The human and mammalian cerebrum scale by computational power and information resistance

The cerebrum of mammals spans a vast range of sizes and yet has a very regular structure. The amount of folding of the cortical surface and the proportion of white matter gradually increase with size, but the underlying mechanisms remain elusive. Here, two laws are derived to fully explain these cerebral scaling relations. The first law holds that the long-range information flow in the cerebrum is determined by the total cortical surface (i.e., the number of neurons) and the increasing information resistance of long-range connections. Despite having just one free parameter, the first law fits the mammalian cerebrum better than any existing function, both across species and within humans. According to the second law, the white matter volume scales, with a few minor corrections, to the cortical surface area. It follows from the first law that large cerebrums have much local processing and little global information flow. Moreover, paradoxically, a further increase in long-range connections would decrease the efficiency of information flow.Comment: 15 pages, 2 figures; 3 supplement

Detection of Gravitational Waves from Inflation

Recent measurements of temperature fluctuations in the cosmic microwave background (CMB) indicate that the Universe is flat and that large-scale structure grew via gravitational infall from primordial adiabatic perturbations. Both of these observations seem to indicate that we are on the right track with inflation. But what is the new physics responsible for inflation? This question can be answered with observations of the polarization of the CMB. Inflation predicts robustly the existence of a stochastic background of cosmological gravitational waves with an amplitude proportional to the square of the energy scale of inflation. This gravitational-wave background induces a unique signature in the polarization of the CMB. If inflation took place at an energy scale much smaller than that of grand unification, then the signal will be too small to be detectable. However, if inflation had something to do with grand unification or Planck-scale physics, then the signal is conceivably detectable in the optimistic case by the Planck satellite, or if not, then by a dedicated post-Planck CMB polarization experiment. Realistic developments in detector technology as well as a proper scan strategy could produce such a post-Planck experiment that would improve on Planck's sensitivity to the gravitational-wave background by several orders of magnitude in a decade timescale.Comment: 13 page, 4 figures. To appear in the proceedings of DPF2000, Columbus, 9-12 August 2000 and (with slight revisions) in the proceedings of, "Gravitational Waves: A Challenge to Theoretical Astrophysics," Trieste, 5-9 June 200

Home biased? : A spatial analysis of the domestic merging behavior of US firms

Using data of US domestic mergers and acquisitions transactions, this paper shows that acquirers have a preference for geographically proximate target companies. We measure the ‘home bias’ against benchmark portfolios of hypothetical deals where the potential targets consist of firms of similar size in the same four-digit SIC code that have been targets in other transactions at about the same time or firms that have been listed at a stock exchange at that time. There is a strong and consistent home bias for M&A transactions in the US, which is significantly declining during the observation period, i.e. between 1990 and 2004. At the same time, the average distances between target and acquirer increase articulately. The home bias is stronger for small and relatively opaque target companies suggesting that local information is the decisive factor in explaining the results. Acquirers that diversify into new business lines also display a stronger preference for more proximate targets. With an event study we show that investors react relatively better to proximate acquisitions than to distant ones. That reaction is more important and becomes significant in times when the average distance between target and acquirer becomes larger, but never becomes economically significant. We interpret this as evidence for the familiarity hypothesis brought forward by Huberman (2001): Acquirers know about the existence of proximate targets and are more likely to merge with them without necessarily being better informed. However, when comparing the best and the worst deals, we are able to show a dramatic difference in distances and home bias: The most successful deals display on average a much stronger home bias and distinctively smaller distance between acquirer and target than the least successful deals. Proximity in M&A transactions therefore is a necessary but not sufficient condition for success. The paper contributes to the growing literature on the role of distance in financial decisions

Reproductive biology of carpenter seabream (Argyrozona argyrozona) (Pisces: Sparidae) in a marine protected area

The carpenter seabream (Argyrozona argyrozona) is an endemic South African sparid that comprises an important part of the handline fishery. A three-year study (1998−2000) into its reproductive biology within the Tsitsikamma National Park revealed that these fishes are serial spawning late gonochorists. The size at 50% maturity (L50) was estimated at 292 and 297 mm FL for both females and males, respectively. A likelihood ratio test revealed that there was no significant difference between male and female L50 (P>0.5). Both monthly gonadosomatic indices and macroscopically determined ovarian stages strongly indicate that A. argyrozona within the Tsitsikamma National Park spawn in the astral summer between November and April. The presence of postovulatory follicles (POFs) confirmed a six-month spawning season, and monthly proportions of early (0−6 hour old) POFs showed that spawning frequency was highest (once every 1−2 days) from December to March. Although spawning season was more highly correlated to photoperiod (r = 0.859) than temperature (r = −0.161), the daily proportion of spawning fish was strongly correlated (r= 0.93) to ambient temperature over the range 9−22oC. These results indicate that short-term upwelling events, a strong feature in the Tsitsikamma National Park during summer, may negatively affect carpenter fecundity. Both spawning frequency and duration (i.e., length of spawning season) increased with fish length. As a result of the allometric relationship between annual fecundity and fish mass a 3-kg fish was calculated to produce fivefold more eggs per kilogram of body weight than a fish of 1 kg. In addition to producing more eggs per unit of weight each year, larger fish also produce significantly larger eggs

Simple model for the Darwinian transition in early evolution

It has been hypothesized that in the era just before the last universal common ancestor emerged, life on earth was fundamentally collective. Ancient life forms shared their genetic material freely through massive horizontal gene transfer (HGT). At a certain point, however, life made a transition to the modern era of individuality and vertical descent. Here we present a minimal model for this hypothesized "Darwinian transition." The model suggests that HGT-dominated dynamics may have been intermittently interrupted by selection-driven processes during which genotypes became fitter and decreased their inclination toward HGT. Stochastic switching in the population dynamics with three-point (hypernetwork) interactions may have destabilized the HGT-dominated collective state and led to the emergence of vertical descent and the first well-defined species in early evolution. A nonlinear analysis of a stochastic model dynamics covering key features of evolutionary processes (such as selection, mutation, drift and HGT) supports this view. Our findings thus suggest a viable route from early collective evolution to the start of individuality and vertical Darwinian evolution, enabling the emergence of the first species.Comment: 9 pages, 5 figures, under review at Physical Review

Examples of scalar-flat hypersurfaces in Rn+1\mathbb{R}^{n+1}

Given a hypersurface $M$ of null scalar curvature in the unit sphere $\mathbb{S}^n$, $n\ge 4$, such that its second fundamental form has rank greater than 2, we construct a singular scalar-flat hypersurface in \Rr^{n+1} as a normal graph over a truncated cone generated by $M$. Furthermore, this graph is 1-stable if the cone is strictly 1-stable.Comment: Paper accepted to publication in Manuscripta Mathematic