Scaling function for the noisy Burgers equation in the soliton approximation

We derive the scaling function for the one dimensional noisy Burgers equation in the two-soliton approximation within the weak noise canonical phase space approach. The result is in agreement with an earlier heuristic expression and exhibits the correct scaling properties. The calculation presents the first step in a many body treatment of the correlations in the Burgers equation.Comment: Replacement: Several corrections, 4 pages, Revtex file, 3 figures. To appear in Europhysics Letter

Biomechanical comparison of the track start and the modified one-handed track start in competitive swimming: an intervention study

This study compared the conventional track and a new one-handed track start in elite age group swimmers to determine if the new technique had biomechanical implications on dive performance. Five male and seven female GB national qualifiers participated (mean ± SD: age 16.7 ± 1.9 years, stretched stature 1.76 ± 0.8 m, body mass 67.4 ± 7.9 kg) and were assigned to a control group (n = 6) or an intervention group (n = 6) that learned the new onehanded dive technique. All swimmers underwent a 4-week intervention comprising 12 ± 3 thirty-minute training sessions. Video cameras synchronized with an audible signal and timing suite captured temporal and kinematic data. A portable force plate and load cell handrail mounted to a swim starting block collected force data over 3 trials of each technique. A MANCOVA identified Block Time (BT), Flight Time (FT), Peak Horizontal Force of the lower limbs (PHF) and Horizontal Velocity at Take-off (Vx) as covariates. During the 10-m swim trial, significant differences were found in Time to 10 m (TT10m), Total Time (TT), Peak Vertical Force (PVF), Flight Distance (FD), and Horizontal Velocity at Take-off (Vx) (p < .05). Results indicated that the conventional track start method was faster over 10 m, and therefore may be seen as a superior start after a short intervention. During training, swimmers and coaches should focus on the most statistically significant dive performance variables: peak horizontal force and velocity at take-off, block and flight time

Characterization and properties of controlled nucleation thermochemical deposited (CNTD) silicon carbide

The microstructure of controlled nucleation thermochemical deposition (CNTD) - SiC material was studied and the room temperature and high temperature bend strength and oxidation resistance was evaluated. Utilizing the CNTD process, ultrafine grained (0.01-0.1 mm) SiC was deposited on W - wires (0.5 mm diameter by 20 cm long) as substrates. The deposited SiC rods had superior surface smoothness and were without any macrocolumnar growth commonly found in conventional CVD material. At both room and high temperature (1200 - 1380 C), the CNTD - SiC exhibited bend strength approximately 200,000 psi (1380 MPa), several times higher than that of hot pressed, sintered, or CVD SiC. The excellent retention of strength at high temperature was attributed to the high purity and fine grain size of the SiC deposit and the apparent absence of grain growth at elevated temperatures. The rates of weight change for CNTD - SiC during oxidation were lower than for NC-203 (hot pressed SiC), higher than for GE's CVD - SiC, and considerably below those for HS-130 (hot pressed Si3N4). The high purity, fully dense, and stable grain size CNTD - SiC material shows potential for high temperature structural applications; however problem areas might include: scaling the process to make larger parts, deposition on removable substrates, and the possible residual tensile stress

Apollonian Circle Packings: Geometry and Group Theory III. Higher Dimensions

This paper gives $n$-dimensional analogues of the Apollonian circle packings in parts I and II. We work in the space \sM_{\dd}^n of all $n$-dimensional oriented Descartes configurations parametrized in a coordinate system, ACC-coordinates, as those $(n+2) \times (n+2)$ real matrices \bW with \bW^T \bQ_{D,n} \bW = \bQ_{W,n} where $Q_{D,n} = x_1^2 +... + x_{n+2}^2 - \frac{1}{n}(x_1 +... + x_{n+2})^2$ is the $n$-dimensional Descartes quadratic form, $Q_{W,n} = -8x_1x_2 + 2x_3^2 + ... + 2x_{n+2}^2$, and \bQ_{D,n} and \bQ_{W,n} are their corresponding symmetric matrices. There are natural actions on the parameter space \sM_{\dd}^n. We introduce $n$-dimensional analogues of the Apollonian group, the dual Apollonian group and the super-Apollonian group. These are finitely generated groups with the following integrality properties: the dual Apollonian group consists of integral matrices in all dimensions, while the other two consist of rational matrices, with denominators having prime divisors drawn from a finite set $S$ depending on the dimension. We show that the the Apollonian group and the dual Apollonian group are finitely presented, and are Coxeter groups. We define an Apollonian cluster ensemble to be any orbit under the Apollonian group, with similar notions for the other two groups. We determine in which dimensions one can find rational Apollonian cluster ensembles (all curvatures rational) and strongly rational Apollonian sphere ensembles (all ACC-coordinates rational).Comment: 37 pages. The third in a series on Apollonian circle packings beginning with math.MG/0010298. Revised and extended. Added: Apollonian groups and Apollonian Cluster Ensembles (Section 4),and Presentation for n-dimensional Apollonian Group (Section 5). Slight revision on March 10, 200

Apollonian Circle Packings: Geometry and Group Theory I. The Apollonian Group

Apollonian circle packings arise by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. We observe that there exist Apollonian packings which have strong integrality properties, in which all circles in the packing have integer curvatures and rational centers such that (curvature)$\times$(center) is an integer vector. This series of papers explain such properties. A {\em Descartes configuration} is a set of four mutually tangent circles with disjoint interiors. We describe the space of all Descartes configurations using a coordinate system \sM_\DD consisting of those $4 \times 4$ real matrices \bW with \bW^T \bQ_{D} \bW = \bQ_{W} where \bQ_D is the matrix of the Descartes quadratic form $Q_D= x_1^2 + x_2^2+ x_3^2 + x_4^2 -{1/2}(x_1 +x_2 +x_3 + x_4)^2$ and \bQ_W of the quadratic form $Q_W = -8x_1x_2 + 2x_3^2 + 2x_4^2$. There are natural group actions on the parameter space \sM_\DD. We observe that the Descartes configurations in each Apollonian packing form an orbit under a certain finitely generated discrete group, the {\em Apollonian group}. This group consists of $4 \times 4$ integer matrices, and its integrality properties lead to the integrality properties observed in some Apollonian circle packings. We introduce two more related finitely generated groups, the dual Apollonian group and the super-Apollonian group, which have nice geometrically interpretations. We show these groups are hyperbolic Coxeter groups.Comment: 42 pages, 11 figures. Extensively revised version on June 14, 2004. Revised Appendix B and a few changes on July, 2004. Slight revision on March 10, 200

Apollonian Circle Packings: Geometry and Group Theory II. Super-Apollonian Group and Integral Packings

Apollonian circle packings arise by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. Such packings can be described in terms of the Descartes configurations they contain. It observed there exist infinitely many types of integral Apollonian packings in which all circles had integer curvatures, with the integral structure being related to the integral nature of the Apollonian group. Here we consider the action of a larger discrete group, the super-Apollonian group, also having an integral structure, whose orbits describe the Descartes quadruples of a geometric object we call a super-packing. The circles in a super-packing never cross each other but are nested to an arbitrary depth. Certain Apollonian packings and super-packings are strongly integral in the sense that the curvatures of all circles are integral and the curvature$\times$centers of all circles are integral. We show that (up to scale) there are exactly 8 different (geometric) strongly integral super-packings, and that each contains a copy of every integral Apollonian circle packing (also up to scale). We show that the super-Apollonian group has finite volume in the group of all automorphisms of the parameter space of Descartes configurations, which is isomorphic to the Lorentz group $O(3, 1)$.Comment: 37 Pages, 11 figures. The second in a series on Apollonian circle packings beginning with math.MG/0010298. Extensively revised in June, 2004. More integral properties are discussed. More revision in July, 2004: interchange sections 7 and 8, revised sections 1 and 2 to match, and added matrix formulations for super-Apollonian group and its Lorentz version. Slight revision in March 10, 200

Finding the way forward for forensic science in the US:a commentary on the PCAST report

A recent report by the US President’s Council of Advisors on Science and Technology (PCAST) [1] has made a number of recommendations for the future development of forensic science. Whereas we all agree that there is much need for change, we find that the PCAST report recommendations are founded on serious misunderstandings. We explain the traditional forensic paradigms of match and identification and the more recent foundation of the logical approach to evidence evaluation. This forms the groundwork for exposing many sources of confusion in the PCAST report. We explain how the notion of treating the scientist as a black box and the assignment of evidential weight through error rates is overly restrictive and misconceived. Our own view sees inferential logic, the development of calibrated knowledge and understanding of scientists as the core of the advance of the profession

Post-Issue Patent "Quality Control": A Comparative Study of US Patent Re-examinations and European Patent Oppositions

We report the results of the first comparative study of the determinants and effects of patent oppositions in Europe and of re-examinations on corresponding patents issued in the United States. The analysis is based on a dataset consisting of matched EPO and US patents. Our analysis focuses on two broad technology categories - biotechnology and pharmaceuticals, and semiconductors and computer software. Within these fields, we collect data on all EPO patents for which oppositions were filed at the EPO. We also construct a random sample of EPO patents with no opposition in these technologies. We match these EPO patents with the 'equivalent' US patents covering the same invention in the United States. Using the matched sample of USPTO and EPO patents, we compare the determinants of opposition and of re-examination. Our results indicate that valuable patents are more likely to be challenged in both jurisdictions. But the rate of opposition at the EPO is more than thirty times higher than the rate of re-examination at the USPTO. Moreover, opposition leads to a revocation of the patent in about 41 percent of the cases, and to a restriction of the patent right in another 30 percent of the cases. Re-examination results in a cancellation of the patent right in only 12.2 percent of all cases. We also find that re-examination is frequently initiated by the patentholders themselves.

Post-Issue Patent "Quality Control": A Comparative Study of US Patent Re-examinations and European Patent Oppositions

We report the results of the first comparative study of the determinants and effects of patent oppositions in Europe and of re- examinations on corresponding patents issued in the United States. The analysis is based on a dataset consisting of matched EPO and US patents. Our analysis focuses on two broad technology categories - biotechnology and pharmaceuticals, and semiconductors and computer software. Within these fields, we collect data on all EPO patents for which oppositions were filed at the EPO. We also construct a random sample of EPO patents with no opposition in these technologies. We match these EPO patents with the “equivalent” US patents covering the same invention in the United States. Using the matched sample of USPTO and EPO patents, we compare the determinants of opposition and of reexamination. Our results indicate that valuable patents are more likely to be challenged in both jurisdictions. But the rate of opposition at the EPO is more than thirty times higher than the rate of reexamination at the USPTO.