A Storm of Feasibility Pumps for Nonconvex MINLP

One of the foremost difficulties in solving Mixed Integer Nonlinear Programs, either with exact or heuristic methods, is to find a feasible point. We address this issue with a new feasibility pump algorithm tailored for nonconvex Mixed Integer Nonlinear Programs. Feasibility pumps are algorithms that iterate between solving a continuous relaxation and a mixed-integer relaxation of the original problems. Such approaches currently exist in the literature for Mixed-Integer Linear Programs and convex Mixed-Integer Nonlinear Programs: both cases exhibit the distinctive property that the continuous relaxation can be solved in polynomial time. In nonconvex Mixed Integer Nonlinear Programming such a property does not hold, and therefore special care has to be exercised in order to allow feasibility pumps algorithms to rely only on local optima of the continuous relaxation. Based on a new, high level view of feasibility pumps algorithms as a special case of the well-known successive projection method, we show that many possible different variants of the approach can be developed, depending on how several different (orthogonal) implementation choices are taken. A remarkable twist of feasibility pumps algorithms is that, unlike most previous successive projection methods from the literature, projection is "naturally" taken in two different norms in the two different subproblems. To cope with this issue while retaining the local convergence properties of standard successive projection methods we propose the introduction of appropriate norm constraints in the subproblems; these actually seem to significantly improve the practical performances of the approach. We present extensive computational results on the MINLPLib, showing the effectiveness and efficiency of our algorithm

Minimizing power consumption in virtualized cellular networks

Cellular network nodes should be dynamically switched on/off based on the load requirements of the network, to save power and minimize inter-cell interference. This should be done keeping into account global interference effects, which requires a centralized approach. In this paper, we present an architecture, realized within the Flex5GWare EU project, that manages a large-scale cellular network, switching on and off nodes based on load requirements and context data. We describe the architectural framework and the optimization model that is used to decide the activity state of the nodes. We present simulation results showing that the framework adapts to the minimum power level based on the cell loads

Practical feasibility, scalability and effectiveness of coordinated scheduling algorithms in cellular networks towards 5G

Coordinated Scheduling (CS) is used to mitigate inter-cell interference in present (4G) and future (5G) cellular networks. We show that coordination of a cluster of nodes can be formulated as an optimization problem, i.e., placing the Resource Blocks (RB) in each node’s subframe with the least possible over-lapping with neighboring nodes. We provide a clever formulation, which allows optimal solutions to be computed in clusters of ten nodes, and algorithms that compute good suboptimal solutions for clusters of tens of nodes, fast enough for a network to respond to traffic changes in real time. This allows us to assess the relationship between the scale at which CS is performed and its benefits in terms of network energy efficiency and cell-edge user rate. Our results, obtained using realistic power, radiation and Signal-to-Interference-and-Noise-Ratio (SINR) models, show that optimal CS allows a significant protection of cell-edge users. Moreover, this goes hand-in-hand with a reduction in the num-ber of allocated RBs, which in turn allows an operator to reduce its energy consumption. Both benefits actually increase with the size of the clusters. The evaluation is carried out in both a 4G and a foreseen 5G setting, using different power models, system bandwidths and SINR-to-datarate mappings

Design Considerations for Tumor-Targeted Nanoparticles

Inorganic/organic hybrid nanoparticles are potentially useful in biomedicine, but to avoid non-specific background fluorescence and long-term toxicity, they need to be cleared from the body within a reasonable timescale1. Previously, we have shown that rigid spherical nanoparticles such as quantum dots can be cleared by the kidneys if they have a hydrodynamic diameter of approximately 5.5 nm and a zwitterionic surface charge2. Here, we show that quantum dots functionalized with high-affinity small-molecule ligands that target tumours can also be cleared by the kidneys if their hydrodynamic diameter is less than this value, which sets an upper limit of 5–10 ligands per quantum dot for renal clearance. Animal models of prostate cancer and melanoma show receptor-specific imaging and renal clearance within 4 h post-injection. This study suggests a set of design rules for the clinical translation of targeted nanoparticles that can be eliminated through the kidneys.National Science Foundation (U.S.) (NSF-0070319)National Institutes of Health (U.S.) (NIH GM68762)National Institutes of Health (U.S.) (NIH grant no. R33-EB-000673)National Institutes of Health (U.S.) ( NIH grant no. R01-CA-115296)National Institutes of Health (U.S.) (MIT-Harvard NanoMedical Consortium (1U54-CA119349, a Center of Cancer Nanotechnology Excellence))Bank of AmericaMedical Foundation, inc. (Charles A. King Trust Postdoctoral Research Fellowship Program)cance

Intraoperative identification of esophageal sentinel lymph nodes with near-infrared fluorescence imaging

ObjectiveIn esophageal cancer, selective removal of involved lymph nodes could improve survival and limit complications from extended lymphadenectomy. Mapping with vital blue dyes or technetium Tc-99m often fails to identify intrathoracic sentinel lymph nodes. Our purpose was to develop an intraoperative method for identifying sentinel lymph nodes of the esophagus with high-sensitivity near-infrared fluorescence imaging.MethodsSix Yorkshire pigs underwent thoracotomy and received submucosal, esophageal injection of quantum dots, a novel near-infrared fluorescent lymph tracer designed for retention in sentinel lymph nodes. Six additional pigs underwent thoracotomy and received submucosal esophageal injection of CW800 conjugated to human serum albumin, another novel lymph tracer designed for uptake into distant lymph nodes. Finally, 6 pigs received submucosal injection of the fluorophore-conjugated albumin with an endoscopic needle through an esophagascope. These lymph tracers fluoresce in the near-infrared, permitting visualization of migration to sentinel lymph nodes with a custom intraoperative imaging system.ResultsInjection of the near-infrared fluorescent lymph tracers into the esophagus revealed communicating lymph nodes within 5 minutes of injection. In all 6 pigs that received quantum dot injection, only a single sentinel lymph node was identified. Among pigs that received fluorophore-conjugated albumin injection, in 5 of 12 a single sentinel lymph node was revealed, but in 7 of 12 two sentinel lymph nodes were identified. There was no dominant pattern in the appearance of the sentinel lymph nodes either cranial or caudal to the injection site.ConclusionNear-infrared fluorescence imaging of sentinel lymph nodes is a novel and reliable intraoperative technique with the power to assist with identification and resection of esophageal sentinel lymph nodes

Near-Infrared Fluorescence Imaging of Liver Metastases in Rats using Indocyanine Green

BackgroundNear-infrared (NIR) fluorescence imaging using indocyanine green (ICG) is a promising technique to obtain real-time assessment of the extent and number of colorectal liver metastases during surgery. The current study aims to optimize dosage and timing of ICG administration.Materials and MethodsLiver tumors were induced in 18 male WAG/Rij rats by subcapsular inoculation of CC531 rat colorectal cancer cells into three distinct liver lobes. Rats were divided in two groups: imaging after 24 and 48 h or 72 and 96 h after intravenous ICG administration. In each time group, rats were allocated to three dose groups: 0.04, 0.08, or 0.16 mg ICG. Intraoperative imaging and ex vivo measurements were performed using the Mini-FLARE imaging system and confirmed by fluorescence microscopy. Fluorescence intensity was quantified using the Mini-FLARE software and the difference between tumor signal and liver signal (tumor-to-liver ratio; TLR) was calculated.ResultsIn all 18 rats, all colorectal liver metastases (n = 34), some as small as 1.2 mm, were identified using ICG and the Mini-FLARE imaging system. Average tumor-to-liver ratio (TLR) over all groups was 3.0 ± 1.2. TLR was significantly higher in the 72 h time group compared with other time points. ICG dose did not significantly influence TLR, but a trend was found favoring the 0.08 mg dose group. Fluorescence microscopy demonstrated a clear fluorescent rim around the tumor.ConclusionsThis study demonstrates that colorectal cancer liver metastases can be clearly identified during surgery using ICG and the Mini-FLARE imaging system, with optimal timing of 72 h post-injection and an optimal dose of 0.08 mg (0.25 mg/kg) ICG. NIR fluorescence imaging has the potential to improve intraoperative detection of micrometastases and, thus, the completeness of resection

Nonlinear Integer Programming

Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject to integrality requirements for the variables. This chapter is dedicated to this topic. The primary goal is a study of a simple version of general nonlinear integer problems, where all constraints are still linear. Our focus is on the computational complexity of the problem, which varies significantly with the type of nonlinear objective function in combination with the underlying combinatorial structure. Numerous boundary cases of complexity emerge, which sometimes surprisingly lead even to polynomial time algorithms. We also cover recent successful approaches for more general classes of problems. Though no positive theoretical efficiency results are available, nor are they likely to ever be available, these seem to be the currently most successful and interesting approaches for solving practical problems. It is our belief that the study of algorithms motivated by theoretical considerations and those motivated by our desire to solve practical instances should and do inform one another. So it is with this viewpoint that we present the subject, and it is in this direction that we hope to spark further research.Comment: 57 pages. To appear in: M. J\"unger, T. Liebling, D. Naddef, G. Nemhauser, W. Pulleyblank, G. Reinelt, G. Rinaldi, and L. Wolsey (eds.), 50 Years of Integer Programming 1958--2008: The Early Years and State-of-the-Art Surveys, Springer-Verlag, 2009, ISBN 354068274

The relationship between redox enzyme activity and electrochemical potential—cellular and mechanistic implications from protein film electrochemistry

In protein film electrochemistry a redox protein of interest is studied as an electroactive film adsorbed on an electrode surface. For redox enzymes this configuration allows quantification of the relationship between catalytic activity and electrochemical potential. Considered as a function of enzyme environment, i.e., pH, substrate concentration etc., the activity–potential relationship provides a fingerprint of activity unique to a given enzyme. Here we consider the nature of the activity–potential relationship in terms of both its cellular impact and its origin in the structure and catalytic mechanism of the enzyme. We propose that the activity–potential relationship of a redox enzyme is tuned to facilitate cellular function and highlight opportunities to test this hypothesis through computational, structural, biochemical and cellular studies

Quantum dots in axillary lymph node mapping: Biodistribution study in healthy mice

<p>Abstract</p> <p>Background</p> <p>Breast cancer is the first cause of cancer death among women and its incidence doubled in the last two decades. Several approaches for the treatment of these cancers have been developed. The axillary lymph node dissection (ALND) leads to numerous morbidity complications and is now advantageously replaced by the dissection and the biopsy of the sentinel lymph node. Although this approach has strong advantages, it has its own limitations which are manipulation of radioactive products and possible anaphylactic reactions to the dye. As recently proposed, these limitations could in principle be by-passed if semiconductor nanoparticles (quantum dots or QDs) were used as fluorescent contrast agents for the <it>in vivo </it>imaging of SLN. QDs are fluorescent nanoparticles with unique optical properties like strong resistance to photobleaching, size dependent emission wavelength, large molar extinction coefficient, and good quantum yield.</p> <p>Methods</p> <p>CdSe/ZnS core/shell QDs emitting around 655 nm were used in our studies. 20 μL of 1 μM (20 pmol) QDs solution were injected subcutaneously in the anterior paw of healthy nude mice and the axillary lymph node (ALN) was identified visually after injection of a blue dye. <it>In vivo </it>fluorescence spectroscopy was performed on ALN before the mice were sacrificed at 5, 15, 30, 60 min and 24 h after QDs injection. ALN and all other organs were removed, cryosectioned and observed in fluorescence microscopy. The organs were then chemically made soluble to extract QDs. Plasmatic, urinary and fecal fluorescence levels were measured.</p> <p>Results</p> <p>QDs were detected in ALN as soon as 5 min and up to 24 h after the injection. The maximum amount of QDs in the ALN was detected 60 min after the injection and corresponds to 2.42% of the injected dose. Most of the injected QDs remained at the injection site. No QDs were detected in other tissues, plasma, urine and feces.</p> <p>Conclusion</p> <p>Effective and rapid (few minutes) detection of sentinel lymph node using fluorescent imaging of quantum dots was demonstrated. This work was done using very low doses of injected QDs and the detection was done using a minimally invasive method.</p