The Richardson–Lucy algorithm, also known as Lucy–Richardson deconvolution, is an iterative procedure for recovering an underlying image that has been blurred by a known point spread function. It was named after William Richardson and Leon B. Lucy, who described it independently. == Description == When an image is produced using an optical system and detected using photographic film, a charge-coupled device or a CMOS sensor, for example, it is inevitably blurred, with an ideal point source not appearing as a point but being spread out into what is known as the point spread function. Extended sources can be decomposed into the sum of many individual point sources, thus the observed image can be represented in terms of a transition matrix p operating on an underlying image: d i = ∑ j p i , j u j , {\displaystyle d_{i}=\sum _{j}p_{i,j}u_{j},} where u j {\displaystyle u_{j}} is the intensity of the underlying image at pixel j {\displaystyle j} , and d i {\displaystyle d_{i}} is the detected intensity at pixel i {\displaystyle i} . In general, a matrix whose elements are p i , j {\displaystyle p_{i,j}} describes the portion of light from source pixel j that is detected in pixel i. In most good optical systems (or in general, linear systems that are described as shift-invariant) the transfer function p can be expressed simply in terms of the spatial offset between the source pixel j and the observation pixel i: p i , j = P ( i − j ) , {\displaystyle p_{i,j}=P(i-j),} where P ( Δ i ) {\displaystyle P(\Delta i)} is called a point spread function. In that case the above equation becomes a convolution. This has been written for one spatial dimension, but most imaging systems are two-dimensional, with the source, detected image, and point spread function all having two indices. So a two-dimensional detected image is a convolution of the underlying image with a two-dimensional point spread function P ( Δ x , Δ y ) {\displaystyle P(\Delta x,\Delta y)} plus added detection noise. In order to estimate u j {\displaystyle u_{j}} given the observed d i {\displaystyle d_{i}} and a known P ( Δ i x , Δ j y ) {\displaystyle P(\Delta i_{x},\Delta j_{y})} , the following iterative procedure is employed in which the estimate of u j {\displaystyle u_{j}} (called u ^ j ( t ) {\displaystyle {\hat {u}}_{j}^{(t)}} ) for iteration number t is updated as follows: u ^ j ( t + 1 ) = u ^ j ( t ) ∑ i d i c i p i j , {\displaystyle {\hat {u}}_{j}^{(t+1)}={\hat {u}}_{j}^{(t)}\sum _{i}{\frac {d_{i}}{c_{i}}}p_{ij},} where c i = ∑ j p i j u ^ j ( t ) , {\displaystyle c_{i}=\sum _{j}p_{ij}{\hat {u}}_{j}^{(t)},} and ∑ j p i j = 1 {\displaystyle \sum _{j}p_{ij}=1} is assumed. It has been shown empirically that if this iteration converges, it converges to the maximum likelihood solution for u j {\displaystyle u_{j}} . Writing this more generally for two (or more) dimensions in terms of convolution with a point spread function P: u ^ ( t + 1 ) = u ^ ( t ) ⋅ ( d u ^ ( t ) ⊗ P ⊗ P ∗ ) , {\displaystyle {\hat {u}}^{(t+1)}={\hat {u}}^{(t)}\cdot \left({\frac {d}{{\hat {u}}^{(t)}\otimes P}}\otimes P^{}\right),} where the division and multiplication are element-wise, ⊗ {\displaystyle \otimes } indicates a 2D convolution, and P ∗ {\displaystyle P^{}} is the mirrored point spread function, or the inverse Fourier transform of the Hermitian transpose of the optical transfer function. In problems where the point spread function p i j {\displaystyle p_{ij}} is not known a priori, a modification of the Richardson–Lucy algorithm has been proposed, in order to accomplish blind deconvolution. == Derivation == In the context of fluorescence microscopy, the probability of measuring a set of number of photons (or digitalization counts proportional to detected light) m = [ m 0 , … , m K ] {\displaystyle \mathbf {m} =[m_{0},\dots ,m_{K}]} for expected values E = [ E 0 , … , E K ] {\displaystyle \mathbf {E} =[E_{0},\dots ,E_{K}]} for a detector with K + 1 {\displaystyle K+1} pixels is given by P ( m ∣ E ) = ∏ i K Poisson ( E i ) = ∏ i K E i m i e − E i m i ! . {\displaystyle P(\mathbf {m} \mid \mathbf {E} )=\prod _{i}^{K}\operatorname {Poisson} (E_{i})=\prod _{i}^{K}{\frac {E_{i}^{m_{i}}e^{-E_{i}}}{m_{i}!}}.} Since in the context of maximum-likelihood estimation the aim is to locate the maximum of the likelihood function without concern for its absolute value, it is convenient to work with ln ( P ) {\displaystyle \ln(P)} : ln P ( m ∣ E ) = ∑ i K [ ( m i ln E i − E i ) − ln ( m i ! ) ] . {\displaystyle \ln P(\mathbf {m} \mid \mathbf {E} )=\sum _{i}^{K}[(m_{i}\ln E_{i}-E_{i})-\ln(m_{i}!)].} Moreover, since ln ( m i ! ) {\displaystyle \ln(m_{i}!)} is a constant, it does not give any additional information regarding the position of the maximum, so consider α ( m ∣ E ) = ∑ i K [ m i ln E i − E i ] , {\displaystyle \alpha (\mathbf {m} \mid \mathbf {E} )=\sum _{i}^{K}[m_{i}\ln E_{i}-E_{i}],} where α {\displaystyle \alpha } is something that shares the same maximum position as P ( m ∣ E ) {\displaystyle P(\mathbf {m} \mid \mathbf {E} )} . Now consider that E {\displaystyle \mathbf {E} } comes from a ground truth x {\displaystyle \mathbf {x} } and a measurement H {\displaystyle \mathbf {H} } which is assumed to be linear. Then E = H x , {\displaystyle \mathbf {E} =\mathbf {H} \mathbf {x} ,} where a matrix multiplication is implied. This can also be written in the form E m = ∑ n K H m n x n , {\displaystyle E_{m}=\sum _{n}^{K}H_{mn}x_{n},} where it can be seen how H {\displaystyle H} mixes or blurs the ground truth. It can also be shown that the derivative of an element of E {\displaystyle \mathbf {E} } , ( E i ) {\displaystyle (E_{i})} with respect to some other element of x j {\displaystyle x_{j}} can be written as It is easy to see this by writing a matrix H {\displaystyle \mathbf {H} } of, say, 5 × 5 and two arrays E {\displaystyle \mathbf {E} } and x {\displaystyle \mathbf {x} } of 5 elements and check it. This last equation can be interpreted as how much one element of x {\displaystyle \mathbf {x} } , say element i {\displaystyle i} , influences the other elements j ≠ i {\displaystyle j\neq i} (and of course the case i = j {\displaystyle i=j} is also taken into account). For example, in a typical case an element of the ground truth x {\displaystyle \mathbf {x} } will influence nearby elements in E {\displaystyle \mathbf {E} } but not the very distant ones (a value of 0 {\displaystyle 0} is expected on those matrix elements). Now, the key and arbitrary step: x {\displaystyle \mathbf {x} } is not known but may be estimated by x ^ {\displaystyle {\hat {\mathbf {x} }}} . Let's call x ^ old {\displaystyle {\hat {\mathbf {x} }}_{\text{old}}} and x ^ new {\displaystyle {\hat {\mathbf {x} }}_{\text{new}}} the estimated ground truths while using the RL algorithm, where the hat symbol is used to distinguish ground truth from estimator of the ground truth where ∂ ∂ x {\displaystyle {\frac {\partial }{\partial \mathbf {x} }}} stands for a K {\displaystyle K} -dimensional gradient. Performing the partial derivative of α ( m ∣ E ( x ) ) {\displaystyle \alpha (\mathbf {m} \mid \mathbf {E} (\mathbf {x} ))} yields the following expression: ∂ α ( m ∣ E ( x ) ) ∂ x j = ∂ ∂ x j ∑ i K [ m i ln E i − E i ] = ∑ i K [ m i E i ∂ ∂ x j E i − ∂ ∂ x j E i ] = ∑ i K ∂ E i ∂ x j [ m i E i − 1 ] . {\displaystyle {\frac {\partial \alpha (\mathbf {m} \mid \mathbf {E} (\mathbf {x} ))}{\partial x_{j}}}={\frac {\partial }{\partial x_{j}}}\sum _{i}^{K}[m_{i}\ln E_{i}-E_{i}]=\sum _{i}^{K}\left[{\frac {m_{i}}{E_{i}}}{\frac {\partial }{\partial x_{j}}}E_{i}-{\frac {\partial }{\partial x_{j}}}E_{i}\right]=\sum _{i}^{K}{\frac {\partial E_{i}}{\partial x_{j}}}\left[{\frac {m_{i}}{E_{i}}}-1\right].} By substituting (1), it follows that ∂ α ( m ∣ E ( x ) ) ∂ x j = ∑ i K H i j [ m i E i − 1 ] . {\displaystyle {\frac {\partial \alpha (\mathbf {m} \mid \mathbf {E} (\mathbf {x} ))}{\partial x_{j}}}=\sum _{i}^{K}H_{ij}\left[{\frac {m_{i}}{E_{i}}}-1\right].} Note that H j i T = H i j {\displaystyle H_{ji}^{T}=H_{ij}} by the definition of a matrix transpose. And hence Since this equation is true for all j {\displaystyle j} spanning all the elements from 1 {\displaystyle 1} to K {\displaystyle K} , these K {\displaystyle K} equations may be compactly rewritten as a single vectorial equation ∂ α ( m ∣ E ( x ) ) ∂ x = H T [ m E − 1 ] , {\displaystyle {\frac {\partial \alpha (\mathbf {m} \mid \mathbf {E} (\mathbf {x} ))}{\partial \mathbf {x} }}=\mathbf {H} ^{T}\left[{\frac {\mathbf {m} }{\mathbf {E} }}-\mathbf {1} \right],} where H T {\displaystyle \mathbf {H} ^{T}} is a matrix, and m {\displaystyle \mathbf {m} } , E {\displaystyle \mathbf {E} } and 1 {\displaystyle \mathbf {1} } are vectors. Now, as a seemingly arbitrary but key step, let where 1 {\displaystyle \mathbf {1} } is a vector of ones of size K {\displaystyle K} (same as m {\displaystyle \mathbf {m} } , E {\displaystyle \mathbf {E} } and x {\displaystyle \mathbf {x} } ), and the d
Secure coding
Secure coding is the practice of developing computer software in such a way that guards against the accidental introduction of security vulnerabilities. Defects, bugs and logic flaws are consistently the primary cause of commonly exploited software vulnerabilities. Through the analysis of thousands of reported vulnerabilities, security professionals have discovered that most vulnerabilities stem from a relatively small number of common software programming errors. By identifying the insecure coding practices that lead to these errors and educating developers on secure alternatives, organizations can take proactive steps to help significantly reduce or eliminate vulnerabilities in software before deployment. Some scholars have suggested that in order to effectively confront threats related to cybersecurity, proper security should be coded or "baked in" to the systems. With security being designed into the software, this ensures that there will be protection against insider attacks and reduces the threat to application security. Implementing secure coding practices is part of the secure by design approach to security engineering. == Buffer-overflow prevention == Buffer overflows, a common software security vulnerability, happen when a process tries to store data beyond a fixed-length buffer. For example, if there are 8 slots to store items in, there will be a problem if there is an attempt to store 9 items. In computer memory the overflowed data may overwrite data in the next location which can result in a security vulnerability (stack smashing) or program termination (segmentation fault). An example of a C program prone to a buffer overflow is If the user input is larger than the destination buffer, a buffer overflow will occur. To fix this unsafe program, use strncpy to prevent a possible buffer overflow. Another secure alternative is to dynamically allocate memory on the heap using malloc. In the above code snippet, the program attempts to copy the contents of src into dst, while also checking the return value of malloc() to ensure that enough memory was able to be allocated for the destination buffer. == Format-string attack prevention == A Format String Attack is when a malicious user supplies specific inputs that will eventually be entered as an argument to a function that performs formatting, such as printf(). The attack involves the adversary reading from or writing to the stack. The C printf function writes output to stdout. If the parameter of the printf function is not properly formatted, several security bugs can be introduced. Below is a program that is vulnerable to a format string attack. A malicious argument passed to the program could be "%s%s%s%s%s%s%s", which can crash the program from improper memory reads. == Integer-overflow prevention == Integer overflow occurs when an arithmetic operation results in an integer too large to be represented within the available space. A program which does not properly check for integer overflow introduces potential software bugs and exploits. Below is a function in C++ which attempts to confirm that the sum of x and y is less than or equal to a defined value MAX: The problem with the code is it does not check for integer overflow on the addition operation. If the sum of x and y is greater than the maximum possible value of an unsigned int, the addition operation will overflow and perhaps result in a value less than or equal to MAX, even though the sum of x and y is greater than MAX. Below is a function which checks for overflow by confirming the sum is greater than or equal to both x and y. If the sum did overflow, the sum would be less than x or less than y. == Path traversal prevention == Path traversal is a vulnerability whereby paths provided from an untrusted source are interpreted in such a way that unauthorised file access is possible. For example, consider a script that fetches an article by taking a filename, which is then read by the script and parsed. Such a script might use the following hypothetical URL to retrieve an article about dog food: https://www.example.net/cgi-bin/article.sh?name=dogfood.html If the script has no input checking, instead trusting that the filename is always valid, a malicious user could forge a URL to retrieve configuration files from the web server: https://www.example.net/cgi-bin/article.sh?name=../../../../../etc/passwd Depending on the script, this may expose the /etc/passwd file, which on Unix-like systems contains (among others) user IDs, their login names, home directory paths and shells. (See SQL injection for a similar attack.) == Regulatory drivers == Secure coding practices are increasingly mandated by regulatory frameworks governing the development and maintenance of software systems that process sensitive data. The Health Insurance Portability and Accountability Act (HIPAA) Security Rule requires covered entities to protect the integrity of protected health information through technical safeguards under 45 CFR 164.312(c)(1) and to implement mechanisms to authenticate electronic protected health information under 45 CFR 164.312(c)(2). The Payment Card Industry Data Security Standard (PCI DSS) version 4.0 Requirement 6.2 mandates that custom software is developed securely, including training developers in secure coding techniques (6.2.2), reviewing custom code for vulnerabilities before release (6.2.3), and addressing common software attacks in development practices (6.2.4).
Virtual intelligence
Virtual intelligence (VI) is the term given to artificial intelligence that exists within a virtual world. Many virtual worlds have options for persistent avatars that provide information, training, role-playing, and social interactions. The immersion in virtual worlds provides a platform for VI beyond the traditional paradigm of past user interfaces (UIs). What Alan Turing established as a benchmark for telling the difference between human and computerized intelligence was devoid of visual influences. With today's VI bots, virtual intelligence has evolved past the constraints of past testing into a new level of the machine's ability to demonstrate intelligence. The immersive features of these environments provide nonverbal elements that affect the realism provided by virtually intelligent agents. Virtual intelligence is the intersection of these two technologies: Virtual environments: Immersive 3D spaces provide for collaboration, simulations, and role-playing interactions for training. Many of these virtual environments are currently being used for government and academic projects, including Second Life, VastPark, Olive, OpenSim, Outerra, Oracle's Open Wonderland, Duke University's Open Cobalt, and many others. Some of the commercial virtual worlds are also taking this technology into new directions, including the high-definition virtual world Blue Mars. Artificial intelligence (AI): AI is a branch of computer science that aims to create intelligent machines capable of performing tasks that typically require human intelligence. VI is a type of AI that operates within virtual environments to simulate human-like interactions and responses. == Applications == Cutlass Bomb Disposal Robot: Northrop Grumman developed a virtual training opportunity because of the prohibitive real-world cost and dangers associated with bomb disposal. By replicating a complicated system without having to learn advanced code, the virtual robot has no risk of damage, trainee safety hazards, or accessibility constraints. MyCyberTwin: NASA is among the companies that have used the MyCyberTwin AI technologies. They used it for the Phoenix rover in the virtual world Second Life. Their MyCyberTwin used a programmed profile to relay information about what the Phoenix rover was doing and its purpose. Second China: The University of Florida developed the "Second China" project as an immersive training experience for learning how to interact with the culture and language in a foreign country. Students are immersed in an environment that provides role-playing challenges coupled with language and cultural sensitivities magnified during country-level diplomatic missions or during times of potential conflict or regional destabilization. The virtual training provides participants with opportunities to access information, take part in guided learning scenarios, communicate, collaborate, and role-play. While China was the country for the prototype, this model can be modified for use with any culture to help better understand social and cultural interactions and see how other people think and what their actions imply. Duke School of Nursing Training Simulation: Extreme Reality developed virtual training to test critical thinking with a nurse performing trained procedures to identify critical data to make decisions and performing the correct steps for intervention. Bots are programmed to respond to the nurse's actions as the patient with their conditions improving if the nurse performs the correct actions.
Cognitive philology
Cognitive philology is the science that studies written and oral texts as the product of human mental processes. Studies in cognitive philology compare documentary evidence emerging from textual investigations with results of experimental research, especially in the fields of cognitive and ecological psychology, neurosciences and artificial intelligence. "The point is not the text, but the mind that made it". Cognitive Philology aims to foster communication between literary, textual, philological disciplines on the one hand and researches across the whole range of the cognitive, evolutionary, ecological and human sciences on the other. Cognitive philology: investigates transmission of oral and written text, and categorization processes which lead to classification of knowledge, mostly relying on the information theory; studies how narratives emerge in so called natural conversation and selective process which lead to the rise of literary standards for storytelling, mostly relying on embodied semantics; explores the evolutive and evolutionary role played by rhythm and metre in human ontogenetic and phylogenetic development and the pertinence of the semantic association during processing of cognitive maps; Provides the scientific ground for multimedia critical editions of literary texts. Among the founding thinkers and noteworthy scholars devoted to such investigations are: Alan Richardson: Studies Theory of Mind in early-modern and contemporary literature. Anatole Pierre Fuksas Benoît de Cornulier David Herman: Professor of English at North Carolina State University and an adjunct professor of linguistics at Duke University. He is the author of "Universal Grammar and Narrative Form" and the editor of "Narratologies: New Perspectives on Narrative Analysis". Domenico Fiormonte François Recanati Gilles Fauconnier, a professor in Cognitive science at the University of California, San Diego. He was one of the founders of cognitive linguistics in the 1970s through his work on pragmatic scales and mental spaces. His research explores the areas of conceptual integration and compressions of conceptual mappings in terms of the emergent structure in language. Julián Santano Moreno Luca Nobile Manfred Jahn in Germany Mark Turner Paolo Canettieri
Google Clips
Google Clips is a discontinued miniature clip-on camera device developed by Google. == History == It was announced on October 4, 2017 and went on sale on January 27, 2018. Google Clips automatically captured video clips (without audio) at moments its machine learning algorithms determined to be interesting or relevant. An indicator flashed when the camera was looking for scenes to capture. Google Clips' artificial intelligence (AI) could learn the faces of people to take photographs with certain people, and could automatically set lighting and framing. It had 16 GB of storage built-in storage and could record clips for up to 3 hours. This camera was originally priced at US$249 in the United States. It was withdrawn from sale on October 15, 2019, but supported until the end of December 2021. == Reception == The Independent wrote that Google Clips is "an impressive little device, but one that also has the potential to feel very creepy." According to The Verge's generally negative review, "it didn't capture anything special" over two weeks of testing.
Shepp–Logan phantom
The Shepp–Logan phantom is a standard test image created by Larry Shepp and Benjamin F. Logan for their 1974 paper "The Fourier Reconstruction of a Head Section". It serves as the model of a human head in the development and testing of image reconstruction algorithms. == Definition == The function describing the phantom is defined as the sum of 10 ellipses inside a 2×2 square:
AI-assisted software development
AI-assisted software development is the use of artificial intelligence (AI) to augment software development. It uses large language models (LLMs), AI agents and other AI technologies to assist software developers. It helps in a range of tasks of the software development life cycle, from code generation to debugging, editing, testing, UI design, understanding the code, and documentation. Agentic coding denotes the use of AI agents for software development. == Technologies == === Source code generation === Large language models trained or fine-tuned on source-code corpora can generate source code from natural-language descriptions, comments, or docstrings. Research on code-generation systems often evaluates generated programs by functional correctness, such as whether the output passes automated test cases, rather than by syntax alone. Such tools can be features or extensions of integrated development environments (IDEs). === Intelligent code completion === AI agents using pre-trained and fine-tuned LLMs can predict and suggest code completions based on context. According to Husein, Aburajouh & Catal in a 2025 literature review in Computer Standards & Interfaces, "LLMs significantly enhance code completion performance across several programming languages and contexts, and their capability to predict relevant code snippets based on context and partial input boosts developer productivity substantially." === Testing, debugging, code review and analysis === AI is used to automatically generate test cases, identify potential bugs and security vulnerabilities, and suggest fixes. AI can also be used to perform static code analysis and suggest potential performance improvements. == Limitations == Both ownership of and responsibility for AI-generated code is disputed. According to a report from the German Federal Office for Information Security, the use of AI coding assistants without careful oversight from experienced developers can introduce both minor and major security vulnerabilities, and any potential gain in productivity should be weighed against the cost of additional quality control and security measures. According to Deloitte, outputs from AI-assisted software development must be validated through a combination of automated testing, static analysis tools and human review, creating a governance layer to improve quality and accountability. == Vibe coding ==