Laplace Functional Ordering of Point Processes in Large-scale Wireless Networks

Stochastic orders on point processes are partial orders which capture notions like being larger or more variable. Laplace functional ordering of point processes is a useful stochastic order for comparing spatial deployments of wireless networks. It is shown that the ordering of point processes is preserved under independent operations such as marking, thinning, clustering, superposition, and random translation. Laplace functional ordering can be used to establish comparisons of several performance metrics such as coverage probability, achievable rate, and resource allocation even when closed form expressions of such metrics are unavailable. Applications in several network scenarios are also provided where tradeoffs between coverage and interference as well as fairness and peakyness are studied. Monte-Carlo simulations are used to supplement our analytical results.Comment: 30 pages, 5 figures, Submitted to Hindawi Wireless Communications and Mobile Computin

Walking across Wikipedia: a scale-free network model of semantic memory retrieval.

Semantic knowledge has been investigated using both online and offline methods. One common online method is category recall, in which members of a semantic category like "animals" are retrieved in a given period of time. The order, timing, and number of retrievals are used as assays of semantic memory processes. One common offline method is corpus analysis, in which the structure of semantic knowledge is extracted from texts using co-occurrence or encyclopedic methods. Online measures of semantic processing, as well as offline measures of semantic structure, have yielded data resembling inverse power law distributions. The aim of the present study is to investigate whether these patterns in data might be related. A semantic network model of animal knowledge is formulated on the basis of Wikipedia pages and their overlap in word probability distributions. The network is scale-free, in that node degree is related to node frequency as an inverse power law. A random walk over this network is shown to simulate a number of results from a category recall experiment, including power law-like distributions of inter-response intervals. Results are discussed in terms of theories of semantic structure and processing

Entropic measures of individual mobility patterns

Understanding human mobility from a microscopic point of view may represent a fundamental breakthrough for the development of a statistical physics for cognitive systems and it can shed light on the applicability of macroscopic statistical laws for social systems. Even if the complexity of individual behaviors prevents a true microscopic approach, the introduction of mesoscopic models allows the study of the dynamical properties for the non-stationary states of the considered system. We propose to compute various entropy measures of the individual mobility patterns obtained from GPS data that record the movements of private vehicles in the Florence district, in order to point out new features of human mobility related to the use of time and space and to define the dynamical properties of a stochastic model that could generate similar patterns. Moreover, we can relate the predictability properties of human mobility to the distribution of time passed between two successive trips. Our analysis suggests the existence of a hierarchical structure in the mobility patterns which divides the performed activities into three different categories, according to the time cost, with different information contents. We show that a Markov process defined by using the individual mobility network is not able to reproduce this hierarchy, which seems the consequence of different strategies in the activity choice. Our results could contribute to the development of governance policies for a sustainable mobility in modern cities

Possible Roles of Neural Electron Spin Networks in Memory and Consciousness

Spin is the origin of quantum effects in both Bohm and Hestenes quantum formulism and a fundamental quantum process associated with the structure of space-time. Thus, we have recently theorized that spin is the mind-pixel and developed a qualitative model of consciousness based on nuclear spins inside neural membranes and proteins. In this paper, we explore the possibility of unpaired electron spins being the mind-pixels. Besides free O2 and NO, the main sources of unpaired electron spins in neural membranes and proteins are transition metal ions and O2 and NO bound/absorbed to large molecules, free radicals produced through biochemical reactions and excited molecular triplet states induced by fluctuating internal magnetic fields. We show that unpaired electron spin networks inside neural membranes and proteins are modulated by action potentials through exchange and dipolar coupling tensors and spin-orbital coupling and g-factor tensors and perturbed by microscopically strong and fluctuating internal magnetic fields produced largely by diffusing O2. We argue that these spin networks could be involved in brain functions since said modulation inputs information carried by the neural spike trains into them, said perturbation activates various dynamics within them and the combination of the two likely produce stochastic resonance thus synchronizing said dynamics to the neural firings. Although quantum coherence is desirable, it is not required for these spin networks to serve as the microscopic components for the classical neural networks. On the quantum aspect, we speculate that human brain works as follows with unpaired electron spins being the mind-pixels: Through action potential modulated electron spin interactions and fluctuating internal magnetic field driven activations, the neural electron spin networks inside neural membranes and proteins form various entangled quantum states some of which survive decoherence through quantum Zeno effects or in decoherence-free subspaces and then collapse contextually via irreversible and non-computable means producing consciousness and, in turn, the collective spin dynamics associated with said collapses have effects through spin chemistry on classical neural activities thus influencing the neural networks of the brain. Thus, according to this alternative model, the unpaired electron spin networks are the “mind-screen,” the neural membranes and proteins are the mind-screen and memory matrices, and diffusing O2 and NO are pixel-activating agents. Together, they form the neural substrates of consciousness