Study geodesic string counts on Riemann-Finsler manifolds, linking to KAM theory.
problem Counting geodesic strings on Riemann-Finsler manifolds.
method Using Fuller index and KAM theory, derive product formula for counts.
result Arithmetic constraints on geodesic string counts and existence of negative curvature metrics.
We combine and extend the work of Alexander & Antman \cite{alexander.82} and Fuller \cite{fuller.71,fuller.78} to give a framework within which precise definitions can be given of topological and geometrical quantities characterising the contortion of open rods undergoing large deformations under end loading. We use th…
High-frequency data cointegration framework developed with rigorous theory and tests.
problem Cointegration in high-frequency data with jumps and infinite activity.
method Regression-based estimation method and Dickey-Fuller type residual tests.
result Consistent and asymptotic limit theory for cointegration tests.
Study of Gromov-Witten theory on locally conformally symplectic manifolds, focusing on non-squeezing and holomorphic curves.
problem Understanding Gromov-Witten theory in the context of locally conformally symplectic manifolds.
method Analyzing holomorphic curves and applying Gromov non-squeezing theorem to $\lcs$ manifolds.
result Gromov non-squeezing theorem has C0 rigidity in dimension 4 for $\lcs$ manifolds. For the geodesic flow of an odd dimensional hyperbolic manifold we prove a Lefschetz type formula. The local terms are Fuller indices of the closed orbits. The global "Frobenius operator" is the generator of the flow and its action on tangential cohomology.
Study forecasts U.S. bond index using deep learning, finding persistence is key.
problem Forecasting U.S. aggregate bond index with deep learning methods.
method Constructed a stationary but maximally persistent representation of the bond index, evaluated using MLPs and CNNs.
result Deep learning models outperform traditional methods in short-horizon forecasting of bond indices.
The Weinstein conjecture is extended to a new class of manifolds.
problem Existence of Reeb 2-curves in locally conformally symplectic manifolds.
method Extended Gromov-Witten theory and elliptic curve counts.
result Partial verification of the conjecture in higher dimensions.
We find bounds on the difference between the writhing number of a smooth curve, and the writhing number of a polygon inscribed within. The proof is based on an extension of Fuller's difference of writhe formula to the case of polygonal curves. The results establish error bounds useful in the computation of writhe.
Study confirms weak-form market efficiency using machine learning on US stock data.
problem Validating weak-form market efficiency using machine learning.
method Conducted econometric tests and implemented algorithmic trading with five machine learning algorithms.
result No predictive power found in any machine learning model, reinforcing weak-form market efficiency.
The main ob jective of this research is to find the different types of elliptic triangulations for planar discs and spheres. We begin in Chapter 1 with the mandatory introduction. In the second chapter we define and study the notion of a patch, that is, a triangulation of a planar disc. By introducing a suitable notion…
Study detects Chinese stock market bubbles using LPPLS confidence indicator.
problem Early detection of stock market bubbles in China.
method LPPLS confidence indicator applied to CSI 300 index data.
result LPPLS detects positive and negative bubbles with high accuracy.
Optimal control trajectories have limited irregularities.
problem Regularity of time-optimal control trajectories in control-affine systems.
method Generic conditions on drift and controlled vector field are used to prove smoothness out of a countable set of times, up to K-th order iterated singularities.
result Control trajectories are smooth out of a countable set of times, with singularities limited to K-th order iterated.
The paper examines market efficiency in China and India post financial crises.
problem Testing market efficiency in emerging markets post crises.
method Examined daily returns using auto correlation tests, runs tests, and unit root tests.
result Both Chinese and Indian stock markets do not exhibit weak form of market efficiency.
Paper analyzes electricity price and demand data to detect cyber-attacks using time series methods.
problem Detecting cyber-attacks in electricity price and demand data.
method Time series analysis, including moving average, moving standard deviation, and augmented Dickey-Fuller test.
result Identified anomalies in the data using time-series stationary criteria.
Label aggregation makes learning robust to noisy labels.
problem Learning from noisy labels.
method Label aggregation and risk consistency.
result Aggregated labels lead to stronger consistency guarantees.
Temporal difference learning explained through gradient splitting, improving convergence times.
problem Learning value functions in Markov Decision Processes with linear approximations.
method Interpreting TD learning as gradient splitting and applying convergence proofs from gradient descent.
result Improved convergence times for TD learning, especially with a minor variation.
The purpose of this study is to estimate the production function and examine the structure of production in the mining sector of Iran. Several studies have already been conducted in estimating production functions of various economic sectors; however, less attention has been paid to mining sectors. After examining the …
Study on decentralization in DAOs and its effect on financial efficiency in DeFi.
problem Understanding the impact of decentralization on financial efficiency in blockchain-based governance.
method Analysis using Gini coefficient as an inequality indicator, comparing ROI of token owners.
result Real decentralization affects financial efficiency positively in DeFi.
Defines new invariants for Riemann-Finsler manifolds, generalizing Preissman's theorem.
problem Finding metrics with negative sectional curvature on compact products.
method Defining a Q-valued deformation invariant and using it to generalize Preissman's theorem. result First and mostly sharp generalizations of Preissman's theorem on non-existence of negative sectional curvature metrics.
Researchers analyze Gromov-Witten potentials of elliptic orbifolds, proving modularity.
problem Understanding modularity properties of Gromov-Witten potentials for elliptic orbifolds.
method Developed identities and identities between functions with properties generalizing mock modular forms.
result Complete understanding of modularity transformation properties of Cho, Hong, Kim, and Lau's functions.
Deep learning models outperform traditional methods in stock price prediction.
problem Improving stock price prediction accuracy using deep learning.
method Comparative analysis of deep learning models (LSTM, GRU) and traditional methods (ARIMA, ARMA) on historical data.
result Deep learning models, particularly LSTM, outperform traditional methods in predicting stock prices across different time horizons.
Paper proposes new estimators for error variance in high-dimensional linear models.
problem Estimating error variance in high-dimensional linear models.
method Proposes natural lasso and organic lasso estimators.
result Natural lasso estimator maximizes a penalized likelihood objective and has provably good performance.
A new clustering evaluation index based on density estimation.
problem Improving internal clustering evaluation indices.
method The index is a mixture of Ambiguous and Similarity sub-indices, calculated using density estimation.
result The new index significantly outperforms other internal clustering evaluation indices.
Study on symmetric operators on non-compact manifolds, focusing on their index modulo 2.
problem Investigating elliptic operators with a specific symmetry and their index modulo 2.
method Analysis of Callias-type operators on non-compact manifolds, establishing mod 2 versions of index theorems.
result Established mod 2 versions of the Gromov-Lawson relative index theorem, Callias index theorem, and Boutet de Monvel's index theorem for Toeplitz operators.
New index formula connects numerical and K-theoretic indices.
problem Equivariant index for proper group actions on manifolds.
method Developed a trace on group conjugacy classes to relate numerical and K-theoretic indices. result Shows that numerical index equals K-theoretic index under certain conditions. Researchers prove index invariance under cobordism for Callias-type operators.
problem Index calculation for elliptic operators on compact manifolds.
method Introduce cobordism of Callias-type operators and prove index invariance.
result Index is preserved by cobordism of Callias-type operators.
New index connects Diederich-Fornæss index to boundary conditions.
problem Understanding the Diederich-Fornæss index for complex domains.
method Defined and proved new index equivalence; used complex geometric analytic techniques.
result First precise non-trivial Diederich-Fornæss index in Euclidean spaces.
The paper explores global index formulas for one-dimensional holomorphic foliations.
problem Global index formulas for one-dimensional holomorphic foliations.
method Microlocal point of view and short proofs for existing index formulas.
result Generalizations of existing index formulas.
CCI30 is a new cryptocurrency index.
problem None explicitly stated in the abstract.
method Not specified in the abstract.
result Not specified in the abstract.
Explain Arnold's proof of the Morse index theorem using Maslov index.
problem Proving the Morse index theorem in Riemannian geometry.
method Using symplectic arguments and the Maslov index.
result Self-contained exposition of Arnold's proof.
The p-index improves investment performance for NYSE stocks but not for SSE stocks.
problem Improving investment performance for stocks using the p-index.
method Comparing different p-ratio strategies and empirical efficient frontiers for SSE and NYSE stocks.
result The p-index enhances investment performance for NYSE stocks but not for SSE stocks.
Study Whittle index learning algorithms for restless bandits with constant stepsizes.
problem Optimizing decisions in restless multi-armed bandits with constant stepsizes.
method Developed Q-learning algorithms with constant stepsizes for index learning in restless bandits, extending to DQN and function approximations.
result The algorithms learn the Whittle index effectively.
Paper introduces danceability index as a new bridge index definition.
problem Defining the bridge index in various mathematical contexts.
method Proves danceability index as equivalent to bridge index, extends to virtual knots.
result Danceability index is a new equivalent definition of the bridge index.
Constructs index class for manifolds with group action.
problem Index class construction for manifolds with group action.
method Constructs coarse index class with support condition using equivariant Dirac operator.
result Shows coarse relative index theorem and compatibility with suspension isomorphism.
New techniques simplify computing geometric index of links in solid tori.
problem Computing the geometric index of links in solid tori.
method Introducing geometric index for solid chambers and proving its computation under specific conditions.
result Simplified computation of geometric index for new examples.
A new index rebalancing strategy reduces large constituent weights without undesirable effects.
problem Undesirable effects of current Nasdaq-100 index rebalancing.
method A simple rebalancing strategy that avoids undesirable effects.
result Preserves the order of index weights and prevents maximum weight increase.
Study on symmetric braid index of ribbon knots, deriving bounds and characterizations.
problem Understanding the symmetric braid index of ribbon knots.
method Defining symmetric braid index, using Khovanov homology, and calculating bounds.
result Existence of knots with symmetric braid index greater than braid index.
Study proves bridge and braid indices match for twist positive knots.
problem Determining when bridge and braid indices are equal for knots.
method Used knot Floer torsion order to prove for all twist positive knots.
result Bridge and braid indices coincide for all twist positive knots.
Minimal grid diagrams for 15,735 knots with 14 crossings and arc index 14.
problem Representing prime knots with 14 crossings and specific arc indices using grid diagrams.
method Enumerated all prime knots with 14 crossings, categorized by arc index, and found minimal grid diagrams for those with arc index 14.
result 8,027 knots with arc index 13 and 15,735 knots with arc index 14 were represented by minimal grid diagrams.
The chord index extends knot invariants and has applications in virtual knot theory.
problem Defining and applying finite type invariants to virtual knots.
method Introducing chord index, indexed Jones polynomial, and indexed quandle.
result The chord index generalizes classical knot invariants and has applications in twisted knot theory.
Given a proper, cocompact action of a Lie groupoid, we define a higher index pairing between invariant elliptic differential operators and smooth groupoid cohomology classes. We prove a cohomological index formula for this pairing by applying the van Est map and algebraic index theory. Finally we discuss in examples th…
Proves the index of a Möbius band in 4D ball equals 5.
problem Determining the Morse index of critical non-orientable surfaces.
method Comparison theorem between Steklov spectral index and energy index.
result Proves the index of critical Möbius band in B4 equals 5. Enhanced indexation uses equity and index options for better performance.
problem Improving portfolio performance through enhanced indexation.
method Integrating index options into an enhanced indexation strategy based on second-order stochastic dominance.
result Introducing option strategies in enhanced indexation leads to improved out-of-sample performance.
Finite index subgroups of relatively hyperbolic groups have equal index.
problem Finite index subgroups of relatively hyperbolic groups have equal index.
method Demonstrating that the number of simplices in a simplicial classifying space grows linearly with index.
result Finite index subgroups of relatively hyperbolic groups have equal index.
The abstract discusses connecting quantum mechanics and algebraic index theories.
problem Exploring the connection between quantum mechanics and algebraic index theories.
method Explains how the classical algebraic index theorem can be proved in terms of BV quantization of topological quantum mechanics and 2d chiral CFT.
result Shows how the generating function of all genus Gromov-Witten invariants on elliptic curves is mirror equivalent to an elliptic chiral index.
Researchers construct an index map for contact manifolds using K-theory.
problem Constructing an index for maximally hypoelliptic operators on contact manifolds.
method Using Higson's construction for symbol class in K-theory, they derive a series of maps whose induced map in K-theory is the Heisenberg Atiyah-Singer index map.
result Explicit construction of a series of maps leading to the Heisenberg Atiyah-Singer index map.
Study of differential operators on von Neumann algebras with applications to index theory.
problem Index theory for differential operators on non-compact manifolds.
method Relative index and Callias-type index theorems for von Neumann indexes.
result Cobordism invariance of the index of Callias-type operators.
Analyzes necessary and sufficient conditions for domains to have trivial Diederich-Fornæss index.
problem Understanding domains with trivial Diederich-Fornæss index in complex spaces.
method New geometric analysis method based on Riemannian geometry and de Rham cohomology.
result Analytical and geometric conditions for domains to have trivial index.