Grass(mannian) trees and forests: Variations of the exponential formula, with applications to the momentum amplituhedron

© 2023 by the author(s). This work is made available under the terms of a Creative Commons Attribution License, available at https://creativecommons.org/licenses/by/4.0/The Exponential Formula allows one to enumerate any class of combinatorial objects built by choosing a set of connected components and placing a structure on each connected component which depends only on its size. There are multiple variants of this result, including Speicher’s result for noncrossing partitions, as well as analogues of the Exponential Formula for series-reduced planar trees and forests. In this paper we use these formulae to give generating functions for contracted Grassmannian trees and forests, certain graphs whose vertices are decorated with a helicity. Along the way we enumerate bipartite planar trees and forests, and we apply our results to enumerate various families of permutations: for example, bipartite planar trees are in bijection with separable permutations. It is postulated by Livia Ferro, Tomasz Łukowski and Robert Moerman (2020) that contracted Grassmannian forests are in bijection with boundary strata of the momentum amplituhedron, an object encoding the tree-level S-matrix of maximally supersymmetric Yang–Mills theory. With this assumption, our results give a rank generating function for the boundary strata of the momentum amplituhedron, and imply that the Euler characteristic of the momentum amplituhedron is 1.Peer reviewe

Experimental optimization of exposure index and quality of service in WLAN networks

This paper presents the first real-life optimization of the Exposure Index (EI). A genetic optimization algorithm is developed and applied to three real-life Wireless Local Area Network scenarios in an experimental testbed. The optimization accounts for downlink, uplink and uplink of other users, for realistic duty cycles, and ensures a sufficient Quality of Service to all users. EI reductions up to 97.5% compared to a reference configuration can be achieved in a downlink-only scenario, in combination with an improved Quality of Service. Due to the dominance of uplink exposure and the lack of WiFi power control, no optimizations are possible in scenarios that also consider uplink traffic. However, future deployments that do implement WiFi power control can be successfully optimized, with EI reductions up to 86% compared to a reference configuration and an EI that is 278 times lower than optimized configurations under the absence of power control

Control of Tension-Compression Asymmetry in Ogden Hyperelasticity with Application to Soft Tissue Modelling

This paper discusses tension-compression asymmetry properties of Ogden hyperelastic formulations. It is shown that if all negative or all positive Ogden coefficients are used, tension-compression asymmetry occurs the degree of which cannot be separately controlled from the degree of non-linearity. A simple hybrid form is therefore proposed providing separate control over the tension-compression asymmetry. It is demonstrated how this form relates to a newly introduced generalised strain tensor class which encompasses both the tension-compression asymmetric Seth-Hill strain class and the tension-compression symmetric Ba\v{z}ant strain class. If the control parameter is set to q=0.5 a tension-compression symmetric form involving Ba\v{z}ant strains is obtained with the property {\Psi}({\lambda}_1,{\lambda}_2,{\lambda}_3 )={\Psi}(1/{\lambda}_1 ,1/{\lambda}_2 ,1/{\lambda}_3 ). The symmetric form may be desirable for the definition of ground matrix contributions in soft tissue modelling allowing all deviation from the symmetry to stem solely from fibrous reinforcement. Such an application is also presented demonstrating the use of the proposed formulation in the modelling of the non-linear elastic and transversely isotropic behaviour of skeletal muscle tissue in compression (the model implementation and fitting procedure have been made freely available). The presented hyperelastic formulations may aid researchers in independently controlling the degree of tension-compression asymmetry from the degree of non-linearity, and in the case of anisotropic materials may assist in determining the role played by, either the ground matrix, or the fibrous reinforcing structures, in generating asymmetry.Comment: 20 page

Mandate-driven networking eco-system : a paradigm shift in end-to-end communications

The wireless industry is driven by key stakeholders that follow a holistic approach of "one-system-fits-all" that leads to moving network functionality of meeting stringent End-to-End (E2E) communication requirements towards the core and cloud infrastructures. This trend is limiting smaller and new players for bringing in new and novel solutions. For meeting these E2E requirements, tenants and end-users need to be active players for bringing their needs and innovations. Driving E2E communication not only in terms of quality of service (QoS) but also overall carbon footprint and spectrum efficiency from one specific community may lead to undesirable simplifications and a higher level of abstraction of other network segments may lead to sub-optimal operations. Based on this, the paper presents a paradigm shift that will enlarge the role of wireless innovation at academia, Small and Medium-sized Enterprises (SME)'s, industries and start-ups while taking into account decentralized mandate-driven intelligence in E2E communications

Optimization of the processing of bio based polymer sustainable products

Polylactic Acid (PLA) is processed by injection moulding technology. The main aim of this study is to provide guidelines for mould and part design, namely to cope with the shrinkage effect and the ejection forces related to the use of bio based polymers. Furthermore optimization of the overall process will be investigated as well as the influence of different parameters to the process and product properties. Draft angle, mould temperature and holding pressure will be related to the ejection forces and the level of shrinkage that occurs

Tridimensional assessment of adductor spasmodic dysphonia pre- and post-treatment with Botulinum toxin

Spasmodic dysphonia voices form, in the same way as substitution voices, a particular category of dysphonia that seems not suited for a standardized basic multidimensional assessment protocol, like the one proposed by the European Laryngological Society. Thirty-three exhaustive analyses were performed on voices of 19 patients diagnosed with adductor spasmodic dysphonia (SD), before and after treatment with Botulinum toxin. The speech material consisted of 40 short sentences phonetically selected for constant voicing. Seven perceptual parameters (traditional and dedicated) were blindly rated by a panel of experienced clinicians. Nine acoustic measures (mainly based on voicing evidence and periodicity) were achieved by a special analysis program suited for strongly irregular signals and validated with synthesized deviant voices. Patients also filled in a VHI-questionnaire. Significant improvement is shown by all three approaches. The traditional GRB perceptual parameters appear to be adequate for these patients. Conversely, the special acoustic analysis program is successful in objectivating the improved regularity of vocal fold vibration: the basic jitter remains the most valuable parameter, when reliably quantified. The VHI is well suited for the voice-related quality of life. Nevertheless, when considering pre-therapy and post-therapy changes, the current study illustrates a complete lack of correlation between the perceptual, acoustic, and self-assessment dimensions. Assessment of SD-voices needs to be tridimensional