On finiteness of log canonical models

Let [Formula: see text] be klt pairs with [Formula: see text] a convex set of divisors. Assuming that the relative Kodaira dimensions of such pairs are non-negative, then there are only finitely many log canonical models when the boundary divisors vary in a rational polytope in [Formula: see text]. As a consequence, we show the existence of the log canonical model for a klt pair [Formula: see text] with real coefficients.

Documenting design research by structured multilevel analysis: supporting the diversity of the design research community of practice

The diversity of design research studies and their associated methods and reporting style make it difficult for the design research community of practice to leverage its work into further advancing the field. We illustrate how a structured multilevel analysis of diverse studies creates a canonical model that allows for the transfer of insight between studies, enhances their comprehension, and supports improved study designs. The benefits of such an approach will increase if different stakeholders adopt such structured approaches to enrich the design research community of practice.

Hyperbolicity for Log Smooth Families with Maximal Variation

We prove that the base space of a log smooth family of log canonical pairs of log general type is of log general type as well as algebraically degenerate, when the family admits a relative good minimal model over a Zariski open subset of the base and the relative log canonical model is of maximal variation.

Perspective Cues Make Eye-specific Contributions to 3-D Motion Perception

Robust 3-D visual perception is achieved by integrating stereoscopic and perspective cues. The canonical model describing the integration of these cues assumes that perspective signals sensed by the left and right eyes are indiscriminately pooled into a single representation that contributes to perception. Here, we show that this model fails to account for 3-D motion perception. We measured the sensitivity of male macaque monkeys to 3-D motion signaled by left-eye perspective cues, right-eye perspective cues, stereoscopic cues, and all three cues combined. The monkeys exhibited idiosyncratic differences in their biases and sensitivities for each cue, including left- and right-eye perspective cues, suggesting that the signals undergo at least partially separate neural processing. Importantly, sensitivity to combined cue stimuli was greater than predicted by the canonical model, which previous studies found to account for the perception of 3-D orientation in both humans and monkeys. Instead, 3-D motion sensitivity was best explained by a model in which stereoscopic cues were integrated with left- and right-eye perspective cues whose representations were at least partially independent. These results indicate that the integration of perspective and stereoscopic cues is a shared computational strategy across 3-D processing domains. However, they also reveal a fundamental difference in how left- and right-eye perspective signals are represented for 3-D orientation versus motion perception. This difference results in more effective use of available sensory information in the processing of 3-D motion than orientation and may reflect the temporal urgency of avoiding and intercepting moving objects.

Cardinality Queries over DL-Lite Ontologies

Ontology-mediated query answering (OMQA) employs structured knowledge and automated reasoning in order to facilitate access to incomplete and possibly heterogeneous data. While most research on OMQA adopts (unions of) conjunctive queries as the query language, there has been recent interest in handling queries that involve counting. In this paper, we advance this line of research by investigating cardinality queries (which correspond to Boolean atomic counting queries) coupled with DL-Lite ontologies. Despite its apparent simplicity, we show that such an OMQA setting gives rise to rich and complex behaviour. While we prove that cardinality query answering is tractable (TC0) in data complexity when the ontology is formulated in DL-Lite-core, the problem becomes coNP-hard as soon as role inclusions are allowed. For DL-Lite-pos-H (which allows only positive axioms), we establish a P-coNP dichotomy and pinpoint the TC0 cases; for DL-Lite-core-H (allowing also negative axioms), we identify new sources of coNP complexity and also exhibit L-complete cases. Interestingly, and in contrast to related tractability results, we observe that the canonical model may not give the optimal count value in the tractable cases, which led us to develop an entirely new approach based upon exploring a space of strategies to determine the minimum possible number of query matches.

WHAT IS GENERATIVE IN GENERATIVE DESIGN TOOLS? UNCOVERING TOPOLOGICAL GENERATIVITY WITH A C-K MODEL OF EVOLUTIONARY ALGORITHMS

Generative design (GD) algorithms is a fast growing field. From the point of view of Design Science, this fast growth leads to wonder what exactly is 'generated' by GD algorithms and how? In the last decades, advances in design theory enabled to establish conditions and operators that characterize design generativity. Thus, it is now possible to study GD algorithms with the lenses of Design Science in order to reach a deeper and unified understanding of their generative techniques, their differences and, if possible, find new paths for improving their generativity.In this paper, first, we rely on C-K ttheory to build a canonical model of GD, based independent of the field of application of the algorithm. This model shows that GD is generative if and only if it builds, not one single artefact, but a “topology of artefacts” that allows for design constructability, covering strategies, and functional comparability of designs. Second, we use the canonical model to compare four well documented and most advanced types of GD algorithms. From these cases, it appears that generating a topology enables the analyses of interdependences and the design of resilience.