Perfect Sets and ff-Ideals

A square-free monomial ideal $I$ is called an {\it $f$-ideal}, if both $\delta_{\mathcal{F}}(I)$ and $\delta_{\mathcal{N}}(I)$ have the same $f$-vector, where $\delta_{\mathcal{F}}(I)$ ($\delta_{\mathcal{N}}(I)$, respectively) is the facet (Stanley-Reisner, respectively) complex related to $I$. In this paper, we introduce and study perfect subsets of $2^{[n]}$ and use them to characterize the $f$-ideals of degree $d$. We give a decomposition of $V(n, 2)$ by taking advantage of a correspondence between graphs and sets of square-free monomials of degree $2$, and then give a formula for counting the number of $f$-ideals of degree $2$, where $V(n, 2)$ is the set of $f$-ideals of degree 2 in $K[x_1,\ldots,x_n]$. We also consider the relation between an $f$-ideal and an unmixed monomial ideal.Comment: 15 page

Traffic Control Strategy Formulation and Optimization Enabled by Homogenous Connected and Autonomous Vehicle Systems.

Ph.D. Thesis. University of Hawaiʻi at Mānoa 2017

Morphometric reorganization induced by working memory training: perspective from vertex and network levels

Der sich beschleunigende globale Alterungsprozess und die Tatsache, dass sich die kog-nitiven Fähigkeiten mit dem Alter verschlechtern, was sich erheblich auf die Lebensquali-tät älterer Erwachsener auswirkt, insbesondere bei altersbedingten Störungen (z. B. kogni-tiver Beeinträchtigung, Demenz), weisen auf einen dringenden Bedarf an Ansätzen zum Schutz und zur Verbesserung der kognitiven Fähigkeiten sowie an Untersuchungen der neuronalen Substrate altersbedingter Veränderungen und der Neuroplastizität hin. Da man davon ausgeht, dass das Arbeitsgedächtnis (WM) die grundlegende Ursache für altersbe-dingte kognitive Beeinträchtigungen bei einer Vielzahl von kognitiven Fähigkeiten dar-stellt, ist das Arbeitsgedächtnistraining (WMT) zu einem aktuellen Thema und einem be-liebten Ansatz geworden. Frühere Studien haben gezeigt, dass das Arbeitsgedächtnistrai-ning (WMT) die kognitive Leistung verbessert. Die spezifischen Auswirkungen sowie die zugrunde liegenden neurobiologischen Mechanismen sind jedoch nach wie vor um-stritten. Ziel dieser Arbeit ist es, die durch das WMT induzierte neuronale strukturelle Plastizität auf mehreren Ebenen sowie die Verhaltenseffekte des WMT zu untersuchen. In der ers-ten Studie untersuchten wir die topographischen Veränderungen der Morphologie der grauen Substanz durch WMT, indem wir vier strukturelle Metriken (d.h. die kortikale Dicke, das kortikale Volumen, die kortikale Oberfläche und den lokalen Gyrifikationsin-dex, LGI) sowie die subkortikalen Volumina explorierten. Konkret wurden 59 gesunde Probanden mittleren Alters nach dem Zufallsprinzip entweder einem adaptiven WMT oder einer nicht-adaptiven Intervention zugewiesen. Alle Teilnehmer unterzogen sich vor und nach der 8-wöchigen WMT-Phase einer Neurobildgebung sowie kognitiven Tests. Vor und nach dem WMT wurden vier kortikale Metriken auf Scheitelpunktniveau und sieben subkortikale Volumina sowie die globale mittlere kortikale Dicke berechnet. Das wich-tigste Ergebnis war, dass die WMT-Gruppe im Vergleich zur aktiven Kontrollgruppe eine größere Zunahme der kortikalen Faltung in den bilateralen parietalen Regionen zeigte. Die Ergebnisse deuten darauf hin, dass strukturelle Veränderungen durch WMT in WM-bezogenen Regionen, insbesondere in parietalen Regionen, die Verarbeitung einer höhe-ren WM-Belastung erleichtern können. Darüber hinaus könnte die kortikale Faltung das relevanteste und plastischste Merkmal von WM und Lernen sein und WMT-Effekte stär-ker widerspiegeln als andere Metriken. Basierend auf den Ergebnissen der ersten Studie haben wir darüber hinaus untersucht, ob die trainingsinduzierten Effekte des WMT in der kortikalen Faltung auf Vertex-Ebene von topologischen Veränderungen begleitet werden. Zu diesem Zweck untersuchten wir in Studie zwei die durch WMT verursachte Plastizität auf Netzwerkebene mit Hilfe eines strukturellen Kovarianzansatzes (SC), der auf denselben Stichproben basiert. Es wurden gyrifikationsbasierte SC-Matrizen für jede Gruppe vor und nach dem Training sowie lon-gitudinale gyrifikationsbasierte SC-Matrizen erstellt. Innerhalb jeder Gruppe ergab die LGI-basierte SC-Analyse keine Hinweise auf WMT-induzierte Veränderungen der kor-tiko-kortikalen Verbindungen, weder in der WMT- noch in der aktiven Kontrollgruppe. Die Ergebnisse der longitudinalen SC-Analyse (unkorrigiert p < 0,005) zeigten, dass die trainingsinduzierten Veränderungen der kortikalen Faltungsintensität signifikante Unter-schiede zwischen Paaren von parietalen Regionen sowie Paaren von frontalen Regionen aufwiesen. Insgesamt deuten die kombinierten Ergebnisse dieser beiden Studien darauf hin, dass ers-tens WMT neuronale strukturelle Plastizität hervorrufen kann; zweitens die kortikale Fal-tung das relevanteste und plastischste Merkmal von WM und Lernen sein könnte, das die Auswirkungen von WMT besser widerspiegelt als andere Indikatoren auf Vertex-Ebene; und drittens die trainingsinduzierten lokalisierten Veränderungen der kortikalen Faltung von einem ähnlichen Muster vergleichbarer struktureller Veränderungen zwischen ROIs innerhalb der Regionen begleitet wurden. In Zukunft sind weitere Forschungen erforder-lich, um diese Ergebnisse zu wiederholen und zu validieren sowie um trainingsinduzierte topologische und topografische Veränderungen anhand einer breiteren Palette von Metri-ken und Eigenschaften zu untersuchen.The accelerating global aging process and the fact that cognitive abilities deteriorate with age, which has a significant impact on the quality of life of older adults, particularly those with age-related disorders (e.g., cognitive impairment, dementia), all point to an urgent need for approaches to protect and enhance cognitive abilities, as well as studies of the neural substrates of aging-related changes and neuroplasticity. Since working memory (WM) has been assumed to be the fundamental source of age-related cognitive impair-ments in a variety of cognitive abilities, working memory training (WMT) has become a hot topic as well as a popular approach. Previous studies have established that working memory training (WMT) improves cognitive performance. However, the specific effects, as well as the underlying neurobiological mechanisms, remain a matter of controversy. The purpose of this thesis is to investigate WMT-induced neural structural plasticity at multiple levels together with the behavioral effects of WMT. In study one, we investigated the topographic changes of grey matter morphology due to WMT by combining four structural metrics (i.e., cortical thickness (CT), cortical volume (CV), cortical surface area (CSA), and local gyrification index (LGI)) as well as subcortical volumes. Specifically, 59 healthy volunteers between the ages of 50 and 65 were randomly assigned to either an adaptive or a non-adaptive intervention. All participants underwent neuroimaging as well as cognitive testing before and after the 8-week intervention. Four cortical metrics at ver-tex level and seven subcortical volumes, as well as global mean cortical thickness, were calculated before and after the intervention. The most important finding was that the adap-tive WMT group showed greater increases in cortical folding in bilateral parietal regions in comparison to the active control group who performed the non-adaptive intervention. The results indicate that structural changes due to adaptive WMT in WM related regions, particularly parietal regions, may facilitate the processing of a higher WM load. In addi-tion, the cortical folding might be the most relevant and plastic feature of WM and learn-ing, reflecting WMT effects more than other metrics. Based on the findings of study one, we further asked whether the training-induced effects of WMT in cortical folding at vertex-level are accompanied by topological changes. To this end, study two investigated network-level plasticity due to WMT by using the struc-tural covariance (SC) approach based on the same samples. Gyrification based SC matri-ces for each group before and after training, together with longitudinal gyrification SC matrices, were constructed. Within each group, the LGI-based SC analysis revealed no evidence of WMT-induced changes in cortical-cortical connections, either in the WMT or the active control groups. The results of the longitudinal SC analysis (uncorrected p < 0.005) revealed that the training induced changes of cortical folding intensity showed sig-nificant difference between pairs of parietal regions as well as pairs of frontal regions. Overall, the combined findings of these two studies indicate that: firstly, WMT can pro-duce neural structural plasticity; secondly, cortical folding might be the most relevant and plastic feature of WM and learning, better reflecting the effects of WMT than other vertex-level indicators; and thirdly, the training induced localized changes in cortical folding were accompanied by the pattern of similar structural changes between ROIs within the regions. In the future, more research is required to replicate and validate these findings, as well as to investigate training-induced topological and topographic changes using a broader set of metrics and properties

Integrative high-throughput study of arsenic hyper-accumulation in Pteris vittata

Arsenic is a natural contaminant in the soil and ground water, which raises considerable concerns in food safety and human health worldwide. The fernPteris vittata (Chinese brake fern) is the first identified arsenic hyperaccumulator[1]. It and its close relatives have un-paralleled ability to tolerant arsenic and feature unique arsenic metabolisms. The focus of the research presented in this thesis is to elucidate the fundamentals of arsenic tolerance and hyper-accumulation in Pteris vittata through high throughput technology and bioinformatics tools. The transcriptome of the P. vittatagametophyte under arsenate stress was obtained using RNA-Seq technology and Trinity de novo assembly. Functional annotation of the transcriptome was performed in terms of blast search, Gene Ontology term assignment, Eukaryotic Orthologous Groups (KOG) classification, and pathway analysis. Differentially expressed genes induced by arsenic stress were identified, which revealed several key players in arsenic hyper-accumulation. As part of the efforts to annotate differentially expressed genes, literature of plant arsenic tolerance was collected and built into a searchable database using the Textpresso text-mining tool, which greatly facilitates the retrieval of biological facts involving arsenic related gene. In addition, an SVM-based named-entity recognition system was constructed to identify new references to genes in literature. The results provide excellent sequence resources for arsenic tolerance study in P.vittata, and establish a platform for integrative study using data of multiple types

L2L_2-Box Optimization for Green Cloud-RAN via Network Adaptation

In this paper, we propose a reformulation for the Mixed Integer Programming (MIP) problem into an exact and continuous model through using the $\ell_2$-box technique to recast the binary constraints into a box with an $\ell_2$ sphere constraint. The reformulated problem can be tackled by a dual ascent algorithm combined with a Majorization-Minimization (MM) method for the subproblems to solve the network power consumption problem of the Cloud Radio Access Network (Cloud-RAN), and which leads to solving a sequence of Difference of Convex (DC) subproblems handled by an inexact MM algorithm. After obtaining the final solution, we use it as the initial result of the bi-section Group Sparse Beamforming (GSBF) algorithm to promote the group-sparsity of beamformers, rather than using the weighted $\ell_1 / \ell_2$-norm. Simulation results indicate that the new method outperforms the bi-section GSBF algorithm by achieving smaller network power consumption, especially in sparser cases, i.e., Cloud-RANs with a lot of Remote Radio Heads (RRHs) but fewer users.Comment: 4 pages, 4 figure