The Neurocognitive Process of Digital Radicalization: A Theoretical Model and Analytical Framework

Recent studies suggest that empathy induced by narrative messages can effectively facilitate persuasion and reduce psychological reactance. Although limited, emerging research on the etiology of radical political behavior has begun to explore the role of narratives in shaping an individual’s beliefs, attitudes, and intentions that culminate in radicalization. The existing studies focus exclusively on the influence of narrative persuasion on an individual, but they overlook the necessity of empathy and that in the absence of empathy, persuasion is not salient. We argue that terrorist organizations are strategic in cultivating empathetic-persuasive messages using audiovisual materials, and disseminating their message within the digital medium. Therefore, in this paper we propose a theoretical model and analytical framework capable of helping us better understand the neurocognitive process of digital radicalization

An Information-geometric Approach to Sensor Management

An information-geometric approach to sensor management is introduced that is based on following geodesic curves in a manifold of possible sensor configurations. This perspective arises by observing that, given a parameter estimation problem to be addressed through management of sensor assets, any particular sensor configuration corresponds to a Riemannian metric on the parameter manifold. With this perspective, managing sensors involves navigation on the space of all Riemannian metrics on the parameter manifold, which is itself a Riemannian manifold. Existing work assumes the metric on the parameter manifold is one that, in statistical terms, corresponds to a Jeffreys prior on the parameter to be estimated. It is observed that informative priors, as arise in sensor management, can also be accommodated. Given an initial sensor configuration, the trajectory along which to move in sensor configuration space to gather most information is seen to be locally defined by the geodesic structure of this manifold. Further, divergences based on Fisher and Shannon information lead to the same Riemannian metric and geodesics.Comment: 4 pages, 3 figures, to appear in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, March 201

Ferreting out the Fluffy Bunnies: Entanglement constrained by Generalized superselection rules

Entanglement is a resource central to quantum information (QI). In particular, entanglement shared between two distant parties allows them to do certain tasks that would otherwise be impossible. In this context, we study the effect on the available entanglement of physical restrictions on the local operations that can be performed by the two parties. We enforce these physical restrictions by generalized superselection rules (SSRs), which we define to be associated with a given group of physical transformations. Specifically the generalized SSR is that the local operations must be covariant with respect to that group. Then we operationally define the entanglement constrained by a SSR, and show that it may be far below that expected on the basis of a naive (or ``fluffy bunny'') calculation. We consider two examples. The first is a particle number SSR. Using this we show that for a two-mode BEC (with Alice owning mode $A$ and Bob mode $B$), the useful entanglement shared by Alice and Bob is identically zero. The second, a SSR associated with the symmetric group, is applicable to ensemble QI processing such as in liquid-NMR. We prove that even for an ensemble comprising many pairs of qubits, with each pair described by a pure Bell state, the entanglement per pair constrained by this SSR goes to zero for a large ensemble.Comment: 8 pages, proceedings paper for an invited talk at 16th International Conference on Laser Spectroscopy (2003

Operator-Valued Frames for the Heisenberg Group

A classical result of Duffin and Schaeffer gives conditions under which a discrete collection of characters on $\mathbb{R}$, restricted to $E = (-1/2, 1/2)$, forms a Hilbert-space frame for $L^2(E)$. For the case of characters with period one, this is just the Poisson Summation Formula. Duffin and Schaeffer show that perturbations preserve the frame condition in this case. This paper gives analogous results for the real Heisenberg group $H_n$, where frames are replaced by operator-valued frames. The Selberg Trace Formula is used to show that perturbations of the orthogonal case continue to behave as operator-valued frames. This technique enables the construction of decompositions of elements of $L^2(E)$ for suitable subsets $E$ of $H_n$ in terms of representations of $H_n$

Maximum-entropy Surrogation in Network Signal Detection

Multiple-channel detection is considered in the context of a sensor network where raw data are shared only by nodes that have a common edge in the network graph. Established multiple-channel detectors, such as those based on generalized coherence or multiple coherence, use pairwise measurements from every pair of sensors in the network and are thus directly applicable only to networks whose graphs are completely connected. An approach introduced here uses a maximum-entropy technique to formulate surrogate values for missing measurements corresponding to pairs of nodes that do not share an edge in the network graph. The broader potential merit of maximum-entropy baselines in quantifying the value of information in sensor network applications is also noted.Comment: 4 pages, submitted to IEEE Statistical Signal Processing Workshop, August 201

Analysis of Fisher Information and the Cram\'{e}r-Rao Bound for Nonlinear Parameter Estimation after Compressed Sensing

In this paper, we analyze the impact of compressed sensing with complex random matrices on Fisher information and the Cram\'{e}r-Rao Bound (CRB) for estimating unknown parameters in the mean value function of a complex multivariate normal distribution. We consider the class of random compression matrices whose distribution is right-orthogonally invariant. The compression matrix whose elements are i.i.d. standard normal random variables is one such matrix. We show that for all such compression matrices, the Fisher information matrix has a complex matrix beta distribution. We also derive the distribution of CRB. These distributions can be used to quantify the loss in CRB as a function of the Fisher information of the non-compressed data. In our numerical examples, we consider a direction of arrival estimation problem and discuss the use of these distributions as guidelines for choosing compression ratios based on the resulting loss in CRB.Comment: 12 pages, 3figure