Vector quantization

Vector quantization (VQ) is a classical quantization technique from signal processing that allows the modeling of probability density functions by the distribution of prototype vectors. Developed in the early 1980s by Robert M. Gray, it was originally used for data compression. It works by dividing a large set of points (vectors) into groups having approximately the same number of points closest to them. Each group is represented by its centroid point, as in k-means and some other clustering algorithms. In simpler terms, vector quantization chooses a set of points to represent a larger set of points. The density matching property of vector quantization is powerful, especially for identifying the density of large and high-dimensional data. Since data points are represented by the index of their closest centroid, commonly occurring data have low error, and rare data high error. This is why VQ is suitable for lossy data compression. It can also be used for lossy data correction and density estimation. Vector quantization is based on the competitive learning paradigm, so it is closely related to the self-organizing map model and to sparse coding models used in deep learning algorithms such as autoencoder. == Training == One simple training algorithm for vector quantization is: Pick a sample point at random Move the nearest quantization vector centroid towards this sample point, by a small fraction of the distance Repeat A more sophisticated algorithm reduces the bias in the density matching estimation and ensures that all points are used, by including an extra sensitivity parameter: Increase each centroid's sensitivity s i {\displaystyle s_{i}} by a small amount Pick a sample point P {\displaystyle P} at random For each quantization vector centroid c i {\displaystyle c_{i}} , let d ( P , c i ) {\displaystyle d(P,c_{i})} denote the distance of P {\displaystyle P} and c i {\displaystyle c_{i}} Find the centroid c i {\displaystyle c_{i}} for which d ( P , c i ) − s i {\displaystyle d(P,c_{i})-s_{i}} is the smallest Move c i {\displaystyle c_{i}} towards P {\displaystyle P} by a small fraction of the distance Set s i {\displaystyle s_{i}} to zero Repeat It is desirable to use a cooling schedule to produce convergence: see Simulated annealing. Another simple method is LBG, which is based on k-means. The algorithm can be iteratively updated with "live" data, rather than by picking random points from a data set, but this will introduce some bias if the data are temporally correlated over many samples. == Applications == Vector quantization is used for lossy data compression, lossy data correction, pattern recognition, density estimation and clustering. Lossy data correction, or prediction, is used to recover data missing from some dimensions. It is done by finding the nearest group with the data dimensions available, then predicting the result based on the values for the missing dimensions, assuming that they will have the same value as the group's centroid. For density estimation, the area/volume that is closer to a particular centroid than to any other is inversely proportional to the density (due to the density matching property of the algorithm). === Use in data compression === Vector quantization, also called "block quantization" or "pattern matching quantization" is often used in lossy data compression. It works by encoding values from a multidimensional vector space into a finite set of values from a discrete subspace of lower dimension. A lower-space vector requires less storage space, so the data is compressed. Due to the density matching property of vector quantization, the compressed data has errors that are inversely proportional to density. The transformation is usually done by projection or by using a codebook. In some cases, a codebook can be also used to entropy code the discrete value in the same step, by generating a prefix coded variable-length encoded value as its output. The set of discrete amplitude levels is quantized jointly rather than each sample being quantized separately. Consider a k-dimensional vector [ x 1 , x 2 , . . . , x k ] {\displaystyle [x_{1},x_{2},...,x_{k}]} of amplitude levels. It is compressed by choosing the nearest matching vector from a set of n-dimensional vectors [ y 1 , y 2 , . . . , y n ] {\displaystyle [y_{1},y_{2},...,y_{n}]} , with n < k. All possible combinations of the n-dimensional vector [ y 1 , y 2 , . . . , y n ] {\displaystyle [y_{1},y_{2},...,y_{n}]} form the vector space to which all the quantized vectors belong. Only the index of the codeword in the codebook is sent instead of the quantized values. This conserves space and achieves more compression. Twin vector quantization (VQF) is part of the MPEG-4 standard dealing with time domain weighted interleaved vector quantization. === Video codecs based on vector quantization === Bink video Cinepak Daala is transform-based but uses pyramid vector quantization on transformed coefficients Digital Video Interactive: Production-Level Video and Real-Time Video Indeo Microsoft Video 1 QuickTime: Apple Video (RPZA) and Graphics Codec (SMC) Sorenson SVQ1 and SVQ3 Smacker video VQA format, used in many games The usage of video codecs based on vector quantization has declined significantly in favor of those based on motion compensated prediction combined with transform coding, e.g. those defined in MPEG standards, as the low decoding complexity of vector quantization has become less relevant. === Audio codecs based on vector quantization === AMR-WB+ CELP CELT (now part of Opus) is transform-based but uses pyramid vector quantization on transformed coefficients Codec 2 DTS G.729 iLBC Ogg Vorbis TwinVQ === Use in pattern recognition === VQ was also used in the eighties for speech and speaker recognition. Recently it has also been used for efficient nearest neighbor search and on-line signature recognition. In pattern recognition applications, one codebook is constructed for each class (each class being a user in biometric applications) using acoustic vectors of this user. In the testing phase the quantization distortion of a testing signal is worked out with the whole set of codebooks obtained in the training phase. The codebook that provides the smallest vector quantization distortion indicates the identified user. The main advantage of VQ in pattern recognition is its low computational burden when compared with other techniques such as dynamic time warping (DTW) and hidden Markov model (HMM). The main drawback when compared to DTW and HMM is that it does not take into account the temporal evolution of the signals (speech, signature, etc.) because all the vectors are mixed up. In order to overcome this problem a multi-section codebook approach has been proposed. The multi-section approach consists of modelling the signal with several sections (for instance, one codebook for the initial part, another one for the center and a last codebook for the ending part). === Use as clustering algorithm === As VQ is seeking for centroids as density points of nearby lying samples, it can be also directly used as a prototype-based clustering method: each centroid is then associated with one prototype. By aiming to minimize the expected squared quantization error and introducing a decreasing learning gain fulfilling the Robbins-Monro conditions, multiple iterations over the whole data set with a concrete but fixed number of prototypes converges to the solution of k-means clustering algorithm in an incremental manner. === Generative adversarial networks (GAN) === VQ has been used to quantize a feature representation layer in the discriminator of generative adversarial networks. The feature quantization (FQ) technique performs implicit feature matching. It improves the GAN training, and yields an improved performance on a variety of popular GAN models: BigGAN for image generation, StyleGAN for face synthesis, and U-GAT-IT for unsupervised image-to-image translation.

Semi-automation

Semi-automation is a process or procedure that is performed by the combined activities of man and machine with both human and machine steps typically orchestrated by a centralized computer controller. Within manufacturing, production processes may be fully manual, semi-automated, or fully automated. In this case, semi-automation may vary in its degree of manual and automated steps. Semi-automated manufacturing processes are typically orchestrated by a computer controller which sends messages to the worker at the time in which he/she should perform a step. The controller typically waits for feedback that the human performed step has been completed via either a human-machine interface or via electronic sensors distributed within the process. Controllers within semi-automated processes may either directly control machinery or send signals to machinery distributed within the process. Centralized computer controllers within semi-automated processes orchestrate processes by instructing the worker, providing electronic communication and control to process equipment, tools, or machines, as well as perform data management to record and ensure that the process meets established process criteria. Many manufacturers choose not to fully automate a process, and instead implement semi-automation due to the complexity of the task, or the number of products produced is too low to justify the investment in full automation. Other processes may not be fully automated because it may reduce the flexibility to easily adapt the processes to reflect production needs.

G.9970

G.9970 (also known as G.hnta) is a Recommendation developed by ITU-T that describes the generic transport architecture for home networks and their interfaces to a provider's access network. G.9970 was developed by Study Group 15, Question 1. G.9970 received Consent on December 12, 2008 and was Approved on January 13, 2009. == Relationship with G.hn == G.9970 (G.hnta) and G.9960 (G.hn) are two ITU-T Recommendations that address home networking in a complementary manner. While G.9970 addresses layer 3 (network layer) of the home network architecture, G.9960 addresses layers 1 (physical layer) and 2 (data link layer).

Coreu

COREU (French: Correspondance Européenne – Telex network of European correspondents, also EUKOR-Netzwerk in Austria) is a communication network of the European Union for the communication of the Council of the European Union, the European correspondents of the foreign ministries of the EU member states, permanent representatives of member states in Brussels, the European Commission, and the General Secretariat of the Council of the European Union. The European Parliament is not among the participants. COREU is the European equivalent of the American Secret Internet Protocol Router Network (SIPRNet, also known as Intelink-S). COREU's official aim is fast communication in case of crisis. The network enables a closer cooperation in matters regarding foreign affairs. In actuality the system's function exceeds that of mere communication, it also enables decision-making. COREU's first goal is to enable the exchange of information before and after decisions. Relaying upfront negotiations in preparation of meetings is the second goal. In addition, the system also allows the editing of documents and the decision-making, especially if there is little time. While the first two goals are preparatory measures for a shared foreign policy, the third is a methodical variant marked by practise that is defining for the image of the Common Foreign and Security Policy. == Members == (The following information dates from 2013): There is one representative in each of the capital cities in the EU.(since 1973) In Germany for example, this is the European correspondent (EU-KOR) from the Foreign Office. In Austria it is the European correspondent from the Referat II.1.a in the Federal Ministry for Europe, Integration and Foreign Affairs They are the correspondents (since 1982) for the European Commission They comprise the secretariat for the European Council They also make up the European External Action Service (EEAS) (responsible for foreign policy issues, since 1987) == Data volume and technical details == COREU functions as a spoke-hub distribution paradigm system with the hub in Brussels. The network is operated by the European Union Intelligence and Situation Centre (formerly Joint Situation Center, JSC). The technical infrastructure is located in a building of the European Council. COREU may be described as an advanced telex system with encrypted messages via dedicated terminals. Once a message has reached the destination, it is then redistributed via the local media. In contrast, messages of governments are transmitted via local media to the correspondents and from there delivered point-to-point to Brussels via COREU. In 2010, approximately 8500 communications had been distributed over this network. == History == A telex-based communication system under the name COREU was established in 1973. Originally, only the ministries of Foreign Affairs in the European capitals were connected to it. This telex system was replaced in 1997 by the mail system CORTESY (COREU Terminal Equipment System). The name was retained despite the technical innovation. COREU was reportedly compromised by hackers working for the People's Liberation Army Strategic Support Force, allowing for the theft of thousands of low-classified documents and diplomatic cables.

Correlation immunity

In mathematics, the correlation immunity of a Boolean function is a measure of the degree to which its outputs are uncorrelated with some subset of its inputs. Specifically, a Boolean function is said to be correlation-immune of order m if every subset of m or fewer variables in x 1 , x 2 , … , x n {\displaystyle x_{1},x_{2},\ldots ,x_{n}} is statistically independent of the value of f ( x 1 , x 2 , … , x n ) {\displaystyle f(x_{1},x_{2},\ldots ,x_{n})} . == Definition == A function f : F 2 n → F 2 {\displaystyle f:\mathbb {F} _{2}^{n}\rightarrow \mathbb {F} _{2}} is k {\displaystyle k} -th order correlation immune if for any independent n {\displaystyle n} binary random variables X 0 … X n − 1 {\displaystyle X_{0}\ldots X_{n-1}} , the random variable Z = f ( X 0 , … , X n − 1 ) {\displaystyle Z=f(X_{0},\ldots ,X_{n-1})} is independent from any random vector ( X i 1 … X i k ) {\displaystyle (X_{i_{1}}\ldots X_{i_{k}})} with 0 ≤ i 1 < … < i k < n {\displaystyle 0\leq i_{1}<\ldots

Dental AI

Dental artificial intelligence (Dental AI) refers to the application of artificial intelligence (AI) and machine-learning methods to oral healthcare data. These systems can be used to find patterns or make predictions that can aid in diagnosis, treatment, patient communication, or practice management. == History and development == Research into AI for dentistry dates to the 1990s and 2000s, alongside early CAD/CAM and image-analysis work in dental radiology. Recent developments in deep learning, especially those involving computer vision, such as convolutional neural networks, trained on large image datasets, led to a rapid improvement in performance, as well as a move from prototype technology to productization suitable for use in dental chairs. Dental schools and continuing education programs started incorporating AI content in the 2020s. == Definition and core technologies == The dental AI software accomplishes this task by using various dental images and patient data. Dental images and data used by the dental AI software include bitewing and periapical X-rays, complete mouth X-rays, detailed 3D images, intraoral images, and the patient’s medical history. The dental AI software utilizes several core technologies in accomplishing its task of assisting the dentist. First, the dental AI software utilizes machine learning and deep learning using programs that can learn from examples. Such programs are referred to as convolutional neural network (CNN) and can detect cavities and identify bone changes related to gum disease. The dental AI software utilizes computer vision, which enables the AI software to identify and quantify important features in images and data, whether they are 2D images or 3D images. Natural language processing (NLP) is used for the AI software to understand written text and can automatically generate dental notes and communicate with the patient. Furthermore, the dental AI software utilizes predictive analytics to identify patients that are more prone to dental complications and can suggest the best intervals for checkups or future dental procedures. == Applications in dentistry == Reported clinical and operational applications include diagnostic assistance for caries and periodontal disease, treatment planning assistance, patient education overlays, quality assurance, curriculum assistance for dental education, and claims documentation. Systematic reviews continue to find image-based applications such as caries detection with some variability in study design and a need for prospective validation. == Academic research and clinical validation == Several peer-reviewed studies have measured the effectiveness of AI for applications such as interproximal caries detection and periodontal bone level assessment, showing improvements over unaided readings with a focus on bias within the dataset. The Dental AI Council found variability among clinicians for diagnosis and treatment planning, suggesting the use of a standard tool as an assist. == Industry adoption == Multiple vendors offer FDA-cleared chairside AI for dental imaging: Pearl — Received U.S. FDA 510(k) clearance for its real-time radiologic aid (“Second Opinion”) in 2022 (2D), with subsequent clearances including pediatric and CBCT (“Second Opinion 3D”). TIME gave “Second Opinion” a special mention on its Best Inventions of 2022 list. Overjet — FDA-cleared for bone-level quantification and detection/outline of caries and calculus (e.g., K210187), with additional clearances expanding capabilities. VideaHealth — Received an FDA 510(k) covering 30+ detections across common dental findings (K232384), including indications for patients ages 3 and up; trade coverage has described elements of this as the first pediatric dental-AI clearance. == Regulations == In the U.S., AI-enabled dental imaging software is generally reviewed via the FDA’s 510(k) pathway. The FDA maintains a public AI-Enabled Medical Devices List, which includes numerous medical-imaging AI tools (including dental). Specific dental clearances include Overjet (K210187), VideaHealth (K232384), and Pearl entries such as “Second Opinion 3D” (K243989).

Trace zero cryptography

First proposed by Gerhard Frey in 1998, trace zero cryptography refers to the use of trace zero varieties (TZV) for cryptographic purpose. Trace zero varieties are subgroups of the divisor class group on a low genus hyperelliptic curve defined over a finite field. These groups can be used to establish asymmetric cryptography using the discrete logarithm problem as cryptographic primitive. Trace zero varieties feature a better scalar multiplication performance than elliptic curves. This allows fast arithmetic in these groups, which can speed up the calculations with a factor 3 compared with elliptic curves and hence speed up the cryptosystem. Another advantage is that for groups of cryptographically relevant size, the order of the group can simply be calculated using the characteristic polynomial of the Frobenius endomorphism. This is not the case, for example, in elliptic curve cryptography when the group of points of an elliptic curve over a prime field is used for cryptographic purpose. However, to represent an element of the trace zero variety more bits are needed compared with elements of elliptic or hyperelliptic curves. Another disadvantage is the fact that it is possible to reduce the security of the TZV of 1/6th of the bit length using cover attack. == Mathematical background == A hyperelliptic curve C of genus g over a prime field F q {\displaystyle \mathbb {F} _{q}} where q = pn (p prime) of odd characteristic is defined as C : y 2 + h ( x ) y = f ( x ) , {\displaystyle C:~y^{2}+h(x)y=f(x),} where f monic, deg(f) = 2g + 1 and deg(h) ≤ g. The curve has at least one F q {\displaystyle \mathbb {F} _{q}} -rational Weierstraßpoint. The Jacobian variety J C ( F q n ) {\displaystyle J_{C}(\mathbb {F} _{q^{n}})} of C is for all finite extension F q n {\displaystyle \mathbb {F} _{q^{n}}} isomorphic to the ideal class group Cl ⁡ ( C / F q n ) {\displaystyle \operatorname {Cl} (C/\mathbb {F} _{q^{n}})} . With the Mumford's representation it is possible to represent the elements of J C ( F q n ) {\displaystyle J_{C}(\mathbb {F} _{q^{n}})} with a pair of polynomials [u, v], where u, v ∈ F q n [ x ] {\displaystyle \mathbb {F} _{q^{n}}[x]} . The Frobenius endomorphism σ is used on an element [u, v] of J C ( F q n ) {\displaystyle J_{C}(\mathbb {F} _{q^{n}})} to raise the power of each coefficient of that element to q: σ([u, v]) = [uq(x), vq(x)]. The characteristic polynomial of this endomorphism has the following form: χ ( T ) = T 2 g + a 1 T 2 g − 1 + ⋯ + a g T g + ⋯ + a 1 q g − 1 T + q g , {\displaystyle \chi (T)=T^{2g}+a_{1}T^{2g-1}+\cdots +a_{g}T^{g}+\cdots +a_{1}q^{g-1}T+q^{g},} where ai in Z {\displaystyle \mathbb {Z} } With the Hasse–Weil theorem it is possible to receive the group order of any extension field F q n {\displaystyle \mathbb {F} _{q^{n}}} by using the complex roots τi of χ(T): | J C ( F q n ) | = ∏ i = 1 2 g ( 1 − τ i n ) {\displaystyle |J_{C}(\mathbb {F} _{q^{n}})|=\prod _{i=1}^{2g}(1-\tau _{i}^{n})} Let D be an element of the J C ( F q n ) {\displaystyle J_{C}(\mathbb {F} _{q^{n}})} of C, then it is possible to define an endomorphism of J C ( F q n ) {\displaystyle J_{C}(\mathbb {F} _{q^{n}})} , the so-called trace of D: Tr ⁡ ( D ) = ∑ i = 0 n − 1 σ i ( D ) = D + σ ( D ) + ⋯ + σ n − 1 ( D ) {\displaystyle \operatorname {Tr} (D)=\sum _{i=0}^{n-1}\sigma ^{i}(D)=D+\sigma (D)+\cdots +\sigma ^{n-1}(D)} Based on this endomorphism one can reduce the Jacobian variety to a subgroup G with the property, that every element is of trace zero: G = { D ∈ J C ( F q n ) | Tr ( D ) = 0 } , ( 0 neutral element in J C ( F q n ) {\displaystyle G=\{D\in J_{C}(\mathbb {F} _{q^{n}})~|~{\text{Tr}}(D)={\textbf {0}}\},~~~({\textbf {0}}{\text{ neutral element in }}J_{C}(\mathbb {F} _{q^{n}})} G is the kernel of the trace endomorphism and thus G is a group, the so-called trace zero (sub)variety (TZV) of J C ( F q n ) {\displaystyle J_{C}(\mathbb {F} _{q^{n}})} . The intersection of G and J C ( F q ) {\displaystyle J_{C}(\mathbb {F} _{q})} is produced by the n-torsion elements of J C ( F q ) {\displaystyle J_{C}(\mathbb {F} _{q})} . If the greatest common divisor gcd ( n , | J C ( F q ) | ) = 1 {\displaystyle \gcd(n,|J_{C}(\mathbb {F} _{q})|)=1} the intersection is empty and one can compute the group order of G: | G | = | J C ( F q n ) | | J C ( F q ) | = ∏ i = 1 2 g ( 1 − τ i n ) ∏ i = 1 2 g ( 1 − τ i ) {\displaystyle |G|={\dfrac {|J_{C}(\mathbb {F} _{q^{n}})|}{|J_{C}(\mathbb {F} _{q})|}}={\dfrac {\prod _{i=1}^{2g}(1-\tau _{i}^{n})}{\prod _{i=1}^{2g}(1-\tau _{i})}}} The actual group used in cryptographic applications is a subgroup G0 of G of a large prime order l. This group may be G itself. There exist three different cases of cryptographical relevance for TZV: g = 1, n = 3 g = 1, n = 5 g = 2, n = 3 == Arithmetic == The arithmetic used in the TZV group G0 based on the arithmetic for the whole group J C ( F q n ) {\displaystyle J_{C}(\mathbb {F} _{q^{n}})} , But it is possible to use the Frobenius endomorphism σ to speed up the scalar multiplication. This can be archived if G0 is generated by D of order l then σ(D) = sD, for some integers s. For the given cases of TZV s can be computed as follows, where ai come from the characteristic polynomial of the Frobenius endomorphism : For g = 1, n = 3: s = q − 1 1 − a 1 mod ℓ {\displaystyle s={\dfrac {q-1}{1-a_{1}}}{\bmod {\ell }}} For g = 1, n = 5: s = q 2 − q − a 1 2 q + a 1 q + 1 q − 2 a 1 q + a 1 3 − a 1 2 + a 1 − 1 mod ℓ {\displaystyle s={\dfrac {q^{2}-q-a_{1}^{2}q+a_{1}q+1}{q-2a_{1}q+a_{1}^{3}-a_{1}^{2}+a_{1}-1}}{\bmod {\ell }}} For g = 2, n = 3: s = − q 2 − a 2 + a 1 a 1 q − a 2 + 1 mod ℓ {\displaystyle s=-{\dfrac {q^{2}-a_{2}+a_{1}}{a_{1}q-a_{2}+1}}{\bmod {\ell }}} Knowing this, it is possible to replace any scalar multiplication mD (|m| ≤ l/2) with: m 0 D + m 1 σ ( D ) + ⋯ + m n − 1 σ n − 1 ( D ) , where m i = O ( ℓ 1 / ( n − 1 ) ) = O ( q g ) {\displaystyle m_{0}D+m_{1}\sigma (D)+\cdots +m_{n-1}\sigma ^{n-1}(D),~~~~{\text{where }}m_{i}=O(\ell ^{1/(n-1)})=O(q^{g})} With this trick the multiple scalar product can be reduced to about 1/(n − 1)th of doublings necessary for calculating mD, if the implied constants are small enough. == Security == The security of cryptographic systems based on trace zero subvarieties according to the results of the papers comparable to the security of hyper-elliptic curves of low genus g' over F p ′ {\displaystyle \mathbb {F} _{p'}} , where p' ~ (n − 1)(g/g' ) for |G| ~128 bits. For the cases where n = 3, g = 2 and n = 5, g = 1 it is possible to reduce the security for at most 6 bits, where |G| ~ 2256, because one can not be sure that G is contained in a Jacobian of a curve of genus 6. The security of curves of genus 4 for similar fields are far less secure. == Cover attack on a trace zero crypto-system == The attack published in shows, that the DLP in trace zero groups of genus 2 over finite fields of characteristic diverse than 2 or 3 and a field extension of degree 3 can be transformed into a DLP in a class group of degree 0 with genus of at most 6 over the base field. In this new class group the DLP can be attacked with the index calculus methods. This leads to a reduction of the bit length 1/6th.