In search of the best AI copywriting tool? An AI copywriting tool is software that uses machine learning to help you get more done — it turns a rough idea into a polished result in seconds. When choosing one, weigh output quality, pricing, export formats, and how well it fits the tools you already use. Whether you are a beginner or a pro, the right AI copywriting tool slots into your workflow and pays for itself fast. Below we compare features, pricing, and real output so you can choose with confidence.
Non-separable wavelet
Non-separable wavelets are multi-dimensional wavelets that are not directly implemented as tensor products of wavelets on some lower-dimensional space. They have been studied since 1992. They offer a few important advantages. Notably, using non-separable filters leads to more parameters in design, and consequently better filters. The main difference, when compared to the one-dimensional wavelets, is that multi-dimensional sampling requires the use of lattices (e.g., the quincunx lattice). The wavelet filters themselves can be separable or non-separable regardless of the sampling lattice. Thus, in some cases, the non-separable wavelets can be implemented in a separable fashion. Unlike separable wavelet, the non-separable wavelets are capable of detecting structures that are not only horizontal, vertical or diagonal (show less anisotropy). == Examples == Red-black wavelets Contourlets Shearlets Directionlets Steerable pyramids Non-separable schemes for tensor-product wavelets
Azure Stream Analytics
Microsoft Azure Stream Analytics is a serverless scalable complex event processing engine by Microsoft that enables users to develop and run real-time analytics on multiple streams of data from sources such as devices, sensors, web sites, social media, and other applications. Users can set up alerts to detect anomalies, predict trends, trigger necessary workflows when certain conditions are observed, and make data available to other downstream applications and services for presentation, archiving, or further analysis. == Query Language == Users can author real-time analytics using a simple declarative SQL-like language with embedded support for temporal logic. Callouts to custom code with JavaScript user defined functions extend the streaming logic written in SQL. Callouts to Azure Machine Learning helps with predictive scoring on streaming data. == Scalability == Azure Stream Analytics is a serverless job service on Azure that eliminates the need for infrastructure, servers, virtual machines, or managed clusters. Users only pay for the processing used for the running jobs. == IoT applications == Azure Stream Analytics integrates with Azure IoT Hub to enable real-time analytics on data from IoT devices and applications. == Real-time Dashboards == Users can build real-time dashboards with Power BI for a live command and control view. Real-time dashboards help transform live data into actionable and insightful visuals. == Data Input Sources == Stream Analytics supports three different types of input sources - Azure Event Hubs, Azure IoT Hubs, and Azure Blob Storage. Additionally, stream analytics supports Azure Blob storage as the input reference data to help augment fast moving event data streams with static data. Stream analytics supports a wide variety of output targets. Support for Power BI allows for real-time dashboarding. Event Hub, Service bus topics and queues help trigger downstream workflows. Support for Azure Table Storage, Azure SQL Databases, Azure SQL Data Warehouse, Azure SQL, Document DB, Azure Data Lake Store enable a variety of downstream analysis and archiving capabilities.
30 Boxes
30 Boxes is a minimalist calendaring IOS application created by 83 Degrees. Originating as a web application in March 2006, 30 Boxes was founded by Webshots cofounder Narendra Rocherolle. The website shut down some time in 2020, but relaunched for the IOS in February 2021. The original website was tailored towards "social media junkies". == Reception == Barry Collins of The Sunday Times appreciated the website's plain-language event adding feature, but did not appreciate that he was unable to see more than one month of events at a time. Collins was also unhappy that the website was not capable of warning him when he had two events scheduled at the same time. In a list of the best web-based calendar software for small businesses, Forbes ranked 30 Boxes second, after Google Calendar. They described 30 Boxes like “buying a new car with manual transmission and lots of extras—you don't just want to drive it, you want to fool around with it to see what it can do”.
Pandas (software)
Pandas (styled as pandas) is a software library written for the Python programming language for data manipulation and analysis. In particular, it offers data structures and operations for manipulating numerical tables and time series. It is free software released under the three-clause BSD license. The name is derived from the term "panel data", an econometrics term for data sets that include observations over multiple time periods for the same individuals, as well as a play on the phrase "Python data analysis". Wes McKinney started building what would become Pandas at AQR Capital while he was a researcher there from 2007 to 2010. The development of Pandas introduced into Python many comparable features of working with DataFrames that were established in the R programming language. The library is built upon another library, NumPy. == History == Developer Wes McKinney started working on Pandas in 2008 while at AQR Capital Management out of the need for a high performance, flexible tool to perform quantitative analysis on financial data. Before leaving AQR, he was able to convince management to allow him to open source the library in 2009. Another AQR employee, Chang She, joined the effort in 2012 as the second major contributor to the library. In 2015, Pandas signed on as a fiscally sponsored project of NumFOCUS, a 501(c)(3) nonprofit charity in the United States. == Data model == Pandas is built around data structures called Series and DataFrames. Data for these collections can be imported from various file formats such as comma-separated values, JSON, Parquet, SQL database tables or queries, and Microsoft Excel. === Series === A Series is a one-dimensional array-like object that stores a sequence of values together with an associated set of labels, called an index. It is built on top of NumPy's array and affords many similar functionalities, but instead of using implicit integer positions, a Series allows explicit index labels of many data types. A Series can be created from Python lists, dictionaries, or NumPy arrays. If no index is provided, pandas automatically assigns a default integer index ranging from 0 to n-1, where n is the number of items in the Series. A simple example with customized labels is: To access a value or list of values from a Series, use its index or list of indices: Series can be used arithmetically, as in the statement series_3 = series_1 + series_2. This will align data points with corresponding index values in series_1 and series_2 (similar to a join in relational algebra), then add them together to produce new values in series_3. A Series has various attributes, such as name (Series name), dtype (data type of values), shape (number of rows), values, and index. They can be used in many of the same operations as NumPy arrays, with additional methods for reindexing, label-based selection, and handling missing data. === DataFrame === A DataFrame is a two-dimensional, tabular data structure with labeled rows and columns. Each column is stored internally as a Series and may hold a different data type (numeric, string, boolean, etc.). DataFrames can be created by a variety of means, including dictionaries of lists, NumPy arrays, and external files such as CSV or Excel spreadsheets: To retrieve a DataFrame column as a Series, use either 1) the index (dict-like notation) or 2) the name of column if the name is a valid Python identifier (attribute-like access). DataFrames support operations such as column assignment, row and column deletion, label-based indexing with loc, position-based indexing with iloc, reshaping, grouping, and joining. Merge operations implement a subset of relational algebra and allow one-to-one, many-to-one, and many-to-many joins. Some common attributes of a DataFrame include dtypes (data type of each column), shape (dimensions of the DataFrame returned as a tuple with form (number of rows, number of columns)), index/columns (labels of the DataFrame's rows/columns, respectively, returned as an Index object), values (data in the DataFrame returned as a 2D array), and empty (returns True if the DataFrame is empty). === Index === Index objects hold metadata for Series and Dataframe objects, such as axis labels and names, and are automatically created from input data. By default, a pandas index is a series of integers ascending from 0, similar to the indices of Python arrays. However, indices can also use any NumPy data type, including floating point, timestamps, or strings. Indices are also immutable, which allows them to be safely shared across multiple objects. pandas' syntax for mapping index values to relevant data is the same syntax Python uses to map dictionary keys to values. For example, if s is a Series, s['a'] will return the data point at index a. Unlike dictionary keys, index values are not guaranteed to be unique. If a Series uses the index value a for multiple data points, then s['a'] will instead return a new Series containing all matching values. A DataFrame's column names are stored and implemented identically to an index. As such, a DataFrame can be thought of as having two indices: one column-based and one row-based. Because column names are stored as an index, these are not required to be unique. If data is a Series, then data['a'] returns all values with the index value of a. However, if data is a DataFrame, then data['a'] returns all values in the column(s) named a. To avoid this ambiguity, Pandas supports the syntax data.loc['a'] as an alternative way to filter using the index. Pandas also supports the syntax data.iloc[n], which always takes an integer n and returns the nth value, counting from 0. This allows a user to act as though the index is an array-like sequence of integers, regardless of how it is actually defined. pandas also supports hierarchical indices with multiple values per data point through the "MultiIndex" class. MultiIndex objects allow a single DataFrame to represent multiple dimensions, similar to a pivot table in Microsoft Excel, where each level can optionally carry its own unique name. In practice, data with more than 2 dimensions is often represented using DataFrames with hierarchical indices, instead of the higher-dimension Panel and Panel4D data structures. == Functionality == pandas supports a variety of indexing and subsetting techniques, allowing data to be selected by label, index, or Boolean conditions. For example, df[df['col1'] > 5] will return all rows in the DataFrame df for which the value of the column col1 exceeds 5. The library also implements grouping operations based on the split-apply-combine approach, enabling users to aggregate, transform, or restructure data according to column values or functions applied to index labels. For example, df['col1'].groupby(df['col2']) groups the data in 'col1' by their values in 'col2', while df.groupby(lambda i: i % 2) groups all data in the whole DataFrame by whether their index is even. The library also provides extensive tools for transforming, filtering and summarizing data. Users may apply arbitrary functions to Series and DataFrames, and because the library is built on top of Numpy, most NumPy functions can be applied directly to pandas objects as well. The library also includes built-in operations for arithmetic operations, string processing, and descriptive statistics such as mean, median, and standard deviation. These built-in functions are designed to handle missing data, usually represented by the floating-point value NaN. In addition, pandas includes tools for reorganizing data into different structural formats, with methods that can reshape tabular data between "wide" and "long" formats and pivot values based on column labels. pandas also implements a flexible set of relational operations for combining datasets. For instance, merge() links row in DataFrames based on one or more shared keys or indices, supporting one-to-one, one-to-many, and many-to-many relationships in a manner analogous to join operations in relational databases like SQL. DataFrames can also be concatenated or stacked together along an axis through the concat() method, and overlapping data can be further spliced together using combine_first() to fill in missing values. Furthermore, the library includes specialized support for working with time-series data. Features include the ability to interpolate values and filter using a range of timestamps, such as data['1/1/2023':'2/2/2023'] , which will return all dates between January 1 and February 2. Missing values in time-series data are represented by a dedicated NaT (Not a Timestamp) object, instead of the NaN value it uses elsewhere. == Criticisms == Pandas has been criticized for its inefficiency. The entire dataset must be loaded in RAM, and the library does not optimize query plans or support parallel computing across multiple cores. Wes McKinney, the creator of Pandas, has recommended Apache Arrow as an alternative to address these performance concerns and ot
Actor-critic algorithm
The actor-critic algorithm (AC) is a family of reinforcement learning (RL) algorithms that combine policy-based RL algorithms such as policy gradient methods, and value-based RL algorithms such as value iteration, Q-learning, SARSA, and TD learning. An AC algorithm consists of two main components: an "actor" that determines which actions to take according to a policy function, and a "critic" that evaluates those actions according to a value function. Some AC algorithms are on-policy, some are off-policy. Some apply to either continuous or discrete action spaces. Some work in both cases. == Overview == The actor-critic methods can be understood as an improvement over pure policy gradient methods like REINFORCE via introducing a baseline. === Actor === The actor uses a policy function π ( a | s ) {\displaystyle \pi (a|s)} , while the critic estimates either the value function V ( s ) {\displaystyle V(s)} , the action-value Q-function Q ( s , a ) , {\displaystyle Q(s,a),} the advantage function A ( s , a ) {\displaystyle A(s,a)} , or any combination thereof. The actor is a parameterized function π θ {\displaystyle \pi _{\theta }} , where θ {\displaystyle \theta } are the parameters of the actor. The actor takes as argument the state of the environment s {\displaystyle s} and produces a probability distribution π θ ( ⋅ | s ) {\displaystyle \pi _{\theta }(\cdot |s)} . If the action space is discrete, then ∑ a π θ ( a | s ) = 1 {\displaystyle \sum _{a}\pi _{\theta }(a|s)=1} . If the action space is continuous, then ∫ a π θ ( a | s ) d a = 1 {\displaystyle \int _{a}\pi _{\theta }(a|s)da=1} . The goal of policy optimization is to improve the actor. That is, to find some θ {\displaystyle \theta } that maximizes the expected episodic reward J ( θ ) {\displaystyle J(\theta )} : J ( θ ) = E π θ [ ∑ t = 0 T γ t r t ] {\displaystyle J(\theta )=\mathbb {E} _{\pi _{\theta }}\left[\sum _{t=0}^{T}\gamma ^{t}r_{t}\right]} where γ {\displaystyle \gamma } is the discount factor, r t {\displaystyle r_{t}} is the reward at step t {\displaystyle t} , and T {\displaystyle T} is the time-horizon (which can be infinite). The goal of policy gradient method is to optimize J ( θ ) {\displaystyle J(\theta )} by gradient ascent on the policy gradient ∇ J ( θ ) {\displaystyle \nabla J(\theta )} . As detailed on the policy gradient method page, there are many unbiased estimators of the policy gradient: ∇ θ J ( θ ) = E π θ [ ∑ 0 ≤ j ≤ T ∇ θ ln π θ ( A j | S j ) ⋅ Ψ j | S 0 = s 0 ] {\displaystyle \nabla _{\theta }J(\theta )=\mathbb {E} _{\pi _{\theta }}\left[\sum _{0\leq j\leq T}\nabla _{\theta }\ln \pi _{\theta }(A_{j}|S_{j})\cdot \Psi _{j}{\Big |}S_{0}=s_{0}\right]} where Ψ j {\textstyle \Psi _{j}} is a linear sum of the following: ∑ 0 ≤ i ≤ T ( γ i R i ) {\textstyle \sum _{0\leq i\leq T}(\gamma ^{i}R_{i})} . γ j ∑ j ≤ i ≤ T ( γ i − j R i ) {\textstyle \gamma ^{j}\sum _{j\leq i\leq T}(\gamma ^{i-j}R_{i})} : the REINFORCE algorithm. γ j ∑ j ≤ i ≤ T ( γ i − j R i ) − b ( S j ) {\textstyle \gamma ^{j}\sum _{j\leq i\leq T}(\gamma ^{i-j}R_{i})-b(S_{j})} : the REINFORCE with baseline algorithm. Here b {\displaystyle b} is an arbitrary function. γ j ( R j + γ V π θ ( S j + 1 ) − V π θ ( S j ) ) {\textstyle \gamma ^{j}\left(R_{j}+\gamma V^{\pi _{\theta }}(S_{j+1})-V^{\pi _{\theta }}(S_{j})\right)} : TD(1) learning. γ j Q π θ ( S j , A j ) {\textstyle \gamma ^{j}Q^{\pi _{\theta }}(S_{j},A_{j})} . γ j A π θ ( S j , A j ) {\textstyle \gamma ^{j}A^{\pi _{\theta }}(S_{j},A_{j})} : Advantage Actor-Critic (A2C). γ j ( R j + γ R j + 1 + γ 2 V π θ ( S j + 2 ) − V π θ ( S j ) ) {\textstyle \gamma ^{j}\left(R_{j}+\gamma R_{j+1}+\gamma ^{2}V^{\pi _{\theta }}(S_{j+2})-V^{\pi _{\theta }}(S_{j})\right)} : TD(2) learning. γ j ( ∑ k = 0 n − 1 γ k R j + k + γ n V π θ ( S j + n ) − V π θ ( S j ) ) {\textstyle \gamma ^{j}\left(\sum _{k=0}^{n-1}\gamma ^{k}R_{j+k}+\gamma ^{n}V^{\pi _{\theta }}(S_{j+n})-V^{\pi _{\theta }}(S_{j})\right)} : TD(n) learning. γ j ∑ n = 1 ∞ λ n − 1 1 − λ ⋅ ( ∑ k = 0 n − 1 γ k R j + k + γ n V π θ ( S j + n ) − V π θ ( S j ) ) {\textstyle \gamma ^{j}\sum _{n=1}^{\infty }{\frac {\lambda ^{n-1}}{1-\lambda }}\cdot \left(\sum _{k=0}^{n-1}\gamma ^{k}R_{j+k}+\gamma ^{n}V^{\pi _{\theta }}(S_{j+n})-V^{\pi _{\theta }}(S_{j})\right)} : TD(λ) learning, also known as GAE (generalized advantage estimate). This is obtained by an exponentially decaying sum of the TD(n) learning terms. === Critic === In the unbiased estimators given above, certain functions such as V π θ , Q π θ , A π θ {\displaystyle V^{\pi _{\theta }},Q^{\pi _{\theta }},A^{\pi _{\theta }}} appear. These are approximated by the critic. Since these functions all depend on the actor, the critic must learn alongside the actor. The critic is learned by value-based RL algorithms. For example, if the critic is estimating the state-value function V π θ ( s ) {\displaystyle V^{\pi _{\theta }}(s)} , then it can be learned by any value function approximation method. Let the critic be a function approximator V ϕ ( s ) {\displaystyle V_{\phi }(s)} with parameters ϕ {\displaystyle \phi } . The simplest example is TD(1) learning, which trains the critic to minimize the TD(1) error: δ i = R i + γ V ϕ ( S i + 1 ) − V ϕ ( S i ) {\displaystyle \delta _{i}=R_{i}+\gamma V_{\phi }(S_{i+1})-V_{\phi }(S_{i})} The critic parameters are updated by gradient descent on the squared TD error: ϕ ← ϕ − α ∇ ϕ ( δ i ) 2 = ϕ + α δ i ∇ ϕ V ϕ ( S i ) {\displaystyle \phi \leftarrow \phi -\alpha \nabla _{\phi }(\delta _{i})^{2}=\phi +\alpha \delta _{i}\nabla _{\phi }V_{\phi }(S_{i})} where α {\displaystyle \alpha } is the learning rate. Note that the gradient is taken with respect to the ϕ {\displaystyle \phi } in V ϕ ( S i ) {\displaystyle V_{\phi }(S_{i})} only, since the ϕ {\displaystyle \phi } in γ V ϕ ( S i + 1 ) {\displaystyle \gamma V_{\phi }(S_{i+1})} constitutes a moving target, and the gradient is not taken with respect to that. This is a common source of error in implementations that use automatic differentiation, and requires "stopping the gradient" at that point. Similarly, if the critic is estimating the action-value function Q π θ {\displaystyle Q^{\pi _{\theta }}} , then it can be learned by Q-learning or SARSA. In SARSA, the critic maintains an estimate of the Q-function, parameterized by ϕ {\displaystyle \phi } , denoted as Q ϕ ( s , a ) {\displaystyle Q_{\phi }(s,a)} . The temporal difference error is then calculated as δ i = R i + γ Q θ ( S i + 1 , A i + 1 ) − Q θ ( S i , A i ) {\displaystyle \delta _{i}=R_{i}+\gamma Q_{\theta }(S_{i+1},A_{i+1})-Q_{\theta }(S_{i},A_{i})} . The critic is then updated by θ ← θ + α δ i ∇ θ Q θ ( S i , A i ) {\displaystyle \theta \leftarrow \theta +\alpha \delta _{i}\nabla _{\theta }Q_{\theta }(S_{i},A_{i})} The advantage critic can be trained by training both a Q-function Q ϕ ( s , a ) {\displaystyle Q_{\phi }(s,a)} and a state-value function V ϕ ( s ) {\displaystyle V_{\phi }(s)} , then let A ϕ ( s , a ) = Q ϕ ( s , a ) − V ϕ ( s ) {\displaystyle A_{\phi }(s,a)=Q_{\phi }(s,a)-V_{\phi }(s)} . Although, it is more common to train just a state-value function V ϕ ( s ) {\displaystyle V_{\phi }(s)} , then estimate the advantage by A ϕ ( S i , A i ) ≈ ∑ j ∈ 0 : n − 1 γ j R i + j + γ n V ϕ ( S i + n ) − V ϕ ( S i ) {\displaystyle A_{\phi }(S_{i},A_{i})\approx \sum _{j\in 0:n-1}\gamma ^{j}R_{i+j}+\gamma ^{n}V_{\phi }(S_{i+n})-V_{\phi }(S_{i})} Here, n {\displaystyle n} is a positive integer. The higher n {\displaystyle n} is, the more lower is the bias in the advantage estimation, but at the price of higher variance. The Generalized Advantage Estimation (GAE) introduces a hyperparameter λ {\displaystyle \lambda } that smoothly interpolates between Monte Carlo returns ( λ = 1 {\displaystyle \lambda =1} , high variance, no bias) and 1-step TD learning ( λ = 0 {\displaystyle \lambda =0} , low variance, high bias). This hyperparameter can be adjusted to pick the optimal bias-variance trade-off in advantage estimation. It uses an exponentially decaying average of n-step returns with λ {\displaystyle \lambda } being the decay strength. == Variants == Asynchronous Advantage Actor-Critic (A3C): Parallel and asynchronous version of A2C. Soft Actor-Critic (SAC): Incorporates entropy maximization for improved exploration. Deep Deterministic Policy Gradient (DDPG): Specialized for continuous action spaces.
ZygoteBody
ZygoteBody, formerly Google Body, is a web application by Zygote Media Group that renders manipulable 3D anatomical models of the human body. Several layers, from muscle tissues down to blood vessels, can be removed or made transparent to allow better study of individual body parts. Most of the body parts are labelled and are searchable. == Technology == The human models are based on data from the Zygote Media Group. The website uses JavaScript and WebGL technology to display 3D images inside the web browser without requiring the installation of external browser plug-ins. == History == ZygoteBody was launched as Google Body on December 15, 2010. On April Fools' Day 2011, users were greeted with the anatomy of a cow on the home page. The cow model is still available as part of the open-3d-viewer open source project. As part of the wind down on Google Labs, it was announced that Google Body will be shut down but will continue to be maintained by Zygote as ZygoteBody. On October 13, 2011, the Google Body site was shut down. Then, on January 9, 2012, ZygoteBody was launched and core code base (with the Google Cow model as a demo) was made available as an open source project called open-3d-viewer.