Spectral measures of small index principal graphs

The principal graph $X$ of a subfactor with finite Jones index is one of the important algebraic invariants of the subfactor. If $\Delta$ is the adjacency matrix of $X$ we consider the equation $\Delta=U+U^{-1}$. When $X$ has square norm $\leq 4$ the spectral measure of $U$ can be averaged by using the map $u\to u^{-1}$, and we get a probability measure $\epsilon$ on the unit circle which does not depend on $U$. We find explicit formulae for this measure $\epsilon$ for the principal graphs of subfactors with index $\le 4$, the (extended) Coxeter-Dynkin graphs of type $A$, $D$ and $E$. The moment generating function of $\epsilon$ is closely related to Jones' $\Theta$-series.Comment: 23 page

Root exudate carbon mitigates nitrogen loss in a semi-arid soil

AbstractThe need for increased food production to support the growing global population requires more efficient nutrient management and prevention of nitrogen (N) losses from both applied fertiliser and organic matter (OM) decomposition. This is particularly important in semi-arid rainfed cropping soils, where soil water and temperature are the dominant drivers of N cycling rather than agricultural management. Here we used 14C and 15N techniques to examine how peptide/amino acid turnover, gross and net N transformation rates and nitrous oxide (N2O) emissions responded to long-term plant residue additions and/or short-term root exudate additions. Soil was collected from a semi-arid rainfed field trial with one winter crop per year followed by a summer fallow period, where additional inputs of straw/chaff over 10 years had increased total soil organic C (SOC) by 76% compared to no extra additions (control). These field soils were incubated in the laboratory with or without a synthetic root exudate mixture at a range of temperatures reflecting regional field conditions (5–50 °C). Long-term plant residue additions (to build up total soil OM) did not decrease the risk of N loss as defined by the nitrification:immobilisation (N:I) ratio at most temperatures, so was not an effective management tool to control N losses. In comparison, short-term root exudate additions decreased the risk of N loss at all temperatures in both the control and plant residue treatment field soils. Increased net N mineralisation and decreased microbial C use efficiency at temperatures greater than 30 °C resulted in significant ammonium (NH4+) accumulation. Microbial decomposers appeared to use amino acid-C for growth but peptide-C for energy production. Findings indicate that the greatest risk of N loss in these semi-arid soils will occur during rains at the start of the growing season, due to inorganic N accumulation over summer fallow when there are high soil temperatures, occasional significant rainfall events and no growing plants to release root exudates. While most attempts to manipulate the soil N cycle have occurred during the winter cropping period, our findings highlight the need to manage N supply during summer fallow if we are to minimise losses to the environment from semi-arid soils

Competition between plant and bacterial cells at the microscale regulates the dynamics of nitrogen acquisition in wheat (Triticum aestivum)

The ability of plants to compete effectively for nitrogen (N) resources is critical to plant survival. However, controversy surrounds the importance of organic and inorganic sources of N in plant nutrition because of our poor ability to visualize and understand processes happening at the root�microbial�soil interface. Using high-resolution nano-scale secondary ion mass spectrometry stable isotope imaging (NanoSIMS-SII), we quantified the fate of 15N over both space and time within the rhizosphere. We pulse-labelled the soil surrounding wheat (Triticum aestivum) roots with either inline image or 15N-glutamate and traced the movement of 15N over 24 h. Imaging revealed that glutamate was rapidly depleted from the rhizosphere and that most 15N was captured by rhizobacteria, leading to very high 15N microbial enrichment. After microbial capture, approximately half of the 15N-glutamate was rapidly mineralized, leading to the excretion of inline image, which became available for plant capture. Roots proved to be poor competitors for 15N-glutamate and took up N mainly as inline image. Spatial mapping of 15N revealed differential patterns of 15N uptake within bacteria and the rapid uptake and redistribution of 15N within roots. In conclusion, we demonstrate the rapid cycling and transformation of N at the soil�root interface and that wheat capture of organic N is low in comparison to inorganic N under the conditions tested

Leaching of phthalate acid esters from plastic mulch films and their degradation in response to UV irradiation and contrasting soil conditions

Phthalate acid esters (PAEs) are commonly used plastic additives, not chemically bound to the plastic that migrate into surrounding environments, posing a threat to environmental and human health. Dibutyl phthalate (DBP) and di(2-ethylhexyl) phthalate (DEHP) are two common PAEs found in agricultural soils, where degradation is attributed to microbial decomposition. Yet the impact of the plastic matrix on PAE degradation rates is poorly understood. Using 14C-labelled DBP and DEHP we show that migration from the plastic matrix into soil represents a key rate limiting step in their bioavailability and subsequent degradation. Incorporating PAEs into plastic film decreased their degradation in soil, DBP (DEHP) from 79% to 21% (9% to <1%), over four months when compared to direct application of PAEs. Mimicking surface soil conditions, we demonstrated that exposure to ultraviolet radiation accelerated PAE mineralisation twofold. Turnover of PAE was promoted by the addition of biosolids, while the presence of plants and other organic residues failed to promote degradation. We conclude that PAEs persist in soil for longer than previously thought due to physical trapping within the plastic matrix, suggesting PAEs released from plastics over very long time periods lead to increasing levels of contamination

Deep-C storage: Biological, chemical and physical strategies to enhance carbon stocks in agricultural subsoils

Due to their substantial volume, subsoils contain more of the total soil carbon (C) pool than topsoils. Much of this C is thousands of years old, suggesting that subsoils offer considerable potential for long-term C sequestration. However, knowledge of subsoil C behaviour and manageability remains incomplete, and subsoil C storage potential has yet to be realised at a large scale, particularly in agricultural systems. A range of biological (e.g. deep-rooting), chemical (e.g. biochar burial) and physical (e.g. deep ploughing) C sequestration strategies have been proposed, but are yet to be assessed. In this review, we identify the main factors that regulate subsoil C cycling and critically evaluate the evidence and mechanistic basis of subsoil strategies designed to promote greater C storage, with particular emphasis on agroecosystems. We assess the barriers and opportunities for the implementation of strategies to enhance subsoil C sequestration and identify 5 key current gaps in scientific understanding. We conclude that subsoils, while highly heterogeneous, are in many cases more suited to long-term C sequestration than topsoils. The proposed strategies may also bring other tangible benefits to cropping systems (e.g. enhanced water holding capacity and nutrient use efficiency). Furthermore, while the subsoil C sequestration strategies we reviewed have large potential, more long-term studies are needed across a diverse range of soils and climates, in conjunction with chronosequence and space-for-time substitutions. Also, it is vital that subsoils are more consistently included in modelled estimations of soil C stocks and C sequestration potential, and that subsoil-explicit C models are developed to specifically reflect subsoil processes. Finally, further mapping of subsoil C is needed in specific regions (e.g. in the Middle East, Eastern Europe, South and Central America, South Asia and Africa). Conducting both immediate and long-term subsoil C studies will fill the knowledge gaps to devise appropriate soil C sequestration strategies and policies to help in the global fight against climate change and decline in soil quality. In conclusion, our evidence-based analysis reveals that subsoils offer an untapped potential to enhance global C storage in terrestrial ecosystems

Adiabatic evolution of a coupled-qubit Hamiltonian

We present a general method for studying coupled qubits driven by adiabatically changing external parameters. Extended calculations are provided for a two-bit Hamiltonian whose eigenstates can be used as logical states for a quantum CNOT gate. From a numerical analysis of the stationary Schroedinger equation we find a set of parameters suitable for representing CNOT, while from a time-dependent study the conditions for adiabatic evolution are determined. Specializing to a concrete physical system involving SQUIDs, we determine reasonable parameters for experimental purposes. The dissipation for SQUIDs is discussed by fitting experimental data. The low dissipation obtained supports the idea that adiabatic operations could be performed on a time scale shorter than the decoherence time.Comment: 10 pages, 4 figures, to be pub.in Phys Rev

Osteochondral allograft transplantation for femoral trochlear dysplasia

Background: The risk factors for patellofemoral joint instability include laxity of medial patellar restraints, abnormal limb geometry, femoral and tibial malrotation, patella alta, and trochlear dysplasia. Femoral trochlear dysplasia is characterized by a hypoplastic or shallow trochlear groove. Case Report: We report the case of a 31-year-old female with trochlear dysplasia and recurrent patella dislocations, laxity of the medial patellofemoral ligament (MPFL), and high-grade chondromalacia of the trochlea and the patella. Surgical treatment goals were to re-create a trochlear groove, restore bony restraint, and realign and offload the patella. First, a triplane tibial tubercle osteotomy (TTO) was performed, and the patella was everted 360° with a subvastus approach. The MPFL was reconstructed using a gracilis allograft. A fresh osteochondral allograft transplant trochlea was sized, and a 35-mm diameter graft was transplanted to re-create the groove. The TTO was secured in a new anterior, medial, and distal position. The patient was braced for 6 weeks and completed a rehabilitation protocol. At 9-month follow-up, she had made significant gains in range of motion (0°-140°) and activity compared to her preoperative status. She reported no pain or recurrent dislocations. Conclusion: This case demonstrates a viable surgical option for treatment of instability resulting from trochlear dysplasia with patellofemoral chondromalacia. The osteochondral allograft transplantation surgery technique allows patients to have a stable, pain-free knee joint and participate in activities compared to nonoperative management. However, the long-term outcomes of this procedure are unknown

Neutron-3^3H potentials and the 5^5H-properties

The continuum resonance spectrum of $^5$H ($^3$H+$n$+$n$) is investigated by use of the complex scaled hyperspherical adiabatic expansion method. The crucial $^3$H-neutron potential is obtained by switching off the Coulomb part from successful fits to $^3$He-proton experimental data. These two-body potentials must be expressed exclusively by operators conserving the nucleon-core mean field angular momentum quantum numbers. The energies $E_R$ and widths $\Gamma_R$ of the $1/2^+$ ground-state resonance and the lowest two excited $5/2^+$ and $3/2^+$-resonances are found to be $(1.6,1.5)$ MeV, $(2.8,2.5)$ MeV and $(3.2,3.9)$ MeV, respectively. These results agree with most of the experimental data. The energy distributions of the fragments after decay of the resonances are predicted.Comment: 26 pages, 8 tables, 7 figures. Accepted for publication in Nucl. Phys.

Factors affecting the union of opening wedge high tibial osteotomy using a titanium wedge plate

Background: Factors that can affect the success rate of high tibial osteotomy (HTO) include patient selection, surgical technique, type of fixation hardware, supplemental fixation, choice of bone graft, and rehabilitation protocol. The purpose of this study was to define the role of cortical hinge fractures in the risk of nonunion and collapse of opening wedge high tibial osteotomy. Methods: A total of 60 patients (mean age, 40 years) who underwent 64 primary HTO procedures were identified from our operational database and observed at a mean follow-up of 2 years. Surgical correction was followed by immediate range of motion and a progressive weight-bearing protocol. Clinical and radiographic data were reviewed for patient demographics, bony union, cortical hinge fractures, loss of correction, and other complications. Results: The average time to radiographic union was 14.8 weeks (range, 8-24). Loss of correction and/or collapse occurred in 6 cases (9.4%). Nine unrecognized cortical hinge fractures were retrospectively identified, of which 4 resulted in nonunion and collapse. We found a significantly higher incidence of unrecognized cortical hinge fractures in cases that collapsed (4/6, 66.7%) compared to cases that healed uneventfully (5/58, 8.6%) (P=0.003). Conclusion: A high index of suspicion must be maintained intraoperatively and postoperatively to identify and treat unstable constructs that increase the risk of nonunion and collapse after opening wedge HTO. This study’s patient series explores the relationship between cortical hinge fracture and patient outcomes in the clinical setting by demonstrating a significantly higher rate of collapse and nonunion with unstable constructs