Industry Dive is a United States-based business-to-business news organization with an estimated 18 million readers in more than 25 industries, such as banking and waste management. Since 2022, it has been owned by Informa plc. Industry Dive aims to serve business executives who read news on their mobile phones. The company had an estimated revenue of more than of more than $110 million in 2023. As of 2020, it has more than 300 employees, including 80 journalists and 12 engineers. Its headquarters is in Washington, D.C. == History == Industry Dive was formed in 2012 by Sean Griffey (president), Eli Dickinson (chief technology officer), and Ryan Willumson (chief revenue officer). It was funded with $900,000 from private investors in 2012 and 2013. The company covered five industries: construction, education, marketing, utility, and waste. In 2016, it began its Dive Awards. Industry Dive's revenues quadrupled from 2015 to 2018, putting it in the top half of the Deloitte Technology Fast 500 and the top 20 percent of the Inc. Top 5000 list. In 2019, Falfurrias Capital Partners acquired a majority stake in the company. ID's content marketing clients included IBM, Siemens, and UPS. In 2020, DCA Live named Industry Dive to its "Red Hot Companies" list, which recognizes the D.C. area's 'fastest-growing' companies. In the same year, Industry Dive acquired CFO. In 2021, Industry Dive acquired PharmaVOICE. In 2022, it was purchased by Informa plc, which bought its majority stake from Falfurrias Capital Partners for about $530 million. == Publications == Industry Dive provides news coverage of a variety of industries including agriculture, banking, construction, education, fashion, healthcare, and manufacturing, each using a different website: == Awards == Industry Dive publications have received several national and regional Awards of Excellence from the American Society of Business Publication Editors, including for a series of 2020 articles about Big Pharma and the race for the coronavirus vaccine. The Washington Post recognized Industry Dive as a top place to work for four consecutive years, from 2016 to 2020.
Pill reminder
A pill reminder is any device that reminds users to take medications. Traditional pill reminders are pill containers with electric timers attached, which can be preset for certain times of the day to set off an alarm. More sophisticated pill reminders can also detect when they have been opened, and therefore when the user is away during the time they were supposed to take their medication, they will be reminded of it when they return. This reminder can be in the form of a light, which also helps for deaf or hearing-impaired users. == Mobile app == A newer type of pill reminder is a mobile app that reminds the owner to take the medication. Some of these applications might effectively support adherence to taking medications.
Paper data storage
Paper data storage refers to the use of paper as a data storage device. This includes writing, illustrating, and the use of data that can be interpreted by a machine or is the result of the functioning of a machine. A defining feature of paper data storage is the ability of humans to produce it with only simple tools and interpret it visually. Though now mostly obsolete, paper was once an important form of computer data storage as both paper tape and punch cards were a common staple of working with computers before the 1980s. == History == Before paper was used for storing data, it had been used in several applications for storing instructions to specify a machine's operation. The earliest use of paper to store instructions for a machine was the work of Basile Bouchon who, in 1725, used punched paper rolls to control textile looms. This technology was later developed into the wildly successful Jacquard loom. The 19th century saw several other uses of paper for controlling machines. In 1846, telegrams could be prerecorded on punched tape and rapidly transmitted using Alexander Bain's automatic telegraph. Several inventors took the concept of a mechanical organ and used paper to represent the music. In the late 1880s Herman Hollerith invented the recording of data on a medium that could then be read by a machine. Prior uses of machine readable media, above, had been for control (automatons, piano rolls, looms, ...), not data. "After some initial trials with paper tape, he settled on punched cards..." Hollerith's method was used in the 1890 census. Hollerith's company eventually became the core of IBM. Other technologies were also developed that allowed machines to work with marks on paper instead of punched holes. This technology was widely used for tabulating votes and grading standardized tests. Banks used magnetic ink on checks, supporting MICR scanning. In an early electronic computing device, the Atanasoff–Berry Computer, electric sparks were used to singe small holes in paper cards to represent binary data. The altered dielectric constant of the paper at the location of the holes could then be used to read the binary data back into the machine by means of electric sparks of lower voltage than the sparks used to create the holes. This form of paper data storage was never made reliable and was not used in any subsequent machine. == Modern techniques == === 1D barcodes === Barcodes make it possible for any object that was to be sold or transported to have some computer readable information securely attached to it. Universal Product Code barcodes, first used in 1974, are ubiquitous today. Some people recommend a width of at least 3 pixels for each minimum-width gap and each minimum-width bar for 1D barcodes. The density is about 50 bits per linear inch (about 2 bit/mm). === 2D barcodes === 2D barcodes allow to store much more data on paper, up to 2.9 kbyte per barcode. It is recommended to have a width of at least 4 pixels—e.g., a 4 × 4 pixel = 16 pixel module. == Limits == The limits of data storage depend on the technology to write and read such data. The theoretical limits assume a scanner that can perfectly reproduce the printed image at its printing resolution, and a program which can accurately interpret such an image. For example, an 8 in × 10 in (200 mm × 250 mm) 600 dpi black-and-white image contains 3.43 MiB of data, as does a 300 dpi CMYK printed image. A 2,400 ppi True color (24-bit) image contains about 1.29 GiB of information; printing an image maintaining this data would require a printing resolution of about 120,000 dpi in black and white, or 60,000 dpi with CMYK dots.
Leiden algorithm
The Leiden algorithm is a community detection algorithm developed by Traag et al at Leiden University. It was developed as a modification of the Louvain method. Like the Louvain method, the Leiden algorithm attempts to optimize modularity in extracting communities from networks; however, it addresses key issues present in the Louvain method, namely poorly connected communities and the resolution limit of modularity. == Improvement over Louvain method == Broadly, the Leiden algorithm uses the same two primary phases as the Louvain algorithm: a local node moving step (though, the method by which nodes are considered in Leiden is more efficient) and a graph aggregation step. However, to address the issues with poorly-connected communities and the merging of smaller communities into larger communities (the resolution limit of modularity), the Leiden algorithm employs an intermediate refinement phase in which communities may be split to guarantee that all communities are well-connected. Consider, for example, the following graph: Three communities are present in this graph (each color represents a community). Additionally, the center "bridge" node (represented with an extra circle) is a member of the community represented by blue nodes. Now consider the result of a node-moving step which merges the communities denoted by red and green nodes into a single community (as the two communities are highly connected): Notably, the center "bridge" node is now a member of the larger red community after node moving occurs (due to the greedy nature of the local node moving algorithm). In the Louvain method, such a merging would be followed immediately by the graph aggregation phase. However, this causes a disconnection between two different sections of the community represented by blue nodes. In the Leiden algorithm, the graph is instead refined: The Leiden algorithm's refinement step ensures that the center "bridge" node is kept in the blue community to ensure that it remains intact and connected, despite the potential improvement in modularity from adding the center "bridge" node to the red community. == Graph components == Before defining the Leiden algorithm, it will be helpful to define some of the components of a graph. === Vertices and edges === A graph is composed of vertices (nodes) and edges. Each edge is connected to two vertices, and each vertex may be connected to zero or more edges. Edges are typically represented by straight lines, while nodes are represented by circles or points. In set notation, let V {\displaystyle V} be the set of vertices, and E {\displaystyle E} be the set of edges: V := { v 1 , v 2 , … , v n } E := { e i j , e i k , … , e k l } {\displaystyle {\begin{aligned}V&:=\{v_{1},v_{2},\dots ,v_{n}\}\\E&:=\{e_{ij},e_{ik},\dots ,e_{kl}\}\end{aligned}}} where e i j {\displaystyle e_{ij}} is the directed edge from vertex v i {\displaystyle v_{i}} to vertex v j {\displaystyle v_{j}} . We can also write this as an ordered pair: e i j := ( v i , v j ) {\displaystyle {\begin{aligned}e_{ij}&:=(v_{i},v_{j})\end{aligned}}} === Community === A community is a unique set of nodes: C i ⊆ V C i ⋂ C j = ∅ ∀ i ≠ j {\displaystyle {\begin{aligned}C_{i}&\subseteq V\\C_{i}&\bigcap C_{j}=\emptyset ~\forall ~i\neq j\end{aligned}}} and the union of all communities must be the total set of vertices: V = ⋃ i = 1 C i {\displaystyle {\begin{aligned}V&=\bigcup _{i=1}C_{i}\end{aligned}}} === Partition === A partition is the set of all communities: P = { C 1 , C 2 , … , C n } {\displaystyle {\begin{aligned}{\mathcal {P}}&=\{C_{1},C_{2},\dots ,C_{n}\}\end{aligned}}} == Partition quality == How communities are partitioned is an integral part on the Leiden algorithm. How partitions are decided can depend on how their quality is measured. Additionally, many of these metrics contain parameters of their own that can change the outcome of their communities. === Modularity === Modularity is a highly used quality metric for assessing how well a set of communities partition a graph. The equation for this metric is defined for an adjacency matrix, A, as: Q = 1 2 m ∑ i j ( A i j − k i k j 2 m ) δ ( c i , c j ) {\displaystyle Q={\frac {1}{2m}}\sum _{ij}(A_{ij}-{\frac {k_{i}k_{j}}{2m}})\delta (c_{i},c_{j})} where: A i j {\displaystyle A_{ij}} represents the edge weight between nodes i {\displaystyle i} and j {\displaystyle j} ; see Adjacency matrix; k i {\displaystyle k_{i}} and k j {\displaystyle k_{j}} are the sum of the weights of the edges attached to nodes i {\displaystyle i} and j {\displaystyle j} , respectively; m {\displaystyle m} is the sum of all of the edge weights in the graph; c i {\displaystyle c_{i}} and c j {\displaystyle c_{j}} are the communities to which the nodes i {\displaystyle i} and j {\displaystyle j} belong; and δ {\displaystyle \delta } is Kronecker delta function: δ ( c i , c j ) = { 1 if c i and c j are the same community 0 otherwise {\displaystyle {\begin{aligned}\delta (c_{i},c_{j})&={\begin{cases}1&{\text{if }}c_{i}{\text{ and }}c_{j}{\text{ are the same community}}\\0&{\text{otherwise}}\end{cases}}\end{aligned}}} === Reichardt Bornholdt Potts Model (RB) === One of the most well used metrics for the Leiden algorithm is the Reichardt Bornholdt Potts Model (RB). This model is used by default in most mainstream Leiden algorithm libraries under the name RBConfigurationVertexPartition. This model introduces a resolution parameter γ {\displaystyle \gamma } and is highly similar to the equation for modularity. This model is defined by the following quality function for an adjacency matrix, A, as: Q = ∑ i j ( A i j − γ k i k j 2 m ) δ ( c i , c j ) {\displaystyle Q=\sum _{ij}(A_{ij}-\gamma {\frac {k_{i}k_{j}}{2m}})\delta (c_{i},c_{j})} where: γ {\displaystyle \gamma } represents a linear resolution parameter === Constant Potts Model (CPM) === Another metric similar to RB is the Constant Potts Model (CPM). This metric also relies on a resolution parameter γ {\displaystyle \gamma } The quality function is defined as: H = − ∑ i j ( A i j w i j − γ ) δ ( c i , c j ) {\displaystyle H=-\sum _{ij}(A_{ij}w_{ij}-\gamma )\delta (c_{i},c_{j})} === Understanding Potts Model resolution parameters/Resolution limit === Typically Potts models such as RB or CPM include a resolution parameter in their calculation. Potts models are introduced as a response to the resolution limit problem that is present in modularity maximization based community detection. The resolution limit problem is that, for some graphs, maximizing modularity may cause substructures of a graph to merge and become a single community and thus smaller structures are lost. These resolution parameters allow modularity adjacent methods to be modified to suit the requirements of the user applying the Leiden algorithm to account for small substructures at a certain granularity. The figure on the right illustrates why resolution can be a helpful parameter when using modularity based quality metrics. In the first graph, modularity only captures the large scale structures of the graph; however, in the second example, a more granular quality metric could potentially detect all substructures in a graph. == Algorithm == The Leiden algorithm starts with a graph of disorganized nodes (a) and sorts it by partitioning them to maximize modularity (the difference in quality between the generated partition and a hypothetical randomized partition of communities). The method it uses is similar to the Louvain algorithm, except that after moving each node it also considers that node's neighbors that are not already in the community it was placed in. This process results in our first partition (b), also referred to as P {\displaystyle {\mathcal {P}}} . Then the algorithm refines this partition by first placing each node into its own individual community and then moving them from one community to another to maximize modularity. It does this iteratively until each node has been visited and moved, and each community has been refined - this creates partition (c), which is the initial partition of P refined {\displaystyle {\mathcal {P}}_{\text{refined}}} . Then an aggregate network (d) is created by turning each community into a node. P refined {\displaystyle {\mathcal {P}}_{\text{refined}}} is used as the basis for the aggregate network while P {\displaystyle {\mathcal {P}}} is used to create its initial partition. Because we use the original partition P {\displaystyle {\mathcal {P}}} in this step, we must retain it so that it can be used in future iterations. These steps together form the first iteration of the algorithm. In subsequent iterations, the nodes of the aggregate network (which each represent a community) are once again placed into their own individual communities and then sorted according to modularity to form a new P refined {\displaystyle {\mathcal {P}}_{\text{refined}}} , forming (e) in the above graphic. In the case depicted by the graph, the nodes were already sorted optimally, so no change too
Broadcast (parallel pattern)
Broadcast is a collective communication primitive in parallel programming to distribute programming instructions or data to nodes in a cluster. It is the reverse operation of reduction. The broadcast operation is widely used in parallel algorithms, such as matrix-vector multiplication, Gaussian elimination and shortest paths. The Message Passing Interface implements broadcast in MPI_Bcast. == Definition == A message M [ 1.. m ] {\displaystyle M[1..m]} of length m {\displaystyle m} should be distributed from one node to all other p − 1 {\displaystyle p-1} nodes. T byte {\displaystyle T_{\text{byte}}} is the time it takes to send one byte. T start {\displaystyle T_{\text{start}}} is the time it takes for a message to travel to another node, independent of its length. Therefore, the time to send a package from one node to another is t = s i z e × T byte + T start {\displaystyle t=\mathrm {size} \times T_{\text{byte}}+T_{\text{start}}} . p {\displaystyle p} is the number of nodes and the number of processors. == Binomial Tree Broadcast == With Binomial Tree Broadcast the whole message is sent at once. Each node that has already received the message sends it on further. This grows exponentially as each time step the amount of sending nodes is doubled. The algorithm is ideal for short messages but falls short with longer ones as during the time when the first transfer happens only one node is busy. Sending a message to all nodes takes log 2 ( p ) t {\displaystyle \log _{2}(p)t} time which results in a runtime of log 2 ( p ) ( m T byte + T start ) {\displaystyle \log _{2}(p)(mT_{\text{byte}}+T_{\text{start}})} == Linear Pipeline Broadcast == The message is split up into k {\displaystyle k} packages and sent piecewise from node n {\displaystyle n} to node n + 1 {\displaystyle n+1} . The time needed to distribute the first message piece is p t = m k T byte + T start {\textstyle pt={\frac {m}{k}}T_{\text{byte}}+T_{\text{start}}} whereby t {\displaystyle t} is the time needed to send a package from one processor to another. Sending a whole message takes ( p + k ) ( m T byte k + T start ) = ( p + k ) t = p t + k t {\displaystyle (p+k)\left({\frac {mT_{\text{byte}}}{k}}+T_{\text{start}}\right)=(p+k)t=pt+kt} . Optimal is to choose k = m ( p − 2 ) T byte T start {\displaystyle k={\sqrt {\frac {m(p-2)T_{\text{byte}}}{T_{\text{start}}}}}} resulting in a runtime of approximately m T byte + p T start + m p T start T byte {\displaystyle mT_{\text{byte}}+pT_{\text{start}}+{\sqrt {mpT_{\text{start}}T_{\text{byte}}}}} The run time is dependent on not only message length but also the number of processors that play roles. This approach shines when the length of the message is much larger than the amount of processors. == Pipelined Binary Tree Broadcast == This algorithm combines Binomial Tree Broadcast and Linear Pipeline Broadcast, which makes the algorithm work well for both short and long messages. The aim is to have as many nodes work as possible while maintaining the ability to send short messages quickly. A good approach is to use Fibonacci trees for splitting up the tree, which are a good choice as a message cannot be sent to both children at the same time. This results in a binary tree structure. We will assume in the following that communication is full-duplex. The Fibonacci tree structure has a depth of about d ≈ log Φ ( p ) {\displaystyle d\approx \log _{\Phi }(p)} whereby Φ = 1 + 5 2 {\displaystyle \Phi ={\frac {1+{\sqrt {5}}}{2}}} the golden ratio. The resulting runtime is ( m k T byte + T start ) ( d + 2 k − 2 ) {\textstyle ({\frac {m}{k}}T_{\text{byte}}+T_{\text{start}})(d+2k-2)} . Optimal is k = n ( d − 2 ) T byte 3 T start {\displaystyle k={\sqrt {\frac {n(d-2)T_{\text{byte}}}{3T_{\text{start}}}}}} . This results in a runtime of 2 m T byte + T start log Φ ( p ) + 2 m log Φ ( p ) T start T byte {\displaystyle 2mT_{\text{byte}}+T_{\text{start}}\log _{\Phi }(p)+{\sqrt {2m\log _{\Phi }(p)T_{\text{start}}T_{\text{byte}}}}} . == Two Tree Broadcast (23-Broadcast) == === Definition === This algorithm aims to improve on some disadvantages of tree structure models with pipelines. Normally in tree structure models with pipelines (see above methods), leaves receive just their data and cannot contribute to send and spread data. The algorithm concurrently uses two binary trees to communicate over. Those trees will be called tree A and B. Structurally in binary trees there are relatively more leave nodes than inner nodes. Basic Idea of this algorithm is to make a leaf node of tree A be an inner node of tree B. It has also the same technical function in opposite side from B to A tree. This means, two packets are sent and received by inner nodes and leaves in different steps. === Tree construction === The number of steps needed to construct two parallel-working binary trees is dependent on the amount of processors. Like with other structures one processor can is the root node who sends messages to two trees. It is not necessary to set a root node, because it is not hard to recognize that the direction of sending messages in binary tree is normally top to bottom. There is no limitation on the number of processors to build two binary trees. Let the height of the combined tree be h = ⌈log(p + 2)⌉. Tree A and B can have a height of h − 1 {\displaystyle h-1} . Especially, if the number of processors correspond to p = 2 h − 1 {\displaystyle p=2^{h}-1} , we can make both sides trees and a root node. To construct this model efficiently and easily with a fully built tree, we can use two methods called "Shifting" and "Mirroring" to get second tree. Let assume tree A is already modeled and tree B is supposed to be constructed based on tree A. We assume that we have p {\displaystyle p} processors ordered from 0 to p − 1 {\displaystyle p-1} . ==== Shifting ==== The "Shifting" method, first copies tree A and moves every node one position to the left to get tree B. The node, which will be located on -1, becomes a child of processor p − 2 {\displaystyle p-2} . ==== Mirroring ==== "Mirroring" is ideal for an even number of processors. With this method tree B can be more easily constructed by tree A, because there are no structural transformations in order to create the new tree. In addition, a symmetric process makes this approach simple. This method can also handle an odd number of processors, in this case, we can set processor p − 1 {\displaystyle p-1} as root node for both trees. For the remaining processors "Mirroring" can be used. === Coloring === We need to find a schedule in order to make sure that no processor has to send or receive two messages from two trees in a step. The edge, is a communication connection to connect two nodes, and can be labelled as either 0 or 1 to make sure that every processor can alternate between 0 and 1-labelled edges. The edges of A and B can be colored with two colors (0 and 1) such that no processor is connected to its parent nodes in A and B using edges of the same color- no processor is connected to its children nodes in A or B using edges of the same color. In every even step the edges with 0 are activated and edges with 1 are activated in every odd step. === Time complexity === In this case the number of packet k is divided in half for each tree. Both trees are working together the total number of packets k = k / 2 + k / 2 {\displaystyle k=k/2+k/2} (upper tree + bottom tree) In each binary tree sending a message to another nodes takes 2 i {\displaystyle 2i} steps until a processor has at least a packet in step i {\displaystyle i} . Therefore, we can calculate all steps as d := log 2 ( p + 1 ) ⇒ log 2 ( p + 1 ) ≈ log 2 ( p ) {\displaystyle d:=\log _{2}(p+1)\Rightarrow \log _{2}(p+1)\approx \log _{2}(p)} . The resulting run time is T ( m , p , k ) ≈ ( m k T byte + T start ) ( 2 d + k − 1 ) {\textstyle T(m,p,k)\approx ({\frac {m}{k}}T_{\text{byte}}+T_{\text{start}})(2d+k-1)} . (Optimal k = m ( 2 d − 1 ) T byte / T start {\textstyle k={\sqrt {{m(2d-1)T_{\text{byte}}}/{T_{\text{start}}}}}} ) This results in a run time of T ( m , p ) ≈ m T byte + T start ⋅ 2 log 2 ( p ) + m ⋅ 2 log 2 ( p ) T start T byte {\displaystyle T(m,p)\approx mT_{\text{byte}}+T_{\text{start}}\cdot 2\log _{2}(p)+{\sqrt {m\cdot 2\log _{2}(p)T_{\text{start}}T_{\text{byte}}}}} . == ESBT-Broadcasting (Edge-disjoint Spanning Binomial Trees) == In this section, another broadcasting algorithm with an underlying telephone communication model will be introduced. A Hypercube creates network system with p = 2 d ( d = 0 , 1 , 2 , 3 , . . . ) {\displaystyle p=2^{d}(d=0,1,2,3,...)} . Every node is represented by binary 0 , 1 {\displaystyle {0,1}} depending on the number of dimensions. Fundamentally ESBT(Edge-disjoint Spanning Binomial Trees) is based on hypercube graphs, pipelining( m {\displaystyle m} messages are divided by k {\displaystyle k} packets) and binomial trees. The Processor 0 d {\displaystyle 0^{d}} cyclically spreads packets to roots of ESB
Symbolic regression
Symbolic regression (SR) is a type of regression analysis that searches the space of mathematical expressions to find the model that best fits a given dataset, both in terms of accuracy and simplicity. No particular model is provided as a starting point for symbolic regression. Instead, initial expressions are formed by randomly combining mathematical building blocks such as mathematical operators, analytic functions, constants, and state variables. Usually, a subset of these primitives will be specified by the person operating it, but that's not a requirement of the technique. The symbolic regression problem for mathematical functions has been tackled with a variety of methods, including recombining equations most commonly using genetic programming, as well as more recent methods utilizing Bayesian methods and neural networks. Another non-classical alternative method to SR is called Universal Functions Originator (UFO), which has a different mechanism, search-space, and building strategy. Further methods such as Exact Learning attempt to transform the fitting problem into a moments problem in a natural function space, usually built around generalizations of the Meijer-G function. By not requiring a priori specification of a model, symbolic regression isn't affected by human bias, or unknown gaps in domain knowledge. It attempts to uncover the intrinsic relationships of the dataset, by letting the patterns in the data itself reveal the appropriate models, rather than imposing a model structure that is deemed mathematically tractable from a human perspective. The fitness function that drives the evolution of the models takes into account not only error metrics (to ensure the models accurately predict the data), but also special complexity measures, thus ensuring that the resulting models reveal the data's underlying structure in a way that's understandable from a human perspective. This facilitates reasoning and favors the odds of getting insights about the data-generating system, as well as improving generalisability and extrapolation behaviour by preventing overfitting. Accuracy and simplicity may be left as two separate objectives of the regression—in which case the optimum solutions form a Pareto front—or they may be combined into a single objective by means of a model selection principle such as minimum description length. It has been proven that symbolic regression is an NP-hard problem. Nevertheless, if the sought-for equation is not too complex it is possible to solve the symbolic regression problem exactly by generating every possible function (built from some predefined set of operators) and evaluating them on the dataset in question. == Difference from classical regression == While conventional regression techniques seek to optimize the parameters for a pre-specified model structure, symbolic regression avoids imposing prior assumptions, and instead infers the model from the data. In other words, it attempts to discover both model structures and model parameters. This approach has the disadvantage of having a much larger space to search, because not only the search space in symbolic regression is infinite, but there are an infinite number of models which will perfectly fit a finite data set (provided that the model complexity isn't artificially limited). This means that it will possibly take a symbolic regression algorithm longer to find an appropriate model and parametrization, than traditional regression techniques. This can be attenuated by limiting the set of building blocks provided to the algorithm, based on existing knowledge of the system that produced the data; but in the end, using symbolic regression is a decision that has to be balanced with how much is known about the underlying system. Nevertheless, this characteristic of symbolic regression also has advantages: because the evolutionary algorithm requires diversity in order to effectively explore the search space, the result is likely to be a selection of high-scoring models (and their corresponding set of parameters). Examining this collection could provide better insight into the underlying process, and allows the user to identify an approximation that better fits their needs in terms of accuracy and simplicity. == Benchmarking == === SRBench === In 2021, SRBench was proposed as a large benchmark for symbolic regression. In its inception, SRBench featured 14 symbolic regression methods, 7 other ML methods, and 252 datasets from PMLB. The benchmark intends to be a living project: it encourages the submission of improvements, new datasets, and new methods, to keep track of the state of the art in SR. === SRBench Competition 2022 === In 2022, SRBench announced the competition Interpretable Symbolic Regression for Data Science, which was held at the GECCO conference in Boston, MA. The competition pitted nine leading symbolic regression algorithms against each other on a novel set of data problems and considered different evaluation criteria. The competition was organized in two tracks, a synthetic track and a real-world data track. ==== Synthetic Track ==== In the synthetic track, methods were compared according to five properties: re-discovery of exact expressions; feature selection; resistance to local optima; extrapolation; and sensitivity to noise. Rankings of the methods were: QLattice PySR (Python Symbolic Regression) uDSR (Deep Symbolic Optimization) ==== Real-world Track ==== In the real-world track, methods were trained to build interpretable predictive models for 14-day forecast counts of COVID-19 cases, hospitalizations, and deaths in New York State. These models were reviewed by a subject expert and assigned trust ratings and evaluated for accuracy and simplicity. The ranking of the methods was: uDSR (Deep Symbolic Optimization) QLattice geneticengine (Genetic Engine) == Non-standard methods == Most symbolic regression algorithms prevent combinatorial explosion by implementing evolutionary algorithms that iteratively improve the best-fit expression over many generations. Recently, researchers have proposed algorithms utilizing other tactics in AI. Silviu-Marian Udrescu and Max Tegmark developed the "AI Feynman" algorithm, which attempts symbolic regression by training a neural network to represent the mystery function, then runs tests against the neural network to attempt to break up the problem into smaller parts. For example, if f ( x 1 , . . . , x i , x i + 1 , . . . , x n ) = g ( x 1 , . . . , x i ) + h ( x i + 1 , . . . , x n ) {\displaystyle f(x_{1},...,x_{i},x_{i+1},...,x_{n})=g(x_{1},...,x_{i})+h(x_{i+1},...,x_{n})} , tests against the neural network can recognize the separation and proceed to solve for g {\displaystyle g} and h {\displaystyle h} separately and with different variables as inputs. This is an example of divide and conquer, which reduces the size of the problem to be more manageable. AI Feynman also transforms the inputs and outputs of the mystery function in order to produce a new function which can be solved with other techniques, and performs dimensional analysis to reduce the number of independent variables involved. The algorithm was able to "discover" 100 equations from The Feynman Lectures on Physics, while a leading software using evolutionary algorithms, Eureqa, solved only 71. AI Feynman, in contrast to classic symbolic regression methods, requires a very large dataset in order to first train the neural network and is naturally biased towards equations that are common in elementary physics.
Relational data stream management system
A relational data stream management system (RDSMS) is a distributed, in-memory data stream management system (DSMS) that is designed to use standards-compliant SQL queries to process unstructured and structured data streams in real-time. Unlike SQL queries executed in a traditional RDBMS, which return a result and exit, SQL queries executed in a RDSMS do not exit, generating results continuously as new data become available. Continuous SQL queries in a RDSMS use the SQL Window function to analyze, join and aggregate data streams over fixed or sliding windows. Windows can be specified as time-based or row-based. == RDSMS SQL Query Examples == Continuous SQL queries in a RDSMS conform to the ANSI SQL standards. The most common RDSMS SQL query is performed with the declarative SELECT statement. A continuous SQL SELECT operates on data across one or more data streams, with optional keywords and clauses that include FROM with an optional JOIN subclause to specify the rules for joining multiple data streams, the WHERE clause and comparison predicate to restrict the records returned by the query, GROUP BY to project streams with common values into a smaller set, HAVING to filter records resulting from a GROUP BY, and ORDER BY to sort the results. The following is an example of a continuous data stream aggregation using a SELECT query that aggregates a sensor stream from a weather monitoring station. The SELECTquery aggregates the minimum, maximum and average temperature values over a one-second time period, returning a continuous stream of aggregated results at one second intervals. RDSMS SQL queries also operate on data streams over time or row-based windows. The following example shows a second continuous SQL query using the WINDOW clause with a one-second duration. The WINDOW clause changes the behavior of the query, to output a result for each new record as it arrives. Hence the output is a stream of incrementally updated results with zero result latency.