Graph Morphology of Non-Hermitian Bands

Non-Hermitian systems exhibit diverse graph patterns of energy spectra under open boundary conditions. Here we present an algebraic framework to comprehensively characterize the spectral geometry and graph topology of non-Bloch bands. Using a locally defined potential function, we unravel the spectral-collapse mechanism from Bloch to non-Bloch bands, delicately placing the spectral graph at the troughs of the potential landscape. The potential formalism deduces non-Bloch band theory and generates the density of states via Poisson equation. We further investigate the Euler-graph topology by classifying spectral vertices based on their multiplicities and projections onto the generalized Brillouin zone. Through concrete models, we identify three elementary graph-topology transitions (UVY, PT-like, and self-crossing), accompanied by the emergence of singularities in the generalized Brillouin zone. Lastly, we unveil how to generally account for isolated edge states outside the spectral graph. Our work lays the cornerstone for exploring the versatile spectral geometry and graph topology of non-Hermitian non-Bloch bands.Comment: 6+8 pages, 4+3 figure

A graph-based mathematical morphology reader

This survey paper aims at providing a "literary" anthology of mathematical morphology on graphs. It describes in the English language many ideas stemming from a large number of different papers, hence providing a unified view of an active and diverse field of research

Nanoparticle enhanced evaporation of liquids: A case study of silicone oil and water

Evaporation is a fundamental physical phenomenon, of which many challenging questions remain unanswered. Enhanced evaporation of liquids in some occasions is of enormous practical significance. Here we report the enhanced evaporation of the nearly permanently stable silicone oil by dispersing with nanopariticles including CaTiO3, anatase and rutile TiO2. The results can inspire the research of atomistic mechanism for nanoparticle enhanced evaporation and exploration of evaporation control techniques for treatment of oil pollution and restoration of dirty water

The Role of Morphosyntactic Awareness in Conventional Lexical Segmentation

A partir do estágio alfabético de aquisição da escrita o aprendiz precisa enfrentar questões relativas à ortografia, entre elas a segmentação do escrito em palavras gráficas. O objetivo deste estudo foi investigar a segmentação convencional de palavras e sua relação com a consciência morfossintática em uma amostra de alunos de 4º e 5º anos do ensino fundamental de escolas públicas. Os resultados revelaram uma discrepância entre a identificação oral de palavras e o desempenho na segmentação da escrita, sendo três os critérios utilizados pelos alunos para definição de “palavra”: 1º) sentido pleno; 2º) sequência de letras e não apenas uma ou duas; 3º) frequência de utilização do vocábulo. Análises estatísticas mostraram correlações positivas e significativas entre segmentação convencional e consciência morfossintática. Infere-se que as habilidades morfossintáticas favorecem o estabelecimento da noção convencional de palavra e sugere-se que os professores promovam o desenvolvimento dessas habilidades para garantir aos alunos maior domínio na linguagem escrita.Desde la etapa alfabética de adquisición de la escritura, el aprendiz necesita enfrentar cuestiones relativas a la ortografía, entre ellas la segmentación de la escritura en palabras gráficas. Se investigó la segmentación convencional de palabras y su relación con la consciencia morfosintáctica en una muestra de alumnos de 4º y 5º año de la enseñanza primaria de escuelas públicas. Los resultados revelaron discrepancia entre la identificación oral de palabras y el desempeño en la segmentación de la escritura. Los alumnos utilizaron tres criterios para la definición de “palabra”: 1º) sentido pleno; 2º) secuencia de letras, no sólo una o dos; 3º) frecuencia de utilización del vocablo. Análisis estadísticos mostraron correlaciones positivas y significativas entre segmentación convencional y conciencia morfosintáctica. Se infiere que las habilidades morfosintácticas favorecen la noción convencional de palabra y se sugiere que los profesores promuevan el desarrollo de esas habilidades, garantizando mayor dominio del lenguaje escrito.Starting with the alphabetic stage of writing acquisition, the learner struggles with issues related to spelling, including the segmentation of writing in graphic words. This study examined the conventional segmentation of words and its relation to morphosyntactic awareness in a sample of students in the 4th and 5th years of elementary education in public schools. Results reveal a discrepancy between the oral identification of words and performance in the segmentation of writing, with three criteria being used by students to define “word”: (1st) full meaning; (2nd) sequence of letters, not only one or two; (3rd) frequency of word use. Statistical analyses revealed significant positive correlations between conventional segmentation and morphosyntactic awareness. It is inferred that morphosyntactic skills support the establishment of the conventional notion of the word, and it is suggested that teachers promote the development of these skills, in order to ensure a greater command of the written language

The Role of Morphosyntactic Awareness in Conventional Lexical Segmentation

Starting with the alphabetic stage of writing acquisition, the learner struggles with issues related to spelling, including the segmentation of writing in graphic words. This study examined the conventional segmentation of words and its relation to morphosyntactic awareness in a sample of students in the 4th and 5th years of elementary education in public schools. Results reveal a discrepancy between the oral identification of words and performance in the segmentation of writing, with three criteria being used by students to define “word”: (1st) full meaning; (2nd) sequence of letters, not only one or two; (3rd) frequency of word use. Statistical analyses revealed significant positive correlations between conventional segmentation and morphosyntactic awareness. It is inferred that morphosyntactic skills support the establishment of the conventional notion of the word, and it is suggested that teachers promote the development of these skills, in order to ensure a greater command of the written language

Morphological filtering on hypergraphs

The focus of this article is to develop computationally efficient mathematical morphology operators on hypergraphs. To this aim we consider lattice structures on hypergraphs on which we build morphological operators. We develop a pair of dual adjunctions between the vertex set and the hyper edge set of a hypergraph H, by defining a vertex-hyperedge correspondence. This allows us to recover the classical notion of a dilation/erosion of a subset of vertices and to extend it to subhypergraphs of H. Afterward, we propose several new openings, closings, granulometries and alternate sequential filters acting (i) on the subsets of the vertex and hyperedge set of H and (ii) on the subhypergraphs of a hypergraph

TRANSDUCER FOR AUTO-CONVERT OF ARCHAIC TO PRESENT DAY ENGLISH FOR MACHINE READABLE TEXT: A SUPPORT FOR COMPUTER ASSISTED LANGUAGE LEARNING

There exist some English literary works where some archaic words are still used; they are relatively distinct from Present Day English (PDE). We might observe some archaic words that have undergone regular changing patterns: for instances, archaic modal verbs like mightst, darest, wouldst. The –st ending historically disappears, resulting on might, dare and would. (wouldst > would). However, some archaic words undergo distinct processes, resulting on unpredictable pattern; The occurrence frequency for archaic english pronouns like thee ‘you’, thy ‘your’, thyself ‘yourself’ are quite high. Students that are Non-Native speakers of English might come across many difficulties when they encounter English texts which include these kinds of archaic words. How might computer be a help for the student? This paper aims on providing some supports from the perspective of Computer Assisted Language Learning (CALL). It proposes some designs of lexicon transducers by using Local Grammar Graphs (LGG) for auto-convert of the archaic words to PDE in a literature machine readable text. The transducer is applied to a machine readable text that is taken from Sir Walter Scott’s Ivanhoe. The archaic words in the corpus can be converted automatically to PDE. The transducer also allows the presentation of the two forms (Arhaic and PDE), the PDE lexicons-only, or the original (Archaic Lexicons) form-only. This will help students in understanding English literature works better. All the linguistic resources here are machine readable, ready to use, maintainable and open for further development. The method might be adopted for lexicon tranducer for another language too