Dense Packings of Congruent Circles in Rectangles with a Variable Aspect Ratio

We use computational experiments to find the rectangles of minimum area into which a given number n of non-overlapping congruent circles can be packed. No assumption is made on the shape of the rectangles. Most of the packings found have the usual regular square or hexagonal pattern. However, for 1495 values of n in the tested range n =< 5000, specifically, for n = 49, 61, 79, 97, 107,... 4999, we prove that the optimum cannot possibly be achieved by such regular arrangements. The evidence suggests that the limiting height-to-width ratio of rectangles containing an optimal hexagonal packing of circles tends to 2-sqrt(3) as n tends to infinity, if the limit exists.Comment: 21 pages, 13 figure

Interaction effects at crossings of spin-polarized one-dimensional subbands

We report conductance measurements of ballistic one-dimensional (1D) wires defined in GaAs/AlGaAs heterostructures in an in-plane magnetic field, B. When the Zeeman energy is equal to the 1D subband energy spacing, the spin-split subband Nup arrow intersects (N+1)down arrow, where N is the index of the spin-degenerate 1D subband. At the crossing of N=1up arrow and N=2down arrow subbands, there is a spontaneous splitting giving rise to an additional conductance structure evolving from the 1.5(2e(2)/h) plateau. With further increase in B, the structure develops into a plateau and lowers to 2e(2)/h. With increasing temperature and magnetic field the structure shows characteristics of the 0.7 structure. Our results suggest that at low densities a spontaneous spin splitting occurs whenever two 1D subbands of opposite spins cross

Learning the subtle dance: the experience of therapists who deliver mentalisation-based therapy for borderline personality disorder

Objectives: This study aimed to understand therapists’ lived experiences of delivering mentalisation-based therapy (MBT), including their experiences of service user change. / Method: One-to-one semi-structured interviews or focus groups were conducted with 14 MBT therapists and analysed using interpretative phenomenological analysis (IPA). / Results: Four superordinate themes were identified: 1) experiencing the challenges and complexities of being with service users during MBT; 2) being on a journey of discovery and change; 3) being an MBT therapist: a new way of working and developing a new therapeutic identity; and 4) being a therapist in the group: seeing it all come together / Conclusion: Our findings highlight the complexity, challenges and individualised experience of working therapeutically with service users with a diagnosis of BPD. The study provides a perspective of service use change that is enriched by idiosyncrasies within the therapeutic encounter. We conclude with a consideration of implications for MBT research and clinical practice

How large dimension guarantees a given angle?

We study the following two problems: (1) Given $n\ge 2$ and \al, how large Hausdorff dimension can a compact set A\su\Rn have if $A$ does not contain three points that form an angle \al? (2) Given \al and \de, how large Hausdorff dimension can a %compact subset $A$ of a Euclidean space have if $A$ does not contain three points that form an angle in the \de-neighborhood of \al? An interesting phenomenon is that different angles show different behaviour in the above problems. Apart from the clearly special extreme angles 0 and $180^\circ$, the angles $60^\circ,90^\circ$ and $120^\circ$ also play special role in problem (2): the maximal dimension is smaller for these special angles than for the other angles. In problem (1) the angle $90^\circ$ seems to behave differently from other angles

Modern dietary guidelines for healthy pregnancy; maximising maternal and foetal outcomes and limiting excessive gestational weight gain

Maternal dietary habits influence maternal and foetal health, representing a pathway for intervention to maximise pregnancy outcomes. Advice on energy intake is provided on a trimester basis, with no additional calories required in the first trimester and an additional 340 kcal∙d-1 and 452 kcal∙d-1 needed for the second and third trimesters. Energy intake depends on pre-gravid body mass index (BMI); underweight women are recommended an increase of 150, 200 and 300 kcal∙d-1 during the first, second and third trimester, normal weight women an increase of 0, 350 and 500 kcal∙d-1 and obese women an increase of 0, 450 and 350 kcal∙day-1. The recommendations for carbohydrate and protein intake are 175 g∙d-1 and 0.88-1.1 g∙kgBM∙d−1, with no change to fat intake. The number of pre-gravid obese women is rising; therefore, we need to regulate weight in women of childbearing age and limit gestational weight gain to within the recommended ranges [overweight women 6.8–11.3 kg and obese women 5.0–9.1 kg]. This can be achieved using nutritional interventions, as dietary changes have been shown to help with gestational weight management. As pregnancy has been identified as a risk factor for the development of obesity, normal weight women should gain 11.5-16.0 kg during pregnancy. Whilst some research has shown that dietary interventions help to regulate gestational weight gain and promote postpartum weight loss to some extent, future research is needed to provide safe and effective guidelines to maximise these effects, whist benefitting maternal and foetal health

Omacetaxine may have a role in chronic myeloid leukaemia eradication through downregulation of Mcl-1 and induction of apoptosis in stem/progenitor cells

Chronic myeloid leukaemia (CML) is maintained by a rare population of tyrosine kinase inhibitor (TKI)-insensitive malignant stem cells. Our long-term aim is to find a BcrAbl-independent drug that can be combined with a TKI to improve overall disease response in chronic-phase CML. Omacetaxine mepesuccinate, a first in class cetaxine, has been evaluated by clinical trials in TKI-insensitive/resistant CML. Omacetaxine inhibits synthesis of anti-apoptotic proteins of the Bcl-2 family, including (myeloid cell leukaemia) Mcl-1, leading to cell death. Omacetaxine effectively induced apoptosis in primary CML stem cells (CD34&lt;sup&gt;+&lt;/sup&gt;38&lt;sup&gt;lo&lt;/sup&gt;) by downregulation of Mcl-1 protein. In contrast to our previous findings with TKIs, omacetaxine did not accumulate undivided cells &lt;i&gt;in vitro&lt;/i&gt;. Furthermore, the functionality of surviving stem cells following omacetaxine exposure was significantly reduced in a dose-dependant manner, as determined by colony forming cell and the more stringent long-term culture initiating cell colony assays. This stem cell-directed activity was not limited to CML stem cells as both normal and non-CML CD34&lt;sup&gt;+&lt;/sup&gt; cells were sensitive to inhibition. Thus, although omacetaxine is not leukaemia stem cell specific, its ability to induce apoptosis of leukaemic stem cells distinguishes it from TKIs and creates the potential for a curative strategy for persistent disease

Changes in use of herbs and dietary supplements (HDS) among clinicians enrolled in an online curriculum

<p>Abstract</p> <p>Background</p> <p>Little is known about clinicians' use of herbs and dietary supplements (HDS), how their personal HDS use changes with time and training, and how changes in their personal use affect their confidence or communication with patients about HDS.</p> <p>Methods</p> <p>We conducted a prospective cohort study of clinicians before and after an on-line curriculum about HDS in winter-spring, 2005.</p> <p>Results</p> <p>Of the 569 clinicians who completed surveys both at baseline and after the course, 25% were male and the average age was 42 years old; 88% used HDS before and after the course. The average number of supplements used fell slightly from 6.2 at baseline to 5.8 after the course (P < 0.01). The most commonly used supplements at baseline were: multivitamins (65%), calcium (42%), B vitamins (34%), vitamin C (34%), green tea (27%), fish oil (27%) and vitamin E (25%). Use of fish oil increased to 30% after the course (P = 0.01). Use of supplements traditionally used to treat colds decreased: vitamin C (34% to 27%), zinc (13% to 10%), and echinacea (7% to 5%, P < 0.05 for all three). Changes in personal HDS use were not associated with significant changes in confidence or communication with patients.</p> <p>Conclusion</p> <p>Many clinicians use HDS personally; use changes seasonally and to a small extent with professional education. Professional use of HDS is dynamic and seasonal. Additional research is needed to understand the impact of personal use on professional attitudes and behavior in populations with lower baseline uses of HDS.</p

No excess of mitochondrial DNA deletions within muscle in progressive multiple sclerosis

BACKGROUND: Mitochondrial dysfunction is an established feature of multiple sclerosis (MS). We recently described high levels of mitochondrial DNA (mtDNA) deletions within respiratory enzyme-deficient (lacking mitochondrial respiratory chain complex IV with intact complex II) neurons and choroid plexus epithelial cells in progressive MS. OBJECTIVES: The objective of this paper is to determine whether respiratory enzyme deficiency and mtDNA deletions in MS were in excess of age-related changes within muscle, which, like neurons, are post-mitotic cells that frequently harbour mtDNA deletions with ageing and in disease. METHODS: In progressive MS cases (n=17), known to harbour an excess of mtDNA deletions in the central nervous system (CNS), and controls (n=15), we studied muscle (paraspinal) and explored mitochondria in single fibres. Histochemistry, immunohistochemistry, laser microdissection, real-time polymerase chain reaction (PCR), long-range PCR and sequencing were used to resolve the single muscle fibres. RESULTS: The percentage of respiratory enzyme-deficient muscle fibres, mtDNA deletion level and percentage of muscle fibres harbouring high levels of mtDNA deletions were not significantly different in MS compared with controls. CONCLUSION: Our findings do not provide support to the existence of a diffuse mitochondrial abnormality involving multiple systems in MS. Understanding the cause(s) of the CNS mitochondrial dysfunction in progressive MS remains a research priority