arXiv research

3D flying wings created for any angle asymptotic cones.

Researchers discover a new family of 3D solitons that are flying wings.

3D steady gradient Ricci solitons are all O(2)-symmetric.

Constructs new steady gradient Ricci solitons for higher dimensions.

New Kähler solitons found that are not $U(n)$-invariant.

Resolves conjecture on cylindrical mean curvature flows in all dimensions.

Paper proves conjecture about star-shaped curves evolving under GAPF, but not always preserves star shape.

The paper explores new translating solitons and their relation to $Δ$-wings.

Finite entropy translating solitons in slabs have quantized entropy and unique structure.

In this final part of a 3-part paper we introduce the pair of "wings" of the abstract PL-colored complexes $\mathcal{H}_{m}^\star$, described in the second paper. The wings, via a weight enhanced Tutte's barycentric embedding of a planar map, produce the unexpected reformutation of a 3-dimensionl problem into a 2-dimen…

We propose a multi-wing harmonium model for mining multimedia data that extends and improves on earlier models based on two-layer random fields, which capture bidirectional dependencies between hidden topic aspects and observed inputs. This model can be viewed as an undirected counterpart of the two-layer directed mode…

The paper studies bowl solitons and their asymptotic expansions.

We consider implied volatilities in asset pricing models, where the discounted underlying is a strict local martingale under the pricing measure. Our main result gives an asymptotic expansion of the right wing of the implied volatility smile and shows that the strict local martingale property can be determined from thi…

New method predicts quasar continuum near Lyman-α with high precision and accuracy.

A new classifier encodes local neighborhoods for each class using Fly Bloom Filters.

In the paper, we characterize the asymptotic behavior of the implied volatility of a basket call option at large and small strikes in a variety of settings with increasing generality. First, we obtain an asymptotic formula with an error bound for the left wing of the implied volatility, under the assumption that the dy…

We determine the distribution of size and growthrates of German business firms in 1987-1997. We find a log-normal size distribution. The distribution of growth rates has fat tails. It can be fitted to an exponential in a narrow central region and is dominated by finite-sample-size effects far in its wings. We study the…

Traditional anatomical analyses captured only a fraction of real phenomic information. Here, we apply deep learning to quantify total phenotypic similarity across 2468 butterfly photographs, covering 38 subspecies from the polymorphic mimicry complex of $\textit{Heliconius erato}$ and $\textit{Heliconius melpomene}$. E…

Fruit fly brain network learns word embeddings using sparse binary codes.

In recent years, air traffic communication data has become easy to access, enabling novel research in many fields. Exploiting this new data source, a wide range of applications have emerged, from weather forecasting to stock market prediction, or the collection of information about military and government movements. Ty…

We analyse the behaviour of the implied volatility smile for options close to expiry in the exponential Lévy class of asset price models with jumps. We introduce a new renormalisation of the strike variable with the property that the implied volatility converges to a non-constant limiting shape, which is a function of …

Refining previously known estimates, we give large-strike asymptotics for the implied volatility of Merton's and Kou's jump diffusion models. They are deduced from call price approximations by transfer results of Gao and Lee. For the Merton model, we also analyse the density of the underlying and show that it features …

The densification of small-cell base stations in a 5G architecture is a promising approach to enhance the coverage area and facilitate the ever increasing capacity demand of end users. However, the bottleneck is an intelligent management of a backhaul/fronthaul network for these small-cell base stations. This involves …

Paper disproves potential singularity models for 3D hypersurfaces in R^4.

Among the central tenets of globalization is free migration of labor. Although much has been written about its benefits, little is known about the limitations of globalization, including how immigration affects the anti-globalist sentiment. Analyzing polls data, we find that over the last three years in a group of EU c…

Second order Sobolev metrics are a useful tool in the shape analysis of curves. In this paper we combine these metrics with varifold-based inexact matching to explore a new strategy of computing geodesics between unparametrized curves. We describe the numerical method used for solving the inexact matching problem, appl…

We prove that the Lawson surface $ξ_{g,1}$ in Lawson's original notation, which has genus $g$ and can be viewed as a desingularization of two orthogonal great two-spheres in the round three-sphere ${\mathbb{S}}^3$, has index $2g+3$ and nullity $6$ for any genus $g\ge2$. In particular $ξ_{g,1}$ has no exceptional Jacobi…

ADVISOR dynamically balances imitation and reinforcement learning to overcome the imitation gap.

We consider the asymptotic behavior of the implied volatility in stochastic asset price models with atoms. In such models, the asset price distribution has a singular component at zero. Examples of models with atoms include the constant elasticity of variance model, jump-to-default models, and stochastic models describ…

We consider the at-the-money strike derivative of implied volatility as the maturity tends to zero. Our main results quantify the behavior of the slope for infinite activity exponential Lévy models including a Brownian component. As auxiliary results, we obtain asymptotic expansions of short maturity at-the-money digit…

Given a tiling $\mathcal{T}$ of the plane by straight edge polygons, which is invariant by two independent translations, we construct a family of embedded triply periodic minimal surfaces which desingularizes $\mathcal{T}\times\mathbb{R}$. For this purpose, inspired by the work of Martin Traizet, we open the nodes of s…

In this paper, we obtain asymptotic formulas with error estimates for the implied volatility associated with a European call pricing function. We show that these formulas imply Lee's moment formulas for the implied volatility and the tail-wing formulas due to Benaim and Friz. In addition, we analyze Pareto-type tails o…

Proposes on-the-fly joint feature selection and classification for time-sensitive decisions.

We identify various structures on the configuration space C of a flying saucer, moving in a three-dimensional smooth manifold M. Always C is a five-dimensional contact manifold. If M has a projective structure, then C is its twistor space and is equipped with an almost contact Legendrean structure. Instead, if M has a …

Structural optimization is a popular method for designing objects such as bridge trusses, airplane wings, and optical devices. Unfortunately, the quality of solutions depends heavily on how the problem is parameterized. In this paper, we propose using the implicit bias over functions induced by neural networks to impro…

In this work we show that $2$-dimensional, simply connected, translating solitons of the mean curvature flow embedded in a slab of $\mathbb{R}^3$ with entropy strictly less than $3$ must be mean convex and thus, thanks to a result by J. Spruck and L. Xiao, are convex. Recently, such $2$-dimensional convex translating s…

Adapts agent strategies on-the-fly for better cross-play in cooperative settings.

APINNs use neural networks to solve MCMC problems efficiently.

Dynamic neural network toolkits such as PyTorch, DyNet, and Chainer offer more flexibility for implementing models that cope with data of varying dimensions and structure, relative to toolkits that operate on statically declared computations (e.g., TensorFlow, CNTK, and Theano). However, existing toolkits - both static…

We introduce a method by which a generative model learning the joint distribution between actions and future states can be used to automatically infer a control scheme for any desired reward function, which may be altered on the fly without retraining the model. In this method, the problem of action selection is reduce…

Wind speed prediction improved using a novel deep ensemble learning model inspired by jet aerodynamics.

Ensuring secure and reliable operations of the power grid is a primary concern of system operators. Phasor measurement units (PMUs) are rapidly being deployed in the grid to provide fast-sampled operational data that should enable quicker decision-making. This work presents a general interpretable framework for analyzi…

Deep reinforcement learning controls drones without model knowledge.

Assemblies of modular subsystems are being pressed into service to perform sensing, reasoning, and decision making in high-stakes, time-critical tasks in such areas as transportation, healthcare, and industrial automation. We address the opportunity to maximize the utility of an overall computing system by employing re…

Binary autoencoder with sparse hidden layer preserves information and zero reconstruction error.

Starting from the observation that a flying saucer is a nonholonomic mechanical system whose 5-dimensional configuration space is a contact manifold, we show how to enrich this space with a number of geometric structures by imposing further nonlinear restrictions on the saucer's velocity. These restrictions define cert…

The goal of eXtreme Multi-label Learning (XML) is to automatically annotate a given data point with the most relevant subset of labels from an extremely large vocabulary of labels (e.g., a million labels). Lately, many attempts have been made to address this problem that achieve reasonable performance on benchmark data…

A new method for generating replay samples on the fly, optimizing for not forgetting.