scholarly journals Model structures on categories of models of type theories

2017 ◽  
Vol 28 (10) ◽  
pp. 1695-1722 ◽  
Author(s):  
VALERY ISAEV
Keyword(s):  
Model Category ◽  
Additional Structure ◽  
Model Structures ◽  
Dependent Type

Models of dependent type theories are contextual categories with some additional structure. We prove that if a theory T has enough structure, then the category T-Mod of its models carries the structure of a model category. We also show that if T has Σ-types, then weak equivalences can be characterized in terms of homotopy categories of models.

scholarly journals Model category structures and spectral sequences

2019 ◽  
Vol 150 (6) ◽  
pp. 2815-2848
Author(s):  
Joana Cirici ◽  
Daniela Egas Santander ◽  
Muriel Livernet ◽  
Sarah Whitehouse
Keyword(s):  
Spectral Sequence ◽  
Commutative Ring ◽  
Model Category ◽  
Spectral Sequences ◽  
Model Structures

AbstractLet R be a commutative ring with unit. We endow the categories of filtered complexes and of bicomplexes of R-modules, with cofibrantly generated model structures, where the class of weak equivalences is given by those morphisms inducing a quasi-isomorphism at a certain fixed stage of the associated spectral sequence. For filtered complexes, we relate the different model structures obtained, when we vary the stage of the spectral sequence, using the functors shift and décalage.

scholarly journals Quillen model structures for relative homological algebra

2002 ◽  
Vol 133 (2) ◽  
pp. 261-293 ◽  
Author(s):  
J. DANIEL CHRISTENSEN ◽  
MARK HOVEY
Keyword(s):  
Homotopy Theory ◽  
Homological Algebra ◽  
Abelian Category ◽  
Derived Categories ◽  
Derived Category ◽  
Category Structure ◽  
Model Category ◽  
Projective Class ◽  
Chain Complexes ◽  
Model Structures

An important example of a model category is the category of unbounded chain complexes of R-modules, which has as its homotopy category the derived category of the ring R. This example shows that traditional homological algebra is encompassed by Quillen's homotopical algebra. The goal of this paper is to show that more general forms of homological algebra also fit into Quillen's framework. Specifically, a projective class on a complete and cocomplete abelian category [Ascr ] is exactly the information needed to do homological algebra in [Ascr ]. The main result is that, under weak hypotheses, the category of chain complexes of objects of [Ascr ] has a model category structure that reflects the homological algebra of the projective class in the sense that it encodes the Ext groups and more general derived functors. Examples include the ‘pure derived category’ of a ring R, and derived categories capturing relative situations, including the projective class for Hochschild homology and co-homology. We characterize the model structures that are cofibrantly generated, and show that this fails for many interesting examples. Finally, we explain how the category of simplicial objects in a possibly non-abelian category can be equipped with a model category structure reflecting a given projective class, and give examples that include equivariant homotopy theory and bounded below derived categories.

scholarly journals An interpretation of dependent type theory in a model category of locally cartesian closed categories

2021 ◽  
pp. 1-26
Author(s):  
Martin E. Bidlingmaier
Keyword(s):  
Type Theory ◽  
Model Category ◽  
Model Categories ◽  
Dependent Type Theory ◽  
Categorical Structure ◽  
Categorical Models ◽  
Cartesian Closed Categories ◽  
Cartesian Closed ◽  
Original Interpretation ◽  
Dependent Type

Abstract Locally cartesian closed (lcc) categories are natural categorical models of extensional dependent type theory. This paper introduces the “gros” semantics in the category of lcc categories: Instead of constructing an interpretation in a given individual lcc category, we show that also the category of all lcc categories can be endowed with the structure of a model of dependent type theory. The original interpretation in an individual lcc category can then be recovered by slicing. As in the original interpretation, we face the issue of coherence: Categorical structure is usually preserved by functors only up to isomorphism, whereas syntactic substitution commutes strictly with all type-theoretic structures. Our solution involves a suitable presentation of the higher category of lcc categories as model category. To that end, we construct a model category of lcc sketches, from which we obtain by the formalism of algebraically (co)fibrant objects model categories of strict lcc categories and then algebraically cofibrant strict lcc categories. The latter is our model of dependent type theory.

scholarly journals Abelian model structures on categories of quiver representations

2019 ◽  
Vol 19 (10) ◽  
pp. 2050195
Author(s):  
Georgios Dalezios
Keyword(s):  
Large Class ◽  
Recent Work ◽  
Model Category ◽  
Quiver Representations ◽  
Representations Of Quivers ◽  
Cotorsion Pairs ◽  
Model Structures

Let [Formula: see text] be an abelian model category (in the sense of Hovey). For a large class of quivers, we describe associated abelian model structures on categories of quiver representations with values in [Formula: see text]. This is based on recent work of Holm and Jørgensen on cotorsion pairs in categories of quiver representations. An application on Ding projective and Ding injective representations of quivers over Ding–Chen rings is given.

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.

Products of therapeutic insulins in the blood of insulin-dependent (type I) diabetic patients

Diabetes ◽  
1985 ◽  
Vol 34 (5) ◽  
pp. 510-519 ◽  
Author(s):  
D. C. Robbins ◽  
S. E. Shoelson ◽  
H. S. Tager ◽  
P. M. Mead ◽  
D. H. Gaynor
Keyword(s):  
Diabetic Patients ◽  
Type I ◽  
Insulin Dependent ◽  
Dependent Type

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 DECOMPOSITION OF UNITARY MATRICES AND QUANTUM GATES

2013 ◽  
Vol 11 (01) ◽  
pp. 1350015 ◽  
Author(s):  
CHI-KWONG LI ◽  
REBECCA ROBERTS ◽  
XIAOYAN YIN
Keyword(s):  
General Scheme ◽  
Quantum Gate ◽  
Quantum Gates ◽  
Unitary Matrix ◽  
Additional Structure ◽  
Unitary Matrices ◽  
Decomposition Scheme ◽  
Single Qubit ◽  
Matlab Program

A general scheme is presented to decompose a d-by-d unitary matrix as the product of two-level unitary matrices with additional structure and prescribed determinants. In particular, the decomposition can be done by using two-level matrices in d - 1 classes, where each class is isomorphic to the group of 2 × 2 unitary matrices. The proposed scheme is easy to apply, and useful in treating problems with the additional structural restrictions. A Matlab program is written to implement the scheme, and the result is used to deduce the fact that every quantum gate acting on n-qubit registers can be expressed as no more than 2n-1(2n-1) fully controlled single-qubit gates chosen from 2n-1 classes, where the quantum gates in each class share the same n - 1 control qubits. Moreover, it is shown that one can easily adjust the proposed decomposition scheme to take advantage of additional structure evolving in the process.

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