Counting Popular Matchings in House Allocation Problems

We study the problem of counting the number of popular matchings in a given instance. A popular matching instance consists of agents A and houses H, where each agent ranks a subset of houses according to their preferences. A matching is an assignment of agents to houses. A matching M is more popular than matching M' if the number of agents that prefer M to M' is more than the number of people that prefer M' to M. A matching M is called popular if there exists no matching more popular than M. McDermid and Irving gave a poly-time algorithm for counting the number of popular matchings when the preference lists are strictly ordered. We first consider the case of ties in preference lists. Nasre proved that the problem of counting the number of popular matching is #P-hard when there are ties. We give an FPRAS for this problem. We then consider the popular matching problem where preference lists are strictly ordered but each house has a capacity associated with it. We give a switching graph characterization of popular matchings in this case. Such characterizations were studied earlier for the case of strictly ordered preference lists (McDermid and Irving) and for preference lists with ties (Nasre). We use our characterization to prove that counting popular matchings in capacitated case is #P-hard

Face selectivity in electrophilic additions to methylenenorsnoutanes: relative importance of through-space, through-bond and electrostatic interactions

4-Substituted 9-methylenenorsnoutanes undergo a variety of electrophilic additions with a small but consistent syn preference; ab initio MESP maps indicate that electrostatic factors and through-space interaction between the double bond and cyclopropane Walsh orbitals are unimportant in determining the face selectivity, while AM1 transition state energetics suggest that the observed preferences are determined primarily by through-bond interactions

Vigilance, arousal, and acetylcholine: Optimal control of attention in a simple detection task

Paying attention to particular aspects of the world or being more vigilant in general can be interpreted as forms of 'internal' action. Such arousal-related choices come with the benefit of increasing the quality and situational appropriateness of information acquisition and processing, but incur potentially expensive energetic and opportunity costs. One implementational route for these choices is widespread ascending neuromodulation, including by acetylcholine (ACh). The key computational question that elective attention poses for sensory processing is when it is worthwhile paying these costs, and this includes consideration of whether sufficient information has yet been collected to justify the higher signal-to-noise ratio afforded by greater attention and, particularly if a change in attentional state is more expensive than its maintenance, when states of heightened attention ought to persist. We offer a partially observable Markov decision-process treatment of optional attention in a detection task, and use it to provide a qualitative model of the results of studies using modern techniques to measure and manipulate ACh in rodents performing a similar task

Fast ACh signals and the optimal control of attention in a detection task

Understanding how the brain represents, updates, and accommodates uncertainty is a key challenge for computational neuroscience. Neuromodulators such as acetylcholine (ACh) have been suggested as playing important roles over multiple timescales, regulating excitability and plasticity to mediate various effects of uncertainty on inference and learning. While these influences are consistent with ACh’s long-standing association with general functions of attention and arousal, recent studies using novel techniques to measure and manipulate this system with increasing exactitude have revealed intriguing patterns of activity at fast timescales. Notably, Sarter and colleagues used ACh amperometry (Howe et al., 2013, J.Neurosci., 33(20):8742-8752) and optogenetics (Gritton et al., 2016, PNAS, 113(8):E1089-E1097) as rodents performed a challenging signal detection task; they reported effects such as a serial dependency over multiple trials as to whether ACh is released, and increased false alarm rates when optogenetic stimulation is applied during non-signal trials. Inspired by their task and findings, we construct an abstract detection task, and consider how attentional state might be optimally controlled over each trial, assuming that more focused attention improves sensory information but incurs costs. We show similarities between the resulting attentional dynamics and task performance in the model and experimental results

Face selectivity in electrophilic additions to methylenenorsnoutanes: relative importance of through-space, through-bond and electrostatic interactions

4-Substituted 9-methylenenorsnoutanes undergo a variety of electrophilic additions with a small but consistent syn preference; ab initio MESP maps indicate that electrostatic factors and through-space interaction between the double bond and cyclopropane Walsh orbitals are unimportant in determining the face selectivity, while AM1 transition state energetics suggest that the observed preferences are determined primarily by through-bond interactions

Influence of Epoxy/Nanosilica on Mechanical Performance of Hemp/Kevlar Fiber Reinforced Hybrid Composite with an Ultrasonic Frequency

Ultrasonic vibration was employed in blending the nanosilica into epoxy resin to manufacture hemp/kevlar/nanosilica-based epoxy composites, with an ultrasonic occurrence of 20 kHz and a 900 W capacity of power. An ultrasonic probe was utilized to ensure the consistent dispersion of the nanoparticles in the epoxy. The mechanical characteristics of hemp/kevlar fiber reinforced with epoxy/nanosilica in a mat form have been studied. Hand layup procedures were used to create these composites, including varying weight % of nanosilica and variable fiber stacking sequencing. The different weight % are 3, 6, and 9, and the stacking sequences are B, C, and D. The effectiveness of ultrasonic irradiation on mechanical characteristics was investigated and related. The inclusion of 6 wt.% of SiO2 to the B type resulted in a 25% rise in tension and a 37% in bending. The addition of 6 wt.% silica to the C-type hybridization nanocomposite results in a 34% rise in tension and a 38% rise in bending. Extreme tension behavior is attained at 6 wt.% SiO2 with epoxy with the B type piling order, and extreme bending behavior is obtained at 6 wt.% SiO2 with the C type piling order. A B-type model composite with a 6-wt.% SiO2 addition performed better in hygroscopic than A, C, and D type model composites. An SEM is utilized to observe the microstructure of shattered materials