Infinity Research Articles

Bootstrap Estimation of Long-Range Dependence in Arfima Processes

Long-memory or long-range dependence (LRD) denotes the property of a time series to exhibit a significant dependence between very distant observations. The presence of long-memory is established in diverse fields, for example, in hydrology, finance, network traffic, psychology, etc. From a practical point of view an important issue is the estimation of LRD parameters, especially the estimation of the Hurst parameter proposed in [19]. The Hurst parameter, usually referred as the H parameter, indicates the intensity of LRD.Various methods for estimating the H parameter in a time series data are available some of which are described in [3]. They are validated by appealing to an asymptotic analysis supposing that the sample size of the time series converges to infinity. Taqqu et al. [37] investigated empirical performance of nine methods for estimating the LRD in simulated autoregressive fractionally integrated moving average (ARFIMA) processes for a fairly large sample size of 10000 terms.The bootstrap is a general statistical procedure for statistical inference, originally introduced by Efron [11] that generally yields better estimations in finite sample sizes, than the classical methods. In this paper, we consider a bootstrap technique, which uses blocks composed of cycles, to estimate the H parameter in ARFIMA processes. The bias and the root mean square error (RMSE) of five estimators and their corresponded bootstrap estimators are obtained by a Monte Carlo study.

Review of from zero to infinity

No abstract available.

Affine Reconstruction Based on Parallel Plane and Infinity Point

Affine reconstruction is to restore the affine shape of the object. Generally, there are two ways of achieving, one is to determine the plane at infinity, another is to determine the plane homography. Using the homography which had determined the plane at infinity achieve affine reconstruction. In this paper, firstly give out the homography of infinity plane and the algorithm of affine reconstruction, then proved: if the scene contains a set of parallel planes and a infinity point, the homography of infinity plane can be obtained and affine reconstruction can be linearly got in the scene. Computer simulation and real experiments show that the linear affine reconstruction algorithm is correct, and the approach has a good precision.

Imitation, opposition and innovation of social forms: Finitude and infinitude in Gabriel Tarde’s Social Laws

En este texto presento una seleccion de fragmentos del libro “Las leyes sociales” de Gabriel Tarde (1843-1904), publicado originalmente en 1898, y traducido en castellano a principios del siglo XX. Despues de un largo olvido Tarde ha sido revigorizado para el panteon de las ciencias sociales, llegando a ser convertido en un autor muy relevante para la teoria del actor-red (incluso siendo mencionado por Bruno Latour como su antepasado). Pero creo que la recuperacion a la que ha sido sometida la obra de Tarde puede llevarnos a discusiones mas interesantes que las de una nueva mitica de las figuras ancestrales. En esta introduccion abogo mas bien por una aproximacion directa a la propia obra de Tarde, lo que nos permitiria ir mas alla de cualquier uso presentista de una figura historica para apuntalar una teoria precocinada para el consumo de masas. Es por esto que propongo nos centremos criticamente en los propios argumentos de Tarde, que describe “las leyes” de la vida social, hecha de formas potencialmente infinitesimales que se repiten y se diferencian (a lo que el se refiere como procesos de imitacion, oposicion e innovacion). Y mencionare a tal efecto algunas consideraciones criticas contemporaneas que ha recibido esta formulacion en terminos de leyes o su tratamiento sobre la escala de lo social, haciendo especial hincapie en la relacion que establece entre la finitud y la infinitud de las formas sociales.

Time-optimal Control of Petrowsky Systems with Infinitely Many Variables and Control-state Constraints

In this paper, the time-optimal control problem for n × n differential systems of Petrowsky type with infinitely many variables and control-state constraints are considered. For some different cases of the observation, the necessary optimality conditions of optimal control are obtained by using the generalized Dubovitskii-Milyutin Theorem (Theorem 1.8.1, [1]). Key Words: Time-optimal control problem; Petrowsky systems; Dubovitskii-Milyutin method; Canonical approximations; Optimality conditions

Review of Thomas A. Carlson, The Indiscrete Image: Infinitude and Creation of the Human

George Aichele reviews Thomas A. Carlson, The Indiscrete Image: Infinitude and Creation of the Human (Chicago: University of Chicago Press, 2008).

On Leray’s problem under Navier boundary conditions

We consider the stationary motions of a viscous incompressible fluid, of kinematical viscosity ν, in domains with cylindrical outlets to infinity of section &Sigma, and axis e 1 (distorted cylinders). We require that the fluid satisfies the classical boundary Navier condition u·n=0, [&gamma u+T (u,p)·n] &tau =0 (&gamma&ge 0) and tends at infinity to the laminar flow u N in the cylinder with section &Sigma having an assigned flux through &Sigma (Leray problem). We prove that there is a computable positive constant c 0 depending only on &Sigma, such that if ||u N || L &infin (&Sigma) 0 &nu, then the problem has at least a weak solution. Moreover, for &gamma=0 we can alternatively require that u tends at infinity to an assigned constant vector &mu e 1 , &mu&ne 0. In contrast with the most part of the known existence theorems for the steady--state Navier--Stokes problem we show that a solution (u,p) of such a problem exists for every &mu and &nu, is unique for large &nu and converges to &mu e 1 at infinity according to u(x)=&mu e 1 +O(e -&zeta |x 1 | ) for some positive constant &zeta .

Upper bounds of the risk of nearest neighbor rules for finite samples

In this paper, based on the integral expressions for the conditional risk and the risk ,we evaluate the upper bounds of the risk for some important distributions with unbounded support

CUBIC FORMAL POWER SERIES IN CHARACTERISTIC 2 WITH UNBOUNDED PARTIAL QUOTIENTS

There is a theory of continued fractions for formal power seriesin x−1 with coefficients in a field Fq. This theory bears a close analogywith classical continued fractions for real numbers with formal power seriesplaying the role of real numbers and the sum of the terms of non-negativedegree in x playing the role of the integral part. We give a family of cubicpower series over F2 with unbounded partial quotients. To be more precise, letf ∈ F2((x−1)) such that f is not polynomial but f3 is polynomial with degreed ∈ 3N, we prove that the continued fraction expansion of f is unbounded.

Strong and Weak Convergence Theorems for Generalized Mixed Equilibrium Problem with Perturbation and Fixed Pointed Problem of Infinitely Many Nonexpansive Mappings

Very recently, Plubtieng and Kumam [S. Plubtieng, P. Kumam, Weak convergence theorem for monotone mappings and a countable family of nonexpansive mappings, J. Comput. Appl. Math. 224 (2009) 614-621] proposed an iterative algorithm for finding a common solution of a variational inequality problem for an inverse-strongly monotone mapping and a fixed point problem of a countable family of nonexpansive mappings, and obtained a weak convergence theorem. In this paper, based on Plubtieng-Kumam's iterative algorithm we introduce a new iterative algorithm for finding a common solution of a generalized mixed equilibrium problem with perturbation and a fixed point problem of a countable family of nonexpansive mappings in a Hilbert space. We first derive a strong convergence theorem for this new algorithm under appropriate assumptions and then consider a special case of this new algorithm. Moreover, we establish a weak convergence theorem for this special case under some weaker assumptions. Such a weak convergence theorem unifies, improves and extends Plubtieng-Kumam's weak convergence theorem. It is worth pointing out that the proof method of strong convergence theorem is very different from the one of weak convergence theorem.

Quantum addition circuits and unbounded fan-out

We first show how to construct an O(n)-depth O(n)-size quantum circuit for additionof two n-bit binary numbers with no ancillary qubits. The exact size is 7n-6, whichis smaller than that of any oth...

Erratum to: Monotone and Čebyšev arcs in hyperspaces

1. Proposition 5.4 (ii) should read: A monotone arc indexed by (0, 1] in Kn 0 or On 0 attains its infimum distance from every element of the hyperspace if and only if it is unbounded or is nested and collapses at 0. 2. Theorem 5.6 should read: A monotone arc in Kn 0 is Cebysev if and only if it is nested and at either end it is closed, is unbounded, or collapses. 3. Theorem 5.8 should read: A monotone arc in On 0 is Cebysev if and only if at either end, it is closed, is unbounded, or is nested and collapses.

Explicit Solution for M/M/1 Preemptive Priority Queue

The stationary queue length distribution for the M/M/1 preemptive priority queue with two classes of customers is studied using the quasi-birth-and-death (QBD) process with infinitely many phases. For the QBD process, we obtain explicit form of the operator- geometric solution such that we can exactly compute its stationary distribution in principle.

Review of Thomas A. Carlson,The Indiscrete Image: Infinitude and Creation of the Human

Review of Thomas A. Carlson,<i>The Indiscrete Image: Infinitude and Creation of the Human</i>

Theoretic explanation about visual disorder induced by fibrous dysplasia of skull: pressure disequilibrium between lamina cribrosa

To investigate the causes for changes in optic nerve head and visual impairment caused by fibrous dysplasia (FD) of optic canal stenosis. A total of 12 FD patients, diagnosed by CT, received the fundus and optical coherence tomography (OCT). Those with FD involving optic canal underwent decompression. The examination of OCT showed that lamina cribrosa located at the top was the exposure factor for retinal pigment epithelium (RPE). There were decreased vision or edematous optic nerve and atrophic lesion. Odds ratio was calculated by Fisher's exact test. The examination of CT showed the results of optic canal stenosis caused by lesions involving 18 sides: 8-sides with normal vision. Among which, 6 showing that lamina cribrosa was located below RPE and a lamina cribrosa plate near RPE at follow-up, 1 side OCT showing lamina cribrosa above RPE with normal optic nerve; a lateral lamina cribrosa was located above RPE with edematous optic nerve. Visual impairment at 10 sides, normal papillary 2 sides, atrophic papillary 8 sides, OCT showed that lamina cribrosa was located above RPE, postoperatively OCT showed that lamina cribrosa below with 7 sides having improved visual acuity. Fisher's exact test was performed (P = 0.000, odds ratio = infinity). The optic canal stenosis causes a rising pressure of lamina cribrosa zone to shift above RPE. The channel becomes distorted so as to squeeze and cut the ganglion cell axons of optic nerve, block the axoplasmic transport and result in blood circulation disorder. The above factors are the etiologies of visual impairments. Postoperatively lamina cribrosa zone pressure drops so that depressed lamina cribrosa and channel deformation recover and visual acuity improves.

A Theory Bite on Infinity: A Companion to Falk

A Theory Bite on Infinity: A Companion to Falk

Information-Theoretically Secure Protocols and Security under Composition

We investigate the question of whether the security of protocols in the information-theoretic setting (where the adversary is computationally unbounded) implies the security of these protocols unde...

Dynamic Response of Unlined Circular Tunnels Subjected to Internal Explosion

Due to the development of urban areas, underground structures are increasingly needed. Therefore, not only it is likely to have two tunnels located close to each other, but also it happens frequently.Because of the complexity of realistic problems, closed form analytical solutions are not accessible for them. However, latest advances in computational techniques have made numerical approaches more practical for realistic problems. Boundary element method (BEM) is one of such approaches. This technique formulates the problem in terms of boundary values. The main advantage of BEM, especially in comparison with finite element and finite difference methods, is that the discretization is only applied to the boundary, thus reducing the volume of modeling and the number of unknown variables. Moreover, the radiation condition at infinity is exactly satisfied in this method which is very striking for wave propagation problems. First the formulation of boundary element method in the time domain is presented and then a parametric study on the dynamic response of unlined circular tunnels subjected to internal explosion is done. Depth of tunnels, vertical and horizontal distance between two tunnels, diameter of tunnels, and other parameters related to geometry are important factors which can affect displacements and stresses of tunnels under explosive loading. In the present study, effect of two parameters has been investigated: changing the depth of the tunnel that is subjected to internal explosion (case A) and changing the horizontal distance between two shallow tunnels subjected to explosion (case B). Radial displacements and circumferential stresses are the results obtained. Case A- Tunnel depth: The tunnel behavior in depth of H=50R is alike to behavior of same tunnel in infinite depth. Also, radial displacement in upper point of tunnel in depth of H=2R is about 2.7 times of the same tunnel in infinite depth. Circumferential stress in points placed on horizontal diameter of tunnel in depth of H=2R is about 1.8 times of the same tunnel in infinite depth. Case B- Tunnels distance: Two tunnels with horizontal distance of greater than L=50R don’t affect each other. When horizontal distance parameter of two tunnels is L=2.5R then the maximum normalized displacement of the side point of the loaded tunnel, is approximately 2.15 times of the same tunnels with distance of infinite. Also, when horizontal distance of two tunnels is L=2.5R, circumferential stress in lower point of the loaded tunnel, which is normalized with static stress, is approximately 1.2 times of the same tunnels with distance of infinite. Normalized results calculated here display the importance of the geometric parameters on the behavior of unlined tunnels subjected to internal explosion and provide suitable criteria for displacement design of shallow tunnels that are subjected to internal explosion. The accuracy of the present study for the computation of radial displacements and circumferential stresses is verified by solving several problems.

Assessing the Probabilistic Fuzzy Net Present Value for a Capital Investment Choice Using Fuzzy Arithmetic

This work applies fuzzy theory to capital budgeting and combines with a probability method in developing the fuzzy net present value algorithms for evaluating the investment projects. The estimation of cash flows in fuzzy numbers catches the vague characteristics of estimation, and the forecast of probabilities of economic prospects describes the randomness of outcomes. Using α-cuts and the interval of confidence of fuzzy numbers, this study defines the fuzzy net present value (FNPV), expected FNPV, and deviation, and derives their membership functions. The fuzzy performance index (FPI), the fuzzy expected value to standard deviation, is them proposed to be the decision indicator. After a ranking procedure, the higher-FPT project is a better choice. The situations of unequal durations and unequal costs of capital for mutually exclusive projects, which are seldom discussed in previous studies, are considered by estimating the fuzzy equivalent annuity (FEA) and fuzzy equivalent annuity to infinity (FEAI). The ranking of their FPIs is also derived. The proposed step-by-step operational algorithms of the membership functions hopefully conduce to more convenient practical implementation. Finally, a numerical example demonstrates the feasibility of the proposed algorithms.

A formula for gap between two closed operators

Aim of this short note is to obtain a formula for the gap between two densely defined unbounded closed operators. It is interesting to note that the formula is very similar to the corresponding formula for the gap between two bounded operators.