Stevens Institute of Technology

About: Stevens Institute of Technology is a education organization based out in Hoboken, New Jersey, United States. It is known for research contribution in the topics: Computer science & Cognitive radio. The organization has 5440 authors who have published 12684 publications receiving 296875 citations. The organization is also known as: Stevens & Stevens Tech.

Asymptotic Solution of the Dirac Equation

Abstract: The WKB method is applied to solve the Dirac equation and the modified Dirac equation appropriate to a spin-\textonehalf{} particle with an anomalous magnetic moment. The solution consists of a phase factor multiplied by a spinor amplitude which is a power series in Planck's constant. The phase is a solution of the Hamilton-Jacobi equation of relativistic mechanics for a spinless particle without electric or magnetic moments. Each term in the spinor amplitude satisfies an ordinary differential equation along the relativistic trajectories. The equation for the leading amplitude yields an equation for the polarization four-vector which is identical with that derived classically by Bargmann, Michel, and Telegdi. It also yields the law of conservation of probability in a tube of trajectories. In addition, it gives rise to an equation for a supplementary phase factor. By using the classical Hamilton-Jacobi function, the law of probability conservation, the polarization four-vector and the supplementary phase factor, the leading term in the solution of the Dirac or modified Dirac equation can be constructed. This solution should be useful when the wavelength of the particle is small compared to the characteristic distance associated with the electromagnetic potential through which the particle moves. When applied to the bound states of a particle without an anomalous moment in a spherically symmetric electrostatic potential, it yields the same results as are usually obtained by separation of variables and use of the ordinary WKB method. The advantage of the present method is that it applies equally well to nonseparable problems.

Semisupervised Feature Selection Based on Relevance and Redundancy Criteria

Abstract: Feature selection aims to gain relevant features for improved classification performance and remove redundant features for reduced computational cost. How to balance these two factors is a problem especially when the categorical labels are costly to obtain. In this paper, we address this problem using semisupervised learning method and propose a max-relevance and min-redundancy criterion based on Pearson’s correlation (RRPC) coefficient. This new method uses the incremental search technique to select optimal feature subsets. The new selected features have strong relevance to the labels in supervised manner, and avoid redundancy to the selected feature subsets under unsupervised constraints. Comparative studies are performed on binary data and multicategory data from benchmark data sets. The results show that the RRPC can achieve a good balance between relevance and redundancy in semisupervised feature selection. We also compare the RRPC with classic supervised feature selection criteria (such as mRMR and Fisher score), unsupervised feature selection criteria (such as Laplacian score), and semisupervised feature selection criteria (such as sSelect and locality sensitive). Experimental results demonstrate the effectiveness of our method.

On the limits of predictability in real-world radio spectrum state dynamics: from entropy theory to 5G spectrum sharing

Abstract: A range of applications in cognitive radio networks, from adaptive spectrum sensing to predictive spectrum mobility and dynamic spectrum access, depend on our ability to foresee the state evolution of radio spectrum, raising a fundamental question: To what degree is radio spectrum state (RSS) predictable? In this article we explore the fundamental limits of predictability in RSS dynamics by studying the RSS evolution patterns in spectrum bands of several popular services, including TV bands, ISM bands, cellular bands, and so on. From an information theory perspective, we introduce a methodology of using statistical entropy measures and Fano inequality to quantify the degree of predictability underlying real-world spectrum measurements. Despite the apparent randomness, we find a remarkable predictability, as large as 90 percent, in real-world RSS dynamics over a number of spectrum bands for all popular services. Furthermore, we discuss the potential applications of prediction-based spectrum sharing in 5G wireless communications.

Master Funds in Portfolio Analysis with General Deviation Measures

Abstract: Generalized measures of deviation are considered as substitutes for standard deviation in a framework like that of classical portfolio theory for coping with the uncertainty inherent in achieving rates of return beyond the risk-free rate. Such measures, derived for example from conditional value-at-risk and its variants, can reflect the different attitudes of different classes of investors. They lead nonetheless to generalized one-fund theorems in which a more customized version of portfolio optimization is the aim, rather than the idea that a single "master fund" might arise from market equilibrium and serve the interests of all investors. The results that are obtained cover discrete distributions along with continuous distributions. They are applicable therefore to portfolios involving derivatives, which create jumps in distribution functions at specific gain or loss values, well as to financial models involving finitely many scenarios. Furthermore, they deal rigorously with issues that come up at that level of generality, but have not received adequate attention, including possible lack of differentiability of the deviation expression with respect to the portfolio weights, and the potential nonuniqueness of optimal weights. The results also address in detail the phenomenon that if the risk-free rate lies above a certain threshold, the usually envisioned master fund must be replaced by one of alternative type, representing a "net short position" instead of a "net long position" in the risky instruments. For nonsymmetric deviation measures, the second type need not just be the reverse of the first type, and there can sometimes even be an interval for the risk-free rate in which no master fund of either type exists. A notion of basic fund, in place of master fund, is brought in to get around this difficulty and serve as a single guide to optimality regardless of such circumstances.