arXiv research

This note explains Ricci flow method for Kähler-Einstein metrics.

Study confirms conjecture about Kähler metrics on smooth minimal models.

Compact metrics found near Kähler manifold's canonical class.

Researchers prove existence of cscK metrics on smooth minimal models.

Improved cover song detection with neural networks.

In this work, we attempt to solve the Hit Song Science problem, which aims to predict which songs will become chart-topping hits. We constructed a dataset with approximately 1.8 million hit and non-hit songs and extracted their audio features using the Spotify Web API. We test four models on our dataset. Our best model…

A model for hit song prediction can be used in the pop music industry to identify emerging trends and potential artists or songs before they are marketed to the public. While most previous work formulates hit song prediction as a regression or classification problem, we present in this paper a convolutional neural netw…

Have you ever wondered how a song might sound if performed by a different artist? In this work, we propose SCM-GAN, an end-to-end non-parallel song conversion system powered by generative adversarial and transfer learning that allows users to listen to a selected target singer singing any song. SCM-GAN first separates …

Record companies invest billions of dollars in new talent around the globe each year. Gaining insight into what actually makes a hit song would provide tremendous benefits for the music industry. In this research we tackle this question by focussing on the dance hit song classification problem. A database of dance hit …

Playlist recommendation involves producing a set of songs that a user might enjoy. We investigate this problem in three cold-start scenarios: (i) cold playlists, where we recommend songs to form new personalised playlists for an existing user; (ii) cold users, where we recommend songs to form new playlists for a new us…

The use of community detection algorithms is explored within the framework of cover song identification, i.e. the automatic detection of different audio renditions of the same underlying musical piece. Until now, this task has been posed as a typical query-by-example task, where one submits a query song and the system …

We conjecture that the Joyce-Song wall-crossing formula for Donaldson-Thomas invariants arises naturally from an asymptotic expansion in the field theoretic work of Gaiotto, Moore and Neitzke. This would also give a new perspective on how the formulae of Joyce-Song and Kontsevich-Soibelman are related. We check the con…

Being able to predict whether a song can be a hit has impor- tant applications in the music industry. Although it is true that the popularity of a song can be greatly affected by exter- nal factors such as social and commercial influences, to which degree audio features computed from musical signals (whom we regard as …

State of the art music recommender systems mainly rely on either matrix factorization-based collaborative filtering approaches or deep learning architectures. Deep learning models usually use metadata for content-based filtering or predict the next user interaction by learning from temporal sequences of user actions. D…

This paper investigates methods for quantifying similarity between audio signals, specifically for the task of of cover song detection. We consider an information-theoretic approach, where we compute pairwise measures of predictability between time series. We compare discrete-valued approaches operating on quantised au…

The task of determining item similarity is a crucial one in a recommender system. This constitutes the base upon which the recommender system will work to determine which items are more likely to be enjoyed by a user, resulting in more user engagement. In this paper we tackle the problem of determining song similarity …

This paper concerns the global theory of properly embedded spacelike surfaces in three-dimensional Minkowski space in relation to their Gaussian curvature. We prove that every regular domain which is not a wedge is uniquely foliated by properly embedded convex surfaces of constant Gaussian curvature. This is a conseque…

Paper classifies Brazilian music genres using song lyrics with BLSTM network.

We find the minimum dilatation of pseudo-Anosov braids on n-punctured discs for 3 <= n <= 8. This covers the results of Song-Ko-Los (n=4) and Ham-Song (n=5). The proof is elementary, and uses the Lefschetz formula.

This work formulates a novel song recommender system as a matrix completion problem that benefits from collaborative filtering through Non-negative Matrix Factorization (NMF) and content-based filtering via total variation (TV) on graphs. The graphs encode both playlist proximity information and song similarity, using …

The study uses historical revenue data to forecast music catalog cashflows and multipliers.

Paper connects 3D gravity averages to 2D CFT correlators.

Minimal surfaces with negative curvature found in large spheres.

Rating prediction is an important application, and a popular research topic in collaborative filtering. However, both the validity of learning algorithms, and the validity of standard testing procedures rest on the assumption that missing ratings are missing at random (MAR). In this paper we present the results of a us…

Study bounds Kähler current diameters on manifolds.

Estimates the growth of Morse index for free boundary minimal hypersurfaces.

In this paper, we give a criterion for the properness of the K-energy in a general Kahler class of a compact Kahler manifold by using Song-Weinkove's result. As applications, we give some Kahler classes on $\mathbb{C}\mathbb{P}^2\#3\overline {\mathbb{C}\mathbb{P}^2}$ and $\mathbb{C}\mathbb{P}^2\#8\overline {\mathbb{C}\…

A classical result by Marston Morse asserts that on some ellipsoids of ${\mathbb R}^3$ there exists exactly 3 closed and simple geodesics. The goal of this presentation is to prove that this rigidity result does not extend to higher dimensions and, more precisely, on any smooth closed riemannian manifod of arbitrary di…

Cai, Song and Kou (2015) [Cai, N., Y. Song, S. Kou (2015) A general framework for pricing Asian options under Markov processes. Oper. Res. 63(3): 540-554] made a breakthrough by proposing a general framework for pricing both discretely and continuously monitored Asian options under one-dimensional Markov processes. In …

Music genre classification is a widely researched topic in music information retrieval (MIR). Being able to automatically tag genres will benefit music streaming service providers such as JOOX, Apple Music, and Spotify for their content-based recommendation. However, most studies on music classification have been done …

Jukebox generates high-fidelity songs with singing in raw audio.

The paper solves a 5-manifold foliation problem using a Sasaki-Ricci flow.

Which song will Smith listen to next? Which restaurant will Alice go to tomorrow? Which product will John click next? These applications have in common the prediction of user trajectories that are in a constant state of flux over a hidden network (e.g. website links, geographic location). What users are doing now may b…

We give examples of smooth surfaces with negative first Chern class which are slope unstable with respect to certain polarisations, and so have Kahler classes that do not admit any constant scalar curvature Kahler metrics. We also compare this to the work of Song-Weinkove on the J-flow.

Researchers prove a Penrose inequality for spacetime with specific conditions.

We contribute a pop-song automation framework for lead melody generation and accompaniment arrangement. The framework reflects the major procedures of human music composition, generating both lead melody and piano accompaniment by a unified strategy. Specifically, we take chord progression as an input and propose three…

Uniform estimates for Kaehler metrics' diameters and volumes.

In this paper, we give a result on the properness of the K-energy, which answers a question of Song-Weinkove in any dimensions. Moreover, we extend our previous result on the properness of K-energy to the case of modified K-energy associated to extremal Kahler metrics.

We generalize the maximal time existence of Kähler-Ricci flow in Tian-Zhang and Song-Tian to conical case. Furthermore, if the twisted canonical bundle $K_{M}+(1-β)[D]$ is big or big and nef, we can expect more on the limit behaviors of such conical Kähler-Ricci flow. Moreover, the results still hold for simple normal …

We prove that, on a minimal elliptic Kähler surface of Kodaira dimension one, the continuity method introduced by La Nave and Tian in \cite{LT} starting from any initial Kähler metric converges in Gromov-Hausdorff topology to the metric completion of the generalized Kähler-Einstein metric on its canonical model constru…

Let $X = M \times E$ where $M$ is an $m$-dimensional Kähler manifold with negative first Chern class and $E$ is an $n$-dimensional complex torus. We obtain $C^\infty$ convergence of the normalized Kähler-Ricci flow on $X$ to a Kähler-Einstein metric on $M$. This strengthens a convergence result of Song-Weinkove and con…

In the domain of algorithmic music composition, machine learning-driven systems eliminate the need for carefully hand-crafting rules for composition. In particular, the capability of recurrent neural networks to learn complex temporal patterns lends itself well to the musical domain. Promising results have been observe…

A crossing in a knot is nugatory if changing the crossing does not change the knot type. Using an invariant of certain types of closed 3-braid diagrams, we show that if a closed 3-braid contains a nugatory crossing then its braid index is one or two. This proves a special case of a conjecture on nugatory crossings due …

The paper analyzes skewness and kurtosis measures for skew-elliptical distributions.

Given a matrix $A\in \mathbb{R}^{n\times d}$ and a vector $b\in \mathbb{R}^n$, we consider the regression problem with $\ell_\infty$ guarantees: finding a vector $x'\in \mathbb{R}^d$ such that $\|x'-x^*\|_\infty \leq \fracε{\sqrt{d}}\cdot \|Ax^*-b\|_2\cdot \|A^\dagger\|$ where $x^*=\arg\min_{x\in \mathbb{R}^d}\|Ax-b\|…

Flow analysis leads to metric completion in Kähler geometry.

We introduce a new continuity method which provides an alternative way of carrying out the Analytic Minimal Model Program introduced by G. Tian and J. Song and G. Tian. This equation -- unlike the Ricci flow -- has the advantage of having Ricci curvature bounded from below along the deformation, so that the compactness…

We investigate the Kahler-Ricci flow on holomorphic fiber spaces whose generic fiber is a Calabi-Yau manifold. We establish uniform metric convergence to a metric on the base, away from the singular fibers, and show that the rescaled metrics on the fibers converge to Ricci-flat Kahler metrics. This strengthens previous…