From average case complexity to improper learning complexity

The basic problem in the PAC model of computational learning theory is to determine which hypothesis classes are efficiently learnable. There is presently a dearth of results showing hardness of learning problems. Moreover, the existing lower bounds fall short of the best known algorithms. The biggest challenge in proving complexity results is to establish hardness of {\em improper learning} (a.k.a. representation independent learning).The difficulty in proving lower bounds for improper learning is that the standard reductions from $\mathbf{NP}$-hard problems do not seem to apply in this context. There is essentially only one known approach to proving lower bounds on improper learning. It was initiated in (Kearns and Valiant 89) and relies on cryptographic assumptions. We introduce a new technique for proving hardness of improper learning, based on reductions from problems that are hard on average. We put forward a (fairly strong) generalization of Feige's assumption (Feige 02) about the complexity of refuting random constraint satisfaction problems. Combining this assumption with our new technique yields far reaching implications. In particular, 1. Learning $\mathrm{DNF}$'s is hard. 2. Agnostically learning halfspaces with a constant approximation ratio is hard. 3. Learning an intersection of $\omega(1)$ halfspaces is hard.Comment: 34 page

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

Scattering of first and second sound waves by quantum vorticity in superfluid Helium

We study the scattering of first and second sound waves by quantum vorticity in superfluid Helium using two-fluid hydrodynamics. The vorticity of the superfluid component and the sound interact because of the nonlinear character of these equations. Explicit expressions for the scattered pressure and temperature are worked out in a first Born approximation, and care is exercised in delimiting the range of validity of the assumptions needed for this approximation to hold. An incident second sound wave will partly convert into first sound, and an incident first sound wave will partly convert into second sound. General considerations show that most incident first sound converts into second sound, but not the other way around. These considerations are validated using a vortex dipole as an explicitely worked out example.Comment: 24 pages, Latex, to appear in Journal of Low Temperature Physic

Model-free tuning of laguerre network for impedance matching in bilateral teleoperation system

This paper addresses the tuning method to attain symmetry between the master and slave manipulators of a bilateral teleoperation system. In the proposed structure, an equalizer based on the Laguerre network connected in-feedback loop to the master manipulator has been introduced. A set of input-output data were first generated and recorded which later be used in two-steps tuning procedure. A fictitious reference signal was formulated based on these data. In addition, a metaheuristic optimization algorithm namely the Particle Swarm Optimization has been employed in seeking the optimal controller’s parameters. Numerical analyses utilizing Matlab software has been performed. The results exhibited that the dynamic of the master manipulator with the added controller is almost identical to the dynamic of the slave systems. Hence, it is verified that the proposed tuning technique is feasible to achieve symmetry between both sides of the manipulators

Stratospheric aerosols from the Sarychev volcano eruption in the 2009 Arctic summer

Aerosols from the Sarychev volcano eruption (Kuril Islands, northeast of Japan) were observed in the Arctic lower stratosphere a few days after the strongest SO2 injection which occurred on 15 and 16 June 2009. From the observations provided by the Infrared Atmospheric Sounding Interferometer (IASI) an estimated 0.9 Tg of sulphur dioxide was injected into the upper troposphere and lower stratosphere (UTLS). The resultant stratospheric sulphate aerosols were detected from satellites by the Optical Spectrograph and Infrared Imaging System (OSIRIS) limb sounder and by the Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) and from the surface by the Network for the Detection of Atmospheric Composition Changes (NDACC) lidar deployed at OHP (Observatoire de Haute-Provence, France). By the first week of July the aerosol plume had spread out over the entire Arctic region. The Sarychev-induced stratospheric aerosol over the Kiruna region (north of Sweden) was measured by the Stratospheric and Tropospheric Aerosol Counter (STAC) during eight balloon flights planned in August and September 2009. During this balloon campaign the Micro Radiomètre Ballon (MicroRADIBAL) and the Spectroscopie d'Absorption Lunaire pour l'Observation des Minoritaires Ozone et NOx (SALOMON) remote-sensing instruments also observed these aerosols. Aerosol concentrations returned to near-background levels by spring 2010. The effective radius, the surface area density (SAD), the aerosol extinction, and the total sulphur mass from STAC in situ measurements are enhanced with mean values in the range 0.15-0.21 μm, 5.5-14.7 μm2 cm-3, 5.5-29.5 × 10-4 km-1, and 4.9-12.6 × 10-10 kg[S] kg-1[air], respectively, between 14 km and 18 km. The observed and modelled e-folding time of sulphate aerosols from the Sarychev eruption is around 70-80 days, a value much shorter than the 12-14 months calculated for aerosols from the 1991 eruption of Mt Pinatubo. The OSIRIS stratospheric aerosol optical depth (AOD) at 750 nm is enhanced by a factor of 6, with a value of 0.02 in late July compared to 0.0035 before the eruption. The HadGEM2 and MIMOSA model outputs indicate that aerosol layers in polar region up to 14-15 km are largely modulated by stratosphere-troposphere exchange processes. The spatial extent of the Sarychev plume is well represented in the HadGEM2 model with lower altitudes of the plume being controlled by upper tropospheric troughs which displace the plume downward and upper altitudes around 18-20 km, in agreement with lidar observations. Good consistency is found between the HadGEM2 sulphur mass density and the value inferred from the STAC observations, with a maximum located about 1 km above the tropopause ranging from 1 to 2 × 10 -9 kg[S] kg-1[air], which is one order of magnitude higher than the background level. © Author(s) 2013.The authors thank the CNES balloon launching team for successful operations and the Swedish Space Corporation at Esrange. The ETHER database (CNES-INSUCNRS) and the CNES “sous-direction Ballon” are partners of the project. The StraPolEt ´ e project has been funded by the French ´ “Agence Nationale de la Recherche” (ANR-BLAN08-1-31627), the “Centre National d’Etudes Spatiales” (CNES), and the “Institut ´ Polaire Paul-Emile Victor” (IPEV). The AEROWAVE (Aerosols, Water Vapor and Electricity) and the HALOHA (HALOgen in High Altitudes) projects have been funded by the recently created French CNES-INSU Balloon Committee (so-called CSTB). We are grateful to Slimane Bekki and David Cugniet for their constructive comments about the AER-UPMC 2-D model, to Marc-Antoine Drouin for his help about the MIMOSA model, and to the LPC2E technical team for this successful campaign. Jim Haywood and Andy Jones were supported by the Joint DECC/Defra Met Office Hadley Centre Climate Programme (GA01101). IASI was developed and built under the responsibility of the Centre National d’Etudes Spatiales (CNES, France). It is flown on board the Metop ´ satellites as part of the EUMETSAT Polar System. The IASI L1 data are received through the EUMETCast near-real-time data distribution service. L. Clarisse is a postdoctoral researcher with FRS-FNRS. We acknowledge the CALIOP team for acquiring and processing data as well as the ICARE team for providing and maintaining the computational facilities to store them. Odin is a Swedish-led satellite project funded jointly by Sweden (SNSB), Canada (CSA), France (CNES), and Finland (Tekes). This study was supported by the French VOLTAIRE Labex (Laboratoire d’Excellence ANR-10-LABX-100-01) managed by the University of Orleans

Cdk2 Is Required for p53-Independent G2/M Checkpoint Control

The activation of phase-specific cyclin-dependent kinases (Cdks) is associated with ordered cell cycle transitions. Among the mammalian Cdks, only Cdk1 is essential for somatic cell proliferation. Cdk1 can apparently substitute for Cdk2, Cdk4, and Cdk6, which are individually dispensable in mice. It is unclear if all functions of non-essential Cdks are fully redundant with Cdk1. Using a genetic approach, we show that Cdk2, the S-phase Cdk, uniquely controls the G2/M checkpoint that prevents cells with damaged DNA from initiating mitosis. CDK2-nullizygous human cells exposed to ionizing radiation failed to exclude Cdk1 from the nucleus and exhibited a marked defect in G2/M arrest that was unmasked by the disruption of P53. The DNA replication licensing protein Cdc6, which is normally stabilized by Cdk2, was physically associated with the checkpoint regulator ATR and was required for efficient ATR-Chk1-Cdc25A signaling. These findings demonstrate that Cdk2 maintains a balance of S-phase regulatory proteins and thereby coordinates subsequent p53-independent G2/M checkpoint activation

Dynamic Distribution of Histone H4 Arginine 3 Methylation Marks in the Developing Murine Cortex

Epigenetic modifications regulate key transitions in cell fate during development of the central nervous system (CNS). During cortical development the initial population of proliferative neuroepithelial precursor cells give rise to neurons and then glia in a strict temporal order. Neurogenesis and gliogenesis are accompanied by a switch from symmetric to asymmetric divisions of the neural precursor cells generating another precursor and a differentiated progeny. To investigate whether specific post-translational histone modifications define specific stages of neural precursor differentiation during cortical development I focussed on the appearance of two different types of histone arginine methylation, the dimethyl symmetric H4R3 (H4R3me2s) and dimethyl asymmetric H4R3 (H4R3me2a) in the developing mouse cortex.An immunohistochemical study of the developing cortex at different developmental stages was performed to detect the distribution of H4R3me2s and H4R3me2a modifications. I analysed the distribution of these modifications in: 1) undifferentiated neural precursors, 2) post-mitotic neurons and 3) developing oligodendrocyte precursors (OLPs) using lineage-specific and histone modification-specific antibodies to co-label the cells. I found that the proliferative neuroepithelium during the stage of mainly symmetric expansive divisions is characterised by the prevalence of H4R3me2s modification and almost no detectable H4R3me2a modification. However, at a later stage, when the cortical layers with post-mitotic neurons have begun forming, both H4R3me2a and H4R3me2s modifications are detected in the post-mitotic neurons and in the developing OLPs.I propose that the H4R3me2s modification forms part of the "histone code" of undifferentiated neural precursors. The later appearance of the H4R3me2a modifications specifies the onset of neurogenesis and gliogenesis and the commitment of the NSCs to differentiate. Thus, the sequential appearance of the two different H4R3 methylation marks may define a particular cellular state of the NSCs during their development and differentiation demonstrating the role of histone arginine methylation in cortical development

Approaches in biotechnological applications of natural polymers

Natural polymers, such as gums and mucilage, are biocompatible, cheap, easily available and non-toxic materials of native origin. These polymers are increasingly preferred over synthetic materials for industrial applications due to their intrinsic properties, as well as they are considered alternative sources of raw materials since they present characteristics of sustainability, biodegradability and biosafety. As definition, gums and mucilages are polysaccharides or complex carbohydrates consisting of one or more monosaccharides or their derivatives linked in bewildering variety of linkages and structures. Natural gums are considered polysaccharides naturally occurring in varieties of plant seeds and exudates, tree or shrub exudates, seaweed extracts, fungi, bacteria, and animal sources. Water-soluble gums, also known as hydrocolloids, are considered exudates and are pathological products; therefore, they do not form a part of cell wall. On the other hand, mucilages are part of cell and physiological products. It is important to highlight that gums represent the largest amounts of polymer materials derived from plants. Gums have enormously large and broad applications in both food and non-food industries, being commonly used as thickening, binding, emulsifying, suspending, stabilizing agents and matrices for drug release in pharmaceutical and cosmetic industries. In the food industry, their gelling properties and the ability to mold edible films and coatings are extensively studied. The use of gums depends on the intrinsic properties that they provide, often at costs below those of synthetic polymers. For upgrading the value of gums, they are being processed into various forms, including the most recent nanomaterials, for various biotechnological applications. Thus, the main natural polymers including galactomannans, cellulose, chitin, agar, carrageenan, alginate, cashew gum, pectin and starch, in addition to the current researches about them are reviewed in this article.. }To the Conselho Nacional de Desenvolvimento Cientfíico e Tecnológico (CNPq) for fellowships (LCBBC and MGCC) and the Coordenação de Aperfeiçoamento de Pessoal de Nvíel Superior (CAPES) (PBSA). This study was supported by the Portuguese Foundation for Science and Technology (FCT) under the scope of the strategic funding of UID/BIO/04469/2013 unit, the Project RECI/BBB-EBI/0179/2012 (FCOMP-01-0124-FEDER-027462) and COMPETE 2020 (POCI-01-0145-FEDER-006684) (JAT)

Functional mechanisms underlying pleiotropic risk alleles at the 19p13.1 breast-ovarian cancer susceptibility locus

A locus at 19p13 is associated with breast cancer (BC) and ovarian cancer (OC) risk. Here we analyse 438 SNPs in this region in 46,451 BC and 15,438 OC cases, 15,252 BRCA1 mutation carriers and 73,444 controls and identify 13 candidate causal SNPs associated with serous OC (P=9.2 × 10-20), ER-negative BC (P=1.1 × 10-13), BRCA1-associated BC (P=7.7 × 10-16) and triple negative BC (P-diff=2 × 10-5). Genotype-gene expression associations are identified for candidate target genes ANKLE1 (P=2 × 10-3) and ABHD8 (P<2 × 10-3). Chromosome conformation capture identifies interactions between four candidate SNPs and ABHD8, and luciferase assays indicate six risk alleles increased transactivation of the ADHD8 promoter. Targeted deletion of a region containing risk SNP rs56069439 in a putative enhancer induces ANKLE1 downregulation; and mRNA stability assays indicate functional effects for an ANKLE1 3′-UTR SNP. Altogether, these data suggest that multiple SNPs at 19p13 regulate ABHD8 and perhaps ANKLE1 expression, and indicate common mechanisms underlying breast and ovarian cancer risk