arXiv research

Differentially private data structures for estimating distances between strings.

String graphs are closely related to planar graphs in terms of distances.

New theory connects string theory to swampland distance conjecture.

We prove that every Teichmuller geodesic of a finite type surface contains a string of intersecting long, thick and dominant segments, such that the distance between consecutive segments is bounded. This is key to obtaining some results about Teichmuller geodesics which mimic those for hyperbolic geodesics. These resul…

Here we prove the existence of a new type of the world-sheet string singularities - the cusps that are stable during the finite time. These singularities make the emission of the captured massive quantum particle possible in the frames of the author's model suggested earlier. In aggregate, we have a new mechanism of qu…

String kernels are attractive data analysis tools for analyzing string data. Among them, alignment kernels are known for their high prediction accuracies in string classifications when tested in combination with SVM in various applications. However, alignment kernels have a crucial drawback in that they scale poorly du…

New string kernels discover global properties through random feature maps, avoiding quadratic complexity.

A new smooth edit distance for easier optimization in machine learning.

Random deep neural networks favor simple functions.

Derives path integrals for perturbative strings on various backgrounds.

Chemical autoencoders are attractive models as they combine chemical space navigation with possibilities for de-novo molecule generation in areas of interest. This enables them to produce focused chemical libraries around a single lead compound for employment early in a drug discovery project. Here it is shown that the…

Topological string theory derived from string geometry for non-perturbative effects.

Identifies all perturbative vacua in bosonic string theory.

String geometry theory connects strings to space-time and finds string vacua.

Derives path-integrals for superstrings on curved backgrounds using string geometry theory.

This paper classifies virtual string links up to cobordism using group theory.

Chiral string integrands simplify to ambitwistor string integrands in the tensionless limit.

New method embeds DNA sequences for faster, more informative gene comparison.

A virtual string can be defined as an equivalence class of planar diagrams under certain kinds of diagrammatic moves. Virtual strings are related to virtual knots in that a simple operation on a virtual knot diagram produces a diagram for a virtual string. In this paper we consider three operations on a virtual string …

A virtual string is a scheme of self-intersections of a closed curve on a surface. We study algebraic invariants of strings as well as two equivalence relations on the set of strings: homotopy and cobordism. We show that the homotopy invariants of strings form an infinite dimensional Lie group. We also discuss connecti…

The crucial importance of metrics in machine learning algorithms has led to an increasing interest in optimizing distance and similarity functions, an area of research known as metric learning. When data consist of feature vectors, a large body of work has focused on learning a Mahalanobis distance. Less work has been …

There is an interpretation of open string field theory in algebraic topology. An interpretation of closed string field theory can be deduced from this open string theory to obtain as well the interpretation of open and closed string field theory combined.

This work verifies recurrent neural networks using DFA and shows some are robust to adversarial samples.

New formulas link string bordism to integers.

Extended Alexander groups are used to define an invariant for open virtual strings. Examples of non-commuting open strings and a ribbon-concordance obstruction are given. An example is given of a slice virtual open string that is not ribbon. Definitions are extended to open n-strings.

BOSS optimizes string inputs using string kernels and genetic algorithms.

Paper presents a new trie for integer sketches to improve similarity searches.

String topology coproduct and Turaev cobracket computed for surfaces.

For many machine learning problem settings, particularly with structured inputs such as sequences or sets of objects, a distance measure between inputs can be specified more naturally than a feature representation. However, most standard machine models are designed for inputs with a vector feature representation. In th…

We present a finite-dimensional and smooth formulation of string structures on spin bundles. It uses trivializations of the Chern-Simons 2-gerbe associated to this bundle. Our formulation is particularly suitable to deal with string connections: it enables us to prove that every string structure admits a string connect…

Paper shows string cobordism at 24 dims can be determined by elliptic genus.

The actions, anomalies, and quantization conditions allow the M2-brane and the M5-brane to support, in a natural way, structures beyond Spin on their worldvolumes. The main examples are twisted String structures. This also extends to twisted String^c structures, which we introduce and relate to twisted String structure…

Introduces string structures linking to loop spaces.

Study topological G₂ and Spin(7) strings at 1-loop using double complexes.

In this note we revisit the subject of anomaly cancelation in string theory and M-theory on manifolds with String structure and give three observations. First, that on String manifolds there is no E8 x E8 global anomaly in heterotic string theory. Second, that the description of the anomaly in the phase of the M-theory…

A virtual string is a scheme of self-intersections of a closed curve on a surface. We introduce virtual strings and study their geometric properties and homotopy invariants. We also discuss connections between virtual strings, Gauss words, and virtual knots.

String vertices proven in hyperbolic geometry, unique up to transformations.

End-to-end solution for recognizing handwritten numerals, avoiding traditional preprocessing steps.

A virtual $n$-string $α$ is a collection of $n$ oriented smooth generic loops on a surface $M$. A stabilization of $α$ is a surgery that results in attaching a handle to $M$ along disks avoiding $α$, and the inverse operation is a destabilization of $α$. We consider virtual $n$-strings up to virtual homotopy, i.e., seq…

We derive a recursion relation for hyperbolic string vertices and apply it to string field theory.

The multi dimensional string objects are introduced as a new alternative for an application of string models for time series forecasting in trading on financial markets. The objects are represented by open string with 2-endpoints and D2-brane, which are continuous enhancement of 1-endpoint open string model. We show ho…

Developing tools for computing string amplitudes with hyperbolic vertices.

STRING improves 2D and 3D position encodings for better performance.

Compact K3 metrics derived from string theory vacua.

In this paper we use 3-manifold techniques to illuminate the structure of the string link monoid. In particular, we give a prime decomposition theorem for string links on two components as well as give necessary conditions for string links to commute under the stacking operation.

This paper investigates methods for quantifying similarity between audio signals, specifically for the task of of cover song detection. We consider an information-theoretic approach, where we compute pairwise measures of predictability between time series. We compare discrete-valued approaches operating on quantised au…

Phylogenetic tree reconstruction is traditionally based on multiple sequence alignments (MSAs) and heavily depends on the validity of this information bottleneck. With increasing sequence divergence, the quality of MSAs decays quickly. Alignment-free methods, on the other hand, are based on abstract string comparisons …

Numbers and numerical vectors account for a large portion of data. However, recently the amount of string data generated has increased dramatically. Consequently, classifying string data is a common problem in many fields. The most widely used approach to this problem is to convert strings into numerical vectors using …