Study the Hessian geometry of an ideal gas in a centrifuge.
problem Understanding the Hessian geometry of an ideal gas in a centrifuge.
method Investigate the Hessian geometry associated with an ideal gas in a spherical centrifuge, using the action of the Euclidean rotation group.
result The Hessian geometry of a spherical rigid body is isometric to a hyperbolic space in the high angular velocity limit.
RotatE embeds knowledge graphs using rotations in complex space for better link prediction.
problem Predicting missing links in knowledge graphs.
method RotatE models relations as rotations in complex vector space, using self-adversarial negative sampling.
result RotatE models and infers various relation patterns, outperforming existing models.
RotRNN uses rotations to simplify long sequence modelling.
problem Complex initialisation and normalisation schemes in linear recurrent models.
method RotRNN employs rotation matrices to simplify and normalise linear recurrent models.
result RotRNN achieves competitive performance on long sequence modelling datasets.
We add prior knowledge to deep networks to make them invariant to transformations.
problem Creating deep networks invariant to transformations like rotation.
method A novel layer based on invariant integration to enforce feature space invariances.
result State-of-the-art performance on the Rotated-MNIST dataset.
Study on unfolding maps of surfaces in 3D space, proving versality conditions.
problem Investigating the versality of rotation unfolding of folding maps for surfaces in R3. method Introducing and analyzing the rotation unfolding of folding maps, proving versality conditions in terms of geometry.
result Proved conditions for the rotation unfolding to be versal, showing diffeomorphic type of tangent plane locus.
Deep learning predicts nuclear equation of state from rotating core collapse GW signals.
problem Classifying the nuclear equation of state from rotating core collapse gravitational wave signals.
method Employed deep convolutional neural networks to classify visual and temporal patterns in GW signals.
result Up to 97% correct classifications of nuclear equation of state in the test set.
Study on rotating surfaces in 4D space with matrices.
problem Understanding rotational surfaces in pseudo-Euclidean 4-space.
method Defined hyperbolic and elliptic rotational surfaces using curves and matrices in 4D semi-Euclidean space.
result Generated rotated surfaces using specific rotation matrices.
Quaternion embeddings model entities and relations in knowledge graphs.
problem Modeling latent inter-dependencies and expressive rotations in knowledge graphs.
method Quaternion-valued embeddings and rotations in hypercomplex space.
result Quaternion embeddings achieve state-of-the-art performance on knowledge graph benchmarks.
The paper proposes a method to learn 3D object pose manifolds using GANs and elasticae.
problem Learning image manifolds of 3D objects with limited data.
method Geom-SGAN and elasticae for geometry-preserving image interpolation.
result The method outperforms state-of-the-art GANs and VAEs in learning rotation paths.
We define general rotational surfaces of elliptic and hyperbolic type in the pseudo-Euclidean 4-space with neutral metric which are analogous to the general rotational surfaces of C. Moore in the Euclidean 4-space. We study Lorentz general rotational surfaces with plane meridian curves and give the complete classificat…
Study of timelike surfaces in Minkowski space with specific geometric properties.
problem Characterizing geometric properties of timelike surfaces in Minkowski space.
method Analytical study of two types of timelike general rotational surfaces.
result Explicit descriptions of minimal and surfaces with specific curvature properties.
The paper applies Clairaut's theorem to rotational surfaces in pseudo-Euclidean 4-space.
problem Exploring geodesic curves on rotational surfaces in pseudo-Euclidean 4-space.
method Expressing Clairaut's theorem and deriving equations for geodesic curves.
result Characterization of geodesic curves on hyperbolic and elliptic surfaces of rotation.
General rotational surfaces as a source of examples of surfaces in the four-dimensional Euclidean space have been introduced by C. Moore. In this paper we consider the analogue of these surfaces in the Minkowski 4-space. On the base of our invariant theory of spacelike surfaces we study general rotational surfaces with…
Study on dual surfaces of rotational minimal and maximal in Euclidean and Lorentz-Minkowski spaces.
problem Investigating the duality between minimal and maximal surfaces in different spaces.
method Analysis of rotational surfaces and use of one-parameter group of rotations.
result Family of Bonnet minimal and maximal surfaces emerge in the duality process.
The study characterizes helices in Euclidean and hyperbolic spaces.
problem Characterizing helices in Euclidean and hyperbolic spaces.
method Analyzing Killing vector fields associated with rotations in both spaces.
result Helices in hyperbolic space are geodesics on suitable surfaces.
Quantum mechanics applied to credit loans for better repayment schedules.
problem Improving repayment schedules for credit loans.
method Introducing quantum mechanics concepts to credit loans, defining operators for debt, amortization, interest, and installments, and using SO(M) symmetry to optimize periodic payments.
result Optimized repayment schedules for borrowers without altering lender's earnings.
The study characterizes loxodromes on specific rotational surfaces in 3D space.
problem Characterizing loxodromes on rotational surfaces with special geometric properties.
method Parametrizations and curvature/torsion calculations for loxodromes on various rotational surfaces.
result The loxodrome on a flat rotational surface is a general helix.
Unified method for efficient pricing of multivariate options.
problem Efficient pricing of complex financial options under multivariate models.
method Unified method using quadrature integration of multi-asset BSM prices, state space rotation.
result Unified method provides accurate and efficient pricing for basket, spread, and Asian options.
The study explores special surfaces in a normed space.
problem Constant Gaussian and mean curvature surfaces in normed spaces.
method Analyzes rotational surfaces with specific curvature properties.
result Generalizes catenoid, pseudo-sphere, and Delaunay surfaces.
The paper defines and analyzes homotopic rotation sets for surfaces of higher genus.
problem Defining and analyzing homotopic rotation sets for surfaces of higher genus.
method Developed a definition and proved several results using the theory of Le Calvez and Tal.
result Found that the homotopic rotation set can imply the existence of infinitely many periodic orbits under certain conditions.
Researchers create an exact entangling gate using braiding and measurement of Fibonacci anyons.
problem No known leakage-free entangling gate using braiding of Fibonacci anyons.
method Supplement braiding with measurement operations to produce an exact controlled rotation gate.
result Exact entangling gate on two qubits created using Fibonacci anyons and measurement.
Finite translation surfaces can be classified by the order of their singularities. When generalizing to infinite translation surfaces, however, the notion of order of a singularity is no longer well-defined and has to be replaced by new concepts. This article discusses the nature of two such concepts, recently introduc…
Quantum method prices options by evolving a state in imaginary time.
problem Pricing options in a quantum setting.
method Prepares an initial state, evolves it using imaginary time algorithms, and maps to quantum state.
result Numerical verification for European options; extension to path-dependent options.
Study rotational surfaces with prescribed Gauss curvature in 3D space.
problem Classify and analyze rotational surfaces with prescribed Gauss curvature.
method Phase plane analysis and mild assumptions on the prescribed function.
result Existence of singular radial solutions intersecting orthogonally the axis of rotation.
Wick rotations between pseudo-Riemannian spaces using real GIT.
problem Existence and non-existence of Wick-rotations between different pseudo-Riemannian spaces.
method Using real GIT to study structure groups of pseudo-Riemannian spaces as real forms of complex Lie groups.
result Derivation of new results regarding the existence and non-existence of Wick-rotations.
Classifies surfaces with special curvature properties.
problem Rotational surfaces with specific curvature conditions.
method Classifies surfaces with rotationally symmetric norms and linear curvature relations.
result Rotational surfaces with linearly related curvatures are classified.
Study on rotational surfaces in de Sitter space with specific curvature conditions.
problem Characterizing rotational surfaces in de Sitter space with Weingarten conditions.
method Analyzing spacelike and timelike rotational surfaces in 3D de Sitter space, determining profile curves, and classifying surfaces based on curvature relations.
result Classification of Weingarten rotational surfaces in de Sitter space with specific curvature relations.
Study on hypersurfaces in pseudo-Euclidean space with constant curvature or rotational properties.
problem Characterizing hypersurfaces in pseudo-Euclidean space.
method Defined and studied warped product hypersurfaces with constant sectional curvature or rotational properties.
result Hypersurfaces in pseudo-Euclidean space either have constant curvature or are contained in rotational hypersurfaces.
The paper classifies and constructs rotational surfaces with constant astigmatism in space forms.
problem Classifying surfaces with constant astigmatism in space forms.
method Classification and construction of surfaces using variational problems and binormal evolution.
result Locally constructed all rotational surfaces of constant astigmatism.
Review of conformal geometry in irrational rotation algebra.
problem Understanding conformal geometry of irrational rotation algebra.
method Review of recent progress by Connes and others.
result Recent progress in understanding conformal geometry.
In this work, we study a class of rotational surfaces in the pseudo-Euclidean space E24 whose profile curves lie in two-dimensional planes. We solve the differential equation that characterizes the rotational surfaces with zero mean curvature to determine the profile curves of such rotational surfaces. The…
New approach classifies rotational Weingarten surfaces in Lorentz-Minkowski space.
problem Classifying rotational Weingarten surfaces in Lorentz-Minkowski space.
method Using geometric linear momentum of generatrix curves with respect to axes of revolution.
result Unified framework for three causal types of rotation axes.
Improved CNNs for image classification tasks with rotational invariance.
problem Improving CNN performance for tasks with rotation invariance.
method Rotation-equivariant and rotation-invariant encoding using 2D-DFT magnitude responses and efficient convolutional schemes.
result Significant improvement in classification accuracy and robustness to hyperparameters.
Efficiently estimates rotations with corrupted data.
problem Rotation synchronization under high corruption and noise.
method Message passing algorithm with reweighted least squares.
result Superior performance over state-of-the-art methods.
In the four-dimensional pseudo-Euclidean space with neutral metric there are three types of rotational surfaces with two-dimensional axis - rotational surfaces of elliptic, hyperbolic or parabolic type. A surface whose mean curvature vector field is lightlike is said to be quasi-minimal. In this paper we classify all q…
Harmonic Networks make images equivariant to translation and rotation.
problem Making CNNs equivariant to rotation.
method Replacing CNN filters with circular harmonics to achieve patch-wise translation and 360-degree rotation equivariance.
result Deep feature maps encode complicated rotational invariants.
The paper explores connections between three equations via Wick rotations and symmetries.
problem Investigating relations between solutions to specific equations under Wick rotations.
method Analyzing symmetries and transformations of solutions to the minimal surface, zero mean curvature, and Born-Infeld equations.
result Existence conditions and transformations of real and imaginary solutions under Wick rotations.
The study disproves rotating ancient flows in 4D space.
problem The existence of rotating ancient flows in R4. method Analysis of ancient noncollapsed flows in R4. result Nonexistence of rotating ancient flows among ancient noncollapsed flows in R4. Solves scalar curvature equations for rotation invariant Kähler metrics on complex space.
problem Finding rotation invariant Kähler metrics with constant scalar curvature on complex space.
method Reduces the scalar curvature equation to a system of ODEs and solves them.
result Obtains complete lists of rotation invariant metrics with zero or positive scalar curvature in lower dimensions.
New surfaces in Lorentz-Minkowski space with constant mean curvature identified.
problem Identifying surfaces with constant mean curvature in Lorentz-Minkowski space.
method Using a specific coordinate system and properties of the Weingarten endomorphism, the mean curvature is shown to be constant under certain conditions.
result Constant mean curvature surfaces identified, including spacelike and timelike Enneper surfaces.
In this paper, we study general rotational surfaces in the 4- dimensional pseudo-Euclidean space E4-2 and obtain a characterization of flat general rotation surfaces with pointwise 1-type Gauss map in E4-2 and give an example of such surfaces.
Study proves stability of slowly rotating Kerr black holes.
problem Stability of slowly rotating Kerr black holes.
method Linear stability analysis using wave map/DeTurck gauge, microlocal analysis, and non-elliptic Fredholm theory.
result Linearized perturbations decay at an inverse polynomial rate.
Study classifies rotational hypersurfaces with prescribed mean curvature.
problem Classifying rotational hypersurfaces with prescribed mean curvature.
method Phase space analysis to classify hypersurfaces.
result Delacunay-type classification for even prescribed functions.
In this paper, we study rotational surfaces of elliptic, hyperbolic and parabolic type with pointwise 1-type Gauss map which have spacelike profile curve in four dimensional pseudo Euclidean space E4-2 and obtain some characterizations for these rotational surfaces to have pointwise 1-type Gauss map.
Minimal surfaces found in 4D space.
problem Minimal surfaces in 4D space.
method Reduced biharmonic equation to ODEs, excluded non-minimal solutions.
result Biharmonic rotational surfaces in 4D are minimal.
The paper classifies surfaces with constant skew curvature in 3-space forms.
problem Classifying surfaces with constant skew curvature in 3-space forms.
method Variational characterization and flow of binormal vector field.
result Classification of rotational surfaces with constant skew curvature.
The paper characterizes special curves and generalizes rectifying-type curves in n-dimensional space.
problem Characterizing and generalizing special curves in higher dimensions.
method Characterization through Rotation minimizing frame (RMF) and generalization of rectifying-type curves.
result Rectifying-type curves are generalized in n-dimensional space.
We study the third Laplace-Beltrami operator of timelike rotational surface of (T,L)-type in three dimensional Lorentz-Minkowski space.