Study the hitting density of Ornstein-Uhlenbeck process, providing semi-analytical solutions.
problem First passage hitting density of Ornstein-Uhlenbeck process.
method Two complementary formulations, heat potentials, linear Volterra integral equations, Abel equation approximation, numerical solutions.
result Semi-analytical solutions for hitting density of Ornstein-Uhlenbeck process.
Generalizes entropy-drift inequality for specific geometric spaces.
problem Entropy, drift, and critical exponent in Gibbs measures on geometrically finite manifolds.
method Generalization of Guivarc'h's inequality for CAT(-1) spaces, analysis of random walks.
result Equality in entropy-drift inequality achieved if and only if Gibbs density is equivalent to hitting measure.
Simplified derivation and simulation of Feller Diffusion.
problem Deriving the probability density function of Feller Diffusion.
method Fourier Transform and Method of Characteristics for derivation; simulation algorithms for validation.
result Confirmation of hitting time probabilities via simulation.
We analyze the hitting time distributions of stock price returns in different time windows, characterized by different levels of noise present in the market. The study has been performed on two sets of data from US markets. The first one is composed by daily price of 1071 stocks trade for the 12-year period 1987-1998, …
Predicts which songs will be Billboard hits using Spotify data.
problem Predicting which songs will become chart-topping hits.
method Used a dataset of 1.8 million hit and non-hit songs, extracted audio features, and tested four models (random forest achieved 88% accuracy).
result Random forest model achieved 88% accuracy in predicting Billboard song success.
Solves financial and non-financial problems using heat potentials.
problem Calibrating default boundaries, calculating default probabilities, and finding hitting time probabilities.
method Classical method of heat potentials, recently extended by the author.
result Successfully solved several financial and non-financial problems.
Equity default-swaps pay the holder a fixed amount of money when the underlying spot level touches a (far-down) barrier during the life of the instrument. While most pricing models give reasonable results when the barrier lies within the range of liquidly traded strikes of plain-vanilla option prices, the situation is …
Predicting dance hits from 1985-2013 using musical features.
problem Predicting which songs will be dance hits.
method Built a database of dance hit songs with features, used multiple classifiers.
result Best model predicts top 10 dance hits with good accuracy.
Faster algorithm for sampling logconcave densities in high dimensions.
problem Cubic barrier in sampling logconcave densities from a cold start.
method Two key ingredients: weaker distance sampling and refined log-Sobolev inequality.
result First sub-cubic sampling algorithms for isotropic position.
In this paper, we propose a new fuzzy clustering algorithm based on the mode-seeking framework. Given a dataset in Rd, we define regions of high density that we call cluster cores. We then consider a random walk on a neighborhood graph built on top of our data points which is designed to be attracted by hig…
Minimal hitting time on origami equals diophantine type for certain slopes.
problem Determining hitting time on origami surfaces.
method Analyzing hitting time and diophantine type on specific origami models.
result For genus 4 origami, hitting time equals diophantine type for certain slopes.
Price limit trading rules are adopted in some stock markets (especially emerging markets) trying to cool off traders' short-term trading mania on individual stocks and increase market efficiency. Under such a microstructure, stocks may hit their up-limits and down-limits from time to time. However, the behaviors of pri…
This paper improves bond market making by adjusting hit-ratios for client flow quality.
problem Economic misleading of raw hit-ratios in corporate bond market making.
method Stochastic-control framework with residual-quality-adjusted hit-ratio.
result Optimal quotes decompose into various components, improving service/economics frontier.
We show that the family of probability measures on the n-dimensional unit sphere, having density proportional to: \[ S^n \ni y \mapsto \frac{1}{|y - x|^{n+α}}, \] satisfies the Curvature-Dimension condition CD(n−1−4n+α,−α), for all ∣x∣<1, α≥−n and n≥2. The case α=1 corresponds to the hit…
Study bond market making with hit-ratio target using optimal control and HJB equations.
problem Optimizing bond market making with hit-ratio target in OTC markets.
method Stochastic optimal control approach, dualizing hit-ratio target, HJB equation, Riccati equation, linearization.
result Explicit quote decompositions into riskless spread, inventory-risk correction, and hit-ratio correction.
Directly analyzes SGLD hitting times for stationary points, providing tighter bounds.
problem Analyzing the hitting time of SGLD to stationary points.
method Direct analysis using linear algebra and probability theory, avoiding complex Cheeger's constant bounds.
result Tighter bounds on hitting times compared to previous work, showing dimension-independent behavior under suitable conditions.
Paper analyzes Hit-and-Run's convergence rates and applies similar methods to randomized Kaczmarz.
problem Quantifying advantages of Hit-and-Run's coordinate-free property.
method Sharp estimates via coupling methods and mixing time bounds.
result Ballistic and superdiffusive convergence rates in certain settings.
In this paper, we investigate the cooling-off effect (opposite to the magnet effect) from two aspects. Firstly, from the viewpoint of dynamics, we study the existence of the cooling-off effect by following the dynamical evolution of some financial variables over a period of time before the stock price hits its limit. S…
In this paper, we study the non-linear diffusion equation associated with a particle system where the common drift depends on the rate of absorption of particles at a boundary. We provide an interpretation as a structural credit risk model with default contagion in a large interconnected banking system. Using the metho…
The hitting measure is singular and has dimension less than 1 for cocompact Fuchsian groups.
problem Analyzing the hitting measure and Hausdorff dimension for cocompact Fuchsian groups.
method Geometric and probabilistic analysis of random walks on cocompact Fuchsian groups.
result The hitting measure is singular with respect to Lebesgue measure and has a Hausdorff dimension strictly less than 1.
Researchers prove hitting measure singularity for most Fuchsian and Kleinian groups.
problem Singularity of hitting measure for random walks on discrete subgroups.
method Algebraic and geometric convergence, hyperbolic Dehn filling.
result Proved singularity conjecture for certain measures on cocompact Fuchsian and Kleinian groups.
Research in psychology and neuroscience has successfully modeled decision making as a process of noisy evidence accumulation to a decision bound. While there are several variants and implementations of this idea, the majority of these models make use of a noisy accumulation between two absorbing boundaries. A common as…
The paper improves competitive and dynamic regret bounds for smoothed online learning.
problem Smoothed online learning with hitting and switching costs.
method Optimization problems to minimize hitting cost, dynamic regret modification of existing algorithms.
result Improved competitive and dynamic regret bounds for various function classes.
Improved track reconstruction using recurrent neural networks.
problem Reconstructing tracks from hits in detectors with many fake hits.
method Combining hit preprocessing and deep neural network in one stage.
result Proposed method is more accurate, faster, and does not require preprocessing.
KANEL combines models for early hit enrichment in virtual screening.
problem Assessing model accuracy in chemical bioactivity predictions.
method Ensemble workflow using Kolmogorov-Arnold Networks (KANs) and other models.
result Improves early hit enrichment metrics like PPV@N.
Large unweighted directed graphs are commonly used to capture relations between entities. A fundamental problem in the analysis of such networks is to properly define the similarity or dissimilarity between any two vertices. Despite the significance of this problem, statistical characterization of the proposed metrics …
New algorithm tests Markov chains without hitting.
problem Testing Markov chains with unknown transition matrix.
method Combining approximation algorithms and spectral analysis.
result Efficient testing of Markov chains without hitting time dependence.
In this work we study drawdowns and drawups of general diffusion processes. The drawdown process is defined as the current drop of the process from its running maximum, while the drawup process is defined as the current increase over its running minimum. The drawdown and the drawup are the first hitting times of the dr…
Derives integral representations for a Lévy process and its extremum, hitting time, with fast evaluation.
problem Efficiently evaluating the joint probability density function of a Lévy process, its supremum, and hitting time.
method Integral representations, Laplace-Fourier transforms, summation by parts, conformal deformation, trapezoid rules, Gaver-Wynn-Rho algorithm.
result Explicit calculations and fast evaluation of the joint cpdf for Lévy processes.
New deep learning methods improve track reconstruction in particle physics.
problem Reconstructing particle tracks from detector hits in GEM detectors.
method Two-stage approach combining hits preprocessing and deep neural networks.
result Deep neural networks can accurately reconstruct tracks without preprocessing.
We empirically investigated the relationships between the degree of efficiency and the predictability in financial time-series data. The Hurst exponent was used as the measurement of the degree of efficiency, and the hit rate calculated from the nearest-neighbor prediction method was used for the prediction of the dire…
In this paper we consider finite volume hyperbolic manifolds X with non-empty totally geodesic boundary. We consider the distribution of the times for the geodesic flow to hit the boundary and derive a formula for the moments of the associated random variable in terms of the orthospectrum. We show that the the first tw…
Model financial default cascades on sparse graphs via hitting times.
problem Capturing systemic risk in large, sparsely-connected financial networks.
method Dynamic particle systems with hitting times and convergence theory.
result Characterization of default time distribution in tree-like networks.
ConfHit provides valid guarantees for generative models without oracle access.
problem Reliable guarantees for novel candidate generation in generative models.
method Formalizes certification and refinement of generated sets, leveraging weighted exchangeability and density-ratio weighted conformal p-values.
result Consistently delivers valid coverage guarantees and compact certified sets across various generative tasks.
HitNet uses a Hit-or-Miss layer to enhance feature interpretability in capsule networks.
problem Difficulty in interpreting complex neural network architectures.
method Replacing the last layer with a Hit-or-Miss layer that trains capsules to hit or miss a target capsule using centripetal loss.
result HitNet achieves better performance than initial CapsNet on various datasets and provides interpretable feature representations.
This study compares two neural models for financial forecasting, showing their superiority.
problem Improving financial market trend predictions using neural networks.
method Systematic comparison of N-HiTS and N-BEATS with conventional models.
result N-HiTS and N-BEATS enhance forecast accuracy and robustness in financial time series data.
High throughput screening of compounds (chemicals) is an essential part of drug discovery [7], involving thousands to millions of compounds, with the purpose of identifying candidate hits. Most statistical tools, including the industry standard B-score method, work on individual compound plates and do not exploit cross…
Holomorphic map connects Hitchin components to character varieties.
problem Complex affine spheres and their properties.
method Mapping class group equivariant holomorphic map from Hitchin components to character varieties.
result Holomorphic map includes holonomies of SL(3,C)-opers.
Paper reconciles different Ricci flow approaches and proves weak solutions.
problem Proving weak solutions for Ricci flows with singularities.
method Introducing a novel hitting estimate for Brownian motion, compensating for lack of lower heat kernel bounds.
result Every noncollapsed limit of Ricci flows and singular Ricci flows are weak solutions.
The paper analyzes McKean-Vlasov equations with hitting times, proving global solvability.
problem Analyzing blow-ups in McKean-Vlasov equations involving hitting times.
method Connection to the supercooled Stefan problem, comparison principles, and new transform.
result Proves global solvability for McKean-Vlasov dynamics under certain conditions.
New algorithm determines dimensions of hit spaces in polynomial algebra.
problem Determining dimensions of quotient spaces in polynomial algebra.
method Linear algebra criterion and algorithmic approach.
result Determines dimensions of QPk for arbitrary k and positive degrees. A model for hit song prediction can be used in the pop music industry to identify emerging trends and potential artists or songs before they are marketed to the public. While most previous work formulates hit song prediction as a regression or classification problem, we present in this paper a convolutional neural netw…
The paper simulates Lévy processes and their extremum and hitting time.
problem Simulating Lévy processes and their extremum and hitting time accurately and efficiently.
method Using characteristic functions and conditional characteristic functions, with conformal deformations and precalculated values on multi-grids.
result Accurate and fast simulation of Lévy processes and their extremum and hitting time.
SurvSurf predicts first hitting times for intermittent events without monotonic violations.
problem Predicting first hitting times for intermittent events with monotonicity guarantees.
method Partially monotonic neural network for sequential events, incorporating unobserved events.
result SurvSurf outperforms existing models in MSE and IBS metrics.
Algorithm samples composite logconcave densities efficiently.
problem Sampling from composite logconcave densities efficiently.
method Uses a restricted Gaussian oracle and gradient queries.
result Achieves strong total variation distance guarantees.
RLCache uses reinforcement learning to optimize cache management decisions.
problem Optimizing cache hit rate and storage size in computer systems.
method Designing three reinforcement learning agents for cache manager tasks and two advanced architectures.
result Reinforcement learning agents achieve higher cache hit rates and minimize storage space compared to heuristics.
Parrot learns optimal cache replacement policies using imitation learning.
problem Improving cache hit rates in complex access patterns.
method Imitation learning approach using Belady's oracle policy.
result Parrot increases cache hit rates by 61% on a web search benchmark.
We report on results concerning a partially aggregated Stock Flow Consistent (SFC) macroeconomic model in the stationary state where the sectors of banks and firms are aggregated, the sector of households is dis-aggregated, and the probability density function (pdf) of the wealth of households is exogenous, constrained…