arXiv research

Study on ion travel time on curved surfaces.

Study of Lévy flights on Zoll surfaces, revealing geometric information.

Sharp inequalities for matrix means with unknown variance.

Study shows effective resistance distance yields more accurate network barycenter than Hamming distance.

Polynomial-time algorithm estimates mean with bounded covariance using differential privacy.

Graph learning captures financial dynamics over time.

Study of a generalized geometric Brownian motion with varying entry and exit rates.

We study discrete-time mean-field Markov games with infinite numbers of agents where each agent aims to minimize its ergodic cost. We consider the setting where the agents have identical linear state transitions and quadratic cost functions, while the aggregated effect of the agents is captured by the population mean o…

Recurrent major mood episodes and subsyndromal mood instability cause substantial disability in patients with bipolar disorder. Early identification of mood episodes enabling timely mood stabilisation is an important clinical goal. Recent technological advances allow the prospective reporting of mood in real time enabl…

GANs can learn stylized facts of financial time series, but performance varies by architecture.

TS-K-means improves financial data clustering with dynamic time warping.

FCM clustering adapts to persistence diagrams for topological data analysis.

Bayesian nonparametrics are a class of probabilistic models in which the model size is inferred from data. A recently developed methodology in this field is small-variance asymptotic analysis, a mathematical technique for deriving learning algorithms that capture much of the flexibility of Bayesian nonparametric infere…

The paper introduces new KMEs to capture stochastic process filtrations.

Multiscale stochastic volatility models have been developed as an efficient way to capture the principle effects on derivative pricing and portfolio optimization of randomly varying volatility. The recent book Fouque, Papanicolaou, Sircar and Sølna (2011, CUP) analyzes models in which the volatility of the underlying i…

Persistence norms explain financial uncertainty better than volatility.

We study the problem of robust mean estimation and introduce a novel Hamming distance-based measure of distribution shift for coordinate-level corruptions. We show that this measure yields adversary models that capture more realistic corruptions than those used in prior works, and present an information-theoretic analy…

Paper tackles imbalanced time series classification with a novel oversampling method.

Proposes TFDF to learn transferable and discriminative features for unsupervised domain adaptation.

Mean curvature flow shows a surface fattening at its first singular point.

We apply the theory of continuous time random walks to study some aspects of the extreme value problem applied to financial time series. We focus our attention on extreme times, specifically the mean exit time and the mean first-passage time. We set the general equations for these extremes and evaluate the mean exit ti…

Study forecasts stock returns on JSE using SGDLMs capturing cross-series dependencies.

Mean curvature flow shows singularities on smooth surfaces.

Estimates mean and covariance for large, unbalanced stock returns panels.

In this paper, we show that if the mean curvature of a closed smooth embedded mean curvature flow in R^3 is of type-I, then the rescaled flow at the first finite singular time converges smoothly to a self-shrinker flow with multiplicity one. This result confirms Ilmanen's multiplicity-one conjecture under the assumptio…

Modeling glucose distribution changes over time using neural ODEs.

Proposes NDIG model to capture bitcoin volatility and option pricing.

NeuralSurv models survival analysis with Bayesian uncertainty.

The study proposes a new interest rate model that captures long-term periodicity in U.S. Treasury yields.

New methods for private statistical inference under local differential privacy.

This paper studies the portfolio optimization problem when the investor's utility is general and the return and volatility of the risky asset are fast mean-reverting, which are important to capture the fast-time scale in the modeling of stock price volatility. Motivated by the heuristic derivation in [J.-P. Fouque, R. …

Consider a family of smooth immersions $F(\cdot,t): M^n\to \mathbb{R}^{n+1}$ of closed hypersurfaces in $\mathbb{R}^{n+1}$ moving by the mean curvature flow $\frac{\partial F(p,t)}{\partial t} = -H(p,t)\cdot ν(p,t)$, for $t\in [0,T)$. We prove that the mean curvature blows up at the first singular time $T$ if all singu…

It is conjectured that the mean curvature blows up at the first singular time of the mean curvature flow in Euclidean space, at least in dimensions less or equal to 7. We show that the mean curvature blows up at the singularities of the mean curvature flow starting from an immersed closed hypersurface with small L^2-no…

A new model characterizes undocumented and asymptomatic infections to quantify COVID-19 uncertainties.

Word evolution refers to the changing meanings and associations of words throughout time, as a byproduct of human language evolution. By studying word evolution, we can infer social trends and language constructs over different periods of human history. However, traditional techniques such as word representation learni…

DeepBlip estimates treatment effects over time using neural networks.

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…

We introduce Probabilistic FastText, a new model for word embeddings that can capture multiple word senses, sub-word structure, and uncertainty information. In particular, we represent each word with a Gaussian mixture density, where the mean of a mixture component is given by the sum of n-grams. This representation al…

In this note, we first prove that the solution of mean curvature flow on a finite time interval $[0,T)$ can be extended over time $T$ if the space-time integration of the norm of the second fundamental form is finite. Secondly, we prove that the solution of certain mean curvature flow on a finite time interval $[0,T)$ …

We show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow in R^3.

Bayesian model captures mean and variance of response variables.

Existing methods for structure discovery in time series data construct interpretable, compositional kernels for Gaussian process regression models. While the learned Gaussian process model provides posterior mean and variance estimates, typically the structure is learned via a greedy optimization procedure. This restri…

The study shows stability of neckpinch singularities in mean curvature flows.

LSTM improves cross-network recommendations by capturing user preference changes and irregular time intervals.

This paper studies subordinate Ornstein-Uhlenbeck (OU) processes, i.e., OU diffusions time changed by Lévy subordinators. We construct their sample path decomposition, show that they possess mean-reverting jumps, study their equivalent measure transformations, and the spectral representation of their transition semigro…

Constructs ancient solutions to mean curvature flow with prescribed singular sets.

MPPN network improves long-term time series forecasting accuracy.

Differentiates Fréchet mean for hyperbolic space applications.