arXiv research

Develops a new method to model overlapping asymmetric datasets effectively.

Deep P-Spline automates DNN structure selection for complex regression problems.

Adaptive algorithm improves nonlinear data assimilation for non-Gaussian systems.

We investigate the elastic behavior of knotted loops of springy wire. To this end we minimize the classic bending energy $E_{\text{bend}}=\intκ^2$ together with a small multiple of ropelength $\mathcal R=\text{length}/\text{thickness}$ in order to penalize selfintersection. Our main objective is to characterize elastic…

Hedonic models predict 84-92% of U.S. real estate prices, highlighting environmental factors' impact.

A new knot selection method for GAMs reduces model complexity.

Study classifies metrics on a twice-punctured sphere, proving Delaunay metrics are complete.

Connected graph for twice-punctured torus curves.

New algebra for twice-punctured torus curves.

Let $D_n$ be the $n$-punctured disk. We prove that a family of essential simple arcs starting and ending at the boundary and pairwise intersecting at most twice is of size at most $\binom{n+1}{3}$. On the way, we also show that any nontrivial square complex homeomorphic to a disk whose hyperplanes are simple arcs inter…

We calculate the asymptotic behavior of the Kashaev invariant of a twice-itarated torus knot and obtain topological interpretation of the formula in terms of the Chern--Simons invariant and the twisted Reidemeister torsion.

Small sub-Riemannian balls have diameter close to twice their radius.

Model uses GAMs to forecast hourly electricity load weeks to one year ahead.

Hyperbolic links in handlebodies can be composed, unlike in 3-sphere.

Study shows how certain knots and tori are detected by ideal points in character varieties.

New proof of SL(n) skein algebra for twice punctured sphere, showing it's a polynomial algebra.

Conditional Autoregressive Value-at-Risk and Conditional Autoregressive Expectile have become two popular approaches for direct measurement of market risk. Since their introduction several improvements both in the Bayesian and in the classical framework have been proposed to better account for asymmetry and local non-l…

We show for an alternating knot the minimal boundary slope of an essential spanning surface is given by the signature plus twice the minimum degree of the Jones polynomial and the maximal boundary slope of an essential spanning surface is given by the signature plus twice the maximum degree of the Jones polynomial. For…

Let p be a puncture of a punctured sphere, and let Q be the set of all other punctures. We prove that the maximal cardinality of a set of arcs pairwise intersecting at most once, which start at p and end in Q, is |X|(|X| + 1). We deduce that the maximal cardinality of a set of arcs with arbitrary endpoints pairwise int…

Study shows constraints on slopes for knot manifolds with specific tori.

Suppose M is a compact orientable irreducible 3-manifold with Heegaard splitting surfaces P and Q. Then either Q is isotopic to a possibly stabilized copy of P or the Hempel distance of the splitting P is no greater than twice the genus of Q. More generally, if P and Q are bicompressible but weakly incompressible conne…

CD converges linearly for MCP/SCAD penalized least squares.

Pareto's 80/20 rule follows a Gaussian distribution with twice the mean standard deviation.

The total diameter of a closed planar curve $C\subset R^2$ is the integral of its antipodal chord lengths. We show that this quantity is bounded below by twice the area of $C$. Furthermore, when $C$ is convex or centrally symmetric, the lower bound is twice as large. Both inequalities are sharp and the equality holds i…

Model learns brevity by exposing to easy problems, improving efficiency without explicit length penalties.

In this note we construct a family of immersions with constant mean curvature of the twice-punctured Riemann sphere into R^3 from the Bessel equation.

TensorSketch is an oblivious linear sketch introduced in Pagh'13 and later used in Pham, Pagh'13 in the context of SVMs for polynomial kernels. It was shown in Avron, Nguyen, Woodruff'14 that TensorSketch provides a subspace embedding, and therefore can be used for canonical correlation analysis, low rank approximation…

Thompson Sampling is at most twice as bad as any other policy in Bayesian bandit models.

We develop an algebraic representation for (1,1)-knots using the mapping class group of the twice punctured torus MCG(T,2). We prove that every (1,1)-knot in a lens space L(p,q) can be represented by the composition of an element of a certain rank two free subgroup of MCG(T,2) with a standard element only depending on …

AgFlow speeds up model selection in penalized PCA.

We consider the Willmore functional on graphs, with an additional penalization of the area where the curvature is non-zero. Interpreting the penalization parameter as a Lagrange multiplier, this corresponds to the Willmore functional with a constraint on the area where the graph is flat. Sending the penalization parame…

We prove that the Morse-Novikov number of a link L in a 3-sphere is less than or equal to twice the tunnel number of L.

It is shown that the diameter of the boundary slope set is bounded from above by the twice of the minimal crossing number for a Montesinos knot.

Sparse-penalized deep neural networks improve performance in weakly dependent processes.

Develops a method to predict stock returns with time-varying risk premia.

We give two applications of the the duality between the complex Homogeneous Monge-Ampère Equation (HMAE) and the Hele-Shaw flow. First, we prove existence of smooth boundary data for which the weak solution to the Dirichlet problem for the HMAE over $\mathbb P^1\times \overline{\mathbb D}$ is not twice differentiable a…

Trading floors need to be twice as deep as electronic markets to compete.

Paper develops a new method for optimal stopping in American options.

A generalization of the volume conjecture relates the asymptotic behavior of the colored Jones polynomial of a knot to the Chern--Simons invariant and the Reidemeister torsion of the knot complement associated with a representation of the fundamental group to the special linear group of degree two over complex numbers.…

In high-dimensional data analysis, penalized likelihood estimators are shown to provide superior results in both variable selection and parameter estimation. A new algorithm, APPLE, is proposed for calculating the Approximate Path for Penalized Likelihood Estimators. Both the convex penalty (such as LASSO) and the nonc…

We describe a procedure for creating infinite families of knots, each having the maximum degree of their HOMFLY polynomial strictly less than twice their canonical genus. These families build upon examples first found by Stoimenow.

In this paper, we propose a one-pass algorithm on MapReduce for penalized linear regression \[f_λ(α, β) = \|Y - α\mathbf{1} - Xβ\|_2^2 + p_λ(β)\] where $α$ is the intercept which can be omitted depending on application; $β$ is the coefficients and $p_λ$ is the penalized function with penalizing parameter $λ$. $f_λ(α, β…

In the present paper we consider the problem of the existence of pre-semigeodesic coordinates on manifolds with affine connection. We proved that pre-semigeodesic coordinates exist in the case when the components of the affine connection are twice differentiable functions.

In this work we establish the equivalence of algorithmic regularization and explicit convex penalization for generic convex losses. We introduce a geometric condition for the optimization path of a convex function, and show that if such a condition is satisfied, the optimization path of an iterative algorithm on the un…

New insights into balancing reward and fairness in stochastic MAB.

The MM algorithm improves robust penalized estimation for outlier-contaminated data.

The paper classifies and analyzes the stability of elastic curves with fixed endpoints.

We extend the analysis of investment strategies derived from penalized quantile regression models, introducing alternative approaches to improve state\textendash of\textendash art asset allocation rules. First, we use a post\textendash penalization procedure to deal with overshrinking and concentration issues. Second, …