String Length Research Articles

Insertion and Deletion Correction in Polymer-Based Data Storage

Synthetic polymer-based data storage seems to be a particularly promising candidate that could help to cope with the ever-increasing demand for archival storage requirements. It involves designing molecules of distinct masses to represent the respective bits {0, 1}, followed by the synthesis of a polymer of molecular units that reflects the order of bits in the information string. Reading out the stored data requires the use of a tandem mass spectrometer, that fragments the polymer into shorter substrings and provides their corresponding masses, from which the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">composition</i> , i.e. the number of 1s and 0s in the concerned substring can be inferred. Prior works have dealt with the problem of unique string reconstruction from the set of all possible compositions, called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">composition multiset</i> . This was accomplished either by determining which string lengths always allow unique reconstruction, or by formulating coding constraints to facilitate the same for all string lengths. Additionally, error-correcting schemes to deal with substitution errors caused by imprecise fragmentation during the readout process, have also been suggested. This work builds on this research by extending previously considered error models, mainly confined to substitution of compositions. To this end, we define new error models that consider insertions of spurious compositions and deletions of existing ones, thereby corrupting the composition multiset. We analyze if the reconstruction codebook proposed by Pattabiraman <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al</i> . is indeed robust to such errors, and if not, propose new coding constraints to remedy this.

Seeding with minimized subsequence.

Modern methods for computation-intensive tasks in sequence analysis (e.g. read mapping, sequence alignment, genome assembly, etc.) often first transform each sequence into a list of short, regular-length seeds so that compact data structures and efficient algorithms can be employed to handle the ever-growing large-scale data. Seeding methods using kmers (substrings of length k) have gained tremendous success in processing sequencing data with low mutation/error rates. However, they are much less effective for sequencing data with high error rates as kmers cannot tolerate errors. We propose SubseqHash, a strategy that uses subsequences, rather than substrings, as seeds. Formally, SubseqHash maps a string of length n to its smallest subsequence of length k, k < n, according to a given order overall length-k strings. Finding the smallest subsequence of a string by enumeration is impractical as the number of subsequences grows exponentially. To overcome this barrier, we propose a novel algorithmic framework that consists of a specifically designed order (termed ABC order) and an algorithm that computes the minimized subsequence under an ABC order in polynomial time. We first show that the ABC order exhibits the desired property and the probability of hash collision using the ABC order is close to the Jaccard index. We then show that SubseqHash overwhelmingly outperforms the substring-based seeding methods in producing high-quality seed-matches for three critical applications: read mapping, sequence alignment, and overlap detection. SubseqHash presents a major algorithmic breakthrough for tackling the high error rates and we expect it to be widely adapted for long-reads analysis. SubseqHash is freely available at https://github.com/Shao-Group/subseqhash.

Forecasting supercritical behavior of drill strings in horizontal wells

The determining factor in the current changes in the world energy balance and its structure, as well as the global development of the oil and gas industry, is currently the technological factor. As a result, fundamentally new categories of horizontal and inclined wells appeared and developed. They give a multiple increase in flow rates, as they increase the production area many times over. They are used in the development of offshore projects, in swampy and very difficult areas, to increase oil recovery, restoration of inactive wells.&#x0D; New technologies based on the method of horizontal drilling have revolutionized the practice and theory of world oil production, as they have allowed the destruction of offshore oil and gas fields without the construction of expensive offshore foundations and platforms.&#x0D; When drilling horizontal wells, as a rule, the main cause of emergencies is the loss of stability of the drill string, its bifurcation protrusion and the maximum frictional interaction with the well wall. The issues of theoretical modeling of the phenomenon of unstable protrusion of columns are associated with significant difficulties, the main of which is due to the need to set the Sturm-Liouville boundary value problem on a large length of drill string. Because for deep wells, the drill string becomes geometrically similar to a human hair, many traditional mathematical methods used to integrate solving equations become poorly convergent in these cases.&#x0D; Based on the theory of curvilinear flexible rods, the problem of theoretical modeling of supercritical states of drill strings taking into account their contact interaction with the walls of oil and gas wells is set. Analytical solutions of the problem are constructed, which determine the critical values of external tensile or compressive longitudinal force and torque at a given difference in the diameters of the cavity and the drill string, the zones of supercritical states of drill strings are established.

Kissing the cheeks of Huygens

How well do the so-called cheeks of Huygens enforce a constant time of oscillation on a pendulum, independent of the amplitude of the pendulum swing? We use a video measurement tool to test it with a homemade experimental setup that can be fruitfully used in classroom and physics laboratory settings. Data fits reveal how well the setup confirms the usefulness of the cheeks of Huygens. Comparisons of computer model results with recorded data have been made for the same purpose. The equation of motion of a pendulum with a string of arbitrary length that winds along two surfaces of cycloidal cheeks is derived, too. Numerical solutions of this equation are used for the error analysis of measurements with the homemade setup.

Adults systematically underestimate decimals and whole number exposure induces further magnitude-based underestimation.

Decimal numbers are generally assumed to be a straightforward extension of the base-ten system for whole numbers given their shared place value structure. However, in decimal notation, unlike whole numbers, the same magnitude can be expressed in multiple ways (e.g., 0.8, 0.80, 0.800, etc.). Here, we used a number line task with carefully selected stimuli to investigate how equivalent decimals (e.g., 0.8 and 0.80 on a 0-1 number line) and proportionally equivalent whole numbers (e.g., 80 on a 0-100 number line) are estimated. We find that young adults (n = 88, Mage = 20.22 years, SD = 1.65, 57 female) have a linear response pattern for both decimals and whole numbers, but those double-digit decimals (e.g., 0.08, 0.82, 0.80) are systematically underestimated relative to proportionally equivalent whole numbers (e.g., 8, 82, 80). Moreover, decimal string length worsens the underestimation, such that single-digit decimals (e.g., 0.8) are perceived as smaller than their equivalent double-digit decimals (e.g., 0.80). Finally, we find that exposing participants to whole number stimuli before decimal stimuli induces magnitude-based underestimation, that is, greater underestimation for larger decimals. Together, these results suggest a small but persistent underestimation bias for decimals less than one, and further that decimal magnitude estimation is fragile and subject to greater underestimation when exposed to whole numbers. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

A more convenient method to predict gravitational acceleration (g) using smartphone’s proximity sensor in a simple pendulum experiment

The application of smartphones in physics learning is inevitable because of the advanced technology installed in them. The simple pendulum is a classical topic in physics relating to gravitational acceleration. Smartphones are equipped with a proximity sensor that can record the period of an oscillating pendulum. A method to determine gravitational acceleration (g) using a smartphone proximity sensor in a simple pendulum experiment was presented in this study. This proposed method is more convenient and straightforward because it does not require additional equipment apart from string and bob. Furthermore, the simplicity of this method is assisted by software used that is able to display directly the results of period measurement that subsequently were applied to calculate the gravitational acceleration (g). The string length was varied to analyze the consistency of measurement results. The calculated g values were compared to the local gravity value and produced a relative error with a range of 0.11%–0.54%. The reported g value combined with uncertainty propagation was 9.75 ± 0.02 ms−2.

Lie Group Formulation and Sensitivity Analysis for Shape Sensing of Variable Curvature Continuum Robots With General String Encoder Routing

This article considers a combination of actuation tendons and measurement strings to achieve accurate shape sensing and direct kinematics of continuum robots. Assuming general string routing, a methodical Lie group formulation for the shape sensing of these robots is presented. The shape kinematics is expressed using arc-length-dependent curvature distributions parameterized by modal functions, and the Magnus expansion for Lie group integration is used to express the shape as a product of exponentials. The tendon and string length kinematic constraints are solved for the modal coefficients and the configuration space and body Jacobian are derived. The noise amplification index for the shape reconstruction problem is defined and used for optimizing the string/tendon routing paths, and a planar simulation study shows the minimal number of strings/tendons needed for accurate shape reconstruction. A torsionally stiff continuum segment is used for experimental evaluation, demonstrating mean (maximal) end-effector absolute position error of less than 2% (5%) of total length. Finally, a simulation study of a torsionally compliant segment demonstrates the approach for general deflections and string routings. We believe that the methods of this article can benefit the design process, sensing, and control of continuum and soft robots.

Gone Fishin': Perceiving the length of one object that is non-rigidly attached to a wielded object.

We performed four experiments to investigate whether people can perceive the length of a target object (a "fish") that is attached to a freely wielded object (the "fishing pole") by a length of string, and if so, whether this ability is grounded in the sensitivity of the touch system to invariant mechanical parameters that describe the forces and torques required to move the target object. In particular, we investigated sensitivity to mass, static moment, and rotational inertia-the forces required to keep an object from falling due to gravity, the torque required to keep an object from rotating due to gravity, and the torques required to actively rotate an object in different directions, respectively. We manipulated the length of the target object (Experiment 1), the mass of the target object (Experiment 2), and the mass distribution of the target object (Experiments 3 and 4). Overall, the results of the four experiments showed that participants can perform this task. Moreover, when the task is configured such that it more closely approximates a wielding at a distance task, the ability to do so is grounded in sensitivity to such forces and torques.

Differential and Linear properties of vectorial boolean functions based on chi

To evaluate the security of a cryptographic primitive, investigating its resistance against differential and linear cryptanalysis is required. Many modern cryptographic primitives repeatedly apply similar round functions alternated with the addition of round keys or constants. A round function usually consists of a non-linear mapping and a number of linear mappings. The non-linear mapping χ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi$$\\end{document} is used in different cryptographic primitives such as Keccak and Subterranean. An alternative version of χ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi$$\\end{document} is used in Ascon and the non-linear layer of Simon has the same differential and linear properties of χ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi$$\\end{document}. The mapping χ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi$$\\end{document} can be applied to strings with different lengths. For instance, it can be parallelly applied to small-length strings as in Keccak, where it works on 5-bit strings, or it can be applied to big-length strings as in Subterranean, where it works on a string of length 257. Investigating the differential and linear properties of χ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi$$\\end{document} working on alternative lengths of strings, provides useful information to designers to make a better choice for the non-linear layer. Some differential properties of χ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi$$\\end{document} have been analyzed in [8] and in this work we provide a revised presentation of them. We then extend this study and we analyze linear propagation properties of χ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi$$\\end{document}. Thanks to these additional results, we extend the comparison between the application of parallel instances of χ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi$$\\end{document} on small-length strings and the application of a single instance of χ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi$$\\end{document} on a big-length string. We show how we can apply the results of this study also to the non-linear layers of Ascon and Simon thanks to their affine-equivalence with χ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi$$\\end{document}.

Longest bordered and periodic subsequences

We present an algorithm computing the longest periodic subsequence of a string of length n in O(n7) time with O(n3) space. We obtain improvements when restricting the exponents or extending the search allowing the reported subsequence to be subperiodic down to O(n2) time and O(n) space. By allowing subperiodic subsequences in the output, the task becomes finding the longest bordered subsequence, for which we devise a conditional lower bound.

GPU acceleration of Levenshtein distance computation between long strings

Computing edit distance for very long strings has been hampered by quadratic time complexity with respect to string length. The WFA algorithm reduces the time complexity to a quadratic factor with respect to the edit distance between the strings. This work presents a GPU implementation of the WFA algorithm and a new optimization that can halve the elements to be computed, providing additional performance gains. The implementation allows to address the computation of the edit distance between strings having hundreds of millions of characters. The performance of the algorithm depends on the similarity between the strings. For strings longer than million characters, the performance is the best ever reported, which is above TCUPS for strings with similarities greater than 70% and above one hundred TCUPS for 99.9% similarity.

The hardest language for grammars with context operators

In 1973, Greibach (“The hardest context-free language”, SIAM J. Comp., 1973) constructed a context-free language L0 with the property that every context-free language can be reduced to L0 by a homomorphism, thus representing it as an inverse homomorphic image h−1(L0). In this paper, a similar characterization is established for a family of grammars equipped with operators for referring to the left context of any substring, recently defined by Barash and Okhotin (“An extension of context-free grammars with one-sided context specifications”, Inform. Comput., 2014). An essential step of the argument is a new normal form for grammars with context operators, in which every nonterminal symbol defines only strings of odd length in left contexts of even length: the even-odd normal form. The characterization is completed by showing that the language family defined by grammars with context operators is closed under inverse homomorphisms; actually, it is closed under injective nondeterministic finite transductions.

Definitions of entwinement

Entwinement was first introduced as the CFT dual to extremal, non-minimal geodesics of quotiented AdS3 spaces. It was heuristically meant to capture the entanglement of internal, gauged degrees of freedom, for instance in the symmetric product orbifold CFT of the D1/D5 brane system. The literature now contains different, and sometimes inequivalent, field theory definitions of entwinement. In this paper, we build a discretized lattice model of symmetric product orbifold CFTs, and explicitly construct a gauge-invariant reduced density matrix whose von Neumann entropy agrees with the holographic computation of entwinement. Refining earlier notions, our construction gives meaning to the entwinement of an interval of given size within a long string of specific length. We discuss similarities and differences with previous definitions of entwinement.

Regge trajectories of tetraquarks and pentaquarks with massive quarks in the flux tube model

In recent years, many tetraquarks and pentaquarks have been discovered by various experimental groups and [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] are some of the interesting observed tetraquark and pentaquark states. The Regge trajectories of some such states are studied in view of the flux tube model of hadrons with finite quark masses. The effect of flux tube (or string) length variation on the Regge trajectories of these states is analyzed in detail. It is observed that for a fixed angular momentum, the string length has a constant value. Some other states are also proposed and the results obtained are then compared with the studies by others. Our findings correspond rather well with those of other researchers and with those of the experiment.

A symbolic algorithm for the case-split rule in solving word constraints with extensions

Case split is a core proof rule in current decision procedures for the theory of string constraints. Its use is the primary cause of the state space explosion in string constraint solving, since it is the only rule that creates branches in the proof tree. Moreover, explicit handling of the case split rule may cause recomputation of the same tasks in multiple branches of the proof tree. In this paper, we propose a symbolic algorithm that significantly reduces such a redundancy. In particular, we encode a string constraint as a regular language and proof rules as rational transducers. This allows us to perform similar steps in the proof tree only once, alleviating the state space explosion. We also extend the encoding to handle arbitrary Boolean combinations of string constraints, length constraints, and regular constraints. In our experimental results, we validate that our technique works in many practical cases where other state-of-the-art solvers fail to provide an answer; our Python prototype implementation solved over 50% of string constraints that could not be solved by the other tools.

Text Generator using GPT2 Model

Abstract- GPT-2 is state of art algorithm transfer learning with respect to nlp task we can do it like text summarizationand many more applications. The text generation application programming interface is supported by a large-scale unsupervised language model capable of generating paragraphs of text This transformer-based language model, based on OpenAI's GPT-2 model, accepts a sentence or partial sentence as input and predicts subsequent text. GPT-2 uses input textto set the initial context for further text generation. The length of an input string can range from few words to a maximumsequence length of 1024 tokens. The longer an initial input, the more subject context is provided to a model. Generally, longer inputs produce a more coherent text output. It was specifically trained to guess the next word in sentences. GPT-2 isa massive model that contains a massive amount of compressed knowledge from various parts of the internet. It can be usedto forecast the likelihood of a sentence. The model learns an internal representation of the English language, which it can then use to extract features useful for subsequent tasks. We have used a tkinter which is a GUI to display the generated output. Keywords—Text generation, Graphical User Interface, gpt2 transformer,Open AI,tkinter,

Correlating Surface and Downhole Perforation Entry Hole Measurements Leads to Development of Improved Perforating Systems

Summary Studies have shown that achieving a consistent perforation hole size in casing (i.e., entry hole) and zero-phase perforation gun orientation led to improved treatment distribution among multiple perforation clusters in plug-and-perf limited entry treatments. In addition to reducing variation in the perforation entry hole by establishing uniformity in gun clearance and the angle of incidence of the perforation jet at the wall of the casing, oriented perforating has been shown to minimize the tendency of proppant to separate from the fracturing fluid while traveling across the perforated intervals (inertial effect) and mitigate nonuniform entry hole erosion due to gravity-induced proppant stratification. The primary goal of this study was to determine the controllable perforating gun elements and accessories that effect the accuracy of gun orientation and entry hole dimensions. Surface tests were conducted at manufacturing facilities for determining the characteristics of the entry holes in pipe produced by shaped explosive charges using various system configurations and the robustness of various gun orientation devices. Promising perforating systems were then used in wellbores to create calibration entry holes (downhole tests) that were measured for equivalent diameter and orientation accuracy using high-resolution acoustic imaging before conducting treatments. This process enabled components of the perforating system influencing entry hole size and gun orientation to be evaluated and modified, as necessary. Elements of the perforating system and downhole environment that influenced entry hole size and consistency included casing type, cement sheath characteristics, perforating gun clearance and orientation, perforating charge type and density, packing arrangement of multiple charges, charge tube and charge carrier design, gun detonation system, hydrostatic pressure, and locking devices. Achieving tight control of these elements significantly reduced variation in entry hole size. Deviations from surface and downhole testing results were commonly attributed to using perforating system elements in the field that differed from those used by the manufacturer in surface testing. Factors affecting gun orientation accuracy and consistency included weight bar type, gun string length, weight, and stiffness, the presence of modified standoff bands, progressive gun deformation during firing, wellbore tortuosity, and self-orienting devices. Several orientation systems were found that achieved orientation within the target 20°-window. To assess the value of this workflow process, the paper includes information on the results of diagnostic tests for evaluating the accuracy of the ultrasonic measuring device, the derivation process used for determining coefficients for a two-component perforation erosion model, and the use of the derived erosion rate coefficients for computing the mass of proppant that enters each perforation and perforation cluster during a fracturing treatment.

Creating and detecting specious randomness

We present a new test of non-randomness that tests both the lower and the upper critical limit of a chi ^{2}-statistic. While checking the upper critical value has been employed by other tests, we argue that also the lower critical value should be examined for non-randomness. To this end, we prepare a binary sequence where all possible bit strings of a certain length occurs the same number of times and demonstrate that such sequences pass a well-known suite of tests for non-randomness. We show that such sequences can be compressed, and therefore are somewhat predictable and thus not fully random. The presented test can detect such non-randomness, and its novelty rests on analysing fixed-length bit string frequencies that lie closer to the a priori probabilities than could be expected by chance alone.

Gregory-Laflamme encounters Superradiance

We investigate the effect of superradiant scattering of gravitational perturbations on the stability of rotating black strings, focusing on the six dimensional equal-spinning Myers-Perry black string. We find that rapidly rotating black strings are unstable to gravitational superradiant modes within a bounded range of string lengths. The instability occurs because momentum along the string direction creates a potential barrier that allows for the confinement of superradiant modes. Yet, five dimensional Myers-Perry black holes do not have stable particle orbits so, unlike other known superradiant systems, these black strings remain stable to perturbations with sufficiently high azimuthal mode number — this is a ‘finite-m’ superradiant instability. For some parameters, this instability competes with the Gregory-Laflamme instability, but otherwise exists independently. The onset of this instability is degenerate and branches to multiple steady-state solutions. This paper is the first of a trilogy: in the next two, we construct two distinct families of rotating strings emerging from the superradiant onset (the ‘black resonator strings’ and ‘helical black strings’). We argue that similar physics is present in 5-dimensional Kerr black strings, but not in D > 6 equal-spinning Myers-Perry black strings.

Short attribute-based signatures for arbitrary Turing machines from standard assumptions

This paper presents the first attribute-based signature (ABS) scheme supporting signing policies representable by Turing machines (TM), based on well-studied computational assumptions. Our work supports arbitraryTMs as signing policies in the sense that the TMs can accept signing attribute strings of unbounded polynomial length and there is no limit on their running time, description size, or space complexity. Moreover, we are able to achieve input-specific running time for the signing algorithm. All other known expressive ABS schemes could at most support signing policies realizable by either arbitrary polynomial-size circuits or TMs having a pre-determined upper bound on the running time. Consequently, those schemes can only deal with signing attribute strings whose lengths are a priori bounded, as well as suffers from the worst-case running time problem. On a more positive note, for the first time in the literature, the signature size of our ABS scheme only depends on the size of the signed message and is completely independent of the size of the signing policy under which the signature is generated. This is a significant achievement from the point of view of communication efficiency. Our ABS construction makes use of indistinguishability obfuscation (IO) for polynomial-size circuits and certain IO-compatible cryptographic tools. Note that, all of these building blocks including IO for polynomial-size circuits are currently known to be realizable under well-studied computational assumptions.