ASU Scholarship Showcase

The relation between flux and fluctuation is fundamental to complex physical systems that support and transport flows. A recently obtained law predicts monotonous enhancement of fluctuation as the average flux is increased, which in principle is valid but only for large systems. For realistic complex systems of small sizes, this law breaks down when both the average flux and fluctuation become large. Here we demonstrate the failure of this law in small systems using real data and model complex networked systems, derive analytically a modified flux-fluctuation law, and validate it through computations of a large number of complex networked systems. Our law is more general in that its predictions agree with numerics and it reduces naturally to the previous law in the limit of large system size, leading to new insights into the flow dynamics in small-size complex systems with significant implications for the statistical and scaling behaviors of small systems, a topic of great recent interest.

An outstanding and fundamental problem in contemporary physics is to include and probe the many-body effect in the study of relativistic quantum manifestations of classical chaos. We address this problem using graphene systems described by the Hubbard Hamiltonian in the setting of resonant tunneling. Such a system consists of two symmetric potential wells separated by a potential barrier, and the geometric shape of the whole domain can be chosen to generate integrable or chaotic dynamics in the classical limit. Employing a standard mean-field approach to calculating a large number of eigenenergies and eigenstates, we uncover a class of localized states with near-zero tunneling in the integrable systems. These states are not the edge states typically seen in graphene systems, and as such they are the consequence of many-body interactions. The physical origin of the non-edge-state type of localized states can be understood by the one-dimensional relativistic quantum tunneling dynamics through the solutions of the Dirac equation with appropriate boundary conditions. We demonstrate that, when the geometry of the system is modified to one with chaos, the localized states are effectively removed, implying that in realistic situations where many-body interactions are present, classical chaos is capable of facilitating greatly quantum tunneling. This result, besides its fundamental importance, can be useful for the development of nanoscale devices such as graphene-based resonant-tunneling diodes.

Dynamical systems based on the minority game (MG) have been a paradigm for gaining significant insights into a variety of social and biological behaviors. Recently, a grouping phenomenon has been unveiled in MG systems of multiple resources (strategies) in which the strategies spontaneously break into an even number of groups, each exhibiting an identical oscillation pattern in the attendance of game players. Here we report our finding of spontaneous breakup of resources into three groups, each exhibiting period-three oscillations. An analysis is developed to understand the emergence of the striking phenomenon of triple grouping and period-three oscillations. In the presence of random disturbances, the triple-group/period-three state becomes transient, and we obtain explicit formula for the average transient lifetime using two methods of approximation. Our finding indicates that, period-three oscillation, regarded as one of the most fundamental behaviors in smooth nonlinear dynamical systems, can also occur in much more complex, evolutionary-game dynamical systems. Our result also provides a plausible insight for the occurrence of triple grouping observed, for example, in the U.S. housing market.

Understanding the dynamics of human movements is key to issues of significant current interest such as behavioral prediction, recommendation, and control of epidemic spreading. We collect and analyze big data sets of human movements in both cyberspace (through browsing of websites) and physical space (through mobile towers) and find a superlinear scaling relation between the mean frequency of visit〈f〉and its fluctuation σ : σ ∼〈f⟩^β with β ≈ 1.2. The probability distribution of the visiting frequency is found to be a stretched exponential function. We develop a model incorporating two essential ingredients, preferential return and exploration, and show that these are necessary for generating the scaling relation extracted from real data. A striking finding is that human movements in cyberspace and physical space are strongly correlated, indicating a distinctive behavioral identifying characteristic and implying that the behaviors in one space can be used to predict those in the other.

The phenomenon of Fano resonance is ubiquitous in a large variety of wave scattering systems, where the resonance profile is typically asymmetric. Whether the parameter characterizing the asymmetry should be complex or real is an issue of great experimental interest. Using coherent quantum transport as a paradigm and taking into account of the collective contribution from all available scattering channels, we derive a universal formula for the Fano-resonance profile. We show that our formula bridges naturally the traditional Fano formulas with complex and real asymmetry parameters, indicating that the two types of formulas are fundamentally equivalent (except for an offset). The connection also reveals a clear footprint for the conductance resonance during a dephasing process. Therefore, the emergence of complex asymmetric parameter when fitting with experimental data needs to be properly interpreted. Furthermore, we have provided a theory for the width of the resonance, which relates explicitly the width to the degree of localization of the close-by eigenstates and the corresponding coupling matrices or the self-energies caused by the leads. Our work not only resolves the issue about the nature of the asymmetry parameter, but also provides deeper physical insights into the origin of Fano resonance. Since the only assumption in our treatment is that the transport can be described by the Green’s function formalism, our results are also valid for broad disciplines including scattering problems of electromagnetic waves, acoustics, and seismology.

Persistent currents (PCs), one of the most intriguing manifestations of the Aharonov-Bohm (AB) effect, are known to vanish for Schrödinger particles in the presence of random scatterings, e.g., due to classical chaos. But would this still be the case for Dirac fermions? Addressing this question is of significant value due to the tremendous recent interest in two-dimensional Dirac materials. We investigate relativistic quantum AB rings threaded by a magnetic flux and find that PCs are extremely robust. Even for highly asymmetric rings that host fully developed classical chaos, the amplitudes of PCs are of the same order of magnitude as those for integrable rings, henceforth the term superpersistent currents (SPCs). A striking finding is that the SPCs can be attributed to a robust type of relativistic quantum states, i.e., Dirac whispering gallery modes (WGMs) that carry large angular momenta and travel along the boundaries. We propose an experimental scheme using topological insulators to observe and characterize Dirac WGMs and SPCs, and speculate that these features can potentially be the base for a new class of relativistic qubit systems. Our discovery of WGMs in relativistic quantum systems is remarkable because, although WGMs are common in photonic systems, they are relatively rare in electronic systems.

Background: Immunosignaturing is a new peptide microarray based technology for profiling of humoral immune responses. Despite new challenges, immunosignaturing gives us the opportunity to explore new and fundamentally different research questions. In addition to classifying samples based on disease status, the complex patterns and latent factors underlying immunosignatures, which we attempt to model, may have a diverse range of applications.

Methods: We investigate the utility of a number of statistical methods to determine model performance and address challenges inherent in analyzing immunosignatures. Some of these methods include exploratory and confirmatory factor analyses, classical significance testing, structural equation and mixture modeling.

Results: We demonstrate an ability to classify samples based on disease status and show that immunosignaturing is a very promising technology for screening and presymptomatic screening of disease. In addition, we are able to model complex patterns and latent factors underlying immunosignatures. These latent factors may serve as biomarkers for disease and may play a key role in a bioinformatic method for antibody discovery.

Conclusion: Based on this research, we lay out an analytic framework illustrating how immunosignatures may be useful as a general method for screening and presymptomatic screening of disease as well as antibody discovery.

Background: Microarray image analysis processes scanned digital images of hybridized arrays to produce the input spot-level data for downstream analysis, so it can have a potentially large impact on those and subsequent analysis. Signal saturation is an optical effect that occurs when some pixel values for highly expressed genes or peptides exceed the upper detection threshold of the scanner software (2¹⁶ - 1 = 65, 535 for 16-bit images). In practice, spots with a sizable number of saturated pixels are often flagged and discarded. Alternatively, the saturated values are used without adjustments for estimating spot intensities. The resulting expression data tend to be biased downwards and can distort high-level analysis that relies on these data. Hence, it is crucial to effectively correct for signal saturation.

Results: We developed a flexible mixture model-based segmentation and spot intensity estimation procedure that accounts for saturated pixels by incorporating a censored component in the mixture model. As demonstrated with biological data and simulation, our method extends the dynamic range of expression data beyond the saturation threshold and is effective in correcting saturation-induced bias when the lost information is not tremendous. We further illustrate the impact of image processing on downstream classification, showing that the proposed method can increase diagnostic accuracy using data from a lymphoma cancer diagnosis study.

Conclusions: The presented method adjusts for signal saturation at the segmentation stage that identifies a pixel as part of the foreground, background or other. The cluster membership of a pixel can be altered versus treating saturated values as truly observed. Thus, the resulting spot intensity estimates may be more accurate than those obtained from existing methods that correct for saturation based on already segmented data. As a model-based segmentation method, our procedure is able to identify inner holes, fuzzy edges and blank spots that are common in microarray images. The approach is independent of microarray platform and applicable to both single- and dual-channel microarrays.

Background: High-throughput technologies such as DNA, RNA, protein, antibody and peptide microarrays are often used to examine differences across drug treatments, diseases, transgenic animals, and others. Typically one trains a classification system by gathering large amounts of probe-level data, selecting informative features, and classifies test samples using a small number of features. As new microarrays are invented, classification systems that worked well for other array types may not be ideal. Expression microarrays, arguably one of the most prevalent array types, have been used for years to help develop classification algorithms. Many biological assumptions are built into classifiers that were designed for these types of data. One of the more problematic is the assumption of independence, both at the probe level and again at the biological level. Probes for RNA transcripts are designed to bind single transcripts. At the biological level, many genes have dependencies across transcriptional pathways where co-regulation of transcriptional units may make many genes appear as being completely dependent. Thus, algorithms that perform well for gene expression data may not be suitable when other technologies with different binding characteristics exist. The immunosignaturing microarray is based on complex mixtures of antibodies binding to arrays of random sequence peptides. It relies on many-to-many binding of antibodies to the random sequence peptides. Each peptide can bind multiple antibodies and each antibody can bind multiple peptides. This technology has been shown to be highly reproducible and appears promising for diagnosing a variety of disease states. However, it is not clear what is the optimal classification algorithm for analyzing this new type of data.

Results: We characterized several classification algorithms to analyze immunosignaturing data. We selected several datasets that range from easy to difficult to classify, from simple monoclonal binding to complex binding patterns in asthma patients. We then classified the biological samples using 17 different classification algorithms. Using a wide variety of assessment criteria, we found ‘Naïve Bayes’ far more useful than other widely used methods due to its simplicity, robustness, speed and accuracy.

Conclusions: ‘Naïve Bayes’ algorithm appears to accommodate the complex patterns hidden within multilayered immunosignaturing microarray data due to its fundamental mathematical properties.

Introduction: The ketogenic diet (KD) is a high-fat, low-carbohydrate diet that alters metabolism by increasing the level of ketone bodies in the blood. KetoCal® (KC) is a nutritionally complete, commercially available 4∶1 (fat∶ carbohydrate+protein) ketogenic formula that is an effective non-pharmacologic treatment for the management of refractory pediatric epilepsy. Diet-induced ketosis causes changes to brain homeostasis that have potential for the treatment of other neurological diseases such as malignant gliomas.

Methods: We used an intracranial bioluminescent mouse model of malignant glioma. Following implantation animals were maintained on standard diet (SD) or KC. The mice received 2×4 Gy of whole brain radiation and tumor growth was followed by in vivo imaging.

Results: Animals fed KC had elevated levels of β-hydroxybutyrate (p = 0.0173) and an increased median survival of approximately 5 days relative to animals maintained on SD. KC plus radiation treatment were more than additive, and in 9 of 11 irradiated animals maintained on KC the bioluminescent signal from the tumor cells diminished below the level of detection (p<0.0001). Animals were switched to SD 101 days after implantation and no signs of tumor recurrence were seen for over 200 days.

Conclusions: KC significantly enhances the anti-tumor effect of radiation. This suggests that cellular metabolic alterations induced through KC may be useful as an adjuvant to the current standard of care for the treatment of human malignant gliomas.