Capture the flag (cybersecurity)

In computer security, Capture the Flag (CTF) is an exercise in which participants attempt to find text strings, called "flags", which are secretly hidden in purposefully vulnerable programs or websites. They can be used for both competitive or educational purposes. In two main variations of CTFs, participants either steal flags from other participants (attack/defense-style CTFs) or from organizers (jeopardy-style challenges). A mixed competition combines these two styles. Competitions can include hiding flags in hardware devices, they can be both online or in-person, and can be advanced or entry-level. The game is inspired by the traditional outdoor sport with the same name. CTFs are used as a tool for developing and refining cybersecurity skills, making them popular in both professional and academic settings. == Overview == Capture the Flag (CTF) is a cybersecurity competition that is used to test and develop computer security skills. It was first developed in 1996 at DEF CON, the largest cybersecurity conference in the United States which is hosted annually in Las Vegas, Nevada. The conference hosts a weekend of cybersecurity competitions, including their flagship CTF. Two popular CTF formats are jeopardy and attack-defense. Both formats test participant’s knowledge in cybersecurity, but differ in objective. In the Jeopardy format, participating teams must complete as many challenges of varying point values from a various categories such as cryptography, web exploitation, and reverse engineering. In the attack-defense format, competing teams must defend their vulnerable computer systems while attacking their opponent's systems. The exercise involves a diverse array of tasks, including exploitation and cracking passwords, but there is little evidence showing how these tasks translate into cybersecurity knowledge held by security experts. Recent research has shown that the Capture the Flag tasks mainly covered technical knowledge but lacked social topics like social engineering and awareness on cybersecurity. == Educational applications == CTFs have been shown to be an effective way to improve cybersecurity education through gamification. There are many examples of CTFs designed to teach cybersecurity skills to a wide variety of audiences, including PicoCTF, organized by the Carnegie Mellon CyLab, which is oriented towards high school students, and Arizona State University supported pwn.college. Beyond educational CTF events and resources, CTFs has been shown to be a highly effective way to instill cybersecurity concepts in the classroom. CTFs have been included in undergraduate computer science classes such as Introduction to Information Security at the National University of Singapore. CTFs are also popular in military academies. They are often included as part of the curriculum for cybersecurity courses, with the NSA organized Cyber Exercise culminating in a CTF competition between the US service academies and military colleges. == Competitions == Many CTF organizers register their competition with the CTFtime platform. This allows the tracking of the position of teams over time and across competitions. These include "Plaid Parliament of Pwning", "More Smoked Leet Chicken", "Dragon Sector", "dcua", "Eat, Sleep, Pwn, Repeat", "perfect blue", "organizers" and "Blue Water". Overall the "Plaid Parliament of Pwning" and "Dragon Sector" have both placed first worldwide the most with three times each. === Community competitions === Every year there are dozens of CTFs organized in a variety of formats. Many CTFs are associated with cybersecurity conferences such as DEF CON, various editions of SANS Institute's NetWars, HITCON, and BSides. The DEF CON CTF, an attack-defence CTF, is notable for being one of the oldest CTF competitions to exist, and has been variously referred to as the "World Series", "Superbowl", and "Olympics", of hacking by media outlets. The NYU Tandon hosted Cybersecurity Awareness Worldwide (CSAW) CTF is one of the largest open-entry competitions for students learning cybersecurity from around the world. In 2021, it hosted over 1200 teams during the qualification round. In addition to conference organized CTFs, many CTF clubs and teams organize CTF competitions. Many CTF clubs and teams are associated with universities, such as the CMU associated Plaid Parliament of Pwning, which hosts PlaidCTF, and the ASU associated Shellphish. Some community CTFs are online and open to all participants. The SANS Institute Holiday Hack Challenge and TryHackMe Advent of Cyber. === Government-supported competitions === Governmentally supported CTF competitions include the DARPA Cyber Grand Challenge and ENISA European Cybersecurity Challenge. In 2023, the US Space Force-sponsored Hack-a-Sat CTF competition included, for the first time, a live orbital satellite for participants to exploit. === Corporate-supported competitions === Corporations and other organizations sometimes use CTFs as a training or evaluation exercise, with benefits similar to those in educational settings. In addition to internal CTF exercises, some corporations such as Google and Tencent host publicly accessible CTF competitions. == In popular culture == In Mr. Robot, a qualification round for the DEF CON CTF competition is depicted in the season 3 opener "eps3.0_power-saver-mode.h". The logo for DEF CON can be seen in the background. In The Undeclared War, a CTF is depicted in the opening scene of the series as a recruitment exercise used by GCHQ. Go Go Squid!, a Chinese television series, is based around training for and competing in highly stylized CTF competitions .

Tensor operator

In pure and applied mathematics, quantum mechanics and computer graphics, a tensor operator generalizes the notion of operators which are scalars and vectors. A special class of these are spherical tensor operators which apply the notion of the spherical basis and spherical harmonics. The spherical basis closely relates to the description of angular momentum in quantum mechanics and spherical harmonic functions. The coordinate-free generalization of a tensor operator is known as a representation operator. == The general notion of scalar, vector, and tensor operators == In quantum mechanics, physical observables that are scalars, vectors, and tensors, must be represented by scalar, vector, and tensor operators, respectively. Whether something is a scalar, vector, or tensor depends on how it is viewed by two observers whose coordinate frames are related to each other by a rotation. Alternatively, one may ask how, for a single observer, a physical quantity transforms if the state of the system is rotated. Consider, for example, a system consisting of a molecule of mass M {\displaystyle M} , traveling with a definite center of mass momentum, p z ^ {\displaystyle p{\mathbf {\hat {z}} }} , in the z {\displaystyle z} direction. If we rotate the system by 90 ∘ {\displaystyle 90^{\circ }} about the y {\displaystyle y} axis, the momentum will change to p x ^ {\displaystyle p{\mathbf {\hat {x}} }} , which is in the x {\displaystyle x} direction. The center-of-mass kinetic energy of the molecule will, however, be unchanged at p 2 / 2 M {\displaystyle p^{2}/2M} . The kinetic energy is a scalar and the momentum is a vector, and these two quantities must be represented by a scalar and a vector operator, respectively. By the latter in particular, we mean an operator whose expected values in the initial and the rotated states are p z ^ {\displaystyle p{\mathbf {\hat {z}} }} and p x ^ {\displaystyle p{\mathbf {\hat {x}} }} . The kinetic energy on the other hand must be represented by a scalar operator, whose expected value must be the same in the initial and the rotated states. In the same way, tensor quantities must be represented by tensor operators. An example of a tensor quantity (of rank two) is the electrical quadrupole moment of the above molecule. Likewise, the octupole and hexadecapole moments would be tensors of rank three and four, respectively. Other examples of scalar operators are the total energy operator (more commonly called the Hamiltonian), the potential energy, and the dipole-dipole interaction energy of two atoms. Examples of vector operators are the momentum, the position, the orbital angular momentum, L {\displaystyle {\mathbf {L} }} , and the spin angular momentum, S {\displaystyle {\mathbf {S} }} . (Fine print: Angular momentum is a vector as far as rotations are concerned, but unlike position or momentum it does not change sign under space inversion, and when one wishes to provide this information, it is said to be a pseudovector.) Scalar, vector and tensor operators can also be formed by products of operators. For example, the scalar product L ⋅ S {\displaystyle {\mathbf {L} }\cdot {\mathbf {S} }} of the two vector operators, L {\displaystyle {\mathbf {L} }} and S {\displaystyle {\mathbf {S} }} , is a scalar operator, which figures prominently in discussions of the spin–orbit interaction. Similarly, the quadrupole moment tensor of our example molecule has the nine components Q i j = ∑ α q α ( 3 r α , i r α , j − r α 2 δ i j ) . {\displaystyle Q_{ij}=\sum _{\alpha }q_{\alpha }\left(3r_{\alpha ,i}r_{\alpha ,j}-r_{\alpha }^{2}\delta _{ij}\right).} Here, the indices i {\displaystyle i} and j {\displaystyle j} can independently take on the values 1, 2, and 3 (or x {\displaystyle x} , y {\displaystyle y} , and z {\displaystyle z} ) corresponding to the three Cartesian axes, the index α {\displaystyle \alpha } runs over all particles (electrons and nuclei) in the molecule, q α {\displaystyle q_{\alpha }} is the charge on particle α {\displaystyle \alpha } , and r α , i {\displaystyle r_{\alpha ,i}} is the i {\displaystyle i} -th component of the position of this particle. Each term in the sum is a tensor operator. In particular, the nine products r α , i r α , j {\displaystyle r_{\alpha ,i}r_{\alpha ,j}} together form a second rank tensor, formed by taking the outer product of the vector operator r α {\displaystyle {\mathbf {r} }_{\alpha }} with itself. == Rotations of quantum states == === Quantum rotation operator === The rotation operator about the unit vector n (defining the axis of rotation) through angle θ is U [ R ( θ , n ^ ) ] = exp ⁡ ( − i θ ℏ n ^ ⋅ J ) {\displaystyle U[R(\theta ,{\hat {\mathbf {n} }})]=\exp \left(-{\frac {i\theta }{\hbar }}{\hat {\mathbf {n} }}\cdot \mathbf {J} \right)} where J = (Jx, Jy, Jz) are the rotation generators (also the angular momentum matrices): J x = ℏ 2 ( 0 1 0 1 0 1 0 1 0 ) J y = ℏ 2 ( 0 i 0 − i 0 i 0 − i 0 ) J z = ℏ ( − 1 0 0 0 0 0 0 0 1 ) {\displaystyle J_{x}={\frac {\hbar }{\sqrt {2}}}{\begin{pmatrix}0&1&0\\1&0&1\\0&1&0\end{pmatrix}}\,\quad J_{y}={\frac {\hbar }{\sqrt {2}}}{\begin{pmatrix}0&i&0\\-i&0&i\\0&-i&0\end{pmatrix}}\,\quad J_{z}=\hbar {\begin{pmatrix}-1&0&0\\0&0&0\\0&0&1\end{pmatrix}}} and let R ^ = R ^ ( θ , n ^ ) {\displaystyle {\widehat {R}}={\widehat {R}}(\theta ,{\hat {\mathbf {n} }})} be a rotation matrix. According to the Rodrigues' rotation formula, the rotation operator then amounts to U [ R ( θ , n ^ ) ] = 1 1 − i sin ⁡ θ ℏ n ^ ⋅ J − 1 − cos ⁡ θ ℏ 2 ( n ^ ⋅ J ) 2 . {\displaystyle U[R(\theta ,{\hat {\mathbf {n} }})]=1\!\!1-{\frac {i\sin \theta }{\hbar }}{\hat {\mathbf {n} }}\cdot \mathbf {J} -{\frac {1-\cos \theta }{\hbar ^{2}}}({\hat {\mathbf {n} }}\cdot \mathbf {J} )^{2}.} An operator Ω ^ {\displaystyle {\widehat {\Omega }}} is invariant under a unitary transformation U if Ω ^ = U † Ω ^ U ; {\displaystyle {\widehat {\Omega }}={U}^{\dagger }{\widehat {\Omega }}U;} in this case for the rotation U ^ ( R ) {\displaystyle {\widehat {U}}(R)} , Ω ^ = U ( R ) † Ω ^ U ( R ) = exp ⁡ ( i θ ℏ n ^ ⋅ J ) Ω ^ exp ⁡ ( − i θ ℏ n ^ ⋅ J ) . {\displaystyle {\widehat {\Omega }}={U(R)}^{\dagger }{\widehat {\Omega }}U(R)=\exp \left({\frac {i\theta }{\hbar }}{\hat {\mathbf {n} }}\cdot \mathbf {J} \right){\widehat {\Omega }}\exp \left(-{\frac {i\theta }{\hbar }}{\hat {\mathbf {n} }}\cdot \mathbf {J} \right).} === Angular momentum eigenkets === The orthonormal basis set for total angular momentum is | j , m ⟩ {\displaystyle |j,m\rangle } , where j is the total angular momentum quantum number and m is the magnetic angular momentum quantum number, which takes values −j, −j + 1, ..., j − 1, j. A general state within the j subspace | ψ ⟩ = ∑ m c j m | j , m ⟩ {\displaystyle |\psi \rangle =\sum _{m}c_{jm}|j,m\rangle } rotates to a new state by: | ψ ¯ ⟩ = U ( R ) | ψ ⟩ = ∑ m c j m U ( R ) | j , m ⟩ {\displaystyle |{\bar {\psi }}\rangle =U(R)|\psi \rangle =\sum _{m}c_{jm}U(R)|j,m\rangle } Using the completeness condition: I = ∑ m ′ | j , m ′ ⟩ ⟨ j , m ′ | {\displaystyle I=\sum _{m'}|j,m'\rangle \langle j,m'|} we have | ψ ¯ ⟩ = I U ( R ) | ψ ⟩ = ∑ m m ′ c j m | j , m ′ ⟩ ⟨ j , m ′ | U ( R ) | j , m ⟩ {\displaystyle |{\bar {\psi }}\rangle =IU(R)|\psi \rangle =\sum _{mm'}c_{jm}|j,m'\rangle \langle j,m'|U(R)|j,m\rangle } Introducing the Wigner D matrix elements: D ( R ) m ′ m ( j ) = ⟨ j , m ′ | U ( R ) | j , m ⟩ {\displaystyle {D(R)}_{m'm}^{(j)}=\langle j,m'|U(R)|j,m\rangle } gives the matrix multiplication: | ψ ¯ ⟩ = ∑ m m ′ c j m D m ′ m ( j ) | j , m ′ ⟩ ⇒ | ψ ¯ ⟩ = D ( j ) | ψ ⟩ {\displaystyle |{\bar {\psi }}\rangle =\sum _{mm'}c_{jm}D_{m'm}^{(j)}|j,m'\rangle \quad \Rightarrow \quad |{\bar {\psi }}\rangle =D^{(j)}|\psi \rangle } For one basis ket: | j , m ¯ ⟩ = ∑ m ′ D ( R ) m ′ m ( j ) | j , m ′ ⟩ {\displaystyle |{\overline {j,m}}\rangle =\sum _{m'}{D(R)}_{m'm}^{(j)}|j,m'\rangle } For the case of orbital angular momentum, the eigenstates | ℓ , m ⟩ {\displaystyle |\ell ,m\rangle } of the orbital angular momentum operator L and solutions of Laplace's equation on a 3d sphere are spherical harmonics: Y ℓ m ( θ , ϕ ) = ⟨ θ , ϕ | ℓ , m ⟩ = ( 2 ℓ + 1 ) 4 π ( ℓ − m ) ! ( ℓ + m ) ! P ℓ m ( cos ⁡ θ ) e i m ϕ {\displaystyle Y_{\ell }^{m}(\theta ,\phi )=\langle \theta ,\phi |\ell ,m\rangle ={\sqrt {{(2\ell +1) \over 4\pi }{(\ell -m)! \over (\ell +m)!}}}\,P_{\ell }^{m}(\cos {\theta })\,e^{im\phi }} where Pℓm is an associated Legendre polynomial, ℓ is the orbital angular momentum quantum number, and m is the orbital magnetic quantum number which takes the values −ℓ, −ℓ + 1, ... ℓ − 1, ℓ The formalism of spherical harmonics have wide applications in applied mathematics, and are closely related to the formalism of spherical tensors, as shown below. Spherical harmonics are functions of the polar and azimuthal angles, ϕ and θ respectively, which can be conveniently collected into a unit vector n(θ, ϕ) pointing in the direction of those angles, in the Cartesian basis it is: n ^ ( θ , ϕ ) = cos ⁡ ϕ sin ⁡ θ e x + s

Pruning (artificial neural network)

In deep learning, pruning is the practice of removing parameters from an existing artificial neural network. The goal of this process is to reduce the size (parameter count) of the neural network (and therefore the computational resources required to run it) whilst maintaining accuracy. This can be compared to the biological process of synaptic pruning which takes place in mammalian brains during development. == Node (neuron) pruning == A basic algorithm for pruning is as follows: Evaluate the importance of each neuron. Rank the neurons according to their importance (assuming there is a clearly defined measure for "importance"). Remove the least important neuron. Check a termination condition (to be determined by the user) to see whether to continue pruning. == Edge (weight) pruning == Most work on neural network pruning does not remove full neurons or layers (structured pruning). Instead, it focuses on removing the most insignificant weights (unstructured pruning), namely, setting their values to zero. This can either be done globally by comparing weights from all layers in the network or locally by comparing weights in each layer separately. Different metrics can be used to measure the importance of each weight. Weight magnitude as well as combinations of weight and gradient information are commonly used metrics. Early work suggested also to change the values of non-pruned weights. == When to prune the neural network? == Pruning can be applied at three different stages: before training, during training, or after training. When pruning is performed during or after training, additional fine-tuning epochs are typically required. Each approach involves different trade-offs between accuracy and computational cost.

Memtransistor

The memtransistor (a blend word from Memory Transfer Resistor) is an experimental multi-terminal passive electronic component that might be used in the construction of artificial neural networks. It is a combination of the memristor and transistor technology. This technology is different from the 1T-1R approach since the devices are merged into one single entity. Multiple memristors can be embedded with a single transistor, enabling it to more accurately model a neuron with its multiple synaptic connections. A neural network produced from these would provide hardware-based artificial intelligence with a good foundation. == Applications == These types of devices would allow for a synapse model that could realise a learning rule, by which the synaptic efficacy is altered by voltages applied to the terminals of the device. An example of such a learning rule is spike-timing-dependant-plasticty by which the weight of the synapse, in this case the conductivity, could be modulated based on the timing of pre and post synaptic spikes arriving at each terminal. The advantage of this approach over two terminal memristive devices is that read and write protocols have the possibility to occur simultaneously and distinctly.

Differential evolution

Differential evolution (DE) is an evolutionary algorithm to optimize a problem by iteratively trying to improve a candidate solution with regard to a given measure of quality. Such methods are commonly known as metaheuristics as they make few or no assumptions about the optimized problem and can search very large spaces of candidate solutions. However, metaheuristics such as DE do not guarantee an optimal solution is ever found. DE is used for multidimensional real-valued functions but does not use the gradient of the problem being optimized, which means DE does not require the optimization problem to be differentiable, as is required by classic optimization methods such as gradient descent and quasi-newton methods. DE can therefore also be used on optimization problems that are not even continuous, are noisy, change over time, etc. DE optimizes a problem by maintaining a population of candidate solutions and creating new candidate solutions by combining existing ones according to its simple formulae, and then keeping whichever candidate solution has the best score or fitness on the optimization problem at hand. In this way, the optimization problem is treated as a black box that merely provides a measure of quality given a candidate solution and the gradient is therefore not needed. == History == Storn and Price introduced Differential Evolution in 1995. Books have been published on theoretical and practical aspects of using DE in parallel computing, multiobjective optimization, constrained optimization, and the books also contain surveys of application areas. Surveys on the multi-faceted research aspects of DE can be found in journal articles. == Algorithm == A basic variant of the DE algorithm works by having a population of candidate solutions (called agents). These agents are moved around in the search-space by using simple mathematical formulae to combine the positions of existing agents from the population. If the new position of an agent is an improvement then it is accepted and forms part of the population, otherwise the new position is simply discarded. The process is repeated and by doing so it is hoped, but not guaranteed, that a satisfactory solution will eventually be discovered. Formally, let f : R n → R {\displaystyle f:\mathbb {R} ^{n}\to \mathbb {R} } be the fitness function which must be minimized (note that maximization can be performed by considering the function h := − f {\displaystyle h:=-f} instead). The function takes a candidate solution as argument in the form of a vector of real numbers. It produces a real number as output which indicates the fitness of the given candidate solution. The gradient of f {\displaystyle f} is not known. The goal is to find a solution m {\displaystyle \mathbf {m} } for which f ( m ) ≤ f ( p ) {\displaystyle f(\mathbf {m} )\leq f(\mathbf {p} )} for all p {\displaystyle \mathbf {p} } in the search-space, which means that m {\displaystyle \mathbf {m} } is the global minimum. Let x ∈ R n {\displaystyle \mathbf {x} \in \mathbb {R} ^{n}} designate a candidate solution (agent) in the population. The basic DE algorithm can then be described as follows: Choose the parameters NP ≥ 4 {\displaystyle {\text{NP}}\geq 4} , CR ∈ [ 0 , 1 ] {\displaystyle {\text{CR}}\in [0,1]} , and F ∈ [ 0 , 2 ] {\displaystyle F\in [0,2]} . NP : NP {\displaystyle {\text{NP}}} is the population size, i.e. the number of candidate agents or "parents". CR : The parameter CR ∈ [ 0 , 1 ] {\displaystyle {\text{CR}}\in [0,1]} is called the crossover probability. F : The parameter F ∈ [ 0 , 2 ] {\displaystyle F\in [0,2]} is called the differential weight. Typical settings are N P = 10 n {\displaystyle NP=10n} , C R = 0.9 {\displaystyle CR=0.9} and F = 0.8 {\displaystyle F=0.8} . Optimization performance may be greatly impacted by these choices; see below. Initialize all agents x {\displaystyle \mathbf {x} } with random positions in the search-space. Until a termination criterion is met (e.g. number of iterations performed, or adequate fitness reached), repeat the following: For each agent x {\displaystyle \mathbf {x} } in the population do: Pick three agents a , b {\displaystyle \mathbf {a} ,\mathbf {b} } , and c {\displaystyle \mathbf {c} } from the population at random, they must be distinct from each other as well as from agent x {\displaystyle \mathbf {x} } . ( a {\displaystyle \mathbf {a} } is called the "base" vector.) Pick a random index R ∈ { 1 , … , n } {\displaystyle R\in \{1,\ldots ,n\}} where n {\displaystyle n} is the dimensionality of the problem being optimized. Compute the agent's potentially new position y = [ y 1 , … , y n ] {\displaystyle \mathbf {y} =[y_{1},\ldots ,y_{n}]} as follows: For each i ∈ { 1 , … , n } {\displaystyle i\in \{1,\ldots ,n\}} , pick a uniformly distributed random number r i ∼ U ( 0 , 1 ) {\displaystyle r_{i}\sim U(0,1)} If r i < C R {\displaystyle r_{i}

PenTile matrix family

PenTile matrix is a family of patented subpixel matrix schemes used in electronic device displays. PenTile is a trademark of Samsung. PenTile matrices are used in AMOLED and LCD displays. These subpixel layouts are specifically designed to operate with proprietary algorithms for subpixel rendering embedded in the display driver, allowing plug and play compatibility with conventional RGB (Red-Green-Blue) stripe panels. == Overview == "PenTile Matrix" (a neologism from penta-, meaning "five" in Greek and tile) describes the geometric layout of the prototypical subpixel arrangement developed in the early 1990s. The layout consists of a quincunx comprising two red subpixels, two green subpixels, and one central blue subpixel in each unit cell. It was inspired by biomimicry of the human retina, which has nearly equal numbers of L and M type cone cells, but significantly fewer S cones. As the S cones are primarily responsible for perceiving blue colors, which do not appreciably affect the perception of luminance, reducing the number of blue subpixels with respect to the red and green subpixels in a display does not reduce the image quality. However, the layout may cause color leakage image distortion, which can be reduced by filters. In some cases the layout causes reduced moiré and blockiness compared to conventional RGB layouts. The PenTile layout is specifically designed to work with and be dependent upon subpixel rendering that uses only one and a quarter subpixel per pixel, on average, to render an image. That is, that any given input pixel is mapped to either a red-centered logical pixel, or a green-centered logical pixel. === History === PenTile was invented by Candice H. Brown Elliott, for which she was awarded the Society for Information Display's Otto Schade Prize in 2014. The technology was licensed by the company Clairvoyante from 2000 until 2008, during which time several prototype PenTile displays were developed by a number of Asian liquid crystal display (LCD) manufacturers. In March 2008, Samsung Electronics acquired Clairvoyante's PenTile IP assets. Samsung then funded a new company, Nouvoyance, Inc. to continue development of the PenTile technology. == PenTile RGBG == PenTile RGBG layout used in AMOLED and plasma displays uses green pixels interleaved with alternating red and blue pixels. The human eye is most sensitive to green, especially for high resolution luminance information. The green subpixels are mapped to input pixels on a one-to-one basis. The red and blue subpixels are subsampled, reconstructing the chroma signal at a lower resolution. The luminance signal is processed using adaptive subpixel rendering filters to optimize reconstruction of high spatial frequencies from the input image, wherein the green subpixels provide the majority of the reconstruction. The red and blue subpixels are capable of reconstructing the horizontal and vertical spatial frequencies, but not the highest of the diagonal. Diagonal high spatial frequency information in the red and blue channels of the input image are transferred to the green subpixels for image reconstruction. Thus the RG-BG scheme creates a color display with one third fewer subpixels than a traditional RGB-RGB scheme but with the same measured luminance display resolution. This is similar to the Bayer filter commonly used in digital cameras. === Devices === As of 2021, "almost all" OLED screens in portable consumer devices use some form of Pentile subpixel layout. == PenTile RGBW == PenTile RGBW technology, used in LCD, adds an extra subpixel to the traditional red, green and blue subpixels that is a clear area without color filtering material and with the only purpose of letting backlight come through, hence W for white. This makes it possible to produce a brighter image compared to an RGB-matrix while using the same amount of power, or produce an equally bright image while using less power. The PenTile RGBW layout uses each red, green, blue and white subpixel to present high-resolution luminance information to the human eyes' red-sensing and green-sensing cone cells, while using the combined effect of all the color subpixels to present lower-resolution chroma (color) information to all three cone cell types. Combined, this optimizes the match of display technology to the biological mechanisms of human vision. The layout uses one third fewer subpixels for the same resolution as the RGB stripe (RGB-RGB) layout, in spite of having four color primaries instead of the conventional three, using subpixel rendering combined with metamer rendering. Metamer rendering optimizes the energy distribution between the white subpixel and the combined red, green, and blue subpixels: W <> RGB, to improve image sharpness. The display driver chip has an RGB to RGBW color vector space converter and gamut mapping algorithm, followed by metamer and subpixel rendering algorithms. In order to maintain saturated color quality, to avoid simultaneous contrast error between saturated colors and peak white brightness, while simultaneously reducing backlight power requirements, the display backlight brightness is under control of the PenTile driver engine. When the image is mostly desaturated colors, those near white or grey, the backlight brightness is significantly reduced, often to less than 50% peak, while the LCD levels are increased to compensate. When the image has very bright saturated colors, the backlight brightness is maintained at higher levels. The PenTile RGBW also has an optional high-brightness mode that doubles the brightness of the desaturated color image areas, such as black-and-white text, for improved outdoor viewability. === Devices === Motorola MC65 Motorola ES55 Motorola ES400 Motorola Atrix 4G Samsung Galaxy Note 10.1 2014 version Lenovo Yoga 2 Pro Lenovo Yoga 3 Pro HP ENVY TouchSmart 14-k022tx Sleekbook MSI GS60 Ghost Pro 4K Lenovo IdeaPad Y50 4K Asus ZenBook UX303LN 4K Asus ZenBook Pro UX501JW LG UH7500/6500/6100 LG ThinQ G7/G7+ Oculus Quest 1 == Controversy == An ongoing controversy regarding the definition or measurement of resolution of color subpixelated flat panel displays led many people to question the resolution claims of PenTile display products. Journalists have noted that in "just about every flat-panel TV in existence, each pixel is composed of one red, one green, and one blue subpixel (RGB), all of uniform size". In traditional flat-panel screens, the resolution is defined by the number of red, green, and blue subpixels, in groups of three, in an array in each axis. As a result, each pixel or group of subpixels can render any colour on the screen, regardless of neighbouring pixels. This is not the case with PenTile screens. The Video Electronics Standards Association (VESA) method of measuring and defining resolution in color displays is to measure the contrast of line pairs, requiring a minimum of 50% Michelson contrast for displays intended for rendering text. The developers of PenTile displays use this VESA criterion for contrast of line pairs to calculate the resolutions specified. In the RGBG layout the alternate red and blue subpixels are 'shared' or sub-sampled with neighboring pixels. Due to the one third lower subpixel density on PenTile displays the pixel structure may be more visible when compared to RGB stripe displays with the same pixel density. The loss of subpixels for a given resolution specification has led some journalists to describe the use of PenTile as "shady practice" and "sort of cheating". For a given size and resolution specification, the PenTile screen can appear grainy, pixelated, speckled, with blurred text on some saturated colors and backgrounds when compared to RGB stripe color. This effect is understood to be caused by the restriction of the number of subpixels that may participate in the image reconstruction when colors are highly saturated to primaries. In the RGBW case, this is caused as the W subpixel will not be available in order to maintain the saturated color. In the RGBG case, this effect will occur when the color boundary is primarily red or blue, as the fully populated (one green per pixel) sub-pixel cannot contribute. For all other cases, text and especially full color images are effectively reconstructed. == Advantages and disadvantages == The PenTile layout reduces the number of subpixels needed to create a specified resolution. Consequently it is possible to achieve an HD resolution on a PenTile AMOLED screen at lower cost than other technologies, and most reviewers note that "300 ppi" (as per VESA - not full pixels) resolution displays (such as Samsung Galaxy S III) make the PenTile effect less obvious than lower resolution PenTile displays (Droid Razr). The second advantage is lower power consumption: the HTC One S's use of a PenTile display makes it more energy efficient and thinner than equivalent LCD screens, giving it better battery life than the HTC One X's IPS LCD. A PenTile AMOLED screen is also

Density-based clustering validation

Density-Based Clustering Validation (DBCV) is a metric designed to assess the quality of clustering solutions, particularly for density-based clustering algorithms like DBSCAN, Mean shift, and OPTICS. This metric is particularly suited for identifying concave and nested clusters, where traditional metrics such as the Silhouette coefficient, Davies–Bouldin index, or Calinski–Harabasz index often struggle to provide meaningful evaluations. Unlike traditional validation measures, which often rely on compact and well-separated clusters, DBCV index evaluates how well clusters are defined in terms of local density variations and structural coherence. This metric was introduced in 2014 by David Moulavi and colleagues in their work. It utilizes density connectivity principles to quantify clustering structures, making it especially effective at detecting arbitrarily shaped clusters in concave datasets, where traditional metrics may be less reliable. The DBCV index has been employed for clustering analysis in bioinformatics, ecology, techno-economy, and health informatics , as well as in numerous other fields. == Definition == DBCV index evaluates clustering structures by analyzing the relationships between data points within and across clusters. Given a dataset X = x 1 , x 2 , . . . , x n {\displaystyle X={x_{1},x_{2},...,x_{n}}} , a density-based algorithm partitions it into K clusters C 1 , C 2 , . . . , C K {\displaystyle {C_{1},C_{2},...,C_{K}}} . Each point x i {\displaystyle x_{i}} belongs to a specific cluster, denoted as C c l u s t e r ( x i ) {\displaystyle C_{cluster(x_{i})}} A key concept in DBCV index is the notion of density-connected paths. Two points within the same cluster are considered density-connected if there exists a sequence of intermediate points linking them, where each consecutive pair meets a predefined density criterion. The density-based distance between two points is determined by identifying the optimal path that minimizes the maximum local reachability distance along its trajectory. DBCV index extends the Silhouette coefficient by redefining cluster cohesion and separation using density-based distances: Within-cluster density distance measures how closely a point is related to other members of its cluster: a i = 1 | C c l u s t e r ( x i ) | − 1 ∑ x j ∈ C c l u s t e r ( x i ) , y ≠ x d d e n s i t y ( x j , x i ) {\displaystyle a_{i}={\frac {1}{|C_{cluster(x_{i})}|-1}}\sum _{x_{j}\in C_{cluster(x_{i})},y\neq x}d_{density}(x_{j},x_{i})} Nearest-cluster density distance quantifies how far a point is from the closest external cluster: b i = min C ≠ C cluster ( x i ) C ∈ { C 1 , … , C K } ( 1 | C | ∑ x j ∈ C d density ( x i , x j ) ) . {\displaystyle b_{i}=\min _{C\neq C_{{\text{cluster}}(x_{i})} \atop C\in \{C_{1},\dots ,C_{K}\}}\left({\frac {1}{|C|}}\sum _{x_{j}\in C}d_{\text{density}}(x_{i},x_{j})\right).} Using these measures, the DBCV index is computed as: D B C V = 1 n ∑ i = 1 n b i − a i max ( a i , b i ) {\displaystyle DBCV={\frac {1}{n}}\sum _{i=1}^{n}{\frac {b_{i}-a_{i}}{\max(a_{i},b_{i})}}} == Explanation == DBCV index values range between −1 and +1: +1: Strongly cohesive and well-separated clusters. 0: Ambiguous clustering structure. −1: Poorly formed clusters or incorrect assignments. By leveraging density-based distances instead of traditional Euclidean measures, DBCV index provides a more robust evaluation of clustering performance in datasets with irregular or non-spherical distributions.