A quantitative measure of carrier shocking

I propose a definition for a "shocking coefficient" $S$ intended to make determinations of the degree of waveform shocking, and comparisons thereof, more quantitative. This means we can avoid having to make ad hoc judgements on the basis of the visual comparison of wave profiles.Comment: 5 pages, 6 figure

The quantitative measure and statistical distribution of fame

Fame and celebrity play an ever-increasing role in our culture. However, despite the cultural and economic importance of fame and its gradations, there exists no consensus method for quantifying the fame of an individual, or of comparing that of two individuals. We argue that, even if fame is difficult to measure with precision, one may develop useful metrics for fame that correlate well with intuition and that remain reasonably stable over time. Using datasets of recently deceased individuals who were highly renowned, we have evaluated several internet-based methods for quantifying fame. We find that some widely-used internet-derived metrics, such as search engine results, correlate poorly with human subject judgments of fame. However other metrics exist that agree well with human judgments and appear to offer workable, easily accessible measures of fame. Using such a metric we perform a preliminary investigation of the statistical distribution of fame, which has some of the power law character seen in other natural and social phenomena such as landslides and market crashes. In order to demonstrate how such findings can generate quantitative insight into celebrity culture, we assess some folk ideas regarding the frequency distribution and apparent clustering of celebrity deaths.Comment: 17 pages, 6 figure

A Quantitative Measure of Interference

We introduce an interference measure which allows to quantify the amount of interference present in any physical process that maps an initial density matrix to a final density matrix. In particular, the interference measure enables one to monitor the amount of interference generated in each step of a quantum algorithm. We show that a Hadamard gate acting on a single qubit is a basic building block for interference generation and realizes one bit of interference, an ``i-bit''. We use the interference measure to quantify interference for various examples, including Grover's search algorithm and Shor's factorization algorithm. We distinguish between ``potentially available'' and ``actually used'' interference, and show that for both algorithms the potentially available interference is exponentially large. However, the amount of interference actually used in Grover's algorithm is only about 3 i-bits and asymptotically independent of the number of qubits, while Shor's algorithm indeed uses an exponential amount of interference.Comment: 13 pages of latex; research done at http://www.quantware.ups-tlse.fr

Towards a quantitative measure of rareness

Within the context of detection of incongruent events, an often overlooked aspect is how a system should react to the detection. The set of all the possible actions is certainly conditioned by the task at hand, and by the embodiment of the artificial cognitive system under consideration. Still, we argue that a desirable action that does not depend from these factors is to update the internal model and learn the new detected event. This paper proposes a recent transfer learning algorithm as the way to address this issue. A notable feature of the proposed model is its capability to learn from small samples, even a single one. This is very desirable in this context, as we cannot expect to have too many samples to learn from, given the very nature of incongruent events. We also show that one of the internal parameters of the algorithm makes it possible to quantitatively measure incongruence of detected events. Experiments on two different datasets support our claim

Quantitative measure of evolution of bright cluster galaxies at moderate redshifts

Using archival data from the Hubble Space Telescope, we study the quantitative morphological evolution of spectroscopically confirmed bright galaxies in the core regions of nine clusters ranging in redshift from $z = 0.31$ to $z = 0.84$. We use morphological parameters derived from two dimensional bulge-disk decomposition to study the evolution. We find an increase in the mean bulge-to-total luminosity ratio $B/T$ as the Universe evolves. We also find a corresponding increase in the fraction of early type galaxies and in the mean S\'ersic index. We discuss these results and their implications to physical mechanisms for evolution of galaxy morphology.Comment: 5 pages, 3 figures, Accepted for publication in MNRAS: Letter

A direct quantitative measure of surface mobility in a glassy polymer

Thin polymer films have striking dynamical properties that differ from their bulk counterparts. With the simple geometry of a stepped polymer film on a substrate, we probe mobility above and below the glass transition temperature $T_{\textrm{g}}$. Above $T_{\textrm{g}}$ the entire film flows, while below $T_{\textrm{g}}$ only the near surface region responds to the excess interfacial energy. An analytical thin film model for flow limited to the free surface region shows excellent agreement with sub-$T_{\textrm{g}}$ data. The system transitions from whole film flow to surface localized flow over a narrow temperature region near the bulk $T_{\textrm{g}}$. The experiments and model provide a measure of surface mobility in a sample geometry where confinement and substrate effects are negligible. This fine control of the glassy rheology is of key interest to nanolithography among numerous other applications