Agent based cooperative theory formation in pure mathematics

The HR program, Colton et al. (1999), performs theory formation in domains of pure mathematics. Given only minimal information about a domain, it invents concepts, make conjectures, proves theorems and finds counterexamples to false conjectures. We present here a multi-agent version of HR which may provide a model for how individual mathematicians perform separate investigations but communicate their results to the mathematical community, learning from others as they do. We detail the exhaustive categorisation problem to which we have applied a multi-agent approach.

Fair assignment of indivisible objects under ordinal preferences

We consider the discrete assignment problem in which agents express ordinal preferences over objects and these objects are allocated to the agents in a fair manner. We use the stochastic dominance relation between fractional or randomized allocations to systematically define varying notions of proportionality and envy-freeness for discrete assignments. The computational complexity of checking whether a fair assignment exists is studied for these fairness notions. We also characterize the conditions under which a fair assignment is guaranteed to exist. For a number of fairness concepts, polynomial-time algorithms are presented to check whether a fair assignment exists. Our algorithmic results also extend to the case of unequal entitlements of agents. Our NP-hardness result, which holds for several variants of envy-freeness, answers an open question posed by Bouveret, Endriss, and Lang (ECAI 2010). We also propose fairness concepts that always suggest a non-empty set of assignments with meaningful fairness properties. Among these concepts, optimal proportionality and optimal weak proportionality appear to be desirable fairness concepts.Comment: extended version of a paper presented at AAMAS 201

Planar cell polarity genes Frizzled3a, Vangl2, and Scribble are required for spinal commissural axon guidance

Background A fundamental feature of early nervous system development is the guidance of axonal projections to their targets in order to assemble neural circuits that control behavior. Spinal commissural neurons are an attractive model to investigate the multiple guidance cues that control growth cone navigation both pre- and post-midline crossing, as well as along both the dorsal–ventral (D–V) and anterior–posterior (A–P) axes. Accumulating evidence suggests that guidance of spinal commissural axons along the A–P axis is dependent on components of the planar cell polarity (PCP) signaling pathway. In the zebrafish, the earliest born spinal commissural neuron to navigate the midline and turn rostrally is termed commissural primary ascending (CoPA). Unlike mammalian systems, CoPA axons cross the midline as a single axon and allow an analysis of the role of PCP components in anterior pathfinding in single pioneering axons. Results Here, we establish CoPA cells in the zebrafish spinal cord as a model system for investigating the molecular function of planar cell polarity signaling in axon guidance. Using mutant analysis, we show that the functions of Fzd3a and Vangl2 in the anterior turning of commissural axons are evolutionarily conserved in teleosts. We extend our findings to reveal a role for the PCP gene scribble in the anterior guidance of CoPA axons. Analysis of single CoPA axons reveals that these commissural axons become responsive to PCP-dependent anterior guidance cues even prior to midline crossing. When midline crossing is prevented by dcc gene knockdown, ipsilateral CoPA axons still extend axons anteriorly in response to A–P guidance cues. We show that this ipsilateral anterior pathfinding that occurs in the absence of midline crossing is dependent on PCP signaling. Conclusion Our results demonstrate that anterior guidance decisions by CoPA axons are dependent on the function of planar cell polarity genes both prior to and after midline crossing

Oxygen kinetics and energy expenditure in fulminant hepatic failure and during liver transplantation

This thesis examines aspects of oxygen transport and uptake in patients with acute and chronic liver disease with specific reference to the management of fulminant hepatic failure (FHF) and the intraoperative management of patients undergoing liver transplantation.A prospective randomised controlled study was carried out in patients with FHF evaluating the effect of the drug N- acetylcysteine on DO2, VO2, and tissue oxygen extraction. A previous study showed that this drug increased all of these oxygen kinetic variables, which was considered of therapeutic benefit. The present study showed that this earlier finding was an artifact related to the method of calculating oxygen consumption (the Fick method). This method produced unreliable results in patients with FHF because it was inaccurate, non -reproducible, the the relation between DO2 and VO2 was subject to mathematical couplig error. No clinically significant improvements in any oxygen kinetic variables were observed after N- acetylcysteine administration, even when followed for a prolonged period. Variable effects on cardiovascular parameters were found, but overall no differences from the control group were demonstrated. No relationship was found between plasma Nacetylcysteine concentrations and clinical response.A prospective study examining energy expenditure and the acute phase response was carried out in patients with FHF. Energy expenditure was increased by approximately 20 -25% in FHF in comparison with spontaneously breathing healthy volunteers and physically anhepatic patients with chronic liver disease studied during liver transplantation. Plasma TNFa, IL -6, and C- reactive protein were measured. These were significantly elevated in comparison with healthy controls in keeping with a significant acute phase response. The study indicated hypermetabolism during severe FHF despite the loss of functioning liver cell mass and the effects of sedation, analgesia, and mechanical ventilation. This was most likely attributable to a systemic inflammatory response.In patients undergoing liver transplantation indirect calorimetry was used to examine changes in metabolic rate and pulmonary physiology following graft reperfusion. Significant changes in metabolic rate, oxygen transport, and acid -base balance were demonstrated the factors which influence these changes were discussed. The use of the piggyback surgical technique was associated with greater metabolic stability than the use of venovenous bypass.A prospective observational study compared the two methods for managing the anhepatic phase of liver transplantation, namely venovenous bypass or the piggyback surgical technique. This study demonstrated higher cardiac output, VO2, and blood temperature during the anhepatic phase with the piggyback surgical technique. This suggested better preservation of tissue oxygenation with this approach, which may translate into improved postoperative function.Two techniques of graft reperfusion, namely via the portal vein or the hepatic artery, were compared in another prospective observational study. This study indicated that the increase in VO2 after reperfusion occurred more slowly when the hepatic artery was used, but was accompanied by a slower release of acid load into the circulation and less requirement for vasopressor support. Reperfusion via the hepatic artery may therefore be preferable in the patient at risk of haemodynamic or cerebral decompensation following reperfusion, although further studies are required to ensure graft outcome is equivalent with both techniques

Computational Aspects of Multi-Winner Approval Voting

We study computational aspects of three prominent voting rules that use approval ballots to elect multiple winners. These rules are satisfaction approval voting, proportional approval voting, and reweighted approval voting. We first show that computing the winner for proportional approval voting is NP-hard, closing a long standing open problem. As none of the rules are strategyproof, even for dichotomous preferences, we study various strategic aspects of the rules. In particular, we examine the computational complexity of computing a best response for both a single agent and a group of agents. In many settings, we show that it is NP-hard for an agent or agents to compute how best to vote given a fixed set of approval ballots from the other agents

Equilibria Under the Probabilistic Serial Rule

The probabilistic serial (PS) rule is a prominent randomized rule for assigning indivisible goods to agents. Although it is well known for its good fairness and welfare properties, it is not strategyproof. In view of this, we address several fundamental questions regarding equilibria under PS. Firstly, we show that Nash deviations under the PS rule can cycle. Despite the possibilities of cycles, we prove that a pure Nash equilibrium is guaranteed to exist under the PS rule. We then show that verifying whether a given profile is a pure Nash equilibrium is coNP-complete, and computing a pure Nash equilibrium is NP-hard. For two agents, we present a linear-time algorithm to compute a pure Nash equilibrium which yields the same assignment as the truthful profile. Finally, we conduct experiments to evaluate the quality of the equilibria that exist under the PS rule, finding that the vast majority of pure Nash equilibria yield social welfare that is at least that of the truthful profile.Comment: arXiv admin note: text overlap with arXiv:1401.6523, this paper supersedes the equilibria section in our previous report arXiv:1401.652

Core Structure of Amyloid Fibrils Formed by Residues 106–126 of the Human Prion Protein

SummaryPeptides comprising residues 106–126 of the human prion protein (PrP) exhibit many features of the full-length protein. PrP(106–126) induces apoptosis in neurons, forms fibrillar aggregates, and can mediate the conversion of native cellular PrP (PrPC) to the scrapie form (PrPSc). Despite a wide range of biochemical and biophysical studies on this peptide, including investigation of its propensity for aggregation, interactions with cell membranes, and PrP-like toxicity, the structure of amyloid fibrils formed by PrP(106–126) remains poorly defined. In this study we use solid-state nuclear magnetic resonance to define the secondary and quaternary structure of PrP(106–126) fibrils. Our results reveal that PrP(106–126) forms in-register parallel β sheets, stacked in an antiparallel fashion within the mature fibril. The close intermolecular contacts observed in the fibril core provide a rational for the sequence-dependent behavior of PrP(106–126), and provide a basis for further investigation of its biological properties

Sustainable consumption and third-party certified labels: consumers' perceptions and reactions

Compared with conventional products, sustainable products continue to attract relatively lower market shares. To increase customer acceptance, many sustainable products feature third-party certified labels (TPCL), yet it is unclear whether TPCL are effective and what processes and boundary conditions define their role in consumer decision making. Across three experimental studies, this research determines that sustainable products are characterized by credence qualities, associated with increased perceptions of risk, which negatively influence consumers’ purchase intentions. Drawing on signaling theory, this study also shows that TPCL on sustainable products provide brand-like information cues that reduce the perceived risk of sustainable products. Finally, a third experimental study demonstrates that consumers must perceive TPCL as credible for them to reduce consumers’ risk perceptions