On a Watson-like Uniqueness Theorem and Gevrey Expansions

We present a maximal class of analytic functions, elements of which are in one-to-one correspondence with their asymptotic expansions. In recent decades it has been realized (B. Malgrange, J. Ecalle, J.-P. Ramis, Y. Sibuya et al.), that the formal power series solutions of a wide range of systems of ordinary (even non-linear) analytic differential equations are in fact the Gevrey expansions for the regular solutions. Watson's uniqueness theorem belongs to the foundations of this new theory. This paper contains a discussion of an extension of Watson's uniqueness theorem for classes of functions which admit a Gevrey expansion in angular regions of the complex plane with opening less than or equal to (\frac \pi k,) where (k) is the order of the Gevrey expansion. We present conditions which ensure uniqueness and which suggest an extension of Watson's representation theorem. These results may be applied for solutions of certain classes of differential equations to obtain the best accuracy estimate for the deviation of a solution from a finite sum of the corresponding Gevrey expansion.Comment: 18 pages, 4 figure

Multilayered feed forward Artificial Neural Network model to predict the average summer-monsoon rainfall in India

In the present research, possibility of predicting average summer-monsoon rainfall over India has been analyzed through Artificial Neural Network models. In formulating the Artificial Neural Network based predictive model, three layered networks have been constructed with sigmoid non-linearity. The models under study are different in the number of hidden neurons. After a thorough training and test procedure, neural net with three nodes in the hidden layer is found to be the best predictive model.Comment: 19 pages, 1 table, 3 figure

Assessing the conservation value of waterbodies: the example of the Loire floodplain (France)

In recent decades, two of the main management tools used to stem biodiversity erosion have been biodiversity monitoring and the conservation of natural areas. However, socio-economic pressure means that it is not usually possible to preserve the entire landscape, and so the rational prioritisation of sites has become a crucial issue. In this context, and because floodplains are one of the most threatened ecosystems, we propose a statistical strategy for evaluating conservation value, and used it to prioritise 46 waterbodies in the Loire floodplain (France). We began by determining a synthetic conservation index of fish communities (Q) for each waterbody. This synthetic index includes a conservation status index, an origin index, a rarity index and a richness index. We divided the waterbodies into 6 clusters with distinct structures of the basic indices. One of these clusters, with high Q median value, indicated that 4 waterbodies are important for fish biodiversity conservation. Conversely, two clusters with low Q median values included 11 waterbodies where restoration is called for. The results picked out high connectivity levels and low abundance of aquatic vegetation as the two main environmental characteristics of waterbodies with high conservation value. In addition, assessing the biodiversity and conservation value of territories using our multi-index approach plus an a posteriori hierarchical classification methodology reveals two major interests: (i) a possible geographical extension and (ii) a multi-taxa adaptation

The Chemotactic Defect in Wiskott-Aldrich Syndrome Macrophages Is Due to the Reduced Persistence of Directional Protrusions

Wiskott-Aldrich syndrome protein (WASp) is an actin nucleation promoting factor that is required for macrophages to directionally migrate towards various chemoattractants. The chemotaxis defect of WASp-deficient cells and its activation by Cdc42 in vivo suggest that WASp plays a role in directional sensing, however, its precise role in macrophage chemotaxis is still unclear. Using shRNA-mediated downregulation of WASp in the murine monocyte/macrophage cell line RAW/LR5 (shWASp), we found that WASp was responsible for the initial wave of actin polymerization in response to global stimulation with CSF-1, which in Dictyostelium discoideum amoebae and carcinoma cells has been correlated with the ability to migrate towards chemoattractants. Real-time monitoring of shWASp cells, as well as WASp−/− bone marrow-derived macrophages (BMMs), in response to a CSF-1 gradient revealed that the protrusions from WASp-deficient cells were directional, showing intact directional sensing. However, the protrusions from WASp-deficient cells demonstrated reduced persistence compared to their respective control shRNA and wild-type cells. Further examination showed that tyrosine phosphorylation of WASp was required for both the first wave of actin polymerization following global CSF-1 stimulation and proper directional responses towards CSF-1. Importantly, the PI3K, Rac1 and WAVE2 proteins were incorporated normally in CSF-1 – elicited protrusions in the absence of WASp, suggesting that membrane protrusion driven by the WAVE2 complex signaling is intact. Collectively, these results suggest that WASp and its phosphorylation play critical roles in coordinating the actin cytoskeleton rearrangements necessary for the persistence of protrusions required for directional migration of macrophages towards CSF-1

Comparative Coastal Risk Index (CCRI): A multidisciplinary risk index for Latin America and the Caribbean

As the world's population grows to a projected 11.2 billion by 2100, the number of people living in low-lying areas exposed to coastal hazards is projected to increase. Critical infrastructure and valuable assets continue to be placed in vulnerable areas, and in recent years, millions of people have been displaced by natural hazards. Impacts from coastal hazards depend on the number of people, value of assets, and presence of critical resources in harm's way. Risks related to natural hazards are determined by a complex interaction between physical hazards, the vulnerability of a society or social-ecological system and its exposure to such hazards. Moreover, these risks are amplified by challenging socioeconomic dynamics, including poorly planned urban development, income inequality, and poverty. This study employs a combination of machine learning clustering techniques (Self Organizing Maps and K-Means) and a spatial index, to assess coastal risks in Latin America and the Caribbean (LAC) on a comparative scale. The proposed method meets multiple objectives, including the identification of hotspots and key drivers of coastal risk, and the ability to process large-volume multidimensional and multivariate datasets, effectively reducing sixteen variables related to coastal hazards, geographic exposure, and socioeconomic vulnerability, into a single index. Our results demonstrate that in LAC, more than 500,000 people live in areas where coastal hazards, exposure (of people, assets and ecosystems) and poverty converge, creating the ideal conditions for a perfect storm. Hotspot locations of coastal risk, identified by the proposed Comparative Coastal Risk Index (CCRI), contain more than 300,00 people and include: El Oro, Ecuador; Sinaloa, Mexico; Usulutan, El Salvador; and Chiapas, Mexico. Our results provide important insights into potential adaptation alternatives that could reduce the impacts of future hazards. Effective adaptation options must not only focus on developing coastal defenses, but also on improving practices and policies related to urban development, agricultural land use, and conservation, as well as ameliorating socioeconomic conditions

Quantitative estimates of unique continuation for parabolic equations, determination of unknown time-varying boundaries and optimal stability estimates

In this paper we will review the main results concerning the issue of stability for the determination unknown boundary portion of a thermic conducting body from Cauchy data for parabolic equations. We give detailed and selfcontained proofs. We prove that such problems are severely ill-posed in the sense that under a priori regularity assumptions on the unknown boundaries, up to any finite order of differentiability, the continuous dependence of unknown boundary from the measured data is, at best, of logarithmic type

High-density gene expression analysis of tumor-associated macrophages from mouse mammary tumors

Clinical and experimental evidence indicates that tumor-associated macrophages (TAMs) promote malignant progression. In breast cancer, TAMs enhance tumor angiogenesis, tumor cell invasion, matrix remodeling, and immune suppression against the tumor. In this study, we examined late-stage mammary tumors from a transgenic mouse model of breast cancer. We used flow cytometry under conditions that minimized gene expression changes to isolate a rigorously defined TAM population previously shown to be associated with invasive carcinoma cells. The gene expression signature of this population was compared with a similar population derived from spleens of non-tumor-bearing mice using high-density oligonucleotide arrays. Using stringent selection criteria, transcript abundance of 460 genes was shown to be differentially regulated between the two populations. Bioinformatic analyses of known functions of these genes indicated that formerly ascribed TAM functions, including suppression of immune activation and matrix remodeling, as well as multiple mediators of tumor angiogenesis, were elevated in TAMs. Further bioinformatic analyses confirmed that a pure and valid TAM gene expression signature in mouse tumors could be used to assess expression of TAMs in human breast cancer. The data derived from these more physiologically relevant autochthonous tumors compared with previous studies in tumor xenografts suggest tactics by which TAMs may regulate tumor angiogenesis and thus provide a basis for exploring other transcriptional mediators of TAM trophic functions within the tumor microenvironment