Experience Implementing a Performant Category-Theory Library in Coq

We describe our experience implementing a broad category-theory library in Coq. Category theory and computational performance are not usually mentioned in the same breath, but we have needed substantial engineering effort to teach Coq to cope with large categorical constructions without slowing proof script processing unacceptably. In this paper, we share the lessons we have learned about how to represent very abstract mathematical objects and arguments in Coq and how future proof assistants might be designed to better support such reasoning. One particular encoding trick to which we draw attention allows category-theoretic arguments involving duality to be internalized in Coq's logic with definitional equality. Ours may be the largest Coq development to date that uses the relatively new Coq version developed by homotopy type theorists, and we reflect on which new features were especially helpful.Comment: The final publication will be available at link.springer.com. This version includes a full bibliography which does not fit in the Springer version; other than the more complete references, this is the version submitted as a final copy to ITP 201

Hyperplane Neural Codes and the Polar Complex

Hyperplane codes are a class of convex codes that arise as the output of a one layer feed-forward neural network. Here we establish several natural properties of stable hyperplane codes in terms of the {\it polar complex} of the code, a simplicial complex associated to any combinatorial code. We prove that the polar complex of a stable hyperplane code is shellable and show that most currently known properties of the hyperplane codes follow from the shellability of the appropriate polar complex.Comment: 23 pages, 5 figures. To appear in Proceedings of the Abel Symposiu

Families of Small Regular Graphs of Girth 5

In this paper we obtain $(q+3)$--regular graphs of girth 5 with fewer vertices than previously known ones for $q=13,17,19$ and for any prime $q \ge 23$ performing operations of reductions and amalgams on the Levi graph $B_q$ of an elliptic semiplane of type ${\cal C}$. We also obtain a 13-regular graph of girth 5 on 236 vertices from $B_{11}$ using the same technique

Dynamical model of sequential spatial memory: winnerless competition of patterns

We introduce a new biologically-motivated model of sequential spatial memory which is based on the principle of winnerless competition (WLC). We implement this mechanism in a two-layer neural network structure and present the learning dynamics which leads to the formation of a WLC network. After learning, the system is capable of associative retrieval of pre-recorded sequences of spatial patterns.Comment: 4 pages, submitted to PR

Angiotensin-Converting Enzyme Inhibitors or Angiotensin Receptor Blockers for Prevention of Type 2 Diabetes A Meta-Analysis of Randomized Clinical Trials

ObjectivesWe sought to investigate the role of angiotensin-converting enzyme (ACE) inhibitors and angiotensin receptor blockers (ARBs) in preventing the new onset of type 2 diabetes mellitus.BackgroundDiabetes is a public health problem of epidemic proportions and its prevalence is on the rise. The typical American born today has a one in three chance of developing type 2 diabetes. This diagnosis is associated with an adverse cardiovascular prognosis and is considered the risk equivalent of established coronary disease. Even in high-risk individuals, diabetes is a preventable disease. Several studies have shown that ACE inhibitors and ARBs decrease the incidence of new-onset type 2 diabetes. However, the exact role of these agents in diabetes prevention has not yet been fully elucidated.MethodsWe conducted a meta-analysis of 12 randomized controlled clinical trials of ACE inhibitors or ARBs, identified through a MEDLINE search and a review of reports from scientific meetings, to study the efficacy of these medications in diabetes prevention.ResultsThis showed that ACE inhibitors and ARBs were associated with reductions in the incidence of newly diagnosed diabetes by 27% and 23%, respectively, and by 25% in the pooled analysis.ConclusionsThe use of an ACE inhibitor or ARB should be considered in patients with pre-diabetic conditions such as metabolic syndrome, hypertension, impaired fasting glucose, family history of diabetes, obesity, congestive heart failure, or coronary heart disease

Neutron emissions in brittle rocks during compression tests: Monotonic vs cyclic loading

Neutron emission measurements, by means of 3He devices and neutron bubble detectors, were performed during two different kinds of compression tests on brittle rocks: (i) under displacement control, and (ii) under cyclic loading. The material used for the tests was Green Luserna Granite, with different specimen sizes and shapes, and consequently with different brittleness numbers. Since the analyzed material contains iron, our conjecture is that piezonuclear reactions involving fission of iron into aluminum, or into magnesium and silicon, should have occurred during compression damage and failure. Some studies have been already conducted on the different forms of energy emitted during the failure of brittle materials. They are based on the signals captured by acoustic emission measurement systems, or on the detection of electromagnetic charge. On the other hand, piezonuclear neutron emissions from very brittle rock specimens in compression have been discovered only very recently. In this paper, the authors analyse this phenomenon from an experimental point of vie

Prioritized Sweeping Neural DynaQ with Multiple Predecessors, and Hippocampal Replays

During sleep and awake rest, the hippocampus replays sequences of place cells that have been activated during prior experiences. These have been interpreted as a memory consolidation process, but recent results suggest a possible interpretation in terms of reinforcement learning. The Dyna reinforcement learning algorithms use off-line replays to improve learning. Under limited replay budget, a prioritized sweeping approach, which requires a model of the transitions to the predecessors, can be used to improve performance. We investigate whether such algorithms can explain the experimentally observed replays. We propose a neural network version of prioritized sweeping Q-learning, for which we developed a growing multiple expert algorithm, able to cope with multiple predecessors. The resulting architecture is able to improve the learning of simulated agents confronted to a navigation task. We predict that, in animals, learning the world model should occur during rest periods, and that the corresponding replays should be shuffled.Comment: Living Machines 2018 (Paris, France

Active versus passive acquisition of spatial knowledge while controlling a vehicle in a virtual urban space in drivers and non-drivers

Historically real world studies have indicated a spatial learning advantage for active explorers of environments over those whose experience is more passive; a common contrast is made between car drivers and passengers. An experiment was conducted to explore the dual hypotheses that active explorers learn more about the layout of a virtual environment than passive observers and that real world car drivers will learn more regardless of their experimental Active/Passive status. Consistent with earlier studies in VEs, there was no benefit from activity (controlling exploration/movement), arguably because input control competes with spatial information acquisition. However, the results showed that Drivers were more accurate than Non-Drivers at indicating the positions of target locations on a map, in both active and passive conditions and had better route scores than Non-Drivers in the passive condition. It is argued that driving experience may convey a spatial learning advantage over and above activity per se

Avian Host-Selection by Culex pipiens in Experimental Trials

Evidence from field studies suggests that Culex pipiens, the primary mosquito vector of West Nile virus (WNV) in the northeastern and north central United States, feeds preferentially on American robins (Turdus migratorius). To determine the contribution of innate preferences to observed preference patterns in the field, we conducted host preference trials with a known number of adult female C. pipiens in outdoor cages comparing the relative attractiveness of American robins with two common sympatric bird species, European starling, Sternus vulgaris and house sparrow, Passer domesticus. Host seeking C. pipiens were three times more likely to enter robin-baited traps when with the alternate host was a European starling (n = 4 trials; OR = 3.06; CI [1.42–6.46]) and almost twice more likely when the alternative was a house sparrow (n = 8 trials; OR = 1.80; CI = [1.22–2.90]). There was no difference in the probability of trap entry when two robins were offered (n = 8 trials). Logistic regression analysis determined that the age, sex and weight of the birds, the date of the trial, starting-time, temperature, humidity, wind-speed and age of the mosquitoes had no effect on the probability of a choosing a robin over an alternate bird. Findings indicate that preferential feeding by C. pipiens mosquitoes on certain avian hosts is likely to be inherent, and we discuss the implications innate host preferences may have on enzootic WNV transmission