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Title: Realizations of Isostatic Material Frameworks
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Author(s) / Creator(s):
 ;  ;  ;  ;  ;  ;  ;  ;  
Publisher / Repository:
Wiley Blackwell (John Wiley & Sons)
Date Published:
Journal Name:
physica status solidi (b)
Medium: X
Sponsoring Org:
National Science Foundation
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  1. Abstract

    The well-studied moduli space of complex cubic surfaces has three different, but isomorphic, compact realizations: as a GIT quotient${\mathcal {M}}^{\operatorname {GIT}}$, as a Baily–Borel compactification of a ball quotient${(\mathcal {B}_4/\Gamma )^*}$, and as a compactifiedK-moduli space. From all three perspectives, there is a unique boundary point corresponding to non-stable surfaces. From the GIT point of view, to deal with this point, it is natural to consider the Kirwan blowup${\mathcal {M}}^{\operatorname {K}}\rightarrow {\mathcal {M}}^{\operatorname {GIT}}$, whereas from the ball quotient point of view, it is natural to consider the toroidal compactification${\overline {\mathcal {B}_4/\Gamma }}\rightarrow {(\mathcal {B}_4/\Gamma )^*}$. The spaces${\mathcal {M}}^{\operatorname {K}}$and${\overline {\mathcal {B}_4/\Gamma }}$have the same cohomology, and it is therefore natural to ask whether they are isomorphic. Here, we show that this is in factnotthe case. Indeed, we show the more refined statement that${\mathcal {M}}^{\operatorname {K}}$and${\overline {\mathcal {B}_4/\Gamma }}$are equivalent in the Grothendieck ring, but notK-equivalent. Along the way, we establish a number of results and techniques for dealing with singularities and canonical classes of Kirwan blowups and toroidal compactifications of ball quotients.

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  2. Abstract Motivation

    A chronogram is a dated phylogenetic tree whose branch lengths have been scaled to represent time. Such chronograms are computed based on available date estimates (e.g. from dated fossils), which provide absolute time constraints for one or more nodes of an input undated phylogeny, coupled with an appropriate underlying model for evolutionary rates variation along the branches of the phylogeny. However, traditional methods for phylogenetic dating cannot take into account relative time constraints, such as those provided by inferred horizontal transfer events. In many cases, chronograms computed using only absolute time constraints are inconsistent with known relative time constraints.


    In this work, we introduce a new approach, Dating Trees using Relative constraints (DaTeR), for phylogenetic dating that can take into account both absolute and relative time constraints. The key idea is to use existing Bayesian approaches for phylogenetic dating to sample posterior chronograms satisfying desired absolute time constraints, minimally adjust or ‘error-correct’ these sampled chronograms to satisfy all given relative time constraints, and aggregate across all error-corrected chronograms. DaTeR uses a constrained optimization framework for the error-correction step, finding minimal deviations from previously assigned dates or branch lengths. We applied DaTeR to a biological dataset of 170 Cyanobacterial taxa and a reliable set of 24 transfer-based relative constraints, under six different molecular dating models. Our extensive analysis of this dataset demonstrates that DaTeR is both highly effective and scalable and that its application can significantly improve estimated chronograms.

    Availability and implementation

    Freely available from

    Supplementary information

    Supplementary data are available at Bioinformatics online.

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  3. Abstract Motivation

    Reticulate evolutionary histories, such as those arising in the presence of hybridization, are best modeled as phylogenetic networks. Recently developed methods allow for statistical inference of phylogenetic networks while also accounting for other processes, such as incomplete lineage sorting. However, these methods can only handle a small number of loci from a handful of genomes.


    In this article, we introduce a novel two-step method for scalable inference of phylogenetic networks from the sequence alignments of multiple, unlinked loci. The method infers networks on subproblems and then merges them into a network on the full set of taxa. To reduce the number of trinets to infer, we formulate a Hitting Set version of the problem of finding a small number of subsets, and implement a simple heuristic to solve it. We studied their performance, in terms of both running time and accuracy, on simulated as well as on biological datasets. The two-step method accurately infers phylogenetic networks at a scale that is infeasible with existing methods. The results are a significant and promising step towards accurate, large-scale phylogenetic network inference.

    Availability and implementation

    We implemented the algorithms in the publicly available software package PhyloNet (

    Supplementary information

    Supplementary data are available at Bioinformatics online.

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  4. These datasets accompany a publication in Geophysical Research Letters by Martens et al. (2024), entitled: "GNSS Geodesy Quantifies Water-Storage Gains and Drought Improvements in California Spurred by Atmospheric Rivers." Please refer to the manuscript and supporting information for additional details.

    Dataset 1: Seasonal Changes in TWS based on the Mean and Median of the Solution Set

    We estimate net gains in water storage during the fall and winter of each year (October to March) using the mean TWS solutions from all nine inversion products, subtracting the average storage for October from the average storage for March in the following year. One-sigma standard deviations are computed as the square root of the sum of the variances for October and for March. The variance in each month is computed based on the nine independent estimates of mean monthly storage (see “GNSS Analysis and Inversion” in the Supporting Information).

    The dataset includes net gains in water storage for both the Sierra Nevada and the SST watersheds (see header lines). For each watershed, results are provided in units of volume (km3) and in units of equivalent water height (mm). Furthermore, for each watershed, we also provide the total storage gains based on non-detrended and linearly detrended time series. In columns four and five, respectively, we provide estimates of snow water equivalent (SWE) from SNODAS (National Operational Hydrologic Remote Sensing Center, 2023) and water-storage changes in surface reservoirs from CDEC (California Data Exchange Center, 2023). In the final column, we provide estimates of net gains in subsurface storage (soil moisture plus groundwater), which are computed by subtracting SWE and reservoir storage from total storage.

    For each data block, the columns are: (1) time period (October of the starting year to March of the following year); (2) average gain in total water storage constrained by nine inversions of GNSS data; (3) one-sigma standard deviation in the average gain in total water storage; (4) gain in snow water equivalent, computed by subtracting the average snow storage in October from the average snow storage in March of the following year; (5) gain in reservoir storage (CDEC database; within the boundaries of each watershed), computed by subtracting the average reservoir storage in October from the average reservoir storage in March of the following year; and (6) average gain in subsurface water storage, estimated as the average gain in total water storage minus the average gain in snow storage minus the gain in reservoir storage.

    For the period from October 2022 to March 2023, we also compute mean gains in total water storage using daily estimates of TWS. Here, we subtract the average storage for the first week in October 2022 (1-7 October) from the average storage for the last week in March 2023 (26 March – 1 April). The one-sigma standard deviation is computed as the square root of the sum of the variances for the first week in October and the last week in March. The variance in each week is computed based on the nine independent estimates of daily storage over seven days (63 values per week). The storage gains for 2022-2023 computed using these methods are distinguished in the datafile by an asterisk (2022-2023*; final row in each data section).

    Dataset 1a provides estimates of storage changes based on the mean and standard deviation of the solution set. Dataset 1b provides estimates of storage changes based on the median and inter-quartile range of the solution set.

    Dataset 2: Estimated Changes in TWS in the Sierra Nevada

    Changes in TWS (units of volume: km3) in the Sierra Nevada watersheds. The first column represents the date (YYYY-MM-DD). For monthly solutions, the TWS solutions apply to the month leading up to that date. The remaining nine columns represent each of the nine solutions described in the text. “UM” represents the University of Montana, “SIO” represents the Scripps Institution of Oceanography, and “JPL” represents the Jet Propulsion Laboratory. “NGL” refers to the use of GNSS analysis products from the Nevada Geodetic Laboratory, “CWU” refers to Central Washington University, and “MEaSUREs” refers to the Making Earth System Data Records for Use in Research Environments program. The time series have not been detrended.

    We highlight that we have added changes in reservoir storage (see Dataset 8) back into the JPL solutions, since reservoir storage had been modeled and removed from the GNSS time series prior to inversion in the JPL workflow (see “Detailed Description of Methods” in the Supporting Information). Thus, the storage values presented here for JPL differ slightly from storage values pulled directly from Dataset 6 and integrated over the area of the Sierra Nevada watersheds.

    Dataset 3: Estimated Changes in TWS in the Sacramento-San Joaquin-Tulare Basin

    Same as Dataset 2, except that data apply to the Sacramento-San Joaquin-Tulare (SST) Basin.

    Dataset 4: Inversion Products (SIO)

    Inversion solutions (NetCDF format) for TWS changes across the western US from January 2006 through March 2023. The products were produced at the Scripps Institution of Oceanography (SIO) using the methods described in the Supporting Information.

    Dataset 5: Inversion Products (UM)

    Inversion solutions (NetCDF format) for TWS changes across the western US from January 2006 through March 2023. The products were produced at the University of Montana (UM) using the methods described in the Supporting Information.

    Dataset 6: Inversion Products (JPL)

    Inversion solutions (NetCDF format) for TWS changes across the western US from January 2006 through March 2023. The products were produced at the Jet Propulsion Laboratory (JPL) using the methods described in the Supporting Information.

    Dataset 7: Lists of Excluded Stations

    Stations are excluded from an inversion for TWS change based on a variety of criteria (detailed in the Supporting Information), including poroelastic behavior, high noise levels, and susceptibility to volcanic deformation. This dataset provides lists of excluded stations from each institution generating inversion products (SIO, UM, JPL).

    Dataset 8: Lists of Reservoirs and Lakes

    Lists of reservoirs and lakes from the California Data Exchange Center (CDEC) (California Data Exchange Center, 2023), which are shown in Figures 1 and 2 of the main manuscript. In the interest of figure clarity, Figure 1 depicts only those reservoirs that exhibited volume changes of at least 0.15 km3 during the first half of WY23.

    Dataset 8a includes all reservoirs and lakes in California that exhibited volume changes of at least 0.15 km3 between October 2022 and March 2023. The threshold of 0.15 km3 represents a natural break in the distribution of volume changes at all reservoirs and lakes in California over that period (169 reservoirs and lakes in total). Most of the 169 reservoirs and lakes exhibited volume changes near zero km3. Datasets 8b and 8c include subsets of reservoirs and lakes (from Dataset 8a) that fall within the boundaries of the Sierra Nevada and SST watersheds.

    Furthermore, in the JPL data-processing and inversion workflow (see “Detailed Description of Methods” in the Supporting Information), surface displacements induced by volume changes in select lakes and reservoirs are modeled and removed from GNSS time series prior to inversion. The water-storage changes in the lakes and reservoirs are then added back into the solutions for water storage, derived from the inversion of GNSS data. Dataset 8d includes the list of reservoirs used in the JPL workflow.

    Dataset 9: Interseismic Strain Accumulation along the Cascadia Subduction Zone

    JPL and UM remove interseismic strain accumulation associated with locking of the Cascadia subduction zone using an updated version of the Li et al. model (Li et al., 2018); see Supporting Information Section 2d. The dataset lists the east, north, and up velocity corrections (in the 4th, 5th, and 6th columns of the dataset, respectively) at each station; units are mm/year. The station ID, latitude, and longitude are listed in columns one, two, and three, respectively, of the dataset.

    Dataset 10: Days Impacted by Atmospheric Rivers

    A list of days impacted by atmospheric rivers within (a) the HUC-2 boundary for California from 1 January 2008 until 1 April 2023 [Dataset 10a] and (b) the Sierra Nevada and SST watersheds from 1 October 2022 until 1 April 2023 [Dataset 10b]. File formats: [decimal year; integrated water-vapor transport (IVT) in kg m-1 s-1; AR category; and calendar date as a two-digit year followed by a three-character month followed by a two-digit day]. The AR category reflects the peak intensity anywhere within the watershed. We use the detection and classification methods of (Ralph et al., 2019; Rutz et al., 2014, 2019). See also Supporting Information Section 2i.

    Dataset 10c provides a list of days and times when ARs made landfall along the California coast between October 1980 and September 2023, based on the MERRA-2 reanalysis using the methods of (Rutz et al., 2014, 2019). Only coastal grid cells are included. File format: [year, month, day, hour, latitude, longitude, and IVT in kg m-1 s-1]. Values are sorted by time (year, month, day, hour) and then by latitude. See also Supporting Information Section 2g.

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  5. Embedding properties of network realizations of dissipative reduced order models Jörn Zimmerling, Mikhail Zaslavsky,Rob Remis, Shasri Moskow, Alexander Mamonov, Murthy Guddati, Vladimir Druskin, and Liliana Borcea Mathematical Sciences Department, Worcester Polytechnic Institute Abstract Realizations of reduced order models of passive SISO or MIMO LTI problems can be transformed to tridiagonal and block-tridiagonal forms, respectively, via dierent modications of the Lanczos algorithm. Generally, such realizations can be interpreted as ladder resistor-capacitor-inductor (RCL) networks. They gave rise to network syntheses in the rst half of the 20th century that was at the base of modern electronics design and consecutively to MOR that tremendously impacted many areas of engineering (electrical, mechanical, aerospace, etc.) by enabling ecient compression of the underlining dynamical systems. In his seminal 1950s works Krein realized that in addition to their compressing properties, network realizations can be used to embed the data back into the state space of the underlying continuum problems. In more recent works of the authors Krein's ideas gave rise to so-called nite-dierence Gaussian quadrature rules (FDGQR), allowing to approximately map the ROM state-space representation to its full order continuum counterpart on a judicially chosen grid. Thus, the state variables can be accessed directly from the transfer function without solving the full problem and even explicit knowledge of the PDE coecients in the interior, i.e., the FDGQR directly learns" the problem from its transfer function. This embedding property found applications in PDE solvers, inverse problems and unsupervised machine learning. Here we show a generalization of this approach to dissipative PDE problems, e.g., electromagnetic and acoustic wave propagation in lossy dispersive media. Potential applications include solution of inverse scattering problems in dispersive media, such as seismic exploration, radars and sonars. To x the idea, we consider a passive irreducible SISO ROM fn(s) = Xn j=1 yi s + σj , (62) assuming that all complex terms in (62) come in conjugate pairs. We will seek ladder realization of (62) as rjuj + vj − vj−1 = −shˆjuj , uj+1 − uj + ˆrj vj = −shj vj , (63) for j = 0, . . . , n with boundary conditions un+1 = 0, v1 = −1, and 4n real parameters hi, hˆi, ri and rˆi, i = 1, . . . , n, that can be considered, respectively, as the equivalent discrete inductances, capacitors and also primary and dual conductors. Alternatively, they can be viewed as respectively masses, spring stiness, primary and dual dampers of a mechanical string. Reordering variables would bring (63) into tridiagonal form, so from the spectral measure given by (62 ) the coecients of (63) can be obtained via a non-symmetric Lanczos algorithm written in J-symmetric form and fn(s) can be equivalently computed as fn(s) = u1. The cases considered in the original FDGQR correspond to either (i) real y, θ or (ii) real y and imaginary θ. Both cases are covered by the Stieltjes theorem, that yields in case (i) real positive h, hˆ and trivial r, rˆ, and in case (ii) real positive h,r and trivial hˆ,rˆ. This result allowed us a simple interpretation of (62) as the staggered nite-dierence approximation of the underlying PDE problem [2]. For PDEs in more than one variables (including topologically rich data-manifolds), a nite-dierence interpretation is obtained via a MIMO extensions in block form, e.g., [4, 3]. The main diculty of extending this approach to general passive problems is that the Stieltjes theory is no longer applicable. Moreover, the tridiagonal realization of a passive ROM transfer function (62) via the ladder network (63) cannot always be obtained in port-Hamiltonian form, i.e., the equivalent primary and dual conductors may change sign [1]. 100 Embedding of the Stieltjes problems, e.g., the case (i) was done by mapping h and hˆ into values of acoustic (or electromagnetic) impedance at grid cells, that required a special coordinate stretching (known as travel time coordinate transform) for continuous problems. Likewise, to circumvent possible non-positivity of conductors for the non-Stieltjes case, we introduce an additional complex s-dependent coordinate stretching, vanishing as s → ∞ [1]. This stretching applied in the discrete setting induces a diagonal factorization, removes oscillating coecients, and leads to an accurate embedding for moderate variations of the coecients of the continuum problems, i.e., it maps discrete coecients onto the values of their continuum counterparts. Not only does this embedding yields an approximate linear algebraic algorithm for the solution of the inverse problems for dissipative PDEs, it also leads to new insight into the properties of their ROM realizations. We will also discuss another approach to embedding, based on Krein-Nudelman theory [5], that results in special data-driven adaptive grids. References [1] Borcea, Liliana and Druskin, Vladimir and Zimmerling, Jörn, A reduced order model approach to inverse scattering in lossy layered media, Journal of Scientic Computing, V. 89, N1, pp. 136,2021 [2] Druskin, Vladimir and Knizhnerman, Leonid, Gaussian spectral rules for the three-point second dierences: I. A two-point positive denite problem in a semi-innite domain, SIAM Journal on Numerical Analysis, V. 37, N 2, pp.403422, 1999 [3] Druskin, Vladimir and Mamonov, Alexander V and Zaslavsky, Mikhail, Distance preserving model order reduction of graph-Laplacians and cluster analysis, Druskin, Vladimir and Mamonov, Alexander V and Zaslavsky, Mikhail, Journal of Scientic Computing, V. 90, N 1, pp 130, 2022 [4] Druskin, Vladimir and Moskow, Shari and Zaslavsky, Mikhail LippmannSchwingerLanczos algorithm for inverse scattering problems, Inverse Problems, V. 37, N. 7, 2021, [5] Mark Adolfovich Nudelman The Krein String and Characteristic Functions of Maximal Dissipative Operators, Journal of Mathematical Sciences, 2004, V 124, pp 49184934 Go back to Plenary Speakers Go back to Speakers Go back 
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