Generalized Householder Transformations

The Householder transformation, allowing a rewrite of probabilities into expectations of dichotomic observables, is generalized in terms of its spectral decomposition. Dichotomy is modulated by allowing more than one negative eigenvalues, or by abandoning it altogether, yielding generalized operator valued arguments for contextuality. We also discuss a form of state-dependent contextuality by variation of the functional relations of the operators; in particular, by additivity.

Application of Spectral Decomposition Technique to Delineate the Evolution of Karst on Carbonate Platforms of Central Luconia, Offshore Sarawak, Malaysia

Karstification in carbonate platforms of the Miocene age in Central Luconia province, offshore Sarawak, Malaysia, has been discussed since the onset of exploration and initial discoveries in the region, with over 200 mapped platforms to date. An extensive drilling program over the last decade confirmed the existence of karst during the drilling process where issues such as total loss circulation and bit drops were common. Karst in Central Luconia has been proposed by several authors; however, detailed quantitative description of the observed features have not yet been conducted. This study involves systematic mapping of loss circulation depths, chalkified/rubble/vuggy zones described from cores, and vugs of >2 mm in size and moldic porosity observed on thin sections of the Jintan platform. These data supplement the interpretation of karst from multiple 3D seismic attributes. Seismic interpretation of the Jintan and M1 platforms revealed an extensive dendritic pattern which is on average 70–100 m deep and 3–5 km long, and circular geobodies of 1 km in width that exist on the upper part of the platform. Spectral decomposition, also known as time-frequency analysis, was used to enhance the interpretation of karst features on seismics within a specific wavelength. In this study, a comparison of three spectral decomposition methods applied on the 3D seismic cube of the Jintan and M1 platforms was undertaken to determine the method which allowed for better delineation of the karst features. The results show that the short-time Fourier transform (STFT) method using frequencies of 46, 54, and 60 Hz delineated most of the karst features compared to the continuous wavelet transform (CWT) Morlet and CWT Ricker wavelet methods. This paper aims to discuss the dimensions, evolution and geometry of the karst features quantitatively on three selected karst horizons named “K1”, “K2”, “K3”. Interpretation revealed that the dendritic karst features were found to be most prominent on the K2 horizon which lies below a conspicuous change of the external geomorphology of the platform. Backstepping of the platform margin by 12 km is observed in both platforms. Quantitative seismic interpretation shows that the karst observed in M1 platform is approximately 70–100 m deep, and the dendritic features are around 1–2 km in length and approximately 500 m wide; whereas, in the Jintan platform the dendritic features observed are up to 5 km in length with several 1 km wide circular/sinkhole features. More than 20 dendritic features orientated SE and NS were mapped mainly in the transitional area as well as the center of both platforms. The nature of the karst morphology in Central Luconia remains controversial; however, it is proposed to be of mixing zone karst origin.

Mathematical Model of the Delay in Communication Networks Based on QS with a Time Lag

In the mathematical modeling of modern computer networks, telecommunication networks, traffic flows, logistics and many others, the methods of queuing theory are widely used. In turn, in studies of queuing systems (QS) G/G/1 with arbitrary distribution laws of intervals between adjacent requirements of the incoming flow and their service time, the spectral decomposition method (MSD) of solving the Lindley integral equation is often used. This method is based on the search for zeros and poles of the constructed spectral decomposition in the form of some fractional-rational function using numerical methods to determine the roots of polynomials. In this case, the coefficients of the polynomial in the numerator of the expansion are expressed through the unknown parameters of the distribution laws used to describe the QS. In the case of teletraffic research, usually these unknown parameters of the distribution laws can be determined through the numerical characteristics of the intervals between traffic packets by the method of moments. The purpose of this article is to present a fundamentally new mathematical model of a system formed by two flows with distribution laws shifted to the right. This is possible only for those probability distribution laws whose density functions are Laplace transformable. The main advantages of such systems, let us call them time lag systems, are that they provide less queue latency compared to conventional systems, and that they extend the range of traffic parameters. The article presents the results obtained on the average delay of requests in the queue for a system with exponential and hyper-Erlang distributions, an algorithm for calculating the average delay and the results of computational experiments in the Mathcad package.

Spectral Analysis of Translation-Invariant Mechanical Systems with Application to Structural Vibrations and Stability

The paper considers the problems and the methods of spectral analysis of elastic structural systems. The presented consideration focuses on the translation-invariant spectral formulations. Some periodic representations and the spectral decomposition are derived. In the context of general analysis of translation-invariant systems, the particular problems of structural vibration and stability are solved in analytical form.

Lateral Line Ablation by Toxins Results in Distinct Rheotaxis Profiles in Fish

Zebrafish lateral line is an established model for hair cell organ damage, yet few studies link mechanistic disruptions to changes in biologically relevant behavior. We used larval zebrafish to determine how damage via ototoxic chemicals impact rheotaxis. Larvae were treated with CuSO4 or neomycin to disrupt lateral line function then exposed to water flow stimuli. Their swimming behavior was recorded, and DeepLabCut and SimBA software were used to track movements and classify rheotaxis behavior. Lateral line-disrupted fish performed rheotaxis, but they swam greater distances, for shorter durations, and with greater angular variance than controls. Further, spectral decomposition analyses demonstrated that lesioned fish exhibited toxin-specific behavioral profiles with distinct fluctuations in the magnitude, timing, and cross-correlation between changes in linear and angular movements. Our observations support that lateral-line input is needed for fish to perform rheotaxis efficiently in flow and reveals commonly used lesion methods have unique effects on behavior.

Zircon U-Pb ages of the Benom Complex: Implications for a Late Triassic uplift event in Central Peninsular Malaysia

Over two decades, analysis of seismic attributes had been an integral part of seismic reflection interpretation. Seismic attributes are an influential assistance to seismic interpretation, delivering geoscientists with alternative images of structural (faults) and stratigraphic features (channels), which can be utilised as mechanisms to identify prospects, ascertain depositional environment and structural deformation history more rapidly even provide direct hydrocarbon indicators. The additional steps are obligatory to compute and interpret the attributes of faults and channels from seismic images, which are often sensitive to noise due to the characteristically computed as discontinuities of seismic reflections. Furthermore, on a conventional seismic profile or poor quality data, faults and channels are hard to visible. The current research review these geological structures through a case study of 3D seismic data from N-field in the viewpoint of Malay Basin. This study aimed to characterise the structure and stratigraphic features by using seismic attributes on the N-field below seismic resolution. Also, two different methods are proposed to improve seismic reflections, i.e., faults and channels that are hard to see on the conventional 3D data set. The first method, to detect faults in seismic data, which this paper employs the ant tracking attribute as a unique algorithm to be an advanced forwarding that introduces a new tool in the interpretation of fault. The effective implementation of ant tracking can be achieved when the output of other faults sensitive attributes are used as input data. In this work, the seismic data used are carefully conditioned using a signal. Chaos and variance that are sensitive to faults are applied to the seismic data set, and the output from these processes are used as input data that run the ant tracking attribute, which the faults were seen difficult to display on the raw seismic data. Meanwhile, for the second method, spectral decomposition was adopted to deliberate the way its method could be utilised to augment stratigraphic features (channels) of the N-field, where the channel is ultimately considered being one of the largest formations of the petroleum entrapment. The spectral decomposition analysis method is an alternative practice concentrated on processing S-transform that can offer better results. Spectral decomposition has been completed over the Pleistocene channels, and results propose that application of its methods directs to dependable implications. Respective channel in this area stands out more obviously within the specific frequency range. The thinner layer demonstrates higher amplitude reading at a higher frequency, and the thicker channel displays higher amplitude reading at a lower frequency. Implementation of spectral decomposition assists in deciding the channels that were placed within incised valleys and helps in recognising the orientation and the relative thickness of each channel. By doing this, the ant tracking attribute and spectral decomposition approach have generated the details of subsurface geologic features through attributes by obtaining enhanced reflections and channels and sharpened faults, respectively.

Seismic Attributes For Enhancing Structural And Stratigraphic Features: Application To N-Field, Malay Basin, Malaysia

Over two decades, analysis of seismic attributes had been an integral part of seismic reflection interpretation. Seismic attributes are an influential assistance to seismic interpretation, delivering geoscientists with alternative images of structural (faults) and stratigraphic features (channels), which can be utilised as mechanisms to identify prospects, ascertain depositional environment and structural deformation history more rapidly even provide direct hydrocarbon indicators. The additional steps are obligatory to compute and interpret the attributes of faults and channels from seismic images, which are often sensitive to noise due to the characteristically computed as discontinuities of seismic reflections. Furthermore, on a conventional seismic profile or poor quality data, faults and channels are hard to visible. The current research review these geological structures through a case study of 3D seismic data from N-field in the viewpoint of Malay Basin. This study aimed to characterise the structure and stratigraphic features by using seismic attributes on the N-field below seismic resolution. Also, two different methods are proposed to improve seismic reflections, i.e., faults and channels that are hard to see on the conventional 3D data set. The first method, to detect faults in seismic data, which this paper employs the ant tracking attribute as a unique algorithm to be an advanced forwarding that introduces a new tool in the interpretation of fault. The effective implementation of ant tracking can be achieved when the output of other faults sensitive attributes are used as input data. In this work, the seismic data used are carefully conditioned using a signal. Chaos and variance that are sensitive to faults are applied to the seismic data set, and the output from these processes are used as input data that run the ant tracking attribute, which the faults were seen difficult to display on the raw seismic data. Meanwhile, for the second method, spectral decomposition was adopted to deliberate the way its method could be utilised to augment stratigraphic features (channels) of the N-field, where the channel is ultimately considered being one of the largest formations of the petroleum entrapment. The spectral decomposition analysis method is an alternative practice concentrated on processing S-transform that can offer better results. Spectral decomposition has been completed over the Pleistocene channels, and results propose that application of its methods directs to dependable implications. Respective channel in this area stands out more obviously within the specific frequency range. The thinner layer demonstrates higher amplitude reading at a higher frequency, and the thicker channel displays higher amplitude reading at a lower frequency. Implementation of spectral decomposition assists in deciding the channels that were placed within incised valleys and helps in recognising the orientation and the relative thickness of each channel. By doing this, the ant tracking attribute and spectral decomposition approach have generated the details of subsurface geologic features through attributes by obtaining enhanced reflections and channels and sharpened faults, respectively.

Non-random behavior in sums of modular symbols

We give explicit expressions for the Fourier coefficients of Eisenstein series twisted by Dirichlet characters and modular symbols on [Formula: see text] in the case where [Formula: see text] is prime and equal to the conductor of the Dirichlet character. We obtain these expressions by computing the spectral decomposition of automorphic functions closely related to these Eisenstein series. As an application, we then evaluate certain sums of modular symbols in a way which parallels past work of Goldfeld, O’Sullivan, Petridis, and Risager. In one case we find less cancelation in this sum than would be predicted by the common phenomenon of “square root cancelation”, while in another case we find more cancelation.