The pseudo-compartment method for coupling PDE and compartment-based models of diffusion

Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted in the literature implements systems of partial differential equations (PDEs), which assumes there are sufficient densities of particles that a continuum approximation is valid. However, due to recent advances in computational power, the simulation, and therefore postulation, of computationally intensive individual-based models has become a popular way to investigate the effects of noise in reaction-diffusion systems in which regions of low copy numbers exist. The stochastic models with which we shall be concerned in this manuscript are referred to as `compartment-based'. These models are characterised by a discretisation of the computational domain into a grid/lattice of `compartments'. Within each compartment particles are assumed to be well-mixed and are permitted to react with other particles within their compartment or to transfer between neighbouring compartments. We develop two hybrid algorithms in which a PDE is coupled to a compartment-based model. Rather than attempting to balance average fluxes, our algorithms answer a more fundamental question: `how are individual particles transported between the vastly different model descriptions?' First, we present an algorithm derived by carefully re-defining the continuous PDE concentration as a probability distribution. Whilst this first algorithm shows strong convergence to analytic solutions of test problems, it can be cumbersome to simulate. Our second algorithm is a simplified and more efficient implementation of the first, it is derived in the continuum limit over the PDE region alone. We test our hybrid methods for functionality and accuracy in a variety of different scenarios by comparing the averaged simulations to analytic solutions of PDEs for mean concentrations.Comment: MAIN - 24 pages, 10 figures, 1 supplementary file - 3 pages, 2 figure

Uplink Linear Receivers for Multi-cell Multiuser MIMO with Pilot Contamination: Large System Analysis

Base stations with a large number of transmit antennas have the potential to serve a large number of users at high rates. However, the receiver processing in the uplink relies on channel estimates which are known to suffer from pilot interference. In this work, making use of the similarity of the uplink received signal in CDMA with that of a multi-cell multi-antenna system, we perform a large system analysis when the receiver employs an MMSE filter with a pilot contaminated estimate. We assume a Rayleigh fading channel with different received powers from users. We find the asymptotic Signal to Interference plus Noise Ratio (SINR) as the number of antennas and number of users per base station grow large while maintaining a fixed ratio. Through the SINR expression we explore the scenario where the number of users being served are comparable to the number of antennas at the base station. The SINR explicitly captures the effect of pilot contamination and is found to be the same as that employing a matched filter with a pilot contaminated estimate. We also find the exact expression for the interference suppression obtained using an MMSE filter which is an important factor when there are significant number of users in the system as compared to the number of antennas. In a typical set up, in terms of the five percentile SINR, the MMSE filter is shown to provide significant gains over matched filtering and is within 5 dB of MMSE filter with perfect channel estimate. Simulation results for achievable rates are close to large system limits for even a 10-antenna base station with 3 or more users per cell.Comment: Accepted for publication in IEEE Transactions on Wireless Communication

Cellular Systems with Many Antennas: Large System Analysis under Pilot Contamination

Base stations with a large number of transmit antennas have the potential to serve a large number of users simultaneously at higher rates. They also promise a lower power consumption due to coherent combining at the receiver. However, the receiver processing in the uplink relies on the channel estimates which are known to suffer from pilot interference. In this work, we perform an uplink large system analysis of multi-cell multi-antenna system when the receiver employs a matched filtering with a pilot contaminated estimate. We find the asymptotic Signal to Interference plus Noise Ratio (SINR) as the number of antennas and number of users per base station grow large while maintaining a fixed ratio. To do this, we make use of the similarity of the uplink received signal in a multi-antenna system to the representation of the received signal in CDMA systems. The asymptotic SINR expression explicitly captures the effect of pilot contamination and that of interference averaging. This also explains the SINR performance of receiver processing schemes at different regimes such as instances when the number of antennas are comparable to number of users as well as when antennas exceed greatly the number of users. Finally, we also propose that the adaptive MMSE symbol detection scheme, which does not require the explicit channel knowledge, can be employed for cellular systems with large number of antennas.Comment: 5 pages, 4 figure

A study of compressible turbulent boundary layers using the method of invariant modeling

Model equations for studying compressible turbulen boundary layer

Women as Party Leaders: Are the Barriers Partisan?

Even though women make up roughly 51% of the population of the United States, they are underrepresented in all branches of American government. Although there has been recent literature on women in politics and women and parties, very little has been done on women in party leadership. Research suggests that there are fewer women in elected office because of a lack of supply, or qualified and willing women, or a lack of demand, an electorate willing to vote for a woman. This study seeks to understand the levels of participation of women as party delegates in state party conventions and whether the barriers that they face are specific to each party Using a survey data set of over 5000 state party convention delegates, I analyze how women participate and the parties’ ideals on women’s role in politics. While I expected to find more Democratic women in leadership roles, this study has shown that perhaps the barriers are not specific to party as more Republican women delegates have held a party or government office than their Democratic women delegate counterparts. This paper suggests that the political culture of the Republican Party discourages women from joining, but once they join, they are equally as likely as Democratic women to hold leadership positions

Suggested Method for Teaching Health Education in the Fourth, Fifth, and Sixth Grades in the Livingston Elementary School

To set up a health program In Livingston Elementary School for teaching health education. To establish in the children in Livingston Elementary School the habits and principles of living which throughout their school life and later years will insure a better and healthier place to live. This study of health education in recent years has around more interest than any other branch in the elementary school. The causes for this interest may be summed up in the following facts: that health education has been neglected in many schools and communities, for instance, the children in the Livingston elementary school did not until recently, have a health program to follow. The textbook was placed in the hands of the child with no definite goal in view, so far as establishing the right health habits and attitudes are concerned. What was the cause for such teaching? To many grades for the number of teachers; (2) teaching load too heavy. Another reason why this study is necessary because the health conditions in the community indicated that a health education program should be set up

Update or Wait: How to Keep Your Data Fresh

In this work, we study how to optimally manage the freshness of information updates sent from a source node to a destination via a channel. A proper metric for data freshness at the destination is the age-of-information, or simply age, which is defined as how old the freshest received update is since the moment that this update was generated at the source node (e.g., a sensor). A reasonable update policy is the zero-wait policy, i.e., the source node submits a fresh update once the previous update is delivered and the channel becomes free, which achieves the maximum throughput and the minimum delay. Surprisingly, this zero-wait policy does not always minimize the age. This counter-intuitive phenomenon motivates us to study how to optimally control information updates to keep the data fresh and to understand when the zero-wait policy is optimal. We introduce a general age penalty function to characterize the level of dissatisfaction on data staleness and formulate the average age penalty minimization problem as a constrained semi-Markov decision problem (SMDP) with an uncountable state space. We develop efficient algorithms to find the optimal update policy among all causal policies, and establish sufficient and necessary conditions for the optimality of the zero-wait policy. Our investigation shows that the zero-wait policy is far from the optimum if (i) the age penalty function grows quickly with respect to the age, (ii) the packet transmission times over the channel are positively correlated over time, or (iii) the packet transmission times are highly random (e.g., following a heavy-tail distribution)

An Assessment of Inheritance Patterns in Two Mutant Eye-color Traits of Drosophila melanogaster

This experiment was a two generation test cross (from F0 to F1 and F1 to F2) to check the patterns of inheritance and their chi-square significance. Wild-type males and females were paired with the opposite sex of the two mutant groups -- Sepia eyes and White eyes. The pairing thus resulted in 4 tube conditions. Generations were counted and identified by sex and phenotype -- Wild-type or Mutant. The next generation was seeded with approximately 6 - 8 individuals from each sex and released once the next generation reached their pupal phase. Fresh tubes were seeded between F1 and F2. Identifying these patterns give us a tried and true method of determining future phenotypes and specific genetic patterns like recessive, dominant, and sex-linked traits. This basic experiment also serves as a baseline experiment to help others in the class with their Drosophila experiments and the data will be shared including several diagrams of inheritance patterns and gene expression