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Optimal Metric Projections for Deformable and Articulated Structure-from-Motion
TLDR
An efficient convex relaxation for the non-convex projection step is introduced to solve for non-rigid 3D shape and motion, associated with a globally optimal projection step of the motion matrices onto the manifold of metric constraints.
Factorization for non-rigid and articulated structure using metric projections
TLDR
An alternating least-squares approach associated with a globally optimal projection step onto the manifold of metric constraints for recovering the 3D shape and motion of deformable and articulated objects purely from uncalibrated 2D image measurements is proposed.
sl.N/-link homology (N 4) using foams and the Kapustin-Li formula
We use foams to give a topological construction of a rational link homology categorifying the slN link invariant, for N>3. To evaluate closed foams we use the Kapustin-Li formula adapted to foams by
Quadruply-graded colored homology of knots
We conjecture the existence of four independent gradings in colored HOMFLYPT homology, and make qualitative predictions of various interesting structures and symmetries in the colored homology of
An Angular Approach for Range-Based Approximate Maximum Likelihood Source Localization Through Convex Relaxation
TLDR
This work considers the problem of locating a single source from noisy range measurements to a set of nodes in a wireless sensor network and proposes two new techniques, which extend to arbitrary real dimensions, which globally outperform state-of-the-art optimization-based methods in different noise scenarios, while exhibiting moderate computational complexity.
Homological algebra of knots and BPS states
It is known that knot homologies admit a physical description as spaces of open BPS states. We study operators and algebras acting on these spaces. This leads to a very rich story, which involves
THE 1,2-COLOURED HOMFLY-PT LINK HOMOLOGY
In this paper we define the 1,2-coloured HOMFLY-PT triply graded link homology and prove that it is a link invariant. We also conjecture on how to generalize our construction for arbitrary colours.
A diagrammatic categorification of the q-Schur algebra
In this paper we categorify the q-Schur algebra Sq(n,d) as a quotient of Khovanov and Lauda’s diagrammatic 2-category Uq(sln)[16]. We also show that our 2-category contains Soergel’s [33] monoidal
On extended graphical calculus for categorified quantum $sl(n)$
We study the properties of the extended graphical calculus for categorified quantum $sl(n)$. The main results include proofs of Reidemeister 2 and Reidemeister 3-like moves involving strands
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