In this paper we combine topological and functional analysis methods to prove that a non-locally trivial quasi-linear map defined on a $C(K)$ must be nontrivial on a subspace isomorphic to $c_0$. We conclude the paper with a few examples showing that the result is optimal, and providing an application to the existence of nontrivial twisted sums of $\ell_1$ and $c_0$.

Quantum information decoupling is a fundamental primitive in quantum information theory, underlying various applications in quantum physics. We prove a novel one-shot decoupling theorem formulated in terms of quantum relative entropy distance, with the decoupling error bounded by two sandwiched Rényi conditional entropies. In the asymptotic i.i.d. setting of standard information decoupling via partial trace, we show that this bound is ensemble-tight in quantum relative entropy distance and thereby yields a characterization of the associated decoupling error exponent in the low-cost-rate regime. Leveraging this framework, we derive several operational applications formulated in terms of purified distance: (i) a single-letter expression for the exact error exponent of quantum state merging in terms of Petz-Rényi conditional entropies, and (ii) regularized expressions for the achievable error exponent of entanglement distillation and quantum channel coding in terms of Petz-Rényi coherent informations. We further prove that these achievable bounds are tight for maximally correlated states and generalized dephasing channels, respectively, for the high distillation-rate/coding-rate regimes.

Self-adaptive systems increasingly operate in close interaction with humans, often sharing the same physical or virtual environments and making decisions with ethical implications at runtime. Current approaches typically encode ethics as fixed, rule-based constraints or as a single chosen ethical theory embedded at design time. This overlooks a fundamental property of human-system interaction settings: ethical preferences vary across individuals and groups, evolve with context, and may conflict, while still needing to remain within a legally and regulatorily defined hard-ethics envelope (e.g., safety and compliance constraints). This paper advocates a shift from static ethical rules to runtime ethical reasoning for self-adaptive systems, where ethical preferences are treated as runtime requirements that must be elicited, represented, and continuously revised as stakeholders and situations change. We argue that satisfying such requirements demands explicit ethics-based negotiation to manage ethical trade-offs among multiple humans who interact with, are represented by, or are affected by a system. We identify key challenges, ethical uncertainty, conflicts among ethical values (including human, societal, and environmental drivers), and multi-dimensional/multi-party/multi-driver negotiation, and outline research directions and questions toward ethically self-adaptive systems.

This paper studies the optimization of the lowest eigenvalue of the magnetic Steklov problem on planar domains. In the bounded domain setting and for magnetic fields of moderate strengths, we prove that among all simply-connected smooth domains of given area, the disk maximises the lowest magnetic Steklov eigenvalue. For exterior domains, we establish a similar isoperimetric inequality for magnetic fields of moderate strength under fixed perimeter constraint and additional geometric and symmetry assumptions. The proofs rely on the method of torsion-type trial functions in the bounded domain case and on the method of trial functions dependent only on the distance to the boundary in the exterior domain case.

We present Nested Sampling with Slice-within-Gibbs (NS-SwiG), an algorithm for Bayesian inference and evidence estimation in high-dimensional models whose likelihood admits a factorization, such as hierarchical Bayesian models. We construct a procedure to sample from the likelihood-constrained prior using a Slice-within-Gibbs kernel: an outer update of hyperparameters followed by inner block updates over local parameters. A likelihood-budget decomposition caches per-block contributions so that each local update checks feasibility in constant time rather than recomputing the global constraint at linearly growing cost. This reduces the per-replacement cost from quadratic to linear in the number of groups, and the overall algorithmic complexity from cubic to quadratic under standard assumptions. The decomposition extends naturally beyond independent observations, and we demonstrate this on Markov-structured latent variables. We evaluate NS-SwiG on challenging benchmarks, demonstrating scalability to thousands of dimensions and accurate evidence estimates even on posterior geometries where state-of-the-art gradient-based samplers can struggle.

How rich is the collection of groups with a given prominent property? In this work we approach this question for property~$R_\infty$, which says that every automorphism $φ$ of a given group has infinitely many orbits under the $φ$-twisted conjugation action $(g,x) \mapsto gxφ(g)^{-1}$. Generalising the soluble groups of Herbert Abels to a large family over many integral domains, we prove that most such groups have property~$R_\infty$ drawing from a classical result of Levchuk and a swift observation by Jabara. Within the broad programme of cataloguing finitely generated groups up to quasi-isometry, our groups can then be separated by finiteness properties and cohomological dimension whilst having~$R_\infty$. Abandoning finite presentability, we establish that property~$R_\infty$ is very abundant in a strong sense: there are uncountably many finitely generated groups (which can all be chosen to be amenable or non-amenable) that have~$R_\infty$ and are pairwise not quasi-isometric. The proofs vary in flavour. On the amenable side we use carefully constructed quotients of Abels' groups and a general strategy for quasi-isometric diversity established by Minasyan, Osin, and Witzel. For the non-amenable constructions we rely on modifications of Leary's type $\mathtt{FP}$ groups, further cohomological arguments, and recent powerful criteria for~$R_\infty$ due to Iveson, Martino, Sgobbi, Wong, and Fournier-Facio.

When increasing the dimensionality of quantum systems, high-dimensional quantum state certification becomes important in quantum information science and technology. However, how to certify ensembles of high-dimensional quantum states in a black-box scenario remains a challenging task. In this work, we report an experimental test of certifying ensembles of high-dimensional quantum states based on prepare-and-measure experiments with \textit{independent devices}, where the state preparation device and the measurement device have no shared randomness. In our experiment, the prepared quantum states are high-dimensional orbital angular momentum states of single photons, and both the preparation fidelity and the measurement fidelity are about 99.0$\%$ for the six-dimensional quantum states. We also measure the crosstalk matrices and calculate the similarity parameter for up to ten dimensions. We not only experimentally certify the ensemble of high-dimensional quantum states in a semi-device-independent manner, but also experimentally investigate the effect of atmospheric turbulent noise on high-dimensional quantum state certification. Our experimental results clearly show that the certification of high-dimensional quantum states can still be achieved even under the influence of atmospheric turbulent noise. Our findings have potential implications in quantum certification and quantum random number generation.

In this paper, we characterize the wave front sets of solutions to fractional Schrödinger equations \(i\partial_{t}u =(-Δ)^{θ/2}u + V(x)u\) with $0<θ<2$ via the wave packet transform (short-time Fourier transform). We clarify the relationship between the order \(θ\) of the fractional Laplacian and the growth rate of the potential in the problem of propagation of singularities. In particular, we present a theorem that bridges the propagation mechanisms of singularities for the Schrödinger and wave equations.

This paper investigates a specific class of nonsmooth nonconvex optimization problems in the face of data uncertainty, namely, robust optimization problems, where the given objective function can be expressed as a difference of two tangentially convex (DTC) functions. More precisely, we develop a range of nonsmooth calculus rules to establish relationships between Frechet and limiting subdifferentials for a particular maximum function and the tangential subdifferential of its constituent functions. Subsequently, we derive optimality conditions for problems involving DTC functions, employing generalized constraint qualifications within the framework of the tangential subdifferential concept. Several illustrative examples are presented to demonstrate the obtained results.

We investigate white dwarfs in the framework of f(R,L_m) and f(R,L_m,T) gravity to explore the Chandrasekhar Limit. We have considered two functional forms of f(R,L_m) and one functional form of f(R,L_m,T) gravity. Considering the matter Lagrangian L_m=p, we calculate modified TOV equations for each of the forms. By employing the fully degenerate electron gas equation of state in the modified TOV equations, we derive the mass-radius relation for each functional form of both f(R,L_m) and f(R,L_m,T) gravity. Our models imply modifications in the Chandrasekhar mass limit that deviate significantly from the GR and the Newtonian cases. In the f(R,L_m, T)$ gravity, the new mass limit of the white dwarf can reach upto 1.537\,\mathrm{M}_\odot while in f(R,L_m) with the quadratic extension can goes upto 1.52\,\mathrm{M}_\odot and with exponential extension upto 2.08\,\mathrm{M}_\odot. Further, we analyze the static stability criterion, the gravitational redshift, and the adiabatic indices. For the power-law form of f(R,L_m) and the non-linear form of f(R,L_m,T) gravity, significant variations are observed at higher densities (ρ_c > 10^{10}\, \mathrm{g/cm^3}), while substantial changes are noted at much lower central densities in the case of exponential form of f(R,L_m) gravity. We also calculate compactness and gravitational redshift, which are much lower than those of neutron stars and black holes. Stability is also confirmed by adiabatic indices, which show that all models yield Γ> 4/3 throughout the interiors of WDs. Overall, our models provide a viable framework for the existence of super-Chandrasekhar mass limit, extending beyond the classical predictions in the Newtonian and/or GR cases.

For a permutation matrix $P$, let $s_P$ denote its Stanley-Wilf limit, the exponential growth rate of the number of $n\times n$ permutation matrices avoiding $P$. Let $c_P$ denote its Füredi-Hajnal limit, which is the limit $\displaystyle \lim_{n \to \infty} \text{ex}(n,P)/n$ where $\text{ex}(n,P)$ is the maximum number of ones in an $n\times n$ $0$-$1$ matrix avoiding $P$. Cibulka proved the universal quadratic bound $s_P\leq 2.88\,c_P^2$. In this note we improve the constants in Cibulka's result through a so-called ``block contraction" argument. Defining \[ F(c)=\inf_{t\in\mathbb{N}} \frac{(t!)^{1/t}\,15^{\,c/t}}{c}, \] for $c>0$, this leads us to the revised inequality $s_P\leq F(c_P)\,c_P^2$. In particular, $F(c)=\log 15+o(1) \approx 2.70805\ldots +o(1)$ as $c\to\infty$, and the constant improves $2.88$ once $c_P \geq 17$.

We perform a theoretical investigation of the nature of vortices in chiral $d+id$ superconductors on the kagome lattice. The study is motivated by recent experimental developments reporting evidence of time-reversal symmetry breaking in the superconducting state of kagome metals. Using self-consistent microscopic calculations that incorporate the characteristics of the band structure of the kagome lattice, we find that fractional vortices permeate the ground state condensate in the presence of an external field. Each fractional vortex carries one third of the superconducting flux quantum and exhibits a characteristic signature related to one of the three sublattice degrees of freedom of the kagome lattice. We discuss the relevance of these results to recent experimental studies of kagome superconductors in the presence of an external magnetic field.

We revisit the construction of the fermionic path-integral representation of overdamped scalar Langevin processes with multiplicative white noise, focusing on the covariance of the generating functional under non-linear changes of variables. We identify the transformations of the auxiliary (commuting and anticommuting) variables that ensure covariance under such transformations. The subtleties induced by the non-differentiable trajectories of the stochastic dynamics are encoded in the fermionic statistics. Upon integrating out the auxiliary variables, we derive the Onsager-Machlup formulation, which agrees with the one recently obtained using a higher-order discretization scheme. In contrast to the latter, the construction proposed here is formulated directly in continuous time.

Dynamic facility location problems predominantly suppose a monopoly over the service or product provided. Nonetheless, this premise can be a severe oversimplification in the presence of market competitors, as customers may prefer facilities installed by one of them. The monopolistic assumption can particularly worsen planning performance when demand depends on prior location decisions of the market participants, namely, when unmet demand from one period carries over to the next. Such a demand behaviour creates an intrinsic relationship between customer demand and location decisions of all market participants, and requires the decision-maker to anticipate the competitor's response. This work studies a novel competitive facility location problem that combines cumulative demand and market competition to devise high-quality solutions. We propose bilevel mixed-integer programming formulations for two variants of our problem, prove that the optimistic variant is $Σ^{p}_{2}$-hard, and develop branch-and-cut algorithms with tightened value-function cuts that significantly outperform general-purpose bilevel solvers. Our results quantify the severe cost of planning under a monopolistic assumption (profit drops by half on average) and the gains from cooperation over competition (6% more joint profit), while drawing managerial guidelines on how instance attributes and duopolistic modelling choices shape robust location schedules.

This study investigates a robust reconfigurable intelligent surface (RIS)-assisted multiple-input multiple-output (MIMO) system for secure wireless communication, in which a multi-antenna transmitter (Alice) sends confidential messages to a multi-antenna receiver (Bob) in the presence of an eavesdropper (Eve). Unlike idealized models, the reflecting elements (REs) of the RIS are assumed to possess inherent electrical resistance, introducing a practical non-ideal effect often neglected in prior research. The aim of the study is to maximize the secrecy rate of the MIMO system under perfect knowledge of the channel state information (CSI). To achieve this, the secrecy rate maximization problem is formulated and solved using a low-complexity joint optimization framework based on an adaptive projected gradient method (PGM), which simultaneously updates both the transmit precoding matrix and the RIS phase shifts. Solving the exact problem is computationally complex. Thus, a simplified variant is further introduced that maximizes the channel power difference rather than the exact secrecy rate. The simulation results show that this approximation yields a secrecy rate close to the true optimum while significantly reducing the computational cost. In addition, the proposed PGM with an adaptive step size initialization and control mechanism substantially improves the secrecy rate and reduces the computational time compared to the conventional fixed step size PGM. Overall, the simulation results confirm the effectiveness of the proposed PGM and demonstrate that adopting a practical RIS model is essential for establishing secure RIS-assisted MIMO communication links, especially under varying RE resistance values.

Condensed water on vertical surfaces ultimately leaves the substrate at the lower edge, where accumulated liquid detaches as drops. While droplet growth and surface transport have been extensively studied, this final release step remains poorly understood and largely uncontrolled. Yet this boundary event determines how and when condensed water is removed. We ask whether geometry can replace randomness as the governing mechanism of edge dripping. By engraving vertical grooves upstream, we redirect water from surface flow into groove-guided drainage toward the boundary. This switch in transport mode changes how liquid accumulates and detaches at the edge. Using rapid forced condensation and high-resolution imaging, we systematically vary groove spacing s, aspect ratio d/w, and orientation. We then analyse how these geometric parameters influence the formation, stability, and spatial organization of droplets hanging below the edge. Smooth substrates exhibit irregular, impact-driven detachment. Grooved substrates produce localized and steady dripping points. When grooves converge, dripping occurs at fixed, geometry-defined locations. For convergent designs, a simple condensation-capillarity model captures the dependence of the dripping period on the area of the drainage basin. Together, these results demonstrate that geometry alone can transform stochastic edge dripping into spatially organized and temporally regular release, with implications for dew harvesting, passive cooling, and millifluidic transport.

Breastfeeding efficiency relies on coordinated tongue motion, sustained tissue contact and maintenance of an effective intraoral seal. Current assessments of seal formation mainly use local kinematic descriptors or pressure recordings, which do not capture the global structural continuity of the sealing region. We introduce a systolic geometry based approach in which each sagittal ultrasound frame is modeled as a two dimensional deformable domain bounded by tongue, palate and nipple contours. Global seal continuity is formalized through the shortest closed curve that cannot be contracted to a point because of the overall geometry of the domain. The nipple defines a central region that must be circumferentially enclosed by a contact band to maintain suction. Within this band, closed curves encircling the nipple exactly once can be identified; the shortest of these curves defines a normalized systolic index representing the tightest admissible sealing loop. Simulations of symmetric thinning, localized discontinuities and cyclic perturbations reveal feasibility boundaries separating seal preserving from seal breaking configurations. Notably, admissible encircling curves may transiently disappear even when overall geometric motion remains smooth. By capturing global circumferential continuity that cannot be inferred from local metrics alone, our approach generates testable hypotheses linking the existence and temporal stability of admissible encircling curves to milk transfer efficiency and vacuum stability. Applied to segmented ultrasound data and integrated with pressure measurements, our systolic approach could provide a quantitative framework for objective assessment of seal integrity and longitudinal monitoring of latch stability.

Epitaxial single-crystalline CsPbBr3 perovskite films on mica, prepared ex-situ, are explored using a low-temperature scanning tunneling microscope (STM) by probing the unoccupied electronic states of their surface in ultra-high vacuum (UHV) at 80 K. Light-assisted STM measurements under a broadband illumination with visible light were employed to enhance and stabilize surface conductivity. STM imaging across the surface of macroscopic bulk CsPbBr3 films reveals large flat terraces characterized by a specific type of surface reconstruction, consisting of parallel rows of U-shaped atomic nanostructures. These structures are spaced by 12 angstroms and exhibit an internal periodicity of 5.1 angstroms. Density functional theory (DFT) calculations reproduce the experimental observations and reveal a competition between different orthorhombic CsPbBr3(110) surface reconstructions: a Cs-rich structure, identified as the most energetically stable, and three alternative PbBr rich reconstructions, which are slightly higher in energy yet remain consistent with the STM data. Additional analyses that explicitly account for the mica substrate exclude the cubic CsPbBr3 phase and other orthorhombic surface orientations, while showing that variations in the mica surface termination do not alter the preferred CsPbBr3(110) reconstruction. This combined approach thereby confirms our assignment and resolves previous STM interpretations of CsPbBr3.

Magnetization dynamics is commonly described by the stochastic Landau-Lifshitz-Gilbert (LLG) equation. On picosecond timescales, inertial and open-system extensions of the LLG equation are necessary to interpret recent experiments. We show analytically and numerically that the standard LLG equation exhibits strictly positive entropy production rates, while inertial and open-system LLG dynamics display temporarily negative entropy production rates indicating non-Markovianity. Here we quantify the degree of non-Markovianity using established measures. Our numerical calculations show that the open-system LLG equation consistently exhibits the highest magnitude of non-Markovianity for different initial conditions and magnetic field orientations.

Speculative thinking about the capabilities and implications of artificial intelligence (AI) influences computer science research, drives AI industry practices, feeds academic studies of existential hazards, and stirs a global political debate. It primarily concerns predictions about the possibilities, benefits, and risks of reaching artificial general intelligence, artificial superintelligence, and technological singularity. It permeates technophilic philosophies and social movements, fuels the corporate and pundit rhetoric, and remains a potent source of inspiration for the media, popular culture, and arts. However, speculative AI is not just a discursive matter. Steeped in vagueness and brimming with unfounded assertions, manipulative claims, and extreme futuristic scenarios, it often has wide-reaching practical consequences. This paper offers a critical overview of AI speculations. In three central sections, it traces the intertwined sway of science fiction, religiosity, intellectual charlatanism, dubious academic research, suspicious entrepreneurship, and ominous sociopolitical worldviews that make AI speculations troublesome and sometimes harmful. The focus is on the field of existential risk studies and the effective altruism movement, whose ideological flux of techno-utopianism, longtermism, and transhumanism aligns with the power struggles in the AI industry to emblematize speculative AI's conceptual, methodological, ethical, and social issues. The following discussion traverses these issues within a wider context to inform the closing summary of suggestions for a more comprehensive appraisal, practical handling, and further study of the potentially impactful AI imaginaries.

We curate a large-scale dataset of low frequency dielectric anisotropy values for low molecular weight liquid crystals. Using this dataset, we demonstrate that supervised machine-learning models can predict dielectric anisotropy with substantially improved accuracy (RMSE 2.6) compared to estimates obtained from the Maier-Meier relations using molecular properties from both the widely used semiempirical AM1 method (RMSE 9.7) and the modern r2scan-3c composite method (RMSE 11.2). Realising the potential of machine learning techniques for liquid crystalline materials requires carefully curated data to be accessible, and on this basis we propose a simple and standard template for reporting data.

Connected and Autonomous Vehicles (CAVs) continue to evolve rapidly, and system latency remains one of their most critical performance parameters, particularly when vehicles are operated remotely. Existing latency-assessment methodologies focus predominantly on Glass-to-Glass (G2G) latency, defined as the delay between an event occurring in the operational environment, its capture by a camera, and its subsequent display to the remote operator. However, G2G latency accounts for only one component of the total delay experienced by the driver. The complementary component, Motion-to-Motion (M2M) latency, represents the delay between the initiation of a control input by the remote driver and the corresponding physical actuation by the vehicle. Together, M2M and G2G constitute the overall End-to-End (E2E) latency. This paper introduces a measurement framework capable of quantifying M2M, G2G, and E2E latencies using gyroscopes, a phototransistor, and two GPS-synchronized Raspberry Pi 5 units. The system employs low-pass filtering and threshold-based detection to identify steering-wheel motion on both the remote operator and vehicle sides. An interrupt is generated when the phototransistor detects the activation of an LED positioned within the camera's Field Of View (FOV). Initial measurements obtained from our teleoperated prototype vehicle over commercial 4G and 5G networks indicate an average E2E latency of approximately 500 ms (measurement precision +/- 4 ms). The M2M latency contributes up to 60% of this value.

This paper proposes a novel robust Model Predictive Control (MPC) scheme for linear discrete-time systems affected by model uncertainty described by interval matrices. The key feature of the proposed method is a bound on the uncertainty propagation along the prediction horizon which exploits a set-theoretic over-approximation of each term of the uncertain system impulse response. Such an approximation is based on matrix zonotopes and leverages the interval matrix structure of the uncertainty model. Its main advantage is that all the relevant bounds are computed offline, thus making the online computational load independent of the number of uncertain parameters. A variable-horizon MPC formulation is adopted to guarantee recursive feasibility and to ensure robust asymptotic stability of the closed-loop system. Numerical simulations demonstrate that the proposed approach is able to match the feasibility regions of the most effective state-of-the-art methods, while significantly reducing the computational burden, thereby enabling the treatment of nontrivial dimensional systems with multiple uncertain parameters.

We consider the maximal regularity of a specific Vlasov-Fokker-Planck equation $\mathcal{A}u=f$ in the Euclidean space. The operator $\mathcal{A}=Δ_{y}u-y\cdot \nabla_x{u}$ is an example of the Ornstein-Uhlenbeck operators. We prove the existence of a solution that satisfies the anisotropic maximal regularity estimates. To prove this we also show a similar estimates and a weak (1, 1) estimate for $L=\partial_t-\mathcal{A}$, which is of independent interest. These results rely on the pointwise estimates of the fundamental solution of $L$.

We study the orbital magnetic moment of Bogoliubov quasiparticles in superconductors with the semiclassical approach. We derive the orbital magnetic moment of a quasiparticle wavepacket by considering the energy correction of the wavepacket to the linear order of the magnetic field. The semiclassical result is further verified by a linear response calculation with a full quantum mechanical method. From the analytical expression we find that nontrivial structure in the superconducting pairing gap alone is unable to produce quasiparticle orbital magnetic moment, which is in sharp contrast to the behavior of quasiparticle Berry curvatures. We apply the formula to study a tight-binding model with chiral $d$-wave superconducting gap, and show the influence of orbital magnetic moment on the energy spectrum and local density of states. We also calculate the orbital Nernst effect driven by the interplay between the orbital magnetic moment and the Berry curvature of Bogoliubov quasiparticles.

We study the effective behavior of heterogeneous energies arising in the modeling of material voids in geometrically linear elastic materials. Specifically, we consider functionals featuring bulk terms depending on the symmetrized gradient of the displacement and terms comparable to the surface area of the material voids inside the material. Under suitable growth conditions for the bulk and surface densities we prove that, as the microscale $\varepsilon$ tends to zero, the $Γ$-limit admits an integral representation that contains an additional surface term expressed by jump discontinuities of the displacement outside of the void region. This term is related to the phenomenon of collapsing of voids in the effective limit. Under a continuity assumption of the surface density at the $\varepsilon$-scale, we show that the limiting density related to jumps is twice the energy density for voids.

In this paper, we analyse the impacts of exogenous and endogenous factors on wealth distribution in the Bitcoin token economy, where wealth distribution refers to the distribution of BTC between economic participants or groups of economic participants. The objective of the paper is to analyse the impact of economic policies on wealth distribution in the Bitcoin ecosystem. Different macroeconomic and microeconomic time series are used to eliminate noise in the wealth distribution time series, and the causality analysis is performed between Bitcoin Improvement Proposals (i.e., BIPs) and the cleaned wealth distribution data to reveal possible patterns in the impacts that the endogenous policies have on wealth distribution in token economies. Lastly, a structure for economic policy taxonomy in token economies is proposed where different the policy implementations are illustrated by existing BIPs. This approach highlights the actions available to the policy makers, as well as providing a technique for analysis of policy impacts in token economies and their categorization.

The advent of integral field data has revolutionised the study of galaxy evolution. A key component of this is dynamical modelling methods which have allowed for crucial insights to be made from kinematic data. Despite this importance, most dynamical models make a number of key assumptions which do not hold for real galaxies. These include assumptions about the geometry (axisymmetry or triaxiality), the shape of the velocity ellipsoid, and the shape of the underlying stellar distribution. At the same time, machine learning methods are becoming increasingly powerful, with many applications appearing in astronomy. As a first step towards building new dynamical modelling methods with machine learning, it is important to understand the types of machine learning architectures that are best fit for dynamical modelling. To investigate this, we construct a training set of dynamical models of early-type galaxies using Jeans Anisotropic Modelling (JAM). We then train a neural network on this data using the parameters of JAM and mock photometry as the input. We are able to accurately model JAM galaxies with relatively simple machine learning architectures, leading to a significant speed increase over traditional JAM modelling.

We give an introduction to partially wrapped Fukaya categories of surfaces with orbifold singularities. Dissecting an orbifold surface $\mathbf S$ into polygons, certain dissections give rise to formal generators, inducing a triangulated equivalence between the derived Fukaya category of $\mathbf S$ and the perfect derived category of a graded associative algebra. This provides a geometric means for obtaining associative algebras -- conjecturally all -- which are derived equivalent to skew-gentle algebras. We include a new perspective on the partially wrapped Fukaya category of an orbifold disk which serves as a local model for the Fukaya categories of general orbifold surfaces. This perspective yields an equivalence between the perfect derived category of a quiver of type $\mathrm D_{n+1}$ and the perfect derived category of a graded quiver of type $\widetilde{\mathrm A}_{n-1}$, the latter being equipped with quadratic zero relations and a nontrivial A$_\infty$ structure. This equivalence elucidates the relationship between skew-gentle algebras and orbifold surfaces, and the role of deformation theory in this relationship.

We consider the variance renormalisation of a singular SPDE for which a Da Prato-Debussche trick is not applicable. The example taken is the $2$-dimensional generalised parabolic Anderson model (gPAM), driven by a much rougher than white noise, necessitating both a multiplicative and an additive renormalisation. To handle the discrepancy between the regularity structures of the approximate and the limiting equations, we consider models that lift $0$ noises to nontrivial models, in analogy with ``pure area'' from rough paths. The convergence to such a model is shown for the BPHZ model over the vanishing noise via graphical computations.