In automata theory (a branch of theoretical computer science), NFA minimization is the task of transforming a given nondeterministic finite automaton (NFA) into an equivalent NFA that has a minimum number of states, transitions, or both. While efficient algorithms exist for DFA minimization, NFA minimization is PSPACE-complete. No efficient (polynomial time) algorithms are known, and under the standard assumption that P ≠ PSPACE, none exist. The most efficient known algorithm is the Kameda–Weiner algorithm. == Non-uniqueness of minimal NFA == Unlike deterministic finite automata, minimal NFAs may not be unique. There may be multiple NFAs with the same number of states that accept the same regular language, but for which there is no equivalent NFA or DFA with fewer states.
Neural radiance field
A neural radiance field (NeRF) is a neural field for reconstructing a three-dimensional representation of a scene from two-dimensional images. The NeRF model enables downstream applications of novel view synthesis, scene geometry reconstruction, and obtaining the reflectance properties of the scene. Additional scene properties such as camera poses may also be jointly learned. First introduced in 2020, it has since gained significant attention for its potential applications in computer graphics and content creation. == Algorithm == The NeRF algorithm represents a scene as a radiance field parametrized by a deep neural network (DNN). The network predicts a volume density and view-dependent emitted radiance given the spatial location ( x , y , z ) {\displaystyle (x,y,z)} and viewing direction in Euler angles ( θ , Φ ) {\displaystyle (\theta ,\Phi )} of the camera. By sampling many points along camera rays, traditional volume rendering techniques can produce an image. === Data collection === A NeRF needs to be retrained for each unique scene. The first step is to collect images of the scene from different angles and their respective camera pose. These images are standard 2D images and do not require a specialized camera or software. Any camera is able to generate datasets, provided the settings and capture method meet the requirements for SfM (Structure from Motion). This requires tracking of the camera position and orientation, often through some combination of SLAM, GPS, or inertial estimation. Researchers often use synthetic data to evaluate NeRF and related techniques. For such data, images (rendered through traditional non-learned methods) and respective camera poses are reproducible and error-free. === Training === For each sparse viewpoint (image and camera pose) provided, camera rays are marched through the scene, generating a set of 3D points with a given radiance direction (into the camera). For these points, volume density and emitted radiance are predicted using the multi-layer perceptron (MLP). An image is then generated through classical volume rendering. Because this process is fully differentiable, the error between the predicted image and the original image can be minimized with gradient descent over multiple viewpoints, encouraging the MLP to develop a coherent model of the scene. == Variations and improvements == Early versions of NeRF were slow to optimize and required that all input views were taken with the same camera in the same lighting conditions. These performed best when limited to orbiting around individual objects, such as a drum set, plants or small toys. Since the original paper in 2020, many improvements have been made to the NeRF algorithm, with variations for special use cases. === Fourier feature mapping === In 2020, shortly after the release of NeRF, the addition of Fourier Feature Mapping improved training speed and image accuracy. Deep neural networks struggle to learn high frequency functions in low dimensional domains; a phenomenon known as spectral bias. To overcome this shortcoming, points are mapped to a higher dimensional feature space before being fed into the MLP. γ ( v ) = [ a 1 cos ( 2 π B 1 T v ) a 1 sin ( 2 π B 1 T v ) ⋮ a m cos ( 2 π B m T v ) a m sin ( 2 π B m T v ) ] {\displaystyle \gamma (\mathrm {v} )={\begin{bmatrix}a_{1}\cos(2{\pi }{\mathrm {B} }_{1}^{T}\mathrm {v} )\\a_{1}\sin(2\pi {\mathrm {B} }_{1}^{T}\mathrm {v} )\\\vdots \\a_{m}\cos(2{\pi }{\mathrm {B} }_{m}^{T}\mathrm {v} )\\a_{m}\sin(2{\pi }{\mathrm {B} }_{m}^{T}\mathrm {v} )\end{bmatrix}}} Where v {\displaystyle \mathrm {v} } is the input point, B i {\displaystyle \mathrm {B} _{i}} are the frequency vectors, and a i {\displaystyle a_{i}} are coefficients. This allows for rapid convergence to high frequency functions, such as pixels in a detailed image. === Bundle-adjusting neural radiance fields === One limitation of NeRFs is the requirement of knowing accurate camera poses to train the model. Often times, pose estimation methods are not completely accurate, nor is the camera pose even possible to know. These imperfections result in artifacts and suboptimal convergence. So, a method was developed to optimize the camera pose along with the volumetric function itself. Called Bundle-Adjusting Neural Radiance Field (BARF), the technique uses a dynamic low-pass filter (DLPF) to go from coarse to fine adjustment, minimizing error by finding the geometric transformation to the desired image. This corrects imperfect camera poses and greatly improves the quality of NeRF renders. === Multiscale representation === Conventional NeRFs struggle to represent detail at all viewing distances, producing blurry images up close and overly aliased images from distant views. In 2021, researchers introduced a technique to improve the sharpness of details at different viewing scales known as mip-NeRF (comes from mipmap). Rather than sampling a single ray per pixel, the technique fits a gaussian to the conical frustum cast by the camera. This improvement effectively anti-aliases across all viewing scales. mip-NeRF also reduces overall image error and is faster to converge at about half the size of ray-based NeRF. === Learned initializations === In 2021, researchers applied meta-learning to assign initial weights to the MLP. This rapidly speeds up convergence by effectively giving the network a head start in gradient descent. Meta-learning also allowed the MLP to learn an underlying representation of certain scene types. For example, given a dataset of famous tourist landmarks, an initialized NeRF could partially reconstruct a scene given one image. === NeRF in the wild === Conventional NeRFs are vulnerable to slight variations in input images (objects, lighting) often resulting in ghosting and artifacts. As a result, NeRFs struggle to represent dynamic scenes, such as bustling city streets with changes in lighting and dynamic objects. In 2021, researchers at Google developed a new method for accounting for these variations, named NeRF in the Wild (NeRF-W). This method splits the neural network (MLP) into three separate models. The main MLP is retained to encode the static volumetric radiance. However, it operates in sequence with a separate MLP for appearance embedding (changes in lighting, camera properties) and an MLP for transient embedding (changes in scene objects). This allows the NeRF to be trained on diverse photo collections, such as those taken by mobile phones at different times of day. === Relighting === In 2021, researchers added more outputs to the MLP at the heart of NeRFs. The output now included: volume density, surface normal, material parameters, distance to the first surface intersection (in any direction), and visibility of the external environment in any direction. The inclusion of these new parameters lets the MLP learn material properties, rather than pure radiance values. This facilitates a more complex rendering pipeline, calculating direct and global illumination, specular highlights, and shadows. As a result, the NeRF can render the scene under any lighting conditions with no re-training. === Plenoctrees === Although NeRFs had reached high levels of fidelity, their costly compute time made them useless for many applications requiring real-time rendering, such as VR/AR and interactive content. Introduced in 2021, Plenoctrees (plenoptic octrees) enabled real-time rendering of pre-trained NeRFs through division of the volumetric radiance function into an octree. Rather than assigning a radiance direction into the camera, viewing direction is taken out of the network input and spherical radiance is predicted for each region. This makes rendering over 3000x faster than conventional NeRFs. === Sparse Neural Radiance Grid === Similar to Plenoctrees, this method enabled real-time rendering of pretrained NeRFs. To avoid querying the large MLP for each point, this method bakes NeRFs into Sparse Neural Radiance Grids (SNeRG). A SNeRG is a sparse voxel grid containing opacity and color, with learned feature vectors to encode view-dependent information. A lightweight, more efficient MLP is then used to produce view-dependent residuals to modify the color and opacity. To enable this compressive baking, small changes to the NeRF architecture were made, such as running the MLP once per pixel rather than for each point along the ray. These improvements make SNeRG extremely efficient, outperforming Plenoctrees. === Instant NeRFs === In 2022, researchers at Nvidia enabled real-time training of NeRFs through a technique known as Instant Neural Graphics Primitives. An innovative input encoding reduces computation, enabling real-time training of a NeRF, an improvement orders of magnitude above previous methods. The speedup stems from the use of spatial hash functions, which have O ( 1 ) {\displaystyle O(1)} access times, and parallelized architectures which run fast on modern GPUs. == Related techniques == === Plenoxels === Plen
MIDI Show Control
MIDI Show Control (MSC), is a real-time System Exclusive extension of the international Musical Instrument Digital Interface (MIDI) standard. MSC enables all types of entertainment equipment to communicate with each other through the process of show control. The MIDI Show Control protocol is a technical standard ratified by the MIDI Manufacturers Association in 1991, which allows entertainment control devices to talk with each other and with computers to perform show control functions in live and prerecorded entertainment applications. Just like musical MIDI, MSC does not transmit the actual show media - it simply transmits digital information about a multimedia performance. == How MSC works == When any cue is called by a user (typically a stage manager) and/or preprogrammed timeline in a show control software application, the show controller transmits one or more MSC messages from its 'MIDI Out' port. A typical MSC message sequence is: the user has just called a cue the cue is for lighting device 3 the cue is number 45.8 the cue is in cue list 7 MSC messages are serially transmitted in the same way as musical messages and are fully compatible with all conventional MIDI hardware; however, many modern MSC devices now use Ethernet communications for higher bandwidth and the flexibility afforded by networks. Other performance parameters are also transmitted, such as lighting desk submaster settings using MSC SET messages. All cues that a media control device is capable of playing are assigned MSC messages within the Show Controller's cue list and they are transmitted from its MIDI Out port at the appropriate show time, depending on the actions of the user and the show controller's internally timed sequences. All MSC-compatible instruments follow the MSC specification and thus transmit identical MSC messages for identical MSC events, such as the playing of a certain cue on the media controller. Since they follow a published standard, all MSC devices can communicate with and understand each other, as well as with computers that have been programmed to understand MSC messages using the MSC Command Set. All MSC compatible instruments have a built-in MIDI interface and many now follow one of the various MIDI-over-Ethernet protocols. == History == To create the MSC spec, Charlie Richmond headed the USITT MIDI Forum on their Callboard Network in 1990, which included developers and designers from the theatre sound and lighting industry from around the world. It is believed that this was the first international standard to be developed without a single physical meeting of the participants. This Forum created the MSC standard between January and September 1990. This was ratified by the MIDI Manufacturers Association (MMA) in January 1991, and the Japan MIDI Standards Committee (JMSC) later that year, becoming a part of the standard MIDI specification in August 1991. The first show to fully use the MSC specification was the Magic Kingdom Parade at Walt Disney World's Magic Kingdom in September 1991. == MIDI Show Control software ==
Hardware trojan
A hardware trojan (HT) is a malicious modification of the circuitry of an integrated circuit. A hardware trojan is completely characterized by its physical representation and its behavior. The payload of an HT is the entire activity that the Trojan executes when it is triggered. In general, trojans try to bypass or disable the security fence of a system: for example, leaking confidential information by radio emission. HTs also could disable, damage or destroy the entire chip or components of it. Hardware trojans may be introduced as hidden front-doors that are inserted while designing a computer chip, by using a pre-made application-specific integrated circuit (ASIC) semiconductor intellectual property core (IP core) that have been purchased from a non-reputable source, or inserted internally by a rogue employee, either acting on their own, or on behalf of rogue special interest groups, or state sponsored spying and espionage. One paper published by IEEE in 2015 explains how a hardware design containing a trojan could leak a cryptographic key leaked over an antenna or network connection, provided that the correct "easter egg" trigger is applied to activate the data leak. In high security governmental IT departments, hardware trojans are a well known problem when buying hardware such as: a KVM switch, keyboards, mice, network cards, or other network equipment. This is especially the case when purchasing such equipment from non-reputable sources that could have placed hardware trojans to leak keyboard passwords, or provide remote unauthorized entry. == Background == In a diverse global economy, outsourcing of production tasks is a common way to lower a product's cost. Embedded hardware devices are not always produced by the firms that design and/or sell them, nor in the same country where they will be used. Outsourced manufacturing can raise doubt about the evidence for the integrity of the manufactured product (i.e., one's certainty that the end-product has no design modifications compared to its original design). Anyone with access to the manufacturing process could, in theory, introduce some change to the final product. For complex products, small changes with large effects can be difficult to detect. The threat of a serious, malicious, design alteration can be especially relevant to government agencies. Resolving doubt about hardware integrity is one way to reduce technology vulnerabilities in the military, finance, energy and political sectors of an economy. Since fabrication of integrated circuits in untrustworthy factories is common, advanced detection techniques have emerged to discover when an adversary has hidden additional components in, or otherwise sabotaged, the circuit's function. == Characterization of hardware trojans == An HT can be characterized by several methods such as by its physical representation, activation phase and its action phase. Alternative methods characterize the HT by trigger, payload and stealth. === Physical characteristics === One of this physical trojan characteristics is the type. The type of a trojan can be either functional or parametric. A trojan is functional if the adversary adds or deletes any transistors or gates to the original chip design. The other kind of trojan, the parametric trojan, modifies the original circuitry, e.g. thinning of wires, weakening of flip-flops or transistors, subjecting the chip to radiation, or using focused ion-beams (FIB) to reduce the reliability of a chip. The size of a trojan is its physical extension or the number of components it is made of. Because a trojan can consist of many components, the designer can distribute the parts of a malicious logic on the chip. The additional logic can occupy the chip wherever it is needed to modify, add, or remove a function. Malicious components can be scattered, called loose distribution, or consist of only few components, called tight distribution, so the area is small where the malicious logic occupies the layout of the chip. In some cases, high-effort adversaries in may regenerate the layout so that the placement of the components of the IC is altered. In rare cases the chip dimension is altered. These changes are structural alterations. === Activation characteristics === The typical trojan is condition-based: It is triggered by sensors, internal logic states, a particular input pattern or an internal counter value. Condition-based trojans are detectable with power traces to some degree when inactive. That is due to the leakage currents generated by the trigger or counter circuit activating the trojan. Hardware trojans can be triggered in different ways. A trojan can be internally activated, which means it monitors one or more signals inside the IC. The malicious circuitry could wait for a count down logic an attacker added to the chip, so that the trojan awakes after a specific time-span. The opposite is externally activated. There can be malicious logic inside a chip, that uses an antenna or other sensors the adversary can reach from outside the chip. For example, a trojan could be inside the control system of a cruising missile. The owner of the missile does not know, that the enemy will be able to switch off the rockets by radio. A trojan which is always-on can be a reduced wire. A chip that is modified in this way produces errors or fails every time the wire is used intensely. Always-on circuits are hard to detect with power trace. In this context combinational trojans and sequential trojans are distinguished. A combinational trojan monitors internal signals until a specific condition happens. A sequential trojan is also an internally activated condition-based circuit, but it monitors the internal signals and searches for sequences not for a specific state or condition like the combinational trojans do. ==== Cryptographic key extraction ==== Extraction of secret keys by means of a hardware trojan without detecting the trojan requires that the trojan uses a random signal or some cryptographic implementation itself. To avoid storing a cryptographic key in the trojan itself and reduction, a physical unclonable function can be used. Physical unclonable functions are small in size and can have an identical layout while the cryptographic properties are different. === Action characteristics === A HT could modify the chip's function or could change the chip's parametric properties (e.g. provokes a process delay). Confidential information can also be transmitted to the adversary (transmission of key information). === Peripheral device hardware trojans === A relatively new threat vector to networks and network endpoints is a HT appearing as a physical peripheral device that is designed to interact with the network endpoint using the approved peripheral device's communication protocol. For example, a USB keyboard that hides all malicious processing cycles from the target network endpoint to which it is attached by communicating with the target network endpoint using unintended USB channels. Once sensitive data is ex-filtrated from the target network endpoint to the HT, the HT can process the data and decide what to do with the data: store the data to memory for later physical retrieval of the HT or possibly ex-filtrate the data to the internet using wireless or using the compromised network endpoint as a pivot. == Potential of threat == A common trojan is passive most of the time-span an altered device is in use. If a trojan is activated the device functionality can be changed, the device can be destroyed or disabled, the device can leak confidential information or the HT may tear down the security and safety of the device. Trojans are stealthy, to avoid detection of the trojan the precondition for activation is a very rare event. Traditional testing techniques are not sufficient. A manufacturing fault happens at a random position while malicious changes are well placed to avoid detection. == Detection == === Physical inspection === First, the molding coat is cut to reveal the circuitry. Then, the engineer repeatedly scans the surface while grinding the layers of the chip. There are several operations to scan the circuitry. Typical visual inspection methods are: scanning optical microscopy (SOM), scanning electron microscopy (SEM), pico-second imaging circuit analysis (PICA), voltage contrast imaging (VCI), light induced voltage alteration (LIVA) or charge induced voltage alteration (CIVA). To compare the floor plan of the chip has to be compared with the image of the actual chip. This is still quite challenging to do. To detect Trojan hardware which include (crypto) keys which are different, an image diff can be taken to reveal the different structure on the chip. The only known hardware Trojan using unique crypto keys but having the same structure is. This property enhances the undetectability of the trojan. === Functional testing === This detection method stimulates the input ports of a chip and monitors the output
Interference (communication)
In telecommunications, an interference is that which modifies a signal in a disruptive manner, as it travels along a communication channel between its source and receiver. The term is often used to refer to the addition of unwanted signals to a useful signal. Common examples include: Electromagnetic interference (EMI) Co-channel interference (CCI), also known as crosstalk Adjacent-channel interference (ACI) Intersymbol interference (ISI) Inter-carrier interference (ICI), caused by doppler shift in OFDM modulation (multitone modulation). Common-mode interference (CMI) Conducted interference Noise is a form of interference but not all interference is noise. Radio resource management aims at reducing and controlling the co-channel and adjacent-channel interference. == Interference alignment == A solution to interference problems in wireless communication networks is interference alignment, which was crystallized by Syed Ali Jafar at the University of California, Irvine. A specialized application was previously studied by Yitzhak Birk and Tomer Kol for an index coding problem in 1998. For interference management in wireless communication, interference alignment was originally introduced by Mohammad Ali Maddah-Ali, Abolfazl S. Motahari, and Amir Keyvan Khandani, at the University of Waterloo, for communication over wireless X channels. Interference alignment was eventually established as a general principle by Jafar and Viveck R. Cadambe in 2008, when they introduced "a mechanism to align an arbitrarily large number of interferers, leading to the surprising conclusion that wireless networks are not essentially interference limited." This led to the adoption of interference alignment in the design of wireless networks. Jafar explained: My research group crystallized the concept of interference alignment and showed that through interference alignment, it is possible for everyone to access half of the total bandwidth free from interference. Initially this result was shown under a number of idealized assumptions that are typical in theoretical studies. We have since continued to work on peeling off these idealizations one at a time, to bring the theory closer to practice. Along the way we have made numerous discoveries through the lens of interference alignment, which reveal new and powerful signaling schemes. According to New York University senior researcher Paul Horn: Syed Jafar revolutionized our understanding of the capacity limits of wireless networks. He demonstrated the astounding result that each user in a wireless network can access half of the spectrum without interference from other users, regardless of how many users are sharing the spectrum. This is a truly remarkable result that has a tremendous impact on both information theory and the design of wireless networks.
Digital Michelangelo Project
The Digital Michelangelo Project was a pioneering initiative undertaken during the 1998–1999 academic year to digitize the sculptures and architecture of Michelangelo using advanced laser scanning technology. The project was led by a team of 30 faculty, staff, and students from Stanford University and the University of Washington, with the aim of creating high-resolution 3D models of Michelangelo's works for scholarly, educational, and preservation purposes. == Objectives == The primary goals of the Digital Michelangelo Project were: To apply recent advancements in laser rangefinder technology for digitizing large cultural artifacts. To create detailed digital archives of Michelangelo's sculptures and architectural spaces for future study and analysis. To explore potential educational and curatorial applications for 3D scanned data. === Artworks digitized === The project involved scanning several iconic works by Michelangelo, including: David The Unfinished Slaves (Atlas, Awakening, Bearded, and Youthful) St. Matthew The allegorical statues from the Medici tombs (Night, Day, Dawn, and Dusk) The architectural interiors of the Tribuna del David at the Galleria dell'Accademia and the New Sacristy in the Medici Chapels. == Technology and methodology == === 3D scanning === The project's primary scanner was a laser triangulation rangefinder mounted on a motorized gantry, custom-built by Cyberware Inc. The scanner used a laser sheet to project onto an object, capturing its shape through triangulation. Multiple scans were taken from various angles and combined into a single, detailed 3D mesh. The resolution achieved was fine enough to capture even Michelangelo's chisel marks, with triangles approximately 0.25 mm on each side. In addition to shape data, color data was captured using a spotlight and a secondary camera, enabling the creation of textured 3D models. === Data processing === The project developed a software suite for processing the scanned data. This included: Aligning and merging multiple scans into a seamless 3D model. Filling holes in the geometry caused by inaccessible areas. Correcting color data for lighting inconsistencies and shadowing. Non-photorealistic rendering techniques were also applied, highlighting surface features such as Michelangelo’s chisel marks for enhanced visualization. == Logistical challenges == The scale and complexity of the project presented several challenges: Data size: The dataset for David alone comprised 2 billion polygons and 7,000 color images, occupying 60 GB of storage. Artifact safety: Ensuring the safety of the statues during scanning required extensive crew training, foam-encased equipment, and collision-prevention mechanisms. == Applications and impact == The digitized models have numerous potential applications: Art history: Allowing precise measurements and geometric analysis, such as determining chisel types or evaluating structural balance. Education: Providing new ways to study art, including interactive viewing from unconventional angles and with custom lighting. Museum curation: Enhancing visitor experiences through interactive kiosks and virtual models. The project demonstrated the potential for 3D technology to preserve and disseminate cultural heritage. == Data distribution == The project's models are available through Stanford University for scholarly purposes, under strict licensing due to Italian intellectual property laws. === ScanView === To provide public access to the 3D models while respecting usage restrictions, the project developed ScanView, a client/server rendering system. ScanView allows users to view and interact with high-resolution 3D models without downloading the data. The client component consists of a freely available viewer program and simplified 3D models. Users can navigate these models locally, adjusting position, orientation, lighting, and surface appearance. When a user finalizes a view, the client queries a remote server for a high-resolution rendering of the model, which is sent back to overwrite the simplified version on the user’s screen. A typical query-response cycle takes 1–2 seconds, depending on network conditions. To protect the models from unauthorized reconstruction, the system employs several security measures, including: Encrypting queries Perturbing viewpoint and lighting parameters Adding noise and warping rendered images Compressing images before transmission ScanView operates on Windows-based PCs and provides access to selected models, including David and St. Matthew, as well as other artifacts such as fragments of the Forma Urbis Romae and items from the Stanford 3D Scanning Repository. == Sponsors == The Digital Michelangelo Project was supported by Stanford University, Interval Research Corporation, and the Paul G. Allen Foundation for the Arts.
Mike Little
Mike Little (born 12 May 1962) is an English web developer and writer. He is the co-founder of the free and open source web publishing software WordPress. == Biography == Mike Little was born in Manchester, England in 1962 to a Nigerian father, who was a mathematics lecturer and musician, and an English mother who worked as a primary school teacher. Little was placed into foster care when he was four months of age, and was later adopted by the same family. He grew up on a council estate in Brinnington, Stockport, and was educated at Stockport School. In 2003, Little and Matt Mullenweg started working on a project in which they built on b2/cafelog and later named it WordPress, releasing the first version on 27 May 2003. Little states that, despite not being invited to join his co-founder's for-profit business Automattic, he and Mullenweg remain on good terms. He clarified: "I don’t want it to sound like he cheated me out of something or ripped me off in some way. He didn’t." In June 2013, Little was awarded the SAScon's "Outstanding Contribution to Digital" award for his part in co-founding and developing WordPress. Little has been described as "modest" and living in "virtual anonymity". He has one daughter. He identifies as a follower of Stoicism and a humanist, and in 2021, he became a patron of charity Humanists UK.