New formula calculates volumes of ideal hyperbolic drums.
problem Computing volumes of ideal hyperbolic drums.
method Proved a volume formula for arbitrary ideal hyperbolic antiprisms (drums).
result Volume formula for ideal hyperbolic drums.
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48 results for “ideal drums”
The Inverse Drum Machine: Source Separation Through Joint Transcription and Analysis-by-Synthesiscs.SD
Inverse Drum Machine separates drum mixes using transcription and synthesis.
problem Separating individual drum tracks from mixed recordings.
method Analysis-by-synthesis framework combining deep learning and automatic transcription.
result Separation quality comparable to supervised methods requiring isolated stems.
DRUM discovers interpretable rules from knowledge graphs for unseen entities.
problem Inductive link prediction on unseen entities and lack of interpretability.
method Differentiable approach using bidirectional RNNs for low-rank tensor approximation.
result DRUM outperforms existing methods in inductive link prediction.
DeepDrummer generates drum loops with human preferences via active learning.
problem Creating drum loops efficiently with user preferences.
method Active learning with a deep neural network classifier.
result System converges to user preferences after few interactions.
Corners can be identified by a drum's sound spectrum.
problem Determining the presence of corners in a drum's shape from its sound.
method Proving spectral invariance of corners in domains with Lipschitz, piecewise smooth boundaries.
result Corners are uniquely determined by a drum's spectrum among domains with fixed genus.
DRUM transfers cardiac arrest models across registries with missing covariates.
problem Clinical prediction models fail when key training covariates are unavailable at deployment.
method DRUM transfers models to target populations with structurally missing covariates, optimizing worst-case predictive performance over unknown target distributions.
result DRUM yields better-calibrated predictions and improved clinical classification performance across sites.
We use an extension of Sunada's theorem to construct a nonisometric pair of isospectral simply connected domains in the Euclidean plane, thus answering negatively Kac's question, ``can one hear the shape of a drum?'' In order to construct simply connected examples, we exploit the observation that an orbifold whose unde…
New method reveals corners of drum shapes.
problem Determining the shape of drum corners from its sound.
method Locality principle and calculations of heat kernels.
result Corners are spectral invariants of the Laplacian.
Considering music as a sequence of events with multiple complex dependencies, the Long Short-Term Memory (LSTM) architecture has proven very efficient in learning and reproducing musical styles. However, the generation of rhythms requires additional information regarding musical structure and accompanying instruments. …
The sound of symmetrymath.SP
Inverse spectral theory reveals shapes from sound.
problem Can the shape of a drum be determined by its sound?
method Inverse isospectral techniques applied to specific shapes.
result The regular n-gon can be uniquely determined by its eigenvalues.
We explore models for translating abstract musical ideas (scores, rhythms) into expressive performances using Seq2Seq and recurrent Variational Information Bottleneck (VIB) models. Though Seq2Seq models usually require painstakingly aligned corpora, we show that it is possible to adapt an approach from the Generative A…
Study uses deep reinforcement learning for real-time control of nuclear microreactors, achieving similar or superior performance to traditional PID controllers.
problem Minimizing operating costs of nuclear microreactors through autonomous control, especially in load-following scenarios.
method Application of deep reinforcement learning (RL) for real-time drum control in microreactors, using point kinetics model with thermal and xenon feedback.
result Deep reinforcement learning controllers, including single- and multi-agent RL frameworks, can achieve similar or superior load-following performance to traditional PID control across various scenarios.
Conway's drum quiltsmath.GT
John Conway created pairs of domains that sound the same for a special kind of music.
problem Creating domains that sound the same for a special kind of music.
method Using his theory of quilts, Conway developed pairs of glueing diagrams.
result Conway's pairs of domains are isospectral for the Laplace operator.
We give a number of examples of isospectral pairs of plane domains, and a particularly simple method of proving isospectrality. One of our examples is a pair of domains that are not only isospectral but homophonic: Each domain has a distinguished point such that corresponding normalized Dirichlet eigenfunctions take eq…
We answer Mark Kac's famous question, "can one hear the shape of a drum?" in the positive for orbifolds that are 3-dimensional and 4-dimensional lens spaces; we thus complete the answer to this question for orbifold lens spaces in all dimensions. We also show that the coefficients of the asymptotic expansion of the tra…
We study isospectrality for manifolds with mixed Dirichlet-Neumann boundary conditions and express the well-known transplantation method in graph- and representation-theoretic terms. This leads to a characterization of transplantability in terms of monomial relations in finite groups and allows for the generating of ne…
We answer Mark Kacs famous question - can one hear the shape of a drum - in the negative for orbifolds that are spherical space forms. This is done by extending the techniques developed by A. Ikeda on Lens Spaces to the orbifold setting. Several results are proved to show that with certain restrictions on the dimension…
We prove an upper bound for the evaluation of all classical SU(2) spin networks conjectured by Garoufalidis and van der Veen. This implies one half of the analogue of the volume conjecture which they proposed for classical spin networks. We are also able to obtain the other half, namely, an exact determination of the s…
In this paper we study deep learning-based music source separation, and explore using an alternative loss to the standard spectrogram pixel-level L2 loss for model training. Our main contribution is in demonstrating that adding a high-level feature loss term, extracted from the spectrograms using a VGG net, can improve…
We propose a novel model for temporal detection and localization which allows the training of deep neural networks using only counts of event occurrences as training labels. This powerful weakly-supervised framework alleviates the burden of the imprecise and time-consuming process of annotating event locations in tempo…
The study proves poor ideal three-edge triangulations are minimal for certain 3-manifolds.
problem Finding minimal ideal triangulations for specific 3-manifolds.
method Analyzing properties of poor ideal three-edge triangulations and applying them to construct minimal triangulations.
result Poor ideal three-edge triangulations are proven to be minimal for certain 3-manifolds.
We give a simple method to find ideal points of the character variety of a 3-manifold from an ideal triangulation.
Paper provides new Alexander ideal-based obstruction to 0-concordance of knotted surfaces.
problem Tackles the 0-concordance problem for knotted surfaces in .
method Uses Alexander ideals to induce a homomorphism and prove non-sliceness.
result Alexander ideal determines 0-concordance classes and non-sliceness.
Short proof for ideal polygons with near optimal orthogeodesic decomposition.
problem Decomposing ideal polygons into orthogeodesics.
method Short proof with orthogeodesic decomposition of length at most .
result Optimal orthogeodesic decomposition of ideal polygons with length .
A method uses CG to create efficient channels for ideal observers.
problem Computational intractability of ideal observers for high-dimensional image data.
method Conjugate gradient (CG) method for constructing efficient channels.
result CG-based channels approximate IO and HO performance efficiently.
The goal of this work is to study the ideals of the Goldman Lie algebra . To do so, we construct an algebra homomorphism from to a simpler algebraic structure, and focus on finding ideals of this new structure instead. The structure can be regarded as either a -module or a -module gen…
Study introduces dynamical ideals for non-commutative rings and classifies knots and links.
problem Classifying surface knots and links in smooth 4-manifolds.
method Introduced dynamical analog of prime ideals for non-commutative rings and proved a factorization theorem.
result Classified surface knots and links in smooth 4-manifolds.
We investigate the rigidity of hyperbolic cone metrics on -manifolds which are isometric gluing of ideal and hyper-ideal tetrahedra in hyperbolic spaces. These metrics will be called ideal and hyper-ideal hyperbolic polyhedral metrics. It is shown that a hyper-ideal hyperbolic polyhedral metric is determined up to i…
Defines timelike ideal boundary for non-positively curved Lorentzian spaces.
problem Understanding the geometry of non-positively curved Lorentzian spaces.
method Introduces timelike ideal boundary as asymptotic classes of geodesic rays, endows with topology and metric, and studies upper curvature bounds.
result Established upper curvature bounds for the resulting metric space.
A taut ideal triangulation of a 3-manifold is a topological ideal triangulation with extra combinatorial structure: a choice of transverse orientation on each ideal 2-simplex, satisfying two simple conditions. The aim of this paper is to demonstrate that taut ideal triangulations are very common, and that their behavio…
The paper studies dynamical properties in semigroups modulo ideals.
problem Analyzing shadowing, expansivity, and stability in semigroups with ideals.
method Investigates shadowing, expansivity, and stability properties in uniform transformation semigroups modulo an ideal.
result Establishes that if a semigroup exhibits shadowing and expansivity modulo an ideal, it is also topologically stable modulo that ideal.
We define the ideal simplicial volume for compact manifolds with boundary. Roughly speaking, the ideal simplicial volume of a manifold measures the minimal size of possibly ideal triangulations of "with real coefficients", thus providing a variation of the ordinary simplicial volume defined by Gromov in 1982, t…
The notion of ideal immersions was introduced by the author in 1990s. Roughly speaking, an ideal immersion of a Riemannian manifold into a real space form is a nice isometric immersion which produces the least possible amount of tension from the ambient space at each point. In this paper, we classify all ideal hypersur…
Study of combinatorial Calabi flow on ideal circle patterns.
problem Finding ideal circle patterns with prescribed curvatures.
method Combinatorial Calabi flow in hyperbolic and Euclidean geometry.
result Flow converges exponentially to ideal circle patterns.
A biconservative submanifold of a Riemannian manifold is a sub- manifold with divergence free stress-energy tensor with respect to bienergy. These are generalizations of biharamonic submanifolds. In 2013, B. Y. Chen and M.I. Munteanu proved that -ideal and -ideal biharmonic hypersurfaces in Euclidean space …
The paper studies deformations of Lie ideals in Lie algebras.
problem Understanding deformations of Lie ideals in Lie algebras.
method Develops deformation theory, compares cohomologies, enriches deformation complex.
result Deformation cohomology classes differentiate smooth deformations of ideals.
Characterization of Infinite Ideal Polyhedra in Hyperbolic 3-Space via Combinatorial Ricci Flowmath.GT
Paper solves long-standing problem of infinite ideal polyhedra in hyperbolic space.
problem Characterize infinite ideal polyhedra in hyperbolic 3-space.
method Introduced combinatorial Ricci flow for infinite ideal circle patterns.
result Proved characterization of infinite ideal circle patterns under specific conditions.
Wintgen ideal surfaces in E^4 form an important family of surfaces, namely surfaces with circular ellipse of curvature. Obviously, Wintgen ideal surfaces satisfy the pointwise equality K+K_N=H^2. In the present study we consider the Wintgen ideal surfaces in n-dimensional Euclidean space E^4. We have shown that Wintgen…
We discuss two different in general natural approaches to the ideal closure and ideal boundary of Busemann nonpositively curved metric space. It is shown that the identity map of the space admits surjective continuation from its coarse ideal closure to the weak one. We consider some situations when these closures coinc…
Combinatorial description of 3-manifolds using ordered triangulations.
problem Understanding closed 3-manifolds through ideal triangulations.
method Combining ordered ideal triangulations and Pachner moves.
result Closed 3-manifolds can be described via ordered triangulations and moves.
Proof of existence for ideal triangulations that normalize fibers in certain 3-manifolds.
problem Existence of ideal triangulations that normalize fibers in specific 3-manifolds.
method Proof and algorithm construction for ideal triangulations.
result Existence of ideal triangulations that normalize fibers in certain 3-manifolds.
Paper connects fair machine learning to political philosophy, highlighting flaws in ideal approaches.
problem Lack of natural formulation for social desiderata in machine learning.
method Proposes metrics and algorithms to satisfy subsets of fairness parities, trading off against utility.
result Misguided fair machine learning algorithms reflect broader flaws in ideal methodological approaches.
Graph Neural Networks model 3D granular flow simulations.
problem Accurate modeling of complex 3D granular flow processes.
method Graph Neural Networks approach to simulate 3D granular flow using LIGGGHTS.
result Machine learning trajectories match physical granular flow processes.
Biharmonic Wintgen ideal submanifolds in Riemannian manifolds of constant sectional curvaturemath.DG
Every biharmonic Wintgen ideal submanifold in a Riemannian manifold of constant sectional curvature is either minimal or has constant mean curvature.
problem Biharmonic Wintgen ideal submanifolds in Riemannian manifolds of constant sectional curvature
method Show that every biharmonic Wintgen ideal submanifold in a Riemannian manifold of nonpositive constant sectional curvature is minimal and that every biharmonic Wintgen ideal submanifold in a Riemannian manifold of positive constant sectional curvature has constant mean curvature.
result Partial affirmative answers to Chen's conjecture, generalized Chen's conjecture in hyperbolic spaces, and Balmuş-Montaldo-Oniciuc conjecture in spheres within the class of Wintgen ideal submanifolds.
Study on Hermitian metrics on Lie algebras with specific ideals.
problem Classifying Hermitian metrics on Lie algebras with abelian ideals.
method Examined unimodular Lie algebras with abelian ideals of codimension two, classified metrics.
result Classification of Bismut Kähler-like and Bismut torsion-parallel metrics.
TBIP uses texts to quantify lawmakers' political positions.
problem Quantifying lawmakers' political positions from speeches, tweets, etc.
method Unsupervised probabilistic topic model analyzing texts.
result TBIP separates lawmakers by party and infers ideal points close to vote-based.
The notion of ideal embeddings was introduced in [B.-Y. Chen, {Strings of Riemannian invariants, inequalities, ideal immersions and their applications.} The Third Pacific Rim Geometry Conference (Seoul, 1996), 7-60, Int. Press, Cambridge, MA, 1998]. Roughly speaking, an ideal embedding (or a best of living) is an isome…
We generalise work of Young-Eun Choi to the setting of ideal triangulations with vertex links of arbitrary genus, showing that the set of all (possibly incomplete) hyperbolic cone-manifold structures realised by positively oriented hyperbolic ideal tetrahedra on a given topological ideal triangulation and with prescrib…