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We applied Bayesian Optimal Experimental Design (OED) in the estimation of parameters involved in the Equilibrium Dispersive Model for chromatography with two components with the Langmuir adsorption isotherm. The coefficients estimated were Henry's coefficients, the total absorption capacity and the number of theoretical plates, while the design variables were the injection time and the initial concentration. The Bayesian OED algorithm is based on nested Monte Carlo estimation, which becomes computationally challenging due to the simulation time of the PDE involved in the dispersive model. This complication was relaxed by introducing a surrogate model based on Piecewise Sparse Linear Interpolation. Using the surrogate model instead the original reduces significantly the simulation time and it approximates the solution of the PDE with high degree of accuracy. The estimation of the parameters over strategical design points provided by OED reduces the uncertainty in the estimation of parameters. Additionally, the Bayesian OED methodology indicates no improvements when increasing the number of measurements in temporal nodes above a threshold value.

In this paper we introduce a Meshfree Variational Physics Informed Neural Network. It is a Variational Physics Informed Neural Network that does not require the generation of a triangulation of the entire domain and that can be trained with an adaptive set of test functions. In order to generate the test space we exploit an a posteriori error indicator and add test functions only where the error is higher. Four training strategies are proposed and compared. Numerical results show that the accuracy is higher than the one of a Variational Physics Informed Neural Network trained with the same number of test functions but defined on a quasi-uniform mesh.

Weakly Supervised Semantic Segmentation (WSSS) employs weak supervision, such as image-level labels, to train the segmentation model. Despite the impressive achievement in recent WSSS methods, we identify that introducing weak labels with high mean Intersection of Union (mIoU) does not guarantee high segmentation performance. Existing studies have emphasized the importance of prioritizing precision and reducing noise to improve overall performance. In the same vein, we propose ORANDNet, an advanced ensemble approach tailored for WSSS. ORANDNet combines Class Activation Maps (CAMs) from two different classifiers to increase the precision of pseudo-masks (PMs). To further mitigate small noise in the PMs, we incorporate curriculum learning. This involves training the segmentation model initially with pairs of smaller-sized images and corresponding PMs, gradually transitioning to the original-sized pairs. By combining the original CAMs of ResNet-50 and ViT, we significantly improve the segmentation performance over the single-best model and the naive ensemble model, respectively. We further extend our ensemble method to CAMs from AMN (ResNet-like) and MCTformer (ViT-like) models, achieving performance benefits in advanced WSSS models. It highlights the potential of our ORANDNet as a final add-on module for WSSS models.

In this paper, we investigate the degree to which fine-tuning in Large Language Models (LLMs) effectively mitigates versus merely conceals undesirable behavior. Through the lens of semi-realistic role-playing exercises designed to elicit such behaviors, we explore the response dynamics of LLMs post fine-tuning interventions. Our methodology involves prompting models for Chain-of-Thought (CoT) reasoning and analyzing the coherence between the reasoning traces and the resultant outputs. Notably, we identify a pervasive phenomenon we term \emph{reason-based deception}, where models either stop producing reasoning traces or produce seemingly ethical reasoning traces that belie the unethical nature of their final outputs. We further examine the efficacy of response strategies (polite refusal versus explicit rebuttal) in curbing the occurrence of undesired behavior in subsequent outputs of multi-turn interactions. Our findings reveal that explicit rebuttals significantly outperform polite refusals in preventing the continuation of undesired outputs and nearly eliminate reason-based deception, challenging current practices in model fine-tuning. Accordingly, the two key contributions of this paper are (1) defining and studying reason-based deception, a new type of hidden behavior, and (2) demonstrating that rebuttals provide a more robust response model to harmful requests than refusals, thereby highlighting the need to reconsider the response strategies in fine-tuning approaches.

This paper contains two major contributions. First we derive, following the discrete de Rham (DDR) and Virtual Element (VEM) paradigms, pressure-robust methods for the Stokes equations that support arbitrary orders and polyhedral meshes. Unlike other methods presented in the literature, pressure-robustness is achieved here without resorting to an $\boldsymbol{H}({\rm div})$-conforming construction on a submesh, but rather projecting the volumetric force onto the discrete $\boldsymbol{H}({\bf curl})$ space. The cancellation of the pressure error contribution stems from key commutation properties of the underlying DDR and VEM complexes. The pressure-robust error estimates in $h^{k+1}$ (with $h$ denoting the meshsize and $k\ge 0$ the polynomial degree of the DDR or VEM complex) are proven theoretically and supported by a panel of three-dimensional numerical tests. The second major contribution of the paper is an in-depth study of the relations between the DDR and VEM approaches. We show, in particular, that a complex developed following one paradigm admits a reformulation in the other, and that couples of related DDR and VEM complexes satisfy commuting diagram properties with the degrees of freedom maps.

In this paper, we apply the Paired-Explicit Runge-Kutta (P-ERK) schemes by Vermeire et. al. (2019, 2022) to dynamically partitioned systems arising from adaptive mesh refinement. The P-ERK schemes enable multirate time-integration with no changes in the spatial discretization methodology, making them readily implementable in existing codes that employ a method-of-lines approach. We show that speedup compared to a range of state of the art Runge-Kutta methods can be realized, despite additional overhead due to the dynamic re-assignment of flagging variables and restricting nonlinear stability properties. The effectiveness of the approach is demonstrated for a range of simulation setups for viscous and inviscid convection-dominated compressible flows for which we provide a reproducibility repository. In addition, we perform a thorough investigation of the nonlinear stability properties of the Paired-Explicit Runge-Kutta schemes regarding limitations due to the violation of monotonicity properties of the underlying spatial discretization. Furthermore, we present a novel approach for estimating the relevant eigenvalues of large Jacobians required for the optimization of stability polynomials.

In this short paper, we present a simple variant of the recursive path ordering, specified for Logically Constrained Simply Typed Rewriting Systems (LCSTRSs). This is a method for curried systems, without lambda but with partially applied function symbols, which can deal with logical constraints. As it is designed for use in the dependency pair framework, it is defined as reduction pair, allowing weak monotonicity.

We investigate the stability of two families of three-level two-step schemes that extend the classical second order BDF (BDF2) and second order Adams-Moulton (AM2) schemes. For a free parameter restricted to an appropriate range that covers the classical case, we show that both the generalized BDF2 and the generalized AM2 schemes are A-stable. We also introduce the concept of uniform-in-time stability which characterizes a scheme's ability to inherit the uniform boundedness over all time of the solution of damped and forced equation with the force uniformly bounded in time. We then demonstrate that A-stability and uniform-in-time stability are equivalent for three-level two-step schemes. Next, these two families of schemes are utilized to construct efficient and unconditionally stable IMEX schemes for systems that involve a damping term, a skew symmetric term, and a forcing term. These novel IMEX schemes are shown to be uniform-in-time energy stable in the sense that the norm of any numerical solution is bounded uniformly over all time, provided that the forcing term is uniformly bounded time, the skew symmetric term is dominated by the dissipative term, together with a mild time-step restriction. Numerical experiments verify our theoretical results. They also indicate that the generalized schemes could be more accurate and/or more stable than the classical ones for suitable choice of the parameter.

In this paper, we propose nonparametric estimators for varextropy function of an absolutely continuous random variable. Consistency of the estimators is established under suitable regularity conditions. Moreover, a simulation study is performed to compare the performance of the proposed estimators based on mean squared error (MSE) and bias. Furthermore, by using the proposed estimators some tests are constructed for uniformity. It is shown that the varextropybased test proposed here performs well compared to the power of the other uniformity hypothesis tests.

This paper presents the development of a speech synthesis system for the LIMMITS'24 Challenge, focusing primarily on Track 2. The objective of the challenge is to establish a multi-speaker, multi-lingual Indic Text-to-Speech system with voice cloning capabilities, covering seven Indian languages with both male and female speakers. The system was trained using challenge data and fine-tuned for few-shot voice cloning on target speakers. Evaluation included both mono-lingual and cross-lingual synthesis across all seven languages, with subjective tests assessing naturalness and speaker similarity. Our system uses the VITS2 architecture, augmented with a multi-lingual ID and a BERT model to enhance contextual language comprehension. In Track 1, where no additional data usage was permitted, our model achieved a Speaker Similarity score of 4.02. In Track 2, which allowed the use of extra data, it attained a Speaker Similarity score of 4.17.