arXiv research

Dilated CNN improves multivariate time series classification.

New hybrid model predicts carbon prices using blockchain data.

Different types of Convolutional Neural Networks (CNNs) have been applied to detect cancerous lung nodules from computed tomography (CT) scans. However, the size of a nodule is very diverse and can range anywhere between 3 and 30 millimeters. The high variation of nodule sizes makes classifying them a difficult and cha…

Deep CNN predicts disruptions in fusion plasmas with high accuracy.

We present an updated version of the VESICLE-CNN algorithm presented by Roncal et al. (2014). The original implementation makes use of a patch-based approach. This methodology is known to be slow due to repeated computations. We update this implementation to be fully convolutional through the use of dilated convolution…

New models explain residual and dilated dense neural networks using sparse coding.

Improved VGG networks enhance image classification accuracy.

Improved volatility forecasting using 1D CNNs with transfer learning.

The paper improves DFA for CNN and RNN training to match BP accuracy.

Large receptive field CNNs improve distant speech recognition.

Volatility is a quantity of measurement for the price movements of stocks or options which indicates the uncertainty within financial markets. As an indicator of the level of risk or the degree of variation, volatility is important to analyse the financial market, and it is taken into consideration in various decision-…

RDL-Net improves speech enhancement with fewer parameters and better performance.

Seq-U-Net improves sequence modeling efficiency with dilated U-Net.

Smartphone app counts grapes for accurate yield estimation.

We consider a general framework for reducing the number of trainable model parameters in deep learning networks by decomposing linear operators as a product of sums of simpler linear operators. Recently proposed deep learning architectures such as CNN, KFC, Dilated CNN, etc. are all subsumed in this framework and we il…

LipKernel adds robustness to CNNs by enforcing Lipschitz bounds.

The study of which mapping class group elements can be realized as affine automorphisms of dilation surfaces.

We find the minimum dilatation of pseudo-Anosov braids with many strands.

Proposes flexible dilation networks for better time series analysis.

Closed geodesics densely cover a circle in dilation surfaces.

The dilatation of a pseudo-Anosov braid is a conjugacy invariant. In this paper, we study the dilatation of a special family of pseudo-Anosov braids. We prove an inductive formula to compute their dilatation, a monotonicity and an asymptotic behavior of the dilatation for this family of braids. We also give an example …

This paper describes a family of pseudo-Anosov braids with small dilatation. The smallest dilatations occurring for braids with 3, 4 and 5 strands appear in this family. A pseudo-Anosov braid with 2g+1 strands determines a hyperelliptic mapping class with the same dilatation on a genus-g surface. Penner showed that log…

Modern audio source separation techniques rely on optimizing sequence model architectures such as, 1D-CNNs, on mixture recordings to generalize well to unseen mixtures. Specifically, recent focus is on time-domain based architectures such as Wave-U-Net which exploit temporal context by extracting multi-scale features. …

Horizon saddle connections imply dense hyperbolic geodesics on dilation surfaces.

For any nonorientable closed surface, we determine the minimal dilatation among pseudo-Anosov mapping classes arising from Penner's construction. We deduce that the sequence of minimal Penner dilatations has exactly two accumulation points, in contrast to the case of orientable surfaces where there is only one accumula…

In this paper we study the minimum dilatation pseudo-Anosov mapping classes coming from fibrations over the circle of a single 3-manifold, the mapping torus for the "simplest pseudo-Anosov braid". The dilatations that arise include the minimum dilatations for orientable mapping classes for genus g=2,3,4,5,8 as well as …

The paper explores inequalities for strongly-convex sets in weighted Riemannian manifolds.

The paper introduces horizon saddle connections to study dilation surfaces.

Maximal dilatation found on nonorientable surfaces.

Constructs moduli spaces for complex affine and dilation surfaces.

Based on the notion of dilatation structure arXiv:math/0608536, we give an intrinsic treatment to sub-riemannian geometry, started in the paper arXiv:0706.3644 . Here we prove that regular sub-riemannian manifolds admit dilatation structures. From the existence of normal frames proved by Bellaiche we deduce the rest of…

We study normed groupoids with dilations and their induced deformations.

Geometric models improve feature extraction and equivariance in image generation.

We find the minimum dilatation of pseudo-Anosov homeomorphisms that stabilize an orientable foliation on surfaces of genus three, four, or five, and provide a lower bound for genus six to eight. Our technique also simplifies Cho and Ham's proof of the least dilatation of pseudo-Anosov homeomorphisms on a genus two surf…

Computes minimal dilatation for Thurston maps on surfaces.

We exhibit low-dilatation families of surface homeomorphisms among monodromies of Lorenz knots.

This paper concerns a family of pseudo-Anosov braids with dilatations arbitrarily close to one. The associated graph maps and train tracks have stable "star-like" shapes, and the characteristic polynomials of their transition matrices form Salem-Boyd sequences. These examples show that the logarithms of least dilatatio…

The Hopf invariant is linked to null-homotopy properties of maps.

We consider the quasiconformal dilatation of projective transformations of the real projective plane. For non-affine transformations, the contour lines of dilatation form a hyperbolic pencil of circles, and these are the only circles that are mapped to circles. We apply this result to analyze the dilatation of the circ…

This note gives a brief survey of the minimum dilatation problem for pseudo-Anosov mapping classes, and the first explicit train track description of an infinite family of pseudo-Anosov mapping classes with orientable stable foliations and the conjectural minimum dilatation for closed surfaces of even genus $g \ge 2$.

A relation between the dilatation of pseudo-Anosov braids and fixed point theory was studied by Ivanov. In this paper we reveal a new relationship between the above two subjects by showing a formula for the dilatation of pseudo-Anosov braids by means of the representations of braid groups due to B. Jiang and H. Zheng.

Method detects airway dilatation with high accuracy.

The study improves bounds on pseudo-Anosov maps and certifies minimum and accumulation points of normalized dilatations.

We introduce length dilatation structures on metric spaces, tempered dilatation structures and coherent projections and explore the relations between these objects and the Radon-Nikodym property and Gamma-convergence of length functionals. Then we show that the main properties of sub-riemannian spaces can be obtained f…

For all orientable closed surfaces, we determine the minimal dilatation among mapping classes arising from Penner's construction. We also discuss generalisations to surfaces with punctures.

We study the minimal dilatation of pseudo-Anosov pure surface braids and provide upper and lower bounds as a function of genus and the number of punctures. For a fixed number of punctures, these bounds tend to infinity as the genus does. We also bound the dilatation of pseudo-Anosov pure surface braids away from zero a…

It has been known since 1981 that if one fixes an orientable surface $S$ of genus $g$, then there is a real number $λ_{min,g} > 1$ that is the dilatation of a pA diffeomorphism of $S$, and every other pA diffeomorphism of $S$ has dilatation $\geq λ_{min,g}$. We will show how a little-known theorem about digraphs gives …

We construct homotopically non-trivial maps from S^m to S^n with arbitrarily small 3-dilation for certain pairs (m,n). The simplest example is m=4, n=3. Other examples include arbitrarily large values of m and n. We show that a homotopy class in pi_7(S^4) can be represented by maps with arbitrarily small 4-dilation if …