Roman Domination in Complementary Prism Graphs

A Roman domination function on a complementary prism graph GGc is a function f : V [ V c ! {0, 1, 2} such that every vertex with label 0 has a neighbor with label 2. The Roman domination number R(GGc) of a graph G = (V,E) is the minimum of Px2V [V c f(x) over such functions, where the complementary prism GGc of G is graph obtained from disjoint union of G and its complement Gc by adding edges of a perfect matching between corresponding vertices of G and Gc. In this paper, we have investigated few properties of R(GGc) and its relation with other parameters are obtaine

International Journal of Mathematical Combinatorics, Vol.6A

The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly comprising 460 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences

Study of Some Interesting Topics in the Theory of Graphs

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Learning-based Segmentation for Connectomics

Recent advances in electron microscopy techniques make it possible to acquire highresolution, isotropic volume images of neural circuitry. In connectomics, neuroscientists seek to obtain the circuit diagram involving all neurons and synapses in such a volume image. Mapping neuron connectivity requires tracing each and every neural process through terabytes of image data. Due to the size and complexity of these volume images, fully automated analysis methods are desperately needed. In this thesis, I consider automated, machine learning-based neurite segmentation approaches based on a simultaneous merge decision of adjacent supervoxels. - Given a learned likelihood of merging adjacent supervoxels, Chapter 4 adapts a probabilistic graphical model which ensures that merge decisions are consistent and the surfaces of final segments are closed. This model can be posed as a multicut optimization problem and is solved with the cutting-plane method. In order to scale to large datasets, a fast search for (and good choice of) violated cycle constraints is crucial. Quantitative experiments show that the proposed closed-surface regularization significantly improves segmentation performance. - In Chapter 5, I investigate whether the edge weights of the previous model can be chosen to minimize the loss with respect to non-local segmentation quality measures (e.g. Rand Index). Suitable w are obtained from a structured learning approach. In the Structured Support Vector Machine formulation, a novel fast enumeration scheme is used to find the most violated constraint. Quantitative experiments show that structured learning can improve upon unstructured methods. Furthermore, I introduce a new approximate, hierarchical and blockwise optimization approach for large-scale multicut segmentation. Using this method, high-quality approximate solutions for large problem instances are found quickly. - Chapter 6 introduces another novel approximate scheme for multicut segmentation -- Cut, Glue&Cut -- which is based on the move-making paradigm. First, the graph is recursively partitioned into small regions (cut phase). Then, for any two adjacent regions, alternative cuts of these two regions define possible moves (glue&cut phase). The proposed algorithm finds segmentations that are { as measured by a loss function { as close to the ground-truth as the global optimum found by exact solvers, while being significantly faster than existing methods. - In order to jointly label resulting segments as well as to label the boundaries between segments, Chapter 7 proposes the Asymmetric Multi-way Cut model, a variant of Multi-way Cut. In this new model, within-class cuts are allowed for some labels, while being forbidden for other labels. Qualitative experiments show when such a formulation can be beneficial. In particular, an application to joint neurite and cell organelle labeling in EM volume images is discussed. - Custom software tools that can cope with the large data volumes common in the field of connectomics are a prerequisite for the implementation and evaluation of novel segmentation techniques. Chapter 3 presents version 1.0 of ilastik, a joint effort of multiple researchers. I have co-written its volume viewing component, volumina. ilastik provides an interactive pixel classification work ow on largerthan-RAM datasets as well as a semi-automated segmentation module useful for acquiring gold standard segmentations. Furthermore, I describe new software for dealing with hierarchies of cell complexes as well as for blockwise image processing operations on large datasets. The different segmentation methods presented in this thesis provide a promising direction towards reaching the required reliability as well as the required data throughput necessary for connectomics applications

Augmenting Wiring Diagrams of Neural Circuits with Activity in Larval Drosophila

Neural circuit models explain an animal's behavior as evoked activity of different circuit elements of its nervous system. Synaptic wiring diagrams mapped from structural imaging of nervous systems guide modeling of neural circuits on the basis of connectivity. However, connectivity alone may not sufficiently constrain the set of plausible circuit hypotheses for empirical study. Combining structural imaging of synaptic connectivity with functional information from activity imaging can further constrain these hypotheses to create unequivocal neural circuit models. This thesis develops computational methods and tools to cross-reference structural and activity imaging of explant larval Drosophila central nervous systems at cellular resolution. Augmenting synaptic wiring diagrams with activity maps via these methods relates circuit structure and function at the neuronal level on a per-behavior basis. Neuronal activity of larval central nervous systems expressing pan-neuronal calcium indicators is imaged in a light sheet microscope, which are then structurally imaged with high throughput electron microscopy. Methods and tools are provided for the assembly of these image volumes, spatial registration between imaging modalities, automated detection of relevant tissue and cellular structures in each, extraction of activity time series, and morphological identification of neurons in structural imaging using reference wiring diagrams mapped from other larvae. Using these methods, existing wiring diagrams mapped from a reference first instar larva were identified with neurons in a larva augmented with activity information for a neural circuit involved in peristaltic motor control. This demonstrates the feasibility of the contributed methods to associate the wiring diagrams of arbitrary circuits of interest with activity timeseries across multiple individuals, behaviors, and behavioral bouts. To demonstrate capability to augment wiring diagrams with information besides activity, these methods are also applied to multiple larvae each expressing specific neurotransmitter labels rather than calcium indicators in the light sheet microscopy. This work scaffolds future modeling of circuits underlying behavior that can only be mechanistically understood in the context of multi-modal observation of synaptic connectivity, functional activity and molecular markers. The methods developed also enable comparative connectomics between multiple individuals, which is necessary to study inter-individual variability in circuits and to observe experimental intervention in the development, structure, and function of neural circuits.Howard Hughes Medical Institute Janelia Research Campu

Graph Theoretic Algorithms Adaptable to Quantum Computing

Computational methods are rapidly emerging as an essential tool for understanding and solving complex engineering problems, which complement the traditional tools of experimentation and theory. When considered in a discrete computational setting, many engineering problems can be reduced to a graph coloring problem. Examples range from systems design, airline scheduling, image segmentation to pattern recognition, where energy cost functions with discrete variables are extremized. However, using discrete variables over continuous variables introduces some complications when defining differential quantities, such as gradients and Hessians involved in scientific computations within solid and fluid mechanics. Consequently, graph techniques are under-utilized in this important domain. However, we have recently witnessed great developments in quantum computing where physical devices can solve discrete optimization problems faster than most well-known classical algorithms. This warrants further investigation into the re-formulation of scientific computation problems into graph-theoretic problems, thus enabling rapid engineering simulations in a soon-to-be quantum computing world. The computational techniques developed in this thesis allow the representation of surface scalars, such as perimeter and area, using discrete variables in a graph. Results from integral geometry, specifically Cauchy-Crofton relations, are used to estimate these scalars via submodular functions. With this framework, several quantities important to engineering applications can be represented in graph-based algorithms. These include the surface energy of cracks for fracture prediction, grain boundary energy to model microstructure evolution, and surface area estimates (of grains and fibers) for generating conformal meshes. Combinatorial optimization problems for these applications are presented first. The last two chapters describe two new graph coloring algorithms implemented on a physical quantum computing device: the D-wave quantum annealer. The first algorithm describes a functional minimization approach to solve differential equations. The second algorithm describes a realization of the Boltzmann machine learning algorithm on a quantum annealer. The latter allows generative and discriminative learning of data, which has vast applications in many fields. Theoretical aspects and the implementation of these problems are outlined with a focus on engineering applications.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/168116/1/sidsriva_1.pd

Exploring Multi-Level Parallelism For Graph-Based Applications Via Algorithm And System Co-Design

Graph processing is at the heart of many modern applications where graphs are used as the basic data structure to represent the entities of interest and the relationships between them. Improving the performance of graph-based applications, especially using parallelism techniques, has drawn significant interest both in academia and industry. On the one hand, modern CPU architectures are able to provide massive computational power by using sophisticated memory hierarchy and multi-level parallelism, including thread-level parallelism, data-level parallelism, etc. On the other hand, graph processing workloads are notoriously challenging for achieving high performance due to their irregular computation pattern and unpredictable control flow. Therefore, how to accelerate the performance of graph-based applications using parallelism is still an open question. This dissertation focuses on providing high performance for graph-based applications. To take full advantage of multi-level parallelism resources provided by CPUs, this dissertation studies the characteristics of graph-based applications and matches their parallel solutions with the underlying hardware via algorithm and system co-design. This dissertation divides graph-based applications into three categories: typical graph algorithms, sequential graph-based applications, and applications with graph-based solutions. The first category comprises typical graph algorithms with available parallel solutions. This dissertation proposes GraphPhi as a new approach to graph processing on emerging Intel Xeon Phi-like architectures. The second category includes specialized graph applications without nontrivial parallel solutions. This dissertation studies a state-of-the-art 2-hop labeling approach named Pruned Landmark Labeling (PLL). This dissertation proposes Batched Vertex-Centric PLL (BVC-PLL), which breaks PLL\u27s inherent dependencies and parallelizes it in a scalable way. The third category includes applications that rely on graph-based solutions. This dissertation studies the sequential search algorithm for the graph-based indexing methods used for the Approximate Nearest Neighbor Search (ANNS) problem. This dissertation proposes Speed-ANN, a parallel similarity search algorithm that reveals hidden intra-query parallelism to accelerate the search speed while fulfilling the high accuracy requirement. Moreover, this dissertation further explores the optimization opportunities for computational graph-based deep neural network inference running on tiny devices, specifically microcontrollers (MCUs). Altogether, this dissertation studies graph-based applications and improves their performance by providing solutions of multi-level parallelism via algorithm and system co-design to match them with the underlying multi-core CPU architectures

Doctor of Philosophy

dissertationWith modern computational resources rapidly advancing towards exascale, large-scale simulations useful for understanding natural and man-made phenomena are becoming in- creasingly accessible. As a result, the size and complexity of data representing such phenom- ena are also increasing, making the role of data analysis to propel science even more integral. This dissertation presents research on addressing some of the contemporary challenges in the analysis of vector fields--an important type of scientific data useful for representing a multitude of physical phenomena, such as wind flow and ocean currents. In particular, new theories and computational frameworks to enable consistent feature extraction from vector fields are presented. One of the most fundamental challenges in the analysis of vector fields is that their features are defined with respect to reference frames. Unfortunately, there is no single ""correct"" reference frame for analysis, and an unsuitable frame may cause features of interest to remain undetected, thus creating serious physical consequences. This work develops new reference frames that enable extraction of localized features that other techniques and frames fail to detect. As a result, these reference frames objectify the notion of ""correctness"" of features for certain goals by revealing the phenomena of importance from the underlying data. An important consequence of using these local frames is that the analysis of unsteady (time-varying) vector fields can be reduced to the analysis of sequences of steady (time- independent) vector fields, which can be performed using simpler and scalable techniques that allow better data management by accessing the data on a per-time-step basis. Nevertheless, the state-of-the-art analysis of steady vector fields is not robust, as most techniques are numerical in nature. The residing numerical errors can violate consistency with the underlying theory by breaching important fundamental laws, which may lead to serious physical consequences. This dissertation considers consistency as the most fundamental characteristic of computational analysis that must always be preserved, and presents a new discrete theory that uses combinatorial representations and algorithms to provide consistency guarantees during vector field analysis along with the uncertainty visualization of unavoidable discretization errors. Together, the two main contributions of this dissertation address two important concerns regarding feature extraction from scientific data: correctness and precision. The work presented here also opens new avenues for further research by exploring more-general reference frames and more-sophisticated domain discretizations

Model Adaptation for Sentence Unit Segmentation from Speech

The sentence segmentation task is a classification task that aims at inserting sentence boundaries in a sequence of words. One of the applications of sentence segmentation is to detect the sentence boundaries in the sequence of words that is output by an automatic speech recognition system (ASR). The purpose of correctly finding the sentence boundaries in ASR transcriptions is to make it possible to use further processing tasks, such as automatic summarization, machine translation, and information extraction. Being a classification task, sentence segmentation requires training data. To reduce the labor-intensive labeling task, available labeled data can be used to train the classifier. The high variability of speech among the various speech styles makes it inefficient to use the classifier from one speech style (designated as out-of-domain) to detect sentence boundaries on another speech style (in-domain) and thus, makes it necessary for one classifier to be adapted before it is used on another speech style. In this work, we first justify the need for adapting data among the broadcast news, conversational telephone and meeting speech styles. We then propose methods to adapt sentence segmentation models trained on conversational telephone speech to meeting conversations style. Our results show that using the model adapted from the telephone conversations, instead of the model trained only on meetings conversation style, significantly improves the performance of the sentence segmentation. Moreover, this improvement holds independently from the amount of in-domain data used. In addition, we also study the differences between speech styles, with statistical measures and by examining the performances of various subsets of features. Focusing on broadcast news and meeting speech style, we show that on the meeting speech style, lexical features are more correlated with the sentence boundaries than the prosodic features, whereas it is the contrary on the broadcast news. Furthermore, we observe that prosodic features are more independent from the speech style than lexical features