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We develop a theory of rewriting for structured cospans in order to extend compositional methods for modeling open networks. First, we introduce a category whose objects are structured cospans, and establish conditions under which it is…
Already in the 1960s, Levenshtein and others studied error-correcting codes that protect against synchronization errors, such as symbol insertions and deletions. However, despite significant efforts, progress on designing such codes has…
Automatic segmentation has great potential to facilitate morphological measurements while simultaneously increasing efficiency. Nevertheless often users want to edit the segmentation to their own needs and will need different tools for…
The concept of a system has proliferated through natural and social sciences. While myriad theories of systems exist, there is no mathematical general theory of systems. In this thesis, we take a first step towards formulating such a…
RNA-Seq is a widely-used method for studying the behavior of genes under different biological conditions. An essential step in an RNA-Seq study is normalization, in which raw data are adjusted to account for factors that prevent direct…
Recurrent neural networks (RNNs) are powerful models of sequential data. They have been successfully used in domains such as text and speech. However, RNNs are susceptible to overfitting; regularization is important. In this paper we…
A fundamental property of DNA is that the reverse complement (RC) of a sequence often carries identical biological meaning. However, state-of-the-art DNA language models frequently fail to capture this symmetry, producing inconsistent…
An RNA molecule is structured on several layers. The primary and most obvious structure is its sequence of bases, i.e. a word over the alphabet {A,C,G,U}. The higher structure is a set of one-to-one base-pairings resulting in a…
Unsupervised learning-based medical image registration approaches have witnessed rapid development in recent years. We propose to revisit a commonly ignored while simple and well-established principle: recursive refinement of deformation…
Registration is the process that computes the transformation that aligns sets of data. Commonly, a registration process can be divided into four main steps: target selection, feature extraction, feature matching, and transform computation…
In natural language processing, it has been observed recently that generalization could be greatly improved by finetuning a large-scale language model pretrained on a large unlabeled corpus. Despite its recent success and wide adoption,…
Optimization acceleration techniques such as momentum play a key role in state-of-the-art machine learning algorithms. Recently, generic vector sequence extrapolation techniques, such as regularized nonlinear acceleration (RNA) of Scieur et…
The basic principle of graph rewriting is the stepwise replacement of subgraphs inside a host graph. A challenge in such replacement steps is the treatment of the patch graph, consisting of those edges of the host graph that touch the…
Composite DNA is a recent method to increase the base alphabet size in DNA-based data storage.This paper models synthesizing and sequencing of composite DNA and introduces coding techniques to correct substitutions, losses of entire…
RNA-seq allows detection and precise quantification of transcripts, provides comprehensive understanding of exon/intron boundaries, aids discovery of alternatively spliced isoforms and fusion transcripts along with measurement of…
Non-confluent and non-terminating constructor-based term rewrite systems are useful for the purpose of specification and programming. In particular, existing functional logic languages use such kind of rewrite systems to define possibly…
The (.)_reg construction was introduced in order to make an arbitrary semigroup S divide a regular semigroup (S)_reg which shares some important properties with S (e.g., finiteness, subgroups, torsion bounds, J-order structure). We show…
The problem of reconstructing strings from their substring spectra has a long history and in its most simple incarnation asks for determining under which conditions the spectrum uniquely determines the string. We study the problem of coded…
Jim Shapiro synthesizes a great many observations about the mechanisms of evolution to reach the remarkable conclusion that large-scale modification, exchange, and rearrangement of the genome are common and should be viewed as fundamental…
A key feature of human intelligence is the ability to generalize beyond the training distribution, for instance, parsing longer sentences than seen in the past. Currently, deep neural networks struggle to generalize robustly to such shifts…