Differentiable imaging is a method within computational imaging that incorporates differentiable programming to design imaging systems. It treats the entire imaging process - from light passing through optical components to the numerical reconstruction—as a differentiable programming problem. This approach links optical hardware with numerical reconstruction, enabling joint optimization of both parts through differentiable programming. Differentiable imaging additionally extends the scope of computational imaging beyond image reconstruction, such as by aiding in characterization of optical components. == Background == Computational imaging combines optical hardware and computational algorithms to capture and reconstruct information that conventional imaging system cannot. This is achieved from a combination of the imaging system and the software used in the image reconstruction. Since the captured information may not directly show the image of the target, these systems often rely on numerical models that describe how light encodes the target. In practice, such models may deviate from the physical systems due to uncertainties such as noise, misalignments, manufacturing imperfections, environmental variations, etc. These uncertainties can cause a mismatch between the physical system and its numerical model, which may degrade reconstruction quality and limit the effectiveness of the hardware–software co-design. Uncertainty quantification is also studied in other hybrid physical–numerical systems, such as digital twin. While numerical modeling imaging systems date back to the several decades, such as the multislice method in electron microscopy or X-Ray nanotomography, differentiable imaging emphasizes jointly modeling uncertainties and solving inverse problems with image reconstruction simultaneously. Differentiable imaging transforms the traditional encoding model y = f ( x ) {\textstyle y=f(x)} into a more comprehensive formulation y = f ( x , θ ) {\textstyle y=f(x,\theta )} , where θ {\displaystyle \theta } represents a parameter set of mismatches between physical systems and numerical models. The forward model captures the entire imaging pipeline through a series of interconnected component functions: y = f ( x , θ ) , f = f n o i s e ∘ f c ∘ f o c ∘ f x ∘ f o i ∘ f i , {\displaystyle y=f(x,\theta ),\qquad f=f_{noise}\circ f_{c}\circ f_{oc}\circ f_{x}\circ f_{oi}\circ f_{i},} where the function composition operator ∘ {\displaystyle \circ } connects each system component, and θ = { θ c , θ o c , … } {\displaystyle \theta =\{\theta _{c},\theta _{oc},\ldots \}} encompasses uncertainty system parameters. Each component corresponds to specific physical processes within the imaging system, from illumination through object interactions to sensor behavior and noises. This forward model enables the formulation of an inverse problem that simultaneously optimizes system parameters while reconstructing images: x ∗ , θ ∗ = argmin x , θ L ( f ( x , θ ) , y ) + ∑ n = 1 N β n R n ( x ) {\displaystyle x^{},\theta ^{}={\text{argmin}}_{x,\theta }{\mathcal {L}}(f(x,\theta ),y)+\sum _{n=1}^{N}\beta _{n}{\mathcal {R}}_{n}(x)} s . t . x ∈ Ω x , θ ∈ Ω θ {\displaystyle s.t.\quad x\in \Omega _{x},\theta \in \Omega _{\theta }} Here, L ( f ( x , θ ) , y ) {\displaystyle {\mathcal {L}}(f(x,\theta ),y)} represents the fidelity term that quantifies the discrepancy between the model predictions and measured data. The whole process of the y = f ( x , θ ) {\displaystyle y=f(x,\theta )} is constructed as a computer graph based on differentiable programming, and the inverse problem is solved with gradient based algorithm, while the gradient is calculated with automatic differentiation. == Applications == One application of differentiable imaging is uncertainty management, which seeks to quantify and mitigate the impact of factors induce reality-numerical mismatch. Explicitly accounting for uncertainties can improve reconstruction accuracy and system robustness. Examples include: Model-related uncertainties: unknown or unmeasurable variables—for instance, optical system quantities that differ from the design specifications Data and system uncertainties: artifacts introduced during image acquisition, such as low-quality data, noise, or hardware imperfections Manufacturing uncertainties: variability in the production of imaging hardware—such as slight deviations in lens curvature or sensor alignment—that alters the physical system's behavior
Candid (app)
Candid was a mobile app for anonymous discussions. It used machine learning to create personalized newsfeeds of opinions and real conversations, and also for moderation and filtering. Users posted under pseudonyms such as "HyperMantis", "SincereGiraffe", "GroundedTurtle" and "ExuberantRaptor", that are unique for each thread. Founder and CEO Bindu Reddy said that she needed "a place to express myself and engage in discussions where ideas can be debated on their own merits instead of being used to attack me as a person", which Candid tried to solve by redirecting off-topic comments to their appropriate groups, removing spam and flagging negative posts. They used natural language processing to identify hate speech, slander and threats, and removed them accordingly with human intervention. Candid software analyzed topics and tried to flag rumors and lies as such. Users could flag problematic posts and a team of ten contractors would review them individually. With time the system analyzed a user's interactions and give them labels, such as socializer, explorer, positive, influencer, hater, gossip, etc. In June 2017, Candid announced that it would be shut down because its parent company, Post Intelligence, was being acquired. The app was forecast to close on June 23, 2017, but didn't actually close until June 25, 2017.
Giditraffic
GidiTraffic (or GIDITRAFFIC) is an online social service started on 23 September 2011. Based primarily on social media, the service employs crowdsourcing as its primary means of providing real-time traffic updates to subscribers on its platform. The service, delivered free of charge, affords its users access to various types of information. Though its broadest category of users is road users and motorists, GIDITRAFFIC lends itself as a platform for answering inquiries from anyone who requires information on any subject of interest. GIDITRAFFIC's core competence is in vehicular traffic reports, however, the service also handles all other forms of traffic (going by the fact that the word traffic also means "the mutual exchange of information"). == Operation == Users of the service log on to its Twitter feed to get up-to-date traffic information or to post a general inquiry, which GIDITRAFFIC then publishes to all subscribers. Through crowdsourced replies, a requester receives numerous responses from other subscribers who have seen the question and can provide a relevant answer. In addition, updates are provided by subscribers to the platform via their mobile devices, thereby making the service effective in delivering traffic updates as they occur, and providing timely answers to other user inquiries. This informs GIDITRAFFIC's motto of "Lending each other an eye", alluding to the collaboration and cooperation between the platform's users in making the service indispensable to its users. == Reception == On Twitter, which is its primary platform, the service caters to over 1,800,000 subscribers, with the number increasing daily. The popularity of the platform stems from the fact that it not only keeps its subscribers abreast of the traffic situation in Lagos, the commercial capital city of Nigeria (well known for its many traffic jams), but users in other parts of the world. For a regular user of the platform, knowing where to avoid getting to a set destination in good time is well worth the two or three minutes it takes to access and scroll through the GIDITRAFFIC feed for updates. Another interesting aspect of this platform is the identity of the person behind it. The sustained anonymity of this individual has sparked many discussions centering on his or her possible identity. Online, GIDITRAFFIC continuously publishes traffic updates and user questions, while keeping up witty interactions with the platform's followers round the clock – adding to the mystery and persona of the GIDITRAFFIC owner. == Awards and recognition == In early 2012, GIDITRAFFIC received a nomination for a Shorty Award in the Life-Saving Hero category. Although this did not translate into a win, it brought recognition and wider exposure for the service from international news outlets such as the BBC, Washington Post. and New York Times. Back home in Nigeria, also in 2012, GIDITRAFFIC was honored with a Future Award for Best Use of New Media in recognition of the huge impact the service has had in terms of helping Lagos residents better manage time spent in traffic. == Mobile Applications == In 2012, GIDITRAFFIC partnered with telecommunications company Nokia to produce a downloadable mobile traffic application (the GIDITRAFFIC application, available for Nokia Asha phones on Nokia's online store). There are plans to extend the application to a wider range of mobile phone platforms. On 4 September 2013, the GIDITRAFFIC application for Nokia Lumia phones using Windows Phone 8 was launched on the Windows App Store.
Vacuum tube characteristics
Vacuum tube characteristics (also called tube curves, valve characteristics or valve curves) describes the electrical relationships between electrode voltages and currents in a vacuum tube. These relationships are commonly presented as characteristic curves in tube manuals and engineering references. The curves typically show plate current versus plate voltage for several fixed control-grid voltages, showing how current varies with electrode potentials under controlled conditions. Designers use them to select operating points, determine voltage gain, estimate output power, and construct graphical load-line analyses. The use of characteristic curves as an engineering tool for analyzing vacuum-tube operation was established in the 1910s, notably in work by Edwin Howard Armstrong. Examples of such curves appear in early tube manuals and textbooks and form the basis of classical vacuum-tube circuit design. Different types of vacuum tubes are characterized using plots appropriate to their electrode structure and intended use. Two-electrode devices such as diodes are described primarily by the relation between plate voltage and plate current. Amplifying tubes containing control grids, such as triodes, tetrodes, pentodes, and beam tetrodes, are represented by families of curves measured for different grid voltages. From these families additional parameters such as amplification factor (μ), transconductance (gm), and plate resistance (rp) may be obtained. Although these plots are used primarily for circuit design, their shapes arise from the underlying physics of electron flow in vacuum tubes. The physical principles responsible for the observed characteristics are discussed in later sections. == 3/2 power law == In high-vacuum thermionic diodes operating under normal conditions, plate current increases nonlinearly with plate voltage. Over the space-charge-limited region, the current is well approximated by the three-halves power relation I p = P ⋅ V p 3 / 2 {\displaystyle I_{p}=P\cdot V_{p}^{3/2}} where P {\displaystyle P} is the perveance of the tube. Perveance is determined primarily by electrode geometry, including cathode area and cathode-to-plate spacing. It provides a practical measure of current-producing capability and is often used in tube manuals in place of a complete family of plate-characteristic curves. == Signal diode characterization == For small-signal diodes, tube manuals typically publish a single static anode characteristic showing anode current (Ia) as a function of anode voltage (Va), measured with the heater operating at its rated voltage. Because the diode contains no control grid, only one such I–V curve is required. The low-voltage portion of the curve is particularly important in detector service, where the nonlinear curvature of the current–voltage relation allows a small alternating signal to produce a net direct-current output, resulting in rectification. In addition to the static characteristic, tube manuals specify heater ratings, maximum plate voltage, permissible average current, and interelectrode capacitance. These parameters define the allowable operating region and high-frequency behavior. Another typical data sheet for a diode is for the Philips EB91 double diode. This book includes curves of the diode response in use as a detector. The output voltage is non-zero for an input voltage of 0 due to the Edison effect. == Rectifier characterization == Vacuum-tube rectifiers intended for power-supply service are specified differently from signal diodes. Their data emphasize heater requirements, peak inverse voltage, maximum peak plate current, permissible DC output current for various filter configurations, and regulation characteristics. Rectifier tubes exhibit nonlinear voltage drop that increases with current. For limited operating ranges this behavior may be represented by an equivalent or effective series resistance corresponding to the local slope of the plate characteristic (dynamic plate resistance, dV/dI). Diode voltages can be determied by use of a graphical aide. In capacitor-input supplies, conduction occurs in pulses near the peaks of the AC waveform, producing peak currents substantially greater than the average DC load current. Data sheets therefore specify maximum peak plate current and permissible filter capacitance in addition to average DC ratings. Under varying load conditions, the supply voltage changes in accordance with the rectifier's nonlinear characteristic and effective impedance. == Triode characterization == === Early use === The systematic use of characteristic curves to explain and quantify vacuum-tube amplification was introduced by Edwin Howard Armstrong in 1914. Using measured plate voltage-current curves, Armstrong demonstrated the mechanism of triode amplification and clarified the operation of grid-leak detection. ==== Plate and transfer characteristics ==== Triode data sheets present families of plate characteristics showing plate current I p {\displaystyle I_{p}} as a function of plate voltage E p {\displaystyle E_{p}} for several fixed grid voltages E g {\displaystyle E_{g}} . From these curves the operating point, voltage gain, and load-line behavior may be determined graphically. In normal operation, plate current depends on both grid and plate voltage. Classical analysis shows that the characteristics for different grid voltages are similar in form and differ primarily by horizontal displacement. In triodes, plate current may be approximated by I p = k ( E g + E p μ ) 3 / 2 {\displaystyle I_{p}=k\left(E_{g}+{\frac {E_{p}}{\mu }}\right)^{3/2}} where E g {\displaystyle E_{g}} is the grid voltage, E p {\displaystyle E_{p}} the plate voltage, μ {\displaystyle \mu } the amplification factor, and k {\displaystyle k} a constant determined by the tube geometry.. The amplification factor μ represents the relative effectiveness of grid voltage compared with plate voltage in controlling current. It is fundamentally determined by structural dimensions, particularly grid-to-cathode spacing relative to plate-to-cathode spacing. ==== Small-signal parameters ==== Triodes are commonly characterized by three interrelated small-signal parameters: Amplification factor ( μ {\displaystyle \mu } ) — the change in plate voltage divided by the change in grid voltage at constant plate current: μ = ( ∂ E p ∂ E g ) I p {\displaystyle \mu =\left({\frac {\partial E_{p}}{\partial E_{g}}}\right)_{I_{p}}} Transconductance ( g m {\displaystyle g_{m}} ) — the change in plate current divided by the change in grid voltage at constant plate voltage: g m = ( ∂ I p ∂ E g ) E p {\displaystyle g_{m}=\left({\frac {\partial I_{p}}{\partial E_{g}}}\right)_{E_{p}}} Plate resistance ( r p {\displaystyle r_{p}} ) — the change in plate voltage divided by the change in plate current at constant grid voltage: r p = ( ∂ E p ∂ I p ) E g {\displaystyle r_{p}=\left({\frac {\partial E_{p}}{\partial I_{p}}}\right)_{E_{g}}} These parameters are related by μ = g m r p {\displaystyle \mu =g_{m}r_{p}} as shown in classical tube theory treatments. These parameters are obtained either from slopes of the characteristic curves or from tabulated operating-point data. ==== Comparison of ECC81, ECC82, and ECC83 ==== The ECC81, ECC82, and ECC83 (also known respectively as 12AT7, 12AU7, and 12AX7) are closely related dual triodes widely used in small-signal amplifier stages. Although similar in construction and envelope size, they differ significantly in electrical parameters due to differences in electrode spacing and grid structure. (Data representative of manufacturer specifications.) The ECC83 exhibits high μ {\displaystyle \mu } and high plate resistance, producing large voltage gain but relatively low current drive capability. The ECC82 has lower μ {\displaystyle \mu } and lower plate resistance, allowing greater current delivery and reduced voltage gain. The ECC81 occupies an intermediate position with comparatively high transconductance and moderate amplification factor. These differences arise primarily from variations in grid pitch, cathode area, and electrode spacing, which determine perveance and amplification factor. Although the external envelope is similar, the internal geometry governs the characteristic curves and small-signal parameters. == Tetrode (screen-grid) characterization == The screen-grid tube (tetrode) was developed primarily to reduce the electrostatic coupling between plate and control grid that limited gain and stability in radio-frequency triode amplifiers. In triodes, the grid–plate capacitance provides feedback from plate to grid, restricting obtainable gain and often requiring neutralization circuits such as those used in neutrodyne receivers. By inserting a positively biased screen grid between control grid and plate, this capacitive coupling is greatly reduced, permitting higher stable gain at radio frequencies. The screen grid, also known as the shield grid or grid 2 (to distinguish it from t
Filter (social media)
Filters are digital image effects often used on social media. They initially simulated the effects of camera filters, and they have since developed with facial recognition technology and computer-generated augmented reality. Social media filters—especially beauty filters—are often used to alter the appearance of selfies taken on smartphones or other similar devices. While filters are commonly associated with beauty enhancement and feature alterations, there is a wide range of filters that have different functions. From adjusting photo tones to using face animations and interactive elements, users have access to a range of tools. These filters allow users to enhance photos and allow room for creative expression and fun interactions with digital content. == History == Beauty filters originate from Purikura ("print club"), a type of Japanese photographic arcade game machine conceived in 1994 by Sasaki Miho, a female employee at Atlus, and released in 1995 by Atlus and Sega primarily for female visitors at Japanese arcades. They allowed the manipulation of digital selfie photos with kawaii beauty filters similar to later Snapchat filters. Purikura filters included beautifying the image, cat whiskers, bunny ears, writing text, scribbling graffiti, selecting backdrops, borders, insertable decorations, icons, hair extensions, twinkling diamond tiaras, tenderized light effects, and predesigned decorative margins. To capitalize on the Purikura phenomenon in Japan during the late 1990s, Japanese mobile phones began including a front-facing camera, starting with the Kyocera Visual Phone VP‑210 in 1999. The Sanyo SCP-5300 released in 2002 was the first camera phone with filter effects, such as illumination, white‑balance control, sepia, black and white, and negative colors. Purikura-like beauty filters later appeared in smartphone apps such as Instagram and Snapchat in the 2010s. In 2010, Apple introduced the iPhone 4—the first iPhone model with a front-facing camera. It gave rise to a dramatic increase in selfies, which could be touched up with more flattering lighting effects with applications such as Instagram. The American photographer Cole Rise was involved in the creation of the original filters for Instagram around 2010, designing several of them himself, including Sierra, Mayfair, Sutro, Amaro, and Willow. However, the technology for virtual lens filters was invented and patented by Patrick Levy-Rosenthal in 2007. The patent received 100 citations, including Facebook, Nvidia, Microsoft, Samsung, and Snap. In September, 2011, the Instagram 2.0 update for the application introduced "live filters," which allowed the user to preview the effect of the filter while shooting with the application's camera. #NoFilter, a hashtag label to describe an image that had not been filtered, became popular around 2013. An update in 2014 allowed users to adjust the intensity of the filters as well as fine-tune other aspects of the image, features that had been available for years on applications such as VSCO and Litely. In 2014, Snapchat started releasing sponsored filters to monetize the participatory use of the application. In September 2015, Snapchat acquired Looksery and released a feature called "lenses," animated filters using facial recognition technology. Some of the early lenses available on Snapchat at the time were Heart Eyes, Terminator, Puke Rainbows, Old, Scary, Rage Face, Heart Avalanche. The Coachella filter released April 2016 was a popular early augmented reality filter. In April 2017, Facebook released the Camera Effects Platform, which is the first augmented reality platform that allows developers to create their own filters and effects on Facebook's Camera. In December 2017, Snapchat also launched their Lens Studio augmented reality developer tool that allows users and advertisers to do the same on the Snapchat application. In April 2022,TikTok joined the two, and launched their own augmented reality developer platform called Effect house. In February 2023, Effect House gave opened up the access to generative AI tools that allowed creators to change facial features in real time. In November 2023, TikTok released a feature where users no longer needed Effect House to create their own filters, as they are now able to create their own effects on the TikTok application. In August 2024, Meta announced that it would be removing third-party filter effects from its family of apps by January 14, 2025. The AR development software Meta Spark AR will also be retired at the same time; it was at one point the "world's largest mobile AR platform". Brand and creator effects represent the vast majority of filters available on Meta platforms, with over 2 million third-party filters available as of 2021. == Beauty filter == A beauty filter is a filter applied to still photographs, or to video in real time, to enhance the physical attractiveness of the subject. Typical effects of such filters include smoothing skin texture and modifying the proportions of facial features, for example enlarging the eyes or narrowing the nose. Filters may be included as a built-in feature of social media apps such as Instagram or Snapchat, or implemented through standalone applications such as Facetune. In 2020, the "Perfect Skin" filter for Snapchat and Instagram which was created by Brazilian augmented reality developer Brenno Faustino gained more than 36 million impressions in the first 24 hours of its release. In 2021, TikTok users pointed out how the default front-facing camera on the platform automatically applied the retouch and other feature-altering filters. Users noted that these filters slimmed down faces, smoothed skin, whitened teeth, and altered facial features such as nose and eye size, without the option to disable this feature through settings. In March 2023, the "Bold Glamour" filter was released on TikTok and instantly went viral with over 18 million videos created within its first week. This filter subtly enhances the user's facial features seamlessly, giving the illusion of fuller eyebrows, taller cheekbones, enhanced eye make up, a smaller nose, plumper lips, and clearer skin, giving off a natural yet distinct effect. As of May 2024, the filter has been used in over 220 million videos and has become a pivotal moment for beauty filters on digital platforms. Critics have raised concerns that the widespread use of such filters on social media may lead to negative body image, particularly among girls. Though Meta's intention of removing third-party filters will likely see all beauty filters removed, academics feel that the damage of beautifying filters is already done. === Background === The manipulation of photos to enhance attractiveness has long been possible using software such as Adobe Photoshop and, before that, analogue techniques such as airbrushing. However, such tools required considerable technical and artistic skill, and so their use was mostly limited to professional contexts, such as magazines or advertisements. By contrast, filters work in an automated fashion through the use of complex algorithms, requiring little or no input from the user. This ease of use, in combination with the increase in processing power of smartphones, and the rise of social media and selfie culture, have led to photographic manipulation occurring on a much wider scale than ever before. One of the earliest examples of a content-aware digital photographic filter is red-eye reduction. === Effects === Typical changes applied by beauty filters include: Smoothing skin texture; minimizing fine lines and blemishes Erasing under-eye bags Erasing naso-labial lines ("laugh lines") Application of virtual makeup, such as lipstick or eyeshadow Slimming the face; erasing double chins Enlarging the eyes Whitening teeth Narrowing the nose Increasing fullness of the lips Beauty filters most frequently target the face, though in some cases they may affect other body parts. For example, the app "Retouch Me" was reported to have a feature which allows users to superimpose visible abdominal muscles (a "six pack") onto photos featuring the subject's bare stomach. === Reception and psychological effects === Some commentators have expressed concern that beauty filters may create unrealistic beauty standards, particularly among girls, and contribute to rates of body dysmorphic disorder. A correlation has been established between negative body image and the use of beautifying filters, though the direction of causation is unknown. The inability to discern whether a particular image has been filtered is thought to exacerbate their negative psychological effects. Policymakers have advocated for social networks to disclose the use of filters; TikTok, Instagram, and Snapchat all label filtered photos and videos with the name of the filter applied. It has also been noted that beauty filters on social media tend to highlight Eurocentric features, like lighter eyes, a smaller nose, and flushed ch
Dynamic epistemic logic
Dynamic epistemic logic (DEL) is a logical framework dealing with knowledge and information change. Typically, DEL focuses on situations involving multiple agents and studies how their knowledge changes when events occur. These events can change factual properties of the actual world (they are called ontic events): for example a red card is painted in blue. They can also bring about changes of knowledge without changing factual properties of the world (they are called epistemic events): for example, a card is revealed publicly (or privately) to be red. Originally, DEL focused on epistemic events. Only some of the basic ideas are present in this entry of the original DEL framework; more details about DEL in general can be found in the references. Due to the nature of its object of study and its abstract approach, DEL is related and has applications to numerous research areas, such as computer science (artificial intelligence), philosophy (formal epistemology), economics (game theory) and cognitive science. In computer science, DEL is for example very much related to multi-agent systems, which are systems where multiple intelligent agents interact and exchange information. As a combination of dynamic logic and epistemic logic, dynamic epistemic logic is a young field of research. It really started in 1989 with Plaza's logic of public announcement. Independently, Gerbrandy and Groeneveld proposed a system dealing moreover with private announcement and that was inspired by the work of Veltman. Another system was proposed by van Ditmarsch whose main inspiration was the Cluedo game. But the most influential and original system was the system proposed by Baltag, Moss and Solecki. This system can deal with all the types of situations studied in the works above and its underlying methodology is conceptually grounded. This entry will present some of its basic ideas. Formally, DEL extends ordinary epistemic logic by the inclusion of event models to describe actions, and a product update operator that defines how epistemic models are updated as the consequence of executing actions described through event models. Epistemic logic will first be recalled. Then, actions and events will enter into the picture and we will introduce the DEL framework. == Epistemic logic == Epistemic logic is a modal logic dealing with the notions of knowledge and belief. As a logic, it is concerned with understanding the process of reasoning about knowledge and belief: which principles relating the notions of knowledge and belief are intuitively plausible? Like epistemology, it stems from the Greek word ϵ π ι σ τ η μ η {\displaystyle \epsilon \pi \iota \sigma \tau \eta \mu \eta } or ‘episteme’ meaning knowledge. Epistemology is nevertheless more concerned with analyzing the very nature and scope of knowledge, addressing questions such as “What is the definition of knowledge?” or “How is knowledge acquired?”. In fact, epistemic logic grew out of epistemology in the Middle Ages thanks to the efforts of Burley and Ockham. The formal work, based on modal logic, that inaugurated contemporary research into epistemic logic dates back only to 1962 and is due to Hintikka. It then sparked in the 1960s discussions about the principles of knowledge and belief and many axioms for these notions were proposed and discussed. For example, the interaction axioms K p → B p {\displaystyle Kp\rightarrow Bp} and B p → K B p {\displaystyle Bp\rightarrow KBp} are often considered to be intuitive principles: if an agent Knows p {\displaystyle p} then (s)he also Believes p {\displaystyle p} , or if an agent Believes p {\displaystyle p} , then (s)he Knows that (s)he Believes p {\displaystyle p} . More recently, these kinds of philosophical theories were taken up by researchers in economics, artificial intelligence and theoretical computer science where reasoning about knowledge is a central topic. Due to the new setting in which epistemic logic was used, new perspectives and new features such as computability issues were then added to the research agenda of epistemic logic. === Syntax === In the sequel, A G T S = { 1 , … , n } {\displaystyle AGTS=\{1,\ldots ,n\}} is a finite set whose elements are called agents and P R O P {\displaystyle PROP} is a set of propositional letters. The epistemic language is an extension of the basic multi-modal language of modal logic with a common knowledge operator C A {\displaystyle C_{A}} and a distributed knowledge operator D A {\displaystyle D_{A}} . Formally, the epistemic language L EL C {\displaystyle {\mathcal {L}}_{\textsf {EL}}^{C}} is defined inductively by the following grammar in BNF: L EL C : ϕ ::= p ∣ ¬ ϕ ∣ ( ϕ ∧ ϕ ) ∣ K j ϕ ∣ C A ϕ ∣ D A ϕ {\displaystyle {\mathcal {L}}_{\textsf {EL}}^{C}:\phi ~~::=~~p~\mid ~\neg \phi ~\mid ~(\phi \land \phi )~\mid ~K_{j}\phi ~\mid ~C_{A}\phi ~\mid ~D_{A}\phi } where p ∈ P R O P {\displaystyle p\in PROP} , j ∈ A G T S {\displaystyle j\in {AGTS}} and A ⊆ A G T S {\displaystyle A\subseteq {AGTS}} . The basic epistemic language L E L {\displaystyle {\mathcal {L}}_{EL}} is the language L E L C {\displaystyle {\mathcal {L}}_{EL}^{C}} without the common knowledge and distributed knowledge operators. The formula ⊥ {\displaystyle \bot } is an abbreviation for ¬ p ∧ p {\displaystyle \neg p\land p} (for a given p ∈ P R O P {\displaystyle p\in PROP} ), ⟨ K j ⟩ ϕ {\displaystyle \langle K_{j}\rangle \phi } is an abbreviation for ¬ K j ¬ ϕ {\displaystyle \neg K_{j}\neg \phi } , E A ϕ {\displaystyle E_{A}\phi } is an abbreviation for ⋀ j ∈ A K j ϕ {\displaystyle \bigwedge \limits _{j\in A}K_{j}\phi } and C ϕ {\displaystyle C\phi } an abbreviation for C A G T S ϕ {\displaystyle C_{AGTS}\phi } . Group notions: general, common and distributed knowledge. In a multi-agent setting there are three important epistemic concepts: general knowledge, distributed knowledge and common knowledge. The notion of common knowledge was first studied by Lewis in the context of conventions. It was then applied to distributed systems and to game theory, where it allows to express that the rationality of the players, the rules of the game and the set of players are commonly known. General knowledge. General knowledge of ϕ {\displaystyle \phi } means that everybody in the group of agents A G T S {\displaystyle {AGTS}} knows that ϕ {\displaystyle \phi } . Formally, this corresponds to the following formula: E ϕ := ⋀ j ∈ A G T S K j ϕ . {\displaystyle E\phi :={\underset {j\in {AGTS}}{\bigwedge }}K_{j}\phi .} Common knowledge. Common knowledge of ϕ {\displaystyle \phi } means that everybody knows ϕ {\displaystyle \phi } but also that everybody knows that everybody knows ϕ {\displaystyle \phi } , that everybody knows that everybody knows that everybody knows ϕ {\displaystyle \phi } , and so on ad infinitum. Formally, this corresponds to the following formula C ϕ := E ϕ ∧ E E ϕ ∧ E E E ϕ ∧ … {\displaystyle C\phi :=E\phi \land EE\phi \land EEE\phi \land \ldots } As we do not allow infinite conjunction the notion of common knowledge will have to be introduced as a primitive in our language. Before defining the language with this new operator, we are going to give an example introduced by Lewis that illustrates the difference between the notions of general knowledge and common knowledge. Lewis wanted to know what kind of knowledge is needed so that the statement p {\displaystyle p} : “every driver must drive on the right” be a convention among a group of agents. In other words, he wanted to know what kind of knowledge is needed so that everybody feels safe to drive on the right. Suppose there are only two agents i {\displaystyle i} and j {\displaystyle j} . Then everybody knowing p {\displaystyle p} (formally E p {\displaystyle Ep} ) is not enough. Indeed, it might still be possible that the agent i {\displaystyle i} considers possible that the agent j {\displaystyle j} does not know p {\displaystyle p} (formally ¬ K i K j p {\displaystyle \neg K_{i}K_{j}p} ). In that case the agent i {\displaystyle i} will not feel safe to drive on the right because he might consider that the agent j {\displaystyle j} , not knowing p {\displaystyle p} , could drive on the left. To avoid this problem, we could then assume that everybody knows that everybody knows that p {\displaystyle p} (formally E E p {\displaystyle EEp} ). This is again not enough to ensure that everybody feels safe to drive on the right. Indeed, it might still be possible that agent i {\displaystyle i} considers possible that agent j {\displaystyle j} considers possible that agent i {\displaystyle i} does not know p {\displaystyle p} (formally ¬ K i K j K i p {\displaystyle \neg K_{i}K_{j}K_{i}p} ). In that case and from i {\displaystyle i} ’s point of view, j {\displaystyle j} considers possible that i {\displaystyle i} , not knowing p {\displaystyle p} , will drive on the left. So from i {\displaystyle i} ’s point of view, j {\displaystyle j} might drive on the left as well (by the same argument as abov
Proximedia Group
Proximedia Group is a Belgian media group. == History == Proximedia Belgium was founded in 1998, by Fabrice Wuyts and Eric Glachant. The company specializes in providing websites for SMEs. The Proximedia Group SA was founded in 1999 and became the coordinating organization of Proximedia Belgium, Online, Bizbook Channel, Globule Bleu bvba, Click+, Proximedia France, Proximedia Nederland, and Proximedia Spain. The Proximedia Group has been listed at the Free Market of Euronext Brussels since 2005. In 2007, the Proximedia Group founded the Bizbook Channel. This branch specialized in creating corporate videos. In 2008, Proximedia SA took over the web agency Globule Bleu. The following year, Proximedia launched the brand BeUP. They were also elected ‘Enterprise of The Year 2009’ by Ernst & Young. Proximedia launched two new services in 2011: Videobiz and Promobook. In 2012, the Bizbook Channel was launched. Proximedia was acquired by Publicis Groupe S.A. in July 2014. == Branches == Proximedia Belgium: the oldest branch of the Proximedia Group. It makes websites and provides support for their customers. Similar branches are Proximedia France and Proximedia Nederland. Batibouw +: specialized in bringing contractors and clients together. Bizbook Channel: specialized in creating corporate videos for SMEs. Click+: offers the management of Google AdWords campaigns. This contains advertising in Google's search results. Globule Bleu: specialized in digital campaigns for larger companies or organisations. Online: an Internet Service Provider (ISP) that provides internet access, domain names, hosting of websites and data centers, email service, etc. Bizbook: an online guestbook where users can post reviews on products and services of a company. Promobook: an online service which can be used to print promotions and coupons. == Key figures == == Sale tactics and lawsuits == There are a lot of websites, forums and blogs that warn for Proximedia. This is because of the long duration of the contract, the inability to terminate the contract and the alleged aggressive approach of Proximedia and the alleged low quality of service that Proximedia offers. Also, there are a lot of lawsuits every month, some of which are customers that wish to terminate the contract, others that allege Proximedia of misguiding. List of some example lawsuits: Mitigation of contractual termination compensation on the basis of article 6:248 paragraph 2 of the Dutch Civil Code A clause on the basis of which a termination fee is claimed can be considered a penalty clause. Mitigation of the penalty based on article 6:94 of the Dutch Civil Code? Performance claim rejected; successful appeal to breach of contract; dissolution; restitution claim awarded. Agreement for IT services. Contents of the agreement. No reflex effect of the Door-to-Door Sales Act for small entrepreneurs. Implementation Act of the Consumer Rights Directive. Breach of contract? Unreasonably onerous clause? Cassation: ECLI:NL:HR:2016:996, (Partial) annulment with referral. Final judgment: ECLI:NL:GHSHE:2014:4228 Error. Reflex effect of the unfair commercial practices law? Compelling evidentiary force of written agreement. (No summary provided by court) Proximedia case. No valid defense against the claim concerning a number of monthly invoices. Article 7.1 of the agreement (containing a termination fee) is a general term in the sense of article 6:231 introductory text and under a of the Dutch Civil Code. No "reflex effect" of article 6:237 introductory text and under i of the Dutch Civil Code. Insufficiently argued why article 7.1 would be unreasonably onerous in the sense of article 6:233 of the Dutch Civil Code and that granting the claim would be unacceptable according to standards of reasonableness and fairness. Termination fee is not a penalty in the sense of article 6:91 of the Dutch Civil Code. A retailer (sole proprietorship) is approached by a representative of a company and enters into an "agreement for IT services" with a term of four years, which includes a dissolution fee of 60% of the not yet due monthly payments. The retailer is instructed to prove that, at the time of entering the agreement, the company promised him that he could terminate the agreement without any further obligations if he terminated his business. The retailer is considered to have succeeded in the burden of proof, and the company's claim for payment of the dissolution fee is rejected.