scholarly journals A minimalist model for coevolving supply and drainage networks

2021 ◽  
Vol 8 (2) ◽  
pp. 201407
Author(s):  
Shashank Kumar Anand ◽  
Milad Hooshyar ◽  
Jan Martin Nordbotten ◽  
Amilcare Porporato
Keyword(s):  
Scalar Field ◽  
Nonlinear Partial Differential Equations ◽  
Three Dimensional ◽  
Dimensional Case ◽  
Spatial Density ◽  
Chemical Signal ◽  
Input And Output ◽  
Drainage Networks ◽  
Steady State Solutions

Numerous complex systems, both natural and artificial, are characterized by the presence of intertwined supply and/or drainage networks. Here, we present a minimalist model of such coevolving networks in a spatially continuous domain, where the obtained networks can be interpreted as a part of either the counter-flowing drainage or co-flowing supply and drainage mechanisms. The model consists of three coupled, nonlinear partial differential equations that describe spatial density patterns of input and output materials by modifying a mediating scalar field, on which supply and drainage networks are carved. In the two-dimensional case, the scalar field can be viewed as the elevation of a hypothetical landscape, of which supply and drainage networks are ridges and valleys, respectively. In the three-dimensional case, the scalar field serves the role of a chemical signal, according to which vascularization of the supply and drainage networks occurs above a critical ‘erosion’ strength. The steady-state solutions are presented as a function of non-dimensional channelization indices for both materials. The spatial patterns of the emerging networks are classified within the branched and congested extreme regimes, within which the resulting networks are characterized based on the absolute as well as the relative values of two non-dimensional indices.

Spherical Geometries and Multigroups

1950 ◽  
Vol 2 ◽  
pp. 100-119 ◽  
Author(s):  
Walter Prenowitz
Keyword(s):  
Three Dimensional ◽  
Spherical Geometry ◽  
Great Circle ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Elliptic Geometry ◽  
The Subject ◽  
Case Based

1. Introduction. The notion spherical geometry is suggested by the familiar geometry of the Euclidean 2-sphere in which the role of path is played by “arc of great circle”. The first postulational treatment of the subject seems to be that of Halsted [10] for the two-dimensional case. Kline [11] under the name double elliptic geometry, gave a greatly simplified foundation for the three-dimensional case based on the primitive notions point and order. Halsted and Kline study not merely descriptive (that is positional, non-metrical) properties of figures but also introduce metrical notions by postulating or defining congruence. Kline includes a continuity postulate designed to yield real spherical geometry.

Reconstruction of Objects from their Projections Using Orthogonal Functions

1973 ◽  
Vol 31 ◽  
pp. 268-269
Author(s):  
Elrnar Zeitler
Keyword(s):  
Unit Area ◽  
Three Dimensional ◽  
One Dimension ◽  
Spatial Density ◽  
Dimensional Representation ◽  
Orthogonal Functions ◽  
Object A ◽  
Plane Normal ◽  
Dimensional Object ◽  
Spatial Density Distribution

Considering any finite three-dimensional object, a “projection” is here defined as a two-dimensional representation of the object's mass per unit area on a plane normal to a given projection axis, here taken as they-axis. Since the object can be seen as being built from parallel, thin slices, the relation between object structure and its projection can be reduced by one dimension. It is assumed that an electron microscope equipped with a tilting stage records the projectionWhere the object has a spatial density distribution p(r,ϕ) within a limiting radius taken to be unity, and the stage is tilted by an angle 9 with respect to the x-axis of the recording plane.

The Role of Three-Dimensional Imaging in Evaluation of the Sinonasal Mass

1996 ◽  
Vol 34 (1) ◽  
pp. 27
Author(s):  
Sue Yon Shim ◽  
Ki Joon Sung ◽  
Young Ju Kim ◽  
In Soo Hong ◽  
Myung Soon Kim ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Three Dimensional Imaging ◽  
Sinonasal Mass

Homogenization and Mass Identity vs. Individual Identity. An Analysis in the Light of the Theory of “The Three Dimensional Spiral of Sense

2016 ◽  
Vol 2 (2) ◽  
pp. 40
Author(s):  
Miriam Aparicio
Keyword(s):  
Three Dimensional ◽  
Individual Identity ◽  
Cognitive Effects ◽  
The Media

This study tests some hypotheses included in the psycho-social-communicational paradigm, which emphasizes the cognitive effects of the media and the role of the psychosocial subject as the recipient

Dysregulation of HOX as a Potential Therapeutic Target in Breast Cancer

2020 ◽  
Vol 27 ◽  
Author(s):  
Ji-Yeon Lee ◽  
Myoung Hee Kim
Keyword(s):  
Breast Cancer ◽  
Hox Genes ◽  
Therapeutic Potential ◽  
Expression Patterns ◽  
Genome Structure ◽  
Control Cell ◽  
Three Dimensional ◽  
Cellular Processes ◽  
Hox Protein

: HOX genes belong to the highly conserved homeobox superfamily, responsible for the regulation of various cellular processes that control cell homeostasis, from embryogenesis to carcinogenesis. The abnormal expression of HOX genes is observed in various cancers, including breast cancer; they act as oncogenes or as suppressors of cancer, according to context. In this review, we analyze HOX gene expression patterns in breast cancer and examine their relationship, based on the three-dimensional genome structure of the HOX locus. The presence of non-coding RNAs, embedded within the HOX cluster, and the role of these molecules in breast cancer have been reviewed. We further evaluate the characteristic activity of HOX protein in breast cancer and its therapeutic potential.

Central ossifying fibroma of mandible

2020 ◽  
Vol 13 (12) ◽  
pp. e239286
Author(s):  
Kumar Nilesh ◽  
Prashant Punde ◽  
Nitin Shivajirao Patil ◽  
Amol Gautam
Keyword(s):  
Fibrous Tissue ◽  
Three Dimensional ◽  
Facial Asymmetry ◽  
Ossifying Fibroma ◽  
Mandible Reconstruction ◽  
Three Dimensional Printing ◽  
Osseous Lesion ◽  
Large Size ◽  
Dimensional Printing

Ossifying fibroma (OF) is a rare, benign, fibro-osseous lesion of the jawbone characterised by replacement of the normal bone with fibrous tissue. The fibrous tissue shows varying amount of calcified structures resembling bone and/or cementum. The central variant of OF is rare, and shows predilection for mandible among the jawbone. Although it is classified as fibro-osseous lesion, it clinically behaves as a benign tumour and can grow to large size, causing bony swelling and facial asymmetry. This paper reports a case of large central OF of mandible in a 40-year-old male patient. The lesion was treated by segmental resection of mandible. Reconstruction of the surgical defect was done using avascular fibula bone graft. Role of three-dimensional printing of jaw and its benefits in surgical planning and reconstruction are also highlighted.

scholarly journals Charge algebra in Al(A)dSn spacetimes

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Adrien Fiorucci ◽  
Romain Ruzziconi
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Three Dimensional ◽  
Dirichlet Boundary Conditions ◽  
Boundary Structure ◽  
Asymptotic Symmetry ◽  
Renormalization Procedure ◽  
Field Dependent ◽  
Odd Dimensions

Abstract The gravitational charge algebra of generic asymptotically locally (A)dS spacetimes is derived in n dimensions. The analysis is performed in the Starobinsky/Fefferman-Graham gauge, without assuming any further boundary condition than the minimal falloffs for conformal compactification. In particular, the boundary structure is allowed to fluctuate and plays the role of source yielding some symplectic flux at the boundary. Using the holographic renormalization procedure, the divergences are removed from the symplectic structure, which leads to finite expressions. The charges associated with boundary diffeomorphisms are generically non-vanishing, non-integrable and not conserved, while those associated with boundary Weyl rescalings are non-vanishing only in odd dimensions due to the presence of Weyl anomalies in the dual theory. The charge algebra exhibits a field-dependent 2-cocycle in odd dimensions. When the general framework is restricted to three-dimensional asymptotically AdS spacetimes with Dirichlet boundary conditions, the 2-cocycle reduces to the Brown-Henneaux central extension. The analysis is also specified to leaky boundary conditions in asymptotically locally (A)dS spacetimes that lead to the Λ-BMS asymptotic symmetry group. In the flat limit, the latter contracts into the BMS group in n dimensions.

scholarly journals Learning by Doing: The Use of Distance, Corners and Length in Rewarded Geometric Tasks by Zebrafish (Danio rerio)

Animals ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 2001
Author(s):  
Greta Baratti ◽  
Angelo Rizzo ◽  
Maria Elena Miletto Petrazzini ◽  
Valeria Anna Sovrano
Keyword(s):  
Danio Rerio ◽  
Three Dimensional ◽  
Reference Memory ◽  
Spatial Abilities ◽  
Learning By Doing ◽  
Surface Distance ◽  
Extended Surfaces ◽  
Unequal Length ◽  
Over Time

Zebrafish spontaneously use distance and directional relationships among three-dimensional extended surfaces to reorient within a rectangular arena. However, they fail to take advantage of either an array of freestanding corners or an array of unequal-length surfaces to search for a no-longer-present goal under a spontaneous cued memory procedure, being unable to use the information supplied by corners and length without some kind of rewarded training. The present study aimed to tease apart the geometric components characterizing a rectangular enclosure under a procedure recruiting the reference memory, thus training zebrafish in fragmented layouts that provided differences in surface distance, corners, and length. Results showed that fish, besides the distance, easily learned to use both corners and length if subjected to a rewarded exit task over time, suggesting that they can represent all the geometrically informative parts of a rectangular arena when consistently exposed to them. Altogether, these findings highlight crucially important issues apropos the employment of different behavioral protocols (spontaneous choice versus training over time) to assess spatial abilities of zebrafish, further paving the way to deepen the role of visual and nonvisual encodings of isolated geometric components in relation to macrostructural boundaries.

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