2063 research outputs found
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How particular is the physics of the free energy principle?
No full textThe free energy principle (FEP) states that any dynamical system can be interpreted as performing Bayesian inference upon its surrounding environment. Although, in theory, the FEP applies to a wide variety of systems, there has been almost no direct exploration or demonstration of the principle in concrete systems. In this work, we examine in depth the assumptions required to derive the FEP in the simplest possible set of systems – weakly-coupled non-equilibrium linear stochastic systems. Specifically, we explore (i) how general the requirements imposed on the statistical structure of a system are and (ii) how informative the FEP is about the behaviour of such systems. We discover that two requirements of the FEP – the Markov blanket condition (i.e. a statistical boundary precluding direct coupling between internal and external states) and stringent restrictions on its solenoidal flows (i.e. tendencies driving a system out of equilibrium) – are only valid for a very narrow space of parameters. Suitable systems require an absence of perception-action asymmetries that is highly unusual for living systems interacting with an environment. More importantly, we observe that a mathematically central step in the argument, connecting the behaviour of a system to variational inference, relies on an implicit equivalence between the dynamics of the average states of a system with the average of the dynamics of those states. This equivalence does not hold in general even for linear stochastic systems, since it requires an effective decoupling from the system's history of interactions. These observations are critical for evaluating the generality and applicability of the FEP and indicate the existence of significant problems of the theory in its current form. These issues make the FEP, as it stands, not straightforwardly applicable to the simple linear systems studied here and suggest that more development is needed before the theory could be applied to the kind of complex systems that describe living and cognitive processes
Maximal subspace averages
No full textWe study maximal operators associated to singular averages along finite subsets Σ
of the Grassmannian Gr(, ) of -dimensional subspaces of R. The well studied = 1 case
corresponds to the the directional maximal function with respect to arbitrary finite subsets of
Gr(1, ) = S−1. We provide a systematic study of all cases 1 ≤ < and prove essentially
sharp 2 (R) bounds for the maximal subspace averaging operator in terms of the cardinality
of Σ, with no assumption on the structure of Σ. In the codimension 1 case, that is = + 1, we
prove the precise critical weak (2, 2)-bound.
Drawing on the analogy between maximal subspace averages and (, )-Nikodym maximal
averages, we also formulate the appropriate maximal Nikodym conjecture for general 1 < <
by providing examples that determine the critical -space for the (, )-Nikodym problem. Unlike
the = 1 case, the maximal Kakeya and Nikodym problems are shown not to be equivalent
when > 1. In this context, we prove the best possible 2 (R)-bound for the (, )-Nikodym
maximal function for all combinations of dimension and codimension.
Our estimates rely on Fourier analytic almost orthogonality principles, combined with polynomial
partitioning, but we also use spatial analysis based on the precise calculation of intersections
of -dimensional plates in R
Notes on Hlog: structural properties, dyadic variants, and bilinear H1-BMO mappings
No full textThis article is devoted to a study of the Hardy space Hlog(Rd) introduced by Bonami, Grellier, and Ky. We present an alternative approach to their result relating the product of a function in the real Hardy space H1 and a function in BMO to distributions that belong to Hlog based on dyadic paraproducts. We also point out analogues of classical results of Hardy-Littlewood, Zygmund, and Stein for Hlog and related Musielak-Orlicz spaces
A mathematical analysis of EDAs with distance-based exponential models
Get PDFEstimation of Distribution Algorithms have been successfully used to solve permutation-based Combinatorial Optimization Problems. In this case, the algorithms use probabilistic models specifically designed for codifying probability distributions over permutation spaces. One class of these probability models are distance-based exponential models, and one example of this class is the Mallows model. In spite of its practical success, the theoretical analysis of Estimation of Distribution Algorithms for permutation-based Combinatorial Optimization Problems has not been developed as extensively as it has been for binary problems. With this motivation, this paper presents a first mathematical analysis of the convergence behavior of Estimation of Distribution Algorithms based on Mallows models. The model removes the randomness of the algorithm in order to associate a dynamical system to it. Several scenarios of increasing complexity with different fitness functions and initial probability distributions are analyzed. The obtained results show: a) the strong dependence of the final results on the initial population, and b) the possibility to converge to non-degenerate distributions even in very simple scenarios, which has not been reported before in the literature.Spanish Ministry of Science and Innovation through the projects
PID2019-104966GB-I00/AEI/10.13039/501100011033,
PID2019-104933GB-I00/AEI/10.13039/501100011033,
PID2019-106453GA-I00/AEI/10.13039/501100011033 and
BCAM Severo Ochoa accreditation SEV-2017-0718; and by the Basque Government through
the program BERC 2022-2025 and
the projects IT1504-22 and
IT1494-22; and
by UPV/EHU through the project GIU20/054.
Imanol holds a grant from the Department of Education of the Basque Government (PRE_2021_2_0224)
Trajectory optimization of space vehicle in rendezvous proximity operation with evolutionary feasibility conserving techniques
Get PDFIn this paper, a direct approach is developed for discovering optimal transfer trajectories of close-range rendezvous of satellites considering disturbances in elliptical orbits. The control vector representing the inputs is parameterized via different interpolation methods, and an Estimation of Distribution Algorithm (EDA) that implements mixtures of probability models is presented. To satisfy the terminal conditions, which are represented as non-linear inequality constraints, several feasibility conserving mechanisms associated with learning and sampling methods of the EDAs are proposed, which guarantee the feasibility of the explored solutions. They include a particular implementation of a clustering algorithm, outlier detection, and several heuristic mapping methods. The combination of the proposed operators guides the optimization process in achieving the optimal solution by surfing the regions of the search domain associated with feasible solutions. Numerical simulations confirm that space transfer trajectories with minimum-fuel consumption for the chaser spacecraft can be obtained with terminal condition satisfaction in rendezvous proximity operation.KK-2021/00065
KK-2022/00106;
PID2019-104933GB-10/AEI/10.13039/501100011033
PID2019-106453GAI00/AEI/10.13039/501100011033
IT1504-2
Surface-Surface-Intersection Computation using a Bounding Volume Hierarchy with Osculating Toroidal Patches in the Leaf Nodes
Get PDFWe present an efficient and robust algorithm for computing the intersection curve of two freeform surfaces using a Bounding Volume
Hierarchy (BVH), where the leaf nodes contain osculating toroidal patches. The covering of each surface by a union of tightly fitting
toroidal patches greatly simplifies the geometric operations involved in the surface-surface-intersection computation, i.e., the bounding
of surface normals, the detection of surface binormals, the point projection from one surface to the other surface, and the intersection
of local surface patches. Moreover, the hierarchy of simple bounding volumes (such as rectangle-swept spheres) accelerates the
geometric search for the potential pairs of surface patches that may generate some curve segments in the surface-surface-intersection.
We demonstrate the effectiveness of our approach by using test examples of intersecting two freeform surfaces, including some highly
non-trivial examples with tangential intersections. In particular, we test the intersection of two almost identical surfaces, where one
surface is obtained from the same surface, using a rotation around a normal line by a smaller and smaller angle θ = 10−k degree,
k = 0, · · · , 5. The intersection results are often given as surface subpatches in some highly tangential areas, and even as the whole
surface itself, when θ = 0.00001◦
Mathematical models for dengue fever epidemiology: a 10-year systematic review
Get PDFMathematical models have a long history in epidemiological research, and as the COVID-19 pandemic progressed, research on mathematical modeling became imperative and very influential to understand the epidemiological dynamics of disease spreading.
Mathematical models describing dengue fever epidemiological dynamics are found back from 1970. Dengue fever is a viral mosquito-borne infection caused by four antigenically related but distinct serotypes (DENV-1 to DENV-4). With 2.5 billion people at risk of acquiring the infection, it is a major international public health concern. Although most of the cases are asymptomatic or mild, the disease immunological response is complex, with severe disease linked to the antibody-dependent enhancement (ADE) - a disease augmentation phenomenon where pre-existing antibodies to previous dengue infection do not neutralize but rather enhance the new infection. Here, we present a 10-year systematic review on mathematical models for dengue fever epidemiology. Specifically, we review multi-strain frameworks describing host-to-host and vector-host transmission models and within-host models describing viral replication and the respective immune response.
Following a detailed literature search in standard scientific databases, different mathematical models in terms of their scope, analytical approach and structural form, including model validation and parameter estimation using empirical data, are described and analysed.
Aiming to identify a consensus on infectious diseases modeling aspects that can contribute to public health authorities for disease control, we revise the current understanding of epidemiological and immunological factors influencing the transmission dynamics of dengue. This review provide insights on general features to be considered to model aspects of real-world public health problems, such as the current epidemiological scenario we are living in.M. A. has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 792494
Derivation of a Cost-Sensitive COVID-19 Mortality Risk Indicator Using a Multistart Framework
Get PDFThe overall global death rate for COVID-19 patients
has escalated to 2.13% after more than a year of worldwide
spread. Despite strong research on the infection pathogenesis, the
molecular mechanisms involved in a fatal course are still poorly
understood.Machine learning constitutes a perfect tool to develop
algorithms for predicting a patient’s hospitalization outcome at
triage. This paper presents a probabilistic model, referred to
as a mortality risk indicator, able to assess the risk of a fatal
outcome for new patients. The derivation of the model was done
over a database of 2,547 patients from the first COVID-19 wave
in Spain. Model learning was tackled through a five multistart
configuration that guaranteed good generalization power and
low variance error estimators. The training algorithm made use
of a class weighting correction to account for the mortality
class imbalance and two regularization learners, logistic and
lasso regressors. Outcome probabilities were adjusted to obtain
cost-sensitive predictions by minimizing the type II error. Our
mortality indicator returns both a binary outcome and a threestage
mortality risk level. The estimated AUC across multistarts
reaches an average of 0.907. At the optimal cutoff for the binary
outcome, the model attains an average sensitivity of 0.898, with
a 0.745 specificity. An independent set of 121 patients later
released from the same consortium attained perfect sensitivity
(1), with a 0.759 specificity when predicted by our model. Best
performance for the indicator is achieved when the prediction’s
time horizon is within two weeks since admission to hospital. In
addition to a strong predictive performance, the set of selected
features highlights the relevance of several underrated molecules
in COVID-19 research, such as blood eosinophils, bilirubin, and
urea levels.AXA Research Fund project "Early prognosis of COVID-19 infections via machine learning"
Basque Government special funding on Mathematical Modelling Applied to
Healt
Attraction-repulsion clustering: a way of promoting diversity linked to demographic parity in fair clustering
Get PDFWe consider the problem of diversity enhancing clustering, i.e, developing clustering methods which produce clusters that favour diversity with respect to a set of protected attributes such as race, sex, age, etc. In the context of fair clustering, diversity plays a major role when fairness is understood as demographic parity. To promote diversity, we introduce perturbations to the distance in the unprotected attributes that account for protected attributes in a way that resembles attraction-repulsion of charged particles in Physics. These perturbations are defined through dissimilarities with a tractable interpretation. Cluster analysis based on attraction-repulsion dissimilarities penalizes homogeneity of the clusters with respect to the protected attributes and leads to an improvement in diversity. An advantage of our approach, which falls into a pre-processing set-up, is its compatibility with a wide variety of clustering methods and whit non-Euclidean data. We illustrate the use of our procedures with both synthetic and real data and provide discussion about the relation between diversity, fairness, and cluster structure.MTM2017-86061-C2-1-P
VA005P17
ANITI program and DEEL IR
Preference incorporation in MOEA/D using an outranking approach with imprecise model parameters
Get PDFMulti-objective Optimization Evolutionary Algorithms (MOEAs) face numerous challenges when they are used to solve Many-objective Optimization Problems (MaOPs). Decomposition-based strategies, such as MOEA/D, divide an MaOP into multiple single-optimization sub-problems, achieving better diversity and a better approximation of the Pareto front, and dealing with some of the challenges of MaOPs. However, these approaches still require one to solve a multi-criteria selection problem that will allow a Decision-Maker (DM) to choose the final solution. Incorporating preferences may provide results that are closer to the region of interest of a DM. Most of the proposals to integrate preferences in decomposition-based MOEAs prefer progressive articulation over the “a priori” incorporation of preferences. Progressive articulation methods can hardly work without comparable and transitive preferences, and they can significantly increase the cognitive effort required of a DM. On the other hand, the “a priori” strategies do not demand transitive judgements from the DM but require a direct parameter elicitation that usually is subject to imprecision. Outranking approaches have properties that allow them to suitably handle non-transitive preferences, veto conditions, and incomparability, which are typical characteristics of many real DMs. This paper explores how to incorporate DM preferences into MOEA/D using the “a priori” incorporation of preferences, based on interval outranking relations, to handle imprecision when preference parameters are elicited. Several experiments make it possible to analyze the proposal's performance on benchmark problems and to compare the results with the classic MOEA/D without preference incorporation and with a recent, state-of-the-art preference-based decomposition algorithm. In many instances, our results are closer to the Region of Interest, particularly when the number of objectives increases