We present recent achievement on manufacturing optical filter and multilayers done with two complementary RF magnetron sputtering approaches: deposition duration control and in situ optical reflectance monitoring. Those approaches were greatly improved thanks to ellipsometry and spectrophotometry cross-studies of optical refractive indexes of Nb2O5, TiO2 and SiO2 materials grown using two sputtering systems. At the same time, we conducted deposition studies of these three materials which have increased the manufacturing reliability and allowed us to consider developing complex optical multilayers with more than 100 layers.

We introduce an algebraic structure for studying state-independent contextuality arguments, a key form of quantum non-classicality exemplified by the well-known Peres-Mermin magic square, and used as a source of quantum advantage. We introduce \emph{commutation groups} presented by generators and relations, and analyse them in terms of a string rewriting system. There is also a linear algebraic construction, a directed version of the Heisenberg group. We introduce \emph{contextual words} as a general form of contextuality witness. We characterise when contextual words can arise in commutation groups, and explicitly construct non-contextual value assignments in other cases. We give unitary representations of commutation groups as subgroups of generalized Pauli $n$-groups.

The mathematical characterization of social-distancing games in classical epidemic theory remains an important question, for their applications to both infectious-disease theory and memetic theory. We consider a special case of the dynamic finite-duration SI social-distancing game where payoffs are accounted using Markov decision theory with zero-discounting, while distancing is constrained by threshold-linear running-costs, and the running-cost of perfect-distancing is finite. In this special case, we are able construct strategic equilibria satisfying the Nash best-response condition explicitly by integration. Our constructions are obtained using a new change of variables which simplifies the geometry and analysis. As it turns out, there are no singular solutions, and a time-dependent bang-bang strategy consisting of a wait-and-see phase followed by a lock-down phase is always the unique strategic equilibrium. We also show that in a restricted strategy space the bang-bang Nash equilibrium is an ESS, and that the optimal public policy exactly corresponds with the equilibrium strategy.

Artificial intelligence (AI)-driven decision support systems can improve diagnostic accuracy and efficiency in computational pathology. However, collaboration between human experts and AI may introduce cognitive biases such as automation and anchoring bias, where users adopt system predictions blindly or are disproportionately influenced by AI advice, even when inaccurate. These effects may be amplified under time pressure, common in routine pathology, or shaped by individual user characteristics. We conducted an online experiment in which pathology experts (n = 28) estimated tumor cell percentages: once independently and once with AI support. A subset of estimations in each condition was performed under time strain. Overall, AI assistance improved diagnostic performance but introduced a 7% automation bias rate, defined as accepted negative consultations where previously correct independent judgments were overturned by incorrect AI advice. While time pressure did not increase the frequency of automation bias, it appeared to intensify its severity, reflected in stronger performance declines associated with increased AI reliance under cognitive load. A linear mixed-effects model (LMM) simulating weighted averaging showed a statistically significant positive coefficient for AI advice, indicating moderate anchoring on system output. This effect increased under time pressure, suggesting anchoring bias becomes more pronounced when cognitive resources are limited. A second LMM assessing automation reliance, a proxy for automation and anchoring bias, showed that professional experience and self-efficacy were associated with lower dependence on AI, whereas higher confidence during AI-assisted decisions was tied to increased AI reliance. These findings highlight the dual nature of AI integration in clinical workflows: improving performance while introducing risks of bias-driven diagnostic errors.

Representations learned by convolutional neural networks (CNNs) exhibit a remarkable resemblance to information processing patterns observed in the primate visual system on large neuroimaging datasets collected under diverse, naturalistic visual stimulation, but with instruction for participants to maintain central fixation. This viewing condition, however, diverges significantly from ecologically valid visual behaviour, suppresses activity in visually active regions, and imposes substantial cognitive load on the viewing task. We present a modification of the encoding model framework, adapting it for use with naturalistic vision datasets acquired under fully natural viewing conditions, without fixation, by incorporating eye-tracking data. Our gaze-aware encoding models were trained on the StudyForrest dataset, which features task-free naturalistic movie viewing. By combining eye-tracking data with the visual content of movie frames, we generate combined subject-wise gaze-stimulus specific feature time series. These time series are constructed by sampling only the locally and temporally relevant elements of the CNN feature map for each fixation. Our results demonstrate that gaze-aware encoding models match the performance of conventional encoding models with 112x fewer model parameters. Gaze-aware encoding models were especially beneficial for participants with more dynamic eye-movement patterns. Therefore, this approach opens the door to more ecologically valid models that can be built in more naturalistic settings, such as playing games or navigating virtual environments.

Research and Development is the largest budget position in the pharmaceutical industry, with clinical trials being a critical, yet costly and time-consuming component to inform decisions. Beyond drug efficacy, the probability of success and efficiency of research and development are highly dependent on the approaches used for designing, analyzing, and interpreting clinical trials. Deep understanding of statistical methodology and quantitative approaches is therefore essential. Consequently, dedicated methodology groups have emerged in mid-size and large pharmaceutical companies and CROs. Their remit is to lead the conception and implementation of innovative quantitative methodologies in order to improve drug development, often by addressing complexities or offering more efficient designs. To achieve this, they collaborate internally and externally (e.g., with academics, regulators) to identify common challenges and tear down silos in order to invest in methods with the highest impact on efficiency and value to the portfolio. Given the immense financial stakes of drug development -- where delays carry massive implications -- these groups represent a critical strategic investment. However, to realize this business impact, statistical innovations must be rigorously validated and seamlessly integrated. This manuscript explores the setup, remit, and value of dedicated methodology groups, alongside the critical organizational considerations and success factors required to maximize their impact on the speed, efficiency, and probability of success.

Recently, Andrews and Dastidar introduced the partition function $SOME(n)$, defined as the sum of all the odd parts in the partitions of $n$ minus the sum of all the even parts in the partitions of $n$. They derived its generating function and established some congruences satisfied by \(SOME(n)\). In this paper, we introduce an overpartition analogue of $SOME(n)$, denoted by $\overline{SOME}(n)$, the sum of all the odd parts in the overpartitions of \(n\) minus the sum of all the even parts in the overpartitions of \(n\). We derive the generating function for $\overline{SOME}(n)$ and obtain congruences modulo \(3, \ 5\) and powers of \(2\). Our method is based on classical $q$-series identities and manipulations of infinite products and sums.

We introduce the TTStack sketch, a structured random projection tailored to the tensor train (TT) format that unifies existing TT-adapted sketching operators. By varying two integer parameters $P$ and $R$, TTStack interpolates between the Khatri-Rao sketch ($R=1$) and the Gaussian TT sketch ($P=1$). We prove that TTStack satisfies an oblivious subspace embedding (OSE) property with parameters $R = \mathcal{O}(d(r+\log 1/δ))$ and $P = \mathcal{O}(\varepsilon^{-2})$, and an oblivious subspace injection (OSI) property under the condition $R = \mathcal{O}(d)$ and $P = \mathcal{O}(\varepsilon^{-2}(r + \log r/δ))$. Both guarantees depend only linearly on the tensor order $d$ and on the subspace dimension $r$, in contrast to prior constructions that suffer from exponential scaling in $d$. As direct consequences, we derive quasi-optimal error bounds for the QB factorization and randomized TT rounding. The theoretical results are supported by numerical experiments on synthetic tensors, Hadamard products, and a quantum chemistry application.

When single-shot qubit readout protocols are adapted for multilevel systems, theoretical $T_1$ lifetime calculations often fall short of capturing the experimental lifetime trends. We identify extrinsic population dynamics as the fundamental origin of this disparity, establishing that the lifetime estimates can, in certain operating regions, be distinct from the intrinsic $T_1$ time. We clarify these aspects with an integrated theory to address recent measurements [Nat. Nano, 20, 494, (2025)] on spin-valley states in bilayer graphene. While confirming that phonon and Johnson noise are the dominant intrinsic sources, we show that the inclusion of extrinsic factors provide the critical match to the experimental estimates. The extrinsic factors also effectuate violations of generalized Mathiessen's rules. With an improved handle on the design space, a revised readout protocol to estimate the $T_1$ lifetime of the valley qubit is proposed.

In [AJM26], we gave large-time asymptotic bounds on the annealed survival probability of a moving polymer taking values in ${\mathbb R}^d, d \geq 1$. This polymer is a solution of a stochastic heat equation driven by additive spacetime white noise on $[0,T] \times [0,J]$, in an environment of Poisson traps. For fixed $J$, the annealed survivial probability decays exponentially with rate proportional to $T^{d/(d+2)}$. In this work we examine the large $J$ asymptotics of the annealed survival probability for any fixed time $T>0$. We prove upper and lower bounds for the annealed survival probability in the cases of hard obstacles. Our bounds decay exponentially with rate proportional to $J^{d/(d+2)}$. The exponents also depend on time $T >0$.

Altermagnetism is a recently identified magnetic state in which time-reversal symmetry is broken despite a collinear compensated spin structure. The response of altermagnets is determined not only by their $d$-, $g$-, or $i$-wave spin order, but also the orientation of their Néel vector $\mathbf{L}$. Therefore, accessing a response that fundamentally depends on the orientation of $\mathbf{L}$, such as the anomalous Hall effect, remains experimentally challenging in particular at the nanoscale. Here, we harness nano-spectroscopic X-ray magnetic circular dichroism (XMCD) to investigate nanoscale modulated altermagnetic responses in $α$-Fe$_2$O$_3$ (Hematite). By performing spectroscopy across the temperature-induced $\mathbf{L}$-reorientation Morin transition, we observe the on-and-off switching of XMCD, in agreement with our theoretical calculations. Although the bulk XMCD vanishes below the Morin temperature, we confirm the reorientation of $\mathbf{L}$ by harnessing polarization-independent X-ray absorption spectroscopy. Moreover, we observe a finite XMCD signal in nanoscale domain walls with locally modulated Néel vectors, while the surrounding domains exhibit no XMCD. At room temperature, we instead identify altermagnetic meron spin textures that exhibit XMCD in their planar regions but no XMCD in their nanoscopic cores. Our results establish a pathway to harness complex spin textures with nanoscale functionalities in a broader class of altermagnets with various $\mathbf{L}$-orientations and using light, earth-abundant elements.

Quadratic Unconstrained Binary Optimization (QUBO) is a standard NP-hard optimization problem. Recently, it has gained renewed interest through quantum computing, as QUBOs directly reduce to the Ising model, on which quantum annealing devices are based. We introduce a QUBO formulation for permutations using compare-exchange networks, with only $O(n \log^2 n)$ binary variables. This is a substantial improvement over the standard permutation matrix encoding, which requires $n^2$ variables and has a much denser interaction graph. A central feature of our approach is uniformity: each permutation corresponds to a unique variable assignment, enabling unbiased sampling. Our construction also allows additional constraints, including fixed points and parity. Moreover, it provides a representation of permutations that supports the operations multiplication and inversion, and also makes it possible to check the order of a permutation. This can be used to uniformly generate permutations of a given order or, for example, permutations that commute with a specified permutation. To our knowledge, this is the first result linking oblivious compare-exchange networks with QUBO encodings. While similar functionality can be achieved using permutation matrices, our method yields QUBOs that are both smaller and sparser. We expect this method to be practically useful in areas where unbiased sampling of constrained permutations is important, including cryptography and combinatorial design.

We quantify changes DeltaQ in 100-year return values for regional annual maxima and minima of near-surface atmospheric temperature from output of five CMIP6 models, for five of the Earth's desert regions, over the interval (2025,2125). We use generalised extreme value (GEV) regression to characterise changes in extremes, considering a range of different parametric forms for the variation of GEV parameters with time, and coupling models for different scenarios so that they provide a common GEV tail in the first year of observation. Parameters are estimated using Bayesian inference. We perform a simulation study using ground truth models generating data qualitatively similar to the CMIP6 output, to assess the relative performance of different information criteria in selecting models from a set of candidates, to minimise error in predictions of DeltaQ. The Bayesian information criterion (BIC) provides best performance, out-performing the divergence and widely-applicable information criteria in particular. Using BIC-selected GEV regression models, we estimate joint posterior distributions of DeltaQ over three forcing scenarios, for different combinations of region, GCM and climate ensemble. Estimates show a consistent trend across regions, GCMs and climate ensembles, of DeltaQ increasing with climate scenario for both regional annual maxima and minima. Aggregating posterior distributions over climate ensembles and GCMs, we find evidence for significant increases in DeltaQ for regional annual maxima under more severe forcing scenarios for all desert regions. Similar but weaker and less significant trends are observed for regional annual minima.

Identifying governing partial differential equations (PDEs) from noisy spatiotemporal data remains challenging due to differentiation-induced noise amplification and ambiguity from overcomplete libraries. We propose a prior-informed weak-form sparse-regression framework that resolves both issues by refining the dictionary before regression and shifting derivatives onto smooth test functions. Our design encodes three compact physics priors-Hamiltonian (skew-gradient and energy-conserving), conservation-law (flux-form with shared cross-directional coefficients), and energy-minimization (variational, dissipative)-so that all candidate features are physically admissible by construction. These prior-consistent libraries are coupled with a subspace-pursuit pipeline enhanced by trimming and residual-reduction model selection to yield parsimonious, interpretable models. Across canonical systems-including Hamiltonian oscillators and the three-body problem, viscous Burgers and two-dimensional shallow-water equations, and diffusion and Allen--Cahn dynamics-our method achieves higher true-positive rates, stable coefficient recovery, and structure-preserving dynamics under substantial noise, consistently outperforming no-prior baselines in both strong- and weak-form settings. The results demonstrate that compact structural priors, when combined with weak formulations, provide a robust and unified route to physically faithful PDE identification from noisy data.

An algorithm for the generation of shuttling sequences is necessary for the operation of a linear segmented ion-trap quantum computer. The present work provides an implementation of an algorithm that produces sequences proved to be optimal for circuits with a quantum Fourier transform-like structure. Such optimality was proved in previous work of our group. We first present an approach for qubit mapping, i.e. determining the initial ordering of the ions, termed the common ion order, and develop a heuristic algorithm for its implementation. We explain how this heuristic is integrated in the shuttling sequence generation algorithm described in the previous work. The results show the increased performance of the heuristic in terms of reducing the number of required shuttling operations. The number of ion displacements required exhibits a polynomial increase in terms of the number of qubits, such that these operations become the main contribution to the overall resource cost. Furthermore, we show that multiple zones for gate interactions can reduce the amount of qubit register reordering.

Maximum-likelihood (ML) detection in high-order MIMO systems is computationally prohibitive due to exponential complexity in the number of transmit layers and constellation size. In this white paper, we demonstrate that for practical MIMO dimensions (up to 8x8) and modulation orders, near-ML hard-decision performance can be achieved using a structured reduced-search strategy with complexity linear in constellation size. Extensive simulations over i.i.d. Rayleigh fading channels show that list sizes of 3|X| for 3x3, 4|X| for 4x4, and 8|X| for 8x8 systems closely match full ML performance, even under high channel condition numbers, |X| being the constellation size. In addition, we provide a trellis based interpretation of the method. We further discuss implications for soft LLR generation and FEC interaction.

We study Li--Yorke and mean Li--Yorke chaos for weighted composition operators $C_{w,φ}$ on Banach spaces of analytic functions on the unit disk $\mathbb{D}$. Under natural conditions on the space, we show that $C_{w,φ}$ is (densely) Li--Yorke chaotic if and only if it is not power-bounded, and (densely) mean Li--Yorke chaotic if and only if it is not absolutely Cesàro bounded. These results are applied to Hardy spaces $H^p(\mathbb{D})$, $1 \le p \le \infty$, and weighted Bergman spaces $A^p_β(\mathbb{D})$, $-1 < β< \infty$ and $1 < p < \infty$.

Ropelength, L, is a parameter characterizing the minimum contour length of a knot or link. There exist upper and lower bounds on ropelength with respect to crossing number, C, including a universal lower bound constraining $L\geqα_0 C^{3/4}$ for some constant $α_0$. There is currently an order-of-magnitude range for the value of $α_0$ between 1.105 and 10.76. In this work, we show that T(Q,Q) torus links can be constructed such that the upper bound is within a factor of 1.77 of the lower bound. We derive a stronger lower bound based on the convex hull around close-packed disks of approximately $α_{T_{QQ}}>\sqrt{8π\sqrt{3}}+(2π+\sqrt{2π+7\sqrt{3}-12}\ )Q^{-1/2}\approx6.60+7.61Q^{-1/2}$, significantly higher than the best universal lower bound of 1.105. We show that a link can be constructed without any free parameters or geometric optimization that, when $Q$ is large, has a coefficient $α_{T_{QQ}}<1.005\cdot 4π(5\sqrt{5}-8)/3\approx13.39$, and can be improved to to 11.68 by solving a helical no-overlap constraint equation that requires a conjectural approximation. For $Q$ up to 20 we construct links from smooth planar curves or toroidal helices minimized with respect to a small number of geometric parameters, that are between 6 and 60% greater in ropelength than the lower bound. Many such links can be annealed to within 10% of the lower bound using gradient descent. This represents significant progress towards developing sharp bounds on the ropelengths of specific classes of knots and links.

We introduce a novel online convex optimization (OCO) framework to estimate the user's signal-to-interference-plus-noise ratio (SINR) from ACK/NACK feedback, channel quality indicator (CQI) reports, and previously selected modulation and coding scheme (MCS) values. Specifically, the proposed approach minimizes a regularized binary cross-entropy loss using mirror descent enhanced with Nesterov momentum for accelerated SINR tracking. Its parameters are tuned online via an expert-advice algorithm, endowing the estimator with continual learning capabilities. Numerical experiments in ray-traced scenarios show that the proposed method outperforms state-of-the-art schemes in estimation accuracy and adapts robustly to time-varying SINR regimes.

In a recent breakthrough, Kalmynin resolved conjectures of Lev--Sonn and Sárközy on additive decompositions of multiplicative subgroups of prime fields. In this paper, inspired by a related conjecture of Sárközy, we prove multiplicative analogues of Kalmynin's results. We show that for every proper multiplicative subgroup $G$, the shifted set $(G-1)\setminus\{0\}$ cannot be written as a product set nontrivially, addressing a conjecture of Sárközy. In addition, we prove that no nonzero shift of any coset of a proper multiplicative subgroup is a ratio set of the form $A/A$. Our results substantially sharpen previous theorems of Shkredov and the authors.

Multi-die FPGAs enable device scaling beyond reticle limits but introduce severe interconnect overhead across die boundaries. Inter-die connections, commonly referred to as super-long lines (SLLs), incur high delay and consume scarce interposer interconnect resources, often dominating critical paths and complicating physical design. To address this, this work proposes an interconnect-aware logic resynthesis method that restructures the LUT-level netlist to reduce the number of SLLs. The resynthesis engine uses die partitioning information to apply logic resubstitutions, which simplifies local circuit structures and eliminates SLLs. By reducing the number of SLLs early in the design flow, prior to physical implementation, the proposed method shortens critical paths, alleviates pressure on scarce interposer interconnect resources, and improves overall physical design flexibility. We further build a tool flow for multi-die FPGAs by integrating the proposed resynthesis method with packing and placement. Experimental results on the EPFL benchmarks show that, compared with a state-of-the-art framework, the proposed method reduces the number of SLLs by up to 24.8% for a 2-die FPGA and up to 27.38% for a 3-die FPGA. On MCNC benchmarks, our tool flow achieves an average SLL reduction of 1.65% while preserving placement quality. On Koios benchmarks, where fewer removable SLLs exist, several designs still exhibit considerable inter-die edge reductions. Overall, the results confirm that reducing inter-die connections at the logic level is an effective approach for multi-die FPGAs.

We develop a trajectory-based Koopman method for sea surface temperature (SST) that lifts annual SST segments using a signature kernel -- a reproducing kernel Hilbert space (RKHS) kernel that compares paths via iterated-integral features -- and learns the one-year shift operator. By operating on annual trajectory segments rather than instantaneous fields, the method encodes finite-time history, which helps capture memory effects in SST-only evolution. The resulting operator improves out-of-sample multi-year forecast skill relative to a climatology baseline and reveals coherent spectral modes. We implement the approach via kernel extended dynamic mode decomposition (EDMD) on signature-kernel Gram matrices, yielding a single pipeline for forecasting and spectral diagnostics of high-dimensional SST dynamics.

The spin dynamics of a trimer with Dzyaloshinsky-Moriya (DM) interaction are investigated within a unified Hamiltonian framework that connects quantum-mechanical and semiclassical descriptions. The interpolation between the two regimes is realised by solving the modified Gisin-Schrödinger equation, in which the relative weight of a quantum coherence and local mean-field contributions is continuously tuned. The resulting dynamical behaviour is analysed and summarised in a ground state diagram that illustrates how the character of the spin motion evolves from fully quantum to semiclassical as the DM interaction is treated at different levels of approximation. In the last part of the publication, the chiral spin dynamics proposed by Da-Wei Wang et al. is examined theoretically, taking into account its behaviour at the boundary between quantum and classical physics.

Let $\bk $ be a field of characteristic $p\geq 0$ and $X$ a simply connected finite CW complex. In this text, we prove that: {\sl if the cohomology algebra $H^*(X;\bk)$ is generated, as an algebra, by at least two linearly independent elements, then the sequence of Betti numbers $ \left( \dim H^n(LX;\bk)\right)_{n\geq 1 }$ grows unbounded.} This provides a complete solution of the closed geodesics problem.

In June 2026, the UK government will set its carbon budget for the period 2038 to 2042, the seventh such carbon budget (CB7) since the Climate Change Act became law in 2008. For the first time, this carbon budget will be accompanied by a macroeconomic assessment of its impact on growth, employment, inflation and inequality. Researchers from the Institute of New Economic Thinking (INET) Oxford are working in partnership with the Department for Energy Security and Net Zero to deliver this assessment using our data-driven macroeconomic agent-based model (ABM). This extended abstract presents the work in progress towards this pioneering policymaking using our data-driven macroeconomic ABM. We are conducting our work in three work packages. By the time of the workshop, we hope to be able to present preliminary findings from the first two work packages. In WP1, we adapt an existing macro-ABM prototype and build a UK macroeconomic baseline. The main task for this is initialising the model with suitable UK household microdata. We present the options considered and the approach settled upon. In WP2, we conduct preliminary modelling that represents UK decarbonisation as an external shock to financial flows and technical coefficients. In order to present results in time to influence the June 2026 policy decision, this second work package exogenously forces the ABM to follow the CB7 green investment and associated technological change projections provided by the Climate Change Committee. Finally, we will implement more sophisticated social and technological learning packages in WP3, building our own projections of likely decarbonisation pathways that may diverge from UK government plans. For the workshop, we will present the progress of WP1 and WP2.

This article's aim is to provide the solution to the equity premium puzzle without using calibrated values. Calibrated values of subjective time discount factor were used in my prior derived models because 4 variables were determined from 3 different equations. Furthermore, calculated values and risk behavior determination of my prior models were compatible with empirical literature. 4 unknown variables are now calculated from 4 different equations in the new derived model in this article. Subjective time discount factor and coefficient of relative risk aversion are found 0.9581 and 1.0319, respectively from the system of equations which are compatible with empirical studies. Micro and macro studies about CRRA value affirm each other for the first time in the literature. Furthermore, equity and risk-free asset investors are pinned down to be insufficient risk-loving, which can be considered a type of risk-averse behavior. Hence it can be said that calculated values and risk attitude determination align with empirical literature. This shows that derived model is valid and make CCAPM work without calibration.

Experience shows that disciplinary science cannot describe life without contradictions. We show that one of the fundamental reasons is the disciplinarity itself: the disciplines deal with a limited set of quantities. This way some 'outlaw' quantities are not measured and the discipline does not have laws about them. All laws of science are based on approximations and the approximations must be different for inanimate and life sciences. Studying ions is special because ions belong simultaneously to thermodynamics and electricity, but neither of those disciplines alone can describe biological processes. One needs a cross-disciplinary discussion and maybe a new scientific discipline. We provide a method for handling the different interaction speeds characterizing the ion transport. Electrolytes in living matter introduce further peculiarities with their closed volumes, internal structure, and slow processes. Their meticulous analysis led to the appropriate approximations, leading to the correct scientific description. As a success story, the cross-disciplinary theory of neuronal operation has been developed.

In this work, we investigate the generation and propagation of gravitational waves within a minimal gravitational SME (Standard Model Extension). Starting from the modified graviton dispersion relation derived in the linearized gravity sector, we analyze the polarization properties of gravitational waves in the transverse-traceless tensor sector. We then construct the retarded Green function associated with the Lorentz-violating wave operator, explicitly verifying the causal structure of the theory and identifying the modified propagation speeds of the tensorial modes. In addition, we study the source-induced emission of gravitational waves from a binary black-hole system. We show that the gravitational waveform preserves the standard quadrupolar amplitude and polarization structure, while Lorentz-violating effects enter exclusively through a modification of the retarded time. As a result, the spatial components of the metric perturbation $h_{ij}(t,r)$ acquire a phase shift determined by the SME coefficients. Finally, we estimate phenomenological bounds to the model under consideration.

In this paper, we construct a functorial quantization of (co)Poisson Hopf algebras within a broad categorical framework. We further introduce categories naturally associated with (co)Poisson Hopf algebras, namely Drinfeld-Yetter modules. These categories provide a canonical setting in which we define explicit dequantization functors that are inverse to the quantization functors. Using this framework, we also establish functorial (de)quantization results for the corresponding module categories. Finally, we recover the classical results of Etingof and Kazhdan as special cases of our construction and discuss applications to deformation quantization à la Tamarkin.

In this article, for a large class of rational self-similar IFS's wich contains the middle-third Cantor set, we compute the Hausdorff dimension of elements a self-similar set that are $ψ$-approximable by rational belonging to this set and satisfying that its numerator has a bounded number of distinct prime divisors. This paper is based on a previous version in which the proof of a lemma (Lemma 3.8) was incorrect.