Smoothed Analysis of the Minimum-Mean Cycle Canceling Algorithm and the Network Simplex Algorithm

The minimum-cost flow (MCF) problem is a fundamental optimization problem with many applications and seems to be well understood. Over the last half century many algorithms have been developed to solve the MCF problem and these algorithms have varying worst-case bounds on their running time. However, these worst-case bounds are not always a good indication of the algorithms' performance in practice. The Network Simplex (NS) algorithm needs an exponential number of iterations for some instances, but it is considered the best algorithm in practice and performs best in experimental studies. On the other hand, the Minimum-Mean Cycle Canceling (MMCC) algorithm is strongly polynomial, but performs badly in experimental studies. To explain these differences in performance in practice we apply the framework of smoothed analysis. We show an upper bound of $O(mn^2\log(n)\log(\phi))$ for the number of iterations of the MMCC algorithm. Here $n$ is the number of nodes, $m$ is the number of edges, and $\phi$ is a parameter limiting the degree to which the edge costs are perturbed. We also show a lower bound of $\Omega(m\log(\phi))$ for the number of iterations of the MMCC algorithm, which can be strengthened to $\Omega(mn)$ when $\phi=\Theta(n^2)$. For the number of iterations of the NS algorithm we show a smoothed lower bound of $\Omega(m \cdot \min \{ n, \phi \} \cdot \phi)$.Comment: Extended abstract to appear in the proceedings of COCOON 201

Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator

The reliable detection of single quantum particles has revolutionized the field of quantum optics and quantum information processing. For several years, researchers have aspired to extend such detection possibilities to larger scale strongly correlated quantum systems, in order to record in-situ images of a quantum fluid in which each underlying quantum particle is detected. Here we report on fluorescence imaging of strongly interacting bosonic Mott insulators in an optical lattice with single-atom and single-site resolution. From our images, we fully reconstruct the atom distribution on the lattice and identify individual excitations with high fidelity. A comparison of the radial density and variance distributions with theory provides a precise in-situ temperature and entropy measurement from single images. We observe Mott-insulating plateaus with near zero entropy and clearly resolve the high entropy rings separating them although their width is of the order of only a single lattice site. Furthermore, we show how a Mott insulator melts for increasing temperatures due to a proliferation of local defects. Our experiments open a new avenue for the manipulation and analysis of strongly interacting quantum gases on a lattice, as well as for quantum information processing with ultracold atoms. Using the high spatial resolution, it is now possible to directly address individual lattice sites. One could, e.g., introduce local perturbations or access regions of high entropy, a crucial requirement for the implementation of novel cooling schemes for atoms on a lattice

Interaction and filling induced quantum phases of dual Mott insulators of bosons and fermions

Many-body effects are at the very heart of diverse phenomena found in condensed-matter physics. One striking example is the Mott insulator phase where conductivity is suppressed as a result of a strong repulsive interaction. Advances in cold atom physics have led to the realization of the Mott insulating phases of atoms in an optical lattice, mimicking the corresponding condensed matter systems. Here, we explore an exotic strongly-correlated system of Interacting Dual Mott Insulators of bosons and fermions. We reveal that an inter-species interaction between bosons and fermions drastically modifies each Mott insulator, causing effects that include melting, generation of composite particles, an anti-correlated phase, and complete phase-separation. Comparisons between the experimental results and numerical simulations indicate intrinsic adiabatic heating and cooling for the attractively and repulsively interacting dual Mott Insulators, respectively

Identification of Copy Number Variants Defining Genomic Differences among Major Human Groups

BACKGROUND:Understanding the genetic contribution to phenotype variation of human groups is necessary to elucidate differences in disease predisposition and response to pharmaceutical treatments in different human populations. METHODOLOGY/PRINCIPAL FINDINGS:We have investigated the genome-wide profile of structural variation on pooled samples from the three populations studied in the HapMap project by comparative genome hybridization (CGH) in different array platforms. We have identified and experimentally validated 33 genomic loci that show significant copy number differences from one population to the other. Interestingly, we found an enrichment of genes related to environment adaptation (immune response, lipid metabolism and extracellular space) within these regions and the study of expression data revealed that more than half of the copy number variants (CNVs) translate into gene-expression differences among populations, suggesting that they could have functional consequences. In addition, the identification of single nucleotide polymorphisms (SNPs) that are in linkage disequilibrium with the copy number alleles allowed us to detect evidences of population differentiation and recent selection at the nucleotide variation level. CONCLUSIONS:Overall, our results provide a comprehensive view of relevant copy number changes that might play a role in phenotypic differences among major human populations, and generate a list of interesting candidates for future studies

Brain energy rescue:an emerging therapeutic concept for neurodegenerative disorders of ageing

The brain requires a continuous supply of energy in the form of ATP, most of which is produced from glucose by oxidative phosphorylation in mitochondria, complemented by aerobic glycolysis in the cytoplasm. When glucose levels are limited, ketone bodies generated in the liver and lactate derived from exercising skeletal muscle can also become important energy substrates for the brain. In neurodegenerative disorders of ageing, brain glucose metabolism deteriorates in a progressive, region-specific and disease-specific manner — a problem that is best characterized in Alzheimer disease, where it begins presymptomatically. This Review discusses the status and prospects of therapeutic strategies for countering neurodegenerative disorders of ageing by improving, preserving or rescuing brain energetics. The approaches described include restoring oxidative phosphorylation and glycolysis, increasing insulin sensitivity, correcting mitochondrial dysfunction, ketone-based interventions, acting via hormones that modulate cerebral energetics, RNA therapeutics and complementary multimodal lifestyle changes

Direct vasoconstriction evoked by A1-adenosine receptor stimulation in the cutaneous microcirculation.

To determine whether the vasoconstriction evoked by A1-adenosine receptor stimulation in the skin circulation caused the release of other substances or whether A1 stimulation modulated the vasoconstriction evoked by other compounds, a potent A1-selective, synthetic agonist, cyclohexyladenosine (CHA), was topically applied simultaneously with several different vasoconstrictor agonists or antagonists. CHA was chosen instead of adenosine because the parent compound is metabolized quickly and also does not discriminate between A1 or A2 receptors. Blood flow was calculated from measurements of arteriolar diameter (40–60 μm) and red blood cell velocity using intravital videomicroscopy. Responses were recorded only in a steady state. The dose-related vasoconstriction evoked by CHA (ED50, 2.07±0.80 nM; half-minimal response, 93±1%) was not attenuated by antagonists to norepinephrine (phentolamine [11 μM] or prazosin [10 μM]), serotonin (methysergide [11 μM]), angiotensin II (saralasin [0.11 μM]), thromboxane (SK&F 88046 [13 μM]), or leukotrienes (SK&F 102922 [2.1 μM]). The vasoconstriction evoked by 2 nM CHA was attenuated by a subthreshold concentration (1 nM) of norepinephrine, whereas the vasoconstriction evoked by 0.1–1 μM norepinephrine was attenuated by a threshold concentration (1 nM) of CHA. Higher concentrations (10–100 nM) of CHA had no additional inhibitory effect. In contrast, CHA had no effect on the vasoconstrictions evoked by angiotensin II (10 nM or 1 μM) or serotonin (100 or 500 nM). Therefore, it is unlikely that A1-receptor stimulation causes the release of norepinephrine, serotonin, angiotensin, thromboxane, or leukotrienes in the skin microcirculation. Because norepinephrine attenuated the vasoconstriction evoked by CHA while CHA attenuated that evoked by norepinephrine, there appears to be a negative interaction between α-adrenergic and A1-adenosinergic receptors