Second-Generation Objects in the Universe: Radiative Cooling and Collapse of Halos with Virial Temperatures Above 10^4 Kelvin

The first generation of protogalaxies likely formed out of primordial gas via H2-cooling in cosmological minihalos with virial temperatures of a few 1000K. However, their abundance is likely to have been severely limited by feedback processes which suppressed H2 formation. The formation of the protogalaxies responsible for reionization and metal-enrichment of the intergalactic medium, then had to await the collapse of larger halos. Here we investigate the radiative cooling and collapse of gas in halos with virial temperatures Tvir > 10^4K. In these halos, efficient atomic line radiation allows rapid cooling of the gas to 8000 K; subsequently the gas can contract nearly isothermally at this temperature. Without an additional coolant, the gas would likely settle into a locally gravitationally stable disk; only disks with unusually low spin would be unstable. However, we find that the initial atomic line cooling leaves a large, out-of-equilibrium residual free electron fraction. This allows the molecular fraction to build up to a universal value of about x(H2) = 10^-3, almost independently of initial density and temperature. We show that this is a non--equilibrium freezeout value that can be understood in terms of timescale arguments. Furthermore, unlike in less massive halos, H2 formation is largely impervious to feedback from external UV fields, due to the high initial densities achieved by atomic cooling. The H2 molecules cool the gas further to about 100K, and allow the gas to fragment on scales of a few 100 Msun. We investigate the importance of various feedback effects such as H2-photodissociation from internal UV fields and radiation pressure due to Ly-alpha photon trapping, which are likely to regulate the efficiency of star formation.Comment: Revised version accepted by ApJ; some reorganization for clarit

Near-optimal Linear Decision Trees for k-SUM and Related Problems

We construct near-optimal linear decision trees for a variety of decision problems in combinatorics and discrete geometry. For example, for any constant k , we construct linear decision trees that solve the k -SUM problem on n elements using O ( n log 2 n ) linear queries. Moreover, the queries we use are comparison queries, which compare the sums of two k -subsets; when viewed as linear queries, comparison queries are 2 k -sparse and have only { −1,0,1} coefficients. We give similar constructions for sorting sumsets A+B and for solving the SUBSET-SUM problem, both with optimal number of queries, up to poly-logarithmic terms. Our constructions are based on the notion of “inference dimension,” recently introduced by the authors in the context of active classification with comparison queries. This can be viewed as another contribution to the fruitful link between machine learning and discrete geometry, which goes back to the discovery of the VC dimension

Superregular grammars do not provide additional explanatory power but allow for a compact analysis of animal song

A pervasive belief with regard to the differences between human language and animal vocal sequences (song) is that they belong to different classes of computational complexity, with animal song belonging to regular languages, whereas human language is superregular. This argument, however, lacks empirical evidence since superregular analyses of animal song are understudied. The goal of this paper is to perform a superregular analysis of animal song, using data from gibbons as a case study, and demonstrate that a superregular analysis can be effectively used with non-human data. A key finding is that a superregular analysis does not increase explanatory power but rather provides for compact analysis: Fewer grammatical rules are necessary once superregularity is allowed. This pattern is analogous to a previous computational analysis of human language, and accordingly, the null hypothesis, that human language and animal song are governed by the same type of grammatical systems, cannot be rejected.Comment: Accepted for publication by Royal Society Open Scienc

A Logic for Non-Deterministic Parallel Abstract State Machines

We develop a logic which enables reasoning about single steps of non-deterministic parallel Abstract State Machines (ASMs). Our logic builds upon the unifying logic introduced by Nanchen and St\"ark for reasoning about hierarchical (parallel) ASMs. Our main contribution to this regard is the handling of non-determinism (both bounded and unbounded) within the logical formalism. Moreover, we do this without sacrificing the completeness of the logic for statements about single steps of non-deterministic parallel ASMs, such as invariants of rules, consistency conditions for rules, or step-by-step equivalence of rules.Comment: arXiv admin note: substantial text overlap with arXiv:1602.0748

Further advantages of data augmentation on convolutional neural networks

Data augmentation is a popular technique largely used to enhance the training of convolutional neural networks. Although many of its benefits are well known by deep learning researchers and practitioners, its implicit regularization effects, as compared to popular explicit regularization techniques, such as weight decay and dropout, remain largely unstudied. As a matter of fact, convolutional neural networks for image object classification are typically trained with both data augmentation and explicit regularization, assuming the benefits of all techniques are complementary. In this paper, we systematically analyze these techniques through ablation studies of different network architectures trained with different amounts of training data. Our results unveil a largely ignored advantage of data augmentation: networks trained with just data augmentation more easily adapt to different architectures and amount of training data, as opposed to weight decay and dropout, which require specific fine-tuning of their hyperparameters.Comment: Preprint of the manuscript accepted for presentation at the International Conference on Artificial Neural Networks (ICANN) 2018. Best Paper Awar

Quantum machine learning: a classical perspective

Recently, increased computational power and data availability, as well as algorithmic advances, have led machine learning techniques to impressive results in regression, classification, data-generation and reinforcement learning tasks. Despite these successes, the proximity to the physical limits of chip fabrication alongside the increasing size of datasets are motivating a growing number of researchers to explore the possibility of harnessing the power of quantum computation to speed-up classical machine learning algorithms. Here we review the literature in quantum machine learning and discuss perspectives for a mixed readership of classical machine learning and quantum computation experts. Particular emphasis will be placed on clarifying the limitations of quantum algorithms, how they compare with their best classical counterparts and why quantum resources are expected to provide advantages for learning problems. Learning in the presence of noise and certain computationally hard problems in machine learning are identified as promising directions for the field. Practical questions, like how to upload classical data into quantum form, will also be addressed.Comment: v3 33 pages; typos corrected and references adde

Walker-Independent Features for Gait Recognition from Motion Capture Data

MoCap-based human identification, as a pattern recognition discipline, can be optimized using a machine learning approach. Yet in some applications such as video surveillance new identities can appear on the fly and labeled data for all encountered people may not always be available. This work introduces the concept of learning walker-independent gait features directly from raw joint coordinates by a modification of the Fisher’s Linear Discriminant Analysis with Maximum Margin Criterion. Our new approach shows not only that these features can discriminate different people than who they are learned on, but also that the number of learning identities can be much smaller than the number of walkers encountered in the real operation

A comparison of machine learning methods for classification using simulation with multiple real data examples from mental health studies

Background: Recent literature on the comparison of machine learning methods has raised questions about the neutrality, unbiasedness and utility of many comparative studies. Reporting of results on favourable datasets and sampling error in the estimated performance measures based on single samples are thought to be the major sources of bias in such comparisons. Better performance in one or a few instances does not necessarily imply so on an average or on a population level and simulation studies may be a better alternative for objectively comparing the performances of machine learning algorithms. Methods: We compare the classification performance of a number of important and widely used machine learning algorithms, namely the Random Forests (RF), Support Vector Machines (SVM), Linear Discriminant Analysis (LDA) and k-Nearest Neighbour (kNN). Using massively parallel processing on high-performance supercomputers, we compare the generalisation errors at various combinations of levels of several factors: number of features, training sample size, biological variation, experimental variation, effect size, replication and correlation between features. Results: For smaller number of correlated features, number of features not exceeding approximately half the sample size, LDA was found to be the method of choice in terms of average generalisation errors as well as stability (precision) of error estimates. SVM (with RBF kernel) outperforms LDA as well as RF and kNN by a clear margin as the feature set gets larger provided the sample size is not too small (at least 20). The performance of kNN also improves as the number of features grows and outplays that of LDA and RF unless the data variability is too high and/or effect sizes are too small. RF was found to outperform only kNN in some instances where the data are more variable and have smaller effect sizes, in which cases it also provide more stable error estimates than kNN and LDA. Applications to a number of real datasets supported the findings from the simulation study

Top-percentile traffic routing problem by dynamic programming

Multi-homing is a technology used by Internet Service Provider (ISP) to connect to the Internet via different network providers. To make full use of the underlying networks with minimum cost, an optimal routing strategy is required by ISPs. This study investigates the optimal routing strategy in case where network providers charge ISPs according to top-percentile pricing. We call this problem the Top-percentile Traffic Routing Problem (TpTRP). The TpTRP is a multistage stochastic optimisation problem in which routing decision should be made before knowing the amount of traffic that is to be routed in the following time period. The stochastic nature of the problem forms the critical difficulty of this study. In this paper several approaches are investigated in modelling and solving the problem. We begin by modelling the TpTRP as a multi-stage stochastic programming problem, which is hard to solve due to the integer variables introduced by top-percentile pricing. Several simplifications of the original TpTRP are then explored in the second part of this work. Some of these allow analytical solutions which lead to bounds on the achievable optimal solution. We also establish bounds by investigation several "naive" routing policies. In the end, we explore the solution of the TpTRP as a stochastic dynamic programming problem by a discretization of the state space. This SDP model gives us achievable routing policies on medium size instances of TpTRP, which of course improve the naive routing policies. With a classification of the SDP decision table, a crude routing policy for realistic size instances can be developed from the smaller size SDP model. © 2011 Springer Science+Business Media, LLC