A vinyl cutter is an entry-level machine for making signs. Computer-designed vector files with patterns and letters are directly cut on the roll of vinyl which is mounted and fed into the vinyl cutter through USB or serial cable. Vinyl cutters are mainly used to make signs, banners and advertisements. Advertisements seen on automobiles and vans are often made with vinyl cut letters. While these machines were designed for cutting vinyl, they can also cut through computer and specialty papers, as well as thicker items like thin sheets of magnet. In addition to sign business, vinyl cutters are commonly used for apparel decoration. To decorate apparel, a vector design needs to be cut in mirror image, weeded, and then heat applied using a commercial heat press or a hand iron for home use. Some businesses use their vinyl cutter to produce both signs and custom apparel. Many crafters also have vinyl cutters for home use. These require little maintenance, and the vinyl can be bought in bulk relatively cheaply. Vinyl cutters are also often used by stencil artists to create single use or reusable stencil art and lettering == How it works == A vinyl cutter is a type of computer-controlled machine tool. The computer controls the movement of a sharp blade over the surface of the material as it would the nozzles of an ink-jet printer. This blade is used to cut out shapes and letters from sheets of thin self-adhesive plastic (vinyl). The vinyl can then be stuck to a variety of surfaces depending on the adhesive and type of material. To cut out a design, a vector-based image must be created using vector drawing software. Some vinyl cutters are marketed to small in-home businesses and require download and use of a proprietary editing software. The design is then sent to the cutter where it cuts along the vector paths laid out in the design. The cutter is capable of moving the blade on an X and Y axis over the material, cutting it into the required shapes. The vinyl material comes in long rolls allowing projects with significant length like banners or billboards to be easily cut. A major limitation with vinyl cutters is that they can only cut shapes from solid colours of vinyl, paper, card or thin plastic sheets such as Mylar. The type and thickness of material will vary for each cutter and how much downforce the cutter is capable of. If the material has no backing, a backing sheet, material or cutting mat and a temporary adhesive are needed to allow the cutter to cut through the material. A design with multiple colours must have each colour cut separately and then layered on top of each other as it is applied to the substrate. This is a process that is often applied in stencil art. Also, since the shapes are cut out of solid colours, photographs and gradients cannot be reproduced with a stand-alone cutter. === Design creation === Designs are created using vector-based software like Adobe Illustrator, FlexiSign, EasyCutPro, or other software. Vector artwork is either drawn with lines, shapes and text or images are vectorized thus create vector shapes. Most cutters (also called plotters) require special software to load/edit the artwork and communicate with the cutter. Computer designed images are loaded onto the vinyl cutter via a wired connection or over a wireless protocol. Then the vinyl is loaded into the machine where it is automatically fed through and cut to follow the set design. The vinyl can be placed on an adhesive mat to stabilize the vinyl when cutting smaller designs. === Types of vinyl === Adhesive vinyl is the type of vinyl used for store windows, car decals, signage, and more. Adhesive vinyl is applied with a transfer medium often called "transfer tape" or "carrier sheet". Heat transfer vinyl is the type of vinyl used to apply a design to fabric including t-shirts, tea towels, canvas bags, and more. Heat Transfer vinyl can be applied using a heat press or an iron, though the constant pressure and heat from a heat press is recommended by experts. === Using other materials === In addition to vinyl some cutters are capable of cutting other materials such as paper, card, plastic sheets and even thin wood. The thickness and type of material that can be cut will depend on the model of the cutter and heavily depends on the downforce. Cricut is a popular home cutter used by arts and craft enthusiasts since it allows for a wide use of different materials and is similar in size to a household printer and has strong downforce for its size. === Backing and cutting mat === If you cut material that doesn't have an adhesive backing you will require a cutting mat that you need to attach your material to. Some cutting mats are sticky, others will require you to use a temporary adhesive and/or masking tape to keep the material in place when cutting. === Cutting === The vinyl cutter uses a small knife or blade to precisely cut the outline of figures into a sheet or piece of vinyl, but not the release liner. The process of cutting vinyl material without penetrating it completely is referred to as "kiss cutting". The knife moves side to side and turns, while the vinyl is moved beneath the knife. The results from the cut process is an image cut into the material. === Weeding === The material is then 'weeded' where the excess parts of the figures are removed from the release liner. It is possible to remove the positive parts, which would give a negative decal, or remove the negative parts, giving a positive decal. Removing the figure would be like removing the positive, giving a negative image of the figures. === Transfer tape === A sheet of transfer tape with an adhesive backing is laid on the weeded vinyl when necessary. Heat Transfer vinyl often does not require use of a separate transfer tape. A roller is applied to the tape, causing it to adhere to the vinyl. The transfer tape and the weeded vinyl is pulled off the release liner, and applied to a substrate, such as a sheet of aluminium. This results in an aluminium sign with vinyl figures. == Uses == In addition to the capabilities of the cutter itself, adhesive vinyl comes in a wide variety of colors and materials including gold and silver foil, vinyl that simulates frosted glass, holographic vinyl, reflective vinyl, thermal transfer material, and even clear vinyl embedded with gold leaf. (Often used in the lettering on fire trucks and rescue vehicles.) As the vinyl film is supplied by the manufacturer, it comes attached to a release liner. == Challenges when cutting on a vinyl cutter == Cutting on a vinyl cutter requires careful calibration to achieve clean and accurate results, especially when the goal is to cut through only the top layer of material while leaving the backing intact. One of the most common challenges is setting the correct cutting depth. If the blade is not lowered enough, the vinyl material may not separate properly; if it goes too deep, it can cut through the backing layer and potentially damage the cutting mat. The cutting depth on the vinyl cutter machines typically does not exceed 1 mm. Another frequent issue is the mismatch between the blade and the type of material being processed. Using an inappropriate blade can lead to uneven cuts, premature dulling of the edge, and torn or frayed material. The overall quality of the output also depends on factors such as the cutting speed, blade sharpening and cutting angle, and the material the knife is made of.
List of computer graphics journals
List of computer graphics journals includes notable peer-reviewed scientific and academic journals that focus on computer graphics, visualization, and related areas such as rendering, animation, image processing, and geometric modeling. == Journals == ACM Transactions on Graphics Computers & Graphics IEEE Computer Graphics and Applications IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems Graphical Models Journal of Computer Graphics Techniques Presence: Teleoperators and Virtual Environments Virtual Reality Simulation & Gaming
Regularization perspectives on support vector machines
Within mathematical analysis, Regularization perspectives on support-vector machines provide a way of interpreting support-vector machines (SVMs) in the context of other regularization-based machine-learning algorithms. SVM algorithms categorize binary data, with the goal of fitting the training set data in a way that minimizes the average of the hinge-loss function and L2 norm of the learned weights. This strategy avoids overfitting via Tikhonov regularization and in the L2 norm sense and also corresponds to minimizing the bias and variance of our estimator of the weights. Estimators with lower Mean squared error predict better or generalize better when given unseen data. Specifically, Tikhonov regularization algorithms produce a decision boundary that minimizes the average training-set error and constrain the Decision boundary not to be excessively complicated or overfit the training data via a L2 norm of the weights term. The training and test-set errors can be measured without bias and in a fair way using accuracy, precision, Auc-Roc, precision-recall, and other metrics. Regularization perspectives on support-vector machines interpret SVM as a special case of Tikhonov regularization, specifically Tikhonov regularization with the hinge loss for a loss function. This provides a theoretical framework with which to analyze SVM algorithms and compare them to other algorithms with the same goals: to generalize without overfitting. SVM was first proposed in 1995 by Corinna Cortes and Vladimir Vapnik, and framed geometrically as a method for finding hyperplanes that can separate multidimensional data into two categories. This traditional geometric interpretation of SVMs provides useful intuition about how SVMs work, but is difficult to relate to other machine-learning techniques for avoiding overfitting, like regularization, early stopping, sparsity and Bayesian inference. However, once it was discovered that SVM is also a special case of Tikhonov regularization, regularization perspectives on SVM provided the theory necessary to fit SVM within a broader class of algorithms. This has enabled detailed comparisons between SVM and other forms of Tikhonov regularization, and theoretical grounding for why it is beneficial to use SVM's loss function, the hinge loss. == Theoretical background == In the statistical learning theory framework, an algorithm is a strategy for choosing a function f : X → Y {\displaystyle f\colon \mathbf {X} \to \mathbf {Y} } given a training set S = { ( x 1 , y 1 ) , … , ( x n , y n ) } {\displaystyle S=\{(x_{1},y_{1}),\ldots ,(x_{n},y_{n})\}} of inputs x i {\displaystyle x_{i}} and their labels y i {\displaystyle y_{i}} (the labels are usually ± 1 {\displaystyle \pm 1} ). Regularization strategies avoid overfitting by choosing a function that fits the data, but is not too complex. Specifically: f = argmin f ∈ H { 1 n ∑ i = 1 n V ( y i , f ( x i ) ) + λ ‖ f ‖ H 2 } , {\displaystyle f={\underset {f\in {\mathcal {H}}}{\operatorname {argmin} }}\left\{{\frac {1}{n}}\sum _{i=1}^{n}V(y_{i},f(x_{i}))+\lambda \|f\|_{\mathcal {H}}^{2}\right\},} where H {\displaystyle {\mathcal {H}}} is a hypothesis space of functions, V : Y × Y → R {\displaystyle V\colon \mathbf {Y} \times \mathbf {Y} \to \mathbb {R} } is the loss function, ‖ ⋅ ‖ H {\displaystyle \|\cdot \|_{\mathcal {H}}} is a norm on the hypothesis space of functions, and λ ∈ R {\displaystyle \lambda \in \mathbb {R} } is the regularization parameter. When H {\displaystyle {\mathcal {H}}} is a reproducing kernel Hilbert space, there exists a kernel function K : X × X → R {\displaystyle K\colon \mathbf {X} \times \mathbf {X} \to \mathbb {R} } that can be written as an n × n {\displaystyle n\times n} symmetric positive-definite matrix K {\displaystyle \mathbf {K} } . By the representer theorem, f ( x i ) = ∑ j = 1 n c j K i j , and ‖ f ‖ H 2 = ⟨ f , f ⟩ H = ∑ i = 1 n ∑ j = 1 n c i c j K ( x i , x j ) = c T K c . {\displaystyle f(x_{i})=\sum _{j=1}^{n}c_{j}\mathbf {K} _{ij},{\text{ and }}\|f\|_{\mathcal {H}}^{2}=\langle f,f\rangle _{\mathcal {H}}=\sum _{i=1}^{n}\sum _{j=1}^{n}c_{i}c_{j}K(x_{i},x_{j})=c^{T}\mathbf {K} c.} == Special properties of the hinge loss == The simplest and most intuitive loss function for categorization is the misclassification loss, or 0–1 loss, which is 0 if f ( x i ) = y i {\displaystyle f(x_{i})=y_{i}} and 1 if f ( x i ) ≠ y i {\displaystyle f(x_{i})\neq y_{i}} , i.e. the Heaviside step function on − y i f ( x i ) {\displaystyle -y_{i}f(x_{i})} . However, this loss function is not convex, which makes the regularization problem very difficult to minimize computationally. Therefore, we look for convex substitutes for the 0–1 loss. The hinge loss, V ( y i , f ( x i ) ) = ( 1 − y f ( x ) ) + {\displaystyle V{\big (}y_{i},f(x_{i}){\big )}={\big (}1-yf(x){\big )}_{+}} , where ( s ) + = max ( s , 0 ) {\displaystyle (s)_{+}=\max(s,0)} , provides such a convex relaxation. In fact, the hinge loss is the tightest convex upper bound to the 0–1 misclassification loss function, and with infinite data returns the Bayes-optimal solution: f b ( x ) = { 1 , p ( 1 ∣ x ) > p ( − 1 ∣ x ) , − 1 , p ( 1 ∣ x ) < p ( − 1 ∣ x ) . {\displaystyle f_{b}(x)={\begin{cases}1,&p(1\mid x)>p(-1\mid x),\\-1,&p(1\mid x) Trying to pick the best AI video generator? An AI video generator is software that uses machine learning to help you get more done — it scales effortlessly from a single task to thousands. The best picks balance beginner-friendly simplicity with the depth power users need, and they ship updates often. Whether you are a beginner or a pro, the right AI video generator slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter. In automata theory (a branch of theoretical computer science), DFA minimization is the task of transforming a given deterministic finite automaton (DFA) into an equivalent DFA that has a minimum number of states. Here, two DFAs are called equivalent if they recognize the same regular language. Several different algorithms accomplishing this task are known and described in standard textbooks on automata theory. == Minimal DFA == For each regular language, there also exists a minimal automaton that accepts it, that is, a DFA with a minimum number of states and this DFA is unique (except that states can be given different names). The minimal DFA ensures minimal computational cost for tasks such as pattern matching. There are three classes of states that can be removed or merged from the original DFA without affecting the language it accepts. Unreachable states are the states that are not reachable from the initial state of the DFA, for any input string. These states can be removed. Dead states are the states from which no final state is reachable. These states can be removed unless the automaton is required to be complete. Nondistinguishable states are those that cannot be distinguished from one another for any input string. These states can be merged. DFA minimization is usually done in three steps: remove dead and unreachable states (this will accelerate the following step), merge nondistinguishable states, optionally, re-create a single dead state ("sink" state) if the resulting DFA is required to be complete. == Unreachable states == The state p {\displaystyle p} of a deterministic finite automaton M = ( Q , Σ , δ , q 0 , F ) {\displaystyle M=(Q,\Sigma ,\delta ,q_{0},F)} is unreachable if no string w {\displaystyle w} in Σ ∗ {\displaystyle \Sigma ^{}} exists for which p = δ ∗ ( q 0 , w ) {\displaystyle p=\delta ^{}(q_{0},w)} . In this definition, Q {\displaystyle Q} is the set of states, Σ {\displaystyle \Sigma } is the set of input symbols, δ {\displaystyle \delta } is the transition function (mapping a state and an input symbol to a set of states), δ ∗ {\displaystyle \delta ^{}} is its extension to strings (also known as extended transition function), q 0 {\displaystyle q_{0}} is the initial state, and F {\displaystyle F} is the set of accepting (also known as final) states. Reachable states can be obtained with the following algorithm: Assuming an efficient implementation of the state sets (e.g. new_states) and operations on them (such as adding a state or checking whether it is present), this algorithm can be implemented with time complexity O ( n + m ) {\displaystyle O(n+m)} , where n {\displaystyle n} is the number of states and m {\displaystyle m} is the number of transitions of the input automaton. Unreachable states can be removed from the DFA without affecting the language that it accepts. == Nondistinguishable states == The following algorithms present various approaches to merging nondistinguishable states. === Hopcroft's algorithm === One algorithm for merging the nondistinguishable states of a DFA, due to Hopcroft (1971), is based on partition refinement, partitioning the DFA states into groups by their behavior. These groups represent equivalence classes of the Nerode congruence, whereby every two states are equivalent if they have the same behavior for every input sequence. That is, for every two states p1 and p2 that belong to the same block of the partition P, and every input word w, the transitions determined by w should always take states p1 and p2 to either states that both accept or states that both reject. It should not be possible for w to take p1 to an accepting state and p2 to a rejecting state or vice versa. The following pseudocode describes the form of the algorithm as given by Xu. Alternative forms have also been presented. The algorithm starts with a partition that is too coarse: every pair of states that are equivalent according to the Nerode congruence belong to the same set in the partition, but pairs that are inequivalent might also belong to the same set. It gradually refines the partition into a larger number of smaller sets, at each step splitting sets of states into pairs of subsets that are necessarily inequivalent. The initial partition is a separation of the states into two subsets of states that clearly do not have the same behavior as each other: the accepting states and the rejecting states. The algorithm then repeatedly chooses a set A from the current partition and an input symbol c, and splits each of the sets of the partition into two (possibly empty) subsets: the subset of states that lead to A on input symbol c, and the subset of states that do not lead to A. Since A is already known to have different behavior than the other sets of the partition, the subsets that lead to A also have different behavior than the subsets that do not lead to A. When no more splits of this type can be found, the algorithm terminates. Lemma. Given a fixed character c and an equivalence class Y that splits into equivalence classes B and C, only one of B or C is necessary to refine the whole partition. Example: Suppose we have an equivalence class Y that splits into equivalence classes B and C. Suppose we also have classes D, E, and F; D and E have states with transitions into B on character c, while F has transitions into C on character c. By the Lemma, we can choose either B or C as the distinguisher, let's say B. Then the states of D and E are split by their transitions into B. But F, which doesn't point into B, simply doesn't split during the current iteration of the algorithm; it will be refined by other distinguisher(s). Observation. All of B or C is necessary to split referring classes like D, E, and F correctly—subsets won't do. The purpose of the outermost if statement (if Y is in W) is to patch up W, the set of distinguishers. We see in the previous statement in the algorithm that Y has just been split. If Y is in W, it has just become obsolete as a means to split classes in future iterations. So Y must be replaced by both splits because of the Observation above. If Y is not in W, however, only one of the two splits, not both, needs to be added to W because of the Lemma above. Choosing the smaller of the two splits guarantees that the new addition to W is no more than half the size of Y; this is the core of the Hopcroft algorithm: how it gets its speed, as explained in the next paragraph. The worst case running time of this algorithm is O(ns log n), where n is the number of states and s is the size of the alphabet. This bound follows from the fact that, for each of the ns transitions of the automaton, the sets drawn from Q that contain the target state of the transition have sizes that decrease relative to each other by a factor of two or more, so each transition participates in O(log n) of the splitting steps in the algorithm. The partition refinement data structure allows each splitting step to be performed in time proportional to the number of transitions that participate in it. This remains the most efficient algorithm known for solving the problem, and for certain distributions of inputs its average-case complexity is even better, O(n log log n). Once Hopcroft's algorithm has been used to group the states of the input DFA into equivalence classes, the minimum DFA can be constructed by forming one state for each equivalence class. If S is a set of states in P, s is a state in S, and c is an input character, then the transition in the minimum DFA from the state for S, on input c, goes to the set containing the state that the input automaton would go to from state s on input c. The initial state of the minimum DFA is the one containing the initial state of the input DFA, and the accepting states of the minimum DFA are the ones whose members are accepting states of the input DFA. === Moore's algorithm === Moore's algorithm for DFA minimization is due to Edward F. Moore (1956). Like Hopcroft's algorithm, it maintains a partition that starts off separating the accepting from the rejecting states, and repeatedly refines the partition until no more refinements can be made. At each step, it replaces the current partition with the coarsest common refinement of s + 1 partitions, one of which is the current one and the rest of which are the preimages of the current partition under the transition functions for each of the input symbols. The algorithm terminates when this replacement does not change the current partition. Its worst-case time complexity is O(n2s): each step of the algorithm may be performed in time O(ns) using a variant of radix sort to reorder the states so that states in the same set of the new partition are consecutive in the ordering, and there are at most n steps since each one but the last increases the number of sets in the partition. The instances of the DFA minimization problem that cause the worst-case behavior are the same as for Hopcroft's algorithm. The number of steps th Zoho Office Suite is an online office suite developed by Zoho Corporation. == History == Zoho Office Suite was launched in 2005 with a web-based word processor. Additional products, such as those for spreadsheets and presentations, were incorporated later into the suite. The applications are distributed as software as a service (SaaS). == Products == Zoho uses an open API for its Writer, Sheet, Show, Creator, Meeting, and Planner products. It also has plugins into Microsoft Word and Excel, an OpenOffice.org plugin, and a plugin for Firefox. Zoho Office Suite is free for individuals but offers a plan for teams, which includes Zoho WorkDrive, Zoho Workplace and other Zoho apps. In October 2009, Zoho integrated some of their applications with the Google Apps online suite. Aravind Krishna Joshi (August 5, 1929 – December 31, 2017) was the Henry Salvatori Professor of Computer and Cognitive Science in the computer science department of the University of Pennsylvania. Joshi defined the tree-adjoining grammar formalism which is often used in computational linguistics and natural language processing. Joshi studied at Pune University and the Indian Institute of Science, where he was awarded a BE in electrical engineering and a DIISc in communication engineering respectively. Joshi's graduate work was done in the electrical engineering department at the University of Pennsylvania, and he was awarded his PhD in 1960. He became a professor at Penn and was the co-founder and co-director of the Institute for Research in Cognitive Science. == Awards and recognitions == Guggenheim fellow, 1971–72 Fellow of the Institute of Electrical and Electronics Engineers (IEEE), 1976 Best Paper Award at the National Conference on Artificial Intelligence, 1987 Founding Fellow of the American Association for Artificial Intelligence (AAAI), 1990 IJCAI Award for Research Excellence, 1997 Fellow of the Association for Computing Machinery, 1998 Elected to the National Academy of Engineering, 1999 First to be awarded the Association for Computational Linguistics Lifetime Achievement Award at the 40th anniversary meeting of the ACL, 2002 Awarded the Rumelhart Prize, 2003 Benjamin Franklin Medal in Computer and Cognitive Science, 2005 Doctor honoris causa of mathematical and physical sciences, Charles University in Prague, October 30, 2013 S.-Y. Kuroda Prize of the SIG Mathematics of Language of the ACL, 2013 === Awarded history === On April 21, 2005, Joshi was awarded the Franklin Institute's Benjamin Franklin Medal in Computer and Cognitive Science. The Franklin Institute citation states that he was awarded the medal "for his fundamental contributions to our understanding of how language is represented in the mind, and for developing techniques that enable computers to process efficiently the wide range of human languages. These advances have led to new methods for computer translation."The Best Free AI Video Generator for Beginners
DFA minimization
Zoho Office Suite
Aravind Joshi