The Kohn-Luttinger (KL) mechanism of pairing, which describes superconductivity emergent from repulsive interactions, typically yields Cooper pairs at high angular-momentum ($\ell > 0$) and extremely low transition temperatures ($T_c$). Here, we reveal an inter-layer s-wave ($\ell=0$) KL superconductivity with greatly elevated $T_c$ in a multi-layer Hubbard model, which prototypes stacked two-dimensional (2D) electrons in layered van der Waals materials. By employing determinant quantum Monte Carlo and dynamical mean-field theory simulations, we show that a strong pairing attraction $V^{*}$, without the mediation of collective modes, can emerge between inter-layer electrons in the system. As inter-layer repulsion $U$ increases, $V^{*}$ evolves from a conventional KL relation of $V^{*} \propto -U^2$, to a linear strong-coupling scaling of $V^{*} \propto -U$, resulting in enhanced superconductivity at large $U$. This strong-coupling KL pairing is robust against changes in lattice geometries and dimensionalities, and it can persist, in the presence of a large remnant Coulomb repulsion $U^{*}$ between pairing electrons. Using \textit{ab initio} calculations, we propose a few 2D layered van der Waals materials that can potentially realize and control this unconventional superconductivity.

For 20 years the beautiful structure in the grid cell code has presented an attractive puzzle: what computation do these representations subserve, and why does it manifest so curiously in neurons. The first question quickly attracted an answer: grid cells subserve path-integration, the ability to keep track of one's position as you move about the world. Subsequent work has only solidified this link: bottom-up mechanistic models that perform path-integration match the measured neural responses, while experimental perturbations that selectively disrupt grid cell activity impair performance on path-integration dependent tasks. A more controversial area of work has been top-down normative modelling: why has the brain chosen to compute like this? Floods of ink have been spilt attempting to build a precise link between the population's objective and the measured implementation. The holy grail is a normative link with broad predictive power which generalises to other neural systems. We review this literature and argue that, despite some controversies, the literature largely agrees that grid cells can be explained as a (1) biologically plausible (2) high fidelity, non-linearly decodable code for position that (3) subserves path-integration. As a rare area of neuroscience with mature theoretical and experimental work, this story holds lessons for normative theories of neural computations, and on the risks and rewards of integrating task-optimised neural networks into such theorising.

We introduce a two-tooth bosonic quantum comb that captures the sequential interactions between a thermal absorber and a long-lived coherent probe. The comb provides a causal, multi-time description of coherence transport, tracking how the probe records both instantaneous fluctuations and their temporal correlations. Using a process-tensor formulation, we derive closed form expressions showing that interference between the two interaction windows generates a non-monotonic memory response that reflects a fundamental competition between the absorbers thermal population and its dynamical correlations. By sweeping the temporal separation between the interaction windows, the probe directly samples the absorbers population correlator, enabling bosonic noise spectroscopy that discriminates Markovian temperature noise from slow or spectrally structured fluctuations. The approach is readily compatible with circuit-QED platforms and offers a general method for probing fluctuating bosonic environments.

Why do neurons encode information the way they do? Normative answers to this question model neural activity as the solution to an optimisation problem; for example, the celebrated efficient coding hypothesis frames neural activity as the optimal encoding of information under efficiency constraints. Successful normative theories have varied dramatically in complexity, from simple linear models (Atick & Redlich '90), to complex deep neural networks (Lindsay '21). What complex models gain in flexibility, they lose in tractability and often understandability. Here, we split the difference by constructing a set of tractable but flexible normative representational theories. Instead of optimising the neural activities directly, following Sengupta et al. '18, we optimise the representational similarity, a matrix formed from the dot products of each pair of neural responses. Using this, we show that a large family of interesting optimisation problems are convex. This family includes problems corresponding to linear and some non-linear neural networks, and problems from the literature not previously recognised as convex, such as modified versions of semi-nonnegative matrix factorisation or nonnegative sparse coding. We put these findings to work in three ways. First, we provide the first necessary and sufficient identifiability result for a form of semi-nonnegative matrix factorisation. Second, we show that if neural tunings are `different enough' then they are uniquely linked to the optimal representational similarity, partially justifying the use of single neuron tuning analysis in neuroscience. Finally, we use the tractable nonlinearity of some of our problems to explain why dense retinal codes, but not sparse cortical codes, optimally split the coding of a single variable into ON & OFF channels. In sum, we identify a space of convex problems, and use them to derive neural coding results.

In 2006 (J. Differential Equ.), Lou proved that, once the intrinsic growth rate $r$ in the logistic model is proportional to the spatially heterogeneous carrying capacity $K$ ($r=K^1$), the total population under the regular diffusion exceeds the total of the carrying capacity. He also conjectured that the dependency of the total population on the diffusion coefficient is unimodal, increasing to its maximum and then decreasing to the asymptote which is the total of the carrying capacity. DeAngelis et al (J. Math. Biol. 2016) argued that the prevalence of the population over the carrying capacity is only observed when the growth rate and the carrying capacity are positively correlated, at least for slow dispersal. Guo et al (J. Math. Biol. 2020) justified that, once $r$ is constant ($r=K^0$), the total population is less than the cumulative carrying capacity. Our paper fills up the gap for when $r=K^λ$ for any real $λ$, disproving an assumption that there is a critical $λ^{\ast} \in (0,1)$ at which the tendency of the prevalence of the carrying capacity over the total population size changes, demonstrating instead that the relationship is more complicated. In addition, we explore the dependency of the total population size on the diffusion coefficient when the third parameter of the dispersal strategy $P$ is involved: the diffusion term is $d Δ(u/P)$, not just $d Δu$, for any $λ$. We outline some differences from the random diffusion case, in particular, concerning the profile of the total population as a function of the diffusion coefficient.

We confirm a recent conjecture of Xin and Zhang, which establishes a simple product formula for the characteristic polynomial of an $(n-1) \times (n-1)$ tridiagonal matrix $C$. This characteristic polynomial arises from a recurrence relation that enumerates $n \times n$ nonnegative integer matrices with all row and column sums equal to $t$, also called the Ehrhart polynomial of the $n$th Birkhoff polytope. Moreover, we extend our method to broader families of tridiagonal matrices.

The notion of sectional-hyperbolicity is a weakened form of hyperbolicity introduced for vector fields in order to understand the dynamical behavior of certain higher-dimensional systems such as the multidimensional Lorenz attractor. In this paper we address the questions proposed in [\emph{Math. Z.}, \textbf{298} (2021), 469-488] and we provide a partial answer by proving that a $C^1$-generic non-trivial sectional-hyperbolic chain-recurrent class, not necessarily Lyapunov stable, satisfies a trichotomy: it is either a homoclinic loop, a union of saddle connections between singularities, or it is robustly a homoclinic class.

We construct a diagrammatic categorification of the spherical module over the Hecke algebra. We establish a basis for the morphism spaces of this category, and prove that it is equivalent to an existing algebraic spherical category.

In this short review paper the detailed analysis of six two-dimensional quantum {\it superintegrable} systems in flat space is presented. It includes the Smorodinsky-Winternitz potentials I-II (the Holt potential), the Fokas-Lagerstrom model, the 3-body Calogero and Wolfes (equivalently, $G_2$ rational, or $I_6$) models, and the Tremblay-Turbiner-Winternitz (TTW) system with integer index $k$. It is shown that all of them are exactly-solvable, thus, confirming the Montreal conjecture (2001); they admit algebraic forms for the Hamiltonian and both integrals (all three can be written as differential operators with polynomial coefficients without a constant term), they have polynomial eigenfunctions with the invariants of the discrete symmetry group of invariance taken as variables, they have hidden (Lie) algebraic structure $g^{(k)}$ with various $k$, and they possess a (finite order) polynomial algebras of integrals. Each model is characterized by infinitely-many finite-dimensional invariant subspaces, which form the infinite flag. Each subspace coincides with the finite-dimensional representation space of the algebra $g^{(k)}$ for a certain $k$. In all presented cases the algebra of integrals is a 4-generated $(H, I_1, I_2, I_{12}\equiv[I_1, I_2])$ infinite-dimensional algebra of ordered monomials of degrees 2,3,4,5, which is a subalgebra of the universal enveloping algebra of the hidden algebra.

Quantum simulation of non-Abelian gauge theories requires careful handling of gauge redundancy. We address this challenge by presenting universal principles for treating gauge symmetry that apply to any quantum simulation approach, clarifying that physical states need not be represented solely by gauge singlets. Both singlet and non-singlet representations are valid, with distinct practical trade-offs, which we elucidate using analogies to BRST quantization. We demonstrate these principles within a complete quantum simulation framework based on the orbifold lattice, which enables explicit and efficient circuit constructions relevant to real-world QCD. For singlet-based approaches, we introduce a Haar-averaging projection implemented via linear combinations of unitaries, and analyze its cost and truncation errors. We also introduce an efficient simulation protocol with an additional term to the Hamiltonian that eliminates non-singlet states from the low-energy spectrum. Beyond the singlet-approach, we show how non-singlet approaches can yield gauge-invariant observables through wave packets and string excitations. This non-singlet approach is proven to be both universal and efficient. Working in temporal gauge, we provide explicit mappings of lattice Yang-Mills dynamics to Pauli-string Hamiltonians suitable for Trotterization. Classical simulations of small systems validate convergence criteria and quantify truncation and Trotter errors, showing concrete resource estimates and scalable circuit recipes for SU$(N)$ gauge theories. Our framework provides both conceptual clarity and practical tools toward quantum advantage in simulating non-Abelian gauge theories.

Multimodal large language models (MLLMs) are built on text-only LLMs by incorporating additional modalities, enabling multimodal understanding and a broader range of applications. However, these additions introduce a previously unexplored energy trade-off across modalities that remains poorly understood, as most prior work focuses on text-only models. In this paper, we examine modality inflation, a key source of inefficiency in which multimodal inputs increase inference workloads through extra encoding stages and expanded token sequences. We provide the first detailed, stage-level analysis of energy consumption in MLLM inference by breaking the pipeline into vision encoding, prefill, and decoding stages. Using four representative MLLMs evaluated on NVIDIA A100 GPU, we quantify the additional energy required for multimodal inference compared to text-only baselines, observing overheads ranging from 17% to 94% across models for identical inputs. Our results show that energy bottlenecks differ widely across model architectures, stemming either from compute-heavy vision encoders or from the downstream impact of large visual token sequences during prefill. By examining GPU power traces, we further uncover substantial GPU underutilization during multimodal execution and show that input complexity leads to markedly different energy scaling behaviors across models. Finally, we demonstrate that stage-wise dynamic voltage and frequency scaling (DVFS) is an effective optimization, allowing energy savings with only modest performance impact. Together, these findings offer practical insights and concrete guidance for designing more energy-efficient multimodal LLM serving systems.

Similarities and differences between Kolmogorov scale-by-scale equilibria/non-equilibria for velocity and scalar fields are investigated in the intermediate layer of a fully developed turbulent channel flow with a passive scalar/temperature field driven by a uniform heat source. The analysis is based on intermediate asymptotics and direct numerical simulations at different Prandtl numbers lower than unity. Similarly to what happens to the velocity fluctuations, for the fluctuating scalar field Kolmogorov scale-by-scale equilibrium is achieved asymptotically around a length scale $r_{min}$, which is located below the inertial range. The lengthscale $r_{min}$ and the ratio between the inter-scale transfer and dissipation rates at $r_{min}$ vary following power laws of the Prandtl number, with exponents determined by matched asymptotics based on the hypothesis of homogeneous two-point physics in non-homogeneous turbulence. The interscale transfer rates of turbulent kinetic energy and passive scalar variance are globally similar but show evident differences when their aligned/anti-aligned contributions are considered.

Light polarization plays a crucial role in optical-cavity experiments; however, mirror birefringence presents a significant challenge that must be addressed carefully. In this study, a rigorous, nonperturbative framework is developed to quantify birefringence effects by incorporating variations in reflectance and polarization misalignment. We analyze the impact of this framework on the sensitivity of axion-like particle (ALP) dark-matter searches. The results show that both birefringence and misalignment contribute to sensitivity degradation in the low-mass regime; however, the adverse effects of misalignment can be mitigated by selecting a postselection angle greater than the misalignment angle. Furthermore, birefringence produces an additional resonance peak in the high-mass region, which remains largely unaffected by misalignment and postselection variations. This rigorous framework underscores the importance of considering birefringence in high-precision optical-cavity experiments for ALP detection.

We develop a variational regularisation framework that enables analytical solutions of the stationary de~Broglie--Bohm wave equation. The formulation begins with a Fisher-information-augmented action functional for the probability density and phase fields, yielding the Madelung (Hamilton--Jacobi and continuity) equations and, upon complex recombination, a Schrödinger-type equation with a parametric information coupling $μ$. Beyond this density-based formulation, we introduce a variational regularisation scheme for the de~Broglie--Bohm equations that combines a global Fisher-information regularisation at the level of the action functional with a shell-level regularisation arising from stationary flux closure. This reduction isolates the regularisation mechanism in the spatial momentum flow and yields constrained Euler--Lagrange equations governing admissible amplitude configurations. The resulting first integral possesses an elliptic structure whose admissible asymptotic branch enforces a universal canonical relation $p(x)x \to μ/2$ near amplitude zeros. The framework yields closed-form analytical solutions for standard potentials and reveals a systematic inverse-square regularising term in the effective potential. The associated elliptic discriminant defines a geometric length scale that, for $μ=\hbar$, naturally reduces to the reduced Compton wavelength. Canonical Bohmian regularisation therefore appears as a variational admissibility condition on density dynamics, producing structurally stable analytical branches and modified yet consistent energy spectra within stationary dBB mechanics.

Analysis of space-charge effects on electron emission typically makes some assumption of continuity and smoothness, whether this is continuity of charge as in the classical derivation of the Child-Langmuir current, or the mean-field approximation used in particle-in-cell simulations. However, when studying the physics of electron emission and propagation at the mesoscale it becomes necessary to consider the discrete nature of electronic charge to account for the space-charge effect of each individual point charge. In this paper we give an extensive analysis of some previous work on the distribution of electrons under space-charge limited conditions. We examine the spacing of electrons as they are emitted from a planar surface, We present simplified models for analysis of such conditions to derive scaling laws for emission and compare them to computer simulations.

This paper investigates Nekhoroshev-type stability for solutions of ultra-differentiable regularity in Schrödinger equations with non-local nonlinear terms, employing the method of rational normal forms. We establish the first rigorous results for logarithmic ultra-differentiable regularity in infinite-dimensional Hamiltonian systems without external parameters. Under Gevrey class regularity assumptions, we achieve the stability times matching Bourgain's conjectured optimal stability time in \cite{B04}. Furthermore, we introduce a novel global vector field norm adapted to the rational normal form framework. This norm eliminate the need for degree tracking during the iteration process, thereby enabling a unified treatment of nonlinear terms.

Mixture models are widely used in modeling heterogeneous data populations. A standard approach of mixture modeling assumes that the mixture component takes a parametric kernel form. In many applications, making parametric assumptions on the latent subpopulation distributions may be unrealistic, which motivates the need for nonparametric modeling of the mixture components themselves. In this paper, we study finite mixtures with nonparametric mixture components, using a Bayesian nonparametric modeling approach. In particular, it is assumed that the data population is generated according to a finite mixture of latent component distributions, where each component is endowed with a Bayesian nonparametric prior such as the Dirichlet process mixture. We present conditions under which the individual mixture component's distribution can be identified, and establish posterior contraction behavior for the data population's density, as well as densities of the latent mixture components. We develop an efficient MCMC algorithm for posterior inference and demonstrate via simulation studies and real-world data illustrations that it is possible to efficiently learn complex forms of probability distribution for the latent subpopulations. In theory, the posterior contraction rate of the component densities is nearly polynomial, which is a significant improvement over the logarithmic convergence rates of estimating mixing measures via deconvolution.

We study simple extensions of pointed finite tensor categories, that is, tensor categories $\mathcal{C}$ admitting an abelian decomposition $\mathcal{C} \cong \mathcal{D} \oplus \mathcal{M}$ where $\mathcal{D}$ is a pointed tensor subcategory and $\mathcal{M}$ has a unique simple projective object. Such categories provide a natural generalization of near-group categories. Our results concern the braided case. We prove that every non-degenerate braided non-semisimple near-group category is a braided simple extension of $\mathrm{sRep}(W\oplus W^*)$ with non-trivial braiding for which $\mathrm{sRep}(W)$ is Lagrangian. Moreover, any braided non-semisimple near-group category $\mathcal{C}$ arises canonically as an extension of such a category by $\mathrm{Rep}(G)$, where $G$ is the Picard group of a symmetric subcategory determined by the unique simple projective object of $\mathcal{C}$.

Industry 5.0's increasing integration of IT and OT systems is transforming industrial operations but also expanding the cyber-physical attack surface. Industrial Control Systems (ICS) face escalating security challenges as traditional siloed defences fail to provide coherent, cross-domain threat insights. We present BRIDG-ICS (BRIDge for Industrial Control Systems), an AI-driven Knowledge Graph (KG) framework for context-aware threat analysis and quantitative assessment of cyber resilience in smart manufacturing environments. BRIDG-ICS fuses heterogeneous industrial and cybersecurity data into an integrated Industrial Security Knowledge Graph linking assets, vulnerabilities, and adversarial behaviours with probabilistic risk metrics (e.g. exploit likelihood, attack cost). This unified graph representation enables multi-stage attack path simulation using graph-analytic techniques. To enrich the graph's semantic depth, the framework leverages Large Language Models (LLMs): domain-specific LLMs extract cybersecurity entities, predict relationships, and translate natural-language threat descriptions into structured graph triples, thereby populating the knowledge graph with missing associations and latent risk indicators. This unified AI-enriched KG supports multi-hop, causality-aware threat reasoning, improving visibility into complex attack chains and guiding data-driven mitigation. In simulated industrial scenarios, BRIDG-ICS scales well, reduces potential attack exposure, and can enhance cyber-physical system resilience in Industry 5.0 settings.

Precise irrigation management requires robust classification of plant water stress. We expanded a morpho-kinematic (MK) framework that derives canopy-movement features from RGB time-lapse imaging evaluating how methodological refinements affect robustness and fine discrimination across four irrigation treatments representing distinct stress histories. The study tested both a biological (Agg) versus an isogonal (Unif) sectoring of the canopy image, within an additive scheme where to the baseline (i.e. flattened MK features, A0) were sequentially added non-linear descriptors (A1), irrigation-context variables (i.e. dry time, A2), and their interactions with baseline (A3). The multi-class problem was decomposed in biologically meaningful binary tasks, and the final classification confronted an adaptive - to the performance obtained in the out-of-fold predictions inside the leave-one-sample-out validation framework - linear opinion pooling (ALOP) ensemble, evaluated across its full parameter space, against hierarchical cascades (HCC). In our combined dataset from two sequential Lactuca sativa experiments (144 sample-days) ALOP median outperformed HCC in every configuration, while non-linear and contextual enrichments (A1-A2) produced consistent improvements in terms of prediction stability, variability (for ALOP), and balanced accuracy (BA). The highest balanced accuracy (median BA = 0.96) was reached under Unif scheme in A3, yet the Agg configuration in A2 achieved the best compromise between accuracy (median BA approx 0.91) and robustness. Concluding, this study identifies methodological pathways that strengthen resilience and transferability of movement-based water-stress classification, establishing a solid foundation for generalizable, low-cost phenotyping.

We study theoretically the structure and formation of the deeply bound $\bar{p}$ atoms. We find that the widths of the atomic states are narrower than the level spacing even for deeply bound states so that the well-isolated deeply bound $\bar{p}$ atoms are expected to exist. We also find the $\bar{p}$-nuclear states with huge widths. For the observation of the deep $ {\bar p}$-atomic states, we investigate theoretically the $(\bar{p}, p)$ reactions for $^{12}$C, $^{16}$O, and $^{31}$P target nuclei. We find that the momentum transfer of the $( {\bar p},p)$ reaction is small and the formation of the $ {\bar p}$-atomic states can be observed as the discrete peak structures in the $( {\bar p},p)$ spectrum. We conclude that the $(\bar{p}, p)$ reactions are very much suited for the $\bar{p}$ atom formation and the spectra of the reaction are expected to provide new valuable information on the $ {\bar p}$ atoms and $ {\bar p}$-nucleus interaction.

Canada is internationally recognized for its leadership in science and its commitment to equity, diversity, and inclusion (EDI) in STEM (science, technology, engineering, and math) fields. Despite this leadership, limited research has examined gender disparities in scientific publishing within the Canadian context. This study analyzes over 67,000 articles published in 24 Canadian Science Publishing (CSP) journals between 2010 and 2021 to better understand patterns of gender representation. Findings show that women accounted for less than one-third of published authors across CSP journals. Representation varied by discipline, with higher proportions of women in biomedical sciences and lower proportions of women in engineering - trends that mirror broader national and global patterns. Notably, the proportion of women submitting manuscripts closely matched those published, suggesting that broader workforce disparities may play a larger role than publication bias. Women were less likely to be solo authors or to hold prominent authorship positions, such as first or last author - roles typically associated with research leadership and career advancement. These findings point to the need for a two-fold response: continued efforts to address systemic barriers to women's participation in science, and a review of publishing practices to ensure equitable access, recognition, and inclusion for all researchers.

We develop a novel framework to engineer persistent oscillatory modes in Markovian open quantum systems governed by a time-independent Lindblad master equation. We show that oscillatory modes can be created when the Hamiltonian and jump operator can be expressed in the same block-diagonal form. A key feature of the framework is that the dissipator of the Lindblad master equation are generally non-zero. We identify the weak and strong conditions, where the onset of the oscillatory modes is dependent and independent of the parameters of the system, respectively. Our method extends beyond the typical decoherence-free subspace approach, in which the dissipator is zero. We demonstrate the applicability of this framework using various models, showing how carefully tailored system-environment interactions can produce sustained coherent oscillations.

Transformers have gained popularity in machine learning due to their application in the field of natural language processing. They manipulate and process text efficiently, capturing long-range dependencies among data and performing the next word prediction. On the other hand, gate-based quantum computing is based on controlling the register of qubits in the quantum hardware by applying a sequence of gates, a process which can be interpreted as a low level text programming language. We develop a transformer model capable of transpiling quantum circuits from the qasm standard to other sets of gates native suited for a specific target quantum hardware, in our case the set for the trapped-ion quantum computers of IonQ. The feasibility of a translation up to five qubits is demonstrated with a percentage of correctly transpiled target circuits equal or superior to 99.98%. Regardless the depth of the register and the number of gates applied, we prove that the complexity of the transformer model scales, in the worst case scenario, with a polynomial trend by increasing the depth of the register and the length of the circuit, allowing models with a higher number of parameters to be efficiently trained on HPC infrastructures.

We study approximation algorithms for two natural generalizations of the Maximum Quadratic Assignment Problem (MaxQAP). In the Maximum List-Restricted Quadratic Assignment Problem, each node in one partite set may only be matched to nodes from a prescribed list. For instances on $n$ nodes where every list has size at least $n - k$, we design a randomized $O(\sqrt{n}+k)$-approximation algorithm based on the linear-programming relaxation and randomized rounding framework of Makarychev, Manokaran, and Sviridenko. In the Maximum Quadratic $b$-Matching Assignment Problem, we seek a $b$-matching that maximizes the MaxQAP objective. We refine the standard MaxQAP relaxation and combine randomized rounding over $b$ independent iterations with a polynomial-time algorithm for maximum-weight $b$-matching problem to obtain an $O(\sqrt{bn})$-approximation. When $b$ is constant and all lists have size $n - O(\sqrt{n})$, our guarantees asymptotically match the best known approximation factor for MaxQAP, yielding the first approximation algorithms for these two variants.

Understanding how microscopic interactions control macroscopic phase transitions is central to quantum materials, where charge density waves (CDWs), Mott states, and superconductivity often compete. In $1T$-TaS$_2$, this competition is tied to a sequence of CDW phases and a hysteretic metal-insulator transition, but details of the transition, especially the role of interlayer coupling, remain unresolved. In this work, spectroscopic ellipsometry is used to determine the uniaxial dielectric response of bulk $1T$-TaS$_2$ from room temperature down to the commensurate insulating state. The room-temperature data reveal natural type-II hyperbolic behavior in the visible range, with negative in-plane and positive out-of-plane permittivity. Temperature-dependent ellipsometry combined with anisotropic Bruggeman effective medium analysis shows that the metallic domains responsible for percolation evolve from disc-like to needle-like shapes, and that, upon heating, an additional intermediate phase emerges. These results identify the transition in $1T$-TaS$_2$ as a three-dimensional, interlayer-driven percolation process and establish this material as a natural, tunable hyperbolic medium.

Rotational optical tweezers are used to probe the mechanical properties of unknown microsystems. Quantifying the angular trap stiffness is essential for interpreting the rotational dynamics of probe particles. While methods to determine trap stiffness are well established for translational degrees of freedom, angular trapping is often treated analogously even though rotational and translational motions are sensitive to distinct experimental parameters and offer separate insights. This work details passive analysis techniques for determining the angular trap stiffness within the linear restoring torque model and examines the influence of several factors unique to rotational optical tweezers. We show that the parameters of an ancillary measurement beam can be tuned to minimise its influence on angular trapping dynamics, providing necessary improvements for nanoparticle-scale analysis. We also explore the combined effects of shape-induced and material birefringence in spheroidal vaterite probes, and present a framework for assessing hydrodynamic and inertial contributions.

Neuromorphic computing aspires to overcome the intrinsic inefficiencies of von Neumann architectures by co-locating memory and computation in physical devices that emulate biological neurons and synapses. Memristive materials stand at the core of this paradigm, enabling non-volatile, history-dependent electronic responses. While inorganic oxides currently dominate the field, molecular and polymeric systems can offer untapped advantages in terms of chemical tunability, structural flexibility, low-cost processing, and biocompatibility. However, progress has been hindered by the absence of a theoretical framework able to rationalize how molecular structure translates into memristive function. Here, a multiscale computational perspective is presented, outlining how quantum chemistry and molecular dynamics, among other approaches, can be integrated into a coherent methodology to design next-generation organic memristors. Three mechanisms, ionic migration, redox-driven switching, and conduction interplay in chiral molecules are examined as representative routes toward molecular neuromorphic hardware. The opportunities and challenges associated with each mechanism are discussed, together with a view on how a theoretically guided roadmap can accelerate the emergence of chemically engineered synaptic materials.

We explore the leptonic sector of a recently proposed supersymmetric SO(10) model with supersymmetry breaking in the 3-10 TeV range. A new ingredient in this work is the requirement that the observed baryon asymmetry is explained via non-thermal leptogenesis, which can be realized in a large class of supersymmetric hybrid inflation models including SO(10). We provide estimates for the masses of the three Standard Model neutrinos (with the lightest mass $m_1\approx 5$ meV) as well as the three right-handed neutrinos ($M_1\approx 10^9$ GeV and $M_{2,3}\approx 10^{13}$ GeV). The best fit estimate for the leptonic CP violating parameter $δ_\mathrm{PMNS}\approx 235^\circ$, and the value of the neutrinoless double beta decay mass parameter $m_{ββ}\approx 0.18$ meV. A numerical analysis broadens the predicted range for $δ_\mathrm{PMNS}$ ($100^\circ$-$300^\circ$), but leaves largely intact the predictions for the six (light and heavy) neutrino masses and $m_{ββ}$. Our statistical analysis, which yields the likelihood-predicted ranges of the observables, is fully consistent with JUNO's newly released first measurement of reactor neutrino oscillations in the $Δm^2_{12}$-$\sin^2θ_{12}$ plane, with JUNO improving the precision by a factor of 1.6 relative to the combination of all previous measurements. The implementation of successful non-thermal leptogenesis allows us to provide estimates for the inflaton mass ($m_χ\approx 7\times 10^{9}$ GeV) and the reheating temperature ($T_\mathrm{RH}\approx 4\times 10^6$ GeV).

We investigate the conditions under which the mean-field formulation of a probabilistic, totalistic cellular automaton approximates the logistic equation. We show that this goal can be only fulfilled for an infinite-range neighborhood. We numerically study the corresponding one-dimensional implementation, showing that the mean-field description is obviously approached by shuffling the configuration at each time step, but also by rewiring a fraction of links, either at each time step, or using the same random sampling once and for all, in the spirit of the "small-world" mechanism. We show that it is possible to obtain a good approximation of the logistic behavior already with a fraction of rewired links different from one. We also show that there is a bifurcation cascade of the density as a function of the fraction of the rewired links, and that this scenario also holds for a deterministic, totalistic CA with the same basic symmetries of the probabilistic one.