arXiv subjects

Hyunseok Lee

Publications and source records attributed to Hyunseok Lee.

At least 37 records · Page 2Linked to original sources

arXiv2022

Laser pulse compression by a density gradient plasma for exawatt to zettawatt lasers

We propose a new method for laser pulse compression that uses the spatially varying dispersion of a plasma plume with a density gradient. This novel scheme can be used to compress ultrahigh power lasers. A long, negatively frequency-chirped, laser pulse reflects off the plasma ramp of an over-dense plasma. As the density increases longitudinally the high frequency photons at the leading part of the laser pulse propagates more deeply than low frequency photons, the pulse is compressed in a similar way to compression off a chirped mirror. Proof-of-principle simulations, using a one-dimensional (1-D) particle-in-cell (PIC) simulation code demonstrates the compression of 2.35 ps laser pulse to 10.3 fs, with a compression ratio of 225. As plasmas is robust and resistant to high intensities, unlike gratings in a chirped-pulse amplification (CPA) technique [1], the method could be used as a compressor to reach exawatt or zettawatt peak power lasers.

physics.plasm-ph↗

arXiv2022

Assessing generalisability of deep learning-based polyp detection and segmentation methods through a computer vision challenge

Polyps are well-known cancer precursors identified by colonoscopy. However, variability in their size, location, and surface largely affect identification, localisation, and characterisation. Moreover, colonoscopic surveillance and removal of polyps (referred to as polypectomy ) are highly operator-dependent procedures. There exist a high missed detection rate and incomplete removal of colonic polyps due to their variable nature, the difficulties to delineate the abnormality, the high recurrence rates, and the anatomical topography of the colon. There have been several developments in realising automated methods for both detection and segmentation of these polyps using machine learning. However, the major drawback in most of these methods is their ability to generalise to out-of-sample unseen datasets that come from different centres, modalities and acquisition systems. To test this hypothesis rigorously we curated a multi-centre and multi-population dataset acquired from multiple colonoscopy systems and challenged teams comprising machine learning experts to develop robust automated detection and segmentation methods as part of our crowd-sourcing Endoscopic computer vision challenge (EndoCV) 2021. In this paper, we analyse the detection results of the four top (among seven) teams and the segmentation results of the five top teams (among 16). Our analyses demonstrate that the top-ranking teams concentrated on accuracy (i.e., accuracy > 80% on overall Dice score on different validation sets) over real-time performance required for clinical applicability. We further dissect the methods and provide an experiment-based hypothesis that reveals the need for improved generalisability to tackle diversity present in multi-centre datasets.

cs.CV↗

arXiv2021

Dimorphic properties of Bernoulli random variable

The aim of this paper is to study a dimorphic property associated with two different sums of identically independent Bernoulli random variables having two different families of probability mass functions. In addition, we give two expressions on sums of products of degenerate Stirling numbers of the second kind and Stirling numbers of the first kind connected with those two different sums of identically independent Bernoulli random variables.

math.NT↗

arXiv2021

Some identities of fully degenerate Dowling and fully degenerate Bell polynomials arising from lambda-umbral calculus

Recently, Kim-Kim introduced the lambda-umbral calculus, in which the lambda-Sheffer sequences occupy the central position. In this paper, we introduce the fully degenerate Bell and the fully degenerate Dowling polynomials, and investigate some properties and identities relating to those polynomials with the help oflambda-umbral calculus. Here we note that the fully degenerate Bell poynomials and the fully degenerate Dowling polynomials are respectively degenerate versions of the Bell polynomials and the Dowling polynomials, of which the latters are the natural extension of the Whitney numbers of the second kind.

math.NT↗

arXiv2021

Some new properties on degenerate Bell polynomials

The aim of this paper is to study the degenerate Bell numbers and polynomials which are degenerate version of the Bell numbers and polynomials. we derive some new identities and properties of those numbers and polynomials that are associated with the degenerate Stirling numbers of the both kinds.

math.NT↗

arXiv2021

Slow expanders invade by forming dented fronts in microbial colonies

Most organisms grow in space, whether they are viruses spreading within a host tissue or invasive species colonizing a new continent. Evolution typically selects for higher expansion rates during spatial growth, but it has been suggested that slower expanders can take over under certain conditions. Here, we report an experimental observation of such population dynamics. We demonstrate that the slower mutants win not only when the two types are intermixed at the front but also when they are spatially segregated into sectors. The latter was thought to be impossible because previous studies focused exclusively on the global competitions mediated by expansion velocities but overlooked the local competitions at sector boundaries. We developed a theory of sector geometry that accounts for both local and global competitions and describes all possible sector shapes. In particular, the theory predicted that a slower, but more competitive, mutant forms a dented V-shaped sector as it takes over the expansion front. Such sectors were indeed observed experimentally and their shapes matched up quantitatively with the theory. In simulations, we further explored several mechanism that could provide slow expanders with a local competitive advantage and showed that they are all well-described by our theory. Taken together, our results shed light on previously unexplored outcomes of spatial competition and establish a universal framework to understand evolutionary and ecological dynamics in expanding populations.

q-bio.PE↗

arXiv2021

A new approach to Bell and poly-Bell numbers and polynomials

The aim of this paper is to introduce Bell polynomials and numbers of the second kind and poly-Bell polynomials and numbers of the second kind, and to derive their explicit expressions, recurrence relations and some identities involving those polynomials and numbers. We also consider degenerate versions of those polynomials and numbers, namely degenerate Bell polynomials and numbers of the second kind and degenerate poly-Bell polynomials and numbers of the second kind, and deduce their similar results.

math.NT↗

arXiv2021

A study on properties of degenerate and zero-truncated degenerate Poisson random variables

Carlitz [2] initiated a study on degenerate versions of Bernoulli and Euler numbers which has been extended recently to the researches on various degenerate versions of quite a few special numbers and polynomials. They have been explored by using several different tools including generating functions, combinatorial methods, $p$-adic analysis, umbral calculus, special functions, differential equations and probability theory as well. \par The degenerate Poisson random variables are degenerate versions of the Poisson random variables. In [6], studied are the degenerate binomial and degenerate Poisson random variables in relation to the degenerate Lah-Bell polynomials. Among other things, it is shown that the rising factorial moments of the degenerate Poisson random variable are expressed by the degenerate Lah-Bell polynomials. Also, it is shown that the probability-generating function of the degenerate Poisson random variable is equal to the generating function of the degenerate Lah-Bell polynomials. The zero-truncated Poisson distributions (also called the conditional or the positive Poisson distributions) are certain discrete probability distributions whose supports are the set of positive integers. In [10], the zero-truncated degenerate Poisson random variables, whose probability mass functions are a natural extension of the zero-truncated Poisson random variables, are introduced and various properties of those random variables are investigated. Specifically, for those distributions, studied are its expectation, its variance, its n-th moment, its cumulative distribution function and certain expressions for the probability function of a finite sum of independent degenerate zero-truncated Poisson random variables with equal and unequal parameters.

math.NT↗

arXiv2021

Multi-Lah numbers and multi-Stirling numbers of the first kind

In this paper, we introduce multi-Lah numbers and multi-Stirling numbers of the first kind and recall multi-Bernoulli numbers, all of whose generating functions are given with the help of multiple logarithm. The aim of this paper is to study several relations among those three numbers. In more detail, we represent the multi-Bernoulli numbers in terms of the multi-Stirling numbers of the first kind and vice versa, and the multi-Lah numbers in terms of multi-Stirling numbers. In addition, we deduce a recurrence relation for multi-Lah numbers

math.NT↗

arXiv2021

Study on q-analogues of Catala-Daehee numbers and polynomials

Catalan-Daehee numbers and polynomials, generating functions of which can be expressed as p-adic Volkenborn integrals on Zp, were studied previously. The aim of this paper is to introduce q-analogues of the catalan-Daehee numbers and polynomials with the help of p-adic q-integrals von Zp. We derive, among other thing, some explicit expressions for the q-analogues of the Catalan-Daehee numbers and polynomials.

math.NT↗

arXiv2021

Generalized degenerate Bernoulli numbers and polynomials arising from Gauss hypergeometric function

In a previous paper, Rahmani introduced a new family of p-Bernoulli numbers and polynomials by means of the Gauss hypergeometric function. Motivated by this paper and as a degenerate version of those numbers and polynomials, we introduce the generalized degenerate Bernoulli numbers and polynomials again by using the Gauss hypergeometric function. In addition, we introduce the degenerate type Eulerian numbers as a degenerate version of Eulerian numbers. For the generalized degenerate Bernoulli numbers, we express them in terms of the degenerate Stirling numbers of the second kind, of the degenerate type Eulerian numbers, of the degenerate $p$-Stirling numbers of the second kind and of an integral on the unit interval. As to the generalized degenerate Bernoulli polynomials, we represent them in terms of the degenerate Stirling polynomials of the second kind.

math.NT↗

arXiv2021

Complete and incomplete Bell polynomials associated with Lah-Bell numbers and polynomials

The nth r-extended Lah-Bell number is defined as the number of ways a set with $n+r$ elements can be partitioned into ordered blocks such that r distinguished elements have to be in distinct ordered blocks. The aim of this paper is to introduce incomplete r-extended Lah-Bell polynomials and complete $r$-extended Lah-Bell polynomials respectively as multivariate versions of $r$-Lah numbers and the r-extended Lah-Bell numbers and to investigate some properties and identities for these polynomials. From these investigations, we obtain some expressions for the r-Lah numbers and the r-extended Lah-Bell numbers as finite sums.

math.CO↗

arXiv2020

Representations of degenerate poly-Bernoulli polynomials

As is well-known, poly-Bernoulli polynomials are defined in terms of polylogarithm functions. Recently, as degenerate version of such functions and polynomials, degenerate polylogarithm functions were introduced and degenertae poly-Bernoulli polynomials were defined by means of the degenerate polylogarithm functions, and some their properties were investigated. The aim of this paper is to furthur study some properties of the degenertae poly-Bernoulli polynomials by using three formulas coming from the recently developed lambda-umbral calculus. In more detail, among other things, we represent the degenerate poly-Bernoulli polynomials by higher-order degenertae Bernoulli polynomials and by higher-order degenerate derangements polynomials.

math.NT↗

arXiv2020

poly-Dedekind type DC sums involving poly-Euler functions

The classical Dedekind sums appear in the transformation behavior of the logarithm of the Dedekind eta-function under substitutions from the modular group. The Dedekind sums and their generalizations are defined in terms of Bernoulli functions and their generalizations, and are shown to satisfy some reciprocity relations. In contrast, Dedekind type DC (Daehee and Changhee) sums and their generalizations are defined in terms of Euler functions and their generalizations. The purpose of this paper is to introduce the poly-Dedekind type DC sums, which are obtained from the Dedekind type DC sums by replacing the Euler function by poly-Euler functions of arbitrary indices, and to show that those sums satisfy, among other things, a reciprocity relation.

math.NT↗

arXiv2020

A note on degenerate derangement polynomials and numbers

In this paper, we study the degenerate derangement polynomials and numbers, investigate some properties of those polynomials and numbers and explore their connections with the degenerate gamma distributions. In more detail, we derive their explicit expressions, recurrence relations and some identities involving the degenerate derangement polynomials and numbers and other special polynomials and numbers, which include the fully degenerate Bell polynomials, the degenerate Fubini polynomials and the degenerate Stirling numbers of both kinds. We also show that those polynomials and numbers are connected with the moments of some variants of the degenerate gamma distributions.

math.NT↗

arXiv2020

Some identities involving derangement polynomials and numbers

The problem of counting derangements was initiated by Pierre Remonde de Motmort in 1708. A derangement is a permutation that has no fixed points and the derangement number Dn is the number of fixed point free permutations on an n element set. Furthermore, the derangement polynomials are natural extensions of the derangement numbers. In this paper, we study the derangement polynomials and numbers, their connections with cosine-derangement polynomials and sine-derangement polynomials and their applications to moments of some variants of gamma random variables.

math.NT↗

arXiv2020

Representations of degenerate Hermite polynomials

We introduce degenerate Hermite polynomials as a degenerate version of the ordinary Hermite polynomials. Then, among other things, by using the formula about representing one lambda-Sheffer polynomial in terms of other lambda-Sheffer polynomials we represent the degenerate Hermite polynomials in terms of the higher-order degenerate Bernoulli, Euler, and Frobenius-Euler polynomials and vice versa.

math.NT↗

arXiv2020

Identities on poly-Dedekind sums

Dedekind sums occur in the transformation behaviour of the logarithm of the Dedekind eta-function under substitutions from the modular group. In 1892, Dedekind showed a reciprocity relation for the Dedekind sums. Apostol generalized Dedekind sums by replacing the first Bernoulli function appearing in them by any Bernoulli functions and derived a reciprocity relation for the generalized Dedekind sums. In this paper, we consider poly-Dedekind sums which are obtained from the Dedekind sums by replacing the first Bernoulli function by any type 2 poly-Bernoulli functions of arbitrary indices and prove a reciprocity relation for the poly-Dedekind sums.

math.NT↗