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The ordered set is one of the most important data type in both theoretical algorithm design and analysis and practical programming. In this paper we study the set operations on two ordered sets, including Union, Intersect and Difference,…

The statistical modelling of spatial extremes has recently made major advances. Much of its focus so far has been on the modelling of the magnitudes of extreme events but little attention has been paid on the timing of extremes. To address…

Topological Data Analysis (TDA) is an approach to handle with big data by studying its shape. A main tool of TDA is the persistence diagram, and one can use it to compare data sets. One approach to learn on the similarity between two…

Nowadays, numerous services based on large-scale distributed systems have been developed to boost the convenience of human life. On the other side, it becomes a significant challenge to ensure the correctness and properties of these systems…

With web and mobile platforms becoming more prominent devices utilized in data analysis, there are currently few systems which are not without flaw. In order to increase the performance of these systems and decrease errors of data…

Attributed graphs model real networks by enriching their nodes with attributes accounting for properties. Several techniques have been proposed for partitioning these graphs into clusters that are homogeneous with respect to both semantic…

As the sheer amount of computer generated data continues to grow exponentially, new bottlenecks are unveiled that require rethinking our traditional software and hardware architectures. In this paper we present five algorithms and data…

Performance analysis has always been an afterthought during the application development process, focusing on application correctness first. The learning curve of the existing static and dynamic analysis tools are steep, which requires…

The goal of this work is to parallelize the multistep scheme for the numerical approximation of the backward stochastic differential equations (BSDEs) in order to achieve both, a high accuracy and a reduction of the computation time as…

Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…

In this work I present a generalization of Amdahl's law on the limits of a parallel implementation with many processors. In particular I establish some mathematical relations involving the number of processors and the dimension of the…

Identifying and explaining the structure of complex networks at different scales has become an important problem across disciplines. At the mesoscale, modular architecture has attracted most of the attention. At the macroscale, other…

The sheer sizes of modern datasets are forcing data-structure designers to consider seriously both parallel construction and compactness. To achieve those goals we need to design a parallel algorithm with good scalability and with low…

In distributed ML applications, shared parameters are usually replicated among computing nodes to minimize network overhead. Therefore, proper consistency model must be carefully chosen to ensure algorithm's correctness and provide high…

The recent advancements in multicore machines highlight the need to simplify concurrent programming in order to leverage their computational power. One way to achieve this is by designing efficient concurrent data structures (e.g. stacks,…

Adaptive multilevel splitting algorithms have been introduced rather recently for estimating tail distributions in a fast and efficient way. In particular, they can be used for computing the so-called reactive trajectories corresponding to…

Consider a system in which tasks of different execution times arrive continuously and have to be executed by a set of processors that are prone to crashes and restarts. In this paper we model and study the impact of parallelism and failures…

To analyse a very large data set containing lengthy variables, we adopt a sequential estimation idea and propose a parallel divide-and-conquer method. We conduct several conventional sequential estimation procedures separately, and properly…

We consider an asynchronous system with transitions corresponding to the instructions of a computer system. For each instruction, a runtime is given. We propose a mathematical model, allowing us to construct an algorithm for finding the…

Arrival of multicore systems has enforced a new scenario in computing, the parallel and distributed algorithms are fast replacing the older sequential algorithms, with many challenges of these techniques. The distributed algorithms provide…