The Paulsen Problem, Continuous Operator Scaling, and Smoothed Analysis

The Paulsen problem is a basic open problem in operator theory: Given vectors $u_1, \ldots, u_n \in \mathbb R^d$ that are $\epsilon$-nearly satisfying the Parseval's condition and the equal norm condition, is it close to a set of vectors $v_1, \ldots, v_n \in \mathbb R^d$ that exactly satisfy the Parseval's condition and the equal norm condition? Given $u_1, \ldots, u_n$, the squared distance (to the set of exact solutions) is defined as $\inf_{v} \sum_{i=1}^n \| u_i - v_i \|_2^2$ where the infimum is over the set of exact solutions. Previous results show that the squared distance of any $\epsilon$-nearly solution is at most $O({\rm{poly}}(d,n,\epsilon))$ and there are $\epsilon$-nearly solutions with squared distance at least $\Omega(d\epsilon)$. The fundamental open question is whether the squared distance can be independent of the number of vectors $n$. We answer this question affirmatively by proving that the squared distance of any $\epsilon$-nearly solution is $O(d^{13/2} \epsilon)$. Our approach is based on a continuous version of the operator scaling algorithm and consists of two parts. First, we define a dynamical system based on operator scaling and use it to prove that the squared distance of any $\epsilon$-nearly solution is $O(d^2 n \epsilon)$. Then, we show that by randomly perturbing the input vectors, the dynamical system will converge faster and the squared distance of an $\epsilon$-nearly solution is $O(d^{5/2} \epsilon)$ when $n$ is large enough and $\epsilon$ is small enough. To analyze the convergence of the dynamical system, we develop some new techniques in lower bounding the operator capacity, a concept introduced by Gurvits to analyze the operator scaling algorithm.Comment: Added Subsection 1.4; Incorporated comments and fixed typos; Minor changes in various place

Solid wastes wastewater and remediation costs in an urban slum: The case study of A Gypsy Camp in Napoli (S Italy)

Slums represent a sort of black box within the urban environment, generating multiple impacts, that are often acknowledged, but forgotten by urban planners and policy-makers when envisioning the future of cities, due to the dimension of social exclusion in which slum dwellers live. These criticalities pose a further threat to urban sustainability. The first problem is revealed by the lack of quantifications about many environmental and socio-economic factors, as well as by a general lack of understanding about slums as systems. This study is aimed at overcoming the present knowledge weakness, developing a preliminary site-specific system representation of a slum as a system. In particular, a case study of a Gypsy camp in Napoli (S Italy) was chosen for such a purpose. Focusing on solid waste, an approximate evaluation of informal waste picking activity was performed. Basic parameters of generated wastewater, which is dispersed in the environment due to the absence of any sewerage infrastructure, are accounted according to environmental engineering standards. In addition, considering a second abandoned camp (Brecce Sant'Erasmo, Napoli, Italy), specific-site remediation costs were calculated. Results evidence the necessity of a better understanding of resources flows within slums. A first planning action for the studied area would be to separate the areas for waste processing with respect to living areas. Basic infrastructures for solid waste and wastewater management are also necessary to improve the life quality of slum dwellers, while reducing the existing impacts. Finally, also a study to detail atmospheric emissions characteristics would be desirable. Specific upgrading solutions are indicated on the basis of the existing literature. They include planning and monitoring actions, together with the development of engineered solutions for waste and wastewater management

Elevation modelling and palaeo-environmental interpretation in the Siwa area (Egypt): Application of SAR interferometry and radargrammetry to COSMO-SkyMed imagery

PublishedJournal Article© 2015 Elsevier B.V. Digital elevation models produced from COSMO-SkyMed imagery were used to delineate palaeo-drainage in a wide area surrounding the Siwa and Al-Jaghbub oases of the western Sahara Desert (Egypt and Libya).This new generation of synthetic aperture radar imagery is suitable for this purpose because of its high spatial resolution and capacity to penetrate dry surface sediments. Different techniques such as radar interferometry and radargrammetry were used to produce digital elevation models. These were assessed for accuracy and then combined to produce a single elevation model of the area. The resulting elevation model was used to support the geological study and palaeo-environmental interpretation of the area. It revealed buried features of the landscape, including inactive palaeo-drainage systems. Drainage features were extracted from the elevation model using geographical information systems; results were combined and assessed with respect to geological field data, as well as data from the literature. Previous studies in the area suggest that a wide river, probably the old Nile River, flowed into the Libyan palaeo-Sirte before the Late Messinian drawdown of the Mediterranean Sea. During the Late Messinian lowering of the sea the fluvial system changed shape and carved deep canyons throughout north-eastern Africa. The reported findings on the key Siwa area were used to precisely delineate the physiography of the modern drainage network and to confirm findings from our previous geological research in the area.We gratefully acknowledge Ruggero Matteucci and Johannes Pignatti (La Sapienza, University of Rome), Francesco Checchi (ENI S.p.A., IOEC), Filippo Bonciani and Debora Graziosi (University of Siena) for their collaboration. Research was supported by the ASI (Id 2262) in the framework of the COSMO-SkyMed Announcement of Opportunity project “Application of COSMO-SkyMed data for geological researches in Egypt and Libya”

Protective and pathogenic effects of interferon signaling during pregnancy

Immune regulation at the maternal-fetal interface is complex due to conflicting immunological objectives: protection of the fetus from maternal pathogens and prevention of immune-mediated rejection of the semiallogeneic fetus and placenta. Interferon (IFN) signaling plays an important role in restricting congenital infections as well as in the physiology of healthy pregnancies. In this review, we discuss the antiviral and pathogenic effects of type I IFN (IFN-α, IFN-β), type II IFN (IFN-γ), and type III IFN (IFN-λ) during pregnancy, with an emphasis on mouse and non-human primate models of congenital Zika virus infection. In the context of these animal model systems, we examine the role of IFN signaling during healthy pregnancy. Finally, we review mechanisms by which dysregulated type I IFN responses contribute to poor pregnancy outcomes in humans with autoimmune disease, including interferonopathies and systemic lupus erythematosus

Intrinsic Environmental Vulnerability as Shallow Landslide Susceptibility in Environmental Impact Assessment

This work investigated the susceptibility factors that trigger shallow landslides. In particular, the objective of the research was the implementation of a method to determine the relevant factors that can trigger shallow landslide events. However, with respect to the existing methods, the integration with historical datasets and the inclusion of spatial factors displaying dynamics in the same characteristic timescales were specific features of the developed tool. The study area included the watersheds of the Sessera and Strona rivers in the alpine area of the Province of Biella (Piedmont, NW Italy). The method was developed and tested from two sub-datasets derived from an integrated dataset that referred to an intense event, involving the same area, that occurred in 1968 (2\u20133 November). This allowed the implementation of an integrated representation of landslides\u2019 predisposing factors and the identification and classification in dierent groups of the areas susceptible to geo-hydrological instability processes. The previously existing databases were verified and integrated into a geographic information system (GIS) environment, giving a potentially sharable source of information for planning purposes. The obtained maps represent a metric of one of the possible intrinsic environmental vulnerability factors for the area under study. Consequently, this method can represent a future instrument for determining the intrinsic environmental vulnerability dependent on landslides within an environmental impact assessment (EIA), as required by the most recent European regulation on EIA. Moreover, the shared information can be used to implement informed policy and planning processes, based on a bottom-up approach. In particular, the availability online of landslide susceptibility maps could support the generation of augmented information\u2014useful for both local administrators and planners as well as for stakeholders willing to implement specific projects or infrastructure in vulnerable areas, such as mountain

Anguilliform larvae collected off North Carolina

The distinctive larval stage of eels (leptocephalus) facilitates dispersal through prolonged life in the open ocean. Leptocephali are abundant and diverse off North Carolina, yet data on distributions and biology are lacking. The water column (from surface to 1,293 m) was sampled in or near the Gulf Stream off Cape Hatteras, Cape Lookout, and Cape Fear, North Carolina during summer through fall of 1999–2005, and leptocephali were collected by neuston net, plankton net, Tucker trawl, and dip net. Additional samples were collected nearly monthly from a transect across southern Onslow Bay, North Carolina (from surface to 91 m) from April 2000 to December 2001 by bongo and neuston nets, Methot frame trawl, and Tucker trawl. Overall, 584 tows were completed, and 224 of these yielded larval eels. The 1,295 eel leptocephali collected (combining all methods and areas) represented at least 63 species (nine families). Thirteen species were not known previously from the area. Dominant families for all areas were Congridae (44% of individuals, 11 species), Ophichthidae (30% of individuals, 27 species), and Muraenidae (22% of individuals, ten species). Nine taxa accounted for 70% of the overall leptocephalus catches (in order of decreasing abundance): Paraconger caudilimbatus (Poey), Gymnothorax ocellatus Agassiz complex, Ariosoma balearicum (Delaroche), Ophichthus gomesii (Castelnau), Callechelys muraena Jordan and Evermann, Letharchus aliculatus McCosker, Rhynchoconger flavus (Goode and Bean), Ophichthus cruentifer (Goode and Bean), Rhynchoconger gracilior (Ginsburg). The top three species represented 52% of the total eel larvae collected. Most leptocephali were collected at night (79%) and at depths \u3e 45 m. Eighty percent of the eels collected in discrete depth Tucker trawls at night ranged from mean depths of 59–353 m. A substantial number (38% of discrete depth sample total) of larval eels were also collected at the surface (neuston net) at night. Daytime leptocephalus distributions were less clear partly due to low catches and lower Tucker trawl sampling effort. While net avoidance may account for some of the low daytime catches, an alternative explanation is that many species of larval eels occur during the day at depths \u3e 350 m. Larvae of 21 taxa of typically shallow water eels were collected at depths \u3e 350 m, but additional discrete depth diel sampling is needed to resolve leptocephalus vertical distributions. The North Carolina adult eel fauna (estuary to at least 2,000 m) consists of 51 species, 41% of which were represented in these collections. Many species of leptocephali collected are not yet known to have juveniles or adults established in the South Atlantic Bight or north of Cape Hatteras. Despite Gulf Stream transport and a prolonged larval stage, many of these eel leptocephali may not contribute to their respective populations

Management of an invasive plant in a Mediterranean Protected Area: the experience of Senecio deltoideus in Italy

Biological invasions are one of the most serious threats to global biodiversity and ecosystem integrity. The problem is growing year by year and a large number of protected areas worldwide are today invaded by at least one exotic species. In this study, we tested the eco-friendly and cost-effective weeding control of Senecio deltoideus in a Regional Protected Area in the North Mediterranean region. During a two years experiment, four techniques compatible with the local laws on protected areas (natural-herbicide, flame-weeding, mulching and mowing) were applied five times a season on sixty plots, compared with fifteen untreated controls. All techniques were effective in reducing Senecio covering: after the first year the maximum covering was limited to 37.93% (flame weeding) with a mean value of 10%; after second year the covering was further reduced (17.02% max; 2% mean). Interestingly, during the second year all plots submitted to a one-year treatment showed an enduring control of S. deltoideus covering (40.73% max; 20% mean). Taking into account feasibility and their impact on the environment, the weeding control recommendable for S. deltoideus is mowing. In a long-time management strategy, the selected treatment could be applied every two years with a drastic reduction in costs for the manager of the protected area

Range-wide assessment of livestock grazing across the sagebrush biome

Domestic livestock grazing occurs in virtually all sagebrush habitats and is a prominent disturbance factor. By affecting habitat condition and trend, grazing influences the resources required by, and thus, the distribution and abundance of sagebrush-obligate wildlife species (for example, sage-grouse Centrocercus spp.). Yet, the risks that livestock grazing may pose to these species and their habitats are not always clear. Although livestock grazing intensity and associated habitat condition may be known in many places at the local level, we have not yet been able to answer questions about use, condition, and trend at the landscape scale or at the range-wide scale for wildlife species. A great deal of information about grazing use, management regimes, and ecological condition exists at the local level (for individual livestock management units) under the oversight of organizations such as the Bureau of Land Management (BLM). However, the extent, quality, and types of existing data are unknown, which hinders the compilation, mapping, or analysis of these data. Once compiled, these data may be helpful for drawing conclusions about rangeland status, and we may be able to identify relationships between those data and wildlife habitat at the landscape scale