A general wavelet-based profile decomposition in the critical embedding of function spaces

We characterize the lack of compactness in the critical embedding of functions spaces $X\subset Y$ having similar scaling properties in the following terms : a sequence $(u_n)_{n\geq 0}$ bounded in $X$ has a subsequence that can be expressed as a finite sum of translations and dilations of functions $(\phi_l)_{l>0}$ such that the remainder converges to zero in $Y$ as the number of functions in the sum and $n$ tend to $+\infty$. Such a decomposition was established by G\'erard for the embedding of the homogeneous Sobolev space $X=\dot H^s$ into the $Y=L^p$ in $d$ dimensions with $0<s=d/2-d/p$, and then generalized by Jaffard to the case where $X$ is a Riesz potential space, using wavelet expansions. In this paper, we revisit the wavelet-based profile decomposition, in order to treat a larger range of examples of critical embedding in a hopefully simplified way. In particular we identify two generic properties on the spaces $X$ and $Y$ that are of key use in building the profile decomposition. These properties may then easily be checked for typical choices of $X$ and $Y$ satisfying critical embedding properties. These includes Sobolev, Besov, Triebel-Lizorkin, Lorentz, H\"older and BMO spaces.Comment: 24 page

Concentration analysis and cocompactness

Loss of compactness that occurs in may significant PDE settings can be expressed in a well-structured form of profile decomposition for sequences. Profile decompositions are formulated in relation to a triplet $(X,Y,D)$, where $X$ and $Y$ are Banach spaces, $X\hookrightarrow Y$, and $D$ is, typically, a set of surjective isometries on both $X$ and $Y$. A profile decomposition is a representation of a bounded sequence in $X$ as a sum of elementary concentrations of the form $g_kw$, $g_k\in D$, $w\in X$, and a remainder that vanishes in $Y$. A necessary requirement for $Y$ is, therefore, that any sequence in $X$ that develops no $D$-concentrations has a subsequence convergent in the norm of $Y$. An imbedding $X\hookrightarrow Y$ with this property is called $D$-cocompact, a property weaker than, but related to, compactness. We survey known cocompact imbeddings and their role in profile decompositions

EO-ALERT: A Novel Architecture for the Next Generation of Earth Observation Satellites Supporting Rapid Civil Alerts

Satellite Earth Observation (EO) data is ubiquitously used in many applications, providing basic services to society, such as environment monitoring, emergency management and civilian security. Due to the increasing request of EO products by the market, the classical EO data chain generates a severe bottleneck problem, further exacerbated in constellations. A huge amount of EO raw data generated on-board the satellite must be transferred to ground, slowing down the EO product availability, increasing latency, and hampering the growth of applications in accordance with the increased user demand. This paper provides an overview of the results achieved by the EO-ALERT project (http://eo-alert-h2020.eu/), an H2020 European Union research activity led by DEIMOS Space. EO-ALERT proposes the definition and development of the next-generation EO data processing chain, based on a novel flight segment architecture that moves optimised key EO data processing elements from the ground segment to on-board the satellite, with the aim of delivering the EO products to the end user with very low latency (quasi-real-time). EO-ALERT achieves, globally, latencies below five minutes for EO products delivery, reaching latencies below 1 minute in some scenarios. The proposed architecture solves the above challenges through a combination of innovations in the on-board elements of the data chain and the communications. Namely, the architecture introduces innovative technological solutions, including on-board reconfigurable data handling, on-board image generation and processing for the generation of alerts (EO products) using Artificial Intelligence (AI), on-board data compression and encryption using AI, high-speed on-board avionics, and reconfigurable high data rate communication links to ground, including a separate chain for alerts with minimum latency and global coverage. The paper presents the proposed architecture, its performance and hardware, considering two different user scenarios; ship detection and extreme weather observation/nowcasting. The results show that, when implemented using COTS components and available communication links, the proposed architecture can deliver alerts to ground with latency lower than five minutes, for both SAR and Optical missions, demonstrating the viability of the EOALERT concept and architecture. The paper also discusses the implementation on an avionics test bench for testing the architecture with real EO data, with the aim of demonstrating that it can meet the requirements of the considered scenarios in terms of detection performance and provides technologies at a high TRL (4-5). When proven, this will open unprecedented opportunities for the exploitation of civil EO products, especially in latency sensitive scenarios, such as disaster management

EO-ALERT: A Novel Architecture for the Next Generation of Earth Observation Satellites Supporting Rapid Civil Alerts

The EO-ALERT project proposes the definition and development of the next-generation Earth Observation (EO) data processing chain, based on a novel flight segment architecture that moves opti-mised key EO data processing elements from the ground segment to on-board the satellite, with the aim of delivering EO products to the end user with very low latency. EO-ALERT achieves, globally, latencies below five minutes for EO products delivery, and below 1 minute in some scenarios. The proposed archi-tecture combines innovations in the on-board elements of the data chain and the communications, namely: on-board reconfigurable data handling, on-board image generation and processing for the generation of alerts (EO products) using Artificial Intelligence (AI), on-board AI-based data compression and encryption, high-speed on-board avionics, and reconfigurable high data rate communication links to ground, including a separate chain for alerts with minimum latency and global coverage. This paper pre-sents the proposed architecture, its performance and hardware, considering two different user scenarios: ship detection and extreme weather nowcasting. The results show that, when implemented using COTS components and available communication links, the proposed architecture can deliver alerts to ground with latency below five minutes, for both SAR and Optical missions, demonstrating the viability of the EO-ALERT concept

A Novel Satellite Architecture for the Next Generation of Earth Observation Satellites Supporting Rapid Alerts

The EO-ALERT European Commission H2020 project proposes the definition, development, and verification and validation through ground hardware testing, of a next-generation Earth Observation (EO) data processing chain. The proposed data processing chain is based on a novel flight segment architecture that moves EO data processing elements traditionally executed in the ground segment to on-board the satellite, with the aim of delivering EO products to the end user with very low latency. EO-ALERT achieves, globally, latencies below five minutes for EO products delivery, and below one minute in realistic scenarios. The proposed EO-ALERT architecture is enabled by on-board processing, recent improvements in processing hardware using Commercial Off-The-Shelf (COTS) components, and persistent space-to-ground communications links. EO-ALERT combines innovations in the on-board elements of the data chain and the communications, namely: on-board reconfigurable data handling, on-board image generation and processing for the generation of alerts (EO products) using Machine Learning (ML) and Artificial Intelligence (AI), on-board AI-based data compression and encryption, high-speed on-board avionics, and reconfigurable high data rate communication links to ground, including a separate chain for alerts with minimum latency and global coverage. This paper presents the proposed architecture, its hardware realization for the ground testing in a representative environment and its performance. The architecture’s performance is evaluated considering two different user scenarios where very low latency (almost-real-time) EO product delivery is required: ship detection and extreme weather monitoring/nowcasting. The hardware testing results show that, when implemented using COTS components and available communication links, the proposed architecture can deliver alerts to the end user with a latency below five minutes, for both SAR and Optical missions, demonstrating the viability of the EO-ALERT architecture. In particular, in several test scenarios, for both the TerraSAR-X SAR and DEIMOS-2 Optical Very High Resolution (VHR) missions, hardware testing of the proposed architecture has shown it can deliver EO products and alerts to the end user globally, with latency lower than one-point-five minutes

Reversible inhibitor of p97, DBeQ, impairs both ubiquitin-dependent and autophagic protein clearance pathways

A specific small-molecule inhibitor of p97 would provide an important tool to investigate diverse functions of this essential ATPase associated with diverse cellular activities (AAA) ATPase and to evaluate its potential to be a therapeutic target in human disease. We carried out a high-throughput screen to identify inhibitors of p97 ATPase activity. Dual-reporter cell lines that simultaneously express p97-dependent and p97-independent proteasome substrates were used to stratify inhibitors that emerged from the screen. N^2,N^4-dibenzylquinazoline-2,4-diamine (DBeQ) was identified as a selective, potent, reversible, and ATP-competitive p97 inhibitor. DBeQ blocks multiple processes that have been shown by RNAi to depend on p97, including degradation of ubiquitin fusion degradation and endoplasmic reticulum-associated degradation pathway reporters, as well as autophagosome maturation. DBeQ also potently inhibits cancer cell growth and is more rapid than a proteasome inhibitor at mobilizing the executioner caspases-3 and -7. Our results provide a rationale for targeting p97 in cancer therapy

Cancer proliferation gene discovery through functional Genomics

Retroviral short hairpin RNA (shRNA) - mediated genetic screens in mammalian cells are powerful tools for discovering loss- of- function phenotypes. We describe a highly parallel multiplex methodology for screening large pools of shRNAs using half- hairpin barcodes for microarray deconvolution. We carried out dropout screens for shRNAs that affect cell proliferation and viability in cancer cells and normal cells. We identified many shRNAs to be antiproliferative that target core cellular processes, such as the cell cycle and protein translation, in all cells examined. Moreover, we identified genes that are selectively required for proliferation and survival in different cell lines. Our platform enables rapid and cost- effective genome-wide screens to identify cancer proliferation and survival genes for target discovery. Such efforts are complementary to the Cancer Genome Atlas and provide an alternative functional view of cancer cells