12. Model Structures for the A1-homotopy Category

2019 ◽  
pp. 175-212
Keyword(s):  
Homotopy Category ◽  
Model Structures

Model Structures for the 𝔸1-homotopy Category

2019 ◽  
pp. 175-212
Author(s):  
Christian Haesemeyer ◽  
Charles A. Weibel
Keyword(s):  
Full Subcategory ◽  
Homotopy Category ◽  
Symmetric Power ◽  
Model Structure ◽  
Model Categories ◽  
Simplicial Presheaves ◽  
Basic Ideas ◽  
Quillen Model ◽  
Model Structures ◽  
Bousfield Localization

This chapter provides the 𝔸1-local projective model structure on the categories of simplicial presheaves and simplicial presheaves with transfers. These model categories, written as Δ‎opPshv(Sm)𝔸1 and Δ‎op PST(Sm)𝔸1, are first defined. Their respective homotopy categories are Ho(Sm) and the full subcategory DM eff nis ≤0 of DM eff nis. Afterward, this chapter introduces the notions of radditive presheaves and ̅Δ‎-closed classes, and develops their basic properties. The theory of ̅Δ‎-closed classes is needed because the extension of symmetric power functors to simplicial radditive presheaves is not a left adjoint. This chapter uses many of the basic ideas of Quillen model categories, which is a category equipped with three classes of morphisms satisfying five axioms. In addition, much of the material in this chapter is based upon the technique of Bousfield localization.

scholarly journals STABLE LEFT AND RIGHT BOUSFIELD LOCALISATIONS

2013 ◽  
Vol 56 (1) ◽  
pp. 13-42 ◽  
Author(s):  
DAVID BARNES ◽  
CONSTANZE ROITZHEIM
Keyword(s):  
Homology Theory ◽  
Homotopy Category ◽  
Stable Model ◽  
Model Categories ◽  
Morita Theory ◽  
Left And Right ◽  
Torsion Modules ◽  
Model Structures ◽  
Insight Into ◽  
Complete Characterisation

AbstractWe study left and right Bousfield localisations of stable model categories which preserve stability. This follows the lead of the two key examples: localisations of spectra with respect to a homology theory and A-torsion modules over a ring R with A a perfect R-algebra. We exploit stability to see that the resulting model structures are technically far better behaved than the general case. We can give explicit sets of generating cofibrations, show that these localisations preserve properness and give a complete characterisation of when they preserve monoidal structures. We apply these results to obtain convenient assumptions under which a stable model category is spectral. We then use Morita theory to gain an insight into the nature of right localisation and its homotopy category. We finish with a correspondence between left and right localisation.

scholarly journals A monoidal algebraic model for rational SO(2)-spectra

2016 ◽  
Vol 161 (1) ◽  
pp. 167-192 ◽  
Author(s):  
DAVID BARNES
Keyword(s):  
Abelian Category ◽  
Algebraic Model ◽  
Homotopy Category ◽  
Smash Product ◽  
Model Structure ◽  
Joint Work ◽  
Generating Sets ◽  
Stable Homotopy Category ◽  
Equivariant Spectra ◽  
Model Structures

AbstractThe category of rational SO(2)–equivariant spectra admits an algebraic model. That is, there is an abelian category ${\mathcal A}$(SO(2)) whose derived category is equivalent to the homotopy category of rational SO(2)–equivariant spectra. An important question is: does this algebraic model capture the smash product of spectra?The category ${\mathcal A}$(SO(2)) is known as Greenlees' standard model, it is an abelian category that has no projective objects and is constructed from modules over a non–Noetherian ring. As a consequence, the standard techniques for constructing a monoidal model structure cannot be applied. In this paper a monoidal model structure on ${\mathcal A}$(SO(2)) is constructed and the derived tensor product on the homotopy category is shown to be compatible with the smash product of spectra. The method used is related to techniques developed by the author in earlier joint work with Roitzheim. That work constructed a monoidal model structure on Franke's exotic model for the K(p)–local stable homotopy category.A monoidal Quillen equivalence to a simpler monoidal model category R•-mod that has explicit generating sets is also given. Having monoidal model structures on ${\mathcal A}$(SO(2)) and R•-mod removes a serious obstruction to constructing a series of monoidal Quillen equivalences between the algebraic model and rational SO(2)–equivariant spectra.

Localization of DNA in chromatin using ESI and osmium ammine staining

1990 ◽  
Vol 48 (3) ◽  
pp. 116-117
Author(s):  
C.L. Woodcock ◽  
R.A. Horowitz ◽  
D. P. Bazett-Jones ◽  
A.L. Olins
Keyword(s):  
Spectroscopic Imaging ◽  
Energy Losses ◽  
Electron Spectroscopic Imaging ◽  
Feulgen Reaction ◽  
Specific Location ◽  
Eukaryotic Nucleus ◽  
Chromatin Fibers ◽  
Patiria Miniata ◽  
Model Structures

In the eukaryotic nucleus, DNA is packaged into nucleosomes, and the nucleosome chain folded into ‘30nm’ chromatin fibers. A number of different model structures, each with a specific location of nucleosomal and linker DNA have been proposed for the arrangment of nucleosomes within the fiber. We are exploring two strategies for testing the models by localizing DNA within chromatin: electron spectroscopic imaging (ESI) of phosphorus atoms, and osmium ammine (OSAM) staining, a method based on the DNA-specific Feulgen reaction.Sperm were obtained from Patiria miniata (starfish), fixed in 2% GA in 150mM NaCl, 15mM HEPES pH 8.0, and embedded In Lowiciyl K11M at -55C. For OSAM staining, sections 100nm to 150nm thick were treated as described, and stereo pairs recorded at 40,000x and 100KV using a Philips CM10 TEM. (The new osmium ammine-B stain is available from Polysciences Inc). Uranyl-lead (U-Pb) staining was as described. ESI was carried out on unstained, very thin (<30 nm) beveled sections at 80KV using a Zeiss EM902. Images were recorded at 20,000x and 30,000x with median energy losses of 110eV, 120eV and 160eV, and a window of 20eV.

A Note on Confidence Intervals and Model Specification

Marketing ZFP ◽  
2019 ◽  
Vol 41 (4) ◽  
pp. 33-42
Author(s):  
Thomas Otter
Keyword(s):  
Confidence Intervals ◽  
Generalized Linear Model ◽  
Statistical Information ◽  
Regression Coefficients ◽  
Model Specification ◽  
Model Parameters ◽  
Exploratory Research ◽  
Empirical Calibration ◽  
Credible Intervals ◽  
Model Structures

Empirical research in marketing often is, at least in parts, exploratory. The goal of exploratory research, by definition, extends beyond the empirical calibration of parameters in well established models and includes the empirical assessment of different model specifications. In this context researchers often rely on the statistical information about parameters in a given model to learn about likely model structures. An example is the search for the 'true' set of covariates in a regression model based on confidence intervals of regression coefficients. The purpose of this paper is to illustrate and compare different measures of statistical information about model parameters in the context of a generalized linear model: classical confidence intervals, bootstrapped confidence intervals, and Bayesian posterior credible intervals from a model that adapts its dimensionality as a function of the information in the data. I find that inference from the adaptive Bayesian model dominates that based on classical and bootstrapped intervals in a given model.

Analysis and design of suitable model structures for activated sludge tanks with circulating flow

1999 ◽  
Vol 39 (4) ◽  
pp. 55-60 ◽  
Author(s):  
J. Alex ◽  
R. Tschepetzki ◽  
U. Jumar ◽  
F. Obenaus ◽  
K.-H. Rosenwinkel
Keyword(s):  
Activated Sludge ◽  
Large Scale ◽  
Wastewater Treatment Plants ◽  
Treatment Plant ◽  
High Sensitivity ◽  
Suitable Model ◽  
Model Structure ◽  
Analysis And Design ◽  
Hydraulic Behaviour ◽  
Model Structures

Activated sludge models are widely used for planning and optimisation of wastewater treatment plants and on line applications are under development to support the operation of complex treatment plants. A proper model is crucial for all of these applications. The task of parameter calibration is focused in several papers and applications. An essential precondition for this task is an appropriately defined model structure, which is often given much less attention. Different model structures for a large scale treatment plant with circulation flow are discussed in this paper. A more systematic method to derive a suitable model structure is applied to this case. Results of a numerical hydraulic model are used for this purpose. The importance of these efforts are proven by a high sensitivity of the simulation results with respect to the selection of the model structure and the hydraulic conditions. Finally it is shown, that model calibration was possible only by adjusting to the hydraulic behaviour and without any changes of biological parameters.

scholarly journals Path homology theory of edge-colored graphs

2021 ◽  
Vol 19 (1) ◽  
pp. 706-723
Author(s):  
Yuri V. Muranov ◽  
Anna Szczepkowska
Keyword(s):  
Spectral Sequence ◽  
Edge Coloring ◽  
Homology Theory ◽  
Homotopy Category ◽  
Homology Groups ◽  
Colored Graphs ◽  
Natural Filtration ◽  
Definition Of ◽  
Exact Sequences

Abstract In this paper, we introduce the category and the homotopy category of edge-colored digraphs and construct the functorial homology theory on the foundation of the path homology theory provided by Grigoryan, Muranov, and Shing-Tung Yau. We give the construction of the path homology theory for edge-colored graphs that follows immediately from the consideration of natural functor from the category of graphs to the subcategory of symmetrical digraphs. We describe the natural filtration of path homology groups of any digraph equipped with edge coloring, provide the definition of the corresponding spectral sequence, and obtain commutative diagrams and braids of exact sequences.

Sign in / Sign up

Export Citation Format

Share Document