arXiv research

We show a natural relation between the monodromy formula for focus-focus singularities of integrable Hamiltonian systems and a formula of Duistermaat-Heckman, and extend the main results of our previous note on focus-focus singularities ($\bbS^1$-action, monodromy, and topological classification) to the degenerate case…

In this paper, we study hyperkahler metric and practice GMN's construction of hyperkahler metric on focus-focus fibrations. We explicitly compute the action-angel coordinates on the local model of focus-focus fibration, and show its semi-global invariant should be harmonic to admit a compatible holomorphic 2-form. Then…

Study focuses on classifying special geometric structures.

We give a topological and geometrical description of focus-focus singularities of integrable Hamiltonian systems. In particular, we explain why the monodromy around these singularities is non-trivial, a result obtained before by J.J. Duistermaat and others for some concrete systems.

Algorithm classifies saddle-focus singularities in Hamiltonian systems.

This work is devoted to a systematic study of symplectic convexity for integrable Hamiltonian systems with elliptic and focus-focus singularities. A distinctive feature of these systems is that their base spaces are still smooth manifolds (with boundary and corners), similarly to the toric case, but their associated in…

Study the monodromy and center-focus problems for rational maps defined by products of generic lines.

We present an algebraic method to study four-dimensional toric varieties by lifting matrix equations from the special linear group ${\rm SL}_2({\mathbb Z})$ to its preimage in the universal cover of ${\rm SL}_2({\mathbb R})$. With this method we recover the classification of two-dimensional toric fans, and obtain a des…

A symplectic semitoric manifold is a symplectic $4$-manifold endowed with a Hamiltonian $(S^1 \times \mathbb{R})$-action satisfying certain conditions. The goal of this paper is to construct a new symplectic invariant of symplectic semitoric manifolds, the helix, and give applications. The helix is a symplectic analogu…

FOCuS detects changes in mean from high-frequency data efficiently.

Improved online changepoint detection for autocorrelated data.

Model improves information transfer from visual streams.

AR-GANs learn depth and DoF from unlabeled images using aperture rendering and focus cues.

A cone projection maps complex plane arcs to conic sections with fixed focus and directrix.

The aim of our paper is to focus on some properties of submanifolds in Riemannian manifolds endowed with endomorphisms that generalize the Golden Riemannian structure, named metallic Riemannian structures. We focus on the properties of the structure induced on submanifolds, named by us $Σ$-metallic Riemannian structure…

In this paper, we focus on option pricing models based on space-time fractional diffusion. We briefly revise recent results which show that the option price can be represented in the terms of rapidly converging double-series and apply these results to the data from real markets. We focus on estimation of model paramete…

A generalized semitoric system F:=(J,H): M --> R^2 on a symplectic 4-manifold is an integrable system whose essential properties are that F is a proper map, its set of regular values is connected, J generates an S^1-action and is not necessarily proper. These systems can exhibit focus-focus singularities, which corresp…

FOCUS addresses label quality disparity in FL for healthcare applications.

Probabilistic mixture models have been widely used for different machine learning and pattern recognition tasks such as clustering, dimensionality reduction, and classification. In this paper, we focus on trying to solve the most common challenges related to supervised learning algorithms by using mixture probability d…

Optimizes credit index option hedging with reinforcement learning.

This survey is a brief introduction to the theory of hyperbolic buildings and their lattices, with a focus on recent results.

Paper reviews neurolinguistics and language technologies, emphasizing mutual enrichment.

Introduces PIT-plot for prioritizing projects based on their impact.

We give a brief introduction to causal fermion systems with a focus on the geometric structures in space-time.

We survey the theory of Kähler-Einstein metrics, with particular focus on the circle of ideas surrounding the Yau-Tian-Donaldson conjecture for Fano manifolds.

FOCUS method forecasts counterfactuals in panel data with time series dynamics.

We present a method for explaining the image classification predictions of deep convolution neural networks, by highlighting the pixels in the image which influence the final class prediction. Our method requires the identification of a heuristic method to select parameters hypothesized to be most relevant in this pred…

Much of current machine learning (ML) research has lost its connection to problems of import to the larger world of science and society. From this perspective, there exist glaring limitations in the data sets we investigate, the metrics we employ for evaluation, and the degree to which results are communicated back to …

The study explores generalized divergences and exponential families with a focus on sufficient conditions and laws of large numbers.

Classifies almost-toric systems in four dimensions.

This is a survey on the various notions of Kodaira dimension in low dimensional topology. The focus is on progress after the 2006 survey [78].

We summarize properties of 3-manifold groups, with a particular focus on the consequences of the recent results of Ian Agol, Jeremy Kahn, Vladimir Markovic and Dani Wise.

FOCUS improves offline RL by incorporating causal structure into world-models.

A survey on recent developments in (algebraic) integral geometry is given. The main focus lies on algebraic structures on the space of translation invariant valuations and applications in integral geometry.

In this paper, we focus on some characterizations for curves in the Galilean and Pseudo-Galilean space.

We present an overview of recent results in locally conformally Kähler geometry, with focus on the topological properties which obstruct the existence of such structures on compact manifolds.

The areas of machine learning and knowledge discovery in databases have considerably matured in recent years. In this article, we briefly review recent developments as well as classical algorithms that stood the test of time. Our goal is to provide a general introduction into different tasks such as learning from tabul…

We present pomegranate, an open source machine learning package for probabilistic modeling in Python. Probabilistic modeling encompasses a wide range of methods that explicitly describe uncertainty using probability distributions. Three widely used probabilistic models implemented in pomegranate are general mixture mod…

This is a short survey on finite-volume hyperbolic four-manifolds. We describe some general theorems and focus on the concrete examples that we found in the literature. The paper contains no new result.

Article establishes criteria for multiplier Hermitian-Einstein metrics on KSM-manifolds.

In this paper we focus on the problem of finding the optimal weights of the shallowest of neural networks consisting of a single Rectified Linear Unit (ReLU). These functions are of the form $\mathbf{x}\rightarrow \max(0,\langle\mathbf{w},\mathbf{x}\rangle)$ with $\mathbf{w}\in\mathbb{R}^d$ denoting the weight vector. …

This is a survey article for the forthcoming `A Concise Encyclopedia of Knot Theory.' We focus on the topology of spatial graphs with few vertices and edges, paying particular attention to Brunnian $θ$-graphs.

In this work we focus on fine-tuning a pre-trained BERT model and applying it to patent classification. When applied to large datasets of over two millions patents, our approach outperforms the state of the art by an approach using CNN with word embeddings. In addition, we focus on patent claims without other parts in …

We compute lower bounds on the virtual crossing number and minimal surface genus of virtual knot diagrams from the arrow polynomial. In particular, we focus on several interesting examples.

We review the main changes in the interbank market after the financial crisis started in August 2007. In particular, we focus on the fixed income market and we analyse the most relevant empirical evidences regarding the divergence of the existing basis between interbank rates with different tenor, such as Libor and OIS…

The outcome of the explorative data analysis (EDA) phase is vital for successful data analysis. EDA is more effective when the user interacts with the system used to carry out the exploration. In the recently proposed paradigm of iterative data mining the user controls the exploration by inputting knowledge in the form…

Although most knots are nonalternating, modern research in knot theory seems to focus on alternating knots. We consider here nonalternating knots and their properties. Specifically, we show certain classes of knots have nontrivial Jones polynomials.

Recent advances in reinforcement learning have proved that given an environment we can learn to perform a task in that environment if we have access to some form of a reward function (dense, sparse or derived from IRL). But most of the algorithms focus on learning a single best policy to perform a given set of tasks. I…