Fluctuating Lake Levels in Rift Basins and its Impact on Extensional Tectonics

<p>The feedback between climate driven processes; weathering, erosion, sediment transport, and deposition, and extensional tectonics is limited to a few studies (Burov and Cloething, 1997; Burov and Poliakov, 2001; Bialas and Buck, 2009; Theunissen and Huismans, 2019; Andrés-Martínez et al., 2019) despite these processes having been shown to impact the stress state and deformation along active orogens (Koons, 1989; Molnar and England, 1990; Avouac and Burov, 1996; Willett, 1999). Here we utilize a fully coupled landscape evolution and thermomechanical extensional model to investigate the potential impact on faulting and extension due to lake loading changes driven by changes in climate on processional timescales. Fault analyses focusing on heave, throw, and magnitude of dip on faults generated within each model are used to characterize individual faults response to stress changes and rift basin evolution. Preliminary results indicate that fluctuations in lake levels in response to climate change may impact the lithospheric stress state by changing both fault and basin geometries within an extensional basin.</p>

The birth of a forearc: The basal Great Valley Group, California, USA

The Great Valley basin of California (USA) is an archetypal forearc basin, yet the timing, structural style, and location of basin development remain controversial. Eighteen of 20 detrital zircon samples (3711 new U-Pb ages) from basal strata of the Great Valley forearc basin contain Cretaceous grains, with nine samples yielding statistically robust Cretaceous maximum depositional ages (MDAs), two with MDAs that overlap the Jurassic-Cretaceous boundary, suggesting earliest Cretaceous deposition, and nine with Jurassic MDAs consistent with latest Jurassic deposition. In addition, the pre-Mesozoic age populations of our samples are consistent with central North America sources and do not require a southern provenance. We interpret that diachronous initiation of sedimentation reflects the growth of isolated depocenters, consistent with an extensional model for the early stages of forearc basin development.

Approximation Fixpoint Theory and the Well-Founded Semantics of Higher-Order Logic Programs

We define a novel, extensional, three-valued semantics for higher-order logic programs with negation. The new semantics is based on interpreting the types of the source language as three-valued Fitting-monotonic functions at all levels of the type hierarchy. We prove that there exists a bijection between such Fitting-monotonic functions and pairs of two-valued-result functions where the first member of the pair is monotone-antimonotone and the second member is antimonotone-monotone. By deriving an extension ofconsistent approximation fixpoint theory(Deneckeret al.2004) and utilizing the above bijection, we define an iterative procedure that produces for any given higher-order logic program a distinguished extensional model. We demonstrate that this model is actually aminimalone. Moreover, we prove that our construction generalizes the familiar well-founded semantics for classical logic programs, making in this way our proposal an appealing formulation for capturing thewell-founded semantics for higher-order logic programs.

What is a categorical model of the differential and the resource λ-calculi?

The differential λ-calculus is a paradigmatic functional programming language endowed with a syntactical differentiation operator that allows the application of a program to an argument in a linear way. One of the main features of this language is that it is resource conscious and gives the programmer suitable primitives to handle explicitly the resources used by a program during its execution. The differential operator also allows us to write the full Taylor expansion of a program. Through this expansion, every program can be decomposed into an infinite sum (representing non-deterministic choice) of ‘simpler’ programs that are strictly linear.The aim of this paper is to develop an abstract ‘model theory’ for the untyped differential λ-calculus. In particular, we investigate what form a general categorical definition of a denotational model for this calculus should take. Starting from the work of Blute, Cockett and Seely on differential categories, we develop the notion of a Cartesian closed differential category and prove that linear reflexive objects living in such categories constitute sound and complete models of the untyped differential λ-calculus. We also give sufficient conditions for Cartesian closed differential categories to model the Taylor expansion. This requires that every model living in such categories equates all programs having the same full Taylor expansion.We then provide a concrete example of a Cartesian closed differential category modelling the Taylor expansion, namely the category MRel of sets and relations from finite multisets to sets. We prove that the extensional model of λ-calculus we have recently built in MRel is linear, and is thus also an extensional model of the untyped differential λ-calculus. In the same category, we build a non-extensional model and prove that it is, nevertheless, extensional on its differential part.Finally, we study the relationship between the differential λ-calculus and the resource calculus, which is a functional programming language combining the ideas behind the differential λ-calculus with those behind Boudol's λ-calculus with multiplicities. We define two translation maps between these two calculi and study the properties of these translations. In particular, this analysis shows that the two calculi share the same notion of a model, and thus that the resource calculus can be interpreted by translation into every linear reflexive object living in a Cartesian closed differential category.

Extension Model of Influence Diagrams

An influence diagram is a kind of graphical model that can represent both the probabilistic relationship between variables and can easy to make decisions. It can make full use of Bayesian Network and Decisiton Tree. Influence Diagram should be modify to inprove the effiency to express relationships among variables. Extensional model of Influence Diagrams is introduced in this paper to express the new kind influence diagrams. And this kind of new model can be applied in the area of supply chain management.