Dominant resource fairness (DRF) is a rule for fair division. It is particularly useful for dividing computing resources in among users in cloud computing environments, where each user may require a different combination of resources. DRF was presented by Ali Ghodsi, Matei Zaharia, Benjamin Hindman, Andy Konwinski, Scott Shenker and Ion Stoica in 2011. == Motivation == In an environment with a single resource, a widely used criterion is max-min fairness, which aims to maximize the minimum amount of resource given to a user. But in cloud computing, it is required to share different types of resource, such as: memory, CPU, bandwidth and disk-space. Previous fair schedulers, such as in Apache Hadoop, reduced the multi-resource setting to a single-resource setting by defining nodes with a fixed amount of each resource (e.g. 4 CPU, 32 MB memory, etc.), and dividing slots which are fractions of nodes. But this method is inefficient, since not all users need the same ratio of resources. For example, some users need more CPU whereas other users need more memory. As a result, most tasks either under-utilize or over-utilize their resources. DRF solves the problem by maximizing the minimum amount of the dominant resource given to a user (then the second-minimum etc., in a leximin order). The dominant resource may be different for different users. For example, if user A runs CPU-heavy tasks and user B runs memory-heavy tasks, DRF will try to equalize the CPU share given to user A and the memory share given to user B. == Definition == There are m resources. The total capacities of the resources are r1,...,rm. There are n users. Each users runs individual tasks. Each task has a demand-vector (d1,..,dm), representing the amount it needs of each resource. It is implicitly assumed that the utility of a user equals the number of tasks he can perform. For example, if user A runs tasks with demand-vector [1 CPU, 4 GB RAM], and receives 3 CPU and 8 GB RAM, then his utility is 2, since he can perform only 2 tasks. More generally, the utility of a user receiving x1,...,xm resources is minj(xj/dj), that is, the users have Leontief utilities. The demand-vectors are normalized to fractions of the capacities. For example, if the system has 9 CPUs and 18 GB RAM, then the above demand-vector is normalized to [1/9 CPU, 2/9 GB]. For each user, the resource with the highest demand-fraction is called the dominant resource. In the above example, the dominant resource is memory, as 2/9 is the largest fraction. If user B runs a task with demand-vector [3 CPU, 1 GB], which is normalized to [1/3 CPU, 1/18 GB], then his dominant resource is CPU. DRF aims to find the maximum x such that all agents can receive at least x of their dominant resource. In the above example, this maximum x is 2/3: User A gets 3 tasks, which require 3/9 CPU and 2/3 GB. User B gets 2 tasks, which require 2/3 CPU and 1/9 GB. The maximum x can be found by solving a linear program; see Lexicographic max-min optimization. Alternatively, the DRF can be computed sequentially. The algorithm tracks the amount of dominant resource used by each user. At each round, it finds a user with the smallest allocated dominant resource so far, and allocates the next task of this user. Note that this procedure allows the same user to run tasks with different demand vectors. == Properties == DRF has several advantages over other policies for resource allocation. Proportionality: each user receives at least as much resources as they could get in a system in which all resources are partitioned equally among users (the authors call this condition "sharing incentive"). Strategyproofness: a user cannot get a larger allocation by lying about his needs. Strategyproofness is important, as evidence from cloud operators show that users try to manipulate the servers in order to get better allocations. Envy-freeness: no user would prefer the allocation of another user. Pareto efficiency: no other allocation is better for some users and not worse for anyone. Population monotonicity: when a user leaves the system, the allocations of remaining users do not decrease. When there is a single resource that is a bottleneck resource (highly demanded by all users), DRF reduces to max-min fairness. However, DRF violates resource monotonicity: when resources are added to the system, some allocations might decrease. == Extensions == Weighted DRF is an extension of DRF to settings in which different users have different weights (representing their different entitlements). Parkes, Procaccia and Shah formally extend weighted DRF to a setting in which some users do not need all resources (that is, they may have demand 0 to some resource). They prove that the extended version still satisfies proportionality, Pareto-efficiency, envy-freeness, strategyproofness, and even Group strategyproofness. On the other hand, they show that DRF may yield poor utilitarian social welfare, that is, the sum of utilities may be only 1/m of the optimum. However, they prove that any mechanism satisfying one of proportionality, envy-freeness or strategyproofness may suffers from the same low utilitarian welfare. They also extend DRF to the setting in which the users' demands are indivisible (as in fair item allocation). For the indivisible setting, they relax envy-freeness to EF1. They show that strategyproofness is incompatible with PO+EF1 or with PO+proportionality. However, a mechanism called SequentialMinMax satisfies efficiency, proportionality and EF1. Wang, Li and Liang present DRFH - an extension of DRF to a system with several heterogeneous servers. == Implementation == DRF was first implemented in Apache Mesos - a cluster resource manager, and it led to better throughput and fairness than previously used fair-sharing schemes.
Physics-informed neural networks
In machine learning, physics-informed neural networks (PINNs), also referred to as theory-trained neural networks (TTNs), are a type of universal function approximator that can embed the knowledge of any physical laws that govern a given data-set in the learning process, and can be described by partial differential equations (PDEs). Low data availability for some biological and engineering problems limit the robustness of conventional machine learning models used for these applications. The prior knowledge of general physical laws acts in the training of neural networks (NNs) as a regularization agent that limits the space of admissible solutions, increasing the generalizability of the function approximation. This way, embedding this prior information into a neural network results in enhancing the information content of the available data, facilitating the learning algorithm to capture the right solution and to generalize well even with a low amount of training examples. Because they process continuous spatial and time coordinates and output continuous PDE solutions, they can be categorized as neural fields. == Function approximation == Most of the physical laws that govern the dynamics of a system can be described by partial differential equations. For example, the Navier–Stokes equations are a set of partial differential equations derived from the conservation laws (i.e., conservation of mass, momentum, and energy) that govern fluid mechanics. The solution of the Navier–Stokes equations with appropriate initial and boundary conditions allows the quantification of flow dynamics in a precisely defined geometry. However, these equations cannot be solved exactly and therefore numerical methods must be used (such as finite differences, finite elements and finite volumes). In this setting, these governing equations must be solved while accounting for prior assumptions, linearization, and adequate time and space discretization. Recently, solving the governing partial differential equations of physical phenomena using deep learning has emerged as a new field of scientific machine learning (SciML), leveraging the universal approximation theorem and high expressivity of neural networks. In general, deep neural networks could approximate any high-dimensional function given that sufficient training data are supplied. However, such networks do not consider the physical characteristics underlying the problem, and the level of approximation accuracy provided by them is still heavily dependent on careful specifications of the problem geometry as well as the initial and boundary conditions. Without this preliminary information, the solution is not unique and may lose physical correctness. To remedy this, Physics-Informed Neural Networks (PINNs) leverage governing physical equations in neural network training. Namely, PINNs are designed to be trained to satisfy the given training data as well as the imposed governing equations. In this fashion, a neural network can be guided with training datasets that do not necessarily need to be large or complete. An accurate solution of partial differential equations can potentially be found without knowing the boundary conditions. Therefore, with some knowledge about the physical characteristics of the problem and some form of training data (even sparse and incomplete), PINNs may be used for finding an optimal solution with high fidelity. PINNs can be applied to a wide range of problems in computational science, and are a pioneering technology leading to the development of new classes of numerical solvers for PDEs. PINNs can be thought of as a mesh-free alternative to traditional approaches (e.g., CFD for fluid dynamics), and new data-driven approaches for model inversion and system identification. Notably, a trained PINN network can be used to predict values on simulation grids of different resolutions without needing to be retrained. Additionally, the derivatives used in the partial differential equations can be computed using automatic differentiation (AD), which is assessed to be superior to numerical or symbolic differentiation. == Modeling and computation == A general nonlinear partial differential equation can be written as: u t + N [ u ; λ ] = 0 , x ∈ Ω , t ∈ [ 0 , T ] {\displaystyle u_{t}+{\mathcal {N}}[u;\lambda ]=0,\quad x\in \Omega ,\quad t\in [0,T]} where u ( t , x ) {\displaystyle u(t,x)} denotes the solution, N [ ⋅ ; λ ] {\displaystyle {\mathcal {N}}[\cdot ;\lambda ]} is a nonlinear operator parameterized by λ {\displaystyle \lambda } , and Ω {\displaystyle \Omega } is a subset of R D {\displaystyle \mathbb {R} ^{D}} . This general form of governing equations summarizes a wide range of problems in mathematical physics, such as conservative laws, diffusion process, advection-diffusion systems, and kinetic equations. Given noisy measurements of a generic dynamic system described by the equation above, PINNs can be designed to solve two classes of problems: data-driven solutions of partial differential equations data-driven discovery of partial differential equations === Data-driven solution of partial differential equations === The data-driven solution of PDE computes the hidden state u ( t , x ) {\displaystyle u(t,x)} of the system given boundary data and/or measurements z {\displaystyle z} , and fixed model parameters λ {\displaystyle \lambda } . We solve: u t + N [ u ] = 0 , x ∈ Ω , t ∈ [ 0 , T ] {\displaystyle u_{t}+{\mathcal {N}}[u]=0,\quad x\in \Omega ,\quad t\in [0,T]} . by defining the residual f ( t , x ) {\displaystyle f(t,x)} as: f := u t + N [ u ] {\displaystyle f:=u_{t}+{\mathcal {N}}[u]} , and approximating u ( t , x ) {\displaystyle u(t,x)} by a deep neural network. This network can be differentiated using automatic differentiation. The parameters of u ( t , x ) {\displaystyle u(t,x)} and f ( t , x ) {\displaystyle f(t,x)} can be then learned by minimizing the following loss function L tot {\displaystyle L_{\text{tot}}} : L tot = L u + L f {\displaystyle L_{\text{tot}}=L_{u}+L_{f}} where: L u = ‖ u − z ‖ Γ {\displaystyle L_{u}=\Vert u-z\Vert _{\Gamma }} is the error between the PINN u ( t , x ) {\displaystyle u(t,x)} and the set of boundary conditions and measured data on the set of points Γ {\displaystyle \Gamma } where the boundary conditions and data are defined. L f = ‖ f ‖ Γ {\displaystyle L_{f}=\Vert f\Vert _{\Gamma }} is the mean-squared error of the residual function. This second term encourages the PINN to learn the structural information expressed by the PDE during the training process. This approach has been used to yield computationally efficient physics-informed surrogate models with applications in the forecasting of physical processes, model predictive control, multi-physics and multi-scale modeling, and simulation. It has been shown to converge to the solution of the PDE. === Data-driven discovery of partial differential equations === Given noisy and incomplete measurements z {\displaystyle z} of the state of the system, the data-driven discovery of PDEs results in computing the unknown state u ( t , x ) {\displaystyle u(t,x)} and learning model parameters λ {\displaystyle \lambda } that best describe the observed data: u t + N [ u ; λ ] = 0 , x ∈ Ω , t ∈ [ 0 , T ] {\displaystyle u_{t}+{\mathcal {N}}[u;\lambda ]=0,\quad x\in \Omega ,\quad t\in [0,T]} By defining f ( t , x ) {\displaystyle f(t,x)} as: f := u t + N [ u ; λ ] = 0 {\displaystyle f:=u_{t}+{\mathcal {N}}[u;\lambda ]=0} , and approximating u ( t , x ) {\displaystyle u(t,x)} by a deep neural network, f ( t , x ) {\displaystyle f(t,x)} results in a PINN. This network can be derived using automatic differentiation. The parameters of u ( t , x ) {\displaystyle u(t,x)} and f ( t , x ) {\displaystyle f(t,x)} , together with the parameter λ {\displaystyle \lambda } of the differential operator can be then learned by minimizing the following loss function L tot {\displaystyle L_{\text{tot}}} : L tot = L u + L f {\displaystyle L_{\text{tot}}=L_{u}+L_{f}} where: L u = ‖ u − z ‖ Γ {\displaystyle L_{u}=\Vert u-z\Vert _{\Gamma }} , with u {\displaystyle u} and z {\displaystyle z} state solutions and measurements at sparse location Γ {\displaystyle \Gamma } , respectively. L f = ‖ f ‖ Γ {\displaystyle L_{f}=\Vert f\Vert _{\Gamma }} is the residual function. This second term requires the structured information represented by the partial differential equations to be satisfied in the training process. This strategy allows for discovering dynamic models described by nonlinear PDEs assembling computationally efficient and fully differentiable surrogate models that may find application in predictive forecasting, control, and data assimilation. == Extensions and applications == === For piece-wise function approximation === PINNs are unable to approximate PDEs that have strong non-linearity or sharp gradients (such as those that commonly occur in practical fluid flow problems). Piecewise approximation has been an old practic
Xara Designer Pro+
Xara Designer Pro+ is an image editing program incorporating photo editing and vector illustration tools created by British software company Xara. Xara Xtreme LX was an early open source version for Linux. The Windows version was previously sold under the names Xara Studio, Xara X and Xara Xtreme, and traces its origin in the late 1980s to a title called ArtWorks for the Acorn Archimedes line of computers using RISC OS. There is a pro version called Xara Designer Pro (formerly Xara Xtreme Pro). The current commercial version of Xara Photo & Graphic Designer runs only on Windows, although Xara documents can be edited in a web browser on any platform using the Xara Cloud service. Versions up to 4.x can be run on Linux using Wine. == History == ArtWorks, the predecessor of Xara Photo and Graphic Designer, was developed on Acorn Archimedes and Risc PC 32-bit RISC computers running RISC OS by Computer Concepts during the late 1980s. The first version, developed for Microsoft Windows was initially called Xara Studio. It was licensed to Corel Corporation before wide-scale public availability, and from 1995 to 2000 was released as CorelXARA. Corel ceded the licensing rights back to Xara in 2000. The first Xara X version released in 2000 by its original owner. The next version, Xara X¹, was released in 2004. Xara Xtreme was released in 2005. In November 2006, Xara Xtreme PRO (an enhanced version of Xara Xtreme) was released. Xara Xtreme 3.2 and Xtreme Pro 3.2 were released in May 2007. 3.2 Pro included Xara3D, and both versions had more robust typography. In April 2008, Xara Xtreme 4.0 was released. Xara Xtreme and Xara Xtreme Pro 5.1 were released in June 2009. Features included more text-area enhancements, content-aware scaling of bitmap images, improved file import and export, master-page (repeated) objects, an object gallery (replacing the layer gallery), website-creation tools, and multi-stage graduated transparency. In June 2010, Xara Photo & Graphic Designer 6 and Xara Designer Pro 6 were released. Xtreme was renamed Photo & Graphic Designer, and Xtreme Pro was renamed Designer Pro. In May 2011, Xara Photo & Graphic Designer 7 and Xara Designer Pro 7 were released. Features included "magic" photo erase, user interface improvements to docking galleries and snapping alignment, and (in Pro) new webpage and website-design features. In May 2012, Xara Photo & Graphic Designer 2013 and Xara Designer Pro X (v8) were released. Xara Photo & Graphic Designer 9 was released in May 2013. In July of that year, Xara Designer Pro X9 was released. Xara Photo & Graphic Designer 10 was released on 16 July 2014, and Xara Designer Pro X10 on 23 July. Xara Photo & Graphic Designer 11 was released on 29 June 2015, and Xara Designer Pro X11 was released the following month. In 2016, the delivery model was changed to an update service which can be renewed annually. Users are entitled to any updates released while the update service is active. The first update-service updates were in May 2016 for Xara Photo & Graphic Designer, and July 2016 for Xara Designer Pro X. == Features == Xara Photo & Graphic Designer is known for its usability and fast renderer. It provides a fully anti-aliased display, advanced gradient fill, and transparency tools. Among vector editors, Xara Photo & Graphic Designer is considered to be fairly easy to learn, with similarities to CorelDRAW and Inkscape in terms of interface. Alongside the vector illustration tools, Xara Photo & Graphic Designer also includes an integrated photo tool offering manual and automatic photo enhance, cropping, adjustment of brightness levels, red-eye fix, 'magic' erase, photo healing, color and background erase, panoramas and content aware resizing. Designer Pro includes a wider range of tools for other design tasks including the creation of web pages and websites, and text and page layout tools for DTP with the aim of providing a single solution for all graphic and web design tasks.
Morphological antialiasing
Morphological antialiasing (MLAA) is a spatial anti-aliasing technique used in real-time computer graphics. It reduces artifacts, such as jaggies, when representing a high-resolution image at a lower resolution. MLAA is a post-process filtering which detects borders in the resulting image and then finds specific patterns in these. Anti-aliasing is achieved by blending pixels in these borders, according to the pattern they belong to and their position within the pattern. Introduced in 2009, MLAA was an early and influential example of anti-aliasing techniques done in post-processing, which makes them suitable for deferred shading. A similar method in this class is fast approximate anti-aliasing (FXAA). Temporal anti-aliasing, also a post-process, has become the most common anti-aliasing method for real-time rendering and video games. Enhanced subpixel morphological antialiasing, or SMAA, is an image-based GPU-based implementation of MLAA developed by Universidad de Zaragoza and Crytek.
D/Vision Pro
D/Vision Pro was one of the earliest marketed non-linear editing systems. It was released by TouchVision Systems, Inc. in the mid-1990s. The program was DOS-based and worked on either Intel's 386 or 486 processor. The system used AVI compression and worked with the Action Media II board. The system allowed users to digitize video, audio, and timecode, create an edit decision list (EDL), instantly play back the edited program, and output the finished EDL in a wide variety of formats. These cost-effective editing systems were used by numerous independent filmmakers and in low-budget productions during the mid-late 1990s. D/Vision Pro's low-quality compression led TouchVision (later renamed D/Vision Systems) to abandon it in favor of D/Vision Online, which was purchased by Discreet Logic and renamed edit. In June 2002, Discreet discontinued edit, as they did not want it to interfere with smoke sales which were more profitable. Discreet was later purchased by Autodesk.
CloudSim
CloudSim is a framework for modeling and simulation of cloud computing infrastructures and services. Originally built primarily at the Cloud Computing and Distributed Systems (CLOUDS) Laboratory, the University of Melbourne, Australia, CloudSim has become one of the most popular open source cloud simulators in the research and academia. CloudSim is completely written in Java. The latest version of CloudSim is CloudSim v6.0.0-beta on GitHub. Cloudsim is suitable for implementing simulations scenarios based on Infrastructure as a service as well as with latest version Platform as a service, so get started here == CloudSim extensions == Initially developed as a stand-alone cloud simulator, CloudSim has further been extended by independent researchers. GPUCloudSim is an enhanced CloudSim tool for modeling GPU-based cloud infrastructures and data centers. It offers simulations for multi-GPU setups, customizable GPU policies, GPU remoting, etc. It also examines performance impacts and interactions within virtualized GPU environments. CloudSim Plus is a totally re-engineered CloudSim fork providing general-purpose cloud computing simulation and exclusive features such as: multi-cloud simulations, vertical and horizontal VM scaling, host fault injection and recovery, joint power- and network-aware simulations and more. Though CloudSim itself does not have a graphical user interface, extensions such as CloudReports offer a GUI for CloudSim simulations. CloudSimEx extends CloudSim by adding MapReduce simulation capabilities and parallel simulations. Cloud2Sim extends CloudSim to execute on multiple distributed servers, by leveraging Hazelcast distributed execution framework. RECAP DES extends the CloudSim Plus framework to model synchronous hierarchical architectures (such as ElasticSearch). ThermoSim extends CloudSim toolkit by incorporating thermal characteristics, and uses Deep learning-based temperature predictor for cloud nodes.
Abillion
abillion was a mobile application helping users to find vegan and sustainable products. The platform allowed users to review plant-based, cruelty-free and sustainable products, while donating between 0.10 and $1 to nonprofit organisations for each review written. As of May 2023, the company claimed to have donated over $2.8M to various nonprofit organisations including Sea Shepherd and Mercy for Animals. The main objective of the company was to reach the number of one billion people following a vegan diet and lifestyle by 2030. == History == The American entrepreneur Vikas Garg founded the company in Singapore and the app was officially launched in May 2018. The start-up was first named 'abillionveg' and changed its name in 2020 to shorten it to 'abillion'. In 2019, the company raised $3M in its first round of funding (pre-Series A). In 2021, it raised $10M in its Series A funding. In February 2023, the company announced the launch of a community investment round, using the crowdfunding platform Wefunder, which reached a total of $500 000. In May 2023, it celebrated its 5th anniversary and reaching 1M downloads. In March 2026, the company announced that they would be closing down by the end of the month. == Awards == Using data from the reviews published by its users, abillion was awarding the most liked vegan products and brands. In May 2023, the company published a world Top 10 Best Plant Based Burgers, among the winning brands were Beyond Meat, NotCo and Sojasun.