Business process automation (BPA), also known as business automation, refers to the technology-enabled automation of business processes. == Development approaches == There are three main approaches to developing BPA: traditional business process automation involves developing BPA software in a programming language for integrating relevant applications in the digital ecosystem to execute a given process; robotic process automation uses software robots (also called agents, bots, or workers) to emulate human-computer interaction for executing a combination of processes, activities, transactions, and tasks in one or more unrelated software systems; hyperautomation (also called intelligent automation (IA), intelligent process automation (IPA), integrated automation platform (IAP), and cognitive automation (CA) combines business process automation, artificial intelligence (AI), and machine learning (ML) to discover, validate, and execute organizational processes automatically with no or minimal human intervention. == Deployment == BPA toolsets vary in capability. With the increasing adoption of artificial intelligence (AI), organizations are implementing AI-driven technologies that can process natural language, interpret unstructured datasets, and interact with users. These systems are designed to adapt to new types of problems with reduced reliance on human intervention. == Business process management implementation == A business process management system differs from BPA. However, it is possible to implement automation based on a BPM implementation. The methods to achieve this vary, from writing custom application code to using specialist BPA tools. == Robotic process automation == Robotic process automation (RPA) involves the deployment of attended or unattended software agents in an organization's environment. These software agents, or robots, are programmed to perform predefined structured and repetitive sets of business tasks or processes. Robotic process automation is designed to streamline workflows by delegating repetitive tasks to software agents, allowing human workers to focus on more complex and strategic activities. BPA providers typically focus on different industry sectors, but the underlying approach is generally similar in that they aim to provide the shortest route to automation by interacting with the user interface rather than modifying the application code or database behind it. == Use of artificial intelligence == Artificial intelligence software robots are used to handle unstructured data sets (like images, texts, audios) and are often deployed after implementing robotic process automation. They can, for instance, generate an automatic transcript from a video. The combination of automation and artificial intelligence (AI) enables autonomy for robots, along with the capability to perform cognitive tasks. At this stage, robots can learn and improve processes by analyzing and adapting them.
Seam carving
Seam carving (or liquid rescaling) is an algorithm for content-aware image resizing, developed by Shai Avidan, of Mitsubishi Electric Research Laboratories (MERL), and Ariel Shamir, of the Interdisciplinary Center and MERL. It functions by establishing a number of seams (paths of least importance) in an image and automatically removes seams to reduce image size or inserts seams to extend it. Seam carving also allows manually defining areas in which pixels may not be modified, and features the ability to remove whole objects from photographs. The purpose of the algorithm is image retargeting, which is the problem of displaying images without distortion on media of various sizes (cell phones, projection screens) using document standards, like HTML, that already support dynamic changes in page layout and text but not images. Image Retargeting was invented by Vidya Setlur, Saeko Takage, Ramesh Raskar, Michael Gleicher and Bruce Gooch in 2005. The work by Setlur et al. won the 10-year impact award in 2015. == Seams == Seams can be either vertical or horizontal. A vertical seam is a path of pixels connected from top to bottom in an image with one pixel in each row. A horizontal seam is similar with the exception of the connection being from left to right. The importance/energy function values a pixel by measuring its contrast with its neighbor pixels. == Process == The below example describes the process of seam carving: The seams to remove depends only on the dimension (height or width) one wants to shrink. It is also possible to invert step 4 so the algorithm enlarges in one dimension by copying a low energy seam and averaging its pixels with its neighbors. === Computing seams === Computing a seam consists of finding a path of minimum energy cost from one end of the image to another. This can be done via Dijkstra's algorithm, dynamic programming, greedy algorithm or graph cuts among others. ==== Dynamic programming ==== Dynamic programming is a programming method that stores the results of sub-calculations in order to simplify calculating a more complex result. Dynamic programming can be used to compute seams. If attempting to compute a vertical seam (path) of lowest energy, for each pixel in a row we compute the energy of the current pixel plus the energy of one of the three possible pixels above it. The images below depict a DP process to compute one optimal seam. Each square represents a pixel, with the top-left value in red representing the energy value of that pixel. The value in black represents the cumulative sum of energies leading up to and including that pixel. The energy calculation is trivially parallelized for simple functions. The calculation of the DP array can also be parallelized with some interprocess communication. However, the problem of making multiple seams at the same time is harder for two reasons: the energy needs to be regenerated for each removal for correctness and simply tracing back multiple seams can form overlaps. Avidan 2007 computes all seams by removing each seam iteratively and storing an "index map" to record all the seams generated. The map holds a "nth seam" number for each pixel on the image, and can be used later for size adjustment. If one ignores both issues however, a greedy approximation for parallel seam carving is possible. To do so, one starts with the minimum-energy pixel at one end, and keep choosing the minimum energy path to the other end. The used pixels are marked so that they are not picked again. Local seams can also be computed for smaller parts of the image in parallel for a good approximation. == Issues == The algorithm may need user-provided information to reduce errors. This can consist of painting the regions which are to be preserved. With human faces it is possible to use face detection. Sometimes the algorithm, by removing a low energy seam, may end up inadvertently creating a seam of higher energy. The solution to this is to simulate a removal of a seam, and then check the energy delta to see if the energy increases (forward energy). If it does, prefer other seams instead. == Implementations == Adobe Systems acquired a non-exclusive license to seam carving technology from MERL, and implemented it as a feature in Photoshop CS4, where it is called Content Aware Scaling. As the license is non-exclusive, other popular computer graphics applications (e. g. GIMP, digiKam, and ImageMagick) as well as some stand-alone programs (e. g. iResizer) also have implementations of this technique, some of which are released as free and open source software. There also exists an implementation for webpages. == Improvements and extensions == Better energy function and application to video by introducing 2D (time+1D) seams. Faster implementation on GPU. Application of this forward energy function to static images. Multi-operator: Combine with cropping and scaling. Much faster removal of multiple seams. Removing seams through neural deformation fields to extend to continuous domains like 3D scenes. A 2010 review of eight image retargeting methods found that seam carving produced output that was ranked among the worst of the tested algorithms. It was, however, a part of one of the highest-ranking algorithms: the multi-operator extension mentioned above (combined with cropping and scaling).
Application delivery network
An application delivery network (ADN) is a suite of technologies that, when deployed together, provide availability, security, visibility, and acceleration for Internet applications such as websites. ADN components provide supporting functionality that enables website content to be delivered to visitors and other users of that website, in a fast, secure, and reliable way. Gartner defines application delivery networking as the combination of WAN optimization controllers (WOCs) and application delivery controllers (ADCs). At the data center end of an ADN is the ADC, an advanced traffic management device that is often also referred to as a web switch, content switch, or multilayer switch, the purpose of which is to distribute traffic among a number of servers or geographically dislocated sites based on application specific criteria. In the branch office portion of an ADN is the WAN optimization controller, which works to reduce the number of bits that flow over the network using caching and compression, and shapes TCP traffic using prioritization and other optimization techniques. Some WOC components are installed on PCs or mobile clients, and there is typically a portion of the WOC installed in the data center. Application delivery networks are also offered by some CDN vendors. The ADC, one component of an ADN, evolved from layer 4-7 switches in the late 1990s when it became apparent that traditional load balancing techniques were not robust enough to handle the increasingly complex mix of application traffic being delivered over a wider variety of network connectivity options. == Application delivery techniques == The Internet was designed according to the end-to-end principle. This principle keeps the core network relatively simple and moves the intelligence as much as possible to the network end-points: the hosts and clients. An Application Delivery Network (ADN) enhances the delivery of applications across the Internet by employing a number of optimization techniques. Many of these techniques are based on established best-practices employed to efficiently route traffic at the network layer including redundancy and load balancing In theory, an Application Delivery Network (ADN) is closely related to a content delivery network. The difference between the two delivery networks lies in the intelligence of the ADN to understand and optimize applications, usually referred to as application fluency. Application Fluent Network (AFN) is based on the concept of Application Fluency to refer to WAN optimization techniques applied at Layer Four to Layer Seven of the OSI model for networks. Application Fluency implies that the network is fluent or intelligent in understanding and being able to optimize delivery of each application. Application Fluent Network is an addition of SDN capabilities. The acronym 'AFN' is used by Alcatel-Lucent Enterprise to refer to an Application Fluent Network. Application delivery uses one or more layer 4–7 switches, also known as a web switch, content switch, or multilayer switch to intelligently distribute traffic to a pool, also known as a cluster or farm, of servers. The application delivery controller (ADC) is assigned a single virtual IP address (VIP) that represents the pool of servers. Traffic arriving at the ADC is then directed to one of the servers in the pool (cluster, farm) based on a number of factors including application specific data values, application transport protocol, availability of servers, current performance metrics, and client-specific parameters. An ADN provides the advantages of load distribution, increase in capacity of servers, improved scalability, security, and increased reliability through application specific health checks. Increasingly the ADN comprises a redundant pair of ADC on which is integrated a number of different feature sets designed to provide security, availability, reliability, and acceleration functions. In some cases these devices are still separate entities, deployed together as a network of devices through which application traffic is delivered, each providing specific functionality that enhances the delivery of the application. == ADN optimization techniques == === TCP multiplexing === TCP Multiplexing is loosely based on established connection pooling techniques utilized by application server platforms to optimize the execution of database queries from within applications. An ADC establishes a number of connections to the servers in its pool and keeps the connections open. When a request is received by the ADC from the client, the request is evaluated and then directed to a server over an existing connection. This has the effect of reducing the overhead imposed by establishing and tearing down the TCP connection with the server, improving the responsiveness of the application. Some ADN implementations take this technique one step further and also multiplex HTTP and application requests. This has the benefit of executing requests in parallel, which enhances the performance of the application. === TCP optimization === There are a number of Request for Comments (RFCs) which describe mechanisms for improving the performance of TCP. Many ADN implement these RFCs in order to provide enhanced delivery of applications through more efficient use of TCP. The RFCs most commonly implemented are: Delayed Acknowledgements Nagle Algorithm Selective Acknowledgements Explicit Congestion Notification ECN Limited and Fast Retransmits Adaptive Initial Congestion Windows === Data compression and caching === ADNs also provide optimization of application data through caching and compression techniques. There are two types of compression used by ADNs today: industry standard HTTP compression and proprietary data reduction algorithms. It is important to note that the cost in CPU cycles to compress data when traversing a LAN can result in a negative performance impact and therefore best practices are to only utilize compression when delivering applications via a WAN or particularly congested high-speed data link. HTTP compression is asymmetric and transparent to the client. Support for HTTP compression is built into web servers and web browsers. All commercial ADN products currently support HTTP compression. A second compression technique is achieved through data reduction algorithms. Because these algorithms are proprietary and modify the application traffic, they are symmetric and require a device to reassemble the application traffic before the client can receive it. A separate class of devices known as WAN Optimization Controllers (WOC) provide this functionality, but the technology has been slowly added to the ADN portfolio over the past few years as this class of device continues to become more application aware, providing additional features for specific applications such as CIFS and SMB. == ADN reliability and availability techniques == === Advanced health checking === Advanced health checking is the ability of an ADN to determine not only the state of the server on which an application is hosted, but the status of the application it is delivering. Advanced health checking techniques allow the ADC to intelligently determine whether or not the content being returned by the server is correct and should be delivered to the client. This feature enables other reliability features in the ADN, such as resending a request to a different server if the content returned by the original server is found to be erroneous. === Load balancing algorithms === The load balancing algorithms found in today's ADN are far more advanced than the simplistic round-robin and least connections algorithms used in the early 1990s. These algorithms were originally loosely based on operating systems' scheduling algorithms, but have since evolved to factor in conditions peculiar to networking and application environments. It is more accurate to describe today's "load balancing" algorithms as application routing algorithms, as most ADN employ application awareness to determine whether an application is available to respond to a request. This includes the ability of the ADN to determine not only whether the application is available, but whether or not the application can respond to the request within specified parameters, often referred to as a service level agreement. Typical industry standard load balancing algorithms available today include: Round Robin Least Connections Fastest Response Time Weighted Round Robin Weighted Least Connections Custom values assigned to individual servers in a pool based on SNMP or other communication mechanism === Fault tolerance === The ADN provides fault tolerance at the server level, within pools or farms. This is accomplished by designating specific servers as a 'backup' that is activated automatically by the ADN in the event that the primary server(s) in the pool fail. The ADN also ensures application availability and reliability through its ability to seamlessly "failover"
Electronic lab notebook
An electronic lab notebook or electronic laboratory notebook (ELN) is a computer program designed to replace paper laboratory notebooks. Lab notebooks in general are used by scientists, engineers, and technicians to document research, experiments, and procedures performed in a laboratory. A lab notebook is often maintained to be a legal document and may be used in a court of law as evidence. Similar to an inventor's notebook, the lab notebook is also often referred to in patent prosecution and intellectual property litigation. Electronic lab notebooks offer many benefits to the user as well as organizations; they are easier to search upon, simplify data copying and backups, and support collaboration amongst many users. ELNs can have fine-grained access controls, and can be more secure than their paper counterparts. They also allow the direct incorporation of data from instruments, replacing the practice of printing out data to be stapled into a paper notebook. == Types == ELNs can be divided into two categories: "Specific ELNs" contain features designed to work with specific applications, scientific instrumentation or data types. "Cross-disciplinary ELNs" or "Generic ELNs" are designed to support access to all data and information that needs to be recorded in a lab notebook. Lab Platforms that combine an ELN, LIMS, and scientific data management together, all-in-one configurable software environment. Solutions range from specialized programs designed from the ground up for use as an ELN, to modifications or direct use of more general programs. Examples of using more general software as an ELN include using OpenWetWare, a MediaWiki install (running the same software that Wikipedia uses), WordPress, or the use of general note taking software such as OneNote as an ELN. ELN's come in many different forms. They can be standalone programs, use a client-server model, or be entirely web-based. Some use a lab-notebook approach, others resemble a blog. ELNs are embracing artificial intelligence and LLM technology to provide scientific AI chat assistants. A good many variations on the "ELN" acronym have appeared. Differences between systems with different names are often subtle, with considerable functional overlap between them. Examples include "ERN" (Electronic Research Notebook), "ERMS" (Electronic Resource (or Research or Records) Management System (or Software) and SDMS (Scientific Data (or Document) Management System (or Software). Ultimately, these types of systems all strive to do the same thing: Capture, record, centralize and protect scientific data in a way that is highly searchable, historically accurate, and legally stringent, and which also promotes secure collaboration, greater efficiency, reduced mistakes and lowered total research costs. == Objectives == A good electronic laboratory notebook should offer a secure environment to protect the integrity of both data and process, whilst also affording the flexibility to adopt new processes or changes to existing processes without recourse to further software development. The package architecture should be a modular design, so as to offer the benefit of minimizing validation costs of any subsequent changes that you may wish to make in the future as your needs change. A good electronic laboratory notebook should be an "out of the box" solution that, as standard, has fully configurable forms to comply with the requirements of regulated analytical groups through to a sophisticated ELN for inclusion of structures, spectra, chromatograms, pictures, text, etc. where a preconfigured form is less appropriate. All data within the system may be stored in a database (e.g. MySQL, MS-SQL, Oracle) and be fully searchable. The system should enable data to be collected, stored and retrieved through any combination of forms or ELN that best meets the requirements of the user. The application should enable secure forms to be generated that accept laboratory data input via PCs and/or laptops / palmtops, and should be directly linked to electronic devices such as laboratory balances, pH meters, etc. Networked or wireless communications should be accommodated for by the package which will allow data to be interrogated, tabulated, checked, approved, stored and archived to comply with the latest regulatory guidance and legislation. A system should also include a scheduling option for routine procedures such as equipment qualification and study related timelines. It should include configurable qualification requirements to automatically verify that instruments have been cleaned and calibrated within a specified time period, that reagents have been quality-checked and have not expired, and that workers are trained and authorized to use the equipment and perform the procedures. == Regulatory and legal aspects == The laboratory accreditation criteria found in the ISO 17025 standard needs to be considered for the protection and computer backup of electronic records. These criteria can be found specifically in clause 4.13.1.4 of the standard. Electronic lab notebooks used for development or research in regulated industries, such as medical devices or pharmaceuticals, are expected to comply with FDA regulations related to software validation. The purpose of the regulations is to ensure the integrity of the entries in terms of time, authorship, and content. Unlike ELNs for patent protection, FDA is not concerned with patent interference proceedings, but is concerned with avoidance of falsification. Typical provisions related to software validation are included in the medical device regulations at 21 CFR 820 (et seq.) and Title 21 CFR Part 11. Essentially, the requirements are that the software has been designed and implemented to be suitable for its intended purposes. Evidence to show that this is the case is often provided by a Software Requirements Specification (SRS) setting forth the intended uses and the needs that the ELN will meet; one or more testing protocols that, when followed, demonstrate that the ELN meets the requirements of the specification and that the requirements are satisfied under worst-case conditions. Security, audit trails, prevention of unauthorized changes without substantial collusion of otherwise independent personnel (i.e., those having no interest in the content of the ELN such as independent quality unit personnel) and similar tests are fundamental. Finally, one or more reports demonstrating the results of the testing in accordance with the predefined protocols are required prior to release of the ELN software for use. If the reports show that the software failed to satisfy any of the SRS requirements, then corrective and preventive action ("CAPA") must be undertaken and documented. Such CAPA may extend to minor software revisions, or changes in architecture or major revisions. CAPA activities need to be documented as well. Aside from the requirements to follow such steps for regulated industry, such an approach is generally a good practice in terms of development and release of any software to assure its quality and fitness for use. There are standards related to software development and testing that can be applied (see ref.).
Business continuity and disaster recovery auditing
Given organizations' increasing dependency on information technology (IT) to run their operations, business continuity planning (and its subset IT service continuity planning) covers the entire organization, while disaster recovery focuses on IT. Auditing documents covering an organization's business continuity and disaster recovery (BCDR) plans provides a third-party validation to stakeholders that the documentation is complete and does not contain material misrepresentations. == Overview == Often used together, the terms business continuity (BC) and disaster recovery (DR) are very different. BC refers to the ability of a business to continue critical functions and business processes after the occurrence of a disaster, whereas DR refers specifically to the IT functions of the business, albeit a subset of BC. == Metrics == The primary objective is to protect the organization in the event that all or part of its operations and/or computer services are rendered partially or completely unusable. === DR metrics === Minimizing downtime and data loss during disaster recovery is typically measured in terms of two key concepts: Recovery time objective (RTO), time until a system is completely up and running Recovery point objective (RPO), a measure of the ability to recover files by specifying a point in time the backup copy will restore to. == The auditor's role == Role of the Internal Auditor in Auditing a Disaster Recovery Plan (DRP): 1. Governance & Oversight - Confirm roles, responsibilities, and oversight are defined, and DRP aligns with risk appetite and continuity strategy. 2. Risk Assessment & BIA - Verify risk and impact assessments identify critical systems and define RTO/RPO. 3. Plan Design & Documentation - Ensure the DRP is current, complete, and includes key recovery procedures. 4. Testing & Validation - Confirm regular DRP testing occurs and results are used to improve the plan. 5. Backup & Recovery - Assess backup frequency and recovery capabilities against RTO/RPO targets. 6. Communication & Training - Verify staff are trained and communication protocols are in place for crises. 7. Maintenance & Improvement - Ensure the DRP is regularly updated and lessons learned are integrated. == Documentation == === Disaster recovery plan === A disaster recovery plan (DRP) is a documented process or set of procedures to execute an organization's disaster recovery processes and recover and protect a business IT infrastructure in the event of a disaster. It is "a comprehensive statement of consistent actions to be taken before, during and after a disaster". The disaster could be natural, environmental or man-made. Man-made disasters could be intentional (for example, an act of a terrorist) or unintentional (that is, accidental, such as the breakage of a man-made dam or even "fat fingers" - or errant commands entered - on a computer system). ==== Types of plans ==== Although there is no one-size-fits-all plan, there are three basic strategies: prevention, including proper backups, having surge protectors and generators detection, a byproduct of routine inspections, which may discover new (potential) threats correction The latter may include securing proper insurance policies, and holding a "lessons learned" brainstorming session. ==== Best practices ==== To maximize their effectiveness, DRPs are most effective when updated frequently, and should: be an integral part of all business analysis processes, be revisited at every major corporate acquisition, at every new product launch and at every new system development milestone. be thoroughly tested, not just unpracticed bureaucratic documentation Adequate records need to be retained by the organization. The auditor examines records, billings, and contracts to verify that records are being kept. One such record is a current list of the organization's hardware and software vendors. Such list is made and periodically updated to reflect changing business practices and as part of an IT asset management system. Copies of it are stored on and off site and are made available or accessible to those who require them. An auditor tests the procedures used to meet this objective and determine their effectiveness. === Relationship to BCPs === Disaster recovery is a subset of business continuity. Where DRP encompasses the policies, tools and procedures to enable recovery of data following a catastrophic event, BCP involves keeping all aspects of a business functioning regardless of potential disruptive events. As such, a business continuity plan is a comprehensive organizational strategy that includes the DRP as well as threat prevention, detection, recovery, and resumption of operations should a data breach or other disaster event occur. Therefore, BCP consists of five component plans: Business resumption plan Occupant emergency plan Continuity of operations plan Incident management plan Disaster recovery plan The first three components (business resumption, occupant emergency, and continuity of operations plans) do not deal with the IT infrastructure. The incident management plan (IMP) does deal with the IT infrastructure, but since it establishes structure and procedures to address cyber attacks against an organization's IT systems, it generally does not represent an agent for activating the DRP; thus DRP is the only BCP component of active interest to IT. == Testing == The overall categorization of tests are functional- and discussion-based. Types of tests include: tabletop exercises, checklists, simulations, parallel processing (testing recovery site while primary site is in operation), and full interruption (fail over) tests. These apply to both BC and DR. == Benefits == Like every insurance plan, there are benefits that can be obtained from proper business continuity planning, including: Studies have shown a correlation between higher spending on auditing fees and lower rates of Incidents. Minimizing risk of delays Guaranteeing the reliability of standby systems (even automating the failure detection and recovery in certain scenarios) Providing a standard for testing the plan Minimizing decision-making during a disaster Reducing potential legal liabilities Lowering unnecessarily stressful work environment === Planning and testing methodology === According to Geoffrey H. Wold of the Disaster Recovery Journal, the entire process involved in developing a Disaster Recovery Plan consists of 10 steps: Performing a risk assessment: The planning committee prepares a risk analysis and a business impact analysis (BIA) that includes a range of possible disasters. Each functional area of the organization is analyzed to determine potential consequences. Traditionally, fire has posed the greatest threat. A thorough plan provides for "worst case" situations, such as destruction of the main building. Establishing priorities for processing and operations: Critical needs of each department are evaluated and prioritized. Written agreements for alternatives selected are prepared, with details specifying duration, termination conditions, system testing, cost, any special security procedures, procedure for the notification of system changes, hours of operation, the specific hardware and other equipment required for processing, personnel requirements, definition of the circumstances constituting an emergency, process to negotiate service extensions, guarantee of compatibility, availability, non-mainframe resource requirements, priorities, and other contractual issues. Collecting data: This includes various lists (employee backup position listing, critical telephone numbers list, master call list, master vendor list, notification checklist), inventories (communications equipment, documentation, office equipment, forms, insurance policies, workgroup and data center computer hardware, microcomputer hardware and software, office supply, off-site storage location equipment, telephones, etc.), distribution register, software and data files backup/retention schedules, temporary location specifications, any other such lists, materials, inventories, and documentation. Pre-formatted forms are often used to facilitate the data gathering process. Organizing and documenting a written plan Developing testing criteria and procedures: reasons for testing include Determining the feasibility and compatibility of backup facilities and procedures. Identifying areas in the plan that need modification. Providing training to the team managers and team members. Demonstrating the ability of the organization to recover. Providing motivation for maintaining and updating the disaster recovery plan. Testing the plan: An initial "dry run" of the plan is performed by conducting a structured walk-through test. An actual test-run must be performed. Problems are corrected. Initial testing can be plan is done in sections and after normal business hours to minimize disruptions. Subsequent tests occur during normal business hours. === Caveats/controversie
Direct Graphics Access
Direct Graphics Access is a plug-in for the X display servers that allows client programs direct access to the frame buffer. Graphics hardware communicates via a chunk of memory called a frame buffer. This is an array of values that represent pixel color values on the screen. Writing the appropriate values into the frame buffer therefore allows a program to paint areas of the screen. However, as with any shared resource, problems occur when multiple programs attempt to access the same resource, as they tend to write over each other's work. In the X Window System, this is solved by having a central display server that mediates between programs that want to draw on the screen. The display server also used to perform a lot of the drawing work, allowing programs to say Draw me a circle of this radius filled with this pattern or draw this text in this font. The X server does all this work, freeing programmers from having to write their own drawing code. Another advantage of the X architecture is that it works over a network, allowing programs on one machine to display output on the screen of another. Direct Graphics Access allows direct access to the frame buffer and the X-server hands over control of the frame buffer to the client program and waits for the client to hand it back. This means that the client program has control of the whole screen, and so it is mostly used for full-screen video/games.
Superincreasing sequence
In mathematics, a sequence of positive real numbers ( s 1 , s 2 , . . . ) {\displaystyle (s_{1},s_{2},...)} is called superincreasing if every element of the sequence is greater than the sum of all previous elements in the sequence. Formally, this condition can be written as s n + 1 > ∑ j = 1 n s j {\displaystyle s_{n+1}>\sum _{j=1}^{n}s_{j}} for all n ≥ 1. == Program == The following Python source code tests a sequence of numbers to determine if it is superincreasing: This produces the following output: Sum: 0 Element: 1 Sum: 1 Element: 3 Sum: 4 Element: 6 Sum: 10 Element: 13 Sum: 23 Element: 27 Sum: 50 Element: 52 Is it a superincreasing sequence? True == Examples == (1, 3, 6, 13, 27, 52) is a superincreasing sequence, but (1, 3, 4, 9, 15, 25) is not. The series a^x for a>=2 == Properties == Multiplying a superincreasing sequence by a positive real constant keeps it superincreasing.