Critical points of the random cluster model with Newman-Ziff sampling

We present a method for computing transition points of the random cluster model using a generalization of the Newman-Ziff algorithm, a celebrated technique in numerical percolation, to the random cluster model. The new method is straightforward to implement and works for real cluster weight $q>0$. Furthermore, results for an arbitrary number of values of $q$ can be found at once within a single simulation. Because the algorithm used to sweep through bond configurations is identical to that of Newman and Ziff, which was conceived for percolation, the method loses accuracy for large lattices when $q>1$. However, by sampling the critical polynomial, accurate estimates of critical points in two dimensions can be found using relatively small lattice sizes, which we demonstrate here by computing critical points for non-integer values of $q$ on the square lattice, to compare with the exact solution, and on the unsolved non-planar square matching lattice. The latter results would be much more difficult to obtain using other techniques.

Constructing a Life–quality Scale for the teachers of Jordanian ministry of education : بناء مقياس جودة الحياة لدى المعلمين والمعلمات العاملين في وزارة التربية والتعليم الأردنية

his study aimed at building a life quality scale for teachers working in the Jordanian Ministry of Education. This study was conducted in schools affiliated with the Jordanian Ministry of Education, and the researcher used the descriptive approach in this study, and the scale of the study was built then its validity and reliability were confirmed and applied to the study sample, which involved 1780 teachers who were selected by random cluster method from six directorates of education Distributed in three regions, and the results of the study showed that there are statistically significant differences in the level of life quality attributed to the variable of the region and in favor of the central and northern regions. The research came out with several recommendations, most notably the re- application of the scale to other categories, knowing its validity and stability, and the derivation of its criteria.

Keefektifan Penggunaan Metode Clustering dan Show Not Tell terhadap Kemampuan Menulis Teks Deskripsi Peserta Didik SMP Kelas VII Di Kecamatan Binamu Kabupaten Jeneponto

Desain yang digunakan adalah one group pretest-posttest design, yaitu desain penelitian yang diberikan pre-test sebelum diberikan perlakuan dan pemberian post-test setelah diberikan perlakuan atau tindakan. Populasi dalam penelitian ini adalah SMP Negeri se-Kecamatan Binamu yang berjumlah 9 sekolah. Sampel dalam penelitian ini sebanyak 3 kelas pada tiga sekolah dengan jumlah 75 peserta didik. Penarikan sampel dilakukan dengan cara random cluster sampling. Dalam penelitian ini yang menjadi sampel adalah SMP Negeri 9 Binamu sebanyak 33 peserta didik, 27 Peserta didik di SMPN 6 Binamu, dan 25 Peserta didik di SMPN 4 Binamu. Jadi, jumlah keseluruhan peserta didik pada 3 sekolah sebanyak 75 peserta didik.Data yang diperoleh dianalisis dengan statistik deskriptif kuantitatif dan statistik inferensial. Berdasarkan analisis statistik deskriptif kuantitiatif menunjukkan bahwa penggunaan metode clustering dan Show Not Tell efektif dalam pembelajaran menulis teks deskripsi peserta didik SMP kelas VII di Kecamatan Binamu. Hal ini dibuktikan berdasarkan perolehan nilai rata-rata peserta didik pada pre-test 35,62. Selanjutnya, nilai post-test diperoleh nilai rata-rata sebesar 72,24 dengan jumlah sampel sama dengan pretest sebanyak 75. Berdasarkan data statistik tersebut menunjukkan bahwa terjadi peningkatan nilai rata-rata hasil penilaian menulis peserta didik berdasarkan nilai pre-test dan nilai post-test. Hasil analisis inferensial menggunakan uji t model paired sampel test tampak bahwa penggunaan metode clustering dan Show Not Tell efektif diterapkan dalam pembelajran menulis teks deskripsi pada peserta didik SMP kelas VII di Kecamatan Binamu. Hal ini berdasarkan hasil diperoleh nilai Sig. (2 tailed) sebesar 0,000 < 0,05. Ini menunjukkan bahwa terdapat perbedaan yang nyata hasil penilaian menulis teks deskripsi sebelum (pre-test) dan setelah (post-test) menggunakan metode Clustering dan Show Not Tell.

Analysis Of The Effect Of Brand Image On The Sales Volume Of Three Products

Brand image is one of the essential things that must be considered for maintaining the existence of a product. A positive brand image is expected to provide trust and satisfaction’s consumer for the product. It will undoubtedly have an impact on increasing the number of product uses by the customer. The purpose of this study was to analyze the effect of brand image on product sales volume. The sampling technique in this study was random cluster sampling. Meanwhile, the analysis method used is Analysis of Variance (ANOVA). The results of the research that have been done show that there is an effect of brand image on sales volume. It can be a material consideration for the company to continue building a brand image to optimize product sales volume.

Planar random-cluster model: fractal properties of the critical phase

This paper is studying the critical regime of the planar random-cluster model on $${\mathbb {Z}}^2$$ Z 2 with cluster-weight $$q\in [1,4)$$ q ∈ [ 1 , 4 ) . More precisely, we prove crossing estimates in quads which are uniform in their boundary conditions and depend only on their extremal lengths. They imply in particular that any fractal boundary is touched by macroscopic clusters, uniformly in its roughness or the configuration on the boundary. Additionally, they imply that any sub-sequential scaling limit of the collection of interfaces between primal and dual clusters is made of loops that are non-simple. We also obtain a number of properties of so-called arm-events: three universal critical exponents (two arms in the half-plane, three arms in the half-plane and five arms in the bulk), quasi-multiplicativity and well-separation properties (even when arms are not alternating between primal and dual), and the fact that the four-arm exponent is strictly smaller than 2. These results were previously known only for Bernoulli percolation ($$q = 1$$ q = 1 ) and the FK-Ising model ($$q = 2$$ q = 2 ). Finally, we prove new bounds on the one, two and four-arm exponents for $$q\in [1,2]$$ q ∈ [ 1 , 2 ] , as well as the one-arm exponent in the half-plane. These improve the previously known bounds, even for Bernoulli percolation.

Random-Cluster Dynamics on Random Regular Graphs in Tree Uniqueness

We establish rapid mixing of the random-cluster Glauber dynamics on random $$\varDelta $$ Δ -regular graphs for all $$q\ge 1$$ q ≥ 1 and $$p<p_u(q,\varDelta )$$ p < p u ( q , Δ ) , where the threshold $$p_u(q,\varDelta )$$ p u ( q , Δ ) corresponds to a uniqueness/non-uniqueness phase transition for the random-cluster model on the (infinite) $$\varDelta $$ Δ -regular tree. It is expected that this threshold is sharp, and for $$q>2$$ q > 2 the Glauber dynamics on random $$\varDelta $$ Δ -regular graphs undergoes an exponential slowdown at $$p_u(q,\varDelta )$$ p u ( q , Δ ) . More precisely, we show that for every $$q\ge 1$$ q ≥ 1 , $$\varDelta \ge 3$$ Δ ≥ 3 , and $$p<p_u(q,\varDelta )$$ p < p u ( q , Δ ) , with probability $$1-o(1)$$ 1 - o ( 1 ) over the choice of a random $$\varDelta $$ Δ -regular graph on n vertices, the Glauber dynamics for the random-cluster model has $$\varTheta (n \log n)$$ Θ ( n log n ) mixing time. As a corollary, we deduce fast mixing of the Swendsen–Wang dynamics for the Potts model on random $$\varDelta $$ Δ -regular graphs for every $$q\ge 2$$ q ≥ 2 , in the tree uniqueness region. Our proof relies on a sharp bound on the “shattering time”, i.e., the number of steps required to break up any configuration into $$O(\log n)$$ O ( log n ) sized clusters. This is established by analyzing a delicate and novel iterative scheme to simultaneously reveal the underlying random graph with clusters of the Glauber dynamics configuration on it, at a given time.

Compulsive Buying in Adolescents. The Impact of Gender and Alcohol and Cannabis Use

The purpose of this study to analyse whether compulsive buying in teenagers is related to gender and alcohol and cannabis use in a sample of 573 students aged 14–17 from secondary education schools in Burgos (Spain) (M = 15.65; SD = 1.04). Random cluster sampling was performed to select the sample. The Compulsive Buying Questionnaire was used together with two extra promts: ‘Indicate how much alcohol you consume’ and ‘Indicate how much cannabis you take’. Descriptive statistics were used in data analysis, while MANOVA was used to study gender differences in alcohol and cannabis use, compulsive buying and their interaction. The results show higher scores for female compulsive buyers than for men, higher scores for alcohol and cannabis users’ compulsive buying than for non-users, respectively, and higher scores for female users than for male users. A certain interaction was also observed between alcohol and cannabis use. A higher alcohol consumption entailed a higher score in compulsive buying, with cannabis users who did not consume alcohol obtaining the highest scores. Thus, prevention programmes should consider teenagers’ gender and the risk of taking toxic substances.

Rapidly modifiable factors associated with full vaccination status among children in Niamey, Niger: A cross-sectional, random cluster household survey

Background and objectives Vaccination status becomes more equitable when interventions are carried out to eliminate poverty or to improve levels in maternal education. Low-income countries need to identify interventions that would have a more immediate and equitable effect. The present study aimed to identify rapidly modifiable factors associated with full vaccination status among children in Niamey, Niger. Methods A cross-sectional, random cluster household survey was conducted in Niamey’s five health districts. Data on vaccination coverage and socioeconomic household characteristics were collected. Logistic regression analysis was conducted with data on 445 mothers and their children aged 12–23 months. Results Of 445 children, 38% were fully vaccinated. Mothers who were satisfied with their health worker’s attitude and had correct vaccination calendar knowledge (adjusted odds ratio [aOR] 5.32, 95% confidence interval [CI] 2.05–13.82) were more likely to have fully vaccinated children. Mothers who had completed secondary school (aOR 2.04, 95% CI 1.17–3.55) were also associated with having fully vaccinated children. Conclusions A higher rate of full vaccination among children could be achieved by relatively short-term modifiable factors. These modifiable factors are mothers’ satisfaction with health workers’ attitudes and knowledge of the vaccination calendar. Maternal satisfaction with health workers’ attitudes could be improved through better interpersonal communication between health workers and mothers. Specifically, mothers should be given specific information on time intervals between appointments. Strengthened communication interventions may be effective in improving both the acceptability of health services and low vaccination coverage.