We introduce a new class of nonstationary kernels, which we derive as covariance functions of a novel family of stochastic processes we refer to as string Gaussian processes (string GPs). We construct string GPs to allow for multiple types of local patterns in the data, while ensuring a mild global regularity condition…
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48 results for “stochastic string”
The paper models liquidity in financial markets using a string model of order books.
problem Tackles the arbitrage and pricing issues in financial markets.
method Develops a dynamic market model with order books and proves no arbitrage under certain conditions.
result Generically, there is no arbitrage in the model when noise is a stochastic string.
The paper constructs Markov processes for stochastic heat equations on infinite strings with manifold values.
problem Constructing Markov processes for stochastic heat equations on infinite strings with manifold values.
method Constructing conservative Markov processes corresponding to martingale solutions to stochastic heat equations on or with values in a Riemannian manifold.
result The process exhibits exponential ergodicity if the Ricci curvature is strictly positive and non-ergodicity if the sectional curvature is negative.
This paper offers a new class of models of the term structure of interest rates. We allow each instantaneous forward rate to be driven by a different stochastic shock, constrained in such a way as to keep the forward rate curve continuous. We term the process followed by the shocks to the forward curve ``stochastic str…
In this paper we introduce a novel framework for making exact nonparametric Bayesian inference on latent functions, that is particularly suitable for Big Data tasks. Firstly, we introduce a class of stochastic processes we refer to as string Gaussian processes (string GPs), which are not to be mistaken for Gaussian pro…
We propose a formulation of the term structure of interest rates in which the forward curve is seen as the deformation of a string. We derive the general condition that the partial differential equations governing the motion of such string must obey in order to account for the condition of absence of arbitrage opportun…
On Bond Portfolio Managementmath.OC
This paper describes a new method of bond portfolio optimization based on stochastic string models of correlation structure in bond returns. The paper shows how to approximate correlation function of bond returns, compute the optimal portfolio allocation using Wiener-Hopf factorization, and check whether a collection o…
Derives path integrals for perturbative strings on various backgrounds.
problem Calculating path integrals for strings on curved backgrounds.
method Derives path integrals from string geometry theory by considering fluctuations around string backgrounds.
result Derives path integrals of all order perturbative strings on various backgrounds.
Topological string theory derived from string geometry for non-perturbative effects.
problem Deriving non-perturbative effects in string theory.
method Formulating topological string geometry theory and deriving the partition function from fluctuations around a classical solution.
result Perturbative partition function of topological string theory derived.
Identifies all perturbative vacua in bosonic string theory.
problem Identifying all perturbative vacua in bosonic string theory.
method Completely identified perturbative vacua through string fluctuations.
result Derivation of path-integrals up to any order from fluctuations.
String geometry theory connects strings to space-time and finds string vacua.
problem Identify and find the global minimum of the string vacuum.
method Identify perturbative vacua, derive path-integrals, and solve the global minimum using analytical and numerical methods.
result The global minimum of the effective potential is the string vacuum.
Derives path-integrals for superstrings on curved backgrounds using string geometry theory.
problem Calculating path-integrals for superstrings on curved backgrounds.
method Derives path-integrals from string geometry theory by considering fluctuations around string backgrounds.
result Derives path-integrals for perturbative superstrings on all string backgrounds.
This paper classifies virtual string links up to cobordism using group theory.
problem Classifying virtual string links up to cobordism.
method Using group theory, specifically the group .
result Virtual string links up to cobordism are classified by elements of .
Chiral string integrands simplify to ambitwistor string integrands in the tensionless limit.
problem Understanding the relationship between chiral and ambitwistor string integrands.
method Analyzing the tensionless limit of chiral superstring integrands.
result Chiral superstring integrands reduce 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…
Black holes offer insights into machine learning's loss landscapes.
problem Understanding the loss landscape in machine learning.
method Comparing machine learning loss landscapes to black hole entropy.
result Black holes provide an infinite family of potential landscapes with known minima.
Research extends Cahn's results on virtual strings to connected non-parallel strings.
problem Understanding the homotopy of virtual strings and their minimal representatives.
method Generalization of Cahn's results using stabilizations, destabilizations, and homotopies.
result Kadokami's statement about virtual strings holds for connected non-parallel strings but not for all strings.
New formulas link string bordism to integers.
problem Understanding the third string bordism group.
method Geometric string structures and 3d TQFT.
result Integral formulas realize the string bordism isomorphism.
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.
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.
Introduces holomorphic string algebroids and classifies them.
problem Classifying holomorphic string algebroids.
method Using Courant extensions and inner morphisms of holomorphic Courant algebroids.
result Classification of string algebroids via Cech cohomology.
BOSS optimizes string inputs using string kernels and genetic algorithms.
problem Optimizing string inputs with constraints.
method Bayesian optimization over string kernels and genetic algorithms.
result Significantly improved optimization across various string constraints.
String topology coproduct and Turaev cobracket computed for surfaces.
problem Computing string topology coproduct and cobracket for surfaces.
method Algorithm to compute coproduct of cyclic words in terms of generators of the fundamental group.
result String cobracket is the negative of Turaev cobracket.
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.
problem Determining string cobordism at dimension 24.
method Using elliptic genus as an invariant.
result Shows string cobordism at 24 dims can be determined by elliptic genus.
New string and D2-brane models improve financial market trend forecasting.
problem Improving time series forecasting for financial markets.
method Introducing string and D2-brane models to analyze currency rates and their stability.
result New models enhance the accuracy of time series forecasting for currency exchange pairs.
Geometric and topological structures related to M-branes II: Twisted String and String^c structureshep-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.
problem Understanding geometric string structures.
method Explains connections to loop spaces.
result String structures linked to loop spaces.
Multistring based matricesmath.GT
A new method for virtual homotopy classes of virtual strings.
problem Addressing an open problem of Turaev regarding virtual homotopy classes of virtual strings.
method Generalizing Turaev's method to multistring based matrices for virtual n-strings.
result Construction of similar invariants for virtual homotopy classes of virtual n-strings.
Study topological G₂ and Spin(7) strings at 1-loop using double complexes.
problem Calculate topological string partition functions at 1-loop.
method Define double complexes for supersymmetric backgrounds using generalised geometry, compute partition functions as alternating products of determinants of Laplacians.
result Reproduce known results for G₂ string and predict for Spin(7) string.
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…
String vertices proven in hyperbolic geometry, unique up to transformations.
problem Existence and uniqueness of string vertices in string field theory.
method Homological proof using hyperbolic metrics and geodesic boundaries.
result String vertices are sets of surfaces with systole greater than or equal to .
Virtual stringsmath.GT
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.
problem Handwritten numeral string recognition with traditional preprocessing steps.
method YoLo-based model for automatic detection and recognition, avoiding heuristic-based preprocessing and segmentation.
result Proposed method reduces complexity and is a feasible end-to-end solution for numeral string recognition.
We derive a recursion relation for hyperbolic string vertices and apply it to string field theory.
problem Deriving a recursion relation for hyperbolic string vertices and its implications for string field theory.
method Using systolic volumes and a modified Mirzakhani's recursion, we construct a higher-order vertex determination for hyperbolic string field theory.
result The higher order vertices in hyperbolic string field theory are determined by the cubic vertex iteratively for any background.
Proves Witten genus vanishes for certain string intersections.
problem Proving the Witten genus vanishes for specific string intersections.
method Using equivariant localization formula of toric varieties.
result Witten genus vanishes for some string complete intersections.
Summarizes spin geometry in supergravity and string theory.
problem Spin geometry in supergravity and string theory.
method Investigation of real Clifford modules.
result Summary of recent findings in spin geometry.
Global solution found for string heat flow on surfaces.
problem Existence of global weak solutions for bosonic string heat flow.
method Proved existence with smallness conditions on form and potential.
result Global weak solution found, smooth with finitely many singular points.
Developing tools for computing string amplitudes with hyperbolic vertices.
problem Computing off-shell string amplitudes with new vertices.
method Constructing local coordinates and investigating limits for hyperbolic three-string vertex.
result Derived conservation laws and performed sample computations.
New string kernels discover global properties through random feature maps, avoiding quadratic complexity.
problem Existing string kernels struggle with capturing long patterns, maintaining positive definiteness, and handling large datasets efficiently.
method Proposes a new class of global string kernels using random feature maps to discover global properties through global alignments, ensuring positive definiteness and linear computational cost.
result Random String Embeddings (RSE) achieve better or comparable accuracy to state-of-the-art methods, especially for longer strings.
STRING improves 2D and 3D position encodings for better performance.
problem Efficient and accurate position encoding for 2D and 3D applications.
method STRING extends Rotary Position Encodings with a unifying theoretical framework, maintaining translation invariance and low computational cost.
result STRING shows substantial gains in open-vocabulary object detection and robotics.
Space-efficient feature maps improve string alignment kernel scalability.
problem String alignment kernels scale poorly with quadratic complexity, limiting large-scale applications.
method Presented SFMEDM, a space-efficient feature map for edit distance with moves using metric embedding and random Fourier features.
result Demonstrated superior performance of SFMEDM in prediction accuracy, scalability, and computation efficiency.
Compact K3 metrics derived from string theory vacua.
problem Finding Ricci-flat metrics on K3 surfaces.
method Using little string theory and BPS degeneracies.
result Systematic procedure for determining K3 metrics.
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.
problem Extending Tong-Yang-Ma representations to string links and welded string links.
method Using the method of Silver and Williams, the authors extend the Tong-Yang-Ma representations.
result The kernels of the extended representations can be described using linking numbers.
Analyzes string topology operations using Chen's integrals and homotopy transfer.
problem Relating string topology to perturbative Chern-Simons theory.
method Develops integrals over configuration spaces and applies homotopy transfer.
result Intertwines involutive Lie bialgebra structures on homology.