Number Of Possible Sequences Research Articles

A Mathematical Connection Between Single-Elimination Sports Tournaments and Evolutionary Trees

Summary How many ways are there to arrange the sequence of games in a single-elimination sports tournament? We consider the connection between this enumeration problem and the enumeration of “labeled histories,” or sequences of asynchronous branching events, in mathematical phylogenetics. The possibility of playing multiple games simultaneously in different arenas suggests an extension of the enumeration of labeled histories to scenarios in which multiple branching events occur simultaneously. We provide a recursive result enumerating game sequences and labeled histories in which simultaneity is allowed. For a March Madness basketball tournament of 68 labeled teams, the number of possible sequences of games is ∼ 1.91 × 10 78 if arbitrarily many arenas are available, but only ∼ 3.60 × 10 68 if all games must be played sequentially in the same arena.

Discrete production workstation with two types of imperfect items: determining the optimal promise time

This paper presents a discrete production system where units are manufactured and reworked, if needed, one at a time using the same resources. Examples of these systems include products that involve extensive manual operations such as welding or manual assembly of intricate items. This industrial setting is not discussed in the literature. The major difficulty in studying these systems is the huge number of possible sequences of conforming and non-conforming units. This paper presents a very efficient approach to analyse these systems. We generate the system statistics for short production periods. In order to study the long-term behaviour of system statistics, we introduce renewal cycles. A major issue facing a manufacturer using these systems is determining the time it takes to produce a given customer order which is called promise time. This paper aims to find the optimal promise time that maximises the expected profit. Numerical experiments show that the expected profit is inversely proportional to the processing times. In addition, the expected profit is sensitive to the parameters; a change of ± 0.05 in the probability of having a conforming unit may result in a 25% change in the expected profit.

A quantum walks assisted algorithm for peptide and protein folding prediction

Proteins are considered as the working force of cells. Their functionality is determined by their spatial form. In 1973 Anfinsen proposed that the spatial form is determined by the sequence of amino acids in the protein backbone. Yet, the number of possible sequences as well as the possible configurations is very large, making the task of predicting the protein's spatial form very difficult. Many approaches have been proposed, both classical and hybrid quantum – classical ones. We propose a novel hybrid algorithm. In our approach we utilized quantum walks, a proven model for universal quantum computation. We considered a simplified version of the protein backbone to be the evolution space of the quantum walk. The dihedral angles φ and ψ are introduced as phase factors to the quantum walk evolution. We also utilized a cost function to describe the system, where the R – chain, describing the specific amino acid, corresponds to a discrete value, affecting the cost functions value. Our aim is to minimize the cost function value, by updating the dihedral angles for specific regions of the Ramachandran plot, using a Metropolis algorithm.

Innovation versus novelty in microbial systems.

Innovation versus novelty in microbial systems.

Sequence‐defined Pareto frontier of a copolymer structure

AbstractThe correlations between the sequence of monomers in a macromolecule and its three‐dimensional (3D) structure is a grand challenge in polymer science. The properties and functions of macromolecules depend on their 3D shape that has appeared to be dictated by their monomer sequence. However, the progress towards understanding the sequence–structure‐property correlations and their utilization in materials engineering are slow because it is almost impossible to characterize an astronomically large number of possible sequences of a copolymer using traditional experimental and simulation methods. To address this problem, here, we combine evolutionary computing and coarse‐grained molecular dynamics (CGMD) simulation and study the sequence‐structure correlations of a model AB‐type copolymer in a solution and assess the impact of sequence on the packing density in its bulk phase. The CGMD‐based evolutionary algorithm (EA) screens the sequence space of a single chain copolymer efficiently and identifies a wide range of single‐molecule structures including extremal radii of gyration. The data are utilized to estimate the Pareto front of the structure‐space of a binary copolymer as a function of its composition. The monomer packings in single‐molecule solution phase and multimolecular bulk phase are found to be identical. The work highlights the opportunities of sequence‐specific control of macromolecular structure for designing target materials.

Optimizing Cycle Time of Industrial Robotic Tasks with Multiple Feasible Configurations at the Working Points

Industrial robot applications should be designed to allow the robot to provide the best performance for increasing throughput. In this regard, both trajectory and task order optimization are crucial, since they can heavily impact cycle time. Moreover, it is very common for a robotic application to be kinematically or functionally redundant so that multiple arm configurations may fulfill the same task at the working points. In this context, even if the working cycle is composed of a small number of points, the number of possible sequences can be very high, so that the robot programmer usually cannot evaluate them all to obtain the shortest possible cycle time. One of the most well-known problems used to define the optimal task order is the Travelling Salesman Problem (TSP), but in its original formulation, it does not allow to consider different robot configurations at the same working point. This paper aims at overcoming TSP limitations by adding some mathematical and conceptual constraints to the problem. With such improvements, TSP can be used successfully to optimize the cycle time of industrial robotic tasks where multiple configurations are allowed at the working points. Simulation and experimental results are presented to assess how cost (cycle time) and computational time are influenced by the proposed implementation.

Modelling peptide adsorption energies on gold surfaces with an effective implicit solvent and surface model

The interaction of proteins and peptides with inorganic surfaces is relevant in a wide array of technological applications. A rational approach to design peptides for specific surfaces would build on amino-acid and surface specific interaction models, which are difficult to characterize experimentally or by modeling. Even with such a model at hand, the large number of possible sequences and the large conformation space of peptides make comparative simulations challenging. Here we present a computational protocol, the effective implicit surface model (EISM), for efficient in silico evaluation of the binding affinity trends of peptides on parameterized surface, with a specific application to the widely studied gold surface. In EISM the peptide surface interactions are modeled with an amino-acid and surface specific implicit solvent model, which permits rapid exploration of the peptide conformational degrees of freedom. We demonstrate the parametrization of the model and compare the results with all-atom simulations and experimental results for specific peptides.

The identification and characterisation of novel bioactive peptides derived from porcine liver

Bioactive peptides (BAPs) can be derived from a variety of sources; these could be from dietary proteins which are then broken down in the gastrointestinal tract to release BAPs, or they can be isolated from various sources ex vivo. Sources include plant-based proteins such as soy, and chickpeas, and animal proteins from waste from the meat industry and from fish skin. Bioinformatics is also a useful approach to assess the peptides released from digests due to the great number of possible sequences that can be isolated from proteins. Therefore, an in silico analysis of peptides could potentially lead to a more rapid discovery of BAPs. This article investigates a “crude” liver peptide mixture derived from papain hydrolysis of porcine liver and purified peptides derived from the hydrolysates following HPLC fractionation and in silico digestion of the host proteins identified using LC-MS/MS. This allowed the identification of two proteins (cytosol aminopeptidase and haemoglobin subunit alpha) present in the “crude” mixture after LC-MS/MS. In silico hydrolysis of these proteins identified that several peptides were predicted to be both present in the crude mixture using the BIOPEP database and to have potential bioactivity using the Peptide Ranker tool. Peptides (FWG, MFLG and SDPPLVFVG) with the greatest potential bioactivity and which had not previously been reported in the literature were then synthesised. The results indicated that the predicted bioactivity of the synthetic peptides would likely include antioxidant activity. FWG and MFLG derived from the in silico papain hydrolysis of cytosol aminopeptidase showed activity better or comparable to Trolox in the Oxygen Radical Absorbance Capacity (ORAC) assay. The use of these in silico tools, alongside a robust range of biochemical assays which cover a wider range of bioactivities would be a way of improving the discovery of novel bioactive peptides.

An Optimal Robotic Assembly Sequence Planning by Assembly Subsets Detection Method Using Teaching Learning-Based Optimization Algorithm

In recent days, many interacted shape products have been developed by manufacturing industries for different applications in various fields such as defense, aerospace, and space centers. In manufacturing, 30% of time consumption is due to assembly operation compared with the remaining processes in manufacturing. It is very difficult to get optimal sequence because assembly sequence planning is a multimodel optimization problem. As the number of parts in the assembly increases, the possible number of sequences increases exponentially therefore obtaining the optimal assembly sequence becomes more difficult and time consuming. There exist many mathematical algorithms to obtain optimal assembly sequences. But, recent studies state that they perform poorly when it comes to multiobjective optimal assembly sequence. In recent years, researchers have developed several soft computing-based algorithms for solving assembly sequence problems. In this paper, assembly subset detection method has been introduced. The proposed method is applied for the first time to solve assembly sequence problems. This method eliminates those assembly sets that have more directional changes and require more energy. The method is compared with other algorithms, namely, genetic algorithm (GA), enhanced GA, ant colony optimization (ACO), memetic algorithm, imperialistic harmonic search algorithm, and flower pollination algorithm (FPA), and is found to be successful in achieving the optimal assembly sequence for an industrial product with smaller number of iterations. Note to Practitioners —This paper is motivated by the redesign of helicopter cowling of a Canadian aircraft company using concepts of design for assembly. Though we could reduce the number of parts using advanced composite materials and manufacturing processes, obtaining a feasible assembly for the new assembly structure required a lot of computation time. Hence, the researchers studied the existing literature on assembly sequence generation methods and their limitations, and came up with efficient automated optimal sequence generation method.

Building neural network language model with POS-based negative sampling and stochastic conjugate gradient descent

Traditional statistical language model is a probability distribution over sequences of words. It has the problem of curse of dimensionality incurred by the exponentially increasing number of possible sequences of words in training text. To solve this issue, neural network language models are proposed by representing words in a distributed way. Due to computation cost on updating a large number of word vectors’ gradients, neural network model needs much training time to converge. To alleviate this problem, in this paper, we propose a gradient descent algorithm based on stochastic conjugate gradient to accelerate the convergence of the neural network’s parameters. To improve the performance of the neural language model, we also propose a negative sampling algorithm based on POS (part of speech) tagging, which can optimize the negative sampling process and improve the quality of the final language model. A novel evaluation model is also used with perplexity to demonstrate the performance of the improved language model. Experiment results prove the effectiveness of our novel methods.

How Many Protein Sequences Fold to a Given Structure? A Coevolutionary Analysis

Quantifying the relationship between protein sequence and structure is key to understanding the protein universe. A fundamental measure of this relationship is the total number of amino acid sequences that can fold to a target protein structure, known as the “sequence capacity,” which has been suggested as a proxy for how designable a given protein fold is. Although sequence capacity has been extensively studied using lattice models and theory, numerical estimates for real protein structures are currently lacking. In this work, we have quantitatively estimated the sequence capacity of 10 proteins with a variety of different structures using a statistical model based on residue-residue co-evolution to capture the variation of sequences from the same protein family. Remarkably, we find that even for the smallest protein folds, such as the WW domain, the number of foldable sequences is extremely large, exceeding the Avogadro constant. In agreement with earlier theoretical work, the calculated sequence capacity is positively correlated with the size of the protein, or better, the density of contacts. This allows the absolute sequence capacity of a given protein to be approximately predicted from its structure. On the other hand, the relative sequence capacity, i.e., normalized by the total number of possible sequences, is an extremely tiny number and is strongly anti-correlated with the protein length. Thus, although there may be more foldable sequences for larger proteins, it will be much harder to find them. Lastly, we have correlated the evolutionary age of proteins in the CATH database with their sequence capacity as predicted by our model. The results suggest a trade-off between the opposing requirements of high designability and the likelihood of a novel fold emerging by chance.

Creation of Recombinant Antibodies: Using 5'-RACE to Amplify Immunoglobulin Sequences.

Modern molecular biology techniques have been applied to the production of therapeutic antibodies. Nonetheless, recombinant antibodies remain the exception rather than the rule for the antibodies used in most research and diagnostic applications. The lack of penetration of recombinant antibodies into the research arena can be attributed largely to the fact that the Ig gene families are large and the variable region gene segments are, indeed, variable, precluding the use of polymerase chain reaction (PCR) with two simple primers to amplify the heavy and light chain gene segments. Because of the complexity of the V gene family and the number of possible sequences for amplification, there may be a distinct advantage to using a PCR method that does not require a specific 5' primer to amplify the gene segment. 5'-RACE is just such a method. In the original 5'-RACE method, mRNA served as a template for cDNA synthesis using either oligo(dT) priming or a gene-specific primer. Terminal deoxynucleotide transferase (TdT) was used to tail the first strand with a region of known sequence, such as poly(A). Once tailed, the second strand can be amplified using poly(T). This 5'-RACE protocol uses the TdT activity of reverse transcriptase, which allows nontemplated addition of nucleotides to the end of the nascently made cDNA first strand.

Learning the mechanisms of chemical disequilibria.

When at equilibrium, large-scale systems obey thermodynamics because they have microscopic configurations that are typical. "Typical" states are a fraction of those possible with the majority of the probability. A more precise definition of typical states underlies the transmission, coding, and compression of information. However, this definition does not apply to natural systems that are transiently away from equilibrium. Here, we introduce a variational measure of typicality and apply it to atomistic simulations of a model for hydrogen oxidation. While a gaseous mixture of hydrogen and oxygen combusts, reactant molecules transform through a variety of ephemeral species en route to the product, water. Out of the exponentially growing number of possible sequences of chemical species, we find that greater than 95% of the probability concentrates in less than 1% of the possible sequences. Overall, these results extend the notion of typicality across the nonequilibrium regime and suggest that typical sequences are a route to learning mechanisms from experimental measurements. They also open up the possibility of constructing ensembles for computing the macroscopic observables of systems out of equilibrium.

Tool path planning of hole-making operations in ejector plate of injection mould using modified shuffled frog leaping algorithm

Abstract Optimization of hole-making operations in manufacturing industry plays a vital role. Tool travel and tool switch planning are the two major issues in hole-making operations. Many industrial applications such as moulds, dies, engine block, automotive parts etc. requires machining of large number of holes. Large number of machining operations like drilling, enlargement or tapping/reaming are required to achieve the final size of individual hole, which gives rise to number of possible sequences to complete hole-making operations on the part depending upon the location of hole and tool sequence to be followed. It is necessary to find the optimal sequence of operations which minimizes the total processing cost of hole-making operations. In this work, therefore an attempt is made to reduce the total processing cost of hole-making operations by applying relatively new optimization algorithms known as shuffled frog leaping algorithm and proposed modified shuffled frog leaping algorithm for the determination of optimal sequence of hole-making operations. An industrial application example of ejector plate of injection mould is considered in this work to demonstrate the proposed approach. The obtained results by the shuffled frog leaping algorithm and proposed modified shuffled frog leaping algorithm are compared with each other. It is seen from the obtained results that the results of proposed modified shuffled frog leaping algorithm are superior to those obtained using shuffled frog leaping algorithm. Highlights Tool travel and tool switch scheduling are major issues in optimization of hole-making operations. Many industrial applications such as moulds, engine block, automotive parts etc. requires machining of number of holes. It is necessary to achieve a correct sequence of hole-making operations to minimize tool travel and tool switch and finally to minimize total processing cost. In the present work, we have attempted an industrial application example of ejector plate of injection mould using shuffled frog leaping algorithm and modified shuffled frog leaping algorithm.

Virtual Disassembly Sequences Generation and Evaluation

First this paper presents a method for generating selective disassembly sequences. The method is based on the Lowest levels of a disassembly product graph. Instead of considering the geometric constraints for each pair of components, the proposed method considers the geometric contact and collision relationships among the components in order to generate the so-called Disassembly Geometry Contacting Graph (DGCG). The latter is then used for disassembly sequence generation thus allowing the number of possible sequences to be reduced by ignoring the components which are unrelated to the target. A simulation framework was developed and integrated in a Virtual reality environment (VRE) thus allowing generating the minimum number of possible disassembly sequences. Secondly, a method for disassembly operation evaluation by 3D geometric removability analysis in a VRE is proposed. It is based on seven new criteria divided into two categories: i). for ergonomic evaluation, ii). and for traditional processing evaluation. All criteria are presented by dimensionless coefficients automatically calculated, thus allowing evaluating disassembly sequences complexity. For this purpose, a Virtual Reality disassembly environment (VRDE) is developed based on Python programming language, utilizing mixed VTK (Visualization Toolkit) and ODE (Open Dynamics Engine) libraries. The framework is based on STEP, WRL and STL exchange formats. The analysis results and findings demonstrate the feasibility of the proposed approach thus providing significant assistance for the evaluation of disassembly sequences during Product Development Process (PDP).

On the exact size of maximum impulse radio sequences with parameters [formula omitted

Impulse radio sequences (IRSs) were introduced by Chu and Colbourn to study sequence or signal design for ultrawideband radio with unmodulated time-hopping. The central researches on IRSs lie in the determination of the value Ψ(m,k,λa,λc), i.e., the largest possible number of sequences in an (m,k,λa,λc)-IRS. When λa=λc=k−1, Chang and Wang have determined the value of Ψ(m,k,k−1,k−1). As far as the authors know, there has been no study on the case of λa≠λc. So we in this paper focus on this case with λc=k−1. We will determine the exact value of Ψ(m,k,k,k−1) for any positive integers m and k. We also calculate the exact value of Ψ(m,k,λ,k−1) for k=3,4 and 1≤λ≤k−2.

A memetic algorithm for the orienteering problem with hotel selection

In this paper, a memetic algorithm is developed to solve the orienteering problem with hotel selection (OPHS). The algorithm consists of two levels: a genetic component mainly focuses on finding a good sequence of intermediate hotels, whereas six local search moves embedded in a variable neighborhood structure deal with the selection and sequencing of vertices between the hotels. A set of 176 new and larger benchmark instances of OPHS are created based on optimal solutions of regular orienteering problems. Our algorithm is applied on these new instances as well as on 224 benchmark instances from the literature. The results are compared with the known optimal solutions and with the only other existing algorithm for this problem. The results clearly show that our memetic algorithm outperforms the existing algorithm in terms of solution quality and computational time. A sensitivity analysis shows the significant impact of the number of possible sequences of hotels on the difficulty of an OPHS instance.

Structure of the AvrBs3-DNA complex provides new insights into the initial thymine-recognition mechanism.

Transcription activator-like effectors contain a DNA-binding domain organized in tandem repeats. The repeats include two adjacent residues known as the repeat variable di-residue, which recognize a single base pair, establishing a direct code between the dipeptides and the target DNA. This feature suggests this scaffold as an excellent candidate to generate new protein-DNA specificities for biotechnological applications. Here, the crystal structure of AvrBs3 (residues 152-895, molecular mass 82 kDa) in complex with its target DNA sequence is presented, revealing a new mode of interaction with the initial thymine of the target sequence, together with an analysis of both the binding specificity and the thermodynamic properties of AvrBs3. This study quantifies the affinity and the specificity between AvrBs3 and its target DNA. Moreover, in vitro and in vivo analyses reveal that AvrBs3 does not show a strict nucleotide-binding preference for the nucleotide at the zero position of the DNA, widening the number of possible sequences that could be targeted by this scaffold.

Determination of the Exact Value for $\Psi(m,k,k-1)$

Impulse radio sequences (IRSs) were first introduced by Chu and Colbourn in (IEEE Trans. Inf. Theory, Vol. 50, pp. 2402-2407, 2004). Let Ψ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> , λ) denote the maximal possible number of sequences in an ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> , λ)-IRS. In this paper, a fundamental equivalence between impulse radio sequences and strictly cyclic packing having the impulse position property is established. With their relationship, the exact value of Ψ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> - 1) is finally determined for any positive integers <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> .

Tandem mass spectrometric de novo sequencing of oligonucleotides using simulated annealing for stochastic optimization

A global strategy for tandem mass spectrometric de novo sequencing of oligonucleotides is presented which is based on finding among all possible sequences the sequence, whose simulated tandem mass spectrum shows the highest degree of similarity to the measured spectrum. Global de novo sequencing can become a time-consuming task due the exponential increase of the number of possible sequences with increasing oligonucleotide length. For the reduction of sequencing effort and time, simulated annealing was introduced as stochastic optimization technique that is capable to find the optimal sequence by testing only a subset of all possible configurations. We have evaluated the performance of the de novo sequencing approach by sequencing 13 synthetic oligonucleotides ranging in length from 5 to 24 nucleotides. Mass spectrometric and tandem mass spectrometric experiments were performed on a quadrupole-quadrupole-time-of-flight instrument. Accurate molecular mass measurements were used to determine the nucleotide compositions of the oligonucleotides. For the majority of tested oligonucleotides two different charge states were selected as precursor ions. Each precursor ion was fragmented applying several different collision voltages. Overall 107 fragment ion mass spectra were acquired. The nucleotide compositions together with the tandem mass spectral information represented the input for the de novo sequencing algorithm. Sequences of oligonucleotides as large as 22-mers were correctly determined in more than 90% of cases. The optimal sequence was retrieved within 1–2min. Fragment ion mass spectra of larger oligonucleotides were inappropriate for de novo sequencing. The occurrence of extensive internal fragmentation causing low sequence coverage paired with a high probability of assigning fragment ions to wrong sequences gave rise to incorrect results.