Search

Graph theory is a fundamental area that explores the properties and relationships present within graph structures. This paper explores generalized graph complements by examining edge partitioning, a novel approach that extends the traditional graph complement. In analogy to the vertex partition-based definitions of generalized complements, two distinct types of generalized complements for a graph emerge through edge partitioning: k'-complement and k'(i)- complement of a graph. k'-complement of a graph emerges as a versatile tool with applications across multiple domains, due to its maximum edge configuration linked with a Fibonacci polynomial and its role as a maximal outerplanar graph. The paper systematically examines theorems and fundamental properties governing the structural relationships between the original graph and its generalized complements. The characterizations of cycles and paths are also analysed in this study. [ABSTRACT FROM AUTHOR]

A cycle C in a graph G is called a Tutte cycle if, after deleting C from G, each component has at most three neighbors on C. Tutte cycles play an important role in the study of Hamiltonicity of planar graphs. Thomas and Yu and independently Sanders proved the existence of Tutte cycles containing three specified edges of a facial cycle in a 2-connected plane graph. We prove a quantitative version of this result, bounding the number of components of the graph obtained by deleting a Tutte cycle. As a corollary, we can find long cycles in essentially 4-connected plane graphs that also contain three prescribed edges of a facial cycle. [ABSTRACT FROM AUTHOR]

A bisection of a graph is a bipartition of its vertex set in which the two parts differ in size by at most 1, and its size is the number of edges which across the two parts. Let G be a graph with n vertices, m edges and degree sequence d 1 , d 2 , ... , d n . Motivated by a few classical results on Max-Cut of graphs, Lin and Zeng proved that if G is { C 4 , C 6 } -free and has a perfect matching, then G has a bisection of size at least m / 2 + Ω (∑ i = 1 n d i ) , and conjectured the same bound holds for C 4 -free graphs with perfect matchings. In this paper, we confirm the conjecture under the additional condition that G is C 5 -free. [ABSTRACT FROM AUTHOR]

This research proposes integrating a combined system from a supercritical Brayton cycle (SBC) at extremely high temperatures and pressures and a conventional ORC cycle. The ORC cycle was evaluated with three working fluids: acetone, toluene, and cyclohexane. Of these, the cyclohexane, thanks to its dry fluid condition, obtained the best result in the sensitivity analysis for the energetic and exergetic evaluations with the most relevant (net power and exergy destruction) for the variation in the most critical performance parameter of the system for both the configuration with reheat and the configuration with recompression. Between the two proposed configurations, the most favorable performance was obtained with a binary system with reheat and recompression; with reheat, the SBC obtained first- and second-law efficiencies of 45.8% and 25.2%, respectively, while the SBC obtained values of 54.8% and 27.9%, respectively, with reheat and recompression. Thus, an increase in overall system efficiency of 30.3% is obtained. In addition, the destroyed exergy is reduced by 23% due to the bypass before the evaporation process. The SBC-ORC combined hybrid system with reheat and recompression has a solar radiation of 950 W/m2 K, an exhaust heat recovery efficiency of 0.85, and a turbine inlet temperature of 1008.15 K. The high pressure is 25,000 kPa, the isentropic efficiency of the turbines is 0.8, the pressure ratio is 12, and the pinch point of the evaporator is initially 20 °C and reaches values of 45 °C in favorable supercritical conditions. [ABSTRACT FROM AUTHOR]

This study compared heart rate variability (HRV) parameters of cardiovascular autonomic regulation between well-trained masters and young cyclists at rest, during and following a continuous cycle (CTS) protocol. Ten masters (age = 56 ± 5 years) and eight young (age = 26 ± 3 years) cyclists completed a 100 min experimental protocol consisting of a 60 min CTS cycling bout at 95% of Ventilatory Threshold 2 followed by 40 min of supine recovery. Beat-to-beat heart rate was measured continuously, and HRV parameters analysed at standardised 5 min intervals during rest, exercise and recovery. The root mean square of the successive differences (RMSSD), low-frequency power and high-frequency power parameters were corrected by division of the R-R interval (time domain), or R-R interval squared (frequency domain). Further, the RMSSD and RMSSD:RR for successive 60-s R-R intervals at the onset (0–10 min) and offset (60–70 min) of CTS exercise were analysed over 10-min periods. The natural logarithm (Ln) of skewed parameters was taken for analysis. Significant interaction effects (P < 0.05) for 5 min segments were found for (LnRMSSD, LnRMSSD:RR, LnHF and LnHF:RR2. Masters cyclists demonstrated lower values of parasympathetic activity at rest and during recovery (15–20 min and 35–40 min) compared to younger cyclists. However, similar HRV responses were observed during exercise, including throughout the acute onset and offset periods (P > 0.05). This data shows that cardiac autonomic regulation during, or immediately following CTS exercise may not be influenced by age, but masters athletes may exhibit a lower baseline for parasympathetic activity. [ABSTRACT FROM AUTHOR]

The main aim of the paper is to give the crossing number of the join product G* + Dn for the graph G* isomorphic to 4-regular graph on six vertices except for two distinct edges with no common vertex such that two remaining vertices are still adjacent, and where Dn consists of n isolated vertices. The proofs are done with the help of well-known exact values for crossing numbers of join products of four subgraphs Hk of G* with discrete graphs. Further, we give a conjecture concerning crossing numbers of the join products of Dn with Wm\e for both types edges e of wheels Wm of m + 1 vertices. [ABSTRACT FROM AUTHOR]

Let W be any wheel graph and G the class of all countable graphs not containing W as a minor. We show that there exists a graph in G which contains every graph in G as an induced subgraph. [ABSTRACT FROM AUTHOR]

Key message: International forest reporting processes and increasing forest disturbances delineate new requirements regarding the information delivered by national forest inventories (NFI), with implications on their sampling strategies. An original comparative review of the sampling designs of 6 pioneer NFI programs being both annual and 5-year periodic evidences a set of common principles used to meet these demands, but also marked implementation differences, and open questions. Bases for a common framework and persisting research needs are highlighted. Developing virtual forest sampling simulation facilities at large scale is a critical challenge. Context: National forest inventories (NFI) rely on diverse sampling strategies. In view of international forest reporting processes, these surveys are increasingly adopting a 5-year periodicity (their bar). The increased need for delivering updated representative statistics in the context of the environmental crisis is making annual forest inventory (their beat) a growing standard of the forest monitoring approach. To meet both objectives, spatially balanced sampling designs resulting in samples that can be split into yearly systematic subsamples have been devised. They ground the grid-based interpenetrating panel design principle that has generated various ingenious designs, however never presented nor reviewed to date. Aims: The purpose of this review was to explore how the interpenetrating panel design principle has been implemented by the NFIs that have turned annual. The aims were to describe and frame the diversity of their designs, highlight their common bases and differences, and compare their ability to address new reporting needs. A special emphasis was placed on the graphical representation of these sampling designs. The NFI programs of France, Norway, Poland, Romania, Sweden, and of the USA were considered. Results: The interpenetrating panel design principle is effective in reviewed inventories and is associated with the 5-year moving-window estimator. Original and creative design developments were identified, causing substantial variations in its implementation. They concern panel geometry, unaligned sampling options, sampling unit status, and estimation methods, making no-two inventory designs identical among those reviewed. In these inventories, the notions of annual and cyclic inventory do not substitute for each other, but appear to complement themselves to serve distinct reporting purposes. Also, negative coordination among annual samples is observed, questioning their adequacy for trend monitoring purposes. Conclusions: The review evidences that a core sampling design principle, used to simultaneously operate annual and 5-year periodic forest inventory, has given rise to a diversity of implementation options. While it offers an original benchmark for any survey transition toward an annual frequency, it demonstrates the absence of a standardized framework. Developing simulation facilities for the comparison and optimization of associated designs appears as a critical priority, especially in the context of the EC forest monitoring perspective. [ABSTRACT FROM AUTHOR]

Let G be a finite simple graph, and JG denote the binomial edge ideal of G. In this paper, we first compute the v-number of binomial edge ideals corresponding to Cohen–Macaulay closed graphs. As a consequence, we obtain the v-number for paths. For cycle and binary tree graphs, we obtain a sharp upper bound for v(JG) using the number of vertices of the graph. We characterize all connected graphs G with v(JG) = 2. We show that for a given pair (k,m),k ≤ m, there exists a graph G with an associated monomial edge ideal I having v-number equal to k and regularity m. We also show that if 2k ≤ m, then there exists a binomial edge ideal with v-number k and regularity m. Finally, we compute v-number of powers of binomial edge ideals with linear resolution, thus proving a conjecture on the v-number of powers of a graded ideal having linear powers, for the class of binomial edge ideals. [ABSTRACT FROM AUTHOR]

A bisection of a graph is a bipartition of its vertex set such that the number of vertices in the two parts differ by at most one, and its size is the number of edges which go across the two parts. Let G be a graph with n vertices, m edges and degree sequence d 1 , d 2 , … , d n . A celebrated result proved by Shearer shows that if G is triangle-free, then it has a bipartition of size at least m / 2 + Ω (∑ i = 1 n d i) . Lin and Zeng showed that Shearer’s lower bound holds for bisections in a graph with a perfect matching and no cycles of length 4 or 6. In this paper, we prove that if the girth of G is at least 6 and G has a perfect matching, then G has a bisection of size at least m / 2 + Ω (∑ i = 1 n d i) , which partly confirms a conjecture posed by Rao, Hou and Zeng. [ABSTRACT FROM AUTHOR]

Answers are offered to Gould’s question to find spectral sufficient conditions that imply a graph contains a chorded cycle via signless Laplacian spectral radius. The conditions are tight. [ABSTRACT FROM AUTHOR]

We characterize the permutative automorphisms of the Cuntz algebra \mathcal {O}_n (namely, stable permutations) in terms of two sequences of graphs that we associate to any permutation of a discrete hypercube [n]^t. As applications we show that in the limit of large t (resp. n) almost all permutations are not stable, thus proving Conj. 12.5 of Brenti and Conti [Adv. Math. 381 (2021), p. 60], characterize (and enumerate) stable quadratic 4 and 5-cycles, as well as a notable class of stable quadratic r-cycles, i.e. those admitting a compatible cyclic factorization by stable transpositions. Some of our results use new combinatorial concepts that may be of independent interest. [ABSTRACT FROM AUTHOR]

The Software Development Life Cycle (SDLC) is a framework that outlines the various stages of software development, from conception to deployment, and beyond until the software is no longer in use. This study investigated the adherence to software engineering stages of the SDLC within selected software development organizations in Kano State. Data was collected with the use of questionnaire. The findings showed strong adherence across different SDLC stages. During the Requirements Gathering phase, elicitation methods were widely employed, with (90.9%) of organizations using the interview technique. Post-elicitation analysis was common, with all organizations (100%) further analyzing requirements using Data Flow Diagrams (DFDs). In the Design Phase, (81.8%) of the organizations used custom development, (72.7%) created architectural designs, and (81.8%) developed User Interface (UI) designs. In the Implementation Phase, all organizations (100%) utilized Integrated Development Environments (IDEs), while (81.8%) used PHP as their programming language of choice. Good practices such as commenting and code reuse were universally applied. In the Testing Phase, all organizations (100%) conducted Unit, Integration, System, Release, Alpha, Beta, and Acceptance testing. A majority (70%) used a combination of white-box and black-box testing methods. In the Maintenance Phase, all organizations (100%) predominantly performed corrective maintenance and functionality additions. This study aims to contribute to capacity-building and skills development initiatives within the software development community in Kano State by identifying areas of low adherence to SDLC stages and suggesting improvement and training programs. [ABSTRACT FROM AUTHOR]

In strong oriented networks, the strong radius, defined as the minimum strong distance between any two nodes, significantly affects the efficiency of information transmission. A larger radius indicates a greater distance between nodes in the network, which results in decreased transmission efficiency and increased latency. In practice, optimizing the strong radius enhances network structure, accelerating information transmission and significantly reducing energy consumption and costs linked to long-distance transmission. This optimization is crucial for maintaining an efficient and cost-effective network system. In this paper, we used the strong product approach, employing cycles as factor graphs to construct strong product networks of cycles, and determined their minimum strong radius. Additionally, we established the upper and lower bounds for the maximum strong radius of these networks. [ABSTRACT FROM AUTHOR]

Copyright of Operations Research Transactions / Yunchouxue Xuebao is the property of Editorial office of Operations Research Transactions and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

For an even graph G and positive integer p, q, and k, the pair (p, q) is an admissible pair if [Formula: see text]. If a graph G admits a decomposition into p copies of [Formula: see text], the path of length k, and q copies of Ck, the cycle of length k, for every admissible pair (p, q), then G has a [Formula: see text]-decomposition. In this paper, we give necessary and sufficient conditions for the existence of a [Formula: see text]-decomposition of n-dimensional hypercube graphs Qn when n is even, [Formula: see text] and [Formula: see text]

Abstract Key message International forest reporting processes and increasing forest disturbances delineate new requirements regarding the information delivered by national forest inventories (NFI), with implications on their sampling strategies. An original comparative review of the sampling designs of 6 pioneer NFI programs being both annual and 5-year periodic evidences a set of common principles used to meet these demands, but also marked implementation differences, and open questions. Bases for a common framework and persisting research needs are highlighted. Developing virtual forest sampling simulation facilities at large scale is a critical challenge. Context National forest inventories (NFI) rely on diverse sampling strategies. In view of international forest reporting processes, these surveys are increasingly adopting a 5-year periodicity (their bar). The increased need for delivering updated representative statistics in the context of the environmental crisis is making annual forest inventory (their beat) a growing standard of the forest monitoring approach. To meet both objectives, spatially balanced sampling designs resulting in samples that can be split into yearly systematic subsamples have been devised. They ground the grid-based interpenetrating panel design principle that has generated various ingenious designs, however never presented nor reviewed to date. Aims The purpose of this review was to explore how the interpenetrating panel design principle has been implemented by the NFIs that have turned annual. The aims were to describe and frame the diversity of their designs, highlight their common bases and differences, and compare their ability to address new reporting needs. A special emphasis was placed on the graphical representation of these sampling designs. The NFI programs of France, Norway, Poland, Romania, Sweden, and of the USA were considered. Results The interpenetrating panel design principle is effective in reviewed inventories and is associated with the 5-year moving-window estimator. Original and creative design developments were identified, causing substantial variations in its implementation. They concern panel geometry, unaligned sampling options, sampling unit status, and estimation methods, making no-two inventory designs identical among those reviewed. In these inventories, the notions of annual and cyclic inventory do not substitute for each other, but appear to complement themselves to serve distinct reporting purposes. Also, negative coordination among annual samples is observed, questioning their adequacy for trend monitoring purposes. Conclusions The review evidences that a core sampling design principle, used to simultaneously operate annual and 5-year periodic forest inventory, has given rise to a diversity of implementation options. While it offers an original benchmark for any survey transition toward an annual frequency, it demonstrates the absence of a standardized framework. Developing simulation facilities for the comparison and optimization of associated designs appears as a critical priority, especially in the context of the EC forest monitoring perspective.

The study of chemical compounds' molecular structures is one of the most cutting-edge uses of graph theory, along with computer science, nanochemistry, network design in electrical and electronic engineering, and the depiction of graphs in Google Maps. The degree and distance between vertices of a graph are the basis for examining topological indices. The formula for computing the Weighted Padmakar Ivan index (WPI) of a graph G is ...Graph operations have become widely used in many engineering disciplines to create the intricate structure of networks. In this manuscript, we determained theWeighted PI index (WPI index) of the lexicographic product of a few classes of graphs and computation of WPI index of various silicate networks has done. [ABSTRACT FROM AUTHOR]

This study investigated the effect of forkhead box M1 (FOXM1) and Aurora kinase B (AURKB) on the epidermal function of keratinocytes.

The crossing number cr (G) of a graph G is the minimum number of edge crossings over all drawings of G in the plane. The main aim of this paper is to give the crossing numbers of the join products G * + P n and G * + C n for the connected graph G * obtained by removing one edge (incident with the dominating vertex) from the wheel W 5 on six vertices, and where P n and C n are paths and cycles on n vertices, respectively. Finally, we also introduce four new conjectures concerning crossing numbers of the join products of P n and C n with W m ∖ e obtained by removing one edge (of both possible types) from the wheel W m on m + 1 vertices. [ABSTRACT FROM AUTHOR]

Let G=(V,E) be a graph. In the D3, the order of any element x in D3 is denoted by O(x).We define a function χ:V(G)→D3 such that for each edge xy we assign the label 0 if o(u)/o(v) or o(v)/o(u) assign the label 1 if o(u) not divides o(v). Let us define the new function µα(χ) which represent number of edges of G having label α under the mapping χ. Now χ is called D3 divisor cordial labeling if |µ1(χ) − µ0(χ)|≤1 and |Vχ(a)– Vχ(b)|≤1 where Vχ(a) represents number of vertices having label a under χ .The graph which satisfies above condition is calledD3divisor cordial labeling graph. Here we discuss the Dihedral group divisor Cordial Labeling of Path, Cycle, star graph, jelly fish graph and wheel graphs. [ABSTRACT FROM AUTHOR]

Let B n denote the family of all maximal bipartite planar graphs on n vertices. Given a family of graphs H , let B n (H) denote the family of all maximal bipartite planar graphs on n vertices which are not H -free. For graph G and a family of graphs H , if G is not H -free, the rainbow number of H in G , denoted by r b (G , H) , is the minimum positive integer t , such that any t -edge-colored graph G contains a rainbow copy of some graph in H. The rainbow number of H in maximal bipartite planar graph, denoted by r b (B n (H) , H) , is defined as max { r b (G , H) | G ∈ B n (H) }. A cycle on l vertices is denoted by C l. The graph obtained by arbitrarily adding one pendant edge at one vertex of a cycle C l is denoted by C l +. For any positive integer k , let C k ≔ { C 4 , C 6 , ... , C 2 k + 2 } and C k , 2 i 0 + ≔ (C k ∖ { C 2 i 0 }) ∪ { C 2 i 0 + } for some i 0 ∈ { 2 , 3 , ... , k + 1 }. In this paper, we firstly prove that r b (B n , C k) = r b (B n , C k , 2 i 0 +) = n + n − 2 k + 2 − 1 for any n ≥ max { 2 k + 2 , 5 } and k + 1 ≥ i 0 ≥ 2. We then obtain that r b (B n (H) , H) = 2 n − 4 for any n ≥ | V (H) | and k ≥ 3 , where H ∈ { C 2 k , C 2 k + }. [ABSTRACT FROM AUTHOR]

Flow-cytometry (FC) is a powerful tool that can assist in lymphoma diagnosis in lymph node (LN) specimens. Although lymphoma diagnosis and classification are mainly based on tumor cell characteristics, surrounding cells are less employed in this process. We retrospectively investigated alterations in the ploidy status, proliferative cell fraction (PF) and the percentages of surrounding immune cells in 62 consecutive LN specimens with B-Cell Non-Hodgkin Lymphoma (B-NHL) that were submitted for FC evaluation between 2019–2022. Compared with indolent B-NHLs, aggressive B-NHLs show increased DNA aneuploidy and PF, increased monocytes, immature-granulocytes, mature granulocytes, CD8+ T-cells, Double-Negative-T-cells and Double-Positive-T-cells, and decreased total CD45+ cells, total lymphocytes, CD4+ T-cells and CD4/CD8 ratio. Receiver operating characteristic analysis determined PF > 6.8% and immature-granulocytes > 0.9% as optimal cutoffs with highest specificity and sensitivity in differentiating aggressive and indolent B-NHLs. These findings further strength the diagnostic value of DNA content analysis by FC and suggest the utilization of tumor surrounding immune cells in NHL diagnosis and classification. [ABSTRACT FROM AUTHOR]

Let H be a set of graphs. The planar Turán number, e x P (n , H) , is the maximum number of edges in an n-vertex planar graph which does not contain any member of H as a subgraph. When H = { H } has only one element, we usually write e x P (n , H) instead. The study of extremal planar graphs was initiated by Dowden (J Graph Theory 83(3):213–230, 2016). He obtained sharp upper bounds for both e x P (n , C 5) and e x P (n , K 4) . Later on, sharp upper bounds were proved for e x P (n , C 6) and e x P (n , C 7) . In this paper, we show that e x P (n , { K 4 , C 5 }) ≤ 15 7 (n - 2) and e x P (n , { K 4 , C 6 }) ≤ 7 3 (n - 2) . We also give constructions which show the bounds are sharp for infinitely many n. [ABSTRACT FROM AUTHOR]

The crossing number cr(H) of a graph H is the minimum number of edge crossings over all drawings of H in the plane. Let H∗ be the connected graph of order five isomorphic to K5 ∖ e obtained by removing one edge from the complete graph K5. The main aim of the paper is to give the crossing numbers of the join products H∗ + Pn and H∗ + Cn, where Pn and Cn are the path and the cycle on n vertices, respectively. The proofs are done with the help of a suitable classification of a large number of drawings of the graph H∗ in view of the existence of a separating cycle of two possible types. [ABSTRACT FROM AUTHOR]

Sanctuary delves into the realms of memory, forgiveness, and present contemplation through a fourphase journey into the past. Each segment intimately explores significant periods and memories, providing an external lens for reassessment. Employing collage illustrations for world-building and drawing inspiration from common gaming elements, such as an inventory system and interactive dialogue options, the artist reflects on themes of causality and the profound impact decisions make on our lives. This contemplation extends to the construction and dissolution of the foundations of our realities, mirroring the ebb and flow of our homes throughout different life phases. The reiteration of memories and contemplation of choices are seamlessly woven into the narrative through the lens of game mechanics, offering users the agency to shape their own version of the past. The immersive journey culminates in an envisioned 'sanctuary,' a symbolic space that mirrors the user's unique disposition, encapsulating the essence of their inner world. [ABSTRACT FROM AUTHOR]

For a graph G, we define a total k-labeling ϕ as a combination of an edge labeling ϕe : E(G) → {1, 2, . . ., ke} and a vertex labeling ϕv : V (G) → {0, 2, . . ., 2kv}, where k = max {ke, 2kv}. The total k-labeling ϕ is called a vertex irregular reflexive k-labeling of G if any pair of vertices u, u' have distinct vertex weights wtϕ(u) ≠ wtϕ(u'), where wtϕ(u) = ϕ(u) + Σuu'∈E(G) ϕ(uu' ) for any vertex u ∈ V (G). The smallest value of k for which such a labeling exists is called the reflexive vertex strength of G, denoted by rvs(G). In this paper, we present a new lower bound for the reflexive vertex strength of any graph. We investigate the exact values of the reflexive vertex strength of generalized friendship graphs, corona product of two paths, and corona product of a cycle with isolated vertices by referring to the lower bound. This study discovers some interesting open problems that are worth further exploration. [ABSTRACT FROM AUTHOR]

Let a graph G = (V, E) be a (p, q) graph. Define ρ = {p/2, p is even p - 1/2, p is odd, and M = {±1, ±2, ⋯ ± ρ} called the set of labels. Consider a mapping λ : V → by assigning different labels in M to the different elements of V when p is even and different labels in M to p -- 1 elements of V and repeating a label for the remaining one vertex when p is odd. The labeling as defined above is said to be a pair mean cordial labeling if for each edge uv of G, there exists a labeling λ(2)+λ(v)/2 if λ(2) + λ(v) is even and λ(u)+λ(v)+1/2 if λ(u) + λ(v) is odd such that ... ≤ where ... and ... respectively denote the number of edges labeled with 1 and the number of edges not labeled with 1. A graph G with a pair mean cordial labeling is called a pair mean cordial graph. In this paper, we discuss here the pair mean cordial labeling of union graphs like Lm, υ Ln, Pm υ Ln, Cm Ln, Wm υ υ Ln, Sm υ Ln. [ABSTRACT FROM AUTHOR]

A graph is ℓ-holed if all its induced cycles of length at least four have length exactly ℓ. We give a complete description of the ℓ -holed graphs for each ℓ ≥ 7. [ABSTRACT FROM AUTHOR]

We show that for every $\eta \gt 0$ every sufficiently large $n$ -vertex oriented graph $D$ of minimum semidegree exceeding $(1+\eta)\frac k2$ contains every balanced antidirected tree with $k$ edges and bounded maximum degree, if $k\ge \eta n$. In particular, this asymptotically confirms a conjecture of the first author for long antidirected paths and dense digraphs. Further, we show that in the same setting, $D$ contains every $k$ -edge antidirected subdivision of a sufficiently small complete graph, if the paths of the subdivision that have length $1$ or $2$ span a forest. As a special case, we can find all antidirected cycles of length at most $k$. Finally, we address a conjecture of Addario-Berry, Havet, Linhares Sales, Reed, and Thomassé for antidirected trees in digraphs. We show that this conjecture is asymptotically true in $n$ -vertex oriented graphs for all balanced antidirected trees of bounded maximum degree and of size linear in $n$. [ABSTRACT FROM AUTHOR]

Background: Porcine embryonic development is widely utilized in the medical industry. However, the blastocyst development rate in vitro is lower compared to in vivo. To address this issue, various supplements are employed. Extracellular vesicles (EVs) play the role of communicators that carry many bioactive cargoes. Additionally, the contents of EVs can vary on the estrous cycle. Methods: We compared the effects of adding EVs derived from porcine uterine fluid (UF), categorized as non-EV (G1), EVs in estrus (G2) and EVs in diestrus (G3). After in vitro culture (IVC) was performed in three different groups, cleavage rate and blastocyst development rate were examined. In addition, glutathione (GSH) and reactive oxygen species (ROS) levels were measured 2 days after activation to assess oxidative stress. Results: Using NTA and cryo-TEM, we confirmed the presence of EVs with sizes ranging from 30 nm to 200 nm, that the particles were suitable for analysis for analysis. In IVC data, the highest cleavage rate was observed in G2, which was significantly different from G1 but not significantly different from the next highest, G3. Similarly, the highest blastocyst development rate was observed in G2, which was significantly different from G1 but not significantly different from the next highest, G3. Conclusions: These results indicate that estrus derived EVs contain biofactors beneficial for early blastocyst development, including GSH which protects the blastocyst from oxidative stress. Additionally, although diestrus-derived EVs are expected to have some effect on blastocyst development, it appeared to be less effective than estrus-derived EVs.

Let G and H be two graphs, each one of them being a path, a cycle or a star. In this paper, we determine the b-chromatic number of every subdivision-vertex neighbourhood corona G ⊡ H or G ⊡ Kn, where Kn is the complete graph of order n. It is also established for those graphs Kn ⊡ G having m-degree not greater than n + 2. All the proofs are accompanied by illustrative examples.

The abstract highlights the critical need for securing sensitive medical data, emphasizing the challenges in the medical domain due to the confidentiality of patient, disease, doctor, and staff information. The proposed study introduces a novel approach using machine learning, specifically integrating the firefly optimization technique with the random forest algorithm, to classify medical data in a secure manner. The significance lies in addressing the security concerns associated with medical datasets, offering a solution that prioritizes confidentiality throughout the software development life cycle (SDLC). The proposed algorithm achieves an impressive accuracy of 96%, showcasing its efficacy in providing a robust and secure framework for the development of applications involving medical data. This research contributes to advancing the field of medical data security, offering a practical solution for safeguarding sensitive information in healthcare applications. [ABSTRACT FROM AUTHOR]

Copyright of Advances in Earth Science (1001-8166) is the property of Advances in Earth Science Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The doctrine of unity of opposites lays in the centre of the debate on Heraclitus' philosophy. The present article proposes a critical analysis of the mainstream interpretation of geometrical oppositions (fragments DK 22 B 59, B 60 and B 103) as mere examples of different points of view. Instead, we suggest that these fragments are fundamental pieces in Heraclitus cosmology and that they are traces of a circular and archaic paradigm. Indeed, cyclical formulations are spread throughout the fragments and, read in connection with geometrical oppositions, perform a useful model to describe how permanence and change can be complementary events. In this context, circularity can be a key to the comprehension of unity of opposites as a result of interchangeable processes – as day and night, life and death, beginning and end – so that opposites are part of a concrete and vital unity. [ABSTRACT FROM AUTHOR]

Monounary algebras are the most simple type of an algebraic structure. Oriented graphs with one outgoing arrow from every vertex represent them. The aim of this paper is to point out the interdisciplinary relationships concerning this structure. Bernoulli shift is a paradigmatic mapping in dynamical systems. It is also called dyadic, bit shift, doubling or sawtooth. We offer a look at the properties of this mapping via monounary algebras. [ABSTRACT FROM AUTHOR]

Crisis management is a complex process requiring the integration of multiple disciplines, specialists, resources and tools for the prevention and solution of crisis events. To define and characterise the space and time period in which crisis management is applied, modelling is a common approach. It is the crisis management models that allow a better understanding of the specificities, processes and activities carried out during the different periods of crisis. These models also make it possible to identify the links between the different processes and, at the same time, to identify gaps and shortcomings, which are then examined. The article focuses on the analysis of the literature in the field of crisis management and its phases. The aim of the article is to provide a comprehensive overview of the processes and activities carried out in crisis management, while also highlighting the importance of territorial risk management and assessment in crisis management. [ABSTRACT FROM AUTHOR]