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1. Residual Intersections and linear powers

   EISENBUD, David; HUNEKE, CRAIG; ULRICH, BERND (July 2024, Transactions of the American Mathematical Society)

   If I is an ideal in a Gorenstein ring S, and S/I is Cohen-Macaulay, then the same is true for any linked ideal I ; but such statements hold for residual intersections of higher codimension only under restrictive hypotheses, not satisfied even by ideals as simple as the ideal Ln of minors of a generic 2 × n matrix when n > 3. In this paper we initiate the study of a different sort of Cohen-Macaulay property that holds for certain general residual intersections of the maximal (interesting) codimension, one less than the analytic spread of I. For example, suppose that K is the residual intersection of Ln by 2n − 4 general quadratic forms in Ln. In this situation we analyze S/K and show that In−3(S/K) is a self-dual maximal Cohen-Macaulay S/K-module with linear free resolution over S. The technical heart of the paper is a result about ideals of analytic spread 1 whose high powers are linearly presented. 

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2. Blanco DECam Bulge Survey (BDBS). VI. Extinction Maps Toward Southern Galactic Bulge Globular Clusters

   https://doi.org/10.3847/1538-4357/acc79e  

   Kader, Justin A.; Pilachowski, Catherine A.; Johnson, Christian I.; Rich, R. Michael; Young, Michael D.; Simion, Iulia T.; Clarkson, William I.; Michael, Scott; Kunder, Andrea; Vivas, Anna Katherina; et al (June 2023, The Astrophysical Journal)

   Abstract We present wide-field, high resolution maps of the color excess for 14 globular clusters toward the Southern Galactic bulge. The maps were derived using Gaia EDR3 astrometry and stellar photometry from the Blanco DECam Bulge Survey, which is a deep, wide-field ugriz Y photometric survey of the southern Galactic bulge. Comparisons with WISE 12 μ m images of thermal continuum emission demonstrate that the maps presented here trace interstellar extinction by dust down to 5″ scales. We use the reddening-corrected photometry of proper motion-selected cluster stars to build color–magnitude diagrams for the target globular clusters, which show residual broadening in excess of that expected from the photometric errors alone. This residual broadening is likely to be driven by star-to-star elemental abundance variations. 

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3. Dynamic, In-situ, Nonlinear-Inelastic Response and Post-Cyclic Strength of a Plastic Silt Deposit

   https://doi.org/10.1139/cgj-2020-0652  

   Jana, Amalesh; Stuedlein, Armin W. (April 2021, Canadian Geotechnical Journal)

   null (Ed.)

   This study presents the use of controlled blasting as a source of seismic energy to obtain the coupled, dynamic, linear-elastic to nonlinear-inelastic response of a plastic silt deposit. Characterization of blast-induced ground motions indicate that the shear strain and corresponding residual excess pore pressures (EPPs) are associated with low frequency near- and far-field shear waves that are within the range of earthquake frequencies, whereas the effect of high frequency P-waves are negligible. Three blasting programs were used to develop the initial and pre-strained relationships between shear strain, EPP, and nonlinear shear modulus degradation. The initial threshold shear strain to initiate soil nonlinearity and to trigger generation of residual EPP ranging from 0.002 to 0.003% and 0.008 to 0.012%, respectively, where the latter corresponded to ~30% of Gmax. Following pre-straining and dissipation of EPPs within the silt deposit, the shear strain necessary to trigger residual excess pore pressure increased two-fold. Greater excess pore pressures were observed in-situ compared to that of intact direct simple shear (DSS) test specimens at a given shear strain amplitude. The reduction of in-situ undrained shear strength within the blast-induced EPP field measured using vane shear tests compared favorably with that of DSS test specimens. 

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4. Regular Supercuspidal Representations

   Tasho Kaletha (July 2019, Journal of the American Mathematical Society)

   We show that, in good residual characteristic, most supercuspidal representations of a tamely ramified reductive p-adic group G arise from pairs (S,\theta), where S is a tame elliptic maximal torus of G, and \theta is a character of S satisfying a simple root-theoretic property. We then give a new expression for the roots of unity that appear in the Adler-DeBacker-Spice character formula for these supercuspidal representations and use it to show that this formula bears a striking resemblance to the character formula for discrete series representations of real reductive groups. Led by this, we explicitly construct the local Langlands correspondence for these supercuspidal representations and prove stability and endoscopic transfer in the case of toral representations. In large residual characteristic this gives a construction of the local Langlands correspondence for almost all supercuspidal representations of reductive p-adic groups. 

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5. Diffeomorphic Image Registration using Lipschitz Continuous Residual Networks

   Joshi, Ankita; Hong, Yi (October 2022, Proceedings of Machine Learning Research)

   Image registration is an essential task in medical image analysis. We propose two novel unsupervised diffeomorphic image registration networks, which use deep Residual Networks (ResNets) as numerical approximations of the underlying continuous diffeomorphic setting governed by ordinary differential equations (ODEs), viewed as a Eulerian discretization scheme. While considering the ODE-based parameterizations of diffeomorphisms, we consider both stationary and non-stationary (time varying) velocity fields as the driving velocities to solve the ODEs, which give rise to our two proposed architectures for diffeomorphic registration. We also employ Lipschitz-continuity on the Residual Networks in both architectures to define the admissible Hilbert space of velocity fields as a Reproducing Kernel Hilbert Spaces (RKHS) and regularize the smoothness of the velocity fields. We apply both registration networks to align and segment the OASIS brain MRI dataset. Experimental results demonstrate that our models are computational efficient and achieve comparable registration results with a smoother deformation field. 

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