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View article: Restricted projections in positive characteristic via Fourier extension and restriction estimates
Restricted projections in positive characteristic via Fourier extension and restriction estimates Open
Let $d\ge3$ and $\mathbb{F}_q^{\,d}$ be the $d$-dimensional vector space over a finite field of order $q$, where $q$ is an odd prime power. Let $X_π$ be the set of lines through the origin intersecting the slice $π\cap S^{d-1}$, where $π=\…
View article: Frostman random variables, entropy inequalities, and applications
Frostman random variables, entropy inequalities, and applications Open
We introduce Frostman conditions for bivariate random variables and study discretized entropy sum-product phenomena in both independent and dependent settings. Fix $0 < s < 1$, and let $(X,Y)$ be a bivariate real random variable with bound…
View article: On a theorem of Mattila in the finite p-adic setting
On a theorem of Mattila in the finite p-adic setting Open
Let $A\ \mathrm{and}\ B$ be subsets of $(\mathbb {Z}/p^r\mathbb {Z})^2$ . In this note, we provide conditions on the densities of A and B such that $|gA-B|\gg p^{2r}$ for a positive proportion of $g\in SO_2(\mathbb {Z}/p^r\mathbb {Z})$ . T…
View article: Detection of Non-typeable <i>Haemophilus influenzae</i> as a Causative Pathogen of Community-Acquired Pneumonia in Vietnamese Children
Detection of Non-typeable <i>Haemophilus influenzae</i> as a Causative Pathogen of Community-Acquired Pneumonia in Vietnamese Children Open
Background: The prevalence of invasive Haemophilus influenzae type b (Hib) disease—especially community-acquired pneumonia (CAP)—has significantly decreased due to the widespread use of Hib conjugate vaccines. Non-typeable H. influenzae (N…
View article: VN1K: a genome graph-based and function-driven multi-omics and phenomics resource for the Vietnamese population
VN1K: a genome graph-based and function-driven multi-omics and phenomics resource for the Vietnamese population Open
Vietnam, the 16th most populated nation, remains profoundly underrepresented in global genomic databases. Here, we present VN1K, a first-ever comprehensive and well-curated resource of multi-omics data with a wide-range of phenotypic infor…
View article: On a theorem of Mattila in the p-adic setting
On a theorem of Mattila in the p-adic setting Open
Let $A, B$ be subsets of $(\mathbb{Z}/p^r\mathbb{Z})^2$. In this note, we provide conditions on the densities of $A$ and $B$ such that $|gA-B|\gg p^{2r}$ for a positive proportion of $g\in SO_2(\mathbb{Z}/p^r\mathbb{Z})$. The conditions ar…
View article: On the distance problem over finite p-adic rings
On the distance problem over finite p-adic rings Open
In this paper, we study the distance problem in the setting of finite p-adic rings. In odd dimensions, our results are essentially sharp. In even dimensions, we clarify the conjecture and provide examples to support it. Surprisingly, compa…
View article: Geometric structures in pseudo-random graphs
Geometric structures in pseudo-random graphs Open
In this paper, we provide a general framework for counting geometric structures in pseudo-random graphs. As applications, our theorems recover and improve several results on the finite field analog of questions originally raised in the con…
View article: The therapeutic landscape for COVID-19 and post-COVID-19 medications from genetic profiling of the Vietnamese population and a predictive model of drug-drug interaction for comorbid COVID-19 patients
The therapeutic landscape for COVID-19 and post-COVID-19 medications from genetic profiling of the Vietnamese population and a predictive model of drug-drug interaction for comorbid COVID-19 patients Open
View article: A study of genetic variants associated with skin traits in the Vietnamese population
A study of genetic variants associated with skin traits in the Vietnamese population Open
Background Most skin-related traits have been studied in Caucasian genetic backgrounds. A comprehensive study on skin-associated genetic effects on underrepresented populations such as Vietnam is needed to fill the gaps in the field. Objec…
View article: A rapid and reference-free imputation method for low-cost genotyping platforms
A rapid and reference-free imputation method for low-cost genotyping platforms Open
View article: A new R,R-RvD6 isomer with protective actions following corneal nerve injury
A new R,R-RvD6 isomer with protective actions following corneal nerve injury Open
View article: Falconer type functions in three variables
Falconer type functions in three variables Open
View article: On a radial projection conjecture and pinned directions in finite spaces
On a radial projection conjecture and pinned directions in finite spaces Open
We give upper bounds on the number of exceptional radial projections of arbitrary subsets of vector spaces over finite fields. Our bounds do not depend on the dimension of the ambient space. Let $\mathbb{F}_q^d$ be the $d$-dimensional vect…
View article: Orthogonal projections and incidence bounds in planes over prime order fields
Orthogonal projections and incidence bounds in planes over prime order fields Open
We give an upper bound on the number of exceptional orthogonal projections of a small set of points in a plane over a prime order field, which makes progress toward a conjecture of Chen (2018). This theorem relies on a new upper bound on t…
View article: A study of genetic variants associated with skin traits in the Vietnamese population
A study of genetic variants associated with skin traits in the Vietnamese population Open
Background Most skin-related traits have been studied from Caucasian genetic background. A comprehensive study on skin-associated genetic effects on under-represented populations like Vietnam is needed to fill the gaps in the field. Object…
View article: New-type Quasirandom Groups and Applications
New-type Quasirandom Groups and Applications Open
This paper aims to introduce a more general definition of quasirandom groups and generalize several well-known results in the literature in this new setting. More precisely, let $G$ be a semi-direct product of groups and $X\subseteq G$, we…
View article: An energy decomposition theorem for matrices and related questions
An energy decomposition theorem for matrices and related questions Open
Given $A\subseteq GL_2(\mathbb {F}_q)$ , we prove that there exist disjoint subsets $B, C\subseteq A$ such that $A = B \sqcup C$ and their additive and multiplicative energies satisfying $$\begin{align*}\max\{\,E_{+}(B),\, E_{\times}(C)\,\…
View article: Lipoxin A4 (LXA4) Reduces Alkali-Induced Corneal Inflammation and Neovascularization and Upregulates a Repair Transcriptome
Lipoxin A4 (LXA4) Reduces Alkali-Induced Corneal Inflammation and Neovascularization and Upregulates a Repair Transcriptome Open
Purpose: To investigate the anti-inflammatory and anti-angiogenic effects of the bioactive lipid mediator LXA4 on a rat model of severe corneal alkali injury. Methods: To induce a corneal alkali injury in the right eyes of anesthetized Spr…
View article: A promising DNA methylation analysis pipeline for epigenetic studies and clinical implementation in inflammatory bowel disease
A promising DNA methylation analysis pipeline for epigenetic studies and clinical implementation in inflammatory bowel disease Open
Hang Viet Dao, Vinh Chi Duong, Long Van Dao, Long Bao Hoang, Thien Khac Nguyen, Thang Luong Pham, Giang Minh Vu, Tham Hong Hoang
View article: Neuroanatomy of Adult and Aging Chicken Cornea
Neuroanatomy of Adult and Aging Chicken Cornea Open
This is the first study to provide a complete map of the entire corneal nerves and CGRP and SP sensory neuropeptide distribution in the adult chicken cornea. The findings show chicken corneal innervation has many differences to human and m…
View article: New Retinal Pigment Epithelial Cell Model to Unravel Neuroprotection Sensors of Neurodegeneration in Retinal Disease
New Retinal Pigment Epithelial Cell Model to Unravel Neuroprotection Sensors of Neurodegeneration in Retinal Disease Open
Retinal pigment epithelial (RPE) cells sustain photoreceptor integrity, and when this function is disrupted, retinal degenerations ensue. Herein, we characterize a new cell line from human RPE that we termed ABC . These cells remarkably re…
View article: A point-sphere incidence bound in odd dimensions and applications
A point-sphere incidence bound in odd dimensions and applications Open
In this paper, we prove a new point-sphere incidence bound in vector spaces over finite fields. More precisely, let be a set of points and be a set of spheres in . Suppose that , we prove that the number of incidences between and sa…
View article: Neuroanatomy of Adult and Aging Chicken Cornea
Neuroanatomy of Adult and Aging Chicken Cornea Open
To provide a complete nerve architecture and main sensory neuropeptide distribution in the chicken cornea. Adult chickens aged 6 months and 4 years were used. The whole cornea was stained with protein gene product (PGP) 9.5 antibody-a pan …
View article: On the pinned distances problem in positive characteristic
On the pinned distances problem in positive characteristic Open
We study the Erd\\H os-Falconer distance problem for a set $A\\subset\n\\mathbb{F}^2$, where $\\mathbb{F}$ is a field of positive characteristic $p$. If\n$\\mathbb{F}=\\mathbb{F}_p$ and the cardinality $|A|$ exceeds $p^{5/4}$, we prove\nth…
View article: A Point-Conic Incidence Bound and Applications over $\mathbb F_p$
A Point-Conic Incidence Bound and Applications over $\mathbb F_p$ Open
In this paper, we prove the first incidence bound for points and conics over prime fields. As applications, we prove new results on expansion of bivariate polynomial images and on certain variations of distinct distances problems. These in…
View article: An Asymmetric Bound for Sum of Distance Sets
An Asymmetric Bound for Sum of Distance Sets Open
For $ E\subset \mathbb{F}_q^d$, let $Δ(E)$ denote the distance set determined by pairs of points in $E$. By using additive energies of sets on a paraboloid, Koh, Pham, Shen, and Vinh (2020) proved that if $E,F\subset \mathbb{F}_q^d $ are s…
View article: Extension theorems for Hamming varieties over finite fields
Extension theorems for Hamming varieties over finite fields Open
We study the finite field extension estimates for Hamming varieties $H_j, j\in \mathbb F_q^*,$ defined by $H_j=\{x\in \mathbb F_q^d: \prod_{k=1}^d x_k=j\},$ where $\mathbb F_q^d$ denotes the $d$-dimensional vector space over a finite field…
View article: Elucidating the structure and functions of Resolvin D6 isomers on nerve regeneration with a distinctive trigeminal transcriptome
Elucidating the structure and functions of Resolvin D6 isomers on nerve regeneration with a distinctive trigeminal transcriptome Open
Innervation sustains cornea integrity. Pigment epithelium‐derived factor (PEDF) plus docosahexaenoic acid (DHA) regenerated damaged nerves by stimulating the synthesis of a new stereoisomer of Resolvin D6 (RvD6si). Here, we resolved the st…
View article: On the Finite Field Cone Restriction Conjecture in Four Dimensions and Applications in Incidence Geometry
On the Finite Field Cone Restriction Conjecture in Four Dimensions and Applications in Incidence Geometry Open
The first purpose of this paper is to solve completely the finite field cone restriction conjecture in four dimensions with $-1$ non-square. The second is to introduce a new approach to study incidence problems via restriction theory. More…