Graph search via star sampling with and without replacement

Star points on smooth hypersurfaces

This thesis discusses several random walk and sampling algorithms and analyses the expected cost of using these algorithms to find target nodes in large graphs. The first algorithms discussed are degree biased random walks. A degree biased random walk variant is introduced entitled Self Avoiding Walk Jump (SAWJ). The innovation is in roughly upper bounding the expected unit cost for SAWJ to find a maximum degree node using a discrete time Markov chain model. Second this thesis estimates the expected unit and linear cost to find a target node in Erdos Renyi (ER) graphs under three variants of star sampling, where a random node is selected and it and its neighbors are sampled. These estimates are shown numerically to be accurate on ER and some real-world graphs. Third this thesis looks at questions tangentially related to analyzing graph search algorithms. Counter examples are given showing greedy wiring or rewiring algorithms do not necessarily construct maximally assortative simple graphs and an estimate is given of the expected samples to find a near maximum value in a set of elements with known distribution but unknown parameterization.

Star sensor is disturbed by strong straylight, which increases the gray level of the captured star map, and this leads to invalid detection of star points and affects the high-precision location of the centroid. To address this issue, we propose a star centroid localization method based on gradient-oriented multi-directional local contrast enhancement. First, the background gray level distribution patterns of star sensors under various actual straylight interference conditions are analyzed. Based on this analysis, a background imaging model for complex operational scenarios is established. Finally, simulations are conducted under complex conditions with straylight images to test the star point detection rate, false detection rate, centroid localization accuracy, and statistical significance testing. The results show that the proposed algorithm outperforms the TOP-HAT, MAX-BACKG (Max-Background Filtering), LCM (Local Contrast Measure), MPCM (Multiscale Patch-Based Contrast Measure), and CMLCM (Curvature-Based Multidirectional Local Contrast Method for Star Detection of Star Sensor) algorithms in terms of star point detection rate. Additionally, the RMSE centroid localization error is achieved with 0.1 pixels, demonstrating its ability to effectively locate star centroids under complex conditions and meet certain engineering application requirements.

Cost-effectiveness analysis in cardiac surgery: A review of its concepts and methodologies

The estimation of construction costs for shield tunneling projects is typically based on a standard quota, which fails to consider the variation of geological parameters and often results in significant differences in unit cost. To address this issue, we propose a novel model based on a random forest machine learning procedure for analyzing the construction cost of shield tunnelling in complex geological conditions. We focus specifically on the unit consumption of grease, grouting, labor, water, and electricity. Using a dataset of geotechnical parameters and consumption quantities from a shield tunneling project, we employ KNN and correlation analysis to reduce the input dataset dimension from 17 to 6 for improved model accuracy and efficiency. Our proposed approach is applied to a shield tunneling project, with results showing that the compressive strength of geomaterial is the most influential parameter for grease, labor, water, and electricity, while it is the second most influential for grouting quantity. Based on these findings, we calculate the unit consumption and cost of the tunnelling project, which we classify into three geological categories: soil, soft rock, and hard rock. Comparing our results to the standard quota value, it is found that the unit cost of shield tunneling in soil is slightly lower (6%), while that in soft rock is very close to the standard value. However, the cost in the hard rock region is significantly greater (38%), which cannot be ignored in project budgeting. Ultimately, our results support the use of compressive strength as a classification index for shield tunneling in complex geological conditions, representing a valuable contribution to the field of tunneling cost prediction.

Performance measurement encompasses the role of performance indicators, measures, and targets within a performance management system and is designed to improve organizational functioning. Indicators, or key performance indicators, identify key areas of strategic and operational performance in organizations. Measures seek to give a numerical evaluation of their achievement, while targets are designed as aspirational statements of intended future performance. The purpose of performance measurement is to improve organizational performance by focusing on the key functions or activities that are designed to achieve organizational objectives, and motivate and influence behavior through the setting of targets. Performance measurement is central to strategic management approaches, which utilize core mission statements, strategic objectives, and a focus on outputs to drive organizational performance.

Uncorrelated random scale-free (URSF) networks are useful null models for checking the effects of scale-free topology on network-based dynamical processes. Here, we present a comparative study of the jamming level of gradient networks based on URSF networks and Erdős–Rényi (ER) random networks. We find that the URSF networks are less congested than ER random networks for the average degree ⟨k⟩>kc (kc ≈ 2 denotes a critical connectivity). In addition, by investigating the topological properties of the two kinds of gradient networks, we discuss the relations between the topological structure and the transport efficiency of the gradient networks. These findings show that the uncorrelated scale-free structure might allow more efficient transport than the random structure.

For a given graph G, modularity gives a score to each vertex partition, with higher values taken to indicate that the partition better captures community structure in G. The modularity q^*(G) (where 0 <= q^*(G)<= 1) of the graph G is defined to be the maximum over all vertex partitions of the modularity value. Given the prominence of modularity in community detection, it is an important graph parameter to understand mathematically. For the Erdos-Renyi random graph G_{n,p} with n vertices and edge-probability p, the likely modularity has three distinct phases. For np infty the modularity is o(1) whp. Between these regions the modularity is non-trivial: for constants 1 0 such that when c_0 <= np <= c_1 we have delta<q^*(G)<1-delta whp. For this critical region, we show that whp q^*(G_{n,p}) has order (np)^{-1/2}, in accord with a conjecture by Reichardt and Bornholdt in 2006 (and disproving another conjecture from the physics literature).

Classical control theory has always been concerned with uncertain inputs. However, this concern has generally been implicit rather than explicit. Modern control methods tend to be more explicit. In particular, methods based on game theory and methods based on a Lyapunov type of analysis have been proposed. One question which seems to be largely ignored is: how do these various methods compare when applied to a typical control problem? Indeed what performance measures can we use to compare various control designs dealing with uncertain inputs? This paper addresses both of these questions. We define performance measures called the v-reachable set and the v-attractive set. The v-reachable set measures the extent that the uncertain input can drive the system away from the target set and the v-attractive set measures the extent that the uncertainty diminishes the size of the controllable set to the target. An ideal control law would be one in which the v-reachable set is the target set and the v-attractive set is the controllable set. Five different controllers based on five different design philosophies are applied to two different control systems. We find that there can be marked differences in the above performance measures. However using these performance measures as guide to choosing feedback parameters, the differences between the various design methods can be minimized. It is found that for these problems a modified game theoretic approach and the Lyapunov type of approach tend to provide the best designs.

We study a general framework for decentralized search in random graphs. Our main focus is on deterministic memoryless search algorithms that use only local information to reach their destination in a bounded number of steps in expectation. This class includes (with small modifications) the search algorithms used in Kleinberg's pioneering work on long-range percolation graphs and hierarchical network models. We give a characterization of searchable graphs in this model, and use this characterization to prove a monotonicity property for searchability.

Random networks are heterogeneous exhibiting a multi-scaling law

Investigating Best Capacity Scaling Policies for Different Reconfigurable Manufacturing System Scenarios

Synoptic measurements of activity in Sun-like stars have been performed continuously since 1966, and the largest set comes from the Mount Wilson HK project, in the form of the well-known S index. We have been monitoring the activity and variability of the Sun and a large sample of Sun-like stars, in terms of S and absolute flux, since 1994 with the Solar-Stellar Spectrograph (SSS) at Lowell Observatory. Directly inspired by the similar long-term program at Mount Wilson Observatory, the SSS incorporates both an HK spectrograph and an echelle for visible and far-red observations. This is the first of three papers presenting the results of some 20,000 observations of the Sun and Sun-like stars with the SSS. In this paper we describe our program, review the calibration of solar and stellar fluxes to S and the chromospheric emission fraction R'HK, compare our derived stellar activity measures to those from other programs, and discuss the broad characteristics of the activity and variability in our target set, with particular attention to good solar analogs and noncycling stars. In subsequent papers we will discuss the echelle data and present detailed examinations of stars of particular interest.

Networks that are fragmented into small disconnected components are prevalent in a large variety of systems. These include the secure communication networks of commercial enterprises, government agencies, and illicit organizations, as well as networks that suffered multiple failures, attacks, or epidemics. The structural and statistical properties of such networks resemble those of subcritical random networks, which consist of finite components, whose sizes are nonextensive. Surprisingly, such networks do not exhibit the small-world property that is typical in supercritical random networks, where the mean distance between pairs of nodes scales logarithmically with the network size. Unlike supercritical networks whose structure has been studied extensively, subcritical networks have attracted relatively little attention. A special feature of these networks is that the statistical and geometric properties vary between different components and depend on their sizes and topologies. The overall statistics of the network can be obtained by a summation over all the components with suitable weights. We use a topological expansion to perform a systematic analysis of the degree distribution and the distribution of shortest path lengths (DSPL) on components of given sizes and topologies in subcritical Erdős-Rényi (ER) networks. From this expansion we obtain an exact analytical expression for the DSPL of the entire subcritical network, in the asymptotic limit. The DSPL, which accounts for all the pairs of nodes that reside on the same finite component (FC), is found to follow a geometric distribution of the form P_{FC}(L=ℓ|L<∞)=(1-c)c^{ℓ-1}, where c<1 is the mean degree. Using computer simulations we calculate the DSPL in subcritical ER networks of increasing sizes and confirm the convergence to this asymptotic result. We also obtain exact asymptotic results for the mean distance, 〈L〉_{FC}, and for the standard deviation of the DSPL, σ_{L,FC}, and show that the simulation results converge to these asymptotic results. Using the duality relations between subcritical and supercritical ER networks, we obtain the DSPL on the nongiant components of ER networks above the percolation transition.

Finding hidden infected nodes is extremely important when information or diseases spread rapidly in a network because hints regarding the global properties of the diffusion dynamics can be provided, and effective control strategies for mitigating such spread can be derived. In this study, to understand the impact of the structure of the underlying network, a cascade infection-recovery problem is considered over an Erdös-Rényi (ER) random graph when a subset of infected nodes is partially observed. The goal is to reconstruct the underlying cascade that is likely to generate these observations. To address this, two algorithms are proposed: (i) a Neighbor-based recovery algorithm (NBRA(α)), where 0≤α≤1 is a control parameter, and (ii) a BFS tree-source-based recovery algorithm (BSRA). The first one simply counts the number of infected neighbors for candidate hidden cascade nodes and computes the possibility of infection from the neighbors by controlling the parameter α. The latter estimates the cascade sources first and computes the infection probability from the sources. A BFS tree approximation is used for the underlying ER random graph with respect to the sources for computing the infection probability because of the computational complexity in general loopy graphs. We then conducted various simulations to obtain the recovery performance of the two proposed algorithms. As a result, although the NBRA(α) uses only local information of the neighboring infection status, it recovers the hidden cascade infection well and is not significantly affected by the average degree of the ER random graph, whereas the BSRA works well on a local tree-like structure.