Abstract:
While modulating neural activity through stimulation is an effective treatment for neurological diseases such as Parkinson's disease and essential tremor, an opportunity for improving neuromodulation therapy remains in automatically adjusting therapy to continuously optimize patient outcomes. Practical issues associated with achieving this include the paucity of human data related to disease states, poorly validated estimators of patient state, and unknown dynamic mappings of optimal stimulation parameters based on estimated states. To overcome these challenges, we present an investigational platform including: an implanted sensing and stimulation device to collect data and run automated closed-loop algorithms; an external tool to prototype classifier and control-policy algorithms; and real-time telemetry to update the implanted device firmware and monitor its state. The prototyping system was demonstrated in a chronic large animal model studying hippocampal dynamics. We used the platform to find biomarkers of the observed states and transfer functions of different stimulation amplitudes. Data showed that moderate levels of stimulation suppress hippocampal beta activity, while high levels of stimulation produce seizure-like after-discharge activity. The biomarker and transfer function observations were mapped into classifier and control-policy algorithms, which were downloaded to the implanted device to continuously titrate stimulation amplitude for the desired network effect. The platform is designed to be a flexible prototyping tool and could be used to develop improved mechanistic models and automated closed-loop systems for a variety of neurological disorders.

Abstract:
Improving utilization of the radio spectrum is the main goal of Cognitive Radio Networks (CRN). Recent studies made use of cooperative relay technology in cognitive networks, to increase transmission diversity gain. In this paper we consider an OFDM based cooperative cognitive network with a pair of Source-Destination nodes as the primary user (PU), and a pair of Source-Destination nodes—which is assisted with a relay—as the secondary (cognitive) user (SU). Both primary and secondary users share a same spectrum. In a two hop transmission, the source transmits in the first hop, and the half-duplex relay decodes the message, re-encodes and forwards it to the destination in the second hop on a different subcarrier. The cognitive network obeys an underlay paradigm where the SU is allowed to transmit simultaneously with PU, while its power is limited such that the interference caused for PU does not exceed a defined temperature. Under this constraint, a joint subcarrier pairing and power allocation is proposed for SU to maximize its weighted sum rate. The problem is transformed to a convex optimization problem and solved in the dual domain. Then an algorithm to achieve feasible solutions is used based on the optimization results. Through extensive simulations, we compare the spectrum utilization of the proposed approach with the existing ones, and show that interestingly the proposed method improves the weighted sum rate of SU.

Abstract:
Like many movements advocating the human rights of a ‘minority’ group, the gay rights movement in the United States has faced severe opposition. This article examines whether a close correlation exists between the anti-gay rights movement and conservative Christianity. The Religious Right has been a vocal and powerful force opposing equal rights for the lesbian, gay, bisexual and transgender (LGBT) populations. Using the theoretical concept of framing, this article shows that the Religious Right has been active in constructing conservative Christian values and beliefs in order to mobilize voters and activists against the gay rights movement. The historical background of the gay and the anti-gay rights movements will be examined in addition to the change in the anti-gay rights rhetoric and framing strategies. It is argued that hostility towards the gay rights movement has grown as opposition to other minority groups has become socially unacceptable, while the same line of framing strategies persist in the rhetoric of the Religious Right. The arguments of anti-gay rights activists are categorized within two main claims: one, homosexuality is a sin, and two, homosexuality is a threat to society. Various framing strategies are used in order to mobilize against gay rights. Further, as the Religious Right works to oppose gay rights, more liberal religious groups have been less active in making their case for equality, diversity, and welcoming LGBT members. Yet public opinion polls in the US show increasing acceptance of gay rights. The gay rights movement can take advantage of the central role of religion in American society through framing religious values for the promotion of equality, tolerance, and respect.

Abstract:
We find the coordinate space wave functions, maximal localization states, and quasiposition wave functions in a GUP framework that implies a minimal length uncertainty using a formally self-adjoint representation. We show how the boundary conditions in quasiposition space can be exactly determined from the boundary conditions in coordinate space. 1. Introduction The existence of a minimal length uncertainty proportional to the Planck length ~ ？m is one of the common predictions of various candidates of quantum gravity. This idea in the context of the Generalized (Gravitational) Uncertainty Principle (GUP) has attracted much attention in recent years and many papers have appeared in the literature to address the effects of this minimal length on various quantum mechanical systems [1–14]. It is pointed out by Mead that gravity amplifies the Heisenberg’s measurement uncertainty which makes it impossible to measure distances more accurate than Planck’s length [15]. In fact, since the increase of the energies to probe small distances considerably disturbs the spacetime structure because of the gravitational effects, the spatial uncertainty eventually increases at energy scales as large as the Planck scale. This minimal length can be considered as a fundamental property of quantum spacetime, a natural UV regulator, and a solution for the trans-Planckian problem. Since the string theory with large or warped extra dimensions can lower the Planck scale into the TeV range, this fundamental length scale also moved into the reach of the Large Hadron Collider. The thought experiments that support the minimal length proposal include the Heisenberg microscope with Newtonian gravity and its relativistic counterpart [15], limit to distance measurements [16], limit to clock synchronization, and limit to the measurement of the blackhole horizon [4]. Moreover, different approaches to quantum gravity such as string theory, loop quantum gravity, and loop quantum cosmology, quantized conformal fluctuations [17, 18], asymptotically safe gravity [19], and noncommutative geometry all indicate a fundamental limit to the resolution of structure. Based on the Heisenberg’s microscope and taking into account both the normal and the gravitational uncertainties one finds [20] where is the gravitational constant. As Adler and Santiago observed this GUP is invariant under and therefore has a momentum inversion symmetry. Because of the universality of the gravity, this correction modifies all Hamiltonians for the quantum systems near the Planck scale. Recently, an experimental scheme is

Abstract:
We obtain a modified version of Coulomb's law in two- and three-dimensional closed spaces. We demonstrate that in a closed space the total electric charge must be zero. We also discuss the relation between total charge neutrality of a isotropic and homogenous universe to whether or not its spatial sector is closed.

Abstract:
We present an alternative quantization procedure for the one-dimensional non-relativistic quantum mechanics. We show that, for the case of a free particle and a particle in a box, the complete classical and quantum correspondence can be obtained using this formulation. The resulting wave packets do not disperse and strongly peak on the classical paths. Moreover, for the case of the free particle, they satisfy minimum uncertainty relation.

Abstract:
We introduce a method to construct wave packets with complete classical and quantum correspondence in one-dimensional non-relativistic quantum mechanics. First, we consider two similar oscillators with equal total energy. In classical domain, we can easily solve this model and obtain the trajectories in the space of variables. This picture in the quantum level is equivalent with a hyperbolic partial differential equation which gives us a freedom for choosing the initial wave function and its initial slope. By taking advantage of this freedom, we propose a method to choose an appropriate initial condition which is independent from the form of the oscillators. We then construct the wave packets for some cases and show that these wave packets closely follow the whole classical trajectories and peak on them. Moreover, we use de-Broglie Bohm interpretation of quantum mechanics to quantify this correspondence and show that the resulting Bohmian trajectories are also in a complete agreement with their classical counterparts.

Abstract:
We propose a new initial condition for the homogeneous and isotropic quantum cosmology, where the source of the gravitational field is a conformally coupled scalar field, and the maximally symmetric hypersurfaces have positive curvature. After solving corresponding Wheeler-DeWitt equation, we obtain exact solutions in both classical and quantum levels. We propose appropriate initial condition for the wave packets which results in a complete classical and quantum correspondence. These wave packets closely follow the classical trajectories and peak on them. We also quantify this correspondence using de-Broglie Bohm interpretation of quantum mechanics. Using this proposal, the quantum potential vanishes along the Bohmian paths and the classical and Bohmian trajectories coincide with each other. We show that the model contains singularities even at the quantum level. Therefore, the resulting wave packets closely follow the classical trajectories from big-bang to big-crunch.

Abstract:
We present the coherent states of the harmonic oscillator in the framework of the generalized (gravitational) uncertainty principle (GUP). This form of GUP is consistent with various theories of quantum gravity such as string theory, loop quantum gravity, and black-hole physics and implies a minimal measurable length. Using a recently proposed formally self-adjoint representation, we find the GUP-corrected Hamiltonian as a generator of the generalized Heisenberg algebra. Then following Klauder's approach, we construct exact coherent states and obtain the corresponding normalization coefficients, weight functions, and probability distributions. We find the entropy of the system and show that it decreases in the presence of the minimal length. These results could shed light on possible detectable Planck-scale effects within recent experimental tests.

Abstract:
We present exact energy eigenvalues and eigenfunctions of the one-dimensional hydrogen atom in the framework of the Generalized (Gravitational) Uncertainty Principle (GUP). This form of GUP is consistent with various theories of quantum gravity such as string theory, loop quantum gravity, black-hole physics, and doubly special relativity and implies a minimal length uncertainty and a maximal momentum. We show that the quantized energy spectrum exactly agrees with the semiclassical results.