arXiv research

BOSS optimizes string inputs using string kernels and genetic algorithms.

In this paper, we discuss Hochschild chain models for some of the string topology operations. We use these models to simplify the proofs and computations of some of the results in string topology. Along the way we also make some new observations. We further discuss how nonnilpotent local level homology classes with res…

String similarity models are vital for record linkage, entity resolution, and search. In this work, we present STANCE --a learned model for computing the similarity of two strings. Our approach encodes the characters of each string, aligns the encodings using Sinkhorn Iteration (alignment is posed as an instance of opt…

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 …

Variational autoencoders (VAEs) defined over SMILES string and graph-based representations of molecules promise to improve the optimization of molecular properties, thereby revolutionizing the pharmaceuticals and materials industries. However, these VAEs are hindered by the non-unique nature of SMILES strings and the c…

Derives path integrals for perturbative strings on various backgrounds.

Identifies all perturbative vacua in bosonic string theory.

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

Geometric flow on symplectic manifolds connects to Type IIA string theory.

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…

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.

String topology coproduct and Turaev cobracket computed for surfaces.

We have developed a novel prediction method based on string invariants. The method does not require learning but a small set of parameters must be set to achieve optimal performance. We have implemented an evolutionary algorithm for the parametric optimization. We have tested the performance of the method on artificial…

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.

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.

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

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.

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.

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…

Decomposes string links in a surface into prime components.

Cohomotopy charge quantization implies String structure on M5-branes.

Constructs a representation of the string 2-group on a von Neumann algebra.

A virtual string can be defined as a closed curve on a surface modulo certain equivalence relations. Turaev defined several invariants of virtual strings which we use to produce a table of virtual strings up to 4 crossings. We discuss progress in extending the tabulation to 5 crossings. We also provide a counter-exampl…

In this paper, we give a complete set of finite type string link invariants of degree <5. In addition to Milnor invariants, these include several string link invariants constructed by evaluating knot invariants on certain closure of (cabled) string links. We show that finite type invariants classify string links up to …

In this paper we investigate the virtual string links via a probabilistic interpretation. This representation can be used to distinguish some virtual string links from classical string links. In order to study the algebraic structure behind this probabilistic interpretation we introduce the notion of virtual flat biqua…

We give a brief overview of the theory of complex dimensions of real (archimedean) fractal strings via an illustrative example, the ordinary Cantor string, and a detailed survey of the theory of p-adic (nonarchimedean) fractal strings and their complex dimensions. Moreover, we present an explicit volume formula for the…

A virtual $n$-string is a chord diagram with $n$ core circles and a collection of arrows between core circles. We consider virtual $n$-strings up to virtual homotopy, compositions of flat virtual Reidemeister moves on chord diagrams. Given a virtual 1-string $α$, Turaev associated a based matrix that encodes invariants…

Proves Stolz conjecture for specific types of manifolds.