Quantization is an essential and popular technique for improving the accessibility of large language models (LLMs) by reducing memory usage and computational costs while maintaining performance. In this study, we apply 4-bit Group Scaling Quantization (GSQ) and Generative Pretrained Transformer Quantization (GPTQ) to LLaMA 1B, Qwen 0.5B, and PHI 1.5B, evaluating their impact across multiple NLP tasks. We benchmark these models on MS MARCO (Information Retrieval), BoolQ (Boolean Question Answering), and GSM8K (Mathematical Reasoning) datasets, assessing both accuracy and efficiency across various tasks. The study measures the trade-offs between model compression and task performance, analyzing key evaluation metrics, namely accuracy, inference latency, and throughput (total output tokens generated per second), providing insights into the suitability of low-bit quantization for real-world deployment. Using the results, users can then make suitable decisions based on the specifications that need to be met. We discuss the pros and cons of GSQ and GPTQ techniques on models of different sizes, which also serve as a benchmark for future experiments.

The field of partial differential equations (PDEs) is vast in size and diversity. The basic reason for this is that essentially all fundamental laws of physics are formulated in terms of PDEs. In addition, approximations to these fundamental laws, that form a patchwork of mathematical models covering the range from the smallest to the largest observable space-time scales, are also formulated in terms of PDEs. The diverse applications of PDEs in science and technology testify to the flexibility and expressiveness of the language of PDEs, but it also makes it a hard topic to teach right. Exactly because of the diversity of applications, there are just so many different points of view when it comes to PDEs. These lecture notes view the subject through the lens of applied mathematics. From this point of view, the physical context for basic equations like the heat equation, the wave equation and the Laplace equation are introduced early on, and the focus of the lecture notes are on methods, rather than precise mathematical definitions and proofs. With respect to methods, both analytical and numerical approaches are discussed. These lecture notes has been succesfully used as the text for a master class in partial differential equations for several years. The students attending this class are assumed to have previously attended a standard beginners class in ordinary differential equations and a standard beginners class in numerical methods. It is also assumed that they are familiar with programming at the level of a beginners class in informatics at the university level.

Optical Character Recognition (OCR) is crucial to the National Library of Norway's (NLN) digitisation process as it converts scanned documents into machine-readable text. However, for the Sámi documents in NLN's collection, the OCR accuracy is insufficient. Given that OCR quality affects downstream processes, evaluating and improving OCR for text written in Sámi languages is necessary to make these resources accessible. To address this need, this work fine-tunes and evaluates three established OCR approaches, Transkribus, Tesseract and TrOCR, for transcribing Sámi texts from NLN's collection. Our results show that Transkribus and TrOCR outperform Tesseract on this task, while Tesseract achieves superior performance on an out-of-domain dataset. Furthermore, we show that fine-tuning pre-trained models and supplementing manual annotations with machine annotations and synthetic text images can yield accurate OCR for Sámi languages, even with a moderate amount of manually annotated data.

This paper presents a differentially private approach to Kaplan-Meier estimation that achieves accurate survival probability estimates while safeguarding individual privacy. The Kaplan-Meier estimator is widely used in survival analysis to estimate survival functions over time, yet applying it to sensitive datasets, such as clinical records, risks revealing private information. To address this, we introduce a novel algorithm that applies time-indexed Laplace noise, dynamic clipping, and smoothing to produce a privacy-preserving survival curve while maintaining the cumulative structure of the Kaplan-Meier estimator. By scaling noise over time, the algorithm accounts for decreasing sensitivity as fewer individuals remain at risk, while dynamic clipping and smoothing prevent extreme values and reduce fluctuations, preserving the natural shape of the survival curve. Our results, evaluated on the NCCTG lung cancer dataset, show that the proposed method effectively lowers root mean squared error (RMSE) and enhances accuracy across privacy budgets ($\epsilon$). At $\epsilon = 10$, the algorithm achieves an RMSE as low as 0.04, closely approximating non-private estimates. Additionally, membership inference attacks reveal that higher $\epsilon$ values (e.g., $\epsilon \geq 6$) significantly reduce influential points, particularly at higher thresholds, lowering susceptibility to inference attacks. These findings confirm that our approach balances privacy and utility, advancing privacy-preserving survival analysis.

Small language models (SLMs) become unprecedentedly appealing due to their approximately equivalent performance compared to large language models (LLMs) in certain fields with less energy and time consumption during training and inference. However, the personally identifiable information (PII) leakage of SLMs for downstream tasks has yet to be explored. In this study, we investigate the PII leakage of the chatbot based on SLM. We first finetune a new chatbot, i.e., ChatBioGPT based on the backbone of BioGPT using medical datasets Alpaca and HealthCareMagic. It shows a matchable performance in BERTscore compared with previous studies of ChatDoctor and ChatGPT. Based on this model, we prove that the previous template-based PII attacking methods cannot effectively extract the PII in the dataset for leakage detection under the SLM condition. We then propose GEP, which is a greedy coordinate gradient-based (GCG) method specifically designed for PII extraction. We conduct experimental studies of GEP and the results show an increment of up to 60$\times$ more leakage compared with the previous template-based methods. We further expand the capability of GEP in the case of a more complicated and realistic situation by conducting free-style insertion where the inserted PII in the dataset is in the form of various syntactic expressions instead of fixed templates, and GEP is still able to reveal a PII leakage rate of up to 4.53%.

We consider randomly distributed mixtures of bonds of ferromagnetic and antiferromagnetic type in a two-dimensional square lattice with probability $1-p$ and $p$, respectively, according to an i.i.d. random variable. We study minimizers of the corresponding nearest-neighbour spin energy on large domains in ${\mathbb Z}^2$. We prove that there exists $p_0$ such that for $p\le p_0$ such minimizers are characterized by a majority phase; i.e., they take identically the value $1$ or $-1$ except for small disconnected sets. A deterministic analogue is also proved.

Diffraction of light upon interaction with thick slabs of a dielectric material having a periodic modulation of its refractive index (or dielectric tensor) is typically studied with the aid of the method known as the rigorous coupled-wave analysis (RCWA). The method involves solving Maxwell's equations for a large number of coupled electromagnetic plane-waves inside the dielectric slab, then matching the boundary conditions at the interface between the incidence medium and the slab, as well as those at the interface between the slab and the transmittance medium. In this way, one obtains the E-field and H-field amplitudes for all the reflected and transmitted plane-waves (i.e., diffraction orders as well as evanescent waves) that emerge within the incidence and transmittance media. If the refractive index (or dielectric tensor) of the holographic slab happens to vary in the thickness direction, one treats the slab as a number of thin layers stacked upon each other, then computes and combines the scattering matrices of these layers to arrive at the complete solution for the entire stack. The goal of the present paper is to extend the standard RCWA method to the case where the hologram's dielectric tensor varies in the thickness direction (in addition to being periodically modulated along an in-plane axis), without slicing up the thick hologram into a number of thin layers. The reflected and transmitted plane-waves in this case exhibit a large degree of degeneracy, but our numerical results confirm the validity and the accuracy of our proposed algorithm for handling such degeneracies.

The proliferation of healthcare data has expanded opportunities for collaborative research, yet stringent privacy regulations hinder pooling sensitive patient records. We propose a \emph{multiparty homomorphic encryption-based} framework for \emph{privacy-preserving federated Kaplan--Meier survival analysis}, offering native floating-point support, a theoretical model, and explicit reconstruction-attack mitigation. Compared to prior work, our framework ensures encrypted federated survival estimates closely match centralized outcomes, supported by formal utility-loss bounds that demonstrate convergence as aggregation and decryption noise diminish. Extensive experiments on the NCCTG Lung Cancer and synthetic Breast Cancer datasets confirm low \emph{mean absolute error (MAE)} and \emph{root mean squared error (RMSE)}, indicating negligible deviations between encrypted and non-encrypted survival curves. Log-rank and numerical accuracy tests reveal \emph{no significant difference} between federated encrypted and non-encrypted analyses, preserving statistical validity. A reconstruction-attack evaluation shows smaller federations (2--3 providers) with overlapping data between the institutions are vulnerable, a challenge mitigated by multiparty encryption. Larger federations (5--50 sites) degrade reconstruction accuracy further, with encryption improving confidentiality. Despite an 8--19$\times$ computational overhead, threshold-based homomorphic encryption is \emph{feasible for moderate-scale deployments}, balancing security and runtime. By providing robust privacy guarantees alongside high-fidelity survival estimates, our framework advances the state-of-the art in secure multi-institutional survival analysis.

The Cancer Registry of Norway (CRN) is a part of the Norwegian Institute of Public Health (NIPH) and is tasked with producing statistics on cancer among the Norwegian population. For this task, CRN develops, tests, and evolves a software system called Cancer Registration Support System (CaReSS). It is a complex socio-technical software system that interacts with many entities (e.g., hospitals, medical laboratories, and other patient registries) to achieve its task. For cost-effective testing of CaReSS, CRN has employed EvoMaster, an AI-based REST API testing tool combined with an integrated classical machine learning model. Within this context, we propose Qlinical to investigate the feasibility of using, inside EvoMaster, a Quantum Neural Network (QNN) classifier, i.e., a quantum machine learning model, instead of the existing classical machine learning model. Results indicate that Qlinical can achieve performance comparable to that of EvoClass. We further explore the effects of various QNN configurations on performance and offer recommendations for optimal QNN settings for future QNN developers.

We prove a homogenization theorem for quadratic convolution energies defined in perforated domains. The corresponding limit is a Dirichlet-type quadratic energy, whose integrand is defined by a non-local cell-problem formula. The proof relies on an extension theorem from perforated domains belonging to a wide class containing compact periodic perforations.

The goal of this note is to study the spectrum of a self-adjoint convolution operator in $L^2(\mathbb R^d)$ with an integrable kernel that is perturbed by an essentially bounded real-valued potential tending to zero at infinity. We show that the essential spectrum of such operator is the union of the spectrum of the convolution operator and of the essential range of the potential. Then we provide several sufficient conditions for the existence of a countable sequence of discrete eigenvalues. For operators having non-connected essential spectrum we give sufficient conditions for the existence of discrete eigenvalues in the corresponding spectral gaps.

The paper deals with periodic homogenization of nonlocal symmetric convolution type operators in $L^2(\mathbb R^d)$, whose kernel is the product of a density that belongs to the domain of attraction of an $\alpha$-stable law and a rapidly oscillating positive periodic function. Assuming that the local oscillation of the said density satisfies a proper upper bound at infinity, we prove homogenization result for the studied family of operators.

In this paper we introduce a new fix point iteration scheme for solving nonlinear electromagnetic scattering problems. The method is based on a spectral formulation of Maxwell's equations called the Bidirectional Pulse Propagation Equations. The scheme can be applied to a wide array of slab-like geometries, and for arbitrary material responses. We derive the scheme and investigated how it performs with respect to convergence and accuracy by applying it to the case of light scattering from a simple slab whose nonlinear material response is a sum a very fast electronic vibrational response, and a much slower molecular vibrational response.

We study homogenization problem for non-autonomous parabolic equations of the form $\partial_t u=L(t)u$ with an integral convolution type operator $L(t)$ that has a non-symmetric jump kernel which is periodic in spatial variables and in time. It is assumed that the space-time scaling of the environment is not diffusive. We show that asymptotically the spatial and temporal evolutions of the solutions are getting decoupled, and the homogenization result holds in a moving frame.

The paper studies homogenization problem for a bounded in $L_2(\mathbb R^d)$ convolution type operator ${\mathbb A}_\eps$, \eps &gt;0, of the form $$ ({\mathbb A}_\eps u) (\x) = \eps^{-d-2} \int_{\R^d} a((\x-\y)/\eps) \mu(\x/\eps, \y/\eps) \left( u(\x) - u(\y) \right)\,d\y. $$ It is assumed that $a(\x)$ is a non-negative function from $L_1(\R^d)$, and $\mu(\x,\y)$ is a periodic in $\x$ and $\y$ function such that $0< \mu_- \leqslant \mu(\x,\y) \leqslant \mu_+< \infty$. No symmetry assumption on$a(\cdot)$and$\mu(\cdot)$ is imposed, so the operator ${\mathbb A}_\eps$ need not be self-adjoint. Under the assumption that the moments $M_k = \int_{\R^d} |\x|^k a(\x)\,d\x$, $k=1,2,3$, are finite we obtain, for small \eps&gt;0, sharp in order approximation of the resolvent $({\mathbb A}_\eps + I)^{-1}$ in the operator norm in $L_2(\mathbb R^d)$, the discrepancy being of order $O(\eps)$. The approximation is given by an operator of the form $({\mathbb A}^0 + \eps^{-1} \langle \boldsymbol{\alpha},\nabla \rangle + I)^{-1}$ multiplied on the right by a periodic function $q_0(\x/\eps)$; here ${\mathbb A}^0 = - \operatorname{div}g^0 \nabla$ is the effective operator, and $\boldsymbol{\alpha}$ is a constant vector.

We propose Guardian-FC, a novel two-layer framework for privacy preserving federated computing that unifies safety enforcement across diverse privacy preserving mechanisms, including cryptographic back-ends like fully homomorphic encryption (FHE) and multiparty computation (MPC), as well as statistical techniques such as differential privacy (DP). Guardian-FC decouples guard-rails from privacy mechanisms by executing plug-ins (modular computation units), written in a backend-neutral, domain-specific language (DSL) designed specifically for federated computing workflows and interchangeable Execution Providers (EPs), which implement DSL operations for various privacy back-ends. An Agentic-AI control plane enforces a finite-state safety loop through signed telemetry and commands, ensuring consistent risk management and auditability. The manifest-centric design supports fail-fast job admission and seamless extensibility to new privacy back-ends. We present qualitative scenarios illustrating backend-agnostic safety and a formal model foundation for verification. Finally, we outline a research agenda inviting the community to advance adaptive guard-rail tuning, multi-backend composition, DSL specification development, implementation, and compiler extensibility alongside human-override usability.

The paper deals with homogenisation problems for high-contrast symmetric convolution-type operators with integrable kernels in media with a periodic microstructure. We adapt the two-scale convergence method to nonlocal convolution-type operators and obtain the homogenisation result both for problems stated in the whole space and in bounded domains with the homogeneous Dirichlet boundary condition. Our main focus is on spectral analysis. We describe the spectrum of the limit two-scale operator and characterize the limit behaviour of the spectrum of the original problem as the microstructure period tends to zero. It is shown that the spectrum of the limit operator is a subset the limit of the spectrum of the original operator, and that they need not coincide.

Recently, Rozelot & Eren pointed out that the first solar gravitational moment (J2) might exhibit a temporal variation. The suggested explanation is through the temporal variation of the solar rotation with latitude. This issue is deeper developed due to an accurate knowledge of the long-term variations in solar differential rotation regarding solar activity. Here we analyze solar cycles 12-24, investigating the long-term temporal variations in solar differential rotation. It is shown that J2 exhibits a net modulation over the 13 studied cycles of approximately (89.6 +- 0.1) yr, with a peak-to-peak amplitude of approximately 0.1 x 10-7 for a reference value of 2.07 x 10-7). Moreover, J2 exhibits a positive linear trend in the period of minima solar activity (sunspot number up to around 40) and a marked declining trend in the period of maxima (sunspot number above 50). In absolute magnitude, the mean value of J2 is more significant during periods of minimum than in periods of maximum. These findings are based on observational results that are not free of errors and can be refined further by considering torsional oscillations for example. They are comforted by identifying a periodic variation of the J2 term evidenced through the analysis of the perihelion precession of planetary orbits either deduced from ephemerides or computed in the solar equatorial coordinate system instead of the ecliptic coordinate one usually used.