Holomorphic subgraph reduction of higher-point modular graph forms

Modular graph forms are a class of modular covariant functions which appear in the genus-one contribution to the low-energy expansion of closed string scattering amplitudes. Modular graph forms with holomorphic subgraphs enjoy the simplifying property that they may be reduced to sums of products of modular graph forms of strictly lower loop order. In the particular case of dihedral modular graph forms, a closed form expression for this holomorphic subgraph reduction was obtained previously by D'Hoker and Green. In the current work, we extend these results to trihedral modular graph forms. Doing so involves the identification of a modular covariant regularization scheme for certain conditionally convergent sums over discrete momenta, with some elements of the sum being excluded. The appropriate regularization scheme is identified for any number of exclusions, which in principle allows one to perform holomorphic subgraph reduction of higher-point modular graph forms with arbitrary holomorphic subgraphs.Comment: 38 pages; v2: publication versio

Heterotic-string amplitudes at one loop: modular graph forms and relations to open strings

We investigate one-loop four-point scattering of non-abelian gauge bosons in heterotic string theory and identify new connections with the corresponding open-string amplitude. In the low-energy expansion of the heterotic-string amplitude, the integrals over torus punctures are systematically evaluated in terms of modular graph forms, certain non-holomorphic modular forms. For a specific torus integral, the modular graph forms in the low-energy expansion are related to the elliptic multiple zeta values from the analogous open-string integrations over cylinder boundaries. The detailed correspondence between these modular graph forms and elliptic multiple zeta values supports a recent proposal for an elliptic generalization of the single-valued map at genus zero.Comment: 57+22 pages, v2: references updated, version published in JHE

PatMining - Wege zur Erschließung textueller Patentinformationen für das Technologie-Monitoring

Patent have often been seen as a useful information source for technology monitoring. Nevertheless, analyzing patent information remains a demanding task, and this is largely due to the ever increasing number and extent of patent documents. A very useful tool for dealing with the information overflow in order to analyze textual patent information can be found in the application of semantic patent analysis. Following up on this, approaches to the content-based analysis of textual patent information for technology monitoring are introduced in this thesis. Relating to the usefulness of patent information for technology monitoring, it is shown that technologies are published in patents on a large scale. Furthermore, patents provide information about new technologies at an early stage. From a methodological point of view, the role of design decisions for concept extraction is highlighted. Additionally, semantic patent analysis is adapted for technology monitoring and its specific tasks

Exploring AI-enhanced Shared Control for an Assistive Robotic Arm

Assistive technologies and in particular assistive robotic arms have the potential to enable people with motor impairments to live a self-determined life. More and more of these systems have become available for end users in recent years, such as the Kinova Jaco robotic arm. However, they mostly require complex manual control, which can overwhelm users. As a result, researchers have explored ways to let such robots act autonomously. However, at least for this specific group of users, such an approach has shown to be futile. Here, users want to stay in control to achieve a higher level of personal autonomy, to which an autonomous robot runs counter. In our research, we explore how Artifical Intelligence (AI) can be integrated into a shared control paradigm. In particular, we focus on the consequential requirements for the interface between human and robot and how we can keep humans in the loop while still significantly reducing the mental load and required motor skills.Comment: Workshop on Engineering Interactive Systems Embedding AI Technologies (EIS-embedding-AI) at EICS'2

Retrospective Study on Ganglionic and Nerve Block Series as Therapeutic Option for Chronic Pain Patients with Refractory Neuropathic Pain

Objective. Current recommendations controversially discuss local infiltration techniques as specific treatment for refractory pain syndromes. Evidence of effectiveness remains inconclusive and local infiltration series are discussed as a therapeutic option in patients not responding to standard therapy. The aim of this study was to investigate the effectiveness of infiltration series with techniques such as sphenopalatine ganglion (SPG) block and ganglionic local opioid analgesia (GLOA) for the treatment of neuropathic pain in the head and neck area in a selected patient group. Methods. In a retrospective clinical study, 4960 cases presenting to our university hospital outpatient pain clinic between 2009 and 2016 were screened. Altogether, 83 patients with neuropathic pain syndromes receiving local infiltration series were included. Numeric rating scale (NRS) scores before, during, and after infiltration series, comorbidity, and psychological assessment were evaluated. Results. Maximum NRS before infiltration series was median 9 (IQR 8–10). During infiltration series, maximum NRS was reduced by mean 3.2 points (SD 3.3, p < 0.001) equaling a pain reduction of 41.0% (SD 40.4%). With infiltration series, mean pain reduction of at least 30% or 50% NRS was achieved in 54.2% or 44.6% of cases, respectively. In six percent of patients, increased pain intensity was noted. Initial improvement after the first infiltration was strongly associated with overall improvement throughout the series. Conclusion. This study suggests a beneficial effect of local infiltration series as a treatment option for refractory neuropathic pain syndromes in the context of a multimodal approach. This effect is both significant and clinically relevant and therefore highlights the need for further randomized controlled trials

Geometric deep learning and equivariant neural networks

We survey the mathematical foundations of geometric deep learning, focusing on group equivariant and gauge equivariant neural networks. We develop gauge equivariant convolutional neural networks on arbitrary manifolds M using principal bundles with structure group K and equivariant maps between sections of associated vector bundles. We also discuss group equivariant neural networks for homogeneous spaces M= G/ K , which are instead equivariant with respect to the global symmetry G on M . Group equivariant layers can be interpreted as intertwiners between induced representations of G, and we show their relation to gauge equivariant convolutional layers. We analyze several applications of this formalism, including semantic segmentation and object detection networks. We also discuss the case of spherical networks in great detail, corresponding to the case M= S2= SO (3) / SO (2) . Here we emphasize the use of Fourier analysis involving Wigner matrices, spherical harmonics and Clebsch–Gordan coefficients for G= SO (3) , illustrating the power of representation theory for deep learning