arXiv research

Classifies doodles into prime and super prime types, describing them with doodle codes.

We discuss Gauss codes of virtual diagrams and virtual doodles. The notion of a left canonical Gauss code is introduced and it is shown that oriented virtual doodles are uniquely presented by left canonical Gauss codes.

Alexander invariant created for doodles, vanishes on unlinked doodles.

Doodles were introduced in [R. Fenn and P. Taylor, Introducing doodles, Topology of low-dimensional manifolds, pp. 37--43, Lecture Notes in Math., 722, Springer, Berlin, 1979] but were restricted to embedded circles in the 2-sphere. Khovanov, [M. Khovanov, Doodle groups, Trans. Amer. Math. Soc. 349 (1997), 2297--2315],…

Doodles link to commutator identities in a 2-sphere.

Paper introduces skew-symmetric matrices for virtual doodle classification.

Complete invariant defined for doodles on a sphere.

A virtual doodle is an equivalence class of virtual diagrams under an equivalence relation generated by flat version of classical Reidemesiter moves and virtual Reidemsiter moves such that Reidemeister moves of type 3 are forbidden. In this paper we discuss colorings of virtual diagrams using an algebra, called a doodl…

Cactus doodles are geometric objects derived from cactus groups.

Paper defines doodles on closed surfaces, unifying classical and virtual theories.

Paper shows how to represent Milnor's triple linking number using chord diagrams and doodle invariants.

Computes invariants distinguishing between immersions and embeddings of doodles and blobs on surfaces.

In 1997 M.~Khovanov proved that any doodle can be presented as closure of twin, this result is analogue of classical Alexander's theorem for braids and links. We give a description of twins that have equivalent closures, this theorem is analogue of classical Markov theorem.

DOODL learns shared spectral dynamics across related dynamical systems.

To make music composition more approachable, we designed the first AI-powered Google Doodle, the Bach Doodle, where users can create their own melody and have it harmonized by a machine learning model Coconet (Huang et al., 2017) in the style of Bach. For users to input melodies, we designed a simplified sheet-music ba…

The paper classifies 10 antipodal pairings of self-dual maps.

Proves Alexander and Markov theorems for higher genus virtual doodles.

Given a plane curve $γ: S^1\to \mathbb R^2$, we consider the problem of determining the minimal number $I(γ)$ of inflections which curves $\mbox{diff}(γ)$ may have, where $\mbox{diff}$ runs over the group of diffeomorphisms of $\mathbb R^2$. We show that if $γ$ is an immersed curve with $D(γ)$ double points and no othe…

We investigate using reinforcement learning agents as generative models of images (extending arXiv:1804.01118). A generative agent controls a simulated painting environment, and is trained with rewards provided by a discriminator network simultaneously trained to assess the realism of the agent's samples, either uncond…

This paper explores Brunnian twin groups and their properties.

Many software analysis methods have come to rely on machine learning approaches. Code segmentation - the process of decomposing source code into meaningful blocks - can augment these methods by featurizing code, reducing noise, and limiting the problem space. Traditionally, code segmentation has been done using syntact…

Study re-evaluates MIMIC-III codes, finding many are under-coded.

Paper proposes new gradient codes for robust distributed machine learning.

CoNCRA uses CNN to find code snippets matching developer intent.

Contrastive Code Representation Learning improves code summarization and type inference.

Transformer model improves source code summarization.

Investigates neural codes and their embeddings, proving conjectures and introducing new code types.

Characterization of a patient clinical phenotype is central to biomedical informatics. ICD codes, assigned to inpatient encounters by coders, is important for population health and cohort discovery when clinical information is limited. While ICD codes are assigned to patients by professionals trained and certified in c…

Sparse coding approximates the data sample as a sparse linear combination of some basic codewords and uses the sparse codes as new presentations. In this paper, we investigate learning discriminative sparse codes by sparse coding in a semi-supervised manner, where only a few training samples are labeled. By using the m…

Inspired by recent work on convex formulations of clustering (Lashkari & Golland, 2008; Nowozin & Bakir, 2008) we investigate a new formulation of the Sparse Coding Problem (Olshausen & Field, 1997). In sparse coding we attempt to simultaneously represent a sequence of data-vectors sparsely (i.e. sparse approximation (…

Topological theory for qLDPC codes enables non-Clifford gates and magic state injection.

We introduce new definitions of universal and superuniversal computable codes, which are based on a code's ability to approximate Kolmogorov complexity within the prescribed margin for all individual sequences from a given set. Such sets of sequences may be singled out almost surely with respect to certain probability …

We introduce the hemicubic codes, a family of quantum codes obtained by associating qubits with the $p$-faces of the $n$-cube (for $n>p$) and stabilizer constraints with faces of dimension $(p\pm1)$. The quantum code obtained by identifying antipodal faces of the resulting complex encodes one logical qubit into $N = 2^…

Code search and comprehension have become more difficult in recent years due to the rapid expansion of available source code. Current tools lack a way to label arbitrary code at scale while maintaining up-to-date representations of new programming languages, libraries, and functionalities. Comprehensive labeling of sou…

Gradient coding is a technique for straggler mitigation in distributed learning. In this paper we design novel gradient codes using tools from classical coding theory, namely, cyclic MDS codes, which compare favorably with existing solutions, both in the applicable range of parameters and in the complexity of the invol…

The design of codes for communicating reliably over a statistically well defined channel is an important endeavor involving deep mathematical research and wide-ranging practical applications. In this work, we present the first family of codes obtained via deep learning, which significantly beats state-of-the-art codes …

MISIM improves code similarity systems with neural learning.

Khovanov homology helps create quantum error-correcting codes.

Program comprehension is a fundamental task in software development and maintenance processes. Software developers often need to understand a large amount of existing code before they can develop new features or fix bugs in existing programs. Being able to process programming language code automatically and provide sum…

Sparse codes improve optimal control tasks with correlated inputs.

Two new coding schemes improve the efficient communication of noisy data.

The abundance of open-source code, coupled with the success of recent advances in deep learning for natural language processing, has given rise to a promising new application of machine learning to source code. In this work, we explore the use of a Siamese recurrent neural network model on Python source code to create …

We use Khovanov homology to define families of LDPC quantum error-correcting codes: unknot codes with asymptotical parameters [[3^(2l+1)/sqrt(8πl);1;2^l]]; unlink codes with asymptotical parameters [[sqrt(2/2πl)6^l;2^l;2^l]] and (2,l)-torus link codes with asymptotical parameters [[n;1;d_n]] where d_n>\sqrt(n)/1.62.

Sparse coding has been popularly used as an effective data representation method in various applications, such as computer vision, medical imaging and bioinformatics, etc. However, the conventional sparse coding algorithms and its manifold regularized variants (graph sparse coding and Laplacian sparse coding), learn th…

In this paper we formalize a combinatorial object for describing link diagrams called a Planar Diagram Code. PD-codes are used by the KnotTheory Mathematica package developed by Bar-Natan, et al. We present the set of PD-codes as a stand alone object and discuss its relationship with link diagrams. We give an explicit …

Sparse coding, which represents a data point as a sparse reconstruction code with regard to a dictionary, has been a popular data representation method. Meanwhile, in database retrieval problems, learning the ranking scores from data points plays an important role. Up to now, these two problems have always been conside…

Predicting the runtime complexity of a programming code is an arduous task. In fact, even for humans, it requires a subtle analysis and comprehensive knowledge of algorithms to predict time complexity with high fidelity, given any code. As per Turing's Halting problem proof, estimating code complexity is mathematically…

Quantum codes on hyperbolic lattices outperform Euclidean ones with higher rates and lower overhead.