Spatial Irregularity Research Articles

Removing Artefacts From Color and Contrast Modifications

This work is concerned with the modification of the gray level or color distribution of digital images. A common drawback of classical methods aiming at such modifications is the revealing of artefacts or the attenuation of details and textures. In this work, we propose a generic filtering method enabling, given the original image and the radiometrically corrected one, to suppress artefacts while preserving details. The approach relies on the key observation that artefacts correspond to spatial irregularity of the so-called transportation map, defined as the difference between the original and the corrected image. The proposed method draws on the nonlocal Yaroslavsky filter to regularize the transportation map. The efficiency of the method is shown on various radiometric modifications: contrast equalization, midway histogram, color enhancement, and color transfer. A comparison with related approaches is also provided.

Study on Estimation of Subsurface Velocity Structure Model using Waveform Inversion

The estimation of layered velocity model by waveform inversion using observed ground motion records is one of ways for modeling deep subsurface structure for the numerical simulation of long-period ground motion. The effectiveness and problem of the estimation by waveform inversion are examined. The numerical test of the waveform inversion using simulated waveform gives good estimation of velocity model assumed beforehand, without constraints of number of layers and velocity of each layers. The case study of application to strong ground motion records at OJIYA, K-NET is conducted. The estimated velocity model by waveform inversion corresponds to the estimated velocity models based on geophysical exploration, geomorphology and geology in previous research. The effect of spatial irregularity of subsurface structure is examined using FDM simulation and waveform inversion. In waveform inversion, the waveform affected by spatial irregularity of subsurface structure gives distorted estimations of the velocity structure. In the region around epicenter, the waveform is not affected by spatial irregularity of subsurface structure so much. In the estimation of velocity model, therefore, the effect of spatial irregularity is small in the region.

Optical investigations of CDOM-rich coastal waters in Pärnu Bay

Parnu Bay in the Eastern Baltic Sea was chosen for studying the spatial-temporal variability of water parameters as an optically complex and semi-enclosed coastal area. The water properties of Parnu Bay are influenced by the town of Parnu with its 70 000 inhabitants and by the high inflow from the Parnu River. The in situ database was collected during the ice-free period of 2006-2007 (11 sampling stations, 10 series of field trips). According to the results, the main factor influencing the light attenuation in the water was coloured dissolved organic matter (CDOM) which overshadows the relationships between the radiation characteristics and organic/inorganic particles. In April and May, when the freshwater discharge of the Parnu River was highest, the values of aCDOM(380) were between 4.6 and 31.8 m -1 , while in September they varied only within 2.52-10.2 m -1 . The concentrations of chlorophyll a (including its metabolite phaeophytin a) generally ranged from 4 to 12 mg m -3 but during algal blooms they rapidly increased to 31.8 mg m -3 . The temporal and spatial irregularity of suspended matter concentrations was caused by the loading of unpacked peat at the Parnu River mouth as well as by undulation and ship traffic in Parnu Bay. MODIS level 1 data with 250 m resolution were used for illustrative comparison of spatial and temporal variations in the water properties in Parnu Bay and the Gulf of Riga. An attempt to perform the quantitative analysis with the purpose of estimating the concentrations of different optically significant substances separately gave statistically incorrect results.

Spatially mixed crops to control the stratified dispersal of airborne fungal diseases

Intraspecific crop diversification is thought to be a possible solution to the disease susceptibility of monocultured crops. We modelled the stratified dispersal of an airborne pathogen population in order to identify the spatial patterns of cultivar mixtures that could slow epidemic spread driven by dual dispersal mechanisms acting over both short and long distances. We developed a model to simulate the propagation of a fungal disease in a 2D field, including a reaction-diffusion model for short-distance disease dispersal, and a stochastic model for long-distance dispersal. The model was fitted to data for the spatio-temporal spread of faba bean rust (caused by Uromyces viciae- fabae) through a discontinuous field. The model was used to compare the effectiveness of eight different planting patterns of cultivar mixtures against a disease spread by short-distance and stratified dispersal. Our combined modelling approach provides a reasonably good fit with the observed data for the spread of faba bean rust. Similar predictive power could be expected for the management of resource-mediated invasions by other airborne fungi. If a disease spreads by short-distance dispersal, random mixtures can be used to slow the epidemic spread, since their spatial irregularity creates a natural barrier to the progression of a smooth epidemic wave. In the context of stratified dispersal, heterogeneous patterns should be used that include a minimum distance between susceptible units, which decreases the probability of infection by long-distance spore dispersal. We provide a simple framework for modelling the stratified dispersal of disease in a diversified crop. The model suggests that the spatial arrangement of components in cultivar mixtures has to accord with the dispersal characteristics of the pathogen in order to increase the efficiency of diversification strategies in agro-ecosystems and forestry. It can be applied in low input agriculture to manage pathogen invasion by intercropping and cultivar mixtures, and to design sustainable systems of land use.

Cortical mechanisms of normal and abnormal processing in the visual system, Part 1

Vernier thresholds rise much more rapidly in the periphery than do grating thresholds. A similar dissociation between acuity and hyperacuity has been shown to be present in strabismic but not in anisometropic amblyopia, thus leading to the suggestion that the strabismic fovea is similar to the normal periphery. Here it is shown that a quantitative model for spatial pattern discrimination, which accounts for foveal hyperacuity data, can be extended to encompass both the periphery and amblyopia if appropriate alterations are made. For the periphery it is necessary to increase the size of model receptive fields and to introduce both spatial undersampling and position irregularity (i.e. irregularity in the location of cortical filters). The strabismic fovea also requires spatial undersampling and position irregularity but no change in receptive field size. Defects in the good eye of strabismus can be explained by spatial irregularity. Finally, the anisometropic fovea requires a reduction in mechanism sensitivity but neither spatial untersampling nor position irregularity.

Toward the Optimal Itinerary-Based KNN Query Processing in Mobile Sensor Networks

The K-nearest neighbors (KNN) query has been of significant interest in many studies and has become one of the most important spatial queries in mobile sensor networks. Applications of KNN queries may include vehicle navigation, wildlife social discovery, and squad/platoon searching on the battlefields. Current approaches to KNN search in mobile sensor networks require a certain kind of indexing support. This index could be either a centralized spatial index or an in-network data structure that is distributed over the sensor nodes. Creation and maintenance of these index structures, to reflect the network dynamics due to sensor node mobility, may result in long query response time and low battery efficiency, thus limiting their practical use. In this paper, we propose a maintenance-free itinerary-based approach called density-aware itinerary KNN query processing (DIKNN). The DIKNN divides the search area into multiple cone-shape areas centered at the query point. It then performs a query dissemination and response collection itinerary in each of the cone-shape areas in parallel. The design of the DIKNN scheme takes into account several challenging issues such as the trade-off between degree of parallelism and network interference on query response time, and the dynamic adjustment of the search radius (in terms of number of hops) according to spatial irregularity or mobility of sensor nodes. To optimize the performance of DIKNN, a detailed analytical model is derived that automatically determines the most suitable degree of parallelism under various network conditions. This model is validated by extensive simulations. The simulation results show that DIKNN yields substantially better performance and scalability over previous work, both as kappa increases and as the sensor node mobility increases. It outperforms the second runner with up to a 50 percent saving in energy consumption and up to a 40 percent reduction in query response time, while rendering the same level of query result accuracy.

Land use changes in Poland during transformation: Case study of Wielkopolska region

The most popular quantitative measure of landscape is land use. The most frequent data sources of land use are satellite images, aerial photographs and maps. Another source of the data can also be land cadaster. The advantages of research based on data from land registers are their relatively good accessibility, nationwide coverage and updates at equal yearly intervals, and the direct possibility to combine the data with statistics published for administrative units. The author of this paper used the above resources to analyse land use changes in the region of Wielkopolska (Poland) in the period of system transformation (1989–2005). The analysis was performed using a synthetic measure of the landscape change, being a quotient of the share of land where hardened ground are dominant and land where biologically active areas prevail. The analysis showed that although the rate of land use changes decreased after 1989, it was marked with spatial irregularity and the differences became greater over time. The changes depend on environmental conditions to a very small extent. For the most part it was the socio-economic factors that caused land use changes, primarily the economic activity of residents. Economically underdeveloped regions were intensively afforested, nevertheless environmental conditions are favourable to technical development. Therefore underdeveloped areas should be stimulated, particularly in the scope of education and entrepreneurship. Such stimulating actions should be emphasised in regional programming documents, especially in the province development strategy.

Topological properties in the spatial distribution of amphibians in Alabama USA for the use of large scale conservation

Large-scale biodiversity conservation is urgently needed due to increasing habitat loss and fragmentation. Understanding topological perspectives of species’ distribution patterns can provide useful information for linking conservation studies at larger scales. We studied topological properties of localities in Alabama where 60 species of 12 families of amphibians were present. Analysis included a clustering coefficient which measures the strength of a population group, the relationship between occurrence localities and species number, the fractal dimension of occurrence localities (which emphasizes spatial irregularity), and distance to nearest-neighbor. The results indicate that the clustering coefficients of most amphibian species were low, but were higher for species with few occurrence localities, such as Rana sylvatica and Limnaoedus ocularis. The general relationship between species number and occurrence localities was that the majority of species held few localities in their distribution, while the remaining species occupied a greater number of localities. The fractal dimension (FD) for all amphibian localities was about 1.58, although FD was low for most individual species. We identified four relationships in the distribution of distance to nearest-neighbor: linear, logarithmic, power and polynomial. These topological properties may indicate intrinsic features about amphibians in Alabama and provide useful information for regional planning. Enhancing landscape linkages across a large area using undisturbed areas, such as 300-500 km in diameter may be a good approach to conservation practice in this region. Steps needed for biodiversity conservation planning in Alabama include creating or conserving small habitats across agricultural and urban land, and maintaining suitable spatial complexity and distance to nearest neighbors.

Temporal and spatiotemporal variations in a mathematical model of macrophage–tumor interaction

In the present paper we study a three-component mathematical model of tumor–immune system interaction. A number of solid tumors contain a high proportion of macrophages and these immune cells are known to have a remarkable impact on the progression and dormancy of such tumors. We assume these macrophages as the main immune system component facilitating tumor destruction. Stability criteria of the basic model around the steady state of coexistence are derived. Next, we consider the process of macrophage activation as non-instantaneous by using a distributed delay with a weak kernel and obtain a range for the macrophage death rate that ensures system stability. Finally, we incorporate the spatial irregularity of solid tumors by making the delay nonlocal. Analysis of the resulting spatiotemporal model gives a number of thresholds in terms of different system parameters that guarantee tumor stability. Numerical simulations are performed to justify analytical findings.

Exploring hot and baryon-dense matter with nucleus–nucleus collisions

The interest in hot and baryon-dense matter has recently intensified because of the prospects for exploring this phase region by a downgraded RHIC and the future FAIR. The baryon excess, the spatial irregularity of the system and its rapid evolution, and particularly the presence of a phase transition, pose interesting theoretical challenges that must be addressed in the development of the transport models required for the planning and interpretation of the experiments.

Task‐performing dynamics in irregular, biomimetic networks

AbstractUnderstanding self‐organized collective dynamics—especially in sparsely connected, noisy, and imperfect networks—has important implications for designing and optimizing task‐performing technological systems as well as for deciphering biological structures and functions. We note that stomatal arrays on plant leaves might provide an ideal example of task‐performance in this context. Guided by observations of stomatal networks, we examined a simple model of task‐performing, collective dynamics that included state noise, spatial rule heterogeneity, dynamic modules, and network rewiring. Our results indicate that task‐performance in such networks can actually be enhanced by various kinds of spatial and temporal irregularity. © 2007 Wiley Periodicals, Inc. Complexity 12: 14–21, 2007

20: QT dispersion for detection of cardiac allograft vasculopathy in heart transplant patients

Purpose: After heart transplantation, cardiac allograft vasculopathy (CAV) may result in ventricular repolarization abnormalities, which can be detected by an increase in QTc and QT dispersion. Thus, we hypothesize that sequential ECG QT dispersion assessment can serve as a noninvasive marker of CAV. Methods and Materials: We analyzed 24 patients with angiographically confirmed and 22 control transplant patients without CAV. Using the program NIH Image, we analyzed early after heart transplantation (11 20 days), at time of diagnosis (1919 714 days), and at two intermediate time (646 306 days) and (1274 500 days). ECGs from control heart patients were analyzed at similar intervals. Sampling times are similar in both groups. ECG QT intervals were measured for each lead. Between-lead, QT dispersion (QTmax QTmin) and corrected dispersion (QTc QT(ms)/[1000(ms-1) RR(ms)]1/) were measured for spatial irregularity of myocardial electrical conduction. Results: CAV and control groups were similar in age (49 12 v 53 11 years; p NS), sex (all males), ethnicity (Caucasian 75 v 77 %, African American 20 v 22%), pre transplant diagnosis (ischemic 45 v 50 %, idiopathic 37 v 45 %, and viral 4 v 4 %). QTc dispersion (graph) was similar between no CAV (n) and CAV (y) at the first and second time interval, but the CAV (y) is significantly greater than CAV (n) at the third (* p 0.0001) and fourth time intervals (* p .0001). Conclusions: Dispersion of QTc was significantly increased in the heart transplant group with CAV. These data suggest that development of CAV is associated with an increase in QT dispersion, a parameter reflective of repolarization and may serve as a noninvasive predictor for cardiac allograft vasculopathy.

Correction of Inhomogeneous RF Field Using Multiple SPGR Signals for High-Field Spin-Echo MRI

To propose a simple and useful method for correcting nonuniformity of high-field (3 Tesla) T(1)-weighted spin-echo (SE) images based on a B1 field map estimated from gradient recalled echo (GRE) signals. To estimate B1 inhomogeneity, spoiled gradient recalled echo (SPGR) images were collected using a fixed repetition time of 70 ms, flip angles of 45 and 90 degrees, and echo times of 4.8 and 10.4 ms. Selection of flip angles was based on the observation that the relative intensity changes in SPGR signals were very similar among different tissues at larger flip angles than the Ernst angle. Accordingly, spatial irregularity that was observed on a signal ratio map of the SPGR images acquired with these 2 flip angles was ascribed to inhomogeneity of the B1 field. Dual echo time was used to eliminate T(2)(*) effects. The ratio map that was acquired was scaled to provide an intensity correction map for SE images. Both phantom and volunteer studies were performed using a 3T magnetic resonance scanner to validate the method. In the phantom study, the uniformity of the T(1)-weighted SE image improved by 23%. Images of human heads also showed practically sufficient improvement in the image uniformity. The present method improves the image uniformity of high-field T(1)-weighted SE images.

Earthquake related tsunami hazard along the western coast of Thailand

Abstract. The primary background for the present study was a project to assist the authorities in Thailand with development of plans for how to deal with the future tsunami risk in both short and long term perspectives, in the wake of the devastating 26 December 2004 Sumatra-Andaman earthquake and tsunami. The study is focussed on defining and analyzing a number of possible future earthquake scenarios (magnitudes 8.5, 8.0 and 7.5) with associated return periods, each one accompanied by specific tsunami modelling. Along the most affected part of the western coast of Thailand, the 2004 tsunami wave caused a maximum water level ranging from 5 to 15 m above mean sea level. These levels and their spatial distributions have been confirmed by detailed numerical simulations. The applied earthquake source is developed based on available seismological and geodetic inversions, and the simulation using the source as initial condition agree well with sea level records and run-up observations. A conclusion from the study is that another megathrust earthquake generating a tsunami affecting the coastline of western Thailand is not likely to occur again for several hundred years. This is in part based on the assumption that the Southern Andaman Microplate Boundary near the Simeulue Islands constitutes a geologic barrier that will prohibit significant rupture across it, and in part on the decreasing subduction rates north of the Banda Ache region. It is also concluded that the largest credible earthquake to be prepared for along the part of the Sunda-Andaman arc that could affect Thailand, is within the next 50–100 years an earthquake of magnitude 8.5, which is expected to occur with more spatial and temporal irregularity than the megathrust events. Numerical simulations have shown such earthquakes to cause tsunamis with maximum water levels up to 1.5–2.0 m along the western coast of Thailand, possibly 2.5–3.0 m on a high tide. However, in a longer time perspective (say more than 50–100 years) the potentials for earthquakes of similar magnitude and consequences as the 2004 event will become gradually larger and eventually posing an unacceptable societal risk. These conclusions apply only to Thailand, since the effects of an M 8.5 earthquake in the same region could be worse for north-western Sumatra, the Andaman and Nicobar Islands, maybe even for Sri Lanka and parts of the Indian coastline. Moreover, further south along the Sunda arc the potentials for large ruptures are now much higher than for the region that ruptured on 26 December 2004.

Short-Term Retinal Vessel Diameter Variability in Relation to the History of Cold Extremities

To test whether the regularity and short-term changes of retinal vessel diameter are related to the history of cold hands and feet and to nailfold circulatory response to cooling. In 13 vasospastic and 13 nonvasospastic young healthy women (based on their history of cold extremities and nailfold capillaroscopy) 20- to 30-second recordings of the ocular fundus was obtained with a retinal vessel analyzer. The spatial regularity of arterioles and venules was analyzed by means of the coefficient of variation of vessel diameter and by exploratory Fourier analysis of spatial frequencies. Temporal variability was analyzed as excursion amplitude of the vessel diameter, as a correlation of means and standard deviations of vessel diameter within a defined time period, and by Fourier analysis of temporal diameter change in the heartbeat frequency range. Mean diameters of selected segments of arterioles (129.9 +/- 15.3 and 124.4 +/- 24.4 microm) and venules (150.8 +/- 14.6 and 149.3 +/- 19.6 microm) were not different between the vasospastic and nonvasospastic groups, respectively. Spatial variability: The coefficient of variation in arterioles was 8.8% +/- 2.8% and 6.1% +/- 1.7%, in venules 3.8% +/- 1.4%, and 3.6% +/- 0.9% in the vasospastic and nonvasospastic groups, respectively (difference by ANOVA, P = 0.017). Fourier analysis revealed differences between arterioles in the two groups, with relative Fourier power spectrum amplitudes of spatial frequencies higher in vasospastic eyes (Mann-Whitney P = 0.029). Temporal variability: The excursion amplitudes of vessel diameters were comparable in the two groups. Individual coefficients of correlation of successive means and standard deviations of the vessel diameter were 0.11 +/- 0.23 and 0.09 +/- 0.23 in the nonvasospastic group, and 0.25 +/- 0.40 and 0.24 +/- 0.22 in the vasospastic group, in the arterioles and venules, respectively (ANOVA: vasospastic versus nonvasospastic; P = 0.038). Fourier analysis in the heartbeat frequency range revealed differences in relative power spectrum amplitudes of temporal frequencies between arterioles in the two groups (higher in the vasospastic group, Mann-Whitney P = 0.029). Retinal arterioles in healthy vasospastic women show higher spatial irregularity and an increased vessel diameter variation within the temporal frequency of the heartbeat than do arterioles in nonvasospastic women.

Measuring of Mist Flow Rate with Optical Spatial Filter

How to measure the mist flow rate ordering 1 mL/h is the key issue to configure the oil feeding system and/or to monitor the quantity of the lubricating oil for MQL engineering. Here, a new algorithm is reported, which is based on a spatial irregularity of scattered light from the mist particles. The flow rate in the tubing is not even, hence the spatial frequency method was considered not to be applicable to it. However, the core image of scattered light near around the center gives a sharp spectrum of the spatial frequency. To obtain the core image, the light source is focused on the center of fubing flow and the scattered light is formed on a linear CCD. The spatial filter consisted of the combinations of the pixels. And the sinusoidal wiegting-function makes it easy to generate a sharp frequency spectrum. The flow rate is estimated by the spatial velocity and the brightness of scattered light from the mist particles. It has the feasibility to construct a flow transducer for the very low flow rate such as lubricating oil with mist flow. To confirm the effect of proposed technique, a trial model is made and tested with several commercial MQL systems. It has a good agreement with the mass measuring method with bottle and tissu. Furthermore at in-line estimation in the MQL machining process, a transient phenomena of mist flow is detected.

Development of large-area a-Si:H films deposition using controlled VHF plasma

A VHF plasma for a large-area a-Si:H films deposition has been produced using the ladder-shaped electrode and the phase modulation method. These techniques enable to average the voltage distribution along the electrode by a high-speed scanning of the voltage standing wave. The effects of these techniques are demonstrated on the a-Si:H films deposition using 1.4 m × 1.1 m substrates and on the self-cleaning using NF 3 plasmas. The spatial irregularity of the deposition rate is about ± 15% and the self-cleaning rate is 5 nm/s.

The interpretation of fen carr pollen diagrams: The representation of the dry land vegetation

Deposits of fen carr origin are frequently used in pollen-based studies, including those where the primary objective is reconstructing the Holocene history of dry land vegetation. However, there have been few studies of modern pollen–vegetation relationships in these circumstances. Here as an aid to the interpretation of fossil assemblages we determine the distribution of pollen derived from dry land sources within areas of fen carr. In particular, we examine the effect distance from the dry land/fen carr edge has on the pollen representation of the dry land vegetation components. Data on vegetation composition and modern pollen samples (from moss polsters) were collected from a series of sample points within two areas of fen carr and adjacent drier woodlands in Norfolk, UK. The spatial distribution of the pollen derived from dry arboreal elements is explored through trend surfaces and plots of pollen representation against distance away from the dry land/fen carr edge. The pollen assemblages from the fen carr sample points reflect and can be used to infer the composition of adjacent dry woodland areas where they are dominated by the relatively high pollen producers Quercus and Betula. The presence of dry taxa that occur away from the dry land/fen carr edge is difficult to detect even if these taxa are generally regarded as over-represented in the pollen record (e.g. Pinus sylvestris). Arboreal elements that are present in the vegetation close to the edge of the dry land show a general declining trend in pollen representation within the first 80 m of fen carr. Factors influencing this pattern include the variable input of pollen from wetland taxa and the spatial irregularity of the dry land/fen carr edge. Pollen recruitment into fen carr systems resembles other closed canopy sites. Palaeo-sites situated within c. 80 m of the dry land/fen carr edge afford the opportunity to reconstruct vegetation at the stand scale. However, adjustments need to be made for differential pollen dispersal, for example, the local presence of Fraxinus excelsior and Sorbus-type can only be detected within c. 20 m of the dry land edge. The interpretation of pollen sequences must also allow for changes in the position of this edge through time.

SPATIAL AND MECHANOEMISSION CHAOS OF MECHANICALLY DEFORMED TUMOR CELLS

The development and spreading of tumor process is accompanied by changes in nonlinear (chaotic) dynamics of mechanochemical interaction process in the group of cells. Taking into consideration spatial irregularity and heterogeneity of internal structures of tumor cells, we suggested that treatment by mechanically deformed (MD) syngeneic tumor cells (STC) would be accompanied by changed influence on malignant growth. The objective of this work was to compare spatial, mechanoemission (ME) chaos of MD STC of carcinoma Lewis and melanoma B16 and their malignant growth. MD STC preparation included the aseptic removal of the animal tumor, lyophilization and next mechanical deformation in the microvibratory mill. The suspension of non-deformed or MD STC was injected intraperitoneally. Morphological, morphometric and mechanoemission studies used for estimate of spatial chaos and heterogeneity structure in tumor cells and blood. For Lewis carcinoma the reduction of spatial and ME chaos of cells is accompanied by regression in tumor growth and metastasis. For melanoma B16 the decrease of spatial chaos and the increase of ME chaos in cells is accompanied by initiation of tumor growth and metastasis. These results illustrated equivalent tendencies in chaos changing in spatial and ME chaos for carcinoma Lewis, while opposite tendencies were observed for melanoma B16. Blood ME of mice with melanoma B16 have greater ME chaos in comparison with animals with Lewis carcinoma. This confirmed that the concept of deterministic chaos is hierarchical for the host during cancer process. Results of comparative analysis between spatial, mechanoemission chaos of MD STC and malignant growth could be useful for gain a better understanding relationship of nonlinear biomechanical processes to tumor cells.

SPATIAL AND MECHANOEMISSION CHAOS OF MECHANICALLY DEFORMED TUMOR CELLS

The development and spend of the tumor process is accompanied by changes in non-linear (chaotic) dynamics of mechanochemical interaction process in the group of cells. Taking into consideration spatial irregularity and heterogeneity of internal structures of tumor cells, we suggested that treatment by mechanically deformed (MD) syngeneic tumor cells (STC) would be accompanied by changed influence on malignant growth. The objective of this work was to compare spatial, mechanoemission (ME) chaos of MD STC of carcinoma Lewis and melanoma B16 and their malignant growth. MD STC preparation included the aseptic removal of the animal tumor, lyophilization and next mechanical deformation in the microvibratory mill. The suspension of non-deformed or MD STC was injected intraperitoneally. Morphological, morphometric and mechanoemission studies were used for the estimate of spatial chaos and heterogeneity structure in tumor cells and blood. For Lewis carcinoma, the reduction of spatial and ME chaos of cells is accompanied by regression in tumor growth and metastasis. For melanoma B16, the decrease of spatial chaos and the increase of ME chaos in cells are accompanied by the initiation of tumor growth and metastasis. These results illustrated equivalent tendencies in chaos changing in spatial and ME chaos for carcinoma Lewis, while opposite tendencies were observed for melanoma B16. Blood ME of mice with melanoma B16 have greater ME chaos in comparison with animals with Lewis carcinoma. This confirmed that the concept of deterministic chaos is hierarchical for the host during cancer process. Results of comparative analysis between spatial, mechanoemission chaos of MD STC and malignant growth could be useful to gain a better understanding relationship of non-linear biomechanical processes to tumor cells.