Code::Blocks (EPS edition) (debug with ST-LINK no GDB and no OpenOCD required) IDE for Arduino ARM boards Arduino – IDE for Atmel SAM3X (Arduino Due) Energia – Arduino IDE for Texas Instruments Tiva and CC3200 Notes: == Debugging tools == JTAG and/or SWD debug interface host adapters (in alphabetical order): Black Magic Probe by 1BitSquared. CMSIS-DAP by Mbed. Crossconnect by Rowley Associates. DSTREAM by ARM Holdings Green Hills Probe and SuperTrace Probe by Green Hills Software. iTAG by iSYSTEM. I-jet by IAR Systems. Jaguar by Crossware. J-Link by Segger Supports JTAG and SWD. Supports ARM7, ARM9, ARM11, Cortex-A, Cortex-M, Cortex-R, Renesas RX, Microchip PIC32. Eclipse plug-in available. Supports GDB, RDI, Ozone debuggers. J-Trace by Segger. Supports JTAG, SWD, and ETM trace on Cortex-M. JTAGjet by Signum. LPC-LINK by Embedded Artists (for NXP) This is only embedded on NXP LPCXpresso development boards. LPC-LINK 2 by NXP. This device can be reconfigured to support 3 different protocols: J-LINK by Segger, CMSIS-DAP by ARM, Redlink by Code Red. Multilink debug probes, Cyclone in-system programming/debugging interfaces, and a GDB Server plug-in for Eclipse-based ARM IDEs by PEmicro. OpenOCD open source GDB server supports a variety of JTAG probes OpenOCD Eclipse plug-in available in GNU ARM Eclipse Plug-ins. AK-OPENJTAG by Artekit (Open JTAG-compatible). AK-LINK by Artekit. PEEDI by RONETIX Debug Probe by Raspberry Pi. RLink by Raisonance. ST-LINK/V2 by STMicroelectronics The ST-LINK/V2 debugger embedded on STM32 Nucleo and Discovery development boards can be converted to SEGGER J-LINK protocol. TRACE32 Debugger and ETM/ITM Trace by Lauterbach. ULINK by Keil. Debugging tools and/or debugging plug-ins (in alphabetical order): Memfault Error Analysis for post mortem debugging Percepio Tracealyzer, RTOS trace visualizer (with Eclipse plugin). Segger SystemView, RTOS trace visualizer. == Real-time operating systems == Commonly referred to as RTOS: == C/C++ software libraries == The following are free C/C++ libraries: ARM Cortex libraries: Cortex Microcontroller Software Interface Standard (CMSIS) libopencm3 (formerly called libopenstm32) libmaple for STM32F1 chips LPCOpen for NXP LPC chips Alternate C standard libraries: Bionic libc, dietlibc, EGLIBC, glibc, klibc, musl, Newlib, uClibc FAT file system libraries: EFSL, FatFs, Petit FatFs Fixed-point math libraries: libfixmath, fixedptc, FPMLib Encryption libraries: Comparison of TLS implementations wolfSSL == Non-C/C++ computer languages and software libraries ==
Digital artifactual value
Digital artifactual value, a preservation term, is the intrinsic value of a digital object, rather than the informational content of the object. Though standards are lacking, born-digital objects and digital representations of physical objects may have a value attributed to them as artifacts. == Intrinsic value in analog materials == With respect to analog or non-digital materials, artifacts are determined to have singular research or archival value if they possess qualities and characteristics that make them the only acceptable form for long-term preservation. These qualities and characteristics are commonly referred to as the item's intrinsic value and form the basis upon which digital artifactual value is currently evaluated. Artifactual value based on this idea is predicated upon the artifact's originality, faithfulness, fixity, and stability. The intrinsic value of a particular object, as interpreted by archival professionals, largely determines the selection process for archives. The National Archives and Records Administration Committee on Intrinsic Value in "Intrinsic Value in Archival Material" classified an analog object as having intrinsic value if it possessed one or more of the follow qualities: Physical form that may be the subject for study if the records provide meaningful documentation or significant examples of the form. Aesthetic or artistic quality. Unique or curious physical features. Age that provides a quality of uniqueness. Value for use in exhibits. Questionable authenticity, date, author, or other characteristic that is significant and ascertainable by physical examination. General and substantial public interest because of direct association with famous or historically significant people, places, things, issues or events. Significance as documentation of the establishment or continuing legal basis of an agency or institution. Significance as documentation of the formulation of policy at the highest executive levels when the policy has significance and broad effect throughout or beyond the agency or institution. Other archival professionals such as Lynn Westney have written that the characteristics of materials exhibiting intrinsic value include age, content, usage, particularities of creation, signatures, and attached seals. Westney and others have stated that paper-based artifacts can be thought to have evidentiary value, or significant contextual markings, insofar that the original manifestation of the artifact can attest to the originality, faithfulness or authenticity, fixity, and stability of the content. For other analog materials, properly articulating intrinsic value remains essential for determining artifactual value. Similar to paper-based objects in many respects, artifactual value for images typically takes into account artistic value, age, authorial prestige, significant provenance, and institutional priorities. Analog audio preservation is based upon similar factors, including the cultural value of the item, its historical uniqueness, the estimated longevity of the medium, the current condition of the item, and the state of playback equipment, among other things. == Analog conventions in a digital realm == The standard definition of artifactual value, as it has applied to analog or non-digital materials in the twentieth century, is based upon a set of conventions which do not ordinarily apply to digital objects in toto. The Council on Library and Information Resources (CLIR) has stated that printed texts and other paper-based manuscripts, when considered as objects, are imbued with meaning distilled from a general set of understandings inherent to these conventions: The object is of a fixed and stable composition/form. Authorship and intellectual property are a recognizable concept. Duplication is possible. Fungibility of informational content (or, in other words, the ability to be replaced by another identical object). These conventions are important to consider because they help to describe the physical and even metaphysical relationship between a document's content and its physical manifestation. The underpinnings of this relationship are not identical and do not apply with the same degree of clarity to an immaterial digital realm. The idea of fixity with regard to printed materials, for example, is largely predicated on the notion that an object has been recorded on a relatively stable medium. The physical presence of a print text serves as proof of its authenticity as an object or artifact, as well as its scarcity and uniqueness in relation to other print materials. Variations in the chemical properties and storage conditions of print-based materials, as well as other cultural variables, certainly impact the fixity or stability of print materials, but there is little controversy about determining its fundamental existence or originality. However, uniqueness in the physical, paper-based sense does not translate to a digital realm in which immaterial objects are subject to theoretically infinite levels of reproduction and dissemination. Born-digital and digital surrogates may or may not look any different from each other on a server, and alterations can be made without explicit notice to the user. These alterations are normally called migration events, or actions taken on the digital object that change the original object's composition. They can enact subtle but fundamental alterations to the original document, thereby compromising its existence as an original object. Furthermore, because the tools used to generate and access digital objects have historically evolved quite rapidly, issues of playback obsolescence, incapability, data loss, and broken pathways to information have changed traditional ideas of fixity and stability. Therefore, artifactual value in a digital realm requires a modified set of generalized standards for determining artifactual originality. Michael J. Giarlo and Ronald Jantz, only two of many, have posited a list of methods for establishing digital intrinsic value by way of careful metadata generation and records maintenance. In their report, a digital original possesses three key characteristics that distinguishes it from identical copies. These include continuous verification and re-verification of the document's digital signature starting from the date of creation; retaining versions and recordings of all changes to the object in an audit trail; and having the archival master contain the creation date of the digital object. They also reported that originality in digital sources could be verified or produced by the following techniques: Digital object is given a date-time stamp that's automatically inserted into the METS-XML header upon creation. Date-time is inserted into archival metadata. Encapsulation. Digital signatures. == The role of digital surrogates == Digital surrogates are considered a utility for aiding in the preservation and increased access of certain artifacts. However, digital surrogates can have different utilities for objects depending on the nature of the original artifact and the condition the artifact is in. In 2001 the Council on Library and Information Resources (CLIR) published a report on the artifact in library collections. The CLIR states that the utility of the digital surrogate can be determined by dividing the original material (artifact) into two different categories, artifacts that are rare and those that are not. These two categories can be further divided by two categories, artifacts that are frequently used and those that are not. === Materials that are frequently used and not rare === According to the CLIR "it is not obvious that digital surrogates provide all the functionality, all the information, or all the aesthetic value of originals. Therefore, while it may be sensible to recommend that digital surrogates be used to reduce the cost and increase the availability of library holdings that circulate frequently, the decision to deaccession a physical object in library collections and replace it with a digital surrogate should be based on a careful assessment of the way in which library patrons use the original object or objects of its kind." === Materials that are infrequently used and not rare === Keeping the original is always the best solution for libraries and especially archives but in the case of libraries where an artifact is not rare or used infrequently there must be a barometer that is developed to help "balance functionality with actual use in order to help decide when digital surrogates that provide most of the functionality of originals are acceptable." === Materials that are rare and frequently used === A professional in the field of Library and Information Science (LIS) would almost certainly not argue that a digital surrogate could replace a rare object. However, in the case of a rare object that is falling into poor shape due to heavy use a digital surrogate could be extremely useful in reducing the wear a