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Many interesting and useful symbolic computation algorithms manipulate mathematical expressions in mathematically meaningful ways. Although these algorithms are commonplace in computer algebra systems, they can be surprisingly difficult to…

Rule-based models, e.g., decision trees, are widely used in scenarios demanding high model interpretability for their transparent inner structures and good model expressivity. However, rule-based models are hard to optimize, especially on…

Dense and sparse tensors allow the representation of most bulk data structures in computational science applications. We show that sparse tensor algebra can also be used to express many of the transformations on these datasets, especially…

A computational tool for coarse-graining nonlinear systems of ordinary differential equations in time is discussed. Three illustrative model examples are worked out that demonstrate the range of capability of the method. This includes the…

We develop a mathematical model for dynamic simulation of an alkaline electrolyzer plant. The plant includes the stack, a water recirculation system and hydrogen storage with compressor. We model each component of the system with mass and…

Probabilistic behavior is omnipresent in computer controlled systems, in particular, so-called safety-critical hybrid systems, because of various reasons, like uncertain environments, or fundamental properties of nature. In this paper, we…

Data-flow analyses usually associate information with control flow regions. Informally, if these regions are too small, like a point between two consecutive statements, we call the analysis dense. On the other hand, if these regions include…

The paper considers pseudo-differential boundary value control systems. The underlying operators form an algebra D with the help of which we are able to formulate typical boundary value control problems. The symbolic calculus gives tools to…

Programming physicists use, as all programmers, arrays, lists, tuples, records, etc., and this requires some change in their thought patterns while converting their formulae into some code, since the "data structures" operated upon, while…

Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…

Large Language Models (LLMs) are increasingly being adopted as tools for learning; however, most tools remain text-only, limiting their usefulness for domains where visualizations are essential, such as mathematics. Recent work shows that…

We study aggregations for ordinary differential equations induced by fluid semantics for Markovian process algebra which can capture the dynamics of performance models and chemical reaction networks. Whilst previous work has required…

This paper presents the mechanization of a process algebra for Mobile Ad hoc Networks and Wireless Mesh Networks, and the development of a compositional framework for proving invariant properties. Mechanizing the core process algebra in…

We introduce a new dynamic analysis technique to discover invariants in separation logic for heap-manipulating programs. First, we use a debugger to obtain rich program execution traces at locations of interest on sample inputs. These…

In the co-sparse analysis model a set of filters is applied to a signal out of the signal class of interest yielding sparse filter responses. As such, it may serve as a prior in inverse problems, or for structural analysis of signals that…

Developed to alleviate prohibitive labeling costs, active learning (AL) methods aim to reduce label complexity in supervised learning. While recent work has demonstrated the benefit of using AL in combination with large pre-trained language…

Probabilistic programming provides the means to represent and reason about complex probabilistic models using programming language constructs. Even simple probabilistic programs can produce models with infinitely many variables. Factored…

Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…

In the present work, we demonstrate how the pseudoinverse concept from linear algebra can be used to represent and analyze the boundary conditions of linear systems of partial differential equations. This approach has theoretical and…

Active learning (AL) prioritizes the labeling of the most informative data samples. However, the performance of AL heuristics depends on the structure of the underlying classifier model and the data. We propose an imitation learning scheme…