Diffraction of return time measures

Letting $T$ denote an ergodic transformation of the unit interval and letting $f \colon [0,1)\to \mathbb{R}$ denote an observable, we construct the $f$-weighted return time measure $\mu_y$ for a reference point $y\in[0,1)$ as the weighted Dirac comb with support in $\mathbb{Z}$ and weights $f \circ T^z(y)$ at $z\in\mathbb{Z}$, and if $T$ is non-invertible, then we set the weights equal to zero for all $z < 0$. Given such a Dirac comb, we are interested in its diffraction spectrum which emerges from the Fourier transform of its autocorrelation and analyse it for the dependence on the underlying transformation. For certain rapidly mixing transformations and observables of bounded variation, we show that the diffraction of $\mu_{y}$ consists of a trivial atom and an absolutely continuous part, almost surely with respect to $y$. This contrasts what occurs in the setting of regular model sets arising from cut and project schemes and deterministic incommensurate structures. As a prominent example of non-mixing transformations, we consider the family of rigid rotations $T_{\alpha} \colon x \to x + \alpha \bmod{1}$ with rotation number $\alpha \in \mathbb{R}^+$. In contrast to when $T$ is mixing, we observe that the diffraction of $\mu_{y}$ is pure point, almost surely with respect to $y$. Moreover, if $\alpha$ is irrational and the observable $f$ is Riemann integrable, then the diffraction of $\mu_{y}$ is independent of $y$. Finally, for a converging sequence $(\alpha_{i})_{i \in \mathbb{N}}$ of rotation numbers, we provide new results concerning the limiting behaviour of the associated diffractions.Comment: 11 pages, 2 figure

Regularity of aperiodic minimal subshifts

At the turn of this century Durand, and Lagarias and Pleasants established that key features of minimal subshifts (and their higher-dimensional analogues) to be studied are linearly repetitive, repulsive and power free. Since then, generalisations and extensions of these features, namely $\alpha$-repetitive, $\alpha$-repulsive and $\alpha$-finite ($\alpha \geq 1$), have been introduced and studied. We establish the equivalence of $\alpha$-repulsive and $\alpha$-finite for general subshifts over finite alphabets. Further, we studied a family of aperiodic minimal subshifts stemming from Grigorchuk's infinite $2$-group $G$. In particular, we show that these subshifts provide examples that demonstrate $\alpha$-repulsive (and hence $\alpha$-finite) is not equivalent to $\alpha$-repetitive, for $\alpha > 1$. We also give necessary and sufficient conditions for these subshifts to be $\alpha$-repetitive, and $\alpha$-repulsive (and hence $\alpha$-finite). Moreover, we obtain an explicit formula for their complexity functions from which we deduce that they are uniquely ergodic.Comment: 15 page

Efficient Representations of Object Geometry for Reinforcement Learning of Interactive Grasping Policies

Grasping objects of different shapes and sizes - a foundational, effortless skill for humans - remains a challenging task in robotics. Although model-based approaches can predict stable grasp configurations for known object models, they struggle to generalize to novel objects and often operate in a non-interactive open-loop manner. In this work, we present a reinforcement learning framework that learns the interactive grasping of various geometrically distinct real-world objects by continuously controlling an anthropomorphic robotic hand. We explore several explicit representations of object geometry as input to the policy. Moreover, we propose to inform the policy implicitly through signed distances and show that this is naturally suited to guide the search through a shaped reward component. Finally, we demonstrate that the proposed framework is able to learn even in more challenging conditions, such as targeted grasping from a cluttered bin. Necessary pre-grasping behaviors such as object reorientation and utilization of environmental constraints emerge in this case. Videos of learned interactive policies are available at https://maltemosbach.github. io/geometry_aware_grasping_policies

On the Stability of Fine-tuning BERT: Misconceptions, Explanations, and Strong Baselines

Fine-tuning pre-trained transformer-based language models such as BERT has become a common practice dominating leaderboards across various NLP benchmarks. Despite the strong empirical performance of fine-tuned models, fine-tuning is an unstable process: training the same model with multiple random seeds can result in a large variance of the task performance. Previous literature (Devlin et al., 2019; Lee et al., 2020; Dodge et al., 2020) identified two potential reasons for the observed instability: catastrophic forgetting and small size of the fine-tuning datasets. In this paper, we show that both hypotheses fail to explain the fine-tuning instability. We analyze BERT, RoBERTa, and ALBERT, fine-tuned on three commonly used datasets from the GLUE benchmark, and show that the observed instability is caused by optimization difficulties that lead to vanishing gradients. Additionally, we show that the remaining variance of the downstream task performance can be attributed to differences in generalization where fine-tuned models with the same training loss exhibit noticeably different test performance. Based on our analysis, we present a simple but strong baseline that makes fine-tuning BERT-based models significantly more stable than the previously proposed approaches. Code to reproduce our results is available online: https://github.com/uds-lsv/bert-stable-fine-tuning

State Differences in the Application of Medical Frailty Under the Affordable Care Act: 2017 Update

This poster details the effects of Medicaid coverage expansion since the Affordable Care Act began the inclusion of childless adults below the poverty level. This change has created a divide in how different states handle Medicaid coverage and this study examines how states undergoing Medicaid expansion differ in their treatment of individuals who may need the extra benefits offered by traditional Medicaid. Researchers studied 14 different states and found substantial differences in how each state assessed eligibility for Medicaid coverage. In states like Massachusetts, individuals who were applying for disability-based Medicaid could self-declare that they had special medical needs, while in other states like North Dakota, applicants are given a questionnaire which is evaluated by a medical professional and then reviewed by the State Department of Human Services to determine Medicaid eligibility

Construction and characterization of a recombinant tripartite enzyme, galactose dehydrogenase/β-galactosidase/galactokinase

AbstractThe in-frame gene fusion between 3 enzymes, galactose dehydrogenase, β-galactosidase and galactokinase, is described. The purified artificial tripartite enzyme displayed all three enzymic activities. Two major forms of the hybrid protein were found, consisting of 4 and 8 subunits respectively, but other forms could also be identified. Each subunit was made up of one monomer each of galactose dehydrogenase, β-galactosidase and galactokinase. Proximity effects exhibited by the hybrid enzyme could be demonstrated using [14C]galactose as a reporter molecule

Outlier analysis for a silicon nanoparticle population balance model

© 2016 The Combustion Institute We assess the impact of individual experimental observations on a multivariate population balance model for the formation of silicon nanoparticles from the thermal decomposition of silane by means of basic regression influence diagnostics. The nanoparticle model is closely related to one which has been used to simulate soot formation in flames and includes morphological and compositional details which allow re presentation of primary particles within aggregates, and of coagulation, surface growth, and sintering processes. Predicted particle size distributions are optimised against 19 experiments across ranges of initial temperature, pressure, residence time, and initial silane mass fraction. The influence of each experimental observation on the model parameter estimates is then quantified using the Cook distance and DFBETA measures. Seven model parameters are included in the analysis, with five Arrhenius pre-exponential factors in the gas-phase kinetic rate expressions, and two kinetic rate constants in the population balance model. The analysis highlights certain experimental conditions and kinetic parameters which warrant closer inspection due to large influence, thus providing clues as to which aspects of the model require improvement. We find the insights provided can be useful for future model development and planning of experiments.This work was partly funded by the Cambridge Australia Trust, by the National Research Foundation (NRF), Prime Minister’s Office, Singapore under its Campus for Research Excellence and Technological Enterprise (CREATE) programme, and by the European Union Horizon 2020 Research and Innovation Programme under Grant agreement 646121

State Differences in the Application of Medical Frailty under the Affordable Care Act

This poster explains a study that examines how states undergoing Medicaid expansion differ in their treatment of the “medically frail” population. The medically frail are individuals who may need the extra benefits offered by traditional Medicaid. The results provide needed information to policymakers that are interested in improving access among vulnerable populations in the 23 states that have not yet implemented Medicaid expansion, but may do so in the future. While regulations provide categories that qualify for medical frailty, each state is free to use their own method of determining who meets the definition. There is a need for ongoing study to determine whether state differences in how medical frailty is addressed are associated with differences in access by persons with high medical need. Presented at the AcademyHealth Annual Research Meeting