Rejewski’s equations: Solving for the entry permutation

In 1932, Marian Rejewski, who was a young mathematician working at the Polish Cipher Bureau, brilliantly recovered the internal wiring of the military Enigma. His initial efforts were unsuccessful because he assumed that the entry permutation was the same as in the commercial machine. Luckily he tried the identity permutation as an alternative and that proved to be correct. This note describes how Rejewski’s equations may be used to deduce the entry permutation without any guesswork, a technique that was later rediscovered by Alan Turing and by Lieutenant Andrew Gleason.     

Ethanol dehydration activity on hydrothermally stable LaPxOy catalysts synthesized using CTAB template

Nanocrystalline LaP_xO_y with various starting P to La ratios from 0.5 to 2.0 catalysts were prepared by a sol?Cgel method using cetyl trimethylammonium bromide (CTAB) as template. The catalysts were thoroughly characterized by N₂ physisorption, powder X-ray diffraction (XRD), temperature programmed desorption (TPD) of NH₃, solid state ³¹P and ¹H nuclear magnetic resonance (NMR), and transmission electron microscopy (TEM) techniques. XRD results indicate the presence of predominantly monazite LaPO₄ with minor amounts of (??3.0 wt%) rhabdophane LaPO₄ phase in the samples with starting P/La ratios of 1.0 and 1.5. NH₃-TPD results show an increasing trend in the total acidity with increase in P/La ratio. These catalysts were tested in the selective ethanol dehydration in the temperature range between 250 and 400?°C. The catalyst activity (??mol/h/m²) is increased with P/La ratio and the catalyst with highest P/La ratio of 2.0 exhibiting the highest ethanol dehydration activity. The ethanol conversion increased with reaction temperature, reaching 100% at 350?°C and remains unchanged at higher temperatures. On the other hand, the ethylene selectivity is also increased up to 350?°C and then decreased with further increase of reaction temperature. At a P/La ratio of 2, the CTAB templated LaP_xO_y catalyst showed higher catalytic activities compared to the LaP_xO_y by hydrothermal method without any template.     

Complexity: learning to muddle through

The articles in this special issue are placed in the context of the literature of general systems theory. The focus is on the complexity (or requisite variety) of complex work domains and the implications for control. Following the insights of Ashby’s law of requisite variety, it is concluded that classical hierarchical or servomechanism-type control systems are inadequate as a basis for dealing with the unanticipated variability endemic to complex work domains. Alternative types of control (e.g., self-organizing systems) and alternative images of cognition are suggested as a theoretical context for modeling performance in complex work domains.     

Base invariance of feasible dimension

Effective fractal dimensions were introduced by Lutz (2003) in order to study the dimensions of individual sequences and quantitatively analyze the structure of complexity classes. Interesting connections of effective dimensions with information theory were also found, implying that constructive dimension as well as polynomial-space dimension are invariant under base change while finite-state dimension is not.We consider the intermediate case, polynomial-time dimension, and prove that it is indeed invariant under base change by a nontrivial argument which is quite different from the Kolmogorov complexity ones used in the other cases.Polynomial-time dimension can be characterized in terms of prediction loss rate, entropy, and compression algorithms. Our result implies that in an asymptotic way each of these concepts is invariant under base change.A corollary of the main theorem is any polynomial-time dimension 1 number (which may be established in any base) is an absolutely normal number, providing an interesting source of absolute normality.     

Improved spatial resolution in soil moisture retrieval at arid mining area using apparent thermal inertia

A surface soil moisture model with improved spatial resolution was developed using remotely sensed apparent thermal inertia (ATI). The model integrates the surface temperature derived from TM/ETM+ image and the mean surface temperature from MODIS images to improve the spatial resolution of soil temperature difference based on the heat conduction equation, which is necessary to calculate the ATI. Consequently, the spatial resolution of ATI and SMC can be enhanced from 1 km to 120 m (TM) or 60 m (ETM+). Moreover, the enhanced ATI has a much stronger correlation coefficient (R²) with SMC (0.789) than the surface reflectance (0.108) or the ATI derived only from MODIS images (0.264). Based on the regression statistics of the field SMC measurement and enhanced ATI, a linear regression model with an RMS error of 1.90% was found.     

Evidence for behavioural thermoregulation by the world's largest fish

Many fishes make frequent ascents to surface waters and often show prolonged surface swimming following descents to deep water. This affinity for the surface is thought to be related to the recovery of body heat lost at depth. We tested this hypothesis using data from time–depth recorders deployed on four whale sharks (Rhincodon typus). We summarized vertical movements into bouts of dives and classified these into three main types, using cluster analysis. In addition to day and night ‘bounce’ dives where sharks rapidly descended and ascended, we found a third type: single deep (mean: 340 m), long (mean: 169 min) dives, occurring in daytime with extremely long post-dive surface durations (mean: 146 min). Only sharks that were not constrained by shallow bathymetry performed these dives. We found a negative relationship between the mean surface duration of dives in the bout and the mean minimum temperature of dives in the bout that is consistent with the hypothesis that thermoregulation was a major factor driving use of the surface. The relationship broke down when sharks were diving in mean minimum temperatures around 25°C, suggesting that warmer waters did not incur a large metabolic cost for diving and that other factors may also influence surface use.     

Critical transition between cohesive and population-dividing responses to change

Globalization and global climate change will probably be accompanied by rapid social and biophysical changes that may be caused by external forcing or internal nonlinear dynamics. These changes often subject residing populations (human or otherwise) to harsh environments and force them to respond. Research efforts have mostly focused on the underlying mechanisms that drive these changes and the characteristics of new equilibria towards which populations would adapt. However, the transient dynamics of how populations respond under these new regimes is equally, if not more, important, and systematic analysis of such dynamics has received less attention. Here, we investigate this problem under the framework of replicator dynamics with fixed reward kernels. We show that at least two types of population responses are possible—cohesive and population-dividing transitions—and demonstrate that the critical transition between the two, as well as other important properties, can be expressed in simple relationships between the shape of reward structure, shift magnitude and initial strategy diversity. Importantly, these relationships are derived from a simple, yet powerful and versatile, method. As many important phenomena, from political polarization to the evolution of distinct ecological traits, may be cast in terms of division of populations, we expect our findings and method to be useful and applicable for understanding population responses to change in a wide range of contexts.     

Wide Range Control of Microstructure and Mechanical Properties of Carbon Nanotube Forests: A Comparison Between Fixed and Floating Catalyst CVD Techniques

Vertically aligned carbon nanotube (CNT) forests may be used as miniature springs, compliant thermal interfaces, and shock absorbers, and for these and other applications it is vital to understand how to engineer their mechanical properties. Herein is investigated how the diameter and packing density within CNT forests govern their deformation behavior, structural stiffness, and elastic energy absorption properties. The mechanical behavior of low‐density CNT forests grown by fixed catalyst CVD methods and high‐density CNT forests grown by a floating catalyst CVD method are studied by in situ SEM compression testing and tribometer measurements of force‐displacement relationships. Low‐density and small‐diameter CNT columns (fixed catalyst) exhibit large plastic deformation and can be pre‐deformed to act as springs within a specified elastic range, whereas high‐density and large‐diameter CNT columns (floating catalyst) exhibit significant elastic recovery after deformation. In this work the energy absorption capacity of CNT forests is tuned over three orders of magnitude and it is shown that CNT forest density can be tuned over a range of conventional foam materials, but corresponding stiffness is ～10× higher. It is proposed that the elastic behavior of CNT forests is analogous to open‐cell foams and a simple model is presented. It is also shown that this model can be useful as a first‐order design tool to establish design guidelines for the mechanical properties of CNT forests and selection of the appropriate synthesis method.