Sum-of-squares lower bounds for planted clique

Finding cliques in random graphs and the closely related "planted" clique variant, where a clique of size k is planted in a random G(n, 1/2) graph, have been the focus of substantial study in algorithm design. Despite much effort, the best known polynomial-time algorithms only solve the problem for k ~ sqrt(n). In this paper we study the complexity of the planted clique problem under algorithms from the Sum-of-squares hierarchy. We prove the first average case lower bound for this model: for almost all graphs in G(n,1/2), r rounds of the SOS hierarchy cannot find a planted k-clique unless k > n^{1/2r} (up to logarithmic factors). Thus, for any constant number of rounds planted cliques of size n^{o(1)} cannot be found by this powerful class of algorithms. This is shown via an integrability gap for the natural formulation of maximum clique problem on random graphs for SOS and Lasserre hierarchies, which in turn follow from degree lower bounds for the Positivestellensatz proof system. We follow the usual recipe for such proofs. First, we introduce a natural "dual certificate" (also known as a "vector-solution" or "pseudo-expectation") for the given system of polynomial equations representing the problem for every fixed input graph. Then we show that the matrix associated with this dual certificate is PSD (positive semi-definite) with high probability over the choice of the input graph.This requires the use of certain tools. One is the theory of association schemes, and in particular the eigenspaces and eigenvalues of the Johnson scheme. Another is a combinatorial method we develop to compute (via traces) norm bounds for certain random matrices whose entries are highly dependent; we hope this method will be useful elsewhere

Evidence for impurity-induced frustration in La2CuO4

Zero-field muon spin rotation and magnetization measurements were performed in La2Cu{1-x}MxO4, for 0<x< 0.12, where Cu2+ is replaced either by M=Zn2+ or by M=Mg2+ spinless impurity. It is shown that while the doping dependence of the sublattice magnetization (M(x)) is nearly the same for both compounds, the N\'eel temperature (T_N(x)) decreases unambiguously more rapidly in the Zn-doped compound. This difference, not taken into account within a simple dilution model, is associated with the frustration induced by the Zn2+ impurity onto the Cu2+ antiferromagnetic lattice. In fact, from T_N(x) and M(x) the spin stiffness is derived and found to be reduced by Zn doping more significantly than expected within a dilution model. The effect of the structural modifications induced by doping on the exchange coupling is also discussed.Comment: 4 pages, 4 figure

The impact of a hot spot policing program in Montevideo, Uruguay: an evaluation using a quasi-experimental difference-in-difference negative binomial approach

Hot spot policing has proven to be effective in reducing crime in cities in North America, Europe and Australasia, but to date, its application and evaluation in Latin American settings has been limited. PADO (Programa de Alta Dedicación Operativa) is a large-scale hot spot policing program implemented by the Uruguay Police in April 2016 in the city of Montevideo. Using an evaluation technique that compares the differential effect between areas where PADO was deployed and control areas, a 23 percent reduction in the rate at which robberies occurred was experienced in the PADO areas, with no significant displacement to neighboring areas, or other areas of the city during the study period. The study indicates that hot spot policing programs can be effective in reducing crime in Latin American urban environments and illustrates how targeted police interventions can be robustly evaluated when control areas are not established at the outset of an intervention

The Evolution of the EH4 Chondrite Indarch at High Pressure and Temperature: The First Experimental Results

Chondrite groups are characterized by variations in bulk composition and oxidation state, illustrating in part heterogeneity in the early solar nebula. Planetary accretion could be explained by at least two different scenarios: the homogeneous [1] and heterogeneous accretion models [2, 3]. In particular, for the formation of the Earth, some studies (e.g. [2, 3]) assume that one component is highly reduced material comparable to enstatite chondrites, devoid of volatile elements but containing all other elements in C1 abundance ratios. To derive constraints on the understanding of early differentiation processes, studies of the silicate phase relations and their interactions with metal, at relevant P-T-fO2, are required. Melting relations and equilibrium partitioning behaviour have been studied on peridotitic and chondritic starting compositions at pressures and temperatures corresponding to the transition zone and lower mantle [4, 5, 6]. However, enstatite chondrites, which are highly reduced primitive meteorites, have not yet been studied experimentally under such conditions. Thus, multianvil experiments have been performed at 20-25 GPa and 2000-2400 C on the EH4 chondrite Indarch

Dynamin-related protein 1 is required for normal mitochondrial bioenergetic and synaptic function in CA1 hippocampal neurons.

Disrupting particular mitochondrial fission and fusion proteins leads to the death of specific neuronal populations; however, the normal functions of mitochondrial fission in neurons are poorly understood, especially in vivo, which limits the understanding of mitochondrial changes in disease. Altered activity of the central mitochondrial fission protein dynamin-related protein 1 (Drp1) may contribute to the pathophysiology of several neurologic diseases. To study Drp1 in a neuronal population affected by Alzheimer's disease (AD), stroke, and seizure disorders, we postnatally deleted Drp1 from CA1 and other forebrain neurons in mice (CamKII-Cre, Drp1lox/lox (Drp1cKO)). Although most CA1 neurons survived for more than 1 year, their synaptic transmission was impaired, and Drp1cKO mice had impaired memory. In Drp1cKO cell bodies, we observed marked mitochondrial swelling but no change in the number of mitochondria in individual synaptic terminals. Using ATP FRET sensors, we found that cultured neurons lacking Drp1 (Drp1KO) could not maintain normal levels of mitochondrial-derived ATP when energy consumption was increased by neural activity. These deficits occurred specifically at the nerve terminal, but not the cell body, and were sufficient to impair synaptic vesicle cycling. Although Drp1KO increased the distance between axonal mitochondria, mitochondrial-derived ATP still decreased similarly in Drp1KO boutons with and without mitochondria. This indicates that mitochondrial-derived ATP is rapidly dispersed in Drp1KO axons, and that the deficits in axonal bioenergetics and function are not caused by regional energy gradients. Instead, loss of Drp1 compromises the intrinsic bioenergetic function of axonal mitochondria, thus revealing a mechanism by which disrupting mitochondrial dynamics can cause dysfunction of axons

3^3He Structure and Mechanisms of p3p^3He Backward Elastic Scattering

The mechanism of $p^3$He backward elastic scattering is studied. It is found that the triangle diagrams with the subprocesses $pd\to ^3$He$\pi^0$, $pd^*\to ^3$He$\pi^0$ and $p(pp)\to^3$He$\pi^+$, where $d^*$ and $pp$ denote the singlet deuteron and diproton pair in the $^1S_0$ state, respectively, dominate in the cross section at 0.3-0.8 GeV, and their contribution is comparable with that for a sequential transfer of a $np$ pair at 1-1.5 GeV. The contribution of the $d^*+pp$, estimated on the basis of the spectator mechanism of the $p(NN)\to ^3$He$\pi$ reaction, increases the $p^3$He$\to ^3$He$p$ cross section by one order of magnitude as compared to the contribution of the deuteron alone. Effects of the initial and final states interaction are taken into account.Comment: 17 pages, Latex, 4 postscript figures, expanded version, accepted by Physical Review

An evaluation of a hot spot policing programme in four Argentinian cities

In 2017, hot spot policing interventions were implemented in four cities in Argentina: La Plata, Morón, Santa Fe and Tres de Febrero. Each intervention was similarly designed, organized and implemented. Results differed between cities. La Plata experienced the largest decreases, including a significant 31% decrease in robbery (while controlling for geographic displacement), whereas in other cities, a mix of non-significant decreases and increases in robbery and theft were observed. No displacement was observed to assaults or vehicle crime. The differences in impact between cities were likely to be associated with differences in the project management of each intervention

Rapid Liquid Chromatography-Tandem Mass Spectrometry Analysis of Two Urinary Oxidative Stress Biomarkers: 8-oxodG and 8-isoprostane.

Human biomonitoring of oxidative stress relies on urinary effect biomarkers such as 8-oxo-7,8-dihydro-2'-deoxyguanosine (8-oxodG), and 8-iso-prostaglandin F2α (8-isoprostane); however, their levels reported for similar populations are inconsistent in the scientific literature. One of the reasons is the multitude of analytical methods with varying degrees of selectivity used to quantify these biomarkers. Single-analyte methods are often used, requiring multiple injections that increase both time and cost. We developed a rapid ultra-high-performance liquid chromatography-tandem mass spectrometry (UPLC-MS/MS) method to quantify both urinary biomarkers simultaneously. A reversed-phase column using a gradient consisting of 0.1% acetic acid in water and 0.1% acetic acid in methanol/acetonitrile (70:30) was used for separation. The MS detection was by positive (8-oxodG) and negative (8-isoprostane) ion-mode by multiple reaction monitoring. Very low limit of detection (&lt;20 pg/mL), excellent linearity (R2 &gt; 0.999), accuracy (near 100%), and precision (CV &lt; 10%) both for intra-day and inter-day experiments were achieved, as well as high recovery rates (&gt;91%). Matrix effects were observed but were compensated by using internal standards. Our newly developed method is applicable for biomonitoring studies as well as large epidemiological studies investigating the effect of oxidative damage, as it requires only minimal clean up using solid phase extraction

Non-invasive diagnostic biomarkers for estimating the onset time of permanent cerebral ischemia.

The treatments for ischemic stroke can only be administered in a narrow time-window. However, the ischemia onset time is unknown in ~30% of stroke patients (wake-up strokes). The objective of this study was to determine whether MR spectra of ischemic brains might allow the precise estimation of cerebral ischemia onset time. We modeled ischemic stroke in male ICR-CD1 mice using a permanent middle cerebral artery filament occlusion model with laser Doppler control of the regional cerebral blood flow. Mice were then subjected to repeated MRS measurements of ipsilateral striatum at 14.1 T. A striking initial increase in γ-aminobutyric acid (GABA) and no increase in glutamine were observed. A steady decline was observed for taurine (Tau), N-acetyl-aspartate (NAA) and similarly for the sum of NAA+Tau+glutamate that mimicked an exponential function. The estimation of the time of onset of permanent ischemia within 6 hours in a blinded experiment with mice showed an accuracy of 33±10 minutes. A plot of GABA, Tau, and neuronal marker concentrations against the ratio of acetate/NAA allowed precise separation of mice whose ischemia onset lay within arbitrarily chosen time-windows. We conclude that (1)H-MRS has the potential to detect the clinically relevant time of onset of ischemic stroke