Chain Partitioning Research Articles

Inferring B Cell Phylogenies from Paired H and L Chain BCR Sequences with Dowser.

Abs are vital to human immune responses and are composed of genetically variable H and L chains. These structures are initially expressed as BCRs. BCR diversity is shaped through somatic hypermutation and selection during immune responses. This evolutionary process produces B cell clones, cells that descend from a common ancestor but differ by mutations. Phylogenetic trees inferred from BCR sequences can reconstruct the history of mutations within a clone. Until recently, BCR sequencing technologies separated H and L chains, but advancements in single-cell sequencing now pair H and L chains from individual cells. However, it is unclear how these separate genes should be combined to infer B cell phylogenies. In this study, we investigated strategies for using paired H and L chain sequences to build phylogenetic trees. We found that incorporating L chains significantly improved tree accuracy and reproducibility across all methods tested. This improvement was greater than the difference between tree-building methods and persisted even when mixing bulk and single-cell sequencing data. However, we also found that many phylogenetic methods estimated significantly biased branch lengths when some L chains were missing, such as when mixing single-cell and bulk BCR data. This bias was eliminated using maximum likelihood methods with separate branch lengths for H and L chain gene partitions. Thus, we recommend using maximum likelihood methods with separate H and L chain partitions, especially when mixing data types. We implemented these methods in the R package Dowser: https://dowser.readthedocs.io.

LATTICE TILINGS OF A PLANE BY POLYOMINOS AND MOLECULAR LAYERS IN CRYSTAL STRUCTURES. STRUCTURAL CLASS CM, Z = 2(M)

Lattice partitions of a plane into polyominoes were constructed for N from 3 to 12, where N is the order of the packing space. We obtained 5191 symmetric independent lattice partitions of a plane with one polyomino in a reduced (primitive) cell, among which 122 variants belong to the structural class cm, Z = 2(m), with the elementary conventional cell being rectangular (centered). Chain partitions of planes have been derived, for which both structural class and structural subclass were identified. The results of the analysis of lattice partitions of a plane into polyominoes were illustrated with examples of real molecular layers in crystal structures.

Improved lower bound on the on-line chain partitioning of semi-orders with representation

An on-line chain partitioning algorithm receives a poset, one element at a time, and irrevocably assigns the element to one of the chains in the partition. The on-line chain partitioning problem involves finding the minimal number of chains needed by an on-line algorithm. Chrobak and Ślusarek considered variants of the on-line chain partitioning problem in which the elements are presented as intervals and intersecting intervals are incomparable. They constructed an on-line algorithm which uses at most 3w−2 chains, where w is the width of the interval order, and showed that this algorithm is optimal. They also considered the problem restricted to intervals of unit-length and while they showed that first-fit needs at most 2w−1 chains, over 30 years later, it remains unknown whether this is an optimal algorithm. In this paper, we improve upon previously known bounds and show that any on-line algorithm can be forced to use ⌈32w⌉ chains to partition an order presented in the form of its unit interval representation. As a consequence, we completely solve the problem for w=3. Lastly, we show that loosening the restriction from unit intervals to proper intervals in the bandwidth variant allows us to improve the lower bound by w/3.

Improved Lower Bounds on the On-line Chain Partitioning of Posets of Bounded Dimension

Improved Lower Bounds on the On-line Chain Partitioning of Posets of Bounded Dimension

Chain enumeration, partition lattices and polynomials with only real roots

The coefficients of the chain polynomial of a finite poset enumerate chains in the poset by their number of elements. The chain polynomials of the partition lattices and their standard type \(B\) analogues are shown to have only real roots. The real-rootedness of the chain polynomial is conjectured for all geometric lattices and is shown to be preserved by the pyramid and the prism operations on Cohen-Macaulay posets. As a result, new families of convex polytopes whose barycentric subdivisions have real-rooted \(f\)-polynomials are presented. An application to the face enumeration of the second barycentric subdivision of the boundary complex of the simplex is also included.Mathematics Subject Classifications: 05A05, 05A18, 05E45, 06A07, 26C10Keywords: Chain polynomial, geometric lattice, partition lattice, real-rooted polynomial, flag \(h\)-vector, convex polytope, barycentric subdivision

Measurement and modelling of the intra-particle diffusion and b-term in reversed-phase liquid chromatography

In an ongoing effort to better understand the underlying mechanisms of band broadening in particle-packed reversed-phase liquid chromatography columns, new models for intra-particle diffusion, representing an adsorption- and partition-type retention behavior, are proposed. These models assume the mesoporous zone inside the particles is subdivided in four distinct regions: a fraction f1 filled with bulk mobile phase, a fraction f2 enriched in pure organic modifier extending outside the stationary phase layer, a fraction f3 comprising the liquid surrounding the alkyl chains and a fraction f4 consisting of the stationary phase alkyl chains. Intra-particle diffusion is calculated as a residence time weighted average of the diffusion in these different regions.Experimental procedures and models are proposed to determine the volumes of these four regions and applied to three reversed-phase liquid chromatography columns with different pore sizes (80 Å versus 300 Å) and different stationary phase types (C18 versus C8). The newly proposed models are then applied to predict the intra-particle diffusion of butyrophenone across a wide range of retention factors (1 ≤ k” ≤ 40) in each of these columns. These predictions are compared to experimental data that are extracted from the effective diffusion coefficients of butyrophenone obtained via peak parking experiments.It is demonstrated that both adsorption- and partition-type models for intra-particle diffusion model the actual behavior of the test compound well, and require the determination of only one (partition) or two (adsorption) fitting factors: the obstruction to free movement the analytes experience from the alkyl chains in the retained state (partition and adsorption) and in the unretained state (adsorption). Finally, it is demonstrated that the major contributor to the intra-particle diffusion of retained compounds (k” > 2) is the diffusion these analytes undergo when retained in the organic-modifier enriched zone surrounding the alkyl chains (partition model) or when adsorbed onto the alkyl chains (adsorption model), confirming that surface diffusion plays an important role in the mass transfer of retained compounds in reversed-phase liquid chromatography columns.

On-line partitioning of width [formula omitted] posets into [formula omitted] chains

An on-line chain partitioning algorithm receives the elements of a poset one at a time, and when an element is received, irrevocably assigns it to one of the chains. In this paper, we present an on-line algorithm that partitions posets of width w into wO(loglogw) chains. This improves over previously best known algorithms using wO(logw) chains by Bosek and Krawczyk and by Bosek, Kierstead, Krawczyk, Matecki, and Smith. Our algorithm runs in wO(w)n time, where w is the width and n is the size of a presented poset.

A Dichotomy Theorem for First-Fit Chain Partitions

First-Fit is a greedy algorithm for partitioning the elements of a poset into chains. Let $\mathrm{FF}(w,Q)$ be the maximum number of chains that First-Fit uses on a $Q$-free poset of width $w$. A result due to Bosek, Krawczyk, and Matecki states that $\mathrm{FF}(w,Q)$ is finite when $Q$ has width at most $2$. We describe a family of posets $\mathcal{Q}$ and show that the following dichotomy holds: if $Q\in\mathcal{Q}$, then $\mathrm{FF}(w,Q) \le 2^{c(\log w)^2}$ for some constant $c$ depending only on $Q$, and if $Q\not\in\mathcal{Q}$, then $\mathrm{FF}(w,Q) \ge 2^w - 1$.

A scalable network-aware framework for cloud monitoring orchestration

Monitoring components are implanted in clouds to evaluate performance, detect the failures, and assess component interactions by message analysis. In this paper, we propose Monitoring as a Service (MaaS) installed across its software defined network in the cloud. All switches in datacenter only forward traffic. Specific SDN application on top of the network controller has been implemented in order to orchestrate multiple network tenants monitoring needs. Applications declare the required observation for traffics and their specific monitoring needs to the Maas. Therefore, a set of virtual monitoring functions (vMF) are prescribed to be placed in datacenter for flows. An optimal placement algorithm places vMF with respect to the network and computing utilization maximization objectives. Network objective refers to minimize traffic delay for flows needed to be monitored and computing objective expresses balancing nodes computing resources. The optimal placement of virtual network functions is known to be an NP-hard problem. Compared to the existing work, we discovered different problem which how a vMF can be split into smaller pieces to decrease the total placement cost for a set of flows required, based on four patterns: free, parser-collocation, job-collocation, and full-collocation. Moreover, we proposed three heuristics to make our placement algorithm scalable for a large network, called, chain partitioning, topology partitioning, and zoning. We show the feasibility of our approach in a large dataset consists of 540k nodes and 11.5M edges, with about 40 requests (flows) at the same time. Furthermore, the proposed solution saves at least 20 percent of total monitoring cost, in average, compared to the latest related work.

On-Chip Self-Test Methodology With All Deterministic Compressed Test Patterns Recorded in Scan Chains

This paper presents a novel test architecture that combines the advantages of high-quality deterministic scan-based test and low-cost built-in self-test. The main idea is to record (store) all required compressed test data in a novel scan chain structure, and extract and decompress them during testing. This requires a very high compression ratio to obtain a low test data volume, that is, smaller than the number of scan cells in the circuit under test. To achieve such a high compression ratio, we propose a novel compression method that combines broadcast scan as well as a tailored single-input compression architecture. We also utilize the concept of scan chain partitioning and clock gating to reduce the test time and test power. An on-chip test controller is employed to automatically generate all required control signals for the whole test procedure. This significantly reduces the requirements on external automatic test equipment. Experimental results show that our method is well suitable for multicore designs. For example, experiments on the 8-core open-source OpenSPARC T2 processor with 5.7M gates show that all required test data for 100% testable stuck-at fault coverage can be stored in just 59.4% of the scan cells of the processor. Experimental results for transition faults are also presented, which show that more identical cores are needed in order to store all test data for transition faults. We also discuss how to extend this paper to address fault diagnosis and engineering change order problems.

Inverse Langevin-like function for statistical description of the polymer chain in orienting fields

The inverse Langevin-like function in the presence of an orienting field is calculated via inversion of the exact, numerically calculated Langevin-like function and/or inversion of its Taylor representation. This representation is obtained using the cumulant method for the natural logarithm of the chain partition function. As a result, a power series representation of the inverse function is obtained. A simple algorithm is formulated for the calculation of this series. The chain free energy and the deformation work and force are calculated. For various strengths of the field and relative orientations of the chain end-to-end distance and the orienting field direction, the convergence of results obtained by using of the exact inverse Langevin-like function or its Taylor representation is discussed.

Anomalous packing and dynamics of a polymer chain confined in a static porous environment.

Polymers in confined porous environments are ubiquitous throughout biology, physics, materials science, and engineering. Several experiments have suggested that in some porous environments, chain dynamics can become extremely slow. While phenomenological explanations exist, the exact mechanisms for these slow dynamics have not been fully characterized. In this work, we initiate a joint simulation-theory study to investigate chain packing and dynamics in a static porous environment. The main theoretical concept is the free energy of the chain partitioning into several chambers of the porous environment. Both the theoretical results and Langevin dynamics simulations show that chain packing in each of the chambers is predominantly independent of chain length; it is determined by the maximal packing of segments in each chamber. Dynamically, short chains (compared to the chamber size) become trapped in a single chamber and dynamics become extremely slow, characteristic of an Ogston sieving-like behavior. For longer chains, on the other hand, a hierarchy of slow dynamics is observed due to entropic trapping, characterized by sub-diffusive behavior and a temporary plateau in the mean square displacement. Due to the slow nature of the dynamics, the inevitable long-time diffusive behavior of the chains is not captured by our simulations. Theoretically, the slow dynamics are understood in terms of a free energy barrier required to thread the chain from one chamber to the next. There is overall qualitative and quantitative agreement between simulations and theory. This work provides foundations for a better understanding of how chain dynamics are affected by porous environments.

Randomized testing of distributed systems with probabilistic guarantees

Several recently proposed randomized testing tools for concurrent and distributed systems come with theoretical guarantees on their success. The key to these guarantees is a notion of bug depth—the minimum length of a sequence of events sufficient to expose the bug—and a characterization of d -hitting families of schedules—a set of schedules guaranteed to cover every bug of given depth d . Previous results show that in certain cases the size of a d -hitting family can be significantly smaller than the total number of possible schedules. However, these results either assume shared-memory multithreading, or that the underlying partial ordering of events is known statically and has special structure. These assumptions are not met by distributed message-passing applications. In this paper, we present a randomized scheduling algorithm for testing distributed systems. In contrast to previous approaches, our algorithm works for arbitrary partially ordered sets of events revealed online as the program is being executed. We show that for partial orders of width at most w and size at most n (both statically unknown), our algorithm is guaranteed to sample from at most w 2 n d −1 schedules, for every fixed bug depth d . Thus, our algorithm discovers a bug of depth d with probability at least 1 / ( w 2 n d −1 ). As a special case, our algorithm recovers a previous randomized testing algorithm for multithreaded programs. Our algorithm is simple to implement, but the correctness arguments depend on difficult combinatorial results about online dimension and online chain partitioning of partially ordered sets. We have implemented our algorithm in a randomized testing tool for distributed message-passing programs. We show that our algorithm can find bugs in distributed systems such as Zookeeper and Cassandra, and empirically outperforms naive random exploration while providing theoretical guarantees.

Mapping Coexistence Phase Diagrams of Block Copolymer Micelles and Free Unimer Chains

Block copolymer micelles can carry molecular cargo in a nanoscopic package that is tunable via polymer structure in combination with cargo and/or solution properties. We use NMR spectroscopy and diffusometry to investigate spherical micelles that self-assemble from diblock poly(ethylene oxide)-b-(ε-caprolactone) (PEO–PCL) at 1% w/v in D2O–THF-d8 mixed solvents. For two series of micelles with block masses of 2 and 3 kg/mol (PEO and PCL, respectively) and 5 and 8 kg/mol, we quantify diffusion coefficients and relative populations of micelles and free unimers over a range of temperatures (21–50 °C) and solvent compositions (10–100 vol % THF-d8). Micelles and free unimers coexist over surprisingly large areas of these micelle–unimer phase diagrams and with a large variation of relative populations. This study provides a new avenue for understanding how inter- and intramolecular interactions fundamentally affect unimer exchange, cargo release, the thermodynamics of chain partitioning, and the tuning of micelle structure and dynamics.

Mitigating Observability Loss of Toggle-Based X-Masking via Scan Chain Partitioning

The Toggle-based X -masking method requires a single toggle at a given cycle, there is a chance that non- X values are also masked. Hence, the non- X value over-masking problem may cause a fault coverage degradation. In this paper, a scan chain partitioning scheme is described to alleviate non- X bit over-masking problem arising from Toggle-based X -Masking method. The scan chain partitioning method finds a scan chain combination that gives the least toggling conflicts. The experimental results show that the amount of over-masked bits is significantly reduced, and it is further reduced when the proposed method is incorporated with X -canceling method. However, as the number of scan chain partitions increases, the control data for decoder increases. To reduce a control data overhead, this paper exploits a Huffman coding based data compression. Assuming two partitions, the size of control bits is even smaller than the conventional X -toggling method that uses only one decoder. In addition, selection rules of X -bits delivered to X -Canceling MISR are also proposed. With the selection rules, a significant test time increase can be prevented.

An Easy Subexponential Bound for Online Chain Partitioning

Bosek and Krawczyk exhibited an online algorithm for partitioning an online poset of width $w$ into $w^{14\lg w}$ chains. We improve this to $w^{6.5 \lg w + 7}$ with a simpler and shorter proof by combining the work of Bosek & Krawczyk with work of Kierstead & Smith on First-Fit chain partitioning of ladder-free posets. We also provide examples illustrating the limits of our approach.

Nutritive value of cowpea fodder cultivars and their effect on nutrients intake, digestibility and nitrogen balance in sheep

Three cowpea fodder varieties (BL-1, BL-2 and BL-4) developed by IGFRI were evaluated against check Kohinoor for their nutritional attributes by in vitro and in vivo means. Varieties were grown under identical agronomic practices in Kharif 2016 and animal feeding was started at flower initiation stage. For feeding trial, 20 growing sheep (mean body weight 19.85±0.45 kg) were randomly distributed to 4 varieties (Kohinoor, BL-1, BL-2 and BL- 4) with 5 animals to each. After 3 weeks of feeding, a digestion cum- metabolism trial was conducted to assess the nutrients intake, digestibility and nitrogen balance in sheep. The cowpea fodder varieties CP, NDF and lignin contents differed and values ranged between 22.23–23.41, 50.54–55.10 and 8.48–10.76%, respectively. Protein and carbohydrate fractions of cowpea varieties were similar except the NSC (% DM) and CC (% CHO) which were lower and higher, respectively in BL-2. Cowpea varieties energy values as TDN, DE, NEL, NEM and NEG were identical. In vitro gas and methane production (ml/g DM) was lower from Kohinoor (86.57 and 10.67) and BL-2 (90.79 and 11.40) than BL-1 (104.83 and 13.96) and BL-4 (98.86 and 13.08), respectively. Short chain fatty acids, partition factor and efficiency for microbial production differed significantly amongst the cowpea varieties. Sheep DM, CP and ME intake (% body wt and g/kg W0.75) was comparable on evaluated cowpea varieties. Digestibility of DM, OM and CP in sheep was similar on cowpea varieties; however, NDF and ADF digestibility tended to be lower of BL-4 (63.88 and 61.70%) than BL-2. Sheep nitrogen balance was identical on all the cowpea varieties and ranged between 16.92–18.32 g/d. Cowpea varieties DCP and DE contents were similar and ranged between 18.36– 20.30% and 13.63–14.72 kjoules/g DM, respectively. Results showed that nutritive value of cowpea varieties differed significantly in terms of CP, NDF, NSC%DM, fermentation pattern, and cell wall (NDF and ADF) digestibility.

Perfect Phylogenies via Branchings in Acyclic Digraphs and a Generalization of Dilworth’s Theorem

Motivated by applications in cancer genomics and following the work of Hajirasouliha and Raphael (WABI 2014), Hujdurović et al. (IEEE TCBB, 2018) introduced the minimum conflict-free row split (MCRS) problem: split each row of a given binary matrix into a bitwise OR of a set of rows so that the resulting matrix corresponds to a perfect phylogeny and has the minimum possible number of rows among all matrices with this property. Hajirasouliha and Raphael also proposed the study of a similar problem, in which the task is to minimize the number of distinct rows of the resulting matrix. Hujdurović et al. proved that both problems are NP-hard, gave a related characterization of transitively orientable graphs, and proposed a polynomial-time heuristic algorithm for the MCRS problem based on coloring cocomparability graphs. We give new, more transparent formulations of the two problems, showing that the problems are equivalent to two optimization problems on branchings in a derived directed acyclic graph. Building on these formulations, we obtain new results on the two problems, including (1) a strengthening of the heuristic by Hujdurović et al. via a new min-max result in digraphs generalizing Dilworth’s theorem, which may be of independent interest; (2) APX-hardness results for both problems; (3) approximation algorithms; and (4) exponential-time algorithms solving the two problems to optimality faster than the naïve brute-force approach. Our work relates to several well-studied notions in combinatorial optimization: chain partitions in partially ordered sets, laminar hypergraphs, and (classical and weighted) colorings of graphs.

Allosteric Activation of Unliganded AChRs: Multiple, Bumpy Pathways

Acetylcholine receptors (AChRs) are allosteric proteins that isomerize (‘gates’) between resting and active conformations. We used single-channel electrophysiology to study gating of mouse adult-type endplate AChRs in the absence of agonists (free energy change, ΔG0). Many different point mutations in AChRs change ΔG0. For pairs of mutations, the net change in ΔG0 was about the same as the sum of the individual changes, indicating that mutations were independent and had mostly local effects. By correlating changes in ΔG0 with side chain partition coefficients, we could infer the hydrophobicity and volume of each residue's local environment. The kinetics of unliganded gating is complex, but was explained by schemes having 3-shut and 2-open states that all produced the same ΔG0. The longest-lived open component was eliminated by some mutations (aromatic residues at the agonist-binding site and in M1) and α-conotoxin (a specific blocker of the α-δ binding site), without affecting ΔG0. This suggests that long-lived unliganded openings are outside of the main activation sequence. In diliganded gating, in the α subunit there is a coarse-grained gradient in gating ϕ values (a conformational ‘wave’) that is less distinct in unliganded gating. Furthermore, without agonists the relative position of the gating transition state was more malleable compared to with agonists (larger Hammond shifts). The degree of shift (dϕ/dΔG0) was a function of the residue ϕ-value, and was largest at ϕ∼0.5. We hypothesize that without agonists, there are multiple activation pathways that traverse a rugged potential energy surface.

Low Latency Security Function Chain Embedding Across Multiple Domains

5G network is envisioned to provide massive connectivity for a wide range of applications, such as ultra-clear media, internet of vehicles, and smart home. The traditional way of providing security services is difficult to support these new 5G applications flexibly and effectively. In our previous work, we proposed a SFC-based framework that chains security functions in different domains to provide security services on demand. However, creating cross-domain service function chains will inevitably result in the additional network latency. In this paper, we study this problem of minimizing the end-to-end latency when deploying cross-domain service function chains for 5G applications. First, an exact approach, consisting of service chain partition and service subchain embedding, is proposed to derive an optimal solution for cross-domain service function chain placement. Second, we improve the Viterbi algorithm and propose an efficient heuristic approach to derive near-optimal solutions for large networks. We also compare the performance of the proposed exact approach, the proposed heuristic approach, and the simple greedy approach in different scales of network infrastructures. Simulation results are presented to demonstrate the effectiveness of the proposed approaches.