Invariants for neural automata

Computational modeling of neurodynamical systems often deploys neural networks and symbolic dynamics. One particular way for combining these approaches within a framework called vector symbolic architectures leads to neural automata. Specifically, neural automata result from the assignment of symbols and symbol strings to numbers, known as Gödel encoding. Under this assignment, symbolic computation becomes represented by trajectories of state vectors in a real phase space, that allows for statistical correlation analyses with real-world measurements and experimental data. However, these assignments are usually completely arbitrary. Hence, it makes sense to address the problem which aspects of the dynamics observed under a Gödel representation is intrinsic to the dynamics and which are not. In this study, we develop a formally rigorous mathematical framework for the investigation of symmetries and invariants of neural automata under different encodings. As a central concept we define patterns of equality for such systems. We consider different macroscopic observables, such as the mean activation level of the neural network, and ask for their invariance properties. Our main result shows that only step functions that are defined over those patterns of equality are invariant under symbolic recodings, while the mean activation, e.g., is not. Our work could be of substantial importance for related regression studies of real-world measurements with neurosymbolic processors for avoiding confounding results that are dependant on a particular encoding and not intrinsic to the dynamics.RTI2018-093860-BC21 funded by (AEI/FEDER, UE) and acronym MathNEURO PID2020-117281GB-I00 PID2019-107444GA-I00 European Regional Development Fund (ERDF) Basque Government, grant IT1483-2

Complementarity in classical dynamical systems

The concept of complementarity, originally defined for non-commuting observables of quantum systems with states of non-vanishing dispersion, is extended to classical dynamical systems with a partitioned phase space. Interpreting partitions in terms of ensembles of epistemic states (symbols) with corresponding classical observables, it is shown that such observables are complementary to each other with respect to particular partitions unless those partitions are generating. This explains why symbolic descriptions based on an \emph{ad hoc} partition of an underlying phase space description should generally be expected to be incompatible. Related approaches with different background and different objectives are discussed.Comment: 18 pages, no figure

FORUM:Remote testing for psychological and physiological acoustics

Acoustics research involving human participants typically takes place in specialized laboratory settings. Listening studies, for example, may present controlled sounds using calibrated transducers in sound-attenuating or anechoic chambers. In contrast, remote testing takes place outside of the laboratory in everyday settings (e.g., participants' homes). Remote testing could provide greater access to participants, larger sample sizes, and opportunities to characterize performance in typical listening environments at the cost of reduced control of environmental conditions, less precise calibration, and inconsistency in attentional state and/or response behaviors from relatively smaller sample sizes and unintuitive experimental tasks. The Acoustical Society of America Technical Committee on Psychological and Physiological Acoustics launched the Task Force on Remote Testing (https://tcppasa.org/remotetesting/) in May 2020 with goals of surveying approaches and platforms available to support remote testing and identifying challenges and considerations for prospective investigators. The results of this task force survey were made available online in the form of a set of Wiki pages and summarized in this report. This report outlines the state-of-the-art of remote testing in auditory-related research as of August 2021, which is based on the Wiki and a literature search of papers published in this area since 2020, and provides three case studies to demonstrate feasibility during practice

Kernel reconstruction for delayed neural field equations

Understanding the neural field activity for realistic living systems is a challenging task in contemporary neuroscience. Neural fields have been studied and developed theoretically and numerically with considerable success over the past four decades. However, to make effective use of such models, we need to identify their constituents in practical systems. This includes the determination of model parameters and in particular the reconstruction of the underlying effective connectivity in biological tissues. In this work, we provide an integral equation approach to the reconstruction of the neural connectivity in the case where the neural activity is governed by a delay neural field equation. As preparation, we study the solution of the direct problem based on the Banach fixed point theorem. Then we reformulate the inverse problem into a family of integral equations of the first kind. This equation will be vector valued when several neural activity trajectories are taken as input for the inverse problem. We employ spectral regularization techniques for its stable solution. A sensitivity analysis of the regularized kernel reconstruction with respect to the input signal u is carried out, investigating the Frechet differentiability of the kernel with respect to the signal. Finally, we use numerical examples to show the feasibility of the approach for kernel reconstruction, including numerical sensitivity tests, which show that the integral equation approach is a very stable and promising approach for practical computational neuroscience

Empirical Research on Sovereign Debt and Default

The long history of sovereign debt and the associated enforcement problem have attracted researchers in many fields. In this paper, we survey empirical work by economists, historians, and political scientists. As we review the empirical literature, we emphasize parallel developments in the theory of sovereign debt. One major theme emerges. Although recent research has sought to balance theoretical and empirical considerations, there remains a gap between theories of sovereign debt and the data used to test them. We recommend a number of steps that researchers can take to improve the correspondence between theory and data

The genetic basis of endometriosis and comorbidity with other pain and inflammatory conditions

Endometriosis is a common condition associated with debilitating pelvic pain and infertility. A genome-wide association study meta-analysis, including 60,674 cases and 701,926 controls of European and East Asian descent, identified 42 genome-wide significant loci comprising 49 distinct association signals. Effect sizes were largest for stage 3/4 disease, driven by ovarian endometriosis. Identified signals explained up to 5.01% of disease variance and regulated expression or methylation of genes in endometrium and blood, many of which were associated with pain perception/maintenance (SRP14/BMF, GDAP1, MLLT10, BSN and NGF). We observed significant genetic correlations between endometriosis and 11 pain conditions, including migraine, back and multisite chronic pain (MCP), as well as inflammatory conditions, including asthma and osteoarthritis. Multitrait genetic analyses identified substantial sharing of variants associated with endometriosis and MCP/migraine. Targeted investigations of genetically regulated mechanisms shared between endometriosis and other pain conditions are needed to aid the development of new treatments and facilitate early symptomatic intervention

The genetic basis of endometriosis and comorbidity with other pain and inflammatory conditions

Endometriosis is a common condition associated with debilitating pelvic pain and infertility. A genome-wide association study meta-analysis, including 60,674 cases and 701,926 controls of European and East Asian descent, identified 42 genome-wide significant loci comprising 49 distinct association signals. Effect sizes were largest for stage 3/4 disease, driven by ovarian endometriosis. Identified signals explained up to 5.01% of disease variance and regulated expression or methylation of genes in endometrium and blood, many of which were associated with pain perception/maintenance (SRP14/BMF, GDAP1, MLLT10, BSN and NGF). We observed significant genetic correlations between endometriosis and 11 pain conditions, including migraine, back and multisite chronic pain (MCP), as well as inflammatory conditions, including asthma and osteoarthritis. Multitrait genetic analyses identified substantial sharing of variants associated with endometriosis and MCP/migraine. Targeted investigations of genetically regulated mechanisms shared between endometriosis and other pain conditions are needed to aid the development of new treatments and facilitate early symptomatic intervention