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  • Hierarchical RBF

    Hierarchical RBF

    In computer graphics, hierarchical RBF is an interpolation method based on radial basis functions (RBFs). Hierarchical RBF interpolation has applications in treatment of results from a 3D scanner, terrain reconstruction, and the construction of shape models in 3D computer graphics (such as the Stanford bunny, a popular 3D model). This problem is informally named as "large scattered data point set interpolation." == Method == The steps of the interpolation method (in three dimensions) are as follows: Let the scattered points be presented as set P = { c i = ( x i , y i , z i ) | i = 1 N ⊂ R 3 } {\displaystyle \mathbf {P} =\{\mathbf {c} _{i}=(\mathbf {x} _{i},\mathbf {y} _{i},\mathbf {z} _{i})\vert _{i=1}^{N}\subset \mathbb {R} ^{3}\}} Let there exist a set of values of some function in scattered points H = { h i | i = 1 N ⊂ R } {\displaystyle \mathbf {H} =\{\mathbf {h} _{i}\vert _{i=1}^{N}\subset \mathbb {R} \}} Find a function f ( x ) {\displaystyle \mathbf {f} (\mathbf {x} )} that will meet the condition f ( x ) = 1 {\displaystyle \mathbf {f} (\mathbf {x} )=1} for points lying on the shape and f ( x ) ≠ 1 {\displaystyle \mathbf {f} (\mathbf {x} )\neq 1} for points not lying on the shape As J. C. Carr et al. showed, this function takes the form f ( x ) = ∑ i = 1 N λ i φ ( x , c i ) {\displaystyle \mathbf {f} (\mathbf {x} )=\sum _{i=1}^{N}\lambda _{i}\varphi (\mathbf {x} ,\mathbf {c} _{i})} where φ {\displaystyle \varphi } is a radial basis function and λ {\displaystyle \lambda } are the coefficients that are the solution of the following linear system of equations: [ φ ( c 1 , c 1 ) φ ( c 1 , c 2 ) . . . φ ( c 1 , c N ) φ ( c 2 , c 1 ) φ ( c 2 , c 2 ) . . . φ ( c 2 , c N ) . . . . . . . . . . . . φ ( c N , c 1 ) φ ( c N , c 2 ) . . . φ ( c N , c N ) ] ∗ [ λ 1 λ 2 . . . λ N ] = [ h 1 h 2 . . . h N ] {\displaystyle {\begin{bmatrix}\varphi (c_{1},c_{1})&\varphi (c_{1},c_{2})&...&\varphi (c_{1},c_{N})\\\varphi (c_{2},c_{1})&\varphi (c_{2},c_{2})&...&\varphi (c_{2},c_{N})\\...&...&...&...\\\varphi (c_{N},c_{1})&\varphi (c_{N},c_{2})&...&\varphi (c_{N},c_{N})\end{bmatrix}}{\begin{bmatrix}\lambda _{1}\\\lambda _{2}\\...\\\lambda _{N}\end{bmatrix}}={\begin{bmatrix}h_{1}\\h_{2}\\...\\h_{N}\end{bmatrix}}} For determination of surface, it is necessary to estimate the value of function f ( x ) {\displaystyle \mathbf {f} (\mathbf {x} )} in specific points x. A lack of such method is a considerable complication on the order of O ( n 2 ) {\displaystyle \mathbf {O} (\mathbf {n} ^{2})} to calculate RBF, solve system, and determine surface. == Other methods == Reduce interpolation centers ( O ( n 2 ) {\displaystyle \mathbf {O} (\mathbf {n} ^{2})} to calculate RBF and solve system, O ( m n ) {\displaystyle \mathbf {O} (\mathbf {m} \mathbf {n} )} to determine surface) Compactly support RBF ( O ( n log ⁡ n ) {\displaystyle \mathbf {O} (\mathbf {n} \log {\mathbf {n} })} to calculate RBF, O ( n 1.2..1.5 ) {\displaystyle \mathbf {O} (\mathbf {n} ^{1.2..1.5})} to solve system, O ( m log ⁡ n ) {\displaystyle \mathbf {O} (\mathbf {m} \log {\mathbf {n} })} to determine surface) FMM ( O ( n 2 ) {\displaystyle \mathbf {O} (\mathbf {n} ^{2})} to calculate RBF, O ( n log ⁡ n ) {\displaystyle \mathbf {O} (\mathbf {n} \log {\mathbf {n} })} to solve system, O ( m + n log ⁡ n ) {\displaystyle \mathbf {O} (\mathbf {m} +\mathbf {n} \log {\mathbf {n} })} to determine surface) == Hierarchical algorithm == A hierarchical algorithm allows for an acceleration of calculations due to decomposition of intricate problems on the great number of simple (see picture). In this case, hierarchical division of space contains points on elementary parts, and the system of small dimension solves for each. The calculation of surface in this case is taken to the hierarchical (on the basis of tree-structure) calculation of interpolant. A method for a 2D case is offered by Pouderoux J. et al. For a 3D case, a method is used in the tasks of 3D graphics by W. Qiang et al. and modified by Babkov V.

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  • Project workforce management

    Project workforce management

    Project workforce management is the practice of combining the coordination of all logistic elements of a project through a single software application (or workflow engine). This includes planning and tracking of schedules and mileposts, cost and revenue, resource allocation, as well as overall management of these project elements. Efficiency is improved by eliminating manual processes, like spreadsheet tracking to monitor project progress. It also allows for at-a-glance status updates and ideally integrates with existing legacy applications in order to unify ongoing projects, enterprise resource planning (ERP) and broader organizational goals. There are a lot of logistic elements in a project. Different team members are responsible for managing each element and often, the organisation may have a mechanism to manage some logistic areas as well. By coordinating these various components of project management, workforce management and financials through a single solution, the process of configuring and changing project and workforce details is simplified. == Introduction == A project workforce management system defines project tasks, project positions, and assigns personnel to the project positions. The project tasks and positions are correlated to assign a responsible project position or even multiple positions to complete each project task. Because each project position may be assigned to a specific person, the qualifications and availabilities of that person can be taken into account when determining the assignment. By associating project tasks and project positions, a manager can better control the assignment of the workforce and complete the project more efficiently. When it comes to project workforce management, it is all about managing all the logistic aspects of a project or an organisation through a software application. Usually, this software has a workflow engine defined. Therefore, all the logistic processes take place in the workflow engine. == About == === Technical field === This invention relates to project management systems and methods, more particularly to a software-based system and method for project and workforce management. === Software usage === Due to the software usage, all the project workflow management tasks can be fully automated without leaving many tasks for the project managers. This returns high efficiency to the project management when it comes to project tracking proposes. In addition to different tracking mechanisms, project workforce management software also offer a dashboard for the project team. Through the dashboard, the project team has a glance view of the overall progress of the project elements. Most of the times, project workforce management software can work with the existing legacy software systems such as ERP (enterprise resource planning) systems. This easy integration allows the organisation to use a combination of software systems for management purposes. === Background === Good project management is an important factor for the success of a project. A project may be thought of as a collection of activities and tasks designed to achieve a specific goal of the organisation, with specific performance or quality requirements while meeting any subject time and cost constraints. Project management refers to managing the activities that lead to the successful completion of a project. Furthermore, it focuses on finite deadlines and objectives. A number of tools may be used to assist with this as well as with assessment. Project management may be used when planning personnel resources and capabilities. The project may be linked to the objects in a professional services life cycle and may accompany the objects from the opportunity over quotation, contract, time and expense recording, billing, period-end-activities to the final reporting. Naturally the project gets even more detailed when moving through this cycle. For any given project, several project tasks should be defined. Project tasks describe the activities and phases that have to be performed in the project such as writing of layouts, customising, testing. What is needed is a system that allows project positions to be correlated with project tasks. Project positions describe project roles like project manager, consultant, tester, etc. Project-positions are typically arranged linearly within the project. By correlating project tasks with project positions, the qualifications and availability of personnel assigned to the project positions may be considered. == Benefits of project management == Good project management should: Reduce the chance of a project failing Ensure a minimum level of quality and that results meet requirements and expectations Free up other staff members to get on with their area of work and increase efficiency both on the project and within the business Make things simpler and easier for staff with a single point of contact running the overall project Encourage consistent communications amongst staff and suppliers Keep costs, timeframes and resources to budget == Workflow engine == When it comes to project workforce management, it is all about managing all the logistic aspects of a project or an organisation through a software application. Usually, this software has a workflow engine defined in them. So, all the logistic processes take place in the workflow engine. The regular and most common types of tasks handled by project workforce management software or a similar workflow engine are: === Planning and monitoring project schedules and milestones === Regularly monitoring your project's schedule performance can provide early indications of possible activity-coordination problems, resource conflicts, and possible cost overruns. To monitor schedule performance. Collecting information and evaluating it ensure a project accuracy. The project schedule outlines the intended result of the project and what's required to bring it to completion. In the schedule, we need to include all the resources involved and cost and time constraints through a work breakdown structure (WBS). The WBS outlines all the tasks and breaks them down into specific deliverables. === Tracking the cost and revenue aspects of projects === The importance of tracking actual costs and resource usage in projects depends upon the project situation. Tracking actual costs and resource usage is an essential aspect of the project control function. === Resource utilisation and monitoring === Organisational profitability is directly connected to project management efficiency and optimal resource utilisation. To sum up, organisations that struggle with either or both of these core competencies typically experience cost overruns, schedule delays and unhappy customers. The focus for project management is the analysis of project performance to determine whether a change is needed in the plan for the remaining project activities to achieve the project goals. == Other management aspects of project management == === Project risk management === Risk identification consists of determining which risks are likely to affect the project and documenting the characteristics of each. === Project communication management === Project communication management is about how communication is carried out during the course of the project === Project quality management === It is of no use completing a project within the set time and budget if the final product is of poor quality. The project manager has to ensure that the final product meets the quality expectations of the stakeholders. This is done by good: Quality planning: Identifying what quality standards are relevant to the project and determining how to meet them. Quality assurance: Evaluating overall project performance on a regular basis to provide confidence that the project will satisfy the relevant quality standards. Quality control: Monitoring specific project results to determine if they comply with relevant quality standards and identifying ways to remove causes of poor performance. == Project workforce management vs. traditional management == There are three main differences between Project Workforce Management and traditional project management and workforce management disciplines and solutions: === Workflow-driven === All project and workforce processes are designed, controlled and audited using a built-in graphical workflow engine. Users can design, control and audit the different processes involved in the project. The graphical workflow is quite attractive for the users of the system and allows the users to have a clear idea of the workflow engine. === Organisation and work breakdown structures === Project Workforce Management provides organization and work breakdown structures to create, manage and report on functional and approval hierarchies, and to track information at any level of detail. Users can create, manage, edit and report work breakdown structures. Work breakdown structures have different abstraction

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  • Artificial imagination

    Artificial imagination

    Artificial imagination is a narrow subcomponent of artificial general intelligence which generates, simulates, and facilitates real or possible fiction models to create predictions, inventions, or conscious experiences. The term artificial imagination is also used to describe a property of machines or programs. Some of the traits that researchers hope to simulate include creativity, vision, digital art, humor, and satire. Practitioners in the field are researching various aspects of Artificial imagination, such as Artificial (visual) imagination, Artificial (aural) Imagination, modeling/filtering content based on human emotions and Interactive Search. Some articles on the topic speculate on how artificial imagination may evolve to create an artificial world "people may be comfortable enough to escape from the real world". Some researchers such as G. Schleis and M. Rizki have focused on using artificial neural networks to simulate artificial imagination. Another important project is being led by Hiroharu Kato and Tatsuya Harada at the University of Tokyo in Japan. They have developed a computer capable of translating a description of an object into an image, which could be the easiest way to define what imagination is. Their idea is based on the concept of an image as a series of pixels divided into short sequences that correspond to a specific part of an image. The scientists call this sequences "visual words" and those can be interpreted by the machine using statistical distribution to read an create an image of an object the machine has not encountered. The topic of artificial imagination has garnered interest from scholars outside the computer science domain, such as noted communications scholar Ernest Bormann, who came up with the Symbolic Convergence Theory and worked on a project to develop artificial imagination in computer systems. An interdisciplinary research seminar organized by the artist Grégory Chatonsky on artificial imagination and postdigital art has taken place since 2017 at the Ecole Normale Supérieure in Paris. == Use in interactive search == The typical application of artificial imagination is for an interactive search. Interactive searching has been developed since the mid-1990s, accompanied by the World Wide Web's development and the optimization of search engines. Based on the first query and feedback from a user, the databases to be searched are reorganized to improve the searching results. Artificial imagination allows us to synthesize images and to develop a new image, whether it is in the database, regardless its existence in the real world. For example, the computer shows results that are based on the answer from the initial query. The user selects several relevant images, and then the technology analyzes these selections and reorganizes the images' ranks to fit the query. In this process, artificial imagination is used to synthesize the selected images and to improve the searching result with additional relevant synthesized images. This technique is based on several algorithms, including the Rocchio algorithm and the evolutionary algorithm. The Rocchio algorithm, locating a query point near relevant examples and far away from irrelevant examples, is simple and works well in a small system where the databases are arranged in certain ranks. The evolutionary synthesis is composed of two steps: a standard algorithm and an enhancement of the standard algorithm. Through feedback from the user, there would be additional images synthesized so as to be suited to what the user is looking for. == General artificial imagination == Artificial imagination has a more general definition and wide applications. The traditional fields of artificial imagination include visual imagination and aural imagination. More generally, all the actions to form ideas, images and concepts can be linked to imagination. Thus, artificial imagination means more than only generating graphs. For example, moral imagination is an important research subfield of artificial imagination, although classification of artificial imagination is difficult. Morals are an important part to human beings' logic, while artificial morals are important in artificial imagination and artificial intelligence. A common criticism of artificial intelligence is whether human beings should take responsibility for machines' mistakes or decisions and how to develop well-behaved machines. As nobody can give a clear description of the best moral rules, it is impossible to create machines with commonly accepted moral rules. However, recent research about artificial morals circumvent the definition of moral. Instead, machine learning methods are applied to train machines to imitate human morals. As the data about moral decisions from thousands of different people are considered, the trained moral model can reflect widely accepted rules. Memory is another major field of artificial imagination. Researchers such as Aude Oliva have performed extensive work on artificial memory, especially visual memory. Compared to visual imagination, the visual memory focuses more on how machine understand, analyse and store pictures in a human way. In addition, characters like spatial features are also considered. As this field is based on the brains' biological structures, extensive research on neuroscience has also been performed, which makes it a large intersection between biology and computer science.

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  • KiSAO

    KiSAO

    The Kinetic Simulation Algorithm Ontology (KiSAO) supplies information about existing algorithms available for the simulation of systems biology models, their characterization and interrelationships. KiSAO is part of the BioModels.net project and of the COMBINE initiative. == Structure == KiSAO consists of three main branches: simulation algorithm simulation algorithm characteristic simulation algorithm parameter The elements of each algorithm branch are linked to characteristic and parameter branches using has characteristic and has parameter relationships accordingly. The algorithm branch itself is hierarchically structured using relationships which denote that the descendant algorithms were derived from, or specify, more general ancestors.

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  • Social software engineering

    Social software engineering

    Social software engineering (SSE) is a branch of software engineering that is concerned with the social aspects of software development and the developed software. SSE focuses on the socialness of both software engineering and developed software. On the one hand, the consideration of social factors in software engineering activities, processes and CASE tools is deemed to be useful to improve the quality of both development process and produced software. Examples include the role of situational awareness and multi-cultural factors in collaborative software development. On the other hand, the dynamicity of the social contexts in which software could operate (e.g., in a cloud environment) calls for engineering social adaptability as a runtime iterative activity. Examples include approaches which enable software to gather users' quality feedback and use it to adapt autonomously or semi-autonomously. SSE studies and builds socially-oriented tools to support collaboration and knowledge sharing in software engineering. SSE also investigates the adaptability of software to the dynamic social contexts in which it could operate and the involvement of clients and end-users in shaping software adaptation decisions at runtime. Social context includes norms, culture, roles and responsibilities, stakeholder's goals and interdependencies, end-users perception of the quality and appropriateness of each software behaviour, etc. The participants of the 1st International Workshop on Social Software Engineering and Applications (SoSEA 2008) proposed the following characterization: Community-centered: Software is produced and consumed by and/or for a community rather than focusing on individuals Collaboration/collectiveness: Exploiting the collaborative and collective capacity of human beings Companionship/relationship: Making explicit the various associations among people Human/social activities: Software is designed consciously to support human activities and to address social problems Social inclusion: Software should enable social inclusion enforcing links and trust in communities Thus, SSE can be defined as "the application of processes, methods, and tools to enable community-driven creation, management, deployment, and use of software in online environments". One of the main observations in the field of SSE is that the concepts, principles, and technologies made for social software applications are applicable to software development itself as software engineering is inherently a social activity. SSE is not limited to specific activities of software development. Accordingly, tools have been proposed supporting different parts of SSE, for instance, social system design or social requirements engineering. Consequently vertical market software, such as software development tools, engineering tools, marketing tools or software that helps users in a decision-making process can profit from social components. Such vertical social software differentiates strongly in its user-base from traditional social software such as Yammer.

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  • ArchiMate

    ArchiMate

    ArchiMate ( AR-ki-mayt) is an open and independent enterprise architecture modeling language to support the description, analysis and visualization of architecture within and across business domains in an unambiguous way. ArchiMate is a technical standard from The Open Group and is based on concepts from the now superseded IEEE 1471 standard. It is supported by various tool vendors and consulting firms. ArchiMate is also a registered trademark of The Open Group. The Open Group has a certification program for ArchiMate users, software tools and courses. ArchiMate distinguishes itself from other languages such as Unified Modeling Language (UML) and Business Process Modeling and Notation (BPMN) by its enterprise modelling scope. Also, UML and BPMN are meant for a specific use and they are quite heavy – containing about 150 (UML) and 250 (BPMN) modeling concepts whereas ArchiMate works with just about 50 (in version 2.0). The goal of ArchiMate is to be ”as small as possible”, not to cover every edge scenario imaginable. To be easy to learn and apply, ArchiMate was intentionally restricted “to the concepts that suffice for modeling the proverbial 80% of practical cases". == Overview == ArchiMate offers a common language for describing the construction and operation of business processes, organizational structures, information flows, IT systems, and technical infrastructure. This insight helps the different stakeholders to design, assess, and communicate the consequences of decisions and changes within and between these business domains. The main concepts and relationships of the ArchiMate language can be seen as a framework, the so-called Archimate Framework: It divides the enterprise architecture into a business, application and technology layer. In each layer, three aspects are considered: active elements, an internal structure and elements that define use or communicate information. One of the objectives of the ArchiMate language is to define the relationships between concepts in different architecture domains. The concepts of this language therefore hold the middle between the detailed concepts, which are used for modeling individual domains (for example, the Unified Modeling Language (UML) for modeling software products), and Business Process Model and Notation (BPMN), which is used for business process modeling. == History == ArchiMate is partly based on the now superseded IEEE 1471 standard. It was developed in the Netherlands by a project team from the Telematica Instituut in cooperation with several Dutch partners from government, industry and academia. Among the partners were Ordina NV, Radboud Universiteit Nijmegen, the Leiden Institute for Advanced Computer Science (LIACS) and the Centrum Wiskunde & Informatica (CWI). Later, tests were performed in organizations such as ABN AMRO, the Dutch Tax and Customs Administration and the ABP. The development process lasted from July 2002 to December 2004, and took about 35 person years and approximately 4 million euros. The development was funded by the Dutch government (Dutch Tax and Customs Administration), and business partners, including ABN AMRO and the ABP Pension Fund. In 2008 the ownership and stewardship of ArchiMate was transferred to The Open Group. It is now managed by the ArchiMate Forum within The Open Group. In February 2009 The Open Group published the ArchiMate 1.0 standard as a formal technical standard. In January 2012 the ArchiMate 2.0 standard, and in 2013 the ArchiMate 2.1 standard was released. In June 2016, the Open Group released version 3.0 of the ArchiMate Specification. An update to Archimate 3.0.1 came out in August 2017. Archimate 3.1 was published 5 November 2019. The latest version of the ArchiMate Specification is version 3.2 released October 2022. Version 3.0 adds enhanced support for capability-oriented strategic modelling, new entities representing physical resources (for modelling the ingredients, equipment and transport resources used in the physical world) and a generic metamodel showing the entity types and the relationships between them. == ArchiMate framework == === Core framework === The main concepts and elements of the ArchiMate language are being presented as ArchiMate core framework. It consists of three layers and three aspects. This creates a matrix of combinations. Every layer has its passive structure, behavior and active structure aspects. ==== Layers ==== ArchiMate has a layered and service-oriented look on architectural models. The higher layers make use of services that are provided by the lower layers. Although, at an abstract level, the concepts that are used within each layer are similar, we define more concrete concepts that are specific for a certain layer. In this context, we distinguish three main layers: The business layer is about business processes, services, functions and events of business units. This layer "offers products and services to external customers, which are realized in the organization by business processes performed by business actors and roles". The application layer is about software applications that "support the components in the business with application services". The technology layer deals "with the hardware and communication infrastructure to support the application layer. This layer offers infrastructural services needed to run applications, realized by computer and communication hardware and system software". Each of these main layers can be further divided in sub-layers. For example, in the business layer, the primary business processes realising the products of a company may make use of a layer of secondary (supporting) business processes; in the application layer, the end-user applications may make use of generic services offered by supporting applications. On top of the business layer, a separate environment layer may be added, modelling the external customers that make use of the services of the organisation (although these may also be considered part of the business layer). In line with service orientation, the most important relation between layers is formed by use relations, which show how the higher layers make use of the services of lower layers. However, a second type of link is formed by realisation relations: elements in lower layers may realise comparable elements in higher layers; e.g., a ‘data object’ (application layer) may realise a ‘business object’ (business layer); or an ‘artifact’ (technology layer) may realise either a ‘data object’ or an ‘application component’ (application layer). ==== Aspects ==== Passive structure is the set of entities on which actions are conducted. In the business layer the example would be information objects, in the application layer data objects and in the technology layer, they could include physical objects. Behavior refers to the processes and functions performed by the actors. "Structural elements are assigned to behavioral elements, to show who or what displays the behavior". Active structure is the set of entities that display some behavior, e.g. business actors, devices, or application components. === Full framework === The Full ArchiMate framework is enriched by the physical layer, which was added to allow modeling of “physical equipment, materials, and distribution networks” and was not present in the previous version. The implementation and migration layer adds elements that allow architects to model a state of transition, to mark parts of the architecture that are temporary for the purpose, as the name says, of implementation and migration. Strategy layer adds three elements: resource, capability and course of action. These elements help to incorporate strategic dimension to the ArchiMate language by allowing it to depict the usage of resources and capabilities in order to achieve some strategic goals. Finally, there is a motivation aspect that allows different stakeholders to describe the motivation of specific actors or domains, which can be quite important when looking at one thing from several different angles. It adds several elements like stakeholder, value, driver, goal, meaning etc. == ArchiMate language == The ArchiMate language is formed as a top-level and is hierarchical. On the top, there is a model. A model is a collection of concepts. A concept can be either an element or a relationship. An element can be either of behavior type, structure, motivation or a so-called composite element (which means that it does not fit just one aspect of the framework, but two or more). The functionality of all concepts without a dependency on a specific layer is described by the generic metamodel. This layer-independent description of concepts is useful when trying to understand the mechanics of the Archimate language. === Concepts === ==== Elements ==== The generic elements are distributed into the same categories as the layers: Active structure elements Behavior elements Passive structure elements Motivation elements Active structure e

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  • Randomized rounding

    Randomized rounding

    In computer science and operations research, randomized rounding is a widely used approach for designing and analyzing approximation algorithms. Many combinatorial optimization problems are computationally intractable to solve exactly (to optimality). For such problems, randomized rounding can be used to design fast (polynomial time) approximation algorithms—that is, algorithms that are guaranteed to return an approximately optimal solution given any input. The basic idea of randomized rounding is to convert an optimal solution of a relaxation of the problem into an approximately-optimal solution to the original problem. The resulting algorithm is usually analyzed using the probabilistic method. == Overview == The basic approach has three steps: Formulate the problem to be solved as an integer linear program (ILP). Compute an optimal fractional solution x {\displaystyle x} to the linear programming relaxation (LP) of the ILP. Round the fractional solution x {\displaystyle x} of the LP to an integer solution x ′ {\displaystyle x'} of the ILP. (Although the approach is most commonly applied with linear programs, other kinds of relaxations are sometimes used. For example, see Goemans' and Williamson's semidefinite programming-based Max-Cut approximation algorithm.) In the first step, the challenge is to choose a suitable integer linear program. Familiarity with linear programming, in particular modelling using linear programs and integer linear programs, is required. For many problems, there is a natural integer linear program that works well, such as in the Set Cover example below. (The integer linear program should have a small integrality gap; indeed randomized rounding is often used to prove bounds on integrality gaps.) In the second step, the optimal fractional solution can typically be computed in polynomial time using any standard linear programming algorithm. In the third step, the fractional solution must be converted into an integer solution (and thus a solution to the original problem). This is called rounding the fractional solution. The resulting integer solution should (provably) have cost not much larger than the cost of the fractional solution. This will ensure that the cost of the integer solution is not much larger than the cost of the optimal integer solution. The main technique used to do the third step (rounding) is to use randomization, and then to use probabilistic arguments to bound the increase in cost due to the rounding (following the probabilistic method from combinatorics). Therein, probabilistic arguments are used to show the existence of discrete structures with desired properties. In this context, one uses such arguments to show the following: Given any fractional solution x {\displaystyle x} of the LP, with positive probability the randomized rounding process produces an integer solution x ′ {\displaystyle x'} that approximates x {\displaystyle x} according to some desired criterion. Finally, to make the third step computationally efficient, one either shows that x ′ {\displaystyle x'} approximates x {\displaystyle x} with high probability (so that the step can remain randomized) or one derandomizes the rounding step, typically using the method of conditional probabilities. The latter method converts the randomized rounding process into an efficient deterministic process that is guaranteed to reach a good outcome. == Example: the set cover problem == The following example illustrates how randomized rounding can be used to design an approximation algorithm for the set cover problem. Fix any instance ⟨ c , S ⟩ {\displaystyle \langle c,{\mathcal {S}}\rangle } of set cover over a universe U {\displaystyle {\mathcal {U}}} . === Computing the fractional solution === For step 1, let IP be the standard integer linear program for set cover for this instance. For step 2, let LP be the linear programming relaxation of IP, and compute an optimal solution x ∗ {\displaystyle x^{}} to LP using any standard linear programming algorithm. This takes time polynomial in the input size. The feasible solutions to LP are the vectors x {\displaystyle x} that assign each set s ∈ S {\displaystyle s\in {\mathcal {S}}} a non-negative weight x s {\displaystyle x_{s}} , such that, for each element e ∈ U {\displaystyle e\in {\mathcal {U}}} , x ′ {\displaystyle x'} covers e {\displaystyle e} —the total weight assigned to the sets containing e {\displaystyle e} is at least 1, that is, ∑ s ∋ e x s ≥ 1. {\displaystyle \sum _{s\ni e}x_{s}\geq 1.} The optimal solution x ∗ {\displaystyle x^{}} is a feasible solution whose cost ∑ s ∈ S c ( S ) x s ∗ {\displaystyle \sum _{s\in {\mathcal {S}}}c(S)x_{s}^{}} is as small as possible. Note that any set cover C {\displaystyle {\mathcal {C}}} for S {\displaystyle {\mathcal {S}}} gives a feasible solution x {\displaystyle x} (where x s = 1 {\displaystyle x_{s}=1} for s ∈ C {\displaystyle s\in {\mathcal {C}}} , x s = 0 {\displaystyle x_{s}=0} otherwise). The cost of this C {\displaystyle {\mathcal {C}}} equals the cost of x {\displaystyle x} , that is, ∑ s ∈ C c ( s ) = ∑ s ∈ S c ( s ) x s . {\displaystyle \sum _{s\in {\mathcal {C}}}c(s)=\sum _{s\in {\mathcal {S}}}c(s)x_{s}.} In other words, the linear program LP is a relaxation of the given set-cover problem. Since x ∗ {\displaystyle x^{}} has minimum cost among feasible solutions to the LP, the cost of x ∗ {\displaystyle x^{}} is a lower bound on the cost of the optimal set cover. === Randomized rounding step === In step 3, we must convert the minimum-cost fractional set cover x ∗ {\displaystyle x^{}} into a feasible integer solution x ′ {\displaystyle x'} (corresponding to a true set cover). The rounding step should produce an x ′ {\displaystyle x'} that, with positive probability, has cost within a small factor of the cost of x ∗ {\displaystyle x^{}} .Then (since the cost of x ∗ {\displaystyle x^{}} is a lower bound on the cost of the optimal set cover), the cost of x ′ {\displaystyle x'} will be within a small factor of the optimal cost. As a starting point, consider the most natural rounding scheme: For each set s ∈ S {\displaystyle s\in {\mathcal {S}}} in turn, take x s ′ = 1 {\displaystyle x'_{s}=1} with probability min ( 1 , x s ∗ ) {\displaystyle \min(1,x_{s}^{})} , otherwise take x s ′ = 0 {\displaystyle x'_{s}=0} . With this rounding scheme, the expected cost of the chosen sets is at most ∑ s c ( s ) x s ∗ {\displaystyle \sum _{s}c(s)x_{s}^{}} , the cost of the fractional cover. This is good. Unfortunately the coverage is not good. When the variables x s ∗ {\displaystyle x_{s}^{}} are small, the probability that an element e {\displaystyle e} is not covered is about ∏ s ∋ e 1 − x s ∗ ≈ ∏ s ∋ e exp ⁡ ( − x s ∗ ) = exp ⁡ ( − ∑ s ∋ e x s ∗ ) ≈ exp ⁡ ( − 1 ) . {\displaystyle \prod _{s\ni e}1-x_{s}^{}\approx \prod _{s\ni e}\exp(-x_{s}^{})=\exp {\Big (}-\sum _{s\ni e}x_{s}^{}{\Big )}\approx \exp(-1).} So only a constant fraction of the elements will be covered in expectation. To make x ′ {\displaystyle x'} cover every element with high probability, the standard rounding scheme first scales up the rounding probabilities by an appropriate factor λ > 1 {\displaystyle \lambda >1} . Here is the standard rounding scheme: Fix a parameter λ ≥ 1 {\displaystyle \lambda \geq 1} . For each set s ∈ S {\displaystyle s\in {\mathcal {S}}} in turn, take x s ′ = 1 {\displaystyle x'_{s}=1} with probability min ( λ x s ∗ , 1 ) {\displaystyle \min(\lambda x_{s}^{},1)} , otherwise take x s ′ = 0 {\displaystyle x'_{s}=0} . Scaling the probabilities up by λ {\displaystyle \lambda } increases the expected cost by λ {\displaystyle \lambda } , but makes coverage of all elements likely. The idea is to choose λ {\displaystyle \lambda } as small as possible so that all elements are provably covered with non-zero probability. Here is a detailed analysis. ==== Lemma (approximation guarantee for rounding scheme) ==== Fix λ = ln ⁡ ( 2 | U | ) {\displaystyle \lambda =\ln(2|{\mathcal {U}}|)} . With positive probability, the rounding scheme returns a set cover x ′ {\displaystyle x'} of cost at most 2 ln ⁡ ( 2 | U | ) c ⋅ x ∗ {\displaystyle 2\ln(2|{\mathcal {U}}|)c\cdot x^{}} (and thus of cost O ( log ⁡ | U | ) {\displaystyle O(\log |{\mathcal {U}}|)} times the cost of the optimal set cover). (Note: with care the O ( log ⁡ | U | ) {\displaystyle O(\log |{\mathcal {U}}|)} can be reduced to ln ⁡ ( | U | ) + O ( log ⁡ log ⁡ | U | ) {\displaystyle \ln(|{\mathcal {U}}|)+O(\log \log |{\mathcal {U}}|)} .) ==== Proof ==== The output x ′ {\displaystyle x'} of the random rounding scheme has the desired properties as long as none of the following "bad" events occur: the cost c ⋅ x ′ {\displaystyle c\cdot x'} of x ′ {\displaystyle x'} exceeds 2 λ c ⋅ x ∗ {\displaystyle 2\lambda c\cdot x^{}} , or for some element e {\displaystyle e} , x ′ {\displaystyle x'} fails to cover e {\displaystyle e} . The expectation of each x s ′ {\displaystyle x'_{s}} is at most λ x s ∗ {\displaystyle \lambda x_{s

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  • Ontology alignment

    Ontology alignment

    Ontology alignment, or ontology matching, is the process of determining correspondences between concepts in ontologies. A set of correspondences is also called an alignment. The phrase takes on a slightly different meaning, in computer science, cognitive science or philosophy. == Computer science == For computer scientists, concepts are expressed as labels for data. Historically, the need for ontology alignment arose out of the need to integrate heterogeneous databases, ones developed independently and thus each having their own data vocabulary. In the Semantic Web context involving many actors providing their own ontologies, ontology matching has taken a critical place for helping heterogeneous resources to interoperate. Ontology alignment tools find classes of data that are semantically equivalent, for example, "truck" and "lorry". The classes are not necessarily logically identical. According to Euzenat and Shvaiko (2007), there are three major dimensions for similarity: syntactic, external, and semantic. Coincidentally, they roughly correspond to the dimensions identified by Cognitive Scientists below. A number of tools and frameworks have been developed for aligning ontologies, some with inspiration from Cognitive Science and some independently. Ontology alignment tools have generally been developed to operate on database schemas, XML schemas, taxonomies, formal languages, entity-relationship models, dictionaries, and other label frameworks. They are usually converted to a graph representation before being matched. Since the emergence of the Semantic Web, such graphs can be represented in the Resource Description Framework line of languages by triples of the form , as illustrated in the Notation 3 syntax. In this context, aligning ontologies is sometimes referred to as "ontology matching". The problem of Ontology Alignment has been tackled recently by trying to compute matching first and mapping (based on the matching) in an automatic fashion. Systems like DSSim, X-SOM or COMA++ obtained at the moment very high precision and recall. The Ontology Alignment Evaluation Initiative aims to evaluate, compare and improve the different approaches. === Formal definition === Given two ontologies i = ⟨ C i , R i , I i , T i , V i ⟩ {\displaystyle i=\langle C_{i},R_{i},I_{i},T_{i},V_{i}\rangle } and j = ⟨ C j , R j , I j , T j , V j ⟩ {\displaystyle j=\langle C_{j},R_{j},I_{j},T_{j},V_{j}\rangle } where C {\displaystyle C} is the set of classes, R {\displaystyle R} is the set of relations, I {\displaystyle I} is the set of individuals, T {\displaystyle T} is the set of data types, and V {\displaystyle V} is the set of values, we can define different types of (inter-ontology) relationships. Such relationships will be called, all together, alignments and can be categorized among different dimensions: similarity vs logic: this is the difference between matchings (predicating about the similarity of ontology terms), and mappings (logical axioms, typically expressing logical equivalence or inclusion among ontology terms) atomic vs complex: whether the alignments we considered are one-to-one, or can involve more terms in a query-like formulation (e.g., LAV/GAV mapping) homogeneous vs heterogeneous: do the alignments predicate on terms of the same type (e.g., classes are related only to classes, individuals to individuals, etc.) or we allow heterogeneity in the relationship? type of alignment: the semantics associated to an alignment. It can be subsumption, equivalence, disjointness, part-of or any user-specified relationship. Subsumption, atomic, homogeneous alignments are the building blocks to obtain richer alignments, and have a well defined semantics in every Description Logic. Let's now introduce more formally ontology matching and mapping. An atomic homogeneous matching is an alignment that carries a similarity degree s ∈ [ 0 , 1 ] {\displaystyle s\in [0,1]} , describing the similarity of two terms of the input ontologies i {\displaystyle i} and j {\displaystyle j} . Matching can be either computed, by means of heuristic algorithms, or inferred from other matchings. Formally we can say that, a matching is a quadruple m = ⟨ i d , t i , t j , s ⟩ {\displaystyle m=\langle id,t_{i},t_{j},s\rangle } , where t i {\displaystyle t_{i}} and t j {\displaystyle t_{j}} are homogeneous ontology terms, s {\displaystyle s} is the similarity degree of m {\displaystyle m} . A (subsumption, homogeneous, atomic) mapping is defined as a pair μ = ⟨ t i , t j ⟩ {\displaystyle \mu =\langle t_{i},t_{j}\rangle } , where t i {\displaystyle t_{i}} and t j {\displaystyle t_{j}} are homogeneous ontology terms. == Cognitive science == For cognitive scientists interested in ontology alignment, the "concepts" are nodes in a semantic network that reside in brains as "conceptual systems." The focal question is: if everyone has unique experiences and thus different semantic networks, then how can we ever understand each other? This question has been addressed by a model called ABSURDIST (Aligning Between Systems Using Relations Derived Inside Systems for Translation). Three major dimensions have been identified for similarity as equations for "internal similarity, external similarity, and mutual inhibition." == Ontology alignment methods == Two sub research fields have emerged in ontology mapping, namely monolingual ontology mapping and cross-lingual ontology mapping. The former refers to the mapping of ontologies in the same natural language, whereas the latter refers to "the process of establishing relationships among ontological resources from two or more independent ontologies where each ontology is labelled in a different natural language". Existing matching methods in monolingual ontology mapping are discussed in Euzenat and Shvaiko (2007). Approaches to cross-lingual ontology mapping are presented in Fu et al. (2011).

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  • Bayesian programming

    Bayesian programming

    Bayesian programming is a formalism and a methodology for having a technique to specify probabilistic models and solve problems when less than the necessary information is available. Edwin T. Jaynes proposed that probability could be considered as an alternative and an extension of logic for rational reasoning with incomplete and uncertain information. In his founding book Probability Theory: The Logic of Science he developed this theory and proposed what he called "the robot," which was not a physical device, but an inference engine to automate probabilistic reasoning—a kind of Prolog for probability instead of logic. Bayesian programming is a formal and concrete implementation of this "robot". Bayesian programming may also be seen as an algebraic formalism to specify graphical models such as, for instance, Bayesian networks, dynamic Bayesian networks, Kalman filters or hidden Markov models. Indeed, Bayesian programming is more general than Bayesian networks and has a power of expression equivalent to probabilistic factor graphs. == Formalism == A Bayesian program is a means of specifying a family of probability distributions. The constituent elements of a Bayesian program are presented below: Program { Description { Specification ( π ) { Variables Decomposition Forms Identification (based on δ ) Question {\displaystyle {\text{Program}}{\begin{cases}{\text{Description}}{\begin{cases}{\text{Specification}}(\pi ){\begin{cases}{\text{Variables}}\\{\text{Decomposition}}\\{\text{Forms}}\\\end{cases}}\\{\text{Identification (based on }}\delta )\end{cases}}\\{\text{Question}}\end{cases}}} A program is constructed from a description and a question. A description is constructed using some specification ( π {\displaystyle \pi } ) as given by the programmer and an identification or learning process for the parameters not completely specified by the specification, using a data set ( δ {\displaystyle \delta } ). A specification is constructed from a set of pertinent variables, a decomposition and a set of forms. Forms are either parametric forms or questions to other Bayesian programs. A question specifies which probability distribution has to be computed. === Description === The purpose of a description is to specify an effective method of computing a joint probability distribution on a set of variables { X 1 , X 2 , ⋯ , X N } {\displaystyle \left\{X_{1},X_{2},\cdots ,X_{N}\right\}} given a set of experimental data δ {\displaystyle \delta } and some specification π {\displaystyle \pi } . This joint distribution is denoted as: P ( X 1 ∧ X 2 ∧ ⋯ ∧ X N ∣ δ ∧ π ) {\displaystyle P\left(X_{1}\wedge X_{2}\wedge \cdots \wedge X_{N}\mid \delta \wedge \pi \right)} . To specify preliminary knowledge π {\displaystyle \pi } , the programmer must undertake the following: Define the set of relevant variables { X 1 , X 2 , ⋯ , X N } {\displaystyle \left\{X_{1},X_{2},\cdots ,X_{N}\right\}} on which the joint distribution is defined. Decompose the joint distribution (break it into relevant independent or conditional probabilities). Define the forms of each of the distributions (e.g., for each variable, one of the list of probability distributions). ==== Decomposition ==== Given a partition of { X 1 , X 2 , … , X N } {\displaystyle \left\{X_{1},X_{2},\ldots ,X_{N}\right\}} containing K {\displaystyle K} subsets, K {\displaystyle K} variables are defined L 1 , ⋯ , L K {\displaystyle L_{1},\cdots ,L_{K}} , each corresponding to one of these subsets. Each variable L k {\displaystyle L_{k}} is obtained as the conjunction of the variables { X k 1 , X k 2 , ⋯ } {\displaystyle \left\{X_{k_{1}},X_{k_{2}},\cdots \right\}} belonging to the k t h {\displaystyle k^{th}} subset. Recursive application of Bayes' theorem leads to: P ( X 1 ∧ X 2 ∧ ⋯ ∧ X N ∣ δ ∧ π ) = P ( L 1 ∧ ⋯ ∧ L K ∣ δ ∧ π ) = P ( L 1 ∣ δ ∧ π ) × P ( L 2 ∣ L 1 ∧ δ ∧ π ) × ⋯ × P ( L K ∣ L K − 1 ∧ ⋯ ∧ L 1 ∧ δ ∧ π ) {\displaystyle {\begin{aligned}&P\left(X_{1}\wedge X_{2}\wedge \cdots \wedge X_{N}\mid \delta \wedge \pi \right)\\={}&P\left(L_{1}\wedge \cdots \wedge L_{K}\mid \delta \wedge \pi \right)\\={}&P\left(L_{1}\mid \delta \wedge \pi \right)\times P\left(L_{2}\mid L_{1}\wedge \delta \wedge \pi \right)\times \cdots \times P\left(L_{K}\mid L_{K-1}\wedge \cdots \wedge L_{1}\wedge \delta \wedge \pi \right)\end{aligned}}} Conditional independence hypotheses then allow further simplifications. A conditional independence hypothesis for variable L k {\displaystyle L_{k}} is defined by choosing some variable X n {\displaystyle X_{n}} among the variables appearing in the conjunction L k − 1 ∧ ⋯ ∧ L 2 ∧ L 1 {\displaystyle L_{k-1}\wedge \cdots \wedge L_{2}\wedge L_{1}} , labelling R k {\displaystyle R_{k}} as the conjunction of these chosen variables and setting: P ( L k ∣ L k − 1 ∧ ⋯ ∧ L 1 ∧ δ ∧ π ) = P ( L k ∣ R k ∧ δ ∧ π ) {\displaystyle P\left(L_{k}\mid L_{k-1}\wedge \cdots \wedge L_{1}\wedge \delta \wedge \pi \right)=P\left(L_{k}\mid R_{k}\wedge \delta \wedge \pi \right)} We then obtain: P ( X 1 ∧ X 2 ∧ ⋯ ∧ X N ∣ δ ∧ π ) = P ( L 1 ∣ δ ∧ π ) × P ( L 2 ∣ R 2 ∧ δ ∧ π ) × ⋯ × P ( L K ∣ R K ∧ δ ∧ π ) {\displaystyle {\begin{aligned}&P\left(X_{1}\wedge X_{2}\wedge \cdots \wedge X_{N}\mid \delta \wedge \pi \right)\\={}&P\left(L_{1}\mid \delta \wedge \pi \right)\times P\left(L_{2}\mid R_{2}\wedge \delta \wedge \pi \right)\times \cdots \times P\left(L_{K}\mid R_{K}\wedge \delta \wedge \pi \right)\end{aligned}}} Such a simplification of the joint distribution as a product of simpler distributions is called a decomposition, derived using the chain rule. This ensures that each variable appears at the most once on the left of a conditioning bar, which is the necessary and sufficient condition to write mathematically valid decompositions. ==== Forms ==== Each distribution P ( L k ∣ R k ∧ δ ∧ π ) {\displaystyle P\left(L_{k}\mid R_{k}\wedge \delta \wedge \pi \right)} appearing in the product is then associated with either a parametric form (i.e., a function f μ ( L k ) {\displaystyle f_{\mu }\left(L_{k}\right)} ) or a question to another Bayesian program P ( L k ∣ R k ∧ δ ∧ π ) = P ( L ∣ R ∧ δ ^ ∧ π ^ ) {\displaystyle P\left(L_{k}\mid R_{k}\wedge \delta \wedge \pi \right)=P\left(L\mid R\wedge {\widehat {\delta }}\wedge {\widehat {\pi }}\right)} . When it is a form f μ ( L k ) {\displaystyle f_{\mu }\left(L_{k}\right)} , in general, μ {\displaystyle \mu } is a vector of parameters that may depend on R k {\displaystyle R_{k}} or δ {\displaystyle \delta } or both. Learning takes place when some of these parameters are computed using the data set δ {\displaystyle \delta } . An important feature of Bayesian programming is this capacity to use questions to other Bayesian programs as components of the definition of a new Bayesian program. P ( L k ∣ R k ∧ δ ∧ π ) {\displaystyle P\left(L_{k}\mid R_{k}\wedge \delta \wedge \pi \right)} is obtained by some inferences done by another Bayesian program defined by the specifications π ^ {\displaystyle {\widehat {\pi }}} and the data δ ^ {\displaystyle {\widehat {\delta }}} . This is similar to calling a subroutine in classical programming and provides an easy way to build hierarchical models. === Question === Given a description (i.e., P ( X 1 ∧ X 2 ∧ ⋯ ∧ X N ∣ δ ∧ π ) {\displaystyle P\left(X_{1}\wedge X_{2}\wedge \cdots \wedge X_{N}\mid \delta \wedge \pi \right)} ), a question is obtained by partitioning { X 1 , X 2 , ⋯ , X N } {\displaystyle \left\{X_{1},X_{2},\cdots ,X_{N}\right\}} into three sets: the searched variables, the known variables and the free variables. The 3 variables S e a r c h e d {\displaystyle Searched} , K n o w n {\displaystyle Known} and F r e e {\displaystyle Free} are defined as the conjunction of the variables belonging to these sets. A question is defined as the set of distributions: P ( S e a r c h e d ∣ Known ∧ δ ∧ π ) {\displaystyle P\left(Searched\mid {\text{Known}}\wedge \delta \wedge \pi \right)} made of many "instantiated questions" as the cardinal of K n o w n {\displaystyle Known} , each instantiated question being the distribution: P ( Searched ∣ Known ∧ δ ∧ π ) {\displaystyle P\left({\text{Searched}}\mid {\text{Known}}\wedge \delta \wedge \pi \right)} === Inference === Given the joint distribution P ( X 1 ∧ X 2 ∧ ⋯ ∧ X N ∣ δ ∧ π ) {\displaystyle P\left(X_{1}\wedge X_{2}\wedge \cdots \wedge X_{N}\mid \delta \wedge \pi \right)} , it is always possible to compute any possible question using the following general inference: P ( Searched ∣ Known ∧ δ ∧ π ) = ∑ Free [ P ( Searched ∧ Free ∣ Known ∧ δ ∧ π ) ] = ∑ Free [ P ( Searched ∧ Free ∧ Known ∣ δ ∧ π ) ] P ( Known ∣ δ ∧ π ) = ∑ Free [ P ( Searched ∧ Free ∧ Known ∣ δ ∧ π ) ] ∑ Free ∧ Searched [ P ( Searched ∧ Free ∧ Known ∣ δ ∧ π ) ] = 1 Z × ∑ Free [ P ( Searched ∧ Free ∧ Known ∣ δ ∧ π ) ] {\displaystyle {\begin{aligned}&P\left({\text{Searched}}\mid {\text{Known}}\wedge \delta \wedge \pi \right)\\={}&\sum _{\text{Free}}\left[P\left({\text{Searched}}\wedge {\text{Free}}\mid {\text{Known}}\wedge \delta \wedge \

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  • Pointer jumping

    Pointer jumping

    Pointer jumping or path doubling is a design technique for parallel algorithms that operate on pointer structures, such as linked lists and directed graphs. Pointer jumping allows an algorithm to follow paths with a time complexity that is logarithmic with respect to the length of the longest path. It does this by "jumping" to the end of the path computed by neighbors. The basic operation of pointer jumping is to replace each neighbor in a pointer structure with its neighbor's neighbor. In each step of the algorithm, this replacement is done for all nodes in the data structure, which can be done independently in parallel. In the next step when a neighbor's neighbor is followed, the neighbor's path already followed in the previous step is added to the node's followed path in a single step. Thus, each step effectively doubles the distance traversed by the explored paths. Pointer jumping is best understood by looking at simple examples such as list ranking and root finding. == List ranking == One of the simpler tasks that can be solved by a pointer jumping algorithm is the list ranking problem. This problem is defined as follows: given a linked list of N nodes, find the distance (measured in the number of nodes) of each node to the end of the list. The distance d(n) is defined as follows, for nodes n that point to their successor by a pointer called next: If n.next is nil, then d(n) = 0. For any other node, d(n) = d(n.next) + 1. This problem can easily be solved in linear time on a sequential machine, but a parallel algorithm can do better: given n processors, the problem can be solved in logarithmic time, O(log N), by the following pointer jumping algorithm: The pointer jumping occurs in the last line of the algorithm, where each node's next pointer is reset to skip the node's direct successor. It is assumed, as in common in the PRAM model of computation, that memory access are performed in lock-step, so that each n.next.next memory fetch is performed before each n.next memory store; otherwise, processors may clobber each other's data, producing inconsistencies. The following diagram follows how the parallel list ranking algorithm uses pointer jumping for a linked list with 11 elements. As the algorithm describes, the first iteration starts initialized with all ranks set to 1 except those with a null pointer for next. The first iteration looks at immediate neighbors. Each subsequent iteration jumps twice as far as the previous. Analyzing the algorithm yields a logarithmic running time. The initialization loop takes constant time, because each of the N processors performs a constant amount of work, all in parallel. The inner loop of the main loop also takes constant time, as does (by assumption) the termination check for the loop, so the running time is determined by how often this inner loop is executed. Since the pointer jumping in each iteration splits the list into two parts, one consisting of the "odd" elements and one of the "even" elements, the length of the list pointed to by each processor's n is halved in each iteration, which can be done at most O(log N) time before each list has a length of at most one. == Root finding == Following a path in a graph is an inherently serial operation, but pointer jumping reduces the total amount of work by following all paths simultaneously and sharing results among dependent operations. Pointer jumping iterates and finds a successor — a vertex closer to the tree root — each time. By following successors computed for other vertices, the traversal down each path can be doubled every iteration, which means that the tree roots can be found in logarithmic time. Pointer doubling operates on an array successor with an entry for every vertex in the graph. Each successor[i] is initialized with the parent index of vertex i if that vertex is not a root or to i itself if that vertex is a root. At each iteration, each successor is updated to its successor's successor. The root is found when the successor's successor points to itself. The following pseudocode demonstrates the algorithm. algorithm Input: An array parent representing a forest of trees. parent[i] is the parent of vertex i or itself for a root Output: An array containing the root ancestor for every vertex for i ← 1 to length(parent) do in parallel successor[i] ← parent[i] while true for i ← 1 to length(successor) do in parallel successor_next[i] ← successor[successor[i]] if successor_next = successor then break for i ← 1 to length(successor) do in parallel successor[i] ← successor_next[i] return successor The following image provides an example of using pointer jumping on a small forest. On each iteration the successor points to the vertex following one more successor. After two iterations, every vertex points to its root node. == History and examples == Although the name pointer jumping would come later, JáJá attributes the first uses of the technique in early parallel graph algorithms and list ranking. The technique has been described with other names such as shortcutting, but by the 1990s textbooks on parallel algorithms consistently used the term pointer jumping. Today, pointer jumping is considered a software design pattern for operating on recursive data types in parallel. As a technique for following linked paths, graph algorithms are a natural fit for pointer jumping. Consequently, several parallel graph algorithms utilizing pointer jumping have been designed. These include algorithms for finding the roots of a forest of rooted trees, connected components, minimum spanning trees, and biconnected components. However, pointer jumping has also shown to be useful in a variety of other problems including computer vision, image compression, and Bayesian inference.

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  • CENDI

    CENDI

    CENDI (Commerce, Energy, NASA, Defense Information Managers Group) is an interagency group of senior Scientific and Technical Information (STI) managers from 14 United States federal agencies. CENDI managers cooperate by exchanging information and ideas, collaborating to address common issues, and undertaking joint initiatives. CENDI's accomplishments range from impacting federal information policy to educating a broad spectrum of stakeholders on all aspects of federal STI systems, including its value to research and the taxpayer, and to operational improvements in agency and interagency STI operations. == History == CENDI traces its roots to the Committee on Scientific and Technical Information (COSATI) of the Federal Council on Science and Technology. COSATI was established in the early 1960s to coordinate the management of the results from the U.S. government's increasing commitment to scientific research and technology development. The scientific and technical information (STI) managers of the government's major research and development (R&D) agencies worked within COSATI to standardize guidelines for cataloging and indexing technical reports. COSATI ceased formal operations in the early 1970s. To continue the cooperation begun under COSATI, managers of agency STI programs from Commerce (National Technical Information Service), Energy (Office of Scientific and Technical Information), NASA (HQ/STI Division), and Defense (Defense Technical Information Center) began meeting periodically to discuss common topics and stimulate more effective cooperation. In 1985, a Memorandum of Understanding was signed by the four charter agencies and CENDI was established. From this small core of STI managers, CENDI has grown to its current membership, which represents the major science agencies, the national libraries, and agencies involved in the dissemination and long-term management of scientific and technical information. The vision of CENDI is to facilitate cooperative enterprise where capabilities are shared and challenges are faced together so that the sum of the accomplishments is greater than each individual agency can achieve on its own amongst federal STI agencies. The abbreviation CENDI refers to the "Commerce, Energy, NASA, Defense Information Managers Group". == Membership == New members from other federal R&D information organizations may be admitted by unanimous agreement of the members. However, it is the intent of the group that membership in CENDI should remain small and focus on organizations with STI or supporting responsibilities. Each agency provides funding to CENDI. == Members == The members of CENDI are: Defense Technical Information Center (United States Department of Defense) Office of Research and Development and Office of Environmental Information (United States Environmental Protection Agency) Government Printing Office Library of Congress NASA Scientific and Technical Information Program National Agricultural Library (United States Department of Agriculture) National Archives and Records Administration National Library of Education (United States Department of Education) National Library of Medicine (United States Department of Health and Human Services) National Science Foundation National Technical Information Service (United States Department of Commerce) National Transportation Library (United States Department of Transportation) Office of Scientific and Technical Information (United States Department of Energy) USGS/Biological Resources Discipline (United States Department of the Interior) == Mission and operation == CENDI's mission is to help improve the productivity of federal science- and technology-based programs through effective scientific, technical, and related information support systems. In fulfilling its mission, CENDI agencies play an important role in addressing science- and technology-based national priorities and strengthening U.S. competitiveness. === Goals === STI Coordination and Leadership: Provide coordination and leadership for information exchange on important STI policy issues. Improvement of STI Systems: Promote the development of improved STI systems through the productive interrelationship of content and technology. STI Understanding: Promote better understanding of STI and STI management. === Principals and Alternates === CENDI is made up of senior federal STI managers and each organization appoints a Principal representative. This person is the point of contact for that organization within CENDI. Each Principal has an Alternate. The Principals and Alternates comprise the main group that meets on a regular basis, usually every other month. === Secretariat === A Tennessee-based information management company, -- Information International Associates, Inc., currently serves as the CENDI Secretariat. The Secretariat provides day-to-day operations to CENDI. The Secretariat prepares the necessary materials for the Principals' meetings, provides support for the working group and task group meetings, assists in developing papers, and maintains the CENDI files and outreach tools. === Task Groups and Working Groups === The chair(s) of a working group is appointed by the Principals and has the overall responsibility for the group's activities. The Secretariat provides support at the request of the Working Group chair(s). The Working Groups and Task Groups that are currently operating are: Copyright and Intellectual Property Working Group Distribution Markings Task Group Digital Preservation Task Group Digitization Specifications Task Group Image Metadata Task Group Science.gov (see below) STI Policy Working Group Terminology Resources Task Group === Science.gov and Worldwidescience.org === In 2001, in response to the April 2001 workshop on "Strengthening the Public Information Infrastructure for Science", and taking into consideration a request from Firstgov (now USA.gov) to develop specialized topical portals, CENDI formed an alliance to develop an interagency website for access to STI. This website, called Science.gov, is a one-stop source of STI, including both selected, authoritative government websites and deep Web databases of technical reports, journal articles, conference proceedings, and other published materials. Through the volunteer efforts of members and involving over 100 staff, content and architecture is developed for the site. The Science.gov website is hosted by the Department of Energy (DOE) Office of Scientific and Technical Information (OSTI). The site was formally launched in December 2002. As a result of the success of Science.gov, under DOE leadership and in cooperation with the International Council of Scientific and Technical Information, a worldwide coordination across national portals called WorldWideScience was launched in 2008. === Work with non-member organizations === CENDI works with several cooperating non-member organizations on a regular basis. These agencies are in academia, federal government, legal and policy analysis, international, non-governmental, and private organizations.

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  • Linguistic categories

    Linguistic categories

    Linguistic categories include Lexical category, a part of speech such as noun, preposition, etc. Syntactic category, a similar concept which can also include phrasal categories Grammatical category, a grammatical feature such as tense, gender, etc. The definition of linguistic categories is a major concern of linguistic theory, and thus, the definition and naming of categories varies across different theoretical frameworks and grammatical traditions for different languages. The operationalization of linguistic categories in lexicography, computational linguistics, natural language processing, corpus linguistics, and terminology management typically requires resource-, problem- or application-specific definitions of linguistic categories. In Cognitive linguistics it has been argued that linguistic categories have a prototype structure like that of the categories of common words in a language. == Linguistic category inventories == To facilitate the interoperability between lexical resources, linguistic annotations and annotation tools and for the systematic handling of linguistic categories across different theoretical frameworks, a number of inventories of linguistic categories have been developed and are being used, with examples as given below. The practical objective of such inventories is to perform quantitative evaluation (for language-specific inventories), to train NLP tools, or to facilitate cross-linguistic evaluation, querying or annotation of language data. At a theoretical level, the existence of universal categories in human language has been postulated, e.g., in Universal grammar, but also heavily criticized. === Part-of-Speech tagsets === Schools commonly teach that there are 9 parts of speech in English: noun, verb, article, adjective, preposition, pronoun, adverb, conjunction, and interjection. However, there are clearly many more categories and sub-categories. For nouns, the plural, possessive, and singular forms can be distinguished. In many languages words are also marked for their case (role as subject, object, etc.), grammatical gender, and so on; while verbs are marked for tense, aspect, and other things. In some tagging systems, different inflections of the same root word will get different parts of speech, resulting in a large number of tags. For example, NN for singular common nouns, NNS for plural common nouns, NP for singular proper nouns (see the POS tags used in the Brown Corpus). Other tagging systems use a smaller number of tags and ignore fine differences or model them as features somewhat independent from part-of-speech. In part-of-speech tagging by computer, it is typical to distinguish from 50 to 150 separate parts of speech for English. POS tagging work has been done in a variety of languages, and the set of POS tags used varies greatly with language. Tags usually are designed to include overt morphological distinctions, although this leads to inconsistencies such as case-marking for pronouns but not nouns in English, and much larger cross-language differences. The tag sets for heavily inflected languages such as Greek and Latin can be very large; tagging words in agglutinative languages such as Inuit languages may be virtually impossible. Work on stochastic methods for tagging Koine Greek (DeRose 1990) has used over 1,000 parts of speech and found that about as many words were ambiguous in that language as in English. A morphosyntactic descriptor in the case of morphologically rich languages is commonly expressed using very short mnemonics, such as ncmsan for category = noun, type = common, gender = masculine, number = singular, case = accusative, animate = no. The most popular tag set for POS tagging for American English is probably the Penn tag set, developed in the Penn Treebank project. === Multilingual annotation schemes === For Western European languages, cross-linguistically applicable annotation schemes for parts-of-speech, morphosyntax and syntax have been developed with the EAGLES Guidelines. The "Expert Advisory Group on Language Engineering Standards" (EAGLES) was an initiative of the European Commission that ran within the DG XIII Linguistic Research and Engineering programme from 1994 to 1998, coordinated by Consorzio Pisa Ricerche, Pisa, Italy. The EAGLES guidelines provide guidance for markup to be used with text corpora, particularly for identifying features relevant in computational linguistics and lexicography. Numerous companies, research centres, universities and professional bodies across the European Union collaborated to produce the EAGLES Guidelines, which set out recommendations for de facto standards and rules of best practice for: Large-scale language resources (such as text corpora, computational lexicons and speech corpora); Means of manipulating such knowledge, via computational linguistic formalisms, mark up languages and various software tools; Means of assessing and evaluating resources, tools and products. The Eagles guidelines have inspired subsequent work on other regions, as well, e.g., Eastern Europe. A generation later, a similar effort was initiated by the research community under the umbrella of Universal Dependencies. Petrov et al. have proposed a "universal", but highly reductionist, tag set, with 12 categories (for example, no subtypes of nouns, verbs, punctuation, etc.; no distinction of "to" as an infinitive marker vs. preposition (hardly a "universal" coincidence), etc.). Subsequently, this was complemented with cross-lingual specifications for dependency syntax (Stanford Dependencies), and morphosyntax (Interset interlingua, partially building on the Multext-East/Eagles tradition) in the context of the Universal Dependencies (UD), an international cooperative project to create treebanks of the world's languages with cross-linguistically applicable ("universal") annotations for parts of speech, dependency syntax, and (optionally) morphosyntactic (morphological) features. Core applications are automated text processing in the field of natural language processing (NLP) and research into natural language syntax and grammar, especially within linguistic typology. The annotation scheme has it roots in three related projects: The UD annotation scheme uses a representation in the form of dependency trees as opposed to a phrase structure trees. At as of February 2019, there are just over 100 treebanks of more than 70 languages available in the UD inventory. The project's primary aim is to achieve cross-linguistic consistency of annotation. However, language-specific extensions are permitted for morphological features (individual languages or resources can introduce additional features). In a more restricted form, dependency relations can be extended with a secondary label that accompanies the UD label, e.g., aux:pass for an auxiliary (UD aux) used to mark passive voice. The Universal Dependencies have inspired similar efforts for the areas of inflectional morphology, frame semantics and coreference. For phrase structure syntax, a comparable effort does not seem to exist, but the specifications of the Penn Treebank have been applied to (and extended for) a broad range of languages, e.g., Icelandic, Old English, Middle English, Middle Low German, Early Modern High German, Yiddish, Portuguese, Japanese, Arabic and Chinese. === Conventions for interlinear glosses === In linguistics, an interlinear gloss is a gloss (series of brief explanations, such as definitions or pronunciations) placed between lines (inter- + linear), such as between a line of original text and its translation into another language. When glossed, each line of the original text acquires one or more lines of transcription known as an interlinear text or interlinear glossed text (IGT)—interlinear for short. Such glosses help the reader follow the relationship between the source text and its translation, and the structure of the original language. There is no standard inventory for glosses, but common labels are collected in the Leipzig Glossing Rules. Wikipedia also provides a List of glossing abbreviations that draws on this and other sources. === General Ontology for Linguistic Description (GOLD) === GOLD ("General Ontology for Linguistic Description") is an ontology for descriptive linguistics. It gives a formalized account of the most basic categories and relations used in the scientific description of human language, e.g., as a formalization of interlinear glosses. GOLD was first introduced by Farrar and Langendoen (2003). Originally, it was envisioned as a solution to the problem of resolving disparate markup schemes for linguistic data, in particular data from endangered languages. However, GOLD is much more general and can be applied to all languages. In this function, GOLD overlaps with the ISO 12620 Data Category Registry (ISOcat); it is, however, more stringently structured. GOLD was maintained by the LINGUIST List and others from 2007 to 2010. The RELISH project created a mirro

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  • Artificial intelligence and elections

    Artificial intelligence and elections

    As artificial intelligence (AI) has become more mainstream, there is growing concern about how this will influence elections. Potential targets of AI include election processes, election offices, election officials and election vendors. There are also global efforts to improve elections using AI. == Tactics == Generative AI capabilities allow creation of misleading content. Examples of this include text-to-video, deepfake videos, text-to-image, AI-altered images, text-to-speech, voice cloning, and text-to-text. In the context of an election, a deepfake video of a candidate may propagate information that the candidate does not endorse. Chatbots could spread misinformation related to election locations, times or voting methods. In contrast to malicious actors in the past, these techniques require little technical skill and can spread rapidly. LLM-generated messages have the capacity to persuade humans on political issues. Researchers have begun to investigate how people rate messages that LLMs generate for how persuasive they are. When it came to policy issues, the LLM-generated messages received a 2.91 compared to a 2.80 when it came to smartness between the AI and humans. The LLM-generated messages were often more technical and analytical than human-generated messages. Generative AI has been used to micro-target people during tight political elections. The generation of targeted large language models has triggered concern that they will be used to leverage readily scale microtargeting. Rephrasing inputs have been used to generate fraudulent emails and phishing websites. Rephrasing inputs in a microtargeting does not violate the terms of OpenAI usage. There are no safeguards to prevent the use of rephrasing and creation of fraudulent emails. Political campaign managers have access to this allowing for them to create targeted content. == Usage by country == === Argentina === ==== 2023 elections ==== During the 2023 Argentine primary elections, Javier Milei's team distributed AI generated images including a fabricated image of his rival Sergio Massa and drew 3 million views. The team also created an unofficial Instagram account entitled "AI for the Homeland." Sergio Massa's team also distributed AI generated images and videos. === Bangladesh === ==== 2024 elections ==== In the run up to the 2024 Bangladeshi general election, deepfake videos of female opposition politicians appeared. Rumin Farhana was pictured in a bikini while Nipun Ray was shown in a swimming pool. === Canada === ==== 2025 elections ==== In the run up to the 2025 Canadian federal election, the use of AI tools is likely to figure prominently. India, Pakistan and Iran are all expected to make efforts to subvert the national vote using disinformation campaigns to deceive voters and sway diaspora communities. In a report by the Canadian Centre for Cyber Security called "Cyber Threats to Canada's Democratic Process: 2025 Update", it states that malicious actors including China and Russia: "are most likely to use generative AI as a means of creating and spreading disinformation, designed to sow division among Canadians and push narratives conducive to the interests of foreign states". === France === ==== 2024 elections ==== In the 2024 French legislative election, deepfake videos appeared claiming: i) That they showed the family of Marine le Pen. In the videos, young women, supposedly Le Pen's nieces, are seen skiing, dancing and at the beach "while making fun of France’s racial minorities": However, the family members don't exist. On social media there were over 2 million views. ii) In a video seen on social media, a deepfake video of a France24 broadcast appeared to report that the Ukrainian leadership had "tried to lure French president Emmanuel Macron to Ukraine to assassinate him and then blame his death on Russia". === Ghana === ==== 2024 elections ==== During the months before the December 2024 Ghanaian general election, a network of at least 171 fake accounts has been used to spam social media. Posts have been used by a group identified as "@TheTPatriots" to promote the New Patriotic Party, although it is not known whether the two are connected. All the networks' posts were "highly likely" to have been generated by ChatGPT and appear to be the "first secretly partisan network using AI to influence elections in Ghana". The opposition National Democratic Congress was also criticized with its leader John Mahama being called a drunkard. === India === ==== 2024 elections ==== In the 2024 Indian general election, politicians used deepfakes in their campaign materials. These deepfakes included politicians who had died prior to the election. Mathuvel Karunanidhi's party posted with his likeness even though he had died 2018. A video The All-India Anna Dravidian Progressive Federation party posted showed an audio clip of Jayaram Jayalalithaa even though she had died in 2016. The Deepfakes Analysis Unit (DAU) is an open source platform created in March 2024 for the public to share misleading content and assess if it had been AI-generated. AI was also used to translate political speeches in real time. This translating ability was widely used to reach more voters. === Indonesia === ==== 2024 elections ==== In the 2024 Indonesian presidential election, Prabowo Subianto made extensive use of AI-generated art in his campaign, which ranged from images of himself as an adorable child to various child portrayals in his advertisements. The Indonesian Children's Protection Commission condemned these ads, labeling them as a form of misuse. Other candidates, Anies Baswedan and Ganjar Pranowo, also incorporated AI art into their campaigns. Throughout the election period, all presidential candidates faced attacks from deepfakes, both in video and audio formats. === Ireland === ==== 2024 elections ==== In the last weeks of the 2024 Irish general election a spoof election poster appeared in Dublin featuring "an AI-generated candidate with three arms". The candidate is called Aidan Irwin, but no-one stood in the election with that name. A slogan on the poster says "put matters into artificial intelligence’s hands". The convincing election poster shows a man that "has six fingers on one hand, three arms, and a distorted thumb". === New Zealand === ==== 2023 elections ==== In May 2023, ahead of the 2023 New Zealand general election in October 2023, the New Zealand National Party published a "series of AI-generated political advertisements" on its Instagram account. After confirming that the images were faked, a party spokesperson said that it was "an innovative way to drive our social media". === Pakistan === ==== 2024 elections ==== AI has been used by the imprisoned ex-Prime Minister Imran Khan and his media team in the 2024 Pakistani general election: i) An AI generated audio of his voice was added to a video clip and was broadcast at a virtual rally. ii) An op-ed in The Economist written by Khan was later claimed by himself to have been written by AI which was later denied by his team. The article was liked and shared on social media by thousands of users. === South Africa === ==== 2024 elections ==== In the 2024 South African general election, there were several uses of AI content: i) A deepfaked video of Joe Biden emerged on social media showing him saying that "The U.S. would place sanctions on SA and declare it an enemy state if the African National Congress (ANC) won". ii) In a deepfake video, Donald Trump was shown endorsing the uMkhonto weSizwe party. It was posted to social media and was viewed more than 158,000 times. iii) Less than 3 months before the elections, a deepfake video showed U.S. rapper Eminem endorsing the Economic Freedom Fighters party while criticizing the ANC. The deepfake was viewed on social media more than 173,000 times. === South Korea === ==== 2022 elections ==== In the 2022 South Korean presidential election, a committee for one presidential candidate Yoon Suk Yeol released an AI avatar 'Al Yoon Seok-yeol' that would campaign in places the candidate could not go. The other presidential candidate Lee Jae-myung introduced a chatbot that provided information about the candidate's pledges. ==== 2024 elections ==== Deepfakes were used to spread misinformation before the 2024 South Korean legislative election with one source reporting 129 deepfake violations of election laws within a two week period. Seoul hosted the 2024 Summit for Democracy, a virtual gathering of world leaders initiated by US President Joe Biden in 2021. The focus of the summit was on digital threats to democracy including artificial intelligence and deepfakes. === Taiwan === ==== 2024 elections ==== AI-generated content was used during the 2024 Taiwanese presidential election. Among the media were: i) A deepfake video of General Secretary of the Chinese Communist Party Xi Jinping which showed him supporting the presidential elections. Created on social media, the video was "widely circulated

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  • Explore-then-commit algorithm

    Explore-then-commit algorithm

    Explore Then Commit (ETC) is an algorithm for the multi-armed bandit problem foc,used on finding the best trade-off between exploration and exploitation. == Multi-armed bandit problem == The multi-armed bandit problem is a sequential game where one player has to choose at each turn between K {\displaystyle K} actions (arms). Behind every arm a {\displaystyle a} is an unknown distribution ν a {\displaystyle \nu _{a}} that lies in a set D {\displaystyle {\mathcal {D}}} known by the player (for example, D {\displaystyle {\mathcal {D}}} can be the set of Gaussian distributions or Bernoulli distributions). At each turn t {\displaystyle t} the player chooses (pulls) an arm a t {\displaystyle a_{t}} , they then get an observation X t {\displaystyle X_{t}} of the distribution ν a t {\displaystyle \nu _{a_{t}}} . === Regret minimization === The goal is to minimize the regret at time T {\displaystyle T} that is defined as R T := ∑ a = 1 K Δ a E [ N a ( T ) ] {\displaystyle R_{T}:=\sum _{a=1}^{K}\Delta _{a}\mathbb {E} [N_{a}(T)]} where μ a := E [ ν a ] {\displaystyle \mu _{a}:=\mathbb {E} [\nu _{a}]} is the mean of arm a {\displaystyle a} μ ∗ := max a μ a {\displaystyle \mu ^{}:=\max _{a}\mu _{a}} is the highest mean Δ a := μ ∗ − μ a {\displaystyle \Delta _{a}:=\mu ^{}-\mu _{a}} N a ( t ) {\displaystyle N_{a}(t)} is the number of pulls of arm a {\displaystyle a} up to turn t {\displaystyle t} The player has to find an algorithm that chooses at each turn t {\displaystyle t} which arm to pull based on the previous actions and observations ( a s , X s ) s < t {\displaystyle (a_{s},X_{s})_{s Read more →

  • Secure Electronic Delivery

    Secure Electronic Delivery

    Secure Electronic Delivery (SED) is a service created in 2003 and provided by the British Library Document Supply Service (BLDSS). Its purpose is to enable faster delivery of digital materials as encrypted, copyright-compliant PDF Documents, to a personal e-mail address. These documents are supplied from the British Library via its On Demand service. When the British Library supplies articles electronically, it sends them securely in order to ensure its usage is permitted (research purposes) and copyright law is observed. == Methods == As the publishing industry, authors and creators become highly protective of their assets and intellectual property, they impose strict rules on delivery methods to prevent copyright infringement. Nowadays, DRM-enabled secure delivery appears to be the most widely used solution to address issues faced by libraries in supplying ebooks and digital materials to their users. SED, one of these solutions, is using Adobe LiveCycle Digital Rights Management (LCDRM) as an encryption method to deliver documents. == Advantages == SED offers convenience, quality and speed as documents are delivered upon request at any location and on any device. Requested articles are scanned for high quality reproduction, opened anywhere on any machine, including mobile devices. == Restrictions == The following are restrictions hold in a SED service implementation: The digital material is accessible only for 14 days via a link sent to a personal message. Due to copyright reasons, the material can be opened only once, saved for 14 days and does not allow a copy-paste action. Upon display, the material must be printed from the same device and reprinted only once. The On Demand encryption technology works best on the default Safari browser although other browsers may accommodate it.

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