String Length Research Articles

The Mechanical Invariance Factor in Musical Acoustics and Perception (Revisited)

Mechanical, acoustical, and neurophysiological investigations in music, acoustics, and auditory perception repose on the Pythagorean string ratio theory of musical pitch intervals (6^th century B.C). Recently, the mechanical validity of the string ratio theory and its psychological import have been challenged and denied on grounds of invariance. In this regard, Essien (2014) demonstrated experimentally that, contrary to established tradition in physics of sound, the tension of a string is not constant when string length is modified even though the balanced-force exerted on the string is held constant. The data revealed the existence of two sources of force in a vibrating string: (1) The oppositely-directed force applied externally to the string (labelled <i>F</i>ex); (2) The force that is the intrinsic property of the string (labelled <i>F</i>in). The latter is the missing parameter in Pythagorean auditory psychophysics. The omission lured researchers into acoustics and neurophysiology of pitch without an invariant physical correlate of pitch. Essien’s (2014) data showed that all transformations to string length or the balanced-force exerted on a string are various ways to modify the string’s resistance to deformation. Thus, the force in a string varies inversely with string length even though <i>F</i>ex is held constant. In the present paper, string length is shown to have very little or no effect at all on a string’s vibrational frequency and subjective pitch. Because psychoacoustic theories of hearing are founded on the string ratio theory, the data not only offer the missing psychological element that deprived the string ratio theory of a scientific status, but also refute both Ohm’s acoustical law (1843) and Helmholtz’s resonance theory (1877). The force in a string is portrayed as the mechanical parameter in control of pitch regardless of vibrational frequency or spectral structure. Implications for future research in musical acoustics and auditory perception are discussed.

Street Performers and Society in Urban Japan, 1600–1900: The Beggar’s Gift by Gerald Groemer

Reviewed by: Street Performers and Society in Urban Japan, 1600–1900: The Beggar’s Gift by Gerald Groemer Adam L. Kern (bio) Street Performers and Society in Urban Japan, 1600–1900: The Beggar’s Gift. By Gerald Groemer. Routledge, London, 2016. xviii, 415 pages. $240.00, cloth; $54.95, E-book. The urban experience has everywhere always derived a lion’s share of its charm from the spectacle of street artists, be they the jongleurs of old-world markets or the jugglers of metropolitan public squares today. In the shogun’s capital of Edo, the proverbial Chinese lion dancers themselves come to mind, though other exemplars of these lowly, and therefore often little-studied, figures abound: standup comic duos (manzai), sand painters, puppeteers, automata operators, peepshow impresarios, blind minstrels, [End Page 142] Zen flutists, Buddhist mendicants reciting benedictions, yin-yang diviners, sacred dancing mimes, vocal impersonators, storytellers, soapbox orators, prestidigitators, conjurers, thimble riggers, acrobats, ladder balancers, basket jumpers, and sword swallowers, to name a few, not to omit professional regurgitators. One such regurgitator (okematsu in Japanese—a term this reviewer admits to not having known previously) would routinely swallow a handful of loose needles and a length of string, then, with neither apparent bodily harm nor dearth of razzmatazz, cough these up perfectly threaded (p. 224). Thrusting us into this dazzling if at times lurid world is Gerald Groemer’s thoroughly researched, well-argued, clarifying, and frequently entertaining Street Performers and Society in Urban Japan, 1600–1900. By “street performers,” Groemer means freelancers who, performing in liminal if public spaces such as street corners and market places, were never beholden to theater managers or highbrow tastes, though these artists occasionally moved to indoor performance halls (yose) and stages. Street Performers presents a wonderfully kaleidoscopic view of urban Japanese society during the Edo (1600–1868) and Meiji (1868–1912) periods through these freelancers without devolving into sentimental eulogy for their lost performance arts. Groemer’s main conviction is that “little tells one more about a society than the way in which the arts it supports can free themselves from their immediate determination by economic, political, and social forces” (p. 7). To this end, Groemer (who teaches ethnomusicology and Western musicology at the University of Yamanashi in Kōfu, Japan) judiciously builds on a dozen of his own articles on street performers and related topics, published in major journals over the past two decades. The result may well be his magnum opus. It certainly represents a considerable achievement and contribution to the study of the period’s urban popular culture. As such, it should be required reading for scholars of literature, culture, and history, though it may not be quite broad enough for general readers, let alone for use in college courses. At least two major challenges must have confronted Groemer, the first being that street arts are notoriously ephemeral. The perceived low social status of performers and a Confucian disdain of amusements do not help matters. Detailed reliable accounts of these arts and their particular performances are scant. What records survive range from the likes of oblique references within comic haiku (senryū) to snippets of dialogue in works of fiction (often illustrated), woodblock prints (often texted), works related to the kabuki stage, even legal documents. Groemer admirably marshals these sources, including 83 images by my count (regrettably, there is no list of illustrations—or credits), with the guidance of Japanese scholarship, providing the most comprehensive account in English of these street arts to date, at least since the pioneering work of Andrew Markus. [End Page 143] The second challenge concerns a basic understanding of the shifting identities of these performers. The conventional wisdom has long been that they were the disenfranchised, particularly “nonhuman” outcastes (hinin), the poor, the homeless, the physically or mentally disabled, the economically hobbled, not to mention Buddhist and other sorts of religious mendicants. One surprise, however, is that members from all four major social classes could and did resort to performing street arts. Given the downward social mobility of the day, this is not surprising. Still, the mental image of samurai literally putting on a song and a dance is striking. Samurai were only willing to do...

Simultaneous Insensitivity for One-Dimensional Wave Equations

We study the simultaneous boundary desensitizing controllability of vibrating elastic strings of the same length and different wave velocities. The problem consists in finding a boundary control for several wave equations such that the solutions are insensitive in some region of the strings with respect to small perturbations of the initial data. The term simultaneous is understood in the sense that the same control function is used to control all the strings. We show that the simultaneous approximate desensitizing controllability holds true in enough large time if and only if the wave velocities of the strings are pairwise incommensurable. The proof is based on a weighted observability inequality for the adjoint system. The inequality also allows us to identify spaces of simultaneously desensitizing controllable initial states depending on Diophantine approximation properties of the ratios of the wave velocities.

High Energy and Large Scale Structures as Gauge Invariant Spectra of Local Super-Symmetry

The least massive fermion generation is attributed to an analogue of Weyl curvature which occurs when a closed, spin-string sweeps out a closed world tube: , where S represents string length. A second order tube and consequent second order fermion mass are associated with a closed tube which circulates and itself sweeps out a closed tube: . Finally a Kth order tube and kth order fermion generation are associated with the general expression . By hypothesis six world tube orders establish an SU(3) symmetry and each closed tube interacts with a SUGRA connection of spin-. Such connections can either be photon-fermion composites or composites that consist strictly of fermions. Interactions that involve no photons are, by hypothesis unobserved and are therefore associated with closed world tubes that are classified as dark mass-energy. It is demonstrated that interactions involving ordinary mass-energy are identities (e.g. interactions that are incapable of generating the proposed SU(3) symmetry). It is therefore concluded that dark mass-energy is a necessary condition for the SU(3) symmetry that by hypothesis characterizes the proposed model. Since 95% of the mass-energy in the universe is regarded as dark, the total mass-energy that constitutes the proposed SU(3) symmetry can be calculated as , where QL is a left-handed quark, where ΨL is a left-handed spin particle and where is a right-handed anti-lepton. Thus the mass-energy that is associated with the wave is about 1067 GeV/c2 (the approximate mass of a typical galaxy). This wave is regarded by hypothesis as a single galactic unit and as the ground state of a large-scale quantization; i.e. as the ground state of a series of abstract waves which mimic de Broglie waves in the sense that the ground state is a wave of one anti-node which oscillates about a wave length that parallels a geodesic on a smallest abstract spherical shell. The first excited state is a wave of two anti-nodes that oscillate about a wave length that parallels a geodesic on the second smallest spherical shell etc. The proposed quantization is calibrated by a boundary condition which is established by observation and which separates galaxies by distances that are about ten times the diameter of a typical galaxy; separates clusters by distances that are about ten times the diameter of a typical cluster etc. Thus the wave Φ is, by hypothesis, the first in a series of gauge transformations that models the galactic hierarchy. By hypothesis the above gauge transformations form an irre-ducible representation of the SU(3) symmetric hierarchy of fermionic generations that is introduced above, providing that tensor products are replaced by the six increments which correspond to the proposed gauge transformations. By hypothesis the local cluster (the state corresponding to n = 2) results from the dispersion of those galaxies that originally form the 2-spherical area by which the local cluster is bounded. This number of galaxies is said to be at least 54. Thus the radius of the concentric sphere which forms the original 2-dimensional boundary of the local cluster is approximately mean radial units. Accordingly the area of the concentric sphere that corresponds to n = 6 is approximately galactic units; or if one predicts 79 galaxies for the local cluster, then the proposed model indicates a universe of approximately 2 × (1012) galaxies, as established by the C. Conselice team at the University of Nottingham and by NASA.

Factorization-Based Approach for Computing a Minimum Makespan Controllable Sublanguage

This paper proposes a decomposition-based approach for computing a controllable sublanguage with minimum makespan. It is applicable to a class of cyclic discrete event system modeled by cyclic timed automata. We introduce the notion of the symmetrically reachable idle state and show that its existence in an automaton allows to decompose a language into a concatenation of smaller languages. We also propose a new technique to compute the makespan of finite length strings. Results are illustrated with a case study of a small factory.

Adiabatic dynamics of one-dimensional classical Hamiltonian dissipative systems

A linearized plane pendulum with the slowly varying mass and length of string and the suspension point moving at a slowly varying speed is presented as an example of a simple 1D mechanical system described by the generalized harmonic oscillator equation, which is a basic model in discussion of the adiabatic dynamics and geometric phase. The expression for the pendulum geometric phase is obtained by three different methods. The pendulum is shown to be canonically equivalent to the damped harmonic oscillator. This supports the mathematical conclusion, not widely accepted in physical community, of no difference between the dissipative and Hamiltonian 1D systems.

An extension of the FFT‐based algorithm for the match‐count problem to weighted scores

The match‐count problem on strings is the basic problem of counting the matches of characters between two strings for every possible alignment. The problem is classically computed in O(σ n log m) time using a fast Fourier transform (FFT) for two strings of lengths m and n (m ≤ n) over an alphabet of size σ. This paper extends the target of this FFT‐based algorithm to a weighted version of the problem, which computes the sum of similarities between characters instead of the number of matches. The algorithm extended in this paper can solve the weighted match‐count problem in O(dn log m) time by mapping characters to numerical vectors of dimensionality d. This paper also evaluates the usefulness of the extended algorithm by applying it to plagiarism detection in documents. The experimental results show that the proposed algorithm is applicable to general vector representation of words and that the obtained plagiarism detection method can extremely reduce the processing time with a slight decrease of accuracy from the method based on the normal match‐count problem.

Optimal choice of k-mer in composition vector method for genome sequence comparison

Several proteins and genes are members of families that share a public evolutionary. In order to outline the evolutionary relationships and to recognize conserved patterns, sequence comparison becomes an emerging process. The current work investigates critically the k-mer role in composition vector method for comparing genome sequences. Generally, composition vector methods using k-mer are applied under choice of different value of k to compare genome sequences. For some values of k, results are satisfactory, but for other values of k, results are unsatisfactory. Standard composition vector method is carried out in the proposed work using 3-mer string length. In addition, special type of information based similarity index is used as a distance measure. It establishes that use of 3-mer and information based similarity index provide satisfactory results especially for comparison of whole genome sequences in all cases. These selections provide a sort of unified approach towards comparison of genome sequences.

Two-string consensus problem under non-overlapping inversion and transposition distance

For biological sequences that can be represented as strings over a finite alphabet, inversion and transposition are commonly observed mutation operations. The non-overlapping inversion and transposition distance (also simply called mutation distance) between two strings is defined as the minimum number of non-overlapping inversion and transposition operations used to transform one string into the other. Given two strings of the same length n and a constant c≥0, the two-string consensus problem under mutation distance is to determine whether or not there exists a string s⁎ such that the mutation distance from s⁎ to each input string does not exceed c. In this study, we present an O(n5) time and O(n4) space algorithm to solve this problem.

Line complexity asymptotics of polynomial cellular automata

Cellular automata are discrete dynamical systems that consist of patterns of symbols on a grid, which change according to a locally determined transition rule. In this paper, we will consider cellular automata that arise from polynomial transition rules, where the symbols are integers modulo some prime p. We consider the asymptotic behavior of the line complexity sequence $$a_T(k)$$ , which counts, for each k, the number of coefficient strings of length k that occur in the automaton. We begin with the modulo 2 case. For a polynomial $$T(x)=c_0+c_1x+\dots +c_nx^n$$ with $$c_0,c_n\ne ~0$$ , we construct odd and even parts of the polynomial from the strings $$0c_1c_3c_5\cdots c_{1+2\lfloor (n-1)/2\rfloor }$$ and $$c_0c_2c_4\cdots c_{2\lfloor n/2\rfloor }$$ , respectively. We prove that $$a_T(k)$$ satisfies recursions of a specific form if the odd and even parts of T are relatively prime. We also define the order of such a recursion and show that the property of “having a recursion of some order” is preserved when the transition rule is raised to a positive integer power. Extending to a more general setting, we consider an abstract generating function $$\phi (z)=\sum _{k=1}^\infty \alpha (k)z^k$$ which satisfies a functional equation relating $$\phi (z)$$ and $$\phi (z^p)$$ . We show that there is a continuous, piecewise quadratic function f on [1 / p, 1] for which $$\lim _{k\rightarrow \infty }(\alpha (k)/k^2-~f(p^{-\langle \log _p k\rangle })) = 0$$ (here $$\langle y\rangle =y-\lfloor y\rfloor $$ ). We use this result to show that for certain positive integer sequences $$s_k(x)\rightarrow \infty $$ with a parameter $$x\in [1/p,1]$$ , the ratio $$\alpha (s_k(x))/s_k(x)^2$$ tends to f(x), and that the limit superior and inferior of $$\alpha (k)/k^2$$ are given by the extremal values of f.

Stability and Vibrations of a Rotating Drill String in a Horizontal Wellbore

In view of the development of new technologies for the production of hydrocarbon fuels from shale rocks, increasing attention in the oil and gas industry is given to the problems of drilling slant and horizontal wells. The specific character of the processes of drilling such wells is that they are strongly acted upon by the forces of contact and frictional interaction between the drill string surface and the borehole wall, which arise in such cases. This paper formulates a problem of the bifurcation buckling and small bending vibrations of a rotating drill string lying in a horizontal wellbore. With allowance for friction forces and additional constraints, differential equations have been derived, for which solutions of eigenvalue problems of free vibrations of drill strings of finite and unlimited length have been constructed.

Vibration characteristics of casing string under the exciting force of an electric vibrator

Vibration cementing is a new technique that can significantly improve the bond strength of cementing interface. To popularize this technique, it is necessary to solve the key problem of how to make cementing string generate downhole radial vibration in the WOC stage. For this purpose, an electric vibrator was developed. With this vibrator, electric energy is converted into mechanical energy by means of a high-temperature motor vibration unit. The motor vibration unit rotates the eccentric block through an output shaft to generate an exciting source, which produces an axial-rotating exciting force at the bottom of the casing string. Then, the vibration characteristics of vertical well casing string under the exciting force were analyzed by using the principal coordinate analysis method, and the response model of casing string to an electric vibrator was developed. Finally, the effects of casing string length, exciting force and vibration frequency on the vibration amplitude at the lowermost of the casing string were analyzed based on a certain casing program. It is indicated that the casing string length and the square of vibration frequency are inversely proportional to the vibration amplitude at the lowermost of the casing string, and the exciting force is proportional to the vibration amplitude at the lowermost of the casing string. These research results provide a theoretical support for the application of vibration cementing technology to the cementing sites with different requirements on well depth and amplitude.

Linear and Logarithmic Time Compositions of Quantum Many-Body Operators.

We develop a generalized framework for constructing many-body-interaction operations either in linear time or in logarithmic time with a linear number of ancilla qubits. Exact gate decompositions are given for Pauli strings, many-control Toffoli gates, number- and parity-conserving interactions, unitary coupled cluster operations, and sparse matrix generators. We provide a linear time protocol that works by creating a superposition of exponentially many different possible operator strings and then uses dynamical decoupling methodology to undo all the unwanted terms. A logarithmic time protocol overcomes the speed limit of the first by using ancilla registers to condition evolution to the support of the desired many-body interaction before using parallel chaining operations to expand the string length. The two techniques improve substantially on current strategies (reductions in time and space ranging from linear to exponential), are applicable to different physical interaction mechanisms such as cnot, XX, and XX+YY, and generalize to a wide range of many-body operators.

Development process of the grand piano duplex scale

Acoustical investigations of the earliest examples of implemented duplex schematics allow to shed light on the question of how much of the piano development in the late 19th century was still a trial and error approach or already a methodical process based on empirical findings. Further, it is investigated if the intended effect was instantly perceivable, or if it was first a theoretical concept, which was later refined to enhance a certain tonal character. For a modern grand piano, the influence of the duplex schematic on the vibroacoustic behavior and the aural impression is extensively covered by Öberg and Askenfelt. By performing measurements on several pianos from the late eighteen hundreds, most prominently the so-called Helmholtz piano, a Steinway grand presented as a gift to von Helmholtz in appreciation of the impact of his work on the company’s piano development, it is possible to retrace development procedures in the workshop in that specific time period. Design parameters from the respective pianos are obtained, e.g., string length ratios, angles from main string to front duplex, boundary conditions, and string diameters. Acoustical measurements, as proposed by Öberg and Askenfelt, are performed to examine if these constructive changes have any significant effect on the generated sound and to allow a comparative analysis of both historical and contemporary instruments.

When black holes collide: Probing the interior composition by the spectrum of ringdown modes and emitted gravitational waves

The merger of colliding black holes (BHs) should lead to the production of ringdown or quasinormal modes (QNMs), which may very well be sensitive to the state of the interior. We put this idea to the test with a recent proposal that the interior of a BH consists of a bound state of highly excited, long, closed, interacting strings; figuratively, a collapsed polymer. We show that such BHs do indeed have a distinct signature in their QNM spectrum: A new class of modes whose frequencies are parametrically lower than the lowest-frequency mode of a classical BH and whose damping times are parametrically longer. The reason for the appearance of the new modes is that our model contains another scale, the string length, which is parametrically larger than the Planck length. This distinction between the collapsed-polymer model and general-relativistic BHs could be made with gravitational-wave observations and offers a means for potentially measuring the strength of the coupling in string theory. For example, GW150914 already allows us to probe the strength of the string coupling near the regime which is predicted by the unification of the gravitational and gauge-theory couplings. We also derive bounds on the amplitude of the collapsed-polymer QNMs that can be placed by current and future gravitational-wave observations.

GPU Based N-Gram String Matching Algorithm with Score Table Approach for String Searching in Many Documents

String searching in documents has become a tedious task with the evolution of Big Data. Generation of large data sets demand for a high performance search algorithm in areas such as text mining, information retrieval and many others. The popularity of GPU’s for general purpose computing has been increasing for various applications. Therefore it is of great interest to exploit the thread feature of a GPU to provide a high performance search algorithm. This paper proposes an optimized new approach to N-gram model for string search in a number of lengthy documents and its GPU implementation. The algorithm exploits GPGPUs for searching strings in many documents employing character level N-gram matching with parallel Score Table approach and search using CUDA API. The new approach of Score table used for frequency storage of N-grams in a document, makes the search independent of the document’s length and allows faster access to the frequency values, thus decreasing the search complexity. The extensive thread feature in a GPU has been exploited to enable parallel pre-processing of trigrams in a document for Score Table creation and parallel search in huge number of documents, thus speeding up the whole search process even for a large pattern size. Experiments were carried out for many documents of varied length and search strings from the standard Lorem Ipsum text on NVIDIA’s GeForce GT 540M GPU with 96 cores. Results prove that the parallel approach for Score Table creation and searching gives a good speed up than the same approach executed serially.

Efficient Length Doubling from Tweakable Block Ciphers

We present a length doubler, LDT, that turns an n-bit tweakable block cipher into an efficient and secure cipher that can encrypt any bit string of length [n..2n − 1]. The LDT mode is simple, uses only two cryptographic primitive calls (while prior work needs at least four), and is a strong length-preserving pseudorandom permutation if the underlying tweakable block ciphers are strong tweakable pseudorandom permutations. We demonstrate that LDT can be used to neatly turn an authenticated encryption scheme for integral data into a mode for arbitrary-length data.

Efficient Length Doubling From Tweakable Block Ciphers

We present a length doubler, LDT, that turns an n-bit tweakable block cipher into an efficient and secure cipher that can encrypt any bit string of length [n..2n − 1]. The LDT mode is simple, uses only two cryptographic primitive calls (while prior work needs at least four), and is a strong length-preserving pseudorandom permutation if the underlying tweakable block ciphers are strong tweakable pseudorandom permutations. We demonstrate that LDT can be used to neatly turn an authenticated encryption scheme for integral data into a mode for arbitrary-length data.

Citation of a taxon name identifier issued by the ICN‐recognized registration repositories instead of taxon name author citation

AbstractProblems with taxon name author citation in the running text of scientific articles are outlined. Particularly, the length of author names strings has significantly increased in the last decades, which could be demonstrated by analysis of names in the LIAS database. In addition, ambiguity of author name citation has increased because of variations in author name abbreviation and incomplete or incorrect citation of authors’ names. It is therefore suggested that in non‐taxonomic scientific publications, author names should be replaced by taxon name identifiers as issued by registration repositories. The advantage of such approach especially in context with linked open data and semantic network challenges is described. An additional recommendation in Article 46 of the ICN with an example is suggested.

Prefix and suffix reversals on strings

The Sorting by Prefix Reversals problem consists in sorting the elements of a given permutation π using a minimum number of prefix reversals, i.e. reversals that always involve the leftmost element of π. A natural extension of this problem is to consider strings, in which any letter may appear several times, rather than permutations. In strings, three different types of problems arise: grouping (given a string S, transform it so that all identical letters are consecutive), sorting (a constrained version of grouping, in which the target string must be lexicographically ordered) and rearranging (given two strings S and T, transform S into T). In this paper, we study these three problems, under an algorithmic viewpoint, in the setting where two operations, rather than one, are allowed: namely, prefix and suffix reversals — where a suffix reversal must always involve the rightmost element of the string. We first compare the “prefix reversals only” case to our case, before presenting a series of algorithmic results on these three problems concerning polynomiality, constant ratio approximation algorithms, NP-hardness and fixed-parameterized tractability. These results depend on the size k of the alphabet on which the strings are built, with a particular focus on small-sized alphabet instances (i.e., k=O(1)) and big-sized alphabet instances (i.e. n−k=O(1), where n is the length of the input string(s)).