Representation Of Strings Research Articles

Engineering perturbative string duals for symmetric product orbifold CFTs

Constructing a holographic string theory dual for a CFT in the perturbative, weakly coupled regime is a holy grail for gauge/string dualities that would not only open the door for proofs of the AdS/CFT correspondence but could also provide novel examples of string duals with and without supersymmetry. In this work we consider some marginal perturbation of a family of symmetric product orbifolds in two dimensions. From their correlation functions we engineer a bosonic string theory whose amplitudes are shown to reproduce the CFT correlation function order-by-order both in the coupling and in 1/N. Our derivation does not require to compute and compare correlation functions explicitly but rather relies on a sequence of identities that can be derived using path integral methods. The bosonic string theory we engineer is based on the field content of the Kac-Wakimoto representation of strings in AdS3 with k units of pure NSNS flux, but the interaction terms we obtain are different. They include current algebra preserving interaction terms with one unit of spectral flow.

Case Study: Optimizing Grading Ring Design for High Voltage Polymeric Insulators in Power Transmission Systems for Enhanced Electric Field and Voltage Distribution by Using a Finite Element Method

This research paper aims to investigate the optimal design of grading rings for high-voltage polymeric insulators in an actual power transmission system, with a focus on improving the electrical representation of the insulator strings. One such subsidiary accessory commonly used with porcelain and polymer insulator strings is the grading ring, which is employed to improve the electric field and voltage distribution surrounding the insulator string. The efficiency of insulator strings can be enhanced by grading rings, as they facilitate a more linear potential division along the strings. The design parameters of grading rings significantly influence their performance on insulator strings. In this study, we examine the optimal design of the grading rings of high-voltage polymer insulators, since no uniform design methodology has been developed for high-voltage polymer insulators, and their optimization is currently the subject of many research studies. The electric field on an outdoor polymeric insulator is examined using finite element method (FEM) software and COMSOL Multi-Physics program. A 2D model is utilized to simulate a 220 kV polymeric insulator. The effectiveness of high-voltage polymeric insulators greatly depends on the dimensions and locations of the grading rings. Therefore, the impacts of the radius of the grading ring and that of its tube and the tube’s vertical position are thoroughly investigated, under dry and humid conditions. To achieve this objective, a search algorithm is employed to adjust the dimensions and locations of the grading ring. The optimization approach in this study is based on determining the maximum electric field across the insulator surface, while ensuring that it remains below the corona initiation level.

Context-sensitive fusion grammars and fusion grammars with forbidden context are universal

Context-sensitive fusion grammars and fusion grammars with forbidden context are special cases of context-dependent fusion grammars where instead of finite sets of positive and negative context conditions in the first case a rule has only a single positive context condition and in the second case a rule has only a finite set of negative context conditions. In this paper, we show that several decision problems can be formulated quite intuitively by these grammars. In particular, we show that the Boolean satisfiability problem as well as the Post correspondence problem can be transformed into a context-sensitive fusion grammar and that the graph coloring problem can be transformed into a fusion grammar with forbidden context such that the generated languages give solutions for the problems. Furthermore, we prove that both grammar types can generate all recursively enumerable string languages (up to representation of strings as graphs) and are universal in this respect.

Is human face recognition lateralized to the right hemisphere due to neural competition with left-lateralized visual word recognition? A critical review.

The right hemispheric lateralization of face recognition, which is well documented and appears to be specific to the human species, remains a scientific mystery. According to a long-standing view, the evolution of language, which is typically substantiated in the left hemisphere, competes with the cortical space in that hemisphere available for visuospatial processes, including face recognition. Over the last decade, a specific hypothesis derived from this view according to which neural competition in the left ventral occipito-temporal cortex with selective representations of letter strings causes right hemispheric lateralization of face recognition, has generated considerable interest and research in the scientific community. Here, a systematic review of studies performed in various populations (infants, children, literate and illiterate adults, left-handed adults) and methodologies (behavior, lesion studies, (intra)electroencephalography, neuroimaging) offers little if any support for this reading lateralized neural competition hypothesis. Specifically, right-lateralized face-selective neural activity already emerges at a few months of age, well before reading acquisition. Moreover, consistent evidence of face recognition performance and its right hemispheric lateralization being modulated by literacy level during development or at adulthood is lacking. Given the absence of solid alternative hypotheses and the key role of neural competition in the sensory-motor cortices for selectivity of representations, learning, and plasticity, a revised language-related neural competition hypothesis for the right hemispheric lateralization of face recognition should be further explored in future research, albeit with substantial conceptual clarification and advances in methodological rigor.

Ambitwistor strings in six and five dimensions

Ambitwistor strings are chiral (holomorphic) strings whose target is the space of complex null geodesics, ambitwistor space. We introduce twistor representations of ambitwistor space in 6 and 5 dimensions. In 6d the twistor representation is naturally conformally invariant. Anomaly cancellation leads to models that describe biadjoint scalar amplitudes and certain conformally invariant gauge and gravity theories, respectively of 4th and 6th order. There are three such models, reflecting triality for the conformal group SO(8) associated to these 6d models. On reduction to five dimensions, gauge anomaly cancellation requires supersymmetry and the resulting models describe maximally supersymmetric Yang-Mills and gravity. The twistor representation of these ambitwistor strings lead to formulæ for maximally supersymmetric gauge and gravity amplitudes based on the polarized scattering equations in 5d, found earlier by the first two authors.

A new approach to regular & indeterminate strings

In this paper we propose a new, more appropriate definition of regular and indeterminate strings. A regular string is one that is “isomorphic” to a string whose entries all consist of a single letter, but which nevertheless may itself include entries containing multiple letters. A string that is not regular is said to be indeterminate. We begin by proposing a new model for the representation of strings, regular or indeterminate, then go on to describe a linear time algorithm to determine whether or not a string x=x[1..n] is regular and, if so, to replace it by a lexicographically least (lex-least) string y whose entries are all single letters. Furthermore, we connect the regularity of a string to the transitive closure problem on a graph, which in our special case can be efficiently solved. We then introduce the idea of a feasible palindrome array MP of a string, and prove that every feasible MP corresponds to some (regular or indeterminate) string. We describe an algorithm that constructs a string x corresponding to given feasible MP, while ensuring that whenever possible x is regular and if so, then lex-least. A final section outlines new research directions suggested by this changed perspective on regular and indeterminate strings.

Supersymmetric S-matrices from the worldsheet in 10 & 11d

We obtain compact formulae for tree super-amplitudes for 10 and 11-dimensional supergravity and 10-dimensional supersymmetric Yang-Mills and Born-Infeld. These are based on the polarised scattering equations. These incorporate polarization data into a spinor field on the Riemann sphere and arise from a twistorial representation of ambitwistor strings in 10 and 11 dimensions. They naturally extend amplitude formulae to manifest maximal supersymmetry. The framework is the natural generalization of twistorial ambitwistor string formulae found previously in four and six dimensions and is informally motivated from a vertex operator prescription for a family of supersymmetric worldsheet ambitwistor string models.

Transformation of Turing Machines into Context-Dependent Fusion Grammars

Context-dependent fusion grammars were recently introduced as devices for the generation of hypergraph languages. In this paper, we show that this new type of hypergraph grammars, where the application of fusion rules is restricted by positive and negative context conditions, is a universal computation model. Our main result is that Turing machines can be transformed into these grammars such that the recognized language of the Turing machine and the generated language of the corresponding context-dependent fusion grammar coincide up to representation of strings as graphs. As a corollary we get that context-dependent fusion grammars can generate all recursively enumerable string languages.

Using RuleBuilder to Graphically Define and Visualize BioNetGen-Language Patterns and Reaction Rules.

RuleBuilder is a tool for drawing graphs that can be represented by the BioNetGen language (BNGL), which is used to formulate mathematical, rule-based models of biochemical systems. BNGL provides an intuitive plain text, or string, representation of such systems, which is based on a graphical formalism. Reactions are defined in terms of graph-rewriting rules that specify the necessary intrinsic properties of the reactants, a transformation, and a rate law. Rules also contain contextual constraints that restrict application of the rule. In some cases, the specification of contextual constraints can be verbose, making a rule difficult to read. RuleBuilder is designed to ease the task of reading and writing individual reaction rules or other BNGL patterns required for model formulation. The software assists in the reading of existing models by converting BNGL strings of interest into a graph-based representation composed of nodes and edges. RuleBuilder also enables the user to construct de novo a visual representation of BNGL strings using drawing tools available in its interface. As objects are added to the drawing canvas, the corresponding BNGL string is generated on the fly, and objects are similarly drawn on the fly as BNGL strings are entered into the application. RuleBuilder thus facilitates construction and interpretation of rule-based models.

Statistical Relational Learning With Unconventional String Models.

This paper shows how methods from statistical relational learning can be used to address problems in grammatical inference using model-theoretic representations of strings. These model-theoretic representations are the basis of representing formal languages logically. Conventional representations include a binary relation for order and unary relations describing mutually exclusive properties of each position in the string. This paper presents experiments on the learning of formal languages, and their stochastic counterparts, with unconventional models, which relax the mutual exclusivity condition. Unconventional models are motivated by domain-specific knowledge. Comparison of conventional and unconventional word models shows that in the domains of phonology and robotic planning and control, Markov Logic Networks With unconventional models achieve better performance and less runtime with smaller networks than Markov Logic Networks With conventional models.

Learning to Represent Handwritten Shapes and Words for Matching and Recognition

Writing is one of the most important forms of communication and for centuries, handwriting had been the most reliable way to preserve knowledge. However, despite the recent development of printing houses and electronic devices, handwriting is still broadly used for taking notes, doing annotations, or sketching ideas. In order to be easily accessed, there is a huge amount of handwritten documents, some of them with uncountable cultural value, that have been recently digitized. This has made necessary the development of methods able to extract information from these document images.Transferring the ability of understanding handwritten text or recognizing handwritten shapes to computers has been the goal of many researches due to its huge importance for many different fields. However, designing good representations to deal with handwritten shapes, e.g. symbols or words, is a very challenging problem due to the large variability of these kinds of shapes. One of the consequences of working with handwritten shapes is that we need representations to be, i.e., able to adapt to large intra-class variability. We need representations to be discriminative, i.e., able to learn what are the differences between classes. And, we need representations to be efficient, i.e., able to be rapidly computed and compared. Unfortunately, current techniques of handwritten shape representation for matching and recognition do not fulfill some or all of these requirements.Through this thesis we focus on the problem of learning to represent handwritten shapes aimed at retrieval and recognition tasks. Concretely, on the first part of the thesis, we focus on the general problem of representing any kind of handwritten shape. We first present a novel shape descriptor based on a deformable grid that deals with large deformations by adapting to the shape and where the cells of the grid can be used to extract different features. Then, we propose to use this descriptor to learn statistical models, based on the Active Appearance Model, that jointly learns the variability in structure and texture of a given class. Then, on the second part, we focus on a concrete application, the problem of representing handwritten words, for the tasks of word spotting, where the goal is to find all instances of a query word in a dataset of images, and recognition. First, we address the segmentation-free problem and propose an unsupervised, sliding-window-based approach that achieves state-of-the-art results in two public datasets.Second, we address the more challenging multi-writer problem, where the variability in words exponentially increases. We describe an approach in which both word images and text strings are embedded in a common vectorial subspace, and where those that represent the same word are close together. This is achieved by a combination of label embedding and attributes learning, and a common subspace regression. This leads to a low-dimensional, unified representation of word images and strings, resulting in a method that allows one to perform either image and text searches, as well as image transcription, in a unified framework. We evaluate our methods on different public datasets of both handwritten documents and natural images showing results comparable or better than the state-of-the-art on spotting and recognition tasks.

A Framework for Succinct Labeled Ordinal Trees over Large Alphabets

We consider succinct representations of labeled ordinal trees that support a rich set of operations. Our new representations support a much broader collection of operations than previous work. In our approach, labels of nodes are stored in a preorder label sequence, which can be compressed using any succinct representation of strings that supports $$\mathtt{{access}}$$ access , $${\mathtt{{rank}}}$$ rank and $$\mathtt{{select}}$$ select operations. Thus, we present a framework for succinct representations of labeled ordinal trees that is able to handle large alphabets. This answers an open problem presented by Geary et al., which asks for representations of labeled ordinal trees that remain space-efficient for large alphabets. We further extend our work and present the first succinct representations for dynamic labeled ordinal trees that support several label-based operations including finding the level ancestor with a given label.

The role of consonant/vowel organization in perceptual discrimination.

According to a recent hypothesis, the CV pattern (i.e., the arrangement of consonant and vowel letters) constrains the mental representation of letter strings, with each vowel or vowel cluster being the core of a unit. Six experiments with the same/different task were conducted to test whether this structure is extracted prelexically. In the mismatching trials, the targets were pseudowords built by the transposition of 2 adjacent letters from base words. In one condition, the pseudowords had the same number of vowel clusters as the base word, whereas in another condition, the transposition modified the number of vowel clusters (e.g., poirver: 2 vowel clusters vs. povirer: 3 vowel clusters, from POIVRER: 2 vowel clusters). In Experiment 1, pseudowords with a different number of vowel clusters were more quickly processed than pseudowords preserving the CV structure of their base word. Experiment 2 further showed that this effect was not due to changes in syllabic structure. In Experiment 3, the pattern of results was also replicated when the category (consonant or vowel) of the transposed letters was strictly equated between conditions. Experiments 4 and 5 confirmed that the effects were not attributable to lexical processing, to differences in letter identity, or to the position of transpositions. The results suggest that the orthographic representation of letter strings is influenced by the CV pattern at an early, prelexical processing stage.

Fast algorithms for finding a minimum repetition representation of strings and trees

A string with many repetitions can be represented compactly by replacing h-fold contiguous repetitions of a string r with (r)h. We present a compact representation, which we call a repetition representation (of a string) or RRS, by which a set of disjoint or nested tandem arrays can be compacted. In this paper, we study the problem of finding a minimum RRS or MRRS, where the size of an RRS is defined by the sum of the length of component letters and the description length of the component repetitions (⋅)h which is defined by wR(h) using a repetition weight function wR. We develop two dynamic programming-based algorithms to solve this problem: CMR, which works for any type of wR, and CMR-C, which is faster but can be applied to a constant wR only. CMR-C is an O(n2logn)-time O(nlogn)-space algorithm, which is more efficient in both time and space than CMR by a ((logn)/n)-factor, where n is the length of the given string. The problem of finding an MRRS for a string can be extended to that of finding a minimum repetition representation (of a tree) or MRRT for a given labeled ordered tree. For this problem, we present two algorithms, CMRT and CMRT-C, by using CMR and CMR-C, respectively, as a subroutine. As well as the theoretical analysis, we confirmed the efficiency of the proposed algorithms by experiments, which consist of the following three parts: First we demonstrated that CMR-C and CMRT-C are fast enough for large-scale data by using synthetic strings and trees, respectively. The size of an MRRS for a given string can be a measure of how compactly the string can be represented, meaning how well the string is structurally organized. This is also true of trees. To check such ability of MRRS-size, second we measured the size of an MRRS for chromosomes of nine different species. We found that all the chromosomes of the same species have a similar compression rate when realized by an MRRS. Run length encoding (RLE) was also shown to have species-specific compression rate, but species were separated more clearly by MRRS than by RLE. Third we examined the size of an MRRT for web pages of world-leading companies by using the tag trees, showing a consistency between the compression rate by an MRRT and visual web page structures.

NUMERICAL NEGATIVE SELECTION ALGORITHM

The artificial immune algorithm is the hot topic in much research such as the intrusion detection system, the information retrieval system and the data mining system. The negative selection algorithm is the typical artificial immune algorithm. A common representation of binary strings for antibody (detector) and antigen have been associated with inefficiencies when generating detector and inspecting antigen. We use a single integer to represent the detector and provide the basis of improving negative selection algorithm efficiency. In the detector generation algorithm, extracting sub-strings in self that its length is larger than threshold and converting them to single integer in numerical interval, then the rest integers in numerical interval are selected as numerical detectors. It can reduce the time and space overhead of detector generation and provide the facility to analyze the positive and negative errors when antigen inspection. The numerical matching rule is given. The B-tree is used to create index of numerical detector. Extracting sub-strings in antigen that its length is larger than threshold and converting them to some integers. If there is the same value as those integers in the index of numerical detector, then the antigen matches one numerical detector. It can improve the efficiency of antigen inspection. Finally the prototype of the numerical negative selection algorithm and negative selection algorithm are realized to test the overhead of the detector generation and antigen inspection using the live data set. The results show that the numerical negative selection algorithm can reduce the time and space overhead and avoid fluctuation of the overhead.

A Novel Approach to Dynamic Representation of Drill Strings in Test Rigs

Drill strings are used in oil and gas production as well as geothermal wells. They experience destructive vibrations, many of which are highly dependent on drill string modes. In this paper, we show that the lowest frequency modes are not necessarily the most critical and we delineate a methodology for reducing the number of modes representing the drill string. The frequency response function and stability diagram are used as measures of dynamic similarity between the proposed model and the drill string. We also introduce a novel approach to represent a drill string in laboratory test rigs. This approach not only represents the drill string dynamics but also offers flexibility to modify, remove, or augment the modes representing the system. The underlying principle is that in a multi-degree-of-freedom in-series spring-mass system with Rayleigh damping, dynamic modes can be decoupled. Applying the force to the end node (bit), the modes can then be configured separately in a parallel arrangement where their contributions to bit displacement are added algebraically. A practical arrangement for this purpose is proposed in this paper. Construction of a test rig that accurately represents the drill string dynamics is critical to validation of any test data on bits, bottom hole assemblies, instrument subs, and so on.

Letter Processing and the Formation of Memory Representations in Children with Naming Speed Deficits

The ability to recognize letter patterns within words as a single unit is important for fluent reading. This skill is based on previously established memory representations of common letter patterns. The ability to form these memory representations may be impaired in some poor readers, particularly readers with naming speed deficits (NSD). This study explored factors that influence letter processing and the subsequent formation of memory representations of letter strings in children with and without a NSD. Children were presented with a letter string, followed by a probe unit that was either a single letter, a two-letter cluster, or a repetition of the whole string. Children indicated whether or not the probe had been present in the preceding string. Two factors were manipulated: (a) amount of time to process the initial letter string, and (b) level of orthographic structure present in the letter string. Results indicated that overall, children with NSD performed less accurately than children without NSD. However, children with NSD showed no differential benefit in performance as a result of longer time to process a letter string. In addition, all readers were able to make use of the orthographic structure in a letter string to aid performance. Implications of results for establishing memory representations of letter strings are discussed.

Semi-classical mechanics in phase space: the quantum target of minimal strings

The target space Mp,q of (p,q) minimal strings is embedded into the phase space of an associated integrable classical mechanical model. This map is derived from the matrix model representation of minimal strings. Quantum effects on the target space are obtained from the semiclassical mechanics in phase space as described by the Wigner function. In the classical limit the target space is a fold catastrophe of the Wigner function that is smoothed out by quantum effects. Double scaling limit is obtained by resolving the singularity of the Wigner function. The quantization rules for backgrounds with ZZ branes are also derived.

Neural networks with chaotic recursive nodes: techniques for the design of associative memories, contrast with Hopfield architectures, and extensions for time-dependent inputs

This paper addresses the coding and storage of information in neural architectures with bifurcating recursive nodes that exhibit chaotic dynamics. It describes architectures of coupled recursive processing elements (RPEs) used to store binary strings, discusses the choices of network parameters related to the coding of zeros and ones, and analyzes several aspects of the network operation in implementing associative memories through populations of logistic maps. Experiments for the performance evaluation of these memories are described, and results addressing the operation under digital noise (flipped bits) and analog noise added to the prompting pattern are presented and analyzed. Quantitative aspects related to the representation of binary strings through cyclic states are equated, and then related to the planning and analysis of several experiments. A simple pre-processing procedure useful in situations of prompting conditions with analog noise is proposed, and the resultant increase in recovery performance presented. The performance of the RPEs associative networks is contrasted with the performance of Hopfield associative memories, and the situations where the RPEs networks present significant superiority are identified. An extended version of the proposed architecture, which allows to address the issues of time-dependent inputs and analog inputs, is analyzed in detail. Experimental results are presented, and the role of this extended architecture in providing mechanisms for modular RPEs architectures is pointed out.

Task demands and representation in long-term repetition priming.

The effects of task demands on the representation of letter strings in long-term repetition priming (LTRP) were explored in two lexical decision experiments. The stimuli in both experiments were words and nonwords, some presented horizontally and some vertically. The only difference between the two experiments was the response required by the participant. In Experiment 1, the participants pressed one of two buttons, indicating whether or not a given stimulus was a word. In Experiment 2, the participants pressed one of four buttons, indicating both the lexical status and the orientation of a given stimulus. The results were that in Experiment 1, LTRP was not disrupted by a change in stimulus orientation, whereas in Experiment 2 it was, suggesting that the nature of the stimulus representation utilized in LTRP is partially dependent on the demands of the task.