Pyramids in the complex projective plane

We study the critical points of the diameter functional on the n-fold Cartesian product of the complex projective plane C P ² with the Fubini-Study metric. Such critical points arise in the calculation of a metric invariant called the filling radius, and are akin to the critical points of the distance function. We study a special family of such critical points, P _kC P ¹C P ², k=1,2... We show that P _k is a local minimum of by verifying the positivity of the Hessian of (a smooth approximation to) at P _k. For this purpose, we use Shirokov's law of cosines and the holonomy of the normal bundle of C P ¹C P ². We also exhibit a critical point of , given by a subset which is not contained in any totally geodesic submanifold of C P ².     

A non-Abelian analogue of Whitney’s 2-isomorphism theorem

We give a non-Abelian analogue of Whitney’s 2-isomorphism theorem for graphs. Whitney’s theorem states that the cycle space determines a graph up to 2-isomorphism. Instead of considering the cycle space of a graph which is an Abelian object, we consider a mildly non-Abelian object, the 2-truncation of the group algebra of the fundamental group of the graph considered as a subalgebra of the 2-truncation of the group algebra of the free group on the edges. The analogue of Whitney’s theorem is that this is a complete invariant of 2-edge connected graphs: let G, G′ be 2-edge connected finite graphs; if there is a bijective correspondence between the edges of G and G′ that induces equality on the 2-truncations of the group algebras of the fundamental groups, then G and G′ are isomorphic.     

Dynamic data structures for fat objects and their applications

We present several efficient dynamic data structures for point-enclosure queries, involving convex fat objects in or. Our planar structures are actually fitted for a more general class of objects – (β,δ)-covered objects – which are not necessarily convex, see definition below. These structures are more efficient than alternative known structures, because they exploit the fatness of the objects. We then apply these structures to obtain efficient solutions to two problems: (i) finding a perfect containment matching between a set of points and a set of convex fat objects, and (ii) finding a piercing set for a collection of convex fat objects, whose size is optimal up to some constant factor.     

Volume Contents

Volume Contents

Volume Contents     

On the degree of Hilbert polynomials associated to the torsion functor

Let be a local, Noetherian ring and an ideal. A question of Kodiyalam asks whether for fixed , the polynomial giving the th Betti number of has degree equal to the analytic spread of minus one. Under mild conditions on , we show that the answer is positive in a number of cases, including when is divisible by or is an integrally closed -primary ideal.

     

Rapid head-related transfer function adaptation using a virtual auditory environment

The paper reports on the ability of people to rapidly adapt in localizing virtual sound sources in both azimuth and elevation when listening to sounds synthesized using non-individualized head-related transfer functions (HRTFs). Participants were placed within an audio-kinesthetic Virtual Auditory Environment (VAE) platform that allows association of the physical position of a virtual sound source with an alternate set of acoustic spectral cues through the use of a tracked physical ball manipulated by the subject. This set-up offers a natural perception-action coupling, which is not limited to the visual field of view. The experiment consisted of three sessions: an initial localization test to evaluate participants' performance, an adaptation session, and a subsequent localization test. A reference control group was included using individual measured HRTFs. Results show significant improvement in localization performance. Relative to the control group, participants using non-individual HRTFs reduced localization errors in elevation by 10° with three sessions of 12 min. No significant improvement was found for azimuthal errors or for single session adaptation.     

Measuring and Modeling the U.S. Regulatory Ecosystem

Over the last 23 years, the U.S. Securities and Exchange Commission has required over 34,000 companies to file over 165,000 annual reports. These reports, the so-called “Form 10-Ks,” contain a characterization of a company’s financial performance and its risks, including the regulatory environment in which a company operates. In this paper, we analyze over 4.5 million references to U.S. Federal Acts and Agencies contained within these reports to measure the regulatory ecosystem, in which companies are organisms inhabiting a regulatory environment. While individuals across the political, economic, and academic world frequently refer to trends in this regulatory ecosystem, far less attention has been paid to supporting such claims with large-scale, longitudinal data. In this paper, in addition to positing a model of regulatory ecosystems, we document an increase in the regulatory energy per filing, i.e., a warming “temperature.” We also find that the diversity of the regulatory ecosystem has been increasing over the past two decades. These findings support the claim that regulatory activity and complexity are increasing, and this framework contributes an important step towards improving academic and policy discussions around legal complexity and regulation.     

Size-dependent tunneling and optical spectroscopy of CdSe quantum rods

Photoluminescence excitation spectroscopy and scanning-tunneling spectroscopy are used to study the electronic states in CdSe quantum rods that manifest a transition from a zero-dimensional to a one-dimensional quantum-confined structure. Both optical and tunneling spectra show that the level structure depends primarily on the diameter of the rod and not its length. With increasing diameter, the band gap and the excited state level spacings shift to the red. The level structure was assigned using a multiband effective-mass model, showing a similar dependence on rod dimensions.     

Determination of plasma lactic acid concentration and specific activity using high-performance liquid chromatography.

Assessment of lactate metabolism is of particular interest during exercise and in disease states such as diabetes, shock, and absorptive abnormalities of short-chain fatty acids by the colon. We describe an analytical method that introduces radio-active tracers and high-performance liquid chromatography (HPLC) to simultaneously analyze concentrations and specific activities (SAs) of plasma lactate. The HPLC conditions included separation on a reversed-phase column (octadecylsilane) and an isocratic buffer (30% acetonitrile in water). [3H]Acetate served as an internal standard. Lactate and acetate were extracted from plasma samples with diethyl ether following a pH adjustment to less than 1.0 and back-extracted into a hydrophilic phase with sodium carbonate (2 mM, pH greater than 10.0). Lactate is detected in the ultraviolet range (242 and 320 nm) by derivatization with alpha-bromoacetophenone. Control plasma samples were studied after an overnight fast for precision and analytical recovery. Calibration curves were linear in the range 0.18-6.0 mM (r = 0.92). The precision was 3% and the analytical recovery was 87%. The detection limit of the method was 36 pmol. Determination of lactate metabolism was performed in a patient with chronic congestive heart failure who was administered primed-continuous L-[U-14C]lactate (10 microCi bolus and 0.3 microCi/min continuously) during a 60-min rest period. Mean arterial lactate concentration and SA were 1.69 +/- 0.2 mM and 253.8 +/- 22 dpm/mumol, respectively. Systemic lactate turnover was 25.65 mumol/kg per min. Lactic acid systemic turnover, organ uptake and release rates can be accurately determined by isocratic HPLC.     

Radiation-induced dechlorination of carbon tetrachloride in cyclohexane Solutions. The kinetics of liquid-phase reactions of trichloromethyl radicals

The kinetics of the gamma-radiation induced free-radical chain reaction in solutions of carbon tetrachloride in cyclohexane (RH) has been investigated in the temperature range of 303–383°K. Trichloromethyl radicals were produced by the reaction of radiolytically generated cyclohexyl radicals with carbon tetrachloride. The kinetics of the following reactions were investigated: The following rate expression was obtained: The error limits are the standard deviation from the least mean square Arrhenius plots. Effects of phase on the kinetics of reactions (3) and (4) are considered.