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Rodents employ a broad spectrum of ultrasonic vocalizations (USVs) for social communication. As these vocalizations offer valuable insights into affective states, social interactions, and developmental stages of animals, various deep learning approaches have aimed to automate both the quantitative (detection) and qualitative (classification) analysis of USVs. Here, we present the first systematic evaluation of different types of neural networks for USV classification. We assessed various feedforward networks, including a custom-built, fully-connected network and convolutional neural network, different residual neural networks (ResNets), an EfficientNet, and a Vision Transformer (ViT). Paired with a refined, entropy-based detection algorithm (achieving recall of 94.9% and precision of 99.3%), the best architecture (achieving 86.79% accuracy) was integrated into a fully automated pipeline capable of analyzing extensive USV datasets with high reliability. Additionally, users can specify an individual minimum accuracy threshold based on their research needs. In this semi-automated setup, the pipeline selectively classifies calls with high pseudo-probability, leaving the rest for manual inspection. Our study focuses exclusively on neonatal USVs. As part of an ongoing phenotyping study, our pipeline has proven to be a valuable tool for identifying key differences in USVs produced by mice with autism-like behaviors.

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Neural operators such as the Fourier Neural Operator (FNO) have been shown to provide resolution-independent deep learning models that can learn mappings between function spaces. For example, an initial condition can be mapped to the solution of a partial differential equation (PDE) at a future time-step using a neural operator. Despite the popularity of neural operators, their use to predict solution functions over a domain given only data over the boundary (such as a spatially varying Dirichlet boundary condition) remains unexplored. In this paper, we refer to such problems as boundary-to-domain problems; they have a wide range of applications in areas such as fluid mechanics, solid mechanics, heat transfer etc. We present a novel FNO-based architecture, named Lifting Product FNO (or LP-FNO) which can map arbitrary boundary functions defined on the lower-dimensional boundary to a solution in the entire domain. Specifically, two FNOs defined on the lower-dimensional boundary are lifted into the higher dimensional domain using our proposed lifting product layer. We demonstrate the efficacy and resolution independence of the proposed LP-FNO for the 2D Poisson equation.

We introduce a new Langevin dynamics based algorithm, called e-TH$\varepsilon$O POULA, to solve optimization problems with discontinuous stochastic gradients which naturally appear in real-world applications such as quantile estimation, vector quantization, CVaR minimization, and regularized optimization problems involving ReLU neural networks. We demonstrate both theoretically and numerically the applicability of the e-TH$\varepsilon$O POULA algorithm. More precisely, under the conditions that the stochastic gradient is locally Lipschitz in average and satisfies a certain convexity at infinity condition, we establish non-asymptotic error bounds for e-TH$\varepsilon$O POULA in Wasserstein distances and provide a non-asymptotic estimate for the expected excess risk, which can be controlled to be arbitrarily small. Three key applications in finance and insurance are provided, namely, multi-period portfolio optimization, transfer learning in multi-period portfolio optimization, and insurance claim prediction, which involve neural networks with (Leaky)-ReLU activation functions. Numerical experiments conducted using real-world datasets illustrate the superior empirical performance of e-TH$\varepsilon$O POULA compared to SGLD, TUSLA, ADAM, and AMSGrad in terms of model accuracy.

We investigate the proof complexity of systems based on positive branching programs, i.e. non-deterministic branching programs (NBPs) where, for any 0-transition between two nodes, there is also a 1-transition. Positive NBPs compute monotone Boolean functions, just like negation-free circuits or formulas, but constitute a positive version of (non-uniform) NL, rather than P or NC1, respectively. The proof complexity of NBPs was investigated in previous work by Buss, Das and Knop, using extension variables to represent the dag-structure, over a language of (non-deterministic) decision trees, yielding the system eLNDT. Our system eLNDT+ is obtained by restricting their systems to a positive syntax, similarly to how the 'monotone sequent calculus' MLK is obtained from the usual sequent calculus LK by restricting to negation-free formulas. Our main result is that eLNDT+ polynomially simulates eLNDT over positive sequents. Our proof method is inspired by a similar result for MLK by Atserias, Galesi and Pudl\'ak, that was recently improved to a bona fide polynomial simulation via works of Je\v{r}\'abek and Buss, Kabanets, Kolokolova and Kouck\'y. Along the way we formalise several properties of counting functions within eLNDT+ by polynomial-size proofs and, as a case study, give explicit polynomial-size poofs of the propositional pigeonhole principle.

Understanding the emergence of data breaches is crucial for cyber insurance. However, analyses of data breach frequency trends in the current literature lead to contradictory conclusions. We put forward that those discrepancies may be (at least partially) due to inconsistent data collection standards, as well as reporting patterns, over time and space. We set out to carefully control both. In this paper, we conduct a joint analysis of state Attorneys General's publications on data breaches across eight states (namely, California, Delaware, Indiana, Maine, Montana, North Dakota, Oregon, and Washington), all of which are subject to established data collection standards-namely, state data breach (mandatory) notification laws. Thanks to our explicit recognition of these notification laws, we are capable of modelling frequency of breaches in a consistent and comparable way over time. Hence, we are able to isolate and capture the complexities of reporting patterns, adequately estimate IBNRs, and yield a highly reliable assessment of historical frequency trends in data breaches. Our analysis also provides a comprehensive comparison of data breach frequency across the eight U.S. states, extending knowledge on state-specific differences in cyber risk, which has not been extensively discussed in the current literature. Furthermore, we uncover novel features not previously discussed in the literature, such as differences in cyber risk frequency trends between large and small data breaches. Overall, we find that the reporting delays are lengthening. We also elicit commonalities and heterogeneities in reporting patterns across states, severity levels, and time periods. After adequately estimating IBNRs, we find that frequency is relatively stable before 2020 and increasing after 2020. This is consistent across states. Implications of our findings for cyber insurance are discussed.

Weakly Supervised Semantic Segmentation (WSSS) employs weak supervision, such as image-level labels, to train the segmentation model. Despite the impressive achievement in recent WSSS methods, we identify that introducing weak labels with high mean Intersection of Union (mIoU) does not guarantee high segmentation performance. Existing studies have emphasized the importance of prioritizing precision and reducing noise to improve overall performance. In the same vein, we propose ORANDNet, an advanced ensemble approach tailored for WSSS. ORANDNet combines Class Activation Maps (CAMs) from two different classifiers to increase the precision of pseudo-masks (PMs). To further mitigate small noise in the PMs, we incorporate curriculum learning. This involves training the segmentation model initially with pairs of smaller-sized images and corresponding PMs, gradually transitioning to the original-sized pairs. By combining the original CAMs of ResNet-50 and ViT, we significantly improve the segmentation performance over the single-best model and the naive ensemble model, respectively. We further extend our ensemble method to CAMs from AMN (ResNet-like) and MCTformer (ViT-like) models, achieving performance benefits in advanced WSSS models. It highlights the potential of our ORANDNet as a final add-on module for WSSS models.

To analyze the topological properties of the given discrete data, one needs to consider a continuous transform called filtration. Persistent homology serves as a tool to track changes of homology in the filtration. The outcome of the topological analysis of data varies depending on the choice of filtration, making the selection of filtration crucial. Filtration learning is an attempt to find an optimal filtration that minimizes the loss function. Exact Multi-parameter Persistent Homology (EMPH) has been recently proposed, particularly for topological time-series analysis, that utilizes the exact formula of rank invariant instead of calculating it. In this paper, we propose a framework for filtration learning of EMPH. We formulate an optimization problem and propose an algorithm for solving the problem. We then apply the proposed algorithm to several classification problems. Particularly, we derive the exact formula of the gradient of the loss function with respect to the filtration parameter, which makes it possible to directly update the filtration without using automatic differentiation, significantly enhancing the learning process.

Magnetic Resonance Imaging (MRI) is a powerful technique employed for non-invasive in vivo visualization of internal structures. Sparsity is often deployed to accelerate the signal acquisition or overcome the presence of motion artifacts, improving the quality of image reconstruction. Image reconstruction algorithms use TV-regularized LASSO (Total Variation-regularized LASSO) to retrieve the missing information of undersampled signals, by cleaning the data of noise and while optimizing sparsity. A tuning parameter moderates the balance between these two aspects; its choice affecting the quality of the reconstructions. Currently, there is a lack of general deterministic techniques to choose these parameters, which are oftentimes manually selected and thus hinder the reliability of the reconstructions. Here, we present ALMA (Algorithm for Lagrange Multipliers Approximation), an iterative mathematics-inspired technique that computes tuning parameters for generalized LASSO problems during MRI reconstruction. We analyze quantitatively the performance of these parameters for imaging reconstructions via TV-LASSO in an MRI context on phantoms. Although our study concentrates on TV-LASSO, the techniques developed here hold significant promise for a wide array of applications. ALMA is not only adaptable to more generalized LASSO problems but is also robust to accommodate other forms of regularization beyond total variation. Moreover, it extends effectively to handle non-Cartesian sampling trajectories, broadening its utility in complex data reconstruction scenarios. More generally, ALMA provides a powerful tool for numerically solving constrained optimization problems across various disciplines, offering a versatile and impactful solution for advanced computational challenges.

General first order methods (GFOMs), including various gradient descent and AMP algorithms, constitute a broad class of iterative algorithms in modern statistical learning problems. Some GFOMs also serve as constructive proof devices, iteratively characterizing the empirical distributions of statistical estimators in the large system limits for any fixed number of iterations. This paper develops a non-asymptotic, entrywise characterization for a general class of GFOMs. Our characterizations capture the precise entrywise behavior of the GFOMs, and hold universally across a broad class of heterogeneous random matrix models. As a corollary, we provide the first non-asymptotic description of the empirical distributions of the GFOMs beyond Gaussian ensembles. We demonstrate the utility of these general results in two applications. In the first application, we prove entrywise universality for regularized least squares estimators in the linear model, by controlling the entrywise error relative to a suitably constructed GFOM. This algorithmic proof method also leads to systematically improved averaged universality results for regularized regression estimators in the linear model, and resolves the universality conjecture for (regularized) MLEs in logistic regression. In the second application, we obtain entrywise Gaussian approximations for a class of gradient descent algorithms. Our approach provides non-asymptotic state evolution for the bias and variance of the algorithm along the iteration path, applicable for non-convex loss functions. The proof relies on a new recursive leave-k-out method that provides almost delocalization for the GFOMs and their derivatives. Crucially, our method ensures entrywise universality for up to poly-logarithmic many iterations, which facilitates effective $\ell_2/\ell_\infty$ control between certain GFOMs and statistical estimators in applications.

A non-linear complex system governed by multi-spatial and multi-temporal physics scales cannot be fully understood with a single diagnostic, as each provides only a partial view and much information is lost during data extraction. Combining multiple diagnostics also results in imperfect projections of the system's physics. By identifying hidden inter-correlations between diagnostics, we can leverage mutual support to fill in these gaps, but uncovering these inter-correlations analytically is too complex. We introduce a groundbreaking machine learning methodology to address this issue. Our multimodal approach generates super resolution data encompassing multiple physics phenomena, capturing detailed structural evolution and responses to perturbations previously unobservable. This methodology addresses a critical problem in fusion plasmas: the Edge Localized Mode (ELM), a plasma instability that can severely damage reactor walls. One method to stabilize ELM is using resonant magnetic perturbation to trigger magnetic islands. However, low spatial and temporal resolution of measurements limits the analysis of these magnetic islands due to their small size, rapid dynamics, and complex interactions within the plasma. With super-resolution diagnostics, we can experimentally verify theoretical models of magnetic islands for the first time, providing unprecedented insights into their role in ELM stabilization. This advancement aids in developing effective ELM suppression strategies for future fusion reactors like ITER and has broader applications, potentially revolutionizing diagnostics in fields such as astronomy, astrophysics, and medical imaging.

This paper presents the first analysis of parameter-uniform convergence for a hybridizable discontinuous Galerkin (HDG) method applied to a singularly perturbed convection-diffusion problem in 2D using a Shishkin mesh. The primary difficulty lies in accurately estimating the convection term in the layer, where existing methods often fall short. To address this, a novel error control technique is employed, along with reasonable assumptions regarding the stabilization function. The results show that, with polynomial degrees not exceeding $k$, the method achieves supercloseness of almost $k+\frac{1}{2}$ order in an energy norm. Numerical experiments confirm the theoretical accuracy and efficiency of the proposed method.

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