COMPLEXITY OF MATHEMATICAL EXPRESSIONS IN ADAPTIVE MULTIMODAL MULTIMEDIA

COMPLEXITY OF MATHEMATICAL EXPRESSIONS IN ADAPTIVE MULTIMODAL MULTIMEDIA SYSTEM ENSURING ACCESS TO MATHEMATICS FOR VISUALLY IMPAIRED USERS Hou Huayang Nov. 23 th AID Team http: //wme. lzu. edu. cn

Agenda www. themegallery. com 1、Challenge 2、Related Work 3、Background 4、Modality, Media and Presentation Format 5、Design 6、Contextual Information 7、Mathematical Taxonomy 8、Evaluation Protocol 9、Experiment Running 10、Results of Experiments 11、Integration of Expression 12、Conclusion http: //wme. lzu. edu. cn

1、Challenge www. themegallery. com v Reasons u Bi-dimensional u One’s knowledge u Further information (e. g. exponent) u Ambiguous (e. g. a minus b minus c) u The limited dots (e. g. X-, x) u …… http: //wme. lzu. edu. cn

2、Related Work www. themegallery. com u u u Repeat it. (Stöger, Miesenberger et Batusic, 2004). Read, write and manipulate mathematics. Speech, Braille and Audio. Mathtalk (Edwards et Stevens, 1994) Maths (Cahill et al. , 1995) La. Tex, Math. ML, HTML to French Braille. VICKIE (Visually Impaired Children Kit for Inclusive Education) (Moço et Archambault, 2003 a) Bra. Ma. Net (Braille Mathématique sur Inter. Net) (Schwebel et Goiffon, 2005) http: //wme. lzu. edu. cn

2、Related Work www. themegallery. com La. Tex to Marburg Braille. Labradoor (La. Tex-to-Braille-Door) (Batusic, Miesenberger et Stöger, 1998). u La. Tex to Nemth Braille. MAVIS (Mathematics Accessible To Visually Impaired Students). (Karshmer et al. , 1998) u Braille and graphic symbols (e. g. +, -, ×, ÷, etc. ) Dots. Plus u Bi-dimensional output (e. g. Π, Σ, etc. ). Easy. Math (Podevin, 2002) u http: //wme. lzu. edu. cn

2、Related Work www. themegallery. com u u La. Tex to Audio. (Audio System for Technical Readings) (Raman, 1998) Germany and Austria Math. ML to vocal output. Audio. Math http: //wme. lzu. edu. cn

3、Background www. themegallery. com u u The Nemeth Math code (Nemeth, 1972) In the USA, Canada, New Zealand, Greece and India The Marburg Math code (Epheser, Pograniczna et Britz, 1992) Germany and Austria French Math code (Commission Evolution du Braille Francais, 2001) Mathematical, physical and chemical symbols of Chinese Braille (2000) http: //wme. lzu. edu. cn

4、Modality, Media and Presentation Format www. themegallery. com u u Modality is defined by the information structure as it is perceived by the user. (e. g. text, speech, Braille, image, etc. ). Media is defined as a device used to acquire or deliver information or data. (e. g. screen, terminal Braille, mouse, keyboard, etc. ). ) http: //wme. lzu. edu. cn

4、Modality, Media and Presentation Format www. themegallery. com u M = {Vin, Tin, Vout, Tout} http: //wme. lzu. edu. cn

4、Modality, Media and Presentation Format www. themegallery. com http: //wme. lzu. edu. cn

5、Design www. themegallery. com Architectural layer view of our multimodal computing system for visually-impaired users. u http: //wme. lzu. edu. cn

6、Contextual Information www. themegallery. com u The User Context u The Environment Context u The System Context u The Expression Complexity 1. The depth of syntax tree 2. The number of operands 3. The number of operators. http: //wme. lzu. edu. cn

6、Contextual Information www. themegallery. com u The User Context u The Environment Context u The System Context u The Expression Complexity 1. The depth of syntax tree 2. The number of operands 3. The number of operators. http: //wme. lzu. edu. cn

6、Contextual Information www. themegallery. com u e. g. A syntax tree of the sample expression http: //wme. lzu. edu. cn

7、Mathematical Taxonomy www. themegallery. com u Arithmetic u Algebra u Analysis u Geometry u Logic u Statistics & Probability http: //wme. lzu. edu. cn

8、Evaluation Protocol www. themegallery. com u WER (Word Error Rate) u I is the number of the insertions u D is the number of the deletions u S is the number of substitutions u N is the number of operators and operands in the expression reference http: //wme. lzu. edu. cn

9、Experiment Running www. themegallery. com u The complexities and its suiting values http: //wme. lzu. edu. cn

10、Results of Experiments www. themegallery. com u Experiment’s results of arithmetic branch http: //wme. lzu. edu. cn

10、Results of Experiments www. themegallery. com u Experiment’s results of algebra branch http: //wme. lzu. edu. cn

10、Results of Experiments www. themegallery. com u Experiment’s results of analysis branch http: //wme. lzu. edu. cn

10、Results of Experiments www. themegallery. com u Experiment’s results of Geometry / Trigonometry branch http: //wme. lzu. edu. cn

10、Results of Experiments www. themegallery. com u Experiment’s results of logic branch http: //wme. lzu. edu. cn

10、Results of Experiments www. themegallery. com u Experiment’s results of statistics & probability branch http: //wme. lzu. edu. cn

10、Results of Experiments www. themegallery. com u Experiment’s results of a collection of 12 expressions http: //wme. lzu. edu. cn

11、Results Analysis www. themegallery. com u Experiment’s results of algebra branch http: //wme. lzu. edu. cn

10、Results of Experiments www. themegallery. com u 4 similar expressions and its average complexity http: //wme. lzu. edu. cn

10、Results of Experiments www. themegallery. com u C is the complexity of the expression u P the number of operands u F the number of operators u D is depth of the tree Experiment’s http: //wme. lzu. edu. cn

10、Results of Experiments www. themegallery. com u x=0. 39; y=0. 10; z=0. 16 http: //wme. lzu. edu. cn

10、Results of Experiments www. themegallery. com u Comparison table of estimated complexity using our formula and average complexity according to experiments. http: //wme. lzu. edu. cn

10、Results of Experiments www. themegallery. com v LSM(Least Squares Method) Evaluate Data Test Data LSM Data Company Logo

10、Results of Experiments www. themegallery. com u The five categories of complexity http: //wme. lzu. edu. cn

11、Integration of Expression www. themegallery. com u Structure of the analysis of a Math. ML expression http: //wme. lzu. edu. cn

11、Integration of Expression www. themegallery. com u A sample analysis of a specimen fraction http: //wme. lzu. edu. cn

www. themegallery. com