arXiv research

MARVIN offers an open ML environment for automated primitive annotation and execution.

Berge introduced knots that are primitive/primitive with respect to the genus 2 Heegaard surface, $F$, in $S^3$; surgery on such knots at the surface slope yields a lens space. Later Dean described a similar class of knots that are primitive/Seifert with respect to $F$; surgery on these knots at the surface slope yield…

The twisted torus knots lie on the standard genus 2 Heegaard surface for $S^3$, as do the primitive/primitive and primitive/Seifert knots. It is known that primitive/primitive knots are fibered, and that not all primitive/Seifert knots are fibered. Since there is a wealth of primitive/Seifert knots that are twisted tor…

Primitive curves in handlebodies form a connected complex.

Note on connectedness of primitive disk complex.

Study primitive cohomology in symplectic manifolds.

Disk surgery on primitive disks of genus-3 Heegaard splittings of 3-sphere yields no primitive disks.

No primitive Teichmüller curves found in Prym(2,2).

The paper analyzes vehicle encounters using driving primitives.

A symplectic form has a primitive with nowhere vanishing $β$.

We show that lens space surgeries on knots in $S^3$ which arise from the primitive/Seifert type construction also arise from the primitive/primitive construction. This is the first step of a three step program to prove the Berge conjecture for tunnel number one knots.

For a genus two Heegaard splitting of a lens space, the primitive disk complex is defined to be the full subcomplex of the disk complex for one of the handlebodies of the splitting spanned by all vertices of primitive disks. In this work, we describe the complete combinatorial structure of the primitive disk complex fo…

We show that the exterior derivative operator on a symplectic manifold has a natural decomposition into two linear differential operators, analogous to the Dolbeault operators in complex geometry. These operators map primitive forms into primitive forms and therefore lead directly to the construction of primitive cohom…

Study primitive decompositions for harmonic forms on almost Kähler manifolds.

In this article, we prove that every arithmetic locally symmetric orbifold of classical type without Euclidean or compact factors has arbitrarily long arithmetic progressions in its primitive length spectrum. Moreover, we show the stronger property that every primitive length occurs in arbitrarily long arithmetic progr…

A twisted torus knot is a knot obtained from a torus knot by twisting adjacent strands by full twists. The twisted torus knots lie in $F$, the genus 2 Heegaard surface for $S^3$. Primitive/primitive and primitive/Seifert knots lie in $F$ in a particular way. Dean gives sufficient conditions for the parameters of the tw…

Two conditions on primitive elements are shown to be equivalent.

A new reinforcement learning approach using competitive primitives that specialize and specialize based on information needs.

Algorithm finds smooth primitives for exact forms.

In this paper, we give a complete criterion for a discrete faithful representation $ρ:F_n \ra \pslc$ to be primitive stable. This will answer Minsky's conjectures about geometric conditions on $\H^3/ρ(F_n)$ regarding the primitive stability of $ρ$.

We call a pair (K, m) of a knot K in the 3-sphere S^3 and an integer m a Seifert fibered surgery if m-surgery on K yields a Seifert fiber space. For most known Seifert fibered surgeries (K, m), K can be embedded in a genus 2 Heegaard surface of S^3 in a primitive/Seifert position, the concept introduced by Dean as a na…

Study shows annotation instrument design affects model performance in hate speech detection.

We give a formula for Alexander polynomials of doubly primitive knots.

Considering the driving habits which are learned from the naturalistic driving data in the path-tracking system can significantly improve the acceptance of intelligent vehicles. Therefore, the goal of this paper is to generate the prediction results of lateral commands with confidence regions according to the reference…

Proves a vanishing property for symplectic manifold cohomology.

Two Riemannian manifolds are called eigenvalue equivalent when their sets of eigenvalues of the Laplace-Beltrami operator are equal (ignoring multiplicities). They are (primitive) length equivalent when the sets of lengths of their (primitive) closed geodesics are equal. We give a general construction of eigenvalue equ…

Clearing algorithm improves CT image segmentation accuracy by merging confident annotations.

We show that closed 3-manifolds with high Heegaard distance and bounded subsurface Heegaard distance are primitive stable when they are regarded as representations from the free group corresponding to the handlebody. This implies that any point on the boundary of Schottky space can be approximated by primitive stable r…

In this article, we investigate when the set of primitive geodesic lengths on a Riemannian manifold have arbitrarily long arithmetic progressions. We prove that in the space of negatively curved metrics, a metric having such arithmetic progressions is quite rare. We introduce almost arithmetic progressions, a coarsific…

New method to estimate doctors' effort in annotating medical images.

We introduce new boundary conditions for differential forms on symplectic manifolds with boundary. These boundary conditions, dependent on the symplectic structure, allows us to write down elliptic boundary value problems for both second-order and fourth-order symplectic Laplacians and establish Hodge theories for the …

Active learning selects both observations and annotation precision for Gaussian Processes.

Study symplectic structures on open 4-manifolds with distinct primitive cohomologies.

Generative model combines multi-dimensional annotations for more accurate ground truth estimation.

A transitive smooth action of a connected Lie group G on a manifold M is called almost primitive (resp. primitive) if G doesn't contain any proper subgroup (resp. any proper normal subgroup) whose induced action on M is transitive as well. The aim of the present work is to investigate some combinatory properties of sym…

Survey on AL strategies for cost-effective annotation in classification.

RAD improves robustness to domain annotation noise without explicit domain annotations.

We construct a sequence of primitive-stable representations of free groups into PSL(2,C) whose ranks go to infinity, but whose images are discrete with quotient manifolds that converge geometrically to a knot complement. In particular this implies that the rank and geometry of the image of a primitive-stable representa…

Decides if elements in free groups are primitive in polynomial time.

Paper adapts and learns movement primitives robustly with probabilistic models.

We construct two infinite families of knots each of which admits a Seifert fibered surgery with none of these surgeries coming from Dean's primitive/Seifert-fibered construction. This disproves a conjecture that all Seifert fibered surgeries arise from Dean's primitive/Seifert-fibered construction. The (-3,3,5)-pretzel…

For random elements in free groups, we find a rank and set of subgroups.

We introduce new finite-dimensional cohomologies on symplectic manifolds. Each exhibits Lefschetz decomposition and contains a unique harmonic representative within each class. Associated with each cohomology is a primitive cohomology defined purely on the space of primitive forms. We identify the dual currents of lagr…

The study challenges the notion that partial data annotation is inferior, suggesting it can sometimes outperform complete annotation.

The goal of this paper is to offer a comprehensive exposition of the current knowledge about Heegaard splittings of exteriors of knots in the 3-sphere. The exposition is done with a historical perspective as to how ideas developed and by whom. Several new notions are introduced and some facts about them are proved. In …

Paper reduces movement primitive dimensionality in parameter space.

Embeddings of pairs of disjoint nonparallel primitive simple closed curves in the boundary of a genus two handlebody are classified. Briefly, two disjoint primitives either lie on opposite ends of a product $F \boldsymbol{\times} I$, or they lie on opposite ends of a kind of "twisted" product $F \widetilde{\boldsymbol{…

A new method uses triplet embeddings to improve human annotation for hidden constructs.