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It is well known that a finite-dimensional Lie algebra over a field of characteristic zero is simple exactly when its derivation algebra is simple. In this paper we characterize those Lie algebras of arbitrary dimension over any field that have a simple derivation algebra. As an application we classify the Lie algebras that have a complete simple derivation algebra and are either finite-dimensional over an algebraically closed field of prime characteristic $p>3$ or $\mathbb{Z}$-graded of finite growth over an algebraically closed field of characteristic zero., Comment: 13 pages

In the era of dense retrieval, document indexing and retrieval is largely based on encoding models that transform text documents into embeddings. The efficiency of retrieval is directly proportional to the number of documents and the size of the embeddings. Recent studies have shown that it is possible to reduce embedding size without sacrificing - and in some cases improving - the retrieval effectiveness. However, the methods introduced by these studies are query-dependent, so they can't be applied offline and require additional computations during query processing, thus negatively impacting the retrieval efficiency. In this paper, we present a novel static pruning method for reducing the dimensionality of embeddings using Principal Components Analysis. This approach is query-independent and can be executed offline, leading to a significant boost in dense retrieval efficiency with a negligible impact on the system effectiveness. Our experiments show that our proposed method reduces the dimensionality of document representations by over 50% with up to a 5% reduction in NDCG@10, for different dense retrieval models.

Recommender Systems (RSs) are pivotal in diverse domains such as e-commerce, music streaming, and social media. This paper conducts a comparative analysis of prevalent loss functions in RSs: Binary Cross-Entropy (BCE), Categorical Cross-Entropy (CCE), and Bayesian Personalized Ranking (BPR). Exploring the behaviour of these loss functions across varying negative sampling settings, we reveal that BPR and CCE are equivalent when one negative sample is used. Additionally, we demonstrate that all losses share a common global minimum. Evaluation of RSs mainly relies on ranking metrics known as Normalized Discounted Cumulative Gain (NDCG) and Mean Reciprocal Rank (MRR). We produce bounds of the different losses for negative sampling settings to establish a probabilistic lower bound for NDCG. We show that the BPR bound on NDCG is weaker than that of BCE, contradicting the common assumption that BPR is superior to BCE in RSs training. Experiments on five datasets and four models empirically support these theoretical findings. Our code is available at \url{https://anonymous.4open.science/r/recsys_losses} ., Comment: main paper 8 pages, 4 figures

Fluorescence imaging allows for non-invasively visualizing and measuring key physiological parameters like pH and dissolved oxygen. In our work, we created two ratiometric fluorescent microsensors designed for accurately tracking dissolved oxygen levels in 3D cell cultures. We developed a simple and cost-effective method to produce hybrid core-shell silica microparticles that are biocompatible and versatile. These sensors incorporate oxygen-sensitive probes (Ru(dpp) or PtOEP) and reference dyes (RBITC or A647 NHS-Ester). SEM analysis confirmed efficient loading and distribution of the sensing dye on the outer shell. Fluorimetric and CLSM tests demonstrated the sensors' reversibility and high sensitivity to oxygen, even when integrated into 3D scaffolds. Aging and bleaching experiments validated the stability of our hybrid core-shell silica microsensors for 3D monitoring. The Ru(dpp)-RBITC microparticles showed the most promising performance, especially in a pancreatic cancer model using alginate microgels. By employing computational segmentation, we generated 3D oxygen maps during live cell imaging, revealing oxygen gradients in the extracellular matrix and indicating a significant decrease in oxygen levels characteristic of solid tumors. Notably, after 12 hours, the oxygen concentration dropped to a hypoxic level of PO2 2.7 +/- 0.1%.

The Zirconium (Z = 40) isotopic chain has attracted interest for more than four decades. The abrupt lowering of the energy of the first $2^+$ state and the increase in the transition strength B(E2; $2_1^\rightarrow 0_1^+$ going from $^{98}$Zr to $^{100}$Zr has been the first example of "quantum phase transition" in nuclear shapes, which has few equivalents in the nuclear chart. Although a multitude of experiments have been performed to measure nuclear properties related to nuclear shapes and collectivity in the region, none of the measured lifetimes were obtained using the Recoil Distance Doppler Shift method in the $\gamma\gamma$-coincidence mode where a gate on the direct feeding transition of the state of interest allows a strict control of systematical errors. This work reports the results of lifetime measurements for the first yrast excited states in $^{98-104}$Zr carried out to extract reduced transition probabilities. The new lifetime values in $\gamma\gamma$-coincidence and $\gamma$-single mode are compared with the results of former experiments. Recent predictions of the Interacting Boson Model with Configuration Mixing, the Symmetry Conserving Configuration Mixing model based on the Hartree-Fock-Bogoliubov approach and the Monte Carlo Shell Model are presented and compared with the experimental data.

The numerical solution of the many-body problem of interacting electrons and ions beyond the adiabatic approximation is a key challenge in condensed matter physics, chemistry, and materials science. Traditional methods to solve the multi-component quantum Hamiltonian tend to be specialized electrons or ions and can suffer from a methodological gap when applied to both electrons and ions simultaneously. In addition, ionic techniques often limited as $T\to$ 0K, whereas electronic methods are designed for 0K. Thus, efficient strategies that simultaneously address the thermal fluctuations of ions at ambient temperature without struggling to describe the electronic quantum state from first principles are missing. This work extends the self-consistent harmonic approximation for the ions to include also the electrons. The approach minimizes the total free energy by optimizing an \emph{ansatz} density matrix, solving a fermionic self-consistent harmonic Hamiltonian on a curved manifold, which is parametrized through a neural network. We demonstrate that this approach, designed initially for a flat Cartesian space to treat quantum nuclei at finite temperatures, can efficiently tackle both the ground and excited state properties of electronic systems, thus paving the way to a unified quantum description for electrons and atomic nuclei. Importantly, this approach preserves an analytical expression for entropy, enabling the direct computation of free energies and phase diagrams of materials. We benchmark the numerical implementation in several prototypical cases, proving that it captures quantum tunneling, electron-ion cusps, and static electronic correlations in the dissociation of H$_2$, where other mean-field approaches fail.

We present the first measurement of the $^{47}$K($d,p\gamma$)$^{48}$K transfer reaction, performed in inverse kinematics using a reaccelerated beam of $^{47}$K. The level scheme of $^{48}$K has been greatly extended with nine new bound excited states identified and spectroscopic factors deduced. Detailed comparisons with SDPF-U and SDPF-MU shell-model calculations reveal a number of discrepancies with these results, and a preference for SDPF-MU is found. Intriguingly, an apparent systematic overestimation of spectroscopic factors and a poor reproduction of the energies for 1$^-$ states suggests that the mixing between the $\pi s^{\,\,\,1}_{1/2} d^{\,\,\,4}_{3/2}$ and $\pi s^{\,\,\,2}_{1/2} d^{\,\,\,3}_{3/2}$ proton configurations in $^{48}$K is not correctly described using current interactions, challenging our descriptions of light $N=28$ nuclei., Comment: 7 pages, 3 figures, 1 table

Descriptive and inferential social network analysis has become common in public administration studies of network governance and management. A large literature has developed in two broad categories: antecedents of network structure, and network effects and outcomes. A new topic is emerging on network interventions that applies knowledge of network formation and effects to actively intervene in the social context of interaction. Yet, the question remains how might scholars deploy and determine the impact of network interventions. Inferential network analysis has primarily focused on statistical simulations of network distributions to produce probability estimates on parameters of interest in observed networks, e.g. ERGMs. There is less attention to design elements for causal inference in the network context, such as experimental interventions, randomization, control and comparison networks, and spillovers. We advance a number of important questions for network research, examine important inferential challenges and other issues related to inference in networks, and focus on a set of possible network inference models. We categorize models of network inference into (i) observational studies of networks, using descriptive and stochastic methods that lack intervention, randomization, or comparison networks; (ii) simulation studies that leverage computational resources for generating inference; (iii) natural network experiments, with unintentional network-based interventions; (iv) network field experiments, with designed interventions accompanied by comparison networks; and (v) laboratory experiments that design and implement randomization to treatment and control networks. The article offers a guide to network researchers interested in questions, challenges, and models of inference for network analysis in public administration.

Low-lying states of $^{94}$Zr were investigated via low-energy multi-step Coulomb excitation. From the measured $\gamma$-ray yields, 13 reduced transition probabilities between low-spin states were determined, together with the spectroscopic quadrupole moments of the $2_{1,2}^+$ states. Based on this information, for the first time in the Zr isotopic chain, the shapes of the $0_{1,2}^+$ states including their deformation softness were inferred in a model-independent way using the quadrupole sum rules approach. The ground state of $^{94}$Zr possesses a rather diffuse shape associated with a spherical configuration, while the $0_2^+$ state is oblate and more strongly deformed. The observed features of shape coexistence in $^{94}$Zr are in agreement with Monte-Carlo shell-model predictions, and the present results are vital to refine the IBM-CM description of the Zr isotopes around $A\approx 100$ in terms of an intertwined quantum phase transition., Comment: 6 pages, 3 figures

Sequential Recommender Systems (SRSs) have emerged as a highly efficient approach to recommendation systems. By leveraging sequential data, SRSs can identify temporal patterns in user behaviour, significantly improving recommendation accuracy and relevance.Ensuring the reproducibility of these models is paramount for advancing research and facilitating comparisons between them. Existing works exhibit shortcomings in reproducibility and replicability of results, leading to inconsistent statements across papers. Our work fills these gaps by standardising data pre-processing and model implementations, providing a comprehensive code resource, including a framework for developing SRSs and establishing a foundation for consistent and reproducible experimentation. We conduct extensive experiments on several benchmark datasets, comparing various SRSs implemented in our resource. We challenge prevailing performance benchmarks, offering new insights into the SR domain. For instance, SASRec does not consistently outperform GRU4Rec. On the contrary, when the number of model parameters becomes substantial, SASRec starts to clearly dominate all the other SRSs. This discrepancy underscores the significant impact that experimental configuration has on the outcomes and the importance of setting it up to ensure precise and comprehensive results. Failure to do so can lead to significantly flawed conclusions, highlighting the need for rigorous experimental design and analysis in SRS research. Our code is available at https://github.com/antoniopurificato/recsys_repro_conf., Comment: 8 pages, 5 figures

The present work provides an application of Global Sensitivity Analysis to supervised machine learning methods such as Random Forests. These methods act as black boxes, selecting features in high--dimensional data sets as to provide accurate classifiers in terms of prediction when new data are fed into the system. In supervised machine learning, predictors are generally ranked by importance based on their contribution to the final prediction. Global Sensitivity Analysis is primarily used in mathematical modelling to investigate the effect of the uncertainties of the input variables on the output. We apply it here as a novel way to rank the input features by their importance to the explainability of the data generating process, shedding light on how the response is determined by the dependence structure of its predictors. A simulation study shows that our proposal can be used to explore what advances can be achieved either in terms of efficiency, explanatory ability, or simply by way of confirming existing results.

The atomic motion in molecular crystals, such as high-pressure hydrogen or hybrid organic-inorganic perovskites, is very complex due to quantum anharmonic effects. In addition, these materials accommodate rotational degrees of freedom. All the approximate methods that describe the nuclei thermodynamics using Cartesian coordinates lead to an unphysical hybridization of roto-librations with other high-energy modes. Hence, they do not accurately account for the free energy contributions of these degrees of freedom. So, a reliable description of a molecular crystal's phase diagram is only possible with Path Integral Molecular Dynamics (PIMD) at a high computational cost. This work shows how to include roto-librational modes in the Self-Consistent Harmonic Approximation (SCHA) framework. SCHA approximates the nuclei Cartesian fluctuations to be Gaussian, thus neglecting curvilinear motion. Keeping its low computational cost, we employ the generalization of SCHA, called nonlinear SCHA (NLSCHA). Our method relies on a Gaussian \textit{ansatz} for the nuclei density matrix on a curved manifold, allowing us to map roto-librations into harmonic modes defined on a surface. By optimizing the surface's curvature variationally, we minimize the free energy, allowing the spontaneous activation of these degrees of freedom without external parameters. Notably, in the limit of vanishing curvature, we recover the standard SCHA.

A distinct feature of pancreatic ductal adenocarcinoma (PDAC) is a prominent tumor microenvironment (TME) with remarkable cellular and spatial heterogeneity that meaningfully impacts disease biology and treatment resistance. The dynamic crosstalk between cancer cells and the dense stromal compartment leads to spatially and temporally heterogeneous metabolic alterations, such as acidic pH that contributes to drug resistance in PDAC. Thus, monitoring the extracellular pH metabolic fluctuations within the TME is crucial to predict and to quantify anticancer drug efficacy. Here, a simple and reliable alginate-based 3D PDAC model embedding ratiometric optical pH sensors and cocultures of tumor (AsPC-1) and stromal cells for simultaneously monitoring metabolic pH variations and quantify drug response is presented. By means of time-lapse confocal laser scanning microscopy (CLSM) coupled with a fully automated computational analysis, the extracellular pH metabolic variations are monitored and quantified over time during drug testing with gemcitabine, folfirinox, and paclitaxel, commonly used in PDAC therapy. In particular, the extracellular acidification is more pronounced after drugs treatment, resulting in increased antitumor effect correlated with apoptotic cell death. These findings highlight the importance of studying the influence of cellular metabolic mechanisms on tumor response to therapy in 3D tumor models, this being crucial for the development of personalized medicine approaches.

The Self-Consistent Harmonic Approximation (SCHA) describes atoms in solids, including quantum fluctuations and anharmonic effects, in a non-perturbative way. It computes ionic free energy variationally, constraining the atomic quantum-thermal fluctuations to be Gaussian. Consequently, the entropy is analytical; there is no need for thermodynamic integration or heavy diagonalization to include finite temperature effects. In addition, as the probability distribution is fixed, SCHA solves all the equations with Monte Carlo integration without employing Metropolis sampling of the quantum phase space. Unfortunately, the Gaussian approximation breaks down for rotational modes and tunneling effects. We show how to describe these non-Gaussian fluctuations using the quantum variational principle at finite temperatures, keeping the main advantage of SCHA: direct access to free energy. Our method, nonlinear SCHA (NLSCHA), employs an invertible nonlinear transformation to map Cartesian coordinates into an auxiliary manifold parametrized by a finite set of variables. So, we adopt a Gaussian \textit{ansatz} for the density matrix in this new coordinate system. The nonlinearity of the mapping ensures that NLSCHA enlarges the SCHA variational subspace, and its invertibility conserves the information encoded in the density matrix. We evaluate the entropy in the auxiliary space, where it has a simple analytical form. As in the SCHA, the variational principle allows for optimizing free parameters to minimize free energy. Finally, we show that, for the first time, NLSCHA gives direct access to the entropy of a crystal with non-Gaussian degrees of freedom.

This letter investigates the problem of controlling an aerial manipulator, composed of an omnidirectional tilting drone equipped with a five-degrees-of-freedom robotic arm. The robot has to interact with the environment to inspect structures and perform non-destructive measurements. A parallel force-impedance control technique is developed to establish contact with the designed surface with a desired force profile. During the interaction, a pushing phase is required to create a vacuum between the surface and the echometer sensor mounted at the end-effector, to measure the thickness of the interaction surface. Repetitive measures are performed to show the repeatability of the algorithm., Comment: In proceedings of 18th International Symposium on Experimental Robotics (ISER 2023)

In this paper, the association scheme defined on the flags of a finite generalized quadrangle is considered. All possible fusions of this scheme are listed, and a full description for those of classes 2 and 3 is given. Furthermore, it is showed that an association scheme with appropriate parameters must arise from the flags of a generalized quadrangle. The same is done for one of its 4-class symmetric fusion.

In this paper, we propose the generalized mixed reduced rank regression method, GMR$^3$ for short. GMR$^3$ is a regression method for a mix of numeric, binary, and ordinal response variables. The predictor variables can be a mix of binary, nominal, ordinal, and numeric variables. For dealing with the categorical predictors we use optimal scaling. A majorization-minimization algorithm is derived for maximum likelihood estimation under a local independence assumption. A series of simulation studies is shown (Section 4) to evaluate the performance of the algorithm with different types of predictor and response variables. In Section 5.2, we briefly discuss the choices to make when applying the model the empirical data and give suggestions for supporting such choices. In Section 6.1, we show an application of GMR$^3$ using the Eurobarometer Surveys data set of 2023., Comment: 29 pages, 4 figures

The excited states of unstable $^{20}$O were investigated via $\gamma$-ray spectroscopy following the $^{19}$O$(d,p)^{20}$O reaction at 8 $A$MeV. By exploiting the Doppler Shift Attenuation Method, the lifetime of the 2$^+_2$ and 3$^+_1$ states were firmly established. From the $\gamma$-ray branching and E2/M1 mixing ratios for transitions deexciting the 2$^+_2$ and 3$^+_1$ states, the B(E2) and B(M1) were determined. Various chiral effective field theory Hamiltonians, describing the nuclear properties beyond ground states, along with a standard USDB interaction, were compared with the experimentally obtained data. Such a comparison for a large set of $\gamma$-ray transition probabilities with the valence space in medium similarity renormalization group ab-initio calculations was performed for the first time in a nucleus far from stability. It was shown that the ab-initio approaches using chiral EFT forces are challenged by detailed high-precision spectroscopic properties of nuclei. The reduced transition probabilities were found to be a very constraining test of the performance of the ab-initio models., Comment: Supplemental Material available

Optical Bound States in the Continuum are peculiar localized states within the continuous spectrum that are unaffected by any far-field radiation and intrinsic absorption, therefore possessing infinite mode lifetime and Q-factor. To date they have been widely studied in dielectric structures whereas their exploitation in lossy media, i.e. plasmonic nanostructures, still remains a challenge. Here, we show the emergence of a hybrid BIC state in a 2D system of silver-filled dimers, quasi-embedded in a high-index dielectric waveguide. The hybrid BIC onset is found to be highly dependent on the bare modes' spectral and spatial overlap, but particularly on the plasmonic field's intensity. By tailoring the hybridizing plasmonic/photonic fractions we select an ideal coupling regime for which the mode exhibits both, high Q-factor values and strong near-field enhancement tightly confined in the nanogap and a consequently extremely small modal volume. We demonstrate that this optical layout can be exploited in a proof-of-concept experiment for the detection of TAR DNA-binding protein 43, which outperforms the sensitivity of current label-free biosensing platforms, reaching the zeptomolar range of concentration.

The tumor microenvironment (TME) features distinct hallmarks, including acidosis, hypoxia, reactive oxygen species (ROS) generation, and altered ion fluxes, which are crucial targets for early cancer biomarker detection, tumor diagnosis, and therapeutic strategies. A variety of imaging and sensing techniques have been developed and employed in both research and clinical settings to visualize and monitor cellular and TME dynamics. Among these, ratiometric fluorescence-based sensors have emerged as powerful analytical tools, providing precise and sensitive insights into the TME and enabling real-time detection and tracking of dynamic changes. In this comprehensive review, we discuss the latest advancements in ratiometric fluorescent probes designed for optical mapping of pH, oxygen, ROS, ions, and biomarkers within the TME. We elucidate their structural designs and sensing mechanisms, as well as their applications in in vitro and in vivo detection. Furthermore, we explore integrated sensing platforms that reveal the spatiotemporal behavior of complex tumor cultures, highlighting the potential of high-resolution imaging techniques combined with computational methods. This review aims to provide a solid foundation for understanding the current state of the art and the future potential of fluorescent nano- and microparticles in the field of cellular microenvironment sensing.

We provide classification results for translation generalized quadrangles of order less or equal to $64$, and hence, for all incidence geometries related to them. The results consist of the classification of all pseudo-ovals in $PG(3n-1,2)$, for $n=3,4$, and that of the pseudo-ovals in $PG(3n-1,q)$, for $n=5,6$, such that one of the associated projective planes is Desarguesian.

Retrieval-Augmented Generation (RAG) has recently emerged as a method to extend beyond the pre-trained knowledge of Large Language Models by augmenting the original prompt with relevant passages or documents retrieved by an Information Retrieval (IR) system. RAG has become increasingly important for Generative AI solutions, especially in enterprise settings or in any domain in which knowledge is constantly refreshed and cannot be memorized in the LLM. We argue here that the retrieval component of RAG systems, be it dense or sparse, deserves increased attention from the research community, and accordingly, we conduct the first comprehensive and systematic examination of the retrieval strategy of RAG systems. We focus, in particular, on the type of passages IR systems within a RAG solution should retrieve. Our analysis considers multiple factors, such as the relevance of the passages included in the prompt context, their position, and their number. One counter-intuitive finding of this work is that the retriever's highest-scoring documents that are not directly relevant to the query (e.g., do not contain the answer) negatively impact the effectiveness of the LLM. Even more surprising, we discovered that adding random documents in the prompt improves the LLM accuracy by up to 35%. These results highlight the need to investigate the appropriate strategies when integrating retrieval with LLMs, thereby laying the groundwork for future research in this area.

Predicting the outcome of antiretroviral therapies for HIV-1 is a pressing clinical challenge, especially when the treatment regimen includes drugs for which limited effectiveness data is available. This scarcity of data can arise either due to the introduction of a new drug to the market or due to limited use in clinical settings. To tackle this issue, we introduce a novel joint fusion model, which combines features from a Fully Connected (FC) Neural Network and a Graph Neural Network (GNN). The FC network employs tabular data with a feature vector made up of viral mutations identified in the most recent genotypic resistance test, along with the drugs used in therapy. Conversely, the GNN leverages knowledge derived from Stanford drug-resistance mutation tables, which serve as benchmark references for deducing in-vivo treatment efficacy based on the viral genetic sequence, to build informative graphs. We evaluated these models' robustness against Out-of-Distribution drugs in the test set, with a specific focus on the GNN's role in handling such scenarios. Our comprehensive analysis demonstrates that the proposed model consistently outperforms the FC model, especially when considering Out-of-Distribution drugs. These results underscore the advantage of integrating Stanford scores in the model, thereby enhancing its generalizability and robustness, but also extending its utility in real-world applications with limited data availability. This research highlights the potential of our approach to inform antiretroviral therapy outcome prediction and contribute to more informed clinical decisions., Comment: 32 pages, 2 figures

Fake news detection models are critical to countering disinformation but can be manipulated through adversarial attacks. In this position paper, we analyze how an attacker can compromise the performance of an online learning detector on specific news content without being able to manipulate the original target news. In some contexts, such as social networks, where the attacker cannot exert complete control over all the information, this scenario can indeed be quite plausible. Therefore, we show how an attacker could potentially introduce poisoning data into the training data to manipulate the behavior of an online learning method. Our initial findings reveal varying susceptibility of logistic regression models based on complexity and attack type.

This report introduces a new family of multimodal models, Gemini, that exhibit remarkable capabilities across image, audio, video, and text understanding. The Gemini family consists of Ultra, Pro, and Nano sizes, suitable for applications ranging from complex reasoning tasks to on-device memory-constrained use-cases. Evaluation on a broad range of benchmarks shows that our most-capable Gemini Ultra model advances the state of the art in 30 of 32 of these benchmarks - notably being the first model to achieve human-expert performance on the well-studied exam benchmark MMLU, and improving the state of the art in every one of the 20 multimodal benchmarks we examined. We believe that the new capabilities of the Gemini family in cross-modal reasoning and language understanding will enable a wide variety of use cases. We discuss our approach toward post-training and deploying Gemini models responsibly to users through services including Gemini, Gemini Advanced, Google AI Studio, and Cloud Vertex AI.

This chapter investigates the complexities surrounding the iron biogeochemical cycle from the Archean to present, with a focus on assessing the balance between iron sources and sinks during long periods of Earth's history with relatively invariable redox conditions, when steady state can be safely assumed. Currently, the residence time of iron in the ocean may be as short as approximately 5 years. The input flux of iron is highly sensitive to redox cycling in sediments, while its removal primarily occurs through dispersed processes of oxidation and precipitation. In the Archean, we find a significant imbalance between continental and hydrothermal inputs, which collectively contribute between 61,500 to 263,000 Gg/yr of dissolved iron to the oceans, and the most obvious sinks such as iron formations (IFs), which sequester up to ~43,000 Gg/yr of iron. A possible solution to this imbalance involves the dispersed abiotic precipitation and removal of iron as silicates, sulfides, and carbonates in marine basins. Additionally, we calculate the residence time of dissolved iron in the Archean oceans to be between 6 kyr and 3 Myr, which is significantly longer than the ocean mixing timescale. Our estimates indicate that under the anoxic Archean atmosphere, the iron cycle was more protracted than today, and the isotopic compositions and concentrations of dissolved iron were likely more uniform. Distinct water bodies were likely confined to limited areas or specific, dynamic systems with intense iron turnover, such as regions where deep-sea upwelling currents brought hydrothermal iron to photic zones rich in biotic or abiotic oxidants., Comment: In press, Treatise on Geochemistry, 3rd Edition. 23954 words, 18 figures, 3 tables

In the paper we consider the following quasilinear Schr\"odinger--Poisson system in the whole space $\mathbb R^{3}$ $$ \begin{cases} - \varepsilon^2 \Delta u + (V + \phi) u = u |u|^{p - 1} \newline - \Delta \phi - \beta \Delta_4 \phi = u^2, \end{cases} $$ where $1 < p < 5, \beta > 0,V :\mathbb R^{3}\to ]0, \infty[$ and look for solutions $u,\phi:\mathbb R^{3}\to \mathbb R$ in the semiclassical regime, namely when $\varepsilon\to 0.$ By means of the Lyapunov--Schmidt method we estimate the number of solutions by the cup-length of the critical manifold of the external potential $V$., Comment: 19 pages; comments are welcome