Frame multipliers are an abstract version of Toeplitz operators in frame theory and consist of a composition of a multiplication operator with the analysis and synthesis operators. Whereas the boundedness properties of frame multipliers on Banach spaces associated to a frame, so-called coorbit spaces, are well understood, their invertibility is much more difficult. We show that frame multipliers with a positive symbol are Banach space isomorphisms between the corresponding coorbit spaces. The results resemble the lifting theorems in the theory of Besov spaces and modulation spaces. Indeed, the application of the abstract lifting theorem to Gabor frames yields a new lifting theorem between modulation spaces. A second application to Fock spaces yields isomorphisms between weighted Fock spaces. The main techniques are taken from the theory of localized frames and the spectral invariance of matrix algebras.

House mice (Mus musculus), like other rodents, communicate using sonic and ultrasonic vocalizations (USVs), but their functions are still poorly understood. One of the main challenges for studying any acoustic communication is processing and analyzing audio files. Our aims here are to provide a critical and comprehensive review of the new bioacoustic tools available for processing and analyzing recordings of mouse vocalizations. We consider each method as used in a serial data processing pipeline and how to minimize errors at each step to prevent error propagation (or error cascades). First, we review methods for processing audio files of recordings of mice. We compare conventional approaches for visualizing vocalizations (time-frequency representations) with an alternative method adapted to the mouse auditory system. We compare machine learning (ML) and signal processing methods for automating USV detection and emphasize the need for better methods for denoising audio files and reliable frequency contour (ridge) tracking and feature extraction. Second, we review methods for analyzing detected USVs, focusing on classification and sequencing approaches. Classifying USVs is a challenging task because, while some calls are discrete, others show graded variation within and between call classes. We compare supervised classifications and unsupervised labeling, and we emphasize the importance of reliable manual (researcher-based) methods as a gold standard for automated ML approaches. We review classifications of mouse vocalizations in the literature, and we propose a new hierarchical framework for the classification of USVs. We examine methods for sequencing USVs and consider their relative advantages. Finally, we address the unresolved technological challenges for these methods to study rodent vocalizations and propose potential solutions for the future.

Bioacoustic recordings are often degraded by ambient noise, which complicates the analysis of weak or noise-overlapped vocalizations. Convolutional neural networks, particularly U-Net architectures, have shown strong denoising performance in speech and music processing. However, their application for denoising bioacoustic signals is limited by the scarcity of clean training data. To address this, we propose a training set synthesis approach and develop a supervised denoising model that predicts a complex ratio mask in the time-frequency domain. The model leverages ridges, or frequency contours, that represent the fundamental frequency together with one or more harmonic partial components of vocalizations. These ridges are used both for the synthesis of training set and for the design of a loss function that assigns higher weights to the ridge regions (ridge-guided loss function). This weighting step helps the network better preserve vocalization details during denoising. As a case study, we evaluate our approach using ultrasonic vocalization (USV) recordings of house mice, which are widely studied in behavioral biology and neuroscience. In field recordings, the proposed method enhances tracking of fundamental and harmonic partial ridges compared to previous signal-processing approaches. In addition, a classifier trained on denoised data improves USV classification on out-of-sample, noisy recordings from wild and domesticated mice compared to classifiers trained on noisy recordings. The proposed method also substantially improves the scale-invariant signal-to-distortion ratio on synthetic testing data across a wide range of input signal-to-noise ratios. While focused on USVs, the proposed approach is broadly applicable to other bioacoustic signals with trackable ridges, and thus enables ridge-based training set synthesis and denoising.

Male house mice (Mus musculus) emit ultrasonic vocalizations (USVs) during courtship and mating, which influence their copulatory success. Several studies have found that playbacks of male USVs attract females, though this response may depend on the presence of male scent, and one study suggested that females are more attracted to complex than simple USV types. We conducted three playback experiments with wild-derived female house mice to test these predictions. None of our results met our expectations: First, females were not more attracted to sequences of complex versus simple USVs. Second, females were also not more attracted to these syllables when compared to silence. Third, females showed no attraction towards more natural sequences containing simple and complex USVs compared to silence, even in the presence of male scent. Thus, we found no evidence that wild-derived female mice show approach behavior towards male USVs, regardless of their complexity or exposure to male olfactory stimuli. These findings raise questions about the repeatability and generalizability of playback studies in house mice and highlight the need for more studies aimed at determining the types of vocalizations and contexts under which mice do and do not show attraction or other responses to USVs.

In this paper, we investigate whether the tensor product of two frames, each individually localised with respect to a spectral matrix algebra, is also localised with respect to a suitably chosen tensor product algebra. We provide a partial answer by constructing an involutive Banach algebra of rank-four tensors that is built from two solid spectral matrix algebras. We show that this algebra is inverse-closed, given that the original algebras satisfy a specific property related to operator-valued versions of these algebras. This condition is satisfied by all commonly used solid spectral matrix algebras. We then prove that the tensor product of two self-localised frames remains self-localised with respect to our newly constructed tensor algebra. Additionally, we discuss generalisations to localised frames of Hilbert-Schmidt operators, which may not necessarily consist of rank-one operators.

We introduce a localization concept for operator-valued frames, where the quality of localization is measured by the associated operator-valued Gram matrix belonging to some suitable Banach algebra. We prove that intrinsic localization of an operator-valued frame is preserved by its canonical dual. Moreover, we show that the series associated to the perfect reconstruction of an operator-valued frame converges not only in the underlying Hilbert space, but also in a whole class of associated (quasi-)Banach spaces which are carefully introduced and analyzed. Finally, we apply our results to irregular Gabor g-frames.

In this paper, we ask when it is possible to transform a given sequence into a frame or a lower semi frame by multiplying the elements by numbers. In other words, we ask when a given sequence is a weighted frame or a weighted lower semi frame and for each case we formulate a conjecture. We determine several conditions under which these conjectures are true. Finally, we prove an equivalence between two older conjectures. The one being that any unconditionally convergent multiplier can be written as a multiplier of Bessel sequences by shifting weights between the generating sequences of the multiplier. The second one that every unconditionally convergent multiplier which is invertible can be written as a multiplier of frames by a similar shift of weights. We also show that these conjectures are also related to one of the newly posed conjectures.