On The Specialization of Neural Modules

A number of machine learning models have been proposed with the goal of achieving systematic generalization: the ability to reason about new situations by combining aspects of previous experiences. These models leverage compositional architectures which aim to learn specialized modules dedicated to structures in a task that can be composed to solve novel problems with similar structures. While the compositionality of these architectures is guaranteed by design, the modules specializing is not. Here we theoretically study the ability of network modules to specialize to useful structures in a dataset and achieve systematic generalization. To this end we introduce a minimal space of datasets motivated by practical systematic generalization benchmarks. From this space of datasets we present a mathematical definition of systematicity and study the learning dynamics of linear neural modules when solving components of the task. Our results shed light on the difficulty of module specialization, what is required for modules to successfully specialize, and the necessity of modular architectures to achieve systematicity. Finally, we confirm that the theoretical results in our tractable setting generalize to more complex datasets and non-linear architectures

The Marshall Differential Analyzer: a Visual Interpretation of Mathematics

Mechanical integration is an idea dating back to the late 1800\u27s discovered by James Thomson, brother of Lord Kelvin. This idea was then expanded to build a calculating machine, called a differential analyzer, by Vannevar Bush (M.I.T) in 1929. The Marshall University Differential Analyzer Team has followed in the footsteps of Dr. Bush and a gentleman named Dr. Arthur Porter, who was the first to build a differential analyzer in England when he was a student of Dr. Douglas Hartree. He built his machine of Meccano components, the British version of Erector Set. In the early days of Arthur Porter\u27s research, the machine was used to solve ordinary differential equations and the results were compared to those of more sophisticated differential analyzers of that time. Dr. Porter\u27s research proved that the Meccano differential analyzer was well suited for many dynamical systems applications. The Team has recently constructed the only two publicly accessible differential analyzers in the USA, a mini two integrator machine and a larger four integrator machine built in the spirit of the Porter Meccano Manchester Differential Analyzer. They are continuing in the spirit of Dr. Porter\u27s work. In this work we will give a brief overview of the Marshall Differential Analyzer Project, the mechanics of the machine and the mathematics that can be described by the mechanics. An example will be presented to unify the mechanics and the mathematical concepts

The Marshall Differential Analyzer: a Visual Interpretation of Mathematics

Mechanical integration is an idea dating back to the late 1800\u27s discovered by James Thomson, brother of Lord Kelvin. This idea was then expanded to build a calculating machine, called a differential analyzer, by Vannevar Bush (M.I.T) in 1929. The Marshall University Differential Analyzer Team has followed in the footsteps of Dr. Bush and a gentleman named Dr. Arthur Porter, who was the first to build a differential analyzer in England when he was a student of Dr. Douglas Hartree. He built his machine of Meccano components, the British version of Erector Set. In the early days of Arthur Porter\u27s research, the machine was used to solve ordinary differential equations and the results were compared to those of more sophisticated differential analyzers of that time. Dr. Porter\u27s research proved that the Meccano differential analyzer was well suited for many dynamical systems applications. The Team has recently constructed the only two publicly accessible differential analyzers in the USA, a mini two integrator machine and a larger four integrator machine built in the spirit of the Porter Meccano Manchester Differential Analyzer. They are continuing in the spirit of Dr. Porter\u27s work. In this work we will give a brief overview of the Marshall Differential Analyzer Project, the mechanics of the machine and the mathematics that can be described by the mechanics. An example will be presented to unify the mechanics and the mathematical concepts

Dynamics Generalisation in Reinforcement Learning via Adaptive Context-Aware Policies

While reinforcement learning has achieved remarkable successes in several domains, its real-world application is limited due to many methods failing to generalise to unfamiliar conditions. In this work, we consider the problem of generalising to new transition dynamics, corresponding to cases in which the environment's response to the agent's actions differs. For example, the gravitational force exerted on a robot depends on its mass and changes the robot's mobility. Consequently, in such cases, it is necessary to condition an agent's actions on extrinsic state information and pertinent contextual information reflecting how the environment responds. While the need for context-sensitive policies has been established, the manner in which context is incorporated architecturally has received less attention. Thus, in this work, we present an investigation into how context information should be incorporated into behaviour learning to improve generalisation. To this end, we introduce a neural network architecture, the Decision Adapter, which generates the weights of an adapter module and conditions the behaviour of an agent on the context information. We show that the Decision Adapter is a useful generalisation of a previously proposed architecture and empirically demonstrate that it results in superior generalisation performance compared to previous approaches in several environments. Beyond this, the Decision Adapter is more robust to irrelevant distractor variables than several alternative methods.Comment: Accepted to NeurIPS 202

Operational and Research Musculoskeletal Summit: Summit Recommendations

The Medical Informatics and Health Care Systems group in the Office of Space Medicine at NASA Johnson Space Center (JSC) has been tasked by NASA with improving overall medical care on the International Space Station (ISS) and providing insights for medical care for future exploration missions. To accomplish this task, a three day Operational and Research Musculoskeletal Summit was held on August 23-25th, 2005 at Space Center Houston. The purpose of the summit was to review NASA#s a) current strategy for preflight health maintenance and injury screening, b) current treatment methods in-flight, and c) risk mitigation strategy for musculoskeletal injuries or syndromes that could occur or impact the mission. Additionally, summit participants provided a list of research topics NASA should consider to mitigate risks to astronaut health. Prior to the summit, participants participated in a web-based pre-summit forum to review the NASA Space Medical Conditions List (SMCL) of musculoskeletal conditions that may occur on ISS as well as the resources currently available to treat them. Data from the participants were compiled and integrated with the summit proceedings. Summit participants included experts from the extramural physician and researcher communities, and representatives from NASA Headquarters, the astronaut corps, JSC Medical Operations and Human Adaptations and Countermeasures Offices, Glenn Research Center Human Research Office, and the Astronaut Strength, Conditioning, and Reconditioning (ASCR) group. The recommendations in this document are based on a summary of summit discussions and the best possible evidence-based recommendations for musculoskeletal care for astronauts while on the ISS, and include recommendati ons for exploration class missions

Morphology of fluvial networks on Titan: Evidence for structural control

Although Titan’s surface shows clear evidence of erosional modification, such as fluvial incision, evidence for tectonism has been less apparent. On Earth, fluvial networks with strongly preferred orientations are often associated with structural features, such as faults or joints, that influence flow or erodibility. We delineated and classified the morphologies of fluvial drainages on Titan and discovered evidence of structural control. Fluvial networks were delineated both on synthetic aperture radar (SAR) images covering ∼40% of Titan from the Cassini Titan Radar Mapper up through T71 and on visible light images of the Huygens landing site collected by the Descent Imager/Spectral Radiometer (DISR). The delineated networks were assigned to one of three morphologic classes—dendritic, parallel or rectangular—using a quantitative terrestrial drainage pattern classification algorithm modified for use with Titan data. We validated our modified algorithm by applying it to synthetic fluvial networks produced by a landscape evolution model with no structural control of drainage orientations, and confirmed that only a small fraction of the networks are falsely identified as structurally controlled. As a second validation, we confirmed that our modified algorithm correctly classifies terrestrial networks that are classified in multiple previous works as rectangular. Application of this modified algorithm to our Titan networks results in a classification of rectangular for one-half of the SAR and DISR networks. A review of the geological context of the four terrestrial rectangular networks indicates that tensional stresses formed the structures controlling those terrestrial drainages. Based on the similar brittle response of rock and cryogenic ice to stress, we infer that structures formed under tension are the most likely cause of the rectangular Titan networks delineated here. The distribution of these rectangular networks suggests that tensional stresses on Titan may have been widespread.United States. National Aeronautics and Space Administration (NASA Cassini Data Analysis Program Grant NNX08BA81G

The Process and a Pitfall in Developing Biology and Chemistry Problems for Mathematics Courses

In this paper, we describe our process for developing applied problems from biology and chemistry for use in a differential calculus course. We describe our conversations and curricular analyses that led us to change from our initial focus on college algebra to calculus. We provide results that allowed us to see the overlaps between biology and mathematics and chemistry and mathematics and led to a specific focus on problems related to rates of change. Finally, we investigate the problems that were developed by the partner disciplines for use on recitation activities in calculus and how those problems were modified by the calculus coordinator. We compare what partner disciplines emphasize in scientific applications with what mathematics instructors emphasize in calculus and consider what that means for students’ understanding of science in mathematics. We also describe the role of the students, partner discipline colleagues, and calculus instructors in the development, refinement, and use of the problems

Persistent global marine euxinia in the early Silurian

The second pulse of the Late Ordovician mass extinction occurred around the Hirnantian-Rhuddanian boundary (~444 Ma) and has been correlated with expanded marine anoxia lasting into the earliest Silurian. Characterization of the Hirnantian ocean anoxic event has focused on the onset of anoxia, with global reconstructions based on carbonate δ238U modeling. However, there have been limited attempts to quantify uncertainty in metal isotope mass balance approaches. Here, we probabilistically evaluate coupled metal isotopes and sedimentary archives to increase constraint. We present iron speciation, metal concentration, δ98Mo and δ238U measurements of Rhuddanian black shales from the Murzuq Basin, Libya. We evaluate these data (and published carbonate δ238U data) with a coupled stochastic mass balance model. Combined statistical analysis of metal isotopes and sedimentary sinks provides uncertainty-bounded constraints on the intensity of Hirnantian-Rhuddanian euxinia. This work extends the duration of anoxia to >3 Myrs – notably longer than well-studied Mesozoic ocean anoxic events

Mapping our Universe in 3D with MITEoR

Mapping our universe in 3D by imaging the redshifted 21 cm line from neutral hydrogen has the potential to overtake the cosmic microwave background as our most powerful cosmological probe, because it can map a much larger volume of our Universe, shedding new light on the epoch of reionization, inflation, dark matter, dark energy, and neutrino masses. We report on MITEoR, a pathfinder low-frequency radio interferometer whose goal is to test technologies that greatly reduce the cost of such 3D mapping for a given sensitivity. MITEoR accomplishes this by using massive baseline redundancy both to enable automated precision calibration and to cut the correlator cost scaling from N^2 to NlogN, where N is the number of antennas. The success of MITEoR with its 64 dual-polarization elements bodes well for the more ambitious HERA project, which would incorporate many identical or similar technologies using an order of magnitude more antennas, each with dramatically larger collecting area.Comment: To be published in proceedings of 2013 IEEE International Symposium on Phased Array Systems & Technolog