Study proves curvature estimates for Kerr spacetime's linearized perturbations.
problem Proving elliptic L2(S2)-estimates for linearised curvature quantities in Kerr spacetime. method Applies linearised system from doctoral thesis, covers full sub-extremal range of Kerr parameters.
result Elliptic L2(S2)-estimates for linearised curvature quantities in the full sub-extremal range of Kerr parameters. New framework for gravitational perturbations of Kerr spacetimes, focusing on stability.
problem Stability of Kerr spacetimes to gravitational perturbations.
method New geometric framework with tailored null frames and gauge, reformulating Einstein equations.
result Derivation of linearised vacuum Einstein equations in the new framework.
In a recent paper, the authors established the uniqueness of photon spheres in static vacuum asymptotically flat spacetimes by adapting Bunting and Masood-ul-Alam's proof of static vacuum black hole uniqueness. Here, we establish uniqueness of suitably defined sub-extremal photon spheres in static electro-vacuum asympt…
Study on black holes and photon surfaces in 4D spacetimes, proving uniqueness theorems.
problem Uniqueness of black hole and photon surfaces in 4D spacetimes.
method Potential theory approach, self-contained proofs for known and new cases.
result Proves new results for connected photon spheres and photon surfaces in the extremal case, and super-extremal case.
Study axisymmetric waves on extremal Kerr spacetime using physical-space estimates.
problem Obtain integrated local energy decay estimates for axisymmetric waves on extremal Kerr backgrounds.
method Use physical-space analysis and a method introduced by Stogin, simplifying Aretakis' derivation.
result Extend Morawetz estimates to extremal Kerr spacetime using purely classical currents.
Global existence and boundedness proved for quasilinear wave equations on Kerr black holes.
problem Global existence and boundedness for quasilinear wave equations on Kerr black holes.
method Combines linear inhomogeneous estimates on Kerr backgrounds and tailored physical space currents.
result Global existence, boundedness and decay for small data solutions to quasilinear wave equations on Kerr black holes.
This paper constructs charged Riemannian manifolds to test Penrose inequality.
problem Testing the Riemannian Penrose Inequality with charged manifolds.
method Constructing asymptotically hyperbolic or Euclidean extensions with electric charge.
result Suggests instability of the generalized Riemannian Penrose Inequality.
Closed and broken electromagnetic orbits in Kerr-Newman spacetime
problem Constructing closed and broken electromagnetic orbits in the Kerr-Newman spacetime
method Constructing smooth closed electromagnetic orbits tangent to the axial Killing field and proving the existence of spherical electromagnetic orbits
result Proving the existence of spherical electromagnetic orbits and constructing closed broken electromagnetic orbits
Characterizes a general range decreasing group homomorphism.
problem Understanding range decreasing group homomorphisms in the entire mapping group.
method Characterization of a general range decreasing group homomorphism.
result Computes a particular class of homomorphisms and identifies all range decreasing group homomorphisms on specific mapping groups.
This paper looks into the analysis of the long-range auto-correlations and cross-correlations in bond market. Based on Detrended Moving Average (DMA) method, empirical results present a clear evidence of long-range persistence that exists in one year scale. The degree of long-range correlation related to maturities has…
When a feed-forward neural network (FNN) is trained for source ranging in an ocean waveguide, it is difficult evaluating the range accuracy of the FNN on unlabeled test data. A fitting-based early stopping (FEAST) method is introduced to evaluate the range error of the FNN on test data where the distance of source is u…
Transformers can perform well with less long-range memory.
problem The need for deep long-range memory in Transformers for language modeling.
method Performed interventions to show performance can be achieved with fewer long-range memories and by limiting attention range.
result Comparable performance can be achieved with 6X fewer long-range memories and better performance with limited attention range.
Research on long-range memory in financial and social systems using various models.
problem Understanding the nature of long-range memory in socioeconomic systems.
method Various Markov processes including point processes, stochastic differential equations, and agent-based models.
result New estimators of self-similarity and long-range memory for non-Gaussian systems are needed.
In this paper, we present the results of Monte Carlo simulations for two popular techniques of long-range correlations detection - classical and modified rescaled range analyses. A focus is put on an effect of different distributional properties on an ability of the methods to efficiently distinguish between short and …
We introduce a notion of genus range as a set of values of genera over all surfaces into which a graph is embedded cellularly, and we study the genus ranges of a special family of four-regular graphs with rigid vertices that has been used in modeling homologous DNA recombination. We show that the genus ranges are sets …
Paper explores variable skipping to speed up range density estimation.
problem Efficiently estimating range densities over high-dimensional data.
method Variable skipping technique to accelerate range density estimation.
result 10-100x efficiency improvements in challenging high-quantile error metrics.
The paper introduces MRVaR and MRCov for elliptical and log-elliptical distributions.
problem Risk management of regulation and investment purposes.
method Proposes MRVaR and MRCov as risk measures for elliptical and log-elliptical distributions.
result Explicit expressions of MRVaR and MRCov derived for multivariate (log-)elliptical distributions.
A new method uses burst and inter-burst duration to test long-range memory in financial markets.
problem Varying results from long-range memory estimators in financial markets.
method Burst and inter-burst duration statistical analysis of limit order book data.
result The new method provides a more reliable evaluation of the Hurst exponent.
New COS method formula improves option pricing accuracy.
problem Determining the optimal truncation range for COS method.
method Derive new formula using Markov's inequality to ensure convergence.
result New formula leads to more accurate option pricing.
New trade-off found in bandit problems with unknown range.
problem Stochastic bandit problems with unknown range.
method Exhibit a strategy achieving new trade-off between distribution-dependent and distribution-free regret bounds.
result Achieves the rates for regret indicated by the new trade-off.
We present two range characterizations for the attenuated geodesic X-ray transform defined on pairs of functions and one-forms on simple surfaces. Such characterizations are based on first isolating the range over sums of functions and one-forms, then separating each sub-range in two ways, first by implicit conditions,…
Enhances stability ranges for Torelli and congruence subgroup homologies.
problem Improving stability ranges for specific subgroup homologies.
method Analyzes H2(Torelli subgroup of Aut(Fn)'s), H2(Torelli subgroup of mapping class groups), and Hk(congruence subgroups of GL_n(R)'s).
result Improved central stability ranges for various subgroup homologies.
We describe the range of the attenuated ray transform of a unitary connection on a simple surface acting on functions and 1-forms. We use this to determine the range of the ray transform acting on symmetric tensor fields.
Developing a range-aware Bayesian optimization framework for discovering diverse designs within target property windows.
problem Discovering multiple, distinct solutions within target property windows.
method Range-aware Bayesian optimization framework.
result Consistently recovers larger and more diverse sets of valid designs.
Identifies Lorentzian locally symmetric spaces where Calabi operator suffices to determine Killing operator range.
problem Determining when the Calabi operator can identify the range of the Killing operator in Lorentzian locally symmetric spaces.
method Developed criteria for a connection to be in the range of a connection, applied to the Killing connection.
result For indecomposable spaces, the Calabi operator suffices to identify the range of the Killing operator; for products, it fails.
Improved Mamba model for long-range sequence tasks.
problem Mamba's poor performance on long-range sequential tasks.
method Proposed B2S6, combining block-wise selective dynamics and channel-specific bias.
result Empirically, B2S6 outperforms S4 and S4D on LRA tasks.
We report an empirical study of Tehran Price Index (TEPIX). To analyze our data we use various methods like as, rescaled range analysis (R/S), modified rescaled range analysis (Lo's method), Detrended Fluctuation Analysis (DFA) and generalized Hurst exponents analysis. Based on numerical results, the scaling range of…
Improved GNN handles long-range dependencies in multi-relational graphs.
problem Vanishing gradients in GNNs for multi-relational graphs.
method Proposes a Gated Graph Neural Network with improved long-range dependency handling.
result Outperforms popular GNN models in synthetic tasks.
Introduces Spectral Attention for better long-range time series forecasting.
problem Challenges in capturing long-range dependencies in time series forecasting.
method Spectral Attention mechanism that preserves temporal correlations and long-range dependencies.
result Achieves state-of-the-art results on 11 real-world time series datasets.
Fractal analysis is carried out on the stock market indices of seven European countries and the US. We find evidence of long range dependence in the log return series of the Mibtel (Italy) and the PX Glob (Czech Republic). Long range dependence implies that predictable patterns in the log returns do not dissipate quick…
Study finds phase transition in context-sensitive language model with short-range interactions.
problem Understanding phase transitions in language models with short-range interactions.
method Constructed a random language model with short-range interactions and investigated its statistical properties.
result Phase transition occurs in context-sensitive language models with constant context length.
This paper extends homological stability results for configuration spaces of manifolds.
problem Homological stability of configuration spaces of manifolds.
method Analyzing the cohomology of configuration spaces of manifolds, focusing on stability in odd and even degrees.
result The stable range for homology groups of configuration spaces depends on the dimension of the manifold and the number of configuration points.
A new method for forming learning objectives using the sum of ranked range.
problem Forming learning objectives from aggregated values.
method Sum of ranked range (SoRR) minimization with DCA.
result The proposed method effectively forms learning objectives and is applicable to binary and multi-label/multi-class classification.
Novel neural network layer improves long-range interactions in point clouds.
problem Efficiently treating long-range interactions in point clouds.
method Long-range convolutional (LRC)-layer that incorporates Fourier transforms.
result Global all-to-all convolution operation performed in nearly-linear time.
A chord diagram consists of a circle, called the backbone, with line segments, called chords, whose endpoints are attached to distinct points on the circle. The genus of a chord diagram is the genus of the orientable surface obtained by thickening the backbone to an annulus and attaching bands to the inner boundary cir…
We investigate how simultaneously recorded long-range power-law correlated multi-variate signals cross-correlate. To this end we introduce a two-component ARFIMA stochastic process and a two-component FIARCH process to generate coupled fractal signals with long-range power-law correlations which are at the same time lo…
The results of R^2 dynamical random surface model (2-dimensional quantum gravity with a R2 term) are applied to explain the personal income distribution. A scale invariance exists if there is not the R2 term in the action. The R^2 term provides a typical scale and breaks the scale invariance explicitly in the low…
Understanding how funding and 4H context regulate crypto markets.
problem Analyzing the chaotic appearance of financial markets.
method Observing interactions between market context and capital conditions in the 4H timeframe.
result Ranges in crypto markets are strategic positioning by informed participants, not indecision.
New insights into X-ray transform on hyperbolic disk, with functional relations and range characterizations.
problem Understanding the X-ray transform on hyperbolic geometry.
method Derived new singular value decompositions, range characterizations, and intertwining relations with wedge-type differential operators.
result Sharp understanding of boundary behavior and invertibility settings for the X-ray transform.
Computes homotopy groups of diffeomorphism spaces for high-dimensional manifolds.
problem Determining homotopy groups of diffeomorphism spaces for high-dimensional manifolds.
method Computes rational homotopy groups of classifying spaces of diffeomorphisms.
result Determines rational pseudoisotopy stable range for compact spin manifolds.
IGNN captures long-range graph dependencies using fixed-point equations.
problem Limited GNN ability to capture long-range graph dependencies.
method Fixed-point equilibrium equations involving implicitly defined state vectors, leveraging Perron-Frobenius theory and projected gradient descent.
result IGNN consistently captures long-range dependencies and outperforms state-of-the-art GNNs.
Understanding temporal dynamics has proved to be highly valuable for accurate recommendation. Sequential recommenders have been successful in modeling the dynamics of users and items over time. However, while different model architectures excel at capturing various temporal ranges or dynamics, distinct application cont…
Recently, locality sensitive hashing (LSH) was shown to be effective for MIPS and several algorithms including L2-ALSH, Sign-ALSH and Simple-LSH have been proposed. In this paper, we introduce the norm-range partition technique, which partitions the original dataset into sub-datasets containing items with similar 2-…
This paper describes results characterizing the range of the time-t heat operator on various manifolds, including Euclidean spaces, spheres, and hyperbolic spaces. The guiding principle behind these results is this: The functions in the range of the heat operator should be, roughly, those functions having an analytic c…
This study uses moving average cluster entropy to analyze financial market dynamics.
problem Understanding long-range dependence in financial markets.
method Moving average cluster entropy approach applied to ARFIMA and FBM processes.
result Long-range positive correlation in financial markets is linked to the cluster entropy behavior.
Stability of black holes proven in full subextremal range with positive cosmological constant.
problem Stability of Kerr-de Sitter black holes in the full subextremal range.
method Similar to previous proof in slowly rotating case, with implementation of constraint damping and verification of subprincipal symbol condition.
result Stability of Kerr-de Sitter black holes proven in the full subextremal range.
Extended univariate Range Value-at-Risk to multivariate settings.
problem Inability of traditional risk measures for heavy-tail distributions and infinite tail expectations.
method Multivariate definitions of robust truncated tail expectations, robustness and properties derived, closed-form expressions and special cases discussed.
result Empirical estimators accuracy examined through numerical and graphical examples.
Novel graph neural network combines random walks with local message passing.
problem Graph neural networks struggle with long-range dependencies.
method Combines random walks with local message passing in a novel architecture.
result Significant performance improvements on graph benchmarks.