Framebuffer

A framebuffer (frame buffer, or sometimes framestore) is a portion of random-access memory (RAM) containing a bitmap that drives a video display. It is a memory buffer containing data representing all the pixels in a complete video frame. Modern video cards contain framebuffer circuitry in their cores. This circuitry converts an in-memory bitmap into a video signal that can be displayed on a computer monitor. In computing, a screen buffer is a part of computer memory used by a computer application for the representation of the content to be shown on the computer display. The screen buffer may also be called the video buffer, the regeneration buffer, or regen buffer for short. The phrase "screen buffer” refers to a logical function, while video memory refers to a hardware storage location. In particular, the screen buffer may be placed in the main RAM, the video memory, or some other hardware location. To reduce latency and avoid screen tearing, multiple frames can be buffered, and this technique is called multiple buffering. When this is so, at any time, only one frame would be visible, and the others would not be. The currently invisible frames are located in the off-screen buffer. The information in the buffer typically consists of color values for every pixel to be shown on the display. Color values are commonly stored in 1-bit binary (monochrome), 4-bit palettized, 8-bit palettized, 16-bit high color and 24-bit true color formats. An additional alpha channel is sometimes used to retain information about pixel transparency. The total amount of memory required for the framebuffer depends on the resolution of the output signal, and on the color depth or palette size. == History == Computer researchers had long discussed the theoretical advantages of a framebuffer but were unable to produce a machine with sufficient memory at an economically practicable cost. In 1947, the Manchester Baby computer used a Williams tube, later the Williams-Kilburn tube, to store 1024 bits on a cathode-ray tube (CRT) memory and displayed on a second CRT. Other research labs were exploring these techniques with MIT Lincoln Laboratory achieving a 4096 display in 1950. A color-scanned display was implemented in the late 1960s, called the Brookhaven RAster Display (BRAD), which used a drum memory and a television monitor. In 1969, A. Michael Noll of Bell Telephone Laboratories, Inc. implemented a scanned display with a frame buffer, using magnetic-core memory. A year or so later, the Bell Labs system was expanded to display an image with a color depth of three bits on a standard color TV monitor. The vector graphics used in the computer had to be converted for the scanned graphics of a TV display. In the early 1970s, the development of MOS memory (metal–oxide–semiconductor memory) integrated-circuit chips, particularly high-density DRAM (dynamic random-access memory) chips with at least 1 kb memory, made it practical to create, for the first time, a digital memory system with framebuffers capable of holding a standard video image. This led to the development of the SuperPaint system by Richard Shoup at Xerox PARC in 1972. Shoup was able to use the SuperPaint framebuffer to create an early digital video-capture system. By synchronizing the output signal to the input signal, Shoup was able to overwrite each pixel of data as it shifted in. Shoup also experimented with modifying the output signal using color tables. These color tables allowed the SuperPaint system to produce a wide variety of colors outside the range of the limited 8-bit data it contained. This scheme would later become commonplace in computer framebuffers. In 1974, Evans & Sutherland released the first commercial framebuffer, the Picture System, costing about $15,000. It was capable of producing resolutions of up to 512 by 512 pixels in 8-bit grayscale, and became a boon for graphics researchers who did not have the resources to build their own framebuffer. The New York Institute of Technology would later create the first 24-bit color system using three of the Evans & Sutherland framebuffers. Each framebuffer was connected to an RGB color output (one for red, one for green and one for blue), with a Digital Equipment Corporation PDP 11/04 minicomputer controlling the three devices as one. In 1975, the UK company Quantel produced the first commercial full-color broadcast framebuffer, the Quantel DFS 3000. It was first used in TV coverage of the 1976 Montreal Olympics to generate a picture-in-picture inset of the Olympic flaming torch while the rest of the picture featured the runner entering the stadium. The rapid improvement of integrated-circuit technology made it possible for many of the home computers of the late 1970s to contain low-color-depth framebuffers. Today, nearly all computers with graphical capabilities utilize a framebuffer for generating the video signal. Amiga computers, created in the 1980s, featured special design attention to graphics performance and included a unique Hold-And-Modify framebuffer capable of displaying 4096 colors. Framebuffers also became popular in high-end workstations and arcade system boards throughout the 1980s. SGI, Sun Microsystems, HP, DEC and IBM all released framebuffers for their workstation computers in this period. These framebuffers were usually of a much higher quality than could be found in most home computers, and were regularly used in television, printing, computer modeling and 3D graphics. Framebuffers were also used by Sega for its high-end arcade boards, which were also of a higher quality than on home computers. == Display modes == Framebuffers used in personal and home computing often had sets of defined modes under which the framebuffer can operate. These modes reconfigure the hardware to output different resolutions, color depths, memory layouts and refresh rate timings. In the world of Unix machines and operating systems, such conveniences were usually eschewed in favor of directly manipulating the hardware settings. This manipulation was far more flexible in that any resolution, color depth and refresh rate was attainable – limited only by the memory available to the framebuffer. An unfortunate side-effect of this method was that the display device could be driven beyond its capabilities. In some cases, this resulted in hardware damage to the display. More commonly, it simply produced garbled and unusable output. Modern CRT monitors fix this problem through the introduction of protection circuitry. When the display mode is changed, the monitor attempts to obtain a signal lock on the new refresh frequency. If the monitor is unable to obtain a signal lock or if the signal is outside the range of its design limitations, the monitor will ignore the framebuffer signal and possibly present the user with an error message. LCD monitors tend to contain similar protection circuitry, but for different reasons. Since the LCD must digitally sample the display signal (thereby emulating an electron beam), any signal that is out of range cannot be physically displayed on the monitor. == Color palette == Framebuffers have traditionally supported a wide variety of color modes. Due to the expense of memory, most early framebuffers used 1-bit (2 colors per pixel), 2-bit (4 colors), 4-bit (16 colors) or 8-bit (256 colors) color depths. The problem with such small color depths is that a full range of colors cannot be produced. The solution to this problem was indexed color, which adds a lookup table to the framebuffer. Each color stored in framebuffer memory acts as a color index. The lookup table serves as a palette with a limited number of different colors, while the rest is used as an index table. Here is a typical indexed 256-color image and its own palette (shown as a rectangle of swatches): In some designs, it was also possible to write data to the lookup table (or switch between existing palettes) on the fly, allowing dividing the picture into horizontal bars with their own palette and thus rendering an image that had a far wider palette. For example, viewing an outdoor shot photograph, the picture could be divided into four bars: the top one with emphasis on sky tones, the next with foliage tones, the next with skin and clothing tones, and the bottom one with ground colors. This required each palette to have overlapping colors, but, carefully done, allowed great flexibility. == Memory access == While framebuffers are commonly accessed via a memory mapping directly to the CPU memory space, this is not the only method by which they may be accessed. Framebuffers have varied widely in the methods used to access memory. Some of the most common are: Mapping the entire framebuffer to a given memory range. Port commands to set each pixel, range of pixels or palette entry. Mapping a memory range smaller than the framebuffer memory, then bank switching as necessary. The framebuffer organization may be packed pixel or planar. The framebuffer may be all

Empowerment (artificial intelligence)

Empowerment in the field of artificial intelligence formalises and quantifies (via information theory) the potential an agent perceives that it has to influence its environment. An agent which follows an empowerment maximising policy, acts to maximise future options (typically up to some limited horizon). Empowerment can be used as a (pseudo) utility function that depends only on information gathered from the local environment to guide action, rather than seeking an externally imposed goal, thus is a form of intrinsic motivation. The empowerment formalism depends on a probabilistic model commonly used in artificial intelligence. An autonomous agent operates in the world by taking in sensory information and acting to change its state, or that of the environment, in a cycle of perceiving and acting known as the perception-action loop. Agent state and actions are modelled by random variables ( S : s ∈ S , A : a ∈ A {\displaystyle S:s\in {\mathcal {S}},A:a\in {\mathcal {A}}} ) and time ( t {\displaystyle t} ). The choice of action depends on the current state, and the future state depends on the choice of action, thus the perception-action loop unrolled in time forms a causal bayesian network. == Definition == Empowerment ( E {\displaystyle {\mathfrak {E}}} ) is defined as the channel capacity ( C {\displaystyle C} ) of the actuation channel of the agent, and is formalised as the maximal possible information flow between the actions of the agent and the effect of those actions some time later. Empowerment can be thought of as the future potential of the agent to affect its environment, as measured by its sensors. E := C ( A t ⟶ S t + 1 ) ≡ max p ( a t ) I ( A t ; S t + 1 ) {\displaystyle {\mathfrak {E}}:=C(A_{t}\longrightarrow S_{t+1})\equiv \max _{p(a_{t})}I(A_{t};S_{t+1})} In a discrete time model, Empowerment can be computed for a given number of cycles into the future, which is referred to in the literature as 'n-step' empowerment. E ( A t n ⟶ S t + n ) = max p ( a t , . . . , a t + n − 1 ) I ( A t , . . . , A t + n − 1 ; S t + n ) {\displaystyle {\mathfrak {E}}(A_{t}^{n}\longrightarrow S_{t+n})=\max _{p(a_{t},...,a_{t+n-1})}I(A_{t},...,A_{t+n-1};S_{t+n})} The unit of empowerment depends on the logarithm base. Base 2 is commonly used in which case the unit is bits. === Contextual Empowerment === In general the choice of action (action distribution) that maximises empowerment varies from state to state. Knowing the empowerment of an agent in a specific state is useful, for example to construct an empowerment maximising policy. State-specific empowerment can be found using the more general formalism for 'contextual empowerment'. C {\displaystyle C} is a random variable describing the context (e.g. state). E ( A t n ⟶ S t + n ∣ C ) = ∑ c ∈ C p ( c ) E ( A t n ⟶ S t + n ∣ C = c ) {\displaystyle {\mathfrak {E}}(A_{t}^{n}\longrightarrow S_{t+n}{\mid }C)=\sum _{c{\in }C}p(c){\mathfrak {E}}(A_{t}^{n}\longrightarrow S_{t+n}{\mid }C=c)} == Application == Empowerment maximisation can be used as a pseudo-utility function to enable agents to exhibit intelligent behaviour without requiring the definition of external goals, for example balancing a pole in a cart-pole balancing scenario where no indication of the task is provided to the agent. Empowerment has been applied in studies of collective behaviour and in continuous domains. As is the case with Bayesian methods in general, computation of empowerment becomes computationally expensive as the number of actions and time horizon extends, but approaches to improve efficiency have led to usage in real-time control. Empowerment has been used for intrinsically motivated reinforcement learning agents playing video games, and in the control of underwater vehicles.

Commercial skipping

Commercial skipping is a feature of some digital video recorders that makes it possible to automatically skip commercials in recorded programs. This feature created controversy, with major television networks and movie studios claiming it violates copyright and should be banned. == History == After the video cassette recorder (VCR) became popular in the 1980s, the television industry began studying the impact of users fast forwarding through commercials. Advertising agencies fought the trend by making them more entertaining. For many years, video recorders manufactured for the Japanese market have been able to skip advertisements automatically, which is done by detecting when foreign language audio overdub tracks provided for many programmes go silent, as advertisements were broadcast with a single language only. The first digital video recorder (DVR) with a built-in commercial skipping feature was ReplayTV with its "4000 Series" and "5000 Series" units. In 2002, the main television networks and movie studios sued ReplayTV, claiming that skipping advertisements during replay violates copyright. Later, five owners of ReplayTV represented by Electronic Frontier Foundation and attorneys Ira Rothken and Richard Wiebe countersued, asking the federal judge to uphold consumers' rights to record TV shows and skip commercials, claiming that features like commercial skipping help parents protect their kids from excessive consumerism. ReplayTV ended up filing for bankruptcy in 2003 after fighting a copyright infringement suit over the ReplayTV's ability to skip commercials. === Commercial skipping software === In addition to the DVR devices which existed in the private market since the late 1990s, towards the mid-2000s, due to the significant advances in home computers, Home theater PCs started gaining popularity in the private market and many users began using their Home theater PCs in their living room for entertainment purposes. Following this, many DVR programs were developed, including popular programs such as Windows Media Center, which contained all of the features of the DVR devices in addition to advanced features such as HDTV and the use of Multiple TV Tuner Cards. Some independent developers began developing independent software capable of skipping the commercial segments when playing recorded videos, and permanently removing the commercial segments from recorded video files. By 2014, many DVR programs such as Windows Media Center, SageTV and MythTV had the capability to skip commercials segments in recorded TV broadcasts after installing third-party add-ons such as DVRMSToolbox, Comskip and ShowAnalyzer, which use various advanced techniques to locate the commercial segments in the video files and save their locations to text files. The text files can also be fed into programs such as MEncoder or DVRMSToolboxGUI which can delete the commercial segments from the recorded video files. A few third-party tools such as MCEBuddy automate detection and removal/marking of commercials. One of the weaknesses of commercial skippers is that, operating automatically, they may misidentify program material as a commercial. Some programs like MCEBuddy provide the ability to fine-tune commercial detection for groups of files (e.g. by channel or country) and provide tools to manually fine-tune commercial segments for individual files. In May 2012, the US Dish Network began offering a DVR with what it calls AutoHop. The device would automatically skip commercials when displaying programming that the viewer had previously recorded with the PrimeTime Anytime feature. It does not skip ads on any live programs. US broadcasters were angered at the news, and FOX embarked on legal action. Most, but not all, of Fox's claims were dismissed; ultimately an agreement was reached whereby AutoHop would only become available for Fox stations seven days after a program is transmitted; terms of the settlement were not disclosed. == The future of TV advertisements == The introduction of digital video recorders and services with skipping and fast-forward capabilities enables viewers to avoid viewing interruptive advertisements in recorded programs, either manually or automatically. While advertising separate to television shows can be skipped, advertising in TV shows themselves ("product placement") cannot be skipped. Streaming services such as Hulu show shorter advertisements with a countdown timer and tailored to the viewers interests, asking interactive questions like "Is this ad relevant to you?".

Giditraffic

GidiTraffic (or GIDITRAFFIC) is an online social service started on 23 September 2011. Based primarily on social media, the service employs crowdsourcing as its primary means of providing real-time traffic updates to subscribers on its platform. The service, delivered free of charge, affords its users access to various types of information. Though its broadest category of users is road users and motorists, GIDITRAFFIC lends itself as a platform for answering inquiries from anyone who requires information on any subject of interest. GIDITRAFFIC's core competence is in vehicular traffic reports, however, the service also handles all other forms of traffic (going by the fact that the word traffic also means "the mutual exchange of information"). == Operation == Users of the service log on to its Twitter feed to get up-to-date traffic information or to post a general inquiry, which GIDITRAFFIC then publishes to all subscribers. Through crowdsourced replies, a requester receives numerous responses from other subscribers who have seen the question and can provide a relevant answer. In addition, updates are provided by subscribers to the platform via their mobile devices, thereby making the service effective in delivering traffic updates as they occur, and providing timely answers to other user inquiries. This informs GIDITRAFFIC's motto of "Lending each other an eye", alluding to the collaboration and cooperation between the platform's users in making the service indispensable to its users. == Reception == On Twitter, which is its primary platform, the service caters to over 1,800,000 subscribers, with the number increasing daily. The popularity of the platform stems from the fact that it not only keeps its subscribers abreast of the traffic situation in Lagos, the commercial capital city of Nigeria (well known for its many traffic jams), but users in other parts of the world. For a regular user of the platform, knowing where to avoid getting to a set destination in good time is well worth the two or three minutes it takes to access and scroll through the GIDITRAFFIC feed for updates. Another interesting aspect of this platform is the identity of the person behind it. The sustained anonymity of this individual has sparked many discussions centering on his or her possible identity. Online, GIDITRAFFIC continuously publishes traffic updates and user questions, while keeping up witty interactions with the platform's followers round the clock – adding to the mystery and persona of the GIDITRAFFIC owner. == Awards and recognition == In early 2012, GIDITRAFFIC received a nomination for a Shorty Award in the Life-Saving Hero category. Although this did not translate into a win, it brought recognition and wider exposure for the service from international news outlets such as the BBC, Washington Post. and New York Times. Back home in Nigeria, also in 2012, GIDITRAFFIC was honored with a Future Award for Best Use of New Media in recognition of the huge impact the service has had in terms of helping Lagos residents better manage time spent in traffic. == Mobile Applications == In 2012, GIDITRAFFIC partnered with telecommunications company Nokia to produce a downloadable mobile traffic application (the GIDITRAFFIC application, available for Nokia Asha phones on Nokia's online store). There are plans to extend the application to a wider range of mobile phone platforms. On 4 September 2013, the GIDITRAFFIC application for Nokia Lumia phones using Windows Phone 8 was launched on the Windows App Store.

Vinyl cutter

A vinyl cutter is an entry-level machine for making signs. Computer-designed vector files with patterns and letters are directly cut on the roll of vinyl which is mounted and fed into the vinyl cutter through USB or serial cable. Vinyl cutters are mainly used to make signs, banners and advertisements. Advertisements seen on automobiles and vans are often made with vinyl cut letters. While these machines were designed for cutting vinyl, they can also cut through computer and specialty papers, as well as thicker items like thin sheets of magnet. In addition to sign business, vinyl cutters are commonly used for apparel decoration. To decorate apparel, a vector design needs to be cut in mirror image, weeded, and then heat applied using a commercial heat press or a hand iron for home use. Some businesses use their vinyl cutter to produce both signs and custom apparel. Many crafters also have vinyl cutters for home use. These require little maintenance, and the vinyl can be bought in bulk relatively cheaply. Vinyl cutters are also often used by stencil artists to create single use or reusable stencil art and lettering == How it works == A vinyl cutter is a type of computer-controlled machine tool. The computer controls the movement of a sharp blade over the surface of the material as it would the nozzles of an ink-jet printer. This blade is used to cut out shapes and letters from sheets of thin self-adhesive plastic (vinyl). The vinyl can then be stuck to a variety of surfaces depending on the adhesive and type of material. To cut out a design, a vector-based image must be created using vector drawing software. Some vinyl cutters are marketed to small in-home businesses and require download and use of a proprietary editing software. The design is then sent to the cutter where it cuts along the vector paths laid out in the design. The cutter is capable of moving the blade on an X and Y axis over the material, cutting it into the required shapes. The vinyl material comes in long rolls allowing projects with significant length like banners or billboards to be easily cut. A major limitation with vinyl cutters is that they can only cut shapes from solid colours of vinyl, paper, card or thin plastic sheets such as Mylar. The type and thickness of material will vary for each cutter and how much downforce the cutter is capable of. If the material has no backing, a backing sheet, material or cutting mat and a temporary adhesive are needed to allow the cutter to cut through the material. A design with multiple colours must have each colour cut separately and then layered on top of each other as it is applied to the substrate. This is a process that is often applied in stencil art. Also, since the shapes are cut out of solid colours, photographs and gradients cannot be reproduced with a stand-alone cutter. === Design creation === Designs are created using vector-based software like Adobe Illustrator, FlexiSign, EasyCutPro, or other software. Vector artwork is either drawn with lines, shapes and text or images are vectorized thus create vector shapes. Most cutters (also called plotters) require special software to load/edit the artwork and communicate with the cutter. Computer designed images are loaded onto the vinyl cutter via a wired connection or over a wireless protocol. Then the vinyl is loaded into the machine where it is automatically fed through and cut to follow the set design. The vinyl can be placed on an adhesive mat to stabilize the vinyl when cutting smaller designs. === Types of vinyl === Adhesive vinyl is the type of vinyl used for store windows, car decals, signage, and more. Adhesive vinyl is applied with a transfer medium often called "transfer tape" or "carrier sheet". Heat transfer vinyl is the type of vinyl used to apply a design to fabric including t-shirts, tea towels, canvas bags, and more. Heat Transfer vinyl can be applied using a heat press or an iron, though the constant pressure and heat from a heat press is recommended by experts. === Using other materials === In addition to vinyl some cutters are capable of cutting other materials such as paper, card, plastic sheets and even thin wood. The thickness and type of material that can be cut will depend on the model of the cutter and heavily depends on the downforce. Cricut is a popular home cutter used by arts and craft enthusiasts since it allows for a wide use of different materials and is similar in size to a household printer and has strong downforce for its size. === Backing and cutting mat === If you cut material that doesn't have an adhesive backing you will require a cutting mat that you need to attach your material to. Some cutting mats are sticky, others will require you to use a temporary adhesive and/or masking tape to keep the material in place when cutting. === Cutting === The vinyl cutter uses a small knife or blade to precisely cut the outline of figures into a sheet or piece of vinyl, but not the release liner. The process of cutting vinyl material without penetrating it completely is referred to as "kiss cutting". The knife moves side to side and turns, while the vinyl is moved beneath the knife. The results from the cut process is an image cut into the material. === Weeding === The material is then 'weeded' where the excess parts of the figures are removed from the release liner. It is possible to remove the positive parts, which would give a negative decal, or remove the negative parts, giving a positive decal. Removing the figure would be like removing the positive, giving a negative image of the figures. === Transfer tape === A sheet of transfer tape with an adhesive backing is laid on the weeded vinyl when necessary. Heat Transfer vinyl often does not require use of a separate transfer tape. A roller is applied to the tape, causing it to adhere to the vinyl. The transfer tape and the weeded vinyl is pulled off the release liner, and applied to a substrate, such as a sheet of aluminium. This results in an aluminium sign with vinyl figures. == Uses == In addition to the capabilities of the cutter itself, adhesive vinyl comes in a wide variety of colors and materials including gold and silver foil, vinyl that simulates frosted glass, holographic vinyl, reflective vinyl, thermal transfer material, and even clear vinyl embedded with gold leaf. (Often used in the lettering on fire trucks and rescue vehicles.) As the vinyl film is supplied by the manufacturer, it comes attached to a release liner. == Challenges when cutting on a vinyl cutter == Cutting on a vinyl cutter requires careful calibration to achieve clean and accurate results, especially when the goal is to cut through only the top layer of material while leaving the backing intact. One of the most common challenges is setting the correct cutting depth. If the blade is not lowered enough, the vinyl material may not separate properly; if it goes too deep, it can cut through the backing layer and potentially damage the cutting mat. The cutting depth on the vinyl cutter machines typically does not exceed 1 mm. Another frequent issue is the mismatch between the blade and the type of material being processed. Using an inappropriate blade can lead to uneven cuts, premature dulling of the edge, and torn or frayed material. The overall quality of the output also depends on factors such as the cutting speed, blade sharpening and cutting angle, and the material the knife is made of.

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)} .

False answer supervision

False answer supervision (FAS) refers to VoIP fraud where the billed duration for the caller is more than the duration of the actual connection duration. The FAS is usually performed by VoIP wholesalers in their softswitches for randomly selected calls. Adding a small amount of extra billed seconds for many calls results in significant revenue for the VoIP wholesaler. == Implementation of FAS == The FAS fraud can be implemented in a softswitch in many different ways. These include: False billing of party A without calling a party B. Usually a fake ringback tone, loopback audio or voicemail message is played Start of billing before actual answer of party B Extra billing after disconnection of party B == Detection of FAS == The FAS can be detected and blocked in a softswitch. Common methods are: Manual verification of call detail records: listening to voice recordings Identification of FAS types and using algorithms to automatically detect the FAS RTP audio signal processing: detection of voice RTP audio signal processing: detection of silence RTP audio signal processing: detection of ringback tone