Inverse Systems Research Articles

A Duality for Involutive Bisemilattices

We establish a duality between the category of involutive bisemilattices and the category of semilattice inverse systems of Stone spaces, using Stone duality from one side and the representation of involutive bisemilattices as Plonka sum of Boolean algebras, from the other. Furthermore, we show that the dual space of an involutive bisemilattice can be viewed as a GR space with involution, a generalization of the spaces introduced by Gierz and Romanowska equipped with an involution as additional operation.

Some categorical aspects of the inverse limits in ditopological context

<p>This paper considers some various categorical aspects of the inverse systems (projective spectrums) and inverse limits described in the category if<strong>PDitop</strong>, whose objects are ditopological plain texture spaces and morphisms are bicontinuous point functions satisfying a compatibility condition between those spaces. In this context, the category <strong>Inv<sub>ifPDitop</sub></strong> consisting of the inverse systems constructed by the objects and morphisms of if<strong>PDitop</strong>, besides the inverse systems of mappings, described between inverse systems, is introduced, and the related ideas are studied in a categorical - functorial setting. In conclusion, an identity natural transformation is obtained in the context of inverse systems - limits constructed in if<strong>PDitop</strong> and the ditopological infinite products are characterized by the finite products via inverse limits.</p>

Direct limits of generalized pseudo-effect algebras with the Riesz decomposition properties

In this paper, we focus on direct limits and inverse limits in the category with generalized pseudo-effect algebras (GPEAs for short) as objects and GPEA-morphisms as morphisms. We show that direct limits exist in the category of GPEAs and direct limits of GPEAs satisfy the Riesz decomposition properties whenever the directed systems of GPEAs satisfy the Riesz decomposition properties. Then, we give a condition under which the quotient of a direct limit of GPEAs is a direct limit of quotients of GPEAs. Moreover, we prove that if inverse systems of GPEAs satisfy the Riesz decomposition properties, then inverse limits also satisfy the Riesz decomposition properties.

Extensional maps and approximate inverse limits

In 2012, Žiga Virk introduced the notion of an extensional equivalence, herein called an extensional map, and used it to generalize part of the extension theory factorization theorem of M. Levin, L. Rubin, and P. Schapiro. Here were are going to study this notion in the setting of inverse systems of compact Hausdorff spaces and approximate inverse systems of compact metric spaces. In both cases we will show that given a surjective map f to the limit, if each coordinate map pγ∘f is an extensional map, then so is f.

Inverse System Estimation for Feedforward: A Kernel-Based Approach for Non-Causal Systems

Accurate models of inverse systems are required for high performance in inverse model-based feedforward control. Identification of inverse systems can be challenging, especially if the inverse system has poles outside the typical stability region. The aim of this paper is to estimate non-causal models of inverse systems, for intended use in feedforward control, where non-causality can be exploited to compensate ‘unstable’ poles. The developed method employs kernel-based regularization to improve the bias/variance trade-off, where the non-causal kernel is constructed using rational basis functions that include poles outside the usual stability region. The benefits of the developed method are demonstrated on an example, including non-causality.

Popov form and the explicit equations of inverse systems

Popov form and the explicit equations of inverse systems

Extending functors from the category of strict morphisms of inverse systems to the associated pro-category with applications to the first derived limit

We show that functors on the category of strict morphisms of inverse systems which are indexed by arbitrary cofiltered small categories have at most one extension to the associated procategory and give conditions characterizing the existence of extensions. This is applied to provide a concrete extension of the first derived limit to the category of pro-groups.

Activation-Induced Conformational Changes of Dopamine D3 Receptor Promote the Formation of the Internal Water Channel

The atomic-level dopamine activation mechanism for transmitting extracellular ligand binding events through transmembrane helices to the cytoplasmic G protein remains unclear. In the present study, the complete dopamine D3 receptor (D3R), with a homology-modeled N-terminus, was constructed to dock different ligands to simulate conformational alterations in the receptor’s active and inactive forms during microsecond-timescale molecular dynamic simulations. In agonist-bound systems, the D3R N-terminus formed a “lid-like” structure and lay flat on the binding site opening, whereas in antagonist and inverse agonist-bound systems, the N-terminus exposed the binding cavity. Receptor activation was characterized using the different molecular switch residue distances, and G protein-binding site volumes. A continuous water pathway was observed only in the dopamine-Gαi-bound system. In the inactive D3Rs, water entry was hindered by the hydrophobic layers. Finally, a complete activation mechanism of D3R was proposed. Upon agonist binding, the “lid-like” conformation of the N-terminus induces a series of molecular switches to increase the volume of the D3R cytoplasmic binding part for G protein association. Meanwhile, water enters the transmembrane region inducing molecular switches to assist in opening the hydrophobic layers to form a continuous water channel, which is crucial for maintaining a fully active conformation for signal transduction.

Inverse systems and limits in the category of ditopological plain spaces

In this paper, inverse systems (spectrums) and their inverse limits are described and investigated in the some special subcategories of the category whose objects are ditopological texture spaces and morphisms are the point functions satisfying a compatibility condition, besides bicontinuity. According to that, we especially restrict ourselves to the topological subcategory ifPDitop consisting of point functions as above and ditopological spaces that have plain texturing which is proper, but still quite extensive subclass of texturings. Followed by, so many major properties of inverse systems and limits in the context of category ifPDitop are constructed under the most general conditions. In particular, by considering the full subcategory ifPDicomp of ifPDitop, whose objects are dicompact plain spaces, we acquired various results about the theory of inverse systems consisting of dicompact plain spaces.

On Teter rings

We give a new characterization, in the equicharacteristic case, of Teter rings by using Macaulay inverse systems. We extend the previous characterizations due to Teter, to Huneke and Vraciu and to Ananthnarayan et al., to any characteristic of the ground field and remove the hypothesis on the socle ideal. We construct and describe the variety parametrizing Teter covers and we show how to check if an Artin ring is Teter. If this is the case, we show how to compute a Teter cover.

Spontaneous assembly of a hybrid crystal-liquid phase in inverse patchy colloid systems.

Materials with well-defined architectures are heavily sought after in view of their diverse technological applications. Among the desired target architectures, lamellar phases stand out for their exceptional mechanical and optical features. Here we show that charged colloids, decorated on their poles with two oppositely charged regions possess the unusual ability to spontaneously assemble in different morphologies of (semi-)ordered, layered particle arrangements which maintain their structural stability over a surprisingly large temperature range. This remarkable capacity is related to a characteristic bonding mechanism: stable intra-layer bonds guarantee the formation of planar aggregates, while strong inter-layer bonds favor the stacking of the emerging planar assemblies. These two types of bonds together are responsible for the self-healing processes occurring during the spontaneous assembly. The resulting phases are characterized by parallel, densely packed, particle layers connected by a relatively small number of intra-layer particles. We investigate the properties of the (semi-)ordered phases in terms of static and dynamic correlation functions, focusing in particular on a novel hybrid crystal-liquid phase that prevails at intermediate temperatures where the inter-layer particles form a mobile, fluid phase.

Comparative Analysis of Cobalt Oxide Nanoisland Stability and Edge Structures on Three Related Noble Metal Surfaces: Au(111), Pt(111) and Ag(111)

Metal oxide nanostructures and thin films grown on metallic substrates have attracted strong attention as model catalysts and as interesting inverse catalyst systems in their own right. In this study, we investigate the role of metal support in the growth and stabilization of cobalt oxide nanostructures on the three related (111) surfaces of Au, Pt and Ag, as investigated by means of high-resolution scanning tunneling microscopy and DFT calculations. All three substrates promote the growth of crystalline CoOx (x = 1−2) islands under oxidative conditions, but we find several noteworthy differences in the occurrence and stabilization of four distinct cobalt oxide island phases: Co–O bilayers, O–Co–O trilayers, Co–O–Co–O double bilayers and O–Co–O–Co–O multilayers. Using atom-resolved images combined with analysis of defect lines in bilayer islands on Au and Pt, we furthermore unambiguously determine the edge structure. Interestingly, the island shape and abundances of edge types in bilayers change radically from mixed Co/O edge terminations on Au(111) to a predominance of Co terminated edges (~91 %) on Pt(111) which is especially interesting since the Co metal edges are expected to host the most active sites for water dissociation.

Vorticity Deformation in Polymeric Emulsions Induced by Anisotropic Ellipsoids.

We study the influence of particle shape on shear-induced droplet deformation in polymeric emulsions. During shearing, droplets become elongated and rotate periodically about their major axes while aligning along the vorticity direction in ellipsoid-filled emulsions, while similar behavior is not observed in the pristine, microsphere-filled or ellipsoid-filled inverse systems. Based on the Jeffery orbit theory, the formation of anisotropic droplets with extremely small Reynolds number due to arrested coalescence in Newtonian matrix and strong confinement effect are suggested to be responsible for the vorticity alignment of droplets during slow shearing.

Some remarks on a theorem of Bergman

We extend a result of Bergman to show that any object in an arbitrary Grothendieck category may be expressed as an inverse limit of injectives. We also study inverse systems of κ-injective objects, where κ is an infinite regular cardinal.

Thermoresponsive Polymers and Inverse Opal Hydrogels for the Detection of Diols.

Responsive inverse opal hydrogels functionalized by boroxole moieties were synthesized and explored as sensor platforms for various low molar mass as well as polymeric diols and polyols, including saccharides, glycopolymers and catechols, by exploiting the diol induced modulation of their structural color. The underlying thermoresponsive water-soluble copolymers and hydrogels exhibit a coil-to-globule or volume phase transition, respectively, of the LCST-type. They were prepared from oligoethylene oxide methacrylate (macro)monomers and functionalized via copolymerization to bear benzoboroxole moieties. The resulting copolymers represent weak polyacids, which can bind specifically to diols within an appropriate pH window. Due to the resulting modulation of the overall hydrophilicity of the systems and the consequent shift of their phase transition temperature, the usefulness of such systems for indicating the presence of catechols, saccharides, and glycopolymers was studied, exploiting the diol/polyol induced shifts of the soluble polymers' cloud point, or the induced changes of the hydrogels' swelling. In particular, the increased acidity of benzoboroxoles compared to standard phenylboronic acids allowed performing the studies in PBS buffer (phosphate buffered saline) at the physiologically relevant pH of 7.4. The inverse opals constructed of these thermo- and analyte-responsive hydrogels enabled following the binding of specific diols by the induced shift of the optical stop band. Their highly porous structure enabled the facile and specific optical detection of not only low molar mass but also of high molar mass diol/polyol analytes such as glycopolymers. Accordingly, such thermoresponsive inverse opal systems functionalized with recognition units represent attractive and promising platforms for the facile sensing of even rather big analytes by simple optical means, or even by the bare eye.

Categories of inverse systems of compacta with upper semi-continuous bonding functions

We define a category G(Λ) of inverse systems of compacta with upper semi-continuous bonding functions indexed by a given directed set Λ so that the topological generalisation of inverse limits proposed by Mahavier can be characterised by a certain universal property in this category. Our defining new category is justified by generating a class of inverse systems that do not have a categorical limit in the usual sense. We also construct a category Gpro in analogy with pro-categories in an attempt to derive generalisations of some results on classical inverse limits.

Top-down assessment of the Asian carbon budget since the mid 1990s.

Increasing atmospheric carbon dioxide (CO2) is the principal driver of anthropogenic climate change. Asia is an important region for the global carbon budget, with 4 of the world's 10 largest national emitters of CO2. Using an ensemble of seven atmospheric inverse systems, we estimated land biosphere fluxes (natural, land-use change and fires) based on atmospheric observations of CO2 concentration. The Asian land biosphere was a net sink of −0.46 (−0.70–0.24) PgC per year (median and range) for 1996–2012 and was mostly located in East Asia, while in South and Southeast Asia the land biosphere was close to carbon neutral. In East Asia, the annual CO2 sink increased between 1996–2001 and 2008–2012 by 0.56 (0.30–0.81) PgC, accounting for ∼35% of the increase in the global land biosphere sink. Uncertainty in the fossil fuel emissions contributes significantly (32%) to the uncertainty in land biosphere sink change.

A criterion for isomorphism of Artinian Gorenstein algebras

Let $A$ be an Artinian Gorenstein algebra over an infinite field~$k$ of characteristic either 0 or greater than the socle degree of $A$. To every such algebra and a linear projection $\pi $ on its maximal ideal $\mathfrak {m}$ with range equal to the socle $\Soc (A)$ of $A$, one can associate a certain algebraic hypersurface $S_{\pi }\subset \mathfrak {m}$, which is the graph of a polynomial map $P_{\pi }:\ker \pi \to \Soc (A)\simeq k$. Recently, the following surprising criterion has been obtained: two Artinian Gorenstein algebras $A$, $\widetilde {A}$ are isomorphic if and only if any two hypersurfaces $S_{\pi }$ and $S_{\tilde {\pi }}$ arising from $A$ and $\widetilde {A}$, respectively, are affinely equivalent. The proof is indirect and relies on a geometric argument. In the present paper, we give a short algebraic proof of this statement. We also discuss a connection, established elsewhere, between the polynomials $P_{\pi }$ and Macaulay inverse systems.

Inverse and symmetrical voice: On languages with two transitive constructions

AbstractIn voice and alignment typology, a categorical distinction is generally made between inverse systems on the one hand and symmetrical voice systems on the other. A major reason for distinguishing between these two types is the assumption that inverse systems are governed by a hierarchy involving grammatical, semantic, and ontological criteria, while symmetrical voice systems are based on discourse-pragmatic factors. However, the two types also have several important properties in common, in particular the fact that they have more than one nonderived transitive construction. Based on data from three native languages of South America, we show that the line between the two types is not always easy to draw, and that features of the inverse type can coexist with those of the symmetrical-voice type in the same language.

Continuity of coarse shape groups

We show that every coarse shape group can be obtained as the inverse limit of an inverse system of the groups coming from an HPol_{; ; ⋆}; ; -expansion. This provides a way of computing of these interesting topological invariants (whose algebraic structure is significantly richer than those of the homotpy and shape groups) in an easier manner. It is proven that, for inverse systems of compact polyhedra, the coarse shape group functor commutes with the inverse limit.