Lower bounds on multiple sequence alignment using exact 3-way alignment

Background  

Multiple sequence alignment is fundamental. Exponential growth in computation time appears to be inevitable when an optimal alignment is required for many sequences. Exact costs of optimum alignments are therefore rarely computed. Consequently much effort has been invested in algorithms for alignment that are heuristic, or explore a restricted class of solutions. These give an upper bound on the alignment cost, but it is equally important to determine the quality of the solution obtained. In the absence of an optimal alignment with which to compare, lower bounds may be calculated to assess the quality of the alignment. As more effort is invested in improving upper bounds (alignment algorithms), it is therefore important to improve lower bounds as well. Although numerous cost metrics can be used to determine the quality of an alignment, many are based on sum-of-pairs (SP) measures and their generalizations.     

一类具连续时滞的三种群互助模型正平衡态的渐近稳定性

本文研究了一类具连续时滞的三种群互助模型,利用上、下解方法及相应的单调迭代方法,获得了该系统存在唯一正常数平衡态及该平衡态是全局渐近稳定的结论,为讨论时滞三种群模型提供了一种有效方法,所得结果也适用于二种群互助模型及不含时滞和扩散项的互助模型,因而推广了已有的一些结论．     

A composite micromechanical model for connective tissues: Part II--Application to rat tail tendon and joint capsule.

A micromechanical model of fibrous soft tissue has been developed which predicts upper and lower bounds on mechanical properties based on the structure and properties of tissue components by Ault and Hoffman [3, 4]. In this paper, two types of biological tissue are modeled and the results compared to experimental test data. The highly organized structure of rat tail tendon is modeled using the upper bound aggregation rule which predicts uniform strain behavior in the composite material. This model fits the experimental data and results in a correlation coefficient of 0.98. Applied to cat knee joint capsule, the lower bound aggregation rule of the model correlates with the data and predicts uniform stress within this more loosely organized tissue structure. These studies show that the nature of the interactions between the components in tissue differs depending upon its structure and that the biomechanical model is capable of analyzing such differences in structure.     

The optimal configuration and workload allocation problem in flexible manufacturing systems

In this article we consider the problem of determining the minimum cost configuration (number of machines and pallets) for a flexible manufacturing system with the constraint of meeting a prespecified throughput, while simultaneously allocating the total workload among the machines (or groups of machines). Our procedure allows consideration of upper and lower bounds on the workload at each machine group. These bounds arise as a consequence of precedence constraints among the various operations and/or limitations on the number or combinations of operations that can be assigned to a machine because of constraints on tool slots or the space required to store assembly components. Earlier work on problems of this nature assumes that the workload allocation is given. For the single-machine-type problem we develop an efficient implicit enumeration procedure that uses fathoming rules to eliminate dominated configurations, and we present computational results. We discuss how this procedure can be used as a building block in solving the problem with multiple machine types.     

A quantitative model of cellular elasticity based on tensegrity

A tensegrity structure composed of six struts interconnected with 24 elastic cables is used as a quantitative model of the steady-state elastic response of cells, with the struts and cables representing microtubules and actin filaments, respectively. The model is stretched uniaxially and the Young's modulus (E0) is obtained from the initial slope of the stress versus strain curve of an equivalent continuum. It is found that E0 is directly proportional to the pre-existing tension in the cables (or compression in the struts) and inversely proportional to the cable (or strut) length square. This relationship is used to predict the upper and lower bounds of E0 of cells, assuming that the cable tension equals the yield force of actin (approximately 400 pN) for the upper bound, and that the strut compression equals the critical buckling force of microtubules for the lower bound. The cable (or strut) length is determined from the assumption that model dimensions match the diameter of probes used in standard mechanical tests on cells. Predicted values are compared to reported data for the Young's modulus of various cells. If the probe diameter is greater than or equal to 3 microns, these data are closer to the lower bound than to the upper bound. This, in turn, suggests that microtubules of the CSK carry initial compression that exceeds their critical buckling force (order of 10(0)-10(1) pN), but is much smaller than the yield force of actin. If the probe diameter is less than or equal to 2 microns, experimental data fall outside the region defined by the upper and lower bounds.     

Sensitivity of vertebral compressive strength to endplate loading distribution

The sensitivity of vertebral body strength to the distribution of axial forces along the endplate has not been comprehensively evaluated. Using quantitative computed tomography-based finite element models of 13 vertebral bodies, an optimization analysis was performed to determine the endplate force distributions that minimized (lower bound) and maximized (upper bound) vertebral strength for a given set of externally applied axial compressive loads. Vertebral strength was also evaluated for three generic boundary conditions: uniform displacement, uniform force, and a nonuniform force distribution in which the interior of the endplate was loaded with a force that was 1.5 times greater than the periphery. Our results showed that the relative difference between the upper and lower bounds on vertebral strength was 14.2 +/- 7.0% (mean +/- SD). While there was a weak trend for the magnitude of the strength bounds to be inversely proportional to bone mineral density (R2 = 0.32, p = 0.02), both upper and lower bound vertebral strength measures were well predicted by the strength response under uniform displacement loading conditions (R2 = 0.91 and R2 = 0.99, respectively). All three generic boundary conditions resulted in vertebral strength values that were statistically indistinguishable from the loading condition that resulted in an upper bound on strength. The results of this study indicate that the uncertainty in strength arising from the unknown condition of the disc is dependent on the condition of the bone (whether it is osteoporotic or normal). Although bone mineral density is not a good predictor of strength sensitivity, vertebral strength under generic boundary conditions, i.e., uniform displacement or force, was strongly correlated with the relative magnitude of the strength bounds. Thus, explicit disc modeling may not be necessary.     

Dielectric behavior of polyelectrolytes. III. The role of counterion interactions

The role of the Coulomb forces between the counterions on the surface of polyelectrolytes on the dielectric response is analyzed. An estimate of the maximum dielectric increment (as a function of the number of counterions) is found as a function of the molecular length. The minimum-energy configuration of the counterions on a cylinder is found to be a double helix, suggesting the fundamental importance of electrostatic interactions in determining structure. Solutions of the dynamical equations for a few counterions indicate that a single mode dominates the relaxation which is enhanced by the inter-ion repulsions. A lower bound is found for this mode based on analysis of the system response for short lengths. Sum rules for the rates and amplitudes of the dipolar correlation function are derived and lead to an upper bound for the rate of the dominant mode. These bounds approach one another for the parameters characteristic of restriction fragments of DNA. This permits a prediction of the magnitude and time scale of the dielectric response.     

Are moment bounds on the recombination fraction between a marker and a disease locus too good to be true? Allelic association mapping revisited for simple genetic diseases in the Finnish population.

In the past several years, allelic association has helped map a number of rare genetic diseases in the human genome. A commonly used upper bound on the recombination fraction between the disease gene and an associated marker is known to be biased downward, so there is the possibility that an investigator could be misled. This upper bound is based on a moment equation that can be derived within the context of a Poisson branching process, so its performance can be compared with a recently proposed likelihood bound. We show that the confidence level of the moment upper bound is much lower than expected, while the confidence level of the likelihood bound is in line with expectation. The effects of mutation at either the marker or disease locus on the upper bounds are also investigated. Results indicate that mutation is not an important force for typical mutation rates, unless the recombination fraction between the marker and disease locus is very small or the disease allele is very rare in the general population. Finally, the impact of sample size on the likelihood bound is investigated. The results are illustrated with data on 10 simple genetic diseased in the Finnish population.     

Bounds and inequalities relating h-index, g-index, e-index and generalized impact factor: an improvement over existing models

In this paper, we describe some bounds and inequalities relating h-index, g-index, e-index, and generalized impact factor. We derive the bounds and inequalities relating these indexing parameters from their basic definitions and without assuming any continuous model to be followed by any of them. We verify the theorems using citation data for five Price Medalists. We observe that the lower bound for h-index given by Theorem 2, [formula: see text], g ≥ 1, comes out to be more accurate as compared to Schubert-Glanzel relation h is proportional to C(2/3)P(-1/3) for a proportionality constant of 1, where C is the number of citations and P is the number of papers referenced. Also, the values of h-index obtained using Theorem 2 outperform those obtained using Egghe-Liang-Rousseau power law model for the given citation data of Price Medalists. Further, we computed the values of upper bound on g-index given by Theorem 3, g ≤ (h + e), where e denotes the value of e-index. We observe that the upper bound on g-index given by Theorem 3 is reasonably tight for the given citation record of Price Medalists.     

Estimating global arthropod species richness: refining probabilistic models using probability bounds analysis

A key challenge in the estimation of tropical arthropod species richness is the appropriate management of the large uncertainties associated with any model. Such uncertainties had largely been ignored until recently, when we attempted to account for uncertainty associated with model variables, using Monte Carlo analysis. This model is restricted by various assumptions. Here, we use a technique known as probability bounds analysis to assess the influence of assumptions about (1) distributional form and (2) dependencies between variables, and to construct probability bounds around the original model prediction distribution. The original Monte Carlo model yielded a median estimate of 6.1 million species, with a 90 % confidence interval of [3.6, 11.4]. Here we found that the probability bounds (p-bounds) surrounding this cumulative distribution were very broad, owing to uncertainties in distributional form and dependencies between variables. Replacing the implicit assumption of pure statistical independence between variables in the model with no dependency assumptions resulted in lower and upper p-bounds at 0.5 cumulative probability (i.e., at the median estimate) of 2.9–12.7 million. From here, replacing probability distributions with probability boxes, which represent classes of distributions, led to even wider bounds (2.4–20.0 million at 0.5 cumulative probability). Even the 100th percentile of the uppermost bound produced (i.e., the absolutely most conservative scenario) did not encompass the well-known hyper-estimate of 30 million species of tropical arthropods. This supports the lower estimates made by several authors over the last two decades.     

Analytical bounding functions for diffusion problems with michaelis-menten kinetics

Pointwise upper and lower bounds for the solution of a class of nonlinear diffusion problems with Michaelis-Menten kinetics are presented. Simple analytical bounding curves are obtained and for an illustrative case the calculated values bound the recent numerical solution of P. Hiltmann and P. Lory, 1983.Bull. math. Biol. 45, 661–664.     

Algorithms to distinguish the role of gene-conversion from single-crossover recombination in the derivation of SNP sequences in populations.

Meiotic recombination is a fundamental biological event and one of the principal evolutionary forces responsible for shaping genetic variation within species. In addition to its fundamental role, recombination is central to several critical applied problems. The most important example is "association mapping" in populations, which is widely hoped to help find genes that influence genetic diseases (Carlson et al., 2004; Clark, 2003). Hence, a great deal of recent attention has focused on problems of inferring the historical derivation of sequences in populations when both mutations and recombinations have occurred. In the algorithms literature, most of that recent work has been directed to single-crossover recombination. However, gene-conversion is an important, and more common, form of (two-crossover) recombination which has been much less investigated in the algorithms literature. In this paper, we explicitly incorporate gene-conversion into discrete methods to study historical recombination. We are concerned with algorithms for identifying and locating the extent of historical crossing-over and gene-conversion (along with single-nucleotide mutation), and problems of constructing full putative histories of those events. The novel technical issues concern the incorporation of gene-conversion into recently developed discrete methods (Myers and Griffiths, 2003; Song et al., 2005) that compute lower and upper-bound information on the amount of needed recombination without gene-conversion. We first examine the most natural extension of the lower bound methods from Myers and Griffiths (2003), showing that the extension can be computed efficiently, but that this extension can only yield weak lower bounds. We then develop additional ideas that lead to higher lower bounds, and show how to solve, via integer-linear programming, a more biologically realistic version of the lower bound problem. We also show how to compute effective upper bounds on the number of needed single-crossovers and gene-conversions, along with explicit networks showing a putative history of mutations, single-crossovers and gene-conversions. Both lower and upper bound methods can handle data with missing entries, and the upper bound method can be used to infer missing entries with high accuracy. We validate the significance of these methods by showing that they can be effectively used to distinguish simulation-derived sequences generated without gene-conversion from sequences that were generated with gene-conversion. We apply the methods to recently studied sequences of Arabidopsis thaliana, identifying many more regions in the sequences than were previously identified (Plagnol et al., 2006), where gene-conversion may have played a significant role. Demonstration software is available at www.csif.cs.ucdavis.edu/~gusfield.     

A composite micromechanical model for connective tissues: Part I--Theory.

A micromechanical model has been developed to study and predict the mechanical behavior of fibrous soft tissues. The model uses the theorems of least work and minimum potential energy to predict upper and lower bounds on material behavior based on the structure and properties of tissue components. The basic model consists of a composite of crimped collagen fibers embedded in an elastic glycosaminoglycan matrix. Upper and lower bound aggregation rules predict composite material behavior under the assumptions of uniform strain and uniform stress, respectively. Input parameters consist of the component material properties and the geometric configuration of the fibers. The model may be applied to a variety of connective tissue structures and is valuable in giving insight into material behavior and the nature of interactions between tissue components in various structures. Application of the model to rat tail tendon and cat knee joint capsule is described in a companion paper [2].     

A numerical study on the effect of the balance assumption in one-warehouse multi-retailer inventory systems

One-warehouse multi-retailer systems under periodic review have been studied extensively in the literature. The optimal policy has not been characterized yet. It would require solving a multi-dimensional dynamic program, which is hard due to the curse of dimensionality. In order to let the dynamic program decompose, researchers often make the so-called balance assumption. All available heuristics for periodic review distribution systems are based on some form of this assumption. For these heuristics, often further approximate steps are applied. We investigate the pure effect of the balance assumption in this paper. The balance assumption is the relaxation of a set of constraints in the original dynamic program and yields a lower bound model, which we solve exactly. This gives us a lower bound for the optimal cost of the original model. An upper bound for the true optimal cost is obtained by simulating the optimal policy for the relaxed problem with a slightly modified allocation rule. This modified policy is referred to as the LB heuristic policy. We use the relative gap between the upper and lower bound as a measure to assess the impact of the balance assumption. Based on extensive testing, we identify when the gap is small, and when not. For those instances with small gaps, both the lower bound is tight and the performance of the LB heuristic policy is close to the optimal. We also identify many practically relevant settings under which the balance assumption yields large gaps. For these instances, either the lower bound is poor or the LB heuristic policy is far from optimal, or both. In any case, it implies that more research is needed to develop better lower bounds and/or better heuristics for these instances.     

Theoretical and practical advances in genome halving

MOTIVATION: Duplication of an organism's entire genome is a rare but spectacular event, enabling the rapid emergence of multiple new gene functions. Over time, the parallel linkage of duplicated genes across chromosomes may be disrupted by reciprocal translocations, while the intra-chromosomal order of genes may be shuffled by inversions and transpositions. Some duplicate genes may evolve unrecognizably or be deleted. As a consequence, the only detectable signature of an ancient duplication event in a modern genome may be the presence of various chromosomal segments containing parallel paralogous genes, with each segment appearing exactly twice in the genome. The problem of reconstructing the linkage structure of an ancestral genome before duplication is known as genome halving with unordered chromosomes. RESULTS: In this paper, we derive a new upper bound on the genome halving distance that is tighter than the best known, and a new lower bound that is almost always tighter than the best known. We also define the notion of genome halving diameter, and obtain both upper and lower bounds for it. Our tighter bounds on genome halving distance yield a new algorithm for reconstructing an ancestral duplicated genome. We create a software package GenomeHalving based on this new algorithm and test it on the yeast genome, identifying a sequence of translocations for halving the yeast genome that is shorter than previously conjectured possible.     

Upper bounds on maximum likelihood for phylogenetic trees

We introduce a mechanism for analytically deriving upper bounds on the maximum likelihood for genetic sequence data on sets of phylogenies. A simple 'partition' bound is introduced for general models. Tighter bounds are developed for the simplest model of evolution, the two state symmetric model of nucleotide substitution under the molecular clock. This follows earlier theoretical work which has been restricted to this model by analytic complexity. A weakness of current numerical computation is that reported 'maximum likelihood' results cannot be guaranteed, both for a specified tree (because of the possibility of multiple maxima) or over the full tree space (as the computation is intractable for large sets of trees). The bounds we develop here can be used to conclusively eliminate large proportions of tree space in the search for the maximum likelihood tree. This is vital in the development of a branch and bound search strategy for identifying the maximum likelihood tree. We report the results from a simulation study of approximately 10(6) data sets generated on clock-like trees of five leaves. In each trial a likelihood value of one specific instance of a parameterised tree is compared to the bound determined for each of the 105 possible rooted binary trees. The proportion of trees that are eliminated from the search for the maximum likelihood tree ranged from 92% to almost 98%, indicating a computational speed-up factor of between 12 and 44.     

Expected waiting time for the visual response

Let the light-quanta be absorbed in the retina according to a Poisson process. The present paper derives bounds for the expected waiting time for an occurence of a visual response. These bounds can serve as control limits for a proposed coincidence threshold. An upper bound for the probability that a visual response has not occured in (O,t) is derived and is used to obtain an upper bound for the mean visual threshold.     

Capacity optimization of flexible manufacturing systems under budget constraints

The capacity of a flexible manufacturing system (FMS) is optimized with the objective to maximize the system's throughput, while a budget constraint is considered. Decisions are performed on the capacity of machine groups (sets of identical machines), the transportation system and, in case of a significant cost impact, the number of pallets in the system. Throughput evaluation is achieved either by an open finite queueing network or by a closed queueing network if the number of pallets is included in the decision process. For both cases the solution procedure is based on the marginal allocation scheme.     

Measures and limits of models of fixation selection

Models of fixation selection are a central tool in the quest to understand how the human mind selects relevant information. Using this tool in the evaluation of competing claims often requires comparing different models' relative performance in predicting eye movements. However, studies use a wide variety of performance measures with markedly different properties, which makes a comparison difficult. We make three main contributions to this line of research: First we argue for a set of desirable properties, review commonly used measures, and conclude that no single measure unites all desirable properties. However the area under the ROC curve (a classification measure) and the KL-divergence (a distance measure of probability distributions) combine many desirable properties and allow a meaningful comparison of critical model performance. We give an analytical proof of the linearity of the ROC measure with respect to averaging over subjects and demonstrate an appropriate correction of entropy-based measures like KL-divergence for small sample sizes in the context of eye-tracking data. Second, we provide a lower bound and an upper bound of these measures, based on image-independent properties of fixation data and between subject consistency respectively. Based on these bounds it is possible to give a reference frame to judge the predictive power of a model of fixation selection. We provide open-source python code to compute the reference frame. Third, we show that the upper, between subject consistency bound holds only for models that predict averages of subject populations. Departing from this we show that incorporating subject-specific viewing behavior can generate predictions which surpass that upper bound. Taken together, these findings lay out the required information that allow a well-founded judgment of the quality of any model of fixation selection and should therefore be reported when a new model is introduced.     

Pointwise bounds for the solution of a nonlinear problem in cell membrane theory

Pointwise upper and lower bounds for the solution of a class of nonlinear problems arising in the steady-state finite cable model of cell membranes are presented. Simple analytical bounding curves are obtained for an illustrative example in the theory of nerve membranes.