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When a dynamical system is subject to a periodic perturbation, the averaging method can be applied to obtain an autonomous leading order `guiding system', placing the time dependence at higher orders. Recent research focused on investigating invariant structures in non-autonomous differential systems arising from hyperbolic structures in the guiding system, such as periodic orbits and invariant tori. The effect that bifurcations in the guiding system have on the original non-autonomous one has also been recently explored. This paper extends the study by providing a broader description of the dynamics that can emerge from non-hyperbolic structures of the guiding system. Specifically, we prove here that $K$-universal bifurcations in the guiding system persist in the original non-autonomous one, while non-versal bifurcations, such as the transcritical and pitchfork, do not, being instead perturbed into stable bifurcation families. We illustrate the results on examples of a fold, a transcritical, a pitchfork, and a saddle-focus. By applying these results to the physical scenario of systems with time-varying parameters, we show that the average parameter value becomes a bifurcation parameter of the averaged system.

Leveraging the capabilities of Knowledge Distillation (KD) strategies, we devise a strategy to fight the recent retraction of face recognition datasets. Given a pretrained Teacher model trained on a real dataset, we show that carefully utilising synthetic datasets, or a mix between real and synthetic datasets to distil knowledge from this teacher to smaller students can yield surprising results. In this sense, we trained 33 different models with and without KD, on different datasets, with different architectures and losses. And our findings are consistent, using KD leads to performance gains across all ethnicities and decreased bias. In addition, it helps to mitigate the performance gap between real and synthetic datasets. This approach addresses the limitations of synthetic data training, improving both the accuracy and fairness of face recognition models., Comment: Accepted at ECCV 2024 Workshops

As in school, one teacher to cover all subjects is insufficient to distill equally robust information to a student. Hence, each subject is taught by a highly specialised teacher. Following a similar philosophy, we propose a multiple specialized teacher framework to distill knowledge to a student network. In our approach, directed at face recognition use cases, we train four teachers on one specific ethnicity, leading to four highly specialized and biased teachers. Our strategy learns a project of these four teachers into a common space and distill that information to a student network. Our results highlighted increased performance and reduced bias for all our experiments. In addition, we further show that having biased/specialized teachers is crucial by showing that our approach achieves better results than when knowledge is distilled from four teachers trained on balanced datasets. Our approach represents a step forward to the understanding of the importance of ethnicity-specific features., Comment: Accepted at ECCV 2024 ABAW

This work provides a complete rheological characterization of molybdenum disulfide (MoS2) inks in the presence of electric fields. Several concentrations of MoS2 are studied and dispersed in a viscoelastic fluid. The lubrication effects are present in the ink when the MoS2 concentration is higher than 0.10% w/w. The dielectric properties show the impossibility of a positive electrorheological effect for all MoS2-inks studied. The formation of vortices and electromigration of MoS2 particles occur under the influence of an external electric field. These two phenomena affect the rheological behavior of MoS2-inks under shear flow condition. Relatively to the extensional rheology experiments, the particle migration and the vortex formation promote anisotropy on the rheological properties of the inks which affects the relaxation time, the formation of beads-on-a-string and the uniaxial elongational flow condition is no longer valid. When the electric field strength is 1.5 kV/mm, the formation of Taylor's cone is observed and independent of MoS2 concentration.

This study investigates the effects of occlusions on the fairness of face recognition systems, particularly focusing on demographic biases. Using the Racial Faces in the Wild (RFW) dataset and synthetically added realistic occlusions, we evaluate their effect on the performance of face recognition models trained on the BUPT-Balanced and BUPT-GlobalFace datasets. We note increases in the dispersion of FMR, FNMR, and accuracy alongside decreases in fairness according to Equilized Odds, Demographic Parity, STD of Accuracy, and Fairness Discrepancy Rate. Additionally, we utilize a pixel attribution method to understand the importance of occlusions in model predictions, proposing a new metric, Face Occlusion Impact Ratio (FOIR), that quantifies the extent to which occlusions affect model performance across different demographic groups. Our results indicate that occlusions exacerbate existing demographic biases, with models placing higher importance on occlusions in an unequal fashion, particularly affecting African individuals more severely., Comment: Accepted at ECCV Workshop FAILED

Variational quantum algorithms (VQAs) have emerged in recent years as a promise to obtain quantum advantage. These task-oriented algorithms work in a hybrid loop combining a quantum processor and classical optimization. Using a specific class of VQA named variational quantum eigensolvers (VQEs), we choose some parameterized quantum circuits to benchmark them at entanglement witnessing and entangled ground state detection for many-body systems described by Heisenberg Hamiltonian, varying the number of qubits and shots. Quantum circuits whose structure is inspired by the Hamiltonian interactions presented better results on cost function estimation than problem-agnostic circuits.

Parameterized quantum circuits play a key role for the development of quantum variational algorithms in the realm of the NISQ era. Knowing their actual capability of performing different kinds of tasks is then of the utmost importance. By comparing them with a prototypical class of universal random circuits we have found that their approach to the asymptotic complexity defined by the Haar measure is faster, needing less gates to reach it. Topology has been revealed crucial for this. The majorization criterion has proven as a relevant complementary tool to the expressibility and the mean entanglement., Comment: 8 pages, 4 figures

While scalable error correction schemes and fault tolerant quantum computing seem not to be universally accessible in the near sight, the efforts of many researchers have been directed to the exploration of the contemporary available quantum hardware. Due to these limitations, the depth and dimension of the possible quantum circuits are restricted. This motivates the study of circuits with parameterized operations that can be classically optimized in hybrid methods as variational quantum algorithms (VQAs), enabling the reduction of circuit depth and size. The characteristics of these Parameterized Quantum Circuits (PQCs) are still not fully understood outside the scope of their principal application, motivating the study of their intrinsic properties. In this work, we analyse the generation of random states in PQCs under restrictions on the qubits connectivities, justified by different quantum computer architectures. We apply the expressibility quantifier and the average entanglement as diagnostics for the characteristics of the generated states and classify the circuits depending on the topology of the quantum computer where they can be implemented. As a function of the number of layers and qubits, circuits following a Ring topology will have the highest entanglement and expressibility values, followed by Linear/All-to-all almost together and the Star topology. In addition to the characterization of the differences between the entanglement and expressibility of these circuits, we also place a connection between how steep is the increase on the uniformity of the distribution of the generated states and the generation of entanglement. Circuits generating average and standard deviation for entanglement closer to values obtained with the truly uniformly random ensemble of unitaries present a steeper evolution when compared to others., Comment: 14 pages, 13 figures

Face recognition applications have grown in parallel with the size of datasets, complexity of deep learning models and computational power. However, while deep learning models evolve to become more capable and computational power keeps increasing, the datasets available are being retracted and removed from public access. Privacy and ethical concerns are relevant topics within these domains. Through generative artificial intelligence, researchers have put efforts into the development of completely synthetic datasets that can be used to train face recognition systems. Nonetheless, the recent advances have not been sufficient to achieve performance comparable to the state-of-the-art models trained on real data. To study the drift between the performance of models trained on real and synthetic datasets, we leverage a massive attribute classifier (MAC) to create annotations for four datasets: two real and two synthetic. From these annotations, we conduct studies on the distribution of each attribute within all four datasets. Additionally, we further inspect the differences between real and synthetic datasets on the attribute set. When comparing through the Kullback-Leibler divergence we have found differences between real and synthetic samples. Interestingly enough, we have verified that while real samples suffice to explain the synthetic distribution, the opposite could not be further from being true., Comment: Accepted at FG 2024

Synthetic data is gaining increasing relevance for training machine learning models. This is mainly motivated due to several factors such as the lack of real data and intra-class variability, time and errors produced in manual labeling, and in some cases privacy concerns, among others. This paper presents an overview of the 2nd edition of the Face Recognition Challenge in the Era of Synthetic Data (FRCSyn) organized at CVPR 2024. FRCSyn aims to investigate the use of synthetic data in face recognition to address current technological limitations, including data privacy concerns, demographic biases, generalization to novel scenarios, and performance constraints in challenging situations such as aging, pose variations, and occlusions. Unlike the 1st edition, in which synthetic data from DCFace and GANDiffFace methods was only allowed to train face recognition systems, in this 2nd edition we propose new sub-tasks that allow participants to explore novel face generative methods. The outcomes of the 2nd FRCSyn Challenge, along with the proposed experimental protocol and benchmarking contribute significantly to the application of synthetic data to face recognition., Comment: arXiv admin note: text overlap with arXiv:2311.10476

We present S+t-SNE, an adaptation of the t-SNE algorithm designed to handle infinite data streams. The core idea behind S+t-SNE is to update the t-SNE embedding incrementally as new data arrives, ensuring scalability and adaptability to handle streaming scenarios. By selecting the most important points at each step, the algorithm ensures scalability while keeping informative visualisations. Employing a blind method for drift management adjusts the embedding space, facilitating continuous visualisation of evolving data dynamics. Our experimental evaluations demonstrate the effectiveness and efficiency of S+t-SNE. The results highlight its ability to capture patterns in a streaming scenario. We hope our approach offers researchers and practitioners a real-time tool for understanding and interpreting high-dimensional data., Comment: This preprint has not undergone peer review or any post-submission improvements or corrections. We will soon add a link to the final version of this contribution that underwent peer-review and post-acceptance improvements and was presented at IDA2024 (https://ida2024.org/)

In this paper, the time-dependent dielectric breakdown (TDDB) in sub-1-nm equivalent oxide thickness (EOT) n-type bulk FinFETs is studied. The gate stacks consist of an IMEC clean interfacial layer, atomic layer deposition HfO2 high-k and TiN metal electrode. For the 0.8-nm EOT FinFETs, it is found that TDDB lifetime is consistent with results of planar devices for areas around 1e-8 cm2, implying that the FinFET architecture does not seem to introduce new failure mechanisms. However, for devices with smaller area, the extrapolated voltage at a ten-year lifetime for soft breakdown (SBD) does not meet the specifications, and as a consequence, the SBD path wear-out will have to be included in the final extrapolation. Furthermore, it is shown that for EOTs smaller than 0.8 nm, the TDDB reliability on n-type FinFETs is challenged by the high leakage currents., Comment: 15 pages, 7 figures

The solution of large systems of nonlinear differential equations is needed for many applications in science and engineering. In this study, we present three main improvements to existing quantum algorithms based on the Carleman linearisation technique. First, by using a high-precision technique for the solution of the linearised differential equations, we achieve logarithmic dependence of the complexity on the error and near-linear dependence on time. Second, we demonstrate that a rescaling technique can considerably reduce the cost, which would otherwise be exponential in the Carleman order for a system of ODEs, preventing a quantum speedup for PDEs. Third, we provide improved, tighter bounds on the error of Carleman linearisation. We apply our results to a class of discretised reaction-diffusion equations using higher-order finite differences for spatial resolution. We show that providing a stability criterion independent of the discretisation can conflict with the use of the rescaling due to the difference between the max-norm and 2-norm. An efficient solution may still be provided if the number of discretisation points is limited, as is possible when using higher-order discretisations., Comment: 37 pages, 2 figures

The solution of linear systems of equations is the basis of many other quantum algorithms, and recent results provided an algorithm with optimal scaling in both the condition number $\kappa$ and the allowable error $\epsilon$ [PRX Quantum \textbf{3}, 0403003 (2022)]. That work was based on the discrete adiabatic theorem, and worked out an explicit constant factor for an upper bound on the complexity. Here we show via numerical testing on random matrices that the constant factor is in practice about 1,500 times smaller than the upper bound found numerically in the previous results. That means that this approach is far more efficient than might naively be expected from the upper bound. In particular, it is over an order of magnitude more efficient than using a randomised approach from [arXiv:2305.11352] that claimed to be more efficient., Comment: 12 pages, 33 figures

Floquet's Theorem is a celebrated result in the theory of ordinary differential equations. Essentially, the theorem states that, when studying a linear differential system with $T$-periodic coefficients, we can apply a, possibly complex, $T$-periodic change of variables that transforms it into a linear system with constant coefficients. In this paper, we explore further the question of the nature of this change of variables. We state necessary and sufficient conditions for it to be real and $T$-periodic. Failing those conditions, we prove that we can still find a real change of variables that is "partially" $T$-periodic and "partially" $T$-antiperiodic. We also present applications of this new form of Floquet's Theorem to the study of the behavior of solutions of nonlinear differential systems near periodic orbits.

Chemotaxis combines three processes: directional sensing, polarity reorientation and migration. Directed migration plays an important role in immune response, metastasis, wound healing and development. To describe chemotaxis, we extend a previously published computational model of a 3D single cell, that presents three compartments (lamellipodium, nucleus and cytoplasm), whose migration on a flat surface quantitatively describes experiments. The simulation is built in the framework of CompuCell3D, an environment based on the Cellular Potts Model. In our extension, we treat chemotaxis as a compound process rather than a response to a potential force. We propose robust protocols to measure cell persistence, drift speed, terminal speed, chemotactic efficiency, taxis time, and we analyse cell migration dynamics in the cell reference frame from position and polarization recordings through time. Our metrics can be applied to experimental results and allow quantitative comparison between simulations and experiments. We found that our simulated cells exhibit a trade-off between polarization stability and chemotactic efficiency. Specifically, we found that cells with lower protrusion forces and smaller lamellipodia exhibit an increased ability to undergo chemotaxis. We also noticed no significant change in cell movement due to external chemical gradient when analysing cell displacement in the cell reference frame. Our results demonstrate the importance of measuring cell polarity throughout the entire cell trajectory, and treating velocity quantities carefully when cell movement is diffusive at short time intervals. The simulation we developed is adequate to the development of new measurement protocols, and it helps paving the way to more complex multicellular simulations to model collective migration and their interaction with external fields, which are under development on this date., Comment: Download and run (in CompuCell3D version 4) the simulation at https://github.com/pdalcastel/Single_Cell_Chemotaxis_2.3 . See the supplemental materials at https://github.com/pdalcastel/CC3D-Chemotaxis-SuppMat

In this note we study the tensor and vector exchange contributions to the elastic reactions involving the pseudoscalars mesons $\pi^+ \pi^-$, $K^{+}K^{-}$ and $D^{+}D^{-}$. In the case of the tensor-exchange contributions we assume that an intermediate tensor $f_2(1270)$ is dynamically generated from the interaction of two virtual $\rho$ mesons, with the use of a pole approximation. The calculation of the two-loop amplitude is facilitated since the triangle loops can be factorized and computed separately. The results show very small contributions coming from the tensor-exchange mechanisms when compared with those from the vector-exchange processes. We compare our results for $\pi \pi$ and $K\bar{K}$ scattering with those obtained in other works where the $f_2(1270)$ is considered as an ordinary $q\bar{q}$ meson. Our picture provides a smaller contribution but of similar order of magnitude for pion scattering and stabilizes the results in the case of $K\bar{K}$, allowing us to make estimates for $D\bar{D}$ scattering., Comment: 12 pages; 6 figures; revised version with several improvements; a comparison with other works is made

The energy extraction from quantum sources is a key task to develop new quantum devices such as quantum batteries (QB). In this context, one of the main figures of merit is the ergotropy, which measures the maximal amount of energy (as work) that can be extracted from the quantum source by means of unitary operations. One of the main issues to fully extract energy from the quantum source is the assumption that any unitary operation can be done on the system. This assumption, in general, fails in practice since the operations that can be done are limited and depend on the quantum hardware (experimental platform) one has available. In this work, we propose an approach to optimize the extractable energy inspired by the variational quantum eigensolver (VQE) algorithm. In this approach, we explicitly take into account a limited set of unitaries by using the hardware efficient asatz (HEA) class of parameterized quantum circuits. As a QB we use an one-dimensional spin chain described by a family of paradigmatic first neighbor Hamiltonians such as the $XXX$,$XXZ$, $XYZ$, $XX$, $XY$ and transverse Ising models. By building our parameterized quantum circuits assuming that different types of connectivity may be available depending on the quantum hardware, we numerically compare the efficiency of work extraction for each model. Our results show that the best efficiency is generally obtained with quantum circuits that have connectivity between first neighbor spins., Comment: 9 pages, 6 figures

With the ever-growing complexity of deep learning models for face recognition, it becomes hard to deploy these systems in real life. Researchers have two options: 1) use smaller models; 2) compress their current models. Since the usage of smaller models might lead to concerning biases, compression gains relevance. However, compressing might be also responsible for an increase in the bias of the final model. We investigate the overall performance, the performance on each ethnicity subgroup and the racial bias of a State-of-the-Art quantization approach when used with synthetic and real data. This analysis provides a few more details on potential benefits of performing quantization with synthetic data, for instance, the reduction of biases on the majority of test scenarios. We tested five distinct architectures and three different training datasets. The models were evaluated on a fourth dataset which was collected to infer and compare the performance of face recognition models on different ethnicity., Comment: Accepted for Oral at BIOSIG 2023

This work provides a complete rheological characterization of 2D-inks in electric fields with different intensities and orientations to the imposed flow field. 2D nanomaterials used in this study are graphene nanoplatelets, hexagonal boron-nitride, and molybdenum disulfide. These materials with different electric properties are dispersed in a non-polar solvent (Toluene) with different concentrations of Ethyl Cellulose (EC), providing Newtonian or viscoelastic characteristics. Shear rheology tests show that the presence of nanoparticles barely changes the fluid behavior from the carrier fluid, and the application of an electric field perpendicular to the flow does not result in electrorheological behavior. However, extensional experiments, which mimic the actual EHD jet printing conditions, allowed the observation of the influence of both the particles and the electric field aligned on the filament thinning process. It was observed that the electric field generates vortices due to an electrophoretic effect in the carrier fluid when EC is present in the formulations, which has severe consequences on the stability of the liquid bridges, whereas it scarcely affects the shear viscosity; additionally, the kind of 2D nanoparticles modifies also the conductivity and permittivity of the solution, inducing Maxwell stresses that also make the filament more stable against surface tension., Comment: Accepted in Applied Materials Today. https://authors.elsevier.com/tracking/article/details.do?aid=102042&jid=APMT&surname=Galindo-Rosales

We search for a $B$ decay mode where one can find a peak for a $D \bar{D}$ bound state predicted in effective theories and in Lattice QCD calculations, which has also been claimed from some reactions that show an accumulated strength in $D \bar{D}$ production at threshold. We find a good candidate in the $B^+\to K^+ \eta\eta$ reaction, by looking at the $\eta\eta$ mass distribution. The reaction proceeds via a first step in which one has the $B^+\to D_s^{*+} \bar{D}^0$ reaction followed by $D_s^{*+}$ decay to $D^0 K^+$ and a posterior fusion of $D^0 \bar{D}^0$ to $\eta \eta$, implemented trough a triangle diagram that allows the $D^0 \bar{D}^0$ to be virtual and produce the bound state. The choice of $\eta\eta$ to see the peak is based on results of calculations that find the $\eta\eta$ among the light pseudoscalar channels with stronger coupling to the $D \bar{D}$ bound state. We find a neat peak around the predicted mass of that state in the $\eta\eta$ mass distribution, with an integrated branching ratio for $B^+\to K^+$ ($D\bar{D}$, bound) ; ($D\bar{D}$, bound) $\to \eta \eta$ of the order of $1.5 \times 10^{-4}$, a large number for hadronic $B$ decays, which should motivate its experimental search.

Quantum decoherence effects in neutrinos, described by the open quantum systems formalism, serve as a gateway to explore potential new physics, including quantum gravity. Previous research extensively investigated these effects across various neutrino sources, imposing stringent constraints on the spontaneous loss of coherence. In this study, we demonstrate that even within the Supernovae environment, where neutrinos are released as incoherent states, quantum decoherence could influence the flavor equipartition of $3\nu$ mixing. Additionally, we examine the potential energy dependence of quantum decoherence parameters ($\Gamma = \Gamma_0 (E/E_0)^n$) with different power laws ($n = 0, 2, 5/2$). Our findings indicate that future-generation detectors (DUNE, Hyper-K, and JUNO) can significantly constrain quantum decoherence effects under different scenarios. For a Supernova located 10 kpc away from Earth, DUNE could potentially establish $3\sigma$ bounds of $\Gamma \leq 6.2 \times 10^{-14}$ eV in the normal mass hierarchy (NH) scenario, while Hyper-K could impose a $2\sigma$ limit of $\Gamma \leq 3.6 \times 10^{-14}$ eV for the inverted mass hierarchy (IH) scenario with $n=0$ - assuming no energy exchange between the neutrino subsystem and non-standard environment ($[H,V_p] = 0$). These limits become even more restrictive for a closer Supernova. When we relax the assumption of energy exchange ($[H,V_p] \neq 0$), for a 10 kpc SN, DUNE can establish a $3\sigma$ limit of $\Gamma_8 \leq 4.2 \times 10^{-28}$ eV for NH, while Hyper-K could constrain $\Gamma_8 \leq 1.3 \times 10^{-27}$ eV for IH ($n=0$) with $2\sigma$, representing the most stringent bounds reported to date. Furthermore, we examine the impact of neutrino loss during propagation for future Supernova detection.

This study provides a complete rheological characterization of 2D nanomaterial dispersions, employed as 2D-inks precursors in printed electronics. Three different 2D nanomaterials (molybdenum disulfide (MoS2), graphene, and hexagonal boron nitride(hBN)) were dispersed in a Newtonian fluid (toluene) and a viscoelastic fluid (toluene + ethyl cellulose) with different polymer concentrations. The presence of nanoparticles does not change the shear rheology of the carrier fluid. Regarding the extensional rheology, the results showed that the pinch-off phenomenon is present in all Toluene suspensions; however, the presence of the ethyl cellulose introduces elasticity in the system, even leading to the formation of beads-on-a-string, and the relaxation times of the suspensions depends on the kind of nanoparticles present in the fluid. As controlling the droplet size when dispensing 2D-inks is of paramount importance for printed electronics, as well as for many other applications, here it is presented a correlation between the rheological properties of these 2D-inks precursors and their droplet size when generated from a capillary nozzle in dripping regime.

Morphing attacks keep threatening biometric systems, especially face recognition systems. Over time they have become simpler to perform and more realistic, as such, the usage of deep learning systems to detect these attacks has grown. At the same time, there is a constant concern regarding the lack of interpretability of deep learning models. Balancing performance and interpretability has been a difficult task for scientists. However, by leveraging domain information and proving some constraints, we have been able to develop IDistill, an interpretable method with state-of-the-art performance that provides information on both the identity separation on morph samples and their contribution to the final prediction. The domain information is learnt by an autoencoder and distilled to a classifier system in order to teach it to separate identity information. When compared to other methods in the literature it outperforms them in three out of five databases and is competitive in the remaining., Comment: Accepted at EUSIPCO 2023

Important information about the dynamical structure of a differential system can be revealed by looking into its invariant compact manifolds, such as equilibria, periodic orbits, and invariant tori. This knowledge is significantly increased if asymptotic properties of the trajectories nearby such invariant manifolds can be determined. In this paper, we present a result providing sufficient conditions for the existence of invariant tori in perturbative differential systems. The regularity, convergence, and stability of such tori as well as the dynamics defined on them are also investigated. The conditions are given in terms of their so-called higher order averaged equations. This result is an extension to a wider class of differential systems of theorems due to Krylov, Bogoliubov, Mitropolsky, and Hale.

Phase estimation is used in many quantum algorithms, particularly in order to estimate energy eigenvalues for quantum systems. When using a single qubit as the probe (used to control the unitary we wish to estimate the eigenvalue of), it is not possible to measure the phase with a minimum mean-square error. In standard methods, there would be a logarithmic (in error) number of control qubits needed in order to achieve this minimum error. Here show how to perform this measurement using only two control qubits, thereby reducing the qubit requirements of the quantum algorithm. Our method corresponds to preparing the optimal control state one qubit at a time, while it is simultaneously consumed by the measurement procedure., Comment: 11 pages, 7 figures. Paper sent for Jonathan P. Dowling Memorial Special Issue

Considering the profound transformation affecting pathology practice, we aimed to develop a scalable artificial intelligence (AI) system to diagnose colorectal cancer from whole-slide images (WSI). For this, we propose a deep learning (DL) system that learns from weak labels, a sampling strategy that reduces the number of training samples by a factor of six without compromising performance, an approach to leverage a small subset of fully annotated samples, and a prototype with explainable predictions, active learning features and parallelisation. Noting some problems in the literature, this study is conducted with one of the largest WSI colorectal samples dataset with approximately 10,500 WSIs. Of these samples, 900 are testing samples. Furthermore, the robustness of the proposed method is assessed with two additional external datasets (TCGA and PAIP) and a dataset of samples collected directly from the proposed prototype. Our proposed method predicts, for the patch-based tiles, a class based on the severity of the dysplasia and uses that information to classify the whole slide. It is trained with an interpretable mixed-supervision scheme to leverage the domain knowledge introduced by pathologists through spatial annotations. The mixed-supervision scheme allowed for an intelligent sampling strategy effectively evaluated in several different scenarios without compromising the performance. On the internal dataset, the method shows an accuracy of 93.44% and a sensitivity between positive (low-grade and high-grade dysplasia) and non-neoplastic samples of 0.996. On the external test samples varied with TCGA being the most challenging dataset with an overall accuracy of 84.91% and a sensitivity of 0.996., Comment: Accepted at npj Precision Oncology. Available at: https://www.nature.com/articles/s41698-024-00539-4

Hilbert's 16th Problem, about the maximum number of limit cycles of planar polynomial vector fields of a given degree $m$, has been one of the most important driving forces for new developments in the qualitative theory of vector fields. Increasing the dimension, one cannot expect the existence of a finite upper bound for the number of limit cycles of, for instance, $3$D polynomial vector fields of a given degree $m$. Here, as an extension of such a problem in the $3$D space, we investigate the number of isolated invariant tori in $3$D polynomial vector fields. In this context, given a natural number $m$, we denote by $N(m)$ the upper bound for the number of isolated invariant tori of $3$D polynomial vector fields of degree $m$. Based on a recently developed averaging method for detecting invariant tori, our first main result provides a mechanism for constructing $3$D differential vector fields with a number $H$ of normally hyperbolic invariant tori from a given planar differential vector field with $H$ hyperbolic limit cycles. The strength of our mechanism in studying the number $N(m)$ lies in the fact that the constructed $3$D differential vector field is polynomial provided that the given planar differential vector field is polynomial. Accordingly, our second main result establishes a lower bound for $N(m)$ in terms of lower bounds for the number of hyperbolic limit cycles of planar polynomial vector fields of degree $[m/2]-1$. Based on this last result, we apply a methodology due to Christopher & Lloyd to show that $N(m)$ grows as fast as $m^3/128$. Finally, the above-mentioned problem is also formulated for higher dimensional polynomial vector fields.

Time-dependent linear differential equations are a common type of problem that needs to be solved in classical physics. Here we provide a quantum algorithm for solving time-dependent linear differential equations with logarithmic dependence of the complexity on the error and derivative. As usual, there is an exponential improvement over classical approaches in the scaling of the complexity with the dimension, with the caveat that the solution is encoded in the amplitudes of a quantum state. Our method is to encode the Dyson series in a system of linear equations, then solve via the optimal quantum linear equation solver. Our method also provides a simplified approach in the case of time-independent differential equations., Comment: 19 pages

In the context of biometrics, matching confidence refers to the confidence that a given matching decision is correct. Since many biometric systems operate in critical decision-making processes, such as in forensics investigations, accurately and reliably stating the matching confidence becomes of high importance. Previous works on biometric confidence estimation can well differentiate between high and low confidence, but lack interpretability. Therefore, they do not provide accurate probabilistic estimates of the correctness of a decision. In this work, we propose a probabilistic interpretable comparison (PIC) score that accurately reflects the probability that the score originates from samples of the same identity. We prove that the proposed approach provides optimal matching confidence. Contrary to other approaches, it can also optimally combine multiple samples in a joint PIC score which further increases the recognition and confidence estimation performance. In the experiments, the proposed PIC approach is compared against all biometric confidence estimation methods available on four publicly available databases and five state-of-the-art face recognition systems. The results demonstrate that PIC has a significantly more accurate probabilistic interpretation than similar approaches and is highly effective for multi-biometric recognition. The code is publicly-available., Comment: Accepted at IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) 2023 Workshop on Biometrics