arXiv research

Predicting fine-grained interests of users with temporal behavior is important to personalization and information filtering applications. However, existing interest prediction methods are incapable of capturing the subtle degreed user interests towards particular items, and the internal time-varying drifting attention …

The essay discusses Margulis' theorems and their implications.

We characterize the price of an Asian option, a financial contract, as a fixed-point of a non-linear operator. In recent years, there has been interest in incorporating changes of regime into the parameters describing the evolution of the underlying asset price, namely the interest rate and the volatility, to model sud…

Convergence to a saddle point for convex-concave functions has been studied for decades, while recent years has seen a surge of interest in non-convex (zero-sum) smooth games, motivated by their recent wide applications. It remains an intriguing research challenge how local optimal points are defined and which algorith…

The paper models user-advertiser interactions using point processes.

Some years ago Moshé Flato pointed up that it could be interesting to develop the Nambu's idea to generalize Hamiltonian mechanic. An interesting new formalism in that direction was proposed by T. Takhtajan. His theory gave new perspectives concerning deformation quantization, and many authors have developed its mathem…

Bayesian algorithm detects changes in fluctuating baselines.

Fix two points $x,\bar{x}\in S^2$ and two directions (without orientation) $η,\barη$ of the velocities in these points. In this paper we are interested to the problem of minimizing the cost $J[γ]=\int_0^T g_{γ(t)}(\dotγ(t),\dotγ(t))+ K^2_{γ(t)}g_{γ(t)}(\dotγ(t),\dotγ(t)) ~dt$ along all smooth curves starting from $x…

Recent progress in recommender system research has shown the importance of including temporal representations to improve interpretability and performance. Here, we incorporate temporal representations in continuous time via recurrent point process for a dynamical model of reviews. Our goal is to characterize how change…

Study eigenfunctions of Laplacian on sphere with even point removals.

Clustering is an extensive research area in data science. The aim of clustering is to discover groups and to identify interesting patterns in datasets. Crisp (hard) clustering considers that each data point belongs to one and only one cluster. However, it is inadequate as some data points may belong to several clusters…

We show that every source connected Lie groupoid always has global bisections through any given point. This bisection can be chosen to be the multiplication of some exponentials as close as possible to a prescribed curve. The existence of bisections through more than one prescribed points is also discussed. We give som…

In this paper, we present own point of view how the unexpected fluctuations of the long-term real interest rate can be explained. We describe a macroeconomic environment by the modification of the fundamental macroeconomic equilibrium model called the IS-LM model. Last but not least, we suggest a possible cooperation b…

Jakobson and Nadirashvili \cite{JN} constructed a sequence of eigenfunctions on $T^2$ with a bounded number of critical points, answering in the negative the question raised by Yau \cite{Yau1} which asks that whether the number of the critical points of eigenfunctions for the Laplacian increases with the corresponding …

In this paper, we consider the problem of Gaussian process (GP) optimization with an added robustness requirement: The returned point may be perturbed by an adversary, and we require the function value to remain as high as possible even after this perturbation. This problem is motivated by settings in which the underly…

While the Anomaly flow was originally motivated by string theory, its zero slope case is potentially of considerable interest in non-Kahler geometry, as it is a flow of conformally balanced metrics whose stationary points are precisely Kahler metrics. We establish its convergence on Kahler manifolds for suitable initia…

As a means to better understanding manifolds with positive curvature, there has been much recent interest in the study of non-negatively curved manifolds which contain either a point or an open dense set of points at which all 2-planes have positive curvature. We study infinite families of biquotients defined by Eschen…

Method identifies regions of maximum dissimilarity in stochastic processes.

We present a detailed analysis of interest rate derivatives valuation under credit risk and collateral modeling. We show how the credit and collateral extended valuation framework in Pallavicini et al (2011), and the related collateralized valuation measure, can be helpful in defining the key market rates underlying th…

A Steiner deltoid maintains constant area across all boundary points of an ellipse.

We generalize the concept of affine locally symmetric spaces for parabolic geometries. We discuss mainly $|1|$--graded geometries and we show some restrictions on their curvature coming from the existence of symmetries. We use the theory of Weyl structures to discuss more interesting $|1|$--graded geometries which can …

PS-BAX uses posterior sampling to select evaluation points for efficient Bayesian algorithm execution.

The paper characterizes and studies compact subsets of complex projective space with specific line intersection properties.

We argue that a negative interest rate policy (NIRP) can be an effect tool for macroeconomic stabilization. We first discuss how implementing negative rates on reserves held at a central bank does not pose any theoretical difficulty, with a reduction in rates operating in exactly the same way when rates are positive or…

Proposes a new model to handle negative interest rates using CIR framework.

The paper models stochastic interest rates for life insurance using phase-type distributions.

Recently, the online car-hailing service, Didi, has emerged as a leader in the sharing economy. Used by passengers and drivers extensive, it becomes increasingly important for the car-hailing service providers to minimize the waiting time of passengers and optimize the vehicle utilization, thus to improve the overall u…

New method models intensity functions on spheres using normalizing flows.

Investigates chaotic financial time series with monthly contributions and devaluation.

In manifold learning, algorithms based on graph Laplacians constructed from data have received considerable attention both in practical applications and theoretical analysis. In particular, the convergence of graph Laplacians obtained from sampled data to certain continuous operators has become an active research topic…

Researchers discover symmetries in Ricci flows and use them to find invariant solutions.

Point-of-Interest (POI) recommendation is one of the most important location-based services helping people discover interesting venues or services. However, the extreme user-POI matrix sparsity and the varying spatio-temporal context pose challenges for POI systems, which affects the quality of POI recommendations. To …

Italian banks use swaps to hedge against rising interest rates, offsetting losses on debt securities.

Research on refined algebraic domains respecting differential geometry.

The study proves fixed-point theorems for groups acting on CAT(0) spaces.

The paper studies estimation of parameters of diffusion market models from historical data. The standard definition of implied volatility for these models presents its value as an implicit function of several parameters, including the risk-free interest rate. In reality, the risk free interest rate is unknown and need …

Smartphones and portable devices have become ubiquitous and part of everyone's life. Due to the fact of its portability, these devices are perfect to record individuals' traces and life-logging generating vast amounts of data at low costs. These data is emerging as a new source for studies in human mobility patterns ra…

This paper shows that a perturbed form of gradient descent converges to a second-order stationary point in a number iterations which depends only poly-logarithmically on dimension (i.e., it is almost "dimension-free"). The convergence rate of this procedure matches the well-known convergence rate of gradient descent to…

The study models mortgage prepayment risk, accounting for behavioral uncertainty, and provides replication strategies.

New MIP approach for efficient change-point detection.

New boundary and point constraints for controlling conformal surfaces.

The last few years have seen an explosion of academic and popular interest in algorithmic fairness. Despite this interest and the volume and velocity of work that has been produced recently, the fundamental science of fairness in machine learning is still in a nascent state. In March 2018, we convened a group of expert…

Clarifies when solutions to stochastic PDEs stay near given subsets.

The symmetries of two-dimensional supersymmetric sigma models on target spaces with covariantly constant forms associated to special holonomy groups are analysed. It is shown that each pair of such forms gives rise to a new one, called a Nijenhuis form, and that there may be further reductions of the structure group. I…

We solve robust optimization problem and show the example of the market model for which the worst case measure is not a martingale measure. In our model the instantaneous interest rate is determined by the Hull-White model and the investor employs the HARA utility to measure his satisfaction.To protect against the mode…

This paper proposes new get-rich-quick schemes that involve trading in a financial security with a non-degenerate price path. For simplicity the interest rate is assumed zero. If the price path is assumed continuous, the trader can become infinitely rich immediately after it becomes non-constant (if it ever does). If i…

Bayesian model detects sudden changes in stock market correlations during pandemic.

We extend Dupire's formula for stochastic interest rates and local volatility.