Hamiltonicity below Dirac's condition

Dirac's theorem (1952) is a classical result of graph theory, stating that an $n$-vertex graph ($n \geq 3$) is Hamiltonian if every vertex has degree at least $n/2$. Both the value $n/2$ and the requirement for every vertex to have high degree are necessary for the theorem to hold. In this work we give efficient algorithms for determining Hamiltonicity when either of the two conditions are relaxed. More precisely, we show that the Hamiltonian cycle problem can be solved in time $c^k \cdot n^{O(1)}$, for some fixed constant $c$, if at least $n-k$ vertices have degree at least $n/2$, or if all vertices have degree at least $n/2-k$. The running time is, in both cases, asymptotically optimal, under the exponential-time hypothesis (ETH). The results extend the range of tractability of the Hamiltonian cycle problem, showing that it is fixed-parameter tractable when parameterized below a natural bound. In addition, for the first parameterization we show that a kernel with $O(k)$ vertices can be found in polynomial time

To Fear is to Gain? The Role of Fear Recognition in Risky Decision Making in TBI Patients and Healthy Controls

Fear is an important emotional reaction that guides decision making in situations of ambiguity or uncertainty. Both recognition of facial expressions of fear and decision making ability can be impaired after traumatic brain injury (TBI), in particular when the frontal lobe is damaged. So far, it has not been investigated how recognition of fear influences risk behavior in healthy subjects and TBI patients. The ability to recognize fear is thought to be related to the ability to experience fear and to use it as a warning signal to guide decision making. We hypothesized that a better ability to recognize fear would be related to a better regulation of risk behavior, with healthy controls outperforming TBI patients. To investigate this, 59 healthy subjects and 49 TBI patients were assessed with a test for emotion recognition (Facial Expression of Emotion: Stimuli and Tests) and a gambling task (Iowa Gambling Task (IGT)). The results showed that, regardless of post traumatic amnesia duration or the presence of frontal lesions, patients were more impaired than healthy controls on both fear recognition and decision making. In both groups, a significant relationship was found between better fear recognition, the development of an advantageous strategy across the IGT and less risk behavior in the last blocks of the IGT. Educational level moderated this relationship in the final block of the IGT. This study has important clinical implications, indicating that impaired decision making and risk behavior after TBI can be preceded by deficits in the processing of fear

At What Stage of Neural Processing Does Cocaine Act to Boost Pursuit of Rewards?

Dopamine-containing neurons have been implicated in reward and decision making. One element of the supporting evidence is that cocaine, like other drugs that increase dopaminergic neurotransmission, powerfully potentiates reward seeking. We analyze this phenomenon from a novel perspective, introducing a new conceptual framework and new methodology for determining the stage(s) of neural processing at which drugs, lesions and physiological manipulations act to influence reward-seeking behavior. Cocaine strongly boosts the proclivity of rats to work for rewarding electrical brain stimulation. We show that the conventional conceptual framework and methods do not distinguish between three conflicting accounts of how the drug produces this effect: increased sensitivity of brain reward circuitry, increased gain, or decreased subjective reward costs. Sensitivity determines the stimulation strength required to produce a reward of a given intensity (a measure analogous to the KM of an enzyme) whereas gain determines the maximum intensity attainable (a measure analogous to the vmax of an enzyme-catalyzed reaction). To distinguish sensitivity changes from the other determinants, we measured and modeled reward seeking as a function of both stimulation strength and opportunity cost. The principal effect of cocaine was a two-fourfold increase in willingness to pay for the electrical reward, an effect consistent with increased gain or decreased subjective cost. This finding challenges the long-standing view that cocaine increases the sensitivity of brain reward circuitry. We discuss the implications of the results and the analytic approach for theories of how dopaminergic neurons and other diffuse modulatory brain systems contribute to reward pursuit, and we explore the implications of the conceptual framework for the study of natural rewards, drug reward, and mood

Lactate Produced by Glycogenolysis in Astrocytes Regulates Memory Processing

When administered either systemically or centrally, glucose is a potent enhancer of memory processes. Measures of glucose levels in extracellular fluid in the rat hippocampus during memory tests reveal that these levels are dynamic, decreasing in response to memory tasks and loads; exogenous glucose blocks these decreases and enhances memory. The present experiments test the hypothesis that glucose enhancement of memory is mediated by glycogen storage and then metabolism to lactate in astrocytes, which provide lactate to neurons as an energy substrate. Sensitive bioprobes were used to measure brain glucose and lactate levels in 1-sec samples. Extracellular glucose decreased and lactate increased while rats performed a spatial working memory task. Intrahippocampal infusions of lactate enhanced memory in this task. In addition, pharmacological inhibition of astrocytic glycogenolysis impaired memory and this impairment was reversed by administration of lactate or glucose, both of which can provide lactate to neurons in the absence of glycogenolysis. Pharmacological block of the monocarboxylate transporter responsible for lactate uptake into neurons also impaired memory and this impairment was not reversed by either glucose or lactate. These findings support the view that astrocytes regulate memory formation by controlling the provision of lactate to support neuronal functions

Towards topology-free optimization - An application to turbine internal cooling geometries

The application of automated design optimization to real-world, complex geometry problems is a significant challenge - especially if the topology is not known a priori like in turbine internal cooling. The long term goal of our work is to focus on an end-to-end integration of the whole CFD Process, from solid model through meshing, solving and post-processing to enable this type of design optimization to become viable & practical. In recent papers we have reported the integration of a Level Set based geometry kernel with an octree-based cut- Cartesian mesh generator, RANS flow solver, post-processing & geometry editing all within a single piece of software - and all implemented in parallel with commodity PC clusters as the target. The cut-cells which characterize the approach are eliminated by exporting a body-conformal mesh guided by the underpinning Level Set. This paper extends this work still further with a simple scoping study showing how the basic functionality can be scripted & automated and then used as the basis for automated optimization of a generic gas turbine cooling geometry. Copyright © 2008 by W.N.Dawes

Building information modeling in construction conflict management

Dispute is recognized as critical cause of deficiency and low performance in construction projects. Plenty of studies have been done in construction dispute management recently; however, there are no studies on construction dispute elimination. This study aims to propose a building information modeling (BIM) approach to control conflict causes before the occurrenc e of dispute. BIM is one of the latest platforms that promote a high level of collaboration, information sharing, and coordination where its implementation ranges from project initialization to completion stage. The circumstances associating with BIM technology can be utilized to explore the possibilities in conflict and dispute resolution system. Questionnaire surveys are used to collect the primary data. Analytical hierarchy process (AHP) and multi attribute utility technique (MAUT) are adopted to develop an algorithm and a decision-making framework to manage and resolve the potential conflict causes, particularly for the Malaysian construction industry. Data analysis emerged that five critical conflict factors in Malaysian construction industry are insufficient monitoring of CPM scheduling and updates requirements; failures to understand and correctly bid or price the works; delay in running bill payment; inadequate contractors’ management, supervision, and coordination; and error and omission in design that are originated from time, cost, quality, and documentation. Further analysis to prioritize BIM functions in construction conflict management has been done by the combination of AHP and MAUT results. Consequently, it is affirmed that clash detection and cost estimating, 4D scheduling, 3D visualization and structure analysis as BIM functions obtained the highest score to control conflicting factors