A polynomial time algorithm for determining zero Euler–Petrie genus of an Eulerian graph

AbstractA dual-Eulerian graph is a plane graph which has an ordering defined on its edge set which forms simultaneously an Euler circuit in the graph and an Euler circuit in the dual graph. Dual-Eulerian graphs were defined and studied in the context of silicon optimization of cmos layouts. They are necessarily of low connectivity, hence may have many planar embeddings. We give a polynomial time algorithm to answer the question whether or not a planar multigraph admits an embedding which is dual-Eulerian and construct such an embedding, if it exists

New Algorithms in Computational Microscopy

Microscopy plays an important role in providing tools to microscopically observe objects and their surrounding areas with much higher resolution ranging from the scale between molecular machineries (angstrom) and individual cells (micrometer). Under microscopes, illumination, such as visible light and electron-magnetic radiation/electron beam, interacts with samples, then they are scattered to a plane and are recorded. Computational microscopy corresponds to image reconstruction from these measurements as well as improving quality of the images. Along with the evolution of microscopy, new studies are discovered and algorithms need development not only to provide high-resolution imaging but also to decipher new and advanced research. In this dissertation, we focus on algorithm development for inverse problems in microscopy, specifically phase retrieval and tomography, and the application of these techniques to machine learning. The four studies in this dissertation demonstrates the use of optimization and calculus of variation in imaging science and other different disciplines.Study 1 focuses on coherent diffractive imaging (CDI) or phase retrieval, a non-linear inverse problem that aims to recover 2D image from it Fourier transforms in modulus taking into account that extra information provided by oversampling as a second constraint. To solve this two-constraint minimization, we proceed from Hamilton-Jacobi partial differential equation (HJ-PDE) and its Hopf-Lax formula. Introducing generalized Bregman distance to the HJ-PDE and applying Legendre transform, we derive our generalized proximal smoothing (GPS) algorithm under the form of primal-dual hybrid gradient (PDHG). While the reflection operator, known as extrapolating momentum, helps overcome local minima, the smoothing by the generalized Bregman distance is adjusted to improve convergence and consistency of phase retrieval.Study 2 focuses on electron tomography, 3D image reconstruction from a set of 2D projections obtained from a transmission electron microscope (TEM) or X-ray microscope. Notice that current tomography algorithms limit to a single tilt axis and fail to work with fully or partially missing data. In the light of calculus of variations and Fourier slice theorem (FST), we develop a highly accurate tomography iterative algorithm that can provide higher resolution imaging and work with missing data as well as has capability to perform multiple-tilt-axis tomography. The algorithm is further developed to work with non-isolated objects and partially-blocked projections which have become more popular in experiment. The success of real space iterative reconstruction engine (RESIRE) opens a new era to the study of tomography in material science and magnetic structures (vector Tomography).Study 3 and 4 are applications of our algorithms to machine learning. Study 3 develops a backward Euler method in a stochastic manner to solve K-mean clustering, a well-known non-convex optimization problem. The algorithm has been shown to improve minimums and consistency, providing a new powerful tool to the class of classification techniques. Study 4 is a direct application of GPS to deep learning gradient descent algorithms. Linearizing the Hopf-Lax formula derived in GPS, we derive our method Laplacian smoothing gradient descent (LSGD), simply known as gradient smoothing. Our experiment shows that LSGD has the ability to search for better and flatter minimums, reduce variation, and obtain higher accuracy and consistency

Geometric data understanding : deriving case specific features

There exists a tradition using precise geometric modeling, where uncertainties in data can be considered noise. Another tradition relies on statistical nature of vast quantity of data, where geometric regularity is intrinsic to data and statistical models usually grasp this level only indirectly. This work focuses on point cloud data of natural resources and the silhouette recognition from video input as two real world examples of problems having geometric content which is intangible at the raw data presentation. This content could be discovered and modeled to some degree by such machine learning (ML) approaches like deep learning, but either a direct coverage of geometry in samples or addition of special geometry invariant layer is necessary. Geometric content is central when there is a need for direct observations of spatial variables, or one needs to gain a mapping to a geometrically consistent data representation, where e.g. outliers or noise can be easily discerned. In this thesis we consider transformation of original input data to a geometric feature space in two example problems. The first example is curvature of surfaces, which has met renewed interest since the introduction of ubiquitous point cloud data and the maturation of the discrete differential geometry. Curvature spectra can characterize a spatial sample rather well, and provide useful features for ML purposes. The second example involves projective methods used to video stereo-signal analysis in swimming analytics. The aim is to find meaningful local geometric representations for feature generation, which also facilitate additional analysis based on geometric understanding of the model. The features are associated directly to some geometric quantity, and this makes it easier to express the geometric constraints in a natural way, as shown in the thesis. Also, the visualization and further feature generation is much easier. Third, the approach provides sound baseline methods to more traditional ML approaches, e.g. neural network methods. Fourth, most of the ML methods can utilize the geometric features presented in this work as additional features.Geometriassa käytetään perinteisesti tarkkoja malleja, jolloin datassa esiintyvät epätarkkuudet edustavat melua. Toisessa perinteessä nojataan suuren datamäärän tilastolliseen luonteeseen, jolloin geometrinen säännönmukaisuus on datan sisäsyntyinen ominaisuus, joka hahmotetaan tilastollisilla malleilla ainoastaan epäsuorasti. Tämä työ keskittyy kahteen esimerkkiin: luonnonvaroja kuvaaviin pistepilviin ja videohahmontunnistukseen. Nämä ovat todellisia ongelmia, joissa geometrinen sisältö on tavoittamattomissa raakadatan tasolla. Tämä sisältö voitaisiin jossain määrin löytää ja mallintaa koneoppimisen keinoin, esim. syväoppimisen avulla, mutta joko geometria pitää kattaa suoraan näytteistämällä tai tarvitaan neuronien lisäkerros geometrisia invariansseja varten. Geometrinen sisältö on keskeinen, kun tarvitaan suoraa avaruudellisten suureiden havainnointia, tai kun tarvitaan kuvaus geometrisesti yhtenäiseen dataesitykseen, jossa poikkeavat näytteet tai melu voidaan helposti erottaa. Tässä työssä tarkastellaan datan muuntamista geometriseen piirreavaruuteen kahden esimerkkiohjelman suhteen. Ensimmäinen esimerkki on pintakaarevuus, joka on uudelleen virinneen kiinnostuksen kohde kaikkialle saatavissa olevan datan ja diskreetin geometrian kypsymisen takia. Kaarevuusspektrit voivat luonnehtia avaruudellista kohdetta melko hyvin ja tarjota koneoppimisessa hyödyllisiä piirteitä. Toinen esimerkki koskee projektiivisia menetelmiä käytettäessä stereovideosignaalia uinnin analytiikkaan. Tavoite on löytää merkityksellisiä paikallisen geometrian esityksiä, jotka samalla mahdollistavat muun geometrian ymmärrykseen perustuvan analyysin. Piirteet liittyvät suoraan johonkin geometriseen suureeseen, ja tämä helpottaa luonnollisella tavalla geometristen rajoitteiden käsittelyä, kuten väitöstyössä osoitetaan. Myös visualisointi ja lisäpiirteiden luonti muuttuu helpommaksi. Kolmanneksi, lähestymistapa suo selkeän vertailumenetelmän perinteisemmille koneoppimisen lähestymistavoille, esim. hermoverkkomenetelmille. Neljänneksi, useimmat koneoppimismenetelmät voivat hyödyntää tässä työssä esitettyjä geometrisia piirteitä lisäämällä ne muiden piirteiden joukkoon

NASA Thesaurus. Volume 2: Access vocabulary

The NASA Thesaurus -- Volume 2, Access Vocabulary -- contains an alphabetical listing of all Thesaurus terms (postable and nonpostable) and permutations of all multiword and pseudo-multiword terms. Also included are Other Words (non-Thesaurus terms) consisting of abbreviations, chemical symbols, etc. The permutations and Other Words provide 'access' to the appropriate postable entries in the Thesaurus

Deep Learning Based Abnormal Gait Classification System Study with Heterogeneous Sensor Network

Gait is one of the important biological characteristics of the human body. Abnormal gait is mostly related to the lesion site and has been demonstrated to play a guiding role in clinical research such as medical diagnosis and disease prevention. In order to promote the research of automatic gait pattern recognition, this paper introduces the research status of abnormal gait recognition and systems analysis of the common gait recognition technologies. Based on this, two gait information extraction methods, sensor-based and vision-based, are studied, including wearable system design and deep neural network-based algorithm design. In the sensor-based study, we proposed a lower limb data acquisition system. The experiment was designed to collect acceleration signals and sEMG signals under normal and pathological gaits. Specifically, wearable hardware-based on MSP430 and upper computer software based on Labview is designed. The hardware system consists of EMG foot ring, high-precision IMU and pressure-sensitive intelligent insole. Data of 15 healthy persons and 15 hemiplegic patients during walking were collected. The classification of gait was carried out based on sEMG and the average accuracy rate can reach 92.8% for CNN. For IMU signals five kinds of abnormal gait are trained based on three models: BPNN, LSTM, and CNN. The experimental results show that the system combined with the neural network can classify different pathological gaits well, and the average accuracy rate of the six-classifications task can reach 93%. In vision-based research, by using human keypoint detection technology, we obtain the precise location of the key points through the fusion of thermal mapping and offset, thus extracts the space-time information of the key points. However, the results show that even the state-of-the-art is not good enough for replacing IMU in gait analysis and classification. The good news is the rhythm wave can be observed within 2 m, which proves that the temporal and spatial information of the key points extracted is highly correlated with the acceleration information collected by IMU, which paved the way for the visual-based abnormal gait classification algorithm.步态指人走路时表现出来的姿态，是人体重要生物特征之一。异常步态多与病变部位有关，作为反映人体健康状况和行为能力的重要特征，其被论证在医疗诊断、疾病预防等临床研究中具有指导作用。为了促进步态模式自动识别的研究，本文介绍了异常步态识别的研究现状，系统地分析了常见步态识别技术以及算法，以此为基础研究了基于传感器与基于视觉两种步态信息提取方法，内容包括可穿戴系统设计与基于深度神经网络的算法设计。 在基于传感器的研究中，本工作开发了下肢步态信息采集系统，并利用该信息采集系统设计实验，采集正常与不同病理步态下的加速度信号与肌电信号，搭建深度神经网络完成分类任务。具体的，在系统搭建部分设计了基于MSP430的可穿戴硬件设备以及基于Labview的上位机软件，该硬件系统由肌电脚环，高精度IMU以及压感智能鞋垫组成，该上位机软件接收、解包蓝牙数据并计算出步频步长等常用步态参数。 在基于运动信号与基于表面肌电的研究中，采集了15名健康人与15名偏瘫病人的步态数据，并针对表面肌电信号训练卷积神经网络进行帕金森步态的识别与分类，平均准确率可达92.8%。针对运动信号训练了反向传播神经网络，LSTM以及卷积神经网络三种模型进行五种异常步态的分类任务。实验结果表明，本工作中步态信息采集系统结合神经网络模型，可以很好地对不同病理步态进行分类，六分类平均正确率可达93%。 在基于视觉的研究中，本文利用人体关键点检测技术，首先检测出图片中的一个或多个人，接着对边界框做图像分割，接着采用全卷积resnet对每一个边界框中的人物的主要关节点做热力图并分析偏移量，最后通过热力图与偏移的融合得到关键点的精确定位。通过该算法提取了不同步态下姿态关键点时空信息，为基于视觉的步态分析系统提供了基础条件。但实验结果表明目前最高准确率的人体关键点检测算法不足以替代IMU实现步态分析与分类。但在2m之内可以观察到节律信息，证明了所提取的关键点时空信息与IMU采集的加速度信息呈现较高相关度，为基于视觉的异常步态分类算法铺平了道路

NASA thesaurus. Volume 2: Access vocabulary

The Access Vocabulary, which is essentially a permuted index, provides access to any word or number in authorized postable and nonpostable terms. Additional entries include postable and nonpostable terms, other word entries, and pseudo-multiword terms that are permutations of words that contain words within words. The Access Vocabulary contains 40,738 entries that give increased access to the hierarchies in Volume 1 - Hierarchical Listing

NASA thesaurus. Volume 2: Access vocabulary

The access vocabulary, which is essentially a permuted index, provides access to any word or number in authorized postable and nonpostable terms. Additional entries include postable and nonpostable terms, other word entries and pseudo-multiword terms that are permutations of words that contain words within words. The access vocabulary contains almost 42,000 entries that give increased access to the hierarchies in Volume 1 - Hierarchical Listing

Adaptive and learning-based formation control of swarm robots

Autonomous aerial and wheeled mobile robots play a major role in tasks such as search and rescue, transportation, monitoring, and inspection. However, these operations are faced with a few open challenges including robust autonomy, and adaptive coordination based on the environment and operating conditions, particularly in swarm robots with limited communication and perception capabilities. Furthermore, the computational complexity increases exponentially with the number of robots in the swarm. This thesis examines two different aspects of the formation control problem. On the one hand, we investigate how formation could be performed by swarm robots with limited communication and perception (e.g., Crazyflie nano quadrotor). On the other hand, we explore human-swarm interaction (HSI) and different shared-control mechanisms between human and swarm robots (e.g., BristleBot) for artistic creation. In particular, we combine bio-inspired (i.e., flocking, foraging) techniques with learning-based control strategies (using artificial neural networks) for adaptive control of multi- robots. We first review how learning-based control and networked dynamical systems can be used to assign distributed and decentralized policies to individual robots such that the desired formation emerges from their collective behavior. We proceed by presenting a novel flocking control for UAV swarm using deep reinforcement learning. We formulate the flocking formation problem as a partially observable Markov decision process (POMDP), and consider a leader-follower configuration, where consensus among all UAVs is used to train a shared control policy, and each UAV performs actions based on the local information it collects. In addition, to avoid collision among UAVs and guarantee flocking and navigation, a reward function is added with the global flocking maintenance, mutual reward, and a collision penalty. We adapt deep deterministic policy gradient (DDPG) with centralized training and decentralized execution to obtain the flocking control policy using actor-critic networks and a global state space matrix. In the context of swarm robotics in arts, we investigate how the formation paradigm can serve as an interaction modality for artists to aesthetically utilize swarms. In particular, we explore particle swarm optimization (PSO) and random walk to control the communication between a team of robots with swarming behavior for musical creation

Ant Colony Optimization

Ant Colony Optimization (ACO) is the best example of how studies aimed at understanding and modeling the behavior of ants and other social insects can provide inspiration for the development of computational algorithms for the solution of difficult mathematical problems. Introduced by Marco Dorigo in his PhD thesis (1992) and initially applied to the travelling salesman problem, the ACO field has experienced a tremendous growth, standing today as an important nature-inspired stochastic metaheuristic for hard optimization problems. This book presents state-of-the-art ACO methods and is divided into two parts: (I) Techniques, which includes parallel implementations, and (II) Applications, where recent contributions of ACO to diverse fields, such as traffic congestion and control, structural optimization, manufacturing, and genomics are presented