Approximation of Spatio-Temporal Random Processes Using Tensor Decomposition

A new representation of spatio-temporal random processes is proposed in this work. In practical applications, such processes are used to model velocity fields, temperature distributions, response of vibrating systems, to name a few. Finding an efficient representation for any random process leads to encapsulation of information which makes it more convenient for a practical implementations, for instance, in a computational mechanics problem. For a single-parameter process such as spatial or temporal process, the eigenvalue decomposition of the covariance matrix leads to the well-known Karhunen-Loeve (KL) decomposition. However, for multiparameter processes such as a spatio-temporal process, the covariance function itself can be defined in multiple ways. Here the process is assumed to be measured at a finite set of spatial locations and a finite number of time instants. Then the spatial covariance matrix at different time instants are considered to define the covariance of the process. This set of square, symmetric, positive semi-definite matrices is then represented as a third-order tensor. A suitable decomposition of this tensor can identify the dominant components of the process, and these components are then used to define a closed-form representation of the process. The procedure is analogous to the KL decomposition for a single-parameter process, however, the decompositions and interpretations vary significantly. The tensor decompositions are successfully applied on (i) a heat conduction problem, (ii) a vibration problem, and (iii) a covariance function taken from the literature that was fitted to model a measured wind velocity data. It is observed that the proposed representation provides an efficient approximation to some processes. Furthermore, a comparison with KL decomposition showed that the proposed method is computationally cheaper than the KL, both in terms of computer memory and execution time.

Wind speed prediction using spatio-temporal covariance

High wind poses a number of hazards in different areas such as structural safety, aviation, and wind energy-where low wind speed is also a concern, pollutant transport, to name a few. Therefore, usage of a good prediction tool for wind speed is necessary in these areas. Like many other natural processes, behavior of wind is also associated with considerable uncertainties stemming from different sources. Therefore, to develop a reliable prediction tool for wind speed, these uncertainties should be taken into account. In this work, we propose a probabilistic framework for prediction of wind speed from measured spatio-temporal data. The framework is based on decompositions of spatio-temporal covariance and simulation using these decompositions. A novel simulation method based on a tensor decomposition is used here in this context. The proposed framework is composed of a set of four modules, and the modules have flexibility to accommodate further modifications. This framework is applied on measured data on wind speed in Ireland. Both short-and long-term predictions are addressed.

Spatio-temporal Map Formation Based on a Potential Function

We revisit the problem of temporal self organization using activity diffusion based on the neural gas (NGAS) algorithm. Using a potential function formulation motivated by a spatio-temporal metric, we derive an adaptation rule for dynamic vector quantization of data. Simulations results show that our algorithm learns the input distribution and time correlation much faster compared to the static neural gas method over the same data sequence under similar training conditions.

Spatial and Temporal Variation of LURR and Its Implication for the Tendency of Earthquake Occurrence in Southern California

Based on the theory of LURR and its recent development, spatial and temporal variation of Y/Y-c (value of LURR/critical value of LURR) in the Southern California region during the period from 1980 through March, 2001 was studied. According to the previous study on the fault system and stress field in Southern California, we zoned the Southern California region into 11 parts in each of which the stress field is almost uniform. With the time window of one year, time moving step of three months, space window of a circle region with a radius of 100 km and space moving step of 0.25 degree in latitude and longitude direction, the evolution of Y/Y-c were snapshot. The scanning results show that obvious Y/Y-c anomalies occurred before 5/6 of strong earthquakes considered with a magnitude of 6.5 or greater. The critical regions of Y/Y-c are near the epicenters of the strong earthquakes and the Y/Y-c anomalies occur months to years prior to the earthquakes. The tendency of earthquake occurrence in the California region is briefly discussed on the basis of the examination of Y/Y-c.

Spatio-Temporal Scanning and Statistical Test of the Accelerating Moment Release (AMR) Model Using Australian Earthquake Data

The Accelerating Moment Release (AMR) preceding earthquakes with magnitude above 5 in Australia that occurred during the last 20 years was analyzed to test the Critical Point Hypothesis. Twelve earthquakes in the catalog were chosen based on a criterion for the number of nearby events. Results show that seven sequences with numerous events recorded leading up to the main earthquake exhibited accelerating moment release. Two occurred near in time and space to other earthquakes preceded by AM R. The remaining three sequences had very few events in the catalog so the lack of AMR detected in the analysis may be related to catalog incompleteness. Spatio-temporal scanning of AMR parameters shows that 80% of the areas in which AMR occurred experienced large events. In areas of similar background seismicity with no large events, 10 out of 12 cases exhibit no AMR, and two others are false alarms where AMR was observed but no large event followed. The relationship between AMR and Load-Unload Response Ratio (LURR) was studied. Both methods predict similar critical region sizes, however, the critical point time using AMR is slightly earlier than the time of the critical point LURR anomaly.

Systematic liquidity: commonality and inter-temporal variation in the Portuguese stock market

[EN] The aim of this paper is to study systematic liquidity at the Euronext Lisbon Stock Exchange. The motivation for this research is provided by the growing interest in financial literature about stock liquidity and the implications of commonality in liquidity for asset pricing since it could represent a source of non-diversifiable risk. Namely, it is analysed whether there exist common factors that drive the variation in individual stock liquidity and the causes of the inter-temporal variation of aggregate liquidity. Monthly data for the period between January 1988 and December 2011 is used to compute some of the most used proxies for liquidity: bid-ask spreads, turnover rate, trading volume, proportion of zero returns and the illiquidity ratio. Following Chordia et al. (2000) methodology, some evidence of commonality in liquidity is found in the Portuguese stock market when the proportion of zero returns is used as a measure of liquidity. In relation to the factors that drive the inter-temporal variation of the Portuguese stock market liquidity, the results obtained within a VAR framework suggest that changes in real economy activity, monetary policy (proxied by changes in monetary aggregate M1) and stock market returns play an important role as determinants of commonality in liquidity.

Spatial and temporal variation in otolith chemistry for tautog (Tautoga onitis) in Narragansett Bay and Rhode Island coastal ponds

The elemental composition of otoliths may provide valuable information for establishing connectivity between fish nursery grounds and adult fish populations. Concentrations of Rb, Mg, Ca, Mn, Sr, Na, K, Sr, Pb, and Ba were determined by using solution-based inductively coupled plasma mass spectrometry in otoliths of young-of-the year tautog (Tautoga onitis) captured in nursery areas along the Rhode Island coast during two consecutive years. Stable oxygen (δ18O) and carbon (δ13C) isotopic ratios in young-of-the year otoliths were also analyzed with isotope ratio mass spectrometry. Chemical signatures differed significantly among the distinct nurseries within Narragansett Bay and the coastal ponds across years. Significant differences were also observed within nurseries from year to year. Classification accuracy to each of the five tautog nursery areas ranged from 85% to 92% across years. Because accurate classification of juvenile tautog nursery sites was achieved, otolith chemistry can potentially be used as a natural habitat tag.

Temporal variation in growth of yellowfin tuna (Thunnus albacares) larvae in the Panama Bight, 1990

Tuna larvae (at flexion, postflexion, and transformation stages) were collected by dip net and light traps at night in the northwestern Panama Bight during the season of reduced upwelling (June−September) of 1990, 1991, 1992, and 1997. The larvae were identified as yellowfin tuna (Thunnus albacares) by mtDNA analysis. Ichthyoplankton data from bongo and Tucker trawl tows were used to examine the potential prey abundance in relation to the mean size-at-age and growth rates of the yellowfin tuna larvae and their otoliths. The most rapid growth rates occurred during June 1990 when plankton volumes were at their highest levels. The lowest plankton volumes coincided with the lowest growth rates and mean sizes-at-age during the August−September 1991 period. High densities of larval fish were prevalent in the ichthyoplankton tows during the 1991 period; therefore intra- and interspecific competition for limited food resources may have been the cause of slower growth (density-dependent growth) in yellowfin tuna larvae The highest mean seasurface temperature and the lowest mean wind stress occurred during an El Niño-Southern Oscillation (ENSO) event during the 1997 period. There appeared to be no clear association between these environmental factors and larval growth rates, but the higher temperatures may have caused an increase in the short-term growth of otoliths in relat

Spatial and temporal variation in the diet of the California sea lion (Zalophus californianus) in the Gulf of California, Mexico

Between June 1995 and May 1996 seven rookeries in the Gulf of California were visited four times in order to collect scat samples for studying spatial and seasonal variability California sea lion prey. The rookeries studied were San Pedro Mártir, San Esteban, El Rasito, Los Machos, Los Cantiles, Isla Granito, and Isla Lobos. The 1273 scat samples collected yielded 4995 otoliths (95.3%) and 247 (4.7%) cephalopod beaks. Fish were found in 97.4% of scat samples collected, cephalopods in 11.2%, and crustaceans in 12.7%. We identified 92 prey taxa to the species level, 11 to genus level, and 10 to family level, of which the most important were Pacific cutlassfish (Trichiurus lepturus), Pacific sardine (Sardinops caeruleus), plainfin midshipman (Porichthys spp.), myctophid no. 1, northern anchovy (Engraulis mordax), Pacific mackerel (Scomber japonicus), anchoveta (Cetengraulis mysticetus), and jack mackerel (Trachurus symmetricus). Significant differences were found among rookeries in the occurrence of all main prey (P≤0.04), except for myctophid no. 1 (P>0.05). Temporally, significant differences were found in the occurrence of Pacific cutlassfish, Pacific sardine, plainfin midshipman, northern anchovy, and Pacific mackerel (P<0.05), but not in jack mackerel (χ 2=2.94, df=3, P=0.40), myctophid no. 1 (χ 2=1.67, df= 3, P=0.64), or lanternfishes (χ 2=2.08, df=3, P=0.56). Differences were observed in the diet and in trophic diversity among seasons and rookeries. More evident was the variation in diet in relation to availability of Pacific sardine.

Image sequence segmentation using mixture-models with uniqueness and spatio-temporal consistency constraints

The use of mixture-model techniques for motion estimation and image sequence segmentation was discussed. The issues such as modeling of occlusion and uncovering, determining the relative depth of the objects in a scene, and estimating the number of objects in a scene were also investigated. The segmentation algorithm was found to be computationally demanding, but the computational requirements were reduced as the motion parameters and segmentation of the frame were initialized. The method provided a stable description, in whichthe addition and removal of objects from the description corresponded to the entry and exit of objects from the scene.