Asymmetric Ramsey Properties of Random Graphs Involving Cliques

Consider the following problem: Forgiven graphs G and F(1),..., F(k), find a coloring of the edges of G with k colors such that G does not contain F; in color i. Rodl and Rucinski studied this problem for the random graph G,,, in the symmetric case when k is fixed and F(1) = ... = F(k) = F. They proved that such a coloring exists asymptotically almost surely (a.a.s.) provided that p <= bn(-beta) for some constants b = b(F,k) and beta = beta(F). This result is essentially best possible because for p >= Bn(-beta), where B = B(F, k) is a large constant, such an edge-coloring does not exist. Kohayakawa and Kreuter conjectured a threshold function n(-beta(F1,..., Fk)) for arbitrary F(1), ..., F(k). In this article we address the case when F(1),..., F(k) are cliques of different sizes and propose an algorithm that a.a.s. finds a valid k-edge-coloring of G(n,p) with p <= bn(-beta) for some constant b = b(F(1),..., F(k)), where beta = beta(F(1),..., F(k)) as conjectured. With a few exceptions, this algorithm also works in the general symmetric case. We also show that there exists a constant B = B(F,,..., Fk) such that for p >= Bn(-beta) the random graph G(n,p) a.a.s. does not have a valid k-edge-coloring provided the so-called KLR-conjecture holds. (C) 2008 Wiley Periodicals, Inc. Random Struct. Alg., 34, 419-453, 2009

A data driven approach for automating vehicle activated signs

Vehicle activated signs (VAS) display a warning message when drivers exceed a particular threshold. VAS are often installed on local roads to display a warning message depending on the speed of the approaching vehicles. VAS are usually powered by electricity; however, battery and solar powered VAS are also commonplace. This thesis investigated devel-opment of an automatic trigger speed of vehicle activated signs in order to influence driver behaviour, the effect of which has been measured in terms of reduced mean speed and low standard deviation. A comprehen-sive understanding of the effectiveness of the trigger speed of the VAS on driver behaviour was established by systematically collecting data. Specif-ically, data on time of day, speed, length and direction of the vehicle have been collected for the purpose, using Doppler radar installed at the road. A data driven calibration method for the radar used in the experiment has also been developed and evaluated. Results indicate that trigger speed of the VAS had variable effect on driv-ers’ speed at different sites and at different times of the day. It is evident that the optimal trigger speed should be set near the 85th percentile speed, to be able to lower the standard deviation. In the case of battery and solar powered VAS, trigger speeds between the 50th and 85th per-centile offered the best compromise between safety and power consump-tion. Results also indicate that different classes of vehicles report differ-ences in mean speed and standard deviation; on a highway, the mean speed of cars differs slightly from the mean speed of trucks, whereas a significant difference was observed between the classes of vehicles on lo-cal roads. A differential trigger speed was therefore investigated for the sake of completion. A data driven approach using Random forest was found to be appropriate in predicting trigger speeds respective to types of vehicles and traffic conditions. The fact that the predicted trigger speed was found to be consistently around the 85th percentile speed justifies the choice of the automatic model.

Mapping an uncertainty zone between interpolated types of a categorical variable

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

AATS for the (X)over-bar chart with variable parameters

A Fortran computer program is given for the computation of the adjusted average time to signal, or AATS, for adaptive (X) over bar charts with one, two, or all three design parameters variable: the sample size, n, the sampling interval, h, and the factor k used in determining the width of the action limits. The program calculates the threshold limit to switch the adaptive design parameters and also provides the in-control average time to signal, or ATS.

X̄ charts with variable sample size

The usual practice in using a control chart to monitor a process is to take samples of size n from the process every h hours. This article considers the properties of the X̄ chart when the size of each sample depends on what is observed in the preceding sample. The idea is that the sample should be large if the sample point of the preceding sample is close to but not actually outside the control limits and small if the sample point is close to the target. The properties of the variable sample size (VSS) X̄ chart are obtained using Markov chains. The VSS X̄ chart is substantially quicker than the traditional X̄ chart in detecting moderate shifts in the process.

AATS for the X̄ Chart with Variable Parameters

A Fortran computer program is given for the computation of the adjusted average time to signal, or AATS, for adaptive X̄ charts with one, two, or all three design parameters variable: the sample size, n, the sampling interval, h, and the factor k used in determining the width of the action limits. The program calculates the threshold limit to switch the adaptive design parameters and also provides the in-control average time to signal, or ATS.

Upconversion ultraviolet random lasing in Nd 3+ doped fluoroindate glass powder

An upconversion random laser (RL) operating in the ultraviolet is reported for Nd 3+ doped fluoroindate glass powder pumped at 575 nm. The RL is obtained by the resonant excitation of the Nd 3+ state 2G 7/2 followed by energy transfer among two excited ions such that one ion in the pair decays to a lower energy state and the other is promoted to state 4D 7/2 from where it decays emitting light at 381 nm. The RL threshold of 30 kW/cm 2 was determined by monitoring the photoluminescence intensity as a function of the pump laser intensity. The RL pulses have time duration of 29 ns that is 50 times smaller than the decay time of the upconversion signal when the sample is pumped with intensities below the RL laser threshold. © 2011 Optical Society of America.

Random laser action from flexible biocellulose-based device

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Coherence characteristics of random lasing in a dye doped hybrid powder

The photon statistics of the random laser emission of a Rhodamine B doped di-ureasil hybrid powder is investigated to evaluate its degree of coherence above threshold. Although the random laser emission is a weighted average of spatially uncorrelated radiation emitted at different positions in the sample, a spatial coherence control was achieved due to an improved detection configuration based on spatial filtering. By using this experimental approach, which also allows for fine mode discrimination and timeresolved analysis of uncoupled modes from mode competition, an area not larger than the expected coherence size of the random laser is probed. Once the spectral and temporal behavior of nonoverlapping modes is characterized, an assessment of the photon-number probability distribution and the resulting second-order correlation coefficient as a function of time delay and wavelength was performed. The outcome of our single photon counting measurements revealed a high degree of temporal coherence at the time of maximum pump intensity and at wavelengths around the Rhodamine B gain maximum.

Mapping an uncertainty zone between interpolated types of a categorical variable

Categorical data cannot be interpolated directly because they are outcomes of discrete random variables. Thus, types of categorical variables are transformed into indicator functions that can be handled by interpolation methods. Interpolated indicator values are then backtransformed to the original types of categorical variables. However, aspects such as variability and uncertainty of interpolated values of categorical data have never been considered. In this paper we show that the interpolation variance can be used to map an uncertainty zone around boundaries between types of categorical variables. Moreover, it is shown that the interpolation variance is a component of the total variance of the categorical variables, as measured by the coefficient of unalikeability. (C) 2011 Elsevier Ltd. All rights reserved.

Design-based random permutation models with auxiliary information

We extend the random permutation model to obtain the best linear unbiased estimator of a finite population mean accounting for auxiliary variables under simple random sampling without replacement (SRS) or stratified SRS. The proposed method provides a systematic design-based justification for well-known results involving common estimators derived under minimal assumptions that do not require specification of a functional relationship between the response and the auxiliary variables.

Dissipation effects in random transverse-field Ising chains

We study the effects of Ohmic, super-Ohmic, and sub-Ohmic dissipation on the zero-temperature quantum phase transition in the random transverse-field Ising chain by means of an (asymptotically exact) analytical strong-disorder renormalization-group approach. We find that Ohmic damping destabilizes the infinite-randomness critical point and the associated quantum Griffiths singularities of the dissipationless system. The quantum dynamics of large magnetic clusters freezes completely, which destroys the sharp phase transition by smearing. The effects of sub-Ohmic dissipation are similar and also lead to a smeared transition. In contrast, super-Ohmic damping is an irrelevant perturbation; the critical behavior is thus identical to that of the dissipationless system. We discuss the resulting phase diagrams, the behavior of various observables, and the implications to higher dimensions and experiments.

UNIVERSALITY OF RANDOM GRAPHS

We prove that asymptotically (as n -> infinity) almost all graphs with n vertices and C(d)n(2-1/2d) log(1/d) n edges are universal with respect to the family of all graphs with maximum degree bounded by d. Moreover, we provide an efficient deterministic embedding algorithm for finding copies of bounded degree graphs in graphs satisfying certain pseudorandom properties. We also prove a counterpart result for random bipartite graphs, where the threshold number of edges is even smaller but the embedding is randomized.

Pain pressure threshold algometry of the abdominal wall in healthy women

The objective of this study was to determine the inter- and intra-examiner reliability of pain pressure threshold algometry at various points of the abdominal wall of healthy women. Twenty-one healthy women in menacme with a mean age of 28 +/- 5.4 years (range: 19-39 years) were included. All volunteers had regular menstrual cycles (27-33 days) and were right-handed and, to the best of our knowledge, none were taking medications at the time of testing. Women with a diagnosis of depression, anxiety or other mood disturbances were excluded. Women with previous abdominal surgery, any pain condition or any evidence of inflammation, hypertension, smoking, alcoholism, or inflammatory disease were also excluded. Pain perception thresholds were assessed with a pressure algometer with digital traction and compression and a measuring capacity for 5 kg. All points were localized by palpation and marked with a felt-tipped pen and each individual was evaluated over a period of 2 days in two consecutive sessions, each session consisting of a set of 14 point measurements repeated twice by two examiners in random sequence. There was no statistically significant difference in the mean pain threshold obtained by the two examiners on 2 diferent days (examiner A: P = 1.00; examiner B: P = 0.75; Wilcoxon matched pairs test). There was excellent/good agreement between examiners for all days and all points. Our results have established baseline values to which future researchers will be able to refer. They show that pressure algometry is a reliable measure for pain perception in the abdominal wall of healthy women.

Studying the influence of a secondary variable in Collocated Cokriging estimates

In this paper the influence of a secondary variable as a function of the correlation with the primary variable for collocated cokriging is examined. For this study five exhaustive data sets were generated in computer, from which samples with 60 and 104 data points were drawn using the stratified random sampling method. These exhaustive data sets were generated departing from a pair of primary and secondary variables showing a good correlation. Then successive sets were generated by adding an amount of white noise in such a way that the correlation gets poorer. Using these samples, it was possible to find out how primary and secondary information is used to estimate an unsampled location according to the correlation level.