Uniform convergence in probability is a form of convergence in probability in statistical asymptotic theory and probability theory. It means that, under certain conditions, the empirical frequencies of all events in a certain event-family uniformly converge to their theoretical probabilities. Uniform convergence in probability has applications to statistics as well as machine learning as part of statistical learning theory. Specifically, the Glivenko-Cantelli theorem and the homonymous classes of functions are fundamentally related to uniform convergence. The law of large numbers says that, for each single event A {\displaystyle A} , its empirical frequency in a sequence of independent trials converges (with high probability) to its theoretical probability. In many application however, the need arises to judge simultaneously the probabilities of events of an entire class S {\displaystyle S} from one and the same sample. Moreover, it, is required that the relative frequency of the events converge to the probability uniformly over the entire class of events S {\displaystyle S} . The Uniform Convergence Theorem gives a sufficient condition for this convergence to hold. Roughly, if the event-family is sufficiently simple (its VC dimension is sufficiently small) then uniform convergence holds. == Definitions == For a class of predicates H {\displaystyle H} defined on a set X {\displaystyle X} and a set of samples x = ( x 1 , x 2 , … , x m ) {\displaystyle x=(x_{1},x_{2},\dots ,x_{m})} , where x i ∈ X {\displaystyle x_{i}\in X} , the empirical frequency of h ∈ H {\displaystyle h\in H} on x {\displaystyle x} is Q ^ x ( h ) = 1 m | { i : 1 ≤ i ≤ m , h ( x i ) = 1 } | . {\displaystyle {\widehat {Q}}_{x}(h)={\frac {1}{m}}|\{i:1\leq i\leq m,h(x_{i})=1\}|.} The theoretical probability of h ∈ H {\displaystyle h\in H} is defined as Q P ( h ) = P { y ∈ X : h ( y ) = 1 } . {\displaystyle Q_{P}(h)=P\{y\in X:h(y)=1\}.} The Uniform Convergence Theorem states, roughly, that if H {\displaystyle H} is "simple" and we draw samples independently (with replacement) from X {\displaystyle X} according to any distribution P {\displaystyle P} , then with high probability, the empirical frequency will be close to its expected value, which is the theoretical probability. Here "simple" means that the Vapnik–Chervonenkis dimension of the class H {\displaystyle H} is small relative to the size of the sample. In other words, a sufficiently simple collection of functions behaves roughly the same on a small random sample as it does on the distribution as a whole. The Uniform Convergence Theorem was first proved by Vapnik and Chervonenkis using the concept of growth function. == Uniform Convergence Theorem == The statement of the Uniform Convergence Theorem is as follows: If H {\displaystyle H} is a set of { 0 , 1 } {\displaystyle \{0,1\}} -valued functions defined on a set X {\displaystyle X} and P {\displaystyle P} is a probability distribution on X {\displaystyle X} then for ε > 0 {\displaystyle \varepsilon >0} and m {\displaystyle m} a positive integer, we have: P m { | Q P ( h ) − Q x ^ ( h ) | ≥ ε for some h ∈ H } ≤ 4 Π H ( 2 m ) e − ε 2 m / 8 . {\displaystyle P^{m}\{|Q_{P}(h)-{\widehat {Q_{x}}}(h)|\geq \varepsilon {\text{ for some }}h\in H\}\leq 4\Pi _{H}(2m)e^{-\varepsilon ^{2}m/8}.} In the above, for any x ∈ X m , {\displaystyle x\in X^{m},} Q P ( h ) = P { ( y ∈ X : h ( y ) = 1 } , {\displaystyle Q_{P}(h)=P\{(y\in X:h(y)=1\},} Q ^ x ( h ) = 1 m | { i : 1 ≤ i ≤ m , h ( x i ) = 1 } | {\displaystyle {\widehat {Q}}_{x}(h)={\frac {1}{m}}|\{i:1\leq i\leq m,h(x_{i})=1\}|} and | x | = m . {\displaystyle |x|=m.} P m {\displaystyle P^{m}} indicates that the probability is taken over x {\displaystyle x} consisting of m {\displaystyle m} i.i.d. draws from the distribution P . {\displaystyle P.} Finally, the growth function Π H {\displaystyle \Pi _{H}} is defined in the following way, for any { 0 , 1 } {\displaystyle \{0,1\}} -valued functions H {\displaystyle H} over X {\displaystyle X} and for any natural number m {\displaystyle m} : Π H ( m ) = max | { h ∩ D : D ⊆ X , | D | = m , h ∈ H } | . {\displaystyle \Pi _{H}(m)=\max |\{h\cap D:D\subseteq X,|D|=m,h\in H\}|.} From the point of view of Learning Theory one can consider H {\displaystyle H} to be the Concept/Hypothesis class defined over the instance set X {\displaystyle X} . Crucially, the Sauer–Shelah lemma implies that Π H ( m ) ≤ m d {\displaystyle \Pi _{H}(m)\leq m^{d}} , where d {\displaystyle d} is the VC dimension of H {\displaystyle H} . == Proof of the Uniform Convergence Theorem == and are the sources of the proof below. Before we get into the details of the proof of the Uniform Convergence Theorem we will present a high level overview of the proof. Symmetrization: We transform the problem of analyzing | Q P ( h ) − Q ^ x ( h ) | ≥ ε {\displaystyle |Q_{P}(h)-{\widehat {Q}}_{x}(h)|\geq \varepsilon } into the problem of analyzing | Q ^ r ( h ) − Q ^ s ( h ) | ≥ ε / 2 {\displaystyle |{\widehat {Q}}_{r}(h)-{\widehat {Q}}_{s}(h)|\geq \varepsilon /2} , where r {\displaystyle r} and s {\displaystyle s} are i.i.d samples of size m {\displaystyle m} drawn according to the distribution P {\displaystyle P} . One can view r {\displaystyle r} as the original randomly drawn sample of length m {\displaystyle m} , while s {\displaystyle s} may be thought as the testing sample which is used to estimate Q P ( h ) {\displaystyle Q_{P}(h)} . Permutation: Since r {\displaystyle r} and s {\displaystyle s} are picked identically and independently, so swapping elements between them will not change the probability distribution on r {\displaystyle r} and s {\displaystyle s} . So, we will try to bound the probability of | Q ^ r ( h ) − Q ^ s ( h ) | ≥ ε / 2 {\displaystyle |{\widehat {Q}}_{r}(h)-{\widehat {Q}}_{s}(h)|\geq \varepsilon /2} for some h ∈ H {\displaystyle h\in H} by considering the effect of a specific collection of permutations of the joint sample x = r | | s {\displaystyle x=r||s} . Specifically, we consider permutations σ ( x ) {\displaystyle \sigma (x)} which swap x i {\displaystyle x_{i}} and x m + i {\displaystyle x_{m+i}} in some subset of 1 , 2 , . . . , m {\displaystyle {1,2,...,m}} . The symbol r | | s {\displaystyle r||s} means the concatenation of r {\displaystyle r} and s {\displaystyle s} . Reduction to a finite class: We can now restrict the function class H {\displaystyle H} to a fixed joint sample and hence, if H {\displaystyle H} has finite VC Dimension, it reduces to the problem to one involving a finite function class. We present the technical details of the proof. It should be stressed that this proof glosses over details like the measurability of the events V {\displaystyle V} and R {\displaystyle R} ; measurability is granted in the case of H {\displaystyle H} being finite or countable, but this is not normally the case in standard applications of the theorem (e.g. for statistical learning theory or to prove the Glivenko-Cantelli theorem). To get measurability, one needs to use a notion of separability of the underlying space, possibly related to H {\displaystyle H} . === Symmetrization === Lemma: Let V = { x ∈ X m : | Q P ( h ) − Q ^ x ( h ) | ≥ ε for some h ∈ H } {\displaystyle V=\{x\in X^{m}:|Q_{P}(h)-{\widehat {Q}}_{x}(h)|\geq \varepsilon {\text{ for some }}h\in H\}} and R = { ( r , s ) ∈ X m × X m : | Q r ^ ( h ) − Q ^ s ( h ) | ≥ ε / 2 for some h ∈ H } . {\displaystyle R=\{(r,s)\in X^{m}\times X^{m}:|{\widehat {Q_{r}}}(h)-{\widehat {Q}}_{s}(h)|\geq \varepsilon /2{\text{ for some }}h\in H\}.} Then for m ≥ 2 ε 2 {\displaystyle m\geq {\frac {2}{\varepsilon ^{2}}}} , P m ( V ) ≤ 2 P 2 m ( R ) {\displaystyle P^{m}(V)\leq 2P^{2m}(R)} . Proof: By the triangle inequality, if | Q P ( h ) − Q ^ r ( h ) | ≥ ε {\displaystyle |Q_{P}(h)-{\widehat {Q}}_{r}(h)|\geq \varepsilon } and | Q P ( h ) − Q ^ s ( h ) | ≤ ε / 2 {\displaystyle |Q_{P}(h)-{\widehat {Q}}_{s}(h)|\leq \varepsilon /2} then | Q ^ r ( h ) − Q ^ s ( h ) | ≥ ε / 2 {\displaystyle |{\widehat {Q}}_{r}(h)-{\widehat {Q}}_{s}(h)|\geq \varepsilon /2} . Therefore, P 2 m ( R ) ≥ P 2 m { ∃ h ∈ H , | Q P ( h ) − Q ^ r ( h ) | ≥ ε and | Q P ( h ) − Q ^ s ( h ) | ≤ ε / 2 } = ∫ V P m { s : ∃ h ∈ H , | Q P ( h ) − Q ^ r ( h ) | ≥ ε and | Q P ( h ) − Q ^ s ( h ) | ≤ ε / 2 } d P m ( r ) = A {\displaystyle {\begin{aligned}&P^{2m}(R)\\[5pt]\geq {}&P^{2m}\{\exists h\in H,|Q_{P}(h)-{\widehat {Q}}_{r}(h)|\geq \varepsilon {\text{ and }}|Q_{P}(h)-{\widehat {Q}}_{s}(h)|\leq \varepsilon /2\}\\[5pt]={}&\int _{V}P^{m}\{s:\exists h\in H,|Q_{P}(h)-{\widehat {Q}}_{r}(h)|\geq \varepsilon {\text{ and }}|Q_{P}(h)-{\widehat {Q}}_{s}(h)|\leq \varepsilon /2\}\,dP^{m}(r)\\[5pt]={}&A\end{aligned}}} since r {\displaystyle r} and s {\displaystyle s} are independent. Now for r ∈ V {\displaystyle r\in V} fix an h ∈ H {\displaystyle h\in H} such that | Q P ( h ) − Q ^ r ( h ) | ≥ ε {\displaystyle |Q_{P}(h)-{\widehat {Q}}_{r}(h)|\geq \varepsilon } . For this h {\displaystyle h} , we shall
ActivTrak
ActivTrak is an American company that produces workforce analytics and productivity software. The company was founded in 2009 by Birch Grove Software and is headquartered in Austin, Texas. The company has raised US$77.5 million in funding and is backed by Sapphire Ventures and Elsewhere Partners. == History == ActivTrak was founded in 2009 by Herb Axilrod and Anton Seidler in Dallas, Texas. ActivTrak's first on-demand software product launched in 2012, and the workforce analytics platform launched in 2015. It uses data sourced from more than 9,500 customers and 900,000 users. In 2019, ActivTrak raised $20 million in a Series A round of funding with Elsewhere Partners, a growth-stage venture capital firm that principally invests in B2B startups. Rita Selvaggi assumed the role of CEO. In 2020, ActivTrak raised $50M in a Series B round of funding with Sapphire Ventures and Elsewhere Partners. The company also introduced the ActivTrak Productivity Lab, an online resource about workforce productivity research, industry benchmark data, and best practices. == Product == ActivTrak is a workforce analytics and productivity platform that uses reports, dashboards, and data analysis. The platform uses machine learning (AI) to collect and analyze user activity data and produce reports about workforce productivity. The software runs on Microsoft Windows, Mac, Chrome, Terminal Services, and VDI. It includes the ActivTrak Agent, which runs in the background and collects data. It responds to user activity, sensing mouse and keyboard movement in the active window(s) of the user's device. This data is collected and stored in a database that aggregates the data based on the user's request. ActivTrak does not utilize keystroke logging, content scraping, camera access, video recording or mobile device monitoring. The database leverages data analytics to generate account and team benchmarks, and identify productivity patterns and outliers. == Awards == Built In, 100 Best Midsize Places to Work in Austin, 2025 G2, Winter: Best Estimated ROI, High Performer, Best Relationship, Best Support, Users Most Likely to Recommend, Easiest Setup, Easiest Admin, Best Meets Requirements, Users Love Us, 2025 TrustRadius, Buyer’s Choice, 2025 Deloitte Technology Fast 500, No. 468 Fastest-Growing Company, 2024 Product Marketing Alliance, AI Marketing Innovation, 2024 Fortune Best Workplaces in Technology™, 2024 Inc. 5000, No. 2335 of America’s Fastest-Growing Private Companies, 2024 Fortune Best Workplaces in Texas™, 2024 Reworked IMPACT Gold Award: Most Innovative Workplace Productivity Solution, 2024 TrustRadius, Most Loved, 2024 Great Place To Work-Certified™, 2024 Inc. 5000 Regionals: Southwest, 2024 Brandon Hall Group, Best Advance in HR Predictive Analytics Technology, 2024
Electronics (journal)
Electronics is a peer-reviewed, scientific journal that covers the study of electronics, including the design, development, and application of electronic devices, systems, and circuits. The journal is published by MDPI and was established in 2012. The editor-in-chief is Flavio Canavero 'Politecnico di Torino). The journal covers a wide range of topics related to electronics, including: electronic devices, electronic materials, electronic circuits, electronic systems, communication electronics, power electronics, and biomedical electronics. The journal also includes articles on the application of electronics in various fields, such as consumer electronics, industrial electronics, automotive electronics, and military electronics. The journal publishes original research articles, review articles, and short communications. == Abstracting and indexing == EBSCO databases ProQuest databases Scopus According to the Journal Citation Reports, the journal has a 2021 impact factor of 2.690.
Algorithmic amplification
Algorithmic amplification is the process by which automated ranking and recommendation systems on digital platforms increase the visibility of certain content beyond its initial audience. Major platforms including Facebook, YouTube, TikTok, and X (formerly Twitter) use such systems to determine what appears in users' feeds and search results. The term is used in research on social media and digital media regulation to describe how platform design choices influence the distribution of online information. Unlike chronological feeds, algorithmic systems evaluate content using signals such as engagement rates, viewing duration, and predicted relevance to individual users. Content that performs strongly on these metrics may be promoted to progressively larger audiences through feeds, search rankings, or autoplay systems. The process is distinct from content moderation, which involves removing, labelling, or restricting content under platform rules, although the two can interact in practice. The concept is closely connected to the attention economy. Research has linked algorithmic amplification to the spread of misinformation and the circulation of political content, as well as to effects on young users' mental health. The scale and direction of those effects remain debated, in part because independent researchers have limited access to the internal workings of platform recommendation systems. Governments in the European Union, United Kingdom, United States, and China have pursued differing regulatory approaches to recommendation algorithms. The EU's Digital Services Act and the UK's Online Safety Act 2023 impose obligations on large platforms related to recommendation system transparency and risk, while China became the first country to enact binding legislation specifically targeting such systems. Internal documents and whistleblower testimony reported by the BBC in 2026 described how competitive pressure between Meta and TikTok led to trade-offs between engagement and user safety in the design of their recommendation systems. == Terminology == The term algorithmic amplification is used in media studies, platform governance scholarship and regulatory literature to describe how automated systems influence the distribution of content beyond what organic user sharing alone would produce. It is distinct from viral spread, which refers primarily to user-driven sharing behaviour, and from algorithmic bias, which describes systematic errors or unfairness in algorithmic outputs. The related term algorithmic curation is used for the broader process of selecting and ordering content, of which amplification is one possible outcome. The phrase also appears in regulatory and legislative discussion of recommendation systems. The European Union's Digital Services Act (DSA) identifies recommendation systems as a potential source of systemic risk, and the term appears frequently in academic and policy commentary on the regulation. In the United States, proposals including the Filter Bubble Transparency Act and the Kids Online Safety Act (KOSA) have used it to frame requirements around recommendation system transparency. In the United Kingdom, the House of Commons Science, Innovation and Technology Committee used the term in a 2025 report on how recommendation algorithms contributed to the spread of misinformation during the 2024 Southport riots. A Joint Declaration on AI and Freedom of Expression adopted in October 2025 by four international freedom of expression mandate holders, including the UN Special Rapporteur on Freedom of Opinion and Expression and the OSCE Representative on Freedom of the Media, stated that recommender systems and other AI-powered curation tools exert "a large hidden influence and gatekeeper role" over what information people access and consume. == Background == Early internet platforms typically displayed content in reverse-chronological order or through keyword-based search systems. Although the term is most often applied to social media, the underlying logic predates social media itself. A 2021 overview traced the origins of modern recommendation systems to the early 1990s, when they were first used experimentally for personal email and information filtering. The 1992 Tapestry mail system and the 1994 GroupLens news filtering system were early milestones before recommendation systems spread into e-commerce and other online services. As user bases and content volumes grew during the 2000s, major platforms including Google, YouTube, and Facebook developed machine-learning systems to personalise content delivery and prioritise material predicted to generate engagement. Facebook introduced its News Feed in 2006, which gradually shifted from chronological presentation towards algorithmically ranked content. YouTube altered its recommendation system in 2012 to prioritise watch time rather than clicks, a change the platform said was prompted by concerns that click-based metrics encouraged misleading thumbnails and low-quality videos. TikTok, launched internationally in 2018, adopted a model in which its primary content surface, the For You feed, is driven almost entirely by algorithmic recommendation rather than by a user's social graph. An internal document obtained by The New York Times in 2021 showed that the platform's algorithm optimised for retention and time spent, using signals such as watch duration, replays, likes, and comments to score and rank videos. Algorithmic recommendation also became central to platforms outside social media. Spotify's personalised features, including Discover Weekly, Release Radar, and Home recommendations, use behavioural signals and inferred "taste profiles" to surface tracks and artists beyond a listener's existing library. An ethnographic study of music curators at streaming platforms described this blend of algorithmic and human editorial selection as an "algo-torial" model of gatekeeping. Amazon adopted item-based collaborative filtering for product recommendations in 1998, and its recommendation engine has been described as one of the earliest large-scale deployments of recommendation technology in e-commerce. The same dynamics operate on adult content platforms. Law professor Amy Adler has argued that from 2007 onwards the pornography industry migrated to algorithm-driven streaming platforms, most of which are controlled by a single near-monopoly company, Aylo (formerly MindGeek). These platforms use algorithmic search engines, suggestions, rigid categorisation of content, and AI-driven search term optimisation in ways that produce the same distorting effects found on mainstream speech platforms, including filter bubbles, feedback loops, and the tendency of algorithmic recommendations to alter individual preferences. == Mechanisms == Recommendation systems commonly combine collaborative filtering, which predicts a user's preferences from the behaviour of similar users, with machine-learning models that predict which content a user is likely to engage with from their prior activity. In a common two-stage design, a platform first generates a set of candidate items from a large content pool and then ranks them using a scoring model with objectives such as predicted engagement or user satisfaction. Small changes in ranking criteria can shift exposure at scale, particularly when applied repeatedly across multiple browsing sessions. These systems typically rely on signals including engagement rates, viewing duration, click-through rates, and network relationships between users. Modern recommendation pipelines continuously update predictions as new behavioural data arrives, allowing platforms to adjust rankings in near real time. Users' revealed preferences, expressed through behaviour such as clicks and viewing time, do not always align with their stated preferences, expressed through explicit feedback such as surveys or content controls. Popularity signals can create feedback dynamics in which early engagement increases the likelihood that content will be shown to additional users. Experimental research on online cultural markets has demonstrated how such feedback processes can produce unequal visibility outcomes even when initial differences in content quality are small. == Beneficial and public-interest uses == Recommendation systems can help users navigate large volumes of content by surfacing material predicted to match their interests or needs, which can improve discoverability on platforms with large content libraries. In public health communication, platforms can help health authorities distribute timely information at scale, though the same recommendation systems also risk amplifying misinformation alongside official guidance. Sociologist Zeynep Tufekci has argued that the shift from independent blogs to large centralised platforms transferred gatekeeping power from traditional media to corporate algorithms. In the case of the Egyptian uprising of 2011, she noted that ordinary users
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.
Mountain car problem
Mountain Car, a standard testing domain in Reinforcement learning, is a problem in which an under-powered car must drive up a steep hill. Since gravity is stronger than the car's engine, even at full throttle, the car cannot simply accelerate up the steep slope. The car is situated in a valley and must learn to leverage potential energy by driving up the opposite hill before the car is able to make it to the goal at the top of the rightmost hill. The domain has been used as a test bed in various reinforcement learning papers. == Introduction == The mountain car problem, although fairly simple, is commonly applied because it requires a reinforcement learning agent to learn on two continuous variables: position and velocity. For any given state (position and velocity) of the car, the agent is given the possibility of driving left, driving right, or not using the engine at all. In the standard version of the problem, the agent receives a negative reward at every time step when the goal is not reached; the agent has no information about the goal until an initial success. == History == The mountain car problem appeared first in Andrew Moore's PhD thesis (1990). It was later more strictly defined in Singh and Sutton's reinforcement learning paper with eligibility traces. The problem became more widely studied when Sutton and Barto added it to their book Reinforcement Learning: An Introduction (1998). Throughout the years many versions of the problem have been used, such as those which modify the reward function, termination condition, and the start state. == Techniques used to solve mountain car == Q-learning and similar techniques for mapping discrete states to discrete actions need to be extended to be able to deal with the continuous state space of the problem. Approaches often fall into one of two categories, state space discretization or function approximation. === Discretization === In this approach, two continuous state variables are pushed into discrete states by bucketing each continuous variable into multiple discrete states. This approach works with properly tuned parameters but a disadvantage is information gathered from one state is not used to evaluate another state. Tile coding can be used to improve discretization and involves continuous variables mapping into sets of buckets offset from one another. Each step of training has a wider impact on the value function approximation because when the offset grids are summed, the information is diffused. === Function approximation === Function approximation is another way to solve the mountain car. By choosing a set of basis functions beforehand, or by generating them as the car drives, the agent can approximate the value function at each state. Unlike the step-wise version of the value function created with discretization, function approximation can more cleanly estimate the true smooth function of the mountain car domain. === Eligibility traces === One aspect of the problem involves the delay of actual reward. The agent is not able to learn about the goal until a successful completion. Given a naive approach for each trial the car can only backup the reward of the goal slightly. This is a problem for naive discretization because each discrete state will only be backed up once, taking a larger number of episodes to learn the problem. This problem can be alleviated via the mechanism of eligibility traces, which will automatically backup the reward given to states before, dramatically increasing the speed of learning. Eligibility traces can be viewed as a bridge from temporal difference learning methods to Monte Carlo methods. == Technical details == The mountain car problem has undergone many iterations. This section focuses on the standard well-defined version from Sutton (2008). === State variables === Two-dimensional continuous state space. V e l o c i t y = ( − 0.07 , 0.07 ) {\displaystyle Velocity=(-0.07,0.07)} P o s i t i o n = ( − 1.2 , 0.6 ) {\displaystyle Position=(-1.2,0.6)} === Actions === One-dimensional discrete action space. m o t o r = ( l e f t , n e u t r a l , r i g h t ) {\displaystyle motor=(left,neutral,right)} === Reward === For every time step: r e w a r d = − 1 {\displaystyle reward=-1} === Update function === For every time step: A c t i o n = [ − 1 , 0 , 1 ] {\displaystyle Action=[-1,0,1]} V e l o c i t y = V e l o c i t y + ( A c t i o n ) ∗ 0.001 + cos ( 3 ∗ P o s i t i o n ) ∗ ( − 0.0025 ) {\displaystyle Velocity=Velocity+(Action)0.001+\cos(3Position)(-0.0025)} P o s i t i o n = P o s i t i o n + V e l o c i t y {\displaystyle Position=Position+Velocity} === Starting condition === Optionally, many implementations include randomness in both parameters to show better generalized learning. P o s i t i o n = − 0.5 {\displaystyle Position=-0.5} V e l o c i t y = 0.0 {\displaystyle Velocity=0.0} === Termination condition === End the simulation when: P o s i t i o n ≥ 0.6 {\displaystyle Position\geq 0.6} == Variations == There are many versions of the mountain car which deviate in different ways from the standard model. Variables that vary include but are not limited to changing the constants (gravity and steepness) of the problem so specific tuning for specific policies become irrelevant and altering the reward function to affect the agent's ability to learn in a different manner. An example is changing the reward to be equal to the distance from the goal, or changing the reward to zero everywhere and one at the goal. Additionally, a 3D mountain car can be used, with a 4D continuous state space.
CloudLibrary
CloudLibrary (stylized as "cloudLibrary") is a cloud-based software system through which libraries lend electronic books; it is also the name of the app that users download to access the e-books. CloudLibrary was created in 2011 by 3M as part of its library systems unit as a competitor to OverDrive, Inc.; in 2015 3M sold the North American part of that unit to Bibliotheca Group GmbH, a company founded in 2011 that was funded by One Equity Partners Capital Advisors, a division of JP Morgan Chase. By 2019, Bibliotecha had tried, unsuccessfully, to negotiate with Amazon to add Kindle-ebook compatibility to cloudLibrary - something that, as of then, Amazon had only made available to Overdrive. In that year, cloudLibrary, along with hoopla offered by Midwest Tape, ODILO, and Baker & Taylor’s Axis 360, were the main competitors to the Overdrive and Libby apps offered by OverDrive, Inc. in the library e-book market. In April 2024, Bibliotheca sold cloudLibrary to the nonprofit cooperative OCLC. By that time, cloudLibrary was used by around 500 libraries in around 20 countries in around 50 languages, and was used to lend audiobooks, digital magazines, newspapers, and comics, and streaming media, along with e-books.