Negative Drift Research Articles

A General Model of Negative Frequency Dependent Selection Explains Global Patterns of Human ABO Polymorphism.

The ABO locus in humans is characterized by elevated heterozygosity and very similar allele frequencies among populations scattered across the globe. Using knowledge of ABO protein function, we generated a simple model of asymmetric negative frequency dependent selection and genetic drift to explain the maintenance of ABO polymorphism and its loss in human populations. In our models, regardless of the strength of selection, models with large effective population sizes result in ABO allele frequencies that closely match those observed in most continental populations. Populations must be moderately small to fall out of equilibrium and lose either the A or B allele (Ne ≤ 50) and much smaller (N e ≤ 25) for the complete loss of diversity, which nearly always involved the fixation of the O allele. A pattern of low heterozygosity at the ABO locus where loss of polymorphism occurs in our model is consistent with small populations, such as Native American populations. This study provides a general evolutionary model to explain the observed global patterns of polymorphism at the ABO locus and the pattern of allele loss in small populations. Moreover, these results inform the range of population sizes associated with the recent human colonization of the Americas.

Aging studies on micro-fabricated alkali buffer-gas cells for miniature atomic clocks

We report an aging study on micro-fabricated alkali vapor cells using neon as a buffer gas. An experimental atomic clock setup is used to measure the cell's intrinsic frequency, by recording the clock frequency shift at different light intensities and extrapolating to zero intensity. We find a drift of the cell's intrinsic frequency of (−5.2 ± 0.6) × 10−11/day and quantify deterministic variations in sources of clock frequency shifts due to the major physical effects to identify the most probable cause of the drift. The measured drift is one order of magnitude stronger than the total frequency variations expected from clock parameter variations and corresponds to a slow reduction of buffer gas pressure inside the cell, which is compatible with the hypothesis of loss of Ne gas from the cell due to its permeation through the cell windows. A negative drift on the intrinsic cell frequency is reproducible for another cell of the same type. Based on the Ne permeation model and the measured cell frequency drift, we determine the permeation constant of Ne through borosilicate glass as (5.7 ± 0.7) × 10−22 m2 s−1 Pa−1 at 81 °C. We propose this method based on frequency metrology in an alkali vapor cell atomic clock setup based on coherent population trapping for measuring permeation constants of inert gases.

Characterization of Sensitive Marine Clays by Using Cone and Ball Penetrometers: Example of Clays in Eastern Canada

Soundings made by using the standard penetration test in sensitive marine clay in Ottawa (Canada) have been problematic. Negative readings have been recorded. The incorrect estimation of the engineering characteristics of Ottawa clays has been noted. The effect of temperature on the penetrometer load cell output is suspected as the reason for the negative drift in soundings and erroneous estimations of engineering characteristics. Also, focused research is needed to verify existing correlations and empirical factors between the cone penetration test and engineering characteristics of Ottawa clays. These are the reasons for carrying out this research work. Temperature effects have become a significant factor in countries with radical temperature changes, such as Canada. Three types of penetrometer tips have been used at the Canadian Geotechnical Research Site No. 1. The tips used are a 36 mm cone, 40 mm ball, and 113 mm ball. Nilcon field vane testing has also been carried out in the site to determine the undrained shear strength and sensitivity (the ratio of the initial undrained shear strength to the remolded undrained shear strength) from the penetrometer soundings. Undisturbed samples are collected to obtain the engineering characteristics by laboratory testing. Laboratory testing on penetrometer equipment is performed to verify the effects of temperature on the soundings. It is found that temperature changes affect the penetrometer soundings. Temperature effects can cause drifting as indicated by negative tip stress or sleeve friction in soft or low resistance clays. Therefore, temperature effects may increase the errors in the estimation of the engineering characteristics of Ottawa clays. It has also been found that correlations may or may not apply well to Ottawa sensitive marine clay. Temperature corrections could be applied to the penetrometer soundings. From this research, correlations and empirical factors between penetrometers and engineering characteristics are verified for Ottawa sensitive marine clays.

Second Order Approximation for the Distribution of the Maximum of a Random Walk with Negative Drift and Infinite Variance

Let $\xi,\xi_1,\xi_2,\ldots$ be independent identically distributed random variables, and set $a:=-{\bf E}\,\xi> 0$, $S_n:=\sum_{j=1}^n\xi_j$, $S_0=0$, $S:=\sup_{n\ge 0}S_n$, $F_+(t):={\bf P}(\xi\ge t)$, $F_-(t):={\bf P}(\xi\le-t)$, $F_+^I(t)=\int_t^\infty F_+(u)\,du$. It is well known (see, e.g., [N. Veraverbeke, Stoch. Process. Appl., 5 (1977), pp. 27--37], [A. A. Borovkov, Probability Theory, Springer, New York, 2013]) that if the function $F^I_+(t)$ is subexponential, then ${\bf P}(S\ge x)\sim{F_+^I(x)}/{a}$ as $x\to\infty$. Under the condition that ${\bf E}\,\xi^2<\infty$ and the function $F_+(x)$ is either regularly varying at infinity or semiexponential, the next term of the asymptotic expansion for ${\bf P}(S\ge x)$ as $x\to\infty$ (which is of the order of $F_+(x)$) was found in [A. A. Borovkov, Sib. Math. J., 43 (2002), pp. 995--1022] (see also [A. A. Borovkov and K. A. Borovkov, Asymptotic Analysis of Random Walks: Heavy-Tailed Distributions, Cambridge University Press, Cambridge, UK, 2008]). I...

On the Asymptotics of the Ruin Probability

We obtain an asymptotic representation of the ruin probability for a random walk with negative drift when the upper bound of the strip tends to infinity. The result is expressed via distributions of the trajectory supremum and overshoot below negative level. In the subsequent corollaries, we use some known asymptotic formulas for the distribution of the supremum which are valid under various restrictions on the rate of decreasing at infinity for the distribution of jumps of a random walk.

Stability of the Max-Weight Protocol in Adversarial Wireless Networks

In this paper, we consider the Max-Weight protocol for routing and scheduling in wireless networks under an adversarial model. This protocol has received a significant amount of attention dating back to the papers of Tassiulas and Ephremides. In particular, this protocol is known to be throughput-optimal whenever the traffic patterns and propagation conditions are governed by a stationary stochastic process. However, the standard proof of throughput optimality (which is based on the negative drift of a quadratic potential function) does not hold when the traffic patterns and the edge capacity changes over time are governed by an arbitrary adversarial process. Such an environment appears frequently in many practical wireless scenarios when the assumption that channel conditions are governed by a stationary stochastic process does not readily apply. In this paper, we prove that even in the above adversarial setting, the Max-Weight protocol keeps the queues in the network stable (i.e., keeps the queue sizes bounded) whenever this is feasible by some routing and scheduling algorithm. However, the proof is somewhat more complex than the negative potential drift argument that applied in the stationary case. Our proof holds for any arbitrary interference relationships among edges. We also prove the same stability of ε-approximate Max-Weight under the adversarial model. We conclude the paper with a discussion of queue sizes in the adversarial model as well as a set of simulation results.

Sarbanes–Oxley Act and patterns in stock returns around executive stock option exercise disclosures

AbstractWe document negative stock returns and elevated trading volumes around executives’ early option exercise disclosures post‐SOX, but not pre‐SOX. This stock price reaction is incomplete, and the negative stock price drift is smaller post‐SOX compared to pre‐SOX. We also show effects of media coverage in the stock price response to exercise disclosures in the post‐SOX period. These findings provide evidence that the requirement mandated by SOX to disclose executives’ stock option exercises within two business days, and the increased media coverage, improves investors’ ability to incorporate into stock prices in a timely fashion the information conveyed by these exercises.

Nonlinear frequency chirping of toroidal Alfvén eigenmodes in tokamak plasmas

Nonlinear frequency chirping of toroidal Alfén eigenmodes (TAE) driven by energetic particles is investigated by kinetic simulations in toroidal plasmas. It is found that the up–down symmetry of the frequency chirping of a TAE is broken due to an anisotropic pitch-angle distribution with dominant co-passing energetic particles. The nonuniform distribution of the free energy associated with the initial energetic particle distribution causes biased driving forces that result in a strongly asymmetric frequency chirping. The evolution of the perturbed distribution function in the phase space shows that a hole–clump pair moves together towards the magnetic axis for the small pitch-angle parameter cases. The downward chirping of the mode frequency is associated with the negative drift of the phase island in the KAM surfaces or the resonance δf structures in the radial direction. On the other hand, the energetic particle distribution with larger pitch-angle parameters leads to upward chirping of the TAE frequency. The upward chirping is due to the drifting of the resonance structure towards the boundary of the simulation region and overlapping of different poloidal resonances in the (Λ, E) phase space at the late stage. The phase space dynamics provides a key mechanism for understanding the wave chirping direction and particle transport process.

Chernoff's distribution and differential equations of parabolic and Airy type

We give a direct derivation of the distribution of the maximum and the location of the maximum of one-sided and two-sided Brownian motion with a negative parabolic drift. The argument uses a relation between integrals of special functions, in particular involving integrals with respect to functions which can be called “incomplete Scorer functions”. The relation is proved by showing that both integrals, as a function of two parameters, satisfy the same extended heat equation, and the maximum principle is used to show that these solutions must therefore have the stated relation. Once this relation is established, a direct derivation of the distribution of the maximum and location of the maximum of Brownian motion minus a parabola is possible, leading to a considerable shortening of the original proofs.

Exact tail asymptotics of the supremum attained by a Lévy process

In this short communication we analyze the tail asymptotics corresponding to the maximum value attained by a Lévy process with negative drift. The note has two contributions: a short and elementary proof of these asymptotics, and an importance sampling algorithm to estimate the rare-event probabilities under consideration.

Subordinated Brownian Motion: Last Time the Process Reaches its Supremum

The article develops a theory for the last time the subordinated Brownian motion (SBM with negative drift reaches its supremum. The study includes obtaining expressions for the Laplace transform of the last time that the SBM reaches its supremum and also for its density. In the process, we establish that the last time that the SBM reaches its supremum is a member of the generalized gamma convolution (GGC) family. The theoretical results for the general case have been explicitly derived for some well-known subordinators. Numerical investigations show close agreement between the theoretical derivations and empirical computations.

The genetics of human migrations

When our human ancestors began to migrate from the African savannahs across the Alps into Northern Europe and Asia between 200,000 and 60,000 years ago, they encountered a colder climate, different food sources and new predators. Inevitably, evolution began to work on those wandering tribes: their skin became lighter, their metabolism adapted to new food sources, and their immune system had to handle different pathogens. Modern Homo sapiens began to evolve into slightly different subspecies or, as they are referred to in the common vernacular, different races. This shallow notion of race—that differences in our appearance have deep‐seated consequences for who and what we are as human beings—is the root of racism, which has led to slavery, discrimination, murder and genocide throughout the millennia. With the emergence of modern genetics and genomics, scientists had hoped that a better understanding of genetic differences and similarities among humans would eventually help to overcome the controversial and toxic notion of race as having anything to do with a person's ability, intelligence or humanity. As J. Craig Venter, then head of the Celera Genomics Corporation in Rockville, MD, USA, put it in 2000, when the first draft of the human genome was published: “Race is a social concept, not a scientific one”. Since the publication of the human genome, further advances in genomic sequencing and statistical analysis are now yielding new insights into the link between past human migrations and today's variety of genetic differences that govern disease resistance, skin pigmentation, tolerance to cold, and ability to digest or metabolize various nutrients. Such findings are contributing to discussions around the delicate issues of race, ethnicity and identity, but they are also having a significant impact on biomedical research and personalized health care. Furthermore, genetic analysis is shedding light on the migrations themselves, along with …

Control of a finite dam with a Lévy input

Bae et al. [7] consider the problem of optimal control of a finite dam using P λ,τ policies, assuming that the input process is a compound Poisson process with a negative drift. Lam and Lou [9] treat the case where the input is a Wiener process with a reflecting boundary at its infimum, with drift term μ ≥ 0, using the long-run average and total discounted cost criteria. Attia [5] obtains results similar to those of Lam and Lou, through simpler and more direct methods. Zuckermann [12] considers P λ,0 policies when the input process is a Wiener process with drift term μ ≥ 0. The techniques used by the above mentioned authors involve solving systems of differential or integral equations. In this paper we use the theory and methods of scale functions of Levy processes to unify and extend the results of these authors.

Decameter Type III Bursts with Changing Frequency Drift-Rate Signs

We discuss properties of type III bursts which change sign of their drift rate from negative to positive and vice versa. Moreover such bursts may change sign of their drift rates more than once. These specific type III bursts were observed simultaneously by radio telescopes UTR-2, URAN-2 and NDA in frequency band 8-41 MHz. The negative drift rates of these bursts are close to those of usual decameter type III bursts and variate from -0.84 MHz/s to -5.56 MHz/s. The positive drift rates of specific type III bursts vary in the wider range from 0.44MHz/s to 12 MHz/s. Unlike inverted U-bursts these type III bursts still drift from the high frequencies to the low frequencies in spite of the change of the drift rates signs. Our basic explanation of the positive drift rate of these type III burst differs from the common assumption that positive drift rates of Type III bursts are connected with electron beam propagation towards the Sun. We propose that, even if electron beams move outward from the Sun, they can generate type III bursts with positive drift rates if in some regions of the solar corona the group velocities of type III radio emissions are lower than the velocities of the electron beams.

Stock Price Reactions to News and the Momentum Effect in the Korean Stock Market

AbstractBy analyzing how stock prices respond to public news, this paper examines the momentum effect in the Korean stock market. It is true that, as a whole, the momentum strategy generates no profits in Korea. However, among the stocks in a momentum portfolio, loser stocks with news headlines make significantly positive profits caused by negative return drift. These positive profits are cancelled out by negative returns, due mostly to reversals exhibited by winner stocks with and without public news. These reversals stand in contrast to the case of the United States market, where winner stocks show weak drift (Chan, 2003). Reversals of news winners and the drift of news losers in Korea imply that stock prices react asymmetrically to public news, which is overlooked in existing studies on momentum. Further analyses indicate that this asymmetric reaction can be attributed to transaction costs rather than to the incentive of managers to disclose bad news slowly. In addition to the asymmetric reaction of prices to news, we suggest that market misperceptions concerning firms' future prospects may also be a reason for the post‐news return patterns in Korea.

Fast and slow frequency-drifting millisecond bursts in Jovian decametric radio emissions

We present an analysis of several Jovian Io-related decametric radio storms recorded in 2004−2012 at the Ukrainian array UTR-2 using the new generation of baseband digital receivers. Continuous baseband sampling within sessions lasting for several hours enabled us to study the evolution of multiscale spectral patterns during the whole storm at varying time and frequency resolutions and trace the temporal transformation of burst structures in unprecedented detail. In addition to the well-known frequency drifting millisecond patterns known as S bursts we detected two other classes of events that often look like S bursts at low resolution but reveal a more complicated structure in high resolution dynamic spectra. The emissions of the first type (LS bursts, superposition of L and S type emissions) have a much lower frequency drift rate than the usual quasi linearly drifting S bursts (QS) and often occur within a frequency band where L emission is simultaneously present, suggesting that both LS and at least part of L emissions may come from the same source. The bursts of the second type (modulated S bursts called MS) are formed by a wideband frequency-modulated envelope that can mimic S bursts with very steep negative (or even positive) drift rates. Observed with insufficient time-frequency resolution, MS look like S bursts with complex shapes and varying drifts; MS patterns often occur in association with (i) narrowband emission; (ii) S burst trains; or (iii) sequences of fast drift shadow events. We propose a phenomenological description for various types of S emissions, that should include at least three components: high- and low-frequency limitation of the overall frequency band of the emission, fast frequency modulation of emission structures within this band, and emergence of elementary S burst substructures, that we call “forking” structures. All together, these three components can produce most of the observed spectral structures, including S bursts with apparently very complex time-frequency structures.

Theoretical analysis of high-field transport in graphene on a substrate

We investigate transport in graphene supported on various dielectrics (SiO2, BN, Al2O3, and HfO2) through a hydrodynamic model which includes self-heating and thermal coupling to the substrate, scattering with ionized impurities, graphene phonons, and dynamically screened interfacial plasmon-phonon (IPP) modes. We uncover that while low-field transport is largely determined by impurity scattering, high-field transport is defined by scattering with dielectric-induced IPP modes, and a smaller contribution of graphene intrinsic phonons. We also find that lattice heating can lead to negative differential drift velocity (with respect to the electric field), which can be controlled by changing the underlying dielectric thermal properties or thickness. Graphene on BN exhibits the largest high-field drift velocity, while graphene on HfO2 has the lowest one due to strong influence of IPP modes.

Large Deviation Asymptotics for Busy Periods

The busy period for a queue is cast as the area swept under the random walk until it first returns to zero. Encompassing non-i.i.d. increments, the large-deviations asymptotics of the busy period B is addressed, under the assumption that the increments satisfy standard conditions, including a negative drift. The main conclusions provide insight on the probability of a large busy period, and the manner in which this occurs. The scaled probability of a large busy period has the asymptote, for any b &gt; 0, [Formula: see text], where [Formula: see text], with [Formula: see text], and with Λ denoting the scaled cumulant generating function of the increments process. The most likely path to a large swept area is found to be a simple rescaling of the path on [0, 1] given by [Formula: see text]. In contrast to the piecewise linear most likely path leading the random walk to hit a high level, this is strictly concave in general. While these two most likely paths have distinctly different forms, their derivatives coincide at the start of their trajectories, and at their first return to zero. These results partially answer an open problem of Kulick and Palmowski [18] regarding the tail of the work done during a busy period at a single server queue. The paper concludes with applications of these results to the estimation of the busy period statistics (λ*, K) based on observations of the increments, offering the possibility of estimating the likelihood of a large busy period in advance of observing one.

Convergence of Distribution of the Sojourn Time of a Random Walk on a Half-Axis

We generalize the known arcsine law for distribution of the sojourn time of a random walk on a half-axis. Under the Cram’er conditions, we obtain an asymptotic representation of the generating function of the time of sojourn above an increasing level in the case of a random walk with negative drift.

Drift-corrected trends and periodic variations in MIPAS IMK/IAA ozone measurements

Abstract. Drifts, trends and periodic variations were calculated from monthly zonally averaged ozone profiles. The ozone profiles were derived from level-1b data of the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) by means of the scientific level-2 processor run by the Karlsruhe Institute of Technology (KIT), Institute for Meteorology and Climate Research (IMK). All trend and drift analyses were performed using a multilinear parametric trend model which includes a linear term, several harmonics with period lengths from 3 to 24 months and the quasi-biennial oscillation (QBO). Drifts at 2-sigma significance level were mainly negative for ozone relative to Aura MLS and Odin OSIRIS and negative or near zero for most of the comparisons to lidar measurements. Lidar stations used here include those at Hohenpeissenberg (47.8° N, 11.0° E), Lauder (45.0° S, 169.7° E), Mauna Loa (19.5° N, 155.6° W), Observatoire Haute Provence (43.9° N, 5.7° E) and Table Mountain (34.4° N, 117.7° W). Drifts against the Atmospheric Chemistry Experiment Fourier Transform Spectrometer (ACE-FTS) were found to be mostly insignificant. The assessed MIPAS ozone trends cover the time period of July 2002 to April 2012 and range from −0.56 ppmv decade−1 to +0.48 ppmv decade−1 (−0.52 ppmv decade−1 to +0.47 ppmv decade−1 when displayed on pressure coordinates) depending on altitude/pressure and latitude. From the empirical drift analyses we conclude that the real ozone trends might be slightly more positive/less negative than those calculated from the MIPAS data, by conceding the possibility of MIPAS having a very small (approximately within −0.3 ppmv decade−1) negative drift for ozone. This leads to drift-corrected trends of −0.41 ppmv decade−1 to +0.55 ppmv decade−1 (−0.38 ppmv decade−1 to +0.53 ppmv decade−1 when displayed on pressure coordinates) for the time period covered by MIPAS Envisat measurements, with very few negative and large areas of positive trends at mid-latitudes for both hemispheres around and above 30 km (~10 hPa). Negative trends are found in the tropics around 25 and 35 km (~25 and 5 hPa), while an area of positive trends is located right above the tropical tropopause. These findings are in good agreement with the recent literature. Differences of the trends compared with the recent literature could be explained by a possible shift of the subtropical mixing barriers. Results for the altitude–latitude distribution of amplitudes of the quasi-biennial, annual and the semi-annual oscillation are overall in very good agreement with recent findings.