Fault zones are the locations where motion of tectonic plates, often associated with earthquakes, is accommodated. Despite a rapid increase in the understanding of faults in the last decades, our knowledge of their geometry, petrophysical properties, and controlling processes remains incomplete. The central questions addressed here in our study of the Dead Sea Transform (DST) in the Middle East are as follows: (1) What are the structure and kinematics of a large fault zone? (2) What controls its structure and kinematics? (3) How does the DST compare to other plate boundary fault zones? The DST has accommodated a total of 105 km of left-lateral transform motion between the African and Arabian plates since early Miocene (similar to 20 Ma). The DST segment between the Dead Sea and the Red Sea, called the Arava/Araba Fault (AF), is studied here using a multidisciplinary and multiscale approach from the mu m to the plate tectonic scale. We observe that under the DST a narrow, subvertical zone cuts through crust and lithosphere. First, from west to east the crustal thickness increases smoothly from 26 to 39 km, and a subhorizontal lower crustal reflector is detected east of the AF. Second, several faults exist in the upper crust in a 40 km wide zone centered on the AF, but none have kilometer-size zones of decreased seismic velocities or zones of high electrical conductivities in the upper crust expected for large damage zones. Third, the AF is the main branch of the DST system, even though it has accommodated only a part (up to 60 km) of the overall 105 km of sinistral plate motion. Fourth, the AF acts as a barrier to fluids to a depth of 4 km, and the lithology changes abruptly across it. Fifth, in the top few hundred meters of the AF a locally transpressional regime is observed in a 100-300 m wide zone of deformed and displaced material, bordered by subparallel faults forming a positive flower structure. Other segments of the AF have a transtensional character with small pull-aparts along them. The damage zones of the individual faults are only 5-20 m wide at this depth range. Sixth, two areas on the AF show mesoscale to microscale faulting and veining in limestone sequences with faulting depths between 2 and 5 km. Seventh, fluids in the AF are carried downward into the fault zone. Only a minor fraction of fluids is derived from ascending hydrothermal fluids. However, we found that on the kilometer scale the AF does not act as an important fluid conduit. Most of these findings are corroborated using thermomechanical modeling where shear deformation in the upper crust is localized in one or two major faults; at larger depth, shear deformation occurs in a 20-40 km wide zone with a mechanically weak decoupling zone extending subvertically through the entire lithosphere.

The Collatz conjecture is a number theoretical problem, which has puzzled countless researchers using myriad approaches. Presently, there are scarcely any methodologies to describe and treat the problem from the perspective of the Algebraic Theory of Automata. Such an approach is promising with respect to facilitating the comprehension of the Collatz sequences "mechanics". The systematic technique of a state machine is both simpler and can fully be described by the use of algebraic means. The current gap in research forms the motivation behind the present contribution. The present authors are convinced that exploring the Collatz conjecture in an algebraic manner, relying on findings and fundamentals of Graph Theory and Automata Theory, will simplify the problem as a whole.

The Collatz conjecture is a number theoretical problem, which has puzzled countless researchers using myriad approaches. Presently, there are scarcely any methodologies to describe and treat the problem from the perspective of the Algebraic Theory of Automata. Such an approach is promising with respect to facilitating the comprehension of the Collatz sequence’s "mechanics". The systematic technique of a state machine is both simpler and can fully be described by the use of algebraic means. The current gap in research forms the motivation behind the present contribution. The present authors are convinced that exploring the Collatz conjecture in an algebraic manner, relying on findings and fundamentals of Graph Theory and Automata Theory, will simplify the problem as a whole.

It is well known that the inverted Collatz sequence can be represented as a graph or a tree. Similarly, it is acknowledged that in order to prove the Collatz conjecture, one must demonstrate that this tree covers all odd natural numbers. A structured reachability analysis is hitherto not available. This paper investigates the problem from a graph theory perspective. We define a tree that consists of nodes labeled with Collatz sequence numbers. This tree will be transformed into a sub-tree that only contains odd labeled nodes. The analysis of this tree will provide new insights into the structure of Collatz sequences. The findings are of special interest to possible cycles within a sequence. Next, we describe the conditions which must be fulfilled by a cycle. Finally, we demonstrate how these conditions could be used to prove that the only possible cycle within a Collatz sequence is the trivial cycle, starting with the number one, as conjectured by Lothar Collatz.

Perovskite solar cells with all-organic transport layers exhibit efficiencies rivaling their counterparts that employ inorganic transport layers, while avoiding high-temperature processing. Herein, it is investigated how the choice of the fullerene derivative employed in the electron-transporting layer of inverted perovskite cells affects the open-circuit voltage (V-OC). It is shown that nonradiative recombination mediated by the electron-transporting layer is the limiting factor for the V-OC in the cells. By inserting an ultrathin layer of an insulating polymer between the active CH3NH3PbI3 perovskite and the fullerene, an external radiative efficiency of up to 0.3%, a V-OC as high as 1.16 V, and a power conversion efficiency of 19.4% are realized. The results show that the reduction of nonradiative recombination due to charge-blocking at the perovskite/organic interface is more important than proper level alignment in the search for ideal selective contacts toward high V-OC and efficiency.