On The Complexity of Distance-dd Independent Set Reconfiguration

For a fixed positive integer $d \geq 2$, a distance-$d$ independent set (D$d$IS) of a graph is a vertex subset whose distance between any two members is at least $d$. Imagine that there is a token placed on each member of a D$d$IS. Two D$d$ISs are adjacent under Token Sliding ($\mathsf{TS}$) if one can be obtained from the other by moving a token from one vertex to one of its unoccupied adjacent vertices. Under Token Jumping ($\mathsf{TJ}$), the target vertex needs not to be adjacent to the original one. The Distance-$d$ Independent Set Reconfiguration (D$d$ISR) problem under $\mathsf{TS}/\mathsf{TJ}$ asks if there is a corresponding sequence of adjacent D$d$ISs that transforms one given D$d$IS into another. The problem for $d = 2$, also known as the Independent Set Reconfiguration problem, has been well-studied in the literature and its computational complexity on several graph classes has been known. In this paper, we study the computational complexity of D$d$ISR on different graphs under $\mathsf{TS}$ and $\mathsf{TJ}$ for any fixed $d \geq 3$. On chordal graphs, we show that D$d$ISR under $\mathsf{TJ}$ is in $\mathtt{P}$ when $d$ is even and $\mathtt{PSPACE}$-complete when $d$ is odd. On split graphs, there is an interesting complexity dichotomy: D$d$ISR is $\mathtt{PSPACE}$-complete for $d = 2$ but in $\mathtt{P}$ for $d=3$ under $\mathsf{TS}$, while under $\mathsf{TJ}$ it is in $\mathtt{P}$ for $d = 2$ but $\mathtt{PSPACE}$-complete for $d = 3$. Additionally, certain well-known hardness results for $d = 2$ on general graphs, perfect graphs, planar graphs of maximum degree three and bounded bandwidth can be extended for $d \geq 3$.Comment: 14 pages, 8 figures, minor revision, to appear in WALCOM 202

Sliding Tokens on a Cactus

Given two independent sets I and J of a graph G, imagine that a token (coin) is placed on each vertex in I. Then, the Sliding Token problem asks if one could transforms I to J using a sequence of elementary steps, where each step requires sliding a token from one vertex to one of its neighbors, such that the resulting set of vertices where tokens are placed still remains independent. In this paper, we describe a polynomial-time algorithm for solving Sliding Token in case the graph G is a cactus. Our algorithm is designed based on two observations. First, all structures that forbid the existence of a sequence of token slidings between I and J, if exist, can be found in polynomial time. A no-instance may be easily deduced using this characterization. Second, without such forbidden structures, a sequence of token slidings between I and J does exist

Reconfiguring k-Path Vertex Covers

A vertex subset I of a graph G is called a k-path vertex cover if every path on k vertices in G contains at least one vertex from I. The K-PATH VERTEX COVER RECONFIGURATION (K-PVCR) problem asks if one can transform one k-path vertex cover into another via a sequence of k-path vertex covers where each intermediate member is obtained from its predecessor by applying a given reconfiguration rule exactly once. We investigate the computational complexity of K-PVCR from the viewpoint of graph classes under the well-known reconfiguration rules: TS, TJ, and TAR. The problem for k=2, known as the VERTEX COVER RECONFIGURATION (VCR) problem, has been well-studied in the literature. We show that certain known hardness results for VCR on different graph classes can be extended for K-PVCR. In particular, we prove a complexity dichotomy for K-PVCR on general graphs: on those whose maximum degree is three (and even planar), the problem is PSPACE-complete, while on those whose maximum degree is two (i.e., paths and cycles), the problem can be solved in polynomial time. Additionally, we also design polynomial-time algorithms for K-PVCR on trees under each of TJ and TAR. Moreover, on paths, cycles, and trees, we describe how one can construct a reconfiguration sequence between two given k-path vertex covers in a yes-instance. In particular, on paths, our constructed reconfiguration sequence is shortest

Reconfiguring k-path vertex covers

A vertex subset $I$ of a graph $G$ is called a $k$-path vertex cover if every path on $k$ vertices in $G$ contains at least one vertex from $I$. The \textsc{$k$-Path Vertex Cover Reconfiguration ($k$-PVCR)} problem asks if one can transform one $k$-path vertex cover into another via a sequence of $k$-path vertex covers where each intermediate member is obtained from its predecessor by applying a given reconfiguration rule exactly once. We investigate the computational complexity of \textsc{$k$-PVCR} from the viewpoint of graph classes under the well-known reconfiguration rules: $\mathsf{TS}$, $\mathsf{TJ}$, and $\mathsf{TAR}$. The problem for $k=2$, known as the \textsc{Vertex Cover Reconfiguration (VCR)} problem, has been well-studied in the literature. We show that certain known hardness results for \textsc{VCR} on different graph classes including planar graphs, bounded bandwidth graphs, chordal graphs, and bipartite graphs, can be extended for \textsc{$k$-PVCR}. In particular, we prove a complexity dichotomy for \textsc{$k$-PVCR} on general graphs: on those whose maximum degree is $3$ (and even planar), the problem is $\mathtt{PSPACE}$-complete, while on those whose maximum degree is $2$ (i.e., paths and cycles), the problem can be solved in polynomial time. Additionally, we also design polynomial-time algorithms for \textsc{$k$-PVCR} on trees under each of $\mathsf{TJ}$ and $\mathsf{TAR}$. Moreover, on paths, cycles, and trees, we describe how one can construct a reconfiguration sequence between two given $k$-path vertex covers in a yes-instance. In particular, on paths, our constructed reconfiguration sequence is shortest.Comment: 29 pages, 4 figures, to appear in WALCOM 202

Leadership Flaws and Organizational Stages

The paper builds on academic work as well as keynote statements about leadership by prolific figures in research and academics, while examining common leadership flaws and exploring ways to negate them. It describes three stages of a Values Journey, namely pre-orderly, orderly and post-orderly, and within those differentiates six steps, representing followers’ values, each having a typical leadership approach. A summary of academic literature surrounding common leadership flaws and organizational pathologies and an overview of a model depicting followers’ coping mechanisms are provided in support of the paper’s main arguments. Popular leadership principles are examined and related to five basic pillars of intent, developed by the authors, to support effective leadership

On Reconfiguration Graph of Independent Sets under Token Sliding

An independent set of a graph $G$ is a vertex subset $I$ such that there is no edge joining any two vertices in $I$. Imagine that a token is placed on each vertex of an independent set of $G$. The $\mathsf{TS}$- ($\mathsf{TS}_k$-) reconfiguration graph of $G$ takes all non-empty independent sets (of size $k$) as its nodes, where $k$ is some given positive integer. Two nodes are adjacent if one can be obtained from the other by sliding a token on some vertex to one of its unoccupied neighbors. This paper focuses on the structure and realizability of these reconfiguration graphs. More precisely, we study two main questions for a given graph $G$: (1) Whether the $\mathsf{TS}_k$-reconfiguration graph of $G$ belongs to some graph class $\mathcal{G}$ (including complete graphs, paths, cycles, complete bipartite graphs, and connected split graphs) and (2) If $G$ satisfies some property $\mathcal{P}$ (including $s$-partitedness, planarity, Eulerianity, girth, and the clique's size), whether the corresponding $\mathsf{TS}$- ($\mathsf{TS}_k$-) reconfiguration graph of $G$ also satisfies $\mathcal{P}$, and vice versa.Comment: 17 pages, 12 figure

Replacement of freshwater small-size fish by formulated feed in snakehead (Channa striata) aquaculture: Experimental and commercial-scale pond trials, with economic analysis

Traditional snakehead culture in Southeast Asia relies on use of small-size (trash) fish as food, an unsustainable practice. Following development of weaning methods and testing of formulated feed (FF) in laboratory experiments, we conducted feeding trials of FF vs. trash fish (TF) in experimental ponds at Can Tho University (CTU), followed by similar trials on commercial farms in two provinces in Vietnam. CTU pond trials consisted of five treatments (in triplicate), in which TF was replaced by FF in increasing percentages: 0 (control), 25, 50, 75, and 100% replacement of TF by FF (i.e., three treatments had mixed TF/FF diets). Although survival was significantly reduced in the 100% replacement treatment, and growth was significantly reduced in the 75% and 100% replacement treatments, the cost per kg of fish produced was 28–35% less in those high-replacement treatments compared to the 0% replacement treatment. On-farm trials were then conducted at two farms in An Giang and Dong Thap provinces for 6 months with snakehead fed TF only or FF only. At both farms, survival (73–80%) was not significantly different, but growth was significantly better on FF diet at both; however, FF-fed fish at the An Giang farm showed significantly higher levels of abnormal development. Overall production was about twice as high at the An Giang farm as at Dong Thap, but significantly greater production by FF-fed fish vs. TF-fed fish was only seen at Dong Thap. Sensory evaluation by a tasting panel found no difference in product quality between FF-fed fish, TF-fed fish, and a commercial sample bought in the market. Economic analysis indicated that profits were higher for FF-fed fish from both farms, although production costs and sales varied greatly, reflecting market differences in the two provinces

ẢNH HƯỞNG CỦA MÔI TRƯỜNG NUÔI CẤY LÊN SINH TRƯỞNG CỦA CALLUS CÂY GIẢO CỔ LAM (Gynostemma pentaphyllum (Thunb.) Makino) – MỘT CÂY DƯỢC LIỆU CÓ GIÁ TRỊ

Gynostemma pentaphyllum (Thunb.) Makino (Jiaogulan) is a traditional medicinal herb belonging to the Cucurbitaceae family. G. pentaphyllum grows widely in Southern China, Japan, Korea, and Vietnam. The essential bioactive components of Jiaogulan are saponin glycosides (gypenosides) and antioxidants. Jiaogulan exhibits bioactive activities such as anticancer, antioxidant, cholesterol-reducing agent, immunopotentiation, and others. In this study, the primary callus of Jiaogulan was used as a material to evaluate the influence of the culture medium on the induction and growth of secondary calli. The results reveal that the callus cultured on the MS medium supplemented with 2.0 mg/L kinetin and 0.5 mg/L indole-3-butyric acid has the best growth ability, high rate of secondary callus induction (100%), and good callus quality for suspension culture. The concentration of gypenoside and Rb1 in callus is 36.298 and 0.009 mg/g dry weight. The gypenoside concentration of callus is lower than that of leaves (65.58%) and almost similar to that of stems (92.38%) from natural samples. The suitable solvent for the extraction of gypenoside is methanol. The obtained callus will be used as material for cell suspension culture in further studies.Giảo cổ lam (Gynostemma pentaphyllum (Thunb.) Makino) là một cây thuốc dân gian thuộc họ Bầu bí. Cây phân bố rộng ở miền Nam Trung Quốc, Nhật Bản, Hàn Quốc và Việt Nam. Các thành phần có hoạt tính sinh học quan trọng của Giảo cổ làm là saponin glycoside (gypenoside) và các chất chống oxy hóa. Giảo cổ lam được sử dụng hỗ trợ chống ung thư, chống oxy hóa, giảm cholesterol, tăng cường miễn dịch và các tác dụng khác. Trong nghiên cứu này, callus sơ cấp của cây Giảo cổ lam được sử dụng làm nguyên liệu để đánh giá ảnh hưởng của môi trường nuôi cấy lên khả năng phát sinh và sinh trưởng của callus thứ cấp. Kết quả cho thấy, callus được nuôi cấy trên môi trường MS có bổ sung 2,0 mg/L kinetin và 0,5 mg/L indole-3-butyric acid sinh trưởng tốt nhất; tỷ lệ tạo callus thứ cấp cao (100%); callus đáp ứng được tiêu chuẩn để nuôi cấy huyền phù. Hàm lượng gypenoside và Rb1 trong callus là 36,298 và 0,009 mg/g chất khô; gypenoside thấp hơn trong lá (65,58%) và gần tương đương với mẫu thân (92,38%) của sản phẩm thu mua từ thị trường. Dung môi thích hợp để tách chiết gypenoside là methanol. Callus thu được sẽ được sử dụng làm nguyên liệu cho nuôi cấy tế bào huyền phù trong các nghiên cứu tiếp theo

ĐẶC ĐIỂM ĐỊA HÓA THẠCH HỌC ĐÁ MAGMA BAZAN VÀ ĐẶC ĐIỂM NGUỒN MANTI KHU VỰC BIỂN ĐÔNG VÀ LÂN CẬN TRONG KAINOZOI

The East Vietnam Sea is one of the largest marginal basins in western Pacific Ocenan, formed by breaking of continental margin in the Late Mesozoic. Geochemical data of the Miocene - Pleistocene bazanic samples collected in the East Sea and neighboring areas show two major eruption trends that reflect the formation and development of the region. The early eruption event is characterized by low alkaline, TiO2, Na2O, K2O and P2O5, and high SiO2 group, comprising olivine and tholeiitic bazans. The later eruption demonstrates high alkaline, TiO2, Na2O, K2O and P2O5, and low SiO2 group, mainly generated by central-type volcanic eruptions, consisting of alkaline olivine and olivine bazans. Distinctive geochemistry of the volcanic rocks within the East Vietnam Sea and adjacent areas is illustrated by wide range of Magnesium index (Mg#= 35-75). At the values of Mg#>65, the relation between Mg# and major oxides is unclear. In contrast, Mg#65 (Olivine differentiation) the isotope ratios start changing. The primitive components are computed based on the principle of olivine compensation. The computed results show that the critical pressure for Tholeiite melting was estimated from ~11.97-20.33 Kb (ca. 30 - 60 km deep) and the Alkaline melting pressure varies from ~16.87-34.93 Kb (corresponding to the depths of ~60 km to 100 km). The continuous range of melting pressures suggests two trends of tholeiitic and alkaline eruptions occurr at various depths in the same magmatic source. Hight temperature and melting pressure of the primitive magma are dependent on partial melting pressure. Possibly, this process was triggered by the asthenosphere intrusion resulted from the closure of the Neo-Tethys following the India - Eurasia collision. This event has not only made the mantle hotter and easily melted but also triggered the opening of the marginal seas, including the East Vietnam Sea.Biển Đông là một trong những biển rìa lớn nhất thuộc rìa tây Thái Bình Dương hình thành do phá vỡ một bộ phận của rìa lục địa vào cuối Mesozoi. Kết quả thành phần địa hóa các đá bazan tuổi Miocen - Pleitocen khu vực Biển Đông và lân cận cho thấy hai xu thế phun trào chính phản ánh quá trình hình thành và phát triển khu vực. Xu thế phun trào sớm có đặc điểm thấp Kiềm, TiO2 và P2O5 và cao SiO2 chủ yếu là các Tholeit, Olivin bazan. Xu thế phun trào muộn thường cao Kiềm, TiO2 và P2O5 và cao SiO2, chủ yếu tập trung tại các khu vực phun trào kiểu trung tâm, thành phần là các bazan Olivin và Nephenin. Đặc trưng địa hóa của đá núi lửa khu vực Biển Đông và lân cận là sự phân bố rộng của chỉ số Magie (Mg#=35-75). Tại giá trị Mg#>65, quan hệ giữa Mg# và các hợp phần oxit chính là không rõ ràng. Ngược lại, tại giá trị Mg