Cryptocurrencies are ranked for efficiency using a new Complexity-Entropy Plane.
problem Evaluating the efficiency of cryptocurrencies using traditional financial metrics.
method Developed a Binary Complexity-Entropy Plane (BiCEP) to analyze daily price fluctuations of major cryptocurrencies.
result Only Shiba Inu (SHIB) is significantly inefficient, while most cryptocurrencies operate in close-to-efficient conditions.
This study analyzes cryptocurrency price dynamics using complexity-entropy causality.
problem Understanding the price dynamics of cryptocurrencies during market booms and busts.
method Used permutation-information-theory quantifiers and complexity-entropy causality plane.
result Discerned three distinct dynamics in cryptocurrency price data.
Paper analyzes Libor rates using information theory to detect abnormal movements around the financial crisis.
problem Detecting abnormal movements in Libor rates during the financial crisis.
method Complexity-Entropy Causality Plane analysis with moving windows.
result Abnormal movements in Libor rates around the financial crisis period.
This paper analyzes several interest rates time series from the United Kingdom during the period 1999 to 2014. The analysis is carried out using a pioneering statistical tool in the financial literature: the complexity-entropy causality plane. This representation is able to classify different stochastic and chaotic reg…
Machine learning and complexity-entropy methods estimate liquid crystal properties from textures.
problem Extracting physical properties from liquid crystal textures.
method Combining permutation entropy, statistical complexity, and machine learning.
result Significant precision in predicting physical properties of liquid crystals.
The role of credit rating agencies has been under severe scrutiny after the subprime crisis. In this paper we explore the relationship between credit ratings and informational efficiency of a sample of thirty nine corporate bonds of US oil and energy companies from April 2008 to November 2012. For that purpose, we use …
We study the temporal evolution of the market efficiency in the stock markets using the complexity, entropy density, standard deviation, autocorrelation function, and probability distribution of the log return for Standard and Poor's 500 (S&P 500), Nikkei stock average index, and Korean composition stock price index (K…
Cryptocurrency time-series predictability is low, resembling Brownian noise.
problem Low predictability of cryptocurrency exchange rates.
method Complexity and model predictions of Litecoin, Binance Coin, Bitcoin, Ethereum, and XRP exchange rates.
result Simpler models outperform complex ones in cryptocurrency forecasting.
Cognitive abstraction metrics predict deep neural networks' generalization ability.
problem Understanding deep neural networks' generalization ability.
method Defined Cognitive Neural Activation (CNA) metric based on information complexity and activation patterns.
result CNA is highly predictive of generalization ability, outperforming other metrics.
Study examines market response to concentrated policy communication using entropy measures.
problem Characterizing market response under concentrated policy communication.
method Jointly examines dispersion and information complexity (entropy) using sliding window cumulative entropy.
result Entropy captures both market volatility and narrative constraints, signaling coherent policy-driven moves.
Using symplectic topology and the Radon transform, we prove that smooth 4-dimensional projective planes are diffeomorphic to CP2. We define the notion of a plane curve in a smooth projective plane, show that plane curves in high dimensional regular planes are lines, prove that homeomorphisms preserving plan…
We define generalized distance-squared mappings, and we concentrate on the plane to plane case. We classify generalized distance-squared mappings of the plane into the plane in a recognizable way.
The study classifies semiaffine stable planes into affine, projective, or punctured projective planes.
problem Characterizing semiaffine stable planes.
method Analyzing properties of lines and points in stable planes.
result Semiaffine stable planes are either affine, projective, or punctured projective planes.
Extends results on automorphism groups of flat Minkowski planes to toroidal circle planes.
problem Understanding automorphism groups of toroidal circle planes.
method Extending Schenkel's results to toroidal circle planes.
result Automorphism groups of toroidal circle planes have dimensions at most 6 and can have dimensions at least 4 or kernels of dimension 3.
Stable planes are locally isomorphic to classical projective planes.
problem Characterizing stable planes that are locally isomorphic to classical projective planes.
method Analyzing properties of stable planes and comparing them to classical projective planes over specific fields.
result Simply connected stable planes with connected lines are isomorphic to open subplanes of classical projective planes.
Only vertical planes are asymptotic to other planes in 3D space.
problem Characterizing asymptotic planes in 3D space.
method Proof of uniqueness for complete translators with finite topology.
result Vertical planes are the only asymptotic planes in 3D space.
Study of elementary planes in Apollonian orbifold with unusual equidistribution.
problem Equidistribution failure in Apollonian orbifold.
method Complete list of elementary planes, boundary data analysis.
result Uniform boundedness of elementary plane areas and closed union.
Generic smooth plane-to-plane map germs are topologically equivalent to cones of mappings of the circle. We carry out a complete topological classification of smooth stable mappings of the circle and show how this classification leads, via the result mentioned above, to a topological classification of finitely determin…
Criteria for sharksfin and deltoid singularities from plane to plane, with applications.
problem Identifying and understanding singularities in plane-to-plane mappings.
method Providing criteria and geometric meanings for singularities.
result Geometric meanings and criteria for sharksfin and deltoid singularities.
Crooked planes in 3D Minkowski space can be foliated.
problem Understanding foliations between crooked planes in 3D Minkowski space.
method Showed that any two disjoint crooked planes are leaves of a crooked foliation.
result Answered a question about foliations between crooked planes in 3D Minkowski space.
We study two types of isotropic planes: weakly isotropic and strongly isotropic planes. We prove that a Riemannian manifold of indefinite metric is conformally flat if and only if its curvature tensor vanishes on all the strongly isotropic planes. We specialize the plane axiom for Riemannian manifolds of indefinite met…
New manifolds with many hyperbolic planes, not homogeneous.
problem Constructing non-homogeneous manifolds with many hyperbolic planes.
method Constructing manifolds with geodesics in hyperbolic planes.
result Non-homogeneous manifolds with many hyperbolic planes exist.
Researchers found parallel mean curvature tori in complex projective and hyperbolic planes.
problem Finding tori with parallel mean curvature vectors.
method Explicit determination of tori in complex projective and hyperbolic planes.
result Explicit determination of tori with parallel mean curvature vectors in both complex projective and hyperbolic planes.
For a pair of points in a smooth locally convex surface in 3-space, its mid-plane is the plane containing its mid-point and the intersection line of the corresponding pair of tangent planes. In this paper we show that the limit of mid-planes when one point tends to the other along a direction is the Transon plane of th…
The study explores conformal planes with finite areas.
problem Geometry of conformal planes with finite areas.
method Analyzes several questions about conformal planes.
result Exploration of conformal planes with finite areas.
Calculates first exit times for Brownian motion in Euclidean and hyperbolic planes.
problem Computing expected first exit times for Brownian motion.
method Analytical computation for Brownian motion in Euclidean and hyperbolic planes.
result Results in expected first exit times for specified domains.
We construct a compact nonpositively curved squared 2-complex whose universal cover contains a flat plane that is not the limit of periodic flat planes.
This thesis explores bifoliated planes and their group actions from Anosov flows.
problem Understanding bifoliated planes and their group actions from Anosov flows.
method Analyzes bifoliated planes associated with Anosov flows and describes their properties.
result Shows left-orderability of groups acting on bifoliated planes and describes bifoliated planes from specific families of Anosov flows.
We use reduced homogeneous coordinates to study Riemannian geometry of the octonionic (or Cayley) projective plane. Our method extends to the para-octonionic (or split octonionic) projective plane, the octonionic projective plane of indefinite signature, and the hyperbolic dual of the octonionic projective plane; we di…
The paper extends curve curvature types from normed to gauge planes.
problem Extending curve curvature classification to gauge planes.
method Using gauge analogue of Birkhoff orthogonality and differential geometry.
result Four curvature types (Minkowski, normal, circular, arc-length) are identified.
Two proofs show that removing a loop from a plane circuit splits the plane.
problem Proving the Weak Jordan Theorem about plane circuits.
method Detailed presentation of Thomassen's and Filippov's proofs.
result The complement of any loop in a plane circuit is disconnected.
Study fake projective planes using recent results to show bicanonical map is always an embedding and construct an exceptional collection.
problem Analyzing Keum's fake projective planes and their geometric properties.
method Apply recent results from Galkin et al. [GKMS15] to study fake projective planes.
result The bicanonical map of Keum's fake projective planes is always an embedding.
New findings on plane waves in 3D spacetimes, showing non-unimodular elliptic plane waves are unique.
problem Classifying Lorentz homogeneous spaces of dimension 3, focusing on plane waves.
method Revisiting and relaxing usual completeness assumptions, characterizing homogeneous plane waves.
result Non-unimodular elliptic plane waves are unique and non-extendable, geodesically complete only if symmetric.
The paper classifies singularities of plane congruences and affine distance functions.
problem Classifying singularities of plane congruences and affine distance functions.
method Classification through 2-parameter plane congruences in \(\mathbb{R^4}\) and affine normal plane congruences.
result Generic singularities of plane congruences and affine distance functions are classified.
Computed distortion coefficients for the α-Grushin plane.
problem Analyzing the distortion coefficients of the α-Grushin plane.
method Using generalised trigonometric functions and synthetic curvature conditions.
result Estimates for distortion coefficients and a curvature condition conjecture.
Classifies toroidal circle planes with 3D automorphism groups.
problem Classifying toroidal circle planes with specific automorphism groups.
method Using almost simple Lie groups and their isomorphism to PSL(2, R), a framework for classification is described.
result Three-dimensional connected automorphism groups are isomorphic to PSL(2, R).
The paper studies stable mappings of plane curves using distance-squared functions.
problem Stability of mappings of plane curves.
method Investigation of compositions of plane curves and generic distance-squared mappings.
result Stable mappings of plane curves are explored.
Proves Ptolemaean Inequality and Theorem in complex hyperbolic plane.
problem None explicitly stated, but related to complex hyperbolic geometry.
method Proof of Ptolemaean Inequality and Theorem in complex hyperbolic plane with Cygan metric.
result Proves Ptolemaean Inequality and Ptolemaeus' Theorem in the closure of complex hyperbolic plane.
Study compact plane waves, showing they are essentially standard.
problem Understanding the topology and dynamics of compact plane waves.
method Analyzing quotients of homogeneous plane waves by discrete subgroups.
result Compact quotients of homogeneous plane waves are essentially standard.
New harmonic maps to hyperbolic plane via Bäcklund transformation.
problem Constructing new harmonic maps to the hyperbolic plane.
method Using Bäcklund transformation to connect solutions of sinh-Gordon and sine-Gordon equations.
result Construction of new harmonic maps.
Paper generalizes splitting number to classify plane curve arrangements.
problem Distinguishing embedded topology of plane curves.
method Introduces splitting graph to generalize splitting number.
result Classifies embedded topology of specific plane curve arrangements.
New classification of 16D planes with specific automorphism groups.
problem Classifying 16-dimensional projective planes with certain automorphism groups.
method Detailed analysis and classification of 16-dimensional planes with specific automorphism properties.
result Classification of 16-dimensional planes with a group of dimension at least 35, excluding planes fixed by exactly one flag.
The paper examines asymptotic lines of plane fields in 3D space.
problem Qualitative properties of asymptotic lines in plane fields.
method Analysis of null directions and Gaussian curvature.
result Asymptotic lines coincide with classical ones in completely integrable fields.
A 6-regular triangulation for hyperbolic plane created.
problem Creating a 6-regular triangulation for hyperbolic plane.
method Constructed a 6-regular geodesic triangulation.
result A 6-regular geodesic triangulation of the hyperbolic plane was successfully created.
Study local and global aspects of complex plane curve embeddings.
problem Local and global problems of complex plane curve embeddings.
method Braid monodromy, local and global analysis.
result Historical progress in understanding complex plane curve embeddings.
Improved bounds on Laplace-Beltrami operator eigenvalues on real projective plane.
problem Improving upper bounds for Laplace-Beltrami operator eigenvalues.
method Analyzing eigenvalues with even indexes and providing bounds for Dirichlet, Neumann, and Steklov eigenvalues.
result Enhanced upper bounds for Laplace-Beltrami operator eigenvalues on the real projective plane.
A diffeomorphism of pseudo-Riemannian manifolds is called sectional curvature preserving if it preserves the sectional curvature of all the nondegenerate 2-planes. We consider a similar condition for degenerate 2-planes and we prove that the diffeomorphism is conformal (when the condition is fulfilled for weakly degene…
A classical result asserts that the complex projective plane modulo complex conjugation is the 4-dimensional sphere. We generalize this result in two directions by considering the projective planes over the normed real division algebras and by considering the complexifications of these four projective planes.