The Garden Hose Complexity for the Equality Function

The garden hose complexity is a new communication complexity introduced by H. Buhrman, S. Fehr, C. Schaffner and F. Speelman [BFSS13] to analyze position-based cryptography protocols in the quantum setting. We focus on the garden hose complexity of the equality function, and improve on the bounds of O. Margalit and A. Matsliah[MM12] with the help of a new approach and of our handmade simulated annealing based solver. We have also found beautiful symmetries of the solutions that have lead us to develop the notion of garden hose permutation groups. Then, exploiting this new concept, we get even further, although several interesting open problems remain.Comment: 16 page

OCCURRENCE AND ATTRIBUTES OF TWO ECHINODERM-BEARING FAUNAS FROM THE UPPER MISSISSIPPIAN (CHESTERIAN; LOWER SERPUKHOVIAN) RAMEY CREEK MEMBER, SLADE FORMATION, EASTERN KENTUCKY, U.S.A.

Well-preserved echinoderm faunas are rare in the fossil record, and when uncovered, understanding their occurrence can be useful in interpreting other faunas. In this study, two such faunas of the same age from separate localities in the shallow-marine Ramey Creek Member of the Slade Formation in the Upper Mississippian (Chesterian) rocks of eastern Kentucky are examined. Of the more than 5,000 fossil specimens from both localities, only 9–34 percent were echinoderms from 3–5 classes. Nine non-echinoderm (8 invertebrate and one vertebrate) classes occurred at both localities, but of these, bryozoans, brachiopods and sponges dominated. To understand the attributes of both localities (Valley Stone and 213 quarries), the geologic and structural settings, lithofacies and depositional environments, as well as faunal makeup and abundances (diversity, evenness, density), were compared and contrasted. Faunas from the Valley Stone Quarry were located on an uplifted fault block in more shallow, open-marine waters with higher energies. As indicated by four distinct lithofacies, the depositional setting was more extensive and varied with interspersed shoals and basins that could accommodate a greater richness (65 species), even though organism densities and abundance were less. In contrast, fauna from the 213 Quarry were located on a downdropped fault block in a more localized, deeper, storm-shelf setting, characterized by a single lithofacies. Although organism density and abundance were nearly twice as high as that at the Valley Stone Quarry, species richness was lower (45 species), and only one species, a bryozoan, predominated. Overall, echinoderm classes, species and individuals were more abundant at the Valley Stone Quarry, and I suggest that this is related to the shallower and more varied depositional environments that developed in response to presence on the shallow, uplifted fault block. This suggests the importance of regional features like faults in controlling environments and organism distribution through time. Although the faunas were originally collected for their echinoderm-dominated “crinoid gardens,” in fact, echinoderms were in the minority, and bryozoans and brachiopods predominated in the communities. Hence, the communities might better be described as bryozoan “thickets” and brachiopod “pavements.

Robust and real-time control of magnetic bearings for space engines

Currently, NASA Lewis Research Center is developing magnetic bearings for Space Shuttle Main Engine (SSME) turbopumps. The control algorithms which have been used are based on either the proportional-intergral-derivative control (PID) approach or the linear quadratic (LQ) state space approach. These approaches lead to an acceptable performance only when the system model is accurately known, which is seldom true in practice. For example, the rotor eccentricity, which is a major source of vibration at high speeds, cannot be predicted accurately. Furthermore, the dynamics of a rotor shaft, which must be treated as a flexible system to model the elastic rotor shaft, is infinite dimensional in theory and the controller can only be developed on the basis of a finite number of modes. Therefore, the development of the control system is further complicated by the possibility of closed loop system instability because of residual or uncontrolled modes, the so called spillover problem. Consequently, novel control algorithms for magnetic bearings are being developed to be robust to inevitable parametric uncertainties, external disturbances, spillover phenomenon and noise. Also, as pointed out earlier, magnetic bearings must exhibit good performance at a speed over 30,000 rpm. This implies that the sampling period available for the design of a digital control system has to be of the order of 0.5 milli-seconds. Therefore, feedback coefficients and other required controller parameters have to be computed off-line so that the on-line computational burden is extremely small. The development of the robust and real-time control algorithms is based on the sliding mode control theory. In this method, a dynamic system is made to move along a manifold of sliding hyperplanes to the origin of the state space. The number of sliding hyperplanes equals that of actuators. The sliding mode controller has two parts; linear state feedback and nonlinear terms. The nonlinear terms guarantee that the systems would reach the intersection of all sliding hyperplanes and remain on it when bounds on the errors in the system parameters and external disturbances are known. The linear part of the control drives the system to the origin of state space. Another important feature is that the controller parameter can be computed off-line. Consequently, on-line computational burden is small

The mechanism of oxygen isotope fractionation during N2O production by denitrification

The isotopic composition of soil-derived N2O can help differentiate between N2O production pathways and estimate the fraction of N2O reduced to N2. Until now, δ18O of N2O has been rarely used in the interpretation of N2O isotopic signatures because of the rather complex oxygen isotope fractionations during N2O production by denitrification. The latter process involves nitrate reduction mediated through the following three enzymes: nitrate reductase (NAR), nitrite reductase (NIR) and nitric oxide reductase (NOR). Each step removes one oxygen atom as water (H2O), which gives rise to a branching isotope effect. Moreover, denitrification intermediates may partially or fully exchange oxygen isotopes with ambient water, which is associated with an exchange isotope effect. The main objective of this study was to decipher the mechanism of oxygen isotope fractionation during N2O production by denitrification and, in particular, to investigate the relationship between the extent of oxygen isotope exchange with soil water and the δ18O values of the produced N2O. We performed several soil incubation experiments. For the first time, ∆17 O isotope tracing was applied to simultaneously determine the extent of oxygen isotope exchange and any associated oxygen isotope effect. We found bacterial denitrification to be typically associated with almost complete oxygen isotope exchange and a stable difference in δ18O between soil water and the produced N2O of δ18O(N2O / H2O) = (17.5±1.2) ‰. However, some experimental setups yielded oxygen isotope exchange as low as 56 % and a higher δ18O(N2O / H2O) of up to 37‰. The extent of isotope exchange and δ18O(N2O / H2O) showed a very significant correlation (R2 = 0.70, p < 0.00001). We hypothesise that this observation was due to the contribution of N2O from another production process, most probably fungal denitrification. An oxygen isotope fractionation model was used to test various scenarios with different magnitudes of branching isotope effects at different steps in the reduction process. The results suggest that during denitrification the isotope exchange occurs prior to the isotope branching and that the mechanism of this exchange is mostly associated with the enzymatic nitrite reduction mediated by NIR. For bacterial denitrification, the branching isotope effect can be surprisingly low, about (0.0±0.9) ‰; in contrast to fungal denitrification where higher values of up to 30‰ have been reported previously. This suggests that δ18O might be used as a tracer for differentiation between bacte- 5 rial and fungal denitrification, due to their different magnitudes of branching isotope effect

Oxygen isotope fractionation during N2O production by soil denitrification

The isotopic composition of soil-derived N₂O can help differentiate between N₂O production pathways and estimate the fraction of N₂O reduced to N₂. Until now, <i>δ</i>¹⁸O of N₂O has been rarely used in the interpretation of N₂O isotopic signatures because of the rather complex oxygen isotope fractionations during N₂O production by denitrification. The latter process involves nitrate reduction mediated through the following three enzymes: nitrate reductase (NAR), nitrite reductase (NIR) and nitric oxide reductase (NOR). Each step removes one oxygen atom as water (H₂O), which gives rise to a branching isotope effect. Moreover, denitrification intermediates may partially or fully exchange oxygen isotopes with ambient water, which is associated with an exchange isotope effect. The main objective of this study was to decipher the mechanism of oxygen isotope fractionation during N₂O production by soil denitrification and, in particular, to investigate the relationship between the extent of oxygen isotope exchange with soil water and the <i>δ</i>¹⁸O values of the produced N₂O. <br><br> In our soil incubation experiments Δ¹⁷O isotope tracing was applied for the first time to simultaneously determine the extent of oxygen isotope exchange and any associated oxygen isotope effect. We found that N₂O formation in static anoxic incubation experiments was typically associated with oxygen isotope exchange close to 100 % and a stable difference between the ¹⁸O ∕ ¹⁶O ratio of soil water and the N₂O product of <i>δ</i>¹⁸O(N₂O ∕ H₂O)  =  (17.5 ± 1.2) ‰. However, flow-through experiments gave lower oxygen isotope exchange down to 56 % and a higher <i>δ</i>¹⁸O(N₂O ∕ H₂O) of up to 37 ‰. The extent of isotope exchange and <i>δ</i>¹⁸O(N₂O ∕ H₂O) showed a significant correlation (<i>R</i>² = 0.70, <i>p</i> &lt;  0.00001). We hypothesize that this observation was due to the contribution of N₂O from another production process, most probably fungal denitrification. <br><br> An oxygen isotope fractionation model was used to test various scenarios with different magnitudes of branching isotope effects at different steps in the reduction process. The results suggest that during denitrification, isotope exchange occurs prior to isotope branching and that this exchange is mostly associated with the enzymatic nitrite reduction mediated by NIR. For bacterial denitrification, the branching isotope effect can be surprisingly low, about (0.0 ± 0.9) ‰, in contrast to fungal denitrification where higher values of up to 30 ‰ have been reported previously. This suggests that <i>δ</i>¹⁸O might be used as a tracer for differentiation between bacterial and fungal denitrification, due to their different magnitudes of branching isotope effects