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Mathematical modeling can offer valuable insights into the behavior of biological systems upon treatment. Different mathematical models (empirical, semi-empirical, and mechanistic) have been designed to predict the efficacy of either hyperthermia (HT), radiotherapy (RT), or their combination. However, mathematical approaches capable of modeling cell survival from shared general principles for both mono-treatments alone and their co-application are rare. Moreover, some cell cultures show dose-dependent saturation in response to HT or RT, manifesting in survival curve flattenings. An advanced survival model must, therefore, appropriately reflect such behavior. We propose a cell survival model to predict the effect of both treatments based on the general principle of sublethal damage (SLD) accumulation for the induction of cell death and irreversible proliferation arrest. Our approach extends Jung's model on heat-induced cellular inactivation by incorporating dose-dependent recovery rates that delineate changes in SLD restoration. The resulting unified model (Umodel) accurately describes not only HT but also RT survival outcomes, is applicable to simultaneous thermoradiotherapy modeling, and particularly suited to reproduce and predict survival curve flattening phenomena. We demonstrate the Umodel's robust performance (R2 > 0.95) based on numerous clonogenic cell survival data sets from the literature and our experimental studies., Comment: Main text: 20 pages, 6 figures, 2 tables, 90 references. Supplemental information: 25 pages, 10 figures, 11 tables

In this paper, we carry out a rigorous analysis of four-dimensional variational data assimilation problems for linear and semilinear parabolic equations with control in the initial condition, coming from a Lebesgue space. Due to the nature of the data assimilation problem, spatial pointwise observations of the state have to be considered in the cost functional, which requires continuity of the solution with respect to the spatial variable. To obtain this for an initial condition in $L^{\beta}(\Omega)$, with $\beta>d$, we make use of maximal parabolic regularity tools, jointly with real and complex interpolation theory. We prove that the data assimilation problems admit an optimal solution and derive a first-order necessary optimality system. For the semilinear case, the situation is more involved. Indeed, due to the differentiability properties of the control-to-state mapping, we can derive first-order necessary optimality conditions just for values of $\beta>4$. Due to the same reason, the study of the second-order sufficient optimality conditions is carried out for $d=2$ and taking $\beta>6$.

A method for channel estimation in wideband massive Multiple-Input Multiple-Output (MIMO) systems using covariance identification is developed. The method is useful for Frequency-Division Duplex (FDD) at either sub-6GHz or millimeter wave (mmWave) frequency bands and takes into account the beam squint effect caused by the large bandwidth of the signals. The method relies on the slow time variation of the channel covariance matrix and allows for the utilization of very short training sequences thanks to the exploitation of the channel structure, both in the covariance matrix identification and the channel estimation stages. As a consequence of significantly reducing the training overhead, the proposed channel estimator has a computational complexity lower than other existing approaches., Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible

In this paper we propose a bilevel optimization approach for the placement of space and time observations in variational data assimilation problems. Within the framework of supervised learning, we consider a bilevel problem where the lower-level task is the variational reconstruction of the initial condition of a semilinear system, and the upper-level problem solves the optimal placement with help of a sparsity inducing function. Due to the pointwise nature of the observations, an optimality system with regular Borel measures is obtained as necessary optimality condition for the lower-level problem. The latter is then considered as constraint for the upper-level instance, yielding an optimization problem constrained by a multi-state system with measures. We demonstrate existence of Lagrange multipliers and derive a necessary optimality system characterizing the optimal solution of the bilevel problem. The numerical solution is carried out also on two levels. The lower-level problem is solved using a standard BFGS method, while the upper-level one is solved by means of a projected BFGS algorithm based on the estimation of $\epsilon$-active sets. Finally some numerical experiments are presented to illustrate the main features of our approach.

Devices and sensors for identification of fallers can be used to implement actions to prevent falls and to allow the elderly to live an independent life while reducing the long-term care costs. In this study we aimed to investigate the accuracy of Timed Up and Go test, for fallers' identification, using fusion of features extracted from accelerometer data. Single and dual tasks TUG (manual and cognitive) were performed by a final sample (94% power) of 36 community dwelling healthy older persons (18 fallers paired with 18 non-fallers) while they wear a single triaxial accelerometer at waist with sampling rate of 200Hz. The segmentation of the TUG different trials and its comparative analysis allows to better discriminate fallers from non-fallers, while conventional functional tests fail to do so. In addition, we show that the fusion of features improve the discrimination power, achieving AUC of 0.84 (Sensitivity=Specificity=0.83, 95% CI 0.62-0.91), and demonstrating the clinical relevance of the study. We concluded that features extracted from segmented TUG trials acquired with dual tasks has potential to improve performance when identifying fallers via accelerometer sensors, which can improve TUG accuracy for clinical and epidemiological applications., Comment: accepted at PLoS One in Apr/2017