An Algorithm for Calculating the Probability of Classes of Data Patterns on a Genealogy

Felsenstein’s pruning algorithm allows one to calculate the probability of any particular data pattern arising on a phylogeny given a model of character evolution. Here we present a similar dynamic programming algorithm. Our algorithm treats the tree and model as known. The algorithm makes it feasible to calculate the probability that a randomly selected character will be a member of a particular class of character patterns. Specifically, we are interested in binning patterns by the number of parsimony steps and the set of states observed at the tips of the tree. This algorithm was developed to expand the range of data set sizes that can be used with Waddell et al.’s marginal testing approach for assessing the adequacy of a model. The algorithms introduced can also be used in likelihood calculations which correct for ascertainment biases. For example, Lewis introduced an Mkv model which corrects for the lack of constant sites. The probability of a constant pattern arising can be calculated using the algorithm that we present, or by enumerating all possible constant patterns and calculating the probability of each one. Because the number of constant data patterns is small, both methods are efficient. However, elaborations of the Mkv model (such as those in Nylander et al) require calculating the probability of parsimony-uninformative patterns arising. For large trees and characters with many possible character states, the number of possible parismony-uninformative patterns is immense. In these cases, the algorithms introduced here will be more efficient. The algorithm has been implemented in open source software written in C++.JMK would like to thank NIH 5 R25GM62232 and the Initiative for Maximizing Student Development for funding. MTH thanks NSF-DEB-1208393 and NSF-DEB-0732920 for financial support

A Signature of Cosmic Strings Wakes in the CMB Polarization

We calculate a signature of cosmic strings in the polarization of the cosmic microwave background (CMB). We find that ionization in the wakes behind moving strings gives rise to extra polarization in a set of rectangular patches in the sky whose length distribution is scale-invariant. The length of an individual patch is set by the co-moving Hubble radius at the time the string is perturbing the CMB. The polarization signal is largest for string wakes produced at the earliest post-recombination time, and for an alignment in which the photons cross the wake close to the time the wake is created. The maximal amplitude of the polarization relative to the temperature quadrupole is set by the overdensity of free electrons inside a wake which depends on the ionization fraction $f$ inside the wake. The signal can be as high as $0.06 {\rm \mu K}$ in degree scale polarization for a string at high redshift (near recombination) and a string tension $\mu$ given by $G \mu = 10^{-7}$.Comment: 8 pages, 3 figure

Hierarchical Kickstarting for Skill Transfer in Reinforcement Learning

Practising and honing skills forms a fundamental component of how humans learn, yet artificial agents are rarely specifically trained to perform them. Instead, they are usually trained end-to-end, with the hope being that useful skills will be implicitly learned in order to maximise discounted return of some extrinsic reward function. In this paper, we investigate how skills can be incorporated into the training of reinforcement learning (RL) agents in complex environments with large state-action spaces and sparse rewards. To this end, we created SkillHack, a benchmark of tasks and associated skills based on the game of NetHack. We evaluate a number of baselines on this benchmark, as well as our own novel skill-based method Hierarchical Kickstarting (HKS), which is shown to outperform all other evaluated methods. Our experiments show that learning with a prior knowledge of useful skills can significantly improve the performance of agents on complex problems. We ultimately argue that utilising predefined skills provides a useful inductive bias for RL problems, especially those with large state-action spaces and sparse rewards

EIT-MESHER – Segmented FEM Mesh Generation and Refinement

EIT-MESHER (https://github.com/EIT-team/Mesher) is C++ software, based on the CGAL library, which generates high quality Finite Element Model tetrahedral meshes from binary masks of 3D volume segmentations. Originally developed for biomedical applications in Electrical Impedance Tomography (EIT) to address the need for custom, non-linear refinement in certain areas (e.g. around electrodes), EIT-MESHER can also be used in other fields where custom FEM refinement is required, such as Diffuse Optical Tomography (DOT)

Replay-Guided Adversarial Environment Design

Deep reinforcement learning (RL) agents may successfully generalize to new settings if trained on an appropriately diverse set of environment and task configurations. Unsupervised Environment Design (UED) is a promising self-supervised RL paradigm, wherein the free parameters of an underspecified environment are automatically adapted during training to the agent's capabilities, leading to the emergence of diverse training environments. Here, we cast Prioritized Level Replay (PLR), an empirically successful but theoretically unmotivated method that selectively samples randomly-generated training levels, as UED. We argue that by curating completely random levels, PLR, too, can generate novel and complex levels for effective training. This insight reveals a natural class of UED methods we call Dual Curriculum Design (DCD). Crucially, DCD includes both PLR and a popular UED algorithm, PAIRED, as special cases and inherits similar theoretical guarantees. This connection allows us to develop novel theory for PLR, providing a version with a robustness guarantee at Nash equilibria. Furthermore, our theory suggests a highly counterintuitive improvement to PLR: by stopping the agent from updating its policy on uncurated levels (training on less data), we can improve the convergence to Nash equilibria. Indeed, our experiments confirm that our new method, PLR ⊥ , obtains better results on a suite of out-of-distribution, zero-shot transfer tasks, in addition to demonstrating that PLR ⊥ improves the performance of PAIRED, from which it inherited its theoretical framework

Constraints on Cosmological Parameters from Future Galaxy Cluster Surveys

We study the expected redshift evolution of galaxy cluster abundance between 0 < z < 3 in different cosmologies, including the effects of the cosmic equation of state parameter w=p/rho. Using the halo mass function obtained in recent large scale numerical simulations, we model the expected cluster yields in a 12 deg^2 Sunyaev-Zeldovich Effect (SZE) survey and a deep 10^4 deg^2 X-ray survey over a wide range of cosmological parameters. We quantify the statistical differences among cosmologies using both the total number and redshift distribution of clusters. Provided that the local cluster abundance is known to a few percent accuracy, we find only mild degeneracies between w and either Omega_m or h. As a result, both surveys will provide improved constraints on Omega_m and w. The Omega_m-w degeneracy from both surveys is complementary to those found either in studies of CMB anisotropies or of high-redshift Supernovae (SNe). As a result, combining these surveys together with either CMB or SNe studies can reduce the statistical uncertainty on both w and Omega_m to levels below what could be obtained by combining only the latter two data sets. Our results indicate a formal statistical uncertainty of about 3% (68% confidence) on both Omega_m and w when the SZE survey is combined with either the CMB or SN data; the large number of clusters in the X-ray survey further suppresses the degeneracy between w and both Omega_m and h. Systematics and internal evolution of cluster structure at the present pose uncertainties above these levels. We briefly discuss and quantify the relevant systematic errors. By focusing on clusters with measured temperatures in the X-ray survey, we reduce our sensitivity to systematics such as non-standard evolution of internal cluster structure.Comment: ApJ, revised version. Expanded discussion of systematics; Press-Schechter mass function replaced by fit from simulation

Evolving Curricula with Regret-Based Environment Design

Training generally-capable agents with reinforcement learning (RL) remains a significant challenge. A promising avenue for improving the robustness of RL agents is through the use of curricula. One such class of methods frames environment design as a game between a student and a teacher, using regret-based objectives to produce environment instantiations (or levels) at the frontier of the student agent's capabilities. These methods benefit from theoretical robustness guarantees at equilibrium, yet they often struggle to find effective levels in challenging design spaces in practice. By contrast, evolutionary approaches incrementally alter environment complexity, resulting in potentially open-ended learning, but often rely on domain-specific heuristics and vast amounts of computational resources. This work proposes harnessing the power of evolution in a principled, regret-based curriculum. Our approach, which we call Adversarially Compounding Complexity by Editing Levels (ACCEL), seeks to constantly produce levels at the frontier of an agent's capabilities, resulting in curricula that start simple but become increasingly complex. ACCEL maintains the theoretical benefits of prior regret-based methods, while providing significant empirical gains in a diverse set of environments. An interactive version of this paper is available at https://accelagent.github.io

Correlation between oxygen isotope effects on the transition temperature and the magnetic penetration depth in high-temperature superconductors close to optimal doping

The oxygen-isotope (^{16}O/^{18}O) effect (OIE) on the in-plane magnetic penetration depth \lambda_{ab}(0) in optimally-doped YBa_2Cu_3O_{7-\delta} and La_{1.85}Sr_{0.15}CuO_4, and in slightly underdoped YBa_2Cu_4O_8 and Y_{0.8}Pr_{0.2}Ba_2Cu_3O_{7-\delta} was studied by means of muon-spin rotation. A substantial OIE on \lambda_{ab}(0) with an OIE exponent \beta_O=-d\ln\lambda_{ab}(0)/d\ln M_O\approx - 0.2 (M_O is the mass of the oxygen isotope), and a small OIE on the transition temperature T_c with an OIE exponent \alpha_O=-d\ln T_{c}/d \ln M_O\simeq0.02 to 0.1 were observed. The observation of a substantial isotope effect on \lambda_{ab}(0), even in cuprates where the OIE on T_c is small, indicates that lattice effects play an important role in cuprate HTS.Comment: 6 pages, 4 figure

What you think – What you do – What you get?: Exploring the link between Epistemology and PJDM in Cricket coaches

Decision making in elite sport has long been of interest, however only recently has the decision making process of coaches gained an increase in attention. Whilst a number of decision making models have been proposed, it still remains unclear as to how a number of these models may actually interact with one another as opposed to them being individual, discrete and isolated elements. This review is rooted within Cricket, given the idiosyncratic nature of the sport and the unique challenges faced by coaches within it. As a result, the review examines the existing literature around professional judgement and decision making (PJDM) and how this may be applied specifically to coaching in cricket. Secondly, we consider the integration of PJDM principles with coaches’ epistemology and the epistemological chain. Finally, against this theoretical backdrop, we offer some implications for current practice and future research in this demonstrably important and complex area