Levels of discontinuity, limit-computability, and jump operators

We develop a general theory of jump operators, which is intended to provide an abstraction of the notion of "limit-computability" on represented spaces. Jump operators also provide a framework with a strong categorical flavor for investigating degrees of discontinuity of functions and hierarchies of sets on represented spaces. We will provide a thorough investigation within this framework of a hierarchy of $\Delta^0_2$-measurable functions between arbitrary countably based $T_0$-spaces, which captures the notion of computing with ordinal mind-change bounds. Our abstract approach not only raises new questions but also sheds new light on previous results. For example, we introduce a notion of "higher order" descriptive set theoretical objects, we generalize a recent characterization of the computability theoretic notion of "lowness" in terms of adjoint functors, and we show that our framework encompasses ordinal quantifications of the non-constructiveness of Hilbert's finite basis theorem

A generalization of a theorem of Hurewicz for quasi-Polish spaces

We identify four countable topological spaces $S_2$, $S_1$, $S_D$, and $S_0$ which serve as canonical examples of topological spaces which fail to be quasi-Polish. These four spaces respectively correspond to the $T_2$, $T_1$, $T_D$, and $T_0$-separation axioms. $S_2$ is the space of rationals, $S_1$ is the natural numbers with the cofinite topology, $S_D$ is an infinite chain without a top element, and $S_0$ is the set of finite sequences of natural numbers with the lower topology induced by the prefix ordering. Our main result is a generalization of Hurewicz's theorem showing that a co-analytic subset of a quasi-Polish space is either quasi-Polish or else contains a countable $\Pi^0_2$-subset homeomorphic to one of these four spaces

ECAPA-TDNN: Emphasized Channel Attention, Propagation and Aggregation in TDNN Based Speaker Verification

Current speaker verification techniques rely on a neural network to extract speaker representations. The successful x-vector architecture is a Time Delay Neural Network (TDNN) that applies statistics pooling to project variable-length utterances into fixed-length speaker characterizing embeddings. In this paper, we propose multiple enhancements to this architecture based on recent trends in the related fields of face verification and computer vision. Firstly, the initial frame layers can be restructured into 1-dimensional Res2Net modules with impactful skip connections. Similarly to SE-ResNet, we introduce Squeeze-and-Excitation blocks in these modules to explicitly model channel interdependencies. The SE block expands the temporal context of the frame layer by rescaling the channels according to global properties of the recording. Secondly, neural networks are known to learn hierarchical features, with each layer operating on a different level of complexity. To leverage this complementary information, we aggregate and propagate features of different hierarchical levels. Finally, we improve the statistics pooling module with channel-dependent frame attention. This enables the network to focus on different subsets of frames during each of the channel's statistics estimation. The proposed ECAPA-TDNN architecture significantly outperforms state-of-the-art TDNN based systems on the VoxCeleb test sets and the 2019 VoxCeleb Speaker Recognition Challenge.Comment: proceedings of INTERSPEECH 202

Numerical simulation of an array of heaving floating point absorber wave energy converters using OpenFOAM

In this paper we use the CFD toolbox OpenFOAM to perform numerical simulations of multiple floating point absorber Wave Energy Converters (WECs) in a numerical wave basin. The two-phase Navier-Stokes fluid solver is coupled with a motion solver to simulate the wave-induced rigid body heave motion. The key of this paper is to extend numerical simulations of a single WEC unit to multiple WECs and to tackle the issues of modelling individual floating objects close to each other in an array lay-out. The developed numerical model is validated with laboratory experiments for free decay tests and for a regular wave train using two or five WECs in the array. For all the simulations presented, a good agreement is found between the numerical and experimental results for the WECs’ heave motions, the surge forces on the WECs and the perturbed wave field. As a result, our coupled CFD–motion solver proofs to be a suitable and accurate toolbox for the study of wave-structure interaction problems of multiple floating bodies in an array configuration