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  • Thermal attack

    Thermal attack

    A thermal attack (aka thermal imaging attack) is an approach that exploits heat traces to uncover the entered credentials. These attacks rely on the phenomenon of heat transfer from one object to another. During authentication, heat transfers from the users' hands to the surface they are interacting with, leaving heat traces behind that can be analyzed using thermal cameras that operate in the far-infrared spectrum. These traces can be recovered and used to reconstruct the passwords. In some cases, the attack can be successful even 30 seconds after the user has authenticated. Thermal attacks can be performed after the victim had authenticated, alleviating the need for in-situ observation attacks (e.g., shoulder surfing attacks) that can be affected by hand occlusions. While smudge attacks can reveal the order of entries of graphical passwords, such as the Android Lock Patterns, thermal attacks can reveal the order of entries even in the case of PINs or alphanumeric passwords. The reason thermal attacks leak information about the order of entry is because keys and buttons that the user touches first lose heat over time, while recently touched ones maintain the heat signature for a longer time. This results in distinguishable heat patterns that can tell the attacker which entry was entered first. Thermal attacks were shown to be effective against plastic keypads, such as the ones used to enter credit card's PINs in supermarkets and restaurants, and on handheld mobile devices such as smartphones and tablets. In their paper published at the Conference on Human Factors in Computing Systems (CHI 2017), Abdelrahman et al. showed that the attack is feasible on today's smartphones. They also proposed some ways to mitigate the attack, such as swiping randomly on the screen to distort the heat traces, or forcing maximum CPU usage for a few seconds. Thermal attacks can also infer passwords from heat traces on keyboards. Researchers at the University of Glasgow showed that attackers who use AI methods can be more effective in performing thermal attacks. Their study presents a new tool called ThermoSecure and evaluates it in two user studies. The results show that ThermoSecure can successfully attack passwords with an average accuracy of 92% to 55%, depending on the length of the password. The effectiveness of thermal attacks also depends on typing behavior and the material of the keycaps. ABS keycaps, which retain heat traces longer, are more vulnerable to thermal attacks. The study also discusses ways to protect against thermal attacks and presents seven potential mitigation approaches. Dr Khamis, who led the development of the technology with Norah Alotaibi and John Williamson, said with thermal imaging cameras more affordable than ever and machine learning becoming more accessible, it was "very likely that people around the world are developing systems along similar lines to ThermoSecure in order to steal passwords". == Thermal Attack Mitigation == === Simple and Practical Measures === One basic and effective way to mitigate thermal attacks is to deliberately create heat noise over the input interface, such as a keypad or keyboard, after entering a password. For instance, placing one's palm over the entire interface for a few seconds after use can obscure the thermal pattern left by the fingers, making it much more difficult for an unauthorized user to interpret the heat traces. === Range of Proposed Strategies === In addition to simple methods, researchers have developed a spectrum of mitigation strategies to counter thermal attacks. These strategies encompass 15 different approaches including: Use of Biometrics: Replacing traditional pin codes or passwords with biometric authentication, such as fingerprint recognition or facial recognition, eliminates the issue of residual heat on keypads. Heating the Interface: Implementing technology to slightly warm up the keypad can effectively neutralize the heat traces left by fingers, preventing thermal cameras from capturing the pattern. Randomizing Key Layouts: Employing dynamic key layouts that change positions every time the interface is used, making it impossible to correlate heat patterns with static input positions. === Technological Intervention on Thermal Cameras === Another avenue for mitigation is to address the issue at the source by modifying thermal cameras. Proposals have been made to develop thermal cameras that can automatically detect vulnerable interfaces such as keyboards or keypads. When these interfaces are detected within the camera's field of view, the camera would be programmed to prevent the user from recording images of them. This solution, however, would require widespread adoption by thermal camera manufacturers. Additionally, the approach is particularly viable for thermal cameras connected to a computing device, such as a smartphone, which can process the images in real time. Many affordable thermal cameras are standalone and do not have connectivity or processing capabilities. However, thermal cameras designed for connection to mobile devices can utilize the smartphone's processing power, making this mitigation approach feasible for such devices.

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  • Ellen Voorhees

    Ellen Voorhees

    Ellen Marie Voorhees (born March 13, 1958) is an American computer scientist known for her work in document retrieval, information retrieval, and natural language processing. She works in the retrieval group at the National Institute of Standards and Technology (NIST). == Education and career == Voorhees was born in Bensalem Township, Pennsylvania, and was the 1976 valedictorian at Bensalem High School. She completed her undergraduate studies at Pennsylvania State University, graduating in 1979 with a bachelor's degree in computer science. She attended Cornell University, where she received her master's degree and then went on to complete her Ph.D. in 1985. Her dissertation, The Effectiveness and Efficiency of Agglomerative Hierarchic Clustering in Document Retrieval, was supervised by Gerard Salton. Prior to joining NIST, she was a senior member of the technical staff at Siemens Corporate Research in Princeton, New Jersey. == Recognition == Voorhees was elected as an ACM Fellow in 2018 for "contributions in evaluation of information retrieval, question answering, and other language technologies". In 2023, Voorhees was awarded an honorary Doctor of Science degree from the University of Glasgow in recognition of her body of work in the evaluation of information retrieval, question answering, and other language technologies. In 2024, Voorhees received the Gerard Salton Award, a lifetime achievement award given by ACM's Special Interest Group on Information Retrieval (SIGIR).

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  • Top 10 AI Pair Programmers Compared (2026)

    Top 10 AI Pair Programmers Compared (2026)

    Looking for the best AI pair programmer? An AI pair programmer is software that uses machine learning to help you get more done — it can save you hours every week by automating repetitive work. Most options offer a generous free tier, with paid plans unlocking higher limits, faster processing, and team features. Whether you are a beginner or a pro, the right AI pair programmer slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.

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  • Top 10 AI Avatar Generators Compared (2026)

    Top 10 AI Avatar Generators Compared (2026)

    In search of the best AI avatar generator? An AI avatar generator is software that uses machine learning to help you get more done — it turns a rough idea into a polished result in seconds. When choosing one, weigh output quality, pricing, export formats, and how well it fits the tools you already use. Whether you are a beginner or a pro, the right AI avatar generator slots into your workflow and pays for itself fast. Below we compare features, pricing, and real output so you can choose with confidence.

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  • Naked Objects for .NET

    Naked Objects for .NET

    Naked Objects for .NET or Naked Objects MVC is a software framework that builds upon the ASP.NET MVC framework. As the name suggests, the framework synthesizes two architectural patterns: naked objects and model–view–controller (MVC). These two patterns have been considered as antithetical. However, Trygve Reenskaug (the inventor of the MVC pattern) has made it clear that he does not see it that way, in his foreword to Richard Pawson's PhD thesis on the Naked Objects pattern. The Naked Objects MVC framework will take a domain model (written as Plain Old CLR Objects) and render it as a complete HTML application without the need for writing any user interface code - by means of a small set of generic View and Controller classes. The framework uses reflection rather than code generation. The developer may then choose to create customised Views and/or Controllers, using standard ASP.NET MVC patterns, for use where the generic user interface is not suitable.

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  • Richard Zemel

    Richard Zemel

    Richard Stanley Zemel (born 1963) is a Canadian-American computer scientist and professor at Columbia University, Department of Computer Science, and a leading figure in the field of machine learning and computer vision. Zemel studied the history of science at Harvard University and obtained his B.A. in 1984. He continued his study at the Department of Computer Science of the University of Toronto under the supervision of Geoffrey Hinton. He obtained his M.Sc. and Ph.D. both in computer science in 1989 and 1994, respectively.

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  • Is an AI Essay Writer Worth It in 2026?

    Is an AI Essay Writer Worth It in 2026?

    Comparing the best AI essay writer? An AI essay writer is software that uses machine learning to help you get more done — it lowers the barrier so anyone can produce professional output. Privacy matters too: check whether your data trains the model and whether a no-log or enterprise tier is available. Whether you are a beginner or a pro, the right AI essay writer slots into your workflow and pays for itself fast. Below we compare features, pricing, and real output so you can choose with confidence.

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  • Top 10 AI Background Removers Compared (2026)

    Top 10 AI Background Removers Compared (2026)

    Curious about the best AI background remover? An AI background remover is software that uses machine learning to help you get more done — it combines speed, accuracy, and an interface that just works. Hands-on testing shows real-world results vary, so a short free trial is the smartest way to decide. Whether you are a beginner or a pro, the right AI background remover slots into your workflow and pays for itself fast. This guide breaks down the top picks, their pros and cons, and who each one is best for.

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  • Tensor glyph

    Tensor glyph

    In scientific visualization a tensor glyph is an object that can visualize all or most of the nine degrees of freedom, such as acceleration, twist, or shear – of a 3 × 3 {\displaystyle 3\times 3} matrix. It is used for tensor field visualization, where a data-matrix is available at every point in the grid. "Glyphs, or icons, depict multiple data values by mapping them onto the shape, size, orientation, and surface appearance of a base geometric primitive." Tensor glyphs are a particular case of multivariate data glyphs. There are certain types of glyphs that are commonly used: Ellipsoid Cuboid Cylindrical Superquadrics According to Thomas Schultz and Gordon Kindlmann, specific types of tensor fields "play a central role in scientific and biomedical studies as well as in image analysis and feature-extraction methods."

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  • Multiple sequence alignment

    Multiple sequence alignment

    Multiple sequence alignment (MSA) is the process or the result of sequence alignment of three or more biological sequences, generally protein, DNA, or RNA. These alignments are used to infer evolutionary relationships via phylogenetic analysis and can highlight homologous features between sequences. Alignments highlight mutation events such as point mutations (single amino acid or nucleotide changes), insertion mutations and deletion mutations, and alignments are used to assess sequence conservation and infer the presence and activity of protein domains, tertiary structures, secondary structures, and individual amino acids or nucleotides. Multiple sequence alignments require more sophisticated methodologies than pairwise alignments, as they are more computationally complex. Most multiple sequence alignment programs use heuristic methods rather than global optimization because identifying the optimal alignment between more than a few sequences of moderate length is prohibitively computationally expensive. However, heuristic methods generally cannot guarantee high-quality solutions and have been shown to fail to yield near-optimal solutions on benchmark test cases. == Problem statement == Given m {\displaystyle m} sequences S i {\displaystyle S_{i}} , i = 1 , ⋯ , m {\displaystyle i=1,\cdots ,m} similar to the form below: S := { S 1 = ( S 11 , S 12 , … , S 1 n 1 ) S 2 = ( S 21 , S 22 , ⋯ , S 2 n 2 ) ⋮ S m = ( S m 1 , S m 2 , … , S m n m ) {\displaystyle S:={\begin{cases}S_{1}=(S_{11},S_{12},\ldots ,S_{1n_{1}})\\S_{2}=(S_{21},S_{22},\cdots ,S_{2n_{2}})\\\,\,\,\,\,\,\,\,\,\,\vdots \\S_{m}=(S_{m1},S_{m2},\ldots ,S_{mn_{m}})\end{cases}}} A multiple sequence alignment is taken of this set of sequences S {\displaystyle S} by inserting any amount of gaps needed into each of the S i {\displaystyle S_{i}} sequences of S {\displaystyle S} until the modified sequences, S i ′ {\displaystyle S'_{i}} , all conform to length L ≥ max { n i ∣ i = 1 , … , m } {\displaystyle L\geq \max\{n_{i}\mid i=1,\ldots ,m\}} and no values in the sequences of S {\displaystyle S} of the same column consists of only gaps. The mathematical form of an MSA of the above sequence set is shown below: S ′ := { S 1 ′ = ( S 11 ′ , S 12 ′ , … , S 1 L ′ ) S 2 ′ = ( S 21 ′ , S 22 ′ , … , S 2 L ′ ) ⋮ S m ′ = ( S m 1 ′ , S m 2 ′ , … , S m L ′ ) {\displaystyle S':={\begin{cases}S'_{1}=(S'_{11},S'_{12},\ldots ,S'_{1L})\\S'_{2}=(S'_{21},S'_{22},\ldots ,S'_{2L})\\\,\,\,\,\,\,\,\,\,\,\vdots \\S'_{m}=(S'_{m1},S'_{m2},\ldots ,S'_{mL})\end{cases}}} To return from each particular sequence S i ′ {\displaystyle S'_{i}} to S i {\displaystyle S_{i}} , remove all gaps. == Graphing approach == A general approach when calculating multiple sequence alignments is to use graphs to identify all of the different alignments. When finding alignments via graph, a complete alignment is created in a weighted graph that contains a set of vertices and a set of edges. Each of the graph edges has a weight based on a certain heuristic that helps to score each alignment or subset of the original graph. === Tracing alignments === When determining the best suited alignments for each MSA, a trace is usually generated. A trace is a set of realized, or corresponding and aligned, vertices that has a specific weight based on the edges that are selected between corresponding vertices. When choosing traces for a set of sequences it is necessary to choose a trace with a maximum weight to get the best alignment of the sequences. == Alignment methods == There are various alignment methods used within multiple sequence to maximize scores and correctness of alignments. Each is usually based on a certain heuristic with an insight into the evolutionary process. Most try to replicate evolution to get the most realistic alignment possible to best predict relations between sequences. === Dynamic programming === A direct method for producing an MSA uses the dynamic programming technique to identify the globally optimal alignment solution. For proteins, this method usually involves two sets of parameters: a gap penalty and a substitution matrix assigning scores or probabilities to the alignment of each possible pair of amino acids based on the similarity of the amino acids' chemical properties and the evolutionary probability of the mutation. For nucleotide sequences, a similar gap penalty is used, but a much simpler substitution matrix, wherein only identical matches and mismatches are considered, is typical. The scores in the substitution matrix may be either all positive or a mix of positive and negative in the case of a global alignment, but must be both positive and negative, in the case of a local alignment. For n individual sequences, the naive method requires constructing the n-dimensional equivalent of the matrix formed in standard pairwise sequence alignment. The search space thus increases exponentially with increasing n and is also strongly dependent on sequence length. Expressed with the big O notation commonly used to measure computational complexity, a naïve MSA takes O(LengthNseqs) time to produce. To find the global optimum for n sequences this way has been shown to be an NP-complete problem. In 1989, based on Carrillo-Lipman Algorithm, Altschul introduced a practical method that uses pairwise alignments to constrain the n-dimensional search space. In this approach pairwise dynamic programming alignments are performed on each pair of sequences in the query set, and only the space near the n-dimensional intersection of these alignments is searched for the n-way alignment. The MSA program optimizes the sum of all of the pairs of characters at each position in the alignment (the so-called sum of pair score) and has been implemented in a software program for constructing multiple sequence alignments. In 2019, Hosseininasab and van Hoeve showed that by using decision diagrams, MSA may be modeled in polynomial space complexity. === Progressive alignment construction === The most widely used approach to multiple sequence alignments uses a heuristic search known as progressive technique (also known as the hierarchical or tree method) developed by Da-Fei Feng and Doolittle in 1987. Progressive alignment builds up a final MSA by combining pairwise alignments beginning with the most similar pair and progressing to the most distantly related. All progressive alignment methods require two stages: a first stage in which the relationships between the sequences are represented as a phylogenetic tree, called a guide tree, and a second step in which the MSA is built by adding the sequences sequentially to the growing MSA according to the guide tree. The initial guide tree is determined by an efficient clustering method such as neighbor-joining or unweighted pair group method with arithmetic mean (UPGMA), and may use distances based on the number of identical two-letter sub-sequences (as in FASTA rather than a dynamic programming alignment). Progressive alignments are not guaranteed to be globally optimal. The primary problem is that when errors are made at any stage in growing the MSA, these errors are then propagated through to the final result. Performance is also particularly bad when all of the sequences in the set are rather distantly related. Most modern progressive methods modify their scoring function with a secondary weighting function that assigns scaling factors to individual members of the query set in a nonlinear fashion based on their phylogenetic distance from their nearest neighbors. This corrects for non-random selection of the sequences given to the alignment program. Progressive alignment methods are efficient enough to implement on a large scale for many (100s to 1000s) sequences. A popular progressive alignment method has been the Clustal family. ClustalW is used extensively for phylogenetic tree construction, in spite of the author's explicit warnings that unedited alignments should not be used in such studies and as input for protein structure prediction by homology modeling. European Bioinformatics Institute (EMBL-EBI) announced that CLustalW2 will expire in August 2015. They recommend Clustal Omega which performs based on seeded guide trees and HMM profile-profile techniques for protein alignments. An alternative tool for progressive DNA alignments is multiple alignment using fast Fourier transform (MAFFT). Another common progressive alignment method named T-Coffee is slower than Clustal and its derivatives but generally produces more accurate alignments for distantly related sequence sets. T-Coffee calculates pairwise alignments by combining the direct alignment of the pair with indirect alignments that aligns each sequence of the pair to a third sequence. It uses the output from Clustal as well as another local alignment program LALIGN, which finds multiple regions of local alignment between two sequences. The resulting alignment and phylogenetic tree are used as a guide to produce new and more accurate w

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  • Ellen Voorhees

    Ellen Voorhees

    Ellen Marie Voorhees (born March 13, 1958) is an American computer scientist known for her work in document retrieval, information retrieval, and natural language processing. She works in the retrieval group at the National Institute of Standards and Technology (NIST). == Education and career == Voorhees was born in Bensalem Township, Pennsylvania, and was the 1976 valedictorian at Bensalem High School. She completed her undergraduate studies at Pennsylvania State University, graduating in 1979 with a bachelor's degree in computer science. She attended Cornell University, where she received her master's degree and then went on to complete her Ph.D. in 1985. Her dissertation, The Effectiveness and Efficiency of Agglomerative Hierarchic Clustering in Document Retrieval, was supervised by Gerard Salton. Prior to joining NIST, she was a senior member of the technical staff at Siemens Corporate Research in Princeton, New Jersey. == Recognition == Voorhees was elected as an ACM Fellow in 2018 for "contributions in evaluation of information retrieval, question answering, and other language technologies". In 2023, Voorhees was awarded an honorary Doctor of Science degree from the University of Glasgow in recognition of her body of work in the evaluation of information retrieval, question answering, and other language technologies. In 2024, Voorhees received the Gerard Salton Award, a lifetime achievement award given by ACM's Special Interest Group on Information Retrieval (SIGIR).

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  • Best AI Presentation Makers in 2026

    Best AI Presentation Makers in 2026

    In search of the best AI presentation maker? An AI presentation maker is software that uses machine learning to help you get more done — it turns a rough idea into a polished result in seconds. When choosing one, weigh output quality, pricing, export formats, and how well it fits the tools you already use. Whether you are a beginner or a pro, the right AI presentation maker slots into your workflow and pays for itself fast. Below we compare features, pricing, and real output so you can choose with confidence.

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  • Data remanence

    Data remanence

    Data remanence is the residual representation of digital data that remains even after attempts have been made to remove or erase the data. This residue may result from data being left intact by a nominal file deletion operation, by reformatting of storage media that does not remove data previously written to the media, or through physical properties of the storage media that allow previously written data to be recovered. Data remanence may make inadvertent disclosure of sensitive information possible should the storage media be released into an uncontrolled environment (e.g., thrown in refuse containers or lost). Various techniques have been developed to counter data remanence. These techniques are classified as clearing, purging/sanitizing, or destruction. Specific methods include overwriting, degaussing, encryption, and media destruction. Effective application of countermeasures can be complicated by several factors, including media that are inaccessible, media that cannot effectively be erased, advanced storage systems that maintain histories of data throughout the data's life cycle, and persistence of data in memory that is typically considered volatile. Several standards exist for the secure removal of data and the elimination of data remanence. == Causes == Many operating systems, file managers, and other software provide a facility where a file is not immediately deleted when the user requests that action. Instead, the file is moved to a holding area (i.e. the "trash"), making it easy for the user to undo a mistake. Similarly, many software products automatically create backup copies of files that are being edited, to allow the user to restore the original version, or to recover from a possible crash (autosave feature). Even when an explicit deleted file retention facility is not provided or when the user does not use it, operating systems do not actually remove the contents of a file when it is deleted unless they are aware that explicit erasure commands are required, like on a solid-state drive. (In such cases, the operating system will issue the Serial ATA TRIM command or the SCSI UNMAP command to let the drive know to no longer maintain the deleted data.) Instead, they simply remove the file's entry from the file system directory because this requires less work and is therefore faster, and the contents of the file—the actual data—remain on the storage medium. The data will remain there until the operating system reuses the space for new data. In some systems, enough filesystem metadata are also left behind to enable easy undeletion by commonly available utility software. Even when undelete has become impossible, the data, until it has been overwritten, can be read by software that reads disk sectors directly. Computer forensics often employs such software. Likewise, reformatting, repartitioning, or reimaging a system is unlikely to write to every area of the disk, though all will cause the disk to appear empty or, in the case of reimaging, empty except for the files present in the image, to most software. Finally, even when the storage media is overwritten, physical properties of the media may permit recovery of the previous contents. In most cases however, this recovery is not possible by just reading from the storage device in the usual way, but requires using laboratory techniques such as disassembling the device and directly accessing/reading from its components. § Complications below gives further explanations for causes of data remanence. == Countermeasures == There are three levels commonly recognized for eliminating remnant data: === Clearing === Clearing is the removal of sensitive data from storage devices in such a way that there is assurance that the data may not be reconstructed using normal system functions or software file/data recovery utilities. The data may still be recoverable, but not without special laboratory techniques. Clearing is typically an administrative protection against accidental disclosure within an organization. For example, before a hard drive is re-used within an organization, its contents may be cleared to prevent their accidental disclosure to the next user. === Purging === Purging or sanitizing is the physical rewrite of sensitive data from a system or storage device done with the specific intent of rendering the data unrecoverable at a later time. Purging, proportional to the sensitivity of the data, is generally done before releasing media beyond control, such as before discarding old media, or moving media to a computer with different security requirements. === Destruction === The storage media is made unusable for conventional equipment. Effectiveness of destroying the media varies by medium and method. Depending on recording density of the media, and/or the destruction technique, this may leave data recoverable by laboratory methods. Conversely, destruction using appropriate techniques is the most secure method of preventing retrieval. == Specific methods == === Overwriting === A common method used to counter data remanence is to overwrite the storage media with new data. This is often called wiping or shredding a disk or file, by analogy to common methods of destroying print media, although the mechanism bears no similarity to these. Because such a method can often be implemented in software alone, and may be able to selectively target only part of the media, it is a popular, low-cost option for some applications. Overwriting is generally an acceptable method of clearing, as long as the media is writable and not damaged. The simplest overwrite technique writes the same data everywhere—often just a pattern of all zeros. At a minimum, this will prevent the data from being retrieved simply by reading from the media again using standard system functions. The UEFI in modern machines may offer an ATA class disk erase function as well. The ATA-6 standard governs secure erases specifications. Bitlocker is whole disk encryption and illegible without the key. Writing a fresh GPT allows a new file system to be established. Blocks will set empty but LBA read is illegible. New data will be unaffected and work fine. In an attempt to counter more advanced data recovery techniques, specific overwrite patterns and multiple passes have often been prescribed. These may be generic patterns intended to eradicate any trace signatures; an example is the seven-pass pattern 0xF6, 0x00, 0xFF, , 0x00, 0xFF, , sometimes erroneously attributed to US standard DOD 5220.22-M. One challenge with overwriting is that some areas of the disk may be inaccessible, due to media degradation or other errors. Software overwrite may also be problematic in high-security environments, which require stronger controls on data commingling than can be provided by the software in use. The use of advanced storage technologies may also make file-based overwrite ineffective (see the related discussion below under § Complications). There are specialized machines and software that are capable of doing overwriting. The software can sometimes be a standalone operating system specifically designed for data destruction. There are also machines specifically designed to wipe hard drives to the department of defense specifications DOD 5220.22-M. Writing zero to each block on hard disks and SSDs has the advantage of affording the firmware to deploy spare blocks when bad blocks are identified. Bitlocker has the advantage that data is illegible without the key. Seatools and other tools can erase disks with zero which is typical to revive old consumer class disks but they can wipe server disks albeit slowly. Modern 28TB and larger disks have an enormous number of LBA48 blocks. 40TB and 60TB disks will take proportionately longer times to wipe. ==== Feasibility of recovering overwritten data ==== Peter Gutmann investigated data recovery from nominally overwritten media in the mid-1990s. He suggested magnetic force microscopy may be able to recover such data, and developed specific patterns, for specific drive technologies, designed to counter such. These patterns have come to be known as the Gutmann method. Gutmann's belief in the possibility of data recovery is based on many questionable assumptions and factual errors that indicate a low level of understanding of how hard drives work. Daniel Feenberg, an economist at the private National Bureau of Economic Research, claims that the chances of overwritten data being recovered from a modern hard drive amount to "urban legend". He also points to the "18+1⁄2-minute gap" Rose Mary Woods created on a tape of Richard Nixon discussing the Watergate break-in. Erased information in the gap has not been recovered, and Feenberg claims doing so would be an easy task compared to recovery of a modern high density digital signal. As of November 2007, the United States Department of Defense considers overwriting acceptable for clearing magnetic media within the same security area/

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  • Markov property

    Markov property

    In probability theory and statistics, the Markov property is the memoryless property of a stochastic process, which means that its future evolution is independent of its history. It is named after the Russian mathematician Andrey Markov. The term strong Markov property is similar to the Markov property, except that the meaning of "present" is defined in terms of a random variable known as a stopping time. The term Markov assumption is used to describe a model where the Markov property is assumed to hold, such as a hidden Markov model. A Markov random field extends this property to two or more dimensions or to random variables defined for an interconnected network of items. An example of a model for such a field is the Ising model. A discrete-time stochastic process satisfying the Markov property is known as a Markov chain. == Introduction == A stochastic process has the Markov property if the conditional probability distribution of future states of the process (conditional on both past and present values) depends only upon the present state; that is, given the present, the future does not depend on the past. A process with this property is said to be Markov or Markovian and known as a Markov process. Two famous classes of Markov process are the Markov chain and Brownian motion. Note that there is a subtle, often overlooked and very important point that is often missed in the plain English statement of the definition: the statespace of the process is constant through time. The conditional description involves a fixed "bandwidth". For example, without this restriction we could augment any process to one which includes the complete history from a given initial condition and it would be made to be Markovian. But the state space would be of increasing dimensionality over time and does not meet the definition. == History == == Definition == Let ( Ω , F , P ) {\displaystyle (\Omega ,{\mathcal {F}},P)} be a probability space with a filtration ( F s , s ∈ I ) {\displaystyle ({\mathcal {F}}_{s},\ s\in I)} , for some (totally ordered) index set I {\displaystyle I} ; and let ( S , Σ ) {\displaystyle (S,\Sigma )} be a measurable space. An ( S , Σ ) {\displaystyle (S,\Sigma )} -valued stochastic process X = { X t : Ω → S } t ∈ I {\displaystyle X=\{X_{t}:\Omega \to S\}_{t\in I}} adapted to the filtration is said to possess the Markov property if, for each A ∈ Σ {\displaystyle A\in \Sigma } and each s , t ∈ I {\displaystyle s,t\in I} with s < t {\displaystyle s Read more →

  • How to Choose an AI Humanizer

    How to Choose an AI Humanizer

    In search of the best AI humanizer? An AI humanizer is software that uses machine learning to help you get more done — it turns a rough idea into a polished result in seconds. When choosing one, weigh output quality, pricing, export formats, and how well it fits the tools you already use. Whether you are a beginner or a pro, the right AI humanizer slots into your workflow and pays for itself fast. We tested the leading options and ranked them by quality, value, and ease of use.

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