String Length Research Articles

Intrinsic non-commutativity of closed string theory

We show that the proper interpretation of the cocycle operators appearing in the physical vertex operators of compactified strings is that the closed string target is noncommutative. We track down the appearance of this non-commutativity to the Polyakov action of the flat closed string in the presence of translational monodromies (i.e., windings). In view of the unexpected nature of this result, we present detailed calculations from a variety of points of view, including a careful understanding of the consequences of mutual locality in the vertex operator algebra, as well as a detailed analysis of the symplectic structure of the Polyakov string. We also underscore why this non-commutativity was not emphasized previously in the existing literature. This non-commutativity can be thought of as a central extension of the zero-mode operator algebra, an effect set by the string length scale — it is present even in trivial backgrounds. Clearly, this result indicates that the α′ → 0 limit is more subtle than usually assumed.

On the rate of decrease in logical depth

The logical depth with significance b of a string x is the shortest running time of a program for x that can be compressed by at most b bits. Another definition is based on algorithmic probability. We give a simple new proof for the known relation between the two definitions. We also prove the following: Given a string we can consider the maximal decrease in logical depth when the significance parameter increases by 1. There exists a sequence of strings of lengths n=1,2,…, such that this maximal decrease as a function of n rises faster than any computable function but not as fast as the Busy Beaver function. This holds also for the computation times of the shortest programs of these strings.

A stochastic de novo assembly algorithm for viral-sized genomes obtains correct genomes and builds consensus

A genetic algorithm with stochastic macro mutation operators which merge, split, move, reverse and align DNA contigs on a scaffold is shown to accurately and consistently assemble raw DNA reads from an accurately sequenced single-read library into a contiguous genome. A candidate solution is a permutation of DNA reads, segmented into contigs. An interleaved merge operator for contigs allows for the quick minimization of a fitness function measuring the string length of a candidate solution. This study assembles read libraries for three genomic fragments from different organisms, five complete virus genomes, and one complete bacterial genome, with the largest genome length of 159 kbp. To evaluate the accuracy of any assembled genome, test libraries of DNA reads are generated from reference genomes, and the assembly is compared to the reference. The method has very high assembly accuracy: over repeated assemblies for each input genome, the original genome was constructed optimally in over 85% of the runs. Given the consistency of the algorithm, the method is suitable to determine the consensus genome in de-novo assembly problems. There are two limitations to the method: genomes with long repeats may be overcompressed, and the computational complexity is high.

A New Dynamic Model of Coupled Axial–Torsional Vibration of a Drill String for Investigation on the Length Increment Effect on Stick–Slip Instability

In this paper, a new model is proposed to study the coupled axial–torsional vibration of the drill string. It is assumed that rotary table angular speed is constant and equals to the nominal angular speed of the drill string. In addition, axial displacement of any point on the drill string is considered to be as the sum of rigid-body motion and elastic vibrations. The depth of cut is defined using instantaneous dynamic states instead of using the delayed model as presented in previous researches. A velocity-weakening function is introduced for modeling the behavior of the frictional component of the torque-on-bit (TOB) with respect to the bit angular speed. After discretizing vibration equations, stability analysis of the system is investigated by linearizing the nonlinear system around its steady-state response point. Considering nominal weight-on-bit (WOB) (W0) and nominal rotational speed (Ω) as the input parameters of the drilling, variation of maximum allowable value of (W0) is presented with respect to variation of Ω . It is shown that the maximum allowable value of W0 has an increasing–decreasing behavior with respect to Ω. The effect of drill string upper and lower part lengths is studied on the stability of the system, and practical results are presented both in the condition that W0 is constant and in the condition that the hook upward force is constant. It is shown that by increasing the drill string length, the system is more exposed to instability, and this must be considered in regulating the input parameters of drilling.

Upper Bounds on the Domination and Total Domination Number of Fibonacci Cubes

One of the basic model for interconnection networks is the $n$-dimensional hypercube graph $Q_n$ and the vertices of $Q_n$ are represented by all binary strings of length $n$. The Fibonacci cube $\Gamma_n$ of dimension $n$ is a subgraph of $Q_n$, where the vertices correspond to those without two consecutive 1s in their string representation. In this paper, we deal with the domination number and the total domination number of Fibonacci cubes. First we obtain upper bounds on the domination number of $\Gamma_n$ for $n\ge 13$. Then using these result we obtain upper bounds on the total domination number of $\Gamma_n$ for $n\ge 14$ and we see that these upper bounds improve the bounds given in [1].

Quantum stabilization of a hedgehog type of cosmic string

Within a slightly simplified version of the electroweak standard model we investigate the stabilization of cosmic strings by fermion quantum fluctuations. Previous studies of quantum energies considered variants of the Nielsen–Olesen profile embedded in the electroweak gauge group and showed that configurations are favored for which the Higgs vacuum expectation value drops near the string core and the gauge field is suppressed. This work found that the strongest binding was obtained from strings that differ significantly from Nielsen–Olesen configurations, deforming essentially only the Higgs field in order to generate a strong attraction without inducing large gradients. Extending this analysis, we consider the leading quantum correction to the energy per unit length of a hedgehog type string, which, in contrast to the Nielsen–Olesen configuration, contains a pseudoscalar field. To employ the spectral method we develop the scattering and bound state problems for fermions in the background of a hedgehog string. Explicit occupation of bound state levels leads to strings that carry the quantum numbers of the bound fermions. We discuss the parameter space for which stable, hedgehog type cosmic strings emerge and reflect on phenomenological consequences of these findings.

Computing the Expected Edit Distance from a String to a Probabilistic Finite-State Automaton

In a number of fields, it is necessary to compare a witness string with a distribution. One possibility is to compute the probability of the string for that distribution. Another, giving a more global view, is to compute the expected edit distance from a string randomly drawn to the witness string. This number is often used to measure the performance of a prediction, the goal then being to return the median string, or the string with smallest expected distance. To be able to measure this, computing the distance between a hypothesis and that distribution is necessary. This paper proposes two solutions for computing this value, when the distribution is defined with a probabilistic finite state automaton. The first is exact but has a cost which can be exponential in the length of the input string, whereas the second is a fully polynomial-time randomized schema.

Markov chain analysis of Leading Ones problem

Evolutionary algorithms (EAs) are randomized optimization search techniques, and the theoretical study of the first hitting time is very important in the practical applications of EA. We investigate the first hitting time of Leading Ones (LO) problem theoretically on Random Local Search (RLS) algorithm and (1 + 1)EA by absorbing Markov chain. This paper reports the calculation method of the first hitting time on LO problem with (1 + 1)EA and RLS. We found that the results only depend on the length of string, and the hitting times can be given approximately by the quadratic function. In the numerical experiments, we showed the agreement between the results of the practical calculation and the theoretical results. Our results give the good example to predict the running time of the practical EA calculations by Markov chain method.

Gravitational waves generated from the cosmological QCD phase transition within AdS/QCD

We study the gravitational waves produced by the collision of the bubbles as a probe for the cosmological first order QCD phase transition, considering heavy static quarks. Using AdS/QCD and the correspondence between a first order Hawking–Page phase transition and confinement–deconfinement phase transition, we find the spectrum and the strain amplitude of the gravitational wave within the hard and soft wall models. We postulate the duration of the phase transition corresponds to the evaporation time of the black hole in the five dimensional dual gravity space, and thereby obtain a bound on the string length in the space and correspondingly on the duration of the QCD phase transition. We also show that IPTA and SKA detectors will be able to detect these gravitational waves, which can be an evidence for the first order deconfinement transition.

Vehicular Platoons in cyclic interconnections with constant inter-vehicle spacing

This paper investigates homogeneous vehicle platoons with cyclic, bi-directional communication maintaining a constant (velocity independent) target inter vehicle spacing. We investigate stability and disturbance amplification if the string length increases, where the vehicles utilise weighted information from multiple vehicles ahead and behind. We find a condition, independent of the linear controller used, for the weighting factors that is necessary for stability of long platoons. In the second part we investigate disturbance amplification for stable systems. We show that while string instability is unavoidable with an extended but limited range, a communication range that increases with the vehicle platoon size can lead to string stability.

Inferring strings from Lyndon factorization

The Lyndon factorization of a string w is a unique factorization ℓ1p1,…,ℓmpm of w such that ℓ1,…,ℓm is a sequence of Lyndon words that is monotonically decreasing in lexicographic order. In this paper, we consider the reverse-engineering problem on Lyndon factorization: Given a sequence S=((s1,p1),…,(sm,pm)) of ordered pairs of positive integers, find a string w whose Lyndon factorization corresponds to the input sequence S, i.e., the Lyndon factorization of w is in a form of ℓ1p1,…,ℓmpm with |ℓi|=si for all 1≤i≤m. Firstly, we show that there exists a simple O(n)-time algorithm if the size of the alphabet is unbounded, where n is the length of the output string. Secondly, we present an O(n)-time algorithm to compute a string over an alphabet of the smallest size. Thirdly, we show how to compute only the size of the smallest alphabet in O(m) time. Fourthly, we give an O(m)-time algorithm to compute an O(m)-size representation of a string over an alphabet of the smallest size. Finally, we propose an efficient algorithm to enumerate all strings whose Lyndon factorizations correspond to S.

A greedy alignment-free distance estimator for phylogenetic inference

BackgroundAlignment-free sequence comparison approaches have been garnering increasing interest in various data- and compute-intensive applications such as phylogenetic inference for large-scale sequences. While k-mer based methods are predominantly used in real applications, the average common substring (ACS) approach is emerging as one of the prominent alignment-free approaches. This ACS approach has been further generalized by some recent work, either greedily or exactly, by allowing a bounded number of mismatches in the common substrings.ResultsWe present ALFRED-G, a greedy alignment-free distance estimator for phylogenetic tree reconstruction based on the concept of the generalized ACS approach. In this algorithm, we have investigated a new heuristic to efficiently compute the lengths of common strings with mismatches allowed, and have further applied this heuristic to phylogeny reconstruction. Performance evaluation using real sequence datasets shows that our heuristic is able to reconstruct comparable, or even more accurate, phylogenetic tree topologies than the kmacs heuristic algorithm at highly competitive speed.ConclusionsALFRED-G is an alignment-free heuristic for evolutionary distance estimation between two biological sequences. This algorithm is implemented in C++ and has been incorporated into our open-source ALFRED software package (http://alurulab.cc.gatech.edu/phylo).

Implementasi Algoritma Hamming Distance dan Brute Force dalam Mendeteksi Kemiripan Source Code Bahasa Pemrograman C

Plagiarism is a behavior that causes violence of copyrights. Survey shows 55% of college presidents say that plagiarism in students’ papers has increased over the past 10 years. Therefore, an application for detecting plagiarism is needed, especially for teachers. This plagiarism checker application is made by using Visual C# 2010. The plagiarism checker uses hamming distance algorithm for matching line code of the source code. This algorithm works by matching the same length string of the code programs. Thus, it needs brute will be matched with hamming distance. Another important thing for detecting plagiarism is the preprocessing, which is used to help the algorithm for detecting plagiarized source code. This paper shows that the application works good in detecting plagiarism, the hamming distance algorithm and brute force algorithm works better than levenstein distance algorithm for detecting structural type of plagiarism and this thesis also shows that the preprocessing could help the application to increase its percentage and its accuracy.
 Index Terms—Brute Force, Hamming Distance, Plagiarisme, Preprocessing.

A Near-Optimal Algorithm to Count Occurrences of Subsequences of a Given Length.

For k ∈ ℤ+, define Σ k as the set of integers {0, 1, …, k - 1}. Given an integer n and a string t of length m ≥ n over Σ k , we count the number of times that each one of the kn distinct strings of length n over Σ k occurs as a subsequence of t. Our algorithm makes only one scan of t and solves the problem in time complexity mkn-1 and space complexity m + kn . These are very close to best possible.

Irregularly observed time series – some asymptotics and the block bootstrap

ABSTRACTWe consider time series being observed at random time points. In addition to Parzen's classical modelling by amplitude modulating sequences, we state another modelling using an integer-valued sequence as the observation times. Limiting results are presented for the sample mean and are generalized to the class of functions of smooth means. Motivated by the complicated limiting behaviour, (moving) block bootstrap possibilities are investigated. Conditional on the used modelling for the irregular spacings, one is lead to different interpretations for the block length and hence bootstrap approaches. The block length either can be interpreted as the time (resulting in an observation string of fixed length containing a random number of observations) or as the number of observations (resulting in an observation string of variable length containing a fixed number of values). Both bootstrap approaches are shown to be asymptotically valid for the sample mean. Numerical examples and an application to real-world ozone data conclude the study.

Unsteady critical liquid sheet flows

The unsteady global dynamics of a gravitational liquid sheet interacting with a one-sided adjacent air enclosure (commonly referred to as nappe oscillation configuration) is addressed under the assumptions of potential flow and the presence of surface tension effects. From a theoretical viewpoint the problem is challenging, because from previous literature it is known that the equation governing the evolution of small disturbances exhibits a singularity at the vertical station where the local flow velocity equals the capillary wave velocity (local critical condition), although the solution to the problem has not yet been found. The equation governing the local dynamics resembles one featuring the forced vibrations of a string of finite length, formulated in the reference frame moving with the flow velocity, and exhibits both slow and fast characteristic curves. From the global system perspective the nappe behaves as a driven damped spring–mass oscillator, where the inertial effects are linked to the liquid sheet mass and the spring is represented by the equivalent stiffness of the air enclosure acting on the displacement of the compliant nappe centreline. A suited procedure is developed to remove the singularity of the integro-differential operator for Weber numbers less than unity. The investigation is carried out by means of a modal (i.e. time asymptotic) linear approach, which is corroborated by numerical simulations of the governing equation and supported by systematic comparisons with experimental data from the literature, available in the supercritical regime only. As regards the critical regime for the unit Weber number, the major theoretical result is a sharp increase in oscillation frequency as the flow Weber number is gradually reduced from supercritical to subcritical values due to the shift of the prevailing mode from the slow one to the fast one.

Tight lower bounds for the longest common extension problem

The longest common extension problem is to preprocess a given string of length n into a data structure that uses S(n) bits on top of the input and answers in T(n) time the queries LCE(i,j) computing the length of the longest string that occurs at both positions i and j in the input. We prove that the trade-off S(n)T(n)=Ω(nlog⁡n) holds in the non-uniform cell-probe model provided that the input string is read-only, each letter occupies a separate memory cell, S(n)=Ω(n), and the size of the input alphabet is at least 28⌈S(n)/n⌉. It is known that this trade-off is tight.

Disturbance scaling in bidirectional vehicle platoons with different asymmetry in position and velocity coupling

This paper considers a string of vehicles where the local control law uses the states of the vehicle’s immediate predecessor and follower. The coupling towards the preceding vehicle can be chosen different to the coupling with the following vehicle, which is referred to as an asymmetric bidirectional string. Further, the asymmetry for the velocity coupling can be chosen differently to the asymmetry in the position coupling. It is investigated how the effect of the disturbance on the control errors in the string depends on the string length. It is shown, that in case of symmetric position coupling and asymmetric velocity coupling, linear scaling can be achieved. For symmetric interactions, the errors scale quadratically in the number of vehicles. When the coupling in position is asymmetric, exponential scaling may occur or the system might even become unstable. The paper thus gives a comprehensive overview of the achievable performance in linear, asymmetric, bidirectional platoons. The results reveal that symmetry in the position coupling and asymmetry in velocity coupling qualitatively improve the performance of the string. Extensive numerical results illustrate the theoretical findings.

Reconstructing a string from its Lyndon arrays

Given a string x=x[1..n] on an ordered alphabet Σ of size σ, the Lyndon array λ=λx[1..n] of x is an array of positive integers such that λ[i],1≤i≤n, is the length of the maximal Lyndon word over the ordering of Σ that begins at position i in x. The Lyndon array has recently attracted considerable attention due to its pivotal role in establishing the long-standing conjecture that ρ(n)<n, where ρ(n) is the maximum number of maximal periodicities (runs) in any string of length n. Here we first describe two linear-time algorithms that, given a valid Lyndon array λ, compute a corresponding string — one for an alphabet of size n, the other for a smaller alphabet. We go on to describe another linear-time algorithm that determines whether or not a given integer array is a Lyndon array of some string. Finally we show how σ Lyndon arrays λΣ={λ1=λ,λ2,…,λσ} corresponding to σ “rotations” of the alphabet can be used to determine uniquely the string x on Σ such that λx=λ.

Subsequence automata with default transitions

Let S be a string of length n with characters from an alphabet of size σ. The subsequence automaton of S (often called the directed acyclic subsequence graph) is the minimal deterministic finite automaton accepting all subsequences of S. A straightforward construction shows that the size (number of states and transitions) of the subsequence automaton is O(nσ) and that this bound is asymptotically optimal.In this paper, we consider subsequence automata with default transitions, that is, special transitions to be taken only if none of the regular transitions match the current character, and which do not consume the current character. We show that with default transitions, much smaller subsequence automata are possible, and provide a full trade-off between the size of the automaton and the delay, i.e., the maximum number of consecutive default transitions followed before consuming a character.Specifically, given any integer parameter k, 1<k≤σ, we present a subsequence automaton with default transitions of size O(nklogk⁡σ) and delay O(logk⁡σ). Hence, with k=2 we obtain an automaton of size O(nlog⁡σ) and delay O(log⁡σ). At the other extreme, with k=σ, we obtain an automaton of size O(nσ) and delay O(1), thus matching the bound for the standard subsequence automaton construction. Finally, we generalize the result to multiple strings. The key component of our result is a novel hierarchical automata construction of independent interest.