Search for: All records

Buchweitz-Greuel-Schreyer conjectured in 1987 a lower bound on the ranks of matrix factorizations over certain local hypersurface rings [Invent. Math. 88 (1987), pp. 165–182]. We study a graded version of this conjecture, and we show that it implies a novel conjecture concerning the cohomology of sheaves over non-Fano projective hypersurfaces. 

We present a case study of changing campus ecologies for students in life science courses at an urban community college. Through analysis of six surveys (n = 583) over a three-year period, we note how changes in students’ coursework affect their virtual and physical developmental ecologies. Students’ abilities to access peers for academic and social support declined and rose relative to social distancing activities, but upon return even when students could identify accessible peers, they expressed a lack of knowledge for how to form social and academic relationships on campus. Changes in social-distancing policy shaped students’ access to socio-academic integrative moments. Students expressed appreciation for their instructors during the transition to online learning, but encountered a number of social and technical roadblocks to participating effectively. Competing demands on their time, lack of access to the internet and digital tools, constraints produced by digital tools like proctoring software, and a general frustration with the amount of “screen time” that the transition required all undermined students’ formation of learning communities. The lack of third spaces – publicly accessible space that is neither home nor work – created a challenge for students who could not demarcate academic space in their homes. Among life science students were a considerable number who worked in health sciences, a field where pandemic-related burnout was considerably higher. Many of these students expressed plans to slow down their education or leave community college entirely. We identify implications for practice including strategies for instructors to foster community in their classroom. 

Abstract Recent studies have highlighted the importance of accurate meteorological conditions for urban transport and dispersion calculations. In this work, we present a novel scheme to compute the meteorological input in the Quick Urban & Industrial Complex () diagnostic urban wind solver to improve the characterization of upstream wind veer and shear in the Atmospheric Boundary Layer (ABL). The new formulation is based on a coupled set of Ordinary Differential Equations (ODEs) derived from the Reynolds Averaged Navier–Stokes (RANS) equations, and is fast to compute. Building upon recent progress in modeling the idealized ABL, we include effects from surface roughness, turbulent stress, Coriolis force, buoyancy and baroclinicity. We verify the performance of the new scheme with canonical Large Eddy Simulation (LES) tests with the GPU-accelerated FastEddyEquation missing<#comment/>solver in neutral, stable, unstable and baroclinic conditions with different surface roughness. Furthermore, we evaluate QUIC calculations with and without the new inflow scheme with real data from the Urban Threat Dispersion (UTD) field experiment, which includes Lidar-based wind measurements as well as concentration observations from multiple outdoor releases of a non-reactive tracer in downtown New York City. Compared to previous inflow capabilities that were limited to a constant wind direction with height, we show that the new scheme can model wind veer in the ABL and enhance the prediction of the surface cross-isobaric angle, improving evaluation statistics of simulated concentrations paired in time and space with UTD measurements. 

Abstract A foundational principle in the study of modules over standard graded polynomial rings is that geometric positivity conditions imply vanishing of Betti numbers. The main goal of this paper is to determine the extent to which this principle extends to the nonstandard ‐graded case. In this setting, the classical arguments break down, and the results become much more nuanced. We introduce a new notion of Castelnuovo–Mumford regularity and employ exterior algebra techniques to control the shapes of nonstandard ‐graded minimal free resolutions. Our main result reveals a unique feature in the nonstandard ‐graded case: the possible degrees of the syzygies of a graded module in this setting are controlled not only by its regularity, but also by its depth. As an application of our main result, we show that given a simplicial projective toric variety and a module over its coordinate ring, the multigraded Betti numbers of are contained in a particular polytope when satisfies an appropriate positivity condition.