Pants decompositions of random surfaces

Our goal is to show, in two different contexts, that "random" surfaces have large pants decompositions. First we show that there are hyperbolic surfaces of genus $g$ for which any pants decomposition requires curves of total length at least $g^{7/6 - \epsilon}$. Moreover, we prove that this bound holds for most metrics in the moduli space of hyperbolic metrics equipped with the Weil-Petersson volume form. We then consider surfaces obtained by randomly gluing euclidean triangles (with unit side length) together and show that these surfaces have the same property.Comment: 16 pages, 4 figure

Pants Decompositions of Random Surfaces

Our goal is to show, in two different contexts, that "random” surfaces have large pants decompositions. First we show that there are hyperbolic surfaces of genus g for which any pants decomposition requires curves of total length at least g 7/6−ε . Moreover, we prove that this bound holds for most metrics in the moduli space of hyperbolic metrics equipped with the Weil-Petersson volume form. We then consider surfaces obtained by randomly gluing euclidean triangles (with unit side length) together and show that these surfaces have the same propert

Send Your Holy Spirit: Reflections on the Theology of Virtual Eucharist in Times of COVID-19

This article explores the issues concerning the intersection of spirituality, sacramentality, proximity, and health safety in light of extreme circumstances such as the current COVID-19 pandemic. We begin by tracing the origins of the sacrament of the Eucharist, including the Eucharistic agency in the lives of the community. The second part of the analysis discusses the nature of community and how it relates to breaking bread and sharing wine. The last part of the article centers on community practice within the context of queering ecclesiology and rites through two examples, one in Latin America and the other in Asia

DyMo: Dynamic Monitoring of Large Scale LTE-Multicast Systems

LTE evolved Multimedia Broadcast/Multicast Service (eMBMS) is an attractive solution for video delivery to very large groups in crowded venues. However, deployment and management of eMBMS systems is challenging, due to the lack of realtime feedback from the User Equipment (UEs). Therefore, we present the Dynamic Monitoring (DyMo) system for low-overhead feedback collection. DyMo leverages eMBMS for broadcasting Stochastic Group Instructions to all UEs. These instructions indicate the reporting rates as a function of the observed Quality of Service (QoS). This simple feedback mechanism collects very limited QoS reports from the UEs. The reports are used for network optimization, thereby ensuring high QoS to the UEs. We present the design aspects of DyMo and evaluate its performance analytically and via extensive simulations. Specifically, we show that DyMo infers the optimal eMBMS settings with extremely low overhead, while meeting strict QoS requirements under different UE mobility patterns and presence of network component failures. For instance, DyMo can detect the eMBMS Signal-to-Noise Ratio (SNR) experienced by the 0.1% percentile of the UEs with Root Mean Square Error (RMSE) of 0.05% with only 5 to 10 reports per second regardless of the number of UEs

Krylov Complexity in Free and Interacting Scalar Field Theories with Bounded Power Spectrum

We study a notion of operator growth known as Krylov complexity in free and interacting massive scalar quantum field theories in $d$-dimensions at finite temperature. We consider the effects of mass, one-loop self-energy due to perturbative interactions, and finite ultraviolet cutoffs in continuous momentum space. These deformations change the behavior of Lanczos coefficients and Krylov complexity and induce effects such as the "staggering" of the former into two families, a decrease in the exponential growth rate of the latter, and transitions in their asymptotic behavior. We also discuss the relation between the existence of a mass gap and the property of staggering, and the relation between our ultraviolet cutoffs in continuous theories and lattice theories.Comment: 44 pages, 12 figures. Comments are welcome. V2: Note added at the end of the Introduction. Added references and footnotes, corrected typos, modified Figure 5, improved argument in Sec. 2.2, added a discussion of large-N limit in Sec. 3.3 and added an additional future direction in Sec.

A conceptual model for anticipating the impact of landscape evolution on groundwater recharge in degrading permafrost environments

Temperatures in the arctic and subarctic are rising at more than twice the rate of the global average, driving the accelerated thawing of permafrost across the region. The impacts of permafrost degradation have been studied in the discontinuous permafrost zone at Umiujaq, in northern Quebec, Canada, for over 30 years, but the effects of changing land cover on groundwater recharge is not well understood. The water table fluctuation method was used to compute groundwater recharge using four years of water level data and soil moisture readings from five field sites characteristic of different stages of permafrost degradation and vegetation invasion. Results indicate that as vegetation grows taller, groundwater recharge increases, likely due to increased snow thickness. Results were then combined with a preexisting conceptual model that describes the evolution from tundra to shrubland and forests to create a new model for describing how groundwater recharge is affected by landscape evolution

Fragmentation and Evolution of Molecular Clouds. II: The Effect of Dust Heating

We investigate the effect of heating by luminosity sources in a simulation of clustered star formation. Our heating method involves a simplified continuum radiative transfer method that calculates the dust temperature. The gas temperature is set by the dust temperature. We present the results of four simulations, two simulations assume an isothermal equation of state and the two other simulations include dust heating. We investigate two mass regimes, i.e., 84 Msun and 671 Msun, using these two different energetics algorithms. The mass functions for the isothermal simulations and simulations which include dust heating are drastically different. In the isothermal simulation, we do not form any objects with masses above 1 Msun. However, the simulation with dust heating, while missing some of the low-mass objects, forms high-mass objects (~20 Msun) which have a distribution similar to the Salpeter IMF. The envelope density profiles around the stars formed in our simulation match observed values around isolated, low-mass star-forming cores. We find the accretion rates to be highly variable and, on average, increasing with final stellar mass. By including radiative feedback from stars in a cluster-scale simulation, we have determined that it is a very important effect which drastically affects the mass function and yields important insights into the formation of massive stars.Comment: 19 pages, 28 figures. See http://www.astro.phy.ulaval.ca/staff/hugo/dust/ms_dust.big.pdf for high resolution version of documen

Preliminary Analysis: Am-241 RHU/TEG Electric Power Source for Nanosatellites

The Februay 2013 Space Works Commercial report indicates a strong increase in nano/microsatellite (1-50 kg) launch demand globally in future years. Nanosatellites (NanoSats) are small spacecraft in the 1-10 kg range, which present a simple, low-cost option for developing quickly-deployable satellites. CubeSats, a special category of NanoSats, are even being considered for interplanetary missions. However, the small dimensions of CubeSats and the limited mass of the NanoSat class in general place limits of capability on their electrical power systems (especially where typical power sources such as solar panels are considered) and stored energy reserves; restricting the power budget and overall functionality. For example, leveraging NanoSat clusters for computationally intensive problems that are solved collectively becomes more challenging with power related restrictions on communication and data-processing. Further, interplanetary missions that would take NanoSats far from the sun, make the use of solar panels less effective as a power source as their required area would become quite large. To overcome these limitations, americium 241 (Am-241) has been suggested as a low power source option. The Idaho National Laboratory, Center for Space Nuclear Research reports that: (Production) requires small quantities of isotope - 62.5 g of Pu-238; 250 g Am- 241 (for 5 We); Am-241 is available at around 1 kg/yr commercially; Am-241 produces 59 kev gammas which are stopped readily by tungsten so the radiation field is very low. Whereby, an Am-241 source could be placed in among the instruments and the waste heat used to heat the platform; and amounts of isotope are so low that launch approval may be easier, especially with tungsten encapsulation. As further reported, Am-241 has a half-life that is approximately five times greater than that of Pu- 238 and it has been determined that the neutron yield of a 241-AmO(sub 2) source is approximately an order of magnitude lower than that of a 238-PuO(sub 2) source of equal mass and degree of (sup 16)O enrichment. Also it has been demonstrated that shielded heat sources fuelled by oxygen-enriched 238-PuO(sub 2) have masses that are up to 10 times greater than those fuelled by oxygenenriched 241-AmO(sub 2) with equivalent thermal power outputs and neutron dose rates at 1 m radii. For these reasons, Am-241 is well suited to missions that demand long duration electrical power output, such as deep spaceflight missions and similar missions that use radiation-hard electronics and instrumentation that are less susceptible to neutron radiation damage