Ternary Hypothesis Research Articles

About One Linguistic Problem

Introduction. The article continues a series of publications on R-linguistics and is dedicated to the ternary hypothesis and the problem of modeling the world associated with it. The essence of the ternary hypothesis is based on the assumption that any natural language does not use verbs with arity (valency) above three. This hypothesis creates an epistemological problem, the essence of which lies in the mismatch between the constraints of the dimensionality of thinking and the dimensionality of some phenomena and processes of the surrounding world. The indicated problem is directly related to language, since language reflects human thinking and the structure of the world model.Methodology and sources. The results obtained in the previous parts of the series are used as research tools. To develop the necessary mathematical representations for verbs with high valence, the categorization axioms formulated earlier in the series are used.Results and discussion. It has been shown that cases of multiple indirect objects are related to data dependencies in the sentence. Methods of categorization have been developed for ternary relations and relations with higher arity. It has been demonstrated that even in this case, all conditional categorizations and conditional verbs can be reduced to a single categorization.Conclusion. The ternary hypothesis and the ternary problem are formulated. Based on the study of data dependencies, it is shown that the ternary hypothesis is most likely true for all natural languages. Based on the study of methods of categorizing relations with arity higher than three, it is demonstrated that in this case linguistic spaces show stability regardless of the location of categories in the sentence, which makes it possible to describe highdimensional interactions using subordinate clauses. Thus, the appearance of subordinate clauses in all languages of the world is associated with the need to describe highdimensional interactions in the world model human.

Isomorphism of Ternary Hypothesis

Isomorphism of Ternary Hypothesis

Spectrum Sensing Under Illegal Spectrum Access Behaviors in Multiple Authorized Users Scenario

In this paper, we detect illegal spectrum access behaviors in the dynamic spectrum sharing of the cognitive wireless networks, in which multiple authorized users (AUs) work in the same channel. First, we detect whether there are users occupy the channel, and if the channel is occupied, then recognize whether there is the illegal user (IU) and infer the number of AUs roughly. In the light of the thorny challenge that legal spectrum utilization behaviors and illegal spectrum access behaviors coexist probabilistically, the spectrum sensing problem is formulated as a mathematical model of ternary hypothesis test. Moreover, when multiple AUs are working at the same time, it is extremely difficult to detect IU. To tackle the problem, taking into account the various potential combinations of AUs and IU, we exploit a two-step detector and derive related detection schemes based on the generalized likelihood ratio test (GLRT), the Rao test, and the Wald test following the generalized multi-hypothesis Neyman-Pearson (GMNP) criterion respectively. Additionally, we design a cooperative spectrum sensing (CSS) scheme on the basis of the global GMNP criteria, in which the distributed detection framework composed of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${K}$ </tex-math></inline-formula> sensing nodes and a fusion center (FC). Finally, to verify the performance of the proposed detection scheme in a variety of parameter configurations, we provide comprehensive simulations and find that there will be at most <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$({{2^{N}}-1})$ </tex-math></inline-formula> detection valleys when <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${N}$ </tex-math></inline-formula> AUs work at the same time. Compared with single-sensing node detection, the CSS scheme can significantly improve the detection performance of the proposed detection schemes, especially in the upper bound and valley of the detection performance.

Multihypothesis Sequential Testing for Illegitimate Access and Collision-Based Attack Detection in Wireless IoT Networks

Jamming or illegitimate wireless network access interferes with legitimate communication sessions by mimicking the legitimate transmissions and degrades the network performance. In this article, we propose a methodology to detect such attacks by implementing a multiple hypotheses sequential testing-based detection framework with variance and channel state information (CSI)-based algorithms. The detection framework focuses on distinguishing between legitimate and illegitimate transmissions and the nature of illegitimate transmissions with a quaternary hypotheses test. The quaternary hypotheses include no transmission, legitimate node transmission, illegitimate node transmission, and collision-based attack. We first devise a sequential testing problem on a ternary hypothesis problem and then tackle the remaining hypothesis with both variance-based approach and CSI-based approach. We devise algorithms based on the same and compare their performance. We also compare our approach with the generalized Neyman-Pearson approach based on detection speed. In addition, we present a multiple sensor-based approach to further improve the detection performance through soft- and hard-decision combining. We conduct extensive performance evaluations based on both simulated and measurement data. The numerical results show fewer sample size requirements for the proposed algorithms, leading to faster detection.

Solving Two Problems IN Number Theory

In 1995, Olivier Ramaret proved that any even number is the sum of no more than 6 primes. From the validity of Goldbach's ternary hypothesis (proved in 2013 year) it follows that any even number is the sum of not more than 4 numbers [1]. In the article, the author confirms the above and proves that the cause and effect of this is any even number the sum of not more than two prime and twin primes are infinite [8]-[14].

Detection of Transmitted Power Violation Based on Geolocation Spectrum Database in Satellite-Terrestrial Integrated Networks.

This paper investigates the detection of the transmitted power violation (TPV) in the satellite-terrestrial integrated network, where the terrestrial base station may break the spectrum policies so that severe damages are made to the satellite systems. Due to the lack of prior information on specific abnormal behaviors, this problem is complex and challenging. To tackle it, we first turn to the geolocation spectrum database based detecting framework, where not only the tasks of each segment but also the spectrum policies are specified. Then, the ternary hypothesis test and the generalized Neyman–Pearson (GMNP) test criterion are applied to maximize the detection probability under the false-alarm constraint. What is more, the Abnormal after Normal (AaN) detector is developed to simplify the analysis. Finally, simulations are conducted to demonstrate that the proposed detector can realize the detection of TPV in most cases at the expense of less than 10% detection probability.

Detection of Spectrum Misuse Behavior in Satellite-Terrestrial Spectrum Sensing Based on Multi-Hypothesis Tests

As the increasing of both users’ demand and the number of communication satellites, spectrum resource is becoming increasingly scarce. Cognitive radio (CR) can effectively alleviate the scarcity of spectrum resource. By using CR technology in the satellite and terrestrial integrated network, the satellite can share the spectrum resource with the terrestrial communication equipment to improve the spectrum utilization. However, due to the satellite communication’s inherent openness and the increasing intelligent level of devices, it makes the satellite communication vulnerable to spectrum misuse, which seriously threatens the reliability and efficiency of the satellite communication system. This paper studies the detection of spectrum misuse in the satellite-terrestrial spectrum sharing system. First, we model the problem as a ternary hypothesis test problem by using generalized multi-hypothesis Neyman-Pearson (GMNP). Then, we utilize a two-step method to solve the complex formula problem in the multiple authorized users scenario. Reasonable decision thresholds are derived by means of the generalized likelihood ratio test (GLRT) and maximum a posterior (MAP) criterion, respectively. Finally, the performance of detection is evaluated and analyzed comprehensively to verify the feasibility of the study.

Spectrum Sensing Under Spectrum Misuse Behaviors: A Multi-Hypothesis Test Perspective

Spectrum misuse behaviors, brought either by illegitimate access or by rogue power emission, endanger the legitimate communication and deteriorate the spectrum usage environment. In this paper, our aim is to detect whether the spectrum band is occupied, and if it is occupied, recognize whether the misuse behavior exists. One vital challenge is that the legitimate spectrum exploitation and misuse behaviors coexist and the illegitimate user may act in an intermittent and fast-changing manner, which brings about much uncertainty for spectrum sensing. To tackle it, we firstly formulate the spectrum sensing problems under illegitimate access and rogue power emission as a uniform ternary hypothesis test. Then, we develop a novel test criterion, named the generalized multi-hypothesis N-P criterion. Following the criterion, we derive two test rules based on the generalized likelihood ratio test and the R-test, respectively, whose asymptotic performances are analyzed and an upper bound is also given. Furthermore, a cooperative spectrum sensing scheme is designed based on the global N-P criterion to further improve the detection performances. In addition, extensive simulations are provided to verify the proposed schemes' performance under various parameter configurations.

Scheme for opportunistic spectrum access in cognitive radio

In this study, an opportunistic spectrum access model with learning strategy is presented for cognitive radio system. Consider a hidden Markov model in learning process, where the ternary hypothesis testing scheme is proposed to perform sensing with the goodness of fit testing. By using a gradient method, the secondary user can estimate the channel patterns and keep up with the variations of the primary user activities. An opportunistic access channel capacity is introduced to evaluate the quality of service of the objective licensed channel. Also, a partially observable Markov decision process framework is presented to exploit spectrum holes. Further analysis shows that, unlike the binary hypothesis testing where the idle state is always protected, the idea of the proposed ternary hypothesis testing puts both the idle and busy state in the same position, which reflects the real state of the licensed channel more precisely. Simulation results indicate that the proposed ternary hypothesis testing scheme outperforms the conventional binary hypothesis testing for both the goodness of fit testing and the energy detection.

Ternary Hypothesis Testing Scheme for Rapidly Opportunistic Spectrum Access

This letter presents a partially observable Markov decision process framework for the opportunistic spectrum access model, where a ternary hypothesis testing scheme is proposed to perform sensing with the goodness of fit testing. Except for idle and busy states, the proposed ternary hypothesis testing also considers the transition state, which reflects the real state of a licensed channel more precisely. Simulation results indicate that the proposed ternary hypothesis testing scheme achieves better performances in channel utilization and collision rate compared with those of the conventional binary hypothesis testing scheme, especially for the rapid variations of the primary user activities.

A Cauchy distribution-based ternary hypothesis testing for bipolar additive watermark detection in H.264/AVC video

The statistical distribution of discrete cosine transform (DCT) coefficients is important for video watermarking since they are the main carriers for watermark embedding. For the statistical distribution of intra-coded DCT coefficients in the H.264/AVC video stream, non-parametric hypothesis test is utilised to verify that Cauchy distribution is better than generalised Gaussian distribution (GGD). Moreover, ternary hypothesis test is introduced into the detection of bipolar additive watermarks. By adjusting the watermark strength parameter, the detector performance can be guaranteed. Experimental results show that for those bipolar additive watermarks in the H.264/AVC stream, the proposed approach can achieve a detection accuracy of more than 80% on average.

A Bayes decision test for detecting uncovered-background and moving pixels in image sequences

We present a ternary hypothesis test for the detection of stationary, moving, and uncovered-background pixels between two image frames in a noisy image sequence using the Bayes decision criterion. Unlike many uncovered-background detection schemes, our scheme does not require motion estimation for the differentiation between moving pixels and uncovered-background pixels. We formulate the Bayes decision rule using a single intensity-difference measurement at each pixel and using multiple intensity-difference measurements in the neighborhood of each pixel. We quantitatively evaluate our detection algorithm on an image sequence which we have generated and qualitatively on the Trevor White image sequence.

Binary and Ternary Catalytic Mechanisms in the Hydration of Acetaldehyde

IN a recent paper1, C. G. Swain has suggested that reactions which are catalysed by acids and bases normally take place by a ternary mechanism, in which the substrate is attacked simultaneously by an acid and a base. Such a mechanism accounts for the product term k′ [HAc][Ac−] found by Dawson and Spivey2 in the expression for the velocity of iodination of acetone in acetate buffers. It has commonly been held that the magnitude of this term was much too small to justify the assumption that the reaction goes primarily by a ternary mechanism involving water molecules3. However, Swain (loc. cit.) has shown clearly that this criticism of the ternary picture is not a valid one, since it ignores the experimental equivalence of pairs of kinetic terms such as [HAc][H2O] and [Ac−][H3O+], or [Ac−][H2O] and [HAc][OH−]. Swain is, in fact, able to show that the magnitude of the term K′ [HAc][Ac−] observed by Dawson and Spivey is close to that predicted by the ternary hypothesis on the basis of the other observed catalytic coefficients. Similarly, Swain shows that if the mutarotation of glucose also involves a ternary mechanism, the term in [HAc][Ac−] will not con-tribute more than a few per cent of the total velocity, and would thus escape detection.