Average Number Of Maxima Research Articles

ВЕРОЯТНОСТНОЕ ОПИСАНИЕ ПОРЫВОВ ВЕТРА В ЗОНЕ ВЗЛЁТНО-ПОСАДОЧНОЙ ПОЛОСЫ, ВЛИЯЮЩИХ НА БЕЗОПАСНОСТЬ ПОЛЁТОВ ВОЗДУШНЫХ СУДОВ

The influence of wind gusts on the safety of aircraft flights is described. The impulse nature of wind gusts is substantiated. Experimental studies of wind gusts carried out with the help of a parametric recording device on an ultrasonic beam and an anemometer are analyzed, and it is shown that wind gusts have an impulsive nature, similar to atmospheric noise envelope emissions. The results of the analytical description of the probabilistic characteristics of atmospheric noise envelope emissions known from the literature are applied to wind gusts on the runway. Characteristics are given for the average duration of wind gusts, intervals between wind gusts and the average duration of intervals, the distribution of the duration of wind gusts, the average number and distribution of maxima of wind gusts.

Statistical parameters of femtosecond laser pulse post-filament propagation on a 65 m air path with localized optical turbulence

High-power femtosecond laser radiation propagates nonlinearly in air, exhibiting pulse self-focusing and strong multiphoton medium ionization, which leads to the spatial fragmentation of laser pulses into highly localized light channels commonly called filaments. Filaments are characterized by high optical intensity and reduced (even zero) angular spreading and can contain laser plasma or be plasmaless (postfilaments). The presence of optical turbulence on the propagation path dramatically changes pulse filamentation dynamics and in some cases causes pulse fragmentation enhancement and collapse arrest. For the first time, to the best of our knowledge, we experimentally and theoretically investigate the transverse profile of Ti:sapphire femtosecond laser radiation nonlinearly propagating a 65 m air path to the region of postfilament evolution after passing through an artificial localized air turbulence. We show that when a turbulence layer is placed before the filamentation region, the average number of high-intensity local fluence maxima (“hot points”) in the beam profile and their sizes grow as the turbulence strength increases, and then saturates at some levels. On the contrary, the deposition of a turbulence screen within the filamentation region has almost no effect on either the number or the average diameter of postfilaments.

Statistical Features of the Thermal Neutron Capture Cross Sections

We discuss the existence of huge thermal neutron capture cross sections in several nuclei. The values of the cross sections are several orders of magnitude bigger than expected at these very low energies. We lend support to the idea that this phenomenon is random in nature and is similar to what we have learned from the study of parity violation in the actinide region. The idea of statistical doorways is advanced as a unified concept in the delineation of large numbers in the nuclear world. The average number of maxima per unit mass, $<n_A>$ in the capture cross section is calculated and related to the underlying cross section correlation function and found to be $<n_A> = 3/(\pi \sqrt{2}\gamma_{A})$, where $\gamma_{A}$ is a characteristic mass correlation width which designates the degree of remnant coherence in the system. We trace this coherence to nucleosynthesis which produced the nuclei whose neutron capture cross sections are considered here.

Cross-section fluctuations in open microwave billiards and quantum graphs: The counting-of-maxima method revisited.

The fluctuations exhibited by the cross sections generated in a compound-nucleus reaction or, more generally, in a quantum-chaotic scattering process, when varying the excitation energy or another external parameter, are characterized by the width Γcorr of the cross-section correlation function. Brink and Stephen [Phys. Lett. 5, 77 (1963)] proposed a method for its determination by simply counting the number of maxima featured by the cross sections as a function of the parameter under consideration. They stated that the product of the average number of maxima per unit energy range and Γcorr is constant in the Ercison region of strongly overlapping resonances. We use the analogy between the scattering formalism for compound-nucleus reactions and for microwave resonators to test this method experimentally with unprecedented accuracy using large data sets and propose an analytical description for the regions of isolated and overlapping resonances.

The local maxima method for enhancement of time–frequency map and its application to local damage detection in rotating machines

In this paper a new method of fault detection in rotating machinery is presented. It is based on a vibration time series analysis in time–frequency domain. A raw vibration signal is decomposed via the short-time Fourier transform (STFT). The time–frequency map is considered as matrix (M×N) with N sub-signals with length M. Each sub-signal is considered as a time series and might be interpreted as energy variation for narrow frequency bins. Each sub-signal is processed using a novel approach called the local maxima method. Basically, we search for local maxima because they should appear in the signal if local damage in bearings or gearbox exists. Finally, information for all sub-signals is combined in order to validate impulsive behavior of energy. Due to random character of the obtained time series, each maximum occurrence has to be checked for its significance. If there are time points for which the average number of local maxima for all sub-signals is significantly higher than for the other time instances, then location of these maxima is “weighted” as more important (at this time instance local maxima create for a set of Δf a pattern on the time–frequency map). This information, called vector of weights, is used for enhancement of spectrogram. When vector of weights is applied for spectrogram, non-informative energy is suppressed while informative features on spectrogram are enhanced. If the distribution of local maxima on spectrogram creates a pattern of wide-band cyclic energy growth, the machine is suspected of being damaged. For healthy condition, the vector of the average number of maxima for each time point should not have outliers, aggregation of information from all sub-signals is rather random and does not create any pattern. The method is illustrated by analysis of very noisy both real and simulated signals.

Relationship between selectivity and average resolution in comprehensive two-dimensional separations with spectroscopic detection

The average value of the multivariate selectivity ( SEL) of randomly positioned peaks in a multi-component separation is shown to equal the average fraction of peaks that are singlets, as predicted by statistical-overlap theory (SOT). This equality is the basis for proposing a useful metric, specifically the average minimum resolution of nearest-neighbor peaks, for the performance of comprehensive two-dimensional (2D) separations. Furthermore this metric was computed both without ancillary spectroscopic information and with the assistance of such help, specifically multi-wavelength UV–vis spectra, acquired during the separation. Separations are simulated with randomly positioned peaks over wide ranges of total number of peaks, first- and second-dimension peak capacity, dimensionless first-dimension sampling time, and spectral diversity. The specific version of the general multivariate selectivity concept that is used here – identified as SEL – gives the relative precision of quantification when using the PARAFAC (parallel factor analysis) method, a popular curve resolution algorithm. The SEL values of all peaks were calculated, averaged, and compared to the predictions of SOT. In the absence of auxiliary spectral data, the SEL-based average minimum resolution required to separate two peaks in a 2D separation is 0.256, compared to resolution of 0.5 if no chemometric assistance is available. This was found to be valid over a wide range of conditions and is essentially independent of peak crowding. With the assistance of the spectral data, the requisite minimum resolution substantially improves, that is, it decreases, especially when peak crowding is severe. The requisite minimum resolution decreases even further, up to a limit, as the spectral diversity is increased. In contrast, the SEL-based average under-sampling correction factor is virtually independent of the presence of the additional spectral data, and additionally is about the same as calculated with SOT from the average number of maxima in closely analogous simulations. The use of selectivity greatly increases the fraction of peaks that are singlets, relative to the number of singlet maxima, especially when spectral assistance is added. The insensitivity of the under-sampling correction factor to either the use of selectivity or added spectral data simplifies optimization of the corrected peak capacity in on-line comprehensive 2D separations.

Analysis of Local Search Landscapes for k-SAT Instances

Stochastic local search is a successful technique in diverse areas of combinatorial optimisation and is predominantly applied to hard problems. When dealing with individual instances of hard problems, gathering information about specific properties of instances in a pre-processing phase is helpful for an appropriate parameter adjustment of local search-based procedures. In the present paper, we address parameter estimations in the context of landscapes induced by k-SAT instances: at first, we utilise a sampling method devised by Garnier and Kallel in 2002 for approximations of the number of local maxima in landscapes generated by individual k-SAT instances and a simple neighbourhood relation. The objective function is given by the number of satisfied clauses. The procedure provides good approximations of the actual number of local maxima, with a deviation typically around 10%. Secondly, we provide a method for obtaining upper bounds for the average number of local maxima in k-SAT instances. The method allows us to obtain the upper bound \(2^{n-O(\sqrt{n/k})}\) for the average number of local maxima, if m is in the region of 2k· n/k.

A unified approach to the performance analysis of speed estimation techniques in mobile communication

Estimation of the mobile speed, or equivalently, the maximum Doppler frequency, is of importance in a variety of applications in wireless mobile communications. In this paper, a unified framework for the performance analysis of several major speed estimation techniques is presented, which allows a fair comparison between all the methods, analytically. Interestingly, it is proved that all these methods are equivalent, asymptotically, i.e., for large observation intervals. In addition, we have derived closed-from expressions for the bias and variance of a recently proposed covariance-based method. We have also introduced a new estimator which relies on the average number of maxima of the inphase component, and have calculated its variance, analytically. Our extensive performance analysis, supported by Monte Carlo simulations, have revealed that depending on the channel condition and the observation interval, one needs to use a crossing- or a covariance-based technique, to achieve the desired estimation accuracy over a large range of mobile speeds.

A Unified Approach to the Performance Analysis of Speed-Estimation Techniques in Mobile Communication

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> The estimation of the mobile speed, or equivalently, the maximum Doppler frequency, is of importance in a variety of applications in wireless mobile communications. In this paper, a unified framework for the performance analysis of several major speed-estimation techniques is presented, which allows a fair comparison between all the methods, analytically. Interestingly, it is proved that all these methods are equivalent, asymptotically, i.e., for large observation intervals. In addition, we have derived closed-form expressions for the bias and variance of a recently proposed covariance-based method. We have also introduced a new estimator that relies on the average number of maxima of the inphase component, and have calculated its variance, analytically. Our extensive performance analysis, supported by Monte Carlo simulations, have revealed that depending on the channel condition and the observation interval, one needs to use a crossing- or a covariance-based technique, to achieve the desired estimation accuracy over a large range of mobile speeds. </para>

Text sparsification via local maxima

In this paper we investigate some properties and algorithms related to a text sparsification technique based on the identification of local maxima in the given string. As the number of local maxima depends on the order assigned to the alphabet symbols, we first consider the case in which the order can be chosen in an arbitrary way. We show that looking for an order that minimizes the number of local maxima in the given text string is an NP-hard problem. Then, we consider the case in which the order is fixed a priori. Even though the order is not necessarily optimal, we can exploit the property that the average number of local maxima induced by the order in an arbitrary text is approximately one third of the text length. In particular, we describe how to iterate the process of selecting the local maxima by one or more iterations, so as to obtain a sparsified text. We show how to use this technique to filter the access to unstructured texts, which appear to have no natural division in words. Finally, we experimentally show that our approach can be successfully used in order to create a space efficient index for searching sufficiently long patterns in a DNA sequence as quickly as a full index.

On the average number of maxima in a set of vectors

Any of n vectors in d-space is called maximal if none of the remaining vectors dominates it in every component. Assuming that n vectors are distributed identically and that the d components of each vector are distributed independently and continuously, we determine the expected number of maximal vectors explicitly for any n and d. The asymptotic behaviour of this quantity as n tends to infinity, which was investigated by Bentley, Kung, Schkolnick, Thompson and Devroye, follows immediately from our result.

Effects of parameter uncertainty on the response of vibratory systems to random excitation

Vibratory systems subjected to a stationary random external excitation and having random uncertainties in parameters are analyzed. Some quantities characterizing the quality of such systems (quality measures) are defined and evaluated; they are, for example, the average number of level crossings, the average number of maxima, and the departure from normality. The effects of random uncertainty in system parameters on the quality measures are investigated (analytically and numerically) via conditioning. This means that first the conditional quantities (obtained for fixed parameters) are used and then integration with respect to the appropriate distribution is performed. The analysis includes also a discussion of the quality predictions for systems subjected to a random excitation with an exponential correlation by considering a system with an “equivalent” white noise excitation.

On the average oscillation of a stack

Evaluating a binary tree in postorder we assume that in one unit of time zero or two nodes are removed from the top of the stack and one node is stored in the stack. The oscillation of the stack can be described by a functionf wheref(t) is the number of nodes in the stack aftert units of time. In this paper we shall first derive several new enumeration results concerning planted plane trees. In the second part we shall prove, that the average number of maxima (MAX-turns) and minima (MIN-turns) of the functionf isn/2 andn/2—1, respectively, provided that all binary trees withn leaves are equally likely. Finally, we shall compute for largen and fixedj the average increase (decrease) of the length of the stack between thej-th MIN-turn and (j+1)-th MAX-turn (between thej-th MAX-turn and thej-th MIN-turn). This result implies that the average oscillation of the stack can be described by the functionf(j)=4√j/π−(−1) j +O(1/√j) for largen and fixed turn-numberj.

An investigation of the frequencydistributions of annual sea level maxima at ports around Great Britain

Observed sea level maxima in the form of annual extremes have been analysedfor 67 ports around the British Isles. The ports give a coverage of all principal estuarine and open coast regions. The average number of annual maxima per port is 45, ranging from a minimum number of 10 to a maximum of over 130. The data are analysed by a standard method of extreme value analysis. It is shown that for certain ports the frequency distributions of the maxima are time dependent; this time dependency is most pronounced in estuarine regions. The results show the local and regional distribution of frequency statistics and the relative magnitude of their variation through time. The limitations of using annual sea level maxima as a basis for computing frequency statistics are examined.

On the Average Number of Maxima in a Set of Vectors and Applications

A maximal vector of a set ~s one which is not less than any other vector m all components We derive a recurrence relation for computing the average number of maxunal vectors m a set of n vectors m d-space under the assumpUon that all (nl) a relative ordermgs are equally probable. Solving the recurrence shows that the average number of maxmaa is O((ln n) a-~) for fixed d We use this result to construct an algorithm for finding all the maxima that have expected running tmae hnear m n (for sets of vectors drawn under our assumptions) We then use the result to find an upper bound on the expected number of convex hull points m a random point set

Use of Mean Squared Pressure along a Reverberant Room Diagonal for Sound Power Measurement

The mean of the squared pressure along part of a room diagonal is frequently used to determine the sound power using the reverberant room technique. The spatial pressure along a room diagonal has been evaluated experimentally and theoretically for a source located in the corner of a 300-m3 and a 150-m3 reverberant room. For frequencies between 100 and 2000 Hz, the average number of maxima in the mean squared pressure 〈p2〉 is given by N=4L/πλ, where L is the length along the diagonal and is independent of absorption, room size, and stationary diffusers. The variation of 〈p2〉 at a maxima is given by 〈p2〉=An cos(πkx/4), where the An possesses a gamma probability distribution that depends on absorption. It is shown that the value of the mean of 〈p2〉 for white noise with a 6-Hz bandwidth depends on the traverse length selected and is independent of damping while the standard deviation is improved by adding damping. Experimental results substantiate this conclusion.

The average number of maxima of a random algebraic curve

AbstractLet g0, gl, g2,…be a sequence of mutually independent, normally distributed random variables with mathematical expectation zero and variance unity. In this work, we obtain the average number of maxima (minima) of the random algebraic curves with the equationsThis average is (½(3½ + 1)) log N + O((log N)⅔ (log log N)½), when N is large.

The theory of fluctuations in nuclear reaction cross sections

A Monte Carlo calculation of cross sections was carried out to illustrate probability density distribution, energy autocorrelation function, average number of maxima per unit energy, and the mean varintion of a partial cross section. (R.E.U.)

Widths of fluctuations in nuclear cross sections

At high energies cross section resonances due to states of compound nuclei in nuclear reactions overlap, and the partial reaction cross sections fluctuate as a function of energy. Ericson's formuias for the probability distribution of a partial cross section sigma are obtained. Additionally, relations for the average number of maxima in the cross section per unit energy and for the probability distribution of d sigma /dE are derived. (D.C.W.)