Graph-Theoretic Simplicial Complexes, Hajos-type Constructions, and k-Matchings

A graph property is monotone if it is closed under the removal of edges and vertices. Given a graph G and a monotone graph property P, one can associate to the pair (G,P) a simplicial complex, which serves as a way to encode graph properties within faces of a topological space. We study these graph-theoretic simplicial complexes using combinatorial and topological approaches as a way to inform our understanding of the graphs and their properties. In this dissertation, we study two families of simplicial complexes: (1) neighborhood complexes and (2) k-matching complexes. A neighborhood complex is a simplicial complex of a graph with vertex set the vertices of the graph and facets given by neighborhoods of each vertex of the graph. In 1978, Lov\\u27asz used neighborhood complexes as a tool for studying lower bounds for the chromatic number of graphs. In Chapter 2, we will prove results about the connectivity of neighborhood complexes in relation to Haj\\u27os-type constructions and analyze randomly generated graphs arising from two Haj\\u27os-type stochastic algorithms using SageMath. Chapter 3 will focus on k-matching complexes. A k-matching complex of a graph is a simplicial complex with vertex set given by edges of the graph and faces given sets of edges in the graph such that each vertex of the induced graph has degree at most k. We pursue the study of k-matching complexes and investigate 2-matching complexes of wheel graphs and caterpillar graphs

Hamiltonicity, Pancyclicity, and Cycle Extendability in Graphs

The study of cycles, particularly Hamiltonian cycles, is very important in many applications. Bondy posited his famous metaconjecture, that every condition sufficient for Hamiltonicity actually guarantees a graph is pancyclic. Pancyclicity is a stronger structural property than Hamiltonicity. An even stronger structural property is for a graph to be cycle extendable. Hendry conjectured that any graph which is Hamiltonian and chordal is cycle extendable. In this dissertation, cycle extendability is investigated and generalized. It is proved that chordal 2-connected K1,3-free graphs are cycle extendable. S-cycle extendability was defined by Beasley and Brown, where S is any set of positive integers. A conjecture is presented that Hamiltonian chordal graphs are {1, 2}-cycle extendable. Dirac’s Theorem is an classic result establishing a minimum degree condition for a graph to be Hamiltonian. Ore’s condition is another early result giving a sufficient condition for Hamiltonicity. In this dissertation, generalizations of Dirac’s and Ore’s Theorems are presented. The Chvatal-Erdos condition is a result showing that if the maximum size of an independent set in a graph G is less than or equal to the minimum number of vertices whose deletion increases the number of components of G, then G is Hamiltonian. It is proved here that the Chvatal-Erdos condition guarantees that a graph is cycle extendable. It is also shown that a graph having a Hamiltonian elimination ordering is cycle extendable. The existence of Hamiltonian cycles which avoid sets of edges of a certain size and certain subgraphs is a new topic recently investigated by Harlan, et al., which clearly has applications to scheduling and communication networks among other things. The theory is extended here to bipartite graphs. Specifically, the conditions for the existence of a Hamiltonian cycle that avoids edges, or some subgraph of a certain size, are determined for the bipartite case. Briefly, this dissertation contributes to the state of the art of Hamiltonian cycles, cycle extendability and edge and graph avoiding Hamiltonian cycles, which is an important area of graph theory

Prefrontal rhythms for cognitive control

Goal-directed behavior requires flexible selection among action plans and updating behavioral strategies when they fail to achieve desired goals. Lateral prefrontal cortex (LPFC) is implicated in the execution of behavior-guiding rule-based cognitive control while anterior cingulate cortex (ACC) is implicated in monitoring processes and updating rules. Rule-based cognitive control requires selective processing while process monitoring benefits from combinatorial processing. I used a combination of computational and experimental methods to investigate how network oscillations and neuronal heterogeneity contribute to cognitive control through their effects on selective versus combinatorial processing modes in LPFC and ACC. First, I adapted an existing LPFC model to explore input frequency- and coherence-based output selection mechanisms for flexible routing of rate-coded signals. I show that the oscillatory states of input encoding populations can exhibit a stronger influence over downstream competition than their activity levels. This enables an output driven by a weaker resonant input signal to suppress lower-frequency competing responses to stronger, less resonant (though possibly higher-frequency) input signals. While signals are encoded in population firing rates, output selection and signal routing can be governed independently by the frequency and coherence of oscillatory inputs and their correspondence with output resonant properties. Flexible response selection and gating can be achieved by oscillatory state control mechanisms operating on input encoding populations. These dynamic mechanisms enable experimentally-observed LPFC beta and gamma oscillations to flexibly govern the selection and gating of rate-coded signals for downstream read-out. Furthermore, I demonstrate how differential drives to distinct interneuron populations can switch working memory representations between asynchronous and oscillatory states that support rule-based selection. Next, I analyzed physiological data from the LeBeau laboratory and built a de novo model constrained by the biological data. Experimental data demonstrated that fast network oscillations at both the beta- and gamma frequency bands could be elicited in vitro in ACC and neurons exhibited a wide range of intrinsic properties. Computational modeling of the ACC network revealed that the frequency of network oscillation generated was dependent upon the time course of inhibition. Principal cell heterogeneity broadened the range of frequencies generated by the model network. In addition, with different frequency inputs to two neuronal assemblies, heterogeneity decreased competition and increased spike coherence between the networks thus conferring a combinatorial advantage to the network. These findings suggest that oscillating neuronal populations can support either response selection (routing), or combination, depending on the interplay between the kinetics of synaptic inhibition and the degree of heterogeneity of principal cell intrinsic conductances. Such differences may support functional differences between the roles of LPFC and ACC in cognitive control

Cooking with plants in ancient Europe and beyond

Plants have constituted the basis of human subsistence. This volume focuses on plant food ingredients that were consumed by the members of past societies and on the ways these ingredients were transformed into food. The thirty chapters of this book unfold the story of culinary transformation of cereals, pulses as well as of a wide range of wild and cultivated edible plants. Regional syntheses provide insights on plant species choices and changes over time and fragments of recipes locked inside amorphous charred masses. Grinding equipment, cooking installations and cooking pots are used to reveal the ancient cooking steps in order to pull together the pieces of a culinary puzzle of the past. From the big picture of spatiotemporal patterns and changes to the micro-imaging of usewear on grinding tool surfaces, the book attempts for the first time a comprehensive and systematic approach to ancient plant food culinary transformation. Focusing mainly on Europe and the Mediterranean world in prehistory, the book expands to other regions such as South Asia and Latin America and covers a time span from the Palaeolithic to the historic periods. Several of the contributions stem from original research conducted in the context of ERC project PlantCult: Investigating the Plant Food Cultures of Ancient Europe. The book’s exploration into ancient cuisines culminates with an investigation of the significance of ethnoarchaeology towards a better understanding of past foodways as well as of the impact of archaeology in shaping modern culinary and consumer trends. The book will be of interest to archaeologists, food historians, agronomists, botanists as well as the wider public with an interest in ancient cooking

Regulation of System Xc-by the Neuropeptide PACAP: Implications for Glutamate Transmission in Drug Addiction

Drug addiction is a chronic brain disorder characterized by heightened relapse susceptibility. Drug-induced aberrant glutamate signaling in corticostriatal circuitry contributes to behaviors in virtually every preclinical model of drug seeking and correlates with drug craving in human. Here, we propose that glutamate signaling is a product of integrated activity between neurons and astrocytes, such that disruptions within astrocytes can stem from abnormal neuronal signaling (e.g., altered corticostriatal firing) and be the source of additional disruptions in other neuronal circuits. The astrocytic mechanism studied in these experiments is system xc- (Sxc) since drug-induced changes to this non-vesicular glutamate release mechanism contribute to heightened relapse vulnerability in preclinical models of addiction. My first objective was to determine whether neurons or neuronal factors regulate Sxc activity in astrocytes (Chapter II and III) since this would illustrate the degree to which glutamate signaling involves integrated activity of multiple cell types. We found that neurons release a soluble factor that potently increases Sxc activity. Moreover, we discovered that the neuropeptide PACAP (pituitary adenylate cyclase-activating peptide) likely contributes to this effect since it upregulates Sxc activity in astrocytes (Chapters II and III). Next, we focused on the importance of PACAP regulation of Sxc to synaptic transmission in the nucleus accumbens (NAc), since this structure is highly implicated in drug addiction (Chapter IV). PACAP depressed synaptic transmission in NAc neurons projecting to the substantia nigra, an important efferent that encodes motivated behaviors. Interestingly, PACAP-induced control over synaptic transmission required enhanced Sxc activity. Given this, we then determined the behavioral impact of increasing PACAP signaling in the NAc on drug-seeking behavior (Chapter IV). Specifically, we found that microinfusion of PACAP into the NAc attenuated cocaine-primed reinstatement of drug seeking. Lastly, we determined that PACAP is expressed in corticostriatal projections to the NAc, and that endogenous PACAP is an unrecognized factor influencing relapse vulnerability (Chapter IV). Collectively, this dissertation reveals that a novel form of neuron-astrocyte communication, namely PACAP regulation of Sxc, is a critical link integrating the glutamate network that mediates motivated behavior