Making Multiple Decisions Adaptively

The asymptotic behavior of multiple decision procedures is studied when the underlying distributions depend on an unknown nuisance parameter. An adaptive procedure must be asymptotically optimal for each value of this nuisance parameter, and it should not depend on its value. A necessary and sufficient condition for the existence of such a procedure is derived. Several examples are investigated in detail, and possible lack of adaptation of the traditional overall maximum likelihood rule is discussed

Cryptanalysis of two chaotic encryption schemes based on circular bit shift and XOR operations

Recently two encryption schemes were proposed by combining circular bit shift and XOR operations, under the control of a pseudorandom bit sequence (PRBS) generated from a chaotic system. This paper studies the security of these two encryption schemes and reports the following findings: 1) there exist some security defects in both schemes; 2) the underlying chaotic PRBS can be reconstructed as an equivalent key by using only two chosen plaintexts; 3) most elements in the underlying chaotic PRBS can be obtained by a differential known-plaintext attack using only two known plaintexts. Experimental results are given to demonstrate the feasibility of the proposed attack.Comment: 17 pages, 8 figure

Neighborhood Homogeneous Labelings of Graphs

Given a labeling of the vertices and edges of a graph, we define a type of homogeneity that requires that the neighborhood of every vertex contains the same number of each of the labels. This homogeneity constraint is a generalization of regularity – all such graphs are regular. We consider a specific condition in which both the edge and vertex label sets have two elements and every neighborhood contains two of each label. We show that vertex homogeneity implies edge homogeneity (so long as the number of edges in any neighborhood is four), and give two theorems describing how to build new homogeneous graphs (or multigraphs) from others. Keywords: vertex labeling; edge labeling; homogenous graph; regular graph 1

On the Parallel Tower of Hanoi Puzzle: Acyclicity and a Conditional Triangle Inequality

A generalization of the Tower of Hanoi Puzzle---the Parallel Tower of Hanoi Puzzle--is described herein. Within this context, two theorems on minimal walks in the state space of configurations, along with their algorithmic proofs, are provided.Comment: To be presented at the SIAM Conference on Discrete Mathematic

PENGEMBANGAN BUKU ELEKTRONIK BERBASIS 7E (ELICITE, ENGAGE, EXPLORE, EXPLAIN, ELABORATE, EVALUATE, AND EXTEND) BERMUATAN LITERASI DIGITAL PADA MATERI ARITMATIKA SOSIAL KELAS VII

Abstrak: Pengembangan ini bertujuan untuk menghasilkan produk yang berupa buku elektronik berbasisis7e bermuatanliterasi digital pada materi aritmatika sosial SMP kelas VIII. Model penelitian pengembangan yang digunakan yaitu model ADDIE yang terdiri atas 5 tahapan diantaranya; (1) tahap Analysis (menganalisis), (2) tahap design (perencanaan), (3) tahap develop (pengembangan) dan (4) tahap implementation  (implementasi) dan (5) evaluation. Subjek dalam penelitian ini adalah, ahli materi, ahli media dan desain serta  ahli praktisi guru dari  sekolah MTs. Negeri 7 Nganjuk, dan 10 siswa dari MTs. MTs. Negeri 7 Nganjuk sebagai pengguna (user). Tujuannya untuk mengetahui kevalidan produk dan kepraktisan produk yang dihasilkan. Analisis data yang digunakan adalah kuantitatif dan kualitatif, menurut penilaian ahli materi memperoleh hasil skor 3.13 ahli media dan desain dengan hasil skor 3.1 dan praktisi dengan hasil skor 3.4. Berdasarkan hasil analisis data validasi ahli dan praktisi, secara keseluruhan buku elektronik yang dikembangkan dinyatakan valid dengan hasil rata-rata penilaian sebesar 3.21 Sedangkan pada validasi pengguna (user), dinyatakan praktis dengan diperoleh rata-rata hasil skor sebesar 3.21. Berdasarkan hasil analisis tersebut, dapat disimpulkan bahwa buku elektronik telah memenuhi kriteria layak digunakan dalam proses pembelajaran.Kata kunci: pengembangan, buku elektronik, 7e, literasi digital, aritmatika sosia

Beta-binomial model for meta-analysis of odds ratios

In meta-analysis of odds ratios ({\OR}s), heterogeneity between the studies is usually modelled via the additive random effects model (REM). An alternative, multiplicative random effects model for {\OR}s uses overdispersion. The multiplicative factor in this overdispersion model (ODM) can be interpreted as an intra-class correlation (ICC) parameter. This model naturally arises when the probabilities of an event in one or both arms of a comparative study are themselves beta-distributed, resulting in beta-binomial distributions. We propose two new estimators of the ICC for meta-analysis in this setting. One is based on the inverted Breslow-Day test, and the other on the improved gamma approximation by Kulinskaya and Dollinger (2015, p. 26) to the distribution of Cochran's $Q$. The performance of these and several other estimators of ICC on bias and coverage is studied by simulation. Additionally, the Mantel-Haenszel approach to estimation of odds ratios is extended to the beta-binomial model, and we study performance of various ICC estimators when used in the Mantel-Haenszel or the inverse-variance method to combine odds ratios in meta-analysis. The results of the simulations show that the improved gamma-based estimator of ICC is superior for small sample sizes, and the Breslow-Day-based estimator is the best for $n\geq100$. The Mantel-Haenszel-based estimator of {\OR} is very biased and is not recommended. The inverse-variance approach is also somewhat biased for {\OR}s\neq1, but this bias is not very large in practical settings. Developed methods and R programs, provided in the Web Appendix, make the beta-binomial model a feasible alternative to the standard REM for meta-analysis of odds ratios

Assessing historical realibility of the agent-based model of the global energy system

This study looks at the historical reliability of the agent-based model of the global energy system. We present a mathematical framework for the agent-based model calibration and sensitivity analysis based on historical observations. Simulation consistency with the historical record is measured as a distance between two vectors of data points and inference on parameter values is done from the probability distribution of this stochastic estimate. Proposed methodology is applied to the model of the global energy system. Some model properties and limitations followed from calibration results are discussed