Multireference Alignment using Semidefinite Programming

The multireference alignment problem consists of estimating a signal from multiple noisy shifted observations. Inspired by existing Unique-Games approximation algorithms, we provide a semidefinite program (SDP) based relaxation which approximates the maximum likelihood estimator (MLE) for the multireference alignment problem. Although we show that the MLE problem is Unique-Games hard to approximate within any constant, we observe that our poly-time approximation algorithm for the MLE appears to perform quite well in typical instances, outperforming existing methods. In an attempt to explain this behavior we provide stability guarantees for our SDP under a random noise model on the observations. This case is more challenging to analyze than traditional semi-random instances of Unique-Games: the noise model is on vertices of a graph and translates into dependent noise on the edges. Interestingly, we show that if certain positivity constraints in the SDP are dropped, its solution becomes equivalent to performing phase correlation, a popular method used for pairwise alignment in imaging applications. Finally, we show how symmetry reduction techniques from matrix representation theory can simplify the analysis and computation of the SDP, greatly decreasing its computational cost

Shortest Path and Distance Queries on Road Networks: An Experimental Evaluation

Computing the shortest path between two given locations in a road network is an important problem that finds applications in various map services and commercial navigation products. The state-of-the-art solutions for the problem can be divided into two categories: spatial-coherence-based methods and vertex-importance-based approaches. The two categories of techniques, however, have not been compared systematically under the same experimental framework, as they were developed from two independent lines of research that do not refer to each other. This renders it difficult for a practitioner to decide which technique should be adopted for a specific application. Furthermore, the experimental evaluation of the existing techniques, as presented in previous work, falls short in several aspects. Some methods were tested only on small road networks with up to one hundred thousand vertices; some approaches were evaluated using distance queries (instead of shortest path queries), namely, queries that ask only for the length of the shortest path; a state-of-the-art technique was examined based on a faulty implementation that led to incorrect query results. To address the above issues, this paper presents a comprehensive comparison of the most advanced spatial-coherence-based and vertex-importance-based approaches. Using a variety of real road networks with up to twenty million vertices, we evaluated each technique in terms of its preprocessing time, space consumption, and query efficiency (for both shortest path and distance queries). Our experimental results reveal the characteristics of different techniques, based on which we provide guidelines on selecting appropriate methods for various scenarios.Comment: VLDB201

Orion: Design of a system for assured low-cost human access to space

In recent years, Congress and the American people have begun to seriously question the role and importance of future manned spaceflight. This is mainly due to two factors: a decline in technical competition caused by the collapse of communism, and the high costs associated with the Space Shuttle transportation system. With these factors in mind, the ORION system was designed to enable manned spaceflight at a low cost, while maintaining the ability to carry out diverse missions, each with a high degree of flexibility. It is capable of performing satellite servicing missions, supporting a space station via crew rotation and resupply, and delivering satellites into geosynchronous orbit. The components of the system are a primary launch module, an upper stage, and a manned spacecraft capable of dynamic reentry. For satellite servicing and space station resupply missions, the ORION system utilizes three primary modules, an upper stage, and the spacecraft, which is delivered to low earth orbit and used to rendezvous, transfer materials, and make repairs. For launching a geosynchronous satellite, one primary module and an upper stage are used to deliver the satellite, along with an apogee kick motor, into orbit. The system is designed with reusability and modularity in mind in an attempt to lower cost

An analysis on stochastic Lanczos quadrature with asymmetric quadrature nodes

The stochastic Lanczos quadrature method has garnered significant attention recently. Upon examination of the error analyses given by Ubaru, Chen and Saad and Cortinovis and Kressner, certain notable inconsistencies arise. It turns out that the former's results are valid for cases with symmetric quadrature nodes and may not be adequate for many practical cases such as estimating log determinant of matrices. This paper analyzes probabilistic error bound of the stochastic Lanczos quadrature method for cases with asymmetric quadrature nodes. Besides, an optimized error allocation technique is employed to minimize the overall number of matrix vector multiplications required by the stochastic Lanczos quadrature method.Comment: 20 pages, 3 figure

The impact of planetary boundary layer parameterisation over the Yangtze River Delta region, China, part 1: meteorological simulation.

The planetary boundary layer (PBL) is the main region for the exchange of matter, momentum, and energy between land and atmosphere. The transport processes in the PBL determine the distribution of temperature, water vapour, wind speed and other physical quantities and are very important for the simulation of the physical characteristics of the meteorology. Based on the two non-local (YSU, ACM2) and two local closure PBL schemes (MYJ, MYNN) in the Weather Research and Forecasting (WRF) model, seasonal and daily cycles of meteorological variables over the Yangtze River Delta (YRD) region are investigated. It is shown that all four PBL schemes overestimate 10-m wind speed and 2-m temperature, while underestimate relative humidity. Inter-comparisons among the different PBL schemes show that the MYNN scheme results in closer match of 2-m temperature and 10-m wind speed to surface observations in summer, while the MYJ scheme shows the smallest bias of 2-m temperature and relative humidity in winter. Compared to the observed PBL height obtained from a micro-pulse lidar system, the MYNN scheme exhibits lowest mean bias while the ACM2 scheme shows the highest correlation. It is also found that there is a varying degree of sensitivity of the PBL height in winter and summer, respectively; a best-performing PBL scheme should be chosen under different seasons to predict various meteorological conditions over complicated topography like the YRD region

The impact of planetary boundary layer parameterisation scheme over the Yangtze River Delta region, China, part I: seasonal and diurnal sensitivity studies.

The planetary boundary layer (PBL) is the main region for the exchange of matter, momentum and energy between land and atmosphere. The transport processes in the PBL determine the distribution of temperature, water vapour, wind speed and other physical quantities within the PBL and are very important for the simulation of the physical characteristics of the meteorology. Based on the two non-local closure PBL schemes (YSU, ACM2) and two local closure PBL schemes (MYJ, MYNN) in the Weather Research and Forecasting (WRF) model, seasonal and daily cycles of meteorological variables over the Yangtze River Delta (YRD) region are investigated. It is shown that all the four PBL schemes overestimate 10-m wind speed and 2-m temperature, while underestimate relative humidity. The MYJ scheme produces the largest biases on 10-m wind speed and the smallest biases on humidity, while the ACM2 scheme show WRF-simulated 2-m temperature and 10-m wind speed are closer to surface meteorological observations in summer. The ACM2 scheme performs well with daytime PBL height, the MYNN scheme performs the lowest mean bias of 0.04 km and the ACM2 scheme shows the highest correlation coefficient of 0.59 compared with observational data. It is found that there is a varying degree of sensitivity of the respective PBL in winter and summer and a best-performing PBL scheme should be chosen to predict various meteorological conditions under different seasons over a complicated region like the YRD