The Significance of the CC-Numerical Range and the Local CC-Numerical Range in Quantum Control and Quantum Information

This paper shows how C-numerical-range related new strucures may arise from practical problems in quantum control--and vice versa, how an understanding of these structures helps to tackle hot topics in quantum information. We start out with an overview on the role of C-numerical ranges in current research problems in quantum theory: the quantum mechanical task of maximising the projection of a point on the unitary orbit of an initial state onto a target state C relates to the C-numerical radius of A via maximising the trace function |\tr \{C^\dagger UAU^\dagger\}|. In quantum control of n qubits one may be interested (i) in having U\in SU(2^n) for the entire dynamics, or (ii) in restricting the dynamics to {\em local} operations on each qubit, i.e. to the n-fold tensor product SU(2)\otimes SU(2)\otimes >...\otimes SU(2). Interestingly, the latter then leads to a novel entity, the {\em local} C-numerical range W_{\rm loc}(C,A), whose intricate geometry is neither star-shaped nor simply connected in contrast to the conventional C-numerical range. This is shown in the accompanying paper (math-ph/0702005). We present novel applications of the C-numerical range in quantum control assisted by gradient flows on the local unitary group: (1) they serve as powerful tools for deciding whether a quantum interaction can be inverted in time (in a sense generalising Hahn's famous spin echo); (2) they allow for optimising witnesses of quantum entanglement. We conclude by relating the relative C-numerical range to problems of constrained quantum optimisation, for which we also give Lagrange-type gradient flow algorithms.Comment: update relating to math-ph/070200

Studying the Salt Dependence of the Binding of σ70 and σ32 to Core RNA Polymerase Using Luminescence Resonance Energy Transfer

The study of protein-protein interactions is becoming increasingly important for understanding the regulation of many cellular processes. The ability to quantify the strength with which two binding partners interact is desirable but the accurate determination of equilibrium binding constants is a difficult process. The use of Luminescence Resonance Energy Transfer (LRET) provides a homogeneous binding assay that can be used for the detection of protein-protein interactions. Previously, we developed an LRET assay to screen for small molecule inhibitors of the interaction of σ70 with theβ' coiled-coil fragment (amino acids 100–309). Here we describe an LRET binding assay used to monitor the interaction of E. coli σ70 and σ32 with core RNA polymerase along with the controls to verify the system. This approach generates fluorescently labeled proteins through the random labeling of lysine residues which enables the use of the LRET assay for proteins for which the creation of single cysteine mutants is not feasible. With the LRET binding assay, we are able to show that the interaction of σ70 with core RNAP is much more sensitive to NaCl than to potassium glutamate (KGlu), whereas the σ32 interaction with core RNAP is insensitive to both salts even at concentrations >500 mM. We also find that the interaction of σ32 with core RNAP is stronger than σ70 with core RNAP, under all conditions tested. This work establishes a consistent set of conditions for the comparison of the binding affinities of the E.coli sigma factors with core RNA polymerase. The examination of the importance of salt conditions in the binding of these proteins could have implications in both in vitro assay conditions and in vivo function

From whole bodies to single cells : a guide to transcriptomic approaches for ecology and evolutionary biology

Funding: The authors were assisted by a Special Topics Network (STN) grant from the European Society for Evolutionary Biology (ESEB) to facilitate networking of the European Drosophila Population Genomics consortium (DrosEU; https://droseu.net/). SG and NP are supported by a Deutsche Forschungsgemeinschaft grant (GR 4495/4-1, PO 1648/7-1, PO 1648/4-1). MGR is supported by Natural Environment Research Council, UK (NE/V001566/1). CS is supported by the Austrian Science Funds (P32935, P33734, W1225). TF is supported by the Swiss National Science Foundation (310030_219283, FZEB-0-214654, 31003A-182262). JG is supported by grant PID2020-115874GB-I00 funded by MCIN/AEI/10.13039/501100011033 and from grant 2021 SGR 00417 funded by Departament de Recerca i Universitats, Generalitat de Catalunya. MK was supported by the grant 322980 from The Research Council of Finland.RNA sequencing (RNAseq) methodology has experienced a burst of technological developments in the last decade, which has opened up opportunities for studying the mechanisms of adaptation to environmental factors at both the organismal and cellular level. Selecting the most suitable experimental approach for specific research questions and model systems can, however, be a challenge and researchers in ecology and evolution are commonly faced with the choice of whether to study gene expression variation in whole bodies, specific tissues, and/or single cells. A wide range of sometimes polarised opinions exists over which approach is best. Here, we highlight the advantages and disadvantages of each of these approaches to provide a guide to help researchers make informed decisions and maximise the power of their study. Using illustrative examples of various ecological and evolutionary research questions, we guide the readers through the different RNAseq approaches and help them identify the most suitable design for their own projects.Peer reviewe

Challenges of maintaining research protocol fidelity in a clinical care setting: A qualitative study of the experiences and views of patients and staff participating in a randomized controlled trial

<p>Abstract</p> <p>Background</p> <p>Trial research has predominantly focused on patient and staff understandings of trial concepts and/or motivations for taking part, rather than why treatment recommendations may or may not be followed during trial delivery. This study sought to understand why there was limited attainment of the glycaemic target (HbA_1c≤6.5%) among patients who participated in the Treating to Target in Type 2 Diabetes Trial (4-T). The objective was to inform interpretation of trial outcomes and provide recommendations for future trial delivery.</p> <p>Methods</p> <p>In-depth interviews were conducted with 45 patients and 21 health professionals recruited from 11 of 58 trial centres in the UK. Patients were broadly representative of those in the main trial in terms of treatment allocation, demographics and glycaemic control. Both physicians and research nurses were interviewed.</p> <p>Results</p> <p>Most patients were committed to taking insulin as recommended by 4-T staff. To avoid hypoglycaemia, patients occasionally altered or skipped insulin doses, normally in consultation with staff. Patients were usually unaware of the trial's glycaemic target. Positive staff feedback could lead patients to believe they had been 'successful' trial participants even when their HbA_1cexceeded 6.5%. While some staff felt that the 4-T automated insulin dose adjustment algorithm had increased their confidence to prescribe larger insulin doses than in routine clinical practice, all described situations where they had not followed its recommendations. Staff regarded the application of a 'one size fits all' glycaemic target during the trial as contradicting routine clinical practice where they would tailor treatments to individuals. Staff also expressed concerns that 'tight' glycaemic control might impose an unacceptably high risk of hypoglycaemia, thus compromising trust and safety, especially amongst older patients. To address these concerns, staff tended to adapt the trial protocol to align it with their clinical practices and experiences.</p> <p>Conclusions</p> <p>To understand trial findings, foster attainment of endpoints, and promote protocol fidelity, it may be necessary to look beyond individual patient characteristics and experiences. Specifically, the context of trial delivery, the impact of staff involvement, and the difficulties staff may encounter in balancing competing 'clinical' and 'research' roles and responsibilities may need to be considered and addressed.</p

Genome sequencing of the extinct Eurasian wild aurochs, Bos primigenius, illuminates the phylogeography and evolution of cattle

Background Domestication of the now-extinct wild aurochs, Bos primigenius, gave rise to the two major domestic extant cattle taxa, B. taurus and B. indicus. While previous genetic studies have shed some light on the evolutionary relationships between European aurochs and modern cattle, important questions remain unanswered, including the phylogenetic status of aurochs, whether gene flow from aurochs into early domestic populations occurred, and which genomic regions were subject to selection processes during and after domestication. Here, we address these questions using whole-genome sequencing data generated from an approximately 6,750-year-old British aurochs bone and genome sequence data from 81 additional cattle plus genome-wide single nucleotide polymorphism data from a diverse panel of 1,225 modern animals. Results Phylogenomic analyses place the aurochs as a distinct outgroup to the domestic B. taurus lineage, supporting the predominant Near Eastern origin of European cattle. Conversely, traditional British and Irish breeds share more genetic variants with this aurochs specimen than other European populations, supporting localized gene flow from aurochs into the ancestors of modern British and Irish cattle, perhaps through purposeful restocking by early herders in Britain. Finally, the functions of genes showing evidence for positive selection in B. taurus are enriched for neurobiology, growth, metabolism and immunobiology, suggesting that these biological processes have been important in the domestication of cattle. Conclusions This work provides important new information regarding the origins and functional evolution of modern cattle, revealing that the interface between early European domestic populations and wild aurochs was significantly more complex than previously thought

Parental diabetes status reveals association of mitochondrial DNA haplogroup J1 with type 2 diabetes

<p>Abstract</p> <p>Background</p> <p>Although mitochondrial dysfunction is consistently manifested in patients with Type 2 Diabetes mellitus (T2DM), the association of mitochondrial DNA (mtDNA) sequence variants with T2DM varies among populations. These differences might stem from differing environmental influences among populations. However, other potentially important considerations emanate from the very nature of mitochondrial genetics, namely the notable high degree of partitioning in the distribution of human mtDNA variants among populations, as well as the interaction of mtDNA and nuclear DNA-encoded factors working in concert to govern mitochondrial function. We hypothesized that association of mtDNA genetic variants with T2DM could be revealed while controlling for the effect of additional inherited factors, reflected in family history information.</p> <p>Methods</p> <p>To test this hypothesis we set out to investigate whether mtDNA genetic variants will be differentially associated with T2DM depending on the diabetes status of the parents. To this end, association of mtDNA genetic backgrounds (haplogroups) with T2DM was assessed in 1055 Jewish patients with and without T2DM parents ('DP' and 'HP', respectively).</p> <p>Results</p> <p>Haplogroup J1 was found to be 2.4 fold under-represented in the 'HP' patients (p = 0.0035). These results are consistent with a previous observation made in Finnish T2DM patients. Moreover, assessing the haplogroup distribution in 'DP' versus 'HP' patients having diabetic siblings revealed that haplogroup J1 was virtually absent in the 'HP' group.</p> <p>Conclusion</p> <p>These results imply the involvement of inherited factors, which modulate the susceptibility of haplogroup J1 to T2DM.</p

Endometrial stromal sarcoma: a population-based analysis

To determine independent prognostic factors for the survival of patients with endometrial stromal sarcoma (ESS), data were abstracted from the Surveillance, Epidemiology, and End Results (SEER) database of the National Cancer Institute from 1988 to 2003. Kaplan–Meier and Cox proportional hazards models were used for analyses. Of 831 women diagnosed with ESS, the median age was 52 years (range: 17–96 years). In total, 59.9% had stage I, 5.1% stage II, 14.9% stage III, and 20.1% had stage IV disease. Overall, 13.0, 36.1, and 34.7% presented with grades 1, 2, and 3, respectively. Patients with stage I–II vs III–IV disease had 5 years DSS of 89.3% vs 50.3% (P<0.001) and those with grades 1, 2, and 3 cancers had survivals of 91.4, 95.4, and 42.1% (P<0.001). In multivariate analysis, older patients, black race, advanced stage, higher grade, lack of primary surgery, and nodal metastasis were independent prognostic factors for poorer survival. In younger women (<50 years) with stage I–II disease, ovarian-sparing procedures did not adversely impact survival (91.9 vs 96.2%; P=0.1). Age, race, primary surgery, stage, and grade are important prognostic factors for ESS. Excellent survival in patients with grade 1 and 2 disease of all stages supports the concept that these tumors are significantly different from grade 3 tumors. Ovarian-sparing surgeries may be considered in younger patients with early-stage disease