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Genuine Multipartite Entanglement Detection with Imperfect Measurements: Concept and Experiment
No full textStandard procedures for entanglement detection assume that experimenters can exactly implement specific quantum measurements. Here, we depart from such idealizations and investigate, in both theory and experiment, the detection of genuine multipartite entanglement when measurements are subject to small imperfections. For arbitrary qubits number n, we construct multipartite entanglement witnesses where the detrimental influence of the imperfection is independent of n. In a tabletop four-partite photonic experiment, we demonstrate first how a small amount of alignment error can undermine the conclusions drawn from standard entanglement witnesses and then perform the correction analysis. Furthermore, since we consider quantum devices that are trusted but not perfectly controlled, we showcase advantages in terms of noise resilience as compared to device-independent models
Extending the learning using privileged information paradigm to logistic regression
No full textLearning using privileged information paradigm is a learning scenario that exploits privileged features, available at training time, but not at prediction, as additional information for training models. This paper delves into the learning of logistic regression models using privileged information. We provide two new algorithms. For its development, the parameters of a conventional logistic regression trained with all available features, privileged and regular, are projected onto the parameter space associated to regular features (available at training and prediction time). The projection to obtain the model parameters is performed by the minimization of two different loss functions governed by logit terms and posterior probabilities. In addition, a metric is proposed to determine whether the use of privileged information can enhance performance. Experimental results report improvements of our proposals over the performance of conventional logistic regression learned without privileged information.PID2022-137442NB-I00
PRE2021-09927
Colloidal homogenization for the hydrodynamics of nematic liquid crystals
No full textThis paper analytically explores a simplified model
for the hydrodynamics of nematic liquid crystal
colloids. We integrate a Stokes equation for the
velocity field with a Ginzburg–Landau transported
heat flow for the director field. The study focuses
on a bounded spatial domain containing periodically
distributed colloidal particles with no-anchoring
conditions on the nematic liquid crystal. By
progressively reducing the particle size to zero and
simultaneously increasing the number of particles,
we delve into the associated homogenization
problem. Our analysis uncovers a form of decoupling
where the velocity field asymptotically satisfies a
Darcy equation, independent of the director, while
the director follows a gradient flow, unaffected
by the velocity field. One of the most intricate
aspects of the homogenization process is the absence
of an extension operator for the director field
that preserves the uniform estimates related to
the system’s energy. We address this challenge
with a novel variation of the Aubin–Lions lemma,
specifically adapted for homogenization problems
Displacement processes with random shifting and their applications
Get PDFThe thesis starts with a generalized model of Stochastic resetting that extends the classical concept through a random resetting amplitude. In particular there are two scenarios: independent and dependent Random amplitude stochastic resetting (RASR). A general analytical formalism of RASR is provided explicitly based on the first renewal picture, whereby the reduction to special cases is provided. The quantitative analysis is specified through the discussion of the mean value and the variance of the height in presence of a ballistic free propagation for Poissonian and constant pace resetting. These choices of resetting interval lengths are based on the geophysical application of sediment dynamics, in which the free propagation mimics the gradual increase (deposition) or decrease (erosion) of a sedimentation profile, whereas the resets represent an additional erosion mechanism. The latter mechanism could be seasonal (constant pace resetting) or random in time weather events such as extreme floods. The qualitative difference between independent and dependent RASR is that the latter class becomes stationary, whereas the former remains nonstationary. Apart from the above geophysical scenarios, this extension of the resetting dynamics can be applied to population dynamics interrupted by epidemics or crises-interrupted financial markets. All these applications correspond to the intermittent picture of a parent process with superimposed resetting statistic, which motivates the investigations of the RASR-model as a random search strategy.
The following chapter investigates the search properties of the continuous time random walk (CTRW), which can be derived from the independent RASR-class. The problem leads to the derivation of a nonhomogeneous Wiener-Hopf equation that exactly calculates the mean first-passage time (MFPT). Apart from the fact, that the derived formalism may also be used for the indirect estimation of the jump-length PDF by assuming a given MFPT, it is shown by use of a specific jump-size PDF that the MFPT is infinite for symmetric random walks, but it becomes finite only for asymmetric jumps with a negative mean. Asymmetric jumps can be physically explained through an active movement as, e.g., chemotaxis or animal movement. However, for the quantitative
description of molecular dynamics, symmetric CTRWs are presumed, for which the MFPT is not a proper quantity. In the subsequent chapters the author extended and modified these calculations for removing this failure of the MFPT for the investigation of symmetric random walks.
In the fourth chapter of the thesis, a formalism for the calculation of the survival probability in first-passage time problems for symmetric random walks in semi-infinite space is provided. Therefore, a Sturm-Liouville system of equations may provide the unique solution, which is shown for a concrete example of jump-size densities in the discrete time scenario. In addition, the Sturm-Liouville system is also derived for the survival probability of a CTRW. The previous example of jump-size PDF is applied also in the continuous-time setting for arbitrary waiting-time distribution, that holds for Markovian and non-Markovian CTRW.
In the last chapter of this thesis, the MFPT of a CTRW in the presence of a uniformly moving target is discussed. Formally, the MFPT depends on the whole jump-sizes and waiting-times distributions within this configuration. Thus, the simple picture that emerged for a fixed target, when the MFPT depends on the mean waiting time, only, is (almost always) broken. Nevertheless, for a uniformly departing target, the MFPT of a CTRW may fulfill the property to be independent of the entire waiting-time PDF for a certain class of jump-size densities, that is derived within the thesis. Moreover, it is shown that the average of the entire process, i.e., jumps plus uniform movement must be negative to provide a finite MFPT, which is not satisfied by symmetric jump-size PDFs in the presence of a departing target. However, for an arriving target, the MFPT is finite even for symmetric CTRWs. This has been observed for a paradigmatic setting for waiting-time PDF and jump-size density, for which the exact result is provided analytically.BERC 2018–2021, Predoc Severo Ochoa. PRE2018-08442
On the embedded Nash problem
No full textThe embedded Nash problem for a hypersurface in a smooth algebraic variety is to characterize geometrically the maximal irreducible families of arcs with fixed order of contact along the hypersurface. We show that divisors on minimal models of the pair contribute with such families. We solve the problem for unibranch plane curve germs, in terms of the resolution graph. These are embedded analogs of known results for the classical Nash problem on singular varieties
Design, motion-planning, and manufacturing of custom-shaped tools for 5-axis super abrasive machining of a turbomachinary blade like component
Get PDFFree-form surfaces generated by Non-Uniform Rational B-Splines (NURBS) are evolving to face turbomachinery components requirements, such as turbine blades to enhanced efficiency. Super Abrasive Machining (SAM) is presented as a potential process for high-added value components using custom-shaped tools to be adapted to any surface. The adaptability and flexibility of these tool concepts are specifically designed to fit these complex surfaces. This paper presents an innovative manufacturing approach for blade type components using a custom-shaped tool designed through an optimization process that simultaneously optimizes both the shape of the tool and its motion. The proposed method with SAM finishing using a custom-shaped tool is compared
against a standard tool and traditional machining process. The result obtained on the blade test case show that the custom-shaped tools need fewer paths, yet produce more accurate surface finish
Beyond the biting - limited impact of explicit mosquito dynamics in dengue models
Get PDFMathematical models play a crucial role in assisting public health authorities in timely disease control decision-making. For vector-borne diseases, integrating host and vector dynamics into models can be highly complex, particularly due to limited data availability, making system validation challenging. In this study, two compartmental models akin to the SIR type were developed to characterize vector-borne infectious disease dynamics. Motivated by dengue fever epidemiology, the models varied in their treatment of vector dynamics, one with implicit vector dynamics and the other explicitly modeling mosquito-host contact. Both considered temporary immunity after primary infection and disease enhancement in secondary infection, analogous to the temporary cross-immunity and the Antibody-dependent enhancement biological processes observed in dengue epidemiology. Qualitative analysis using bifurcation theory and numerical experiments revealed that the immunity period and disease enhancement outweighed the impact of explicit vector dynamics. Both models demonstrated similar bifurcation structures, indicating that explicit vector dynamics are only justified when assessing the effects of vector control methods. Otherwise, the extra equations are irrelevant, as both systems display similar dynamics scenarios. The study underscores the importance of using simple models for mathematical analysis, initiating crucial discussions among the modeling community in vector-borne diseases.MA recieve Ramon y Cajal Grant RYC2021-031380-I funded by MICIU/AEI/10.13039/501100011033 and by the European Union NextGenerationEU/PRTR. A.K.S. receives financial support by the Ministerio de Ciencia e Innovación (MICINN) of the Spanish Government through the Juan de la Cierva grant FJC-2021-046826-I / MICIU/AEI /10.13039/501100011033 and by the European Union NextGenerationEU/PRTR
Within-host models unravelling the dynamics of dengue reinfections
Get PDFCaused by four serotypes, dengue fever is a major public health concern worldwide. Current modeling efforts have mostly focused on primary and heterologous secondary infections, assuming that lifelong immunity prevents reinfections by the same serotype. However, recent findings challenge this assumption, prompting a reevaluation of dengue immunity dynamics.
In this study, we develop a within-host modeling framework to explore different scenarios of dengue infections. Unlike previous studies, we go beyond a deterministic framework, considering individual immunological variability. Both deterministic and stochastic models are calibrated using empirical data on viral load and antibody (IgM and IgG) concentrations for all dengue serotypes, incorporating confidence intervals derived from stochastic realizations.
With good agreement between the mean of the stochastic realizations and the mean field solution for each model, our approach not only successfully captures primary and heterologous secondary infection dynamics facilitated by antibody-dependent enhancement (ADE) but also provides, for the first time, insights into homotypic reinfection dynamics. Our study discusses the relevance of homotypic reinfections in dengue transmission at the population level, highlighting potential implications for disease prevention and control strategies
Semi-blind-trace algorithm for self-supervised attenuation of trace-wise coherent noise
Get PDFTrace-wise noise is a type of noise often seen in seismic data, which is characterized by vertical coherency and horizontal incoherency. Using self-supervised deep learning to attenuate this type of noise, the conventional blind-trace deep learning trains a network to blindly reconstruct each trace in the data from its surrounding traces; it attenuates isolated trace-wise noise but causes signal leakage in clean and noisy traces and reconstruction errors next to each noisy trace. To reduce signal leakage and improve denoising, we propose a new loss function and masking procedure in a semi-blind-trace deep learning framework. Our hybrid loss function has weighted active zones that cover masked and non-masked traces. Therefore, the network is not blinded to clean traces during their reconstruction. During training, we dynamically change the masks' characteristics. The goal is to train the network to learn the characteristics of the signal instead of noise. The proposed algorithm enables the designed U-net to detect and attenuate trace-wise noise without having prior information about the noise. A new hyperparameter of our method is the relative weight between the masked and non-masked traces' contribution to the loss function. Numerical experiments show that selecting a small value for this parameter is enough to significantly decrease signal leakage. The proposed algorithm is tested on synthetic and real off-shore and land data sets with different noises. The results show the superb ability of the method to attenuate trace-wise noise while preserving other events. An implementation of the proposed algorithm as a Python code is also made available