DDR game charts generated from raw audio tracks.
problem Creating new step charts for songs without existing charts.
method Combining recurrent and convolutional neural networks for step placement and a conditional LSTM for step selection.
result Improved step charts generated from raw audio tracks.
Generative model creates realistic dance poses from music.
problem Generating human-like dance poses from music.
method Music feature encoder, pose generator, music genre classifier integrated.
result Generative autoregressive model synthesizes dance sequences up to 5,000 frames.
Automates honeybee dance analysis for real-time food source information.
problem Manual labeling of honeybee dance videos for extracting food source information is time-consuming and inaccurate.
method Proposes an automated process to monitor and segment honeybee dance components.
result Highly accurate real-time analysis of honeybee dance components.
Predicting dance hits from 1985-2013 using musical features.
problem Predicting which songs will be dance hits.
method Built a database of dance hit songs with features, used multiple classifiers.
result Best model predicts top 10 dance hits with good accuracy.
Math and dance blend in choreographer's research.
problem Exploring intersections between dance and mathematics.
method Choreographic practice and mathematical concepts.
result Examples of fractals, braids in choreography.
Dancing polygons and rolling balls linked via a special geometric distribution.
problem Understanding the geometric and mechanical relationship between dancing polygons and rolling balls.
method Mapping dancing polygons to trajectories of a rolling ball on a 3D surface, both described by a specific geometric distribution.
result Non-degenerate dancing pairs of polygons exist for all n≥6 and correspond to rolling ball trajectories. Deep neural networks generate dance steps from music with minimal labeled data.
problem Generating dance steps from music with little labeled data and maintaining timing accuracy.
method Weakly supervised deep recurrent neural network with convolutional and LSTM layers.
result Model generates dance steps with low cross entropy and maintains timing accuracy.
DANCE improves prediction set efficiency for deep learning models.
problem Inefficient, overly conservative prediction sets for pre-trained models.
method DANCE combines adaptive kernel regression and nearest-neighbor approach.
result DANCE produces more efficient and robust prediction sets.
New AI tools generate and vary dance choreographies.
problem Creating original and customizable dance choreographies.
method Recurrent neural networks and autoencoders trained on movement data.
result Generated and varied dance sequences using machine learning.
The "dancing metric" is a pseudo-riemannian metric g of signature (2,2) on the space M4 of non-incident point-line pairs in the real projective plane RP2. The null-curves of (M4,g) are given by the "dancing condition": the point is moving towards a point on the line, about which the li…
This paper extends danceability concept to twisted virtual knots.
problem Danceability of knot diagrams on non-orientable surfaces.
method Expanding danceability concept to twisted virtual knot diagrams.
result Danceability properties of twisted virtual knots.
DANCE optimizes neural network and accelerator design for faster, more efficient DNN execution.
problem Challenges in optimizing neural network and accelerator design for efficient DNN execution.
method Differentiable approach to co-exploration of accelerator and network architecture design.
result Significantly shorter time to achieve superior accuracy and hardware cost metrics.
RFC enhances humanoid control to imitate complex human motions.
problem Dynamics mismatch between humanoid models and real humans.
method Residual Force Control (RFC) augments control policies with external forces.
result RFC outperforms state-of-the-art methods in convergence speed and motion quality.
We present recent results on counting and distribution of circles in a given circle packing invariant under a geometrically finite Kleinian group and discuss how the dynamics of flows on geometrically finite hyperbolic 3 manifolds are related. Our results apply to Apollonian circle packings, Sierpinski curves, Schott…
DANCE method improves large-scale learning efficiency via accumulating sample strategy.
problem Efficiently solving large-scale empirical risk minimization problems.
method Distributed Accumulated Newton Conjugate gradient (DANCE) method with multistage approach.
result The method achieves satisfactory statistical accuracy with fewer passes over data.
Study identifies personality traits from dance movements in music.
problem Predicting individual differences from music-induced movement.
method Identified Big Five personality traits and EQ/SQ scores from dance movements.
result Successfully explored unseen space for personality and EQ/SQ.
DANCE improves saliency maps by adding subtle input variations.
problem Poor performance of saliency methods in saturated gradients, adversarial perturbations, and inter-feature dependence.
method Two-step procedure: 1) Perturbation mechanism, 2) Aggregation of saliency maps.
result DANCE saliency method outperforms existing methods qualitatively and quantitatively.
Products of Hidden Markov Models(PoHMMs) are an interesting class of generative models which have received little attention since their introduction. This maybe in part due to their more computationally expensive gradient-based learning algorithm,and the intractability of computing the log likelihood of sequences under…
Let P be a locally finite circle packing in the plane invariant under a non-elementary Kleinian group Gamma and with finitely many Gamma-orbits. When Gamma is geometrically finite, we construct an explicit Borel measure on the plane which describes the asymptotic distribution of small circles in P, assuming that either…
The abstract discusses a new causal structure on manifolds using paths and points.
problem Constructing a causal structure on manifolds using paths and points.
method Constructing a four-manifold from pairs of points and paths, and a seven-dimensional manifold from pairs of points and conics.
result The causal structure corresponds to a conformal structure only when the underlying surface is a real projective plane.
Many complex dynamical phenomena can be effectively modeled by a system that switches among a set of conditionally linear dynamical modes. We consider two such models: the switching linear dynamical system (SLDS) and the switching vector autoregressive (VAR) process. Our Bayesian nonparametric approach utilizes a hiera…
Double descent in portfolio optimization shows improved performance with complexity, then declines, due to overfitting.
problem Improving portfolio optimization performance with model complexity.
method Investigates the relationship between model complexity and out-of-sample performance in mean-variance portfolio optimization.
result Performance of low-dimensional models initially improves with complexity but declines due to overfitting. High-dimensional models show double ascent Sharpe ratio curve.
Study surfaces of revolution from frontals in Euclidean space.
problem Characterize surfaces of revolution from frontals.
method Analyze curvatures and invariants of Legendre curves to derive properties of surfaces of revolution.
result Properties of surfaces of revolution with singularities and cones are defined.
In this paper we consider the conformal type (parabolicity or non-parabolicity) of complete ends of revolution immersed in simply connected space forms of constant sectional curvature. We show that any complete end of revolution in the 3-dimensional Euclidean space or in the 3-dimensional sphere is parabolic. In th…
Sharp upper bound found for Steklov spectrum on revolution submanifolds.
problem Finding bounds for Steklov spectrum on specific submanifolds.
method Analyzing submanifolds of revolution in Euclidean space.
result Sharp upper bound established for Steklov spectrum.
The study defines new surfaces with specific cut locus properties and provides conditions for their existence.
problem Understanding the properties of surfaces of revolution with specific cut locus structures.
method Analyzing the Gaussian curvature function and proving conditions for surfaces to be generalized von Mangoldt.
result For any surface of revolution with finite total curvature, there exists a generalized von Mangoldt surface with the same total curvature and non-monotone Gaussian curvature function along a meridian.
We prove here that when all planes transverse and nearly perpendicular to the axis of a surface of revolution intersect it in loops having central symmetry, the surface must be quadric. It follows that the quadrics are the only surfaces of revolution without skewloops. Similar statements hold for hypersurfaces of revol…
Upper bound found for Steklov eigenvalue of a surface of revolution.
problem Finding an upper limit for Steklov eigenvalues of a specific surface.
method Analyzing a surface of revolution with boundary conditions of two spheres.
result An upper bound for the first Steklov eigenvalue is derived and shown to be sharp in some cases.
Study examines noncompact cases of Gauss Curvature Flow on revolution surfaces.
problem Noncompact cases of Gauss Curvature Flow on revolution surfaces.
method Examines two noncompact cases of Gauss Curvature Flow on revolution surfaces.
result Examines noncompact cases of Gauss Curvature Flow on revolution surfaces.
Characterizes rotational solitons for curve shortening flow on revolution surfaces.
problem Understanding the behavior of curves under curve shortening flow on revolution surfaces.
method Characterization and asymptotic behavior analysis.
result Asymptotic behavior of rotational solitons to parallel geodesics.
In this paper we study geodesic mappings of n-dimensional surfaces of revolution. From the general theory of geodesic mappings of equidistant spaces we specialize to surfaces of revolution and apply the obtained formulas to the case of rotational ellipsoids. We prove that such n-dimensional ellipsoids admit non tri…
Smooth maps preserve distances on specific revolution surfaces.
problem Existence of smooth maps on revolution surfaces.
method Proving existence of maps preserving distances on meridians and parallels.
result Smooth maps exist from revolution surfaces to Euclidean plane.
This paper establishes an interesting connection between the family of CMC surfaces of revolution in E13 and some specific families of elliptic curves. As a consequence of this connection, we show in the class of spacelike CMC surfaces of revolution in the E13, only spacelike cylinders and stand…
Fermat constants fail to fully identify Clairaut constants for certain geodesics on a surface of revolution.
problem Identifying Clairaut constants from Fermat constants for specific geodesics.
method Analytical proof for a specific class of geodesics on a surface of revolution.
result Fermat constants do not fully determine Clairaut constants for some geodesics, except for a standard sphere.
New 2-spheres of revolution with simple cut locus structures.
problem Determining surfaces of revolution with simple cut locus structures.
method Introducing a new family of 2-spheres of revolution.
result The new family {M_n}_n has a simple cut locus structure.
Study of Ricci flow on discrete surfaces of revolution with constant Gaussian curvature.
problem Understanding Ricci flow on discrete surfaces of revolution.
method Explicit parametrizations and Ricci flow analysis for discrete surfaces of revolution.
result Discrete surfaces of revolution approach constant Gaussian curvature under Ricci flow.
We consider surfaces of revolution in the three-dimensional Euclidean space which are of coordinate finite type with respect to the third fundamental form. We show that a surface of revolution satisfying the preceding relation is a catenoid or part of a sphere.
The study finds conditions for certain surfaces to have a specific type of metric.
problem Understanding the geometry of surfaces with specific metrics.
method Analyzes surfaces of revolution and derives conditions for a strongly convex slope metric.
result Necessary and sufficient conditions for surfaces of revolution to admit a strongly convex slope metric are established.
The paper studies surfaces of revolution in a semi-isotropic space.
problem Characterizing surfaces of revolution in a semi-isotropic space.
method Analyzing surfaces using the position vector and Laplace operators.
result Described surfaces of revolution in terms of fundamental forms.
Proves inequality for special 3D shapes, generalizing to non-symmetric ones.
problem Proving a mathematical inequality for specific 3D shapes.
method Operator theoretic approach combined with spherical function decomposition.
result Generalized inequality for non-symmetric bodies of revolution.
Using the theory of geodesics on surfaces of revolution, we introduce the period function. We use this as our main tool in showing that any two-dimensional orbifold of revolution homeomorphic to S^2 must contain an infinite number of geometrically distinct closed geodesics. Since any such orbifold of revolution can be …
In the previous paper, the structure of the cut locus was determined for a class of surfaces of revolution homeomorphic to a cylinder. In this paper, we prove the structure theorem of the cut locus for a wider class of surfaces of revolution homeomorphic to a cylinder.
We present numerical visualizations of Ricci Flow of surfaces and 3-dimensional manifolds of revolution. Ricci_rot is an educational tool which visualizes surfaces of revolution moving under Ricci flow. That these surfaces tend to remain embedded in R3 is what makes direct visualization possible. The numerical lessons …
We show that the surface energy introduced by Auckly and Sadun attains the minimum value at the Clifford torus among tori of revolution.
The study finds parametrizations for surfaces of revolution with a linear curvature ratio.
problem Deriving surfaces of revolution with a specific curvature ratio.
method Derives parametrizations for surfaces of revolution with an affine-linear relation between their curvature radii.
result Explicit parametrizations found for a countably-infinite number of surfaces.
Study of tori of revolution under Willmore flow converges to Clifford Torus.
problem Long-time behavior and convergence of Willmore flow for tori of revolution.
method Gradient flow of Willmore energy for tori of revolution, analyzing energy threshold and convergence to Clifford Torus.
result Convergence of Willmore flow to Clifford Torus for initial energy below 8π.
An extrinsic representation of a Ricci flow on a differentiable n-manifold M is a family of submanifolds S(t), each smoothly embedded in R^{n+k}, evolving as a function of time t such that the metrics induced on the submanifolds S(t) by the ambient Euclidean metric yield the Ricci flow on M. When does such a representa…
Study properties of surfaces with nonvanishing third fundamental form.
problem Investigate surfaces with finite III-type properties.
method Analyze Laplace operators and third fundamental form of surfaces in E3.
result Present surfaces of revolution with constant R and nonvanishing Gauss curvature.