Scientific computing applications are being increasingly deployed on cloud computing platforms. Transient servers such as EC2 spot instances and Google Preemptible VMs, can be used to lower the costs of running applications on the cloud by up to$10\times$. However, the frequent preemptions and resource heterogeneity of these transient servers introduces many challenges in their effective and efficient use. In this paper, we develop techniques for modeling and mitigating preemptions of transient servers, and present SciSpot, a software framework that enables low-cost scientific computing on the cloud. SciSpot deploys applications on Google Cloud Preemptible Virtual Machines that exhibit temporally constrained preemptions: VMs are always preempted in a 24 hour interval. Our empirical analysis shows that the preemption rate is generally bathtub shaped, which raises multiple fundamental challenges in performance modeling and policy design. We develop a new reliability model for temporally constrained preemptions, and use statistical mechanics to show why the bathtub shape is generally exhibited. SciSpot’s design is guided by our observation that many emerging scientific computing applications that integrate machine learning with simulations, can be deployed as “bags” of jobs, which represent multiple instantiations of the same computation with different physical model parameters. For a bag of jobs, SciSpot finds the optimal transient server on-the-fly, by taking into account the price, performance, and preemption rates of different servers. SciSpot reduces costs by$5\times$compared to conventional cloud deployments, and reduces makespans by up to$10\times$compared to conventional high performance computing clusters.

Mathematical word problems can be broadly divided into two categories as numerical word problems and algebraic word problems. These can be further categorised according to the domain, such as interest calculation and mensuration. Although most of the popular Mathematics examinations contain word problems, there are slight differences in the syllabi. The existing research has produced solutions for some categories of the word type problems. However, these solutions cannot be used for other types of word problems nor can these systems be used in the context of other examinations where there are differences in the grading schemes. We introduce a system that can be easily used to assess answers to both numerical and algebraic type word problems and automatically identifies the exact errors (if any) made by students by using a (teacher provided) marking rubric. The system is modularized and can be extended to support different types of word problems. If the answer contains a short textual phrase along with the numerical or algebraic expression, it is also evaluated in order to check whether the student has actually understood the question.

Venn and Euler diagrams are well-defined mathematical diagram types, which are the major representation methods of Set Theory. Venn and Euler diagrams are part of major Mathematics examinations in secondary education such as London Ordinary Level and SAT. Although computer assessment of different diagram types has been addressed, no such research has been done for Venn and Euler diagrams. In this research, we present a system capable of automatically assessing student answers consisting of Venn and Euler diagrams. The student answer is compared against a model answer, and marks are allocated according to a marking rubric.