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SHARP EMBEDDINGS BETWEEN WEIGHTED PALEY-WIENER SPACES
Get PDFIn this paper we address the problem of estimating the operator norm of the embed- dings between multidimensional weighted Paley-Wiener spaces. These can be equivalently thought as Fourier uncertainty principles for bandlimited functions. By means of radial symmetrization mechanisms, we show that such problems can all be shifted to dimension one. We provide precise asymptotics in the general case and, in some particular situations, we are able to identify the sharp constants and characterize the extremizers. The sharp constant study is actually a consequence of a more general result we prove in the setup of de Branges spaces of entire functions, addressing the operator given by multiplication by zk, k ∈ N. Applications to sharp higher order Poincar ́e inequalities and other related extremal problems are discussed
ON (GLOBAL) UNIQUE CONTINUATION PROPERTIES OF THE FRACTIONAL DISCRETE LAPLACIAN
Get PDFWe study various qualitative and quantitative (global) unique continuation prop- erties for the fractional discrete Laplacian. We show that while the fractional Laplacian enjoys striking rigidity properties in the form of (global) unique continuation properties, the fractional discrete Laplacian does not enjoy these in general. While discretization thus counteracts the strong rigidity properties of the continuum fractional Laplacian, by discussing quantitative forms of unique continuation, we illustrate that these properties can be recovered if exponen- tially small (in the lattice size) correction terms are added. In particular, this allows us to deduce stability properties for a discrete, linear inverse problem for the fractional Laplacian. We complement these observations with a transference principle and the discussion of these properties on the discrete torus
AN HOMAGE TO GUIDO WEISS AND HIS LEADERSHIP OF THE SAINT LOUIS TEAM: COMMUTATORS OF SINGULAR INTEGRALS AND SOBOLEV INEQUALITIES
Get PDFWe extend some classical Sobolev type inequalities for linear and non-linear commutators
A Variational Learning Approach for Concurrent Distance Estimation and Environmental Identification
Get PDFWireless propagated signals encapsulate rich information
for high-accuracy localization and environment sensing.
However, the full exploitation of positional and environmental
features as well as their correlation remains challenging in
complex propagation environments. In this paper, we propose
a methodology of variational inference over deep neural networks
for concurrent distance estimation and environmental
identification. The proposed approach, namely inter-instance
variational auto-encoders (IIns-VAEs), conducts inference with
latent variables that encapsulate information about both distance
and environmental labels. A deep learning network with instance
normalization is designed to approximate the inference concurrently
via deep learning. We conduct extensive experiments on
real-world datasets and the results show the superiority of the
proposed IIns-VAE in both distance estimation and environmental
identification compared to conventional approaches
An ACO-based Hyper-heuristic for Sequencing Many-objective Evolutionary Algorithms that Consider Different Ways to Incorporate the DM's Preferences
Get PDFMany-objective optimization is an area of interest common to researchers, professionals, and practitioners because of its real-world implications. Preference incorporation into Multi-Objective Evolutionary Algorithms (MOEAs) is one of the current approaches to treat Many-Objective Optimization Problems (MaOPs). Some recent studies have focused on the advantages of embedding preference models based on interval outranking into MOEAs; several models have been proposed to achieve it. Since there are many factors influencing the choice of the best outranking model, there is no clear notion of which is the best model to incorporate the preferences of the decision maker into a particular problem. This paper proposes a hyper-heuristic algorithm—named HyperACO—that searches for the best combination of several interval outranking models embedded into MOEAs to solve MaOPs. HyperACO is able not only to select the most appropriate model but also to combine the already existing models to solve a specific MaOP correctly. The results obtained on the DTLZ and WFG test suites corroborate that HyperACO can hybridize MOEAs with a combined preference model that is suitable to the problem being solved. Performance comparisons with other state-of-the-art MOEAs and tests for statistical significance validate this conclusion
Prescriptive, descriptive or predictive models: What approach should be taken when empirical data is limited? Reply to comments on “Mathematical models for Dengue fever epidemiology: A 10-year systematic review”
Get PDF1. BERC 2022-2025 program
2. Ministry of Sciences, Innovation and Universi-
ties: BCAM Severo Ochoa accreditation CEX2021-001142-S / MICIN / AEI /
10.13039/501100011033
3. M.A. has received funding from the European Union’s
Horizon 2020 research and innovation program under the Marie Sklodowska-
Curie grant agreement No 792494
Extrapolation in general quasi-Banach function spaces
Get PDFIn this work we prove off-diagonal, limited range, multilinear, vector-valued, and two-weight versions of the Rubio de Francia extrapolation theorem in general quasi-Banach function spaces. We prove mapping properties of the generalization of the Hardy-Littlewood maximal operator to very general bases that includes a method to obtain self-improvement results that are sharp with respect to its operator norm. Furthermore, we prove bounds for the Hardy-Littlewood maximal operator in weighted Lorentz, variable Lebesgue, and Morrey spaces, and recover and extend several extrapolation theorems in the literature. Finally, we provide an application of our results to the Riesz potential and the Bilinear Hilbert transform
Five-year follow-up mortality prognostic index for colorectal patients
Get PDFPurpose: To identify 5-year survival prognostic variables in patients with colorectal cancer (CRC) and to propose a survival prognostic score that also takes into account changes over time in the patient's health-related quality of life (HRQoL) status.
Methods: Prospective observational cohort study of CRC patients. We collected data from their diagnosis, intervention, and at 1, 2, 3, and 5 years following the index intervention, also collecting HRQoL data using the EuroQol-5D-5L (EQ-5D-5L), European Organization for Research and Treatment of Cancer's Quality of Life Questionnaire-Core 30 (EORTC-QLQ-C30), and Hospital Anxiety and Depression Scale (HADS) questionnaires. Multivariate Cox proportional models were used.
Results: We found predictors of mortality over the 5-year follow-up to be being older; being male; having a higher TNM stage; having a higher lymph node ratio; having a result of CRC surgery classified as R1 or R2; invasion of neighboring organs; having a higher score on the Charlson comorbidity index; having an ASA IV; and having worse scores, worse quality of life, on the EORTC and EQ-5D questionnaires, as compared to those with higher scores in each of those questionnaires respectively.
Conclusions: These results allow preventive and controlling measures to be established on long-term follow-up of these patients, based on a few easily measurable variables.
Implications for cancer survivors: Patients with colorectal cancer should be monitored more closely depending on the severity of their disease and comorbidities as well as the perceived health-related quality of life, and preventive measures should be established to prevent adverse outcomes and therefore to ensure that better treatment is received.
Trial registration: ClinicalTrials.gov identifier: NCT02488161Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. This work was supported in part by grants from the Instituto de Salud Carlos III and the European Regional Development Fund (PS09/00314, PS09/00910, PS09/00746, PS09/00805, PI09/90460, PI09/90490, PI09/90453, PI09/90441, PI09/90397); the Spanish Ministry of the Economy (PID2020-115738 GB-I00); the Departments of Health (2010111098) and Education, Language Policy and Culture (IT1456-22; IT1598-22; IT-1187–19) of the Basque Government; the Research Committee of Galdakao Hospital; the REDISSEC (Red de Investigación en Servicios de Salud en Enfermedades Crónicas) thematic network of the Instituto de Salud Carlos III; and the Department of Education of the Basque Government through the Consolidated Research Group MATHMODE (IT1456-22) and the Basque Government through BMTF “Mathematical Modeling Applied to Health” Project
An Error-Based Approximation Sensing Circuit for Event-Triggered Low-Power Wearable Sensors
Get PDFEvent-based sensors have the potential to optimize energy consumption at every stage in the signal processing pipeline, including data acquisition, transmission, processing, and storage. However, almost all state-of-the-art systems are still built upon the classical Nyquist-based periodic signal acquisition. In this work, we design and validate the Polygonal Approximation Sampler (PAS), a novel circuit to implement a general-purpose event-based sampler using a polygonal approximation algorithm as the underlying sampling trigger. The circuit can be dynamically reconfigured to produce either a coarse or detailed reconstruction of the analog input by adjusting the error threshold of the approximation. The proposed circuit is designed at the Register Transfer Level and processes each input sample received from the analog-to-digital converter (ADC) in a single clock cycle. The PAS has been tested with three different types of archetypal signals captured by wearable devices (electrocardiogram, accelerometer, and respiration data) and compared with a standard periodic ADC. These tests show that single-channel signals, with slow variations and constant segments (like the used single-lead ECG and the respiration signals), take great advantage of the used sampling technique, reducing the amount of data used up to 99% without significant performance degradation. At the same time, multi-channel signals (like the six-dimensional accelerometer signal) can still benefit from the designed circuit, achieving a reduction factor of up to 80% with minor performance degradation. These results open the door to new types of wearable sensors with reduced size and higher battery lifetime.RYC2021-032853-
Towards -continuous multi-strip path-planning for 5-axis flank CNC machining of free-form surfaces using conical cutting tools
No full textExisting flank milling path-planning methods typically lead to tiny gaps or overlaps between neighboring paths, which causes artifacts and imperfections in the workpiece. We propose a new multi-strip path-planning method for 5-axis flank milling of free-form surfaces which targets (tangent-plane) continuity of the neighboring strips along shared boundaries. While for some geometries one cannot achieve continuity and high approximation quality at the same time, our optimization framework offers a good trade-off between machining accuracy in terms of distance error and the connection of neighboring strips. We demonstrate our algorithm on synthetic free-form surfaces as well as on industrial benchmark datasets, showing that we are able to meet fine industrial tolerances and simultaneously significantly reduce the kink angle of adjacent strips, and consequently to improve the surface finish in terms of smoothness