Multiple object tracking with non-unique data-to-object association via generalized hypothesis testing

A generalized hypothesis testing approach is applied to the problem of tracking several objects where several different associations of data with objects are possible. Such problems occur, for instance, when attempting to distinctly track several aircraft maneuvering near each other or when tracking ships at sea. Conceptually, the problem is solved by first, associating data with objects in a statistically reasonable fashion and then, tracking with a bank of Kalman filters. The objects are assumed to have motion characterized by a fixed but unknown deterministic portion plus a random process portion modeled by a shaping filter. For example, the object might be assumed to have a mean straight line path about which it maneuvers in a random manner. Several hypothesized associations of data with objects are possible because of ambiguity as to which object the data comes from, false alarm/detection errors, and possible uncertainty in the number of objects being tracked. The statistical likelihood function is computed for each possible hypothesized association of data with objects. Then the generalized likelihood is computed by maximizing the likelihood over parameters that define the deterministic motion of the object

Conformal Parametrisation of Loxodromes by Triples of Circles

We provide a parametrisation of a loxodrome by three specially arranged cycles. The parametrisation is covariant under fractional linear transformations of the complex plane and naturally encodes conformal properties of loxodromes. Selected geometrical examples illustrate the usage of parametrisation. Our work extends the set of objects in Lie sphere geometry---circle, lines and points---to the natural maximal conformally-invariant family, which also includes loxodromes.Comment: 14 pages. 9 PDF in four figures, AMS-LaTe

Giant Electron-hole Charging Energy Asymmetry in Ultra-short Carbon Nanotubes

Making full usage of bipolar transport in single-wall carbon nanotube (SWCNT) transistors could permit the development of two-in-one quantum devices with ultra-short channels. We report on clean $\sim$10 to 100 nm long suspended SWCNT transistors which display a large electron-hole transport asymmetry. The devices consist of naked SWCNT channels contacted with sections of SWCNT-under-annealed-gold. The annealed gold acts as an n-doping top gate which creates nm-sharp barriers at the junctions between the contacts and naked channel. These tunnel barriers define a single quantum dot (QD) whose charging energies to add an electron or a hole are vastly different ($e-h$ charging energy asymmetry). We parameterize the $e-h$ transport asymmetry by the ratio of the hole and electron charging energies $\eta_{e-h}$. We show that this asymmetry is maximized for short channels and small band gap SWCNTs. In a small band gap SWCNT device, we demonstrate the fabrication of a two-in-one quantum device acting as a QD for holes, and a much longer quantum bus for electrons. In a 14 nm long channel, $\eta_{e-h}$ reaches up to 2.6 for a device with a band gap of 270 meV. This strong $e-h$ transport asymmetry survives even at room temperature

Severity of disease and risk of malignant change in hereditary multiple exostoses. A genotype-phenotype study

We performed a prospective genotype-phenotype study using molecular screening and clinical assessment to compare the severity of disease and the risk of sarcoma in 172 individuals (78 families) with hereditary multiple exostoses. We calculated the severity of disease including stature, number of exostoses, number of surgical procedures that were necessary, deformity and functional parameters and used molecular techniques to identify the genetic mutations in affected individuals. Each arm of the genotype-phenotype study was blind to the outcome of the other. Mutations EXT1 and EXT2 were almost equally common, and were identified in 83% of individuals. Non-parametric statistical tests were used. There was a wide variation in the severity of disease. Children under ten years of age had fewer exostoses, consistent with the known age-related penetrance of this condition. The severity of the disease did not differ significantly with gender and was very variable within any given family. The sites of mutation affected the severity of disease with patients with EXT1 mutations having a significantly worse condition than those with EXT2 mutations in three of five parameters of severity (stature, deformity and functional parameters). A single sarcoma developed in an EXT2 mutation carrier, compared with seven in EXT1 mutation carriers. There was no evidence that sarcomas arose more commonly in families in whom the disease was more severe. The sarcoma risk in EXT1 carriers is similar to the risk of breast cancer in an older population subjected to breast-screening, suggesting that a role for regular screening in patients with hereditary multiple exostoses is justifiable. ©2004 British Editorial Society of Bone and Joint Surgery

Accurate determination of the free-free Gaunt factor. II - relativistic Gaunt factors

When modelling an ionised plasma, all spectral synthesis codes need the thermally averaged free-free Gaunt factor defined over a very wide range of parameter space in order to produce an accurate prediction for the spectrum. Until now no data set exists that would meet these needs completely. We have therefore produced a table of relativistic Gaunt factors over a much wider range of parameter space than has ever been produced before. We present tables of the thermally averaged Gaunt factor covering the range log10(gamma^2) = -6 to 10 and log10(u) = -16 to 13 for all atomic numbers Z = 1 through 36. The data were calculated using the relativistic Bethe-Heitler-Elwert (BHE) approximation and were subsequently merged with accurate non-relativistic results in those parts of the parameter space where the BHE approximation is not valid. These data will be incorporated in the next major release of the spectral synthesis code Cloudy. We also produced tables of the frequency integrated Gaunt factor covering the parameter space log10(gamma^2) = -6 to 10 for all values of Z between 1 and 36. All the data presented in this paper are available online.Comment: 8 pages, 8 figures, 2 table

Improved He I Emissivities in the Case B Approximation

We update our prior work on the case B collisional-recombination spectrum of He I to incorporate \textit{ab initio} photoionisation cross-sections. This large set of accurate, self-consistent cross-sections represents a significant improvement in He I emissivity calculations because it largely obviates the piecemeal nature that has marked all modern works. A second, more recent set of \textit{ab initio} cross-sections is also available, but we show that those are less consistent with bound-bound transition probabilities than our adopted set. We compare our new effective recombination coefficients with our prior work and our new emissivities with those by other researchers, and we conclude with brief remarks on the effects of the present work on the He I error budget. Our calculations cover temperatures $5000 \le T_e \le 25000$ K and densities $10^1 \le n_e \le 10^{14}$ cm$^{-3}$. Full results are available online.Comment: Accepted to MNRAS Letters; 4 pages, 4 figures, 2 tables, 1 supplemental fil