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

Phonon and crystal field excitations in geometrically frustrated rare earth titanates

The phonon and crystal field excitations in several rare earth titanate pyrochlores are investigated. Magnetic measurements on single crystals of Gd2Ti2O7, Tb2Ti2O7, Dy2Ti2O7 and Ho2Ti2O7 are used for characterization, while Raman spectroscopy and terahertz time domain spectroscopy are employed to probe the excitations of the materials. The lattice excitations are found to be analogous across the compounds over the whole temperature range investigated (295-4 K). The resulting full phononic characterization of the R2Ti2O7 pyrochlore structure is then used to identify crystal field excitations observed in the materials. Several crystal field excitations have been observed in Tb2Ti2O7 in Raman spectroscopy for the first time, among which all of the previously reported excitations. The presence of additional crystal field excitations, however, suggests the presence of two inequivalent Tb3+ sites in the low temperature structure. Furthermore, the crystal field level at approximately 13 cm-1 is found to be both Raman and dipole active, indicating broken inversion symmetry in the system and thus undermining its current symmetry interpretation. In addition, evidence is found for a significant crystal field-phonon coupling in Tb2Ti2O7. These findings call for a careful reassessment of the low temperature structure of Tb2Ti2O7, which may serve to improve its theoretical understanding.Comment: 13 pages, 7 figure

Observation of the algebraic localization-delocalization transition in a 1D disordered potential with a bias force

In a one-dimensional (1D) disordered potential, quantum interferences leading to Anderson lo-calization are ubiquitous, such that all wave-functions are exponentially localized. Moreover, no phase transition toward delocalization is expected in 1D. This behavior is strongly modified in the presence of a bias force. We experimentally study this case, launching a non-interacting 39 K Bose-Einstein condensate in a 1D disordered potential induced by a far-off-resonance laser speckle, while controlling a bias force. In agreement with theoretical predictions, we observe a transition between algebraic localization and delocalization as a function of our control parameter that is the relative strength of the disorder against the bias force. We also demonstrate that the initial velocity of the wave-packet only plays a role through an effective disorder strength due to the correlation of the disorder. Adding a bias force is a quite natural way to probe the transport properties of quantum systems, a subject of broad interest that can be in particular addressed with atomic quantum gases thanks to their high degree of control and versatility [1]. For example, Bloch oscillations has been measured through the addition of a constant force to atoms in periodic potential induced by an optical lattice [2]. A force applied to a harmonic trap is equivalent to a trap displacement. The response to such a displacement permits to reveal the fluid or insulating behavior of atomic systems. In 1D interacting Bose gases, the pinning transition by an optical lattice [3] or the insulating transition in quasi-disordered optical lattice [4, 5] have been studied in this manner. More recently, transport in quantum gases is also studied in junction-type setup more analogous to condensed-matter systems: two reservoirs with different chemical potentials are connected through a constriction. For example, in a gas of fermions, the quantization of conductance through a quantum point contact [6] and the superfluid to normal transition in a disordered thin film have been observed [7]. In our work, we focus on the transport of non-interacting particles in disordered media. Without a bias force, quantum interferences between multiple paths lead to Anderson localization [8] whose signature is an exponential decay in space of single particle wave-function [9]. This phenomenon is ubiquitous in wave/quantum physics and it has been observed in many physical contexts [10] including condensed-matter [11] and ultra-cold atoms [12-14]. One-dimensional truly disordered systems are always localized [15], contrary to the 3D case where a phase transition between localized and extended single particle wave-functions takes place as a function of the disorder strength [16-18]. The localization properties of 1D disordered systems are modified in the presence of a bias force. Theoretical studies predict a transition from algebraic localization to delocalization as a function of a single control non-dimensional parameter α which is the ratio of the force to the disorder strength [19, 20]. Physically, α is the relative energy gain ∆E/E of a particle of energy E when moving over a localization length. Interestingly, in a 1D white noise disorder, this quantity is independent of E as the localization length is proportional to E. If α is small, the force does not considerably change the localization behavior of the particle while for large α its dynamics is severely affected leading to delocalization. This localization-delocalization transition is predicted in the infinite time limit for white noise disorder [20]. In a correlated disorder, as the one produced from a far-off-resonance laser speckle [21], the situation is more complicated. Speckles have no Fourier component beyond a spatial frequency 2k c. As a consequence, back-scattering and localization are not expected in the framework of Born approximation for atoms with wavevectors k > k c [12, 22]. Since localized wave-functions always have a small fraction at long distance corresponding to large energies and momenta in the presence of a bias force, we thus expect correlation-induced delocalization at infinite time. However, signatures of the algebraic localization-delocalization transition are predicted to be observable at transient times [20]. In this paper, we report on the observation of the algebraic localization-delocalization transition with cold-atoms propagating in a one dimensional disordered potential in the presence of a controlled bias force. We experimentally show that the non-dimensional parameter α is the only relevant parameter to describe the transition. We notice that the initial velocity of the quantum wave packet only plays a role through the correlation of the disordered potential, showing that the transition is in-trinsically energy independent. In the localized regime, we demonstrate an algebraic decay of the density and measure the corresponding decay exponent as a function of α. At large disorder strength, a saturation of the exp

On the Design of Sidelink for Cellular V2X: A Literature Review and Outlook for Future

Connected and fully automated vehicles are expected to revolutionize our mobility in the near future on a global scale, by significantly improving road safety, traffic efficiency, and traveling experience. Enhanced vehicular applications, such as cooperative sensing and maneuvering or vehicle platooning, heavily rely on direct connectivity among vehicles, which is enabled by sidelink communications. In order to set the ground for the core contribution of this paper, we first analyze the main streams of the cellular-vehicle-to-everything (C-V2X) technology evolution within the Third Generation Partnership Project (3GPP), with focus on the sidelink air interface. Then, we provide a comprehensive survey of the related literature, which is classified and critically dissected, considering both the Long-Term Evolution-based solutions and the 5G New Radio-based latest advancements that promise substantial improvements in terms of latency and reliability. The wide literature review is used as a basis to finally identify further challenges and perspectives, which may shape the C-V2X sidelink developments in the next-generation vehicles beyond 5G

Parental occupational exposure to pesticides and risk of childhood cancer in Switzerland: a census-based cohort study.

Pesticide exposure is a suspected risk factor for childhood cancer. We investigated the risk of developing childhood cancer in relation to parental occupational exposure to pesticides in Switzerland for the period 1990-2015. From a nationwide census-based cohort study in Switzerland, we included children aged < 16 years at national censuses of 1990 and 2000 and followed them until 2015. We extracted parental occupations reported at the census closest to the birth year of the child and estimated exposure to pesticides using a job exposure matrix. Cox proportional hazards models, adjusted for potential confounders, were fitted for the following outcomes: any cancer, leukaemia, central nervous system tumours (CNST), lymphoma, non-CNS solid tumours. Analyses of maternal (paternal) exposure were based on approximately 15.9 (15.1) million-person years at risk and included 1891 (1808) cases of cancer, of which 532 (503) were leukaemia, 348 (337) lymphomas, 423 (399) CNST, and 588 (569) non-CNS solid tumours. The prevalence of high likelihood of exposure was 2.9% for mothers and 6.7% for fathers. No evidence of an association was found with maternal or paternal exposure for any of the outcomes, except for "non-CNS solid tumours" (High versus None; Father: adjusted HR [95%CI] =1.84 [1.31-2.58]; Mother: 1.79 [1.13-2.84]). No evidence of an association was found for main subtypes of leukaemia and lymphoma. A post-hoc analysis on frequent subtypes of "non-CNS solid tumours" showed positive associations with wide CIs for some cancers. Our study suggests an increased risk for solid tumours other than in the CNS among children whose parents were occupationally exposed to pesticides; however, the small numbers of cases limited a closer investigation of cancer subtypes. Better exposure assessment and pooled studies are needed to further explore a possible link between specific childhood cancers types and parental occupational exposure to pesticides

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

Neonatal treatment of CINCA syndrome.

ABSTRACT: Chronic Infantile Neurological Cutaneous Articular (CINCA) syndrome, also called Neonatal Onset Multisystem Inflammatory Disease (NOMID) is a chronic disease with early onset affecting mainly the central nervous system, bones and joints and may lead to permanent damage. We report two preterm infants with severe CINCA syndrome treated by anti-interleukin-1 in the neonatal period, although, so far, no experience with this treatment in infants younger than three months of age has been reported. A review of the literature was performed with focus on treatment and neonatal features of CINCA syndrome. CASE REPORT: Two cases suspected to have CINCA syndrome were put on treatment with anakinra in the early neonatal period due to severe clinical presentation. We observed a rapid and persistent decline of clinical signs and systemic inflammation and good drug tolerance. Diagnosis was confirmed in both cases by mutations in the NLRP3/CIAS1-gene coding for cryopyrin. As particular neonatal clinical signs polyhydramnios and endocardial overgrowth are to be mentioned. CONCLUSION: We strongly suggest that specific treatment targeting interleukin-1 activity should be started early. Being well tolerated, it can be introduced already in neonates presenting clinical signs of severe CINCA syndrome in order to rapidly control inflammation and to prevent life-long disability

Highly efficient separation of actinides from lanthanides by a phenanthroline-derived bis-triazine ligand

The synthesis, lanthanide complexation, and solvent ex- traction of actinide(III) and lanthanide(III) radiotracers from nitric acid solutions by a phenanthroline-derived quadridentate bis-triazine ligand are described. The ligand separates Am(III) and Cm(III) from the lanthanides with remarkably high efficiency, high selectivity, and fast extraction kinetics compared to its 2,2'-bipyridine counterpart. Structures of the 1:2 bis-complexes of the ligand with Eu(III) and Yb(III) were elucidated by X-ray crystallography and force field calculations, respec-tively. The Eu(III) bis-complex is the first 1:2 bis-complex of a quadridentate bis-triazine ligand to be characterized by crystallography. The faster rates of extraction were verified by kinetics measurements using the rotating membrane cell technique in several diluents. The improved kinetics of metal ion extraction are related to the higher surface activity of the ligand at the phase interface. The improvement in the ligand's properties on replacing the bipyridine unit with a phenanthroline unit far exceeds what was anticipated based on ligand design alone

Urinary biomarker concentrations of captan, chlormequat, chlorpyrifos and cypermethrin in UK adults and children living near agricultural land

There is limited information on the exposure to pesticides experienced by UK residents living near agricultural land. This study aimed to investigate their pesticide exposure in relation to spray events. Farmers treating crops with captan, chlormequat, chlorpyrifos or cypermethrin provided spray event information. Adults and children residing ≤100 m from sprayed fields provided first-morning void urine samples during and outwith the spray season. Selected samples (1–2 days after a spray event and at other times (background samples)) were analysed and creatinine adjusted. Generalised Linear Mixed Models were used to investigate if urinary biomarkers of these pesticides were elevated after spray events. The final data set for statistical analysis contained 1518 urine samples from 140 participants, consisting of 523 spray event and 995 background samples which were analysed for pesticide urinary biomarkers. For captan and cypermethrin, the proportion of values below the limit of detection was greater than 80%, with no difference between spray event and background samples. For chlormequat and chlorpyrifos, the geometric mean urinary biomarker concentrations following spray events were 15.4 μg/g creatinine and 2.5 μg/g creatinine, respectively, compared with 16.5 μg/g creatinine and 3.0 μg/g creatinine for background samples within the spraying season. Outwith the spraying season, concentrations for chlorpyrifos were the same as those within spraying season backgrounds, but for chlormequat, lower concentrations were observed outwith the spraying season (12.3 μg/g creatinine). Overall, we observed no evidence indicative of additional urinary pesticide biomarker excretion as a result of spray events, suggesting that sources other than local spraying are responsible for the relatively low urinary pesticide biomarkers detected in the study population

Estimating cortical thickness trajectories in children across different scanners using transfer learning from normative models

This work illustrates the use of normative models in a longitudinal neuroimaging study of children aged 6–17 years and demonstrates how such models can be used to make meaningful comparisons in longitudinal studies, even when individuals are scanned with different scanners across successive study waves. More specifically, we first estimated a large-scale reference normative model using Hierarchical Bayesian Regression from N = 42,993 individuals across the lifespan and from dozens of sites. We then transfer these models to a longitudinal developmental cohort (N = 6285) with three measurement waves acquired on two different scanners that were unseen during estimation of the reference models. We show that the use of normative models provides individual deviation scores that are independent of scanner effects and efficiently accommodate inter-site variations. Moreover, we provide empirical evidence to guide the optimization of sample size for the transfer of prior knowledge about the distribution of regional cortical thicknesses. We show that a transfer set containing as few as 25 samples per site can lead to good performance metrics on the test set. Finally, we demonstrate the clinical utility of this approach by showing that deviation scores obtained from the transferred normative models are able to detect and chart morphological heterogeneity in individuals born preterm.</p