Search results for: Tsallis%20entropy

Authors: Muhammad Sheraz, Vasile Preda, Silvia Dedu

Abstract:

Concepts of econophysics are usually used to solve problems related to uncertainty and nonlinear dynamics. In the theory of option pricing the risk neutral probabilities play very important role. The application of entropy in finance can be regarded as the extension of both information entropy and the probability entropy. It can be an important tool in various financial methods such as measure of risk, portfolio selection, option pricing and asset pricing. Gulko applied Entropy Pricing Theory (EPT) for pricing stock options and introduced an alternative framework of Black-Scholes model for pricing European stock option. In this article, we present solutions to maximum entropy problems based on Tsallis, Weighted-Tsallis, Kaniadakis, Weighted-Kaniadakies entropies, to obtain risk-neutral densities. We have also obtained the value of European call and put in this framework.

Keywords: option pricing, Black-Scholes model, Tsallis entropy, Kaniadakis entropy, weighted entropy, risk-neutral density

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Authors: J. Juan Peña, J. Morales, J. García-Ravelo, J. García-Martínes

Abstract:

It is known that by introducing alternative forms of exponential and logarithmic functions, the Tsallis entropy Sq is itself a generalization of Shannon entropy S. In this work, from a deformation through a scaling function applied to the differential operator, it is possible to generate a q-deformed calculus as well as a q-deformed arithmetic, which not only allows generalizing the exponential and logarithmic functions but also any other standard function. The updated q-deformed differential operator leads to an updated integral operator under which the functions are integrated together with a weight function. For each differentiable function, it is possible to identify its q-deformed partner, which is useful to generalize other algebraic relations proper of the original functions. As an application of this proposal, in this work, a generalization of exponential and logarithmic functions is studied in such a way that their relationship with the thermodynamic functions, particularly the entropy, allows us to have a q-deformed expression of these. As a result, from a particular scaling function applied to the differential operator, a q-deformed arithmetic is obtained, leading to the generalization of the Tsallis entropy.

Keywords: q-calculus, q-deformed arithmetic, entropy, exponential functions, thermodynamic functions

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Authors: Neda Seyyedi, Reza Berangi

Abstract:

Voice over IP (VOIP) network, also known as Internet telephony, is growing increasingly having occupied a large part of the communications market. With the growth of each technology, the related security issues become of particular importance. Taking advantage of this technology in different environments with numerous features put at our disposal, there arises an increasing need to address the security threats. Being IP-based and playing a signaling role in VOIP networks, Session Initiation Protocol (SIP) lets the invaders use weaknesses of the protocol to disable VOIP service. One of the most important threats is denial of service attack, a branch of which in this article we have discussed as flooding attacks. These attacks make server resources wasted and deprive it from delivering service to authorized users. Distributed denial of service attacks and attacks with a low rate can mislead many attack detection mechanisms. In this paper, we introduce a mechanism which not only detects distributed denial of service attacks and low rate attacks, but can also identify the attackers accurately. We detect and prevent flooding attacks in SIP protocol using Shannon (FDP-S), Renyi (FDP-R) and Tsallis (FDP-T) entropy. We conducted an experiment to compare the percentage of detection and rate of false alarm messages using any of the Shannon, Renyi and Tsallis entropy as a measure of disorder. Implementation results show that, according to the parametric nature of the Renyi and Tsallis entropy, by changing the parameters, different detection percentages and false alarm rates will be gained with the possibility to adjust the sensitivity of the detection mechanism.

Keywords: VOIP networks, flooding attacks, entropy, computer networks

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Authors: Sheema Shuja Khattak, Gule Saman, Imran Khan, Abdus Salam

Abstract:

Image segmentation plays an important role in medical imaging applications. Therefore, accurate methods are needed for the successful segmentation of medical images for diagnosis and detection of various diseases. In this paper, we have used maximum entropy to achieve image segmentation. Maximum entropy has been calculated using Shannon, Renyi, and Tsallis entropies. This work has novelty based on the detection of skin lesion caused by the bite of a parasite called Sand Fly causing the disease is called Cutaneous Leishmaniasis.

Keywords: shannon, maximum entropy, Renyi, Tsallis entropy

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Authors: Naydelis Brito Suárez, Deni Librado Torres Román, Fernando Hermosillo Reynoso

Abstract:

Automatic detection and generation of a dynamic ROI (Region of Interest) in vehicle traffic surveillance videos based on a static camera in Intelligent Transportation Systems is challenging for computer vision-based systems. The dynamic ROI, being a changing ROI, should capture any other moving object located outside of a static ROI. In this work, the video is represented by a Tensor model composed of a Background and a Foreground Tensor, which contains all moving vehicles or objects. The values of each pixel over a time interval are represented by time series, and some pixel rows were selected. This paper proposes a pixel entropy-based algorithm for automatic detection and generation of a dynamic ROI in traffic videos under the assumption of two types of theoretical pixel entropy behaviors: (1) a pixel located at the road shows a high entropy value due to disturbances in this zone by vehicle traffic, (2) a pixel located outside the road shows a relatively low entropy value. To study the statistical behavior of the selected pixels, detecting the entropy changes and consequently moving objects, Shannon, Tsallis, and Approximate entropies were employed. Although Tsallis entropy achieved very high results in real-time, Approximate entropy showed results slightly better but in greater time.

Keywords: convex hull, dynamic ROI detection, pixel entropy, time series, moving objects

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Authors: Gabriel I. Loaiza Ossa, Carlos A. Cadavid Moreno, Juan C. Arango Parra

Abstract:

It is known that the Riemannian manifold determined by the family of inverse Gaussian distributions endowed with the Fisher metric has negative constant curvature κ= -1/2, as does the family of usual Gaussian distributions. In the present paper, firstly, we arrive at this result by following a different path, much simpler than the previous ones. We first put the family in exponential form, thus endowing the family with a new set of parameters, or coordinates, θ₁, θ₂; then we determine the matrix of the Fisher metric in terms of these parameters; and finally we compute this matrix in the original parameters. Secondly, we define the inverse q-Gaussian distribution family (q < 3) as the family obtained by replacing the usual exponential function with the Tsallis q-exponential function in the expression for the inverse Gaussian distribution and observe that it supports two possible geometries, the Fisher and the q-Fisher geometry. And finally, we apply our strategy to obtain results about the Fisher and q-Fisher geometry of the inverse q-Gaussian distribution family, similar to the ones obtained in the case of the inverse Gaussian distribution family.

Keywords: base of changes, information geometry, inverse Gaussian distribution, inverse q-Gaussian distribution, statistical manifolds

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