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We investigate how elimination of variables can affect the asymptotic dynamics and phenotype control of Boolean networks. In particular, we look at the impact on minimal trap spaces, and identify a structural condition that guarantees their preservation. We examine the possible effects of variable elimination under three of the most popular approaches to control (attractor-based control, value propagation and control of minimal trap spaces), and under different update schemes (synchronous, asynchronous, generalized asynchronous). We provide some insights on the application of reduction, and an ample inventory of examples and counterexamples.

The paper presents the kinematic modelling for the coupled motion of a 6-DOF surgical parallel robot PARA-SILSROB which guides a mobile platform carrying the surgical instruments, and the actuators of the sub-modules which hold these tools. To increase the surgical procedure safety, a closed form solution for the kinematic model is derived and then, the forward and inverse kinematic models for the mobile orientation platform are obtained. The kinematic models are used in numerical simulations for the reorientation of the endoscopic camera, which imposes an automated compensatory motion from the active instruments' mod-ules.

The delimitation of biological species, i.e., deciding which individuals belong to the same species and whether and how many different species are represented in a data set, is key to the conservation of biodiversity. Much existing work uses only genetic data for species delimitation, often employing some kind of cluster analysis. This can be misleading, because geographically distant groups of individuals can be genetically quite different even if they belong to the same species. We investigate the problem of testing whether two potentially separated groups of individuals can belong to a single species or not based on genetic and spatial data. Existing methods such as the partial Mantel test and jackknife-based distance-distance regression are considered. New approaches, i.e., an adaptation of a mixed effects model, a bootstrap approach, and a jackknife version of partial Mantel, are proposed. All these methods address the issue that distance data violate the independence assumption for standard inference regarding correlation and regression; a standard linear regression is also considered. The approaches are compared on simulated meta-populations generated with SLiM and GSpace - two software packages that can simulate spatially-explicit genetic data at an individual level. Simulations show that the new jackknife version of the partial Mantel test provides a good compromise between power and respecting the nominal type I error rate. Mixed-effects models have larger power than jackknife-based methods, but tend to display type I error rates slightly above the significance level. An application on brassy ringlets concludes the paper.

In this work, we analyze the convergence rate of randomized quasi-Monte Carlo (RQMC) methods under Owen's boundary growth condition [Owen, 2006] via spectral analysis. Specifically, we examine the RQMC estimator variance for the two commonly studied sequences: the lattice rule and the Sobol' sequence, applying the Fourier transform and Walsh--Fourier transform, respectively, for this analysis. Assuming certain regularity conditions, our findings reveal that the asymptotic convergence rate of the RQMC estimator's variance closely aligns with the exponent specified in Owen's boundary growth condition for both sequence types. We also provide analysis for certain discontinuous integrands.

Symplectic integrators are widely implemented numerical integrators for Hamiltonian mechanics, which preserve the Hamiltonian structure (symplecticity) of the system. Although the symplectic integrator does not conserve the energy of the system, it is well known that there exists a conserving modified Hamiltonian, called the shadow Hamiltonian. For the Nambu mechanics, which is a kind of generalized Hamiltonian mechanics, we can also construct structure-preserving integrators by the same procedure used to construct the symplectic integrators. In the structure-preserving integrator, however, the existence of shadow Hamiltonians is nontrivial. This is because the Nambu mechanics is driven by multiple Hamiltonians and it is nontrivial whether the time evolution by the integrator can be cast into the Nambu mechanical time evolution driven by multiple shadow Hamiltonians. In this paper we present a general procedure to calculate the shadow Hamiltonians of structure-preserving integrators for Nambu mechanics, and give an example where the shadow Hamiltonians exist. This is the first attempt to determine the concrete forms of the shadow Hamiltonians for a Nambu mechanical system. We show that the fundamental identity, which corresponds to the Jacobi identity in Hamiltonian mechanics, plays an important role in calculating the shadow Hamiltonians using the Baker-Campbell-Hausdorff formula. It turns out that the resulting shadow Hamiltonians have indefinite forms depending on how the fundamental identities are used. This is not a technical artifact, because the exact shadow Hamiltonians obtained independently have the same indefiniteness.

Recurrent neural networks (RNNs) notoriously struggle to learn long-term memories, primarily due to vanishing and exploding gradients. The recent success of state-space models (SSMs), a subclass of RNNs, to overcome such difficulties challenges our theoretical understanding. In this paper, we delve into the optimization challenges of RNNs and discover that, as the memory of a network increases, changes in its parameters result in increasingly large output variations, making gradient-based learning highly sensitive, even without exploding gradients. Our analysis further reveals the importance of the element-wise recurrence design pattern combined with careful parametrizations in mitigating this effect. This feature is present in SSMs, as well as in other architectures, such as LSTMs. Overall, our insights provide a new explanation for some of the difficulties in gradient-based learning of RNNs and why some architectures perform better than others.

We consider the nonparametric regression problem when the covariates are located on an unknown smooth compact submanifold of a Euclidean space. Under defining a random geometric graph structure over the covariates we analyze the asymptotic frequentist behaviour of the posterior distribution arising from Bayesian priors designed through random basis expansion in the graph Laplacian eigenbasis. Under Holder smoothness assumption on the regression function and the density of the covariates over the submanifold, we prove that the posterior contraction rates of such methods are minimax optimal (up to logarithmic factors) for any positive smoothness index.

Studies intended to estimate the effect of a treatment, like randomized trials, may not be sampled from the desired target population. To correct for this discrepancy, estimates can be transported to the target population. Methods for transporting between populations are often premised on a positivity assumption, such that all relevant covariate patterns in one population are also present in the other. However, eligibility criteria, particularly in the case of trials, can result in violations of positivity when transporting to external populations. To address nonpositivity, a synthesis of statistical and mathematical models can be considered. This approach integrates multiple data sources (e.g. trials, observational, pharmacokinetic studies) to estimate treatment effects, leveraging mathematical models to handle positivity violations. This approach was previously demonstrated for positivity violations by a single binary covariate. Here, we extend the synthesis approach for positivity violations with a continuous covariate. For estimation, two novel augmented inverse probability weighting estimators are proposed. Both estimators are contrasted with other common approaches for addressing nonpositivity. Empirical performance is compared via Monte Carlo simulation. Finally, the competing approaches are illustrated with an example in the context of two-drug versus one-drug antiretroviral therapy on CD4 T cell counts among women with HIV.

Background: The aim of this study was to investigate the role of clinical, dosimetric and pretherapeutic magnetic resonance imaging (MRI) features for lesion-specific outcome prediction of stereotactic radiotherapy (SRT) in patients with brain metastases from malignant melanoma (MBM). Methods: In this multicenter, retrospective analysis, we reviewed 517 MBM from 130 patients treated with SRT (single fraction or hypofractionated). For each gross tumor volume (GTV) 1576 radiomic features (RF) were calculated (788 each for the GTV and for a 3 mm margin around the GTV). Clinical parameters, radiation dose and RF from pretherapeutic contrast-enhanced T1-weighted MRI from different institutions were evaluated with a feature processing and elimination pipeline in a nested cross-validation scheme. Results: Seventy-two (72) of 517 lesions (13.9%) showed a local failure (LF) after SRT. The processing pipeline showed clinical, dosimetric and radiomic features providing information for LF prediction. The most prominent ones were the correlation of the gray level co-occurrence matrix of the margin (hazard ratio (HR): 0.37, confidence interval (CI): 0.23-0.58) and systemic therapy before SRT (HR: 0.55, CI: 0.42-0.70). The majority of RF associated with LF was calculated in the margin around the GTV. Conclusions: Pretherapeutic MRI based RF connected with lesion-specific outcome after SRT could be identified, despite multicentric data and minor differences in imaging protocols. Image data analysis of the surrounding metastatic environment may provide therapy-relevant information with the potential to further individualize radiotherapy strategies.

This study explores the impact of adversarial perturbations on Convolutional Neural Networks (CNNs) with the aim of enhancing the understanding of their underlying mechanisms. Despite numerous defense methods proposed in the literature, there is still an incomplete understanding of this phenomenon. Instead of treating the entire model as vulnerable, we propose that specific feature maps learned during training contribute to the overall vulnerability. To investigate how the hidden representations learned by a CNN affect its vulnerability, we introduce the Adversarial Intervention framework. Experiments were conducted on models trained on three well-known computer vision datasets, subjecting them to attacks of different nature. Our focus centers on the effects that adversarial perturbations to a model's initial layer have on the overall behavior of the model. Empirical results revealed compelling insights: a) perturbing selected channel combinations in shallow layers causes significant disruptions; b) the channel combinations most responsible for the disruptions are common among different types of attacks; c) despite shared vulnerable combinations of channels, different attacks affect hidden representations with varying magnitudes; d) there exists a positive correlation between a kernel's magnitude and its vulnerability. In conclusion, this work introduces a novel framework to study the vulnerability of a CNN model to adversarial perturbations, revealing insights that contribute to a deeper understanding of the phenomenon. The identified properties pave the way for the development of efficient ad-hoc defense mechanisms in future applications.