Partition Complex Research Articles

Addressing the role of centromere sites in activation of ParB proteins for partition complex assembly.

The ParB-parS partition complexes that bacterial replicons use to ensure their faithful inheritance also find employment in visualization of DNA loci, as less intrusive alternatives to fluorescent repressor-operator systems. The ability of ParB molecules to interact via their N-terminal domains and to bind to non-specific DNA enables expansion of the initial complex to a size both functional in partition and, via fusion to fluorescent peptides, visible by light microscopy. We have investigated whether it is possible to dispense with the need to insert parS in the genomic locus of interest, by determining whether ParB fused to proteins that bind specifically to natural DNA sequences can still assemble visible complexes. In yeast cells, coproduction of fusions of ParB to a fluorescent peptide and to a TALE protein targeting an endogenous sequence did not yield visible foci; nor did any of several variants of these components. In E.coli, coproduction of fusions of SopB (F plasmid ParB) to fluorescent peptide, and to dCas9 together with specific guide RNAs, likewise yielded no foci. The result of coproducing analogous fusions of SopB proteins with distinct binding specificities was also negative. Our observations imply that in order to assemble higher order partition complexes, ParB proteins need specific activation through binding to their cognate parS sites.

The Complexity of Tree Partitioning

Given a tree T on n vertices, and $$k, b, s_1, \ldots , s_b \in \mathbb {N}$$ , the Tree Partitioning problem asks if at most k edges can be removed from T so that the resulting components can be grouped into b groups such that the number of vertices in group i is $$s_i$$ , for $$i =1, \ldots , b$$ . The case where $$s_1=\cdots =s_b =n/b$$ , referred to as the Balanced Tree Partitioning problem, was shown to be $${\mathcal {NP}}$$ -complete for trees of maximum degree at most 5, and the complexity of the problem for trees of maximum degree 4 and 3 was posed as an open question. The parameterized complexity of Balanced Tree Partitioning was also posed as an open question in another work. In this paper, we answer both open questions negatively. We show that Balanced Tree Partitioning (and hence, Tree Partitioning) is $${\mathcal {NP}}$$ -complete for trees of maximum degree 3, thus closing the door on the complexity of Balanced Tree Partitioning, as the simple case when T is a path is in $${\mathcal {P}}$$ . In terms of the parameterized complexity of the problems, we show that both Balanced Tree Partitioning and Tree Partitioning are W[1]-complete parameterized by k. Using a compact representation of the solution space for an instance of the problem, we present a dynamic programming algorithm for the weighted version of Tree Partitioning (and hence for that of Balanced Tree Partitioning) that runs in subexponential-time $$2^{O(\sqrt{n})}$$ , adding a natural problem to the list of problems that can be solved in subexponential time. Finally, we extend this subexponential-time algorithm to the Weighted Graph Partitioning problem on graphs of treewidth $$o(n/\lg {n})$$ , and we also show an application of this subexponential-time algorithm for approximating the Weighted Graph Partitioning problem.

Dynamics and Complexity of Computrons.

We investigate chaoticity and complexity of a binary general network automata of finite size with external input which we call a computron. As a generalization of cellular automata, computrons can have non-uniform cell rules, non-regular cell connectivity and an external input. We show that any finite-state machine can be represented as a computron and develop two novel set-theoretic concepts: (i) diversity space as a metric space that captures similarity of configurations on a given graph and (ii) basin complexity as a measure of complexity of partitions of the diversity space. We use these concepts to quantify chaoticity of computrons’ dynamics and the complexity of their basins of attraction. The theory is then extended into probabilistic machines where we define fuzzy basin partitioning of recurrent classes and introduce the concept of ergodic decomposition. A case study on 1D cyclic computron is provided with both deterministic and probabilistic versions.

IMPROVING PSNR AND PROCESSING SPEED FOR HEVC USING HYBRID PSO FOR INTRA FRAME PREDICTION

High efficiency video coding (HEVC) is the newest video codec to increase significantly the coding efficiency of its ancestor H.264/Advance Video Coding. However, the HEVC delivers a highly increased computation complexity. In this paper, a coding unit partitioning pattern optimization method based on particle swarm optimization (PSO) is proposed to reduce the computational complexity of hierarchical quadtree-based coding unit partitioning. The required coding unit partitioning pattern for exhaustive partitioning and the rate distortion cost are efficiently considered as the chromosome and the fitness function of the PSO, respectively. To reduce the computational time, the cellular automata-based (CA) rule based time limit is used in order to find out the best possible modes of operation. Compared to the current state of the art algorithms, this scheme is computationally simple and achieves superior reconstructed video quality (12% increase in PSNR compared to existing methods) at less computational complexity (overall delay by 40%).

Analysis of Learning Patterns and Performance—A Case Study of 3-D Modeling Lessons in the K-12 Classrooms

As more schools incorporate 3D printing into their curriculum to stimulate the creativity of K-12 students with a learning-by-doing approach, it becomes crucial to understand how users work with 3D modeling tools and to evaluate integrated lesson plans in the STEAM (Science, Technology, Engineering, Arts and Math) educational framework. Our work consists of two stages: an investigation of usage patterns of modeling, and an evaluation of the usability of Qmodel Creator, in collaboration with Lanyu Primary and Junior High School, Sanchong High School, and Affiliated Experimental Elementary School of National Chengchi University. Participants operation logs, screen recordings, and finished work for respective 3D modeling software were recorded and analyzed. Two types of indicators have been developed. One is concerned with the quantification of learning behavior, including Effective Operating Period (EOP), Trial-and-Error Period (TEP), and Implementation Period (IP). The other has to do with the evaluation of learning outcome, i.e., the complexity of 3D models, including the Degree of Detail ( DoD ), shape ( $C_{f}$ ), partition ( $C_{p}$ ), and block-ratio ( $C_{r}$ ) complexity. Based on the proposed features, we are able to identify the key factors that affect students’ learning experiences and performance in terms of learning patterns and model completeness. Through these indicators, instructors can gain better insights into student’s learning status of 3D modeling software.

Scalable Spectral Clustering With Nyström Approximation: Practical and Theoretical Aspects

Spectral clustering techniques are valuable tools in signal processing and machine learning for partitioning complex data sets. The effectiveness of spectral clustering stems from constructing a non-linear embedding based on creating a similarity graph and computing the spectral decomposition of the Laplacian matrix. However, spectral clustering methods fail to scale to large data sets because of high computational cost and memory usage. A popular approach for addressing these problems utilizes the Nystrom method, an efficient sampling-based algorithm for computing low-rank approximations to large positive semi-definite matrices. This paper demonstrates how the previously popular approach of Nystrom-based spectral clustering has severe limitations. Existing time-efficient methods ignore critical information by prematurely reducing the rank of the similarity matrix associated with sampled points. Also, current understanding is limited regarding how utilizing the Nystrom approximation will affect the quality of spectral embedding approximations. To address the limitations, this work presents a principled spectral clustering algorithm that exploits spectral properties of the similarity matrix associated with sampled points to regulate accuracy-efficiency trade-offs. We provide theoretical results to reduce the current gap and present numerical experiments with real and synthetic data. Empirical results demonstrate the efficacy and efficiency of the proposed method compared to existing spectral clustering techniques based on the Nystrom method and other efficient methods. The overarching goal of this work is to provide an improved baseline for future research directions to accelerate spectral clustering.

Approximate Multiparametric Mixed-Integer Convex Programming

We propose an algorithm for generating explicit solutions of multiparametric mixed-integer convex programs to within a given suboptimality tolerance. The algorithm is applicable to a very general class of optimization problems, but is most useful for hybrid model predictive control, where online implementation is hampered by the worst-case exponential complexity of mixed-integer solvers. The output is a simplicial partition which defines a static map from the current state to a suboptimal solution. The primary theoretical contribution of this letter is to introduce a non-zero optimal cost overlap metric which is necessary and sufficient for convergence. The overlap size is also linked to partition complexity. The algorithm is massively parallelizable and our implementation, which is publicly available, is run on a cluster of several hundred processors. Not only does our solution have a deterministic runtime, simulations show that our approach is faster than online optimization by up to three orders of magnitude.

Steroidal antibiotics are antimetabolites of Acanthamoeba steroidogenesis with phylogenetic implications

Pathogenic organisms may be sensitive to inhibitors of sterol biosynthesis, which carry antimetabolite properties, through manipulation of the key enzyme, sterol methyltransferase (SMT). Here, we isolated natural suicide substrates of the ergosterol biosynthesis pathway, cholesta-5,7,22,24-tetraenol (CHT) and ergosta-5,7,22,24(28)-tetraenol (ERGT), and demonstrated their interference in Acanthamoeba castellanii steroidogenesis: CHT and ERGT inhibit trophozoite growth (EC50 of 51 nM) without affecting cultured human cell growth. Washout experiments confirmed that the target for vulnerability was SMT. Chemical, kinetic, and protein-binding studies of inhibitors assayed with 24-AcSMT [catalyzing C28-sterol via Δ24(28)-olefin production] and 28-AcSMT [catalyzing C29-sterol via Δ25(27)-olefin production] revealed interrupted partitioning and irreversible complex formation from the conjugated double bond system in the side chain of either analog, particularly with 28-AcSMT. Replacement of active site Tyr62 with Phe or Leu residues involved in cation-π interactions that model product specificity prevented protein inactivation. The alkylating properties and high selective index of 103 for CHT and ERGT against 28-AcSMT are indicative of a new class of steroidal antibiotic that, as an antimetabolite, can limit sterol expansion across phylogeny and provide a novel scaffold in the design of amoebicidal drugs. Animal studies of these suicide substrates can further explore the potential of their antibiotic properties.

Efficient and simple scalable image compression algorithms

Abstract Most wavelet-based scalable image compression algorithms are optimized for performance only, i.e., they try to produce a compressed bit-stream that gives the best image quality for the selected bit-rate. Unfortunately, the optimization of the coding method may result in a bit-stream that cannot be rearranged easily to support resolution scalability. This paper proposes two algorithms. The first algorithm produces a rate scalable bit-stream that is optimized for performance and scalability. That is, it has good performance and at the same time it produces bit-stream that can be easily rearranged to become highly (rate and resolution) scalable. To this end, the algorithm combines the low complexity and rate scalability features of the set partitioning coding approach, and it exploits the resolution scalability characteristics of the block-based systems. The second algorithm upgrades the first algorithm to produce a highly scalable bit-stream by only arranging and identifying the different resolutions within the bit-stream.

A conserved mechanism drives partition complex assembly on bacterial chromosomes and plasmids

Chromosome and plasmid segregation in bacteria are mostly driven by ParABS systems. These DNA partitioning machineries rely on large nucleoprotein complexes assembled on centromere sites (parS). However, the mechanism of how a few parS‐bound ParB proteins nucleate the formation of highly concentrated ParB clusters remains unclear despite several proposed physico‐mathematical models. We discriminated between these different models by varying some key parameters in vivo using the F plasmid partition system. We found that “Nucleation & caging” is the only coherent model recapitulating in vivo data. We also showed that the stochastic self‐assembly of partition complexes (i) is a robust mechanism, (ii) does not directly involve ParA ATPase, (iii) results in a dynamic structure of discrete size independent of ParB concentration, and (iv) is not perturbed by active transcription but is by protein complexes. We refined the “Nucleation & caging” model and successfully applied it to the chromosomally encoded Par system of Vibrio cholerae, indicating that this stochastic self‐assembly mechanism is widely conserved from plasmids to chromosomes.

High-fidelity reversible data hiding by Quadtree-based pixel value ordering

Recently, the pixel value ordering (PVO) method has received a great deal of attention in the field of high-fidelity reversible data hiding. To improve the embedding performance of the PVO-based method, a quadtree-based pixel value ordering (QPVO) method based on dynamic quadtree partition is proposed in this paper. Instead of using equal-sized blocks, blocks in various sizes are adaptively generated based on the quadtree partitioning and block complexity. Smooth regions are divided into smaller blocks to obtain high embedding capacity, while rough regions are divided into larger blocks to avoid distortion. The decoder can recover the original image as well as the original quadtree structure by the block complexity. Extensive experiments demonstrate that the proposed QPVO method could significantly improve the embedding performance of these PVO-based methods, especially for a relatively small embedding payload.

A Comparison of Partitioning Strategies for Fixed Points Based Limited Preemptive Scheduling

The increasing industrial demand for handling complex functionalities has influenced the design of hardware architectures for time critical embedded systems, during the past decade. Multicore systems facilitate the inclusion of many complex functionalities, while, at the same time, inducing cache related overheads, as well as adding partitioning complexity to the overall system schedulability. One of the efficient paradigms for controlling and reducing the cache related costs in real-time systems is limited preemptive scheduling (LPS), with its particular instance fixed preemption points scheduling (LP-FPPS), which has been shown to outperform other alternatives as well as has been supported by and investigated in the automotive domain. With respect to the partitioning constraints, partitioned scheduling has been widely used to preruntime allocate tasks to specific cores, resulting in predictable cache-related preemption delays estimations. In this paper, we propose to integrate the LP-FPPS and partitioned scheduling on fixed-priority multicore real-time systems in order to increase the overall system schedulability. We define a new joint approach for task partitioning and preemption point selection, which is based on the computation of the maximum blocking tolerance upon each allocation, thus being able to quantify the schedulability of the taskset on each processor. Furthermore, we investigate the partitioning strategies based on different heuristics, i.e., first fit decreasing and worst fit decreasing, and priority and density taskset orderings. The evaluation performed on randomly generated tasksets shows that in the general case, no single partitioning strategy fully dominates the others. However, the evaluation results reveal that the certain partitioning strategies perform significantly better with respect to the overall schedulability for specific taskset characteristics. The results also reveal that the proposed partitioning strategies outperform fully preemptive and nonpreemptive partitioned scheduling in terms of successful partitioning.

Surfing on Protein Waves: Proteophoresis as a Mechanism for Bacterial Genome Partitioning.

Efficient bacterial chromosome segregation typically requires the coordinated action of a three-component machinery, fueled by adenosine triphosphate, called the partition complex. We present a phenomenological model accounting for the dynamic activity of this system that is also relevant for the physics of catalytic particles in active environments. The model is obtained by coupling simple linear reaction-diffusion equations with a proteophoresis, or "volumetric" chemophoresis, force field that arises from protein-protein interactions and provides a physically viable mechanism for complex translocation. This minimal description captures most known experimental observations: dynamic oscillations of complex components, complex separation, and subsequent symmetrical positioning. The predictions of our model are in phenomenological agreement with and provide substantial insight into recent experiments. From a nonlinear physics view point, this system explores the active separation of matter at micrometric scales with a dynamical instability between static positioning and traveling wave regimes triggered by the dynamical spontaneous breaking of rotational symmetry.

Higher equivariant excision

We develop a theory of Goodwillie calculus for functors between G-equivariant homotopy theories, where G is a finite group. We construct J-excisive approximations for any finite G-set J. These combine into a poset, the Goodwillie tree, that extends the classical Goodwillie tower. We prove convergence results for the tree of a functor on pointed G-spaces that commutes with fixed-points, and we reinterpret the Tom Dieck-splitting as an instance of a more general splitting phenomenon that occurs for the fixed-points of the equivariant derivatives of these functors. As our main example we describe the layers of the tree of the identity functor in terms of the equivariant Spanier–Whitehead duals of the partition complexes.

The complexity of partitioning into disjoint cliques and a triangle-free graph

Motivated by Chudnovsky’s structure theorem of bull-free graphs, Abu-Khzam, Feghali, and Müller have recently proved that deciding if a graph has a vertex partition into disjoint cliques and a triangle-free graph is NP-complete for five graph classes. The problem is trivial for the intersection of these five classes. We prove that the problem is NP-complete for the intersection of two subsets of size four among the five classes. We also show NP-completeness for other small classes, such as graphs with maximum degree 4 and line graphs.

Partitioning (hierarchically clustered) complex networks via size-constrained graph clustering

The most commonly used method to tackle the graph partitioning problem in practice is the multilevel metaheuristic. In this paper we introduce size-constrained label propagation (SCLaP) and show how it can be used to instantiate both the coarsening phase and the refinement phase of multilevel graph partitioning. We mainly target networks with highly irregular and hierarchically clustered structure (but other network types can be partitioned as well). Additionally, we augment the basic algorithm with several extensions to further improve its speed and/or solution quality. Depending on the configuration of the resulting partitioner using SCLaP, we are able to compute high-quality partitions outperforming all competitors, or instead, to compute similarly good partitions as the best competitor in terms of quality, hMetis, while being an order of magnitude faster. Our fastest configuration partitions the largest real-world graph in our study (it has 3.3 billion edges) with sequential code in about ten minutes while cutting less than half of the edges than the fastest competitor, kMetis.

ParB Partition Proteins: Complex Formation and Spreading at Bacterial and Plasmid Centromeres.

In bacteria, active partition systems contribute to the faithful segregation of both chromosomes and low-copy-number plasmids. Each system depends on a site-specific DNA binding protein to recognize and assemble a partition complex at a centromere-like site, commonly called parS. Many plasmid, and all chromosomal centromere-binding proteins are dimeric helix-turn-helix DNA binding proteins, which are commonly named ParB. Although the overall sequence conservation among ParBs is not high, the proteins share similar domain and functional organization, and they assemble into similar higher-order complexes. In vivo, ParBs “spread,” that is, DNA binding extends away from the parS site into the surrounding non-specific DNA, a feature that reflects higher-order complex assembly. ParBs bridge and pair DNA at parS and non-specific DNA sites. ParB dimers interact with each other via flexible conformations of an N-terminal region. This review will focus on the properties of the HTH centromere-binding protein, in light of recent experimental evidence and models that are adding to our understanding of how these proteins assemble into large and dynamic partition complexes at and around their specific DNA sites.

Bacterial partition complexes segregate within the volume of the nucleoid.

Precise and rapid DNA segregation is required for proper inheritance of genetic material. In most bacteria and archaea, this process is assured by a broadly conserved mitotic-like apparatus in which a NTPase (ParA) displaces the partition complex. Competing observations and models imply starkly different 3D localization patterns of the components of the partition machinery during segregation. Here we use super-resolution microscopies to localize in 3D each component of the segregation apparatus with respect to the bacterial chromosome. We show that Par proteins locate within the nucleoid volume and reveal that proper volumetric localization and segregation of partition complexes requires ATPase and DNA-binding activities of ParA. Finally, we find that the localization patterns of the different components of the partition system highly correlate with dense chromosomal regions. We propose a new mechanism in which the nucleoid provides a scaffold to guide the proper segregation of partition complexes.

The Slow Mobility of the ParA Partitioning Protein Underlies Its Steady-State Patterning in Caulobacter

In bacteria, ParABS systems mediate intracellular transport of various cargos, including chromosomal regions in Caulobacter crescentus. Transport of the ParB/parS partition complex requires the DNA-binding activity of ParA, which transiently tethers the partition complex during translocation. In C. crescentus, the directionality of the transport is set up by a gradient of ParA whose concentration gradually increases from one end of the cell (old pole) to the other (new pole). Importantly, this ParA gradient is already observed before DNA replication and segregation are initiated when the partition complex is anchored at the old pole. How such micron-scale ParA pattern is established and maintained before the initiation of chromosome segregation has not been experimentally established. Although the stimulation of ParA ATPase activity by the localized ParB/parS partition complex is thought to be involved, this activity alone cannot quantitatively describe the ParA pattern observed inside cells. Instead, our experimental and theoretical study shows that the missing key component for achieving the experimentally observed steady-state ParA patterning is the slow mobility of ParA dimers (D ∼10−3μm2/s) due to intermittent DNA binding. Our model recapitulates the entire steady-state ParA distribution observed experimentally, including the shape of the gradient as well as ParA accumulation at the location of the partition complex. Stochastic simulations suggest that cell-to-cell variability in ParA pattern is due to the low ParA copy number in C. crescentus cells. The model also accounts for an apparent exclusion of ParA from regions with small spacing between partition complexes observed in filamentous cells. Collectively, our work demonstrates that in addition to its function in mediating transport, the conserved DNA-binding property of ParA has a critical function before DNA segregation by setting up a ParA pattern required for transport directionality.

The 6-strand braid group is CAT(0)

We show that braid groups with at most 6 strands are CAT(0) using the close connection between these groups, the associated non-crossing partition complexes and the embeddability of their diagonal links into spherical buildings of type A. Furthermore, we prove that the orthoscheme complex of any bounded graded modular complemented lattice is CAT(0), giving a partial answer to a conjecture of Brady and McCammond.