Least-squares spectral analysis (LSSA) is a class of methods for estimating a frequency spectrum by fitting sinusoids to data using a least-squares fit. Unlike Fourier analysis, the most widely used spectral method in science, data need not be equally spaced to use LSSA. Furthermore, while Fourier analysis generally amplifies long-period noise in long or gapped records, LSSA mitigates such problems. The first strictly least-squares LSSA method was developed in 1969 and 1971, and is known as the Vaníček method or the Gauss–Vaniček method, after its inventor Petr Vaníček and Carl Friedrich Gauss, the inventor of the least-squares method for error minimization. A widely known LSSA variant is the Lomb method or the Lomb–Scargle periodogram, based on dated computational simplifications of the Vaníček method introduced in the 1970s and 1980s, first by Nicholas R. Lomb and later by Jeffrey D. Scargle. Other LSSA variants have been subsequently developed. == Historical background == The close connections between Fourier analysis, the periodogram, and the least-squares fitting of sinusoids have been known for a long time. However, most developments are restricted to complete data sets of equally spaced samples. In 1963, Freek J. M. Barning of Mathematisch Centrum, Amsterdam, handled unequally spaced data by similar techniques, including both a periodogram analysis equivalent to what nowadays is called the Lomb method and least-squares fitting of selected frequencies of sinusoids determined from such periodograms — and connected by a procedure known today as the matching pursuit with post-back fitting or the orthogonal matching pursuit. Petr Vaníček, a Canadian geophysicist and geodesist of the University of New Brunswick, proposed in 1969 also the matching-pursuit approach for equally and unequally spaced data, which he called "successive spectral analysis" and the result a "least-squares periodogram". He generalized this method to account for any systematic components beyond a simple mean, such as a "predicted linear (quadratic, exponential, ...) secular trend of unknown magnitude", and applied it to a variety of samples, in 1971. Vaníček's strictly least-squares method was then simplified in 1976 by Nicholas R. Lomb of the University of Sydney, who pointed out its close connection to periodogram analysis. Subsequently, the definition of a periodogram of unequally spaced data was modified and analyzed by Jeffrey D. Scargle of NASA Ames Research Center, who showed that, with minor changes, it becomes identical to Lomb's least-squares formula for fitting individual sinusoid frequencies. Scargle states that his paper "does not introduce a new detection technique, but instead studies the reliability and efficiency of detection with the most commonly used technique, the periodogram, in the case where the observation times are unevenly spaced," and further points out regarding least-squares fitting of sinusoids compared to periodogram analysis, that his paper "establishes, apparently for the first time, that (with the proposed modifications) these two methods are exactly equivalent." Press summarizes the development this way: A completely different method of spectral analysis for unevenly sampled data, one that mitigates these difficulties and has some other very desirable properties, was developed by Lomb, based in part on earlier work by Barning and Vanicek, and additionally elaborated by Scargle. In 1989, Michael J. Korenberg of Queen's University in Kingston, Ontario, developed the "fast orthogonal search" method of more quickly finding a near-optimal decomposition of spectra or other problems, similar to the technique that later became known as the orthogonal matching pursuit. == Development of LSSA and variants == === The Vaníček method === In the Vaníček method, a discrete data set is approximated by a weighted sum of sinusoids of progressively determined frequencies using a standard linear regression or least-squares fit. The frequencies are chosen using a method similar to Barning's, but going further in optimizing the choice of each successive new frequency by picking the frequency that minimizes the residual after least-squares fitting (equivalent to the fitting technique now known as matching pursuit with pre-backfitting). The number of sinusoids must be less than or equal to the number of data samples (counting sines and cosines of the same frequency as separate sinusoids). The relationship between the DFT and the approximation of trigonometric functions using the least-squares method is well explained in (Strutz, 2017). A data vector Φ is represented as a weighted sum of sinusoidal basis functions, tabulated in a matrix A by evaluating each function at the sample times, with weight vector x: ϕ ≈ A x , {\displaystyle \phi \approx {\textbf {A}}x,} where the weights vector x is chosen to minimize the sum of squared errors in approximating Φ. The solution for x is closed-form, using standard linear regression: x = ( A T A ) − 1 A T ϕ . {\displaystyle x=({\textbf {A}}^{\mathrm {T} }{\textbf {A}})^{-1}{\textbf {A}}^{\mathrm {T} }\phi .} Here the matrix A can be based on any set of functions mutually independent (not necessarily orthogonal) when evaluated at the sample times; functions used for spectral analysis are typically sines and cosines evenly distributed over the frequency range of interest. If we choose too many frequencies in a too-narrow frequency range, the functions will be insufficiently independent, the matrix ill-conditioned, and the resulting spectrum meaningless. When the basis functions in A are orthogonal (that is, not correlated, meaning the columns have zero pair-wise dot products), the matrix ATA is diagonal; when the columns all have the same power (sum of squares of elements), then that matrix is an identity matrix times a constant, so the inversion is trivial. The latter is the case when the sample times are equally spaced and sinusoids chosen as sines and cosines equally spaced in pairs on the frequency interval 0 to a half cycle per sample (spaced by 1/N cycles per sample, omitting the sine phases at 0 and maximum frequency where they are identically zero). This case is known as the discrete Fourier transform, slightly rewritten in terms of measurements and coefficients. x = A T ϕ {\displaystyle x={\textbf {A}}^{\mathrm {T} }\phi } — DFT case for N equally spaced samples and frequencies, within a scalar factor. === The Lomb method === Trying to lower the computational burden of the Vaníček method in 1976 (no longer an issue), Lomb proposed using the above simplification in general, except for pair-wise correlations between sine and cosine bases of the same frequency, since the correlations between pairs of sinusoids are often small, at least when they are not tightly spaced. This formulation is essentially that of the traditional periodogram but adapted for use with unevenly spaced samples. The vector x is a reasonably good estimate of an underlying spectrum, but since we ignore any correlations, Ax is no longer a good approximation to the signal, and the method is no longer a least-squares method — yet in the literature continues to be referred to as such. Rather than just taking dot products of the data with sine and cosine waveforms directly, Scargle modified the standard periodogram formula so to find a time delay τ {\displaystyle \tau } first, such that this pair of sinusoids would be mutually orthogonal at sample times t j {\displaystyle t_{j}} and also adjusted for the potentially unequal powers of these two basis functions, to obtain a better estimate of the power at a frequency. This procedure made his modified periodogram method exactly equivalent to Lomb's method. Time delay τ {\displaystyle \tau } by definition equals to tan 2 ω τ = ∑ j sin 2 ω t j ∑ j cos 2 ω t j . {\displaystyle \tan {2\omega \tau }={\frac {\sum _{j}\sin 2\omega t_{j}}{\sum _{j}\cos 2\omega t_{j}}}.} Then the periodogram at frequency ω {\displaystyle \omega } is estimated as: P x ( ω ) = 1 2 [ [ ∑ j X j cos ω ( t j − τ ) ] 2 ∑ j cos 2 ω ( t j − τ ) + [ ∑ j X j sin ω ( t j − τ ) ] 2 ∑ j sin 2 ω ( t j − τ ) ] , {\displaystyle P_{x}(\omega )={\frac {1}{2}}\left[{\frac {\left[\sum _{j}X_{j}\cos \omega (t_{j}-\tau )\right]^{2}}{\sum _{j}\cos ^{2}\omega (t_{j}-\tau )}}+{\frac {\left[\sum _{j}X_{j}\sin \omega (t_{j}-\tau )\right]^{2}}{\sum _{j}\sin ^{2}\omega (t_{j}-\tau )}}\right],} which, as Scargle reports, has the same statistical distribution as the periodogram in the evenly sampled case. At any individual frequency ω {\displaystyle \omega } , this method gives the same power as does a least-squares fit to sinusoids of that frequency and of the form: ϕ ( t ) = A sin ω t + B cos ω t . {\displaystyle \phi (t)=A\sin \omega t+B\cos \omega t.} In practice, it is always difficult to judge if a given Lomb peak is significant or not, especially when the nature of the noise is unknown, so for example a false-alarm spectr
Xiaomi MiMo
Xiaomi MiMo is a family of large language models (LLMs) developed by Xiaomi. It was initially released in April 2025 with the MiMo-7B model. Currently, MiMo is available for developers through API service. It is used as the key AI model in Xiaomi's "Human x Car x Home" ecosystem. == Development == Xiaomi developed MiMo as a reasoning-focused language model. Its development team was led by Luo Fuli, who had previously worked at DeepSeek before joining Xiaomi in late 2025. The model was trained using multi-token prediction and reinforcement learning, with a particular emphasis on mathematical reasoning and code generation tasks. In March 2026, Xiaomi CEO Lei Jun announced that the company planned to invest at least US$8.7 billion in artificial intelligence over the following three years. == Models == === List of models === === MiMo-7B === MiMo-7B is the first model of this LLM. The base model, MiMo-7B-Base, was pre-trained on approximately 25 trillion tokens using web pages, academic papers, books, and synthetic reasoning data. MiMo-7B-RL underwent supervised fine-tuning and reinforcement learning on 130,000 mathematics and code problems. MiMo-7B-RL-0530 was released in May 2025. It scaled the fine-tuning dataset from 500,000 to 6 million instances and extended the RL window from 32,000 to 48,000 tokens and improved AIME 2024 scores from 68.2 to 80.1. MiMo-VL-7B was a vision-language model combining a Vision Transformer encoder with the MiMo-7B backbone. It was trained in four stages consuming 2.4 trillion tokens. Its reinforcement learning variant used Mixed On-Policy Reinforcement Learning (MORL) which integrated reward signals across perception, grounding, and reasoning. Xiaomi also released MiMo-Audio-7B, an audio-language model for voice conversion, style transfer, and speech editing. === MiMo-V2-Flash === MiMo-V2-Flash was launched in December 2025. It is a open-sourced Mixture-of-experts model with 309 billion total parameters and 15 billion active parameters. It was trained on 27 trillion tokens using FP8 mixed precision. It used hybrid attention interleaving Sliding Window and Global Attention at a 5:1 ratio. === MiMo-V2-Pro === Xiaomi publicly introduced MiMo-V2-Pro on 18 March 2026. It has over 1 trillion total parameters, 42 billion active, and a 1-million-token context window. Before the official release, the model had appeared anonymously on OpenRouter under the codename "Hunter Alpha," where it drew substantial usage and topped daily charts for several days, according to Xiaomi and Reuters. During its listing on OpenRouter, the model reportedly processed over one trillion tokens in total usage. Xiaomi later said Hunter Alpha was an early internal test build of MiMo-V2-Pro, and Reuters reported that the model had been mistaken by some users for a possible DeepSeek system before Xiaomi confirmed its origin. The model was released as a proprietary API product, and Luo Fuli stated that Xiaomi intended to open-source a variant at an unspecified future date. Xiaomi has partnered with several API web platforms like OpenClaw to launch the model. All these websites initially offered a free trial of this model for a week, but due to the overwhelming response, Xiaomi later extended the free trial period of the model until 2 April 2026. === MiMo-V2-Omni === Alongside MiMo-V2-Pro, Xiaomi launched MiMo-V2-Omni on 18 March 2026. It handles image, video, audio, and text inputs. Before the official release, it was codenamed "Healer Alpha" in OpenRouter. === MiMo-V2-TTS === On the same date as the release of MiMo-V2-Pro and MiMo-V2-Omni, a Text-to-Speech model named MiMo-V2-TTS was released also. It is a speech synthesis model. It was trained on audio data, which makes it capable of emotional transitions, mid-sentence tone shifts, singing, and synthesis of regional dialects like Sichuan, Cantonese, Henan, and Taiwanese. == Licensing == Xiaomi has used different licensing approaches for different models in the MiMo family. The MiMo-7B series and MiMo-V2-Flash were released as open-weight models. MiMo-V2-Flash was published under the MIT license with model weights and inference code available on Hugging Face. MiMo-V2-Pro and MiMo-V2-Omni were released as proprietary models. It was accessible through Xiaomi's API platform and third-party API providers. Luo Fuli stated that Xiaomi intended to open-source a variant of MiMo-V2-Pro. Although, she did not specify any timeline. MiMo-V2-TTS was released as a proprietary model with no publicly available weights.
Display list
A display list, also called a command list in Direct3D 12 and a command buffer in Vulkan, is a series of graphics commands or instructions that are run when the list is executed. Systems that make use of display list functionality are called retained mode systems, while systems that do not are as opposed to immediate mode systems. In OpenGL, display lists are useful to redraw the same geometry or apply a set of state changes multiple times. This benefit is also used with Direct3D 12's bundle command lists. In Direct3D 12 and Vulkan, display lists are regularly used for per-frame recording and execution. == Origins in vector displays == The vector monitors or calligraphic displays of the 1960s and 1970s used electron beam deflection to draw line segments, points, and sometimes curves directly on a CRT screen. Because the image would immediately fade, it needed to be redrawn many times a second (storage tube CRTs retained the image until blanked, but they were unsuitable for interactive graphics). To refresh the display, a dedicated CPU called a Display Processor or Display Processing Unit (DPU) was used, which had a memory buffer for a "display list", "display file", or "display program" containing line segment coordinates and other information. Advanced Display Processors also supported control flow instructions, which were useful for drawing repetitive graphics such as text, and some could perform coordinate transformations such as 3D projection. == Home computer display list functionality == One of the earliest systems with a true display list was the Atari 8-bit computers. The display list (actually called so in Atari terminology) is a series of instructions for ANTIC, the video co-processor used in these machines. This program, stored in the computer's memory and executed by ANTIC in real-time, can specify blank lines, any of six text modes and eight graphics modes, which sections of the screen can be horizontally or vertically fine-scrolled, and trigger Display List Interrupts (called raster interrupts or HBI on other systems). The Amstrad PCW family contains a Display List function called the 'Roller RAM'. This is a 512-byte RAM area consisting of 256 16-bit pointers in RAM, one for each line of the 720 × 256 pixel display. Each pointer identifies the location of 90 bytes of monochrome pixels that hold the line's 720 pixel states. The 90 bytes of 8 pixel states are spaced at 8-byte intervals, so there are 7 unused bytes between each byte of pixel data. This suits how the text-orientated PCW constructs a typical screen buffer in RAM, where the first character's 8 rows are stored in the first 8 bytes, the second character's rows in the next 8 bytes, and so on. The Roller RAM was implemented to speed up display scrolling as it would have been unacceptably slow for its 3.4 MHz Z80 to move up the 23 KB display buffer 'by hand' i.e. in software. The Roller RAM starting entry used at the beginning of a screen refresh is controlled by a Z80-writable I/O register. Therefore, the screen can be scrolled simply by changing this I/O register. Another system using a Display List-like feature in hardware is the Amiga, which, not coincidentally, was also designed by some of the same people who developed the custom hardware for the Atari 8-bit computers. Once directed to produce a display mode, it would continue to do so automatically for every following scan line. The computer also included a dedicated co-processor, called "Copper", which ran a simple program or 'Copper List' intended for modifying hardware registers in sync with the display. The Copper List instructions could direct the Copper to wait for the display to reach a specific position on the screen, and then change the contents of hardware registers. In effect, it was a processor dedicated to servicing raster interrupts. The Copper was used by Workbench to mix multiple display modes (multiple resolutions and color palettes on the monitor at the same time), and by numerous programs to create rainbow and gradient effects on the screen. The Amiga Copper was also capable of reconfiguring the sprite engine mid-frame, with only one scanline of delay. This allowed the Amiga to draw more than its 8 hardware sprites, so long as the additional sprites did not share scanlines (or the one scanline gap) with more than 7 other sprites. i.e., so long as at least one sprite had finished drawing, another sprite could be added below it on the screen. Additionally, the later 32-bit AGA chipset allowed the drawing of bigger sprites (more pixels per row) while retaining the same multiplexing. The Amiga also had dedicated block-shifter ("blitter") hardware, which could draw larger objects into a framebuffer. This was often used in place of, or in addition to, sprites. In more primitive systems, the results of a display list can be simulated, though at the cost of CPU-intensive writes to certain display modes, color control, or other visual effect registers in the video device, rather than a series of rendering commands executed by the device. Thus, one must create the displayed image using some other rendering process, either before or while the CPU-driven display generation executes. In many cases, the image is also modified or re-rendered between frames. The image is then displayed in various ways, depending on the exact way in which the CPU-driven display code is implemented. Examples of the results possible on these older machines requiring CPU-driven video include effects such as Commodore 64/128's FLI mode, or Rainbow Processing on the ZX Spectrum. == Usage in OpenGL == To delimit a display list, the glNewList and glEndList functions are used, and to execute the list, the glCallList function is used. Almost all rendering commands that occur between the function calls are stored in the display list. Commands that affect the client state are not stored in display lists. Display lists are named with an integer value, and creating a display list with the same name as one already created overrides the first. The glNewList function expects two arguments: an integer representing the name of the list, and an enumeration for the compilation mode. The two modes include GL_COMPILE_AND_EXECUTE, which compiles and immediately executes, and GL_COMPILE, which only compiles the list. Display lists enable the use of the retained mode rendering pattern, which is a system in which graphics commands are recorded (retained) to execute in succession at a later time. This is contrary to immediate mode, where graphics commands are immediately executed on client calls. == Usage in Direct3D 12 == Command lists are created using the ID3D12Device::CreateCommandList function. Command lists may be created in several types: direct, bundle, compute, copy, video decode, video process, and video encoding. Direct command lists specify that a command list the GPU can execute, and doesn't inherit any GPU state. Bundles, are best used for storing and executing small sets of commands any number of times. This is used differently than regular command lists, where commands stored in a command list are typically executed only once. Compute command lists are used for general computations, with a common use being calculating mipmaps. A copy command list is strictly for copying and the video decode and video process command lists are for video decoding and processing respectively. Upon creation, command lists are in the recording state. Command lists may be re-used by calling the ID3D12GraphicsCommandList::Reset function. After recording commands, the command list must be transitioned out of the recording state by calling ID3D12GraphicsCommandList::Close. The command list is then executed by calling ID3D12CommandQueue::ExecuteCommandLists.
RFPolicy
The RFPolicy outlines a method for contacting vendors about security vulnerabilities found in their products. It was initially written in 2000 by hacker and security consultant Rain Forest Puppy. It was perhaps the second disclosure policy, following Simple Nomad's. The policy gives the vendor five working days to respond to the reporter of the bug. If the vendor fails to contact the reporter within those five days, the issue is recommended to be disclosed to the general community. The reporter should help the vendor reproduce the bug and work out a fix. The reporter should delay notifying the general community about the bug if the vendor provides feasible reasons for requiring so. If the vendor fails to respond or shuts down communication with the reporter of the problem within five working days, the reporter should disclose the issue to the general community. When issuing an alert or fix, the vendor should give the reporter proper credit for reporting the bug. Context for the history of vulnerability disclosure is available in a history article.
Z-order
Z-order is an ordering of overlapping two-dimensional objects, such as windows in a stacking window manager, shapes in a vector graphics editor, or objects in a 3D application. One of the features of a typical GUI is that windows may overlap, so that one window hides part or all of another. When two windows overlap, their Z-order determines which one appears on top of the other. == Definition == The term "Z-order" refers to the order of objects along the Z-axis. In coordinate geometry, X typically refers to the horizontal axis (left to right), Y to the vertical axis (up and down), and Z refers to the axis perpendicular to the other two (forward or backward). One can think of the windows in a GUI as a series of planes parallel to the surface of the monitor. The windows are therefore stacked along the Z-axis, and the Z-order information thus specifies the front-to-back ordering of the windows on the screen. An analogy would be some sheets of paper scattered on top of a table, each sheet being a window, the table your computer screen, and the top sheet having the highest Z value. == Use == Typically, users of a GUI can affect the Z-order by selecting a window to be brought to the foreground (that is, "above" or "in front of" all the other windows). Some window managers allow interaction with windows while they are not in the foreground, while others will bring a window to the front whenever it receives input from the user. It is also possible for special windows to be designated "always on top"; these are then fixed to the top of the Z-order so that (with few exceptions) no other window can overlap them. When dealing with visual objects on a computer screen, an object with a Z-order of 1 would be visually "underneath" an object with a Z-order of 2 or greater. This is the same as making "layers" of objects where the Z-order determines what object is on top of another. An HTML page can use CSS to specify the Z-order so that some objects can be layered over others. Z-ordering is also used in 3D applications to determine object visibility based on overlap from other objects. This confers a speed advantage to the user as the computer does not need to render unseen objects. In practice, of course, some objects may be only partially obscured, and this is a complication that must be taken into account. In early real-time 3D graphics, Z-order was applied on a per-polygon basis to avoid using Z-buffer, which was considered expensive at the time. In modern 3D graphics, Z-order is used for order-dependent rendering, for example with semi-transparent objects. It can also be used to reduce the problem of Z-fighting, by either rendering farther objects first and then using weak inequality as the depth test or, conversely, rendering front-to-back and using strict inequality. == z-index == The actual number assigned to a particular place in the Z-order is sometimes known as the z-index. In particular the CSS property that sets the stack order of specific elements is known as the z-index. An element with greater stack order is always in front of another element with lower stack order. Negative values can also be used in the same manner. A negative value will appear behind a positive one. z-index only works on elements that have a position value (e.g. position: relative;) and for many coders, this one of the first things to investigate when debugging why the z-index isn't working. Like all other CSS properties, it can be set with JavaScript, with the following syntax:
Computer Graphics International
Computer Graphics International (CGI) is one of the oldest annual international conferences on computer graphics. It is organized by the Computer Graphics Society (CGS). Researchers across the whole world are invited to share their experiences and novel achievements in various fields - like computer graphics and human-computer interaction. Former conferences have been held recently in Hong Kong (China), Geneva (Switzerland), Shanghai (China), Geneva (virtually), Calgary (Canada), Bintan (Indonesia) and Yokohama (Japan). == Awards == Starting in the year of 2013, CGI has given yearly a Best Paper Award and a Career Achievement Award. == Venues ==
Fragment (computer graphics)
In computer graphics, a fragment is the data necessary to generate a single pixel's worth of a drawing primitive in the frame buffer. These data may include, but are not limited to: raster position depth interpolated attributes (color, texture coordinates, etc.) stencil alpha window ID As a scene is drawn, drawing primitives (the basic elements of graphics output, such as points, lines, circles, text etc.) are rasterized into fragments which are textured and combined with the existing frame buffer. How a fragment is combined with the data already in the frame buffer depends on various settings. In a typical case, a fragment may be discarded if it is further away than the pixel which is already at that location (according to the depth buffer). If it is nearer than the existing pixel, it may replace what is already there, or, if alpha blending is in use, the pixel's color may be replaced with a mixture of the fragment's color and the pixel's existing color, as in the case of drawing a translucent object. In general, a fragment can be thought of as the data needed to shade the pixel, plus the data needed to test whether the fragment survives to become a pixel (depth, alpha, stencil, scissor, window ID, etc.). Shading a fragment is done through a fragment shader (or pixel shaders in Direct3D). In computer graphics, a fragment is not necessarily opaque, and could contain an alpha value specifying its degree of transparency. The alpha is typically normalized to the range of [0, 1], with 0 denotes totally transparent and 1 denotes totally opaque. If the fragment is not totally opaque, then part of its background object could show through, which is known as alpha blending.