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With distributed computing and mobile applications, synchronizing diverging replicas of data structures is a more and more common problem. We use algebraic methods to reason about filesystem operations, and introduce a simplified definition…

Points-to analysis is the problem of approximating run-time values of pointers statically or at compile-time. Points-to sets are used to store the approximated values of pointers during points-to analysis. Memory usage and running time…

There is a lot of research interest in encoding variable length sentences into fixed length vectors, in a way that preserves the sentence meanings. Two common methods include representations based on averaging word vectors, and…

Traditional software engineering programming paradigms are mostly object or procedure oriented, driven by deterministic algorithms. With the advent of deep learning and cognitive sciences there is an emerging trend for data-driven…

Decision trees have been a very popular class of predictive models for decades due to their interpretability and good performance on categorical features. However, they are not always robust and tend to overfit the data. Additionally, if…

Classic grammars and regular expressions can be used for a variety of purposes, including parsing, intent detection, and matching. However, the comparisons are performed at a structural level, with constituent elements (words or characters)…

Recently, there has been a lot of effort to represent words in continuous vector spaces. Those representations have been shown to capture both semantic and syntactic information about words. However, distributed representations of phrases…

Stochastic variational inference (SVI), the state-of-the-art algorithm for scaling variational inference to large-datasets, is inherently serial. Moreover, it requires the parameters to fit in the memory of a single processor; this is…

State-of-the-art clustering algorithms use heuristics to partition the feature space and provide little insight into the rationale for cluster membership, limiting their interpretability. In healthcare applications, the latter poses a…

An affine vector space partition of $\operatorname{AG}(n,q)$ is a set of proper affine subspaces that partitions the set of points. Here we determine minimum sizes and enumerate equivalence classes of affine vector space partitions for…

Harmonic sums and their generalizations are extremely useful in the evaluation of higher-order perturbative corrections in quantum field theory. Of particular interest have been the so-called nested sums,where the harmonic sums and their…

The ageing algebra is a local dynamical symmetry of many ageing systems, far from equilibrium, and with a dynamical exponent z=2. Here, new representations for an integer dynamical exponent z=n are constructed, which act non-locally on the…

The Binary Space Partitioning-Tree~(BSP-Tree) process was recently proposed as an efficient strategy for space partitioning tasks. Because it uses more than one dimension to partition the space, the BSP-Tree Process is more efficient and…

Tensor Networks are graph representations of summation expressions in which vertices represent tensors and edges represent tensor indices or vector spaces. In this work, we present EinExprs.jl, a Julia package for contraction path…

Abstract meaning representations (AMRs) are broad-coverage sentence-level semantic representations. AMRs represent sentences as rooted labeled directed acyclic graphs. AMR parsing is challenging partly due to the lack of annotated…

The interpretability of models has become a crucial issue in Machine Learning because of algorithmic decisions' growing impact on real-world applications. Tree ensemble methods, such as Random Forests or XgBoost, are powerful learning tools…

Ren et al. recently introduced a method for aggregating multiple decision trees into a strong predictor by interpreting a path taken by a sample down each tree as a binary vector and performing linear regression on top of these vectors…

This paper discusses the practical use of the saddle variational formulation for the weakly-constrained 4D-VAR method in data assimilation. It is shown that the method, in its original form, may produce erratic results or diverge because of…

In this work, we present a translation of the complete pipeline for variational shape approximation (VSA) to the setting of point sets. First, we describe an explicit example for the theoretically known non-convergence of the currently…

Staged trees are a relatively recent class of probabilistic graphical models that extend Bayesian networks to formally and graphically account for non-symmetric patterns of dependence. Machine learning algorithms to learn them from data…