Tutte's 5-flow conjecture

The aim of this thesis is to show and put together the results, obtained so far, useful to tackle a conjecture of graph theory proposed in 1954 by William Thomas Tutte. The conjecture in question is Tutte's 5-flow conjecture, which states that every bridgeless graph admits a nowhere-zero 5-flow, namely a flow with non-zero integer values between -4 and 4. We will start by giving some basics on graph theory, useful for the followings, and proving some results about flows on oriented graphs and in particular about the flow polynomial. Next we will treat two cases: graphs embeddable in the plane $\mathbb{R}^2$ and graphs embeddable in the projective plane $\mathbb{P}^2$. In the first case we will see the correlation between flows and colorings and prove a theorem even stronger than Tutte's conjecture, using the 4-color theorem. In the second case we will see how in 1984 Richard Steinberg used Fleischner's Splitting Lemma to show that there can be no minimal counterexample of the conjecture in the case of graphs in the projective plane. In the fourth chapter we will look at the theorems of François Jaeger (1976) and Paul D. Seymour (1981). The former proved that every bridgeless graph admits a nowhere-zero 8-flow, the latter managed to go even further showing that every bridgeless graph admits a nowhere-zero 6-flow. In the fifth and final chapter there will be a short introduction to the Tutte polynomial and it will be shown how it is related to the flow polynomial via the Recipe Theorem. Finally we will see some applications of flows through the study of networks and their properties.

An Error-Localization, Validation and Optimization Tool for Embedded Code Augmentation: an Architecture Oriented Approach

Embedded systems are usually designed for a single or a specified set of tasks. This specificity means the system design as well as its hardware/software development can be highly optimized. Embedded software must meet the requirements such as high reliability operation on resource-constrained platforms, real time constraints and rapid development. This necessitates the adoption of static machine codes analysis tools running on a host machine for the validation and optimization of embedded system codes, which can help meet all of these goals. This could significantly augment the software quality and is still a challenging field.Embedded systems are usually designed for a single or a specified set of tasks. This specificity means the system design as well as its hardware/software development can be highly optimized. Embedded software must meet the requirements such as high reliability operation on resource-constrained platforms, real time constraints and rapid development. This necessitates the adoption of static machine codes analysis tools running on a host machine for the validation and optimization of embedded system codes, which can help meet all of these goals. This could significantly augment the software quality and is still a challenging field.Embedded systems are usually designed for a single or a specified set of tasks. This specificity means the system design as well as its hardware/software development can be highly optimized. Embedded software must meet the requirements such as high reliability operation on resource-constrained platforms, real time constraints and rapid development. This necessitates the adoption of static machine codes analysis tools running on a host machine for the validation and optimization of embedded system codes, which can help meet all of these goals. This could significantly augment the software quality and is still a challenging field.Embedded systems are usually designed for a single or a specified set of tasks. This specificity means the system design as well as its hardware/software development can be highly optimized. Embedded software must meet the requirements such as high reliability operation on resource-constrained platforms, real time constraints and rapid development. This necessitates the adoption of static machine codes analysis tools running on a host machine for the validation and optimization of embedded system codes, which can help meet all of these goals. This could significantly augment the software quality and is still a challenging field.This dissertation contributes to an architecture oriented code validation, error localization and optimization technique assisting the embedded system designer in software debugging, to make it more effective at early detection of software bugs that are otherwise hard to detect, using the static analysis of machine codes. The focus of this work is to develop methods that automatically localize faults as well as optimize the code and thus improve the debugging process as well as quality of the code.Validation is done with the help of rules of inferences formulated for the target processor. The rules govern the occurrence of illegitimate/out of place instructions and code sequences for executing the computational and integrated peripheral functions. The stipulated rules are encoded in propositional logic formulae and their compliance is tested individually in all possible execution paths of the application programs. An incorrect sequence of machine code pattern is identified using slicing techniques on the control flow graph generated from the machine code.An algorithm to assist the compiler to eliminate the redundant bank switching codes and decide on optimum data allocation to banked memory resulting in minimum number of bank switching codes in embedded system software is proposed. A relation matrix and a state transition diagram formed for the active memory bank state transition corresponding to each bank selection instruction is used for the detection of redundant codes. Instances of code redundancy based on the stipulated rules for the target processor are identified.This validation and optimization tool can be integrated to the system development environment. It is a novel approach independent of compiler/assembler, applicable to a wide range of processors once appropriate rules are formulated. Program states are identified mainly with machine code pattern, which drastically reduces the state space creation contributing to an improved state-of-the-art model checking. Though the technique described is general, the implementation is architecture oriented, and hence the feasibility study is conducted on PIC16F87X microcontrollers. The proposed tool will be very useful in steering novices towards correct use of difficult microcontroller features in developing embedded systems.

Estudo da viabilidade do desenvolvimento de sistemas integrados baseados em redes em chip sem processadores: sistema IPNoSys

The increase of capacity to integrate transistors permitted to develop completed systems, with several components, in single chip, they are called SoC (System-on-Chip). However, the interconnection subsystem cans influence the scalability of SoCs, like buses, or can be an ad hoc solution, like bus hierarchy. Thus, the ideal interconnection subsystem to SoCs is the Network-on-Chip (NoC). The NoCs permit to use simultaneous point-to-point channels between components and they can be reused in other projects. However, the NoCs can raise the complexity of project, the area in chip and the dissipated power. Thus, it is necessary or to modify the way how to use them or to change the development paradigm. Thus, a system based on NoC is proposed, where the applications are described through packages and performed in each router between source and destination, without traditional processors. To perform applications, independent of number of instructions and of the NoC dimensions, it was developed the spiral complement algorithm, which finds other destination until all instructions has been performed. Therefore, the objective is to study the viability of development that system, denominated IPNoSys system. In this study, it was developed a tool in SystemC, using accurate cycle, to simulate the system that performs applications, which was implemented in a package description language, also developed to this study. Through the simulation tool, several result were obtained that could be used to evaluate the system performance. The methodology used to describe the application corresponds to transform the high level application in data-flow graph that become one or more packages. This methodology was used in three applications: a counter, DCT-2D and float add. The counter was used to evaluate a deadlock solution and to perform parallel application. The DCT was used to compare to STORM platform. Finally, the float add aimed to evaluate the efficiency of the software routine to perform a unimplemented hardware instruction. The results from simulation confirm the viability of development of IPNoSys system. They showed that is possible to perform application described in packages, sequentially or parallelly, without interruptions caused by deadlock, and also showed that the execution time of IPNoSys is more efficient than the STORM platform

Context-sensitive analysis of obfuscated x86 executables

A method for context-sensitive analysis of binaries that may have obfuscated procedure call and return operations is presented. Such binaries may use operators to directly manipulate stack instead of using native call and ret instructions to achieve equivalent behavior. Since definition of context-sensitivity and algorithms for context-sensitive analysis have thus far been based on the specific semantics associated to procedure call and return operations, classic interprocedural analyses cannot be used reliably for analyzing programs in which these operations cannot be discerned. A new notion of context-sensitivity is introduced that is based on the state of the stack at any instruction. While changes in 'calling'-context are associated with transfer of control, and hence can be reasoned in terms of paths in an interprocedural control flow graph (ICFG), the same is not true of changes in 'stack'-context. An abstract interpretation based framework is developed to reason about stack-contexts and to derive analogues of call-strings based methods for the context-sensitive analysis using stack-context. The method presented is used to create a context-sensitive version of Venable et al.'s algorithm for detecting obfuscated calls. Experimental results show that the context-sensitive version of the algorithm generates more precise results and is also computationally more efficient than its context-insensitive counterpart. Copyright © 2010 ACM.

Context-sensitive analysis without calling-context

Since Sharir and Pnueli, algorithms for context-sensitivity have been defined in terms of 'valid' paths in an interprocedural flow graph. The definition of valid paths requires atomic call and ret statements, and encapsulated procedures. Thus, the resulting algorithms are not directly applicable when behavior similar to call and ret instructions may be realized using non-atomic statements, or when procedures do not have rigid boundaries, such as with programs in low level languages like assembly or RTL. We present a framework for context-sensitive analysis that requires neither atomic call and ret instructions, nor encapsulated procedures. The framework presented decouples the transfer of control semantics and the context manipulation semantics of statements. A new definition of context-sensitivity, called stack contexts, is developed. A stack context, which is defined using trace semantics, is more general than Sharir and Pnueli's interprocedural path based calling-context. An abstract interpretation based framework is developed to reason about stack-contexts and to derive analogues of calling-context based algorithms using stack-context. The framework presented is suitable for deriving algorithms for analyzing binary programs, such as malware, that employ obfuscations with the deliberate intent of defeating automated analysis. The framework is used to create a context-sensitive version of Venable et al.'s algorithm for analyzing x86 binaries without requiring that a binary conforms to a standard compilation model for maintaining procedures, calls, and returns. Experimental results show that a context-sensitive analysis using stack-context performs just as well for programs where the use of Sharir and Pnueli's calling-context produces correct approximations. However, if those programs are transformed to use call obfuscations, a contextsensitive analysis using stack-context still provides the same, correct results and without any additional overhead. © Springer Science+Business Media, LLC 2011.

System Architecture of a Mixed Reality Framework

In this paper the software architecture of a framework which simplifies the development of applications in the area of Virtual and Augmented Reality is presented. It is based on VRML/X3D to enable rendering of audio-visual information. We extended our VRML rendering system by a device management system that is based on the concept of a data-flow graph. The aim of the system is to create Mixed Reality (MR) applications simply by plugging together small prefabricated software components, instead of compiling monolithic C++ applications. The flexibility and the advantages of the presented framework are explained on the basis of an exemplary implementation of a classic Augmented Realityapplication and its extension to a collaborative remote expert scenario.

A flexible (C)LP-based approach to the analysis of object-oriented programs

Static analyses of object-oriented programs usually rely on intermediate representations that respect the original semantics while having a more uniform and basic syntax. Most of the work involving object-oriented languages and abstract interpretation usually omits the description of that language or just refers to the Control Flow Graph(CFG) it represents. However, this lack of formalization on one hand results in an absence of assurances regarding the correctness of the transformation and on the other it typically strongly couples the analysis to the source language. In this work we present a framework for analysis of object-oriented languages in which in a first phase we transform the input program into a representation based on Horn clauses. This allows on one hand proving the transformation correct attending to a simple condition and on the other being able to apply an existing analyzer for (constraint) logic programming to automatically derive a safe approximation of the semantics of the original program. The approach is flexible in the sense that the first phase decouples the analyzer from most languagedependent features, and correct because the set of Horn clauses returned by the transformation phase safely approximates the standard semantics of the input program. The resulting analysis is also reasonably scalable due to the use of mature, modular (C)LP-based analyzers. The overall approach allows us to report results for medium-sized programs.

A generic, context sensitive analysis framework for object oriented programs

Abstract interpreters rely on the existence of a nxpoint algorithm that calculates a least upper bound approximation of the semantics of the program. Usually, that algorithm is described in terms of the particular language in study and therefore it is not directly applicable to programs written in a different source language. In this paper we introduce a generic, block-based, and uniform representation of the program control flow graph and a language-independent nxpoint algorithm that can be applied to a variety of languages and, in particular, Java. Two major characteristics of our approach are accuracy (obtained through a topdown, context sensitive approach) and reasonable efficiency (achieved by means of memoization and dependency tracking techniques). We have also implemented the proposed framework and show some initial experimental results for standard benchmarks, which further support the feasibility of the solution adopted.

A Flow Trace Generator using Graph-based Traffic Classification Techniques

We propose a novel methodology to generate realistic network flow traces to enable systematic evaluation of network monitoring systems in various traffic conditions. Our technique uses a graph-based approach to model the communication structure observed in real-world traces and to extract traffic templates. By combining extracted and user-defined traffic templates, realistic network flow traces that comprise normal traffic and customized conditions are generated in a scalable manner. A proof-of-concept implementation demonstrates the utility and simplicity of our method to produce a variety of evaluation scenarios. We show that the extraction of templates from real-world traffic leads to a manageable number of templates that still enable accurate re-creation of the original communication properties on the network flow level.

ANALYSIS AND VISUALIZATION OF FLOW FIELDS USING INFORMATION-THEORETIC TECHNIQUES AND GRAPH-BASED REPRESENTATIONS

Three-dimensional flow visualization plays an essential role in many areas of science and engineering, such as aero- and hydro-dynamical systems which dominate various physical and natural phenomena. For popular methods such as the streamline visualization to be effective, they should capture the underlying flow features while facilitating user observation and understanding of the flow field in a clear manner. My research mainly focuses on the analysis and visualization of flow fields using various techniques, e.g. information-theoretic techniques and graph-based representations. Since the streamline visualization is a popular technique in flow field visualization, how to select good streamlines to capture flow patterns and how to pick good viewpoints to observe flow fields become critical. We treat streamline selection and viewpoint selection as symmetric problems and solve them simultaneously using the dual information channel [81]. To the best of my knowledge, this is the first attempt in flow visualization to combine these two selection problems in a unified approach. This work selects streamline in a view-independent manner and the selected streamlines will not change for all viewpoints. My another work [56] uses an information-theoretic approach to evaluate the importance of each streamline under various sample viewpoints and presents a solution for view-dependent streamline selection that guarantees coherent streamline update when the view changes gradually. When projecting 3D streamlines to 2D images for viewing, occlusion and clutter become inevitable. To address this challenge, we design FlowGraph [57, 58], a novel compound graph representation that organizes field line clusters and spatiotemporal regions hierarchically for occlusion-free and controllable visual exploration. We enable observation and exploration of the relationships among field line clusters, spatiotemporal regions and their interconnection in the transformed space. Most viewpoint selection methods only consider the external viewpoints outside of the flow field. This will not convey a clear observation when the flow field is clutter on the boundary side. Therefore, we propose a new way to explore flow fields by selecting several internal viewpoints around the flow features inside of the flow field and then generating a B-Spline curve path traversing these viewpoints to provide users with closeup views of the flow field for detailed observation of hidden or occluded internal flow features [54]. This work is also extended to deal with unsteady flow fields. Besides flow field visualization, some other topics relevant to visualization also attract my attention. In iGraph [31], we leverage a distributed system along with a tiled display wall to provide users with high-resolution visual analytics of big image and text collections in real time. Developing pedagogical visualization tools forms my other research focus. Since most cryptography algorithms use sophisticated mathematics, it is difficult for beginners to understand both what the algorithm does and how the algorithm does that. Therefore, we develop a set of visualization tools to provide users with an intuitive way to learn and understand these algorithms.

Galerkin finite element method for incompressible thermofluid flows framed within the bond graph theory

In this paper a bond graph methodology is used to model incompressible fluid flows with viscous and thermal effects. The distinctive characteristic of these flows is the role of pressure, which does not behave as a state variable but as a function that must act in such a way that the resulting velocity field has divergence zero. Velocity and entropy per unit volume are used as independent variables for a single-phase, single-component flow. Time-dependent nodal values and interpolation functions are introduced to represent the flow field, from which nodal vectors of velocity and entropy are defined as state variables. The system for momentum and continuity equations is coincident with the one obtained by using the Galerkin method for the weak formulation of the problem in finite elements. The integral incompressibility constraint is derived based on the integral conservation of mechanical energy. The weak formulation for thermal energy equation is modeled with true bond graph elements in terms of nodal vectors of temperature and entropy rates, resulting a Petrov-Galerkin method. The resulting bond graph shows the coupling between mechanical and thermal energy domains through the viscous dissipation term. All kind of boundary conditions are handled consistently and can be represented as generalized effort or flow sources. A procedure for causality assignment is derived for the resulting graph, satisfying the Second principle of Thermodynamics. (C) 2007 Elsevier B.V. All rights reserved.

A multicommuted flow-system for spectrophotometric determination of tannin exploiting the Cu(I)/BCA complex formation

A flow system exploiting the multicommutation approach is proposed for spectrophotometric determination of tannin in beverages. The procedure is based on the reduction of Cu(II) in the presence of 4,4`-dicarboxy-2,2`-biquinoline, yielding a complex with maximum absorption at 558 nm. Calibration graph was linear (r=0.999) for tannic acid concentrations up to 5.00 mu mol L-1. The detection limit and coefficient of variation were estimated as 10 nmol L-1 (99.7% confidence level) and 1% (1.78 mu mol L-1 tannic acid, n=10), respectively. The sampling rate was 50 determinations per hour. The proposed procedure is more sensitive and selective than the official Folin-Denis method, also minimizing drastically waste generation. Recoveries within 91.8 and 115% were estimated for total tannin determination in tea and wine samples. (C) 2007 Elsevier B.V. All rights reserved.

Fuzzy Connectedness Image Segmentation in Graph Cut Formulation: A Linear-Time Algorithm and a Comparative Analysis

A deep theoretical analysis of the graph cut image segmentation framework presented in this paper simultaneously translates into important contributions in several directions. The most important practical contribution of this work is a full theoretical description, and implementation, of a novel powerful segmentation algorithm, GC(max). The output of GC(max) coincides with a version of a segmentation algorithm known as Iterative Relative Fuzzy Connectedness, IRFC. However, GC(max) is considerably faster than the classic IRFC algorithm, which we prove theoretically and show experimentally. Specifically, we prove that, in the worst case scenario, the GC(max) algorithm runs in linear time with respect to the variable M=|C|+|Z|, where |C| is the image scene size and |Z| is the size of the allowable range, Z, of the associated weight/affinity function. For most implementations, Z is identical to the set of allowable image intensity values, and its size can be treated as small with respect to |C|, meaning that O(M)=O(|C|). In such a situation, GC(max) runs in linear time with respect to the image size |C|. We show that the output of GC(max) constitutes a solution of a graph cut energy minimization problem, in which the energy is defined as the a"" (a) norm ayenF (P) ayen(a) of the map F (P) that associates, with every element e from the boundary of an object P, its weight w(e). This formulation brings IRFC algorithms to the realm of the graph cut energy minimizers, with energy functions ayenF (P) ayen (q) for qa[1,a]. Of these, the best known minimization problem is for the energy ayenF (P) ayen(1), which is solved by the classic min-cut/max-flow algorithm, referred to often as the Graph Cut algorithm. We notice that a minimization problem for ayenF (P) ayen (q) , qa[1,a), is identical to that for ayenF (P) ayen(1), when the original weight function w is replaced by w (q) . Thus, any algorithm GC(sum) solving the ayenF (P) ayen(1) minimization problem, solves also one for ayenF (P) ayen (q) with qa[1,a), so just two algorithms, GC(sum) and GC(max), are enough to solve all ayenF (P) ayen (q) -minimization problems. We also show that, for any fixed weight assignment, the solutions of the ayenF (P) ayen (q) -minimization problems converge to a solution of the ayenF (P) ayen(a)-minimization problem (ayenF (P) ayen(a)=lim (q -> a)ayenF (P) ayen (q) is not enough to deduce that). An experimental comparison of the performance of GC(max) and GC(sum) algorithms is included. This concentrates on comparing the actual (as opposed to provable worst scenario) algorithms' running time, as well as the influence of the choice of the seeds on the output.

Electroencephalogram based Causality Graph Analysis in Behavior Tasks of Parkinson’s Disease Patients

Electroencephalographic (EEG) signals of the human brains represent electrical activities for a number of channels recorded over a the scalp. The main purpose of this thesis is to investigate the interactions and causality of different parts of a brain using EEG signals recorded during a performance subjects of verbal fluency tasks. Subjects who have Parkinson's Disease (PD) have difficulties with mental tasks, such as switching between one behavior task and another. The behavior tasks include phonemic fluency, semantic fluency, category semantic fluency and reading fluency. This method uses verbal generation skills, activating different Broca's areas of the Brodmann's areas (BA44 and BA45). Advanced signal processing techniques are used in order to determine the activated frequency bands in the granger causality for verbal fluency tasks. The graph learning technique for channel strength is used to characterize the complex graph of Granger causality. Also, the support vector machine (SVM) method is used for training a classifier between two subjects with PD and two healthy controls. Neural data from the study was recorded at the Colorado Neurological Institute (CNI). The study reveals significant difference between PD subjects and healthy controls in terms of brain connectivities in the Broca's Area BA44 and BA45 corresponding to EEG electrodes. The results in this thesis also demonstrate the possibility to classify based on the flow of information and causality in the brain of verbal fluency tasks. These methods have the potential to be applied in the future to identify pathological information flow and causality of neurological diseases.

A Novel Framework for Real-time Traffic Flow Parameter Estimation from Aerial Videos

Thesis (Master's)--University of Washington, 2016-06