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Mathematical formulae represent complex semantic information in a concise form. Especially in Science, Technology, Engineering, and Mathematics, mathematical formulae are crucial to communicate information, e.g., in scientific papers, and…
Column-sparse packing problems arise in several contexts in both deterministic and stochastic discrete optimization. We present two unifying ideas, (non-uniform) attenuation and multiple-chance algorithms, to obtain improved approximation…
Deep ensembles can be considered as the current state-of-the-art for uncertainty quantification in deep learning. While the approach was originally proposed as a non-Bayesian technique, arguments supporting its Bayesian footing have been…
The availability of working quantum computers has led to several proposals and claims of quantum advantage. In 2023, this has included claims that quantum computers can successfully factor large integers, by optimizing the search for nearby…
Indexed languages are a classical notion in formal language theory, which has attracted attention in recent decades due to its role in higher-order model checking: They are precisely the languages accepted by order-2 pushdown automata. The…
In the literature on algorithms for performing the multi-term addition $s_n=\sum_{i=1}^n x_i$ using floating-point arithmetic it is often shown that a hardware unit that has single normalization and rounding improves precision, area,…
In this paper, starting from a generalized coherent (i.e. avoiding uniform loss) intervalvalued probability assessment on a finite family of conditional events, we construct conditional probabilities with quasi additive classes of…
We use the martingale-theoretic approach of game-theoretic probability to incorporate imprecision into the study of randomness. In particular, we define a notion of computable randomness associated with interval, rather than precise,…
In this paper, an application of automated theorem proving techniques to computational semantics is considered. In order to compute the presuppositions of a natural language discourse, several inference tasks arise. Instead of treating…
Though many safety-critical software systems use floating point to represent real-world input and output, programmers usually have idealized versions in mind that compute with real numbers. Significant deviations from the ideal can cause…
In this paper the local order of convergence used in iterative methods to solve nonlinear systems of equations is revisited, where shorter alternative analytic proofs of the order based on developments of multilineal functions are shown.…
Hybrid automata are a natural framework for modeling and analyzing systems which exhibit a mixed discrete continuous behaviour. However, the standard operational semantics defined over such models implicitly assume perfect knowledge of the…
The numerical solution of an ordinary differential equation can be interpreted as the exact solution of a nearby modified equation. Investigating the behaviour of numerical solutions by analysing the modified equation is known as backward…
A finite sum of exponential functions may be expressed by a linear combination of powers of the independent variable and by successive integrals of the sum. This is proved for the general case and the connection between the parameters in…
Several researchers have experimentally shown that substantial improvements can be obtained in difficult pattern recognition problems by combining or integrating the outputs of multiple classifiers. This chapter provides an analytical…
Efficient number representation is essential for federated learning, natural language processing, and network measurement solutions. Due to timing, area, and power constraints, such applications use narrow bit-width (e.g., 8-bit) number…
We propose a new perspective for the evaluation of matching procedures by considering the complexity of the function class they belong to. Under this perspective we provide theoretical guarantees on post-matching covariate balance through a…
Beginning with the projectively invariant method for linear programming, interior point methods have led to powerful algorithms for many difficult computing problems, in combinatorial optimization, logic, number theory and non-convex…
Scientific computing programs often undergo aggressive compiler optimization to achieve high performance and efficient resource utilization. While performance is critical, we also need to ensure that these optimizations are correct. In this…
Computational feasibility is a widespread concern that guides the framing and modeling of biological and artificial intelligence. The specification of cognitive system capacities is often shaped by unexamined intuitive assumptions about the…