Counting triangles in graphs without vertex disjoint odd cycles

Given two graphs $H$ and $F$, the maximum possible number of copies of $H$ in an $F$-free graph on $n$ vertices is denoted by $\mathrm{ex}(n, H, F)$. Let $(\ell+1) \cdot F$ denote $\ell+1$ vertex disjoint copies of $F$. In this paper, we determine the exact value of $\mathrm{ex}(n, C_3, (\ell+1)\cdot C_{2k+1})$ and its extremal graph, which generalizes some known results

Intelligent Optimized Combined Model Based on GARCH and SVM for Forecasting Electricity Price of New South Wales, Australia

Daily electricity price forecasting plays an essential role in electrical power system operation and planning. The accuracy of forecasting electricity price can ensure that consumers minimize their electricity costs and make producers maximize their profits and avoid volatility. However, the fluctuation of electricity price depends on other commodities and there is a very complicated randomization in its evolution process. Therefore, in recent years, although large number of forecasting methods have been proposed and researched in this domain, it is very difficult to forecast electricity price with only one traditional model for different behaviors of electricity price. In this paper, we propose an optimized combined forecasting model by ant colony optimization algorithm (ACO) based on the generalized autoregressive conditional heteroskedasticity (GARCH) model and support vector machine (SVM) to improve the forecasting accuracy. First, both GARCH model and SVM are developed to forecast short-term electricity price of New South Wales in Australia. Then, ACO algorithm is applied to determine the weight coefficients. Finally, the forecasting errors by three models are analyzed and compared. The experiment results demonstrate that the combined model makes accuracy higher than the single models

Analysis of risk factors for recurrence in infertile endometrial cancer patients after in vitro fertilization treatment

PurposeTo investigate the oncologic outcomes of patients with early-stage endometrioid endometrial cancer (EEC) treated with in vitro fertilization/intracytoplasmic sperm injection (IVF/ICSI) following fertility-sparing treatment (FST).MethodsA total of 62 patients who underwent IVF/ICSI treatment in a single fertility center between June 2010 and December 2021 after conservative treatment for early-stage EEC were assigned to a recurrence group and a non-recurrence group. Their clinical characteristics and disease outcomes were retrospectively evaluated.ResultsThe 62 women with complete remission (CR) after FST for EEC underwent 103 IVF cycles, resulting in 41 fresh embryo transfers (ETs) and 70 frozen–thawed transfers; 27 (43.55%) achieved clinical pregnancies, and 20 (32.26%) gave birth to a total of 23 live neonates. Additionally, nine patients had live births from natural pregnancies after IVF failure, bringing the cumulative live birth rate to 46.77% (29/62). After a median follow-up period of 53.88 months (range 20.2–127.5 months), 17 patients (27.42%) experienced recurrence within 2.8 to 57.9 months after the first controlled ovarian stimulation (COS). The probability of relapse at 1, 2, and 3 years after the initiation of COS was 14.52% (9/62), 21% (13/62), and 25.81% (16/62), respectively. Factors such as the time to CR, the time to IVF, the frequency of COS, maintenance treatment before IVF, and histology type were not found to significantly affect recurrence (p = 0.079, 0.182, 0.093, 0.267, and 0.41, respectively). Live births (hazard ratio (HR): 0.28, 95% CI: 0.082–0.962, p = 0.043) and the protocol of letrozole plus gonadotropin-releasing hormone (GnRH) antagonist/agonist used during IVF (HR: 0.1, 95% CI: 0.011–0.882, p = 0.038) were identified as independent favorable factors for recurrence.ConclusionsLive birth was associated with decreased recurrence of EEC. Reducing estrogen levels during COS may serve to mitigate the risk of endometrial cancer recurrence

CAF: Cluster Algorithm and A-Star with Fuzzy Approach for Lifetime Enhancement in Wireless Sensor Networks

Energy is a major factor in designing wireless sensor networks (WSNs). In particular, in the real world, battery energy is limited; thus the effective improvement of the energy becomes the key of the routing protocols. Besides, the sensor nodes are always deployed far away from the base station and the transmission energy consumption is index times increasing with the increase of distance as well. This paper proposes a new routing method for WSNs to extend the network lifetime using a combination of a clustering algorithm, a fuzzy approach, and an A-star method. The proposal is divided into two steps. Firstly, WSNs are separated into clusters using the Stable Election Protocol (SEP) method. Secondly, the combined methods of fuzzy inference and A-star algorithm are adopted, taking into account the factors such as the remaining power, the minimum hops, and the traffic numbers of nodes. Simulation results demonstrate that the proposed method has significant effectiveness in terms of balancing energy consumption as well as maximizing the network lifetime by comparing the performance of the A-star and fuzzy (AF) approach, cluster and fuzzy (CF)method, cluster and A-star (CA)method, A-star method, and SEP algorithm under the same routing criteria

Two stability theorems for Kℓ+1r\mathcal{K}_{\ell + 1}^{r}-saturated hypergraphs

An $\mathcal{F}$-saturated $r$-graph is a maximal $r$-graph not containing any member of $\mathcal{F}$ as a subgraph. Let $\mathcal{K}_{\ell + 1}^{r}$ be the collection of all $r$-graphs $F$ with at most $\binom{\ell+1}{2}$ edges such that for some $\left(\ell+1\right)$-set $S$ every pair $\{u, v\} \subset S$ is covered by an edge in $F$. Our first result shows that for each $\ell \geq r \geq 2$ every $\mathcal{K}_{\ell+1}^{r}$-saturated $r$-graph on $n$ vertices with $t_{r}(n, \ell) - o(n^{r-1+1/\ell})$ edges contains a complete $\ell$-partite subgraph on $(1-o(1))n$ vertices, which extends a stability theorem for $K_{\ell+1}$-saturated graphs given by Popielarz, Sahasrabudhe and Snyder. We also show that the bound is best possible. Our second result is motivated by a celebrated theorem of Andr\'{a}sfai, Erd\H{o}s and S\'{o}s which states that for $\ell \geq 2$ every $K_{\ell+1}$-free graph $G$ on $n$ vertices with minimum degree $\delta(G) > \frac{3\ell-4}{3\ell-1}n$ is $\ell$-partite. We give a hypergraph version of it. The \emph{minimum positive co-degree} of an $r$-graph $\mathcal{H}$, denoted by $\delta_{r-1}^{+}(\mathcal{H})$, is the maximum $k$ such that if $S$ is an $(r-1)$-set contained in a edge of $\mathcal{H}$, then $S$ is contained in at least $k$ distinct edges of $\mathcal{H}$. Let $\ell\ge 3$ be an integer and $\mathcal{H}$ be a $\mathcal{K}_{\ell+1}^3$-saturated $3$-graph on $n$ vertices. We prove that if either $\ell \ge 4$ and $\delta_{2}^{+}(\mathcal{H}) > \frac{3\ell-7}{3\ell-1}n$; or $\ell = 3$ and $\delta_{2}^{+}(\mathcal{H}) > 2n/7$, then $\mathcal{H}$ is $\ell$-partite; and the bound is best possible. This is the first stability result on minimum positive co-degree for hypergraphs

Toward a density Corr\'{a}di--Hajnal theorem for degenerate hypergraphs

Given an $r$-graph $F$ with $r \ge 2$, let $\mathrm{ex}(n, (t+1) F)$ denote the maximum number of edges in an $n$-vertex $r$-graph with at most $t$ pairwise vertex-disjoint copies of $F$. Extending several old results and complementing prior work [J. Hou, H. Li, X. Liu, L.-T. Yuan, and Y. Zhang. A step towards a general density Corr\'{a}di--Hajnal theorem. arXiv:2302.09849, 2023.] on nondegenerate hypergraphs, we initiate a systematic study on $\mathrm{ex}(n, (t+1) F)$ for degenerate hypergraphs $F$. For a broad class of degenerate hypergraphs $F$, we present near-optimal upper bounds for $\mathrm{ex}(n, (t+1) F)$ when $n$ is sufficiently large and $t$ lies in intervals $\left[0, \frac{\varepsilon \cdot \mathrm{ex}(n,F)}{n^{r-1}}\right]$, $\left[\frac{\mathrm{ex}(n,F)}{\varepsilon n^{r-1}}, \varepsilon n \right]$, and $\left[ (1-\varepsilon)\frac{n}{v(F)}, \frac{n}{v(F)} \right]$, where $\varepsilon > 0$ is a constant depending only on $F$. Our results reveal very different structures for extremal constructions across the three intervals, and we provide characterizations of extremal constructions within the first interval. Additionally, for graphs, we offer a characterization of extremal constructions within the second interval. Our proof for the first interval also applies to a special class of nondegenerate hypergraphs, including those with undetermined Tur\'{a}n densities, partially improving a result in [J. Hou, H. Li, X. Liu, L.-T. Yuan, and Y. Zhang. A step towards a general density Corr\'{a}di--Hajnal theorem. arXiv:2302.09849, 2023.]Comment: 37 pages, 4 figures, comments are welcom

Increased both cortical activation and functional connectivity after transcranial direct current stimulation in patients with post-stroke: A functional near-infrared spectroscopy study

BackgroundPrevious studies have shown that cognitive impairment is common after stroke. Transcranial direct current stimulation (tDCS) is a promising tool for rehabilitating cognitive impairment. This study aimed to investigate the effects of tDCS on the rehabilitation of cognitive impairment in patients with stroke.MethodsTwenty-two mild–moderate post-stroke patients with cognitive impairments were treated with 14 tDCS sessions. A total of 14 healthy individuals were included in the control group. Cognitive function was assessed using the Mini-Mental State Examination (MMSE) and the Montreal Cognitive Assessment (MoCA). Cortical activation was assessed using functional near-infrared spectroscopy (fNIRS) during the verbal fluency task (VFT).ResultsThe cognitive function of patients with stroke, as assessed by the MMSE and MoCA scores, was lower than that of healthy individuals but improved after tDCS. The cortical activation of patients with stroke was lower than that of healthy individuals in the left superior temporal cortex (lSTC), right superior temporal cortex (rSTC), right dorsolateral prefrontal cortex (rDLPFC), right ventrolateral prefrontal cortex (rVLPFC), and left ventrolateral prefrontal cortex (lVLPFC) cortical regions. Cortical activation increased in the lSTC cortex after tDCS. The functional connectivity (FC) between the cerebral hemispheres of patients with stroke was lower than that of healthy individuals but increased after tDCS.ConclusionThe cognitive and brain functions of patients with mild-to-moderate stroke were damaged but recovered to a degree after tDCS. Increased cortical activation and increased FC between the bilateral cerebral hemispheres measured by fNIRS are promising biomarkers to assess the effectiveness of tDCS in stroke

Designing a Programming Contract Library for Java

Programmers are now developing large and complex software systems, so it’s important to have software that is consistent, efficient, and robust. Programming contracts allow developers to specify preconditions, postconditions, and invariants in order to more easily identify programming errors. The design by contract principle [1] was first used in the Eiffel programming language [2], and has since been extended to libraries in many other languages. The purpose of my project is to design a programming contract library for Java. The library supports a set of preconditions, postconditions, and invariants that are specified in Java annotations. It incorporates contract checking for objects of classes following the bean notation [3]. The library also supports checking for user-defined functions as contract conditions. This feature allows the user to check for complex contract conditions. In addition to these, the library supports contracts using lambdas in Java 8 [4], which to our knowledge has not been done in previous works on Java contracts. While the results show us that enabling contracts lowers the performance of the system, especially when lambda contracts are used, we also demonstrate how careful design can significantly reduce the overhead

PpNAC187 Enhances Lignin Synthesis in ‘Whangkeumbae’ Pear (Pyrus pyrifolia) ‘Hard-End’ Fruit

A disorder in pears that is known as ‘hard-end’ fruit affects the appearance, edible quality, and market value of pear fruit. RNA-Seq was carried out on the calyx end of ‘Whangkeumbae’ pear fruit with and without the hard-end symptom to explore the mechanism underlying the formation of hard-end. The results indicated that the genes in the phenylpropanoid pathway affecting lignification were up-regulated in hard-end fruit. An analysis of differentially expressed genes (DEGs) identified three NAC transcription factors, and RT-qPCR analysis of PpNAC138, PpNAC186, and PpNAC187 confirmed that PpNAC187 gene expression was correlated with the hard-end disorder in pear fruit. A transient increase in PpNAC187 was observed in the calyx end of ‘Whangkeumbae’ fruit when they began to exhibit hard-end symptom. Concomitantly, the higher level of PpCCR and PpCOMT transcripts was observed, which are the key genes in lignin biosynthesis. Notably, lignin content in the stem and leaf tissues of transgenic tobacco overexpressing PpNAC187 was significantly higher than in the control plants that were transformed with an empty vector. Furthermore, transgenic tobacco overexpressing PpNAC187 had a larger number of xylem vessel elements. The results of this study confirmed that PpNAC187 functions in inducing lignification in pear fruit during the development of the hard-end disorder. View Full-Tex