708 research outputs found

    Relative CC"-Numerical Ranges for Applications in Quantum Control and Quantum Information

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    Motivated by applications in quantum information and quantum control, a new type of CC"-numerical range, the relative CC"-numerical range denoted WK(C,A)W_K(C,A), is introduced. It arises upon replacing the unitary group U(N) in the definition of the classical CC"-numerical range by any of its compact and connected subgroups KU(N)K \subset U(N). The geometric properties of the relative CC"-numerical range are analysed in detail. Counterexamples prove its geometry is more intricate than in the classical case: e.g. WK(C,A)W_K(C,A) is neither star-shaped nor simply-connected. Yet, a well-known result on the rotational symmetry of the classical CC"-numerical range extends to WK(C,A)W_K(C,A), as shown by a new approach based on Lie theory. Furthermore, we concentrate on the subgroup SUloc(2n):=SU(2)...SU(2)SU_{\rm loc}(2^n) := SU(2)\otimes ... \otimes SU(2), i.e. the nn-fold tensor product of SU(2), which is of particular interest in applications. In this case, sufficient conditions are derived for WK(C,A)W_{K}(C,A) being a circular disc centered at origin of the complex plane. Finally, the previous results are illustrated in detail for SU(2)SU(2)SU(2) \otimes SU(2).Comment: accompanying paper to math-ph/070103

    Resolution requirements for numerical simulations of transition

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    The resolution requirements for direct numerical simulations of transition to turbulence are investigated. A reliable resolution criterion is determined from the results of several detailed simulations of channel and boundary-layer transition

    Goltz syndrome (focal dermal hypoplasia) with unilateral ocular, cutaneous and skeletal features: case report

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    <p>Abstract</p> <p>Background</p> <p>Goltz syndrome or focal dermal hypoplasia (FDH) is an uncommon multisystem disorder. Herein, we report a typical case of FDH with unilateral ocular, cutaneous and skeletal features.</p> <p>Case Presentation</p> <p>a 4-year-old girl presented with microphthalmos and iris coloboma of the left eye, facial asymmetry, and a low-set protruding ear. Cutaneous changes included hypopigmented atrophic macules on the left side of the face, chest, abdomen and limbs. Characteristic lobster claw deformity of left hand and oligodactyly and syndactyly of left foot were present.</p> <p>Conclusions</p> <p>FDH usually affects both sides of the body. This case represents the unusual unilateral manifestation of the syndrome.</p

    Cognitive and behavioral predictors of light therapy use

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    Objective: Although light therapy is effective in the treatment of seasonal affective disorder (SAD) and other mood disorders, only 53-79% of individuals with SAD meet remission criteria after light therapy. Perhaps more importantly, only 12-41% of individuals with SAD continue to use the treatment even after a previous winter of successful treatment. Method: Participants completed surveys regarding (1) social, cognitive, and behavioral variables used to evaluate treatment adherence for other health-related issues, expectations and credibility of light therapy, (2) a depression symptoms scale, and (3) self-reported light therapy use. Results: Individuals age 18 or older responded (n = 40), all reporting having been diagnosed with a mood disorder for which light therapy is indicated. Social support and self-efficacy scores were predictive of light therapy use (p's<.05). Conclusion: The findings suggest that testing social support and self-efficacy in a diagnosed patient population may identify factors related to the decision to use light therapy. Treatments that impact social support and self-efficacy may improve treatment response to light therapy in SAD. © 2012 Roecklein et al

    Clinical Experience and Results of Microsurgical Resection of Arterioveonous Malformation in the Presence of Space-Occupying Intracerebral Hematoma

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    BACKGROUND: Management of ruptured arteriovenous malformations (AVMs) with a mass-producing intracerebral hematoma (ICH) represents a surgical dilemma. OBJECTIVE: To evaluate the clinical outcome and obliteration rates of microsurgical resection of AVM when performed concomitantly with evacuation of an associated space-occupying ICH. METHODS: Data of patients with AVM were collected prospectively. Cases were identified in which an AVM was resected and an associated space-occupying ICH was evacuated at the same time, and divided into "group 1," in which the surgery was performed acutely within 48 h of presentation (secondary to elevated intracranial pressure); and "group 2," in which selected patients were operated upon in the presence of a liquefying ICH in the "subacute" stage. Clinical outcomes were assessed using the modified Rankin Scale, with a score of 0 to 2 considered a good outcome. Obliteration rates were assessed using postoperative angiography. RESULTS: From 2001 to 2015, 131 patients underwent microsurgical resection of an AVM, of which 65 cases were included. In "group 1" (n = 21; Spetzler-Ponce class A = 13, class B = 5, and class C = 3), 11 of 21 (52%) had a good outcome and in 18 of 19 (95%) of those who had a postoperative angiogram the AVMs were completely obliterated. In "group 2" (n = 44; Spetzler-Ponce class A = 33, class B = 9, and class C = 2), 31 of 44 (93%) had a good outcome and 42 of 44 (95%) were obliterated with a single procedure. For supratentorial AVMs, the ICH cavity was utilized to provide an operative trajectory to a deep AVM in 11 cases, and in 26 cases the ICH cavity was deep to the AVM and hence facilitated the deep dissection of the nidus. CONCLUSION: In selected patients the presence of a liquefying ICH cavity may facilitate the resection of AVMs when performed in the subacute stage resulting in a good neurological outcome and high obliteration rate

    On the Importance of Countergradients for the Development of Retinotopy: Insights from a Generalised Gierer Model

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    During the development of the topographic map from vertebrate retina to superior colliculus (SC), EphA receptors are expressed in a gradient along the nasotemporal retinal axis. Their ligands, ephrin-As, are expressed in a gradient along the rostrocaudal axis of the SC. Countergradients of ephrin-As in the retina and EphAs in the SC are also expressed. Disruption of any of these gradients leads to mapping errors. Gierer's (1981) model, which uses well-matched pairs of gradients and countergradients to establish the mapping, can account for the formation of wild type maps, but not the double maps found in EphA knock-in experiments. I show that these maps can be explained by models, such as Gierer's (1983), which have gradients and no countergradients, together with a powerful compensatory mechanism that helps to distribute connections evenly over the target region. However, this type of model cannot explain mapping errors found when the countergradients are knocked out partially. I examine the relative importance of countergradients as against compensatory mechanisms by generalising Gierer's (1983) model so that the strength of compensation is adjustable. Either matching gradients and countergradients alone or poorly matching gradients and countergradients together with a strong compensatory mechanism are sufficient to establish an ordered mapping. With a weaker compensatory mechanism, gradients without countergradients lead to a poorer map, but the addition of countergradients improves the mapping. This model produces the double maps in simulated EphA knock-in experiments and a map consistent with the Math5 knock-out phenotype. Simulations of a set of phenotypes from the literature substantiate the finding that countergradients and compensation can be traded off against each other to give similar maps. I conclude that a successful model of retinotopy should contain countergradients and some form of compensation mechanism, but not in the strong form put forward by Gierer

    Two Earth-sized planets orbiting Kepler-20

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    Since the discovery of the first extrasolar giant planets around Sun-like stars, evolving observational capabilities have brought us closer to the detection of true Earth analogues. The size of an exoplanet can be determined when it periodically passes in front of (transits) its parent star, causing a decrease in starlight proportional to its radius. The smallest exoplanet hitherto discovered has a radius 1.42 times that of the Earth's radius (R Earth), and hence has 2.9 times its volume. Here we report the discovery of two planets, one Earth-sized (1.03R Earth) and the other smaller than the Earth (0.87R Earth), orbiting the star Kepler-20, which is already known to host three other, larger, transiting planets. The gravitational pull of the new planets on the parent star is too small to measure with current instrumentation. We apply a statistical method to show that the likelihood of the planetary interpretation of the transit signals is more than three orders of magnitude larger than that of the alternative hypothesis that the signals result from an eclipsing binary star. Theoretical considerations imply that these planets are rocky, with a composition of iron and silicate. The outer planet could have developed a thick water vapour atmosphere.Comment: Letter to Nature; Received 8 November; accepted 13 December 2011; Published online 20 December 201

    Acute presentation of a heterotopic pregnancy following spontaneous conception: a case report

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    Spontaneous heterotopic pregnancy is a rare clinical condition in which intrauterine and extra uterine pregnancies occur at the same time. It can be a life threatening condition and can be easily missed with the diagnosis being overlooked. We present the case of a 40 year old patient who was treated for a heterotopic pregnancy. She had a transvaginal ultrasound because of a previous ectopic pregnancy and an intrauterine gestational sac was seen with false reassurances. The patient presented acutely with a ruptured tubal pregnancy and this was managed laparoscopically. The ectopic pregnancy was not suspected at her initial presentation. A high index of suspicion is needed in women with risk factors for an ectopic pregnancy and in low risk women who have free fluid with or without an adnexal mass with an intrauterine gestation

    Resistance to autosomal dominant Alzheimer's disease in an APOE3 Christchurch homozygote: a case report.

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    We identified a PSEN1 (presenilin 1) mutation carrier from the world's largest autosomal dominant Alzheimer's disease kindred, who did not develop mild cognitive impairment until her seventies, three decades after the expected age of clinical onset. The individual had two copies of the APOE3 Christchurch (R136S) mutation, unusually high brain amyloid levels and limited tau and neurodegenerative measurements. Our findings have implications for the role of APOE in the pathogenesis, treatment and prevention of Alzheimer's disease
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