Symbol Alphabet Research Articles

Hopf algebra structure of the two loop three mass nonplanar Feynman diagram

The method of using Hopf algebras for calculating Feynman integrals developed by Abreu et al. is applied to the two-loop non-planar on-shell diagram with massless propagators and three external mass scales. We show that the existence of the method of cut Feynman diagrams comprising of the coproduct, the first entry condition and integrability condition that was found to be true for the planar case also holds for the non-planar case; furthermore, the non-planar symbol alphabet is the same as for the planar case. This is one of the main results of this work, and they have been obtained by a systematic analysis of the relevant cuts, using the symbolic manipulation codes HypExp and PolyLogTools. The obtained result for the symbol is cross-checked by an analysis of the known two-loop original Feynman integral result. In addition, we also reconstruct the full result from the symbol. This is the other main result in this paper.

Children with handwriting difficulties: developing orthographic knowledge of alphabet-letters to improve capacity to write alphabet symbols

Children with handwriting difficulties: developing orthographic knowledge of alphabet-letters to improve capacity to write alphabet symbols

Symbol alphabets from plabic graphs III: n = 9

Symbol alphabets of n-particle amplitudes in mathcal{N} = 4 super-Yang-Mills theory are known to contain certain cluster variables of G(4, n) as well as certain algebraic functions of cluster variables. In this paper we solve the C Z = 0 matrix equations associated to several cells of the totally non-negative Grassmannian, combining methods of arXiv:2012.15812 for rational letters and arXiv:2007.00646 for algebraic letters. We identify sets of parameterizations of the top cell of G+(5, 9) for which the solutions produce all of (and only) the cluster variable letters of the 2-loop nine-particle NMHV amplitude, and identify plabic graphs from which all of its algebraic letters originate.

Effects of underwater optical turbulence on light carrying orbital angular momentum and its classification using machine learning

Laser-based optical links offer the possibility of secure, high data rate underwater communication. Challenges include quickly modulating the light, and rapidly and reliably decoding the received symbols, despite degradation due to optical turbulence and scattering. This paper builds upon a framework introduced in 2016 to address these challenges. We constructed two novel 5-beam Laguerre-Gaussian basis sets, creating 25 symbol alphabets via superposition. We collected 139,000 images of the symbols, transmitted 4.3 meters through water with very strong optical turbulence. We use a novel convolutional neural network to decode them. We believe this work is the first to achieve high accuracy (93.7–99.9%) in an environment with extremely high levels (2∼107-108 m-2/3) of carefully documented experimentallyinduced optical turbulence. We improve upon previous work in several ways: using a larger alphabet (47 vs. 32), faster classification rates (10,000 Hz vs. 1,000 Hz), and a larger set of test images (96,000 vs 9,600).

PORTABILITY OF CARTOGRAPHIC SYMBOLS LIBRARY FOR OPEN STANDARDS

Abstract. The Geological Survey of Brazil has a library of palaeontology symbols to use in geological mapping works, currently in bitmap format and adapted for ESRI platform. This type of representation has presented anti-aliasing problems when reduced, in addition to not being suitable for map presentation on the web, according to OGC (Open Geospatial Consortium) specifications. This work presents a reproducible method in any symbol library type. The method consists of converting the symbol library to open-source format, resulting an OpenType font file, which can be installed on any operating system and view each symbol font in any software that has this functionality, such as a GIS (Geographic Information Systems) software. The need to develop font construction technique is due to improving typographic quality of cartographic representations and making library compatible with main GIS softwares. Those 61 pictorial palaeontology symbols were converted, one by one, to SVG (Scalable Vector Graphics) format. We imported each symbol as a glyph in FontForge font editor. Major computer platforms use OpenType format due to its wide availability and typographic flexibility, including provisions to deal with diverse characteristics of internationally symbolic alphabet systems. There is even the possibility of symbols standardizing in the UTF-8 alphabet system, an issue for the scientific community to study. The advantage of using the SVG format is its size, a compact text file, and has an excellent compression factor. In addition, version-control repositories, like GitHub, can store SVG files, which would facilitate content management. The adopted method proved to be applicable to any cartographic symbols library with good results. Rendering tests on different platforms (web or desktop) showed no noticeable differences. One of the most important aspects of the method presented in this work was to make cartographic symbols library public and open-source for use by the geoscientific community, regardless whether an open-source or proprietary platform is used, and so, the Geological Survey of Brazil will be able to distribute geological symbology patterns, according to Open Data definition.

Algebraic branch points at all loop orders from positive kinematics and wall crossing

There is a remarkable connection between the boundary structure of the positive kinematic region and branch points of integrated amplitudes in planar mathcal{N} = 4 SYM. A long-standing question has been precisely how algebraic branch points emerge from this picture. We use wall crossing and scattering diagrams to systematically study the boundary structure of the positive kinematic regions associated with MHV amplitudes. The notion of asymptotic chambers in the scattering diagram naturally explains the appearance of algebraic branch points. Furthermore, the scattering diagram construction also motivates a new coordinate system for kinematic space that rationalizes the relations between algebraic letters in the symbol alphabet. As a direct application, we conjecture a complete list of all algebraic letters that could appear in the symbol alphabet of the 8-point MHV amplitude.

Interdisciplinary and Intercultural Development of an Early Literacy App in Dhuwaya

Phonological awareness is a skill which is crucial in learning to read. In this paper, we report on the challenges encountered while developing a digital application (app) for teaching phonological awareness and early literacy skills in Dhuwaya. Dhuwaya is a Yolŋu language variety spoken in Yirrkala and surrounding areas in East Arnhem Land. Dhuwaya is the first language of the children who attend a bilingual school in which Dhuwaya and English are the languages of instruction. Dhuwaya and English have different phonemic inventories and different alphabets. The Dhuwaya alphabet is based on Roman alphabet symbols and has 31 graphemes (compared to 26 in English). The app was designed to teach children how to segment and blend syllables and phonemes and to identify common words as well as suffixes used in the language. However, the development was not straightforward, and the impact of the linguistic, cultural and educational challenges could not have been predicted. Amongst these was the inherent variation in the language, including glottal stops, the pronunciation of stops, the focus on syllables as a decoding strategy for literacy development and challenges of finding one-syllable words such as those initially used with English-speaking children. Another challenge was identifying culturally appropriate images which the children could relate to and which were not copyrighted. In this paper, we discuss these plus a range of other issues that emerged, identifying how these problems were addressed and resolved by the interdisciplinary and intercultural team.

Notes on cluster algebras and some all-loop Feynman integrals

We study cluster algebras for some all-loop Feynman integrals, including box-ladder, penta-box-ladder, and double-penta-ladder integrals. In addition to the well-known box ladder whose symbol alphabet is {D}_2simeq {A}_1^2 , we show that penta-box ladder has an alphabet of D3 ≃ A3 and provide strong evidence that the alphabet of seven-point double-penta ladders can be identified with a D4 cluster algebra. We relate the symbol letters to the u variables of cluster configuration space, which provide a gauge-invariant description of the cluster algebra, and we find various sub-algebras associated with limits of the integrals. We comment on constraints similar to extended-Steinmann relations or cluster adjacency conditions on cluster function spaces. Our study of the symbol and alphabet is based on the recently proposed Wilson-loop d log representation, which allows us to predict higher-loop alphabet recursively; by applying it to certain eight-point and nine-point double-penta ladders, we also find D5 and D6 cluster functions respectively.

The Wilson-loop d log representation for Feynman integrals

We introduce and study a so-called Wilson-loop d log representation of certain Feynman integrals for scattering amplitudes in mathcal{N} = 4 SYM and beyond, which makes their evaluation completely straightforward. Such a representation was motivated by the dual Wilson loop picture, and it can also be derived by partial Feynman parametrization of loop integrals. We first introduce it for the simplest one-loop examples, the chiral pentagon in four dimensions and the three-mass-easy hexagon in six dimensions, which are represented by two- and three-fold d log integrals that are nicely related to each other. For multi-loop examples, we write the L-loop generalized penta-ladders as 2(L − 1)-fold d log integrals of some one-loop integral, so that once the latter is known, the integration can be performed in a systematic way. In particular, we write the eight-point penta-ladder as a 2L-fold d log integral whose symbol can be computed without performing any integration; we also obtain the last entries and the symbol alphabet of these integrals. Similarly we study the symbol of the seven-point double-penta-ladder, which is represented by a 2(L − 1)-fold integral of a hexagon; the latter can be written as a two-fold d log integral plus a boundary term. We comment on the relation of our representation to differential equations and resumming the ladders by solving certain integral equations.

Symbol alphabets from plabic graphs II: rational letters

Symbol alphabets of n-particle amplitudes in mathcal{N} = 4 super-Yang-Mills theory are known to contain certain cluster variables of G(4, n) as well as certain algebraic functions of cluster variables. The first paper arXiv:2007.00646 in this series focused on n = 8 algebraic letters. In this paper we show that it is possible to obtain all rational symbol letters (in fact all cluster variables) by solving matrix equations of the form C Z = 0 if one allows C to be an arbitrary cluster parameterization of the top cell of G+(n−4, n).

Algebraic singularities of scattering amplitudes from tropical geometry

We address the appearance of algebraic singularities in the symbol alphabet of scattering amplitudes in the context of planar mathcal{N} = 4 super Yang-Mills theory. We argue that connections between cluster algebras and tropical geometry provide a natural language for postulating a finite alphabet for scattering amplitudes beyond six and seven points where the corresponding Grassmannian cluster algebras are finite. As well as generating natural finite sets of letters, the tropical fans we discuss provide letters containing square roots. Remarkably, the minimal fan we consider provides all the square root letters recently discovered in an explicit two-loop eight-point NMHV calculation.

An automated tool for comparing phonetic transcriptions

ABSTRACT Many computerized tools for comparing phonetic transcriptions have been proposed and shared in the past; however, previous tools are relatively difficult to access and incorporate into clinical and research practice, or require users to learn additional phonetic symbol systems. The purpose of this project was to develop and test a readily available web-based application for quantitatively comparing phonetic transcriptions that are input using International Phonetic Alphabet (IPA) symbols. A web-based computer application was developed to allow for IPA phonetic transcription comparison. A point-and-click keyboard was developed to provide support for character input of the full IPA, as well as most symbols in the extIPA set. The application compares phonetic transcriptions using a modified edit distance algorithm following phonologically informed alignment. Visualizations of the algorithm’s optimal alignment and scoring operations are shown for each comparison input by a user. The application, named the Automated Phonetic Transcription Comparison Tool (APTct), was thoroughly tested for accurate implementation of the algorithm principles. Validity tests through two sample use cases were also performed by comparison of hand calculations to APTct calculations. In function testing, the APTct showed excellent agreement with an expert’s hand scoring using the same algorithm principles. In a validity test, only minor differences between the APTct and hand calculations were observed, primarily due to errors inputting the transcriptions into the APTct. The web-based APTct is a validated and versatile tool for quantitatively comparing even complex IPA phonetic transcriptions. It is freely available to clinicians and researchers, who may find it useful for a variety of potential scenarios. We invite researchers, clinicians, and other individuals to use the tool in their clinical and research work. The permalink for the website is as follows: https://aptct.auburn.edu

A note on letters of Yangian invariants

Motivated by reformulating Yangian invariants in planar mathcal{N} = 4 SYM directly as d log forms on momentum-twistor space, we propose a purely algebraic problem of determining the arguments of the d log’s, which we call “letters”, for any Yangian invariant. These are functions of momentum twistors Z ’s, given by the positive coordinates α’s of parametrizations of the matrix C(α), evaluated on the support of polynomial equations C(α) · Z = 0. We provide evidence that the letters of Yangian invariants are related to the cluster algebra of Grassmannian G(4, n), which is relevant for the symbol alphabet of n-point scattering amplitudes. For n = 6, 7, the collection of letters for all Yangian invariants contains the cluster mathcal{A} coordinates of G(4, n). We determine algebraic letters of Yangian invariant associated with any “four-mass” box, which for n = 8 reproduce the 18 multiplicative-independent, algebraic symbol letters discovered recently for two-loop amplitudes.

СРЕДСТВА СИМВОЛИКИ В ГРАФИЧЕСКОМ МЕТАЯЗЫКЕ РУССКОЙ ЛИНГВИСТИКИ

The article is devoted to the definition of the concept symbols, graphic tools, graphs, tables, diagrams and other elements of the graphic metalanguage of linguistics as a means of non-verbal expression of linguistic concepts. The purpose of the article is to describe the general characteristics of the of Russian metalanguage as a means of language research and to determine the general patterns of functioning of non-verbal units of the metalanguage and symbols above all. A metalanguage is a language intended and used to describe a natural language and including general scientific vocabulary, terms, alphabetic, numeric, spatial and other symbols, tables, diagrams, etc. The formation of a linduistic symbols is carried out, as a rule, on the basis of the language material and other sciences metalanguages material in existence. As bearers of specific information, symbols are important means of fixing, storing and developing professional and scientific knowledge. Information expressed by symbols in a linguistic text is a non-verbally expressed generalization which accumulates specialized knowledge and is used in professional and scholarly pursuits. Conducted study suggests that terms, as a verbal manifestation of special concepts, and graphic symbols, as a non-verbal manifestation of special concepts, are a key tool for scientific activity including the field of linguistic research.

Multi-Resonant Frequency Shift Keying: A Novel and Efficient Modulation Scheme for Magnetic Communication

Magnetic communication is a promising technique in harsh environments, such as seawater. To enable efficient communication, transmitting and receiving coils are conventionally operated as part of resonant circuits. However, this results in narrow bandwidths and the associated disadvantages. Thus, most digital modulation schemes cannot be used efficiently on these systems. In this contribution, a mixed hardware/software approach for efficient frequency shift keying is presented. With this energy-efficient modulation concept, the full available bandwidth of a receiver can be utilized for data transmission, while all advantages of using a resonant circuit on the transmitter side can be retained. Towards this goal, a transmitter-side resonant circuit is designed, which supports discrete switching between multiple resonant frequencies. The data symbols are mapped onto these unique resonant frequencies. This prevents the parasitic amplitude modulation associated with conventional frequency shift keying applied to narrow bandwidth circuits, resulting in maximum transmitted magnitude and minimum symbol distortion without need for any further measures. Furthermore, the frequency spacing and/or the cardinality of the symbol alphabet can be increased considerably. At the receiver side, the classical pick-up coil is replaced by a high-sensitivity broadband magnetic field sensor. Numerical results of the mixed hardware/software scheme are provided, and are verified by an experimental setup. This setup is constructed using principles from the field of power electronics and demonstrates, how this modulation concept can be implemented with relatively simple and highly energy efficient electronics and without the use of linear amplifiers in particular.

Analysis of an invented writing system for the Shanghainese language

The present study uses qualitative methods to analyze and restore an invented missionary writing system for the Shanghainese language, and uses the restoration to check for historical sound change. The project consists of two parts: the analysis and restoration of the orthography and the confirmation of historical sound changes in Shanghainese. The restoration of the writing system provides all symbols with equivalent International Phonetic Alphabet (IPA) symbols. Following the restoration to IPA is an explanation of the rules for combining initial and final symbols to form a single character, as well as rules for tonal distinction. The analysis of the restored orthography compares its development with the academic criteria for orthography development, and finds that it is a sound writing system. The evaluation also reviews the sociolinguistic criteria crucial for orthography acceptance, and shows that the writing system does not meet these criteria in present day Shanghai. The results of the check for historical sound change confirm that many of the sounds not found in present day Shanghainese existed in this writing system. The phones found in this writing system are able to confirm the disappearance or merger of various sounds in Shanghainese since the mid 19th century. Overall, the study shows that the invented writing system is sound, but would not be accepted in Shanghai today. However, it should be reviewed by other linguists as having the possibility to represent other languages.

Decision problems and projection languages for restricted variants of two-dimensional automata

A two-dimensional automaton has a read-only input head that moves in four directions on a finite array of cells labeled by symbols of the input alphabet. A three-way two-dimensional automaton is prohibited from making upward moves, while a two-way two-dimensional automaton can only move downward and rightward.We show that the language emptiness problem for unary three-way nondeterministic two-dimensional automata is NP-complete, and is in P for general-alphabet two-way nondeterministic two-dimensional automata. We also show that the language equivalence and inclusion problems for two-way deterministic two-dimensional automata are decidable, while the language universality, equivalence, and inclusion problems for two-way nondeterministic two-dimensional automata are undecidable. The deterministic case is the first known positive decidability result for a language equivalence problem on two-dimensional automata over a general alphabet.Finally, we discuss the notion of row and column projection languages. We show that the row projection language of a unary three-way nondeterministic two-dimensional automaton is always regular, and that there exists a unary three-way deterministic two-dimensional automaton with a nonregular column projection language. For two-way nondeterministic two-dimensional automata, on the other hand, both the row and column projection languages are always regular.

Solving a PSPACE-complete problem with cP systems

There have been a few NP-hard problems solved using cP systems including the travelling salesman problem. However, these problems are typically in NP rather than higher in the polynomial time hierarchy. In this paper, we solve QSAT (also known as TQBF), which is a well-known PSPACE-complete problem. Compared to other extant confluent P systems solutions, our deterministic cP solution only uses a small constant number of custom alphabet symbols (19), a small constant number of rules (10) and a small constant upper limit of membrane nesting depth (6), independent of the problem size.

Two-loop integrals for planar five-point one-mass processes

We present the computation of a full set of planar five-point two-loop master integrals with one external mass. These integrals are an important ingredient for two-loop scattering amplitudes for two-jet-associated W-boson production at leading color in QCD. We provide a set of pure integrals together with differential equations in canonical form. We obtain analytic differential equations efficiently from numerical samples over finite fields, fitting an ansatz built from symbol letters. The symbol alphabet itself is constructed from cut differential equations and we find that it can be written in a remarkably compact form. We comment on the analytic properties of the integrals and confirm the extended Steinmann relations, which govern the double discontinuities of Feynman integrals, to all orders in ϵ. We solve the differential equations in terms of generalized power series on single-parameter contours in the space of Mandelstam invariants. This form of the solution trivializes the analytic continuation and the integrals can be evaluated in all kinematic regions with arbitrary numerical precision.

Symbol alphabets from plabic graphs

Symbol alphabets of n-particle amplitudes in mathcal{N} = 4 super-Yang-Mills theory are known to contain certain cluster variables of Gr(4, n) as well as certain algebraic functions of cluster variables. In this paper we suggest an algorithm for computing these symbol alphabets from plabic graphs by solving matrix equations of the form C ∙ Z = 0 to associate functions on Gr(m, n) to parameterizations of certain cells of Gr(k, n) indexed by plabic graphs. For m = 4 and n = 8 we show that this association precisely reproduces the 18 algebraic symbol letters of the two-loop NMHV eight-particle amplitude from four plabic graphs.