TDOA--based localization in two dimensions: the bifurcation curve

In this paper, we complete the study of the geometry of the TDOA map that encodes the noiseless model for the localization of a source from the range differences between three receivers in a plane, by computing the Cartesian equation of the bifurcation curve in terms of the positions of the receivers. From that equation, we can compute its real asymptotic lines. The present manuscript completes the analysis of [Inverse Problems, Vol. 30, Number 3, Pages 035004]. Our result is useful to check if a source belongs or is closed to the bifurcation curve, where the localization in a noisy scenario is ambiguous.Comment: 11 pages, 3 figures, to appear in Fundamenta Informatica

A comprehensive analysis of the geometry of TDOA maps in localisation problems

In this manuscript we consider the well-established problem of TDOA-based source localization and propose a comprehensive analysis of its solutions for arbitrary sensor measurements and placements. More specifically, we define the TDOA map from the physical space of source locations to the space of range measurements (TDOAs), in the specific case of three receivers in 2D space. We then study the identifiability of the model, giving a complete analytical characterization of the image of this map and its invertibility. This analysis has been conducted in a completely mathematical fashion, using many different tools which make it valid for every sensor configuration. These results are the first step towards the solution of more general problems involving, for example, a larger number of sensors, uncertainty in their placement, or lack of synchronization.Comment: 51 pages (3 appendices of 12 pages), 12 figure

Raman anisotropy in serpentine minerals, with a caveat on identification

AbstractThe serpentine minerals lizardite, polyhedral serpentine, chrysotile, antigorite and 15‐sector and 30‐sector polygonal serpentine have been studied by micro‐Raman spectroscopy, using selected samples, that had been previously characterized. The appropriate crystal orientations were determined by optical microscopy of petrographic sections. Oriented spectra, obtained using Nd‐YAG green laser radiation (532 nm), were deconvolved, extracting wavenumber and intensity values for the peaks, possibly overlapping and forming complex bands. Relevant Raman anisotropy is common and relevant in serpentine. Depending upon the orientation of the impinging laser, significant wavenumber shifts occur (up to 10 cm−1, mostly in polyhedral serpentine and lizardite). Furthermore, also, important intensity variations (up to 1 order of magnitude) occur in polyhedral serpentine, lizardite, chrysotile and antigorite as well. On the one hand, the possibly characteristic peaks have been identified and discussed. On the other hand, caution is suggested as far as the micro‐Raman characterization of polyphasic, variably oriented serpentine minerals is concerned

The algebro-geometric study of range maps

Localizing a radiant source is a widespread problem to many scientific and technological research areas. E.g. localization based on range measurements stays at the core of technologies like radar, sonar and wireless sensors networks. In this manuscript we study in depth the model for source localization based on range measurements obtained from the source signal, from the point of view of algebraic geometry. In the case of three receivers, we find unexpected connections between this problem and the geometry of Kummer's and Cayley's surfaces. Our work gives new insights also on the localization based on range differences.Comment: 38 pages, 18 figure

The Neolithic greenstone industry of Chiomonte (northwestern Italy): mineralogy, petrography and archaeometric implications

Abstract. The polished stone industry of Chiomonte (Piedmont region, northwestern Italy), dating back to the middle to late Neolithic, has been studied with a multi-analytical approach, including mineralogical, petrographic and morpho-typological issues, with the aim of providing information about the sources of the raw materials and determining the function of this particular settlement in the prehistoric Western Alps. Most of the lithic tools are made of sensu stricto greenstones (i.e. "Na pyroxene rocks" and "Na pyroxene and garnet rocks"), though a large number of serpentinite tools (25 %) also exist. The combined application of X-ray powder diffraction (XRPD), polarising microscopy and Scanning Electron Microscopy coupled with Energy Dispersive Spectrometry (SEM-EDS) led to the detection of specific mineral and chemical "markers", pointing to the Chiomonte tools likely having come from the Monviso area. However, other closer supply sources, e.g. small meta-ophiolite units in the Orsiera–Rocciavré mountain range or in the lower Susa valley, cannot be ruled out. The presence, on the many retrieved roughouts and broken tools, of raw, yet unpolished surfaces that are ascribable to pebbles and cobbles from alluvial or glacial deposits, suggests that these rocks had been picked up from local "secondary" sources. The abundance of roughouts and broken tools identifies Chiomonte as a second-order manufacturing site, although it is still unclear whether such an activity was restricted to serving local needs or if it contributed to the circulation of greenstone implements on a wider scale

Geology and petrology of the Austroalpine Châtillon slice, Aosta valley, western Alps

Slices of continental crust pertinent to the lower Austroalpine domain of the western Alps, crop out within the ophiolitic Piemonte Zone. Among them, the Ch (a) over cap tillon slice was studied in detail. The slice consists of orthogneiss with subordinate metabasics and very minor paraschist. The garnet-phengite-epidote-albite orthogneiss is characterised by polyphase garnet porphyroclasts. Metabasics consist of prasinite lenses and eclogite relics. Phengite-clinozoisite eclogite is characterised by small garnet idioblasts with prograde zoning; jadeite content in omphacite increases towards the rim; Si content in phengite decreases towards the rim. Gamet-glaucophane-phengite-paragonite micaschist is characterised by polymetamorphic garnet porphyroclasts, and small Alpine garnet idioblasts. A pre-Alpine amphibolite-facies metamorphism is inferred for the polymetamorphic rocks of the Ch (a) over cap tillon slice. Paragneiss and micaschist probably derive from pre-Alpine "kinzigites"; the orthogneiss protolith was a late-Variscan porphyritic granitoid. Thermobarometry in the eclogite constrains the metamorphic peak at T less than or equal to 560 degreesC and P = 16 kbar. The HP minerals were partly retrogressed to greenschist-facies assemblages during the late Alpine tectono-metamorphic recrystallisation. The inferred Alpine P-T conditions are consistent with those for other Penninic and Austro-Alpine nappes of the northwestern internal Alps. The Ch (a) over cap tillon slice is very similar to the Eclogitic Micas-chists Complex of the Sesia-Lanzo Zone and to the other eclogite-facies Austroalpine slices of the Dent Blanche Nappe, but it could also represent a portion of the Sesia-Lanzo Zone basement, which experienced a somewhat different subduction depth. The tectonic position of the Ch (a) over cap tillon slice within the Piemonte Zone is essential to reconstruct the geometric relationships in the Austroalpine-Piemonte nappe stack of the northwestern internal Alps