arXiv research

Bernstein theorem proven for 2-valued minimal graphs in 4D.

Minimal surfaces with complex branching structures constructed using various methods.

In the 1980's, Almgren developed a theory of multi-valued Dirichlet energy minimizing functions on $n$ dimensional domains and used it, in an essential way, to bound the Hausdorff dimension of the singular sets of area minimizing rectifiable currents of dimension $n$ and codimension $\geq 2$. Recent work of the second …

We derive the joint density of a Skew Brownian motion, its last visit to the origin, local and occupation times. The result is applied to option pricing in a two valued local volatility model and in a displaced diffusion model with constrained volatility.

We prove some epsilon regularity results for n-dimensional minimal two-valued Lipschitz graphs. The main theorems imply uniqueness of tangent cones and regularity of the singular set in a neighbourhood of any point at which at least one tangent cone is equal to a pair of transversely intersecting multiplicity one n-dim…

Study on 2-valued dynamics on complex plane, showing some dynamics can't be group actions.

Optimizes dividend payouts with fixed costs and regime switching.

Study refracted skew Brownian motion, find densities and asymptotics.

Improves RL algorithms with two techniques.

The paper extends risk measures to two-step approximations and studies log-concave distributions.

We prove that the norm of the Euler class E for flat vector bundles is $2^{-n}$ (in even dimension $n$, since it vanishes in odd dimension). This shows that the Sullivan--Smillie bound considered by Gromov and Ivanov--Turaev is sharp. We construct a new cocycle representing E and taking only the two values $\pm 2^{-n}$…

Study proves bridge and braid indices match for twist positive knots.

This paper makes one step forward towards characterizing a new family of \textit{model-free} Deep Reinforcement Learning (DRL) algorithms. The aim of these algorithms is to jointly learn an approximation of the state-value function ($V$), alongside an approximation of the state-action value function ($Q$). Our analysis…

We propose a differentiable sigmoid function for efficient p-value calculation in clustering.

The abstract link L_d of the complex isolated singularity x^2 + y^2 + z^2 + v^{2d} = 0 is diffeomorphic to S^3 \times S^2. We classify the embedded links of these singularities up to regular homotopies precomposed with diffeomorphisms of S^3 \times S^2. Let us denote by i_d the inclusion of L_d in S^7. We show that for…

A new readout layer improves graph property prediction.

We consider a two-valued function $u$ that is either Dirichlet energy minimizing, $C^{1,μ}$ harmonic, or in $C^{1,μ}$ with an area-stationary graph such that Almgren's frequency (restricted to the singular set) is continuous at a singular point $Y_0$. As a corollary of recent work of Wickramasekera and the author, if t…

Deep residual networks can approximate any continuous function using control theory.

Pessimistic Minimax Value Iteration finds efficient NE policies from offline data.

In the early 1980's Almgren developed a theory of Dirichlet energy minimizing multi-valued functions, proving that the Hausdorff dimension of the singular set (including branch points) of such a function is at most $(n-2),$ where $n$ is the dimension of its domain. Almgren used this result in an essential way to show t…

In this paper we extend the concept of Competitivity Graph to compare series of rankings with ties ({\em partial rankings}). We extend the usual method used to compute Kendall's coefficient for two partial rankings to the concept of evolutive Kendall's coefficient for a series of partial rankings. The theoretical frame…

Translation-based embedding models have gained significant attention in link prediction tasks for knowledge graphs. TransE is the primary model among translation-based embeddings and is well-known for its low complexity and high efficiency. Therefore, most of the earlier works have modified the score function of the Tr…

Study optimal transport on null hypersurfaces and null energy condition.

Study non-orientable surfaces to find loops winding around punctures.

Researchers prove an index formula for spinors on 3-manifolds branching along graphs.

Proves regularity for stable varifolds near specific cones.

Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) are popular risk measures from academic, industrial and regulatory perspectives. The problem of minimizing CVaR is theoretically known to be of Neyman-Pearson type binary solution. We add a constraint on expected return to investigate the Mean-CVaR portfolio sele…

Proposes a new algorithm for learning continuous-time Bayesian network structures.

Study evaluates valuation models for UK companies using case studies.

Updating predictive models introduces bias, leading to miscalibration.

Traffic classification has various applications in today's Internet, from resource allocation, billing and QoS purposes in ISPs to firewall and malware detection in clients. Classical machine learning algorithms and deep learning models have been widely used to solve the traffic classification task. However, training s…

We classify the Markov traces factoring through the Birman-Wenzl-Murakami (BMW) algebras. For this purpose, we define a common `cover' for the two variations of the BMW-algebra originating from the quantum orthogonal/symplectic duality, which are responsible for the so-called `Dubrovnik' variation of the Kauffman polyn…

The use of low-precision fixed-point arithmetic along with stochastic rounding has been proposed as a promising alternative to the commonly used 32-bit floating point arithmetic to enhance training neural networks training in terms of performance and energy efficiency. In the first part of this paper, the behaviour of …

Deep convolutional neural networks (CNNs) are powerful tools for a wide range of vision tasks, but the enormous amount of memory and compute resources required by CNNs pose a challenge in deploying them on constrained devices. Existing compression techniques, while excelling at reducing model sizes, struggle to be comp…

Regularized linear regression improves binary classification performance, especially with ridge and $\ell_1$ regularization.

We propose a method for causal inference using satellite image time series, in order to determine the treatment effects of interventions which impact climate change, such as deforestation. Simply put, the aim is to quantify the 'before versus after' effect of climate related human driven interventions, such as urbaniza…

New algorithm reduces regret by allowing free exploration in multi-armed bandits.

Real-world applications of machine learning tools in high-stakes domains are often regulated to be fair, in the sense that the predicted target should satisfy some quantitative notion of parity with respect to a protected attribute. However, the exact tradeoff between fairness and accuracy is not entirely clear, even f…

A new method selects regions of interest in GC-MS data without prior target selection.

New neural network models for complex functional data analysis.

Distance function to a finite set is a topological Morse function.

Introduces new weighted floating functions and affine surface areas.

Develops methods for selecting and estimating smooth functional coefficients in high-dimensional multivariate functional data.

Neural networks can approximate functionals on RKHS with error bounds.

FFBO optimizes functions as inputs and outputs, improving on existing BO methods.

Chirped sinosoids and interferometric phase plots are functions that are not periodic, but are the composition of a smooth function and a periodic function. These functions functions factor into a pair of maps: from their domain to a circle, and from a circle to their codomain. One can easily imagine replacing the circ…

The Fridman function is bounded by the injectivity radius for certain hyperbolic manifolds.

Optimally estimates a functional using nuisance function tuning and sample splitting.