Higher homotopy groups of complements of complex hyperplane arrangements

We generalize results of Hattori on the topology of complements of hyperplane arrangements, from the class of generic arrangements, to the much broader class of hypersolvable arrangements. We show that the higher homotopy groups of the complement vanish in a certain combinatorially determined range, and we give an explicit Z\pi_1-module presentation of \pi_p, the first non-vanishing higher homotopy group. We also give a combinatorial formula for the \pi_1-coinvariants of \pi_p. For affine line arrangements whose cones are hypersolvable, we provide a minimal resolution of \pi_2, and study some of the properties of this module. For graphic arrangements associated to graphs with no 3-cycles, we obtain information on \pi_2, directly from the graph. The \pi_1-coinvariants of \pi_2 may distinguish the homotopy 2-types of arrangement complements with the same \pi_1, and the same Betti numbers in low degrees.Comment: 24 pages, 3 figure

The Generative Capacity of Digital Artifacts: A Mapping of the Field

The concept of generativity as the capacity of a technology or a system to be malleable by diverse groups of actors in unanticipated ways has recently gained considerable traction in information systems research. We review a sample of the body of knowledge and identify that scholars commonly investigated generativity in conjunction with digital infrastructures and digital platforms, both of which are complex, networked, and evolving socio-technical systems. Interestingly, other types of digital artifacts have been neglected, despite our initial assumption that the distinct attributes (e.g., reprogrammability, distributedness) of any digital artifact match well with generativity. The literature review also reveals that innovation brought about heterogeneous groups of actors is universally regarded as the goal of generativity, discounting the possibility of exploiting generative systems towards other valuable ends such as organizational agility. Furthermore, scholars commonly discuss generativity in conjunction with the logic of modularity, leading to unresolved questions on how these two concepts might complement each other. Another important contribution of this paper is the systematization of various meanings of generativity, spanning from the philosophical–e.g., generative mechanisms in critical realist research–to a more literal understanding, for instance generativity as synonym to ‘creation of a particular solution’

Translated tori in the characteristic varieties of complex hyperplane arrangements

We give examples of complex hyperplane arrangements for which the top characteristic variety contains positive-dimensional irreducible components that do not pass through the origin of the character torus. These examples answer several questions of Libgober and Yuzvinsky. As an application, we exhibit a pair of arrangements for which the resonance varieties of the Orlik-Solomon algebra are (abstractly) isomorphic, yet whose characteristic varieties are not isomorphic. The difference comes from translated components, which are not detected by the tangent cone at the origin.Comment: Revised and expanded; 16 pages, 10 figures; to appear in Topology and its Application

Machine learning-based estimation and clustering of statistics within stratigraphic models as exemplified in Denmark

Estimating a covariance model for kriging purposes is traditionally done using semivariogram analyses, where an empirical semivariogram is calculated, and a chosen semivariogram model, usually defined by a sill and a range, is fitted. We demonstrate that a convolutional neural network can estimate such a semivariogram model with comparable accuracy and precision by training it to recognise the relationship between realisations of Gaussian random fields and the sill and range values that define it, for a Gaussian type semivariance model. We do this by training the network with synthetic data consisting of many such realisations with the sill and range as the target variables. Because training takes time, the method is best suited for cases where many models need to be estimated since the actual estimation itself is about 70 times faster with the neural network than with the traditional approach. We demonstrate the viability of the method in three ways: (1) we test the model’s performance on the validation data, (2) we do a test where we compare the model to the traditional approach and (3) we show an example of an actual application of the method using the Danish national hydrostratigraphic model

Leptonic and Semileptonic Decays of Pseudoscalar Mesons

We employ the relativistic constituent quark model to give a unified description of the leptonic and semileptonic decays of pseudoscalar mesons (\pi, K, D, D_s, B, B_s). The calculated leptonic decay constants and form factors are found to be in good agreement with available experimental data and other approaches. We reproduce the results of spin-flavor symmetry in the heavy quark limit.Comment: 12 pages LaTeX (elsart.sty) + 4 figures; added references, to appear in Phys. Lett.

Three-Dimensional Light Bullets in Arrays of Waveguides

We report the first experimental observation of 3D-LBs, excited by femtosecond pulses in a system featuring quasi-instantaneous cubic nonlinearity and a periodic, transversally-modulated refractive index. Stringent evidence of the excitation of LBs is based on time-gated images and spectra which perfectly match our numerical simulations. Furthermore, we reveal a novel evolution mechanism forcing the LBs to follow varying dispersion/diffraction conditions, until they leave their existence range and decay.Comment: 4 pages, 5 figures - Published by the American Physical Societ

Prostate Cancer Nodal Staging: Using Deep Learning to Predict 68Ga-PSMA-Positivity from CT Imaging Alone

Lymphatic spread determines treatment decisions in prostate cancer (PCa) patients. 68Ga-PSMA-PET/CT can be performed, although cost remains high and availability is limited. Therefore, computed tomography (CT) continues to be the most used modality for PCa staging. We assessed if convolutional neural networks (CNNs) can be trained to determine 68Ga-PSMA-PET/CT-lymph node status from CT alone. In 549 patients with 68Ga-PSMA PET/CT imaging, 2616 lymph nodes were segmented. Using PET as a reference standard, three CNNs were trained. Training sets balanced for infiltration status, lymph node location and additionally, masked images, were used for training. CNNs were evaluated using a separate test set and performance was compared to radiologists' assessments and random forest classifiers. Heatmaps maps were used to identify the performance determining image regions. The CNNs performed with an Area-Under-the-Curve of 0.95 (status balanced) and 0.86 (location balanced, masked), compared to an AUC of 0.81 of experienced radiologists. Interestingly, CNNs used anatomical surroundings to increase their performance, "learning" the infiltration probabilities of anatomical locations. In conclusion, CNNs have the potential to build a well performing CT-based biomarker for lymph node metastases in PCa, with different types of class balancing strongly affecting CNN performance