In the mathematical theory of random processes, the Markov chain central limit theorem has a conclusion somewhat similar in form to that of the classic central limit theorem (CLT) of probability theory, but the quantity in the role taken by the variance in the classic CLT has a more complicated definition. See also the general form of Bienaymé's identity. == Statement == Suppose that: the sequence X 1 , X 2 , X 3 , … {\textstyle X_{1},X_{2},X_{3},\ldots } of random elements of some set is a Markov chain that has a stationary probability distribution; and the initial distribution of the process, i.e. the distribution of X 1 {\textstyle X_{1}} , is the stationary distribution, so that X 1 , X 2 , X 3 , … {\textstyle X_{1},X_{2},X_{3},\ldots } are identically distributed. In the classic central limit theorem these random variables would be assumed to be independent, but here we have only the weaker assumption that the process has the Markov property; and g {\textstyle g} is some (measurable) real-valued function for which var ( g ( X 1 ) ) < + ∞ . {\textstyle \operatorname {var} (g(X_{1}))<+\infty .} Now let μ = E ( g ( X 1 ) ) , μ ^ n = 1 n ∑ k = 1 n g ( X k ) σ 2 := lim n → ∞ var ( n μ ^ n ) = lim n → ∞ n var ( μ ^ n ) = var ( g ( X 1 ) ) + 2 ∑ k = 1 ∞ cov ( g ( X 1 ) , g ( X 1 + k ) ) . {\displaystyle {\begin{aligned}\mu &=\operatorname {E} (g(X_{1})),\\{\widehat {\mu }}_{n}&={\frac {1}{n}}\sum _{k=1}^{n}g(X_{k})\\\sigma ^{2}&:=\lim _{n\to \infty }\operatorname {var} ({\sqrt {n}}{\widehat {\mu }}_{n})=\lim _{n\to \infty }n\operatorname {var} ({\widehat {\mu }}_{n})=\operatorname {var} (g(X_{1}))+2\sum _{k=1}^{\infty }\operatorname {cov} (g(X_{1}),g(X_{1+k})).\end{aligned}}} Then as n → ∞ , {\textstyle n\to \infty ,} we have n ( μ ^ n − μ ) → D Normal ( 0 , σ 2 ) , {\displaystyle {\sqrt {n}}({\hat {\mu }}_{n}-\mu )\ {\xrightarrow {\mathcal {D}}}\ {\text{Normal}}(0,\sigma ^{2}),} where the decorated arrow indicates convergence in distribution. == Monte Carlo Setting == The Markov chain central limit theorem can be guaranteed for functionals of general state space Markov chains under certain conditions. In particular, this can be done with a focus on Monte Carlo settings. An example of the application in a MCMC (Markov Chain Monte Carlo) setting is the following: Consider a simple hard spheres model on a grid. Suppose X = { 1 , … , n 1 } × { 1 , … , n 2 } ⊆ Z 2 {\displaystyle X=\{1,\ldots ,n_{1}\}\times \{1,\ldots ,n_{2}\}\subseteq Z^{2}} . A proper configuration on X {\displaystyle X} consists of coloring each point either black or white in such a way that no two adjacent points are white. Let χ {\displaystyle \chi } denote the set of all proper configurations on X {\displaystyle X} , N χ ( n 1 , n 2 ) {\displaystyle N_{\chi }(n_{1},n_{2})} be the total number of proper configurations and π be the uniform distribution on χ {\displaystyle \chi } so that each proper configuration is equally likely. Suppose our goal is to calculate the typical number of white points in a proper configuration; that is, if W ( x ) {\displaystyle W(x)} is the number of white points in x ∈ χ {\displaystyle x\in \chi } then we want the value of E π W = ∑ x ∈ χ W ( x ) N χ ( n 1 , n 2 ) {\displaystyle E_{\pi }W=\sum _{x\in \chi }{\frac {W(x)}{N_{\chi }{\bigl (}n_{1},n_{2}{\bigr )}}}} If n 1 {\displaystyle n_{1}} and n 2 {\displaystyle n_{2}} are even moderately large then we will have to resort to an approximation to E π W {\displaystyle E_{\pi }W} . Consider the following Markov chain on χ {\displaystyle \chi } . Fix p ∈ ( 0 , 1 ) {\displaystyle p\in (0,1)} and set X 1 = x 1 {\displaystyle X_{1}=x_{1}} where x 1 ∈ χ {\displaystyle x_{1}\in \chi } is an arbitrary proper configuration. Randomly choose a point ( x , y ) ∈ X {\displaystyle (x,y)\in X} and independently draw U ∼ U n i f o r m ( 0 , 1 ) {\displaystyle U\sim \mathrm {Uniform} (0,1)} . If u ≤ p {\displaystyle u\leq p} and all of the adjacent points are black then color ( x , y ) {\displaystyle (x,y)} white leaving all other points alone. Otherwise, color ( x , y ) {\displaystyle (x,y)} black and leave all other points alone. Call the resulting configuration X 1 {\displaystyle X_{1}} . Continuing in this fashion yields a Harris ergodic Markov chain { X 1 , X 2 , X 3 , … } {\displaystyle \{X_{1},X_{2},X_{3},\ldots \}} having π {\displaystyle \pi } as its invariant distribution. It is now a simple matter to estimate E π W {\displaystyle E_{\pi }W} with w n ¯ = ∑ i = 1 n W ( X i ) / n {\displaystyle {\overline {w_{n}}}=\sum _{i=1}^{n}W(X_{i})/n} . Also, since χ {\displaystyle \chi } is finite (albeit potentially large) it is well known that X {\displaystyle X} will converge exponentially fast to π {\displaystyle \pi } which implies that a CLT holds for w n ¯ {\displaystyle {\overline {w_{n}}}} . == Implications == Not taking into account the additional terms in the variance which stem from correlations (e.g. serial correlations in markov chain monte carlo simulations) can result in the problem of pseudoreplication when computing e.g. the confidence intervals for the sample mean.
Proximal gradient methods for learning
Proximal gradient (forward backward splitting) methods for learning is an area of research in optimization and statistical learning theory which studies algorithms for a general class of convex regularization problems where the regularization penalty may not be differentiable. One such example is ℓ 1 {\displaystyle \ell _{1}} regularization (also known as Lasso) of the form min w ∈ R d 1 n ∑ i = 1 n ( y i − ⟨ w , x i ⟩ ) 2 + λ ‖ w ‖ 1 , where x i ∈ R d and y i ∈ R . {\displaystyle \min _{w\in \mathbb {R} ^{d}}{\frac {1}{n}}\sum _{i=1}^{n}(y_{i}-\langle w,x_{i}\rangle )^{2}+\lambda \|w\|_{1},\quad {\text{ where }}x_{i}\in \mathbb {R} ^{d}{\text{ and }}y_{i}\in \mathbb {R} .} Proximal gradient methods offer a general framework for solving regularization problems from statistical learning theory with penalties that are tailored to a specific problem application. Such customized penalties can help to induce certain structure in problem solutions, such as sparsity (in the case of lasso) or group structure (in the case of group lasso). == Relevant background == Proximal gradient methods are applicable in a wide variety of scenarios for solving convex optimization problems of the form min x ∈ H F ( x ) + R ( x ) , {\displaystyle \min _{x\in {\mathcal {H}}}F(x)+R(x),} where F {\displaystyle F} is convex and differentiable with Lipschitz continuous gradient, R {\displaystyle R} is a convex, lower semicontinuous function which is possibly nondifferentiable, and H {\displaystyle {\mathcal {H}}} is some set, typically a Hilbert space. The usual criterion of x {\displaystyle x} minimizes F ( x ) + R ( x ) {\displaystyle F(x)+R(x)} if and only if ∇ ( F + R ) ( x ) = 0 {\displaystyle \nabla (F+R)(x)=0} in the convex, differentiable setting is now replaced by 0 ∈ ∂ ( F + R ) ( x ) , {\displaystyle 0\in \partial (F+R)(x),} where ∂ φ {\displaystyle \partial \varphi } denotes the subdifferential of a real-valued, convex function φ {\displaystyle \varphi } . Given a convex function φ : H → R {\displaystyle \varphi :{\mathcal {H}}\to \mathbb {R} } an important operator to consider is its proximal operator prox φ : H → H {\displaystyle \operatorname {prox} _{\varphi }:{\mathcal {H}}\to {\mathcal {H}}} defined by prox φ ( u ) = arg min x ∈ H φ ( x ) + 1 2 ‖ u − x ‖ 2 2 , {\displaystyle \operatorname {prox} _{\varphi }(u)=\operatorname {arg} \min _{x\in {\mathcal {H}}}\varphi (x)+{\frac {1}{2}}\|u-x\|_{2}^{2},} which is well-defined because of the strict convexity of the ℓ 2 {\displaystyle \ell _{2}} norm. The proximal operator can be seen as a generalization of a projection. We see that the proximity operator is important because x ∗ {\displaystyle x^{}} is a minimizer to the problem min x ∈ H F ( x ) + R ( x ) {\displaystyle \min _{x\in {\mathcal {H}}}F(x)+R(x)} if and only if x ∗ = prox γ R ( x ∗ − γ ∇ F ( x ∗ ) ) , {\displaystyle x^{}=\operatorname {prox} _{\gamma R}\left(x^{}-\gamma \nabla F(x^{})\right),} where γ > 0 {\displaystyle \gamma >0} is any positive real number. === Moreau decomposition === One important technique related to proximal gradient methods is the Moreau decomposition, which decomposes the identity operator as the sum of two proximity operators. Namely, let φ : X → R {\displaystyle \varphi :{\mathcal {X}}\to \mathbb {R} } be a lower semicontinuous, convex function on a vector space X {\displaystyle {\mathcal {X}}} . We define its Fenchel conjugate φ ∗ : X → R {\displaystyle \varphi ^{}:{\mathcal {X}}\to \mathbb {R} } to be the function φ ∗ ( u ) := sup x ∈ X ⟨ x , u ⟩ − φ ( x ) . {\displaystyle \varphi ^{}(u):=\sup _{x\in {\mathcal {X}}}\langle x,u\rangle -\varphi (x).} The general form of Moreau's decomposition states that for any x ∈ X {\displaystyle x\in {\mathcal {X}}} and any γ > 0 {\displaystyle \gamma >0} that x = prox γ φ ( x ) + γ prox φ ∗ / γ ( x / γ ) , {\displaystyle x=\operatorname {prox} _{\gamma \varphi }(x)+\gamma \operatorname {prox} _{\varphi ^{}/\gamma }(x/\gamma ),} which for γ = 1 {\displaystyle \gamma =1} implies that x = prox φ ( x ) + prox φ ∗ ( x ) {\displaystyle x=\operatorname {prox} _{\varphi }(x)+\operatorname {prox} _{\varphi ^{}}(x)} . The Moreau decomposition can be seen to be a generalization of the usual orthogonal decomposition of a vector space, analogous with the fact that proximity operators are generalizations of projections. In certain situations it may be easier to compute the proximity operator for the conjugate φ ∗ {\displaystyle \varphi ^{}} instead of the function φ {\displaystyle \varphi } , and therefore the Moreau decomposition can be applied. This is the case for group lasso. == Lasso regularization == Consider the regularized empirical risk minimization problem with square loss and with the ℓ 1 {\displaystyle \ell _{1}} norm as the regularization penalty: min w ∈ R d 1 n ∑ i = 1 n ( y i − ⟨ w , x i ⟩ ) 2 + λ ‖ w ‖ 1 , {\displaystyle \min _{w\in \mathbb {R} ^{d}}{\frac {1}{n}}\sum _{i=1}^{n}(y_{i}-\langle w,x_{i}\rangle )^{2}+\lambda \|w\|_{1},} where x i ∈ R d and y i ∈ R . {\displaystyle x_{i}\in \mathbb {R} ^{d}{\text{ and }}y_{i}\in \mathbb {R} .} The ℓ 1 {\displaystyle \ell _{1}} regularization problem is sometimes referred to as lasso (least absolute shrinkage and selection operator). Such ℓ 1 {\displaystyle \ell _{1}} regularization problems are interesting because they induce sparse solutions, that is, solutions w {\displaystyle w} to the minimization problem have relatively few nonzero components. Lasso can be seen to be a convex relaxation of the non-convex problem min w ∈ R d 1 n ∑ i = 1 n ( y i − ⟨ w , x i ⟩ ) 2 + λ ‖ w ‖ 0 , {\displaystyle \min _{w\in \mathbb {R} ^{d}}{\frac {1}{n}}\sum _{i=1}^{n}(y_{i}-\langle w,x_{i}\rangle )^{2}+\lambda \|w\|_{0},} where ‖ w ‖ 0 {\displaystyle \|w\|_{0}} denotes the ℓ 0 {\displaystyle \ell _{0}} "norm", which is the number of nonzero entries of the vector w {\displaystyle w} . Sparse solutions are of particular interest in learning theory for interpretability of results: a sparse solution can identify a small number of important factors. === Solving for L1 proximity operator === For simplicity we restrict our attention to the problem where λ = 1 {\displaystyle \lambda =1} . To solve the problem min w ∈ R d 1 n ∑ i = 1 n ( y i − ⟨ w , x i ⟩ ) 2 + ‖ w ‖ 1 , {\displaystyle \min _{w\in \mathbb {R} ^{d}}{\frac {1}{n}}\sum _{i=1}^{n}(y_{i}-\langle w,x_{i}\rangle )^{2}+\|w\|_{1},} we consider our objective function in two parts: a convex, differentiable term F ( w ) = 1 n ∑ i = 1 n ( y i − ⟨ w , x i ⟩ ) 2 {\displaystyle F(w)={\frac {1}{n}}\sum _{i=1}^{n}(y_{i}-\langle w,x_{i}\rangle )^{2}} and a convex function R ( w ) = ‖ w ‖ 1 {\displaystyle R(w)=\|w\|_{1}} . Note that R {\displaystyle R} is not strictly convex. Let us compute the proximity operator for R ( w ) {\displaystyle R(w)} . First we find an alternative characterization of the proximity operator prox R ( x ) {\displaystyle \operatorname {prox} _{R}(x)} as follows: u = prox R ( x ) ⟺ 0 ∈ ∂ ( R ( u ) + 1 2 ‖ u − x ‖ 2 2 ) ⟺ 0 ∈ ∂ R ( u ) + u − x ⟺ x − u ∈ ∂ R ( u ) . {\displaystyle {\begin{aligned}u=\operatorname {prox} _{R}(x)\iff &0\in \partial \left(R(u)+{\frac {1}{2}}\|u-x\|_{2}^{2}\right)\\\iff &0\in \partial R(u)+u-x\\\iff &x-u\in \partial R(u).\end{aligned}}} For R ( w ) = ‖ w ‖ 1 {\displaystyle R(w)=\|w\|_{1}} it is easy to compute ∂ R ( w ) {\displaystyle \partial R(w)} : the i {\displaystyle i} th entry of ∂ R ( w ) {\displaystyle \partial R(w)} is precisely ∂ | w i | = { 1 , w i > 0 − 1 , w i < 0 [ − 1 , 1 ] , w i = 0. {\displaystyle \partial |w_{i}|={\begin{cases}1,&w_{i}>0\\-1,&w_{i}<0\\\left[-1,1\right],&w_{i}=0.\end{cases}}} Using the recharacterization of the proximity operator given above, for the choice of R ( w ) = ‖ w ‖ 1 {\displaystyle R(w)=\|w\|_{1}} and γ > 0 {\displaystyle \gamma >0} we have that prox γ R ( x ) {\displaystyle \operatorname {prox} _{\gamma R}(x)} is defined entrywise by ( prox γ R ( x ) ) i = { x i − γ , x i > γ 0 , | x i | ≤ γ x i + γ , x i < − γ , {\displaystyle \left(\operatorname {prox} _{\gamma R}(x)\right)_{i}={\begin{cases}x_{i}-\gamma ,&x_{i}>\gamma \\0,&|x_{i}|\leq \gamma \\x_{i}+\gamma ,&x_{i}<-\gamma ,\end{cases}}} which is known as the soft thresholding operator S γ ( x ) = prox γ ‖ ⋅ ‖ 1 ( x ) {\displaystyle S_{\gamma }(x)=\operatorname {prox} _{\gamma \|\cdot \|_{1}}(x)} . === Fixed point iterative schemes === To finally solve the lasso problem we consider the fixed point equation shown earlier: x ∗ = prox γ R ( x ∗ − γ ∇ F ( x ∗ ) ) . {\displaystyle x^{}=\operatorname {prox} _{\gamma R}\left(x^{}-\gamma \nabla F(x^{})\right).} Given that we have computed the form of the proximity operator explicitly, then we can define a standard fixed point iteration procedure. Namely, fix some initial w 0 ∈ R d {\displaystyle w^{0}\in \mathbb {R} ^{d}} , and for k = 1 , 2 , … {\displaystyle k=1,2,\ldots } define w k + 1 = S γ ( w k − γ ∇ F ( w k ) ) . {\displaystyle w^{k+1}=S_{\gamma }\left(w^{k}-\gamma \nabla F\l
Floyd–Steinberg dithering
Floyd–Steinberg dithering is an image dithering algorithm first published in 1976 by Robert W. Floyd and Louis Steinberg. It is commonly used by image manipulation software, for example, when converting an image from a Truecolor 24-bit PNG format into a GIF format, which is restricted to a maximum of 256 colors. == Implementation == The algorithm achieves dithering using error diffusion, meaning it pushes (adds) the residual quantization error of a pixel onto its neighboring pixels, to be quantized after. It spreads the debt out according to the distribution (shown as a map of the neighboring pixels): [ ∗ 7 16 … … 3 16 5 16 1 16 … ] {\displaystyle {\begin{bmatrix}&&&{\frac {\displaystyle 7}{\displaystyle 16}}&\ldots \\\ldots &{\frac {\displaystyle 3}{\displaystyle 16}}&{\frac {\displaystyle 5}{\displaystyle 16}}&{\frac {\displaystyle 1}{\displaystyle 16}}&\ldots \\\end{bmatrix}}} The pixel indicated with a star () indicates the pixel currently being scanned, and the blank pixels are the previously scanned pixels. The specific values (7/16, 3/16, 5/16, 1/16) were originally found by trial-and-error, "guided by the desire to have a region of desired density 0.5 come out as a checkerboard pattern". The algorithm scans the image from left to right, top to bottom, quantizing pixel values one by one. Each time, the quantization error is transferred to the neighboring pixels, while not affecting the pixels that already have been quantized. Hence, if a number of pixels have been rounded downwards, it becomes more likely that the next pixel is rounded upwards, such that on average, the quantization error is close to zero. The diffusion coefficients have the property that if the original pixel values are exactly halfway in between the nearest available colors, the dithered result is a checkerboard pattern. For example, 50% grey data could be dithered as a black-and-white checkerboard pattern. For optimal dithering, the counting of quantization errors should be in sufficient accuracy to prevent rounding errors from affecting the result. For correct results, all values should be linearized first, rather than operating directly on sRGB values as is common for images stored on computers. In some implementations, the horizontal direction of scan alternates between lines; this is called "serpentine scanning" or boustrophedon transform dithering. The algorithm described above is in the following pseudocode. This works for any approximately linear encoding of pixel values, such as 8-bit integers, 16-bit integers or real numbers in the range [0, 1]. for each y from top to bottom do for each x from left to right do oldpixel := pixels[x][y] newpixel := find_closest_palette_color(oldpixel) pixels[x][y] := newpixel quant_error := oldpixel - newpixel pixels[x + 1][y ] := pixels[x + 1][y ] + quant_error × 7 / 16 pixels[x - 1][y + 1] := pixels[x - 1][y + 1] + quant_error × 3 / 16 pixels[x ][y + 1] := pixels[x ][y + 1] + quant_error × 5 / 16 pixels[x + 1][y + 1] := pixels[x + 1][y + 1] + quant_error × 1 / 16 When converting grayscale pixel values from a high to a low bit depth (e.g. 8-bit grayscale to 1-bit black-and-white), find_closest_palette_color() may perform just a simple rounding, for example: find_closest_palette_color(oldpixel) = round(oldpixel / 255) The pseudocode can result in pixel values exceeding the valid values (such as greater than 255 in 8-bit grayscale images). Such values should ideally be handled by the find_closest_palette_color() function, rather than clipping the intermediate values, since a subsequent error may bring the value back into range. However, if fixed-width integers are used, wrapping of intermediate values would cause inversion of black and white, and so should be avoided. The find_closest_palette_color() implementation is nontrivial for a palette that is not evenly distributed, however small inaccuracies in selecting the correct palette color have minimal visual impact due to error being propagated to future pixels. A nearest neighbor search in 3D is frequently used.
Identi.ca
identi.ca is a free and open-source social networking and blogging service based on the pump.io software, using the Activity Streams protocol. Identi.ca stopped accepting new registrations in 2013, but continues to operate alongside several other pump.io-based hosts provided by E14N which continue to accept new registrations. == Features == Identi.ca is similar to social networking sites like Facebook and Google+, allowing unlimited length status updates, rich text, and images. The Activity Streams protocol supports many kinds of activities such as games. OpenFarmGame is a prototype application for an Activity Streams-based game. Previous features from its StatusNet version such as hashtags, groups, and global search are not supported. == History == === StatusNet === The service received more than 8,000 registrations and 19,000 updates within the first 24 hours of publicly launching on July 2, 2008, and reached its 1,000,000th notice on November 4, 2008. In January 2009, identi.ca received investment funds from venture capital group Montreal Start Up. On March 30, 2009, Control Yourself (since renamed StatusNet Inc) announced that Identi.ca was to become part of a hosted microblogging service called status.net to be launched in May 2009. Status.net offers individual microblogs under a subdomain to be chosen by the customer. Identi.ca will remain a free service. All notices will be published under the Creative Commons Attribution 3.0 license by default, but paying customers will be free to choose a different license. Formerly based on StatusNet, a micro-blogging software package built on the OStatus specification (and earlier based on the OpenMicroBlogging specification), Identi.ca allowed users to send text updates (known as "notices") up to 140 characters long. While similar to Twitter in both concept and operation, Identi.ca/StatusNet provided many features not currently implemented by Twitter, including XMPP support and personal tag clouds. In addition, Identi.ca/StatusNet allowed free export and exchange of personal and "friend" data based on the FOAF standard; therefore, notices could be fed into a Twitter account or other service, and also ported in to a private system similar to Yammer. === pump.io === Developer Evan Prodromou chose to change the site to the pump.io software platform in development, because pump.io offers more features making it technically more advanced. Registration on Identi.ca was closed in December 2012 in preparation for the switch to pump.io software (the popularity of Identi.ca and "official" Status.net hosting were considered a hindrance to the creation of a federated social network). The conversion was completed on 12 July 2013. The 140 character per post limit was removed (in StatusNet, it was a setting, not an inherent limitation); now the blog posts can contain formatting and images. Groups, hashtags, and a page listing popular posts are not yet implemented in pump.io.
GeneTalk
GeneTalk is a web-based platform, tool, and database for filtering, reduction and prioritization of human sequence variants from next-generation sequencing (NGS) data. GeneTalk allows editing annotation about sequence variants and build up a crowd sourced database with clinically relevant information for diagnostics of genetic disorders. GeneTalk allows searching for information about specific sequence variants and connects to experts on variants that are potentially disease-relevant. == Application to diagnostics == Users can upload NGS data in Variant Call Format (VCF) onto the GeneTalk server into their accounts. All entries of the file are preprocessed and shown in the integrated VCF viewer. Filtering tools are set by the user to reduce the number of clinically non-relevant variants. After filtering and prioritization users can interpret relevant variants by retrieving information (annotations) about variants from the GeneTalk database. The communication platform allow users to contact experts about specific variants, genes, or genetic disorders, to exchange knowledge and expertise. === Analysis procedure === Steps required to analyze VCF files Upload VCF file Edit pedigree and phenotype information for segregation filtering Filter VCF file by editing the filtering options View results and annotations Add annotations === Filtering tools === The following filtering options may be used to reduce the non-relevant sequence variants in VCF files. Functional – filter out variants that have effects on protein level Linkage – filter out variants that are on specified chromosomes Gene panel – filter variants by genes or gene panels, subscribe to publicly available gene panels or create own ones Frequency – show only variants with a genotype frequency lower than specified Inheritance – filter out variants by presumed mode of inheritance Annotation – show only variants with a score for medical relevance and scientific evidence == Communication platform and expert network == Users can share VCF files with colleagues and coworkers. The integrated mailing systems allows users to contact experts easily. Users can create annotations and comments and rate annotations regarding medical relevance and scientific evidence, that is helpful for the community of users for diagnosis of genetic disorders. Registered users provide information about their field of knowledge in their profile and can be contacted by other users. == Potential applications == Developing diagnostics Genetic analysis Capturing data generated by community Communication and exchange of knowledge and expertise
Cybersecurity in space
Cybersecurity in space involves the defense of all space assets (e.g. navigation systems, satellites, ground antennas, networks, etc.). The security of space can be affected by attacks such as disruption, corruption as well as the destruction of depended-upon assets/collected data. Government (e.g. militaries) and non-government sectors (e.g. financial industries) have started to become more reliant on numerous space-based services. Due to the criticality of these services, space security experts have identified these assets as high-value targets (HVT) that can cause detrimental consequences to all of Earth. == Scope and definitions == Space assets are broken down by three sub-sectors: the space component, the ground component, and the individual user component. The architecture of space assets is extremely complex and allows for a frequent attack vector utilized, the disruption by radio frequency (RF) cyber-attacks. In 2020, a memorandum was published by President Donald Trump, Space Policy Directive‑5 (SPD‑5). It established principles to ensure the safeguarding of all space assets. In 2023, the National Institute of Standards and Technology’s (NIST) published IR 8270, Introduction to Cybersecurity for Commercial Satellite Operations. This report established a baseline risk-management framework (RMF) to be implemented into space operations. == History == During the Cold War in the 1950s-1960s, the United States and Russia entered what was called the “Space Race”. By 1957, the Soviet Union successfully launched the first satellite into space named Sputnik. By 1961, the first key milestone was accomplished when the Soviet Union’s Yuri Gagarin became the first human to orbit Earth. This was later followed by the first American, Alan Shepard, to be launched into space; this was followed by John Glenn becoming the first American to orbit Earth in 1962. In 1969, a pinnacle milestone was reached when Apollo 11 launched into space and Neil Armstrong became the first man to walk on the moon. As space operations furthered, Commercial off-the-shelf products became increasingly popular but resulted in a rapid increase to the cyber-attack surface. Public awareness of space security did not increase until 2022, when the Viasat KA-SAT incident occurred, resulting in the disruption of a large number of modems across Europe. The attack was later accredited to Russia by the U.S. and the U.K. Policy and standards started to rapidly increase by 2020. The establishment of SPD-5 was released in 2020 followed by asset hardening instructions in 2022, and NIST’s IR 8270 in 2023. It was not until 2025 that Europe published their own findings in the Space Threat Landscape 2025 Report. This document led to the EU’s security proposals and standards. == Threats == === Radio-frequency Interference and Global Navigation Satellite Systems (GNSS) Spoofing === Space services are highly dependent on RF links for systems such as GNSS, however, a consequence of this dependency on RF is denial of service and deception. In 2017, the Black Sea maritime event occurred when numerous ships were subject to spoofing. Space services depend on RF links susceptible to jamming (denial) and spoofing (deception), including for GNSS/Positioning, Navigation, and Timing (PNT). Annotated incidents include the 2017 Black Sea maritime spoofing event affecting numerous ships, and extensive aviation GNSS spoofing patterns surveyed in various regions during 2024–2025. === Network intrusion and malware === Cyber threats can intrude and infect assets with malware. They do this by finding misconfiguration vulnerabilities, remote-management interfaces, and/or supply-chain vulnerabilities mainly in ground networks and user terminals. When KA-SAT occurred, it resulted from bulk modem disturbances. Forensic analysts later suggested malicious management controls and wiper malware as the root cause. === Supply-chain and lifecycle risks === The outsource of COTS components, external vendors, and software defined payloads allowed for vulnerabilities to emerge in the System/Product Lifecycle. In response, EU recommended the implementation of lifecycle-wide controls as mitigating factors. === Espionage, disruption, and influence === As Advanced Persistent Threats (APTs), Global Positioning System (GPS) intervention, and information warfare increased, assets like transponders became more frequent targets of attack. == Noteworthy incidents == The Viasat KA‑SAT incident of 2022, where a large number of modems in Europe were disrupted, resulted in the loss of telemetry access to a significant amount of wind turbines in Germany. The mass GNSS deception of the Black Sea in 2017 affected numerous ships when they started to convey fake central locations in Russia. Between 2024 and 2025, there was a mass, repetitive aviation GNSS spoofing that affected the aircraft of various regions. == Standards, guidelines, and best practices == SPD‑5 (U.S.) – This established risk-based engineering, verifying and ensuring positive control, and the implementation of risk mitigation controls. NIST IR 8270 – This created a RMF for COTS satellites. CISA/FBI SATCOM Advisory (AA22‑076) – Provided guidance on hardening techniques such as least-privileged, access control, encryption, etc.). ENISA Space Threat Landscape 2025 – It established the categorization of assets to organize threats, ensuring the observation of system/product lifecycle, and an RMF for COTS satellites. ECSS‑E‑ST‑80C (2024) – This established a standard for securing lifecycles in space, covering all segments (e.g. ground, launch, etc.). == Regulation and governance == As of 2025, there is no international regulations established for space assets, but the U.S., EU, and ESA institutional initiatives have published standards to address security concerns. The U.S. implemented SPD-5 and the Federal Communications Commission (FCC); the FCC addressed orbital debris. While the EU created standards to address technological mandates and support the implementation of NIS2. Lastly, the ESA created a special operations center to safeguard their satellites. International governance is still evolving, but forums have been held by the United Nations Committee on the Peaceful Uses of Outer Space. International conversations under forums such as the UN Committee on the Peaceful Uses of Outer Space (COPUOS) progressively note the cyber–space safety relationship, though formal global norms specific to space cybersecurity continue evolving. == Risk management approaches == Through RMF, mitigation controls have been implemented to reduce the risk of exploitation while increasing the security of space. Controls addressing mitigation include proper configuration, system hardening, zero-trust architectures, encryption, etc. Both the government and industries have placed an emphasis on incident response procedures to identify, contain, and remediate breaches.
Quickly (software)
Quickly is a framework for creating software programs for a Linux distribution using Python, PyGTK, Glade Interface Designer and Desktop Couch. It then allows for easy publishing using bzr and Launchpad. Quickly is designed to speed up the start of new projects with the use of templates, not only for programs but for any type of project. These templates are used to automate project configuration and maintenance. Delegating into templates and not into a specific library allows projects created using Quickly not to require dependencies on any particular library or runtime of Quickly itself. The project was started by Rick Spencer after his frustration as a beginner Ubuntu developer. == Updates == Last available software update is on 2013-01-31 for Ubuntu 11.04.