Randomized Solutions to Convex Programs with Multiple Chance Constraints

The scenario-based optimization approach (`scenario approach') provides an intuitive way of approximating the solution to chance-constrained optimization programs, based on finding the optimal solution under a finite number of sampled outcomes of the uncertainty (`scenarios'). A key merit of this approach is that it neither assumes knowledge of the uncertainty set, as it is common in robust optimization, nor of its probability distribution, as it is usually required in stochastic optimization. Moreover, the scenario approach is computationally efficient as its solution is based on a deterministic optimization program that is canonically convex, even when the original chance-constrained problem is not. Recently, researchers have obtained theoretical foundations for the scenario approach, providing a direct link between the number of scenarios and bounds on the constraint violation probability. These bounds are tight in the general case of an uncertain optimization problem with a single chance constraint. However, this paper shows that these bounds can be improved in situations where the constraints have a limited `support rank', a new concept that is introduced for the first time. This property is typically found in a large number of practical applications---most importantly, if the problem originally contains multiple chance constraints (e.g. multi-stage uncertain decision problems), or if a chance constraint belongs to a special class of constraints (e.g. linear or quadratic constraints). In these cases the quality of the scenario solution is improved while the same bound on the constraint violation probability is maintained, and also the computational complexity is reduced.Comment: This manuscript is the preprint of a paper submitted to the SIAM Journal on Optimization and it is subject to SIAM copyright. SIAM maintains the sole rights of distribution or publication of the work in all forms and media. If accepted, the copy of record will be available at http://www.siam.or

Rotational and Translational Velocity and Acceleration Thresholds for the Onset of Cybersickness in Virtual Reality

This paper determined rotational and translational velocity and acceleration thresholds for the onset of cybersickness. Cybersickness causes discomfort and discourages the widespread use of virtual reality systems for both recreational and professional use. Visual motion or optic flow is known to be one of the main causes of cybersickness due to the sensory conflict it creates with the vestibular system. The aim of this experiment is to detect rotational and translational velocity and acceleration thresholds that cause the onset of cybersickness. Participants were exposed to a moving particle field in virtual reality for a few seconds per run. The field moved in different directions (longitudinal, lateral, roll, and yaw), with different velocity profiles (steady and accelerating), and different densities. Using a staircase procedure, that controlled the speed or acceleration of the field, we detected the threshold at which participant started to feel temporary symptoms of cybersickness. The optic flow was quantified for each motion type and by modifying the number of features, the same amount of optic flow was present in each scene. Having the same optic flow in each scene allows a direct comparison of the thresholds. The results show that the velocity and acceleration thresholds for rotational optic flow were significantly lower than for translational optic flow. The thresholds suggestively decreased with the decreasing particle density of the scene. Finally, it was found that all the rotational and translational thresholds strongly correlate with each other. While the mean values of the thresholds could be used as guidelines to develop virtual reality applications, the high variability between individuals implies that the individual tuning of motion controls would be more effective to reduce cybersickness while minimizing the impact on the experience of immersion

Comparing Virtual Reality to Conventional Simulator Visuals: Effects of Peripheral Visual Cues in Roll-Axis Tracking Tasks

This paper compares the effects of peripheral visual cues on manual control between a conventional fixed-base simulator and virtual reality. The results were also compared with those from a previous experiment conducted in a motion-base simulator. Fifteen participants controlled a system with second-order dynamics in a disturbance-rejection task. Tracking performance, control activity, simulator sickness questionnaire answers, and biometrics were collected. Manual control behavior was modeled for the first time in a virtual reality environment. Virtual reality did not degrade participants manual control performance or alter their control behavior. However, peripheral cues were significantly more effective in virtual reality. Control activity decreased for all conditions with peripheral cues. The trends introduced by the peripheral visual cues from the previous experiment were replicated. Finally, VR was not more nauseogenic than the conventional simulator. These results suggest that virtual reality might be a good alternative to conventional fixed-base simulators for training manual control skills

Quantum-state transfer via resonant tunnelling through local field induced barriers

Efficient quantum-state transfer is achieved in a uniformly coupled spin-1/2 chain, with open boundaries, by application of local magnetic fields on the second and last-but-one spins, respectively. These effective \textit{barriers} induce appearance of two eigenstates, bi-localized at the edges of the chain, which allow a high quality transfer also at relatively long distances. The same mechanism may be used to send an entire e-bit (e.g., an entangled qubit pair) from one to the other end of the chain

Trace-metaldynamics in response of increase CO₂ and iron availability in a coastal mesocosm experiment

A mesocosm experiment was performed in the Raunefjord (Norway) to study changes in dissolved Cu (dCu) and Fe (dFe), and in the elemental composition of particles during an Emiliania huxleyi dominated bloom. The CO2 treatments consisted of present (LC; 390 ppmV) and predicted levels (HC; 900 ppmV) and iron conditions were created with the addition of the siderophore desferoxamine B (DFB). Our results showed the DFB addition enhanced the solubility of Fe in this fjord environment. Initially, dFe was comparable among treatments but after the addition, the HC and/or +DFB treatments presented higher levels and finally, the only ones maintaining high dFe were the +DFB treatments. Unlike dCu presented indistinguishable levels in all mesocosms over time. Particulate metals were normalised to P and Al to evaluate the relative influence of biotic and abiotic sources. The Fe:P ratios decreased with time and compared to published phytoplankton ratios suggest Fe storage. On the other hand, Fe:Al ratios were relatively closer to the crustal ratios suggesting that the abiotic source was more important for this metal. Trends for other metals will be discussed.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Spectral properties of a two-orbital Anderson impurity model across a non-Fermi liquid fixed point

We study by NRG the spectral properties of a two-orbital Anderson impurity model in the presence of an exchange splitting which follows either regular or inverted Hund's rules. The phase diagram contains a non-Fermi liquid fixed point separating a screened phase, where conventional Kondo effect occurs, from an unscreened one, where the exchange-splitting takes care of quenching the impurity degrees of freedom. On the Kondo screened side close to this fixed point the impurity density of states shows a narrow Kondo-peak on top of a broader resonance. This narrow peak transforms in the unscreened phase into a narrow pseudo-gap inside the broad resonance. Right at the fixed point only the latter survives. The fixed point is therefore identified by a jump of the density of states at the chemical potential. We also show that particle-hole perturbations which simply shift the orbital energies do not wash out the fixed point, unlike those perturbations which hybridize the two orbitals. Consequently the density-of-state jump at the chemical potential remains finite even away from particle-hole symmetry, and the pseudo-gap stays pinned at the chemical potential, although it is partially filled in. We also discuss the relevance of these results for lattice models which map onto this Anderson impurity model in the limit of large lattice-coordination. Upon approaching the Mott metal-insulator transition, these lattice models necessarily enter a region with a local criticality which reflects the impurity non-Fermi liquid fixed point. However, unlike the impurity, the lattice can get rid of the single-impurity fixed-point instability by spontaneously developing bulk-coherent symmetry-broken phases, which we identify for different lattice models.Comment: 43 pages, 11 figures. Minor corrections in the Appendi

Post-Pandemic Urbanism: Criteria for a New Normal

Globalization, tourism, virtuality, climate change, and the explosive growth of cities have generated a wide range of stressors, pollutants, and toxins that have been ravaging populations. This, coupled with viral, bacterial, and other pandemics, is rapidly creating a new reality that requires public health factors to be integrated more thoroughly into the planning and design of city regions. This prompts a questioning of the role and form of city centers as well as the distribution of people and activities in city regions. This goes beyond more outdoor spaces, places, and activities and new criteria for indoor events. Moreover, public transport, mobility, and infrastructure in general need to be retooled to deal with these emergent circumstances