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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 motion of tectonic plates is accommodated at fault zones. One of the unanswered questions about fault zones relates to the role they play in controlling shallow and local hydrology. This study focuses on the Arava/Araba Fault (AF) zone, the southern portion of the Dead Sea Transform (DST) in the Middle East. We combine seismic and electromagnetic methods (EM) to image the geometry and map the petro-physical properties and water occurrence in the top 100 m of this active fault. For three profiles, P-velocity and resistivity images were derived independently. Using a neural network cluster analysis three classes with similar P-velocity and resistivities could then be determined from these images. These classes correspond to spatial domains of specific material and wetness. The first class occurs primarily east of the fault consisting of 'wet' sand (dunes) and brecciated sediments, whereas the second class composed of similar material located west of the fault is 'dry'. The third class lies at depth below ca. 50 m and is composed of highly deformed and weathered Precambrian rocks that constitute the multi-branch fault zone of the AF at this location. The combination of two independent measurements like seismics and EM linked by a stringent mathematical approach has thus shown the potential to delineate the interplay of lithology and water near active faults.

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.

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 1, as conjectured by Lothar Collatz.

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.

In detoxified alcohol-dependent patients, alcohol-related stimuli can promote relapse. However, to date, the mechanisms by which contextual stimuli promote relapse have not been elucidated in detail. One hypothesis is that such contextual stimuli directly stimulate the motivation to drink via associated brain regions like the ventral striatum and thus promote alcohol seeking, intake and relapse. Pavlovian-to-Instrumental-Transfer (PIT) may be one of those behavioral phenomena contributing to relapse, capturing how Pavlovian conditioned (contextual) cues determine instrumental behavior (e.g. alcohol seeking and intake). We used a PIT paradigm during functional magnetic resonance imaging to examine the effects of classically conditioned Pavlovian stimuli on instrumental choices in n=31 detoxified patients diagnosed with alcohol dependence and n=24 healthy controls matched for age and gender. Patients were followed up over a period of 3 months. We observed that (1) there was a significant behavioral PIT effect for all participants, which was significantly more pronounced in alcohol-dependent patients; (2) PIT was significantly associated with blood oxygen level-dependent (BOLD) signals in the nucleus accumbens (NAcc) in subsequent relapsers only; and (3) PIT-related NAcc activation was associated with, and predictive of, critical outcomes (amount of alcohol intake and relapse during a 3 months follow-up period) in alcohol-dependent patients. These observations show for the first time that PIT-related BOLD signals, as a measure of the influence of Pavlovian cues on instrumental behavior, predict alcohol intake and relapse in alcohol dependence.

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.

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 unavailable. 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. Furthermore, we derive and prove several formulas that can be used to traverse the graph. The analysis covers the Collatz problem both in it’s original form 3x + 1 as well as in the generalized variant kx + 1. Finally, we transform the Collatz graph into a binary tree, following the approach of Kleinnijenhuis, which could form the basis for a comprehensive proof of the conjecture.

Reduced Interface-Mediated Recombination for High Open-Circuit Voltages in CH3NH3PbI3 Solar Cells
(2017)

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.

Charge transport layers (CTLs) are key components of diffusion controlled perovskite solar cells, however, they can induce additional non-radiative recombination pathways which limit the open circuit voltage (V-OC) of the cell. In order to realize the full thermodynamic potential of the perovskite absorber, both the electron and hole transport layer (ETL/HTL) need to be as selective as possible. By measuring the photoluminescence yield of perovskite/CTL heterojunctions, we quantify the non-radiative interfacial recombination currents in pin- and nip-type cells including high efficiency devices (21.4%). Our study comprises a wide range of commonly used CTLs, including various hole-transporting polymers, spiro-OMeTAD, metal oxides and fullerenes. We find that all studied CTLs limit the V-OC by inducing an additional non-radiative recombination current that is in most cases substantially larger than the loss in the neat perovskite and that the least-selective interface sets the upper limit for the V-OC of the device. Importantly, the V-OC equals the internal quasi-Fermi level splitting (QFLS) in the absorber layer only in high efficiency cells, while in poor performing devices, the V-OC is substantially lower than the QFLS. Using ultraviolet photoelectron spectroscopy and differential charging capacitance experiments we show that this is due to an energy level mis-alignment at the p-interface. The findings are corroborated by rigorous device simulations which outline important considerations to maximize the V-OC. This work highlights that the challenge to suppress non-radiative recombination losses in perovskite cells on their way to the radiative limit lies in proper energy level alignment and in suppression of defect recombination at the interfaces.