Non-contractible closed geodesics on compact Finsler space forms without self-intersections

Let $M=S^n/ \Gamma$ and $h \in \pi_1(M)$ be a non-trivial element of finite order $p$, where the integers $n, p\geq2$ and $\Gamma$ is a finite abelian group which acts on the sphere freely and isometrically, therefore $M$ is diffeomorphic to a compact space form which is typical a non-simply connected manifold. We prove there exist at least two non-contractible closed geodesics on $\mathbb{R}P^2$ and obtain the upper bounds on their lengths. Moreover, we prove there exist at least $n$ prime non-contractible simple closed geodesics on $(M,F)$ of prescribed class $[h]$, provided $$F^2 <(\frac{\lambda+1}{\lambda})^2 g_0 \;\; \text{ and } \;\; (\frac{\lambda}{\lambda+1})^2 < K \leq 1 \text{ for $n$ is odd or }\; 0<K \leq 1 \text{ for $n$ is even},$$ where $\lambda$ is the reversibility, $K$ is the flag curvature and $g_0$ is standard Riemannian metric. Stability of these non-contractible closed geodesics is also studied.Comment: arXiv admin note: text overlap with arXiv:2202.1000

How does Veteran Status Affect Risk of Cardiovascular Diseases?

There were 20.39 million military veterans in the U.S. in 2016 and more than 65.5% of them being 55 years or older. According to T. Simpson et al. (2012) and Lehavot et al. (2012), veterans had worse overall health, a higher incidence of health risk behavior and chronic health conditions than civilians (non-veterans). However, the causal relationship between the military experience as a veteran and physical health cannot be determined. We applied the Rubin Causal Model on the BRFSS2016 data to find if there is any significant difference between the veterans and the non-veterans in Heart Attack incidence rate. We also used the Logistic Regression Model to understand the effect of being a veteran and predict the probability of each individual having had Heart Attack(s). We first used categorical variables to replace all numerical variables and applied an exact 1-to-1 matching. Then, we applied another exact 1-to-1 matching on the key numerical variable (Age). After the matching, the Heart Attack incidence rates were 9.94% in the veterans and 9.23% in the non-veterans. The difference was 0.71% and the p-value was 0.00035. In the logistic regression model(s), the effect of being a veteran was positive (increasing the probability to have had a heart attack) and significant. Also, we show that when the data size reduces the simple model could predict better than the complex model

A GENERIC BENCHMARK FOR A MINI-SPLIT HEAT PUMP SYSTEM

Heating, Ventilation, and Air Conditioning (HVAC) accounts for half of the building energy consumption in the U.S where Mini-Split Heat Pumps (MSHPs) are an emerging type of HVAC system. Their utilization has greatly increased by 34% from 2009 to 2013 and high potential EER is recognized for MSHPs. However, there is limited research involving MSHPs systems, and there is no generic benchmark for system testing and modeling. The available simulation tools such as VapCyc, GreatLab, and CYCLE_D are either too complicated, difficult to access, or not freely available. Therefore, an accurate and public share generic benchmark is essential and will be researched for researchers and scientists. In this study, the Heat Pump Design Model (HPDM) is utilized to investigate MSHP performance values. There are five different kinds of input parameters necessary for the HPDM, namely a general system description, system refrigerant-side balancing, compressor characteristics which need a compressor scaling method, fin-and-tube heat exchanger parameters, and system operating conditions. Based on systematic inputs of the HPDM, several key outputs can be obtained, including system capacity, power consumption, and mass flow rate. By comparing output values with existing data sets, the capability of a generic model for MSHP can be identified. In order to validate the methodology analyzed above, two kinds of case studies will be presented. In the first study, a comparison of lab data and simulation results is presented, whereas in the second one, a comparison is conducted between manufacturing data and simulation results. By identifying all of the input parameters for the specified unit, which is the LG LA096HV in this study, the HPDM can obtain simulation results immediately. As indicated by simulation results, the HPDM can be a generic benchmark in a certain temperature range with a relative error below 5%. Advisor: Haorong L

A GENERIC BENCHMARK FOR A MINI-SPLIT HEAT PUMP SYSTEM

Heating, Ventilation, and Air Conditioning (HVAC) accounts for half of the building energy consumption in the U.S where Mini-Split Heat Pumps (MSHPs) are an emerging type of HVAC system. Their utilization has greatly increased by 34% from 2009 to 2013 and high potential EER is recognized for MSHPs. However, there is limited research involving MSHPs systems, and there is no generic benchmark for system testing and modeling. The available simulation tools such as VapCyc, GreatLab, and CYCLE_D are either too complicated, difficult to access, or not freely available. Therefore, an accurate and public share generic benchmark is essential and will be researched for researchers and scientists. In this study, the Heat Pump Design Model (HPDM) is utilized to investigate MSHP performance values. There are five different kinds of input parameters necessary for the HPDM, namely a general system description, system refrigerant-side balancing, compressor characteristics which need a compressor scaling method, fin-and-tube heat exchanger parameters, and system operating conditions. Based on systematic inputs of the HPDM, several key outputs can be obtained, including system capacity, power consumption, and mass flow rate. By comparing output values with existing data sets, the capability of a generic model for MSHP can be identified. In order to validate the methodology analyzed above, two kinds of case studies will be presented. In the first study, a comparison of lab data and simulation results is presented, whereas in the second one, a comparison is conducted between manufacturing data and simulation results. By identifying all of the input parameters for the specified unit, which is the LG LA096HV in this study, the HPDM can obtain simulation results immediately. As indicated by simulation results, the HPDM can be a generic benchmark in a certain temperature range with a relative error below 5%. Advisor: Haorong L

Do Stereotype Consistent Media Profiles of Sexual Outgroup Members affect Perceived Entitativity of and Bias Towards Sexual Outgroups?

Intergroup contact has been shown to reduce discrimination towards several derogated social outgroups. In this paper, we examined the application of indirect contact to the reduction of bias towards male homosexuals. Specifically, we used social media to induce a situation in which participants engaged in contact with the media profile of a sexual outgroup member. In the first study, we manipulated whether the online profiles were consistent or inconsistent with social stereotypes towards gay men and examined the relation between outgroup stereotype consistency and entitativity, which may be a mediating variable between contact and bias reduction. We found that viewing stereotype consistent media profiles of sexual outgroup members might lead to perceptions that these sexual outgroup members were less entitative. In the second study, we used the same stimuli to examine the relation between outgroup stereotype consistency and implicit attitudes and affect towards sexual outgroup members. However, we found that there is no significant interaction between outgroup stereotype consistency and implicit attitudes and affect towards outgroups. Therefore, our studies show that outgroup stereotype consistency might be a manipulator of entitativity, but outgroup stereotype consistency does not change individuals’ implicit affect or attitude towards outgroup members. Future studies may further investigate methods other than social media that may alter implicit attitudes and affect towards outgroups. Key word: stereotype, consistency, entitativity, sexual minorit

On the rapidly rotating vorticity in the unit disk

In this paper, we obtain uniformly rotating vorticity with sufficiently large angular velocity in the unit disk. The solution consists of either a small nearly-ellipse vortex patch which is highly concentrated near the origin or a $2+1$ configuration in which the another two vortical components are very close to the boundary of fluid domain. The total vorticity are prescribed and the sizes of vortical domains are not necessarily small in the same order. The construction, which is based on a perturbation argument, exhibits a subtle multiscale phenomenon in this highly rotating fluid

DYNAMIC MEMORY MANAGEMENT FOR KEY-VALUE STORE

To minimize the latency of accessing back-end servers, modern web services often use in-memory key-value (k-v) stores at the front end to cache frequently accessed objects. Due to the limited memory capacity, these stores must be configured with a fixed amount of memory. Consequently, cache replacement is required when the footprint of the accessed objects exceeds the cache size. This thesis presents a comprehensive exploration of advanced dynamic memory management techniques for k-v stores. The first study conducts a detailed analysis of K-LRU, a random sampling-based replacement policy, proposing a dynamic K configuration scheme to exploit the potential miss ratio gap among various Ks. Experimental results demonstrate a throughput improvement of up to 32.5% over the default static K setting. Building on this, the second study extends the exploration of K-LRU to a multi-tenant k-v store environment, introducing a locality- and latency-aware memory partitioning scheme. This approach significantly enhances performance, achieving up to a 50.2% reduction in average access latency and a 262.8% increase in throughput compared to standard Redis. When compared to a state-of-the-art memory allocation design, the proposed scheme shows improvements of up to 24.8% in average access latency and 61.8% in throughput. Finally, inspired by emerging Compute Express Link (CXL) memory-sharing techniques, the third study pushes k-v store memory management into a multi-tier memory environment. This involves designing a software-defined tiered memory management architecture on top of a CXL memory-sharing switch. By dynamically identifying hot application data, efficiently migrating items among memory tiers based on popularity, and implementing multi-tenant memory partitioning, the proposed sdTMM system effectively integrates fast local DRAM with slower but larger CXL-shared memory. Evaluations across various workloads show that, even with 80% of the fast memory replaced by CXL-shared slow memory, sdTMM maintains an average performance impact of 13%, with the best-case impact as low as 2.2% compared to an all-fast memory over-provisioned system. This research collectively advances the techniques of dynamic memory management, demonstrating promising performance improvements in k-v stores