In mathematics and machine learning, the softplus function is f ( x ) = ln ( 1 + e x ) . {\displaystyle f(x)=\ln(1+e^{x}).} It is a smooth approximation (in fact, an analytic function) to the ramp function, which is known as the rectifier or ReLU (rectified linear unit) in machine learning. For large negative x {\displaystyle x} it is ln ( 1 + e x ) = ln ( 1 + ϵ ) ⪆ ln 1 = 0 {\displaystyle \ln(1+e^{x})=\ln(1+\epsilon )\gtrapprox \ln 1=0} , so just above 0, while for large positive x {\displaystyle x} it is ln ( 1 + e x ) ⪆ ln ( e x ) = x {\displaystyle \ln(1+e^{x})\gtrapprox \ln(e^{x})=x} , so just above x {\displaystyle x} . The names softplus and SmoothReLU are used in machine learning. The name "softplus" (2000), by analogy with the earlier softmax (1989) is presumably because it is a smooth (soft) approximation of the positive part of x, which is sometimes denoted with a superscript plus, x + := max ( 0 , x ) {\displaystyle x^{+}:=\max(0,x)} . == Alternative forms == This function can be approximated as: ln ( 1 + e x ) ≈ { ln 2 , x = 0 , x 1 − e − x / ln 2 , x ≠ 0 {\displaystyle \ln \left(1+e^{x}\right)\approx {\begin{cases}\ln 2,&x=0,\\[6pt]{\frac {x}{1-e^{-x/\ln 2}}},&x\neq 0\end{cases}}} By making the change of variables x = y ln ( 2 ) {\displaystyle x=y\ln(2)} , this is equivalent to log 2 ( 1 + 2 y ) ≈ { 1 , y = 0 , y 1 − e − y , y ≠ 0. {\displaystyle \log _{2}(1+2^{y})\approx {\begin{cases}1,&y=0,\\[6pt]{\frac {y}{1-e^{-y}}},&y\neq 0.\end{cases}}} A sharpness parameter k {\displaystyle k} may be included: f ( x ) = ln ( 1 + e k x ) k , f ′ ( x ) = e k x 1 + e k x = 1 1 + e − k x . {\displaystyle f(x)={\frac {\ln(1+e^{kx})}{k}},\qquad \qquad f'(x)={\frac {e^{kx}}{1+e^{kx}}}={\frac {1}{1+e^{-kx}}}.} Additionally, the softplus function is equivalent to the log of the sigmoid function in the following way: − ln ( sigmoid ( − x ) ) = − ln ( 1 1 + e x ) = ln ( 1 + e x ) = softplus ( x ) {\displaystyle -\ln({\text{sigmoid}}(-x))=-\ln \left({\frac {1}{1+e^{x}}}\right)=\ln \left(1+e^{x}\right)={\text{softplus}}(x)} == Related functions == The derivative of softplus is the standard logistic function: f ′ ( x ) = e x 1 + e x = 1 1 + e − x {\displaystyle f'(x)={\frac {e^{x}}{1+e^{x}}}={\frac {1}{1+e^{-x}}}} The logistic function or the sigmoid function is a smooth approximation of the rectifier, the Heaviside step function. === LogSumExp === The multivariable generalization of single-variable softplus is the LogSumExp with the first argument set to zero: L S E 0 + ( x 1 , … , x n ) := LSE ( 0 , x 1 , … , x n ) = ln ( 1 + e x 1 + ⋯ + e x n ) . {\displaystyle \operatorname {LSE_{0}} ^{+}(x_{1},\dots ,x_{n}):=\operatorname {LSE} (0,x_{1},\dots ,x_{n})=\ln(1+e^{x_{1}}+\cdots +e^{x_{n}}).} The LogSumExp function is LSE ( x 1 , … , x n ) = ln ( e x 1 + ⋯ + e x n ) , {\displaystyle \operatorname {LSE} (x_{1},\dots ,x_{n})=\ln(e^{x_{1}}+\cdots +e^{x_{n}}),} and its gradient is the softmax; the softmax with the first argument set to zero is the multivariable generalization of the logistic function. Both LogSumExp and softmax are used in machine learning. === Convex conjugate === The convex conjugate (specifically, the Legendre transformation) of the softplus function is the negative binary entropy function (with base e). This is because (following the definition of the Legendre transformation: the derivatives are inverse functions) the derivative of softplus is the logistic function, whose inverse function is the logit, which is the derivative of negative binary entropy. Softplus can be interpreted as logistic loss (as a positive number), so, by duality, minimizing logistic loss corresponds to maximizing entropy. This justifies the principle of maximum entropy as loss minimization.
Digital Michelangelo Project
The Digital Michelangelo Project was a pioneering initiative undertaken during the 1998–1999 academic year to digitize the sculptures and architecture of Michelangelo using advanced laser scanning technology. The project was led by a team of 30 faculty, staff, and students from Stanford University and the University of Washington, with the aim of creating high-resolution 3D models of Michelangelo's works for scholarly, educational, and preservation purposes. == Objectives == The primary goals of the Digital Michelangelo Project were: To apply recent advancements in laser rangefinder technology for digitizing large cultural artifacts. To create detailed digital archives of Michelangelo's sculptures and architectural spaces for future study and analysis. To explore potential educational and curatorial applications for 3D scanned data. === Artworks digitized === The project involved scanning several iconic works by Michelangelo, including: David The Unfinished Slaves (Atlas, Awakening, Bearded, and Youthful) St. Matthew The allegorical statues from the Medici tombs (Night, Day, Dawn, and Dusk) The architectural interiors of the Tribuna del David at the Galleria dell'Accademia and the New Sacristy in the Medici Chapels. == Technology and methodology == === 3D scanning === The project's primary scanner was a laser triangulation rangefinder mounted on a motorized gantry, custom-built by Cyberware Inc. The scanner used a laser sheet to project onto an object, capturing its shape through triangulation. Multiple scans were taken from various angles and combined into a single, detailed 3D mesh. The resolution achieved was fine enough to capture even Michelangelo's chisel marks, with triangles approximately 0.25 mm on each side. In addition to shape data, color data was captured using a spotlight and a secondary camera, enabling the creation of textured 3D models. === Data processing === The project developed a software suite for processing the scanned data. This included: Aligning and merging multiple scans into a seamless 3D model. Filling holes in the geometry caused by inaccessible areas. Correcting color data for lighting inconsistencies and shadowing. Non-photorealistic rendering techniques were also applied, highlighting surface features such as Michelangelo’s chisel marks for enhanced visualization. == Logistical challenges == The scale and complexity of the project presented several challenges: Data size: The dataset for David alone comprised 2 billion polygons and 7,000 color images, occupying 60 GB of storage. Artifact safety: Ensuring the safety of the statues during scanning required extensive crew training, foam-encased equipment, and collision-prevention mechanisms. == Applications and impact == The digitized models have numerous potential applications: Art history: Allowing precise measurements and geometric analysis, such as determining chisel types or evaluating structural balance. Education: Providing new ways to study art, including interactive viewing from unconventional angles and with custom lighting. Museum curation: Enhancing visitor experiences through interactive kiosks and virtual models. The project demonstrated the potential for 3D technology to preserve and disseminate cultural heritage. == Data distribution == The project's models are available through Stanford University for scholarly purposes, under strict licensing due to Italian intellectual property laws. === ScanView === To provide public access to the 3D models while respecting usage restrictions, the project developed ScanView, a client/server rendering system. ScanView allows users to view and interact with high-resolution 3D models without downloading the data. The client component consists of a freely available viewer program and simplified 3D models. Users can navigate these models locally, adjusting position, orientation, lighting, and surface appearance. When a user finalizes a view, the client queries a remote server for a high-resolution rendering of the model, which is sent back to overwrite the simplified version on the user’s screen. A typical query-response cycle takes 1–2 seconds, depending on network conditions. To protect the models from unauthorized reconstruction, the system employs several security measures, including: Encrypting queries Perturbing viewpoint and lighting parameters Adding noise and warping rendered images Compressing images before transmission ScanView operates on Windows-based PCs and provides access to selected models, including David and St. Matthew, as well as other artifacts such as fragments of the Forma Urbis Romae and items from the Stanford 3D Scanning Repository. == Sponsors == The Digital Michelangelo Project was supported by Stanford University, Interval Research Corporation, and the Paul G. Allen Foundation for the Arts.
New media
New media are communication technologies that enable or enhance interaction between users, as well as interaction between users and content. In the middle of the 1990s, the phrase "new media" became widely used as part of a sales pitch for the influx of interactive CD-ROMs for entertainment and education. The new media technologies, sometimes known as Web 2.0, include a wide range of web-related communication tools such as blogs, wikis, online social networking, virtual worlds, and other social media platforms. The phrase "new media" refers to computational media that share material online and through computers. New media inspire new ways of thinking about older media. Media do not replace one another in a clear, linear succession, instead evolving in a more complicated network of interconnected feedback loops . What is different about new media is how they specifically refashion traditional media and how older media refashion themselves to meet the challenges of new media. Unless they contain technologies that enable digital generative or interactive processes, broadcast television programs, non-interactive news websites, feature films, magazines, and books are not considered to be new media. The term "new media" stands in contrast to old media, which dominated the media landscape as a form of mass media for many years. == History == In the 1950s, connections between computing and radical art began to grow stronger. It was not until the 1980s that Alan Kay and his co-workers at Xerox PARC began to give the computability of a personal computer to the individual, rather than have a big organization be in charge of this. In the late 1980s and early 1990s, however, we seem to witness a different kind of parallel relationship between social changes and computer design. Although causally unrelated, conceptually, it makes sense that the Cold War and the design of the Web took place at exactly the same time. Writers and philosophers such as Marshall McLuhan were instrumental in the development of media theory during this period which is now famous declaration in Understanding Media: The Extensions of Man, that "the medium is the message" drew attention to the too often ignored influence media and technology themselves, rather than their "content," have on humans' experience of the world and on society broadly. Until the 1980s, media relied primarily upon print and analog broadcast models such as television and radio. The last twenty-five years have seen the rapid transformation into media which are predicated upon the use of digital technologies such as the Internet and video games. However, these examples are only a small representation of new media. The use of digital computers has transformed the remaining 'old' media, as suggested by the advent of digital television and online publications. Even traditional media forms such as the printing press have been transformed through the application of technologies by using of image manipulation software like Adobe Photoshop and desktop publishing tools. Andrew L. Shapiro argues that the "emergence of new, digital technologies signals a potentially radical shift of who is in control of information, experience and resources". W. Russell Neuman suggests that whilst the "new media" have technical capabilities to pull in one direction, economic and social forces pull back in the opposite direction. According to Neuman, "We are witnessing the evolution of a universal interconnected network of audio, video, and electronic text communications that will blur the distinction between interpersonal and mass communication; and between public and private communication". Neuman argues that new media will: Alter the meaning of geographic distance. Allow for a huge increase in the volume of communication. Provide the possibility of increasing the speed of communication. Provide opportunities for interactive communication. Allow forms of communication that were previously separate to overlap and interconnect. Consequently, it has been the contention of scholars such as Douglas Kellner and James Bohman that new media and particularly the Internet will provide the potential for a democratic postmodern public sphere, in which citizens can participate in well informed, non-hierarchical debate pertaining to their social structures. Contradicting these positive appraisals of the potential social impacts of new media are scholars such as Edward S. Herman and Robert McChesney who have suggested that the transition to new media has seen a handful of powerful transnational telecommunications corporations who achieve a level of global influence which was hitherto unimaginable. Scholars have highlighted both the positive and negative potential and actual implications of new media technologies, suggesting that some of the early work in new media studies was guilty of technologicaldeterminism – whereby the effects of media were determined by the technologies themselves, rather than by tracing the complex social networks that governed the development, funding, implementation, and future evolution of any technology. Based on the argument that people have a limited amount of time to spend on the consumption of different media, displacement theory argue that the viewership or readership of one particular outlet leads to the reduction in the amount of time spent by the individual on another. The introduction of new media, such as the internet, therefore reduces the amount of time individuals would spend on existing "old" media, which could ultimately lead to the end of such traditional media. == Definition == Although, there are several ways that new media may be described, Lev Manovich, in an introduction to The New Media Reader, defines new media by using eight propositions: New media versus cyberculture – Cyberculture is the various social phenomena that are associated with the Internet and network communications (blogs, online multi-player gaming), whereas new media is concerned more with cultural objects and paradigms (digital to analog television, smartphones). New media as computer technology used as a distribution platform – New media are the cultural objects which use digital computer technology for distribution and exhibition. e.g. (at least for now) Internet, Web sites, computer multimedia, Blu-ray disks etc. The problem with this is that the definition must be revised every few years. The term "new media" will not be "new" anymore, as most forms of culture will be distributed through computers. New media as digital data controlled by software – The language of new media is based on the assumption that, in fact, all cultural objects that rely on digital representation and computer-based delivery do share a number of common qualities. New media is reduced to digital data that can be manipulated by software as any other data. Now media operations can create several versions of the same object. An example is an image stored as matrix data which can be manipulated and altered according to the additional algorithms implemented, such as color inversion, gray-scaling, sharpening, rasterizing, etc. New media as the mix between existing cultural conventions and the conventions of software – New media today can be understood as the mix between older cultural conventions for data representation, access, and manipulation and newer conventions of data representation, access, and manipulation. The "old" data are representations of visual reality and human experience, and the "new" data is numerical data. The computer is kept out of the key "creative" decisions, and is delegated to the position of a technician. e.g. In film, software is used in some areas of production, in others are created using computer animation. New media as the aesthetics that accompanies the early stage of every new modern media and communication technology – While ideological tropes indeed seem to be reappearing rather regularly, many aesthetic strategies may reappear two or three times ... In order for this approach to be truly useful it would be insufficient to simply name the strategies and tropes and to record the moments of their appearance; instead, we would have to develop a much more comprehensive analysis which would correlate the history of technology with social, political, and economical histories or the modern period. New media as faster execution of algorithms previously executed manually or through other technologies – Computers are a huge speed-up of what were previously manual techniques. e.g. calculators. Dramatically speeding up the execution makes possible previously non-existent representational technique. This also makes possible of many new forms of media art such as interactive multimedia and video games. On one level, a modern digital computer is just a faster calculator, we should not ignore its other identity: that of a cybernetic control device. New media as the encoding of modernist avant-garde; new media as metamedia – Manovi
Brand networking
Brand networking is the engagement of a social networking service around a brand by providing consumers with a platform of relevant content, elements of participation, and a currency, score, or ranking. Brand networking creates communities that serve as interactive destinations to encourage brand participation online and off. This evolved level of user participation with the brand facilitates strong relationships with consumers, leverages sales, and generates fan equity. The concept builds on the marketing literature on brand communities, which describes specialized, non-geographically bound groups of consumers organized around shared interest in a brand, and on subsequent research on social-media-based brand communities that examines how such groups operate when embedded in general-purpose networking platforms. == History == The development and growth of social networking in the early 2000s gave birth to brand networking. Brands saw the immediate potential to reach and interact with consumers through online platforms like Facebook and MySpace. At first, the ability to reach consumers through these platforms was inadequate; brands had the option to join as members or simply advertise on these sites. The potential existed to not only display advertisements to consumers, but to encourage them to interact with the brand. This is when brands made the shift to create their own networking platforms. Less evolved attempts to connect brands with consumers via networking are typically built as online platforms meant only to complement a product/service and are limited in functionality. Typically these sites offer consumers the opportunity to interact through discussion boards and group pages. The Guiding Light Community was built to complement the popular CBS television soap opera. The site offers members reward points for contributing content to discussion boards and blogs (which is all geared toward the show). == Structure == Brand networking is more than the utilization of a social networking platform; it is connecting consumers together and constructing relationships directly with the brand. Three key elements, in unity, create effective brand networking: relevant content, elements of participation, and a competitive currency. Websites in conjunction with other media types (television, radio, print) present content around a vertical industry, sector of interest, or cultural and social issues for a brand. This can be in areas such as health, marketing, or business, or any content relevant to the brand message. Such content is not only provided by the brand but also in the form of consumer-generated media. Research on brand-related user-generated content across major platforms suggests that the form and tone of consumer contributions vary by platform, with promotional content more common on some networks and response-oriented content on others. A brand provides participation with consumers online and offline. This is accomplished through the combination of typical social networking features online, such as personalised pages, friend lists, groups, and messaging, alongside elements of involvement offline. This is not simply connecting an online platform with mobile devices, but providing separate mobile features jointly with a secondary media type to drive online usage and build relationships with the brand on the go. By participating in mobile campaigns, users are interacting with the brand outside of traditional brick and mortar or e-commerce destinations. Empirical work on consumer brand engagement in social media frames such participation along cognitive, affective, and behavioural dimensions. The final element of brand networking involves incentivising participation with the other two elements. The addition of a currency or point system acts as an anchor to the brand and network and creates a competitive dynamic between consumers. These points are distributed for activity carried out outside of the networking site. By incentivising usage offline, the brand image is reinforced for the consumer and strengthens the relationship. Consumers are turned into promoters for both the brand and the users' benefit. The use of points, badges, leaderboards, and similar mechanics is described in the marketing literature as gamification, and has been linked to higher participation rates in mobile and loyalty programmes. == Fan equity == Fan equity is the idea that by locking in consumers to a brand, they are turned into fans of the brand. As fans, they promote, interact, and consume on a daily basis and become assets. Apple Inc. is one example of a company often cited as possessing fan equity. Customers of Apple are extremely brand loyal and are assets to the company. Creating a fan-generated brand is a difficult but effective method of business. Through the use of brand networking, a company is able to build a consumer or fan base that provides a strong relationship between business and consumers. The trust is formed and fans do a lot of work for the brand by word of mouth. Peer-to-peer channels are the strongest means of communication for a brand, but also one in which the brand can only influence and not control. Subsequent research links community engagement with brand trust, identifying community engagement as a mediator between social-media brand community participation and trust. This method of business is argued to be a relationship handled by the brand generally for its own gain. Many fans do not realise the work they are doing for companies by using their product or service. Facebook is a fan-based brand that has become a global phenomenon through customer use, with social media features such as sharing and commenting. With the growth of social media, marketing and advertising through social media has continued to expand. Brands can display and promote their products or services at a fast rate, with consumers sharing and contributing to the brand on a global scale. This can also be seen as online word of mouth exposure that can produce positive or negative feedback for brands. Once consumers become fans they are typically loyal, which can create positive word of mouth for a brand. Fans become a valuable asset, boosting the status and reputation of a brand. Different perceptions of brands can be linked to a person's origin or religion, which creates a difficulty when trying to enter a market or gain market share. Businesses need to be aware of the types of products or services they introduce to a specific market, ensuring they are culturally sensitive. Fan pages are created on social media to maintain the relationship between brands and consumers. By engaging and interacting with consumers, brands obtain fans and produce positive imaging. Some fans become attached to brands and are often encouraged to remain as fans through the use of celebrities endorsing the brand. Research on parasocial interaction in social-media environments suggests that one-sided emotional bonds that consumers form with endorsers and brand personae help convert ordinary followers into engaged fans.
Microelectronics
Microelectronics is a subfield of electronics. As the name suggests, microelectronics relates to the study and manufacture (or microfabrication) of very small electronic designs and components. Usually, but not always, this means micrometre-scale or smaller. These devices are typically made from semiconductor materials. Many components of a normal electronic design are available in a microelectronic equivalent. These include transistors, capacitors, inductors, resistors, diodes and (naturally) insulators and conductors can all be found in microelectronic devices. Unique wiring techniques such as wire bonding are also often used in microelectronics because of the unusually small size of the components, leads and pads. This technique requires specialized equipment and is expensive. Digital integrated circuits (ICs) consist of billions of transistors, resistors, diodes, and capacitors. Analog circuits commonly contain resistors and capacitors as well. Inductors are used in some high frequency analog circuits, but tend to occupy larger chip area due to their lower reactance at low frequencies. Gyrators can replace them in many applications. As techniques have improved, the scale of microelectronic components has continued to decrease. At smaller scales, the relative impact of intrinsic circuit properties, such as unintended interactions between components or their parts, may become more significant. These are called parasitic effects, and the goal of the microelectronics design engineer is to find ways to compensate for or to minimize these effects, while delivering smaller, faster, and cheaper devices. Today, microelectronics design is largely aided by electronic design automation (EDA) software.
Deblurring
Deblurring is the process of removing blurring artifacts from images. Deblurring recovers a sharp image S from a blurred image B, where S is convolved with K (the blur kernel) to generate B. Mathematically, this can be represented as B = S ∗ K {\displaystyle B=SK} (where represents convolution). While this process is sometimes known as unblurring, deblurring is the correct technical word. The blur K is typically modeled as point spread function and is convolved with a hypothetical sharp image S to get B, where both the S (which is to be recovered) and the point spread function K are unknown. This is an example of an inverse problem. In almost all cases, there is insufficient information in the blurred image to uniquely determine a plausible original image, making it an ill-posed problem. In addition the blurred image contains additional noise which complicates the task of determining the original image. This is generally solved by the use of a regularization term to attempt to eliminate implausible solutions. This problem is analogous to echo removal in the signal processing domain. Nevertheless, when coherent beam is used for imaging, the point spread function can be modeled mathematically. By proper deconvolution of the point spread function K and the blurred image B, the blurred image B can be deblurred (unblur) and the sharp image S can be recovered.
DBOS
DBOS (Formerly Database-Oriented Operating System, now just DBOS) is an open source durable workflow execution software library written for the Python, TypeScript, Java, and Go programming languages. DBOS arose from a joint open source project from MIT and Stanford, after a discussion between Michael Stonebraker and Matei Zaharia on how to scale and improve scheduling and performance of millions of Apache Spark tasks. Today it is a commercial company that offers an open source system to add durable computing to any software, built on concepts derived from the joint research project. == History == === 2020: Academic R&D Project === DBOS originated in 2020 as a joint open source project between MIT, Stanford, and Carnegie Mellon. The project explored the idea of operating system services built atop a distributed database - a database-oriented operating system meant to simplify and improve the scalability, security and resilience of large-scale distributed applications. The basic concept was to run a multi-node multi-core, transactional, highly-available distributed database, such as VoltDB, as the only application for a microkernel, and then to implement scheduling, messaging, file systems and other operating system services on top of the database. The architectural philosophy is described by this quote from the abstract of their initial preprint: All operating system state should be represented uniformly as database tables, and operations on this state should be made via queries from otherwise stateless tasks. This design makes it easy to scale and evolve the OS without whole-system refactoring, inspect and debug system state, upgrade components without downtime, manage decisions using machine learning, and implement sophisticated security features. A prototype was built with competitive performance to existing systems. ==