A scatter plot is a type of plot or mathematical diagram using Cartesian coordinates to display values for two variables for a set of data. If the points are color-coded, one additional variable can be displayed; the data are displayed as a collection of points, each having the value of one variable determining the position on the horizontal axis and the value of the other variable determining the position on the vertical axis. A scatter plot can be used either when one continuous variable, under the control of the experimenter and the other depends on it or when both continuous variables are independent. If a parameter exists, systematically incremented and/or decremented by the other, it is called the control parameter or independent variable and is customarily plotted along the horizontal axis; the measured or dependent variable is customarily plotted along the vertical axis. If no dependent variable exists, either type of variable can be plotted on either axis and a scatter plot will illustrate only the degree of correlation between two variables.
A scatter plot can suggest various kinds of correlations between variables with a certain confidence interval. For example and height, weight would be on y axis and height would be on the x axis. Correlations may be negative, or null. If the pattern of dots slopes from lower left to upper right, it indicates a positive correlation between the variables being studied. If the pattern of dots slopes from upper left to lower right, it indicates a negative correlation. A line of best fit can be drawn in order to study the relationship between the variables. An equation for the correlation between the variables can be determined by established best-fit procedures. For a linear correlation, the best-fit procedure is known as linear regression and is guaranteed to generate a correct solution in a finite time. No universal best-fit procedure is guaranteed to generate a correct solution for arbitrary relationships. A scatter plot is very useful when we wish to see how two comparable data sets agree to show nonlinear relationships between variables.
The ability to do this can be enhanced by adding a smooth line such as LOESS. Furthermore, if the data are represented by a mixture model of simple relationships, these relationships will be visually evident as superimposed patterns; the scatter diagram is one of the seven basic tools of quality control. Scatter charts can be built in the form of marker, or/and line charts. For example, to display a link between a person's lung capacity, how long that person could hold his/her breath, a researcher would choose a group of people to study measure each one's lung capacity and how long that person could hold his/her breath; the researcher would plot the data in a scatter plot, assigning "lung capacity" to the horizontal axis, "time holding breath" to the vertical axis. A person with a lung capacity of 400 cl who held his/her breath for 21.7 seconds would be represented by a single dot on the scatter plot at the point in the Cartesian coordinates. The scatter plot of all the people in the study would enable the researcher to obtain a visual comparison of the two variables in the data set, will help to determine what kind of relationship there might be between the two variables.
For a set of data variables X1, X2... Xk, the scatter plot matrix shows all the pairwise scatter plots of the variables on a single view with multiple scatterplots in a matrix format. For k variables, the scatterplot matrix will contain k rows and k columns. A plot located on the intersection of i-th row and j-th column is a plot of variables Xj; this means that each row and column is one dimension, each cell plots a scatterplot of two dimensions. A generalized scatterplot matrix offers a range of displays of paired combinations of categorical and quantitative variables. A mosaic plot, fluctuation diagram, or faceted bar chart may be used to display two categorical variables. Other plots are used for one quantitative variables. Rug plot What is a scatterplot? Correlation scatter-plot matrix for ordered-categorical data – Explanation and R code Density scatterplot for large datasets
SageMath is a computer algebra system with features covering many aspects of mathematics, including algebra, graph theory, numerical analysis, number theory and statistics. The first version of SageMath was released on 24 February 2005 as free and open-source software under the terms of the GNU General Public License version 2, with the initial goals of creating an "open source alternative to Magma, Mathematica, MATLAB"; the originator and leader of the SageMath project, William Stein, is a mathematician at the University of Washington. SageMath uses a syntax resembling Python's, supporting procedural and object-oriented constructs. Features of SageMath include: A browser-based notebook for review and re-use of previous inputs and outputs, including graphics and text annotations. Compatible with Firefox, Konqueror, Google Chrome and Safari. Notebooks can be accessed locally or remotely and the connection can be secured with HTTPS. A text-based command-line interface using IPython. Support for parallel processing using multi-core processors, multiple processors, or distributed computing.
Calculus using Maxima and SymPy. Numerical linear algebra using the GSL, SciPy and NumPy. Libraries of elementary and special mathematical functions. 2D and 3D graphs of numerical data. Matrix manipulation, including sparse arrays. Multivariate statistics libraries, using SciPy. A toolkit for adding user interfaces to calculations and applications. Graph theory visualization and analysis tools. Libraries of number theory functions. Support for complex numbers, arbitrary-precision arithmetic, symbolic computation. Technical word processing including formula editing and embedding SageMath within LaTeX documents; the Python standard library, including tools for connecting to SQL, HTTP, HTTPS, NNTP, IMAP, SSH, IRC, FTP and others. Interfaces to some third-party applications like Mathematica, Magma, R, Maple. MoinMoin as a Wiki system for knowledge management. Documentation using Sphinx. An automated test-suite. Execution of Fortran, C, C++, Cython code. SageMath can pull up Mathematica within a program. Interfacing this way is documented to Sage.
William Stein realized when designing Sage that there were many open-source mathematics software packages written in different languages, namely C, C++, Common Lisp and Python. Rather than reinventing the wheel, Sage integrates many specialized mathematics software packages into a common interface, for which a user needs to know only Python. However, Sage contains hundreds of thousands of unique lines of code adding new functions and creating the interface between its components. SageMath uses both professionals for development; the development of SageMath is supported by grants. However, it was not until 2016; the same year, Stein described his disappointment with a lack of academic funding and credentials for software development, citing it as the reason for his decision to leave his tenured academic position to work full-time on the project in a newly founded company, SageMath, Inc. Only the major releases are listed below. SageMath practices the "release early, release often" concept, with releases every few weeks or months.
In total, there have been over 300 releases. 2007: first prize in the scientific software division of Les Trophées du Libre, an international competition for free software. 2012: one of the projects selected for the Google Summer of Code. 2013: ACM/SIGSAM Jenks Prize. SageMath has been cited in a variety of publications. Both binaries and source code are available for SageMath from the download page. If SageMath is built from source code, many of the included libraries such as ATLAS, FLINT, NTL will be tuned and optimized for that computer, taking into account the number of processors, the size of their caches, whether there is hardware support for SSE instructions, etc. Cython can increase the speed of SageMath programs, as the Python code is converted into C. SageMath is free software, distributed under the terms of the GNU General Public License version 3. SageMath is available in many ways: The source code can be downloaded from the downloads page. Although not recommended for end users, development releases of SageMath are available.
Many Linux distributions include SageMath in their repositories. Binaries can be downloaded for macOS and Solaris. A live CD containing a bootable Linux operating system is available; this allows usage of SageMath without Linux installation. Users could have used an online version of SageMath at sagenb.org, but it has been discontinued in April 2015. Users can use an online "single cell" version of SageMath at sagecell.sagemath.org or embed a single SageMath cell into any web page. Users can create permalinks to SageMath computations using the cell server. A new online SageMath notebook is available at cocalc.com. Full documentation for installation is provided at doc.sagemath.org/html/en/installation/. Although Microsoft was sponsoring a native version of SageMath for the Windows operating system, prior to 2016 there were no plans for a native port, users of Windows had to use virtualization technology such as VirtualBox to run SageMath; as of SageMath 8.0, with development funded by the OpenDreamKit project, it builds on Cygwin, a binary installer for 64-bit versions of Windows is available.
Linux distributions in which SageMath is available as a package are Fedora, Arch Linux, Debian and NixOS. In Gentoo, it is av
A finite-state machine or finite-state automaton, finite automaton, or a state machine, is a mathematical model of computation. It is an abstract machine that can be in one of a finite number of states at any given time; the FSM can change from one state to another in response to some external inputs. An FSM is defined by a list of its states, its initial state, the conditions for each transition. Finite state machines are of two types – deterministic finite state machines and non-deterministic finite state machines. A deterministic finite-state machine can be constructed equivalent to any non-deterministic one; the behavior of state machines can be observed in many devices in modern society that perform a predetermined sequence of actions depending on a sequence of events with which they are presented. Simple examples are vending machines, which dispense products when the proper combination of coins is deposited, whose sequence of stops is determined by the floors requested by riders, traffic lights, which change sequence when cars are waiting, combination locks, which require the input of combination numbers in the proper order.
The finite state machine has less computational power than some other models of computation such as the Turing machine. The computational power distinction means there are computational tasks that a Turing machine can do but a FSM cannot; this is because a FSM's memory is limited by the number of states it has. FSMs are studied in the more general field of automata theory. An example of a simple mechanism that can be modeled by a state machine is a turnstile. A turnstile, used to control access to subways and amusement park rides, is a gate with three rotating arms at waist height, one across the entryway; the arms are locked, blocking the entry, preventing patrons from passing through. Depositing a coin or token in a slot on the turnstile unlocks the arms, allowing a single customer to push through. After the customer passes through, the arms are locked again. Considered as a state machine, the turnstile has two possible states: Unlocked. There are two possible inputs that affect its state: pushing the arm.
In the locked state, pushing on the arm has no effect. Putting a coin in – that is, giving the machine a coin input – shifts the state from Locked to Unlocked. In the unlocked state, putting additional coins in has no effect. However, a customer pushing through the arms, giving a push input, shifts the state back to Locked; the turnstile state machine can be represented by a state transition table, showing for each possible state, the transitions between them and the outputs resulting from each input: The turnstile state machine can be represented by a directed graph called a state diagram. Each state is represented by a node. Edges show the transitions from one state to another; each arrow is labeled with the input. An input that doesn't cause a change of state is represented by a circular arrow returning to the original state; the arrow into the Locked node from the black dot indicates. A state is a description of the status of a system, waiting to execute a transition. A transition is a set of actions to be executed when a condition is fulfilled or when an event is received.
For example, when using an audio system to listen to the radio, receiving a "next" stimulus results in moving to the next station. When the system is in the "CD" state, the "next" stimulus results in moving to the next track. Identical stimuli trigger different actions depending on the current state. In some finite-state machine representations, it is possible to associate actions with a state: an entry action: performed when entering the state, an exit action: performed when exiting the state. Several state transition table types are used; the most common representation is shown below: the combination of current state and input shows the next state. The complete action's information is not directly described in the table and can only be added using footnotes. A FSM definition including the full actions information is possible using state tables; the Unified Modeling Language has a notation for describing state machines. UML state machines overcome the limitations of traditional finite state machines while retaining their main benefits.
UML state machines introduce the new concepts of hierarchically nested states and orthogonal regions, while extending the notion of actions. UML state machines have the characteristics of Moore machines, they support actions that depend on both the state of the system and the triggering event, as in Mealy machines, as well as entry and exit actions, which are associated with states rather than transitions, as in Moore machines. The Specification and Description Language is a standard from ITU that includes graphical symbols to describe actions in the transition: send an event receive an event start a timer cancel a timer start another concurrent state machine decisionSDL embeds basic data types called "Abstract Data Types", an action language, an execution semantic in order to make the finite state machine executable. There are a large number of variants to represent an FSM such as the one in figure 3. In addition to their use in modeling reactive systems
An operating system is system software that manages computer hardware and software resources and provides common services for computer programs. Time-sharing operating systems schedule tasks for efficient use of the system and may include accounting software for cost allocation of processor time, mass storage and other resources. For hardware functions such as input and output and memory allocation, the operating system acts as an intermediary between programs and the computer hardware, although the application code is executed directly by the hardware and makes system calls to an OS function or is interrupted by it. Operating systems are found on many devices that contain a computer – from cellular phones and video game consoles to web servers and supercomputers; the dominant desktop operating system is Microsoft Windows with a market share of around 82.74%. MacOS by Apple Inc. is in second place, the varieties of Linux are collectively in third place. In the mobile sector, use in 2017 is up to 70% of Google's Android and according to third quarter 2016 data, Android on smartphones is dominant with 87.5 percent and a growth rate 10.3 percent per year, followed by Apple's iOS with 12.1 percent and a per year decrease in market share of 5.2 percent, while other operating systems amount to just 0.3 percent.
Linux distributions are dominant in supercomputing sectors. Other specialized classes of operating systems, such as embedded and real-time systems, exist for many applications. A single-tasking system can only run one program at a time, while a multi-tasking operating system allows more than one program to be running in concurrency; this is achieved by time-sharing, where the available processor time is divided between multiple processes. These processes are each interrupted in time slices by a task-scheduling subsystem of the operating system. Multi-tasking may be characterized in co-operative types. In preemptive multitasking, the operating system slices the CPU time and dedicates a slot to each of the programs. Unix-like operating systems, such as Solaris and Linux—as well as non-Unix-like, such as AmigaOS—support preemptive multitasking. Cooperative multitasking is achieved by relying on each process to provide time to the other processes in a defined manner. 16-bit versions of Microsoft Windows used cooperative multi-tasking.
32-bit versions of both Windows NT and Win9x, used preemptive multi-tasking. Single-user operating systems have no facilities to distinguish users, but may allow multiple programs to run in tandem. A multi-user operating system extends the basic concept of multi-tasking with facilities that identify processes and resources, such as disk space, belonging to multiple users, the system permits multiple users to interact with the system at the same time. Time-sharing operating systems schedule tasks for efficient use of the system and may include accounting software for cost allocation of processor time, mass storage and other resources to multiple users. A distributed operating system manages a group of distinct computers and makes them appear to be a single computer; the development of networked computers that could be linked and communicate with each other gave rise to distributed computing. Distributed computations are carried out on more than one machine; when computers in a group work in cooperation, they form a distributed system.
In an OS, distributed and cloud computing context, templating refers to creating a single virtual machine image as a guest operating system saving it as a tool for multiple running virtual machines. The technique is used both in virtualization and cloud computing management, is common in large server warehouses. Embedded operating systems are designed to be used in embedded computer systems, they are designed to operate on small machines like PDAs with less autonomy. They are able to operate with a limited number of resources, they are compact and efficient by design. Windows CE and Minix 3 are some examples of embedded operating systems. A real-time operating system is an operating system that guarantees to process events or data by a specific moment in time. A real-time operating system may be single- or multi-tasking, but when multitasking, it uses specialized scheduling algorithms so that a deterministic nature of behavior is achieved. An event-driven system switches between tasks based on their priorities or external events while time-sharing operating systems switch tasks based on clock interrupts.
A library operating system is one in which the services that a typical operating system provides, such as networking, are provided in the form of libraries and composed with the application and configuration code to construct a unikernel: a specialized, single address space, machine image that can be deployed to cloud or embedded environments. Early computers were built to perform a series of single tasks, like a calculator. Basic operating system features were developed in the 1950s, such as resident monitor functions that could automatically run different programs in succession to speed up processing. Operating systems did not exist in their more complex forms until the early 1960s. Hardware features were added, that enabled use of runtime libraries and parallel processing; when personal computers became popular in the 1980s, operating systems were made for them similar in concept to those used on larger computers. In the 1940s, the earliest electronic digital systems had no operating systems.
Electronic systems of this time were programmed on rows of mechanical switches or by jumper wires on plug boards. These were special-purpose systems that, for example, generated ballistics tables for the military or controlled the pri
The plotter is a computer printer for printing vector graphics. Plotters draw pictures on paper using a pen. In the past, plotters were used in applications such as computer-aided design, as they were able to produce line drawings much faster and of a higher quality than contemporary conventional printers, small desktop plotters were used for business graphics. Although they retained a niche for producing large drawings for many years, plotters have now been replaced by wide-format conventional printers. Digitally controlled plotters evolved from earlier analog XY-writers used as output devices for measurement instruments and analog computers. Pen plotters print by moving a pen or other instrument across the surface of a piece of paper; this means that plotters are vector graphics devices, rather than raster graphics as with other printers. Pen plotters can draw complex line art, including text, but do so because of the mechanical movement of the pens, they are incapable of efficiently creating a solid region of color, but can hatch an area by drawing a number of close, regular lines.
Plotters offered the fastest way to efficiently produce large drawings or color high-resolution vector-based artwork when computer memory was expensive and processor power was limited, other types of printers had limited graphic output capabilities. Pen plotters have become obsolete, have been replaced by large-format inkjet printers and LED toner based printers; such devices may still understand vector languages designed for plotter use, because in many uses, they offer a more efficient alternative to raster data. Electrostatic plotters used a dry toner transfer process similar to that in many photocopiers, they were faster than pen plotters and were available in large formats, suitable for reproducing engineering drawings. The quality of image was not as good as contemporary pen plotters. Electrostatic plotters were made in both drum types. Cutting plotters use knives to cut into a piece of material, lying on the flat surface area of the plotter, it is achieved because the cutting plotter is connected to a computer, equipped with specialized cutting design or drawing computer software programs.
Those computer software programs are responsible for sending the necessary cutting dimensions or designs in order to command the cutting knife to produce the correct project cutting needs. In recent years the use of cutting plotters has become popular with home enthusiasts of paper crafts such as cardmaking and scrapbooking; such tools allow desired card shapes to be cut out precisely, repeated identically. A number of printer control languages were created to operate pen plotters, transmit commands like "lift pen from paper", "place pen on paper", or "draw a line from here to here". Three common ASCII-based plotter control languages are Hewlett-Packard's HP-GL, its successor HP-GL/2 and Houston Instruments DMPL. Here is a simple HP-GL script drawing a line: SP1. Programmers using FORTRAN or BASIC did not program these directly, but used software packages, such as the Calcomp library, or device independent graphics packages, such as Hewlett-Packard's AGL libraries or BASIC extensions or high end packages such as DISSPLA.
These would establish scaling factors from world coordinates to device coordinates, translate to the low level device commands. For example, to plot X*X in HP 9830 BASIC, the program would be 10 SCALE -1,1,1,1 20 FOR X =-1 to 1 STEP 0.1 30 PLOT X, X*X 40 NEXT X 50 PEN 60 END Early pen plotters, e.g. the Calcomp 565 of 1959, worked by placing the paper over a roller that moved the paper back and forth for X motion, while the pen moved back and forth on a track for Y motion. The paper was supplied in roll form and had perforations along both edges that were engaged by sprockets on the rollers. Another approach, e.g. Computervision's Interact I, involved attaching ball-point pens to drafting pantographs and driving the machines with stepper motors controlled by the computer; this had the disadvantage of being somewhat slow to move, as well as requiring floor space equal to the size of the paper, but could double as a digitizer. A change was the addition of an electrically controlled clamp to hold the pens, which allowed them to be changed, thus create multi-colored output.
Hewlett Packard and Tektronix produced small, desktop-sized flatbed plotters in the late 1960s and 1970s. The pens were mounted on a traveling bar, whereby the y-axis was represented by motion up and down the length of the bar and the x-axis was represented by motion of the bar back and forth across the plotting table. Due to the mass of the bar, these plotters operated slowly. In the 1980s, the small and lightweight HP 7470 introduced the "grit wheel" mechanism, eliminating the need for perforations along the edges, unlike the Calcomp plotters two decades earlier; the grit wheels at opposite edges of the sheet press against resilient polyurethane-coated rollers and form tiny indentations in the sheet. As the sheet is moved back and forth, the grit wheels keep the sheet in proper registration due to the grit particles falling into the earlier indentations, much like the teeth of two gears meshing; the pen is mounted on a carriage that moves back and forth in a line between the gri