Stationary states of a directed planar growth process

1997 ◽  
Vol 29 (4) ◽  
pp. 857-877 ◽  
Author(s):  
D. J. Gates
Keyword(s):  
Forest Fires ◽  
Two Dimensions ◽  
Growth Patterns ◽  
Transition Rates ◽  
Single Particles ◽  
Growth Behaviour ◽  
Solid Films ◽  
Two Measures ◽  
Voter Models ◽  
Planar Growth

A new Markov process is introduced, describing growth or spread in two dimensions, via the aggregation of particles or the filling of cells. States of the process are configurations of part of the boundary of the growing aggregate, and transitions are captures or escapes of single particles. For suitably chosen transition rates, the process is dynamically reversible, leading to an explicit stationary distribution and a statistical description of the boundary. The growth rate is calculated and growth behaviour described. Different asymptotic relations between transition rates lead to different growth patterns or regimes. Besides the regimes familiar in polymer crystal growth, several new ones are described. The aggregate can have a porous structure resembling thin solid films deposited from vapour. Two measures of porosity, one for the boundary and one for the bulk, are calculated. The process is relevant to growing colonies of bacteria or the like, to the spread of epidemics and grass or forest fires, and to voter models.

Stationary states of a directed planar growth process

1997 ◽  
Vol 29 (04) ◽  
pp. 857-877 ◽  
Author(s):  
D. J. Gates
Keyword(s):  
Forest Fires ◽  
Two Dimensions ◽  
Growth Patterns ◽  
Transition Rates ◽  
Single Particles ◽  
Growth Behaviour ◽  
Solid Films ◽  
Two Measures ◽  
Voter Models ◽  
Planar Growth

A new Markov process is introduced, describing growth or spread in two dimensions, via the aggregation of particles or the filling of cells. States of the process are configurations of part of the boundary of the growing aggregate, and transitions are captures or escapes of single particles. For suitably chosen transition rates, the process is dynamically reversible, leading to an explicit stationary distribution and a statistical description of the boundary. The growth rate is calculated and growth behaviour described. Different asymptotic relations between transition rates lead to different growth patterns or regimes. Besides the regimes familiar in polymer crystal growth, several new ones are described. The aggregate can have a porous structure resembling thin solid films deposited from vapour. Two measures of porosity, one for the boundary and one for the bulk, are calculated. The process is relevant to growing colonies of bacteria or the like, to the spread of epidemics and grass or forest fires, and to voter models.

scholarly journals Combining Mechanistic Models and Machine Learning for Personalized Chemotherapy and Surgery Sequencing in Breast Cancer

2020 ◽  
Author(s):  
Cristian Axenie ◽  
Daria Kurz
Keyword(s):  
Breast Cancer ◽  
Machine Learning ◽  
Tumor Growth ◽  
Predictive Modelling ◽  
Growth Patterns ◽  
Growth Behaviour ◽  
Computational Oncology ◽  
Chemotherapy Protocol ◽  
Clinical Advantage ◽  
Personalized Chemotherapy

AbstractMathematical and computational oncology has increased the pace of cancer research towards the advancement of personalized therapy. Serving the pressing need to exploit the large amounts of currently underutilized data, such approaches bring a significant clinical advantage in tailoring the therapy. CHIMERA is a novel system that combines mechanistic modelling and machine learning for personalized chemotherapy and surgery sequencing in breast cancer. It optimizes decision-making in personalized breast cancer therapy by connecting tumor growth behaviour and chemotherapy effects through predictive modelling and learning. We demonstrate the capabilities of CHIMERA in learning simultaneously the tumor growth patterns, across several types of breast cancer, and the pharmacokinetics of a typical breast cancer chemotoxic drug. The learnt functions are subsequently used to predict how to sequence the intervention. We demonstrate the versatility of CHIMERA in learning from tumor growth and pharmacokinetics data to provide robust predictions under two, typically used, chemotherapy protocol hypotheses.

scholarly journals Policentryczność regionów miejskich w Polsce = Polycentricity of urban regions in Poland

2020 ◽  
Vol 92 (4) ◽  
pp. 455-474
Author(s):  
Bartosz Bartosiewicz ◽  
Szymon Marcińczak
Keyword(s):  
Urban Development ◽  
Statistical Significance ◽  
Regional Distribution ◽  
Two Dimensions ◽  
Morphological Development ◽  
Urban Structure ◽  
Urban Regions ◽  
Two Measures ◽  
Commuting Patterns ◽  
The Relationship

Studies dealing with the issue of polycentric urban development, both functional and morphological, often promote different approaches to the measurement of polycentricity. Relying on data on commuting patterns and the intra-regional distribution of population in Poland in 2011, we apply two measures of polycentricity to shed more light on the functional and morphological development of urban regions in Poland. We also explore the relationship between the two dimensions of polycentricity, using a functional/morphological primacy index and a general functional polycentricity index. The results reveal regions for which the different measures suggest divergent conclusions, while also implying that the measure used can determine the strength and statistical significance of the relationship between the two dimensions to polycentricity. As, in our view, it is the measure advocated by Burger et al. (2011) that best seems to differentiate between the different forms of urban structure, we use this to summarise patterns of polycentric urban development in Poland. The results illustrate: the statistical significance of the relationship between the two (morphological and functional) dimensions to polycentricity in Poland’s urban regions, and the way in which the level of functional polycentricity is higher than the degree of functional polycentricity.

scholarly journals The AGC protein kinase UNICORN controls planar growth by attenuating PDK1 in Arabidopsis thaliana

2018 ◽  
Author(s):  
Sebastian Scholz ◽  
Janys Pleßmann ◽  
Regina Hüttl ◽  
Katrin Wassmer ◽  
Balaji Enugutti ◽  
...  
Keyword(s):  
Transcription Factor ◽  
Protein Kinase ◽  
Seed Coat ◽  
Stress Responses ◽  
Biological Data ◽  
Growth Patterns ◽  
Cellular Growth ◽  
Distinct Cell ◽  
Cell Layers ◽  
Planar Growth

AbstractTissue morphogenesis critically depends on the coordination of cellular growth patterns. In plants, many organs consist of clonally distinct cell layers, such as the epidermis, whose cells undergo divisions that are oriented along the plane of the layer. The developmental control of such planar growth is poorly understood. We have previously identified the Arabidopsis AGCVIII-class protein kinase UNICORN (UCN) as a central regulator of this process. Plants lacking UCN activity show spontaneous formation of ectopic multicellular protrusions in integuments and malformed petals indicating that UCN suppresses uncontrolled growth in those tissues. In the current model UCN regulates planar growth of integuments in part by directly repressing the putative transcription factor ABERRANT TESTA SHAPE (ATS). Here we report on the identification of 3-PHOSPHOINOSITIDE-DEPENDENT PROTEIN KINASE 1 (PDK1) as a novel factor involved in UCN-mediated growth control. PDK1 constitutes a basic component of signaling mediated by AGC protein kinases throughout eukaryotes. Arabidopsis PDK1 is implied in stress responses and growth promotion. Here we show that loss-of-function mutations in PDK1 suppress aberrant growth in integuments and petals of ucn mutants. Additional genetic, in vitro, and cell biological data support the view that UCN functions by repressing PDK1. Furthermore, our data indicate that PDK1 is indirectly required for deregulated growth caused by ATS overexpression. Our findings support a model proposing that UCN suppresses ectopic growth in integuments through two independent processes: the attenuation of the protein kinase PDK1 in the cytoplasm and the repression of the transcription factor ATS in the nucleus.Author SummaryPlant organs, such as petals or roots, are composites of distinct cell layers. As a rule, cells making up a layer, for example the epidermis, the outermost layer of a tissue, divide “within the plane” of the layer. This cellular behavior results in the two-dimensional sheet-like or planar growth of the cell layer. The mechanism orchestrating such a growth pattern is poorly understood. In particular, it is unclear how uncontrolled and “out-of-plane” growth is avoided. Here we provide insight into this process. Our data indicate that higher than normal activity of a central regulator of growth and stress responses results in wavy and malformed petals and in protrusion-like aberrant outgrowths in the tissue that will develop into the seed coat. It is therefore important to keep this factor in check to allow proper formation of those tissues. We further show that a protein called UNICORN attenuates the activity of this regulator thereby ensuring the sheet-like growth of young petals or the developing seed coat.

Fire favours expansion of bamboo-dominated forests in the south-west Amazon

2010 ◽  
Vol 27 (1) ◽  
pp. 59-64 ◽  
Author(s):  
Maira Smith ◽  
Bruce Walker Nelson
Keyword(s):  
Forest Fires ◽  
Basal Area ◽  
Natural Disturbance ◽  
Ground Level ◽  
Control Area ◽  
The South ◽  
South West ◽  
The Face ◽  
Woody Bamboos ◽  
Two Measures

Abstract:Forests dominated by semi-scandent woody bamboos of the genus Guadua cover about 165 000 km2 of the south-west Amazon. Because many woody bamboo species are favoured by disturbance some authors have inferred this landscape to be a consequence of indigenous or natural disturbance. As seen in satellite images, the rounded edges of some bamboo-dominated forests indicate expansion into surrounding forest. These edges are unrelated to topography and resemble the borders of ground fires in unlogged Amazon forests, suggesting that bamboo may have been favoured by past fires. We studied the recovery of Guadua sarcocarpa and its competitors in the face of simulated fire by cutting all plant stems at ground level in ten 100-m2 plots, compared with ten control plots, and by burning a 2500-m2 plot. In the clear-cuts, bamboos recovered more successfully than did palms and dicots, by two measures: biomass accumulated and per cent recovery of pre-disturbance biomass. Resprouted bamboo attained higher stem densities than in control sites at 11 mo. In the burn plot, bamboo basal area recovered to pre-burn levels after 2 y and approached that of an undisturbed control area after 3 y. Though other natural disturbances are relevant, we conclude that forest fires should favour the spread and dominance of Guadua species in the south-west Amazon.

From Festies to Tourrats: Examining the Relationship between Jamband Subculture Involvement and Role Meanings

2008 ◽  
Vol 71 (4) ◽  
pp. 356-378 ◽  
Author(s):  
Pamela M. Hunt
Keyword(s):  
Group Analysis ◽  
Two Dimensions ◽  
Grateful Dead ◽  
Security Officer ◽  
Two Measures ◽  
Using Data ◽  
Affective Meanings ◽  
Continuous Measures ◽  
The Relationship ◽  
Negative Acts

I introduce two continuous measures of subculture involvement (ideological embeddedness and behavioral-relational involvement), and use them to examine the relationship between involvement in the jamband subculture and the affective meanings (evaluation, potency, and activity) associated with 18 roles that are relevant to that subculture. I expect the two measures of involvement to be related positively to the evaluation and potency of fourteen subculture roles (deadhead, drinker, drug user, environmentalist, festie, hippie, phishhead, rainbow person, rastafarian, raver, stoner, tourrat, vendor, wharfrat), and negatively to the evaluation and potency of four authority roles (capitalist, nark, police officer, venue security officer). Using data from self-administered surveys ( N = 418 for familiar subculture and authority roles, N = 219 for less familiar subculture roles), I find that subculture members learn meanings for relevant roles as a result of their socialization in the subculture; more specifically, as a result of their levels of ideological embeddedness and behavioral-relational involvement. This study enhances other investigations of subculture and meaning socialization. First, whereas past studies have examined between-group meaning variation, I investigate within-group meaning variation. A within-group analysis should indicate whether or not groups are heterogeneous, a finding that might reduce negative acts such as stereotyping. Second, I introduce two continuous measures designed to capture two dimensions of subculture involvement: ideological embeddedness and behavioral-relational involvement. Similar to previous conceptualizations of involvement, these two measures represent both attitudinal and behavioral involvement. Third, previous qualitative research within the related Grateful Dead subculture suggests that although not all subculture roles are equal in terms of evaluation, most subculture roles tend to be equal in potency. I further investigate this hypothesis using evaluation and potency to represent the affective meaning of roles, and I examine the implications of these findings for the jamband subculture.

The Glauber and Metropolis Transition Rates on the Stationary States of the Ising Model

1997 ◽  
Vol 11 (13) ◽  
pp. 565-570
Author(s):  
G. L. S. Paula ◽  
W. Figueiredo
Keyword(s):  
Ising Model ◽  
Nearest Neighbor ◽  
Mean Field ◽  
Field Approximation ◽  
Two Dimensions ◽  
Mean Field Approximation ◽  
Stationary States ◽  
Transition Rates ◽  
The Mean ◽  
The One

We have applied the Glauber and Metropolis prescriptions to investigate the stationary states of the Ising model in one and two dimensions. We have employed the formalism of the master equation to follow the evolution of the system towards the stationary states. Although the Glauber and Metropolis transition rates lead the system to the same equilibrium states for the Ising model in the Monte Carlo simulations, we show that they can predict different results if we disregard the correlations between spins. The critical temperature of the one-dimensional Ising model cannot even be found by using the Metropolis algorithm and the mean field approximation. However, taking into account only correlations between nearest neighbor spins, the resulting stationary states become identical for both Glauber and Metropolis transition rates.

Two Measures of Category Breadth: Age, Sex, Examiner Differences and Intercorrelations

1969 ◽  
Vol 25 (3) ◽  
pp. 859-870 ◽  
Author(s):  
Walter Penk
Keyword(s):  
Sex Differences ◽  
Age Differences ◽  
Learning Task ◽  
Growth Patterns ◽  
The Other ◽  
Quadratic Trend ◽  
High Tolerance ◽  
Two Measures ◽  
Psychological Similarity ◽  
Linear Decline

Two measures of category breadth—an adaptation of Pettigrew's (1958) Category-width scale and a learning task called poggles (Wallach & Caron, 1959)—were administered in a battery to 100 children, ages 7 to 11, grades 2 to 6. Sex differences were not replicated. Significant age differences occurred. The two measures of category breadth evidenced different growth patterns: one measure followed a linear decline combined with a resurgence of means; the other measure showed a U-shaped quadratic trend indicating that youngest and oldest children used broader category breadths than intermediate-aged children. Examiner differences were not significant. Intercorrelations suggested that test correlates and behavioral referents of category breadth necessitated redefinition or elaboration. While broader categorization may continue to be defined as high tolerance for deviant instances in psychological similarity, it is not associated with the converse—high tolerance for nondeviant instances. Specifically, broad categorization negatively related to measures of comparatively mature levels of verbal abstractions.

Transitions from Unemployment to Education in Europe: The Role of Educational Policies

2019 ◽  
Vol 48 (4) ◽  
pp. 699-720 ◽  
Author(s):  
BJÖRN HÖGBERG
Keyword(s):  
Young Adults ◽  
Two Dimensions ◽  
Further Education ◽  
Educational Policies ◽  
Educational Systems ◽  
Transition Rates ◽  
Financial Barriers ◽  
Individual Level ◽  
Cross Country

AbstractThe aim of this study is to investigate cross-country variability in transition rates from unemployment to further education among young adults, as well as how barriers in educational systems affect these transition rates. Previous research on adult further education has largely neglected the role of policies, and has not taken unemployed people into account.Two dimensions of educational policies are investigated. (1) Barriers facing prospective students with regard to previous academic achievements (e.g. second chance opportunities); and (2) financial barriers (e.g. high costs). It is hypothesized that low barriers are associated with higher transition rates into education, especially for unemployed young adults with lower levels of education.The aim is approached by investigating how differences in transition rates across countries are linked to the design of educational policies. Cross-country standardised individual-level panel data from 29 European countries are taken from EU-SILC. Multilevel multinomial models are fitted.Results show that lower barriers in the education system are associated with higher probabilities that unemployed young adults leave unemployment to re-enter further education, although only partial support is found for the hypothesis that unemployed young adults with lower levels of education gain relatively more from low barriers. Low barriers are sometimes associated with lower transition rates into employment.

Growth in encrusting cheilostome bryozoans: II. Circum-Atlantic distribution patterns

Paleobiology ◽  
1990 ◽  
Vol 16 (3) ◽  
pp. 304-321 ◽  
Author(s):  
Scott Lidgard
Keyword(s):  
Large Scale ◽  
Environmental Gradients ◽  
Distribution Patterns ◽  
Two Dimensions ◽  
Growth Patterns ◽  
The North ◽  
Upward Growth ◽  
Third Dimension ◽  
Environmental Limits ◽  
Cheilostome Bryozoans

Differences in zooid skeletal ontogeny are strongly linked to the distribution of bryozoan species, even along such large-scale environmental gradients as depth and latitude. Three growth patterns broadly characterize zooid formation for encrusting cheilostome bryozoans: zooidal and intrazooidal budding, which facilitate growth in two dimensions at colony margins; and frontal budding, which also permits upward growth in the third dimension. Analyses of skeletal growth patterns of encrusting species present in 230 Recent assemblages from the North Atlantic, Mediterranean, North Sea, and Gulf of Mexico show that species with zooidal budding dominate overwhelmingly at lower latitudes and in shallower water, as assessed by percentages of species within assemblages. In contrast, patterns within moderately diverse fossil assemblages from North America indicate that within the geographic and environmental limits sampled, species with intrazooidal budding once dominated and probably originated in shallow, warm water environments. Intrazooidal budding now occurs with greater relative frequency among species from deeper and higher latitude assemblages. Patterns for frontal budding suggest a slight decrease with increasing depth, but no consistent relationship with latitude. These paleoenvironmental trends occur withn a putatively monophyletic clade and are markedly similar to onshore/offshore trends recognized in other groups of marine benthos, based on patterns of occurrence of supra-specific taxa and novel morphotypes. Results presented here are based on relative dominance of species within assemblages and thus provide a novel comparative test of these previously reported trends.

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