The Graphical Kernel System (GKS) is a 2D computer graphics system using vector graphics, introduced in 1977. It was suitable for making line and bar charts and similar tasks. A key concept was cross-system portability, based on an underlying coordinate system that could be represented on almost any hardware. GKS is best known as the basis for the graphics in the GEM GUI system used on the Atari ST and as part of Ventura Publisher. A draft international standard was circulated for review in September 1983. Final ratification of the standard was achieved in 1985, making it the first ISO graphics standard. A 3D system modelled on GKS was introduced as PHIGS, which saw some use in the 1980s and early 1990s. == Overview == GKS provides a set of drawing features for two-dimensional vector graphics suitable for charting and similar duties. The calls are designed to be portable across different programming languages, graphics devices and hardware, so that applications written to use GKS will be readily portable to many platforms and devices. GKS was fairly common on computer workstations in the 1980s and early 1990s. GKS formed the basis of Digital Research's GSX which evolved into VDI, one of the core components of GEM. GEM was the native GUI on the Atari ST and was occasionally seen on PCs, particularly in conjunction with Ventura Publisher. GKS was little used commercially outside these markets, but remains in use in some scientific visualization packages. It is also the underlying API defining the Computer Graphics Metafile. One popular application based on an implementation of GKS is the GR Framework, a C library for high-performance scientific visualization that has become a common plotting backend among Julia users. A main developer and promoter of the GKS was José Luis Encarnação, formerly director of the Fraunhofer Institute for Computer Graphics (IGD) in Darmstadt, Germany. GKS has been standardized in the following documents: ANSI standard ANSI X3.124 of 1985. ISO 7942:1985 standard, revised as ISO 7942:1985/Amd 1:1991 and ISO/IEC 7942-1:1994, as well as ISO/IEC 7942-2:1997, ISO/IEC 7942-3:1999 and ISO/IEC 7942-4:1998 The language bindings are ISO standard ISO 8651. GKS-3D (Graphical Kernel System for Three Dimensions) functional definition is ISO standard ISO 8805, and the corresponding C bindings are ISO/IEC 8806. The functionality of GKS is wrapped up as a data model standard in the STEP standard, section ISO 10303-46.
Pwnie Awards
The Pwnie Awards are an annual awards ceremony that recognizes both excellence and incompetence in the field of information security, described by SecurityWeek as an event that "recognizes excellence and mocks incompetence in cybersecurity." Winners are selected by a committee of security industry professionals from nominations collected from the information security community. Nominees are announced yearly at Summercon, and the awards themselves are presented at the Black Hat Security Conference. == Origins == The name Pwnie Award is based on the word "pwn", which is hacker slang meaning to "compromise" or "control" based on the previous usage of the word "own" (and it is pronounced similarly). The name "The Pwnie Awards," pronounced as "Pony," is meant to sound like the Tony Awards, an awards ceremony for Broadway theater in New York City. == History == The Pwnie Awards were founded in 2007 by Alexander Sotirov and Dino Dai Zovi following discussions regarding Dino's discovery of a cross-platform QuickTime vulnerability (CVE-2007-2175) and Alexander's discovery of an ANI file processing vulnerability (CVE-2007-0038) in Internet Explorer. == Winners == === 2024 === Most Epic Fail: Crowdstrike for 2024 CrowdStrike incident Best Mobile Bug: Operation Triangulation Lamest Vendor Response: Xiaomi for obstructing Pwn2Own researchers from using their services Best Cryptographic Attack: GoFetch Best Desktop Bug: forcing realtime WebAudio playback in Chrome (CVE-2023-5996) Best Song: Touch Some Grass by UwU Underground Best Privilege Escalation: Windows Streaming Service UAF (CVE-2024-30089) by Valentina Palmiotti (chompie) Best Remote Code Execution: Microsoft Message Queuing (MSMQ) Remote Code Execution Vulnerability (CVE-2024-30080) Most Epic Achievement: Discovery and reverse engineering of the XZ Utils backdoor Most Innovative Research: Let the Cache Cache and Let the WebAssembly Assemble: Knocking’ on Chrome’s Shell by Edouard Bochin, Tao Yan, and Bo Qu Most Underhyped Research: See No Eval: Runtime Dynamic Code Execution in Objective-C === 2023 === Best Desktop Bug: CountExposure! by RyeLv(@b2ahex) Best Cryptographic Attack: Video-based cryptanalysis: Extracting Cryptographic Keys from Video Footage of a Device’s Power LED by Ben Nassi, Etay Iluz, Or Cohen, Ofek Vayner, Dudi Nassi, Boris Zadov, Yuval Elovici Best Song: Clickin’ Most Innovative Research: Inside Apple’s Lightning: Jtagging the iPhone for Fuzzing and Profit Most Under-Hyped Research: Activation Context Cache Poisoning Best Privilege Escalation Bug: URB Excalibur: Slicing Through the Gordian Knot of VMware VM Escapes Best Remote Code Execution Bug: ClamAV RCE Lamest Vendor Response: Three Lessons From Threema: Analysis of a Secure Messenger Most Epic Fail: “Holy fucking bingle, we have the no fly list,” Epic Achievement: Clement Lecigne: 0-days hunter world champion Lifetime Achievement Award: Mudge === 2022 === Lamest Vendor Response: Google's "TAG" response team for "unilaterally shutting down a counterterrorism operation." Epic Achievement: Yuki Chen’s Windows Server-Side RCE Bugs Most Epic Fail: HackerOne Employee Caught Stealing Vulnerability Reports for Personal Gains Best Desktop Bug: Pietro Borrello, Andreas Kogler, Martin Schwarzl, Moritz Lipp, Daniel Gruss, Michael Schwarz for Architecturally Leaking Data from the Microarchitecture Most Innovative Research: Pietro Borrello, Martin Schwarzl, Moritz Lipp, Daniel Gruss, Michael Schwarz for Custom Processing Unit: Tracing and Patching Intel Atom Microcode Best Cryptographic Attack: Hertzbleed: Turning Power Side-Channel Attacks Into Remote Timing Attacks on x86 by Yingchen Wang, Riccardo Paccagnella, Elizabeth Tang He, Hovav Shacham, Christopher Fletcher, David Kohlbrenner Best Remote Code Execution Bug: KunlunLab for Windows RPC Runtime Remote Code Execution (CVE-2022-26809) Best Privilege Escalation Bug: Qidan He of Dawnslab, for Mystique in the House: The Droid Vulnerability Chain That Owns All Your Userspace Best Mobile Bug: FORCEDENTRY Most Under-Hyped Research: Yannay Livneh for Spoofing IP with IPIP Best Song: Dialed Up by Project Mammoth === 2021 === Lamest Vendor Response: Cellebrite, for their response to Moxie, the creator of Signal, reverse-engineering their UFED and accompanying software and reporting a discovered exploit. Epic Achievement: Ilfak Guilfanov, in honor of IDA's 30th Anniversary. Best Privilege Escalation Bug: Baron Samedit of Qualys, for the discovery of a 10-year-old exploit in sudo. Best Song: The Ransomware Song by Forrest Brazeal Best Server-Side Bug: Orange Tsai, for his Microsoft Exchange Server ProxyLogon attack surface discoveries. Best Cryptographic Attack: The NSA for its disclosure of a bug in the verification of signatures in Windows which breaks the certificate trust chain. Most Innovative Research: Enes Göktaş, Kaveh Razavi, Georgios Portokalidis, Herbert Bos, and Cristiano Giuffrida at VUSec for their research on the "BlindSide" Attack. Most Epic Fail: Microsoft, for their failure to fix PrintNightmare. Best Client-Side Bug: Gunnar Alendal's discovery of a buffer overflow on the Samsung Galaxy S20's secure chip. Most Under-Hyped Research: The Qualys Research Team for 21Nails, 21 vulnerabilities in Exim, the Internet's most popular mail server. === 2020 === Best Server-Side Bug: BraveStarr (CVE-2020-10188) – A Fedora 31 netkit telnetd remote exploit (Ronald Huizer') Best Privilege Escalation Bug: checkm8 – A permanent unpatchable USB bootrom exploit for a billion iOS devices. (axi0mX) Epic Achievement: "Remotely Rooting Modern Android Devices" (Guang Gong) Best Cryptographic Attack: Zerologon vulnerability (Tom Tervoort, CVE-2020-1472) Best Client-Side Bug: RCE on Samsung Phones via MMS (CVE-2020-8899 and -16747), a zero click remote execution attack. (Mateusz Jurczyk) Most Under-Hyped Research: Vulnerabilities in System Management Mode (SMM) and Trusted Execution Technology (TXT) (CVE-2019-0151 and -0152) (Gabriel Negreira Barbosa, Rodrigo Rubira Branco, Joe Cihula) Most Innovative Research: TRRespass: When Memory Vendors Tell You Their Chips Are Rowhammer-free, They Are Not. (Pietro Frigo, Emanuele Vannacci, Hasan Hassan, Victor van der Veen, Onur Mutlu, Cristiano Giuffrida, Herbert Bos, Kaveh Razavi) Most Epic Fail: Microsoft; for the implementation of Elliptic-curve signatures which allowed attackers to generate private pairs for public keys of any signer, allowing HTTPS and signed binary spoofing. (CVE-2020-0601) Best Song: Powertrace by Rebekka Aigner, Daniel Gruss, Manuel Weber, Moritz Lipp, Patrick Radkohl, Andreas Kogler, Maria Eichlseder, ElTonno, tunefish, Yuki and Kater Lamest Vendor Response: Daniel J. Bernstein (CVE-2005-1513) === 2019 === Best Server-Side Bug: Orange Tsai and Meh Chang, for their SSL VPN research. Most Innovative Research: Vectorized Emulation Brandon Falk Best Cryptographic Attack: \m/ Dr4g0nbl00d \m/ Mathy Vanhoef, Eyal Ronen Lamest Vendor Response: Bitfi Most Over-hyped Bug: Allegations of Supermicro hardware backdoors, Bloomberg Most Under-hyped Bug: Thrangrycat, (Jatin Kataria, Red Balloon Security) === 2018 === Most Innovative Research: Spectre/Meltdown (Paul Kocher, Jann Horn, Anders Fogh, Daniel Genkin, Daniel Gruss, Werner Haas, Mike Hamburg, Moritz Lipp, Stefan Mangard, Thomas Prescher, Michael Schwarz, Yuval Yarom) Best Privilege Escalation Bug: Spectre/Meltdown (Paul Kocher, Jann Horn, Anders Fogh, Daniel Genkin, Daniel Gruss, Werner Haas, Mike Hamburg, Moritz Lipp, Stefan Mangard, Thomas Prescher, Michael Schwarz, Yuval Yarom) Lifetime Achievement: Michał Zalewski Best Cryptographic Attack: ROBOT - Return Of Bleichenbacher’s Oracle Threat Hanno Böck, Juraj Somorovsky, Craig Young Lamest Vendor Response: Bitfi hardware crypto-wallet, after the "unhackable" device was hacked to extract the keys required to steal coins and rooted to play Doom. === 2017 === Epic Achievement: Federico Bento for Finally getting TIOCSTI ioctl attack fixed Most Innovative Research: ASLR on the line Ben Gras, Kaveh Razavi, Erik Bosman, Herbert Bos, Cristiano Giuffrida Best Privilege Escalation Bug: DRAMMER Victor van der Veen, Yanick Fratantonio, Martina Lindorfer, Daniel Gruss, Clementine Maurice, Giovanni Vigna, Herbert Bos, Kaveh Razavi, Cristiano Giuffrida Best Cryptographic Attack: The first collision for full SHA-1 Marc Stevens, Elie Bursztein, Pierre Karpman, Ange Albertini, Yarik Markov Lamest Vendor Response: Lennart Poettering - for mishandling security vulnerabilities most spectacularly for multiple critical Systemd bugs Best Song: Hello (From the Other Side) - Manuel Weber, Michael Schwarz, Daniel Gruss, Moritz Lipp, Rebekka Aigner === 2016 === Most Innovative Research: Dedup Est Machina: Memory Deduplication as an Advanced Exploitation Vector Erik Bosman, Kaveh Razavi, Herbert Bos, Cristiano Giuffrida Lifetime Achievement: Peiter Zatko aka Mudge Best Cryptographic Attack: DROWN attack Nimrod Aviram et al. Best Song: Cyberlier - Katie Mous
Kernel method
In machine learning, kernel machines are a class of algorithms for pattern analysis, whose best known member is the support-vector machine (SVM). These methods involve using linear classifiers to solve nonlinear problems. The general task of pattern analysis is to find and study general types of relations (for example clusters, rankings, principal components, correlations, classifications) in datasets. For many algorithms that solve these tasks, the data in raw representation have to be explicitly transformed into feature vector representations via a user-specified feature map: in contrast, kernel methods require only a user-specified kernel, i.e., a similarity function over all pairs of data points computed using inner products. The feature map in kernel machines is infinite dimensional but only requires a finite dimensional matrix from user-input according to the representer theorem. Kernel machines are slow to compute for datasets larger than a couple of thousand examples without parallel processing. Kernel methods owe their name to the use of kernel functions, which enable them to operate in a high-dimensional, implicit feature space without ever computing the coordinates of the data in that space, but rather by simply computing the inner products between the images of all pairs of data in the feature space. This operation is often computationally cheaper than the explicit computation of the coordinates. This approach is called the "kernel trick". Kernel functions have been introduced for sequence data, graphs, text, images, as well as vectors. Algorithms capable of operating with kernels include the kernel perceptron, support-vector machines (SVM), Gaussian processes, principal components analysis (PCA), canonical correlation analysis, ridge regression, spectral clustering, linear adaptive filters and many others. Most kernel algorithms are based on convex optimization or eigenproblems and are statistically well-founded. Typically, their statistical properties are analyzed using statistical learning theory (for example, using Rademacher complexity). == Motivation and informal explanation == Kernel methods can be thought of as instance-based learners: rather than learning some fixed set of parameters corresponding to the features of their inputs, they instead "remember" the i {\displaystyle i} -th training example ( x i , y i ) {\displaystyle (\mathbf {x} _{i},y_{i})} and learn for it a corresponding weight w i {\displaystyle w_{i}} . Prediction for unlabeled inputs, i.e., those not in the training set, are treated by the application of a similarity function k {\displaystyle k} , called a kernel, between the unlabeled input x ′ {\displaystyle \mathbf {x'} } and each of the training inputs x i {\displaystyle \mathbf {x} _{i}} . For instance, a kernelized binary classifier typically computes a weighted sum of similarities y ^ = sgn ∑ i = 1 n w i y i k ( x i , x ′ ) , {\displaystyle {\hat {y}}=\operatorname {sgn} \sum _{i=1}^{n}w_{i}y_{i}k(\mathbf {x} _{i},\mathbf {x'} ),} where y ^ ∈ { − 1 , + 1 } {\displaystyle {\hat {y}}\in \{-1,+1\}} is the kernelized binary classifier's predicted label for the unlabeled input x ′ {\displaystyle \mathbf {x'} } whose hidden true label y {\displaystyle y} is of interest; k : X × X → R {\displaystyle k\colon {\mathcal {X}}\times {\mathcal {X}}\to \mathbb {R} } is the kernel function that measures similarity between any pair of inputs x , x ′ ∈ X {\displaystyle \mathbf {x} ,\mathbf {x'} \in {\mathcal {X}}} ; the sum ranges over the n labeled examples { ( x i , y i ) } i = 1 n {\displaystyle \{(\mathbf {x} _{i},y_{i})\}_{i=1}^{n}} in the classifier's training set, with y i ∈ { − 1 , + 1 } {\displaystyle y_{i}\in \{-1,+1\}} ; the w i ∈ R {\displaystyle w_{i}\in \mathbb {R} } are the weights for the training examples, as determined by the learning algorithm; the sign function sgn {\displaystyle \operatorname {sgn} } determines whether the predicted classification y ^ {\displaystyle {\hat {y}}} comes out positive or negative. Kernel classifiers were described as early as the 1960s, with the invention of the kernel perceptron. They rose to great prominence with the popularity of the support-vector machine (SVM) in the 1990s, when the SVM was found to be competitive with neural networks on tasks such as handwriting recognition. == Mathematics: the kernel trick == The kernel trick avoids the explicit mapping that is needed to get linear learning algorithms to learn a nonlinear function or decision boundary. For all x {\displaystyle \mathbf {x} } and x ′ {\displaystyle \mathbf {x'} } in the input space X {\displaystyle {\mathcal {X}}} , certain functions k ( x , x ′ ) {\displaystyle k(\mathbf {x} ,\mathbf {x'} )} can be expressed as an inner product in another space V {\displaystyle {\mathcal {V}}} . The function k : X × X → R {\displaystyle k\colon {\mathcal {X}}\times {\mathcal {X}}\to \mathbb {R} } is often referred to as a kernel or a kernel function. The word "kernel" is used in mathematics to denote a weighting function for a weighted sum or integral. Certain problems in machine learning have more structure than an arbitrary weighting function k {\displaystyle k} . The computation is made much simpler if the kernel can be written in the form of a "feature map" φ : X → V {\displaystyle \varphi \colon {\mathcal {X}}\to {\mathcal {V}}} which satisfies k ( x , x ′ ) = ⟨ φ ( x ) , φ ( x ′ ) ⟩ V . {\displaystyle k(\mathbf {x} ,\mathbf {x'} )=\langle \varphi (\mathbf {x} ),\varphi (\mathbf {x'} )\rangle _{\mathcal {V}}.} The key restriction is that ⟨ ⋅ , ⋅ ⟩ V {\displaystyle \langle \cdot ,\cdot \rangle _{\mathcal {V}}} must be a proper inner product. On the other hand, an explicit representation for φ {\displaystyle \varphi } is not necessary, as long as V {\displaystyle {\mathcal {V}}} is an inner product space. The alternative follows from Mercer's theorem: an implicitly defined function φ {\displaystyle \varphi } exists whenever the space X {\displaystyle {\mathcal {X}}} can be equipped with a suitable measure ensuring the function k {\displaystyle k} satisfies Mercer's condition. Mercer's theorem is similar to a generalization of the result from linear algebra that associates an inner product to any positive-definite matrix. In fact, Mercer's condition can be reduced to this simpler case. If we choose as our measure the counting measure μ ( T ) = | T | {\displaystyle \mu (T)=|T|} for all T ⊂ X {\displaystyle T\subset X} , which counts the number of points inside the set T {\displaystyle T} , then the integral in Mercer's theorem reduces to a summation ∑ i = 1 n ∑ j = 1 n k ( x i , x j ) c i c j ≥ 0. {\displaystyle \sum _{i=1}^{n}\sum _{j=1}^{n}k(\mathbf {x} _{i},\mathbf {x} _{j})c_{i}c_{j}\geq 0.} If this summation holds for all finite sequences of points ( x 1 , … , x n ) {\displaystyle (\mathbf {x} _{1},\dotsc ,\mathbf {x} _{n})} in X {\displaystyle {\mathcal {X}}} and all choices of n {\displaystyle n} real-valued coefficients ( c 1 , … , c n ) {\displaystyle (c_{1},\dots ,c_{n})} (cf. positive definite kernel), then the function k {\displaystyle k} satisfies Mercer's condition. Some algorithms that depend on arbitrary relationships in the native space X {\displaystyle {\mathcal {X}}} would, in fact, have a linear interpretation in a different setting: the range space of φ {\displaystyle \varphi } . The linear interpretation gives us insight about the algorithm. Furthermore, there is often no need to compute φ {\displaystyle \varphi } directly during computation, as is the case with support-vector machines. Some cite this running time shortcut as the primary benefit. Researchers also use it to justify the meanings and properties of existing algorithms. Theoretically, a Gram matrix K ∈ R n × n {\displaystyle \mathbf {K} \in \mathbb {R} ^{n\times n}} with respect to { x 1 , … , x n } {\displaystyle \{\mathbf {x} _{1},\dotsc ,\mathbf {x} _{n}\}} (sometimes also called a "kernel matrix"), where K i j = k ( x i , x j ) {\displaystyle K_{ij}=k(\mathbf {x} _{i},\mathbf {x} _{j})} , must be positive semi-definite (PSD). Empirically, for machine learning heuristics, choices of a function k {\displaystyle k} that do not satisfy Mercer's condition may still perform reasonably if k {\displaystyle k} at least approximates the intuitive idea of similarity. Regardless of whether k {\displaystyle k} is a Mercer kernel, k {\displaystyle k} may still be referred to as a "kernel". If the kernel function k {\displaystyle k} is also a covariance function as used in Gaussian processes, then the Gram matrix K {\displaystyle \mathbf {K} } can also be called a covariance matrix. == Applications == Application areas of kernel methods are diverse and include geostatistics, kriging, inverse distance weighting, 3D reconstruction, bioinformatics, cheminformatics, information extraction and handwriting recognition. == Popular kernels == Fisher kernel Graph kernels Kernel smoother Polynomial kernel Radial basis function kern
Yooreeka
Yooreeka is a library for data mining, machine learning, soft computing, and mathematical analysis. The project started with the code of the book "Algorithms of the Intelligent Web". Although the term "Web" prevailed in the title, in essence, the algorithms are valuable in any software application. It covers all major algorithms and provides many examples. Yooreeka 2.x is licensed under the Apache License rather than the somewhat more restrictive LGPL (which was the license of v1.x). The library is written 100% in the Java language. == Algorithms == The following algorithms are covered: Clustering Hierarchical—Agglomerative (e.g. MST single link; ROCK) and Divisive Partitional (e.g. k-means) Classification Bayesian Decision trees Neural Networks Rule based (via Drools) Recommendations Collaborative filtering Content based Search PageRank DocRank Personalization
Semantic mapping (statistics)
Semantic mapping (SM) is a statistical method for dimensionality reduction (the transformation of data from a high-dimensional space into a low-dimensional space). SM can be used in a set of multidimensional vectors of features to extract a few new features that preserves the main data characteristics. SM performs dimensionality reduction by clustering the original features in semantic clusters and combining features mapped in the same cluster to generate an extracted feature. Given a data set, this method constructs a projection matrix that can be used to map a data element from a high-dimensional space into a reduced dimensional space. SM can be applied in construction of text mining and information retrieval systems, as well as systems managing vectors of high dimensionality. SM is an alternative to random mapping, principal components analysis and latent semantic indexing methods.
NIS2 Directive
The Directive (EU) 2022/2555, commonly known as NIS2 is a directive of the European Union aimed at protecting digital infrastructure, in particular critical infrastructure. It broadened the sectors covered by EU network and information security rules and updated incident reporting and oversight compared to the NIS1. Member States were required to transpose NIS2 by 17 October 2024, and the earlier NIS Directive was repealed on 18 October 2024. Only 23 Member States have fully implemented the measures contained with the NIS Directive. Infringement proceedings against them to enforce the Directive have not taken place, and they are not expected to take place in the near future. This failed implementation has led to the fragmentation of cybersecurity capabilities across the EU, with differing standards, incident reporting requirements and enforcement requirements being implemented in different Member States. From the EFTA countries (to April 2026) only Liechtenstein has fully transposed the NIS2 Directive. While the EFTA commission is conducting preparations to transpose the directive into its legislation. == National implementations == === Czech Republic === It is implemented through the Act No. 264/2025 Coll. also called Zákon o kybernetické bezpečnosti (Cybersecurity law) and through another five implementing regulations. The transposing legislation came into force on November 1st, 2025. === Germany === It is implemented through the Gesetz zur Umsetzung der NIS-2-Richtlinie und zur Regelung wesentlicher Grundzüge des Informationssicherheitsmanagements in der Bundesverwaltung. === Ireland === It is implemented through the National Cyber Security Bill. === The Netherlands === It is implemented through the Cyberbeveiligingswet (Cbw). === Slovakia === It is implemented through via an amendment of the Act No. 69/2018 Coll. also called Zákon o kybernetickej bezpečnosti a o zmene a doplnení niektorých zákonov (Law on Cybersecurity and change and amendment of certain laws). It came into force on November 1st, 2025. === Spain === It is implemented through the Esquema Nacional de Seguridad (ENS).
Generalized blockmodeling of valued networks
Generalized blockmodeling of valued networks is an approach of the generalized blockmodeling, dealing with valued networks (e.g., non-binary). While the generalized blockmodeling signifies a "formal and integrated approach for the study of the underlying functional anatomies of virtually any set of relational data", it is in principle used for binary networks. This is evident from the set of ideal blocks, which are used to interpret blockmodels, that are binary, based on the characteristic link patterns. Because of this, such templates are "not readily comparable with valued empirical blocks". To allow generalized blockmodeling of valued directional (one-mode) networks (e.g. allowing the direct comparisons of empirical valued blocks with ideal binary blocks), a non–parametric approach is used. With this, "an optional parameter determines the prominence of valued ties as a minimum percentile deviation between observed and expected flows". Such two–sided application of parameter then introduces "the possibility of non–determined ties, i.e. valued relations that are deemed neither prominent (1) nor non–prominent (0)." Resulted occurrences of links then motivate the modification of the calculation of inconsistencies between empirical and ideal blocks. At the same time, such links also give a possibility to measure the interpretational certainty, which is specific to each ideal block. Such maximum two–sided deviation threshold, holding the aggregate uncertainty score at zero or near–zero levels, is then proposed as "a measure of interpretational certainty for valued blockmodels, in effect transforming the optional parameter into an outgoing state". Problem with blockmodeling is the standard set of ideal block, as they are all specified using binary link (tie) patters; this results in "a non–trivial exercise to match and count inconsistencies between such ideal binary ties and empirical valued ties". One approach to solve this is by using dichotomization to transform the network into a binary version. The other two approaches were first proposed by Aleš Žiberna in 2007 by introducing valued (generalized) blockmodeling and also homogeneity blockmodeling. The basic idea of the latter is "that the inconsistency of an empirical block with its ideal block can be measured by within block variability of appropriate values". The newly–formed ideal blocks, which are appropriate for blockmodeling of valued networks, are then presented together with the definitions of their block inconsistencies. Two other approaches were later suggested by Carl Nordlund in 2019: deviational approach and correlation-based generalized approach. Both Nordlund's approaches are based on the idea, that valued networks can be compared with the ideal block without values. With this approach, more information is retained for analysis, which also means, that there are fewer partitions having identical values of the criterion function. This means, that the generalized blockmodeling of valued networks measures the inconsistencies more precisely. Usually, only one optimal partition is found in this approach, especially when it is used by homogeneity blockmodeling. Contrary, while using binary blockmodeling on the same sample, usually more than one optimal partition had occurred on several occasions.