The paper explores constructing an invariant for s-move 3-cells using 2-cell decompositions.
problem Creating an invariant for s-move 3-cells.
method Using elementary 3-expansions and 2-cell decompositions, the paper constructs an invariant.
result The method provides a sequence of 2-cells to decompose s-move 3-cells.
We study capital process behavior in the fair-coin game and biased-coin games in the framework of the game-theoretic probability of Shafer and Vovk (2001). We show that if Skeptic uses a Bayesian strategy with a beta prior, the capital process is lucidly expressed in terms of the past average of Reality's moves. From t…
The Frenet frame generalizes the Park transform for multi-phase circuits.
problem Generalizing the Park transform for multi-phase circuits.
method Using the Frenet frame and Cartan's moving frames.
result The Frenet frame provides a new approach to circuit analysis.
Given a group action, known by its infinitesimal generators, we exhibit a complete set of syzygies on a generating set of differential invariants. For that we elaborate on the reinterpretation of Cartan's moving frame by Fels and Olver (1999). This provides constructive tools for exploring algebras of differential inva…
This research predicts vehicle movements by analyzing their intentions relative to road lanes.
problem Accurately forecasting vehicles' future movements for safe autonomous driving.
method LSTM networks with attention mechanisms applied to spatio-temporal graphs of road lanes.
result The model outperforms other state-of-the-art models in several metrics.
The paper studies relationships between twisted torsion and connected sums of 3-manifolds.
problem Understanding the topology and geometry of 3-manifolds through twisted torsion.
method Investigates the multiplicative property of twisted Reidemeister torsion and its connection to the connected sum operation.
result Establishes a relationship between the multiplicative property of twisted torsion and connected sums of 3-manifolds.
We consider product 4--manifolds S^1 X M, where M is a closed, connected and oriented 3-manifold. We prove that if S^1 X M admits a complex structure or a Lefschetz or Seifert fibration, then the following statement is true: S^1 X M admits a symplectic structure if and only if M fibers over S^1, under the additional as…
0-efficient triangulations of 3-manifolds are defined and studied. It is shown that any triangulation of a closed, orientable, irreducible 3-manifold M can be modified to a 0-efficient triangulation or M can be shown to be one of the manifolds S^3, RP^3 or L(3,1). Similarly, any triangulation of a compact, orientable, …
We study multistep Bayesian betting strategies in coin-tossing games in the framework of game-theoretic probability of Shafer and Vovk (2001). We show that by a countable mixture of these strategies, a gambler or an investor can exploit arbitrary patterns of deviations of nature's moves from independent Bernoulli trial…
New CR structures found for once-punctured torus bundles.
problem No natural CR realisation for hyperbolic once-punctured torus bundles.
method Introduced a new cell decomposition and branched CR structure.
result Every hyperbolic once-punctured torus bundle admits a branched CR structure.
Develops algorithms for constructing moving frames and differential invariants for Lie group actions.
problem Equivalence of submanifolds under Lie group actions.
method Introduces two algorithms: a product group algorithm and a recursive algorithm.
result Constructs differential invariants and moving frames for groups of transformations on the plane.
The paper solves video object segmentation without supervision using nonconvex optimization.
problem Unsupervised video object segmentation via background subtraction.
method Formulates the problem as a nonnegative variant of robust principal component analysis, ensuring global optimality under certain conditions.
result Conditions guaranteeing the uniqueness and global optimality of object segmentation are derived and demonstrated with real data.
New method for curve comparison using iterated integrals and moving frames.
problem Comparing curves robustly to noise and transformations.
method Moving frame method paired with log-signature transform.
result Algorithmic construction of invariants for curve equivalence under rigid motions.
Paper predicts cryptocurrency bull and bear phases using Bitcoin's moving averages.
problem Determining cryptocurrency bull and bear phases based on Bitcoin performance.
method Employing predictive algorithms to forecast Bitcoin's 50 Day and 200 Day Moving Averages.
result Predicted data from Bitcoin's moving averages helps identify potential bull and bear phases.
We create a 3-skeleton for a symmetric group's classifying space.
problem Classifying space construction for symmetric groups.
method Combining rewriting systems and combinatorial methods.
result Correctness of the constructed 3-skeleton.
Study of nonlocal mean curvature and symmetry of surfaces.
problem Symmetry of surfaces with ordered nonlocal mean curvature.
method Generalization of Alexandrov's moving plane method.
result Similar result to classical setting proved in nonlocal setting.
Proves least Gaussian perimeter decomposition conjectures for 2-3 cells in n-dimensional space.
problem Finding least perimeter ways to divide space into cells of prescribed Gaussian measure.
method Analyzes stable clusters and uses Voronoi cells of equidistant points.
result Simplicial clusters are unique minimizers for 2-3 cells in n-dimensional space.
Paper defines a new invariant for 4-manifolds with boundary.
problem Defining a new invariant for 4-manifolds with boundary.
method Defined the relative L-invariant by measuring path lengths in the cut complex of a trisection surface.
result Shows that if a rational homology ball has a zero relative L-invariant, it must be the 4-ball.
Causal classification of three Misner-type spacetimes.
problem Causal structure and isocausality of three spacetimes.
method Formal proof of pairwise isocausality on covers and compactified spacetimes.
result Explicit causal bijections and deck-equivariance criterion for isocausality.
LARNN improves LSTM's performance with attention and multi-head mechanism.
problem Improving LSTM's performance in sequence prediction tasks.
method Derived from LSTM and RNN, LARNN uses attention and multi-head mechanism to query past states.
result LARNN achieves 91.92% test accuracy, significantly better than vanilla LSTM.