A genetic operator is an operator used in evolutionary algorithms (EA) to guide the algorithm towards a solution to a given problem. There are three main types of operators (mutation, crossover and selection), which must work in conjunction with one another in order for the algorithm to be successful. Genetic operators are used to create and maintain genetic diversity (mutation operator), combine existing solutions (also known as chromosomes) into new solutions (crossover) and select between solutions (selection). The classic representatives of evolutionary algorithms include genetic algorithms, evolution strategies, genetic programming and evolutionary programming. In his book discussing the use of genetic programming for the optimization of complex problems, computer scientist John Koza has also identified an 'inversion' or 'permutation' operator; however, the effectiveness of this operator has never been conclusively demonstrated and this operator is rarely discussed in the field of genetic programming. For combinatorial problems, however, these and other operators tailored to permutations are frequently used by other EAs. Mutation (or mutation-like) operators are said to be unary operators, as they only operate on one chromosome at a time. In contrast, crossover operators are said to be binary operators, as they operate on two chromosomes at a time, combining two existing chromosomes into one new chromosome. == Operators == Genetic variation is a necessity for the process of evolution. Genetic operators used in evolutionary algorithms are analogous to those in the natural world: survival of the fittest, or selection; reproduction (crossover, also called recombination); and mutation. === Selection === Selection operators give preference to better candidate solutions (chromosomes), allowing them to pass on their 'genes' to the next generation (iteration) of the algorithm. The best solutions are determined using some form of objective function (also known as a 'fitness function' in evolutionary algorithms), before being passed to the crossover operator. Different methods for choosing the best solutions exist, for example, fitness proportionate selection and tournament selection. A further or the same selection operator is used to determine the individuals for being selected to form the next parental generation. The selection operator may also ensure that the best solution(s) from the current generation always become(s) a member of the next generation without being altered; this is known as elitism or elitist selection. === Crossover === Crossover is the process of taking more than one parent solutions (chromosomes) and producing a child solution from them. By recombining portions of good solutions, the evolutionary algorithm is more likely to create a better solution. As with selection, there are a number of different methods for combining the parent solutions, including the edge recombination operator (ERO) and the 'cut and splice crossover' and 'uniform crossover' methods. The crossover method is often chosen to closely match the chromosome's representation of the solution; this may become particularly important when variables are grouped together as building blocks, which might be disrupted by a non-respectful crossover operator. Similarly, crossover methods may be particularly suited to certain problems; the ERO is considered a good option for solving the travelling salesman problem. === Mutation === The mutation operator encourages genetic diversity amongst solutions and attempts to prevent the evolutionary algorithm converging to a local minimum by stopping the solutions becoming too close to one another. In mutating the current pool of solutions, a given solution may change between slightly and entirely from the previous solution. By mutating the solutions, an evolutionary algorithm can reach an improved solution solely through the mutation operator. Again, different methods of mutation may be used; these range from a simple bit mutation (flipping random bits in a binary string chromosome with some low probability) to more complex mutation methods in which genes in the solution are changed, for example by adding a random value from the Gaussian distribution to the current gene value. As with the crossover operator, the mutation method is usually chosen to match the representation of the solution within the chromosome. == Combining operators == While each operator acts to improve the solutions produced by the evolutionary algorithm working individually, the operators must work in conjunction with each other for the algorithm to be successful in finding a good solution. Using the selection operator on its own will tend to fill the solution population with copies of the best solution from the population. If the selection and crossover operators are used without the mutation operator, the algorithm will tend to converge to a local minimum, that is, a good but sub-optimal solution to the problem. Using the mutation operator on its own leads to a random walk through the search space. Only by using all three operators together can the evolutionary algorithm become a noise-tolerant global search algorithm, yielding good solutions to the problem at hand.
Automated storage and retrieval system
An automated storage and retrieval system (ASRS or AS/RS) consists of a variety of computer-controlled systems for automatically placing and retrieving loads from defined storage locations. Automated storage and retrieval systems (AS/RS) are typically used in applications where: There is a very high volume of loads being moved into and out of storage Storage density is important because of space constraints No value is added in this process (no processing, only storage and transport) Accuracy is critical because of potential expensive damages to the load An AS/RS can be used with standard loads as well as nonstandard loads, meaning that each standard load can fit in a uniformly-sized volume; for example, the film canisters in the image of the Defense Visual Information Center are each stored as part of the contents of the uniformly sized metal boxes, which are shown in the image. Standard loads simplify the handling of a request of an item. In addition, audits of the accuracy of the inventory of contents can be restricted to the contents of an individual metal box, rather than undergoing a top-to-bottom search of the entire facility, for a single item. They can also be used in self storage places. == Overview == AS/RS systems are designed for automated storage and retrieval of parts and items in manufacturing, distribution, retail, wholesale and institutions. They first originated in the 1960s, initially focusing on heavy pallet loads but with the evolution of the technology the handled loads have become smaller. The systems operate under computerized control, maintaining an inventory of stored items. Retrieval of items is accomplished by specifying the item type and quantity to be retrieved. The computer determines where in the storage area the item can be retrieved from and schedules the retrieval. It directs the proper automated storage and retrieval machine (SRM) to the location where the item is stored and directs the machine to deposit the item at a location where it is to be picked up. A system of conveyors and or automated guided vehicles is sometimes part of the AS/RS system. These take loads into and out of the storage area and move them to the manufacturing floor or loading docks. To store items, the pallet or tray is placed at an input station for the system, the information for inventory is entered into a computer terminal and the AS/RS system moves the load to the storage area, determines a suitable location for the item, and stores the load. As items are stored into or retrieved from the racks, the computer updates its inventory accordingly. The benefits of an AS/RS system include reduced labor for transporting items into and out of inventory, reduced inventory levels, more accurate tracking of inventory, and space savings. Items are often stored more densely than in systems where items are stored and retrieved manually. Within the storage, items can be placed on trays or hang from bars, which are attached to chains/drives in order to move up and down. The equipment required for an AS/RS include a storage & retrieval machine (SRM) that is used for rapid storage and retrieval of material. SRMs are used to move loads vertically or horizontally, and can also move laterally to place objects in the correct storage location. The trend towards Just In Time production often requires sub-pallet level availability of production inputs, and AS/RS is a much faster way of organizing the storage of smaller items next to production lines. The Material Handling Institute of America (MHIA), the non-profit trade association for the material handling world, and its members have categorised AS/RS into two primary segments: Fixed Aisle and Carousels/Vertical Lift Modules (VLMs). Both sets of technologies provide automated storage and retrieval for parts and items, but use different technologies. Each technology has its unique set of benefits and disadvantages. Fixed Aisle systems are characteristically larger systems whereas carousels and Vertical Lift Modules are used individually or grouped, but in small to medium-sized applications. A fixed-aisle AS/R machine (stacker crane) is one of two main designs: single-masted or double masted. Most are supported on a track and ceiling guided at the top by guide rails or channels to ensure accurate vertical alignment, although some are suspended from the ceiling. The 'shuttles' that make up the system travel between fixed storage shelves to deposit or retrieve a requested load (ranging from a single book in a library system to a several ton pallet of goods in a warehouse system). The entire unit moves horizontally within an aisle, while the shuttles are able to elevate up to the necessary height to reach the load, and can extend and retract to store or retrieve loads that are several positions deep in the shelving. A semi-automated system can be achieved by utilizing only specialized shuttles within an existing rack system. Another AS/RS technology is known as shuttle technology. In this technology the horizontal movement is made by independent shuttles each operating on one level of the rack while a lift at a fixed position within the rack is responsible for the vertical movement. By using two separate machines for these two axes the shuttle technology is able to provide higher throughput rates than stacker cranes. Storage and Retrieval Machines pick up or drop off loads to the rest of the supporting transportation system at specific stations, where inbound and outbound loads are precisely positioned for proper handling. In addition, there are several types of Automated Storage & Retrieval Systems (AS/RS) devices called Unit-load AS/RS, Mini-load AS/RS, Mid-Load AS/RS, Vertical Lift Modules (VLMs), Horizontal Carousels and Vertical Carousels. These systems are used either as stand-alone units or in integrated workstations called pods or systems. These units are usually integrated with various types of pick to light systems and use either a microprocessor controller for basic usage or inventory management software. These systems are ideal for increasing space utilization up to 90%, productivity levels by 90%, accuracy to 99.9%+ levels and throughput up to 750 lines per hour/per operator or more depending on the configuration of the system. == Horizontal carousels == Robotic Inserter/Extractor devices can be used for horizontal carousels. The robotic device is positioned in the front or rear of up to three horizontal carousels tiered high. The robot grabs the tote required in the order and often replenishes at the same time to speed up throughput. The tote(s) are then delivered to a conveyor, which routes it to a work station for picking or replenishing. Up to eight transactions per minute per unit can be done. Totes or containers up to 36" x 36" x 36" can be used in a system. On a simplistic level, horizontal carousels are also often used as "rotating shelving". With simple "fetch" command, items are brought to the operator and otherwise wasted space is eliminated. AS/RS Applications: Most applications of AS/RS technology have been associated with warehousing and distribution operations. An AS/RS can also be used to store raw materials and work in process in manufacturing. Three application areas can be distinguished for AS/RS: (1) Unit load storage and handling, (2) Order picking, and (3) Work in process storage. Unit load storage and retrieval applications are represented by unit load AS/RS and deep-lane storage systems. These kinds of applications are commonly found in warehousing for finishing goods in a distribution center, rarely in manufacturing. Deep-lane systems are used in the food industry. As described above, order picking involves retrieving materials in less than full unit load quantities. Minilpass, man-on board, and items retrieval systems are used for this second application area. Work in process storage is a more recent application of automated storage technology. While it is desirable to minimize the amount of work in process, WIP is unavoidable and must be effectively managed. Automated storage systems, either automated storage/retrieval systems or carousel systems, represent an efficient way to store materials between processing steps, particularly in batch and job shop production. In high production, work in process is often carried between operations by conveyor system, which this serve both storage and transport functions. === Inventory Category-specific AS/RS === Each inventory category—raw materials, work-in-process, and finished goods—requires its own specialized Automated Storage and Retrieval System (AS/RS). Particularly for work-in-process (WIP) inventories, due to variations in manufacturing processes, the AS/RS systems are significantly different in design and function, tailored specifically to match unique handling, storage, and retrieval requirements === Installed applications === Installed applications of this technology can be wide-ranging. In some librarie
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Weighted automaton
In theoretical computer science and formal language theory, a weighted automaton or weighted finite-state machine is a generalization of a finite-state machine in which the edges have weights, for example real numbers or integers. Finite-state machines are only capable of answering decision problems; they take as input a string and produce a Boolean output, i.e. either "accept" or "reject". In contrast, weighted automata produce a quantitative output, for example a count of how many answers are possible on a given input string, or a probability of how likely the input string is according to a probability distribution. They are one of the simplest studied models of quantitative automata. The definition of a weighted automaton is generally given over an arbitrary semiring R {\displaystyle R} , an abstract set with an addition operation + {\displaystyle +} and a multiplication operation × {\displaystyle \times } . The automaton consists of a finite set of states, a finite input alphabet of characters Σ {\displaystyle \Sigma } and edges which are labeled with both a character in Σ {\displaystyle \Sigma } and a weight in R {\displaystyle R} . The weight of any path in the automaton is defined to be the product of weights along the path, and the weight of a string is the sum of the weights of all paths which are labeled with that string. The weighted automaton thus defines a function from Σ ∗ {\displaystyle \Sigma ^{}} to R {\displaystyle R} . Weighted automata generalize deterministic finite automata (DFAs) and nondeterministic finite automata (NFAs), which correspond to weighted automata over the Boolean semiring, where addition is logical disjunction and multiplication is logical conjunction. In the DFA case, there is only one accepting path for any input string, so disjunction is not applied. When the weights are real numbers and the outgoing weights for each state add to one, weighted automata can be considered a probabilistic model and are also known as probabilistic automata. These machines define a probability distribution over all strings, and are related to other probabilistic models such as Markov decision processes and Markov chains. Weighted automata have applications in natural language processing where they are used to assign weights to words and sentences, as well as in image compression. They were first introduced by Marcel-Paul Schützenberger in his 1961 paper On the definition of a family of automata. Since their introduction, many extensions have been proposed, for example nested weighted automata, cost register automata, and weighted finite-state transducers. Researchers have studied weighted automata from the perspective of learning a machine from its input-output behavior (see computational learning theory) and studying decidability questions. == Definition == A commutative semiring (or rig) is a set R equipped with two distinguished elements 0 ≠ 1 {\displaystyle 0\neq 1} and addition and multiplication operations ⊕ {\displaystyle \oplus } and ⊗ {\displaystyle \otimes } such that ⊕ {\displaystyle \oplus } is commutative and associative with identity 0 {\displaystyle 0} , ⊗ {\displaystyle \otimes } is commutative and associative with identity 1 {\displaystyle 1} , ⊗ {\displaystyle \otimes } distributes over ⊕ {\displaystyle \oplus } , and 0 is an absorbing element for ⊗ {\displaystyle \otimes } . A weighted automaton over R {\displaystyle R} is a tuple A = ( Q , Σ , Δ , I , F ) {\displaystyle {\mathcal {A}}=(Q,\Sigma ,\Delta ,I,F)} where: Q {\displaystyle Q} is a finite set of states. Σ {\displaystyle \Sigma } is a finite alphabet. Δ ⊆ Q × Σ × R × Q {\displaystyle \Delta \subseteq Q\times \Sigma \times R\times Q} is a finite set of transitions ( q , σ , w , q ′ ) {\displaystyle (q,\sigma ,w,q')} , where σ {\displaystyle \sigma } is called a character and w {\displaystyle w} is called a weight. I : Q → R {\displaystyle I:Q\to R} is an initial weight function. F : Q → R {\displaystyle F:Q\to R} is a final weight function. A path on input w ∈ Σ ∗ {\displaystyle w\in \Sigma ^{}} is a finite path in the graph, where the concatenation of the character labels equals w {\displaystyle w} . The weight of the path q 0 , q 1 , … , q n {\displaystyle q_{0},q_{1},\ldots ,q_{n}} is the product ( ⊗ {\displaystyle \otimes } ) of the weights along the path, additionally multiplied by the initial and final weights I ( q 0 ) ⊗ F ( q n ) {\displaystyle I(q_{0})\otimes F(q_{n})} . The weight of the word w {\displaystyle w} is the sum ( ⊕ {\displaystyle \oplus } ) of the weights of all paths on input w {\displaystyle w} (or 0 if there are no accepting paths). In this way the machine defines a function [ [ A ] ] : Σ ∗ → R {\displaystyle [\![{\mathcal {A}}]\!]:\Sigma ^{}\to R} . == Ambiguity and determinism == Since Δ {\displaystyle \Delta } is a set of transitions, weighted automata allow multiple transitions (or paths) on a single input string. Therefore a weighted automaton can be considered analogous to a nondeterministic finite automaton (NFA). As is the case with NFAs, restrictions of weighted automata are considered that correspond to the concepts of deterministic finite automaton and unambiguous finite automaton (deterministic weighted automata and unambiguous weighted automata, respectively). First, a preliminary definition: the underlying NFA of A {\displaystyle {\mathcal {A}}} is an NFA formed by removing all transitions with weight 0 {\displaystyle 0} and then erasing all of the weights on the transitions Δ {\displaystyle \Delta } , so that the new transition set lies in Q × Σ × Q {\displaystyle Q\times \Sigma \times Q} . The initial states and final states are the set of states q {\displaystyle q} such that I ( q ) ≠ 0 {\displaystyle I(q)\neq 0} and F ( q ) ≠ 0 {\displaystyle F(q)\neq 0} , respectively. A weighted automaton is deterministic if the underlying NFA is deterministic and unambiguous if the underlying NFA is unambiguous. Every deterministic weighted automaton is unambiguous. In both the deterministic and unambiguous cases, there is always at most one accepting path, so the ⊕ {\displaystyle \oplus } operation is never applied and can be omitted from the definition. == Variations == The requirement that there is a zero element for ⊕ {\displaystyle \oplus } is sometimes omitted; in this case the machine defines a partial function from Σ ∗ {\displaystyle \Sigma ^{}} to R {\displaystyle R} rather than a total function. It is possible to extend the definition to allow epsilon transitions ( q , ϵ , w , q ′ ) {\displaystyle (q,\epsilon ,w,q')} , where ϵ {\displaystyle \epsilon } is the empty string. In this case, one must then require that there are no cycles of epsilon transitions. This does not increase the expressiveness of weighted automata. If epsilon transitions are allowed, the initial weights and final weights can be replaced by initial and final sets of states without loss of expressiveness. Some authors omit the initial and final weight functions I {\displaystyle I} and F {\displaystyle F} . Instead, I {\displaystyle I} and F {\displaystyle F} are replaced by a set of initial and final states. If epsilon transitions are not present, this technically decreases expressiveness as it forces [ [ A ] ] ( ε ) {\displaystyle [\![{\mathcal {A}}]\!](\varepsilon )} to depend only on the number of states that are both initial and final. The transition function can be given as a matrix Δ σ ∈ R Q × Q {\displaystyle \Delta _{\sigma }\in R^{Q\times Q}} with entries in R {\displaystyle R} for each σ {\displaystyle \sigma } , rather than a set of transitions. The entry of the matrix at ( q , q ′ ) {\displaystyle (q,q')} is the sum of all transitions labeled ( q , σ , q ′ ) {\displaystyle (q,\sigma ,q')} . Some authors restrict to specific semirings, such as N {\displaystyle \mathbb {N} } or Z {\displaystyle \mathbb {Z} } , particularly when studying decidability results.
Deep learning in photoacoustic imaging
Photoacoustic imaging (PA) is based on the photoacoustic effect, in which optical absorption causes a rise in temperature, which causes a subsequent rise in pressure via thermo-elastic expansion. This pressure rise propagates through the tissue and is sensed via ultrasonic transducers. Due to the proportionality between the optical absorption, the rise in temperature, and the rise in pressure, the ultrasound pressure wave signal can be used to quantify the original optical energy deposition within the tissue. Photoacoustic imaging has applications of deep learning in both photoacoustic computed tomography (PACT) and photoacoustic microscopy (PAM). PACT utilizes wide-field optical excitation and an array of unfocused ultrasound transducers. Similar to other computed tomography methods, the sample is imaged at multiple view angles, which are then used to perform an inverse reconstruction algorithm based on the detection geometry (typically through universal backprojection, modified delay-and-sum, or time reversal ) to elicit the initial pressure distribution within the tissue. PAM on the other hand uses focused ultrasound detection combined with weakly focused optical excitation (acoustic resolution PAM or AR-PAM) or tightly focused optical excitation (optical resolution PAM or OR-PAM). PAM typically captures images point-by-point via a mechanical raster scanning pattern. At each scanned point, the acoustic time-of-flight provides axial resolution while the acoustic focusing yields lateral resolution. == Applications of deep learning in PACT == The first application of deep learning in PACT was by Reiter et al. in which a deep neural network was trained to learn spatial impulse responses and locate photoacoustic point sources. The resulting mean axial and lateral point location errors on 2,412 of their randomly selected test images were 0.28 mm and 0.37 mm respectively. After this initial implementation, the applications of deep learning in PACT have branched out primarily into removing artifacts from acoustic reflections, sparse sampling, limited-view, and limited-bandwidth. There has also been some recent work in PACT toward using deep learning for wavefront localization. There have been networks based on fusion of information from two different reconstructions to improve the reconstruction using deep learning fusion based networks. === Using deep learning to locate photoacoustic point sources === Traditional photoacoustic beamforming techniques modeled photoacoustic wave propagation by using detector array geometry and the time-of-flight to account for differences in the PA signal arrival time. However, this technique failed to account for reverberant acoustic signals caused by acoustic reflection, resulting in acoustic reflection artifacts that corrupt the true photoacoustic point source location information. In Reiter et al., a convolutional neural network (similar to a simple VGG-16 style architecture) was used that took pre-beamformed photoacoustic data as input and outputted a classification result specifying the 2-D point source location. ==== Deep learning for PA wavefront localization ==== Johnstonbaugh et al. was able to localize the source of photoacoustic wavefronts with a deep neural network. The network used was an encoder-decoder style convolutional neural network. The encoder-decoder network was made of residual convolution, upsampling, and high field-of-view convolution modules. A Nyquist convolution layer and differentiable spatial-to-numerical transform layer were also used within the architecture. Simulated PA wavefronts served as the input for training the model. To create the wavefronts, the forward simulation of light propagation was done with the NIRFast toolbox and the light-diffusion approximation, while the forward simulation of sound propagation was done with the K-Wave toolbox. The simulated wavefronts were subjected to different scattering mediums and Gaussian noise. The output for the network was an artifact free heat map of the targets axial and lateral position. The network had a mean error rate of less than 30 microns when localizing target below 40 mm and had a mean error rate of 1.06 mm for localizing targets between 40 mm and 60 mm. With a slight modification to the network, the model was able to accommodate multi target localization. A validation experiment was performed in which pencil lead was submerged into an intralipid solution at a depth of 32 mm. The network was able to localize the lead's position when the solution had a reduced scattering coefficient of 0, 5, 10, and 15 cm−1. The results of the network show improvements over standard delay-and-sum or frequency-domain beamforming algorithms and Johnstonbaugh proposes that this technology could be used for optical wavefront shaping, circulating melanoma cell detection, and real-time vascular surgeries. === Removing acoustic reflection artifacts (in the presence of multiple sources and channel noise) === Building on the work of Reiter et al., Allman et al. utilized a full VGG-16 architecture to locate point sources and remove reflection artifacts within raw photoacoustic channel data (in the presence of multiple sources and channel noise). This utilization of deep learning trained on simulated data produced in the MATLAB k-wave library, and then later reaffirmed their results on experimental data. === Ill-posed PACT reconstruction === In PACT, tomographic reconstruction is performed, in which the projections from multiple solid angles are combined to form an image. When reconstruction methods like filtered backprojection or time reversal, are ill-posed inverse problems due to sampling under the Nyquist-Shannon's sampling requirement or with limited-bandwidth/view, the resulting reconstruction contains image artifacts. Traditionally these artifacts were removed with slow iterative methods like total variation minimization, but the advent of deep learning approaches has opened a new avenue that utilizes a priori knowledge from network training to remove artifacts. In the deep learning methods that seek to remove these sparse sampling, limited-bandwidth, and limited-view artifacts, the typical workflow involves first performing the ill-posed reconstruction technique to transform the pre-beamformed data into a 2-D representation of the initial pressure distribution that contains artifacts. Then, a convolutional neural network (CNN) is trained to remove the artifacts, in order to produce an artifact-free representation of the ground truth initial pressure distribution. ==== Using deep learning to remove sparse sampling artifacts ==== When the density of uniform tomographic view angles is under what is prescribed by the Nyquist-Shannon's sampling theorem, it is said that the imaging system is performing sparse sampling. Sparse sampling typically occurs as a way of keeping production costs low and improving image acquisition speed. The typical network architectures used to remove these sparse sampling artifacts are U-net and Fully Dense (FD) U-net. Both of these architectures contain a compression and decompression phase. The compression phase learns to compress the image to a latent representation that lacks the imaging artifacts and other details. The decompression phase then combines with information passed by the residual connections in order to add back image details without adding in the details associated with the artifacts. FD U-net modifies the original U-net architecture by including dense blocks that allow layers to utilize information learned by previous layers within the dense block. Another technique was proposed using a simple CNN based architecture for removal of artifacts and improving the k-wave image reconstruction. ==== Removing limited-view artifacts with deep learning ==== When a region of partial solid angles are not captured, generally due to geometric limitations, the image acquisition is said to have limited-view. As illustrated by the experiments of Davoudi et al., limited-view corruptions can be directly observed as missing information in the frequency domain of the reconstructed image. Limited-view, similar to sparse sampling, makes the initial reconstruction algorithm ill-posed. Prior to deep learning, the limited-view problem was addressed with complex hardware such as acoustic deflectors and full ring-shaped transducer arrays, as well as solutions like compressed sensing, weighted factor, and iterative filtered backprojection. The result of this ill-posed reconstruction is imaging artifacts that can be removed by CNNs. The deep learning algorithms used to remove limited-view artifacts include U-net and FD U-net, as well as generative adversarial networks (GANs) and volumetric versions of U-net. One GAN implementation of note improved upon U-net by using U-net as a generator and VGG as a discriminator, with the Wasserstein metric and gradient penalty to stabilize training (WGAN-GP). ==== Pixel-wise interpolation
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