Formula for foliations' singularities in complex projective spaces.
problem Counting singularities of foliations on complex projective spaces.
method Global residue formula for logarithmic indices of foliations with isolated singularities.
result Formula for the number of singularities in the complement of the invariant divisor on complex projective 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.
Proves a Baum--Bott formula for foliations by curves with logarithmic terms.
problem Analyzing singularities and smoothness in foliations by curves.
method Logarithmic Baum--Bott residues for foliated triples (X,F,D), relating to Poincaré's Problem and GSV indices. result Logarithmic Baum--Bott residues generalize Aleksandrov logarithmic index for vector fields on hypersurfaces.
Logarithmic regret strategies for safe multi-armed bandits with safety risk constraints.
problem Maximizing reward while avoiding unsafe arms under safety risk constraints.
method Doubly optimistic strategies with pseudo-regret formulation.
result Logarithmic regret bounds for safe multi-armed bandits.
Proves new fixed point formulae for complex manifolds with boundary.
problem Fixed points on complex manifolds with boundary conditions.
method Logarithmic Lefschetz fixed point formulae, normal rescaling, relative duality.
result Resonant boundary terms record normal contact and tangential multiplicity.
The study compares differencing methods for financial data and finds fractional differencing improves model performance.
problem Improving financial time series forecasting models using appropriate data transformation techniques.
method Comparative analysis of traditional logarithmic returns and fractional differencing methods, including tempered extensions.
result Fractional differencing methods improve model forecasting performance and trading strategy effectiveness.
We find a nonlinear dependence between an indicator of the degree of multiscaling of log-price time series of a stock and the average correlation of the stock with respect to the other stocks traded in the same market. This result is a robust stylized fact holding for different financial markets. We investigate this re…
A robust bandit algorithm uses Dirichlet sampling to minimize regret under various distributional assumptions.
problem Robustness of bandit algorithms to model misspecification.
method Dirichlet Sampling (DS) algorithm based on pairwise comparisons and re-sampling of arm observations.
result Different DS variants achieve optimal regret guarantees for bounded distributions and logarithmic regret for semi-bounded distributions.
The gain-loss asymmetry, observed in the inverse statistics of stock indices is present for logarithmic return levels that are over 2%, and it is the result of the non-Pearson type auto-correlations in the index. These non-Pearson type correlations can be viewed also as functionally dependent daily volatilities, ext…
This study analyzes economic policy uncertainty indices using visibility graphs.
problem Understanding the role of economic policy uncertainty in global economies.
method Visibility graph algorithm applied to economic policy uncertainty indices.
result The economic policy uncertainty indices exhibit persistent behavior and scale-free networks.
Study improves privacy-preserving online prediction from experts with speed-ups.
problem Privacy-preserving online prediction from experts with speed-ups.
method Differentially private federated online prediction algorithms.
result Achieves m-fold regret speed-up with low-loss expert in federated setting. We make an extensive empirical study of the market impact of large orders (metaorders) executed in the U.S. equity market between 2007 and 2009. We show that the square root market impact formula, which is widely used in the industry and supported by previous published research, provides a good fit only across about tw…
Following our previous investigation of the USA Standard and Poor index anti-bubble that started in August 2000, we analyze thirty eight world stock market indices and identify 21 anti-bubble. An ``anti-bubble'' is defined as a self-fulfilling decreasing price created by positive price-to-price feedbacks feeding overal…
Study predicts NFT bubbles using LPPL model.
problem Tackles bubble prediction of NFTs.
method Applied logarithmic periodic power law (LPPL) model to NFT price data.
result NFTs, Decentraland, and ArtBlocks are in bubbles, while Ethereum Name Service is in a negative bubble.
Modeling financial market dynamics with noise and fundamentalist agents.
problem Understanding opinion formation and market behavior in financial markets.
method Agent-based model with Erdös-Rényi random graph structure, incorporating anxiety parameter.
result Model accurately reproduces key market features like fat-tailed returns and volatility clustering.
Paper tackles confounded ANMs, estimating ACEs with minimal interventions.
problem Estimating causal effects in the presence of unobserved confounders.
method Interventional distributions and randomized algorithm to reduce the number of required interventions.
result Poly-logarithmic number of interventions sufficient to infer causal effects in confounded ANMs.
The paper uses CPI growth rates to improve LGD predictions for CRE loans.
problem Challenges in forecasting LGD for CRE loans due to extended resolution times and restricted data.
method Combines internal and public data, including CPI growth rates, to forecast CRE LGD.
result Incorporating CPI at the time of default improves LGD prediction accuracy.
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.
We investigate the correlation properties of transaction data from the New York Stock Exchange. The trading activity f(t) of each stock displays a crossover from weaker to stronger correlations at time scales 60-390 minutes. In both regimes, the Hurst exponent H depends logarithmically on the liquidity of the stock, me…
In this paper, we introduce the notions of logarithmic Poisson structure and logarithmic principal Poisson structure; we prove that the latter induces a representation by logarithmic derivation of the module of logarithmic Kahler differentials; therefore, it induces a differential complex from which we derive the notio…
The highly detailed international trade data among all countries in the world during 1971-2000 shows that the kinds of export goods and the logarithmic GDP (gross domestic production) of a country has an S-shaped relationship. This indicates all countries can be divided into three stages accordingly. First, the poor co…
Model monthly VIX and stock returns using log-Heston model.
problem Modeling monthly VIX and stock index returns accurately.
method Log-Heston model applied to logarithm of VIX as an autoregression, normalizing stock returns by VIX.
result Model captures independent, identically distributed Gaussian stock returns after normalization.
Study analyzes foreign exchange rates using MFDFA, revealing multifractality and its sources.
problem Analyzing multifractality in foreign exchange rates.
method Multifractal Detrended Fluctuation Analysis (MFDFA) applied to shuffled and phase-randomized return series.
result Sources of multifractality differ among currencies: US dollar fat tails, British Pound and Euro long-range correlations, Japanese Yen broad tails.
Study predicts 2015 Chinese stock market bubble using LPPLS model.
problem Detecting and predicting the 2015 Chinese stock market bubble.
method Calibrated Log Periodic Power Law Singularity (LPPLS) model, Lomb spectral analysis, Unit-root tests, CMA-ES optimization.
result The LPPLS model can predict the actual critical day (tc) two months before the bubble crash.
This paper explores using nonlinear control for robust logarithmic growth in coin flipping games.
problem Tackles the use of nonlinear control in recursive betting games with logarithmic growth.
method Formulates a robust nonlinear control problem for a simple coin flipping game, considering a probability range for the coin's bias.
result Provides a closed-form description of the optimal robust nonlinear controller, which outperforms linear controllers.
Study rigidity by logarithmic capacity and related functions.
problem Rigidity phenomena in kernel functions and capacities.
method Exploration of Bergman kernel, logarithmic capacity, Green's function, and Euclidean distance/volume.
result Established rigidity theorems by logarithmic capacity.
Study excess logarithmic residues for foliations to bound invariant hypersurfaces and test log canonicity.
problem Bounding invariant hypersurfaces and testing log canonicity of singularities.
method Introduce excess logarithmic residues, prove residue formula, derive Poincaré-type bound, and use them to recover log discrepancies.
result Componentwise logarithmic residues of a lifted foliation along the exceptional divisor recover log discrepancies of singularities.
Logarithmic connections on principal bundles over normal varieties are studied.
problem Existence and properties of logarithmic connections on principal bundles over normal varieties.
method Introducing logarithmic connections, showing equivalence to covariant derivatives, and proving existence conditions.
result Existence of logarithmic connections on principal bundles over normal varieties is equivalent to certain conditions on the associated vector bundles and adjoint bundles.
Study real logarithms of semi-simple matrices, focusing on differential structure.
problem Understanding the differential structure of real logarithms of semi-simple matrices.
method Examines the differential structure of real logarithms of semi-simple matrices under specific matrix types.
result Characterizes the differential structure of real logarithms of semi-simple matrices.
Introduces logarithmic Cartan geometry on complex manifolds with singularities.
problem Holomorphic Cartan geometry with singularities.
method Definition and study of logarithmic Cartan geometry on complex manifolds with polar part supported on a normal crossing divisor.
result Push-forward of a Cartan geometry constructed using a finite Galois ramified covering is a logarithmic Cartan geometry.
We present a new method to solve certain ∂ˉ-equations for logarithmic differential forms by using harmonic integral theory for currents on Kahler manifolds. The result can be considered as a ∂ˉ-lemma for logarithmic forms. As applications, we generalize the result of Deligne about closedness…
We extend the lifecycle model (LCM) of consumption over a random horizon (a.k.a. the Yaari model) to a world in which (i.) the force of mortality obeys a diffusion process as opposed to being deterministic, and (ii.) a consumer can adapt their consumption strategy to new information about their mortality rate (a.k.a. h…
Local logarithmic Brunn-Minkowski holds for zonoids.
problem Logarithmic Brunn-Minkowski conjecture for zonoids
method Bochner method variant
result Local form of conjecture proven for zonoids
We present evidence, that if a large enough set of high resolution stock market data is analyzed, certain analogies with physics -- such as scaling and universality -- fail to capture the full complexity of such data. Despite earlier expectations, the mean value per trade, the mean number of trades per minute and the m…
New framework for logarithmically divergent integrals on manifolds with corners.
problem Logarithmically divergent integrals on manifolds with corners.
method Introduces new geometric framework and morphisms in logarithmic geometry.
result Functorial characterization of regularized integration.
Directly proves logarithmic systolic growth for all hyperbolic surfaces.
problem Proving logarithmic systolic growth for all hyperbolic surfaces.
method Using original Brooks/Buser-Sarnak surfaces through a direct approach.
result Directly proves logarithmic systolic growth for all hyperbolic surfaces.
Logarithmic separation profile in hyperbolic groups shows hierarchical structure.
problem Understanding hierarchical structure in hyperbolic groups with logarithmic separation.
method Proving groups with logarithmic separation split over cyclic groups and providing counterexamples.
result Not all groups with hierarchical structure have logarithmic separation profile.
Paper uses ABP method to prove logarithmic Sobolev inequalities on curved spaces.
problem Proving logarithmic Sobolev inequalities on manifolds with nonnegative curvature.
method Employing the ABP method developed by Brendle.
result Sharp L2 and Lp logarithmic Sobolev inequalities established. Investment and consumption strategy optimized under uncertain conditions.
problem Optimal investment and consumption under logarithmic utility and uncertainty model.
method Characterized using quadratic BSDE.
result Optimal solution found.
The paper constructs a Saito basis for a specific class of divisors and applies it to logarithmic Poisson geometry.
problem Investigating a class of non-quasi-homogeneous free divisors and their logarithmic vector fields.
method Explicitly constructing a Saito basis for the module of logarithmic vector fields and applying it to logarithmic Poisson geometry.
result The construction of the Saito basis and the Lie-Rinehart algebra structure on the sheaf of logarithmic 1-forms.
Extended logarithm for solvable elements in mapping class groups.
problem Logarithm of Johnson map extension to solvable elements.
method Extension to exponential solvable elements in mapping class groups using solvable Lie groups.
result Solvability of extended logarithm.
Functorial correspondence found between logarithmic connections and abelian connections.
problem Establishing a relationship between logarithmic sl2-connections and abelian connections. method Constructing inverse functors and a canonical cocycle.
result Functorial correspondence proved between logarithmic sl2-connections and abelian connections. Study of conformal logarithmic Laplacian on sphere, connecting Yamabe problems and Sobolev spaces.
problem Yamabe-type problems and Sobolev spaces on the sphere.
method Detailed spectral analysis, conformal invariance, and Hilbert space introduction.
result Established precise connection between sphere and \(\mathbb{R}^N\) logarithmic Laplacian.
In this work, we give a formula for the logarithmic invariant of knots in terms of certain derivatives of the colored Jones invariant. This invariant is related to the logarithmic conformal field theory, and was defined by using the centers in the radical of the restricted quantum group at root of unity. A relation bet…
Paper finds necessary condition for logarithmic Minkowski problem in higher dimensions.
problem Logarithmic Minkowski problem in higher dimensions.
method Established a necessary condition through generalization and refinement of previous work.
result Generalizes and refines necessary condition for logarithmic Minkowski problem.
Bandit algorithms struggle with consistent performance and robustness.
problem Achieving consistent and robust performance in stochastic multi-armed bandit settings.
method Analyzing regret minimization trade-offs and proposing distribution-oblivious algorithms.
result Logarithmic regret is inconsistent and super-logarithmic regret is necessary for consistent learning.
We construct helicoid-like embedded minimal disks with axes along self-similar curves modeled on logarithmic spirals. The surfaces have a self-similarity inherited from the curves and the nature of the construction. Moreover, inside of a "logarithmic cone", the surfaces are embedded.
Solves a discrete logarithmic Minkowski problem for electrostatic p-capacity.
problem Characterize measures generated by electrostatic p-capacity.
method Solves the discrete logarithmic Minkowski problem for 1 < p < n.
result Solves the discrete logarithmic Minkowski problem for measures in general position.