String Length Research Articles

Shortest covers of all cyclic shifts of a string

A factor C of a string S is called a cover of S, if each position of S is contained in an occurrence of C. Breslauer (1992) [3] proposed a well-known O(n)-time algorithm that computes the shortest cover of every prefix of a string of length n. We show an O(nlog⁡n)-time and O(n)-space algorithm that computes the shortest cover of every cyclic shift of a string of length n and an O(n)-time algorithm that computes the shortest among these covers. We also provide a combinatorial characterization of shortest covers of cyclic shifts of Fibonacci strings that leads to efficient algorithms for computing these covers.We further consider the bound on the number of different lengths of shortest covers of cyclic shifts of the same string of length n. We show that this number is Θ(log⁡n) for Fibonacci strings.

A quantum algorithm for string matching

Algorithms that search for a pattern within a larger data-set appear ubiquitously in text and image processing. Here, we present an explicit, circuit-level implementation of a quantum pattern-matching algorithm that matches a search string (pattern) of length M inside a longer text of length N. Our algorithm has a time complexity of tilde{O}(sqrt{N}), while the space complexity remains modest at O(N + M). We report the quantum gate counts relevant for both pre-fault-tolerant and fault-tolerant regimes.

Longest previous overlapping factor array

In this paper, we introduce the longest previous overlapping factor array of a string – a variant of the longest previous factor array. We show that it can be computed in linear time in the length of the input string, via a reduction to the Max-variant of the Manhattan skyline problem Crochemore et al. (2014) [5].

Improved descriptional complexity results on generalized forbidding grammars

In formal language theory, if a grammar consists of rules of the type ( r , F r ) , where r is a context-free rule and F r is an associated finite set of strings called the forbidding set, such that r can be applied to a string only if none of the strings in F r is present in the string, then the grammar is said to be a generalized forbidding (GF) grammar. There are four main parameters that describe the size of a GF grammar, namely, (1) d , the maximum length of strings in the forbidding sets, (2) i , the maximum cardinality of the forbidding sets, (3) n , the number of nonterminals used in the grammar, and (4) c , the number of rules with nonempty forbidding set. The family of languages described by a GF grammar of size (at most) ( d , i , n , c ) is denoted by GF ( d , i , n , c ) . We study for what sizes of GF grammars one can obtain the computational power of Turing machines. We specifically show this result for sizes (2, 6, 8, 6), (2, 5, 9, 7), (2, 4, 7, 8) and (2, 3, 20, 18).

Computing longest palindromic substring after single-character or block-wise edits

Palindromes are important objects in strings which have been extensively studied from combinatorial, algorithmic, and bioinformatics points of views. It is known that the length of the longest palindromic substrings (LPSs) of a given string T of length n can be computed in O(n) time by Manacher's algorithm [12]. In this paper, we consider the problem of finding the LPS after the string is edited. We present an algorithm that uses O(n) time and space for preprocessing, and answers the length of the LPSs in O(log⁡(min⁡{σ,log⁡n})) time after a single character substitution, insertion, or deletion, where σ denotes the number of distinct characters appearing in T. We also propose an algorithm that uses O(n) time and space for preprocessing, and answers the length of the LPSs in O(ℓ+log⁡log⁡n) time, after an existing substring in T is replaced by a string of arbitrary length ℓ.

Quantitative Evidence of Mobile Ion Hopping in Polymerized Ionic Liquids.

Atomistic molecular dynamics simulations were performed, and an extensive set of analyses were undertaken to understand the ion transport mechanism in the polymerized ionic liquid poly(C2VIm)Tf2N. The ion hopping events were investigated at different time scales. Ion hopping was examined by monitoring the instantaneous cation-anion association and dissociation. Ion diffusion was subsequently evaluated with correlation functions and the calculation of relaxation times at different time scales. Dynamical heterogeneity in the mobility of the ions was observed with only a small portion of the anions classified as fast mobile ions. The mobile ions were characterized as the ones traveling farther than a certain distance during a characteristic period, which was much longer than the time scale of the instant ion pair dissociation. Effective hopping of the mobile ions contributed to the diffusivity which was dominated by interchain hopping and generally facilitated with five associating cations from two different polymer chains. Mobile anions had relatively fewer associating cations from more associating chains than immobile anions. The stringlike cooperative motion was observed in the mobile anions. The string length was determined to decrease with increasing temperature. These findings provided an in-depth understanding of the ion transport in polymerized ionic liquids and important information for the rational design of novel materials.

An Ultra-Fast and Parallelizable Algorithm for Finding k-Mismatch Shortest Unique Substrings.

This paper revisits the k-mismatch shortest unique substring finding problem and demonstrates that a technique recently presented in the context of solving the k-mismatch average common substring problem can be adapted and combined with parts of the existing solution, resulting in a new algorithm which has expected time complexity of O(n logk n), while maintaining a practical space complexity at O(kn), where n is the string length. When , which is the hard case, our new proposal significantly improves the any-case O(n2) time complexity of the prior best method for k-mismatch shortest unique substring finding. Experimental study shows that our new algorithm is practical to implement and demonstrates significant improvements in processing time compared to the prior best solution's implementation when k is small relative to n. For example, our method processes a 200 KB sample DNA sequence with k=1 in just 0.18 seconds compared to 174.37 seconds with the prior best solution. Further, it is observed that significant portions of the adapted technique can be executed in parallel, using two different simple concurrency models, resulting in further significant practical performance improvement. As an example, when using 8 cores, the parallel implementations both achieved processing times that are less than 1/4 of the serial implementation's time cost, when processing a 10 MB sample DNA sequence with k=2. In an age where instances with thousands of gigabytes of RAM are readily available for use through Cloud infrastructure providers, it is likely that the trade-off of additional memory usage for significantly improved processing times will be desirable and needed by many users. For example, the best prior solution may spend years to finish a DNA sample of 200MB for any , while this new proposal, using 24 cores, can finish processing a sample of this size with k=1 in 206.376 seconds with a peak memory usage of 46 GB, which is both easily available and affordable on Cloud. It is expected that this new efficient and practical algorithm for k-mismatch shortest unique substring finding will prove useful to those using the measure on long sequences in fields such as computational biology. We also give a theoretical bound that the k-mismatch shortest unique substring finding problem can be solved using O(n logk n) time and O(n) space, asymptotically much better than the one we implemented, serving as a new discovery of interest.

Introduction to Set Shaping Theory

In this article, we define the Set Shaping Theory whose goal is the study of the bijection functions that transform a set of strings into a set of equal size made up of strings of greater length. The functions that meet this condition are many but since the goal of this theory is the transmission of data, we have analyzed the function that minimizes the average information content. The results obtained show how this type of function can be useful in data compression.

An Incentive and Reputation Mechanism Based on Blockchain for Crowd Sensing Network

Nowadays, sensors inserted in mobile applications are used for gathering data for an explicit assignment that can effectively save cost and time in crowd sensing networks (CSNs). The true value and essence of gathered statistics depend on the participation level from all the members of a CSN, i.e., service providers, data collectors, and service consumers. In comparison with the centralized conventional mechanisms that are susceptible to privacy invasion, attacks, and manipulation, this article proposes a decentralized incentive and reputation mechanism for CSN. The monetary rewards are used to motivate the data collectors and to encourage the participants to take part in the network activities. Whereas the issue of privacy leakage is dealt with using Advanced Encryption Standard (AES128) technique. Additionally, a reputation system is implemented to tackle issues like data integrity, fake reviews, and conflicts among entities. Through registering reviews, the system encourages data utilization by providing correct, consistent, and reliable data. Furthermore, simulations are performed for analyzing the gas consumed by smart contracts. Similarly, the encryption technique is ratified by comparing its execution time with other techniques that are previously used in literature. Lastly, the reputation system is inspected through analyzing the gas consumption and mining time of input string length.

Longest common subsequence in sublinear space

We present the first o(n)-space polynomial-time algorithm for computing the length of a longest common subsequence. Given two strings of length n, the algorithm runs in O(n3) time with O(nlog1.5⁡n2log⁡n) bits of space.

Low energy consequences of loop quantum gravity

Using the loop quantum gravity, based on polymer quantization, we will argue that the polymer length (like string length) can be several orders larger than the Planck length, and this can have low energy consequences. We will demonstrate that a short distance modification of a quantum system by polymer quantization and by string theoretical considerations can produce similar behavior. Moreover, it will be demonstrated that a family of different deformed Heisenberg algebras can produce similar low energy effects. We will analyze such polymer correction to a degenerate Fermi gases in a harmonic trap, and its polymer corrected thermodynamics.

PENGUKURAN MODULUS YOUNG SENAR PANCING DENGAN METODE ANALISIS FREKUENSI DAWAI

The research has been conducted to determine the Young Modulus value of the fishing line with frequency analysis on a string by using a sound sensor. The fishing line made of Nylon Monofilament and Stainless Steel Nylon Coat. The diameter of the fishing line with each material consisted of 0.25 mm. The fishing line vibration events ware displayed on the graph of the relationship between pressure and time in the Logger pro program. The graph of the relationship between pressure and time was then transformed into an FFT graph of the amplitude relationship to frequency. Then the frequency value which was obtained from the FFT was used to determine the wave velocity value of the fishing line. The average wave velocity value was obtained by graphing the frequency relation to one of each string length. After obtained the average wave velocity value of the fishing line the Modulus Young value can be determined by the equation of the square wave velocity relationship times the mass per length times the cross-sectional area. In this study, the Young Modulus value of Nylon Monofilament fishing line was (1.94±0.09) GPa and the Young Modulus value of the Stainless Steel Nylon Coat fishing line was (45.05±2.05) GPa.

New Vertically Planed Pendulum Motion

This article is concerned about the planed rigid body pendulum motion suspended with a spring which is suspended to move on a vertical plane moving uniformly about a horizontal X-axis. This model depends on a system containing three generalized coordinates. The three nonlinear differential equations of motion of the second order are obtained to the elastic string length and the oscillation angles φ 1 and φ 2 which represent the freedom degrees for the pendulum motions. It is assumed that the body moves in a rotating vertical plane uniformly with an arbitrary angular velocity ω . The relative periodic motions of this model are considered. The governing equations of motion are obtained using Lagrange’s equations and represent a nonlinear system of second-order differential equations that can be solved in terms of generalized coordinates. The numerical solutions are investigated using the approximated fourth-order Runge–Kutta method through programming packages. These solutions are represented graphically to describe and discuss the behavior of the body at any instant for different values of the different physical parameters of the body. The obtained results have been discussed and compared with some previously published works. Some concluding remarks have been presented at the end of this work. The value of this study comes from its wide applications in both civil and military life. The main findings and objectives of the current study are obtaining periodic solutions for the problem and satisfying their accuracy and stabilities through the numerical procedure.

New insights into time-series analysis IV: panchromatic and flux-independent period finding methods

ABSTRACT New time-series analysis tools are needed in disciplines as diverse as astronomy, economics, and meteorology. In particular, the increasing rate of data collection at multiple wavelengths requires new approaches able to handle these data. The panchromatic correlated indices $K^{(s)}_{(fi)}$ and $L^{(s)}_{(pfc)}$ are adapted to quantify the smoothness of a phased light-curve resulting in new period-finding methods applicable to single- and multiband data. Simulations and observational data are used to test our approach. The results were used to establish an analytical equation for the amplitude of the noise in the periodogram for different false alarm probability values, to determine the dependency on the signal-to-noise ratio, and to calculate the yield rate for the different methods. The proposed method has similar efficiency to that found for the string length period method. The effectiveness of the panchromatic and flux-independent period finding methods in single as well as multiple wavebands that share a fundamental frequency is also demonstrated in real and simulated data.

Treating the Solid Pendulum Motion by the Large Parameter Procedure

In this paper, we consider the dynamical description of a pendulum model consists of a heavy solid connection to a nonelastic string which suspended on an elliptic path in a vertical plane. We suppose that the dimensions of the solid are large enough to the length of the suspended string, in contrast to previous works which considered that the dimensions of the body are sufficiently small to the length of the string. According to this new assumption, we define a large parameter ε and apply Lagrange’s equation to construct the equations of motion for this case in terms of this large parameter. These equations give a quasi-linear system of second order with two degrees of freedom. The obtained system will be solved in terms of the generalized coordinates θ and φ using the large parameter procedure. This procedure has an advantage over the other methods because it solves the problem in a new domain when fails all other methods for solving the problem in such a domain under these conditions. It is one of the most important applications, when we study the slow spin motion of a rigid body in a Newtonian field of force under an external moment or the rotational motion of a heavy solid in a uniform gravity field or the gyroscopic motions with a sufficiently small angular velocity component about the major or the minor axis of the ellipsoid of inertia. There are many applications of this technique in aerospace science, satellites, navigations, antennas, and solar collectors. This technique is also useful in all perturbed problems in physics and mechanics, for example, the perturbed pendulum motions and the perturbed mechanical systems. The results of this paper also are useful in moving bridges and the swings. For satisfying the validation of the obtained solutions, we consider numerical considerations by one of the numerical methods and compare the obtained analytical and numerical solutions.

Counting profile strings from rectangular tilings

We study the enumeration of profiles, which are outlines that occur when tiling a rectangular board with squares, dominoes, and trominoes. Profiles of length m correspond to a special subset of the set {0,1,2,3}m, called profile strings. Profiles and their corresponding strings first appeared in the enumeration of the tilings of rectangular 2×n and 3×n boards with squares, dominoes, and trominoes. Profiles also play a role in enumerating the tilings of an m×n board for any fixed m≥2. We describe how profiles arise when enumerating tilings, and we prove that the number of profile strings of length m equals m⋅3m−1.

Linear space string correction algorithm using the Damerau-Levenshtein distance

BackgroundThe Damerau-Levenshtein (DL) distance metric has been widely used in the biological science. It tries to identify the similar region of DNA,RNA and protein sequences by transforming one sequence to the another using the substitution, insertion, deletion and transposition operations. Lowrance and Wagner have developed an O(mn) time O(mn) space algorithm to find the minimum cost edit sequence between strings of length m and n, respectively. In our previous research, we have developed algorithms that run in O(mn) time using only O(s∗min{m,n}+m+n) space, where s is the size of the alphabet comprising the strings, to compute the DL distance as well as the corresponding edit sequence. These are so far the fastest and most space efficient algorithms. In this paper, we focus on the development of algorithms whose asymptotic space complexity is linear.ResultsWe develop linear space algorithms to compute the Damerau-Levenshtein (DL) distance between two strings and determine the optimal trace (corresponding edit operations.)Extensive experiments conducted on three computational platforms–Xeon E5 2603, I7-x980 and Xeon E5 2695–show that, our algorithms, in addition to using less space, are much faster than earlier algorithms.ConclusionBesides using less space than the previously known algorithms,significant run-time improvement was seen for our new algorithms on all three of our experimental platforms. On all platforms, our linear-space cache-efficient algorithms reduced run time by as much as 56.4% and 57.4% in respect to compute the DL distance and an optimal edit sequences compared to previous algorithms. Our multi-core algorithms reduced the run time by up to 59.3% compared to the best previously known multi-core algorithms.

Computing the multi-string BWT and LCP array in external memory

Indexing very large collections of strings, such as those produced by the widespread next generation sequencing technologies, heavily relies on multi-string generalization of the Burrows–Wheeler Transform (BWT): large requirements of in-memory approaches have stimulated recent developments on external memory algorithms. The related problem of computing the Longest Common Prefix (LCP) array of a set of strings is instrumental to compute the suffix-prefix overlaps among strings, which is an essential step for many genome assembly algorithms. In a previous paper, we presented an in-memory divide-and-conquer method for building the BWT and LCP where we merge partial BWTs with a forward approach to sort suffixes.In this paper, we propose an alternative backward strategy to develop an external memory method to simultaneously build the BWT and the LCP array on a collection of m strings of different lengths. The algorithm over a set of strings having constant length k has O(mkl) time and I/O volume, using O(k+m) main memory, where l is the maximum value in the LCP array.

Syntactic stochastic processes: Definitions, models, and related inference problems

We define a Syntactic Stochastic Process (SSP) as a stochastic process valued in the set of terminal symbols of a grammar, and whose realizations are terminal strings generated by some stochastic grammar. and show that any SSP generated by a Stochastic Context Free Grammar (SCFG) can be consistently indexed by a subset of nodes of a suitable defined Graphical Random Field (GRF). In the second part of the paper we propose a definition of Stochastic Context-Sensitive Grammar (SCSG), and that the stochastic process generated by a SCFG admits a representation as a GRF. Finally, we show that strings generated by a Stochastic Tree Adjoining Grammar (STAG) are reciprocal processes, which allows the solution of the inference problem with a complexity linear with respect to string length.

LL-PMS8: A time efficient approach to solve planted motif search problem

Among other motif finding algorithms Planted Motif Search (PMS) or (ℓ, d) motif search algorithms are considered as next-generation motif finding algorithms. Here, n strings and two integer ℓ and d are provided as input in PMS. It gives outputs of all sequences of length M in each input string, where each occurrence varies from Min at most d points. This paper proposes a new algorithm, for the (ℓ, d) motif discovery problem in which we find all strings of length ℓ that seems in every string of a provided set of strings with at most d mismatches has been. After proper investigation of the PMS problem, it has been shown that this is an NP-hard exact algorithm. Usually, in the worst-case scenarios, all the known exact algorithms for PMS need exponential time in some of the underlying parameters. In this paper, we proposed a faster approach that reduces the searching time in the sample-driven part of the algorithm. In particular, we used dynamic programming techniques to eliminate the recalculation of the values of some common subtree and introduced some new speedup techniques like using a linked list, reduced ℓ-mers for making the algorithm faster. Due to the use of Linked List as a main speedup technique, we named our proposed algorithm as Linked List Implementation technique of PMS8 (LL-PMS8).