A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Hashing, or learning binary embeddings of data, is frequently used in nearest neighbor retrieval. In this paper, we develop learning to rank formulations for hashing, aimed at directly optimizing ranking-based evaluation metrics such as Average Precision (AP) and Normalized Discounted Cumulative Gain (NDCG). We first o…
Proposes a method to enhance multi-view learning by maximizing higher order correlations.
problem Losing intrinsic interconnections among multiple views in pairwise correlation maximization.
method Formulates multi-view data as a low rank approximation problem using higher order correlation tensor and solves it with the generating polynomial method.
result Consistently outperforms prior methods on real multi-view data.
We show that if a closed manifold M admits an F-structure (possibly of rank 0) then its minimal entropy vanishes. In particular, this is the case if M admits a non-trivial circle action. As a corollary we obtain that the simplicial volume of a colsed manifold admitting an F-structure is zero. We also show that if M adm…
In many applications that require matrix solutions of minimal rank, the underlying cost function is non-convex leading to an intractable, NP-hard optimization problem. Consequently, the convex nuclear norm is frequently used as a surrogate penalty term for matrix rank. The problem is that in many practical scenarios th…
In many applications that require matrix solutions of minimal rank, the underlying cost function is non-convex leading to an intractable, NP-hard optimization problem. Consequently, the convex nuclear norm is frequently used as a surrogate penalty term for matrix rank. The problem is that in many practical scenarios th…
We show the set of faithful representations of a closed orientable hyperbolic surface group is dense in both irreducible components of the PSL(2,K) representation variety, where K is the field of real or complex numbers, answering a question of W. Goldman. We also prove the existence of faithful representations into PU…
The symmetry-rank of a riemannian manifold is by definition the rank of its isometry group. We determine precisely which smooth closed manifolds admit a positively curved metric with maximal symmetry-rank.
Nowadays, how to effectively evaluate visual properties has become a popular topic for fine-grained visual comprehension. In this paper we study the problem of how to estimate such visual properties from a ranking perspective with the help of the annotators from online crowdsourcing platforms. The main challenges of ou…
Ranking stock indices based on causal influence using directed information graphs.
problem Identifying which countries exert the most economic influence in a subset of the global economy.
method Representing indices as nodes in a directed graph, estimating causal influences using directed information functional, ranking indices based on net-flow.
result Indices representing smaller economies can exert significant influence on larger economies.
For a given lattice, we establish an equivalence involving a closed zone of the corresponding Voronoi polytope, a lamina hyperplane of the corresponding Delaunay partition and a quadratic form of rank 1 being an extreme ray of the corresponding L-type domain.
Study on Finsler spaces with unique prime geodesics.
problem Estimating the number of orbits of prime closed geodesics in Finsler manifolds.
method Generalizing works on two prime closed geodesics to equivariant situation, studying homogeneous Finsler geometry.
result Closed Finsler manifold with only one orbit of prime closed geodesic is a compact rank-one Riemannian symmetric space when dimension is even or metric is reversible.
Politicians world-wide frequently promise a better life for their citizens. We find that the probability that a country will increase its {\it per capita} GDP ({\it gdp}) rank within a decade follows an exponential distribution with decay constant λ=0.12. We use the Corruption Perceptions Index (CPI) and the Global …
Study manifolds with positive intermediate Ricci curvature and large symmetry rank.
problem Closed, simply connected manifolds with positive 2nd-intermediate Ricci curvature and large symmetry rank.
method New tools for studying isometric actions on closed manifolds with positive kth-intermediate Ricci curvature, including isotropy rank lemma, symmetry rank bound, and connectedness principle.
result Even dimensional manifolds with large symmetry rank must have trivial odd degree integral cohomology and are either spheres or complex projective spaces.
We observe that stable integral simplicial volume of closed manifolds gives an upper bound for the rank gradient of the corresponding fundamental groups.