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We characterise the slices of the category of graphs that are algebraically universal in terms of the structure of the slicing graph. In particular, we show that algebraic universality is obtained if, and only if, the slicing graph contains one of four fixed graphs as a subgraph.

This study deals with approaches for a social-ecological friendly European bioeconomy based on biomass from industrial crops cultivated on marginal agricultural land. The selected crops to be investigated are: Biomass sorghum, camelina, cardoon, castor, crambe, Ethiopian mustard, giant reed, hemp, lupin, miscanthus, pennycress, poplar, reed canary grass, safflower, Siberian elm, switchgrass, tall wheatgrass, wild sugarcane, and willow. The research question focused on the overall crop growth suitability under low-input management. The study assessed: (i) How the growth suitability of industrial crops can be defined under the given natural constraints of European marginal agricultural lands; and (ii) which agricultural practices are required for marginal agricultural land low-input systems (MALLIS). For the growth-suitability analysis, available thresholds and growth requirements of the selected industrial crops were defined. The marginal agricultural land was categorized according to the agro-ecological zone (AEZ) concept in combination with the marginality constraints, so-called ‘marginal agro-ecological zones’ (M-AEZ). It was found that both large marginal agricultural areas and numerous agricultural practices are available for industrial crop cultivation on European marginal agricultural lands. These results help to further describe the suitability of industrial crops for the development of social-ecologically friendly MALLIS in Europe.

The synthesis and characterization of Cu-, Al-, Zn-, Ni-, Mn- complexes as substitutes for the Cr- and Co-complex acid azo dyes with lower toxicity was carried out and the subsequent use of ultra-filtration was studied with the aim of purifying the metal complex dyes and thus increasing dye strength and solubility and additionally reducing the free metal present in the final dye. A drastic reduction in the content of inorganic additives and free metal was achieved by the ultra-filtration process. The ultra-filtrated and non-ultra-filtrated dyes were used to dye wool and nylon fabrics. Color measurements and fastness properties were performed on the dyeings produced on wool and polyamide and compared with the Cr-complex dyeing, thus examining the possibility of using successfully these complex dyes as possible replacement of the Cr- and Co-complex dyes.

Preservation theorems provide a direct correspondence between the syntactic structure of first-order sentences and the closure properties of their respective classes of models. A line of work has explored preservation theorems relativised to combinatorially tame classes of sparse structures [Atserias et al., JACM 2006; Atserias et al., SiCOMP 2008; Dawar, JCSS 2010; Dawar and Eleftheriadis, 2024]. In this article we initiate the study of preservation theorems for dense graph classes. In contrast to the sparse setting, we show that extension preservation fails on most natural dense classes of low complexity. Nonetheless, we isolate a technical condition which is sufficient for extension preservation to hold, providing a dense analogue to a result of [Atserias et al., SiCOMP 2008].

We characterise the slices of the category of graphs that are algebraically universal in terms of the structure of the slicing graph. In particular, we show that algebraic universality is obtained if, and only if, the slicing graph contains one of four fixed graphs as a subgraph.

We consider categories of relational structures that fully embed every category of universal algebras, and prove a partial characterisation of these in terms of an infinitary variant of the notion of nowhere density of Nešetřil and Ossona de Mendez. More precisely, we show that the Gaifman class of an algebraically universal category contains subdivided complete graphs of any infinite size, and establish that any monotone category satisfying this may be oriented to obtain an algebraically universal category. For the proof of the above, we also develop a categorical framework for relational gadget constructions. This generalises known results about categories of finite graphs to categories of relational structures of unbounded size.

This study deals with approaches for a social-ecological friendly European bioeconomy based on biomass from industrial crops cultivated on marginal agricultural land. The selected crops to be investigated are: Biomass sorghum, camelina, cardoon, castor, crambe, Ethiopian mustard, giant reed, hemp, lupin, miscanthus, pennycress, poplar, reed canary grass, safflower, Siberian elm, switchgrass, tall wheatgrass, wild sugarcane, and willow. The research question focused on the overall crop growth suitability under low-input management. The study assessed: (i) How the growth suitability of industrial crops can be defined under the given natural constraints of European marginal agricultural lands; and (ii) which agricultural practices are required for marginal agricultural land low-input systems (MALLIS). For the growth-suitability analysis, available thresholds and growth requirements of the selected industrial crops were defined. The marginal agricultural land was categorized according to the agro-ecological zone (AEZ) concept in combination with the marginality constraints, so-called ‘marginal agro-ecological zones’ (M-AEZ). It was found that both large marginal agricultural areas and numerous agricultural practices are available for industrial crop cultivation on European marginal agricultural lands. These results help to further describe the suitability of industrial crops for the development of social-ecologically friendly MALLIS in Europe.

We explore the cumulative hierarchy \\(V\\) defined in Chapter 10 of the HoTT book. We begin by showing how to translate formulas of set theory in HoTT, and proceed to examine which axioms are satisfied in \\(V\\). In particular, we show that \\(V\\) models ZF\\(^-\\) in HoTT+PR, while LEM is required to obtain full ZF. Finally, we attempt to model constructive set theories in V, and although this is achieved for ECST, we only obtain IZF and CZF with LEM.

We revisit the work studying homomorphism preservation for first-order logic in sparse classes of structures initiated in [Atserias et al., JACM 2006] and [Dawar, JCSS 2010]. These established that first-order logic has the homomorphism preservation property in any sparse class that is monotone and addable. It turns out that the assumption of addability is not strong enough for the proofs given. We demonstrate this by constructing classes of graphs of bounded treewidth which are monotone and addable but fail to have homomorphism preservation. We also show that homomorphism preservation fails on the class of planar graphs. On the other hand, the proofs of homomorphism preservation can be recovered by replacing addability by a stronger condition of amalgamation over bottlenecks. This is analogous to a similar condition formulated for extension preservation in [Atserias et al., SiCOMP 2008].

A graph class \\( C\\) is monadically dependent if one cannot interpret all graphs in colored graphs from \\( C\\) using a fixed first-order interpretation. We prove that monadically dependent classes can be exactly characterized by the following property, which we call flip-separability: for every \\(rın N\\), \\(>0\\), and every graph \\(Gın C\\) equipped with a weight function on vertices, one can apply a bounded (in terms of \\(C,r,\\)) number of flips (complementations of the adjacency relation on a subset of vertices) to \\(G\\) so that in the resulting graph, every radius-\\(r\\) ball contains at most an \\(\\)-fraction of the total weight. On the way to this result, we introduce a robust toolbox for working with various notions of local separations in monadically dependent classes.