A Logical Calculus of the Ideas Immanent in Nervous Activity

A Logical Calculus of the Ideas Immanent in Nervous Activity

"A Logical Calculus of the Ideas Immanent in Nervous Activity" is a 1943 paper written by Warren Sturgis McCulloch and Walter Pitts, published in the journal The Bulletin of Mathematical Biophysics. The paper proposed a mathematical model of the nervous system as a network of simple logical elements, later known as artificial neurons, or McCulloch–Pitts neurons. These neurons receive inputs, perform a weighted sum, and fire an output signal based on a threshold function. By connecting these units in various configurations, McCulloch and Pitts demonstrated that their model could perform all logical functions. It is a seminal work in cognitive science, computational neuroscience, computer science, and artificial intelligence. It was a foundational result in automata theory. John von Neumann cited it as a significant result. == Mathematics == The artificial neuron used in the original paper is slightly different from the modern version. They considered neural networks that operate in discrete steps of time t = 0 , 1 , … {\displaystyle t=0,1,\dots } . The neural network contains a number of neurons. Let the state of a neuron i {\displaystyle i} at time t {\displaystyle t} be N i ( t ) {\displaystyle N_{i}(t)} . The state of a neuron can either be 0 or 1, standing for "not firing" and "firing". Each neuron also has a firing threshold θ {\displaystyle \theta } , such that it fires if the total input exceeds the threshold. Each neuron can connect to any other neuron (including itself) with positive synapses (excitatory) or negative synapses (inhibitory). That is, each neuron can connect to another neuron with a weight w {\displaystyle w} taking an integer value. A peripheral afferent is a neuron with no incoming synapses. We can regard each neural network as a directed graph, with the nodes being the neurons, and the directed edges being the synapses. A neural network has a circle or a circuit if there exists a directed circle in the graph. Let w i j ( t ) {\displaystyle w_{ij}(t)} be the connection weight from neuron j {\displaystyle j} to neuron i {\displaystyle i} at time t {\displaystyle t} , then its next state is N i ( t + 1 ) = H ( ∑ j = 1 n w i j ( t ) N j ( t ) − θ i ( t ) ) , {\displaystyle N_{i}(t+1)=H\left(\sum _{j=1}^{n}w_{ij}(t)N_{j}(t)-\theta _{i}(t)\right),} where H {\displaystyle H} is the Heaviside step function (outputting 1 if the input is greater than or equal to 0, and 0 otherwise). === Symbolic logic === The paper used, as a logical language for describing neural networks, "Language II" from The Logical Syntax of Language by Rudolf Carnap with some notations taken from Principia Mathematica by Alfred North Whitehead and Bertrand Russell. Language II covers substantial parts of classical mathematics, including real analysis and portions of set theory. To describe a neural network with peripheral afferents N 1 , N 2 , … , N p {\displaystyle N_{1},N_{2},\dots ,N_{p}} and non-peripheral afferents N p + 1 , N p + 2 , … , N n {\displaystyle N_{p+1},N_{p+2},\dots ,N_{n}} they considered logical predicate of form P r ( N 1 , N 2 , … , N p , t ) {\displaystyle Pr(N_{1},N_{2},\dots ,N_{p},t)} where P r {\displaystyle Pr} is a first-order logic predicate function (a function that outputs a boolean), N 1 , … , N p {\displaystyle N_{1},\dots ,N_{p}} are predicates that take t {\displaystyle t} as an argument, and t {\displaystyle t} is the only free variable in the predicate. Intuitively speaking, N 1 , … , N p {\displaystyle N_{1},\dots ,N_{p}} specifies the binary input patterns going into the neural network over all time, and P r ( N 1 , N 2 , … , N n , t ) {\displaystyle Pr(N_{1},N_{2},\dots ,N_{n},t)} is a function that takes some binary input patterns, and constructs an output binary pattern P r ( N 1 , N 2 , … , N n , 0 ) , P r ( N 1 , N 2 , … , N n , 1 ) , … {\displaystyle Pr(N_{1},N_{2},\dots ,N_{n},0),Pr(N_{1},N_{2},\dots ,N_{n},1),\dots } . A logical sentence P r ( N 1 , N 2 , … , N n , t ) {\displaystyle Pr(N_{1},N_{2},\dots ,N_{n},t)} is realized by a neural network iff there exists a time-delay T ≥ 0 {\displaystyle T\geq 0} , a neuron i {\displaystyle i} in the network, and an initial state for the non-peripheral neurons N p + 1 ( 0 ) , … , N n ( 0 ) {\displaystyle N_{p+1}(0),\dots ,N_{n}(0)} , such that for any time t {\displaystyle t} , the truth-value of the logical sentence is equal to the state of the neuron i {\displaystyle i} at time t + T {\displaystyle t+T} . That is, ∀ t = 0 , 1 , 2 , … , P r ( N 1 , N 2 , … , N p , t ) = N i ( t + T ) {\displaystyle \forall t=0,1,2,\dots ,\quad Pr(N_{1},N_{2},\dots ,N_{p},t)=N_{i}(t+T)} === Equivalence === In the paper, they considered some alternative definitions of artificial neural networks, and have shown them to be equivalent, that is, neural networks under one definition realizes precisely the same logical sentences as neural networks under another definition. They considered three forms of inhibition: relative inhibition, absolute inhibition, and extinction. The definition above is relative inhibition. By "absolute inhibition" they meant that if any negative synapse fires, then the neuron will not fire. By "extinction" they meant that if at time t {\displaystyle t} , any inhibitory synapse fires on a neuron i {\displaystyle i} , then θ i ( t + j ) = θ i ( 0 ) + b j {\displaystyle \theta _{i}(t+j)=\theta _{i}(0)+b_{j}} for j = 1 , 2 , 3 , … {\displaystyle j=1,2,3,\dots } , until the next time an inhibitory synapse fires on i {\displaystyle i} . It is required that b j = 0 {\displaystyle b_{j}=0} for all large j {\displaystyle j} . Theorem 4 and 5 state that these are equivalent. They considered three forms of excitation: spatial summation, temporal summation, and facilitation. The definition above is spatial summation (which they pictured as having multiple synapses placed close together, so that the effect of their firing sums up). By "temporal summation" they meant that the total incoming signal is ∑ τ = 0 T ∑ j = 1 n w i j ( t ) N j ( t − τ ) {\displaystyle \sum _{\tau =0}^{T}\sum _{j=1}^{n}w_{ij}(t)N_{j}(t-\tau )} for some T ≥ 1 {\displaystyle T\geq 1} . By "facilitation" they meant the same as extinction, except that b j ≤ 0 {\displaystyle b_{j}\leq 0} . Theorem 6 states that these are equivalent. They considered neural networks that do not change, and those that change by Hebbian learning. That is, they assume that at t = 0 {\displaystyle t=0} , some excitatory synaptic connections are not active. If at any t {\displaystyle t} , both N i ( t ) = 1 , N j ( t ) = 1 {\displaystyle N_{i}(t)=1,N_{j}(t)=1} , then any latent excitatory synapse between i , j {\displaystyle i,j} becomes active. Theorem 7 states that these are equivalent. === Logical expressivity === They considered "temporal propositional expressions" (TPE), which are propositional formulas with one free variable t {\displaystyle t} . For example, N 1 ( t ) ∨ N 2 ( t ) ∧ ¬ N 3 ( t ) {\displaystyle N_{1}(t)\vee N_{2}(t)\wedge \neg N_{3}(t)} is such an expression. Theorem 1 and 2 together showed that neural nets without circles are equivalent to TPE. For neural nets with loops, they noted that "realizable P r {\displaystyle Pr} may involve reference to past events of an indefinite degree of remoteness". These then encodes for sentences like "There was some x such that x was a ψ" or ( ∃ x ) ( ψ x ) {\displaystyle (\exists x)(\psi x)} . Theorems 8 to 10 showed that neural nets with loops can encode all first-order logic with equality and conversely, any looped neural networks is equivalent to a sentence in first-order logic with equality, thus showing that they are equivalent in logical expressiveness. As a remark, they noted that a neural network, if furnished with a tape, scanners, and write-heads, is equivalent to a Turing machine, and conversely, every Turing machine is equivalent to some such neural network. Thus, these neural networks are equivalent to Turing computability and Church's lambda-definability. == Context == === Previous work === The paper built upon several previous strands of work. In the symbolic logic side, it built on the previous work by Carnap, Whitehead, and Russell. This was contributed by Walter Pitts, who had a strong proficiency with symbolic logic. Pitts provided mathematical and logical rigor to McCulloch’s vague ideas on psychons (atoms of psychological events) and circular causality. In the neuroscience side, it built on previous work by the mathematical biology research group centered around Nicolas Rashevsky, of which McCulloch was a member. The paper was published in the Bulletin of Mathematical Biophysics, which was founded by Rashevsky in 1939. During the late 1930s, Rashevsky's research group was producing papers that had difficulty publishing in other journals at the time, so Rashevsky decided to found a new journal exclusively devoted to mathematical biophysics. Also in the Rashevsky's group was Alston Scott Householder, who in 1941 published an abstract model

MeituPic

Meitu Xiu Xiu ("Meitu") (Chinese: 美图秀秀) is an image editing software that is mostly used in Mainland China but is also popular in Hong Kong and Taiwan. It is only available on Google Play and App Store in certain countries. It provides tools for editing photos: filters, retouching, collage, scenes, frames, and photo decorations, as well as generative AI features such as text-to-images, AI removal and AI repainting etc. Meitu is one of the apps developed by Meitu, Inc.; it also produced BeautyCam, Wink and X-Design. == History == Meitu's PC version was created in 2008 by Wu Xinhong, the CEO of Meitu. In 2013, its mobile version became one of the first must-have mobile apps in China. Meitu, Inc. is a photo and video-centered app developer, which was founded in 2008 in Xiamen. Currently, the major revenue source of Meitu is premium subscription. Meitu, Inc. was initially funded by Cai Wensheng, a well-known angel investor. The company has an approximately 250 million monthly active users globally. == Function == === Edit === MeituPic provides a number of photo-editing tools. The major functions are auto enhance, edit, enhance, filters, frames, magic brush, mosaic, text, and blur. Auto enhance focuses on the nature of photos taken, while Edit includes functions of cropping, rotation, sharpening, and adjustment of ratio. For Enhance, users can apply slight adjustment on the photo by controlling the levels of brightness, contrast, colour temperature, saturation, highlight, shadow and smart light. Major types of filters are LOMO, beauty, style as well as art. Different frames can be chosen from poster, simple, and fantasy. Magic brush provides a great variety of brushes with different colours and patterns for users to decorate the photos. Mosaic brush enables users to cover certain parts of the photo. Texts can be added to the photo. Choices of different bubbles, font as well as style of words are available. Blurring effect is also available to make the photo less distinct and clear. === Beauty Retouch === There are seven major functions for retouching a photo: automatic retouch, smooth and whiten skin, remove blemish, make slimmer, remove dark circles and bags under the eyes, make taller, and enhance the eyes. Automatic retouch enhances portraits by lightening the skin tone, brightening the eyes, and simulating a face-lift by tapping on just one button. This helps to remove wrinkles and optimizes the skin tone. Acne, blemishes, and other skin imperfections can also be removed. The face-lift and weight-loss functions in the slimming option can be used to reshape the body. The option to make the subject taller can be used to change the perceived height of the subject and give the impression of slimmer, longer legs. The option to enhance the eyes can enlarge and brighten the eyes. === Collage === Collage has four types: template, freestyle, poster, PicStrip, which all maximize to insert nine photos. Template integrates photos in a vertical rectangle tightly. MeituPic has 15 frames or free download function for users. MeituPic also provides different templates according to number of photos inserted. Freestyle separates photos on a background freely. There are two parts of background: custom and more. For custom, users choose from album. For more, there are plain and picture with 18 choices. Poster makes a poster with photos. Users choose a poster among 8 choices or tap ‘more’ to download a new one. PicStrip combines photos vertically making an elongated file. Users choose a frame from 15 choices. Pinching thumb and forefinger together or apart zooms photos in/out. Putting two fingers and turning hand rotates photos. Pressing moves photos to ideal location. After designing, users tap ‘save/share’ on the upper right corner and the photo made is saved into album automatically. == Awards ==

IDN Times

IDN Times is a digital multi-platform media outlet that provides news and entertainment for Millennials and Gen Z in Indonesia. IDN Times is one of IDN’s business units under the Digital Media pillar, founded by Winston Utomo and William Utomo on June 8, 2014. Currently, senior journalist Uni Zulfiani Lubis serves as the Editor-in-Chief of IDN Times. == History == IDN Times was initially known as Indonesian Times, a blog featuring articles written by Winston Utomo while he was working at Google Singapore. As interest and readership grew, Indonesian Times evolved into IDN Times, a digital multi-platform media company focused on delivering relevant content for Indonesia’s younger generations. == Bureau == IDN Times has a representative bureau that has spread over 12 provinces in Indonesia: == Events == === Indonesia Millennial and Gen Z Summit === The Indonesia Millennial and Gen-Z Summit (IMGS) is an annual event organized by IDN. This event aims to empower Indonesia’s younger generations through discussions and interdisciplinary collaborations. IMGS features inspirational figures, professionals, and leaders from various fields who share insights and drive positive change. The event hosts dozens of discussion sessions in collaboration with eight prominent communities. Topics covered include politics, economics, technology, and pop culture. === Indonesia Writers Festival === The Indonesia Writers Festival is an independent writing festival organized by IDN Times. The event seeks to empower Indonesians through writing by inviting experts and literacy activists from various backgrounds. == Duniaku.com == Duniaku.com is a multi-platform digital media part of IDN Times which presents content about geek culture ranging from video games, anime, comics, films, technology and gadgets. Duniaku.com was officially launched on September 6, 2019 by the Minister of Communication and Informatics Rudiantara together with CEO of IDN Media Winston Utomo and IDN Times and Editor-in-Chief of Duniaku.com Uni Lubis. == Awards == 2019 IDN won WAN-IFRA Asia Digital Media Awards 2019 as the Best Digital Project to Engage Younger and/or Millennial Audiences for IDN Times’ #MillennialsMemilih program 2020 IDN Times (IDN Times Community) won WAN-IFRA Asia Digital Media Awards 2019 in The Best in Audience Engagement category. 2021 IDN Times journalists won awards at the Subroto Award, Ministry of Energy and Mineral Resources (ESDM) on 28 September 2021. 2024 IDN Times won WAN-IFRA event at both the Asia and Global levels in Best Use of AI in Revenue Strategy. === #Interconnected22 by Pulitzer Center === One of the IDN Times journalists, Dhana Kencana, was the speaker at the #Interconnected22 conference held from June 9 to June 10, 2022, in Washington DC, United States of America. Dhana Kencana is also a grant recipient Pulitzer Center through the Rainforest Journalism Fund (RJF) program, a funding program for journalists that makes a number of coverage of the rainforest.

Signal-to-crosstalk ratio

The signal-to-crosstalk ratio at a specified point in a circuit is the ratio of the power of the wanted signal to the power of the unwanted signal from another channel. The signals are adjusted in each channel so that they are of equal power at the zero transmission level point in their respective channels. The signal-to-crosstalk ratio is usually expressed in dB.

Contact cleaner

Contact cleaner, also known as switch-cleaner, is any of various chemicals, or mixtures of chemicals, intended to remove or prevent the build-up of oxides or other unwanted substances on the conductive surfaces of connectors, switches, and other electronic components with moving surface-contacts, and thus reduce the contact resistance encountered. The use of contact cleaner can help to minimize the wetting current across a pair of contacts. An example of a simple contact cleaner is isopropyl alcohol Some contact cleaners are designed to evaporate completely and rapidly, leaving no residue. Others may contain lubricants. Lubricants themselves should not necessarily be used as contact cleaners, especially if they are designed to leave an unsuitable residue. However, appropriate lubricants may work well as contact cleaners.

Eaze

Eaze is an American company based in San Francisco, California that launched a medical cannabis delivery app of the same name in 2014. == History == Eaze was launched in 2014 by Keith McCarty to deliver medical marijuana to patients in California. McCarty started the company in his San Francisco apartment with four employees. The company provides a mobile app to connect users with cannabis dispensaries, but does not grow or sell marijuana itself, and has been nicknamed “the Uber of Weed”. As of 2017, the company operates in more than 100 cities within California. In 2017, Eaze reported 300 percent growth over the previous year. It has 81 employees, and performs 120,000 deliveries per month to 250,000 users. A survey of Eaze users revealed that 66% are male, 57% are between 22 and 34, just over half have a bachelor's degree, and 49% have an annual income over $75,000. The company's vaporizer cartridge sales reached $1 million in sales in 4 months, and 31% of customers had ordered a vaporizer by the end of 2016. In 2016, Eaze founder Keith McCarty stepped down from his position as CEO and was replaced by Jim Patterson, who served as the company's chief product and technology officer. == EazeMD == EazeMD is a service that helps people acquire a medical marijuana card. It is a California-based telemedicine service in which physicians assess patients through an online video chat. It is California's largest telemedicine service for marijuana referrals. In June 2017, a former employee of one of these physicians accessed patient data in the physician's records system, causing a security breach. However, there was no evidence that Eaze data was accessed. == Eaze Insights == Eaze Insights conducts surveys of their users and compiles data into reports on cannabis use. Statistics from their reports have been cited in Seattle Weekly, Forbes, The Huffington Post, Business Insider, Fortune, and other general interest publications. == Financing == The company announced its $10 million Series A funding in April 2015 by multiple venture capital firms, including the Snoop Dogg-backed Casa Verde Capital. In October 2016, Eaze announced its series B funding in the amount of $13 million from five investors, making the company "the highest-funded startup in the history of the cannabis industry, as well as its fastest-growing one". In September 2017, the company raised another $27 million in venture funding. The Series B funding was led by Bailey Capital, joined by DCM Ventures, Kaya Ventures, and FJ Labs. According to the company' officials in 2017, Eaze managed to raise more than $52 million since its inception in 2014.

Digital entertainment

Digital entertainment Industry includes, but is not restricted to, any combination of the following industries (that themselves have a considerable degree of overlap): digital media new media video on demand video games interactive entertainment online gambling mobile entertainment social media streaming services "Digital entertainment", largely a hard to define marketing term, rests upon entertainment technology and ultimately on the enabling basic technologies computers, Internet/World Wide Web, digital rights management, multimedia and streaming media. Apart from pure entertainment, the term rests upon the observation that already in 2011 in the UK, for example, "nearly half of people’s waking hours are spent using media content and communications services" ("screen time"). Digital entertainment is inextricably connected with digital marketing. People who follow influencers on social media for entertainment will receive a fair share of advertising at the same time. Digital merchandise is distributed with every computer game and popup ads or similar are ubiquitous in the online (gaming) world.