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Hypertension, a leading contributor to cardiovascular morbidity, underscores the need for accurate and continuous blood pressure (BP) monitoring. Photoplethysmography (PPG) presents a promising approach to this end. However, the precision of BP estimates derived from PPG signals has been the subject of ongoing debate, necessitating a comprehensive evaluation of their effectiveness and constraints. We developed a calibration-based Siamese ResNet model for BP estimation, using a signal input paired with a reference BP reading. We compared the use of normalized PPG (N-PPG) against the normalized Invasive Arterial Blood Pressure (N-IABP) signals as input. The N-IABP signals do not directly present systolic and diastolic values but theoretically provide a more accurate BP measure than PPG signals since it is a direct pressure sensor inside the body. Our strategy establishes a critical benchmark for PPG performance, realistically calibrating expectations for PPG's BP estimation capabilities. Nonetheless, we compared the performance of our models using different signal-filtering conditions to evaluate the impact of filtering on the results. We evaluated our method using the AAMI and the BHS standards employing the VitalDB dataset. The N-IABP signals meet with AAMI standards for both Systolic Blood Pressure (SBP) and Diastolic Blood Pressure (DBP), with errors of 1.29+-6.33mmHg for systolic pressure and 1.17+-5.78mmHg for systolic and diastolic pressure respectively for the raw N-IABP signal. In contrast, N-PPG signals, in their best setup, exhibited inferior performance than N-IABP, presenting 1.49+-11.82mmHg and 0.89+-7.27mmHg for systolic and diastolic pressure respectively. Our findings highlight the potential and limitations of employing PPG for BP estimation, showing that these signals contain information correlated to BP but may not be sufficient for predicting it accurately., Comment: 17 pages, 7 figures, 3 tables

Sleep is a crucial aspect of our overall health and well-being. It plays a vital role in regulating our mental and physical health, impacting our mood, memory, and cognitive function to our physical resilience and immune system. The classification of sleep stages is a mandatory step to assess sleep quality, providing the metrics to estimate the quality of sleep and how well our body is functioning during this essential period of rest. Photoplethysmography (PPG) has been demonstrated to be an effective signal for sleep stage inference, meaning it can be used on its own or in a combination with others signals to determine sleep stage. This information is valuable in identifying potential sleep issues and developing strategies to improve sleep quality and overall health. In this work, we present a machine learning sleep-wake classification model based on the eXtreme Gradient Boosting (XGBoost) algorithm and features extracted from PPG signal and activity counts. The performance of our method was comparable to current state-of-the-art methods with a Sensitivity of 91.15 $\pm$ 1.16%, Specificity of 53.66 $\pm$ 1.12%, F1-score of 83.88 $\pm$ 0.56%, and Kappa of 48.0 $\pm$ 0.86%. Our method offers a significant improvement over other approaches as it uses a reduced number of features, making it suitable for implementation in wearable devices that have limited computational power., Comment: 8 pages, 3 figures

Diabetes is a prevalent chronic condition that compromises the health of millions of people worldwide. Minimally invasive methods are needed to prevent and control diabetes but most devices for measuring glucose levels are invasive and not amenable for continuous monitoring. Here, we present an alternative method to overcome these shortcomings based on non-invasive optical photoplethysmography (PPG) for detecting diabetes. We classify non-Diabetic and Diabetic patients using the PPG signal and metadata for training Logistic Regression (LR) and eXtreme Gradient Boosting (XGBoost) algorithms. We used PPG signals from a publicly available dataset. To prevent overfitting, we divided the data into five folds for cross-validation. By ensuring that patients in the training set are not in the testing set, the model's performance can be evaluated on unseen subjects' data, providing a more accurate assessment of its generalization. Our model achieved an F1-Score and AUC of $58.8\pm20.0\%$ and $79.2\pm15.0\%$ for LR and $51.7\pm16.5\%$ and $73.6\pm17.0\%$ for XGBoost, respectively. Feature analysis suggested that PPG morphological features contains diabetes-related information alongside metadata. Our findings are within the same range reported in the literature, indicating that machine learning methods are promising for developing remote, non-invasive, and continuous measurement devices for detecting and preventing diabetes., Comment: 11 pages, 6 figures

Photoplethysmography (PPG) is a non-invasive technology that measures changes in blood volume in the microvascular bed of tissue. It is commonly used in medical devices such as pulse oximeters and wrist worn heart rate monitors to monitor cardiovascular hemodynamics. PPG allows for the assessment of parameters (e.g., heart rate, pulse waveform, and peripheral perfusion) that can indicate conditions such as vasoconstriction or vasodilation, and provides information about microvascular blood flow, making it a valuable tool for monitoring cardiovascular health. However, PPG is subject to a number of sources of variations that can impact its accuracy and reliability, especially when using a wearable device for continuous monitoring, such as motion artifacts, skin pigmentation, and vasomotion. In this study, we extracted 27 statistical features from the PPG signal for training machine-learning models based on gradient boosting (XGBoost and CatBoost) and Random Forest (RF) algorithms to assess quality of PPG signals that were labeled as good or poor quality. We used the PPG time series from a publicly available dataset and evaluated the algorithm s performance using Sensitivity (Se), Positive Predicted Value (PPV), and F1-score (F1) metrics. Our model achieved Se, PPV, and F1-score of 94.4, 95.6, and 95.0 for XGBoost, 94.7, 95.9, and 95.3 for CatBoost, and 93.7, 91.3 and 92.5 for RF, respectively. Our findings are comparable to state-of-the-art reported in the literature but using a much simpler model, indicating that ML models are promising for developing remote, non-invasive, and continuous measurement devices., Comment: 9 pages

We consider the problem of establishing nonlinear smoothing as a general feature of nonlinear dispersive equations, i.e. the improved regularity of the integral term in Duhamel's formula, with respect to the initial data and the corresponding regularity of the linear evolution, and how this property relates to local well-posedness. In a first step, we show how the problem generally reduces to the derivation of specific frequency-restricted estimates, which are multiplier estimates in the spatial frequency alone. Then, using a precise methodology, we prove these estimates for the specific cases of the modified Zakharov-Kuznetsov equation, the cubic and quintic nonlinear Schr\"odinger equation and the quartic Korteweg-de Vries equation., Comment: 29 pages

In this paper, we define the constant $D(\varphi, p)$, an analogue for the Davenport constant, for sequences on the finite field $\mathbb{F}_p$, defined via quadratic symmetric polynomials. Next, we state a series of results presenting either the exact value of $D(\varphi, p)$, or lower and upper bounds for this constant.

We study the nonlinear Schr\"odinger equation with initial data in $\mathcal{Z}^s_p(\mathbb{R}^d)=\dot{H}^s(\mathbb{R}^d)\cap L^p(\mathbb{R}^d)$, where $0

We study generic semilinear Schr\"odinger systems which may be written in Hamiltonian form. In the presence of a single gauge invariance, the components of a solution may exchange mass between them while preserving the total mass. We exploit this feature to unravel new orbital instability results for ground-states. More precisely, we first derive a general instability criterion and then apply it to some well-known models arising in several physical contexts. In particular, this mass-transfer instability allows us to exhibit $L^2$-subcritical unstable ground-states.

Let $G$ be a finite abelian group of exponent $n$, written additively, and let $A$ be a subset of $\mathbb{Z}$. The constant $s_A(G)$ is defined as the smallest integer $\ell$ such that any sequence over $G$ of length at least $\ell$ has an $A$-weighted zero-sum of length $n$ and $\eta_A(G)$ defined as the smallest integer $\ell$ such that any sequence over $G$ of length at least $\ell$ has an $A$-weighted zero-sum of length at most $n$. Here we prove that, for $\alpha \geq \beta$, and $A=\left\{x\in\mathbb{N}\; : \; 1 \le a \le p^{\alpha} \; \mbox{ and }\; \gcd(a, p) = 1\right \}$, we have $s_{A}(\mathbb{Z}_{p^{\alpha}}\oplus \mathbb{Z}_{p^\beta}) = \eta_A(\mathbb{Z}_{p^{\alpha}}\oplus \mathbb{Z}_{p^\beta}) + p^{\alpha}-1 = p^{\alpha} + \alpha +\beta$ and classify all the extremal $A$-weighted zero-sum free sequences.

We study the nonlinear Schr\"odinger system \[ \begin{cases} \displaystyle iu_t+\Delta u-u+(\frac{1}{9}|u|^2+2|w|^2)u+\frac{1}{3}\overline{u}^2w=0,\\ i\displaystyle \sigma w_t+\Delta w-\mu w+(9|w|^2+2|u|^2)w+\frac{1}{9}u^3=0, \end{cases} \] for $(x,t)\in \mathbb{R}^n\times\mathbb{R}$, $1\leq n\leq 3$ and $\sigma,\mu>0$. This system models the interaction between an optical beam and its third harmonic in a material with Kerr-type nonlinear response. We prove the existence of ground state solutions, analyse its stability, and establish local and global well-posedness results as well as several criteria for blow-up.

This paper uses typed linear algebra (LA) to represent data and perform analytical querying in a single, unified framework. The typed approach offers strong type checking (as in modern programming languages) and a diagrammatic way of expressing queries (paths in LA diagrams). A kernel of LA operators has been implemented so that paths extracted from LA diagrams can be executed. The approach is validated and evaluated taking TPC-H benchmark queries as reference. The performance of the LA-based approach is compared with popular database competitors (PostgreSQL and MySQL).

We study the Schr\"odinger-Debye system over $\mathbb{R}^d$ iu_t+\frac 12\Delta u=uv,\quad \mu v_t+v=\lambda |u|^2 and establish the global existence and scattering of small solutions for initial data in several function spaces in dimensions $d=2,3,4$. Moreover, in dimension $d=1$, we prove a Hayashi-Naumkin modified scattering result., Comment: 22 pages

We consider the quadratic Schr\"odinger system $$iu_t+\Delta_{\gamma_1}u+\overline{u}v=0$$ $$2iv_t+\Delta_{\gamma_2}v-\beta v+\frac 12 u^2=0,$$ where $t\in\mathbf{R},\,x\in \mathbf{R}^d\times \mathbf{R}$, in dimensions $1\leq d\leq 4$ and for $\gamma_1,\gamma_2>0$, the so-called elliptic-elliptic case. We show the formation of singularities and blow-up in the $L^2$-(super)critical case. Furthermore, we derive several stability results concerning the ground state solutions of this system.