Anomalies in time series in Xevents 12 May Vien, Austria

DMA definition Discrete mathematical analysis (DMA) is an approach to studying of multidimensional massifs and time series, based on modeling of limit in a finite situation, realized in a series of algorithms. The basis of the finite limit was formed on a more stable character, compared to a mathematic character, of human idea of discontinuity and stochasticity. Fuzzy mathematics and fuzzy logic are sufficient for modeling of human ideas and judgments. That was reason why they became technical foundation of DMA. 12 May Vien, Austria

Density as limit measure DMA General Scheme Fuzzy comparisons of positive numbers Proximity in finite metrical space Limit in finite metrical space Multidimensional Discrete spaces Finite time series FTS Recognition of dense subsets: Crystal. Monolith. Clusterization: Rodin Recognition of linear structure: Tracing Smooth FTS: Equilibrium Monotonous FTS Predication of FTS: Forecast Extremums on FTS Anomalies on FTS: DRAS, FLARS, FCARS Convex FTS Fuzzy logic and geometry on FTS: Geometry measures 12 May Vien, Austria

12 May Vien, Austria4 Classical Set Classical set has a clear boundary between elements that do and don’t belong to the set. If U is universal set, then a classical subset A  U is defined by the membership function μ(x) that takes only two values: μ(x) =1 for the elements belonging to A and μ(x) =0 for elements not belonging to A.

12 May Vien, Austria5 Fuzzy Set A is a fuzzy set in U if there is a map μ: U  0,1 , that shows the degree of inclusion of the element x into the fuzzy set A. μ(x) is called by membership function of the fuzzy set A.

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12 May Vien, Austria7 Fuzzy Sets Approach in Geophysics Lofti Zadeh: A human being thinks not in terms of numbers, but rather in terms of fuzzy notions. Норберт Винер: По-видимому, главное преимущество человека перед компьютером – это его способность оперировать с нечетко очерченными понятиями.

FLASAR 12 May Vien, Austria

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Vien, Austria Monitoring of La Fournais volcano, Reunion, France 12 May 2009

Recognition SP- anomalyes, connected with volcanic activity 12 May Vien, Austria Eruption

FCARS: three vision for one time series 12 May Vien, Austria12

FCARS: universality 12 May Vien, Austria13

Agreement “Equilibrium” and “Forecast” Real time series 12 May Vien, Austria

Extremums on time series 12 May Vien, Austria

Etna volcano 2005, 2004, 2003, 2002, 2001, 1994, 1993, 1991, 1989, 1988, 1987, 1986, 1985, 1984, 1983, 1981, 1980, 1979, 1978, 1975, 1974, 1971, 1968, 1966, 1959, 1958, 1957, 1955, 1953, 1951, 1950, 1949, 1947, 1946, 1945, 1942, 1940, 1935, 1934, 1931, 1930, 1929, 1928, 1926, 1924, 1923, 1919, 1918, 1917, 1913, 1912, 1911, 1910, 1908, 1899, 1893, 1892, 1891, 1886, 1884, 1883, 1879, 1878, 1874, 1869, 1868, 1865, 1864, 1863, 1857, 1852, 1843, 1842, 1838, 1833, 1832, 1828, 1827, 1822, 1819, 1816, 1811, 1810, 1809, 1803, 1802, 1797, 1792, 1791, 1787, 1781, 1780, 1776, 1770, 1767, 1766, 1764, 1763, 1758, 1755, 1752, 1747, 1744, 1735, 1732, 1723, 1702, 1693, 1689, 1688, 1682, 1669, 1654, 1651, 1646, 1643, 1640, 1634, 1633, 1614, 1610, 1609, 1607, 1603, 1595, 1579, 1578, 1566, 1554, 1550, 1541, 1540, 1537, 1536, 1535, 1533, 1494, 1470, 1447, 1446, 1444, 1408, 1381, 1350, 1334, 1333, 1329, 1321, 1284, 1250, 1222, 1194, 1175, 1169, 1164, 1160, 1157, 1063, 1044, 1004, 0911, 0859, 0814, 0812, 0644, 0604, 0560, 0500, 0417, 0410, 0400, 0252, 0165, 0080, 0072, 0050, 0039, 0010, , -0032, -0036, -0044, -0049, -0056, -0061, -0122, -0126, -0135, -0141, -0350, -0396, -0425, -0479, -0565, , -0735, -1050, -1470, -1500, -2330, -3050, -3390, -3510, -4150, -5150, May Vien, Austria

Algorithm “Monolith”. Etna volcano Interferogram Smooth points1st iteration2nd iteration3rd iteration4th iterationBorders 12 May Vien, Austria

Algorithm “Monolith”. Etna volcano. Final result 12 May Vien, Austria

GIS Vien, Austria12 May 2009

GIS Vien, Austria Цифровая модель высот (разрешение 30") Площадная гидрография, Гидрорельеф, Естественные формы рельефа, Изогоны (1: ) Фрагмент карты почв (1: ) 12 May 2009

Literature on DMA to Xevents list 12 May Vien, Austria21 Gvishiani A.D., Agayan S.M., Bogoutdinov Sh.R., Ledenev A., Zlotnicki J., Bonnin J. Mathematical Methods of Geoinformatics. II. The algorithms of fuzzy logic in the problem of anomalies recognition in time series / / Cybernetics and system analysis № 4. p Gvishiani A.D., Agayan S.M., Bogoutdinov Sh.R., Zlotnicki J. Algorithms of fuzzy logic in the problem of anomalies recognition in time series / / Sketches of Geophysical Research. By the 75 th anniversary of the Joint Institute of Physics of the Earth RAS. O.Y Schmidt. M.: OIFZ RAS p Zlotnicki J., Agayan S., Gvishiani A., Bogoutdinov Sh. Telematics and artificial intelligence tools in monitoring of volcanoes // WISTCIS Newsletter Vol. 3. November May p Zlotnicki J., Le Mouel J.-L., Gvishiani A., Agayan S., Mikhailov V., Bogoutdinov Sh., Kanwar R., Yvetot P. Automatic fuzzy-logic recognition of anomalous activity on long geophysical records: Application to electric signals associated with the volcanic activity of La Fournaise volcano (Reunion Island) // Earth and Planetary Science Letters Vol p

12 May Vien, Austria22 Gvishiani A.D., Agayan S.M., Bogoutdinov Sh.R., Tikhotsky S.A., Hinderer J., Bonnin J., Diament M. Algorithm FLARS and recognition of time series anomalies // System Research & Information Technologies №. 3. p Agayan S.M., Bogoutdinov Sh.R., Gvishiani A.D., Graeva E.M., Zlotnicki J., Rodkin M.V. Investigation of the morphology of the signal based on the algorithms of fuzzy logic / / Geophysical Research. M.: IFZ RAS Vol.1. p Zlotnicki J., LeMouel J.-L., Gvishiani A., Agayan S., Mikhailov V., Bogoutdinov Sh. Automatic fuzzy-logic recognition of anomalous activity on long geophysical records. Application to electric signals associated with the volcanic activity of la Fournaise volcano (Réunion Island) // Earth and Planetary Science Letters Vol.234. P Bogoutdinov Sh.R., Agayan S.M., Gvishiani A.D., Graeva E.M., Rodkin M.V., Zlotnicki J., Le Mouël J.L. Fuzzy logic algorithms in the analysis of electrotelluric data with reference to monitoring of volcanic activity // Izvestiya, Physics of the Solid Earth. MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC Vol. 43. p Literature on DMA to Xevents list

12 May Vien, Austria23 Gvishiani A.D., Agayan S.M., Bogoutdinov Sh.R. Fuzzy Recognition of Anomalies in Time Series / / Doklady Earth Sciences, June-July 2008, Vol. 421, № 5, p Doklady Earth Sciences Gvishiani A.D., Agayan S.M., Bogoutdinov Sh.R., Zlotnicki J., Bonnin J. Mathematical Methods of Geoinformatics. III. Fuzzy comparison and recognition of anomalies in time series / / Cybernetics and system analysis. 2008, Vol. 44, № 3, p Literature on DMA to Xevents list