Totally frustrated states in the chromatic theory of gain graphs

We generalize proper coloring of gain graphs to totally frustrated states, where each vertex takes a value in a set of `qualities' or `spins' that is permuted by the gain group. (An example is the Potts model.) The number of totally frustrated states satisfies the usual deletion-contraction law but is matroidal only for standard coloring, where the group action is trivial or nearly regular. One can generalize chromatic polynomials by constructing spin sets with repeated transitive components.Comment: 14 pages, 2 figure

An elementary chromatic reduction for gain graphs and special hyperplane arrangements

A gain graph is a graph whose edges are labelled invertibly by "gains" from a group. "Switching" is a transformation of gain graphs that generalizes conjugation in a group. A "weak chromatic function" of gain graphs with gains in a fixed group satisfies three laws: deletion-contraction for links with neutral gain, invariance under switching, and nullity on graphs with a neutral loop. The laws lead to the "weak chromatic group" of gain graphs, which is the universal domain for weak chromatic functions. We find expressions, valid in that group, for a gain graph in terms of minors without neutral-gain edges, or with added complete neutral-gain subgraphs, that generalize the expression of an ordinary chromatic polynomial in terms of monomials or falling factorials. These expressions imply relations for chromatic functions of gain graphs. We apply our relations to some special integral gain graphs including those that correspond to the Shi, Linial, and Catalan arrangements, thereby obtaining new evaluations of and new ways to calculate the zero-free chromatic polynomial and the integral and modular chromatic functions of these gain graphs, hence the characteristic polynomials and hypercubical lattice-point counting functions of the arrangements. We also calculate the total chromatic polynomial of any gain graph and especially of the Catalan, Shi, and Linial gain graphs.Comment: 31 page

Mathematical Knowledge for Teaching as Decision-Making for the University Mathematician Developing Coherence in Review of Discrete Mathematics

Mathematicians teaching at the university level have a deep understanding and appreciation for the mathematics that they teach. However, they rarely receive much formal training in teaching. Thus, university mathematicians must rely on their mathematical understandings and personally developed ideas of teaching to guide their decision-making. Relatively little research exists on mathematicians’ teaching practices. The purpose of this study was to examine the mathematical knowledge for teaching (MKT) of a university mathematician teaching discrete mathematics and how he leveraged his knowledge to make decisions and develop coherence among mathematical ideas during a semester review. An enactivist perspective examining a mathematician’s decision-making in planning, enacting, and reflecting upon their lessons in this study shed light on how this mathematician practically approached his teaching duties. By enacting four distinct coherence strategies, the mathematician in this case study revealed a personal standard for mathematical storytelling which guided his decision enactment. These strategies fostered rich connections among mathematical ideas and among topics from earlier in the semester meaningfully with a single culminating topic: the chromatic polynomial. Implications of this study for research include recognized advantages of graph theoretic visualizations for the analysis of teacher decisions and coherence, benefits of dual coding for the Knowledge Quartet MKT framework, and a stance on inactivism\u27s consideration of cognitive actions. For teaching, this research supports the benefits of mathematical storytelling and review units which feature a new context to reframe previously seen topics

Advances in Optical Amplifiers

Optical amplifiers play a central role in all categories of fibre communications systems and networks. By compensating for the losses exerted by the transmission medium and the components through which the signals pass, they reduce the need for expensive and slow optical-electrical-optical conversion. The photonic gain media, which are normally based on glass- or semiconductor-based waveguides, can amplify many high speed wavelength division multiplexed channels simultaneously. Recent research has also concentrated on wavelength conversion, switching, demultiplexing in the time domain and other enhanced functions. Advances in Optical Amplifiers presents up to date results on amplifier performance, along with explanations of their relevance, from leading researchers in the field. Its chapters cover amplifiers based on rare earth doped fibres and waveguides, stimulated Raman scattering, nonlinear parametric processes and semiconductor media. Wavelength conversion and other enhanced signal processing functions are also considered in depth. This book is targeted at research, development and design engineers from teams in manufacturing industry, academia and telecommunications service operators

Dinámica Cerebral:La actividad cerebral en función de las condiciones dinámicas de la excitabilidad nerviosa. Tomo primero.

This book can be cited as: Gonzalo J. (1945/2010/2022), "Dinámica Cerebral", Tomo I, Consejo Superior de investigaciones Cientificas, Madrid 1945, in: "Dinámica Cerebral" facsimile edition, Gonzalo I. (Ed), Red Temática en Tecnologías de Computación Artificial/Natural, Universidad de Santiago de Compostela 2010 (Open Access http://dspace.usc.es/handle/10347/4341). "Brain Dynamics" Volume 1, Gonzalo I. (Ed), English translation, Madrid 2022 (Open Access in this web page). English translation (2022) of Volume 2 of Brain Dynamics by Justo Gonzalo is freely available at at: https://eprints.ucm.es/id/eprint/72118/ English translation (2015, revised 2022) of ubsequent research by this author is freely available at: https://eprints.ucm.es/id/eprint/30931/This book is the English translation of the published book in Spanish: `Dinámica Cerebral´, by Justo Gonzalo, Volume 1, published by the Consejo Superior de Investigaciones Científicas, Madrid 1945. A facsimile Spanish edition includindg Volume 2 and supplements was published by the Red Temática en Tecnologías de Computación Artificial/Natural (RTNAC) and the University of Santiago de Compostela in 2010, and whose on-line open-access version (http://dspace.usc.es/handle/10347/4341) maintains a significant rate of visits since its publication. Justo Gonzalo (Barcelona 1910 - Madrid 1986), after specialization in Austria and Germany, developed a novel research on the human cerebral cortex, partially exposed in this book. The research described here is surprisingly of current interest, apart from its undoubted historical interest. Some aspects were ahead of discoveries that were made later. Some of the phenomena exposed are still unknown, or have only been observed in the last decades, and the functional dynamic unity of the cortex proposed by the author is closely related to the current trends in the study of the brain. Some singular phenomena are described with extreme detail, such as inverted vision, facilitation, delocalization of colors, reversal of motion, and orientation disorder, among others. From the study of patients with unilateral lesion in an association area of the left parieto-occipital cortex, the author characterized what he called the `central syndrome´ of the cortex as a multisensory disorder in which all functions are affected bilaterally and symmetrically, presenting dynamic phenomena such as disaggregation of a sensory function into partial functions that are united in normal perception. Thus, inverted or tilted vision appears, whose first in-depth study is part of this research. A related phenomenon is partial disappearance of the disorders by intensification of the stimulus, or by means of facilitation, according to which the perception of a stimulus improves by the presence of another stimulus of the same or of a different sensory modality (cross-modal effect), or by a motor stimulus, muscular effort being one of the most efficient and less known means. The greater the brain excitability deficit, the more efficient facilitation is. The first detailed study on multisensory and motor facilitation is part of this research. Multisensoriality is a topic of great interest at present. From the new approach that the author gave to the research, his conception of brain dynamics emerged. The term `brain dynamics´, so widely used today, was introduced here for the first time in relation to sensory organization. This research filled the gap then existing between brain pathology and the physiology of the nervous system since the phenomena described find explanation on a physiological basis governed by the laws of nervous excitability, and provides a dynamic solution to the rigid theory of brain localization by establishing a continuous transition between lower and higher sensory functions, both being based on the same physiological laws. In addition to the patients directly studied by the author, a reference case is also the famous Schneider patient of Goldstein and Gelb studied in 1918-1919, which deserves publications even at present, and which the author interpreted under the central syndrome. In this Volume 1, the first part deals qualitatively with general aspects of the research (findings, new syndrome, dynamic analysis), and a the second part focuses on the quantitative and experimental aspects concerning visual functions. This part covers electrical and light excitability, color vision, visual field, visual forms, color vision, motion perception, motion inversion, visual image orientation, and visual schema. The rich bibliographic documentation on various trends of thought and clinical data adds interest and amenity to the book. This research received international attention from relevant authors shortly after the first publication of the book in Spanish, and more recently found echo in the field of cybernetics and artificial intelligence. A preface introduces some aspects of this research, its author and his subsequent research.Depto. de ÓpticaFac. de Ciencias FísicasFALSEunpu

Cubaneo In Latin Piano: A Parametric Approach To Gesture, Texture, And Motivic Variation

ABSTRACT CUBANEO IN LATIN PIANO: A PARAMETRIC APPROACH TO GESTURE, TEXTURE, AND MOTIVIC VARIATION COPYRIGHT Orlando Enrique Fiol 2018 Dr. Carol A. Muller Over the past century of recorded evidence, Cuban popular music has undergone great stylistic changes, especially regarding the piano tumbao. Hybridity in the Cuban/Latin context has taken place on different levels to varying extents involving instruments, genres, melody, harmony, rhythm, and musical structures. This hybridity has involved melding, fusing, borrowing, repurposing, adopting, adapting, and substituting. But quantifying and pinpointing these processes has been difficult because each variable or parameter embodies a history and a walking archive of sonic aesthetics. In an attempt to classify and quantify precise parameters involved in hybridity, this dissertation presents a paradigmatic model, organizing music into vocabularies, repertories, and abstract procedures. Cuba\u27s pianistic vocabularies are used very interactively, depending on genre, composite ensemble texture, vocal timbre, performing venue, and personal taste. These vocabularies include: melodic phrases, harmonic progressions, rhythmic cells and variation schemes to replace repetition with methodical elaboration of the piano tumbao as a main theme. These pianistic vocabularies comprise what we actually hear. Repertories, such as pre-composed songs, ensemble arrangements, and open- ended montuno and solo sections, situate and contextualize what we hear in real life musical performances. Abstract procedures are the thoughts, aesthetics, intentions, and parametric rules governing what Cuban/Latin pianists consider possible. Abstract procedures alter vocabularies by displacing, expanding, contracting, recombining, permuting, and layering them. As Cuba\u27s popular musics find homes in its musical diaspora (the United States, Latin America and Europe), Cuban pianists have sought to differentiate their craft from global salsa and Latin jazz pianists. Expanding the piano\u27s gestural/textural vocabulary beyond pre-Revolutionary traditions and performance practices, the timba piano tumbao is a powerful marker of Cuban identity and musical pride, transcending national borders and cultural boundaries

Novel up-conversion concentrating photovoltaic concepts

This thesis summarises a set of experiments towards the integration of concentrating optics into up-conversion photovoltaics. Up-conversion in rare earths has been investigated here. This optical process is non-linear therefore a high solar irradiance is required. High solar irradiance is achievable by solar concentration. Two concentrating approaches were investigated in this thesis: The first approach involved the concentration of the incident solar irradiance into optical fibres. An optical system with spherical lenses and dielectric tapers was designed accordingly. A solar concentration of 2000 suns was realised at the end of a single optical fibre. In addition to the total solar concentration, the spectral dependence was characterised to account for the effect of chromatic aberrations. Then, the solar concentration could be transferred into rare earth-doped fibres. For this reason, a series of experiments on double-clad erbium-doped silicate fibres was carried out. Although up-conversion in this type of fibre is minimised, the measured power dependence agrees with up-conversion via excited state absorption. In the second approach, concentrating optics were integrated in up-conversion solar cells. The role of the optics was to couple the photons transmitted by the solar cell to the rare earth up-converter. Therefore, imaging and non-imaging optics were investigated, with the latter exhibiting ideal coupling characteristics; concentration and high transmission of the incident irradiance, but also efficient collection of the up-converted emission. Out of the non-imaging optics, the dielectric compound parabolic concentrator fulfilled these characteristics, indicating its novel use in up-conversion solar cells. Two erbium-doped up-converters were utilised in this approach, beta-phase hexagonal sodium yttrium tetrafluoride (β-NaYF4:25%Er3+) and barium diyttrium octafluoride (BaY2F8:30%Er3+). The latter performed best, with an external quantum efficiency (EQE) of 2.07% under 1493 nm illumination, while the former exhibited an EQE of 1.80% under 1523 nm illumination both at an irradiance of 0.02 W/cm2. This corresponds to a relative conversion efficiency of 0.199% and 0.163% under sub-band-gap illumination, respectively, for a solar cell of 17.6% under standard AM1.5G conditions. These values are among the highest in literature for up-conversion solar cells and show the potential of the concentrating concept that can be important for future directions of photovoltaics.Engineering and Physical Sciences Research Council (EPSRC)European Community's Seventh Framework Program (FP7/2007-2013