Comparative Learning: A Sample Complexity Theory for Two Hypothesis Classes

In many learning theory problems, a central role is played by a hypothesis class: we might assume that the data is labeled according to a hypothesis in the class (usually referred to as the realizable setting), or we might evaluate the learned model by comparing it with the best hypothesis in the class (the agnostic setting). Taking a step beyond these classic setups that involve only a single hypothesis class, we study a variety of problems that involve two hypothesis classes simultaneously. We introduce comparative learning as a combination of the realizable and agnostic settings in PAC learning: given two binary hypothesis classes S and B, we assume that the data is labeled according to a hypothesis in the source class S and require the learned model to achieve an accuracy comparable to the best hypothesis in the benchmark class B. Even when both S and B have infinite VC dimensions, comparative learning can still have a small sample complexity. We show that the sample complexity of comparative learning is characterized by the mutual VC dimension VC(S,B) which we define to be the maximum size of a subset shattered by both S and B. We also show a similar result in the online setting, where we give a regret characterization in terms of the analogous mutual Littlestone dimension Ldim(S,B). These results also hold for partial hypotheses. We additionally show that the insights necessary to characterize the sample complexity of comparative learning can be applied to other tasks involving two hypothesis classes. In particular, we characterize the sample complexity of realizable multiaccuracy and multicalibration using the mutual fat-shattering dimension, an analogue of the mutual VC dimension for real-valued hypotheses. This not only solves an open problem proposed by Hu, Peale, Reingold (2022), but also leads to independently interesting results extending classic ones about regression, boosting, and covering number to our two-hypothesis-class setting

SPECTRUM-BASED AND COLLABORATIVE NETWORK TOPOLOGY ANALYSIS AND VISUALIZATION

Networks are of significant importance in many application domains, such as World Wide Web and social networks, which often embed rich topological information. Since network topology captures the organization of network nodes and links, studying net- work topology is very important to network analysis. In this dissertation, we study networks by analyzing their topology structure to explore community structure, the relationship among network members and links as well as their importance to the belonged communities. We provide new network visualization methods by studying network topology through two aspects: spectrum-based and collaborative visualiza- tion techniques. For the spectrum-based network visualization, we use eigenvalues and eigenvectors to express network topological features instead of using network datasets directly. We provide a visual analytics approach to analyze unsigned networks based on re- cent achievements on spectrum-based analysis techniques which utilize the features of node distribution and coordinates in the high dimensional spectral space. To assist the interactive exploration of network topologies, we have designed network visual- ization and interactive analysis methods allowing users to explore the global topology structure. Further, to address the question of real-life applications involving of both positive and negative relationships, we present a spectral analysis framework to study both signed and unsigned networks. Our framework concentrates on two problems of net- work analysis - what are the important spectral patterns and how to use them to study signed networks. Based on the framework, we present visual analysis methods, which guide the selection of k-dimensional spectral space and interactive exploration of network topology. With the increasing complexity and volume of dynamic networks, it is important to adopt strategies of joint decision-making through developing collaborative visualiza- tion approaches. Thus, we design and develop a collaborative detection mechanism with matrix visualization for complex intrusion detection applications. We establish a set of collaboration guidelines for team coordination with distributed visualization tools. We apply them to generate a prototype system with interactions that facilitates collaborative visual analysis. In order to evaluate the collaborative detection mechanism, a formal user study is presented. The user study monitored participants to collaborate under co-located and distributed collaboration environments to tackle the problems of intrusion detection. We have observed participants’ behaviors and collected their performances from the aspects of coordination and communication. Based on the results, we conclude several coordination strategies and summarize the values of communication for collaborative visualization. Our visualization methods have been demonstrated to be efficient topology explo- ration with both synthetic and real-life datasets in spectrum-based and collaborative exploration. We believe that our methods can provide useful information for future design and development of network topology visualization system

Constructing a Predator Exclusionary Fence to Protect Hawaiian Petrels (Pterodroma sandwichensis) at Hawai῾i Volcanoes National Park

Reports were scanned in black and white at a resolution of 600 dots per inch and were converted to text using Adobe Paper Capture Plug-in.Remnant nesting colonies of endangered Hawaiian Petrels, or ‘Ua’u (Pterodroma sandwichensis), on Mauna Loa, Hawai’i Island, are primarily threatened by feral cats. At Hawai῾i Volcanoes National Park, trapping success has been variable due several challenges, including the difficulty of accessing remote, subalpine (9,000’) sites. To create a core area free from cat predation, the park, with support from multiple partners, constructed a five mile barrier fence encircling 640 acres of the richest known concentration of subalpine Hawaiian Petrel nests on Mauna Loa. We report on key fence design elements, pilot studies, step by step construction details, concurrent and subsequent monitoring, and lessons learned throughout the project for the benefit of other managers considering exclusionary fencing

Mechanically manipulating glymphatic transport by ultrasound combined with microbubbles

The glymphatic system is a perivascular fluid transport system for waste clearance. Glymphatic transport is believed to be driven by the perivascular pumping effect created by the pulsation of the arterial wall caused by the cardiac cycle. Ultrasound sonication of circulating microbubbles (MBs) in the cerebral vasculature induces volumetric expansion and contraction of MBs that push and pull on the vessel wall to generate a MB pumping effect. The objective of this study was to evaluate whether glymphatic transport can be mechanically manipulated by focused ultrasound (FUS) sonication of MBs. The glymphatic pathway in intact mouse brains was studied using intranasal administration of fluorescently labeled albumin as fluid tracers, followed by FUS sonication at a deep brain target (thalamus) in the presence of intravenously injected MBs. Intracisternal magna injection, the conventional technique used in studying glymphatic transport, was employed to provide a comparative reference. Three-dimensional confocal microscopy imaging of optically cleared brain tissue revealed that FUS sonication enhanced the transport of fluorescently labeled albumin tracer in the perivascular space (PVS) along microvessels, primarily the arterioles. We also obtained evidence of FUS-enhanced penetration of the albumin tracer from the PVS into the interstitial space. This study revealed that ultrasound combined with circulating MBs could mechanically enhance glymphatic transport in the brain

Painless causality in defect calculations

Topological defects must respect causality, a statement leading to restrictive constraints on the power spectrum of the total cosmological perturbations they induce. Causality constraints have for long been known to require the presence of an under-density in the surrounding matter compensating the defect network on large scales. This so-called compensation can never be neglected and significantly complicates calculations in defect scenarios, eg. computing cosmic microwave background fluctuations. A quick and dirty way to implement the compensation are the so-called compensation fudge factors. Here we derive the complete photon-baryon-CDM backreaction effects in defect scenarios. The fudge factor comes out as an algebraic identity and so we drop the negative qualifier ``fudge''. The compensation scale is computed and physically interpreted. Secondary backreaction effects exist, and neglecting them constitutes the well-defined approximation scheme within which one should consider compensation factor calculations. We quantitatively assess the accuracy of this approximation, and conclude that the considerable pains associated with improving on it are often a waste of effort

Use of ambient light in remote photoplethysmographic systems: comparison between a high-performance camera and a low-cost webcam

Imaging photoplethysmography (PPG) is able to capture useful physiological data remotely from a wide range of anatomical locations. Recent imaging PPG studies have concentrated on two broad research directions involving either high-performance cameras and or webcam-based systems. However, little has been reported about the difference between these two techniques, particularly in terms of their performance under illumination with ambient light. We explore these two imaging PPG approaches through the simultaneous measurement of the cardiac pulse acquired from the face of 10 male subjects and the spectral characteristics of ambient light. Measurements are made before and after a period of cycling exercise. The physiological pulse waves extracted from both imaging PPG systems using the smoothed pseudo-Wigner-Ville distribution yield functional characteristics comparable to those acquired using gold standard contact PPG sensors. The influence of ambient light intensity on the physiological information is considered, where results reveal an independent relationship between the ambient light intensity and the normalized plethysmographic signals. This provides further support for imaging PPG as a means for practical noncontact physiological assessment with clear applications in several domains, including telemedicine and homecare

Comparison of scientific CMOS camera and webcam for monitoring cardiac pulse after exercise

In light of its capacity for remote physiological assessment over a wide range of anatomical locations, imaging photoplethysmography has become an attractive research area in biomedical and clinical community. Amongst recent iPPG studies, two separate research directions have been revealed, i.e., scientific camera based imaging PPG (iPPG) and webcam based imaging PPG (wPPG). Little is known about the difference between these two techniques. To address this issue, a dual-channel imaging PPG system (iPPG and wPPG) using ambient light as the illumination source has been introduced in this study. The performance of the two imaging PPG techniques was evaluated through the measurement of cardiac pulse acquired from the face of 10 male subjects before and after 10 min of cycling exercise. A time-frequency representation method was used to visualize the time-dependent behaviour of the heart rate. In comparison to the gold standard contact PPG, both imaging PPG techniques exhibit comparable functional characteristics in the context of cardiac pulse assessment. Moreover, the synchronized ambient light intensity recordings in the present study can provide additional information for appraising the performance of the imaging PPG systems. This feasibility study thereby leads to a new route for non-contact monitoring of vital signs, with clear applications in triage and homecare

Prevalence of non-alcoholic fatty liver disease and its relation to hypoadiponectinaemia in the middle-aged and elderly Chinese population

Introduction: Hypoadiponectinaemia is an important risk factor for non-alcoholic fatty liver disease (NAFLD). However, little is known about its role in the Chinese population. This study sought to assess the prevalence of NAFLD and its association with hypoadiponectinaemia in middle-aged and elderly Chinese. Material and methods: We conducted a population-based cross-sectional study in an urban Shanghai sample of 2201 participants age 50 years to 83 years (973 men, 1228 women). Hepatic ultrasonographic examination was performed for all participants. Serum adiponectin concentrations were measured by ELISA methods. Results: The prevalence of NAFLD was 19.8% (16.0% in men, 22.8% in women). Serum adiponectin levels were significantly higher in female than in male subjects (p < 0.001). Serum adiponectin levels were significantly lower in NAFLD subjects than those in control subjects (p < 0.001). The prevalence of NAFLD progressively increased with declining adiponectin levels (p(for) (trend) < 0.001). The participants in the lowest adiponectin quartile had a significantly increased risk for acquiring NAFLD (OR = 2.31, 95% CI 1.72-3.15) after adjustment for potential confounders. Conclusions: Population-based screening suggests that NAFLD is highly prevalent in middle-aged and elderly people in Shanghai, particularly among women. Serum adiponectin level is negatively associated with NAFLD independently of potential cofounders, indicating that hypoadiponectinaemia may contribute to the development of NAFLD

Investigation of Type 2 Diabetes Risk Alleles Support CDKN2A/B, CDKAL1, and TCF7L2 As Susceptibility Genes in a Han Chinese Cohort

Background: Recent genome-wide association studies (GWASs) have reported several genetic variants to be reproducibly associated with type 2 diabetes. Additional variants have also been detected from a metaanalysis of three GWASs, performed in populations of European ancestry. In the present study, we evaluated the influence of 17 genetic variants from 15 candidate loci, identified in type 2 diabetes GWASs and the metaanalysis, in a Han Chinese cohort. Methodology/Principal Findings: Selected type 2 diabetes-associated genetic variants were genotyped in 1,165 type 2 diabetic patients and 1,136 normoglycemic control individuals of Southern Han Chinese ancestry. The OR for risk of developing type 2 diabetes was calculated using a logistic regression model adjusted for age, sex, and BMI. Genotype-phenotype associations were tested using a multivariate linear regression model. Genetic variants in CDKN2A/B, CDKAL1, TCF7L2, TCF2, MC4R, and PPARG showed a nominal association with type 2 diabetes (P <= 0.05), of whom the three first would stand correction for multiple testing: CDKN2A/B rs10811661, OR: 1.26 (1.12-1.43) P = 1.8* 10(-4); CDKAL1 rs10946398, OR: 1.23 (1.09-1.39); P = 7.1* 10(-4), and TCF7L2 rs7903146, OR: 1.61 (1.19-2.18) P = 2.3* 10(-3). Only nominal phenotype associations were observed, notably for rs8050136 in FTO and fasting plasma glucose (P = 0.002), postprandial plasma glucose (P = 0.002), and fasting C-peptide levels (P = 0.006) in the diabetic patients, and with BMI in controls (P = 0.033). Conclusions/Significance: We have identified significant association between variants in CDKN2A/B, CDKAL1 and TCF7L2, and type 2 diabetes in a Han Chinese cohort, indicating these genes as strong candidates conferring susceptibility to type 2 diabetes across different ethnicities

Arithmetic Expression Construction

When can $n$ given numbers be combined using arithmetic operators from a given subset of $\{+, -, \times, \div\}$ to obtain a given target number? We study three variations of this problem of Arithmetic Expression Construction: when the expression (1) is unconstrained; (2) has a specified pattern of parentheses and operators (and only the numbers need to be assigned to blanks); or (3) must match a specified ordering of the numbers (but the operators and parenthesization are free). For each of these variants, and many of the subsets of $\{+,-,\times,\div\}$, we prove the problem NP-complete, sometimes in the weak sense and sometimes in the strong sense. Most of these proofs make use of a "rational function framework" which proves equivalence of these problems for values in rational functions with values in positive integers.Comment: 36 pages, 5 figures. Full version of paper accepted to 31st International Symposium on Algorithms and Computation (ISAAC 2020