Pauli graphs, Riemann hypothesis, Goldbach pairs

Let consider the Pauli group $\mathcal{P}_q=$ with unitary quantum generators $X$ (shift) and $Z$ (clock) acting on the vectors of the $q$-dimensional Hilbert space via $X|s> =|s+1>$ and $Z|s> =\omega^s |s>$, with $\omega=\exp(2i\pi/q)$. It has been found that the number of maximal mutually commuting sets within $\mathcal{P}_q$ is controlled by the Dedekind psi function $\psi(q)=q \prod_{p|q}(1+\frac{1}{p})$ (with $p$ a prime) \cite{Planat2011} and that there exists a specific inequality $\frac{\psi (q)}{q}>e^{\gamma}\log \log q$, involving the Euler constant $\gamma \sim 0.577$, that is only satisfied at specific low dimensions $q \in \mathcal {A}=\{2,3,4,5,6,8,10,12,18,30\}$. The set $\mathcal{A}$ is closely related to the set $\mathcal{A} \cup \{1,24\}$ of integers that are totally Goldbach, i.e. that consist of all primes $p2$) is equivalent to Riemann hypothesis. Introducing the Hardy-Littlewood function $R(q)=2 C_2 \prod_{p|n}\frac{p-1}{p-2}$ (with $C_2 \sim 0.660$ the twin prime constant), that is used for estimating the number $g(q) \sim R(q) \frac{q}{\ln^2 q}$ of Goldbach pairs, one shows that the new inequality $\frac{R(N_r)}{\log \log N_r} \gtrapprox e^{\gamma}$ is also equivalent to Riemann hypothesis. In this paper, these number theoretical properties are discusssed in the context of the qudit commutation structure.Comment: 11 page

Adequate symptom relief justifies hepatic resection for benign disease

BACKGROUND: The purpose of this study was to evaluate the long-term results of partial liver resection for benign liver lesions. METHODS: All patients operated on for benign liver lesions from 1991 to 2002 were included. Information was retrieved from medical records, the hospital registration system and by a telephonic questionnaire. RESULTS: Twenty-eight patients with a median age of 41 years (17–71) were operated on (M/F ratio 5/23). The diagnosis was haemangioma in 8 patients, FNH in 6, HCA in 13 and angiomyolipoma in 1. Eight patients were known to have relevant co-morbidity. Median operating time was 207 minutes (45–360). The morbidity rate was 25% and no postoperative mortality was observed. Twenty-two patients (79%) had symptoms (mainly abdominal pain) prior to surgery. Twenty-five patients were reached for a questionnaire. The median follow up was 55 months (4–150). In 89% of patients preoperative symptoms had decreased or disappeared after surgery. Four patients developed late complications. CONCLUSION: Long-term follow up after liver surgery for benign liver lesions shows considerable symptom relief and patient satisfaction. In addition to a correct indication these results justify major surgery with associated morbidity and mortality

Seizures and disturbed brain potassium dynamics in the leukodystrophy megalencephalic leukoencephalopathy with subcortical cysts

OBJECTIVE: Loss of function of the astrocyte-specific protein MLC1 leads to the childhood-onset leukodystrophy "megalencephalic leukoencephalopathy with subcortical cysts" (MLC). Studies on isolated cells show a role for MLC1 in astrocyte volume regulation and suggest that disturbed brain ion and water homeostasis is central to the disease. Excitability of neuronal networks is particularly sensitive to ion and water homeostasis. In line with this, reports of seizures and epilepsy in MLC patients exist. However, systematic assessment and mechanistic understanding of seizures in MLC are lacking. METHODS: We analyzed an MLC patient inventory to study occurrence of seizures in MLC. We used two distinct genetic mouse models of MLC to further study epileptiform activity and seizure threshold through wireless extracellular field potential recordings. Whole-cell patch-clamp recordings and K+-sensitive electrode recordings in mouse brain slices were used to explore the underlying mechanisms of epilepsy in MLC. RESULTS: An early onset of seizures is common in MLC. Similarly, in MLC mice, we uncovered spontaneous epileptiform brain activity and a lowered threshold for induced seizures. At the cellular level, we found that although passive and active properties of individual pyramidal neurons are unchanged, extracellular K+dynamics and neuronal network activity are abnormal in MLC mice. INTERPRETATION: Disturbed astrocyte regulation of ion and water homeostasis in MLC causes hyperexcitability of neuronal networks and seizures. These findings suggest a role for defective astrocyte volume regulation in epilepsy. Ann Neurol 2018;83:636-649

The Value of 3D Printed Models in Understanding Acetabular Fractures

Acetabular fractures are complex and difficult to classify. Although the Judet-Letournel classification is designed to increase the understanding of acetabular fractures, it remains prone to error when using conventional medical imaging. We hypothesize that three-dimensional (3D) printing, as a new diagnostic imaging tool, will lead to an increased understanding and knowledge of acetabular fractures and an optimal surgical approach. Digital data (DICOM) of 20 acetabular fractures were converted into 3D files [standard tessellation language (STL) data]. These STL files were used to prepare 3D prints of life-size hemipelvic models with acetabular fractures. Seven senior trauma surgeons specializing in pelvic and acetabular surgery, 5 young fellowship-trained trauma surgeons, 5 senior surgical residents, 5 junior surgical residents, and 5 interns classified 20 acetabular cases using X-ray/two-dimensional (2D) computed tomography (CT), 3D reconstructions, and 3D printed models according to the Judet-Letournel classification. Furthermore, all junior and senior surgeons were instructed to evaluate their surgical approach and the positioning of the patient during operation. Time to classify each case was recorded. Calculations were done using Fleiss' κ statistics. Only slight and fair interobserver agreements for senior surgeons (κ = 0.33) and interns (κ = 0.16) were found when using X-ray/2D CT. However, 3D printed models showed moderate and substantial interobserver agreements for senior surgeons (κ = 0.59), junior surgeons (κ = 0.56), senior surgical residents (κ = 0.66), junior surgical residents (κ = 0.51), and interns (κ = 0.61). Compared with X-ray/2D CT, the interobserver agreement regarding the surgical approach for junior surgeons using 3D printed models increased by κ = 0.04 and κ = 0.23, respectively. Except for the interns, a significant time difference for classification was found between X-ray/2D CT and 3D CT and 3D printed models for junior and senior surgical residents and junior and senior surgeons (p < 0.001). 3D printing is of added value in the understanding, classification, and surgical evaluation of acetabular fractures. We recommend the implementation of 3D printed models in trauma surgery training

Human Impacts on Forest Biodiversity in Protected Walnut-Fruit Forests in Kyrgyzstan

We used a spatially explicit model of forest dynamics, supported by empirical field data and socioeconomic data, to examine the impacts of human disturbances on a protected forest landscape in Kyrgyzstan. Local use of 27 fruit and nut species was recorded and modeled. Results indicated that in the presence of fuelwood cutting with or without grazing, species of high socioeconomic impor- tance such as Juglans regia, Malus spp., and Armeniaca vulgaris were largely eliminated from the landscape after 50–150 yr. In the absence of disturbance or in the presence of grazing only, decline of these species occurred at a much lower rate, owing to competi- tive interactions between tree species. This suggests that the current intensity of fuelwood harvesting is not sustainable. Conversely, cur- rent grazing intensities were found to have relatively little impact on forest structure and composition, and could potentially play a positive role in supporting regeneration of tree species. These results indicate that both positive and negative impacts on biodiversity can arise from human populations living within a protected area. Potentially, these could be reconciled through the development of participatory approaches to conservation management within this reserve, to ensure the maintenance of its high conservation value while meeting human needs

UK guideline on transition of adolescent and young persons with chronic digestive diseases from paediatric to adult care

The risks of poor transition include delayed and inappropriate transfer that can result in disengagement with healthcare. Structured transition care can improve control of chronic digestive diseases and long-term health-related outcomes. These are the first nationally developed guidelines on the transition of adolescent and young persons (AYP) with chronic digestive diseases from paediatric to adult care. They were commissioned by the Clinical Services and Standards Committee of the British Society of Gastroenterology under the auspices of the Adolescent and Young Persons (A&YP) Section. Electronic searches for English-language articles were performed with keywords relating to digestive system diseases and transition to adult care in the Medline (via Ovid), PsycInfo (via Ovid), Web of Science and CINAHL databases for studies published from 1980 to September 2014. The quality of evidence and grading of recommendations was appraised using the Grading of Recommendations Assessment, Development and Evaluation (GRADE) system. The limited number of studies in gastroenterology and hepatology required the addition of relevant studies from other chronic diseases to be included. These guidelines deal specifically with the transition of AYP living with a diagnosis of chronic digestive disease and/or liver disease from paediatric to adult healthcare under the following headings; 1. Patient populations involved in AYP transition 2. Risks of failing transition or poor transition 3. Models of AYP transition 4. Patient and carer/parent perspective in AYP transition 5. Surgical perspectiv

Use of population input functions for reduced scan duration whole-body Patlak F-18-FDG PET imaging

Abstract: Whole-body Patlak images can be obtained from an acquisition of first 6 min of dynamic imaging over the heart to obtain the arterial input function (IF), followed by multiple whole-body sweeps up to 60 min pi. The use of a population-averaged IF (PIF) could exclude the first dynamic scan and minimize whole-body sweeps to 30–60 min pi. Here, the effects of (incorrect) PIFs on the accuracy of the proposed Patlak method were assessed. In addition, the extent of mitigating these biases through rescaling of the PIF to image-derived IF values at 30–60 min pi was evaluated. Methods: Using a representative IF and rate constants from the literature, various tumour time-activity curves (TACs) were simulated. Variations included multiplication of the IF with a positive and negative gradual linear bias over 60 min of 5, 10, 15, 20, and 25% (generating TACs using an IF different from the PIF); use of rate constants (K 1, k 3, and both K 1 and k 2) multiplied by 2, 1.5, and 0.75; and addition of noise (μ = 0 and σ = 5, 10 and 15%). Subsequent Patlak analysis using the original IF (representing the PIF) was used to obtain the influx constant (K i) for the differently simulated TACs. Next, the PIF was scaled towards the (simulated) IF value using the 30–60-min pi time interval, simulating scaling of the PIF to image-derived values. Influence of variabilities in IF and rate constants, and rescaling the PIF on bias in K i was evaluated. Results: Percentage bias in K i observed using simulated modified IFs varied from − 16 to 16% depending on the simulated amplitude and direction of the IF modifications. Subsequent scaling of the PIF reduced these K i biases in most cases (287 out of 290) to < 5%. Conclusions: Simulations suggest that scaling of a (possibly incorrect) PIF to IF values seen in whole-body dynamic imaging from 30 to 60 min pi can provide accurate Ki estimates. Consequently, dynamic Patlak imaging protocols may be performed for 30–60 min pi making whole-body Patlak imaging clinically feasible

Dissipation equals production in the log layer of wall-induced turbulence

Asymptotic analysis is presented of the energy balance equations derived from statistically averagedNavier-Stokes equations pertinent to wall-induced turbulence. Attention is focused on the inertialsublayer, the region outside the viscous sublayer, and the buffer layer where the log-law for meanflow holds. Production and dissipation of turbulence are shown to be equal with a relative error of order(x2 /L), where x2 is the distance from the wall and L is the external length (pipe radius, channelhalf-height, boundary layer thickness). Diffusion of pressure and kinetic energy together are only ofrelative magnitude order (x2 /L). Pressure gradient terms are shown to redistribute longitudinalturbulence production in equal portions dissipated in the three orthogonal directions

Update on the Role of [18F]FDOPA PET/CT.

[ 18F]-dihydroxyphenylalanine ([ 18F]FDOPA) is a radiopharmaceutical used in a broad spectrum of diseases, including neuroendocrine tumors (NETs), congenital hyperinsulinism, parkinsonian syndromes and neuro-oncology. Genetic analysis and disease specific biomarkers may guide the optimum selection of patients that may benefit most from [ 18F]FDOPA PET in different stages of several neuroendocrine neoplasms and in congenital hyperinsulinism. For clinical routine in neuro-oncology, indications for [ 18F]FDOPA PET include tumor delineation and distinguishing between treatment related changes and recurrent disease. New developments as the advent of large axial field of view PET/CT or integrated PET/MRI systems may provide more unique opportunities, such as those related to detection of smaller lesions in primary staging of NETs, dose reduction in children with congenital hyperinsulinism, or possibilities to obtain more extensive noninvasive quantification of cerebral uptake by using image derived input functions. Although the widespread use of [ 18F]FDOPA has been hampered by complex synthesis methods and high production costs in the past, significant efforts have been undertaken to provide robust GMP compliant synthesis methods with high activity yield and molar activity. </p

Hypofibrinolysis in diabetes: a therapeutic target for the reduction of cardiovascular risk

An enhanced thrombotic environment and premature atherosclerosis are key factors for the increased cardiovascular risk in diabetes. The occlusive vascular thrombus, formed secondary to interactions between platelets and coagulation proteins, is composed of a skeleton of fibrin fibres with cellular elements embedded in this network. Diabetes is characterised by quantitative and qualitative changes in coagulation proteins, which collectively increase resistance to fibrinolysis, consequently augmenting thrombosis risk. Current long-term therapies to prevent arterial occlusion in diabetes are focussed on anti-platelet agents, a strategy that fails to address the contribution of coagulation proteins to the enhanced thrombotic milieu. Moreover, antiplatelet treatment is associated with bleeding complications, particularly with newer agents and more aggressive combination therapies, questioning the safety of this approach. Therefore, to safely control thrombosis risk in diabetes, an alternative approach is required with the fibrin network representing a credible therapeutic target. In the current review, we address diabetes-specific mechanistic pathways responsible for hypofibrinolysis including the role of clot structure, defects in the fibrinolytic system and increased incorporation of anti-fibrinolytic proteins into the clot. Future anti-thrombotic therapeutic options are discussed with special emphasis on the potential advantages of modulating incorporation of the anti-fibrinolytic proteins into fibrin networks. This latter approach carries theoretical advantages, including specificity for diabetes, ability to target a particular protein with a possible favourable risk of bleeding. The development of alternative treatment strategies to better control residual thrombosis risk in diabetes will help to reduce vascular events, which remain the main cause of mortality in this condition