The Law of Interspersion and the Principle of Edge: Old Arguments and a New Synthesis

Leopold’s interspersion hypothesis has experienced fluctuating acceptance, opposition and neglect due to its unintentional ambiguous description and seemingly simplistically universal application. Originally developed to describe the positive association between animal density and habitat heterogeneity in the landscape, the hypothesis has been mischaracterized as the principle of edge resulting from Guthery and Bingham’s (1992) assertion that the interspersion hypothesis could be modeled by the amount of ‘high contrast’ edge and that edge density and interspersion were synonymous. We contend that Leopold’s original intention was not to promote more edge density is always better but rather to promote interspersion of habitat types within landscapes suitable for bobwhite. We argue that edge density and interspersion are different metrics to describe landscape configuration but are incorrectly used interchangeably. These metrics reflect two unique hypotheses regarding bobwhite relationships with landscape structure. We used a northern bobwhite (Colinus virginianus) monitoring dataset to demonstrate the importance of the proper use of edge density and interspersion metrics. We modeled bobwhite abundance at 160 sites across 6 years using an open N-mixture model. We used Fragstats to calculate edge density and interspersion at the landscape scale. These metrics were not correlated (r \u3c .10) indicating they describe unique aspects of configurational heterogeneity. Both metrics had positive but varying effects on bobwhite abundance. We recommend scientists have explicit a priori hypothesis regarding the differential effects of edge density and interspersion

Prediction of pelvic lymph node metastases and PSMA PET positive pelvic lymph nodes with multiparametric MRI and clinical information in primary staging of prostate cancer

PURPOSE To compare the accuracy of multiparametric MRI (mpMRI), $^{68}$Ga-PSMA PET and the Briganti 2019 nomogram in the prediction of metastatic pelvic lymph nodes (PLN) in prostate cancer, to assess the accuracy of mpMRI and the Briganti nomogram in prediction of PET positive PLN and to investigate the added value of quantitative mpMRI parameters to the Briganti nomogram. METHOD This retrospective IRB-approved study included 41 patients with prostate cancer undergoing mpMRI and $^{68}$Ga-PSMA PET/CT or MR prior to prostatectomy and pelvic lymph node dissection. A board-certified radiologist assessed the index lesion on diffusion-weighted (Apparent Diffusion Coefficient, ADC; mean/volume), T2-weighted (capsular contact length, lesion volume/maximal diameters) and contrast-enhanced (iAUC, k$_{ep}$, K$^{trans}$, v$_{e}$) sequences. The probability for metastatic pelvic lymph nodes was calculated using the Briganti 2019 nomogram. PET examinations were evaluated by two board-certified nuclear medicine physicians. RESULTS The Briganti 2019 nomogram performed superiorly (AUC: 0.89) compared to quantitative mpMRI parameters (AUCs: 0.47-0.73) and $^{68}$Ga-PSMA-11 PET (AUC: 0.82) in the prediction of PLN metastases and superiorly (AUC: 0.77) in the prediction of PSMA PET positive PLN compared to MRI parameters (AUCs: 0.49-0.73). The addition of mean ADC and ADC volume from mpMRI improved the Briganti model by a fraction of new information of 0.21. CONCLUSIONS The Briganti 2019 nomogram performed superiorly in the prediction of metastatic and PSMA PET positive PLN, but the addition of parameters from mpMRI can further improve its accuracy. The combined model could be used to stratify patients requiring ePLND or PSMA PET

Risk estimators for choosing regularization parameters in ill-posed problems - Properties and limitations

This paper discusses the properties of certain risk estimators that recently regained popularity for choosing regularization parameters in ill-posed problems, in particular for sparsity regularization. They apply Stein’s unbiased risk estimator (SURE) to estimate the risk in either the space of the unknown variables or in the data space. We will call the latter PSURE in order to distinguish the two different risk functions. It seems intuitive that SURE is more appropriate for ill-posed problems, since the properties in the data space do not tell much about the quality of the reconstruction. We provide theoretical studies of both approaches for linear Tikhonov regularization in a finite dimensional setting and estimate the quality of the risk estimators, which also leads to asymptotic convergence results as the dimension of the problem tends to infinity. Unlike previous works which studied single realizations of image processing problems with a very low degree of ill-posedness, we are interested in the statistical behaviour of the risk estimators for increasing ill-posedness. Interestingly, our theoretical results indicate that the quality of the SURE risk can deteriorate asymptotically for ill-posed problems, which is confirmed by an extensive numerical study. The latter shows that in many cases the SURE estimator leads to extremely small regularization parameters, which obviously cannot stabilize the reconstruction. Similar but less severe issues with respect to robustness also appear for the PSURE estimator, which in comparison to the rather conservative discrepancy principle leads to the conclusion that regularization parameter choice based on unbiased risk estimation is not a reliable procedure for ill-posed problems. A similar numerical study for sparsity regularization demonstrates that the same issue appears in non-linear variational regularization approaches

The Iteratively Regularized Gau{\ss}-Newton Method with Convex Constraints and Applications in 4Pi-Microscopy

This paper is concerned with the numerical solution of nonlinear ill-posed operator equations involving convex constraints. We study a Newton-type method which consists in applying linear Tikhonov regularization with convex constraints to the Newton equations in each iteration step. Convergence of this iterative regularization method is analyzed if both the operator and the right hand side are given with errors and all error levels tend to zero. Our study has been motivated by the joint estimation of object and phase in 4Pi microscopy, which leads to a semi-blind deconvolution problem with nonnegativity constraints. The performance of the proposed algorithm is illustrated both for simulated and for three-dimensional experimental data

Momentum Enhancement during Kinetic Impacts in the Low-intermediate-strength Regime: Benchmarking and Validation of Impact Shock Physics Codes

In 2022 September, the DART spacecraft (NASA’s contribution to the Asteroid Impact & Deflection Assessment (AIDA) collaboration) will impact the asteroid Dimorphos, the secondary in the Didymos system. The crater formation and material ejection will affect the orbital period. In 2027, Hera (ESA’s contribution to AIDA) will investigate the system, observe the crater caused by DART, and characterize Dimorphos. Before Hera’s arrival, the target properties will not be well-constrained. The relationships between observed orbital change and specific target properties are not unique, but Hera’s observations will add additional constraints for the analysis of the impact event, which will narrow the range of feasible target properties. In this study, we use three different shock physics codes to simulate momentum transfer from impactor to target and investigate the agreement between the results from the codes for well-defined target materials. In contrast to previous studies, care is taken to use consistent crushing behavior (e.g., distension as a function of pressure) for a given porosity for all codes. First, we validate the codes against impact experiments into a regolith simulant. Second, we benchmark the codes at the DART impact scale for a range of target material parameters (10%–50% porosity, 1.4–100 kPa cohesion). Aligning the crushing behavior improves the consistency of the derived momentum enhancement between the three codes to within +/−5% for most materials used. Based on the derived mass–velocity distributions from all three codes, we derive scaling parameters that can be used for studies of the ejecta curtain

Dynamics of Fermionic Four-Wave Mixing

We study the dynamics of a beam of fermions diffracted off a density grating formed by fermionic atoms in the limit of a large grating. An exact description of the system in terms of particle-hole operators is developed. We use a combination of analytical and numerical methods to quantitatively explore the Raman-Nath and the Bragg regimes of diffraction. We discuss the limits in diffraction efficiency resulting from the dephasing of the grating due the distribution of energy states occupied by the fermions. We propose several methods to overcome these limits, including the novel technique of ``atom echoes''.Comment: 8 pages, 7 figure