Exponential Rate Of Decrease Research Articles

Understanding the radial contraction and axial mechanical responses of carbon nanotube yarns under axial tensile loading

Carbon nanotube yarns (CNTYs) are hierarchical fibers with outstanding mechanical and electrical properties, with promising applications in the composite industry and as smart materials. In situ scanning electron microscopy observations are performed herein on individual dry-spun CNTYs during axial tensile testing in order to study their radial contraction response and structural changes. The CNTYs exhibited significant diameter reduction and untwisting due to the rearrangement of their fibrils during axial loading. In situ measurements of CNTY diameter reduction led to an exponential decrease of the radial contraction ratio with axial strain, with average values ranging between 5.43 and 1.08. The major failure mechanism was identified as fibril pull-out triggered by fibril slipping. The simultaneous stress and electrical resistance decay of CNTYs under axial tensile relaxation tests fit to a Wiechert's viscoelastic model using a Prony series. The rate of exponential decrease of the electrical resistance over time, however, is slower than that of the stress relaxation, indicating that additional charge carrier relaxation phenomena are present. Using the measured structural and material data input, a nonlinear analytical model based on classical theory of staple yarns is able to reproduce the mechanical response of the yarn. The model suggests that the most prominent parameters affecting the axial mechanical response of the CNTY are the radial contraction ratio, the slip factor, fibril radius, and fibril length.

Environmental Controls on the Climatological Scaling of Tornado Frequency with Intensity

AbstractThe scaling of U.S. tornado frequency with enhanced Fujita (EF)-rated intensity is examined for the range EF1–EF3. Previous work has found that tornado frequency decreases exponentially with increasing EF rating and that many regions around the world show the same exponential rate of decrease despite having quite different overall tornado frequencies. This scaling is important because it relates the frequency of the most intense tornadoes to the overall tornado frequency. Here we find that U.S. tornado frequency decreases more sharply with increasing intensity during summer than during other times of the year. One implication of this finding is that, despite their rarity, when tornadoes do occur during the cool season, the relative likelihood of more intense tornadoes is higher than during summer. The environmental driver of this scaling variability is explored through new EF-dependent tornado environmental indices (TEI-EF) that are fitted to each EF class. We find that the sensitivity of TEI-EF to storm relative helicity (SRH) increases with increasing EF class. This increasing sensitivity to SRH means that TEI-EF predicts a slower decrease in frequency with increasing intensity for larger values of SRH (e.g., cool season) and a sharper decrease in tornado frequency in summer when wind shear plays a less dominant role. This explanation is also consistent with the fact that the fraction of supercell tornadoes is smaller during summer.

On exponential decay of the variance of BLUE for the mean of a stationary sequence

Abstract In this paper, we obtain necessary as well as sufficient conditions for exponential rate of decrease of the variance of the best linear unbiased estimator (BLUE) for the unknown mean of a stationary sequence possessing a spectral density. In particular, we show that a necessary condition for variance of BLUE to decrease to zero exponentially is that the spectral density vanishes on a set of positive Lebesgue measure in any vicinity of zero.

Asymptotic Behavior of the Variance of the Best Linear Unbiased Estimator for the Mean of a Discrete-time Singular Stationary Process

It is known that for a wide class of discrete-time stationary processes possessing spectral densities f, the variance σ2(f) of the best linear unbiased estimator for the mean depends asymptotically only on the behavior of the spectral density f near the origin, and behaves hyperbolically as n → ∞. In this paper, we obtain necessary as well as sufficient conditions for exponential rate of decrease of σ2(f) as n → ∞. In particular, we show that a necessary condition for σ2(f) to decrease to zero exponentially is that the spectral density f vanishes on a set of positive measure in any vicinity of zero, and if f vanishes only at the origin, then it is impossible to obtain exponential decay of σ2(f), no mater how high the order of the zero of f at the origin.

Unequal Error Protection Querying Policies for the Noisy 20 Questions Problem

In this paper, we propose an open-loop unequal-error-protection querying policy based on superposition coding for the noisy 20 questions problem. In this problem, a player wishes to successively refine an estimate of the value of a continuous random variable by posing binary queries and receiving noisy responses. When the queries are designed non-adaptively as a single block and the noisy responses are modeled as the output of a binary symmetric channel the 20 questions problem can be mapped to an equivalent problem of channel coding with unequal error protection (UEP). A new non-adaptive querying strategy based on UEP superposition coding is introduced whose estimation error decreases with an exponential rate of convergence that is significantly better than that of the UEP repetition coding introduced by Variani et al. (2015). With the proposed querying strategy, the rate of exponential decrease in the number of queries matches the rate of a closed-loop adaptive scheme where queries are sequentially designed with the benefit of feedback. Furthermore, the achievable error exponent is significantly better than that of random block codes employing equal error protection.

Ozone Design Values in Southern California's Air Basins: Temporal Evolution and U.S. Background Contribution

AbstractCalifornia's ambient ozone concentrations have two principal contributions: U.S. background ozone and enhancements produced from anthropogenic precursor emissions; only the latter effectively respond to California emission controls. From 1980 to 2015 ozone has been monitored in eight air basins in Southern California. The temporal evolution of the largest measured concentrations, i.e., those that define the ozone design value (ODV) upon which the National Ambient Air Quality Standard (NAAQS) is based, is described very well by an exponential decrease on top of a positive offset. We identify this offset as the ODV due to the U.S. background ozone (i.e., the concentration that would be present if U.S. anthropogenic precursor emissions were reduced to zero) and is estimated to be 62.0 ± 1.9 ppb in six of the basins. California's emission control efforts have reduced the anthropogenic ozone enhancements by a factor of ~5 since 1980. However, assuming that the current rate of exponential decrease is maintained and that U.S. background ODV remains constant, projections of the past decrease suggest that ~35 years of additional emission control efforts will be required to reach the new NAAQS of 70 ppb in the Los Angeles area. The growing predominance of U.S. background ozone contributions has shifted the maximum ozone concentrations in all air basins from later to earlier in the summer. Comparisons indicate that currently accepted model estimates of U.S. background ozone concentrations in Southern California are somewhat underestimated; thus, reducing ozone in this region to the 2015 NAAQS may be more difficult than currently expected.

Precise Evaluation of Leaked Information with Secure Randomness Extraction in the Presence of Quantum Attacker

We treat secret key extraction when the eavesdropper has correlated quantum states. We propose quantum privacy amplification theorems different from Renner’s, which are based on quantum conditional Rényi entropy of order 1 + s. Using those theorems, we derive an exponential rate of decrease for leaked information and the asymptotic equivocation rate, which have not been derived hitherto in the quantum setting.

Tight Exponential Analysis of Universally Composable Privacy Amplification and Its Applications

Motivated by the desirability of universal composability, we analyze in terms of L_1 distinguishability the task of secret key generation from a joint random variable. Under this secrecy criterion, using the Renyi entropy of order 1+s for s in [0,1, we derive a new upper bound of Eve's distinguishability under the application of the universal2 hash functions. It is also shown that this bound gives the tight exponential rate of decrease in the case of independent and identical distributions. The result is applied to the wire-tap channel model and to secret key generation (distillation) by public discussion.

Stochastic Hybrid Systems with Renewal Transitions: Moment Analysis with Application to Networked Control Systems with Delays

We consider stochastic hybrid systems (SHSs) for which the lengths of times that the system stays in each mode are independent random variables with given distributions. We propose an approach based on a set of Volterra equations to compute any statistical moment of the state of the SHS. Moreover, we provide a method to compute the Lyapunov exponents of a given degree, i.e., the exponential rate of decrease or increase at which statistical moments converge to zero or to infinity, respectively. We also discuss how, by computing the statistical moments, one can provide information about the probability distribution of the state of the SHS. The applicability of the results is illustrated in the analysis of a networked control problem with independently distributed intervals between data transmissions and delays.

Nesting activity and demography of an isolated population of malleefowl (Leipoa ocellata)

Nesting activity of a population of malleefowl (Leipoa ocellata), isolated within a small mallee remnant in central New South Wales, was monitored annually between the summers of 1986–87 and 1998–99. A total of 148 nesting events was recorded. Only once was a new mound constructed rather than an old one reworked. Birds began and finished work on the mound progressively later each month (October to January). Nest-site fidelity was highly variable; some pairs persisted with the same mound for up to nine years while others relocated between a cluster of two, three or four mounds. Males displayed greater nest-site fidelity than females. After the loss of a partner, males tended to continue to use mounds they had used previously whereas females often relocated to a new mound. All individuals were monogamous. Pair bonds were maintained for life but, following the death of a partner, new bonds were quickly established with another unattached individual. Established pairs occasionally failed to breed, all such failures being coincident with years of low rainfall. Pairs that did not breed generally began construction of a nest but failed to complete the task. As far as can be ascertained, unpaired birds did not construct nests. The malleefowl population was characterised by a rapid turnover of breeding individuals, a high rate of adult mortality and a lesser rate of recruitment. The maximum longevity recorded for breeding adults was 12 years; average longevity was 7.5 years. Twenty-five adults were lost from the breeding population over a period of 9 years; meanwhile, 14 birds entered the breeding population. Thus, the ratio of adult mortality to recruitment was 1.79 : 1.00. Between 1986–87 and 1997–98 the population declined from at least 32 breeding adults to 14, at an average exponential rate of decrease of 0.075. Large population decreases were coincident with years of low rainfall. This population of malleefowl is predicted to become extinct by 2008.

An analytical model for the altitude variation of aerosol number densities in the coastal atmospheric boundary layer

A simplified one dimensional analytical model to describe the altitude variation of aerosol number densities in the atmospheric boundary layer during clear sky and calm/moderate wind conditions, over a plane terrain on the tropical seacoast, is developed. The analytical model is mainly defined by two parameters, the aerosol mixing height and the exponential rate of decrease above the mixing height. The effect of surface impaction is also taken into account in this model. It is seen that this parameter varies with season. By matching the analytical profile with the observed mean profile in each month, the surface source strength has been estimated. The seasonal and inter-annual variations of this parameter are studied.

Interaction Between Ionizing Radiation, Estrogens and Antiestrogens in the Modification of Tumor Microenvironment in Estrogen Dependent Multicellular Spheroids

MCF7 human breast cancer cells growing as multicellular spheroids were examined as a model of three-dimensional cellular organization. Estrogen-free medium inhibited spheroid formation. In medium containing estrogens, the antiestrogen hydroxytamoxifen decreased the spheroid growth rate. Analyses with the recursion formula after Gompertz fitting showed that the rate of exponential decrease in growth rate (alpha) was alpha 0.099 +/- 0.013 d-1, and the decrease in alpha' was 0.061 +/- 0.015 d-1 for 0.1 microM hydroxytamoxifen and control spheroids respectively. MCF7 cells which had been growth arrested in an estrogen-free medium showed a significant decrease in radiosensitivity (surviving fraction at 2 Gy, SF2 = 63%) when compared with 0.1 nM 17 beta-estradiol-treated cells (SF2 = 38%). No differences in radiosensitivity were seen in MCF7 spheroids in estrogen-supplemented medium (radiation dose necessary to control 50% of spheroids (SCD50) was 5.51 Gy; derived alpha, beta and SF2 were 0.301 +/- 0.110 Gy-1, 0.018 +/- 0.005 Gy-2, and 51% respectively) when compared with monolayer cultures in the same medium (alpha = 0.316 +/- 0.059 Gy-1, beta = 0.023 +/- 0.006 Gy-2 and SF2 = 50%). In the spheroid model, manipulating the cellular environment, i.e., with estrogen treatment, modulates sensitivity to ionizing radiation.

Sources of variation in post-Chernobyl radiocaesium in brown trout,Salmo truttaL., and Arctic charr,Salvelinus alpinus(L.), from six Cumbrian lakes (northwest England)

The objectives were to evaluate temporal variation in 137Cs in trout and charr from Crummock Water, Wastwater, Ennerdale Water, and to compare levels in trout from six lakes (above three + Windermere, Loweswater, Devoke Water) and charr from four lakes (above three + Windermere). Fish were caught between June 1986 and October 1988, chiefly with fyke nets and gill nets. Overall means for 137Cs in trout were markedly higher than those for charr in the three lakes. Values for individual trout exceeded 1000 Bq.kg-1 in Ennerdale and 500 Bq.kg-1 in Wastwater and Crummock Water, but values for charr never exceeded 350 Bq.kg-1. 137Cs content increased with fish weight for trout from Wastwater and therefore values were scaled to a standard weight in subsequent analyses. No similar relationships were found for trout in Ennerdale or Crummock Water, or for charr in all three lakes. Monthly mean values for 137Cs in trout followed similar temporal patterns in the three lakes and a parabola provided a simple model for these changes. Chernobyl deposition occurred early in May 1986 and maximum values in trout were in December 1986 in Wastwater, January/February 1987 in Ennerdale Water and March 1987 in Crummock Water. The exponential rate of decrease from these maxima did not differ significantly between the three lakes, and ecological half-lives of 137Cs in the trout differed slightly, but not significantly, between lakes : 180 days for Wastwater, 194 days for Crummock Water and 249 days for Ennerdale Water. The equivalent value for Ennerdale charr was lower at 132 days, and it was impossible to fit models or calculate half-lives for Wastwater and Crummock charr. Maximum monthly geometric mean 137Cs values in trout from six lakes and charr from four lakes were related to the initial concentration of 137Cs in both water and sediment, and the maximum monthly geometric mean 137Cs values obtained from the routine water samples. The relationship was curvilinear and approximated, but was not identical to, an asymptotic curve. No similar relationships were found with mean Ca or K levels in the lake water. Metabolic and diet differences may explain the lower 137Cs levels in charr compared with trout and differences for the same species from different lakes may be due to limnological variations and différences between lakes in the nature of their sediments and catchment soils. Both points are discussed in detail.

On universal hypotheses testing via large deviations

A prototype problem in hypotheses testing is discussed. The problem of deciding whether an i.i.d. sequence of random variables has originated from a known source P/sub 1/ or an unknown source P/sub 2/ is considered. The exponential rate of decrease in type II probability of error under a constraint on the minimal rate of decrease in type I probability of error is chosen for a criterion of optimality. Using large deviations estimates, a decision rule that is based on the relative entropy of the empirical measure with respect to P/sub 1/ is proposed. In the case of discrete random variables, this approach yields weaker results than the combinatorial approach used by Hoeffding (1965). However, it enables the analysis to be extended to the general case of R/sup n/-valued random variables. Finally, the results are extended to the case where P/sub 1/ is an unknown parameter-dependent distribution that is known to belong to a set of distributions (P/sup 0//sub 1/, theta in Theta ).< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Large deviation rate calculations for nonlinear detectors in Gaussian noise

An asymptotic analysis based on large deviation theory is presented for three representative nonlinear receivers operating in the presence of Gaussian noise, namely radiometers, differential phase shift keying, and memoryless detectors. En route to the results an extension to the Toeplitz distribution theorem is proved. This extension provides the key to obtaining closed-form expressions for the exponential rate of decrease of the probability of error for the first two detector structures. The solution to the rate constant problem for the memoryless detector is then shown to be given by the solution to a certain nonlinear Hammerstein integral equation. Several examples are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Vascular transport and soybean nodule function: II. A role for phloem supply in product export*

Abstract The ureide content of soybean (Glycine max (L.) Merr.) nodules was unaffected by variations in the transpirational rate, while whole plant manipulations designed to decrease phloem supply to nodules resulted in lower rates of nitrogenase activity and an increase in the ureide content of the nodules. The rate of ureide export from the nodule was estimated from the exponential rate of decrease in the pool size of ureides in nodules, following exposure to an N2‐free atmosphere (Ar:O2). Export was greatly reduced under treatments which reduced phloem supply to the nodule. A water budget for nodules suggested that the delivery of water to the nodule via mass flow in the phloem was comparable to that required for export of ureides from the nodule in the xylem from the nodule. Therefore, we suggest that xylem export from nodules is related to the phloem supply to the nodule rather than to the transpirational flux in the parent root. This suggestion is related to the reported decreases in nodule permeability to gases under conditions of phloem deprivation.

Robust large deviations performance analysis for large sample detectors

Large deviations theory is used to analyze the exponential rate of decrease of error probabilities for a sequence of decisions based on a test statistics sequence (T/sub n/). It is assumed that (for a given statistical hypothesis) the distributions of T/sub n/ are determined by some unknown member of a class of probability distributions. The worst case, or least favorably exponential rate of error probability decrease over this class, is sought. It is shown that the Legendre-Fenchel transform of the maximized cumulant function yields a lower bound for the minimized large deviations rate function, and that in many cases this bound is tight. Application of the result is illustrated by a detailed consideration of i.i.d memoryless detection with an epsilon -contamination distribution family. >

The estimation of the model order in exponential families

Estimators are sought that achieve high exponential rate of decrease in the underestimation probability while keeping the overestimation probability exponent at a certain prescribed level. It is assumed that a given integer is known to upper-bound the true order. Some examples are given of possible applications of the proposed method in specific order estimation and hypothesis testing problems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

An asymptotically least-favorable Chernoff bound for a large class of dependent data processes

It is desired to determine the worst-case asymptotic error probability performance of a given detector operating in an environment of uncertain data dependency. A class of Markov data process distributions is considered which satisfy a one-shift dependency bound and agree with a specified univariate distribution. Within this dependency contamination class the distribution structure which minimizes the exponential rate of decrease of detection error probabilities is identified. This is a uniform least-favorability principle, because the least-favorable dependency structure is the same for all bounded memoryless detectors. The error probability exponential rate criterion used is a device of large deviations theory. The results agree well with previous results obtained using Pitman's asymptotic relative efficiency (ARE), which is a more tractable small-signal performance criterion. In contrast to ARE, large deviations theory is closely related to finite-sample error probabilities via the finite-sample Chernoff bounds and other exponentially tight bounds and other approximations.

Radioisotope-dilution technique for determining endogenous manganese in feces of the growing rat

A conventional balance study with growing rats was conducted to evaluate experimental conditions for determining endogenous fecal manganese (Mn) excretion and, hence, true Mn absorption by the isotope-dilution technique. Thirty-four rats, with a mean initial live weight of 60 g, allotted to three groups of 8 animals and one group of 10 animals, were injected intramuscularly with a(54)Mn tracer dose and sacrificed after 4, 8, 12, and 16 d, respectively.In liver and serum, the specific radioactivity of Mn was the lowest among the tissues analyzed and its exponential rate of decrease over the period of d 4-16 was the highest. During the 8-d period, from d 9-16, apparent Mn absorption averaged 14.1% of intake (128.5 μg Mn/d). Assuming that the specific activity of Mn in liver of d 11 or, alternatively, in serum of d 16, was on the average representative of that of endogenous Mn in feces of d 9-16, it was computed that Mn of endogenous origin accounted for 9.0 and 9.3% of the total fecal excretion of the metal, and that true absorption amounted to 21.9 and 22.1% of Mn intake, respectively.