Performance bounds for Reduced Order Models with Application to Parametric Transport

The Kolmogorov $n$-width is an established benchmark to judge the performance of reduced basis and similar methods that produce linear reduced spaces. Although immensely successful in the elliptic regime, this width, shows unsatisfactory slow convergence rates for transport dominated problems. While this has triggered a large amount of work on nonlinear model reduction techniques, we are lacking a benchmark to evaluate their optimal performance. Nonlinear benchmarks like manifold/stable/Lipschitz width applied to the solution manifold are often trivial if the degrees of freedom exceed the parameter dimension and ignore desirable structure as offline/online decompositions. In this paper, we show that the same benchmarks applied to the full reduced order model pipeline from PDE to parametric quantity of interest provide non-trivial benchmarks and we prove lower bounds for transport equations

Time as a limited resource: Communication Strategy in Mobile Phone Networks

We used a large database of 9 billion calls from 20 million mobile users to examine the relationships between aggregated time spent on the phone, personal network size, tie strength and the way in which users distributed their limited time across their network (disparity). Compared to those with smaller networks, those with large networks did not devote proportionally more time to communication and had on average weaker ties (as measured by time spent communicating). Further, there were not substantially different levels of disparity between individuals, in that mobile users tend to distribute their time very unevenly across their network, with a large proportion of calls going to a small number of individuals. Together, these results suggest that there are time constraints which limit tie strength in large personal networks, and that even high levels of mobile communication do not fundamentally alter the disparity of time allocation across networks.Comment: 10 pages, 3 figures. Accepted for publication in Social Network

The ice-breaker effect: Singing mediates fast social bonding

It has been proposed that singing evolved to facilitate social cohesion. However, it remains unclear whether bonding arises out of properties intrinsic to singing or whether any social engagement can have a similar effect. Furthermore, previous research has used one-off singing sessions without exploring the emergence of social bonding over time. In this semi-naturalistic study, we followed newly formed singing and non-singing (crafts or creative writing) adult education classes over seven months. Participants rated their closeness to their group and their affect, and were given a proxy measure of endorphin release, before and after their class, at three timepoints (months 1, 3 and 7). We show that although singers and non-singers felt equally connected by timepoint 3, singers experienced much faster bonding: singers demonstrated a significantly greater increase in closeness at timepoint 1, but the more gradual increase shown by non-singers caught up over time. This represents the first evidence for an ‘ice-breaker effect’ of singing in promoting fast cohesion between unfamiliar individuals, which bypasses the need for personal knowledge of group members gained through prolonged interaction. We argue that singing may have evolved to quickly bond large human groups of relative strangers, potentially through encouraging willingness to coordinate by enhancing positive affect

Unsupervised machine learning algorithms as support tools in molecular dynamics simulations

Unsupervised Machine Learning algorithms such as clustering offer convenient features for data analysis tasks. When combined with other tools like visualization software, the possibilities of automated analysis may be greatly enhanced. In the context of Molecular Dynamics simulations, in particular asymmetric granular collisions which typically consist of thousands of particles, it is key to distinguish the fragments in which the system is divided after a collision for classification purposes. In this work we explore the unsupervised Machine Learning algorithms k-means and AGNES to distinguish groups of particles in molecular dynamics simulations, with encouraging results according to performance metrics such as accuracy and precision. We also report computational times for each algorithm, where k-means results faster than AGNES. Finally, we delineate the integration of these type of algorithms with a well-known analysis and visualization tool widely used in the physics community.Sociedad Argentina de Informática e Investigación Operativ

In-group Bias and the Police: Evidence from Award Nominations

This paper examines the impact of in-group bias on the internal dynamics of a police department. Prior studies have documented racial bias in policing, but little is known about bias against officers due to lack of available data. We construct a novel panel dataset of Chicago Police Department officers, with detailed information on officer characteristics and work productivity. Exploiting quasi-random variation in supervisor assignment, we find that white supervisors are less likely to nominate black officers than white or Hispanic officers. We find weaker evidence that male supervisors are less likely to nominate female officers than male officers. We explore several theories of discrimination that can explain our main findings. Requiring interaction between supervisors and officers reduces the minority nomination gap, but white supervisors still exhibit in-group favoritism. Our findings suggest departments should focus on policies that address in-group bias due to its effect on career advancement

Relating on-shell and off-shell formalism in perturbative quantum field theory

In the on-shell formalism (mostly used in perturbative quantum field theory) the entries of the time ordered product T are on-shell fields (i.e. the basic fields satisfy the free field equations). With that, (multi)linearity of T is incompatible with the Action Ward identity. This can be circumvented by using the off-shell formalism in which the entries of T are off-shell fields. To relate on- and off-shell formalism correctly, a map sigma from on-shell fields to off-shell fields was introduced axiomatically by Duetsch and Fredenhagen. In that paper it was shown that, in the case of one real scalar field in N=4 dimensional Minkowski space, these axioms have a unique solution. However, this solution was given there only recursively. We solve this recurrence relation and give a fully explicit expression for sigma in the cases of the scalar, Dirac and gauge fields for arbitrary values of the dimension N.Comment: The case of gauge fields was added. 16 page

On a three-dimensional and two four-dimensional oncolytic viro-therapy models

We revisit here and carry out further works on tumor-virotherapy compartmental models of [Tian, 2011, Wang et al., 2013, Phan and Tian, 2017, Guo et al., 2019]. The results of these papers are only slightly pushed further. However, what is new is the fact that we make public our electronic notebooks, since we believe that easy electronic reproducibility is crucial in an era in which the role of the software becomes very important.Comment: 41 pages, 15 figure

Tracking system options for future altimeter satellite missions

Follow-on missions to provide continuity in the observation of the sea surface topography once the successful TOPEX/POSEIDON (T/P) oceanographic satellite mission has ended are discussed. Candidates include orbits which follow the ground tracks of T/P GEOSAT or ERS-1. The T/P precision ephemerides, estimated to be near 3 cm root-mean-square, demonstrate the radial orbit accuracy that can be achieved at 1300 km altitude. However, the radial orbit accuracy which can be achieved for a mission at the 800 km altitudes of GEOSAT and ERS-1 has not been established, and achieving an accuracy commensurate with T/P will pose a great challenge. This investigation focuses on the radial orbit accuracy that can be achieved for a mission in the GEOSAT orbit. Emphasis is given to characterizing the effects of force model errors on the estimated radial orbit accuracy, particularly those due to gravity and drag. The importance of global, continuous tracking of the satellite for reduction in these sources of orbit error is demonstrated with simulated GPS tracking data. A gravity tuning experiment is carried out to show how the effects of gravity error may be reduced. Assuming a GPS flight receiver with a full-sky tracking capability, the simulation results indicate that a 5 cm radial orbit accuracy for an altimeter satellite in GEOSAT orbit should be achievable during low-drag atmospheric conditions and after an acceptable tuning of the gravity model

Boundary Flows in general Coset Theories

In this paper we study the boundary effects for off-critical integrable field theories which have close analogs with integrable lattice models. Our models are the $SU(2)_{k}\otimes SU(2)_{l}/SU(2)_{k+l}$ coset conformal field theories perturbed by integrable boundary and bulk operators. The boundary interactions are encoded into the boundary reflection matrix. Using the TBA method, we verify the flows of the conformal BCs by computing the boundary entropies. These flows of the BCs have direct interpretations for the fusion RSOS lattice models. For super CFTs ($k=2$) we show that these flows are possible only for the Neveu-Schwarz sector and are consistent with the lattice results. The models we considered cover a wide class of integrable models. In particular, we show how the the impurity spin is screened by electrons for the $k$-channel Kondo model by taking $l\to\infty$ limit. We also study the problem using an independent method based on the boundary roaming TBA. Our numerical results are consistent with the boundary CFTs and RSOS TBA analysis.Comment: 22 pages, 3 postscript figure file