Infinitary braid groupsmath.GT
Study of infinite-string braids as a limit of finite ones.
problem Properties of infinite-string braids.
method Investigate via direct limit of finite n-braid groups.
result Basic properties of countable-string braids.
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arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,341 papers · 148 categories
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48 results for “countable strings”
String graphs are closely related to planar graphs in terms of distances.
problem Understanding the relationship between string graphs and planar graphs.
method Proved quasi-isometric relationship between string graphs and planar graphs.
result String graphs are quasi-isometric to planar graphs.
New findings show language models can't simultaneously avoid hallucinations and capture all language richness.
problem Achieving both valid output and full language richness in language generation.
method Investigates language generation within a statistical setting, focusing on consistency and breadth.
result For most collections of candidate languages, a language model cannot simultaneously avoid hallucinations and capture all language richness.
Study on generating and identifying languages privately, showing privacy imposes costs and creates barriers.
problem Generating and identifying languages privately in the limit model.
method Introduced a continual release model under differential privacy constraints, proving both positive and negative results.
result Privacy imposes quantitative and qualitative costs, and creates fundamental barriers for identification.
We show that for every positive curvature Kahler-Einstein manifold in dimension 2n there is a countably infinite class of associated Sasaki-Einstein manifolds X_{2n+3} in dimension 2n+3. When n=1 we recover a recently discovered family of supersymmetric AdS_5 x X_5 solutions of type IIB string theory, while when n=2 we…
On Characterizations for Language Generation: Interplay of Hallucinations, Breadth, and Stabilitycs.LG
We characterize language generation with stability and breadth, proving impossibility results.
problem Characterizing and proving impossibility results for language generation with stability and breadth.
method Analysis of existing notions of breadth and stability, proving lower bounds.
result Proven impossibility of generating with higher perplexity or lower hallucination rate for stable generators.
Countable modular groups found on surfaces with infinite type.
problem Finding modular groups of infinite type surfaces.
method Proving countable modular groups for orientable infinite type surfaces.
result Every orientable infinite type surface has a countable modular group.
Study chaotic behavior in homeomorphism groups of countable products of spaces.
problem Investigate chaotic behavior in homeomorphism groups of countable products of various metrizable topological spaces.
method Construct numerous examples of chaotic groups of homeomorphisms of countable products of spaces.
result New chaotic groups of homeomorphisms of countable products of various metrizable topological spaces are discovered.
Finite groups can be represented as origami automorphisms, extended to countable groups.
problem Representing countable groups as automorphisms of origamis.
method Considering origamis on the Loch Ness monster.
result Every countable group can be represented as origami automorphisms.
We classify up to coarse equivalence all countable abelian groups of finite torsion free rank. The Q-cohomological dimension and the torsion free rank are the two invariants that give us such classification. We also prove that any countable abelian group of finite torsion free rank is coarsely equivalent to Z^n + H whe…
Mixing endomorphisms found on toroidal groups and their products.
problem Finding topologically mixing endomorphisms on toroidal groups and their products.
method Analyzing continuous endomorphisms on toroidal groups and their countable products.
result Proves existence of infinitely many topologically mixing endomorphisms on countable infinite toroidal groups.
Extends inf-convolution to countable risk measures for risk sharing.
problem Limited inf-convolution theory to finite sets of risk measures.
method Extends inf-convolution to countable sets, investigates properties and results.
result Generalizes known properties and results to countable case.
We prove that two countable locally finite-by-abelian groups G,H endowed with proper left-invariant metrics are coarsely equivalent if and only if their asymptotic dimensions coincide and the groups are either both finitely-generated or both are infinitely generated. On the other hand, we show that each countable group…
Every countable compact subset of sphere is tame.
problem Characterizing compact subsets of spheres.
method Proving homeomorphic complements imply homeomorphic subsets.
result Wild subspaces like Antoine contain Cantor sets.
Finite approximations help reconstruct countable metric and ultrametric spaces.
problem Reconstructing countable metric and ultrametric spaces.
method Topological reconstruction using inverse limits of finite spaces.
result Countable metric and ultrametric spaces can be reconstructed as finite approximations.
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.
Compact groups can be represented as dessin automorphisms.
problem Representing all countable groups as automorphisms of dessins.
method Constructive proof using non-compact dessins.
result Any tame action of a countable group is realizable as a dessin automorphism.
Generalizes theorem for topological -manifolds with linear Lie groups .
problem Understanding topological -manifolds with linear Lie groups .
method Using countable CW complexes and Palais-proper actions.
result Topological -manifolds have -homotopy type of countable -CW complexes.
We compute the asymptotic dimension of the rationals given with an invariant proper metric. Also, we show that a countable torsion abelian group taken with an invariant proper metric has asymptotic dimension zero.
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.
Generative models can still learn from contaminated data, but with limitations.
problem How much contamination can generative models tolerate?
method Characterized robustness under contaminated enumerations, proving generation is achievable for all countable collections if contamination fraction converges to zero.
result Generation under contamination is achievable for all countable collections if contamination fraction converges to zero, but dense generation is strictly less robust.
For every countable group G we construct a compact path connected subspace K of R^4 whose fundamental group is isomorphic to G. Our construction is much simpler than the one found recently by Virk.
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…
We prove that for every countable group G there exists a hyperbolic 3-manifold M such that the isometry group of M, the mapping class group of M, and the outer automorphism group of the fundamental group of M are isomorphic to G.
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.
New algorithm for countable bandits with optimal regret.
problem Stochastic bandit problem with countably many arms.
method Fully adaptive online learning algorithm with O(log n) expected cumulative regret.
result Achieves optimal regret of O(log n) after any number of plays n.
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…
We show that C^1 hypersurfaces in the Heisenberg group are countably N-rectifiable. As a corollary, this shows that all C^1_H graphs over the xy-plane are countable N-rectifiable, showing the equivalence of this notion of rectifiability with that of Franchi, Serra Cassano and Serapioni for such surfaces.
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 .