Restricted permutations, antichains, atomic classes and stack sorting

Involvement is a partial order on all finite permutations, of infinite dimension and having subsets isomorphic to every countable partial order with finite descending chains. It has attracted the attention of some celebrated mathematicians including Paul Erdős and, due to its close links with sorting devices, Donald Knuth. We compare and contrast two presentations of closed classes that depend on the partial order of involvement: Basis or Avoidance Set, and Union of Atomic Classes. We examine how the basis is affected by a comprehensive list of closed class constructions and decompositions. The partial order of involvement contains infinite antichains. We develop the concept of a fundamental antichain. We compare the concept of 'fundamental' with other definitions of minimality for antichains, and compare fundamental permutation antichains with fundamental antichains in graph theory. The justification for investigating fundamental antichains is the nice patterns they produce. We forward the case for classifying the fundamental permutation antichains. Sorting devices have close links with closed classes. We consider two sorting devices, constructed from stacks in series, in detail. We give a comment on an enumerative conjecture by Ira Gessel. We demonstrate, with a remarkable example, that there exist two closed classes, equinumerous, one of which has a single basis element, the other infinitely many basis elements. We present this paper as a comprehensive analysis of the partial order of permutation involvement. We regard the main research contributions offered here to be the examples that demonstrate what is, and what is not, possible; although there are numerous structure results that do not fall under this category. We propose the classification of fundamental permutation antichains as one of the principal problems for closed classes today, and consider this as a problem whose solution will have wide significance for the study of partial orders, and mathematics as a whole

Models and Algorithms for Sorting Permutations with Tandem Duplication and Random Loss

A central topic of evolutionary biology is the inference of phylogeny, i. e., the evolutionary history of species. A powerful tool for the inference of such phylogenetic relationships is the arrangement of the genes in mitochondrial genomes. The rationale is that these gene arrangements are subject to different types of mutations in the course of evolution. Hence, a high similarity in the gene arrangement between two species indicates a close evolutionary relation. Metazoan mitochondrial gene arrangements are particularly well suited for such phylogenetic studies as they are available for a wide range of species, their gene content is almost invariant, and usually free of duplicates. With these properties gene arrangements of mitochondrial genomes are modeled by permutations in which each element represents a gene, i. e., a specific genetic sequence. The mutations that shape the gene arrangement of genomes are then represented by operations that rearrange elements in permutations, so-called genome rearrangements, and thereby bridge the gap between evolutionary biology and optimization. Many problems of phylogeny inference can be formulated as challenging combinatorial optimization problems which makes this research area especially interesting for computer scientists. The most prominent examples of such optimization problems are the sorting problem and the distance problem. While the sorting problem requires a minimum length sequence of rearrangements that transforms one given permutation into another given permutation, i. e., it aims for a hypothetical scenario of gene order evolution, the distance problem intends to determine only the length of such a sequence. This minimum length is called distance and used as a (dis)similarity measure quantifying the evolutionary relatedness. Most evolutionary changes occurring in gene arrangements of mitochondrial genomes can be explained by the tandem duplication random loss (TDRL) genome rearrangement model. A TDRL consists of a duplication of a consecutive set of genes in tandem followed by a random loss of one copy of each duplicated gene. In spite of the importance of the TDRL genome rearrangement in mitochondrial evolution, its combinatorial properties have rarely been studied. In addition, models of genome rearrangements which include all types of rearrangement that are relevant for mitochondrial genomes, i. e., inversions, transpositions, inverse transpositions, and TDRLs, while admitting computational tractability are rare. Nevertheless, especially for metazoan gene arrangements the TDRL rearrangement should be considered for the reconstruction of phylogeny. Realizing that a better understanding of the TDRL model is indispensable for the study of mitochondrial gene arrangements, the central theme of this thesis is to broaden the horizon of TDRL genome rearrangements with respect to mitochondrial genome evolution. For this purpose, this thesis provides combinatorial properties of the TDRL model and its variants as well as efficient methods for a plausible reconstruction of rearrangement scenarios between gene arrangements. The methods that are proposed consider all types of genome rearrangements that predominately occur during mitochondrial evolution. More precisely, the main points contained in this thesis are as follows: The distance problem and the sorting problem for the TDRL model are further examined in respect to circular permutations, a formal concept that reflects the circular structure of mitochondrial genomes. As a result, a closed formula for the distance is provided. Recently, evidence for a variant of the TDRL rearrangement model in which the duplicated set of genes is additionally inverted have been found. Initiating the algorithmic study of this new rearrangement model on a certain type of permutations, a closed formula solving the distance problem is proposed as well as a quasilinear time algorithm that solves the corresponding sorting problem. The assumption that only one type of genome rearrangement has occurred during the evolution of certain gene arrangements is most likely unrealistic, e. g., at least three types of rearrangements on top of the TDRL rearrangement have to be considered for the evolution metazoan mitochondrial genomes. Therefore, three different biologically motivated constraints are taken into account in this thesis in order to produce plausible evolutionary rearrangement scenarios. The first constraint is extending the considered set of genome rearrangements to the model that covers all four common types of mitochondrial genome rearrangements. For this 4-type model a sharp lower bound and several close additive upper bounds on the distance are developed. As a byproduct, a polynomial-time approximation algorithm for the corresponding sorting problem is provided that guarantees the computation of pairwise rearrangement scenarios that deviate from a minimum length scenario by at most two rearrangement operations. The second biologically motivated constraint is the relative frequency of the different types of rearrangements occurring during the evolution. The frequency is modeled by employing a weighting scheme on the 4-type model in which every rearrangement is weighted with respect to its type. The resulting NP-hard sorting problem is then solved by means of a polynomial size integer linear program. The third biologically motivated constraint that has been taken into account is that certain subsets of genes are often found in close proximity in the gene arrangements of many different species. This observation is reflected by demanding rearrangement scenarios to preserve certain groups of genes which are modeled by common intervals of permutations. In order to solve the sorting problem that considers all three types of biologically motivated constraints, the exact dynamic programming algorithm CREx2 is proposed. CREx2 has a linear runtime for a large class of problem instances. Otherwise, two versions of the CREx2 are provided: The first version provides exact solutions but has an exponential runtime in the worst case and the second version provides approximated solutions efficiently. CREx2 is evaluated by an empirical study for simulated artificial and real biological mitochondrial gene arrangements

Algorithm Libraries for Multi-Core Processors

By providing parallelized versions of established algorithm libraries, we ease the exploitation of the multiple cores on modern processors for the programmer. The Multi-Core STL provides basic algorithms for internal memory, while the parallelized STXXL enables multi-core acceleration for algorithms on large data sets stored on disk. Some parallelized geometric algorithms are introduced into CGAL. Further, we design and implement sorting algorithms for huge data in distributed external memory

Enhanced Algorithms for Analysis and Design of Nucleic Acid Reaction Pathways

Nucleic acids provide a powerful platform for programming at the molecular level. This is possible because the free energy of nucleic acid structures is dominated by the local interactions of base pairing and base pair stacking. The nearest neighbor secondary structure model implied by these energetics has enabled development of a set of algorithms for calculating thermodynamic quantities of nucleic acid sequences. Molecular programmers and synthetic biologists continue to extend their reach to larger, more complicated nucleic acid complexes, reaction pathways, and systems. This necessitates a focus on new algorithm development and efficient implementations to enable analysis and design of such systems. Concerning analysis of nucleic acids, we collect seemingly diverse algorithms under a unified three-component dynamic programming framework consisting of: 1) recursions that specify the dependencies between subproblems and incorporate the details of the structural ensemble and the free energy model, 2) evaluation algebras that define the mathematical form of each subproblem, 3) operation orders that specify the computational trajectory through the dependency graph of subproblems. Changes to the set of recursions allows operation over the complex ensemble including coaxial and dangle stacking states, affecting all thermodynamic quantities. An updated operation order for structure sampling allows simultaneous generation of a set of structures sampled from the Boltzmann distribution in time that scales empirically sublinearly in the number of samples and leads to an order of magnitude or more speedup over repeated single-structure sampling. For the problem of sequence design for reaction pathway engineering, we introduce an optimization algorithm to minimize the multitstate test tube ensemble defect, which simultaneously designs for reactant, intermediate, and product states along the reaction pathway (positive design) and against crosstalk interactions (negative design). Each of these on-pathway or crosstalk states is represented as a target test tube ensemble containing arbitrary numbers of on-target complexes, each with a target secondary structure and target concentration, and arbitrary numbers of off-target complexes, each with vanishing target concentration. Our test tube specification formalism enables conversion of a reaction pathway specification into a set of target test tubes. Sequences are designed subject to a set of hard constraints allowing specification of properties such as sequence composition, sequence complementarity, prevention of unwanted sequence patterns, and inclusion of biological sequences. We then extend this algorithm with soft constraints, enhancing flexibility through new constraint types and reducing design cost by up to two orders of magnitude in the most highly constrained cases. These soft constraints enable multiobjective design of the multitstate test tube ensemble defect simultaneously with heuristics for avoiding kinetic traps and equalizing reaction rates to further aid reaction pathway engineering.</p

A Survey on Compiler Autotuning using Machine Learning

Since the mid-1990s, researchers have been trying to use machine-learning based approaches to solve a number of different compiler optimization problems. These techniques primarily enhance the quality of the obtained results and, more importantly, make it feasible to tackle two main compiler optimization problems: optimization selection (choosing which optimizations to apply) and phase-ordering (choosing the order of applying optimizations). The compiler optimization space continues to grow due to the advancement of applications, increasing number of compiler optimizations, and new target architectures. Generic optimization passes in compilers cannot fully leverage newly introduced optimizations and, therefore, cannot keep up with the pace of increasing options. This survey summarizes and classifies the recent advances in using machine learning for the compiler optimization field, particularly on the two major problems of (1) selecting the best optimizations and (2) the phase-ordering of optimizations. The survey highlights the approaches taken so far, the obtained results, the fine-grain classification among different approaches and finally, the influential papers of the field.Comment: version 5.0 (updated on September 2018)- Preprint Version For our Accepted Journal @ ACM CSUR 2018 (42 pages) - This survey will be updated quarterly here (Send me your new published papers to be added in the subsequent version) History: Received November 2016; Revised August 2017; Revised February 2018; Accepted March 2018

A Group-Based Ring Oscillator Physical Unclonable Function

Silicon Physical Unclonable Function (PUF) is a physical structure of the chip which has functional characteristics that are hard to predict before fabrication but are expected to be unique after fabrication. This is caused by the random fabrication variations. The secret characteristics can only be extracted through physical measurement and will vanish immediately when the chip is powered down. PUF promises a securer means for cryptographic key generation and storage among many other security applications. However, there are still many practical challenges to cost effectively build secure and reliable PUF secrecy. This dissertation proposes new architectures for ring oscillator (RO) PUFs to answer these challenges. First, our temperature-aware cooperative (TAC) RO PUF can utilize certain ROs that were otherwise discarded due to their instability. Second, our novel group-based algorithm can generate secrecy higher than the theoretical upper bound of the conventional pairwise comparisons approach. Third, we build the first regression-based entropy distiller that can turn the PUF secrecy statistically random and robust, meeting the NIST standards. Fourth, we develop a unique Kendall syndrome coding (KSC) that makes the PUF secrecy error resilient against potential environmental fluctuations. Each of these methods can improve the hardware efficiency of the RO PUF implementation by 1.5X to 8X while improving the security and reliability of the PUF secrecy

Routines and Applications of Symbolic Algebra Software

Computing has become an essential resource in modern research and has found application across a wide range of scientific disciplines. Developments in symbolic algebra tools have been particularly valuable in physics where calculations in fields such as general relativity, quantum field theory and physics beyond the standard model are becoming increasing complex and unpractical to work with by hand. The computer algebra system Cadabra is a tensor-first approach to symbolic algebra based on the programming language Python which has been used extensively in research in these fields while also having a shallow learning curve making it an excellent way to introduce students to methods in computer algebra. The work in this thesis has been concentrated on developing Cadabra, which has involved looking at two different elements which make up a computer algebra program. Firstly, the implementation of algebraic routines is discussed. This has primarily been focused on the introduction of an algorithm for detecting the equivalence of tensorial expressions related by index permutation symmetries. The method employed differs considerably from traditional canonicalisation routines which are commonly used for this purpose by using Young projection operators to make such symmetries manifest. The other element of writing a computer algebra program which is covered is the infrastruc- ture and environment. The importance of this aspect of software design is often overlooked by funding committees and academic software users resulting in an anti-pattern of code not being shared and contributed to in the way in which research itself is published and promulgated. The focus in this area has been on implementing a packaging system for Cadabra which allows the writing of generic libraries which can be shared by the community, and interfacing with other scientific computing packages to increase the capabilities of Cadabra

Evolution of whole genomes through inversions:models and algorithms for duplicates, ancestors, and edit scenarios

Advances in sequencing technology are yielding DNA sequence data at an alarming rate – a rate reminiscent of Moore's law. Biologists' abilities to analyze this data, however, have not kept pace. On the other hand, the discrete and mechanical nature of the cell life-cycle has been tantalizing to computer scientists. Thus in the 1980s, pioneers of the field now called Computational Biology began to uncover a wealth of computer science problems, some confronting modern Biologists and some hidden in the annals of the biological literature. In particular, many interesting twists were introduced to classical string matching, sorting, and graph problems. One such problem, first posed in 1941 but rediscovered in the early 1980s, is that of sorting by inversions (also called reversals): given two permutations, find the minimum number of inversions required to transform one into the other, where an inversion inverts the order of a subpermutation. Indeed, many genomes have evolved mostly or only through inversions. Thus it becomes possible to trace evolutionary histories by inferring sequences of such inversions that led to today's genomes from a distant common ancestor. But unlike the classic edit distance problem where string editing was relatively simple, editing permutation in this way has proved to be more complex. In this dissertation, we extend the theory so as to make these edit distances more broadly applicable and faster to compute, and work towards more powerful tools that can accurately infer evolutionary histories. In particular, we present work that for the first time considers genomic distances between any pair of genomes, with no limitation on the number of occurrences of a gene. Next we show that there are conditions under which an ancestral genome (or one close to the true ancestor) can be reliably reconstructed. Finally we present new methodology that computes a minimum-length sequence of inversions to transform one permutation into another in, on average, O(n log n) steps, whereas the best worst-case algorithm to compute such a sequence uses O(n√n log n) steps

직접 볼륨 렌더링에서 점진적 렌즈 샘플링을 사용한 피사계 심도 렌더링

학위논문 (박사) -- 서울대학교 대학원 : 공과대학 전기·컴퓨터공학부, 2021. 2. 신영길.Direct volume rendering is a widely used technique for extracting information from 3D scalar fields acquired by measurement or numerical simulation. To visualize the structure inside the volume, the voxels scalar value is often represented by a translucent color. This translucency of direct volume rendering makes it difficult to perceive the depth between the nested structures. Various volume rendering techniques to improve depth perception are mainly based on illustrative rendering techniques, and physically based rendering techniques such as depth of field effects are difficult to apply due to long computation time. With the development of immersive systems such as virtual and augmented reality and the growing interest in perceptually motivated medical visualization, it is necessary to implement depth of field in direct volume rendering. This study proposes a novel method for applying depth of field effects to volume ray casting to improve the depth perception. By performing ray casting using multiple rays per pixel, objects at a distance in focus are sharply rendered and objects at an out-of-focus distance are blurred. To achieve these effects, a thin lens camera model is used to simulate rays passing through different parts of the lens. And an effective lens sampling method is used to generate an aliasing-free image with a minimum number of lens samples that directly affect performance. The proposed method is implemented without preprocessing based on the GPU-based volume ray casting pipeline. Therefore, all acceleration techniques of volume ray casting can be applied without restrictions. We also propose multi-pass rendering using progressive lens sampling as an acceleration technique. More lens samples are progressively used for ray generation over multiple render passes. Each pixel has a different final render pass depending on the predicted maximum blurring size based on the circle of confusion. This technique makes it possible to apply a different number of lens samples for each pixel, depending on the degree of blurring of the depth of field effects over distance. This acceleration method reduces unnecessary lens sampling and increases the cache hit rate of the GPU, allowing us to generate the depth of field effects at interactive frame rates in direct volume rendering. In the experiments using various data, the proposed method generated realistic depth of field effects in real time. These results demonstrate that our method produces depth of field effects with similar quality to the offline image synthesis method and is up to 12 times faster than the existing depth of field method in direct volume rendering.직접 볼륨 렌더링(direct volume rendering, DVR)은 측정 또는 수치 시뮬레이션으로 얻은 3차원 공간의 스칼라 필드(3D scalar fields) 데이터에서 정보를 추출하는데 널리 사용되는 기술이다. 볼륨 내부의 구조를 가시화하기 위해 복셀(voxel)의 스칼라 값은 종종 반투명의 색상으로 표현된다. 이러한 직접 볼륨 렌더링의 반투명성은 중첩된 구조 간 깊이 인식을 어렵게 한다. 깊이 인식을 향상시키기 위한 다양한 볼륨 렌더링 기법들은 주로 삽화풍 렌더링(illustrative rendering)을 기반으로 하며, 피사계 심도(depth of field, DoF) 효과와 같은 물리 기반 렌더링(physically based rendering) 기법들은 계산 시간이 오래 걸리기 때문에 적용이 어렵다. 가상 및 증강 현실과 같은 몰입형 시스템의 발전과 인간의 지각에 기반한 의료영상 시각화에 대한 관심이 증가함에 따라 직접 볼륨 렌더링에서 피사계 심도를 구현할 필요가 있다. 본 논문에서는 직접 볼륨 렌더링의 깊이 인식을 향상시키기 위해 볼륨 광선투사법에 피사계 심도 효과를 적용하는 새로운 방법을 제안한다. 픽셀 당 여러 개의 광선을 사용한 광선투사법(ray casting)을 수행하여 초점이 맞는 거리에 있는 물체는 선명하게 표현되고 초점이 맞지 않는 거리에 있는 물체는 흐리게 표현된다. 이러한 효과를 얻기 위하여 렌즈의 서로 다른 부분을 통과하는 광선들을 시뮬레이션 하는 얇은 렌즈 카메라 모델(thin lens camera model)이 사용되었다. 그리고 성능에 직접적으로 영향을 끼치는 렌즈 샘플은 최적의 렌즈 샘플링 방법을 사용하여 최소한의 개수를 가지고 앨리어싱(aliasing)이 없는 이미지를 생성하였다. 제안한 방법은 기존의 GPU 기반 볼륨 광선투사법 파이프라인 내에서 전처리 없이 구현된다. 따라서 볼륨 광선투사법의 모든 가속화 기법을 제한없이 적용할 수 있다. 또한 가속 기술로 누진 렌즈 샘플링(progressive lens sampling)을 사용하는 다중 패스 렌더링(multi-pass rendering)을 제안한다. 더 많은 렌즈 샘플들이 여러 렌더 패스들을 거치면서 점진적으로 사용된다. 각 픽셀은 착란원(circle of confusion)을 기반으로 예측된 최대 흐림 정도에 따라 다른 최종 렌더링 패스를 갖는다. 이 기법은 거리에 따른 피사계 심도 효과의 흐림 정도에 따라 각 픽셀에 다른 개수의 렌즈 샘플을 적용할 수 있게 한다. 이러한 가속화 방법은 불필요한 렌즈 샘플링을 줄이고 GPU의 캐시(cache) 적중률을 높여 직접 볼륨 렌더링에서 상호작용이 가능한 프레임 속도로 피사계 심도 효과를 렌더링 할 수 있게 한다. 다양한 데이터를 사용한 실험에서 제안한 방법은 실시간으로 사실적인 피사계 심도 효과를 생성했다. 이러한 결과는 우리의 방법이 오프라인 이미지 합성 방법과 유사한 품질의 피사계 심도 효과를 생성하면서 직접 볼륨 렌더링의 기존 피사계 심도 렌더링 방법보다 최대 12배까지 빠르다는 것을 보여준다.CHAPTER 1 INTRODUCTION 1 1.1 Motivation 1 1.2 Dissertation Goals 5 1.3 Main Contributions 6 1.4 Organization of Dissertation 8 CHAPTER 2 RELATED WORK 9 2.1 Depth of Field on Surface Rendering 10 2.1.1 Object-Space Approaches 11 2.1.2 Image-Space Approaches 15 2.2 Depth of Field on Volume Rendering 26 2.2.1 Blur Filtering on Slice-Based Volume Rendering 28 2.2.2 Stochastic Sampling on Volume Ray Casting 30 CHAPTER 3 DEPTH OF FIELD VOLUME RAY CASTING 33 3.1 Fundamentals 33 3.1.1 Depth of Field 34 3.1.2 Camera Models 36 3.1.3 Direct Volume Rendering 42 3.2 Geometry Setup 48 3.3 Lens Sampling Strategy 53 3.3.1 Sampling Techniques 53 3.3.2 Disk Mapping 57 3.4 CoC-Based Multi-Pass Rendering 60 3.4.1 Progressive Lens Sample Sequence 60 3.4.2 Final Render Pass Determination 62 CHAPTER 4 GPU IMPLEMENTATION 66 4.1 Overview 66 4.2 Rendering Pipeline 67 4.3 Focal Plane Transformation 74 4.4 Lens Sample Transformation 76 CHAPTER 5 EXPERIMENTAL RESULTS 78 5.1 Number of Lens Samples 79 5.2 Number of Render Passes 82 5.3 Render Pass Parameter 84 5.4 Comparison with Previous Methods 87 CHAPTER 6 CONCLUSION 97 Bibliography 101 Appendix 111Docto

Network-Wide Monitoring And Debugging

Modern networks can encompass over 100,000 servers. Managing such an extensive network with a diverse set of network policies has become more complicated with the introduction of programmable hardwares and distributed network functions. Furthermore, service level agreements (SLAs) require operators to maintain high performance and availability with low latencies. Therefore, it is crucial for operators to resolve any issues in networks quickly. The problems can occur at any layer of stack: network (load imbalance), data-plane (incorrect packet processing), control-plane (bugs in configuration) and the coordination among them. Unfortunately, existing debugging tools are not sufficient to monitor, analyze, or debug modern networks; either they lack visibility in the network, require manual analysis, or cannot check for some properties. These limitations arise from the outdated view of the networks, i.e., that we can look at a single component in isolation. In this thesis, we describe a new approach that looks at measuring, understanding, and debugging the network across devices and time. We also target modern stateful packet processing devices: programmable data-planes and distributed network functions as these becoming increasingly common part of the network. Our key insight is to leverage both in-network packet processing (to collect precise measurements) and out-of-network processing (to coordinate measurements and scale analytics). The resulting systems we design based on this approach can support testing and monitoring at the data center scale, and can handle stateful data in the network. We automate the collection and analysis of measurement data to save operator time and take a step towards self driving networks