Gato is a deep neural network for a range of complex tasks that exhibits multimodality. It can perform tasks such as engaging in a dialogue, playing video games, controlling a robot arm to stack blocks, and more. == Overview == Gato was created by researchers at London-based AI firm DeepMind. It is a transformer, like GPT-3. According to MIT Technology Review, the system "learns multiple different tasks at the same time, which means it can switch between them without having to forget one skill before learning another" whereas "[t]he AI systems of today are called “narrow,” meaning they can only do a specific, restricted set of tasks such as generate text", and according to The Independent, it is a "'generalist agent' that can carry out a huge range of complex tasks, from stacking blocks to writing poetry". It uses supervised learning with 1.2B parameters. The technology has been described as "general purpose" artificial intelligence and a "step toward" artificial general intelligence.
Empirical risk minimization
In statistical learning theory, the principle of empirical risk minimization defines a family of learning algorithms based on evaluating performance over a known and fixed dataset. The core idea is based on an application of the law of large numbers; more specifically, we cannot know exactly how well a predictive algorithm will work in practice (i.e. the "true risk") because we do not know the true distribution of the data, but we can instead estimate and optimize the performance of the algorithm on a known set of training data. The performance over the known set of training data is referred to as the "empirical risk". == Background == The following situation is a general setting of many supervised learning problems. There are two spaces of objects X {\displaystyle X} and Y {\displaystyle Y} and we would like to learn a function h : X → Y {\displaystyle \ h:X\to Y} (often called hypothesis) which outputs an object y ∈ Y {\displaystyle y\in Y} , given x ∈ X {\displaystyle x\in X} . To do so, there is a training set of n {\displaystyle n} examples ( x 1 , y 1 ) , … , ( x n , y n ) {\displaystyle \ (x_{1},y_{1}),\ldots ,(x_{n},y_{n})} where x i ∈ X {\displaystyle x_{i}\in X} is an input and y i ∈ Y {\displaystyle y_{i}\in Y} is the corresponding response that is desired from h ( x i ) {\displaystyle h(x_{i})} . To put it more formally, assuming that there is a joint probability distribution P ( x , y ) {\displaystyle P(x,y)} over X {\displaystyle X} and Y {\displaystyle Y} , and that the training set consists of n {\displaystyle n} instances ( x 1 , y 1 ) , … , ( x n , y n ) {\displaystyle \ (x_{1},y_{1}),\ldots ,(x_{n},y_{n})} drawn i.i.d. from P ( x , y ) {\displaystyle P(x,y)} . The assumption of a joint probability distribution allows for the modelling of uncertainty in predictions (e.g. from noise in data) because y {\displaystyle y} is not a deterministic function of x {\displaystyle x} , but rather a random variable with conditional distribution P ( y | x ) {\displaystyle P(y|x)} for a fixed x {\displaystyle x} . It is also assumed that there is a non-negative real-valued loss function L ( y ^ , y ) {\displaystyle L({\hat {y}},y)} which measures how different the prediction y ^ {\displaystyle {\hat {y}}} of a hypothesis is from the true outcome y {\displaystyle y} . For classification tasks, these loss functions can be scoring rules. The risk associated with hypothesis h ( x ) {\displaystyle h(x)} is then defined as the expectation of the loss function: R ( h ) = E [ L ( h ( x ) , y ) ] = ∫ L ( h ( x ) , y ) d P ( x , y ) . {\displaystyle R(h)=\mathbf {E} [L(h(x),y)]=\int L(h(x),y)\,dP(x,y).} A loss function commonly used in theory is the 0-1 loss function: L ( y ^ , y ) = { 1 if y ^ ≠ y 0 if y ^ = y {\displaystyle L({\hat {y}},y)={\begin{cases}1&{\mbox{ if }}\quad {\hat {y}}\neq y\\0&{\mbox{ if }}\quad {\hat {y}}=y\end{cases}}} . The ultimate goal of a learning algorithm is to find a hypothesis h ∗ {\displaystyle h^{}} among a fixed class of functions H {\displaystyle {\mathcal {H}}} for which the risk R ( h ) {\displaystyle R(h)} is minimal: h ∗ = a r g m i n h ∈ H R ( h ) . {\displaystyle h^{}={\underset {h\in {\mathcal {H}}}{\operatorname {arg\,min} }}\,{R(h)}.} For classification problems, the Bayes classifier is defined to be the classifier minimizing the risk defined with the 0–1 loss function. == Formal definition == In general, the risk R ( h ) {\displaystyle R(h)} cannot be computed because the distribution P ( x , y ) {\displaystyle P(x,y)} is unknown to the learning algorithm. However, given a sample of iid training data points, we can compute an estimate, called the empirical risk, by computing the average of the loss function over the training set; more formally, computing the expectation with respect to the empirical measure: R emp ( h ) = 1 n ∑ i = 1 n L ( h ( x i ) , y i ) . {\displaystyle \!R_{\text{emp}}(h)={\frac {1}{n}}\sum _{i=1}^{n}L(h(x_{i}),y_{i}).} The empirical risk minimization principle states that the learning algorithm should choose a hypothesis h ^ {\displaystyle {\hat {h}}} which minimizes the empirical risk over the hypothesis class H {\displaystyle {\mathcal {H}}} : h ^ = a r g m i n h ∈ H R emp ( h ) . {\displaystyle {\hat {h}}={\underset {h\in {\mathcal {H}}}{\operatorname {arg\,min} }}\,R_{\text{emp}}(h).} Thus, the learning algorithm defined by the empirical risk minimization principle consists in solving the above optimization problem. == Properties == Guarantees for the performance of empirical risk minimization depend strongly on the function class selected as well as the distributional assumptions made. In general, distribution-free methods are too coarse, and do not lead to practical bounds. However, they are still useful in deriving asymptotic properties of learning algorithms, such as consistency. In particular, distribution-free bounds on the performance of empirical risk minimization given a fixed function class can be derived using bounds on the VC complexity of the function class. For simplicity, considering the case of binary classification tasks, it is possible to bound the probability of the selected classifier, ϕ n {\displaystyle \phi _{n}} being much worse than the best possible classifier ϕ ∗ {\displaystyle \phi ^{}} . Consider the risk L {\displaystyle L} defined over the hypothesis class C {\displaystyle {\mathcal {C}}} with growth function S ( C , n ) {\displaystyle {\mathcal {S}}({\mathcal {C}},n)} given a dataset of size n {\displaystyle n} . Then, for every ϵ > 0 {\displaystyle \epsilon >0} : P ( L ( ϕ n ) − L ( ϕ ∗ ) > ϵ ) ≤ 8 S ( C , n ) exp { − n ϵ 2 / 32 } {\displaystyle \mathbb {P} \left(L(\phi _{n})-L(\phi ^{})>\epsilon \right)\leq {\mathcal {8}}S({\mathcal {C}},n)\exp\{-n\epsilon ^{2}/32\}} Similar results hold for regression tasks. These results are often based on uniform laws of large numbers, which control the deviation of the empirical risk from the true risk, uniformly over the hypothesis class. === Impossibility results === It is also possible to show lower bounds on algorithm performance if no distributional assumptions are made. This is sometimes referred to as the No free lunch theorem. Even though a specific learning algorithm may provide the asymptotically optimal performance for any distribution, the finite sample performance is always poor for at least one data distribution. This means that no classifier can improve on the error for a given sample size for all distributions. Specifically, let ϵ > 0 {\displaystyle \epsilon >0} and consider a sample size n {\displaystyle n} and classification rule ϕ n {\displaystyle \phi _{n}} , there exists a distribution of ( X , Y ) {\displaystyle (X,Y)} with risk L ∗ = 0 {\displaystyle L^{}=0} (meaning that perfect prediction is possible) such that: E L n ≥ 1 / 2 − ϵ . {\displaystyle \mathbb {E} L_{n}\geq 1/2-\epsilon .} It is further possible to show that the convergence rate of a learning algorithm is poor for some distributions. Specifically, given a sequence of decreasing positive numbers a i {\displaystyle a_{i}} converging to zero, it is possible to find a distribution such that: E L n ≥ a i {\displaystyle \mathbb {E} L_{n}\geq a_{i}} for all n {\displaystyle n} . This result shows that universally good classification rules do not exist, in the sense that the rule must be low quality for at least one distribution. === Computational complexity === Empirical risk minimization for a classification problem with a 0-1 loss function is known to be an NP-hard problem even for a relatively simple class of functions such as linear classifiers. Nevertheless, it can be solved efficiently when the minimal empirical risk is zero, i.e., data is linearly separable. In practice, machine learning algorithms cope with this issue either by employing a convex approximation to the 0–1 loss function (like hinge loss for SVM), which is easier to optimize, or by imposing assumptions on the distribution P ( x , y ) {\displaystyle P(x,y)} (and thus stop being agnostic learning algorithms to which the above result applies). In the case of convexification, Zhang's lemma majors the excess risk of the original problem using the excess risk of the convexified problem. Minimizing the latter using convex optimization also allow to control the former. == Tilted empirical risk minimization == Tilted empirical risk minimization is a machine learning technique used to modify standard loss functions like squared error, by introducing a tilt parameter. This parameter dynamically adjusts the weight of data points during training, allowing the algorithm to focus on specific regions or characteristics of the data distribution. Tilted empirical risk minimization is particularly useful in scenarios with imbalanced data or when there is a need to emphasize errors in certain parts of the prediction space.
Tapingo
Tapingo was an American mobile commerce application that offers advance ordering for pickup and food delivery services for college campuses. The company was acquired by Grubhub in September 2018 for approximately $150 million. Following the acquisition, Tapingo’s campus-ordering functionality was integrated into the Grubhub app (Grubhub Campus Dining) and the Tapingo service was discontinued during 2019. Tapingo is differentiated from other on-demand delivery/logistics companies, such as Waiter.com, Postmates, or DoorDash, by focusing its efforts on serving the college market. Through Tapingo, users can browse menus, place orders, pay for the meal and schedule the pickup or have it delivered. On certain campuses, students are able to use their university's meal dollars to pay for food. In the spring of 2012, Tapingo first launched its services on five campuses (Santa Clara University, Loyola Marymount University, Biola University, the University of Maine, and California Lutheran University), and has since expanded to more than 200 college campuses across the U.S. and Canada, serving 100 markets. To date, Tapingo has received venture funding from Carmel Ventures, Khosla Ventures, Kinzon Capital, DCM Ventures and Qualcomm Ventures. In fall 2015, Tapingo announced expansion plans through major partnership deals with national brands like Chipotle Mexican Grill and 7-Eleven, regional restaurants such as Taco Bueno, and global foodservice provider Aramark.
Graphics
Graphics (from Ancient Greek γραφικός (graphikós) 'pertaining to drawing, painting, writing, etc.') are visual images or designs on some surface, such as a wall, canvas, screen, paper, or stone, to inform, illustrate, or entertain. In contemporary usage, it includes a pictorial representation of data, as in design and manufacture, in typesetting and the graphic arts, and in educational and recreational software. Images that are generated by a computer are called computer graphics. Examples are photographs, drawings, line art, mathematical graphs, line graphs, charts, diagrams, typography, numbers, symbols, geometric designs, maps, engineering drawings, or other images. Graphics often combine text, illustration, and color. Graphic design may consist of the deliberate selection, creation, or arrangement of typography alone, as in a brochure, flyer, poster, web site, or book without any other element. The objective can be clarity or effective communication, association with other cultural elements, or merely the creation of a distinctive style. Graphics can be functional or artistic. The latter can be a recorded version, such as a photograph, or an interpretation by a scientist to highlight essential features, or an artist, in which case the distinction with imaginary graphics may become blurred. It can also be used for architecture. == History == The earliest graphics known to anthropologists studying prehistoric periods are cave paintings and markings on boulders, bone, ivory, and antlers, which were created during the Upper Palaeolithic period from 40,000 to 10,000 B.C. or earlier. Many of these were found to record astronomical, seasonal, and chronological details. Some of the earliest graphics and drawings are known to the modern world, from almost 6,000 years ago, are that of engraved stone tablets and ceramic cylinder seals, marking the beginning of the historical periods and the keeping of records for accounting and inventory purposes. Records from Egypt predate these and papyrus was used by the Egyptians as a material on which to plan the building of pyramids; they also used slabs of limestone and wood. From 600 to 250 BC, the Greeks played a major role in geometry. They used graphics to represent their mathematical theories such as the Circle Theorem and the Pythagorean theorem. In art, "graphics" is often used to distinguish work in a monotone and made up of lines, as opposed to painting. === Drawing === Drawing generally involves making marks on a surface by applying pressure from a tool or moving a tool across a surface. In which a tool is always used as if there were no tools it would be art. Graphical drawing is an instrumental guided drawing. === Printmaking === Woodblock printing, including images is first seen in China after paper was invented (about A.D. 105). In the West, the main techniques have been woodcut, engraving and etching, but there are many others. ==== Etching ==== Etching is an intaglio method of printmaking in which the image is incised into the surface of a metal plate using an acid. The acid eats the metal, leaving behind roughened areas, or, if the surface exposed to the acid is very thin, burning a line into the plate. The use of the process in printmaking is believed to have been invented by Daniel Hopfer (c. 1470–1536) of Augsburg, Germany, who decorated armour in this way. Etching is also used in the manufacturing of printed circuit boards and semiconductor devices. === Line art === Line art is a rather non-specific term sometimes used for any image that consists of distinct straight and curved lines placed against a (usually plain) background, without gradations in shade (darkness) or hue (color) to represent two-dimensional or three-dimensional objects. Line art is usually monochromatic, although lines may be of different colors. === Illustration === An illustration is a visual representation such as a drawing, painting, photograph or other work of art that stresses the subject more than form. The aim of an illustration is to elucidate or decorate a story, poem or piece of textual information (such as a newspaper article), traditionally by providing a visual representation of something described in the text. The editorial cartoon, also known as a political cartoon, is an illustration containing a political or social message. Illustrations can be used to display a wide range of subject matter and serve a variety of functions, such as: giving faces to characters in a story displaying a number of examples of an item described in an academic textbook (e.g. A Typology) visualizing step-wise sets of instructions in a technical manual communicating subtle thematic tone in a narrative linking brands to the ideas of human expression, individuality, and creativity making a reader laugh or smile for fun (to make laugh) funny === Graphs === A graph or chart is a graphic that represents tabular or numeric data. Charts are often used to make it easier to understand large quantities of data and the relationships between different parts of the data. === Diagrams === A diagram is a simplified and structured visual representation of concepts, ideas, constructions, relations, statistical data, etc., used to visualize and clarify the topic. === Symbols === A symbol, in its basic sense, is a representation of a concept or quantity; i.e., an idea, object, concept, quality, etc. In more psychological and philosophical terms, all concepts are symbolic in nature, and representations for these concepts are simply token artifacts that are allegorical to (but do not directly codify) a symbolic meaning, or symbolism. === Maps === A map is a simplified depiction of a space, a navigational aid which highlights relations between objects within that space. Usually, a map is a two-dimensional, geometrically accurate representation of a three-dimensional space. One of the first 'modern' maps was made by Waldseemüller. === Photography === One difference between photography and other forms of graphics is that a photographer, in principle, just records a single moment in reality, with seemingly no interpretation. However, a photographer can choose the field of view and angle, and may also use other techniques, such as various lenses to choose the view or filters to change the colors. In recent times, digital photography has opened the way to an infinite number of fast, but strong, manipulations. Even in the early days of photography, there was controversy over photographs of enacted scenes that were presented as 'real life' (especially in war photography, where it can be very difficult to record the original events). Shifting the viewer's eyes ever so slightly with simple pinpricks in the negative could have a dramatic effect. The choice of the field of view can have a strong effect, effectively 'censoring out' other parts of the scene, accomplished by cropping them out or simply not including them in the photograph. This even touches on the philosophical question of what reality is. The human brain processes information based on previous experience, making us see what we want to see or what we were taught to see. Photography does the same, although the photographer interprets the scene for their viewer. === Engineering drawings === An engineering drawing is a type of drawing and is technical in nature, used to fully and clearly define requirements for engineered items. It is usually created in accordance with standardized conventions for layout, nomenclature, interpretation, appearance (such as typefaces and line styles), size, etc. === Computer graphics === There are two types of computer graphics: raster graphics, where each pixel is separately defined (as in a digital photograph), and vector graphics, where mathematical formulas are used to draw lines and shapes, which are then interpreted at the viewer's end to produce the graphic. Using vectors results in infinitely sharp graphics and often smaller files, but, when complex, like vectors take time to render and may have larger file sizes than a raster equivalent. In 1950, the first computer-driven display was attached to MIT's Whirlwind I computer to generate simple pictures. This was followed by MIT's TX-0 and TX-2, interactive computing which increased interest in computer graphics during the late 1950s. In 1962, Ivan Sutherland invented Sketchpad, an innovative program that influenced alternative forms of interaction with computers. In the mid-1960s, large computer graphics research projects were begun at MIT, General Motors, Bell Labs, and Lockheed Corporation. Douglas T. Ross of MIT developed an advanced compiler language for graphics programming. S.A.Coons, also at MIT, and J. C. Ferguson at Boeing, began work in sculptured surfaces. GM developed their DAC-1 system, and other companies, such as Douglas, Lockheed, and McDonnell, also made significant developments. In 1968, ray tracing was first described by Arthur Appel of the IBM Research Center, Yorktown Heights, N
Cowrie (honeypot)
Cowrie is a medium interaction SSH and Telnet honeypot designed to log brute force attacks and shell interaction performed by an attacker. Cowrie also functions as an SSH and telnet proxy to observe attacker behavior to another system. Cowrie was developed from Kippo. == Reception == Cowrie has been referenced in published papers. The Book "Hands-On Ethical Hacking and Network Defense" includes Cowrie in a list of 5 commercial honeypots. === Prior uses === Discussing a honeypot effort called the Project Heisenberg Cloud by Rapid7, Bob Rudis, the company's chief data scientist, told eWEEK, "There are custom Rapid7-developed low- and medium-interaction honeypots used within the framework, along with open-source ones, such as Cowrie." Doug Rickert has experimented with the open-source Cowrie SSH honeypot and wrote about it on Medium. Putting up a simple honeypot isn't difficult, and there are many open-source products besides Cowrie, including the original Honeyd to MongoDB and NoSQL honeypots, to ones that emulate web servers. Some appear to be SCADA or other more advanced applications. === Best practices === Researchers at the SysAdmin, Audit, Network and Security (SANS) institute urged administrators and security researchers to run the latest version of Cowrie on a honeypot to monitor shifts in the type of passwords being scanned for and pattern of attacks on IoT devices. === Discussion and further resources === Attack Detection and Forensics Using Honeypot in an IoT Environment calls Cowrie a "medium interaction honeypot" and describes results from using it for 40 days to capture "all communicated sessions in log files." The book Advances on Data Science also devotes chapter two to "Cowrie Honeypot Dataset and Logging." ICCWS 2018 13th International Conference on Cyber Warfare and Security describes using Cowrie. On the Move to Meaningful Internet Systems: OTM 2019 Conferences includes details of using Cowrie. Splunk, a security tool that can receive information from honeypots, outlines how to set up a honeypot using the open-source Cowrie package.
Confidential computing
Confidential computing is a security and privacy-enhancing computational technique focused on protecting data in use. Confidential computing can be used in conjunction with storage and network encryption, which protect data at rest and data in transit respectively. It is designed to address software, protocol, cryptographic, and basic physical and supply-chain attacks, although some critics have demonstrated architectural and side-channel attacks effective against the technology. The technology protects data in use by performing computations in a hardware-based trusted execution environment (TEE). Confidential data is released to the TEE only once it is assessed to be trustworthy. Different types of confidential computing define the level of data isolation used, whether virtual machine, application, or function, and the technology can be deployed in on-premise data centers, edge locations, or the public cloud. It is often compared with other privacy-enhancing computational techniques such as fully homomorphic encryption, secure multi-party computation, and Trusted Computing. Confidential computing is promoted by the Confidential Computing Consortium (CCC) industry group, whose membership includes major providers of the technology. == Properties == Trusted execution environments (TEEs) "prevent unauthorized access or modification of applications and data while they are in use, thereby increasing the security level of organizations that manage sensitive and regulated data". Trusted execution environments can be instantiated on a computer's processing components such as a central processing unit (CPU) or a graphics processing unit (GPU). In their various implementations, TEEs can provide different levels of isolation including virtual machine, individual application, or compute functions. Typically, data in use in a computer's compute components and memory exists in a decrypted state and can be vulnerable to examination or tampering by unauthorized software or administrators. According to the CCC, confidential computing protects data in use through a minimum of three properties: Data confidentiality: "Unauthorized entities cannot view data while it is in use within the TEE". Data integrity: "Unauthorized entities cannot add, remove, or alter data while it is in use within the TEE". Code integrity: "Unauthorized entities cannot add, remove, or alter code executing in the TEE". In addition to trusted execution environments, remote cryptographic attestation is an essential part of confidential computing. The attestation process assesses the trustworthiness of a system and helps ensure that confidential data is released to a TEE only after it presents verifiable evidence that it is genuine and operating with an acceptable security posture. It allows the verifying party to assess the trustworthiness of a confidential computing environment through an "authentic, accurate, and timely report about the software and data state" of that environment. "Hardware-based attestation schemes rely on a trusted hardware component and associated firmware to execute attestation routines in a secure environment". Without attestation, a compromised system could deceive others into trusting it, claim it is running certain software in a TEE, and potentially compromise the confidentiality or integrity of the data being processed or the integrity of the trusted code. == Technical approaches == Technical approaches to confidential computing may vary in which software, infrastructure and administrator elements are allowed to access confidential data. The "trust boundary," which circumscribes a trusted computing base (TCB), defines which elements have the potential to access confidential data, whether they are acting benignly or maliciously. Confidential computing implementations enforce the defined trust boundary at a specific level of data isolation. The three main types of confidential computing are: Virtual machine isolation Application isolation, also known as process isolation Function isolation, also known as library isolation Virtual machine isolation removes the elements controlled by the computer infrastructure or cloud provider, but allows potential data access by elements inside a virtual machine running on the infrastructure. Application or process isolation permits data access only by authorized software applications or processes. Function or library isolation is designed to permit data access only by authorized subroutines or modules within a larger application, blocking access by any other system element, including unauthorized code in the larger application. == Threat model == As confidential computing is concerned with the protection of data in use, only certain threat models can be addressed by this technique. Other types of attacks are better addressed by other privacy-enhancing technologies. === In scope === The following threat vectors are generally considered in scope for confidential computing: Software attacks: including attacks on the host’s software and firmware. This may include the operating system, hypervisor, BIOS, other software and workloads. Protocol attacks: including "attacks on protocols associated with attestation as well as workload and data transport". This includes vulnerabilities in the "provisioning or placement of the workload" or data that could cause a compromise. Cryptographic attacks: including "vulnerabilities found in ciphers and algorithms due to a number of factors, including mathematical breakthroughs, availability of computing power and new computing approaches such as quantum computing". The CCC notes several caveats in this threat vector, including relative difficulty of upgrading cryptographic algorithms in hardware and recommendations that software and firmware be kept up-to-date. A multi-faceted, defense-in-depth strategy is recommended as a best practice. Basic physical attacks: including cold boot attacks, bus and cache snooping and plugging attack devices into an existing port, such as a PCI Express slot or USB port. Basic upstream supply-chain attacks: including attacks that would compromise TEEs through changes such as added debugging ports. The degree and mechanism of protection against these threats varies with specific confidential computing implementations. === Out of scope === Threats generally defined as out of scope for confidential computing include: Sophisticated physical attacks: including physical attacks that "require long-term and/or invasive access to hardware" such as chip scraping techniques and electron microscope probes. Upstream hardware supply-chain attacks: including attacks on the CPU manufacturing process, CPU supply chain in key injection/generation during manufacture. Attacks on components of a host system that are not directly providing the capabilities of the trusted execution environment are also generally out-of-scope. Availability attacks: confidential computing is designed to protect the confidentiality and integrity of protected data and code. It does not address availability attacks such as Denial of Service or Distributed Denial of Service attacks. == Use cases == Confidential computing can be deployed in the public cloud, on-premise data centers, or distributed "edge" locations, including network nodes, branch offices, industrial systems and others. === Data privacy and security === Confidential computing protects the confidentiality and integrity of data and code from the infrastructure provider, unauthorized or malicious software and system administrators, and other cloud tenants, which may be a concern for organizations seeking control over sensitive or regulated data. The additional security capabilities offered by confidential computing can help accelerate the transition of more sensitive workloads to the cloud or edge locations. === Multi-party analytics === Confidential computing can enable multiple parties to engage in joint analysis using confidential or regulated data inside a TEE while preserving privacy and regulatory compliance. In this case, all parties benefit from the shared analysis, but no party's sensitive data or confidential code is exposed to the other parties or system host. Examples include multiple healthcare organizations contributing data to medical research, or multiple banks collaborating to identify financial fraud or money laundering. Oxford University researchers proposed the alternative paradigm called "Confidential Remote Computing" (CRC), which supports confidential operations in Trusted Execution Environments across endpoint computers considering multiple stakeholders as mutually distrustful data, algorithm and hardware providers. === Confidential generative AI === Confidential computing technologies can be applied to various stages of a generative AI deployments to help increase data or model privacy, security, and regulatory compliance. TEEs and remote attestation can protect the integrity of data during AI model training, keep
Supertoroid
In geometry and computer graphics, a supertoroid or supertorus is usually understood to be a family of doughnut-like surfaces (technically, a topological torus) whose shape is defined by mathematical formulas similar to those that define the superellipsoids. The plural of "supertorus" is either supertori or supertoruses. The family was described and named by Alan Barr in 1994. Barr's supertoroids have been fairly popular in computer graphics as a convenient model for many objects, such as smooth frames for rectangular things. One quarter of a supertoroid can provide a smooth and seamless 90-degree joint between two superquadric cylinders. However, they are not algebraic surfaces (except in special cases). == Formulas == Alan Barr's supertoroids are defined by parametric equations similar to the trigonometric equations of the torus, except that the sine and cosine terms are raised to arbitrary powers. Namely, the generic point P(u, v) of the surface is given by P ( u , v ) = ( X ( u , v ) Y ( u , v ) Z ( u , v ) ) = ( ( a + C u s ) C v t ( b + C u s ) S v t S u s ) {\displaystyle P(u,v)=\left({\begin{array}{c}X(u,v)\\Y(u,v)\\Z(u,v)\end{array}}\right)=\left({\begin{array}{c}(a+C_{u}^{s})C_{v}^{t}\\(b+C_{u}^{s})S_{v}^{t}\\S_{u}^{s}\end{array}}\right)} where C θ ε = sgn ( cos θ ) | cos θ | ε , S θ ε = sgn ( sin θ ) | sin θ | ε , {\displaystyle {\begin{aligned}C_{\theta }^{\varepsilon }&=\operatorname {sgn} (\cos \theta )\,\left|\,\cos \theta \,\right|^{\varepsilon },\\S_{\theta }^{\varepsilon }&=\operatorname {sgn} (\sin \theta )\ \left|\,\sin \theta \ \right|^{\varepsilon },\end{aligned}}} sgn is the sign function, and the parameters u, v range from 0 to 360 degrees (0 to 2π radians). In these formulas, the parameter s > 0 controls the "squareness" of the vertical sections, t > 0 controls the squareness of the horizontal sections, and a, b ≥ 1 are the major radii in the x and y directions. With s = t = 1 and a = b = R one obtains the ordinary torus with major radius R and minor radius 1, with the center at the origin and rotational symmetry about the z-axis. In general, the supertorus defined as above spans the intervals: − ( a + 1 ) ≤ x ≤ + ( a + 1 ) − ( b + 1 ) ≤ y ≤ + ( b + 1 ) − 1 ≤ z ≤ + 1 {\displaystyle {\begin{array}{rcccl}-(a+1)&\leq &x&\leq &+(a+1)\\[4pt]-(b+1)&\leq &y&\leq &+(b+1)\\[4pt]-1&\leq &z&\leq &+1\end{array}}} The whole shape is symmetric about the planes x = 0, y = 0, and z = 0. The hole runs in the z direction and spans the intervals − ( a − 1 ) ≤ x ≤ + ( a − 1 ) − ( b − 1 ) ≤ y ≤ + ( b − 1 ) − ∞ ≤ z ≤ + ∞ {\displaystyle {\begin{array}{rcccl}-(a-1)&\leq &x&\leq &+(a-1)\\[4pt]-(b-1)&\leq &y&\leq &+(b-1)\\[4pt]-\infty &\leq &z&\leq &+\infty \end{array}}} A curve of constant u on this surface is a horizontal Lamé curve with exponent 2 t , {\displaystyle {\tfrac {2}{t}},} scaled in x and y and displaced in z. A curve of constant v, projected on the plane x = 0 or y = 0, is a Lamé curve with exponent 2 s , {\displaystyle {\tfrac {2}{s}},} scaled and horizontally shifted. If v = 0, the curve is planar and spans the intervals: a − 1 ≤ x ≤ a + 1 − 1 ≤ z ≤ + 1 {\displaystyle {\begin{array}{rcccl}a-1&\leq &x&\leq &a+1\\[4pt]-1&\leq &z&\leq &+1\end{array}}} and similarly if v = 90°, 180°, 270°. The curve is also planar if a = b. In general, if a ≠ b and v is not a multiple of 90 degrees, the curve of constant v will not be planar; and, conversely, a vertical plane section of the supertorus will not be a Lamé curve. The basic supertoroid shape defined above is often modified by non-uniform scaling to yield supertoroids of specific width, length, and vertical thickness. == Plotting code == The following GNU Octave code generates plots of a supertorus: