Our latest publications

• Moen, Per August Jarval (2027). Minimax rates in variance and covariance changepoint testing. Bernoulli. ISSN 1350-7265. To appear. doi: 10.48550/arXiv.2405.07757. Full text in Research Archive
• Salucci, Clara Bertinelli; Reiersrud, Hedvig Borgen; Read, A. L.; Kvellestad, Anders & Bin, Riccardo De (2026). The asymptotic distribution of the likelihood ratio test statistic in two-peak discovery experiments. European Physical Journal C. ISSN 1434-6044. 86(10). doi: 10.1140/epjc/s10052-026-16439-9. Full text in Research Archive Show summary

  Abstract Likelihood ratio tests are widely used in high-energy physics, where the test statistic is usually assumed to follow a chi-squared distribution with a number of degrees of freedom specified by Wilks’ theorem. This assumption breaks down when parameters such as signal or coupling strengths are restricted to be non-negative and their values under the null hypothesis lie on the boundary of the parameter space. Based on a recent clarification concerning the correct asymptotic distribution of the likelihood ratio test statistic for cases where two of the parameters are on the boundary, we revisit the the question of significance estimation for two-peak signal-plus-background counting experiments. In the high-energy physics literature, such experiments are commonly analyzed using Wilks’ chi-squared distribution or the one-parameter Chernoff limit. We demonstrate that these approaches can lead to strongly miscalibrated significances, and that the test statistic distribution is instead well described by a chi-squared mixture with weights determined by the Fisher information matrix. Our results highlight the need for boundary-aware asymptotics in the analysis of two-peak counting experiments.

• Hubin, Aliaksandr & Storvik, Geir Olve (2026). Estimating the marginal likelihood with Integrated nested Laplace approximation (INLA). Journal of Reproducible Statistics. 1(1), p. 1–13. doi: 10.68365/jrepstat.2026.9. Full text in Research Archive Show summary

  The marginal likelihood is a well established model selection criterion in Bayesian statistics. It also allows to efficiently calculate the marginal posterior model probabilities that can be used for Bayesian model averaging of quantities of interest. For many complex models, including latent modeling approaches, marginal likelihoods are however difficult to compute. One recent promising approach for approximating the marginal likelihood is Integrated Nested Laplace Approximation (INLA), designed for models with latent Gaussian structures. In this study we compare the approximations obtained with INLA to alternative approaches across a progression of models of varying complexity. In particular, we evaluate a simple linear latent model with exact analytical truth, a Bayesian linear regression model, probit and logit Bayesian regression models, a longitudinal Poisson generalized linear mixed model, and two extra simulation scenarios designed to probe the limits of the latent Gaussian approximation.

• Badar, Zanib; Ahmad, Ishfaq; Ahmad, Touqeer & Almanjahie, Ibrahim Mufrah (2026). A novel multivariate vine-copula–based drought index with application to high-elevation catchments. Environmental Science and Pollution Research. ISSN 0944-1344. 33(32), p. 16359–16379. doi: 10.1007/s11356-026-38256-z. Full text in Research Archive Show summary

  Drought is a complex, slowly evolving hazard governed by multiple interacting hydro-climatic factors, making it difficult to monitor, characterize, and predict. Conventional single-variable indices fail to capture the nonlinear, asymmetric dependence between precipitation and temperature—a limitation that is particularly critical in data-scarce, high-mountain catchments, where incomplete drought characterization undermines the reliability of early-warning systems. To address this, we propose a novel vine-copula-based Multivariate Drought Index (VMDI) that integrates the Standardized Precipitation Index (SPI), the Standardized Precipitation Evapotranspiration Index (SPEI), and the Standardized Precipitation Temperature Index (SPTI) within a flexible, station-adaptive dependence-modeling framework. VMDI’s key novelty lies in its station-adaptive canonical vine (C-vine) copula structure in which each index is first transformed into uniform pseudo-observations via rank-based empirical CDFs. Dependence is then decomposed into unconditional (Tree 1) and conditional (Tree 2) pair-copulas with SPTI as the root variable, capturing both direct interactions and joint behavior conditioned on SPTI. Copula families are selected locally via information criteria, and Kendall’s values derived from the fitted vine structure yield physically consistent, station-specific index weights. Validated across six stations in the Upper Indus Basin (UIB), VMDI substantially outperforms benchmark indices for precipitation-driven drought signals, achieving agreement improvements of 15–30%, MAE reductions exceeding 50%, skill-score gains of 30–40%, F1-score improvements of 33–37%, and lower-tail dependence coefficients above 0.70, while maintaining low conditional entropy (CE ). For evapotranspiration-related drought conditions, JSDI outperforms VMDI relative to SPEI by about 27–38%, with the greatest improvements observed at the glacier-influenced stations of Bunji and Gilgit. Overall, VMDI and JSDI offer a complementary and operationally robust framework for comprehensive drought monitoring across complex mountain catchments.

• Arbes, Florian Maurits; Mardal, Kent-Andre & Jensen, Øyvind (2026). Data regularization and deconvolution for non-intrusive reduced-order modeling of transport-dominated problems. Results in Applied Mathematics. ISSN 2590-0382. 32. doi: 10.1016/j.rinam.2026.100775. Full text in Research Archive
• Normann, Dag & Sanders, Sam (2026). The uncountability of the reals and the axiom of choice. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik. ISSN 9122-845X. 72, p. 425–436. doi: 10.60866/CAM.323. Full text in Research Archive Show summary

  Abstract The uncountability of the reals was first established by Cantor in what was later heralded as the first paper on set theory. Since the latter constitutes the de facto foundations of mathematics, the logical study of the uncountability of the reals is a worthy endeavour for historical, foundational, and conceptual reasons. In this paper, we shall study the following principle: NIN[0,1]: there is no injection from the unit interval to the natural numbers. We show that relatively strong logical systems cannot prove NIN[0,1]. In particular, the former system implies second-order arithmetic and fragments of the axiom of choice, including dependent choice. We also study the latter choice fragments in Kohlenbach's higher-order reverse mathematics.

• Cibinel, Luca; Roverato, Alberto & Vinciotti, Veronica (2026). A unified approach to penalized likelihood estimation of covariance matrices in high dimensions. Statistical Science. ISSN 0883-4237. Full text in Research Archive Show summary

  We consider the problem of estimation of a covariance matrix for Gaussian data in a high dimensional setting. Existing approaches include maximum likelihood estimation under a pre-specified sparsity pattern, ℓ1- penalized loglikelihood optimization and ridge regularization of the sample covariance. We show that these three approaches can be addressed in an unified way, by considering the constrained optimization of an objective function that involves two suitably defined penalty terms. This unified procedure exploits the advantages of each individual approach, while bringing novelty in the combination of the three. We provide an efficient algorithm for the optimization of the regularized objective function and describe the relationship between the two penalty terms, thereby highlighting the importance of the joint application of the three methods. A simulation study shows how the sparse estimates of covariance matrices returned by the procedure are stable and accurate, both in low and high dimensional settings, and how their calculation is more efficient than existing approaches under a partially known sparsity pattern. An illustration on sonar data is presented for the identification of the covariance structure among signals bounced off a certain material. The method is implemented in the publicly available R package gicf.

• Bhatt, Bidisha & Carlson, Andreas (2026). Capillary slinky: Equilibrium and dynamics of a droplet in a soft spring. Physical Review Fluids. 11(4), p. 043607-1–043607-14. doi: 10.1103/P9J4-HP5H. Full text in Research Archive
• Jaklitsch, David Alexander & Yamashita, Makoto (2026). The braided monoidal structure of tube algebra representations. Theory and Applications of Categories. 45(49), p. 2115–2152. doi: https:/tac.mta.ca/tac/volumes/45/49/45-49abs.html. Full text in Research Archive Show summary

  We consider the tube algebra of a spherical semisimple multitensor category X, and construct a braided monoidal structure with twist for its representations. We further show that this category is braided tensor equivalent with the Drinfeld center of the ind-category of X, extending the well-known linear equivalence.

• Al-Izzi, Sami Cameron; Du, Yao; Veenstra, Jonas; Morris, Richard G.; Souslov, Anton & Carlson, Andreas [Show all 8 contributors for this article] (2026). Nonreciprocal buckling makes active filaments polyfunctional. Proceedings of the National Academy of Sciences of the United States of America (PNAS). ISSN 0027-8424. 123(11). doi: 10.1073/pnas.2531723123. Full text in Research Archive Show summary

  Active filaments are a workhorse for propulsion and actuation across biology, soft robotics, and mechanical metamaterials. However, artificial active rods suffer from limited robustness and adaptivity because they rely on external control, or are tethered to a substrate. Here, we bypass these constraints by demonstrating that nonreciprocal interactions lead to large-scale unidirectional dynamics in free-standing slender structures. By coupling the bending modes of a buckled beam antisymmetrically, we transform the multistable dynamics of elastic snap-through into persistent cycles of shape change. In contrast to the critical point underpinning beam buckling, this transition to self-snapping is mediated by a critical exceptional point, at which bending modes simultaneously become unstable and degenerate. Upon environmental perturbation, our active filaments exploit self-snapping for a range of functionality including crawling, digging, and walking. Our work advances critical exceptional physics as a guiding principle for programming instabilities into functional active materials.

• Lande, Øystein; Meyer, Herman Martens; Dreyer, Lars Willas; Rabault, Jean; Krzywkowski, Théo & Jensen, Atle (2026). Feasibility Study of an Ultra-Low-Cost 3D-Printed Wave Buoy for Water Wave Measurement. Water Waves. ISSN 2523-367X. p. 1–29. doi: 10.1007/s42286-026-00153-w. Full text in Research Archive Show summary

  This paper presents a feasibility study of an ultra-low-cost wave buoy for measuring water waves, built from a 3D-printed hull and an off-the-shelf data logger with an integrated MEMS inertial measurement unit. The buoy records continuously and carries no telemetry, which reduces the average power consumption to 4.7 mA, so that two D-cell batteries sustain more than 6 months of sampling at 100 Hz. A custom firmware stores the raw sensor data in binary form with a GPS-disciplined UTC time base, and the surface elevation is reconstructed in postprocessing through orientation estimation, removal of the gravity component, adaptive band selection, and double integration. The validation is organized so that each stage isolates a single source of error. Under pure translation, where the orientation of the sensor is constant, the measured acceleration amplitude equals the target on average and three sensors agree with one another to within 1–2%. Under pure rotation about an axis through the sensor, where the true vertical displacement is zero, the reconstructed angle agrees with an exact reference to within 1.6%. The stationary noise of the sensor is propagated through the processing chain to give the smallest resolvable excursion as a function of period, and the response of the hull is computed by a radiation–diffraction analysis and confirmed by free-decay tests. The complete system is then tested in nine irregular sea states in a wave basin, with peak periods from 1 to 3 s and steepness from 0.011 to 0.033. The reconstructed motion reproduces the optically tracked motion of the buoy closely in every sea state. Compared with a fixed wave probe, the buoy records lower crests and deeper troughs, and the difference grows with steepness, which reflects the response of a freely floating body to the wave field rather than an error of the instrument. The total materials cost is below $200, and we conclude that 3D printing combined with low-cost MEMS sensors provides a viable route to affordable wave measurement, in particular for sheltered and nearshore waters where the wave periods are short.

• Barna, Danielle Marie; Engeland, Kolbjørn; Kneib, Thomas; Thorarinsdottir, Thordis Linda & Xu, Chong-Yu (2026). Regional flood frequency analysis at multiple durations: A comparison of duration consistency in quantile and parameter regression techniques. Hydrology Research. ISSN 1998-9563. 57(5). doi: 10.1016/j.hydrch.2026.100002. Full text in Research Archive Show summary

  This study compares two regional flood frequency analysis (RFFA) approaches—the parameter regression technique (PRT) and the quantile regression technique (QRT)—in the context of retention-based hydrologic applications, which require consistent design flood estimates across durations. Using a moving-window approach to estimate average streamflow over fixed durations, we assess whether predicting distribution parameters (PRT) or quantiles directly (QRT) affects the accuracy and duration consistency of flood estimates at ungauged locations. Both methods show similar predictive accuracy at return periods up to 50 years. However, the PRT more reliably preserves duration consistency: at 32 stations, the QRT produced inconsistent estimates at return periods beyond 2 years, while the PRT did not. These inconsistencies were not explained by record length or catchment characteristics. Additionally, at 64 of 239 stations, out-of-sample estimation of the median (index) flood was duration-inconsistent, suggesting difficulties in differentiating between the order of magnitude of floods across durations. Such inconsistencies were not observed in the spread and shape parameters estimated by the PRT. A quantile-based reparameterization of the generalized extreme value distribution was used to align both methods around the median flood, making it easier to compare how the methods behave across durations.

• Kern, Vanessa R.; Moura, Marcel; Olsen, Pål E. S. & Carlson, Andreas (2026). Patterning surface textured plates with a viscoplastic fluid. Physical Review Fluids. 11(9). doi: 10.1103/1jz3-5j4d. Full text in Research Archive Show summary

  The deposition of a viscoplastic fluid onto a substrate can be achieved by moving apart two plates initially separated by a fluid-filled gap, where the footprint shape depends on the initiation of a fingering instability. Here, we present an approach for controlled deposition of a viscoplastic fluid by designing the macroscopic structure of the solid substrate. Through experiments in a lifted Hele-Shaw cell, we explore how slot, square, pyramid, and triangular patterns affect the dynamics of liquid deposition. The substrate structures directly control the symmetry and final shape of the deposited viscoplastic footprint, while having little systematic influence on the maximal normal adhesive force or on the force-gap scaling exponents once the total entrapped volume is accounted for through an effective initial gap. We develop a scaling description for the normal force of a Herschel–Bulkley fluid, showing that the measured force decay reflects a superposition of capillary, yield stress, and viscous contributions. For experiments producing stable patterning, the measured effective exponents are consistent with the theoretical range predicted by this model. Finally, we interpret the pattern-selection mechanism through a dynamical permeability analysis where the substrate texture creates an anisotropic permeability field whose angular maxima correlate with the preferred inward propagation directions of the invading air. Our results highlight a direct link between substrate geometry, interfacial dynamics, and the final deposited morphology, showing how millimetric deposition patterns can be programed using submillimetric surface structures.

• Imkeller, Peter; Pamen, Olivier Menoukeu & Proske, Frank Norbert (2026). TAKAGI TYPE FUNCTIONS AND DYNAMICAL SYSTEMS: THE SMOOTHNESS OF THE SBR MEASURE AND THE EXISTENCE AND SMOOTHNESS OF LOCAL TIME. arXiv.org. ISSN 2331-8422. doi: https:/arxiv.org/pdf/2107.07185v4. Full text in Research Archive Show summary

  We investigate the occupation measures and local times of Takagi-type functions with roughness parameter γ, which are Hölder continuous with exponent H = log γ / log(1/2). Analytical insight is obtained by embedding these functions into a dynamical system related to the baker transform, whose global attractor is the graph of the Takagi function. The associated stable manifolds support Sinai-Bowen-Ruelle (SBR) measures, which we identify with the laws of certain symmetric Bernoulli convolutions. Dually, where duality is induced by time reversal, we derive a representation of the Takagi-type curves centred around the stable fibres in terms of Bernoulli convolutions, thereby relating SBR measures to occupation measures. While Bernoulli convolutions belong to the first Rademacher chaos, we show that the occupation measure is naturally represented as a functional in the second Rademacher chaos within the framework of non-Gaussian Malliavin calculus. Using a Fourier-analytic criterion together with variants of Weyl’s equidistribution theorem, we prove that Takagi-type curves admit square-integrable local times for γ = 2^(-1/m), m ≥ 7, and that the same conclusion holds for drifted Takagi curves for almost every γ ∈ (1/2, 1).

• Mirafzali, Ehsan; Proske, Frank Norbert & Marinescu, Razvan (2026). Logarithmic derivatives of variational and singular stochastic partial differential equations. arXiv.org. ISSN 2331-8422. arXiv:2608.21805 (math). doi: https:/arxiv.org/pdf/2608.21805. Full text in Research Archive Show summary

  For a stochastic partial differential equation posed on a Gelfand triple and satisfying the fully local monotone conditions of Röckner, Shang and Zhang, we compute the logarithmic derivative of the law of the solution at a fixed time along a prescribed direction of the state space. The formula is intrinsic, being expressed through the Hilbert-Schmidt Malliavin derivative Φr=DrX(t) and the covariance γt=∫t0ΦrΦ∗rdr alone, so that neither the inversion of the first variation used in finite dimensions nor uniform Malliavin-Sobolev bounds on the Tikhonov family are called upon. It is obtained from an integration-by-parts identity on an abstract Hilbert space, a Moore-Penrose construction of a covering field on Wiener space, and a trace formula for the Tikhonov limit, specialised to the equation through the representation Φr=Y(t,r)B(r,X(r)) of the Malliavin derivative by the first variation; the stochastic p-Laplacian and the two-dimensional Navier-Stokes equation are treated in detail. Beyond the variational class, a scalar reduction gives an integration-by-parts identity for the law of a pairing ⟨u(t),φ⟩ which passes to the renormalised limit for the singular equations of Bruned, Chandra, Chevyrev and Hairer, and which is represented by a logarithmic derivative under second-order Malliavin smoothness and negative-moment hypotheses.

• Agram, Nacira; Øksendal, Bernt Karsten; Proske, Frank Norbert & Tymochenko, Olena (2026). Optimal Stopping for Systems Driven by the Brownian Sheet. arXiv.org. ISSN 2331-8422. arXiv:2603.12853 (math). doi: https:/arxiv.org/abs/2603.12853. Full text in Research Archive Show summary

  We investigate optimal stopping problems for systems driven by the Brownian sheet. Our analysis is divided into two parts. In the first part, we derive explicit solutions to two optimal stopping problems for the exponentially discounted Brownian sheet. The first problem consists in determining the optimal two parameter first hitting point τ = (τ1,τ2) that maximizes E e−ρτ1τ2 h B(τ1,τ2), where ρ > 0 is a discount factor and h is a reward function. Restricting attention to first hitting points of levels, we obtain a closed form characterization of the optimal stopping threshold. In particular, for linear rewards h(y) = y, the optimal level is y= (2ρ)−1/2 . The second problem concerns optimal stopping of the integrated discounted Brownian sheet: E τ1 0 τ2 0 e−ρtxB(t,x) dtdx . We show that the optimal first hitting level is strictly positive, and provide an explicit representation of the value function in terms of the exponential integral function. The optimal threshold is characterized as the unique solution of a nonlinear equation derived from a Laplace transform identity for the product τ1τ2.The result is surprising, in view of the (well-known) fact that the solution of the corresponding one-parameter problem is to stop at the first time t when B(t) hits the negative level y=−(2ρ)−1/2 . In the second and main part of the paper, we develop a general potential theoretic framework for two parameter optimal stopping problems associated with stochastic partial differential equations (SPDEs) driven by the Brownian sheet. For a class of Itˆo sheets and time space homogeneous SPDEs, we prove that the value function is the least superharmonic majorant of the reward and that the optimal stopping point is given by the first exit point from the continuation region. This yields a general existence theorem for optimal stopping points in the plane, extending classical one parameter theory to the two parameter Brownian sheet setting.

• Mirafzali, Ehsan; Proske, Frank Norbert; Venturi, Daniele & Marinescu, Razvan (2026). SCORE-BASED DIFFUSION MODELS IN INFINITE DIMENSIONS: A MALLIAVIN CALCULUS PERSPECTIVE. Journal of Machine Learning for Modeling and Computing. ISSN 2689-3967. 7(2). doi: https:/www.dl.begellhouse.com/download/article/7de76a605645f298/JMLMC0702(2)-63274.pdf. Full text in Research Archive Show summary

  We study score-based diffusion modelling in infinite-dimensional separable Hilbert spaces through Malliavin calculus, extending the analysis of generative models beyond the finite-dimensional set- ting. The forward diffusion process is formulated as a linear stochastic partial differential equa- tion (SPDE) driven by space–time coloured noise with a trace-class covariance operator, ensuring well-posedness in arbitrary spatial dimensions. Building on Malliavin calculus and an infinite- dimensional extension of the Bismut–Elworthy–Li formula, we derive a closed-form expression for the logarithmic derivative of the transition measure along Cameron–Martin directions, which serves as the natural infinite-dimensional analogue of the score function. Our operator-theoretic approach preserves the intrinsic geometry of Hilbert spaces and accommodates general trace-class operators, thereby incorporating spatially correlated noise without assuming semigroup invertibility. We vali- date the derived score formula numerically for several classes of linear SPDEs in both one and two spatial dimensions using spectral methods.

• Compagnoni, Enea Monzio; Islamov, Rustem; Proske, Frank Norbert; Lucchi, Aurelien; Orvieto, Antonio & Gorbunov, Eduard (2026). On the Interaction of Batch Noise, Adaptivity, and Compression, under (L0, L1)-Smoothness: An SDE Approach. Proceedings of Machine Learning Research (PMLR). ICML 2026. doi: https:/openreview.net/attachment?id=Pmsc4yytlf&name=pdf. Full text in Research Archive Show summary

  Distributed stochastic optimization intertwines (i) stochastic gradient noise, (ii) communication compression, and (iii) adaptive/normalized updates. While each factor has been studied in isolation, their joint effect under realistic assumptions remains poorly understood. In this work, we develop a unified theoretical framework for Distributed Compressed SGD (DCSGD) and its sign variant Distributed SignSGD (DSignSGD) under the recently introduced (L0,L1)- smoothness condition. From a conceptual perspective, we show that the first- and second-order modified equations from the literature do not accurately model the discrete-time stepsize/stability restrictions, especially under (L0,L1)-smoothness. From a technical perspective, we propose new first-order SDEs by carefully incorporating curvature-dependent terms into their drift: This helps capture the fine-grained relationship between learning rate restrictions, gradient noise, compression, and the geometry of the loss landscape. Importantly, we do so under general gradient noise assumptions, including heavy-tailed and affine-variance regimes, which extend beyond the classical bounded-variance setting. Our results suggest that normalizing the updates of DCSGD emerges as a natural condition for stability, with the degree of normalization precisely determined by the gradient noise structure, the landscape’s regularity, and the compression rate. In contrast, DSignSGD converges even under heavy-tailed noise with standard learning rate schedules. Together, these findings offer both new theoretical insights and perspectives, and practical guidance.

• Morale, Daniela; Tarquini, Leonardo & Ugolini, Stefania (2026). A Feynman--Kac representation of a non-conservative and path-dependent nonlinear reaction-diffusion-advection system. arXiv. doi: 10.48550/ARXIV.2407.19301. Full text in Research Archive Show summary

  We provide a probabilistic interpretation of a weakly parabolic PDE--ODE system with a reaction term, which makes the dynamics non-conservative. As a consequence, the solution is represented as the density of a sub-probability measure solving a Feynman--Kac-type equation, where the time-marginal law of the underlying process is weighted by a survival probability induced by the reaction. This leads to a coupled stochastic formulation consisting of a non-Markovian stochastic differential equation with path-dependent coefficients and the associated Feynman--Kac-type equation. We prove well-posedness of the resulting stochastic system. Finally, we introduce the corresponding interacting particle system and show that its empirical measure, suitably weighted by the survival probability associated with the reaction rate, converges to the limiting sub-probability.

• Morale, Daniela; Tarquini, Leonardo & Ugolini, Stefania (2026). Path-dependent McKean PDEs with reaction: a discussion on probabilistic interpretations and particle approximations. arXiv. doi: 10.48550/ARXIV.2602.07255. Full text in Research Archive Show summary

  We discuss and compare two probabilistic approaches for associating a stochastic differential equation with a McKean-type partial differential equation featuring a reaction term and path-dependent coefficients. The non-conservative nature of the macroscopic dynamics leads to two possible interpretations of the sub-probability measure and of the associated SDE equation at the microscale: on the one hand, as a measure-valued solution of a Feynman-Kac-type equation; on the other hand, as the sub-probability associated with an SDE defined up to a survival time with a reaction-dependent rate. These different interpretations give rise to two different microscopic stochastic models and therefore to two different techniques of probabilistic analysis. Finally, by considering the interacting particle systems associated with both models, we discuss how their empirical densities provide two different kernel estimators for the PDE solution.

• Benth, Fred Espen; Ortiz-Latorre, Salvador & Tarquini, Leonardo (2026). Signature McKean-Vlasov stochastic differential equations. arXiv. doi: 10.48550/ARXIV.2606.22964. Full text in Research Archive Show summary

  McKean-Vlasov-type stochastic differential equations (SDEs) are characterized by coefficients depending on both the state and the law of the solution. In this work, we focus on a class of such equations where the coefficients depend on a linear combination of the expected signature of the geometric p-rough path lift of its solution, with $p\in(2,3)$. After establishing the strong existence and uniqueness of a solution, we prove how such an equation can approximate a general class of path-dependent McKean-Vlasov SDEs. Finally, we consider the associated particle system and propagation of chaos is established.

• Biswas, Uddalak; Galland, Olivier & Carlson, Andreas (2026). Laponite® RD and hydroxyethyl cellulose as host rock and magma analogue to simulate a wide range of rheological combinations in the volcanic plumbing system. Tectonophysics. ISSN 0040-1951. 937. doi: 10.1016/j.tecto.2026.231351. Full text in Research Archive Show summary

  Analogue modelling is essential for understanding magma emplacement in the Earth’s crust and requires strict geometric, kinematic and dynamic scaling. Therefore, material selection must satisfy the scaling laws to reproduce the natural rheological variability. Although often represented by end-member rheologies, crustal rocks in nature exhibit complex rheological behaviour. In this study, we analysed two complex materials, Laponite® RD (LRD) and hydroxyethyl cellulose (HEC), to assess their effectiveness as geological analogues for country rock and magma in dyke emplacement experiments. We provide a detailed characterisation of LRD, highlighting its tuneable rheological properties via curing time (t_c). To characterise the complex rheology of the LRD gels, rotational and oscillatory tests, including flow, amplitude, frequency sweep, and creep and recovery tests, were performed at curing times (t_c) ranging from 30 to 240 min. We tested the rheology of aqueous HEC solutions at concentrations of 0.50, 0.75, and 1.00 wt%. Additionally, this study highlights the significant role of surface tension in laboratory analogue experiments, demonstrating the need to minimise interfacial tension by selecting an appropriate magma analogue fluid when using a viscoelastic host. The rheological test results showed that the storage modulus (G^') and yield stress (τ_y) increased systematically with increasing t_c. The flow and surface tension test results indicate that HEC hydrous solutions serve as robust magma analogues, offering variable viscosities with minimal alterations in surface tension and density. Combining the rheological analysis results of LRD and HEC, we propose a new methodology for simulating a wide range of rheological conditions by systematically varying the LRD curing time and employing different concentrations of HEC as a magma analogue. Our approach emphasises precise rheological characterisation together with control of magma-analogue density and surface tension, minimising the interfacial tension and buoyancy contrast with the host for accurate scaling in analogue models of volcanic plumbing systems.

• Lozano, Pere Diaz & Nunno, Giulia Di (2026). Hölder regularity for backward stochastic Volterra integral equations and applications to numerical schemes. arXiv.org. ISSN 2331-8422. doi: 10.48550/ARXIV.2607.04012. Full text in Research Archive Show summary

  We prove a Hölder-type regularity estimate for the martingale integrand of a backward stochastic Volterra integral equation (BSVIE). The estimate is formulated in Lp(Ω) after averaging in L2 over the first time variable, and gives an averaged Hölder estimate of order 1/2 in the second time variable. Our approach is based on the approximation of the BSVIE by a system of BSDEs. For this system, we establish a uniform regularity estimate for the martingale component using Malliavin calculus, and then pass to the limit to obtain the result for the BSVIE. We allow for a general Malliavin differentiable free term and generator. In particular, neither is assumed to come from a forward stochastic differential equation or to have a specific functional form. We also propose an explicit Euler scheme for the approximating BSDE system and show that the regularity estimate yields a convergence rate for the resulting discrete approximation of the BSVIE.

• Lozano, Pere Diaz & Kloster, Thomas K. (2026). A Wiener Chaos Approach to Martingale Modelling and Implied Volatility Calibration. arXiv.org. ISSN 2331-8422. doi: 10.48550/ARXIV.2602.16232. Full text in Research Archive Show summary

  Calibration to a surface of option prices requires specifying a suitably flexible martingale model for the discounted asset price under a risk-neutral measure. Assuming Brownian noise and mean-square integrability, we construct an over-parameterized model based on the martingale representation theorem. In particular, we approximate the terminal value of the martingale via a truncated Wiener--chaos expansion and recover the intermediate dynamics by computing the corresponding conditional expectations. Using the Hermite-polynomial formulation of the Wiener chaos, we obtain easily implementable expressions that enable fast calibration to a target implied-volatility surface. We illustrate the flexibility and expressive power of the resulting model through numerical experiments on both simulated and real market data.

• Diaz-Lozano, Pere & Nunno, Giulia Di (2026). Deep operator BSDE: A numerical scheme to approximate solution operators. The Annals of Applied Probability. ISSN 1050-5164. 36(3), p. 2594–2625. doi: 10.1214/25-aap2289. Full text in Research Archive Show summary

  Motivated by dynamic risk measures and conditional g-expectations, in this work we propose a numerical method to approximate the solution operator given by a backward stochastic differential equation (BSDE). The main ingredients for this are the Wiener chaos decomposition and the classical Euler scheme for BSDEs. We show convergence of this scheme under very mild assumptions, and provide a rate of convergence in more restrictive cases. We then implement it using neural networks, and we present several numerical examples where we can check the accuracy of the method.

• Pérez, Johan Manuel de Aguas & Jullum, Martin (2026). Scope-Restricted Backtracking Counterfactuals. Proceedings of Machine Learning Research (PMLR). 343. doi: https:/openreview.net/forum?id=BEb4fBP6LI. Full text in Research Archive
• Pérez, Johan Manuel de Aguas (2026). Collaborative Representations for Targeted Causal Inference Under Outcome Selection. In Ceci, Michelangelo; Kocev, Dragi; Monreale, Anna; Vens, Celine; Flach, Peter; Manco, Giuseppe; Spiliopoulou, Myra & Masciari, Elio (Ed.), Machine Learning and Knowledge Discovery in Databases. Research Track. Springer Nature Switzerland. ISSN 9783032376541. p. 623–640. doi: 10.1007/978-3-032-37654-1_36. Full text in Research Archive
• Cibinel, Luca; Meggio, Claudio & Zuccato, Lorenzo (2026). Enhancing Quantum Graph Representations via Heuristics and Model-Based Clustering. In Bin, Riccardo De; Salucci, Clara Bertinelli & Hubin, Aliaksandr (Ed.), Proceedings of the 40th International Workshop on Statistical Modelling 28.06 – 03.07.2026, Oslo, Norway. International Workshop on Statistical Modelling. ISSN 9788255325000. Full text in Research Archive Show summary

  We propose a novel class of representations for graph-structured data, with the objective of improving feature prediction performance. We focus on graphs with clearly identifiable and interpretable subgraphs, such as transition metal complexes. Our approach is based on the identification of subgraph popu- lations whose citizens exhibit a similar statistical behaviour. Knowledge of these populations is injected in the original graphs in the form of virtual nodes to make global information available at the local level.

• Tandon, Kushagri; Thorarinsdottir, Thordis Linda & Storvik, Geir Olve (2026). Distributional properties of non-Gaussian spatial fields. In Bin, Riccardo De; Salucci, Clara Bertinelli & Hubin, Aliaksandr (Ed.), Proceedings of the 40th International Workshop on Statistical Modelling 28.06 – 03.07.2026, Oslo, Norway. International Workshop on Statistical Modelling. ISSN 9788255325000. p. 526–529. Full text in Research Archive
• Vittersø, Sigurd Myhre & Hubin, Aliaksandr (2026). BGET: Bayesian Genetic Ensemble of Trees. In Bin, Riccardo De; Salucci, Clara Bertinelli & Hubin, Aliaksandr (Ed.), Proceedings of the 40th International Workshop on Statistical Modelling 28.06 – 03.07.2026, Oslo, Norway. International Workshop on Statistical Modelling. ISSN 9788255325000. p. 592–595. doi: https:/www.mn.uio.no/math/english/research/groups/statistics-data-science/events/conferences/iwsm2026/proceedings/proceedings_iwsm2026_proofonline.pdf. Full text in Research Archive Show summary

  We embed classification and regression trees in the Bayesian generalized nonlinear model framework, defining a Bayesian genetic ensemble of trees with complexity-penalizing priors on tree structures. Inference is performed via genetically modified mode jumping MCMC, which explores large spaces of tree ensembles using posterior inclusion probabilities to guide genetic operators. The approach is evaluated on the Abalone and Boston housing data and performs on par with relevant related baselines.

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• Nunno, Giulia Di; Mishura, Yuliya & Yurchenko-Tytarenko, Anton (2026). Volterra Volatility Models: Option Pricing and Hedging. Springer Nature. ISBN 9783032265753. doi: 10.1007/978-3-032-26576-0. Full text in Research Archive Show summary

  This monograph introduces flexible Hölder‑noise models capturing rough and long‑range dependent volatility, with practical pricing and hedging methods.

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• Fuchs, Franz Georg (2026). QSTAR Center for Quantum Computing and Applications in Norway. doi: https:/enccs.se/event/quantum-computing-school-2026-in-sweden/. Full text in Research Archive
• Lindstrøm, Tom Louis (2026). Matematikkfagets utvikling i norsk skole. Full text in Research Archive
• Lindstrøm, Tom Louis (2026). Talllinjen – eller tallinjer? Full text in Research Archive
• Fuchs, Franz Georg (2026). QSTAR - developing reliable and useful quantum computers. doi: https:/www.uio.no/english/research/interfaculty-research-areas/growth-house/news-and-events/events/2026/science-impact/. Full text in Research Archive
• Eskeland, Gunnar; Glad, Ingrid Kristine & Frigessi, Arnoldo (2026). Europa må regulere KI | DN. Full text in Research Archive Show summary

  Høvdingene innen kunstig intelligens (KI) babler om trusler mot menneskeheten og ber om regulering, og da kreves skepsis i responsen (jf. Mogstad og Hardings kronikk i DN 2. oktober: «Hvorfor innovere når man kan regulere?»).Det de ber om, skal de ikke få.Ikke i Europa.

• Larsen, Nadia S. (2026). Kvanteberegning - et blikk i et nytt univers. Full text in Research Archive
• Austad, Are (2026). Fourier multipliers and quantum metric geometry. Full text in Research Archive
• Kern, Vanessa Ruth; Moura, Marcel; Olsen, Pål Eivind & Carlson, Andreas (2026). Complex Fluids in confinement: instabilities in textured lifting Hele-Shaw cells. Full text in Research Archive
• Moura, Marcel; Lanza, Federico; Kern, Vanessa Ruth; Olsen, Pål Eivind; Carlson, Andreas & Måløy, Knut Jørgen [Show all 7 contributors for this article] (2026). Instabilities in textured lifted Hele-Shaw cells and bubbly flows in a pipe. Full text in Research Archive
• Kern, Vanessa Ruth; Moura, Marcel; Olsen, Pål Eivind & Carlson, Andreas (2026). Instabilities and Pattern Formation in Textured Lifting Hele-Shaw Cells with Viscoplastic Fluids. Full text in Research Archive
• Jaklitsch, David Alexander (2026). Levin-Wen model and tensor product of Tube algebra representations. Full text in Research Archive
• Jaklitsch, David Alexander (2026). The braided monoidal structure of Tube algebra representations. Full text in Research Archive
• Melteig, Elina; Glad, Ingrid Kristine; Ramezani-Kebrya, Ali; Pérez, Johan Manuel de Aguas; Holmsen, Sigurd & Palomares, Alfonso Diz-Lois [Show all 7 contributors for this article] (2026). Blir KI vår dommedag? Ekspertene strides. [Journal]. Titan. Full text in Research Archive
• Ortiz-Latorre, Salvador (2026). Heston-Hawkes stochastic volatility model: Change of measure and Thiele's PIDE. Full text in Research Archive
• Ortiz-Latorre, Salvador (2026). Convergence in law for quasi-linear SPDEs. Full text in Research Archive
• Nunno, Giulia Di (2026). Uncertainties in risk evaluation for long term horizons and computational aspects. doi: https:/www.bacheliercongress.com/2026/eventi.unibo.it/bachelier.html. Full text in Research Archive Show summary

  Long and short-horizons must be treated differently in monetary risk-evaluations. Horizon-risk and h-longevity are identified to capture this. We clarify that classical dynamic risk measures are subject to horizon-risk exposure, and propose to work with fully-dynamic risk-measures. In long horizons, also interest rate uncertainty cannot be underestimated. We combine these aspect working with cash non-additive dynamic risk-measures via BSDEs and generalised shortfalls. We take steps in the numerical quantification relying on a novel use of Wiener-Ito chaos expansions and proposing DeepO BSDEs schemes.

• Nunno, Giulia Di (2026). Optimal control of Volterra dynamics: from finite to infinite dimensions in UMD Banach spaces and return. doi: https:/sites.google.com/view/trr388/events/past-events/workshop-optimal-control-2026?authuser=1. Full text in Research Archive Show summary

  We consider a stochastic optimal control problem for Volterra type forward dynamics, which are typically non-Markovian in nature. A direct application of dynamic pro- gramming is not feasible. So we propose to lift the problem to infinite dimensions, where we can recover Markovianity. For this we work with Banach-valued processes. In this framework we tackle the optimal control problem by studying the corresponding Hamilton-Jacobi-Bellman equation, which can be formulated thanks to the appropriate lift. Our techniques make use of Malliavin calculus in UMD Banach spaces. Finally, we reconnect the solution of the infinite dimensional problem to the original finite dimen- sional one.

• Nunno, Giulia Di (2026). BSDEs and fully-dynamic risk measures. doi: https:/fdnss.fi/44th-finnish-summer-school-on-probability-and-statistics-50-years-jubilee/. Full text in Research Archive
• Nunno, Giulia Di (2026). Malliavin calculus in Sandwich Volterra Volatility models. Full text in Research Archive Show summary

  Sandwich Volterra Volatility models are capturing both the long-memory and rough features of volatility, while also complying with stylised facts observed in volatility markets. Within the analysis of this family, we see how Malliavin calculus has been instrumental to characterise the behaviour of these processes. As supplement, we also discuss generalised product and chain rule.

• Nunno, Giulia Di (2026). BSDEs and Operator Deep BSDEs for dynamic risk evaluation. doi: https:/www.ucc.ie/en/stochastica/events/stochasticadirectionsworkshopapril2026/. Full text in Research Archive Show summary

  Backward SDEs (BSDEs) have been used for dynamic risk measurement, we revise the framework and value of a dynamic risk evaluation. We also indicate some shortcomings, particularly related to the evaluation of risk at different time horizon, introduced as horizon-risk. For this reason we introduce the concept of fully-dynamic risk measurement and show how it is still easily related to BSDEs. As illustration we consider variation to the entropic case as well as we introduce the hq-entropic risk measure inspired by Tsallis general entropy. We discuss computational methods from an operator point of view, proposing an Operator Deep BSDE approach.

• Nunno, Giulia Di (2026). Capturing horizon risk and interest rate uncertainty. doi: https:/sites.google.com/view/mf-osaka/home?authuser=1. Full text in Research Archive Show summary

  Horizon risk is introduced as the evaluation of the exposure to potentially erroneous risk measurement when using a risk measure that is not adequate to the actual time horizon of the position. We clarify that classical dynamic risk measures are subject to horizon risk, so we propose to work with fully-dynamic risk measures, which are then designed to capture horizon risk and evaluate it in terms of an index of h-longevity. For this we use backward stochastic differential equations. In a financial context, we combine horizon risk with interest rates uncertainty, thus we also propose a cash non-additive version of fully- dynamic risk measures. We construct such risk measures via backward stochastic differential equations or via a generalisation of shortfall-type representation. As illustration, we introduce the class of hq-entropic risk measures.

• Gancia, Gino; Mittal, Shivika; Nunno, Giulia Di; Castellacci, Fulvio & Beferull-Lozano, Baltasar (2026). SURE-AI@STAR Workshop on the Environmental Cost of AI. doi: https:/www.mn.uio.no/math/english/research/groups/risk-stochastics/events/seminars/SURE-AI@STARWorkshop-CostAI.html. Full text in Research Archive
• Tarquini, Leonardo (2026). Signature McKean-Vlasov stochastic differential equations. doi: https:/sites.google.com/unipv.it/apmp2026/home-page. Full text in Research Archive Show summary

  McKean--Vlasov-type stochastic differential equations (SDEs) are characterised by coefficients depending on both the state and the law of the solution. In our work, we focus on a class of such equations where the coefficients depend on a linear combination of the expected signature of the geometric p-rough path lift of its solution, with p ∈ (2,3). After establishing the strong existence and uniqueness of a solution, we prove how such an equation can approximate a general class of path-dependent McKean–Vlasov SDEs. Finally, we consider the associated particle system and establish propagation of chaos. This is a joint work with F.E. Benth (BI Norwegian Business School and University of Oslo) and S. Ortiz-Latorre (University of Oslo).

• Lozano, Pere Diaz (2026). Deep operator BSDE: A numerical scheme to approximate solution operators. Full text in Research Archive Show summary

  Motivated by dynamic risk measures and conditional g-expectations, in this work we propose a numerical method to approximate the solution operator given by a backward stochastic differential equation (BSDE). The main ingredients for this are the Wiener chaos decomposition and the classical Euler scheme for BSDEs. We show convergence of this scheme under very mild assumptions, and provide a rate of convergence in more restrictive cases. We then implement it using neural networks, and we present several numerical examples where we can check the accuracy of the method.

• Biswas, Uddalak; Galland, Olivier & Carlson, Andreas (2026). Formation of various geometry by viscous magma intruding into visco-elasto-plastic deep crust: a 2D analogue experiment. Full text in Research Archive Show summary

  Magma ascends to the Earth's surface for eruption by traversing the crust, which is the uppermost layer above the mantle, where the magma originates. As this substantial volume of magma moves through the crust, it deforms the crustal rocks, facilitating its progression toward the surface and subsurface. The resulting geometry, which may manifest as thin sheets, branching fingers, or blunt lobes, is set by the competition between the intruding fluid and the mechanical response of the host material. These deformation mechanisms, which control the geometry of the magmatic bodies, are essential for assessing hazards related to volcanic eruptions, seismic activity due to volcanism, and the localisation of economically valuable ore deposits. As the deformation of the crustal rocks by the intruding magma occurs at a certain depth and natural exposures record only the end state of this strongly dynamic process, the mechanics behind this process can’t be inferred directly. To address this gap, researchers have employed analogue modelling as a tool to simulate a simplified analogous intrusion process of magma at a laboratory scale for decades. Conventionally, in these analogue experiments, crustal rocks have been modelled using elastic or plastic Coulomb materials, whereas magma has been represented as a viscous fluid by previous researchers. However, recent studies have shown that deep crustal rocks exhibit a complex visco-elastic to visco-elasto-plastic rheology in nature. To simulate the crustal rocks more accurately, in this study, we approached the problem by injecting a viscous fluid as a magma analogue into an aqueous Laponite® RD (LRD) gel, which acted as a model host rock, confined in a two-dimensional Hele-Shaw cell. The LRD gel exhibits diverse rheological properties, transitioning progressively from a viscous liquid to a viscoelastic state, and ultimately to an elastico-viscous solid, as its curing time (tc) increases. Considering this property of the LRD gel, we used tc = 30, 60, 90, 150, and 240 min to represent crustal rock under different physical and chemical conditions. On the other hand, magma in nature exhibits variable viscosity depending on its composition, temperature and volatile content. In parallel, we varied the injected fluid using water and hydroxyethyl cellulose solutions at 0.50 and 0.75wt%, to span the range of viscosity. Injection was carried out at a fixed volumetric flow rate of 10 ml/min up to a maximum injected volume of 50 ml, so that the flow rate is held constant while the rheology of the host and viscosity of the fluid are varied. Additionally, polyamide tracer particles with a diameter of 60 μm were embedded in the gel, enabling particle image velocimetry (PIV) to simultaneously resolve the deformation field of the host as the intrusion expanded. The experiments produced distinct intrusion geometries that systematically depended on host rheology and the viscosity of the injected fluid. The velocimetry fields from the PIV analysis further show that intrusions of broadly similar shapes can be accommodated by clearly different velocity and strain distributions within the host. Combining the evolving geometry with the accompanying strain pattern therefore offers a route toward identifying which deformation mechanism accommodated a given volume of magma, and this diagnostic can in principle be applied to interpret the intrusion patterns observed in the field.

• Biswas, Uddalak; Galland, Olivier & Carlson, Andreas (2026). Magma emplacement mechanism in visco-elasto-plastic crustal rock: an insight from quantitative 2D analogue experiments. doi: 10.5194/egusphere-egu26-18980. Full text in Research Archive Show summary

  Magma generated at depth ascends through the crust and erupts at the surface. In this process, the magma volume creates space by deforming the crustal rock. To study this process, researchers have employed analogue experiments for decades. Conventionally, most analogue models assume the crustal rock as a purely elastic, brittle (Coulomb), or viscous material. However, natural rocks exhibit more complex visco-elasto-plastic behaviours, with rheological properties transitioning from elastic-plastic to visco-elasto-plastic with increasing depth. Conversely, magma itself behaves as a Newtonian fluid, exhibiting a range of viscosities influenced by factors such as silica and volatile content. In this study, we conducted scaled 2D analogue magma emplacement experiments using Laponite® RD (LRD), a complex visco-elasto-plastic rheological material, as a host rock analogue. The rheological properties of LRD were systematically varied by changing the curing time (tc) from tc = 30 min to tc = 240 min to simulate a broad range of crustal rheological behaviours, corresponding to different depths from viscous to visco-elasto-plastic regimes. Food-coloured water and hydroxyethyl cellulose (HEC) aqueous solutions, with concentrations of 0.50 wt% and 0.75 wt%, are used to simulate magma with varying viscosities. Polyamide seeding particles (PSPs) of 60µm diameter were incorporated inside the LRD solution to quantify host-rock deformation during magma emplacement via particle image velocimetry (PIV). Our experimental results show that magma intrusions exhibit various shapes, ranging from straight-edged fractures in the case of low-viscosity water and viscoelastic LRD of high tc to bulbous, rounded forms in high-viscosity HEC and viscous LRD of low tc. Furthermore, PIV data enabled the identification of domains exhibiting distinct deformation types, thereby delineating changes in deformation regimes attributable to variations in the rheological properties of the host rock. Finally, by integrating geometric and PIV analyses, we established a relationship between the intrusion morphology and host rock rheology, and propose a mechanical model that elucidates the deformation mechanisms operative within the host during magma emplacement across different rheological combinations of host and magma materials.

• Lozano, Pere Diaz (2026). A Wiener Chaos Approach to Martingale Modelling and Implied Volatility Calibration. Full text in Research Archive Show summary

  Calibration to a surface of option prices requires specifying a suitably flexible martingale model for the discounted asset price under a risk-neutral measure. Assuming Brownian noise and mean-square integrability, we construct an over-parameterized model based on the martingale representation theorem. In particular, we approximate the terminal value of the martingale via a truncated Wiener--chaos expansion and recover the intermediate dynamics by computing the corresponding conditional expectations. Using the Hermite-polynomial formulation of the Wiener chaos, we obtain easily implementable expressions that enable fast calibration to a target implied-volatility surface. We illustrate the flexibility and expressive power of the resulting model through numerical experiments on both simulated and real market data.

• Lozano, Pere Diaz (2026). A Wiener Chaos Approach to Martingale Modelling and Implied Volatility Calibration. Full text in Research Archive Show summary

  Calibration to a surface of option prices requires specifying a suitably flexible martingale model for the discounted asset price under a risk-neutral measure. Assuming Brownian noise and mean-square integrability, we construct an over-parameterized model based on the martingale representation theorem. In particular, we approximate the terminal value of the martingale via a truncated Wiener--chaos expansion and recover the intermediate dynamics by computing the corresponding conditional expectations. Using the Hermite-polynomial formulation of the Wiener chaos, we obtain easily implementable expressions that enable fast calibration to a target implied-volatility surface. We illustrate the flexibility and expressive power of the resulting model through numerical experiments on both simulated and real market data.

• Lozano, Pere Diaz (2026). An Euler scheme for BSDEs via the Wiener chaos decomposition. Full text in Research Archive Show summary

  The Euler scheme is a standard time discretization for BSDEs, but its implementation hinges on approximating conditional expectations and the associated martingale terms at each time step. We propose an implementation based on the Wiener chaos decomposition to approximate these quantities. In contrast to many numerical schemes that rely on a finite-dimensional Markovian representation, our approach accommodates arbitrary FT-measurable square-integrable terminal conditions. We provide a comprehensive convergence analysis under additional Malliavin regularity assumptions and illustrate the method on several numerical examples, including genuinely non-Markovian problems arising, for instance, in the pricing and hedging of contingent claims under rough-volatility models.

• Nunno, Giulia Di (2026). On Sandwiched Volterra Volatility Models. Full text in Research Archive Show summary

  Sandwiched Volterra Volatility (SVV) models are a class of dynamics capable of capturing both the long-memory and rough features of volatility, while also complying with several stylized facts observed in volatility markets. At the same time, price dynamics with SVV volatility remain sufficiently tractable to allow for a rigorous and explicit analysis of pricing and hedging of financial assets. We present an overview of these models, highlighting their main features and potential applications. While pricing aspects are briefly discussed, the main focus of the talk is on the quadratic hedging of financial derivatives within this framework, providing insights into the computational challenges associated with the optimal hedging strategy.

• Nunno, Giulia Di (2026). Quadratic hedging in Sandwiched Volterra Volatility Models. Full text in Research Archive Show summary

  Sandwiched Volterra Volatility (SVV) models are a class of dynamics capable of capturing both the long-memory and rough features of volatility, while also complying with several stylized facts observed in volatility markets. At the same time, price dynamics with SVV volatility remain sufficiently tractable to allow for a rigorous and explicit analysis of pricing and hedging of financial assets. We present an overview of these models, highlighting their main features and potential applications. While pricing aspects are briefly discussed, the main focus of the talk is on the quadratic hedging of financial derivatives within this framework, providing insights into the computational challenges associated with the optimal hedging strategy. The explicit optimal hedging solution is characterized via the non-anticipating derivative, and its numerical implementation is addressed through Markovian approximations.

• Laubo, Sami; Eide, Per Kristian & Rognes, Marie Elisabeth (2026). Predicting individual contrast enrichment and clearance by learning glymphatic magnetic resonance imaging. Full text in Research Archive
• Laubo, Sami; Eide, Per Kristian & Rognes, Marie Elisabeth (2026). Predicting molecular transport in brain fluids using longitudinal MRI. Full text in Research Archive Show summary

  Cerebrospinal fluid (CSF) plays a critical role in the clearance of metabolic waste products from the brain and serves as a delivery route for some neuropharmaceuticals. However, the high inter-patient variability in CSF dynamics observed in various nervous system diseases indicates a need for personalized approaches to understand and predict transport in CSF. A method to observe CSF transport in the brain is via injection of a CSF contrast agent followed by longitudinal magnetic resonance imaging (MRI) sequences. This provides sequential snapshots of the tracer distribution in the brain at different time points. We propose a supervised convolutional neural network (CNN) model to predict the pixel-wise signal increase at peak parenchymal enrichment, 24 hours post-injection, utilizing the longitudinal MRI scans. To incorporate the temporal information inherent in longitudinal scans, we combine a U-Net architecture with a convolutional long short-term memory (ConvLSTM) module modified to integrate the varying time intervals between MRI scans. While models with single-input pre-injection or post-injection MRI scan showed potential, they are often not fully able to capture the temporal evolution of tracer transport. The time-aware ConvLSTM U-Net demonstrates a significant increase in predictive quality compared with the single-input models. The longitudinal model also exhibit improved robustness on patients with varying CSF dynamics which is crucial for trustworthy applications in medicine. Lastly, we discuss the need to incorporate direct physical components to improve patient predictions.

• Laubo, Sami; Eide, Per Kristian & Rognes, Marie Elisabeth (2026). Predicting individual brain contrast enrichment and clearance by learning glymphatic MR. Full text in Research Archive Show summary

  Cerebrospinal fluid (CSF) plays a critical role in the clearance of metabolic waste products from the brain and serves as a delivery route for some neuropharmaceuticals. However, the high inter-patient variability in CSF dynamics observed in various nervous system diseases indicates a need for personalized approaches to understand and predict transport in CSF. A method to observe CSF transport is via intrathecal lumbar injection of the CSF contrast agent gadobutrol followed by longitudinal T1-weighted magnetic resonance imaging (MRI) sequences. This provides sequential snapshots of the tracer distribution in the brain at different time points. We propose a supervised convolutional neural network (CNN) model to predict the pixel-wise signal increase at peak parenchymal enrichment — 24 hours post-injection — utilizing the longitudinal MRI scans. To incorporate the temporal information inherent in longitudinal scans, we combine a U-Net architecture with a convolutional long short-term memory (ConvLSTM) module modified to integrate the varying time intervals between MRI scans. This module recurrently updates feature states extracted from each MRI scan into a combined representation. While baseline models using a single pre-injection or post-injection MRI scan showed potential, they are often not fully able to capture the temporal evolution of tracer transport. The time-aware ConvLSTM U-Net demonstrates a significant increase in predictive quality compared with the baseline models. The model also exhibit improved robustness on patients with varying CSF dynamics, crucial for trustworthy application. Finally, we analyse different image metrics to determine the most clinically relevant quantitative measures, and employ explainable artificial intelligence techniques to better understand the current limitations of CNNs in glymphatic MRI.

• Laubo, Sami; Eide, Per Kristian & Rognes, Marie Elisabeth (2026). Predicting individual contrast enrichment and clearance by learning glymphatic MRI. Full text in Research Archive Show summary

  In and around the brain flows a clear liquid, essential for a healthy and functioning brain. This fluid is called the cerebrospinal fluid (CSF) and plays a critical role in the clearance of metabolic waste products from the brain and serves as a delivery route for nutrients and some neuropharmaceuticals and chemotherapy drugs. Altered CSF dynamics are observed in various nervous system diseases. Alzheimer’s and Parkinson’s disease are two examples where one observes the accumulation of proteins normally cleared by CSF. The variability and altered CSF dynamics seen in both health and disease calls for patient specific planning and dosing of CSF transported drugs. Our goal is to investigate how we can utilize image-based machine learning to predict the distribution of a CSF tracer post-injection. Using longitudinal MRI scans after injecting a CSF tracer allows for snapshots of the tracer distribution in the brain over time, from which we can utilize deep learning to predict the 24 hour post-injection MRI scan. We apply a standard U-Net architecture on the pre-injection MRI scan, as well as a U-Net modified with a proposed Convolutional Time-aware Long Short-term Memory (ConvTLSTM) to utilize the full sequence of MRI scans. The ConvTLSTM U-Net outperforms the pre-injection U-Net, where around half of the predictions have a sufficient clinically relevant quality.

• Moen, Per August Jarval (2026). A Grid-Based Methodology for Fast Online Changepoint Detection. Full text in Research Archive
• Moen, Per August Jarval (2026). A grid-based methodology for fast online changepoint detection. Full text in Research Archive
• Solheim, Andreas & Mardal, Kent-Andre (2026). The importance of barriers and interfaces in brain fluid modeling​. Full text in Research Archive
• Solheim, Andreas & Mardal, Kent-Andre (2026). Data-integrated simulations of solute transport in the rodent brain. Full text in Research Archive
• Solheim, Andreas; Ringstad, Geir; Eide, Per Kristian; Acar, Evrim & Mardal, Kent-Andre (2026). Data-driven insights from glymphatic MRI​. Full text in Research Archive
• Solheim, Andreas; Ringstad, Geir; Eide, Per Kristian; Nordengen, Kaja & Mardal, Kent-Andre (2026). Image registration as a tool for modeling and analysis of brain solute transport​. Full text in Research Archive
• Girelli, Alberto; Solheim, Andreas; Lian, Sofie Lysholm; Storås, Tryggve Holck; Nordengen, Kaja & Mardal, Kent-Andre (2026). Exploring dura hydrodynamics: The Role of the Meningeal Lymphatic Vessels in Brain Clearance. Full text in Research Archive
• Solheim, Andreas; Girelli, Alberto; Lian, Sofie Lysholm; Storås, Tryggve Holck; Nordengen, Kaja & Mardal, Kent-Andre (2026). Exploring the brain dura: Estimating meningeal lymphatic clearance through mathematical models. Full text in Research Archive
• Glad, Ingrid Kristine (2026). Intervju: Pisa-resultater 2025 i matte. [Internet]. Uniforum. Full text in Research Archive
• Girelli, Alberto; Solheim, Andreas; Lian, Sofie Lysholm; Nordengen, Kaja; Storås, Tryggve Holck & Mardal, Kent-Andre (2026). Exploring the brain dura: a multiscale framework for dural lymphatic transport. Full text in Research Archive
• Glad, Ingrid Kristine (2026). On the Move: Real-Time Detection of Distributional Changes and Anomalies in Data Streams. Full text in Research Archive Show summary

  Online change and anomaly detection—the task of automatically detecting distributional changes in data streams in real time—is fundamental in applications such as sensor network monitoring, financial surveillance, cybersecurity, and the monitoring of AI processes and ML operations for anomalous behavior or drift. In this talk, I will present ongoing work on both recurrent-neural-network-based and more statistically grounded methods for fast, automatic, and scalable online detection of changes, to be used in settings where sequential information must be monitored in real time for deviations from some (unknown) baseline behavior. The methods are straightforward to apply and come with mathematical guarantees for optimal performance, for example high probability bounds on detection delays and error rates. I will conclude with a brief overview of the broader context of this project: the CoE Integreat – Norwegian Center for Knowledge-driven Machine Learning.

• Mardal, Kent-Andre (2026). Computational modeling of brain clearance during sleep. Full text in Research Archive
• Girelli, Alberto; Solheim, Andreas; Lian, Sofie Lysholm; Storås, Tryggve Holck; Nordengen, Kaja & Mardal, Kent-Andre (2026). Computational Modeling of transport in the human brain dura. Full text in Research Archive
• Mardal, Kent-Andre (2026). Why do we sleep? -- Computational models of brain clearance. Full text in Research Archive
• Mardal, Kent-Andre (2026). Computational modeling of brain clearance: why do we sleep? Full text in Research Archive
• Chini, Michele (2026). Stor-I presentation. Full text in Research Archive Show summary

  Can large language models (LLMs) capture sequential structure when outcomes depend on order? We study this in a controlled, semantic-free sequence framework with three mechanisms over a hidden set of key letters: ordered compliance, driven by key order at a fixed lag; global-property compliance, driven by the parity of the total key count; and key-inversion parity, driven by the parity of key-order inversions. Theoretically, we prove that ordered-compliance inherently leaks information through frequency patterns, creating predictive shortcuts that allow models to succeed without truly capturing causal sequential structure. To isolate true order learning, we introduce a shortcut-auditing protocol that quantifies the predictive power of non-sequential features (e.g., k-grams, pair counts) under label noise. Empirically, encoder and recurrent models reach the theoretical optimum (measured by AUC and F1) on ordered-compliance more efficiently than fine-tuned decoder-only LLMs. On global-property compliance, the tested sequence models remain near chance under standard training unless explicitly guided on feature relevance. On key-inversion parity, recurrent and transformer models can solve the task with four keys, while all tested models remain near chance with six. Our results demonstrate that high quality performance on order-sensitive tasks often masks shortcut exploitation, highlighting the need to test whether simpler statistical patterns can explain comparable predictive performance.

• Glad, Ingrid Kristine (2026). Women in AI: From Algorithms to Action: Living in the AI Era - NORA - Norwegian Artificial Intelligence Research Consortium. Full text in Research Archive
• Cibinel, Luca; Meggio, Claudio & Zuccato, Lorenzo (2026). Enhancing Quantum Graph Representations via Heuristics and Model-Based Clustering. Full text in Research Archive Show summary

  We propose a novel class of representations for graph-structured data, with the objective of improving feature prediction performance. We focus on graphs with clearly identifiable and interpretable subgraphs, such as transition metal complexes. Our approach is based on the identification of subgraph popu- lations whose citizens exhibit a similar statistical behaviour. Knowledge of these populations is injected in the original graphs in the form of virtual nodes to make global information available at the local level.

• Urheim, Espen Bjørge (2026). Presentation of "gridcp: Fast Online Changepoint Detection in Python" at EMS 2026 in Lugano. Full text in Research Archive
• Friedman, Yael & Smajdor, Anna (2026). Synthetic Medical Data. Full text in Research Archive
• Tandon, Kushagri (2026). Thinking about AI beyond capability: Access, Privacy, and Representation. Full text in Research Archive
• Aastveit, Marthe Elisabeth; Lenkoski, Alex & Thorarinsdottir, Thordis Linda (2026). Predicting partially observed survival curves via factor analysis with application to demand forecasting in short-term rental markets. Full text in Research Archive
• Tandon, Kushagri (2026). Investigating bivariate structure and Gaussian anamorphosis correlation of non-Gaussian spatial fields. Full text in Research Archive
• Tandon, Kushagri (2026). Bivariate structure of non-Gaussian spatial fields. Full text in Research Archive Show summary

  Ongoing work with my supervisors Thordis Linda Thorarinsdottir and Geir Olve Storvik.

• Glad, Ingrid Kristine & Øksnes, Berit Omli (2026). Kvinner og KI - Rådgiverdagen 2026 (UiO). doi: https:/www.integreat.no/news/women-in-ai.html. Full text in Research Archive Show summary

  Rådgiverdagen ved Universitetet i Oslo (UiO) er en faglig samling for rådgivere og andre som jobber med studie- og karriereveiledning. Foredraget handlet om veier inn i matematikk og kunstig intelligens, betydningen av synlige forbilder, og hvorfor mangfold er viktig i forskningsfeltet.

• Thorarinsdottir, Thordis Linda (2026). Proper scoring rules in probabilistic forecasting: Theory, methods and applications. Full text in Research Archive
• Thorarinsdottir, Thordis Linda (2026). Spatio-temporal modelling for environmental data. Full text in Research Archive
• Friedman, Yael & Smajdor, Anna (2026). Synthetic medical data: ethical panacea or invasion of the zombies…? Full text in Research Archive
• Friedman, Yael & Smajdor, Anna (2026). On synthetic medical data: Values hierarchies, reification, and zombies. Full text in Research Archive Show summary

  Synthetic medical data (SMD) has been introduced to address data-acquisition challenges. It has been described as a “magical” solution that enables model training without compromising patients’ privacy and is therefore considered ethically desirable (Bellovin et al. 2019; Savage, 2023). However, as we will show in this article, synthetic data is not value-neutral, and it poses both epistemic and ethical trade-offs that cumulatively affect the medical realm. We focus on three primary methodologies: two key deep learning approaches, namely generative models without privacy guarantees and differential privacy (DP) models. In addition, we will use vine copula models as our primary example to demonstrate the statistical approach. We show that prioritizing privacy over transparency undermines explainability, which in turn hinders trust and fairness, pushing these values down the ladder. We also show that prioritizing scalability over fidelity moves medicine away from personalized, participatory, and patient-centered approaches and toward a naturalistic, mechanistic understanding. The collapse of context and experiential knowledge into “zombie data” yields a narrow conception of utility in medicine that ignores the patient as a person. The absence of a direct real-world reference (combined with the use of this data to train algorithms) is where SMD makes a step forward in the reification process relative to “regular” medical data. The data collected to represent reality may gradually subsume the very thing it is intended to represent. As such, SMD also introduces a new degree of reification in medicine, promoting fungibility, which offers clear advantages for data-intensive enterprises, over patients and minorities.

• Friedman, Yael & Smajdor, Anna (2026). DATA, Synthetic DATA, and the spectrum of reification. Full text in Research Archive Show summary

  With rapid advances in AI technology, there is an increasing demand for data to train AI models. These models are used in medicine and health care for clinical research, diagnosis, drug development, and prevention. However, while significant amounts of health-related data are generated, large datasets may not be available due to privacy concerns and regulatory frameworks (e.g., GDPR). To obtain patients’ data, informed consent is required, therefore creating a high threshold for data sharing. In addition, for rare diseases or cases of “no diagnosis”, large data sets are not available. Synthetic medical data (SMD) has been introduced to address data-acquisition challenges; It has been described as a solution that enables model training without compromising patients’ privacy and is therefore considered "ethically desirable" (Bellovin et al. 2019, Savage, 2023). In this talk, we will introduce three main models of SMD: Generative models, Differential Privacy (DP) models, and the C-vine copula-based synthetic data generator. As we will show, these models are not value-neutral, and they pose both epistemic and ethical trade-offs. We will illustrate how SMD use creates new value hierarchies: Privacy over transparency: SMD can obscure the specific characteristics and nuances of real patient populations, which can create explanation gaps that undermine clinicians’ ability to interpret model outputs, erode trust, hinder bias mitigation (Susser et al., 2024), and knowledge development, and risk long-term de-skilling. These risks are especially relevant in the case of rare diseases, where small original datasets and oversimplified synthetic approaches can lose critical dependencies and idiosyncratic features, leading to misleading clinical insights. Scalability over fidelity: developers of SMD aim for low individual fidelity (to protect privacy) but high distributional fidelity, yet, as we will show, noise and selective-distortion methods can break crucial dependencies or entrench biased dependencies from the original data (ibid.), perpetuating the “garbage in, garbage out” paradox (in the process of keeping what seems as important dependencies in C vein copula models), or even introduce new biases (when adding noise in DP models). The preference for scalable, quantified data over individual experience holds risks of alienating patients, erasing contextual and minority experiences (creating what we call “zombie data”), expanding diagnostic disparities, and institutionalizing these trade-offs as a new normal. We will discuss how this prioritization fosters fungibility in medical practice, which we conceptualize as an advanced stage of the medical reification process. We will distinguish between the stage of “datafication”, which is characterize by decontextualization and translation of messy human experiences into transportable data points that creates a partial, curated technical form of objectivity (Leonelli,2016; Nguyen,2024), and SMD, which goes a step further, generating “zombie data” that deepens reification by stripping lived experience, context and agency from those experiences. Finally, we will argue that this new level of reification is a step forward in the process of commodification and, hence, in capitalism. References Bellovin, S. M., Dutta, P. K., & Reitinger, N. (2019). Privacy and synthetic datasets. Stan. Tech. L. Rev., 22, 1. Leonelli, S. (2019). Data-centric biology: A philosophical study. University of Chicago Press. Nguyen, C. T. (2024). Value capture. J. Ethics & Soc. Phil., 27, 469. Savage, N. (2023). Synthetic data could be better than real data. Susser, D., Schiff, D. S., Gerke, S., Cabrera, L. Y., Cohen, I. G., Doerr, M., ... & Wagner, J. K. (2024). Synthetic health data: real ethical promise and peril. Hastings Center Report, 54(5), 8-13.

• Dahl, Geir & Dar, Ahmad Joukhah (2026). Network Flow Optimization: A Study of Classical Problems and Transformations. Algorithms, Examples, and Relationships. Universitetet i Oslo. Full text in Research Archive Show summary

  Optimizing and improving a network flow might not seem like a difficult task, but such problems may not have a feasible solution if the network has certain constraints or limitations. This thesis provides an introduction to the concept of networks and some important methods for presenting and storing network data in order to numerically solve a specific problem. We will review some of the most common and important problems in the field of network flow optimization. First, we begin with the maximum flow problem to determine the maximum possible flow between a source node and a sink node, provided that each arc carrying the flow has a maximum capacity of flow units. Then we move on to the minimum cut problem to determine the "easiest" way to separate two nodes in the network, mostly the source and sink nodes. The third problem is the shortest path problem, which clearly helps us find the shortest path between two nodes, or between all pairs of nodes. Next, we use the maximum flow problem and the shortest path problem as subproblems within a more general and practical problem we might encounter in the transportation industry: the minimum cost flow problem. This problem allows us to determine how to plan or reroute flow paths to minimize overall costs, since each arc has a maximum capacity for the number of flow units it can carry and a corresponding cost for each unit passing through it. Finally, we address the transportation problem, a special case of the minimum cost flow problem, but one with its own unique characteristics that make it worthy of further investigation. One of the interesting outcomes of this study is the attempt to transform the general case of the minimum cost flow problem into the special case of the transportation problem, thus simplifying its solution.

• Lozano, Pere Diaz; Nunno, Giulia Di & Ortiz-Latorre, Salvador (2026). Backward stochastic equations and martingale modelling. Universitetet i Oslo. Full text in Research Archive Show summary

  This thesis is concerned with numerical methods and regularity properties for backward stochastic equations, together with martingale modelling in mathematical finance. The main tools are Wiener chaos expansions and Malliavin calculus. The first part focuses on backward stochastic differential equations (BSDEs). We develop numerical methods that do not require the terminal condition to be given as a function of a forward diffusion, as is often assumed in the literature. Instead, the terminal condition is represented through its Wiener chaos expansion. This leads to two related approaches: an operator-based Euler scheme that approximates the map sending terminal conditions to BSDE solutions, and a chaos-based Euler scheme in which conditional expectations and martingale integrands are computed through finite chaos projections. Convergence results are obtained for both methods. In the second part, we apply the same Wiener chaos point of view to financial modelling. Starting from the no-arbitrage requirement that discounted prices should be martingales under a risk-neutral measure, we construct an over-parameterized square-integrable martingale model by parameterizing its terminal value through a finite Wiener chaos expansion. The resulting model is arbitrage-free by construction, dense in the space of square-integrable martingales, and can be efficiently calibrated to implied volatility surfaces. The final part of the thesis studies backward stochastic Volterra integral equations (BSVIEs). We establish Hölder-type regularity estimates for the martingale integrand, both for the original BSVIE and for a system of approximating BSDEs. These estimates are then used to prove a convergence rate for an explicit Euler-type approximation of the BSVIE.

• Eidesen, Jonas (2026). Groups and Error Correction in Quantum Communication. Universitetet i Oslo. Full text in Research Archive Show summary

  Quantum error correction is an important component of current scientific efforts towards developing practical realizations of quantum communications. In recent years quantum error correction has also become a melting pot for multiple mathematical disciplines, including representation theory, operator algebras, and noncommutative geometry to name a few. In this thesis we initiate deep investigations into some of the mathematical structures that the field of quantum error correction has to offer. Papers I and II in this thesis investigate the structure of stabilizer codes and Clifford codes using tools from projective representation theory. Paper I serves to establish some technical results, and interesting examples of codes that are best realized using the language of projective representation theory. Paper II builds upon the work of paper I and sets the framework established therein into a broader context. Paper III investigates distances between quantum information-channels from the perspective of noncommutative geometry. The quantum information theoretic properties of stability and chaining are shown to hold for constructions that are natural within noncommutative geometry. The papers are preceded by an introductory section on projective representation theory.

• Nunno, Giulia Di; Aslam, Awais & Sobol, Adam Gabriel (2026). A Unified Framework for Cross-Currency Government Bond Valuation and Relative Value Analysis. Universitetet i Oslo. Full text in Research Archive Show summary

  This thesis builds a framework for relating government bonds across durations, currencies and national issuers by using asset swap spreads and cross-currency asset swap spreads. The construction starts from the ground up. Bonds are first treated as mathematical cash-flow objects, after which discount curves are introduced as the tools needed to value these cash flows. The thesis then studies how these curves are built in practice, with particular focus on modern risk-free rate curve construction using overnight indexed swaps and backward-looking overnight rates. Once the curve machinery is in place, domestic asset swap spreads are constructed and interpreted as market-implied measures of relative bond valuation. The analysis is then extended from a single-currency setting to a multi-currency setting. This requires a treatment of foreign exchange forwards, interest-rate parity and the modern market reality in which observed FX forwards do not generally coincide with their covered-interest-parity-implied values. This break between the theoretical and observed forward curve makes the cross-currency basis an unavoidable object in the construction of market-consistent cross-currency valuation. From this, the thesis constructs cross-currency asset swap spreads. The empirical part of the thesis then asks whether the spreads constructed in this framework actually contain useful structure. The answer appears to be yes. Asset swap spread levels display common valuation components across groups of bonds, while first differences are generally better suited for time-series analysis due to their stationarity. Correlation matrices, hierarchical clustering and autoregressive diagnostics suggest that bonds can be grouped into valuation baskets, although short-term spread changes remain partly bond-specific. The thesis therefore presents both a valuation framework and an empirical motivation for treating asset swap spreads as objects with common structure, rather than as isolated bond-level residuals.

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