arXiv subjects

Shanshan Du

Publications and source records attributed to Shanshan Du.

8 recordsLinked to original sources

arXiv2026

Logic Programming on Knowledge Graph Networks And its Application in Medical Domain

The rash development of knowledge graph research has brought big driving force to its application in many areas, including the medicine and healthcare domain. However, we have found that the application of some major information processing techniques on knowledge graph still lags behind. This defect includes the failure to make sufficient use of advanced logic reasoning, advanced artificial intelligence techniques, special-purpose programming languages, modern probabilistic and statistic theories et al. on knowledge graphs development and application. In particular, the multiple knowledge graphs cooperation and competition techniques have not got enough attention from researchers. This paper develops a systematic theory, technique and application of the concept 'knowledge graph network' and its application in medical and healthcare domain. Our research covers its definition, development, reasoning, computing and application under different conditions such as unsharp, uncertain, multi-modal, vectorized, distributed, federated. Almost in each case we provide (real data) examples and experiment results. Finally, a conclusion of innovation is provided.

cs.AI↗

arXiv2024

The restricted sumsets in finite abelian groups

Suppose that $k\geq 2$ and $A$ is a non-empty subset of a finite abelian group $G$ with $|G|>1$. Then the cardinality of the restricted sumset $$ k^\wedge A:=\{a_1+\cdots+a_k:\,a_1,\ldots,a_k\in A,\ a_i\neq a_j\text{ for }i\neq j\} $$ is at least $$ \min\{p(G), k|A|-k^2+1\}, $$ where $p(G)$ denotes the least prime divisor of $|G|$.

math.CO↗

arXiv2022

Particle manipulation behind turbid medium based on intensity transmission matrix

Optical tweezers can manipulate tiny particles. However, the distortion caused by the scattering medium restricts the applications of optical tweezers. Wavefront shaping techniques including the transmission matrix (TM) method are powerful tools to achieve light focusing behind the scattering medium. In this paper, we propose a new kind of TM, named intensity transmission matrix (ITM). Only relying on the intensity distribution, we can calculate the ITM with only about 1/4 measurement time of the widely used four-phase method. Meanwhile, ITM method can avoid the energy loss in diffraction introduced by holographic modulation. Based on the ITM, we have implemented particle manipulation with a high degree of freedom on single and multiple particles. In addition, the manipulation range is enlarged over twenty times (compared with the memory effect) to 200 μm.

physics.optics↗

arXiv2019

Vinogradov three prime theorem with Piatetski-Shapiro primes

We prove that, for any $c_1,c_2,c_3\in(1,41/35)$, every sufficiently large odd number $N$ can be represented as the sum of three primes $N = p_1 + p_2 +p_3$ such that $p_i = \lfloor n_{i}^{c_i}\rfloor$ for some $n_i \in{\mathbb N}$ for each $1 \leq i \leq 3$. Our arguments are based on a variant of Green's transference principle due to Matom\"aki, Maynard and Shao. We prove a necessary restriction estimate using Bourgain's strategy and employ Harman's sieve method to optimize our upper bound for $c_i$.

math.NT↗

arXiv2016

On the number of three-term arithmetic progressions in a dense subset of $F_q^n$

Let $q$ be an odd prime power. Combining the discussion of Varnavides and a recent theorem of Ellenberg and Gijswijt, we show that a subset $A\subset{\mathbb F}_q^n$ will contain many non-trivial three-term arithmetic progressions, whenever $|A|\geq (c_q q)^n$ for some constant $c_q>0$. After the first version of our manuscript was uploaded in the arXiv, we learned from Professors Jacob Fox and Terence Tao that our result is a special case of a result of Fox and Lovasz [1, Theorem 3]. In fact, [1, Theorem 3] gives a much better bound than ours. For example, when $q=3$, the lower bound given by Fox and Lovasz is $|A|^{2}\cdot (|A|q^{-n})^{11.901}$, while our bound is $|A|^{2}\cdot (|A|q^{-n})^{25.803}$. We thank Professors Jacob Fox and Terence Tao for their helpful comments on our manuscript. [1] Jacob Fox, László Miklós Lovász, A tight bound for Green's arithmetic triangle removal lemma in vector spaces, preprint, arXiv:1606.01230.

math.CO↗

arXiv2016

A generalization of Frieman's 3k-3 theorem

We prove a generalization of Frieman's $3k-3$ theorem for the sumset $$ Σ^{l}(A_1,\ldots,A_k)=\{a_{j_{1}}+\cdots+a_{j_{l}}:\,1\leq j_{1}<\cdots<j_{l}\leq k,\ a_{j_{s}}\in A_{j_{s}}\text{ for all }s\}. $$

math.NT↗

arXiv2016

On the generalized restricted sumsets in abelian groups

Suppose that $A$, $B$ and $S$ are non-empty subsets of a finite abelian group $G$. Then the generalized restricted sumset $$ A\stackrel{S}+B:=\{a+b:\,a\in A,\ b\in B,\ a-b\not\in S\} $$ contains at least $$ \min\{|A|+|B|-3|S|,p(G)\} $$ elements, where $p(G)$ is the least prime factor of $|G|$. Further, we also have $$ |A\stackrel{S}+B|\geq \min\{|A|+|B|-|S|-2,p(G)\}, $$ provided that both $|A|$ and $|B|$ are large with respect to $|S|$.

math.NT↗

arXiv2012

Restricted Sumsets in Finite Nilpotent Groups

Suppose that $A,B$ are two non-empty subsets of the finite nilpotent group $G$. If $A\not=B$, then the cardinality of the restricted sumset $$A\dotplus B={a+b: a\in A, b\in B, a\neq b} $$ is at least $$\min{p(G),|A|+|B|-2},$$ where $p(G)$ denotes the least prime factor of $|G|$.

math.CO↗