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.

We prove that the binary classifiers of bit strings generated by random wide deep neural networks with ReLU activation function are biased towards simple functions. The simplicity is captured by the following two properties. For any given input bit string, the average Hamming distance of the closest input bit string wi…

Edit distance, also known as Levenshtein distance, is an essential way to compare two strings that proved to be particularly useful in the analysis of genetic sequences and natural language processing. However, edit distance is a discrete function that is known to be hard to optimize. This fact hampers the use of this …

Derives path integrals for perturbative strings on various backgrounds.

Gene annotation has traditionally required direct comparison of DNA sequences between an unknown gene and a database of known ones using string comparison methods. However, these methods do not provide useful information when a gene does not have a close match in the database. In addition, each comparison can be costly…

Identifies all perturbative vacua in bosonic string theory.

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…

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

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

Perturbative string amplitudes are correctly derived from the string geometry theory, which is one of the candidates of a non-perturbative formulation of string theory. In order to derive non-perturbative effects rather easily, we formulate topological string geometry theory. We derive the perturbative partition functi…

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

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.

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.

String topology coproduct and Turaev cobracket computed for surfaces.

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…

Cobordism of virtual string links on $n$ strands is a combinatorial generalization of link cobordism. There exists a bijection between virtual string links up to cobordisms and elements of the group $\mathbb{Z}^{n(n-1)}$. This paper also shows that virtual string links up to unwelded equivalence are classified by those…

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

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…

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.

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.

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.

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 …

The Tong-Yang-Ma representations are extended to string links and welded string links.

Analyzes string topology operations using Chen's integrals and homotopy transfer.

Extends Goldberg's result for string links over surfaces.

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 …

In this paper we compute the sharp lower bounds for the crossing number of $n$-string $k$-loop essential tangles. For essential tangles with only string components, we characterise the ones with the minimum crossing number for a given number of components, both when the tangle has knotted strings or only unknotted stri…