ASU Scholarship Showcase

Scattering amplitudes in maximally supersymmetric gauge theory receive a dual description in terms of the expectation value of the super Wilson loop stretched on a null polygonal contour. This makes the analysis amenable to nonperturbative techniques. Presently, we elaborate on a refined form of the operator product expansion in terms of pentagon transitions to compute twist-two contributions to NMHV amplitudes. To start with, we provide a novel derivation of scattering matrices starting from Baxter equations for flux-tube excitations propagating on magnon background. We propose bootstrap equations obeyed by pentagon form factors with nonsinglet quantum numbers with respect to the R-symmetry group and provide solutions to them to all orders in 't Hooft coupling. These are then successfully confronted against available perturbative calculations for NMHV amplitudes to four-loop order.

We address the near-collinear expansion of multiparticle NMHV amplitudes, namely, the heptagon and octagons in the dual language of null polygonal super Wilson loops. In particular, we verify multiparticle factorization of charged pentagon transitions in terms of pentagons for single flux-tube excitations within the framework of refined operator product expansion. We find a perfect agreement with available tree and one-loop data.

A semi-nonparametric generalized multinomial logit model, formulated using orthonormal Legendre polynomials to extend the standard Gumbel distribution, is presented in this paper. The resulting semi-nonparametric function can represent a probability density function for a large family of multimodal distributions. The model has a closed-form log-likelihood function that facilitates model estimation. The proposed method is applied to model commute mode choice among four alternatives (auto, transit, bicycle and walk) using travel behavior data from Argau, Switzerland. Comparisons between the multinomial logit model and the proposed semi-nonparametric model show that violations of the standard Gumbel distribution assumption lead to considerable inconsistency in parameter estimates and model inferences.

A general consensus on the concept of rainfall intermittency has not yet been reached, and intermittency is often attributed to different aspects of rainfall variability, including the fragmentation of the rainfall support (i.e., the alternation of wet and dry intervals) and the strength of intensity fluctuations and bursts. To explore these different aspects, a systematic analysis of rainfall intermittency properties in the time domain is presented using high-resolution (1-min) data recorded by a network of 201 tipping-bucket gauges covering the entire island of Sardinia (Italy). Four techniques, including spectral and scale invariance analysis, and computation of clustering and intermittency exponents, are applied to quantify the contribution of the alternation of dry and wet intervals (i.e., the rainfall support fragmentation), and the fluctuations of intensity amplitudes, to the overall intermittency of the rainfall process. The presence of three ranges of scaling regimes between 1 min to ~ 45 days is first demonstrated. In accordance with past studies, these regimes can be associated with a range dominated by single storms, a regime typical of frontal systems, and a transition zone.

The positions of the breaking points separating these regimes change with the applied technique, suggesting that different tools explain different aspects of rainfall variability. Results indicate that the intermittency properties of rainfall support are fairly similar across the island, while metrics related to rainfall intensity fluctuations are characterized by significant spatial variability, implying that the local climate has a significant effect on the amplitude of rainfall fluctuations and minimal influence on the process of rainfall occurrence. In addition, for each analysis tool, evidence is shown of spatial patterns of the scaling exponents computed in the range of frontal systems. These patterns resemble the main pluviometric regimes observed on the island and, thus, can be associated with the corresponding synoptic circulation patterns. Last but not least, we demonstrate how the methodology adopted to sample the rainfall signal from the records of the tipping instants can significantly affect the intermittency analysis, especially at smaller scales. The multifractal scale invariance analysis is the only tool that is insensitive to the sampling approach. Results of this work may be useful to improve the calibration of stochastic algorithms used to downscale coarse rainfall predictions of climate and weather forecasting models, as well as the parameterization of intensity-duration-frequency curves, adopted for land planning and design of civil infrastructures.

Delays are a major cause for concern in the construction industry in Saudi Arabia. This paper identifies the main causes of delay in infrastructure projects in Mecca, Saudi Arabia, and compares these with projects around the country and other Gulf countries. Data was obtained from 49 infrastructure projects undertaken by the owner and were analyzed quantitatively to understand the severity and causes of delay. 10 risk factors were identified and were grouped into four categories. Average delay in infrastructure projects in Mecca was found to be 39%. The most severe cause of delay was found to be the land acquisition factor. This highlights the critical land ownership and acquisition issues that are prevailing in the city. Additionally, other factors that contribute to delay include contractors’ lack of expertise, re-designing, and haphazard underground utilities (line services). It is concluded that the majority of project delays were caused from the owner's side as compared to contractors, consultants, and other project's stakeholders. This finding matched with the research findings of the Gulf Countries Construction (GCC) Industry's literature. This study fills an important practice and research gap for improving the efficiency in delivering infrastructure projects in the holy city of Mecca and Gulf countries at large.

Scattering amplitudes in maximally supersymmetric gauge theory are dual to super-Wilson loops on null polygonal contours. The operator product expansion for the latter revealed that their dynamics is governed by the evolution of multiparticle GKP excitations. They were shown to emerge from the spectral problem of an underlying open spin chain. In this work we solve this model with the help of the Baxter Q-operator and Sklyanin's Separation of Variables methods. We provide an explicit construction for eigenfunctions and eigenvalues of GKP excitations. We demonstrate how the former define the so-called multiparticle hexagon transitions in super-Wilson loops and prove their factorized form at leading order of 't Hooft coupling for particle number-preserving transitions that were suggested earlier in a generic case.

We compute one-loop renormalization group equations for non-singlet twist-four operators in QCD. The calculation heavily relies on the light-cone gauge formalism in the momentum fraction space that essentially rephrases the analysis of all two-to-two and two-to-three transition kernels to purely algebraic manipulations both for non- and quasipartonic operators. This is the first brute force calculation of this sector available in the literature. Fourier transforming our findings to the coordinate space, we checked them against available results obtained within a conformal symmetry-based formalism that bypasses explicit diagrammatic calculations and confirmed agreement with the latter.

Urban transportation systems are vulnerable to congestion, accidents, weather, special events, and other costly delays. Whereas typical policy responses prioritize reduction of delays under normal conditions to improve the efficiency of urban road systems, analytic support for investments that improve resilience (defined as system recovery from additional disruptions) is still scarce. In this effort, we represent paved roads as a transportation network by mapping intersections to nodes and road segments between the intersections to links. We built road networks for 40 of the urban areas defined by the U.S. Census Bureau. We developed and calibrated a model to evaluate traffic delays using link loads. The loads may be regarded as traffic-based centrality measures, estimating the number of individuals using corresponding road segments. Efficiency was estimated as the average annual delay per peak-period auto commuter, and modeled results were found to be close to observed data, with the notable exception of New York City. Resilience was estimated as the change in efficiency resulting from roadway disruptions and was found to vary between cities, with increased delays due to a 5% random loss of road linkages ranging from 9.5% in Los Angeles to 56.0% in San Francisco. The results demonstrate that many urban road systems that operate inefficiently under normal conditions are nevertheless resilient to disruption, whereas some more efficient cities are more fragile. The implication is that resilience, not just efficiency, should be considered explicitly in roadway project selection and justify investment opportunities related to disaster and other disruptions.

The human hand comprises complex sensorimotor functions that can be impaired by neurological diseases and traumatic injuries. Effective rehabilitation can bring the impaired hand back to a functional state because of the plasticity of the central nervous system to relearn and remodel the lost synapses in the brain. Current rehabilitation therapies focus on strengthening motor skills, such as grasping, employ multiple objects of varying stiffness so that affected persons can experience a wide range of strength training. These devices have limited range of stiffness due to the rigid mechanisms employed in their variable stiffness actuators. This paper presents a novel soft robotic haptic device for neuromuscular rehabilitation of the hand, which is designed to offer adjustable stiffness and can be utilized in both clinical and home settings. The device eliminates the need for multiple objects by employing a pneumatic soft structure made with highly compliant materials that act as the actuator of the haptic interface. It is made with interchangeable sleeves that can be customized to include materials of varying stiffness to increase the upper limit of the stiffness range. The device is fabricated using existing 3D printing technologies, and polymer molding and casting techniques, thus keeping the cost low and throughput high. The haptic interface is linked to either an open-loop system that allows for an increased pressure during usage or closed-loop system that provides pressure regulation in accordance to the stiffness the user specifies. Preliminary evaluation is performed to characterize the effective controllable region of variance in stiffness. It was found that the region of controllable stiffness was between points 3 and 7, where the stiffness appeared to plateau with each increase in pressure. The two control systems are tested to derive relationships between internal pressure, grasping force exertion on the surface, and displacement using multiple probing points on the haptic device. Additional quantitative evaluation is performed with study participants and juxtaposed to a qualitative analysis to ensure adequate perception in compliance variance. The qualitative evaluation showed that greater than 60% of the trials resulted in the correct perception of stiffness in the haptic device.

As gesture interfaces become more main-stream, it is increasingly important to investigate the behavioral characteristics of these interactions – particularly in three-dimensional (3D) space. In this study, Fitts’ method was extended to such input technologies, and the applicability of Fitts’ law to gesture-based interactions was examined. The experiment included three gesture-based input devices that utilize different techniques to capture user movement, and compared them to conventional input technologies like touchscreen and mouse. Participants completed a target-acquisition test and were instructed to move a cursor from a home location to a spherical target as quickly and accurately as possible. Three distances and three target sizes were tested six times in a randomized order for all input devices. A total of 81 participants completed all tasks. Movement time, error rate, and throughput were calculated for each input technology. Results showed that the mean movement time was highly correlated with the target's index of difficulty for all devices, providing evidence that Fitts’ law can be extended and applied to gesture-based devices. Throughputs were found to be significantly lower for the gesture-based devices compared to mouse and touchscreen, and as the index of difficulty increased, the movement time increased significantly more for these gesture technologies. Error counts were statistically higher for all gesture-based input technologies compared to mouse. In addition, error counts for all inputs were highly correlated with target width, but little impact was shown by movement distance. Overall, the findings suggest that gesture-based devices can be characterized by Fitts’ law in a similar fashion to conventional 1D or 2D devices.