scholarly journals On spatial modelling

2015 ◽  
Vol 43 (1) ◽  
pp. 77-101 ◽  
Author(s):  
Leonid Tchertov
Keyword(s):  
Spatial Models ◽  
Structural Similarity ◽  
Spatial Modelling ◽  
Spatial Structures ◽  
Semiotic System ◽  
Important Special Case ◽  
The Third ◽  
Visual Spatial ◽  
Internal Modelling ◽  
Special Case

Spatial modelling concerns both the case when spatial structures have a modelling function and the case when such structures become modelled objects. In the article, spatial models are considered as the means of human activity in both external and internal aspects. External spatial models are tangible objects which have structural similarity with something different from them and can represent it for a subject. These external models can be interpreted on various mental levels: sensorial, perceptual, apperceptual and conceptual ones. Each of them is connected with a peculiar way of internal modelling. Both external and internal spatial models can have a productive or a reproductive character, which depends on whether they serve as patterns for reproduction or if they are copies of originals. It is possible to consider external models as spatial texts if they can be divided into a plane of expression and a plane of content which are connected with each other by a semiotic system. In particular, such division can be revealed in depictions in which the two planes of both depicting and depicted spaces are open for the eye and their connection is regulated by indexes of a special perceptographic code. So, depictions can be treated as spatial texts interpreted firstly on the perceptual level of internal modelling and, secondly, on the higher mental levels by means of other visual-spatial codes.The article is divided into three parts. The first part contains a description of the basic concepts introduced in the author’s interpretation. In the second part, these concepts are applied to description of spatial modelling and its semiotic means. In the third part an important special case of spatial modelling – combination of mimetic and semiotic means in formation of depictions – is discussed.

ON THE DENSITY OF HAUSDORFF DIMENSIONS OF BOUNDED TYPE CONTINUED FRACTION SETS: THE TEXAN CONJECTURE

2004 ◽  
Vol 04 (01) ◽  
pp. 63-76 ◽  
Author(s):  
OLIVER JENKINSON
Keyword(s):  
Hausdorff Dimension ◽  
Finite Subset ◽  
Continued Fraction ◽  
Cantor Set ◽  
Computational Method ◽  
Accurate Approximation ◽  
Natural Numbers ◽  
Important Special Case ◽  
The One ◽  
Special Case

Given a non-empty finite subset A of the natural numbers, let EA denote the set of irrationals x∈[0,1] whose continued fraction digits lie in A. In general, EA is a Cantor set whose Hausdorff dimension dim (EA) is between 0 and 1. It is shown that the set [Formula: see text] intersects [0,1/2] densely. We then describe a method for accurately computing dimensions dim (EA), and employ it to investigate numerically the way in which [Formula: see text] intersects [1/2,1]. These computations tend to support the conjecture, first formulated independently by Hensley, and by Mauldin & Urbański, that [Formula: see text] is dense in [0,1]. In the important special case A={1,2}, we use our computational method to give an accurate approximation of dim (E{1,2}), improving on the one given in [18].

An Elementary Proof of Suslin Reciprocity

2005 ◽  
Vol 48 (2) ◽  
pp. 221-236 ◽  
Author(s):  
Matt Kerr
Keyword(s):  
Elementary Proof ◽  
Function Fields ◽  
Algebraic Cycles ◽  
Important Special Case ◽  
Special Case

AbstractWe state and prove an important special case of Suslin reciprocity that has found significant use in the study of algebraic cycles. An introductory account is provided of the regulator and norm maps on Milnor K2-groups (for function fields) employed in the proof.

scholarly journals The Steady Profile of an Axisymmetric Ice Sheet

1981 ◽  
Vol 27 (95) ◽  
pp. 25-37 ◽  
Author(s):  
I. R. Johnson
Keyword(s):  
Aspect Ratio ◽  
Power Law ◽  
Viscous Incompressible Fluid ◽  
Ice Sheet ◽  
Plane Flow ◽  
The Third ◽  
Basal Sliding ◽  
Steady Plane ◽  
Third Dimension ◽  
Special Case

AbstractSteady plane flow under gravity of an axisymmetric ice sheet resting on a horizontal rigid bed, subject to surface accumulation and ablation, basal drainage, and basal sliding is treated according to a power law between shear traction and velocity. The surface accumulation is taken to depend on height, and the drainage and sliding coefficient also depend on the height of overlying ice. The ice is described as a general non-linearly viscous incompressible fluid, and temperature variation through the ice sheet is neglected. Illustrations are presented for Glen’s power law (including the special case of a Newtonian fluid), and the polynomial law of Colbeck and Evans. The analysis follows that of Morland and Johnson (1980) where the analogous problem for an ice sheet deforming under plane flow was considered. Comparisons are made between the two models and it is found that the effect of the third dimension is to reduce (or leave unchanged) the aspect ratio for the cases considered, although no general formula can be obtained. This reduction is seen to depend on both the surface accumulation and the sliding law.

scholarly journals Spatial models to support the management of coastal marine ecosystems: a short review of the best practices in Liguria, Italy

2013 ◽  
Vol 15 (1) ◽  
pp. 189 ◽  
Author(s):  
M. VACCHI ◽  
M. MONTEFALCONE ◽  
V. PARRAVICINI ◽  
A. ROVERE ◽  
P. VASSALLO ◽  
...  
Keyword(s):  
Human Impacts ◽  
Spatial Models ◽  
Short Review ◽  
Posidonia Oceanica ◽  
Spatial Modelling ◽  
Coastal Development ◽  
Marine Habitat ◽  
Marine Habitats ◽  
Coastal Marine ◽  
The Status

Spatial modelling is an emerging approach to the management of coastal marine habitats, as it helps understanding and predicting the results of global change. This paper reviews critically two recent examples developed in Liguria, an administrative region of NW Italy. The first example, aiming at predicting habitat status depending on pressures, provides managers with the opportunity of envisaging different scenarios for the consequences of coastal development choices. The second example defines the status of an important Mediterranean coastal marine habitat (Posidonia oceanica meadows) under natural conditions, allowing for quantifying human impacts on regressed meadows. Both modelling approaches are useful to define the targets of coastal management, and may help choosing the best management option. Well-planned and sustained monitoring is essential to model validation and improvement.

scholarly journals Loglinear Model Formation using Hierachial Backward Method

2020 ◽  
Vol 2 (1) ◽  
pp. 28-36
Author(s):  
Siti Fatimah Sihotang ◽  
Zuhri
Keyword(s):  
Linear Model ◽  
Good Method ◽  
General Linear Model ◽  
Loglinear Model ◽  
Complete Model ◽  
The Third ◽  
Several Variables ◽  
Model Formation ◽  
Special Case ◽  
Categorical Scale

The loglinear model is a special case of a general linear model for poissondistributed data. The loglinear model is also a number of models in statistics that are used todetermine dependencies between several variables on a categorical scale. The number ofvariables discussed in this study were three variables. After the variables are investigated,the formation of the loglinear model becomes important because not all the modelinteraction factors that exist in the complete model become significant in the resultingmodel. The formation of the loglinear model in this study uses the Backward Hierarchicalmethod. This research makes loglinear modeling to get the model using the HierarchicalBackward method to choose a good method in making models with existing examples.From the challenging examples that have been done, it is known that the HierarchicalReverse method can model the third iteration or scroll. Then, also use better assessmentmethods about faster workmanship and computer-sponsored assessments that are used moreefficiently through compatibility testing for each model made

Exact third-order structure functions for two-dimensional turbulence

2018 ◽  
Vol 851 ◽  
pp. 672-686 ◽  
Author(s):  
Jin-Han Xie ◽  
Oliver Bühler
Keyword(s):  
Structure Functions ◽  
Spectral Energy ◽  
Order Structure ◽  
Two Dimensional ◽  
Third Order ◽  
Transfer Rates ◽  
The Third ◽  
Random Forcing ◽  
Asymptotic Expressions ◽  
Special Case

We derive and investigate exact expressions for third-order structure functions in stationary isotropic two-dimensional turbulence, assuming a statistical balance between random forcing and dissipation both at small and large scales. Our results extend previously derived asymptotic expressions in the enstrophy and energy inertial ranges by providing uniformly valid expressions that apply across the entire non-dissipative range, which, importantly, includes the forcing scales. In the special case of white noise in time forcing this leads to explicit predictions for the third-order structure functions, which are successfully tested against previously published high-resolution numerical simulations. We also consider spectral energy transfer rates and suggest and test a simple robust diagnostic formula that is useful when forcing is applied at more than one scale.

On the Possible Spatial Structures of the β – Amyloid.

2022 ◽  
Vol 7 (1) ◽  
pp. 0-0
Keyword(s):  
Amino Acids ◽  
Amino Acid ◽  
Spatial Structure ◽  
Spatial Models ◽  
Globular Proteins ◽  
Spatial Structures ◽  
Higher Dimensional ◽  
Protein Molecules ◽  
Β Amyloid ◽  
First Time

Spatial models of the β - structures of protein molecules, forming layers of amino acids, in principle, of unlimited length for both antiparallel and parallel conformation have been constructed. It is shown that the simplified flat Pauling models do not reflect the spatial structure of these layers. Using the recently developed theory of higher-dimensional polytopic prismahedrons, models of the volumetric filling of space with amino acid molecules are constructed. The constructed models for the first time mathematically describe the native structures of globular proteins.

Introduction

2020 ◽  
pp. 1-6
Author(s):  
Peter Scholze ◽  
Jared Weinstein
Keyword(s):  
Moduli Spaces ◽  
Function Fields ◽  
Number Fields ◽  
Important Special Case ◽  
Langlands Correspondence ◽  
Key Innovation ◽  
Perfectoid Spaces ◽  
Definition Of ◽  
Special Case

This introductory chapter provides an overview of Drinfeld's work on the global Langlands correspondence over function fields. Whereas the global Langlands correspondence is largely open in the case of number fields K, it is a theorem for function fields, due to Drinfeld and L. Lafforgue. The key innovation in this case is Drinfeld's notion of an X-shtuka (or simply shtuka). The Langlands correspondence for X is obtained by studying moduli spaces of shtukas. A large part of this course is about the definition of perfectoid spaces and diamonds. There is an important special case where the moduli spaces of shtukas are classical rigid-analytic spaces. This is the case of local Shimura varieties. Some examples of these are the Rapoport-Zink spaces.

On the Hyperplane Sections Through two Given Points of an Algebraic Variety

1970 ◽  
Vol 22 (1) ◽  
pp. 128-133 ◽  
Author(s):  
Wei-Eihn Kuan
Keyword(s):  
Simple Proof ◽  
Hyperplane Section ◽  
Rational Points ◽  
Infinite Field ◽  
Important Special Case ◽  
Irreducible Curve ◽  
Irreducible Variety ◽  
Dimension 2 ◽  
Hyperplane Sections ◽  
Special Case

1. Let k be an infinite field and let V/k be an irreducible variety of dimension ≧ 2 in a projective n-space Pn over k. Let P and Q be two k-rational points on V In this paper, we describe ideal-theoretically the generic hyperplane section of V through P and Q (Theorem 1) and prove that the section is almost always an absolutely irreducible variety over k1/pe if V/k is absolutely irreducible (Theorem 3). As an application (Theorem 4), we give a new simple proof of an important special case of the existence of a curve connecting two rational points of an absolutely irreducible variety [4], namely any two k-rational points on V/k can be connected by an irreducible curve.I wish to thank Professor A. Seidenberg for his continued advice and encouragement on my thesis research.

scholarly journals Deception through Half-Truths

2020 ◽  
Vol 34 (06) ◽  
pp. 10110-10117
Author(s):  
Andrew Estornell ◽  
Sanmay Das ◽  
Yevgeniy Vorobeychik
Keyword(s):  
Polynomial Time ◽  
Transition Function ◽  
Np Hard ◽  
Fundamental Issue ◽  
Fake News ◽  
False Information ◽  
Important Special Case ◽  
Bayes Network ◽  
Special Case

Deception is a fundamental issue across a diverse array of settings, from cybersecurity, where decoys (e.g., honeypots) are an important tool, to politics that can feature politically motivated “leaks” and fake news about candidates. Typical considerations of deception view it as providing false information. However, just as important but less frequently studied is a more tacit form where information is strategically hidden or leaked. We consider the problem of how much an adversary can affect a principal's decision by “half-truths”, that is, by masking or hiding bits of information, when the principal is oblivious to the presence of the adversary. The principal's problem can be modeled as one of predicting future states of variables in a dynamic Bayes network, and we show that, while theoretically the principal's decisions can be made arbitrarily bad, the optimal attack is NP-hard to approximate, even under strong assumptions favoring the attacker. However, we also describe an important special case where the dependency of future states on past states is additive, in which we can efficiently compute an approximately optimal attack. Moreover, in networks with a linear transition function we can solve the problem optimally in polynomial time.

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