arXiv subjects

M. Drew LaMar

Publications and source records attributed to M. Drew LaMar.

8 recordsLinked to original sources

arXiv2023

Using Science Education Gateways to improve undergraduate STEM education: The QUBES Platform as a case study

The QUBES platform was conceived as a "science education gateway" and designed to accelerate innovation in undergraduate STEM education. The technical infrastructure was purpose built to provide more equitable access to professional resources, support learning that reflects authentic science, and promote open education practices. Four platform services (OER Library Access; Professional Learning; Partner Support; and Customizable Workspaces) support overlapping faculty user communities, provide multiple points of entry, and enable manifold use case scenarios. The integrated nature of the platform makes it possible to collect, curate, and disseminate a diverse array of reform resources in a scalable and sustainable manner. We believe that the QUBES platform has the capacity to broaden participation in scholarship around teaching and learning and, furthermore, that it can help to lower faculty barriers to the adoption of reform practices. The role of cyberinfrastructure in undergraduate STEM education is generally underappreciated and warrants further exploration.

cs.CY↗

arXiv2017

A "Rule of Five" Framework for Models and Modeling to Unify Mathematicians and Biologists and Improve Student Learning

Despite widespread calls for the incorporation of mathematical modeling into the undergraduate biology curriculum, there is lack of a common understanding around the definition of modeling, which inhibits progress. In this paper, we extend the "Rule of Four," initially used in calculus reform efforts, to a framework for models and modeling that is inclusive of varying disciplinary definitions of each. This unifying framework allows us to both build on strengths that each discipline and its students bring, but also identify gaps in modeling activities practiced by each discipline. We also discuss benefits to student learning and interdisciplinary collaboration.

math.HO↗

arXiv2014

Algorithm and Complexity for a Network Assortativity Measure

We show that finding a graph realization with the minimum Randić index for a given degree sequence is solvable in polynomial time by formulating the problem as a minimum weight perfect b-matching problem. However, the realization found via this reduction is not guaranteed to be connected. Approximating the minimum weight b-matching problem subject to a connectivity constraint is shown to be NP-Hard. For instances in which the optimal solution to the minimum Randić index problem is not connected, we describe a heuristic to connect the graph using pairwise edge exchanges that preserves the degree sequence. In our computational experiments, the heuristic performs well and the Randić index of the realization after our heuristic is within 3% of the unconstrained optimal value on average. Although we focus on minimizing the Randić index, our results extend to maximizing the Randić index as well. Applications of the Randić index to synchronization of neuronal networks controlling respiration in mammals and to normalizing cortical thickness networks in diagnosing individuals with dementia are provided.

math.CO↗

arXiv2014

Split digraphs

We generalize the class of split graphs to the directed case and show that these split digraphs can be identified from their degree sequences. The first degree sequence characterization is an extension of the concept of splittance to directed graphs, while the second characterization says a digraph is split if and only if its degree sequence satisfies one of the Fulkerson inequalities (which determine when an integer-pair sequence is digraphic) with equality.

cs.DM↗

arXiv2012

Threshold Digraphs

A digraph whose degree sequence has a unique vertex labeled realization is called threshold. In this paper we present several characterizations of threshold digraphs and their degree sequences, and show these characterizations to be equivalent. One of the characterizations is new, and allows for a shorter proof of the equivalence of the two known characterizations as well as proving the final characterization which appears without proof in the literature. Using this result, we obtain a new, short proof of the Fulkerson-Chen theorem on degree sequences of general digraphs.

math.CO↗

arXiv2010

Signal processing of acoustic signals in the time domain with an active nonlinear nonlocal cochlear model

A two space dimensional active nonlinear nonlocal cochlear model is formulated in the time domain to capture nonlinear hearing effects such as compression, multi-tone suppression and difference tones. The micromechanics of the basilar membrane (BM) are incorporated to model active cochlear properties. An active gain parameter is constructed in the form of a nonlinear nonlocal functional of BM displacement. The model is discretized with a boundary integral method and numerically solved using an iterative second order accurate finite difference scheme. A block matrix structure of the discrete system is exploited to simplify the numerics with no loss of accuracy. Model responses to multiple frequency stimuli are shown in agreement with hearing experiments. A nonlinear spectrum is computed from the model, and compared with FFT spectrum for noisy tonal inputs. The discretized model is efficient and accurate, and can serve as a useful auditory signal processing tool.

q-bio.QM↗

arXiv2010

Algorithms for realizing degree sequences of directed graphs

The Havel-Hakimi algorithm for constructing realizations of degree sequences for undirected graphs has been used extensively in the literature. A result by Kleitman and Wang extends the Havel-Hakimi algorithm to degree sequences for directed graphs. In this paper we go a step further and describe a modification of Kleitman and Wang's algorithm that is a more natural extension of Havel-Hakimi's algorithm, in the sense that our extension can be made equivalent to Havel-Hakimi's algorithm when the degree sequence has equal in and out degrees and an even degree sum. We identify special degree sequences, called directed 3-cycle anchored, that are ill-defined for the algorithm and force a particular local structure on all directed graph realizations. We give structural characterizations of these realizations, as well as characterizations of the ill-defined degree sequences, leading to a well-defined algorithm.

math.CO↗

arXiv2002

Modeling Vocal Fold Motion with a New Hydrodynamic Semi-Continuum Model

Vocal fold (VF) motion is a fundamental process in voice production, and is also a challenging problem for direct numerical computation because the VF dynamics depend on nonlinear coupling of air flow with the response of elastic channels (VF), which undergo opening and closing, and induce internal flow separation. A traditional modeling approach makes use of steady flow approximation or Bernoulli's law which is known to be invalid during VF opening. We present a new hydrodynamic semi-continuum system for VF motion. The airflow is modeled by a quasi-one dimensional continuum aerodynamic system, and the VF by a classical lumped two mass system. The reduced flow system contains the Bernoulli's law as a special case, and is derivable from the two dimensional compressible Navier-Stokes equations. Since we do not make steady flow approximation, we are able to capture transients and rapid changes of solutions, e.g. the double pressure peaks at opening and closing stages of VF motion consistent with experimental data. We demonstrate numerically that our system is robust, and models in-vivo VF oscillation more physically. It is also much simpler than a full two-dimensional Navier-Stokes system.

nlin.PS↗