Uniform Tail Research Articles

Quick Multiband Spectrum Sensing for Delay-Constraint Cognitive UAV Networks

Unmanned aerial vehicles (UAVs) have gained much popularity for a wide variety of applications that do not require human operators, but also face the spectrum scarcity problem. To address this problem, a cognitive UAV network (CUAVN) framework based on cognitive radio (CR) technology is formulated in this article. On the basis of this, the sequential probability ratio test (SPRT) is used as a fundamental cooperative spectrum sensing (CSS) scheme to significantly reduce the average number of samples, but the uncertainty of its detection delay has a negative impact on the spectrum-sensing performance and the achievable throughput of CUAVNs, especially in the multiband spectrum sensing. Considering the location flexibility and uneven distribution density of UAVs, we design an intraframe CSS structure, with aim of achieving CSS between microsensing slots. Furthermore, a sequential maximal truncation (SMT) is proposed to realize a quick multiband spectrum sensing for delay-constraint CUAVNs. Compared to uniform tail truncation (UTT), simulation results show that the proposed quick multiband spectrum sensing with the help of SMT requires fewer sensing times in support of better sensing performance and achievable throughput, especially under a strict delay constraint.

Existence, exponential mixing and convergence of periodic measures of fractional stochastic delay reaction-diffusion equations on [formula omitted

This paper is concerned with periodic measures of fractional stochastic reaction-diffusion equations with variable time delay defined on unbounded domains. We first prove the existence of periodic measures of the Markov process associated with the equation by showing the weak compactness of distribution laws of a family of solutions based on the uniform estimates and the equicontinuity of solutions in probability. We then establish the regularity of periodic measures and prove the tightness of the set of all periodic measures of the equation for small noise intensity. As a result, any sequence of periodic measures possesses at least one limit point, and we further prove every such limit must be a periodic measure of the corresponding limiting system. Finally, under further assumptions on the nonlinear terms, we establish the uniqueness and the exponential mixing property of periodic measures in the sense of Wasserstein metric. All the results of the paper are also valid for invariant measures of the corresponding autonomous version of the stochastic equation with constant time delay. The idea of uniform tail estimates of solutions in probability is employed to overcome the difficulty introduced by the non-compactness of Sobolev embeddings on unbounded domains.

Uniform tail asymptotics for Airy kernel determinant solutions to KdV and for the narrow wedge solution to KPZ

We obtain uniform asymptotics for deformed Airy kernel determinants, which arise in models of finite temperature free fermions and which characterize the narrow wedge solution of the Kardar–Parisi–Zhang equation. The asymptotics for the determinants yield uniform initial data for an associated family of solutions to the Korteweg–de Vries equation, and uniform lower tail asymptotics for the narrow wedge solution of the Kardar–Parisi–Zhang equation.

Existence and Upper Semi-Continuity of Random Attractors for Nonclassical Diffusion Equation with Multiplicative Noise on R<sup>n</sup>

This paper is concerned with the existence and upper semi-continuity of random attractors for the nonclassical diffusion equation with arbitrary polynomial growth nonlinearity and multiplicative noise in H1(Rn). First, we study the existence and uniqueness of solutions by a noise arising in a continuous random dynamical system and the asymptotic compactness is established by using uniform tail estimate technique, and then the existence of random attractors for the nonclassical diffusion equation with arbitrary polynomial growth nonlinearity. As a motivation of our results, we prove an existence and upper semi-continuity of random attractors with respect to the nonlinearity that enters the system together with the noise.

Random dynamics of non-autonomous fractional stochastic p-Laplacian equations on $${\mathbb {R}}^N$$

This article is concerned with the random dynamics of a wide class of non-autonomous, non-local, fractional, stochastic p-Laplacian equations driven by multiplicative white noise on the entire space $${\mathbb {R}}^N$$ . We first establish the well-posedness of the equations when the time-dependent non-linear drift terms have polynomial growth of arbitrary orders $$p,q\ge 2$$ . We then prove that the equation has a unique bi-spatial pullback random attractor that is measurable, compact in $$L^2({\mathbb {R}}^N)\cap L^p({\mathbb {R}}^N)\cap L^q({\mathbb {R}}^N)$$ and attracts all random subsets of $$L^2({\mathbb {R}}^N)$$ under the topology of $$L^2({\mathbb {R}}^N)\cap L^p({\mathbb {R}}^N)\cap L^q({\mathbb {R}}^N)$$ . In addition, we establish the upper semi-continuity of these attractors in $$L^2({\mathbb {R}}^N)\cap L^p({\mathbb {R}}^N)\cap L^q({\mathbb {R}}^N)$$ when the density of noise shrinks to zero. The idea of uniform tail estimates and the method of asymptotic a priori estimates are applied to prove the pullback asymptotic compactness of the solutions in $$L^2({\mathbb {R}}^N)\cap L^p({\mathbb {R}}^N)\cap L^q({\mathbb {R}}^N)$$ to overcome the non-compactness of Sobolev embeddings on $${\mathbb {R}}^N$$ as well as the almost sure nondifferentiability of the sample paths of the Wiener process.

Uniform Symmetric and Asymmetric Polymer Nanostructures via Directed Chain Organization

Polymer nanostructures can be designed with specific properties and functions, such as controlled shape, size, chemical composition, and adaptive ability to change shape or size in response to environmental cues. Precise control to organize polymer chains into uniform nonspherical symmetric and asymmetric nanostructures and at scale remains a synthetic challenge. Here, by using the temperature-directed morphology transformation (TDMT) method we show through a systematic organization of polymer chains the synthesis of well-defined asymmetric (i.e., tadpole) and symmetric (i.e., worm) nanostructures in water at high polymer concentrations. This method further allowed the production of tadpoles with controlled and uniform tail lengths, ranging from 200 to 800 nm. The organization of chains could be driven by environmental conditions to produce adaptive nanostructure systems.

Uniform tail approximation of homogenous functionals of Gaussian fields

Abstract Let X(t), t ∈ ℝd, be a centered Gaussian random field with continuous trajectories and set ξu(t) = X(f(u)t), t ∈ ℝd, with f some positive function. Using classical results we can establish the tail asymptotics of ℙ{Γ(ξu) > u} as u → ∞ with Γ(ξu) = supt ∈ [0, T]d ξu(t), T > 0, by requiring that f(u) tends to 0 as u → ∞ with speed controlled by the local behavior of the correlation function of X. Recent research shows that for applications, more general functionals than the supremum should be considered and the Gaussian field can depend also on some additional parameter τu ∈ K say ξu,τu(t), t ∈ ℝd. In this paper we derive uniform approximations of ℙ{Γ(ξu,τu) > u} with respect to τu, in some index set Ku as u → ∞. Our main result has important theoretical implications; two applications are already included in Dȩbicki et al. (2016), (2017). In this paper we present three additional applications. First we derive uniform upper bounds for the probability of double maxima. Second, we extend the Piterbarg–Prisyazhnyuk theorem to some large classes of homogeneous functionals of centered Gaussian fields ξu. Finally, we show the finiteness of generalized Piterbarg constants.

Tail behavior for the sum of two correlated classes of discounted aggregate claims in a time-dependent risk model

ABSTRACTConsider a continuous-time risk model with two correlated classes of insurance business and a constant force of interest. Suppose that the correlation comes from a common shock, and that the claim sizes and inter-arrival times correspondingly form a sequence of random pairs, with each pair obeying a dependence structure. By assuming that the claim sizes are heavy tailed, a uniform tail asymptotic formula for the sum of the two correlated classes of discounted aggregate claims is obtained.

Delocalization of eigenvectors of random matrices with independent entries

We prove that an n by n random matrix G with independent entries is completely delocalized. Suppose the entries of G have zero means, variances uniformly bounded below, and a uniform tail decay of exponential type. Then with high probability all unit eigenvectors of G have all coordinates of magnitude O(n^{-1/2}), modulo logarithmic corrections. This comes a consequence of a new, geometric, approach to delocalization for random matrices.

Uniform Estimate for Randomly Weighted Sums of Dependent Subexponential Random Variables

Abstract This paper obtains the uniform tail asymptotics of the maximum of randomly weighted sum max 1 ≤ k ≤ n ∑ i = 1 k θ i X i $$\mathop {\max}\limits_{1 \le k \le n} \sum\nolimits_{i = 1}^k {\theta _i}{X_i}$$ with respective to n, in which the primary random variables X 1 , . . . , X n $${X_1},...,{X_n}$$ are real valued, dependent, and have different subexponential distributions, while the random weights θ 1 , . . . , θ n $${\theta _1},...,{\theta _n}$$ are nonnegative and arbitrarily dependent, but independent of X 1 , . . . , X n $${X_1},...,{X_n}$$ . An application to insurance risk model with investment portfolio is proposed.

Lemon-shaped halo archaeal virus His1 with uniform tail but variable capsid structure

Lemon-shaped viruses are common in nature but so far have been observed to infect only archaea. Due to their unusual shape, the structures of these viruses are challenging to study and therefore poorly characterized. Here, we have studied haloarchaeal virus His1 using cryo-electron tomography as well as biochemical dissociation. The virions have different sizes, but prove to be extremely stable under various biochemical treatments. Subtomogram averaging of the computationally extracted virions resolved a tail-like structure with a central tail hub density and six tail spikes. Inside the tail there are two cavities and a plug density that separates the tail hub from the interior genome. His1 most likely uses the tail spikes to anchor to host cells and the tail hub to eject the genome, analogous to classic tailed bacteriophages. Upon biochemical treatment that releases the genome, the lemon-shaped virion transforms into an empty tube. Such a dramatic transformation demonstrates that the capsid proteins are capable of undergoing substantial quaternary structural changes, which may occur at different stages of the virus life cycle.

Uniform tail asymptotics for the aggregate claims with stochastic discount in the renewal risk models

Considering an insurer who is allowed to make risk-free and risky investments, as in Tang et al. (2010), the price process of the investment portfolio is described as a geometric Levy process. We study the tail probability of the stochastic present value of future aggregate claims. When the clai m -size distribution is of extended regular variation, we obtain an asymptotically equivalent formula which holds uniformly for all time horizons, and furthermore, the same asymptotic formula holds for the finite-time ruin probabilities. The results extend the works of Tang et al. (2010).

Uniform Tail Asymptotics for the Sum of Two Correlated Classes with Stochastic Returns and Dependent Heavy Tails

Consider a continuous-time risk model with two correlated classes of insurance business and risky investments whose price processes are geometric Lévy processes. By assuming that the correlation comes from a common shock, and the claim sizes are heavy-tailed and pairwise quasi-asymptotically independent, we investigate the tail behavior of the sum of the stochastic present values of the two correlated classes, and a uniform asymptotic formula is obtained.

Uniform tail asymptotics for the stochastic present value of aggregate claims in the renewal risk model

Consider an insurer who is allowed to make risk-free and risky investments. The price process of the investment portfolio is described as a geometric Lévy process. We study the tail probability of the stochastic present value of future aggregate claims. When the claim-size distribution is of Pareto type, we obtain a simple asymptotic formula which holds uniformly for all time horizons. The same asymptotic formula holds for the finite-time and infinite-time ruin probabilities. Restricting our attention to the so-called constant investment strategy, we show how the insurer adjusts his investment portfolio to maximize the expected terminal wealth subject to a constraint on the ruin probability.

DYNAMICAL BEHAVIOR OF THE ALMOST-PERIODIC DISCRETE FITZHUGH–NAGUMO SYSTEMS

In this paper, we study the dynamical behavior of nonautonomous, almost-periodic discrete FitzHugh–Nagumo system defined on infinite lattices. We prove that the nonautonomous infinite-dimensional system has a uniform attractor which attracts all solutions uniformly with respect to the translations of external terms. We also establish the upper semicontinuity of uniform attractors when the infinite-dimensional system is approached by a family of finite-dimensional systems. This paper is based on a uniform tail method, which shows that, for large time, the tails of solutions are uniformly small with respect to bounded initial data as well as the translations of external terms. The uniform tail estimates play a crucial role for proving the uniform asymptotic compactness of the system and the upper semicontinuity of attractors.

Evaluation of PEG-FVIII Molecules with Prolonged Half-Lives in a Murine FVIII-Dependent Bleeding Model.

Current treatment of patients with hemophilia A often requires the frequent infusion of Factor VIII (FVIII) due to its short circulating half-life. A longer-acting FVIII molecule could profoundly impact patients' lives by extending bleeding protection with a reduced frequency of infusions. Several strategies to prolong plasma concentrations of FVIII have been attempted. In particular, targeting domains on FVIII that bind to LRP, the putative clearance receptor, has been a popular strategy. We have investigated the use of site-directed pegylation of B-domain deleted (BDD) FVIII to evaluate the utility of PEG as a method to decrease FVIII clearance through steric hindrance of LRP binding, or other unknown clearance mechanisms, while minimizing decreases in vWF binding and in vivo activity. The evaluation of novel constructs required the development of in vivo pharmacokinetic models and a FVIII-dependent bleed model. We describe the development of an acute bleed model following uniform tail transection in the hemophilia A mouse that is FVIII dependent and allows the evaluation of the acute pharmacologic effects of FVIII or variants in vivo. Pharmacokinetic analysis of recombinant FVIII (rFVIII) and its variants was performed in rabbits over 32-hours and rFVIII or variants were measured using a modified Coatest® to differentiate endogenous rabbit FVIII from the administered human FVIII. For efficacy evaluations, hemophilia A mice were anesthetized with isoflurane and their pre-warmed tail was cut by a scalpel and placed into a new tube of warmed saline (37–40°C). Blood was collected over 40 minutes and blood loss was measured gravimetrically. Three modes of treatment were evaluated: prevention of bleeding (drug was administered 5 minutes before injury), treatment of an acute bleeding event (drug was administered 5 minutes after injury), and a delayed injury model (tail cut occurred at 20 or 24 hours after the drug administration). Over the course of 40 minutes control (C57BL6) mice demonstrated negligible bleeding (approximately 41 ± 8 μL) compared to 919 ± 26 μL in hemophilia A mice. A dose response curve was constructed for doses ranging from 0.1 to 5.0 IU of human rFVIII per mouse. Hemophilia A mice treated with 200 IU/kg of human rFVIII (5 IU/mouse) lost a similar volume of blood as control mice. The protective effect was rFVIII dose dependent over a range of 4–200 IU/kg (0.1–5 IU/mouse). In contrast, more rFVIII was required to stop an acute bleeding event when administered after the injury. In the delayed injury model, mice injured 24 hours after drug administration had a significantly larger mean blood volume loss compared to mice injured 20 hours post drug administration. Pegylated rFVIII constructs with longer half-lives also had increased activity over time compared to non-pegylated rFVIII in this mouse model. These results describe a superior hemophilia A tail bleed model that demonstrates FVIII-dependent bleeding reduction in response to acute hemorrhage over a 40 minute time course. This is the first demonstration of a hemophilia A mouse model in which all untreated animals uniformly bleed and all control animals demonstrate negligible bleeding. This model was used to evaluate the in vivo hemostatic efficacy of new rFVIII molecules that were designed to have superior pharmacologic and/or pharmacokinetic properties compared to rFVIII.

On uniform tail expansions of multivariate copulas and wide convergence of measures

The theory of copulas provides a useful tool for modeling dependence in risk management. In insurance and finance, as well as in other applications, dependence of extreme events is particularly important, hence there is a need for a detailed study of the tail behaviour of multivariate copulas. We investigate the class of copulas having regular tails with a uniform expansion. We present several equivalent characterizations of uniform tail expansions. Next, basing on them, we determine the class of all possible leading parts of such expansions; we compute the leading parts of copulas popular in the literature, and discuss the statistical aspects of tail expansions.

Cluster observations of sudden impulses in the magnetotail caused by interplanetary shocks and pressure increases

Abstract. Sudden impulses (SI) in the tail lobe magnetic field associated with solar wind pressure enhancements are investigated using measurements from Cluster. The magnetic field components during the SIs change in a manner consistent with the assumption that an antisunward moving lateral pressure enhancement compresses the magnetotail axisymmetrically. We found that the maximum variance SI unit vectors were nearly aligned with the associated interplanetary shock normals. For two of the tail lobe SI events during which Cluster was located close to the tail boundary, Cluster observed the inward moving magnetopause. During both events, the spacecraft location changed from the lobe to the magnetospheric boundary layer. During the event on 6 November 2001 the magnetopause was compressed past Cluster. We applied the 2-D Cartesian model developed by collier98 in which a vacuum uniform tail lobe magnetic field is compressed by a step-like pressure increase. The model underestimates the compression of the magnetic field, but it fits the magnetic field maximum variance component well. For events for which we could determine the shock normal orientation, the differences between the observed and calculated shock propagation times from the location of WIND/Geotail to the location of Cluster were small. The propagation speeds of the SIs between the Cluster spacecraft were comparable to the solar wind speed. Our results suggest that the observed tail lobe SIs are due to lateral increases in solar wind dynamic pressure outside the magnetotail boundary.

On uniform tail expansions of bivariate copulas

On uniform tail expansions of bivariate copulas

Poisson and Gaussian approximation of weighted local empirical processes

We consider the local empirical process indexed by sets, a substantial generalization of the well-studied uniform tail empirical process. We show that the weak limit of weighted versions of this process is Poisson under certain conditions, whereas it is Gaussian in other situations. Our main theorems provide many new results as well as a unified approach to a number of asymptotic distributional results for weighted empirical processes, which up to now appeared to be isolated facts. Our results have applications in ‘local’ statistical procedures; we will, in particular, show their usefulness in multivariate extreme value theory.