Irregular wakes in reaction-diffusion waves

Reaction-diffusion equations have proved to be highly successful models for a wide range of biological and chemical systems, but chaotic solutions have been very rarely documented. We present a new mechanism for generating apparently chaotic spatiotemporal irregularity in such systems, by analysing in detail the bifurcation structure of a particular set of reaction-diffusion equations on an infinite one-dimensional domain, with particular initial conditions. We show that possible solutions include travelling fronts which leave behind either regular or irregular spatiotemporal oscillations. Using a combination of analytical and numerical analysis, we show that the irregular behaviour arises from the instability of oscillations induced by the passage of the front. Finally, we discuss the generality of this mechanism as a way in which spatiotemporal irregularities can arise naturally in reaction-diffusion systems.     

Mapping Properties of a Projection Related to the Helmholtz Equation

We study the continuity properties of a projection derived from a recent characterization of Herglotz Wave Functions in the plane. Herglotz Wave Functions are the entire solutions of the Helmholtz equation which have L²-Far-Field-Pattern. The behavior of this projection is reminiscent of the Disc Multiplier Operator on both L^p and mixed L^p-normed spaces. In particular a Kakeya type set plays a central role in our analysis. As a consequence we answer a question posed by Alvarez, Folch-Gabayet and Pérez-Esteva.     

The phase structure of the two-dimensionalN=2 Wess-Zumino model

We construct a convergent cluster expansion for the two-dimensionalN=2 Wess-Zumino model, in a region of parameter space where there are multiple phase. As a result of this expansion, we are able to construct the infinite volume field theory and demonstrate exponential decay of correlations. We are also able to investigate the different phases of the model, develop the phase diagram, and show that the free energy of each phase vanishes.Supported in part by National Science Foundation grants DMS 90-08827, PHY/DMS 88-16214 and DMS 88-58073Supported in part by National Science Foundation Mathematical Sciences Postdoctoral Research Fellowship DMS 88-07291     

Randomised circular means of Fourier transforms of measures

We explore decay estimates for circular means of the Fourier transform of a measure on in terms of its -dimensional energy. We find new upper bounds for the decay exponent. We also prove sharp estimates for a certain family of randomised versions of this problem.

     

Analytic models for commuting operator tuples on bounded symmetric domains

For a domain in and a Hilbert space of analytic functions on which satisfies certain conditions, we characterize the commuting -tuples of operators on a separable Hilbert space  such that is unitarily equivalent to the restriction of to an invariant subspace, where is the operator -tuple on the Hilbert space tensor product  . For the unit disc and the Hardy space , this reduces to a well-known theorem of Sz.-Nagy and Foias; for a reproducing kernel Hilbert space on such that the reciprocal of its reproducing kernel is a polynomial in and  , this is a recent result of Ambrozie, Müller and the second author. In this paper, we extend the latter result by treating spaces for which ceases to be a polynomial, or even has a pole: namely, the standard weighted Bergman spaces (or, rather, their analytic continuation) on a Cartan domain corresponding to the parameter in the continuous Wallach set, and reproducing kernel Hilbert spaces for which is a rational function. Further, we treat also the more general problem when the operator is replaced by ,  being a certain generalization of a unitary operator tuple. For the case of the spaces on Cartan domains, our results are based on an analysis of the homogeneous multiplication operators on , which seems to be of an independent interest.

     

Absorption Spectrum of H2O in the Range 12 400-14 520 cm

Fourier transform spectra recorded using (a) natural abundance water vapor, (b) H₂¹⁸O-enriched water vapor, and (c) H₂¹⁷O-enriched water vapor are analyzed. The ratio of intensities in three spectra is used to identify 927 lines due to absorption by H₂¹⁸O. Intensities and self-broadening parameters are derived for these lines. Using theoretical linelists, comparisons with previously assigned H₂¹⁶O spectra, and automatic searches for combination differences, 747 lines are assigned. These lines belong to 14 vibrational states in the 3ν+δ and 4ν polyads. Newly determined H₂¹⁸O vibrational band origins include 4ν₁ at 13 793.09 cm⁻¹, 3ν₁+ν₃ at 13 795.40 cm⁻¹, 2ν₁+2ν₃ at 14 188.82 cm⁻¹, ν₁+3ν₃ at 14 276.34 cm⁻¹, and 2ν₂+2ν₂+ν₃ at 13 612.71 cm⁻¹. These results are compared with data in HITRAN.     

A vanishing theorem for supersymmetric quantum field theory and finite size effects in multiphase cluster expansions

We apply cluster expansion methods to to theN=2 Wess-Zumino models in finite volume, in two space-time dimensions. We show that in the region of convergence of the cluster expansion, a vanishing theorem holds for the supercharge of the theory; that is, the dimension of the kernel of the Hamiltonian is equal to the index of the supercharge.Supported in part by National Science Foundation Mathematical Sciences Postdoctoral Research Fellowship DMS 90-07206Supported in part by National Science Foundation Mathematical Sciences Postodoctoral Research Fellowship DmS 88-07291     

Automated Spleen Injury Detection Using 3D Active Contours and Machine Learning

The spleen is one of the most frequently injured organs in blunt abdominal trauma. Computed tomography (CT) is the imaging modality of choice to assess patients with blunt spleen trauma, which may include lacerations, subcapsular or parenchymal hematomas, active hemorrhage, and vascular injuries. While computer-assisted diagnosis systems exist for other conditions assessed using CT scans, the current method to detect spleen injuries involves the manual review of scans by radiologists, which is a time-consuming and repetitive process. In this study, we propose an automated spleen injury detection method using machine learning. CT scans from patients experiencing traumatic injuries were collected from Michigan Medicine and the Crash Injury Research Engineering Network (CIREN) dataset. Ninety-nine scans of healthy and lacerated spleens were split into disjoint training and test sets, with random forest (RF), naive Bayes, SVM, k-nearest neighbors (k-NN) ensemble, and subspace discriminant ensemble models trained via 5-fold cross validation. Of these models, random forest performed the best, achieving an Area Under the receiver operating characteristic Curve (AUC) of 0.91 and an F1 score of 0.80 on the test set. These results suggest that an automated, quantitative assessment of traumatic spleen injury has the potential to enable faster triage and improve patient outcomes.     

Socio-Economic Impact of the Covid-19 Pandemic in the U.S.

This paper proposes a dynamic cascade model to investigate the systemic risk posed by sector-level industries within the U.S. inter-industry network. We then use this model to study the effect of the disruptions presented by Covid-19 on the U.S. economy. We construct a weighted digraph G = (V,E,W) using the industry-by-industry total requirements table for 2018, provided by the Bureau of Economic Analysis (BEA). We impose an initial shock that disrupts the production capacity of one or more industries, and we calculate the propagation of production shortages with a modified Cobb–Douglas production function. For the Covid-19 case, we model the initial shock based on the loss of labor between March and April 2020 as reported by the Bureau of Labor Statistics (BLS). The industries within the network are assigned a resilience that determines the ability of an industry to absorb input losses, such that if the rate of input loss exceeds the resilience, the industry fails, and its outputs go to zero. We observed a critical resilience, such that, below this critical value, the network experienced a catastrophic cascade resulting in total network collapse. Lastly, we model the economic recovery from June 2020 through March 2021 using BLS data.