arXiv subjects

Seung Jin Lee

Publications and source records attributed to Seung Jin Lee.

23 records · Page 2Linked to original sources

arXiv2014

Distinct mechanisms of DNA sensing based on N-doped carbon nanotubes with enhanced conductance and chemical selectivity

Carrying out first-principles calculations, we study N-doped capped carbon nanotube (CNT) electrodes applied to DNA sequencing. While we obtain for the face-on nucleobase junction configurations a conventional conductance ordering where the largest signal results from guanine according to its high highest occupied molecular orbital (HOMO) level, we extract for the edge-on counterparts a distinct conductance ordering where the low-HOMO thymine provides the largest signal. The edge-on mode is shown to operate based on a novel molecular sensing mechanism that reflects the chemical connectivity between N-doped CNT caps that can act both as electron donors and electron acceptors and DNA functional groups that include the hyperconjugated thymine methyl group.

cond-mat.mes-hall↗

arXiv2012

Explicit constructions of centrally symmetric k-neighborly polytopes and large strictly antipodal sets

We present explicit constructions of centrally symmetric 2-neighborly d-dimensional polytopes with about 3^{d/2} = (1.73)^d vertices and of centrally symmetric k-neighborly d-polytopes with about 2^{c_k d} vertices where c_k=3/20 k^2 2^k. Using this result, we construct for a fixed k > 1 and arbitrarily large d and N, a centrally symmetric d-polytope with N vertices that has at least (1-k^2 (gamma_k)^d) binom(N, k) faces of dimension k-1, where gamma_2=1/\sqrt{3} = 0.58 and gamma_k = 2^{-3/{20k^2 2^k}} for k > 2. Another application is a construction of a set of 3^{d/2 -1}-1 points in R^d every two of which are strictly antipodal as well as a construction of an n-point set (for an arbitrarily large n) in R^d with many pairs of strictly antipodal points. The two latter results significantly improve the previous bounds by Talata, and Makai and Martini, respectively.

math.MG↗

arXiv2011

Centrally symmetric polytopes with many faces

We present explicit constructions of centrally symmetric polytopes with many faces: first, we construct a d-dimensional centrally symmetric polytope P with about (1.316)^d vertices such that every pair of non-antipodal vertices of P spans an edge of P, second, for an integer k>1, we construct a d-dimensional centrally symmetric polytope P of an arbitrarily high dimension d and with an arbitrarily large number N of vertices such that for some 0 < delta_k < 1 at least (1-delta_k^d) {N choose k} k-subsets of the set of vertices span faces of P, and third, for an integer k>1 and a>0, we construct a centrally symmetric polytope Q with an arbitrary large number N of vertices and of dimension d=k^{1+o(1)} such that least (1 - k^{-a}){N choose k} k-subsets of the set of vertices span faces of Q.

math.MG↗

arXiv2011

Neighborliness of the symmetric moment curve

We consider the convex hull B_k of the symmetric moment curve U(t)=(cos t, sin t, cos 3t, sin 3t, ..., cos (2k-1)t, sin (2k-1)t) in R^{2k}, where t ranges over the unit circle S= R/2pi Z. The curve U(t) is locally neighborly: as long as t_1, ..., t_k lie in an open arc of S of a certain length phi_k>0, the convex hull of the points U(t_1), ..., U(t_k) is a face of B_k. We characterize the maximum possible length phi_k, proving, in particular, that phi_k > pi/2 for all k and that the limit of phi_k is pi/2 as k grows. This allows us to construct centrally symmetric polytopes with a record number of faces.

math.MG↗

arXiv2011

Local neighborliness of the symmetric moment curve

A centrally symmetric analogue of the cyclic polytope, the bicyclic polytope, was defined in [BN08]. The bicyclic polytope is defined by the convex hull of finitely many points on the symmetric moment curve where the set of points has a symmetry about the origin. In this paper, we study the Barvinok-Novik orbitope, the convex hull of the symmetric moment curve. It was proven in [BN08] that the orbitope is locally $k$-neighborly, that is, the convex hull of any set of $k$ distinct points on an arc of length not exceeding $ϕ_k$ in $\mathbb{S}^1$ is a $(k-1)$-dimensional face of the orbitope for some positive constant $ϕ_k$. We prove that we can choose $ϕ_k $ bigger than $γk^{-3/2} $ for some positive constant $γ$.

math.CO↗