A dual larynx motor networks hypothesis

Humans are vocal modulators par excellence. This ability is supported in part by the dual representation of the laryngeal muscles in the motor cortex. Movement, however, is not the product of motor cortex alone but of a broader motor network. This network consists of brain regions that contain somatotopic maps that parallel the organization in motor cortex. We therefore present a novel hypothesis that the dual laryngeal representation is repeated throughout the broader motor network. In support of the hypothesis, we review existing literature that demonstrates the existence of network-wide somatotopy and present initial evidence for the hypothesis' plausibility. Understanding how this uniquely human phenotype in motor cortex interacts with broader brain networks is an important step toward understanding how humans evolved the ability to speak. We further suggest that this system may provide a means to study how individual components of the nervous system evolved within the context of neuronal networks. This article is part of the theme issue ‘Voice modulation: from origin and mechanism to social impact (Part I)’.

Scalar Multivariate Risk Measures with a Single Eligible Asset

In this paper, we present results on scalar risk measures in markets with transaction costs. Such risk measures are defined as the minimal capital requirements in the cash asset. First, some results are provided on the dual representation of such risk measures, with particular emphasis given on the space of dual variables as (equivalent) martingale measures and prices consistent with the market model. Then, these dual representations are used to obtain the main results of this paper on time consistency for scalar risk measures in markets with frictions. It is well known from the superhedging risk measure in markets with transaction costs that the usual scalar concept of time consistency is too strong and not satisfied. We will show that a weaker notion of time consistency can be defined, which corresponds to the usual scalar time consistency but under any fixed consistent pricing process. We will prove the equivalence of this weaker notion of time consistency and a certain type of backward recursion with respect to the underlying risk measure with a fixed consistent pricing process. Several examples are given, with special emphasis on the superhedging risk measure.

Set-Valued T-Translative Functions and Their Applications in Finance

A theory for set-valued functions is developed, which are translative with respect to a linear operator. It is shown that such functions cover a wide range of applications, from projections in Hilbert spaces, set-valued quantiles for vector-valued random variables, to scalar or set-valued risk measures in finance with defaultable or nondefaultable securities. Primal, dual, and scalar representation results are given, among them an infimal convolution representation, which is not so well known even in the scalar case. Along the way, new concepts of set-valued lower/upper expectations are introduced and dual representation results are formulated using such expectations. An extension to random sets is discussed at the end. The principal methodology consisted of applying the complete lattice framework of set optimization.

A dual larynx motor networks hypothesis

Humans are vocal modulators par excellence. This ability is supported in part by the dual representation of the laryngeal muscles in the motor cortex. Movement, however, is not the product of motor cortex alone but of a broader motor network. This network consists of brain regions which contain somatotopic maps that parallel the organisation in motor cortex. We therefore present a novel hypothesis that the dual laryngeal representation is repeated throughout the broader motor network. In support of the hypothesis we review existing literature which demonstrates the existence of network-wide somatotopy, and present initial evidence for the hypothesis’ plausibility. Understanding how this uniquely human phenotype in motor cortex interacts with broader brain networks is an important step toward understanding how humans evolved the ability to speak. We further suggest that this system may provide a means to study how individual components of the nervous system evolved within the context of neuronal networks.

Quantum gravity states, entanglement graphs and second-quantized tensor networks

In recent years, the import of quantum information techniques in quantum gravity opened new perspectives in the study of the microscopic structure of spacetime. We contribute to such a program by establishing a precise correspondence between the quantum information formalism of tensor networks (TN), in the case of projected entangled-pair states (PEPS) generalised to a second-quantized framework, and group field theory (GFT) states, and by showing how, in this quantum gravity approach, discrete spatial manifolds arise as entanglement patterns among quanta of space, having a dual representation in terms of graphs and simplicial complexes. We devote special attention to the implementation and consequences of the label independence of the graphs/networks, corresponding to the indistinguishability of the space quanta and representing a discrete counterpart of the diffeomorphism invariance of a consistent quantum gravity formalism. We also outline a relational setting to recover distinguishability of graph/network vertices at an effective and physical level, in a partial semi-classical limit of the theory.

Identifying Critical Isolation Valves in a Water Distribution Network: A Socio-Technical Approach

Isolation valves are critical for reliable functioning of water distribution networks (WDNs). However, it is challenging for utilities to prioritize valve rehabilitation and replacement given it is often unclear if certain valves are operable in a given WDN. This study uses the Gomory-hu tree of the segment-valve representation (or dual representation) of WDNs to obtain logical implications of inoperable valves (i.e., which segments would be isolated and merged unnecessarily due to valve inoperability). Multi-objective optimization is then used to identify the critical valves based on selected attributes (e.g., social vulnerability, flow volume) of segments that would be unnecessarily isolated as a result. This study developed three multi-objective formulations: first, deterministic; second, accounting for uncertainty; and third, accounting or both uncertainty and likelihood of failure of pipes within segments. Identified critical valves are compared between the three developed formulations and a method considering only a single objective. Results demonstrated that the multi-objective optimization provided additional information that can be used to discern valve importance for utilities in comparison with using a single objective. Further, though there was overlap between the results from the three formulations, the third formulation provided the most insight without overwhelming decision-makers with a large number of identified valves.

Dual subtractions

We propose a novel local subtraction scheme for the computation of Next-to-Leading Order contributions to theoretical predictions for scattering processes in perturbative Quantum Field Theory. With respect to well known schemes proposed since many years that build upon the analysis of the real radiation matrix elements, our construction starts from the loop diagrams and exploits their dual representation. Our scheme implements exact phase space factorization, handles final state as well as initial state singularities and is suitable for both massless and massive particles.