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1. ToPoRg-18k: dataset of single-chain radii of gyration distribution for 18,450 architecturally diverse and chemically patterned coarse-grained polymers

   https://doi.org/10.5281/ZENODO.13619700  

   Jiang, Shengli; Michael_A, Webb (January 2025, Zenodo)

   Revision: This revision includes four independent trajectory values of the ensemble averages of the mean squared radii of gyration and their standard deviations, which can be used to compute statistical measures such as the standard error. This distribution provides access to 18,450 configurations of coarse-grained polymers. The data is provided as a serialized object using the `pickle' Python module and in csv format. The data was compiled using Python version 3.8.  ReferencesThe specific applications and analyses of the data are described in 1.  Jiang, S.; Webb, M.A. "Physics-Guided Neural Networks for Transferable Prediction of Polymer Properties" DataThere are seven .pickle files that contain serialized Python objects. pattern_graph_data_*_*_rg_new.pickle: squared radii of gyration distribution from MD simulation. The number indicates the molecular weight range. rg2_baseline_*_new.pickle: squared radii of gyration distribution from Gaussian chain theoretical prediction. delta_data_v0314.pickle: torch_geometric training data. UsageTo access the data in the .pickle file, users can execute the following: # LOAD SIMULATION DATADATA_DIR = "your/custom/dir/"mw = 40 # or 90, 190 MWs filename = os.path.join(DATA_DIR, f"pattern_graph_data_{mw}_{mw+20}_rg_new.pickle")with open(filename, "rb") as handle:    graph = pickle.load(handle)    label = pickle.load(handle)    desc  = pickle.load(handle)    meta  = pickle.load(handle)    mode  = pickle.load(handle)    rg2_mean   = pickle.load(handle)    rg2_std    = pickle.load(handle) ** 0.5 # var # combine asymmetric and symmetric star polymerslabel[label == 'stara'] = 'star'# combine bottlebrush and other comb polymerslabel[label == 'bottlebrush'] = 'comb'  # LOAD GAUSSIAN CHAIN THEORETICAL DATAwith open(os.path.join(DATA_DIR, f"rg2_baseline_{mw}_new.pickle"), "rb") as handle:    rg2_mean_theo = pickle.load(handle)[:, 0]    rg2_std_theo = pickle.load(handle)[:, 0] graph: NetworkX graph representations of polymers. label: Architectural classes of polymers (e.g., linear, cyclic, star, branch, comb, dendrimer). desc: Topological descriptors (optional). meta: Identifiers for unique architectures (optional). mode: Identifiers for unique chemical patterns (optional). rg2_mean: Mean squared radii of gyration from simulations. rg2_std: Corresponding standard deviation from simulations. rg2_mean_theo: Mean squared radii of gyration from theoretical models. rg2_std_theo: Corresponding standard deviation from theoretical models. Help, Suggestions, Corrections?If you need help, have suggestions, identify issues, or have corrections, please send your comments to Shengli Jiang at sj0161@princeton.edu GitHubAdditional data and code relevant for this study is additionally accessible at https://github.com/webbtheosim/gcgnn 

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2. TopoSolv-6k: Radii of Gyration and Shear-Rate Dependent Viscosities for Topologically and Chemically Diverse Coarse-Grained Polymers

   https://doi.org/10.5281/ZENODO.16696725  

   Jiang, Shengli; Webb, Michael (January 2025, Zenodo)

   Dataset Description This dataset contains 6710 structural configurations and solvophobicity values for topologically and chemically diverse coarse-grained polymer chains. Additionally, 480 polymers include shear-rate dependent viscosity profiles at 2 wt% polymer concentration.The data is provided as serialized objects using the pickle Python module.All files were generated using Python version 3.10. Data There are three pickle files containing serialized Python objects. Key files include: data_aug10.pickle  Contains the coarse-grained polymer dataset with 6710 entries.  Each entry includes: Polymer graph Squared radius of gyration (at lambda = 0). Solvophobicity (lambda). Bead count (N). Chain virial number (Xi). topo_param_visc.pickle   Shear-rate-dependent viscosity profiles of 480 polymer systems. target_curves.pickle  Contains 30 target viscosity profiles used for active learning. Usage To load the dataset stored in data_aug10.pickle, use the following code: import pickle with open("data_aug10.pickle", "rb") as handle:    (        (x_train, y_train, c_train, l_train, graph_train),        (x_valid, y_valid, c_valid, l_valid, graph_valid),        (x_test, y_test, c_test, l_test, graph_test),        NAMES,        SCALER,        SCALER_y,        le    ) = pickle.load(handle) x: node features for each polymer graph y: labels (e.g., predicted properties) c: topological class indices l: topological descriptors graph: NetworkX graphs representing polymer topology NAMES: list of topological class names SCALER: fitted scaler for topological descriptors (l) SCALER_y: fitted scaler for property labels (y) le: label encoder for topological class indices   To load the dataset stored in topo_param_visc.pickle, use the following code: import pickle with open("poly_data_ml.pickle", "rb") as handle:    desc_all, ps_all, curve_all, shear_rate, graph_all = pickle.load(handle) desc_all: topological descriptors for each polymer graph ps_all: fitted Carreau–Yasuda model parameters curve_all: fitted viscosity curves shear_rate: shear rates corresponding to each viscosity curve graph_all: polymer graphs represented as NetworkX objects   First 30: seed dataset Next 150: 5 iterations (30 each) from class-balanced space-filling Following 150: space-filling without class balancing Final 150: active learning samples    To load the dataset stored in target_curves.pickle, use the following code: import pickle with open("target_curves.pickle", "rb") as handle:    data = pickle.load(f) curves = data['curves']params = data['params']shear_rate = data["xx"]   curves: target viscosity curves used as design objectives params: Carreau–Yasuda model parameters fitted to the target curves shear_rate: shear rate values associated with the target curves     Help, Suggestions, Corrections?If you need help, have suggestions, identify issues, or have corrections, please send your comments to Shengli Jiang at sj0161@princeton.edu GitHubAdditional data and code relevant for this study is additionally accessible at https://github.com/webbtheosim/cg-topo-solv 

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3. Sketching, Moment Estimation, and the Lévy-Khintchine Representation Theorem

   https://doi.org/10.4230/lipics.itcs.2025.77  

   Pettie, Seth; Wang, Dingyu (January 2025, Schloss Dagstuhl – Leibniz-Zentrum für Informatik)

   Meka, Raghu (Ed.)

   In the d-dimensional turnstile streaming model, a frequency vector 𝐱 = (𝐱(1),…,𝐱(n)) ∈ (ℝ^d)ⁿ is updated entry-wisely over a stream. We consider the problem of f-moment estimation for which one wants to estimate f(𝐱)=∑_{v ∈ [n]}f(𝐱(v)) with a small-space sketch. A function f is tractable if the f-moment can be estimated to within a constant factor using polylog(n) space. The f-moment estimation problem has been intensively studied in the d = 1 case. Flajolet and Martin estimate the F₀-moment (f(x) = 1 (x > 0), incremental stream); Alon, Matias, and Szegedy estimate the L₂-moment (f(x) = x²); Indyk estimates the L_α-moment (f(x) = |x|^α), α ∈ (0,2]. For d ≥ 2, Ganguly, Bansal, and Dube estimate the L_{p,q} hybrid moment (f:ℝ^d → ℝ,f(x) = (∑_{j = 1}^d |x_j|^p)^q), p ∈ (0,2],q ∈ (0,1). For tractability, Bar-Yossef, Jayram, Kumar, and Sivakumar show that f(x) = |x|^α is not tractable for α > 2. Braverman, Chestnut, Woodruff, and Yang characterize the class of tractable one-variable functions except for a class of nearly periodic functions. In this work we present a simple and generic scheme to construct sketches with the novel idea of hashing indices to Lévy processes, from which one can estimate the f-moment f(𝐱) where f is the characteristic exponent of the Lévy process. The fundamental Lévy-Khintchine representation theorem completely characterizes the space of all possible characteristic exponents, which in turn characterizes the set of f-moments that can be estimated by this generic scheme. The new scheme has strong explanatory power. It unifies the construction of many existing sketches (F₀, L₀, L₂, L_α, L_{p,q}, etc.) and it implies the tractability of many nearly periodic functions that were previously unclassified. Furthermore, the scheme can be conveniently generalized to multidimensional cases (d ≥ 2) by considering multidimensional Lévy processes and can be further generalized to estimate heterogeneous moments by projecting different indices with different Lévy processes. We conjecture that the set of tractable functions can be characterized using the Lévy-Khintchine representation theorem via what we called the Fourier-Hahn-Lévy method. 

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4. Popular progression differences in vector spaces II

   Fox, Jacob; Pham, Huy Tuan (November 2019, Discrete analysis)

   Green used an arithmetic analogue of Szemerédi's celebrated regularity lemma to prove the following strengthening of Roth's theorem in vector spaces. For every α>0, β<α3, and prime number p, there is a least positive integer n_p(α,β) such that if n≥n_p(α,β), then for every subset of 𝔽np of density at least α there is a nonzero d for which the density of three-term arithmetic progressions with common difference d is at least β. We determine for p≥19 the tower height of n_p(α,β) up to an absolute constant factor and an additive term depending only on p. In particular, if we want half the random bound (so β=α^{3}/2), then the dimension n required is a tower of twos of height Θ((log p)loglog(1/α)). It turns out that the tower height in general takes on a different form in several different regions of α and β, and different arguments are used both in the upper and lower bounds to handle these cases. 

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5. Thermal stability and phase transformation of α-, κ(ε)-, and γ-Ga2O3 films under different ambient conditions

   https://doi.org/10.1063/5.0214500  

   Tang, Jingyu; Jiang, Kunyao; Tseng, Po-Sen; Kurchin, Rachel C; Porter, Lisa M; Davis, Robert F (August 2024, Applied Physics Letters)

   Phase transitions in metastable α-, κ(ε)-, and γ-Ga2O3 films to thermodynamically stable β-Ga2O3 during annealing in air, N2, and vacuum have been systematically investigated via in situ high-temperature x-ray diffraction (HT-XRD) and scanning electron microscopy (SEM). These respective polymorphs exhibited thermal stability to ∼471–525 °C, ∼773–825 °C, and ∼490–575 °C before transforming into β-Ga2O3, across all tested ambient conditions. Particular crystallographic orientation relationships were observed before and after the phase transitions, i.e., (0001) α-Ga2O3 → (2¯01) β-Ga2O3, (001) κ(ε)-Ga2O3 → (310) and (2¯01) β-Ga2O3, and (100) γ-Ga2O3 → (100) β-Ga2O3. The phase transition of α-Ga2O3 to β-Ga2O3 resulted in catastrophic damage to the film and upheaval of the surface. The respective primary and possibly secondary causes of this damage are the +8.6% volume expansion and the dual displacive and reconstructive transformations that occur during this transition. The κ(ε)- and γ-Ga2O3 films converted to β-Ga2O3 via singular reconstructive transformations with small changes in volume and unchanged surface microstructures. 

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