اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدSimple Derivation of the Lifetime and the Distribution of Faces for a Binary Subdivision Model
299
0
0.0
(
0
)
تأليف
Yukio Hayashi
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
The iterative random subdivision of rectangles is used as a generation model of networks in physics, computer science, and urban planning. However, these researches were independent. We consider some relations in them, and derive fundamental properties for the average lifetime depending on birth-time and the balanced distribution of rectangle faces.
قيم البحث
اقرأ أيضاً
The dynamics of wealth distribution plays a critical role in the economic market, hence an understanding of its nonequilibrium statistical mechanics is of great importance to human society. For this aim, a simple and efficient one-dimensional (1D) la
ttice gas automaton (LGA) is presented for wealth distribution of agents with or without saving propensity. The LGA comprises two stages, i.e., random propagation and economic transaction. During the former phase, an agent either remains motionless or travels to one of its neighboring empty sites with a certain probability. In the subsequent procedure, an economic transaction takes place between a pair of neighboring agents randomly. It requires at least 4 neighbors to present correct simulation results. The LGA reduces to the simplest model with only random economic transaction if all agents are neighbors and no empty sites exist. The 1D-LGA has a higher computational efficiency than the 2D-LGA and the famous Chakraborti-Chakrabarti economic model. Finally, the LGA is validated with two benchmarks, i.e., the wealth distributions of individual agents and dual-earner families. With the increasing saving fraction, both the Gini coefficient and Kolkata index (for individual agents or two-earner families) reduce, while the deviation degree (defined to measure the difference between the probability distributions with and without saving propensities) increases. It is demonstrated that the wealth distribution is changed significantly by the saving propensity which alleviates wealth inequality.
Let $R=K[X_1,dots, X_n]$ be a polynomial ring in $n$ variables over a field $K$ of charactersitic zero and $d$ a $K$-derivation of $R$. Consider the isotropy group if $d$: $ text{Aut}(R)_d :={rho in text{Aut}_K(R)|; rho d rho^{-1}=d}$. In his doctora
l thesis, Baltazar proved that if $d$ is a simple Shamsuddin derivation of $K[X_1,X_2]$, then its isotropy group is trivial. He also gave an example of a non-simple derivation whose isotropy group is infinite. Recently, Mendes and Pan generalized this result to an arbitrary derivation of $K[X_1,X_2]$ proving that a derivation of $K[X_1,X_2]$ is simple if, and only if, its isotropy group is trivial. In this paper, we prove that the isotropy group of a simple Shamsuddin derivation of the polynomial ring $R=K[X_1,dots, X_n]$ is trivial. We also calculate other isotropy groups of (not necessarily simple) derivations of $K[X_1,X_2]$ and prove that they are finite cyclic groups.
A modern graphics processing unit (GPU) is able to perform massively parallel scientific computations at low cost. We extend our implementation of the checkerboard algorithm for the two dimensional Ising model [T. Preis et al., J. Comp. Phys. 228, 44
68 (2009)] in order to overcome the memory limitations of a single GPU which enables us to simulate significantly larger systems. Using multi-spin coding techniques, we are able to accelerate simulations on a single GPU by factors up to 35 compared to an optimized single Central Processor Unit (CPU) core implementation which employs multi-spin coding. By combining the Compute Unified Device Architecture (CUDA) with the Message Parsing Interface (MPI) on the CPU level, a single Ising lattice can be updated by a cluster of GPUs in parallel. For large systems, the computation time scales nearly linearly with the number of GPUs used. As proof of concept we reproduce the critical temperature of the 2D Ising model using finite size scaling techniques.
Human activities increasingly take place in online environments, providing novel opportunities for relating individual behaviours to population-level outcomes. In this paper, we introduce a simple generative model for the collective behaviour of mill
ions of social networking site users who are deciding between different software applications. Our model incorporates two distinct components: one is associated with recent decisions of users, and the other reflects the cumulative popularity of each application. Importantly, although various combinations of the two mechanisms yield long-time behaviour that is consistent with data, the only models that reproduce the observed temporal dynamics are those that strongly emphasize the recent popularity of applications over their cumulative popularity. This demonstrates---even when using purely observational data without experimental design---that temporal data-driven modelling can effectively distinguish between competing microscopic mechanisms, allowing us to uncover new aspects of collective online behaviour.
The growing conflicts in and about oil exporting regions and speculations about volatile oil prices during the last decade have renewed the public interest in predictions for the near future oil production and consumption. Unfortunately, studies from
only 10 years ago, which tried to forecast the oil production during the next 20-30 years, failed to make accurate predictions for todays global oil production and consumption. Forecasts using economic growth scenarios, overestimated the actual oil production, while models which tried to estimate the maximum future oil production/year, using the official country oil reserve data, predicted a too low production. In this paper, a new approach to model the maximal future regional and thus global oil production (part I) and consumption (part II) during the next decades is proposed. Our analysis of the regional oil production data during past decades shows that, in contrast to periods when production was growing and growth rates varied greatly from one country to another, remarkable similarities are found during the plateau and decline periods of different countries. Following this model, the particular production phase of each major oil producing country and region is determined essentially only from the recent past oil production data. Using these data, the model is then used to predict the production from all major oil producing countries, regions and continents up to the year 2050. The limited regional and global potential to compensate this decline with unconventional oil and oil-equivalents is also presented.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
