Feasibility of approximating spatial and local entanglement in long-range interacting systems using the extended Hubbard model

We investigate the extended Hubbard model as an approximation to the local and spatial entanglement of a one-dimensional chain of nanostructures where the particles interact via a long range interaction represented by a `soft' Coulomb potential. In the process we design a protocol to calculate the particle-particle spatial entanglement for the Hubbard model and show that, in striking contrast with the loss of spatial degrees of freedom, the predictions are reasonably accurate. We also compare results for the local entanglement with previous results found using a contact interaction (PRA, 81 (2010) 052321) and show that while the extended Hubbard model recovers a better agreement with the entanglement of a long-range interacting system, there remain realistic parameter regions where it fails to predict the quantitative and qualitative behaviour of the entanglement in the nanostructure system.Comment: 6 pages, 5 figures and 1 table; added results with correlated hopping term; accepted by EP

Hubbard model as an approximation to the entanglement in nanostructures

We investigate how well the one-dimensional Hubbard model describes the entanglement of particles trapped in a string of quantum wells. We calculate the average single-site entanglement for two particles interacting via a contact interaction and consider the effect of varying the interaction strength and the interwell distance. We compare the results with the ones obtained within the one-dimensional Hubbard model with on-site interaction. We suggest an upper bound for the average single-site entanglement for two electrons in M wells and discuss analytical limits for very large repulsive and attractive interactions. We investigate how the interplay between interaction and potential shape in the quantum-well system dictates the position and size of the entanglement maxima and the agreement with the theoretical limits. Finally, we calculate the spatial entanglement for the quantum-well system and compare it to its average single-site entanglement

Spin-1/2 geometric phase driven by decohering quantum fields

We calculate the geometric phase of a spin-1/2 system driven by a one and two mode quantum field subject to decoherence. Using the quantum jump approach, we show that the corrections to the phase in the no-jump trajectory are different when considering an adiabatic and non-adiabatic evolution. We discuss the implications of our results from both the fundamental as well as quantum computational perspective.Comment: 4 page

From Clinical Presentation to the Outcome: the Natural History of PML in a Portuguese Population of HIV Infected Patients

Background Progressive multifocal leukoencephalopathy (PML) is a demyelinating disease of the central nervous system, associated with immunosuppression states. As there are only some non-published documents concerning PML in HIV infected patients in Portugal, we pretend to characterize natural history of PML infection in a population of HIV patients. Methods We retrospectively reviewed, from 1992 to 2009, PML cases in a population of 724 HIV infected patients followed in our institution. Clinical, biological, imagery features and outcomes were characterized. Results Twenty-five (3.45%) patients were identified as having PML. The mean time between HIV and PML diagnosis was 20.4 months. PML was the presentation of HIV infection in 40% of the patients, and 92% had CD4 T cell count lower than 200/mm3. Paresis was the most common clinical presentation. No specific characteristics were found in cerebrospinal fluid and JCV DNA was positive in 3 of 7 patients. MRI revealed characteristic findings. Combined antiretroviral therapy was started or changed in 96% of the patients. Neurological condition got worse in 12 patients. From the 14 deaths, 5 were directly attributed to PML progression. Follow-up was lost in 8 patients. Conclusions PML was the presentation of HIV infection in more than 1/3 of patients, frequently associated with advanced immunocompromise. MRI sensitivity to PML is high, and JCV DNA determination in CSF was not revealed to be sensible. PML diagnosis should be taken into account in HIV patients presenting any neurological symptoms, and HIV infection should be suspected when radiological findings suggest PML lesions even in previously healthy individuals

Liver MRI: From basic protocol to advanced techniques

Liver MR is a well-established modality with multiparametric capabilities. However, to take advantage of its full capacity, it is mandatory to master the technique and optimize imaging protocols, apply advanced imaging concepts and understand the use of different contrast media. Physiologic artefacts although inherent to upper abdominal studies can be minimized using triggering techniques and new strategies for motion control. For standardization, the liver MR protocol should include motion-resistant T2-w sequences, in-op phase GRE T1 and T2-w fast spin echo sequences with fat suppression. Diffusion-weighted imaging (DWI) is mandatory, especially for detection of sub-centimetre metastases. Contrast-enhanced MR is the cornerstone of liver MR, especially for lesion characterization. Although extracellular agents are the most extensively used contrast agents, hepatobiliary contrast media can provide an extra-layer of functional diagnostic information adding to the diagnostic value of liver MR. The use of high field strength (3T) increases SNR but is more challenging especially concerning artefact control. Quantitative MR belongs to the new and evolving field of radiomics where the use of emerging biomarkers such as perfusion or DWI can derive new information regarding disease detection, prognostication and evaluation of tumour response. This information can overcome some of the limitations of current tests, especially when using vascular disruptive agents for oncologic treatment assessment. MR is, today, a robust, mature, multiparametric imaging modality where clinical applications have greatly expanded from morphology to advanced imaging. This new concept should be acknowledged by all those involved in producing high quality, high-end liver MR studies.info:eu-repo/semantics/publishedVersio

Optimization on manifolds: A symplectic approach

There has been great interest in using tools from dynamical systems and numerical analysis of differential equations to understand and construct new optimization methods. In particular, recently a new paradigm has emerged that applies ideas from mechanics and geometric integration to obtain accelerated optimization methods on Euclidean spaces. This has important consequences given that accelerated methods are the workhorses behind many machine learning applications. In this paper we build upon these advances and propose a framework for dissipative and constrained Hamiltonian systems that is suitable for solving optimization problems on arbitrary smooth manifolds. Importantly, this allows us to leverage the well-established theory of symplectic integration to derive "rate-matching" dissipative integrators. This brings a new perspective to optimization on manifolds whereby convergence guarantees follow by construction from classical arguments in symplectic geometry and backward error analysis. Moreover, we construct two dissipative generalizations of leapfrog that are straightforward to implement: one for Lie groups and homogeneous spaces, that relies on the tractable geodesic flow or a retraction thereof, and the other for constrained submanifolds that is based on a dissipative generalization of the famous RATTLE integrator

Melatonin bioengineered: A New Possible Strategy for Treatment of Breast Cancer

Breast cancer is an important public health problem, with an estimated 3.2 million new cases by the year 2050. Diet plays a key role in the etiology of breast cancer and breastfeeding is associated with a lower incidence of breast cancer. On the other hand, the improvement of the therapeutic properties of bioactive compounds through their incorporation into microcarriers is an important strategy in obtaining new therapies, since cyclical changes in concentration are eliminated; there is biological availability of the compound as well as the reduction in toxicity, number dose and suppression of adverse reactions. Studies using hormones such as melatonin extracted from human milk adsorbed onto polyethylene glycol (PEG) microspheres showed that the controlled release of this compound was able to reduce viability and induce apoptosis in MCF-7 cell lines. Colostrum differs from most of the secretions because it contains viable leukocytes during the first days of lactation with a quantity and activity comparable to blood leukocytes, and has several defense components such as antibodies and hormones, such as melatonin (MLT). This review details the influence of the soluble and cellular components present in human colostrum, such as the MLT hormone, as the modified release systems influence the action of MLT and the possible mechanisms involved that contribute to the hypothesis of reduction of breast cancer in women who breastfed