Quantum Topological Excitations: from the Sawtooth Lattice to the Heisenberg Chain

The recently elucidated structure of the delafossite YCuO$_{2.5}$ reveals a Cu-O network with nearly independent $\Delta$ chains having different interactions between the $s=1/2$ spins. Motivated by this result, we study the $\Delta$ chain for various ratios $J_{\rm bb}/J_{\rm bv}$ of the base-base and base-vertex interactions. By exact diagonalization and extrapolation, we show that the elementary excitation spectrum, which (within numerical error) is the same for total spins $S_{\rm tot}=0$ and 1, has a gap only in the interval $0.4874(1) \leq J_{\rm bb}/J_{\rm bv} \leq 1.53(1)$. The gap is dispersionless for $J_{\rm bb}/J_{\rm bv}=1$, but has increasing $k$-dependence as $J_{\rm bb}/J_{\rm bv}$ moves away from unity, related to the instability of dimers in the ground state.Comment: 4 pages, 6 figures (revtex twocolumn

Limits of feedback control in bacterial chemotaxis

Inputs to signaling pathways can have complex statistics that depend on the environment and on the behavioral response to previous stimuli. Such behavioral feedback is particularly important in navigation. Successful navigation relies on proper coupling between sensors, which gather information during motion, and actuators, which control behavior. Because reorientation conditions future inputs, behavioral feedback can place sensors and actuators in an operational regime different from the resting state. How then can organisms maintain proper information transfer through the pathway while navigating diverse environments? In bacterial chemotaxis, robust performance is often attributed to the zero integral feedback control of the sensor, which guarantees that activity returns to resting state when the input remains constant. While this property provides sensitivity over a wide range of signal intensities, it remains unclear how other parameters affect chemotactic performance, especially when considering that the swimming behavior of the cell determines the input signal. Using analytical models and simulations that incorporate recent experimental evidences about behavioral feedback and flagellar motor adaptation we identify an operational regime of the pathway that maximizes drift velocity for various environments and sensor adaptation rates. This optimal regime is outside the dynamic range of the motor response, but maximizes the contrast between run duration up and down gradients. In steep gradients, the feedback from chemotactic drift can push the system through a bifurcation. This creates a non-chemotactic state that traps cells unless the motor is allowed to adapt. Although motor adaptation helps, we find that as the strength of the feedback increases individual phenotypes cannot maintain the optimal operational regime in all environments, suggesting that diversity could be beneficial.Comment: Corrected one typo. First two authors contributed equally. Notably, there were various typos in the values of the parameters in the model of motor adaptation. The results remain unchange

Solution to the Isotropy Problem for Cosmological Hidden Vector Models

Gauge bosons associated to new gauge symmetries under which the standard model particles are not charged are predicted in many extensions of the standard model of particles and interactions. We show that under very general conditions, the average energy-momentum tensor of these rapidly oscillating vector fields is isotropic for any locally inertial observer. This result has a fundamental importance in order to consider coherent vector fields as a viable alternative to support models of dark matter, dark energy or inflation.Comment: 4 pages, 1 figure. Contributed to the 9th Patras Workshop on Axions, WIMPs and WISPs, Mainz, June 24-28, 201

Spherical harmonic decomposition applied to spatial-temporal analysis of human high-density EEG

We demonstrate an application of spherical harmonic decomposition to analysis of the human electroencephalogram (EEG). We implement two methods and discuss issues specific to analysis of hemispherical, irregularly sampled data. Performance of the methods and spatial sampling requirements are quantified using simulated data. The analysis is applied to experimental EEG data, confirming earlier reports of an approximate frequency-wavenumber relationship in some bands.Comment: 12 pages, 8 figures, submitted to Phys. Rev. E, uses APS RevTeX style

Interference Suppression in Multiple Access Communications Using M-Ary Phase Shift Keying Generated via Spectral Encoding

A conceptual transform domain communication system (TDCS) is shown capable of operating successfully using M-Ary phase shift keying (MPSK) data modulation in a multiple access environment. Using spectral encoding, the conceptual TDCS provides an effective means for mitigating interference affects while achieving multiple access communications. The use of transform domain processing with MPSK data modulation (TD-MPSK) provides higher spectral efficiency relative to other modulation techniques (antipodal signaling and cyclic shift keying) considered previously for TDCS applications. The proposed TD-MPSK technique uses spectral encoding for both data and multiple access phase modulations. Demodulation of the spectrally encoded TD-MPSK communication symbols is accomplished using conventional, multi-channel time domain correlation techniques. Analytic expressions for TD-MPSK probability of symbol error (PE) and probability of bit error (PB) are derived and validated using simulated results over the range of signal-to-noise ratios typically considered for communications. This validation includes scenarios with: 1) multiple access interference, 2) spectral notching, 3) jamming present and 4) combinations of all three. For a J/S of 3.14 dB and a Eb/N0 of 6 dB, PB dropped by up to a factor of 3 for TD-QPSK in a MA environment for the case when spectral notching was present versus the case when spectral notching wasn\u27t present. The cross-correlation between communication symbols of different synchronous users can be made identically zero through proper selection of multiple access phase codes (orthogonal signaling). For a synchronous network containing orthogonal users, PE and PB are unaffected as the number of orthogonal network users increases. For a J/S of 3.14 dB and a Eb/N0 of 6 dB, PB dropped by a factor of 12 for TD-QPSK in a MA environment for the case when spectral notching was present versus the case when spectral notching wasn\u27t present

A Physical Model of Human Skin and Its Application for Search and Rescue

For this research we created a human skin reflectance model in the VIS and NIR. We then modeled sensor output for an RGB sensor based on output from the skin reflectance model. The model was also used to create a skin detection algorithm and a skin pigmentation level (skin reflectance at 685nm) estimation algorithm. The average root mean square error across the VIS and NIR between the skin reflectance model and measured data was 2%. The skin reflectance model then allowed us to generate qualitatively accurate responses for an RGB sensor for different biological and lighting conditions. To test the accuracy of the skin detection and skin color estimation algorithms, hyperspectral images of a suburban test scene containing people with various skin colors were collected. The skin detection algorithm had a probability of detection as high as 95% with a probability of false alarm of 0.6%. The skin pigmentation level estimation algorithm had a mean absolute error when compared with data measured by a reflectometer of 2.6% where the reflectance of the individuals at 685nm ranged from 14% to 64%