The Challenge of Modeling the Acquisition of Mathematical Concepts

As a full-blown research topic, numerical cognition is investigated by a variety of disciplines including cognitive science, developmental and educational psychology, linguistics, anthropology and, more recently, biology and neuroscience. However, despite the great progress achieved by such a broad and diversified scientific inquiry, we are still lacking a comprehensive theory that could explain how numerical concepts are learned by the human brain. In this perspective, I argue that computer simulation should have a primary role in filling this gap because it allows identifying the finer-grained computational mechanisms underlying complex behavior and cognition. Modeling efforts will be most effective if carried out at cross-disciplinary intersections, as attested by the recent success in simulating human cognition using techniques developed in the fields of artificial intelligence and machine learning. In this respect, deep learning models have provided valuable insights into our most basic quantification abilities, showing how numerosity perception could emerge in multi-layered neural networks that learn the statistical structure of their visual environment. Nevertheless, this modeling approach has not yet scaled to more sophisticated cognitive skills that are foundational to higher-level mathematical thinking, such as those involving the use of symbolic numbers and arithmetic principles. I will discuss promising directions to push deep learning into this uncharted territory. If successful, such endeavor would allow simulating the acquisition of numerical concepts in its full complexity, guiding empirical investigation on the richest soil and possibly offering far-reaching implications for educational practice

Emergence of network motifs in deep neural networks

Network science can offer fundamental insights into the structural and functional properties of complex systems. For example, it is widely known that neuronal circuits tend to organize into basic functional topological modules, called network motifs. In this article, we show that network science tools can be successfully applied also to the study of artificial neural networks operating according to self-organizing (learning) principles. In particular, we study the emergence of network motifs in multi-layer perceptrons, whose initial connectivity is defined as a stack of fully-connected, bipartite graphs. Simulations show that the final network topology is shaped by learning dynamics, but can be strongly biased by choosing appropriate weight initialization schemes. Overall, our results suggest that non-trivial initialization strategies can make learning more effective by promoting the development of useful network motifs, which are often surprisingly consistent with those observed in general transduction networks

Visual sense of number vs. sense of magnitude in humans and machines

Numerosity perception is thought to be foundational to mathematical learning, but its computational bases are strongly debated. Some investigators argue that humans are endowed with a specialized system supporting numerical representations; others argue that visual numerosity is estimated using continuous magnitudes, such as density or area, which usually co-vary with number. Here we reconcile these contrasting perspectives by testing deep neural networks on the same numerosity comparison task that was administered to human participants, using a stimulus space that allows the precise measurement of the contribution of non-numerical features. Our model accurately simulates the psychophysics of numerosity perception and the associated developmental changes: discrimination is driven by numerosity, but non-numerical features also have a significant impact, especially early during development. Representational similarity analysis further highlights that both numerosity and continuous magnitudes are spontaneously encoded in deep networks even when no task has to be carried out, suggesting that numerosity is a major, salient property of our visual environment

Studying the evolution in time of bimetallic nanoparticles morphology by Cyclic Voltammetry

Over the last decades, bimetallic nanosized systems have attracted more and more interest thanks to their novel optical, catalytic, magnetic, and sensing properties, often different from the ones of their monometallic counterparts. Studies directed towards the size, shape, composition, and functionalization of the bimetallic nanoparticles are optimized to design sophisticated materials for the intended applications. Considering these facts, it is important to evaluate not only the type and the quantity of the two metals involved, but also their morphological distribution (e.g. alloy or core-shell). Characterization techniques normally used to investigate bimetallic systems are HR-TEM and EXAFS, very expensive and not so easily accessible. Recently, electrochemistry has been employed as alternative or complementary, low-cost, efficient technique with very promising results, allowing the discrimination between alloyed and perfect or defective core-shell systems after their synthesis. A further achievement is the possibility to follow step by step the formation morphology of these nanomaterials during their synthetic procedure. In the present work, we present a study on Au-Pt bimetallic nanoparticles, in form of alloy or core-shell. Cyclovoltammetry (CV) is used as a fast, low-cost and simple screening technique to distinguish the general composition of the sample and to understand the evolution in time of the systems morphology during their synthesis. An additional advantage is the possibility to conduct the study of the material simply in liquid form, without the need of using solid supports, as normally required by other characterization techniques. Interesting results are obtained for Au-based bimetallic samples, gaining information in accordance with TEM images and EXAFS spectra. This fact moves the interest towards the study of other bimetallic systems, to be used in catalytic, electrocatalytic and electroanalytical applications

A precise CNOT gate in the presence of large fabrication induced variations of the exchange interaction strength

We demonstrate how using two-qubit composite rotations a high fidelity controlled-NOT (CNOT) gate can be constructed, even when the strength of the interaction between qubits is not accurately known. We focus on the exchange interaction oscillation in silicon based solid-state architectures with a Heisenberg Hamiltonian. This method easily applies to a general two-qubit Hamiltonian. We show how the robust CNOT gate can achieve a very high fidelity when a single application of the composite rotations is combined with a modest level of Hamiltonian characterisation. Operating the robust CNOT gate in a suitably characterised system means concatenation of the composite pulse is unnecessary, hence reducing operation time, and ensuring the gate operates below the threshold required for fault-tolerant quantum computation.Comment: 9 pages, 8 figure

Voltammetric characterization of gold-based bimetallic (AuPt; AuPd; AuAg) nanoparticles

Bimetallic nanoparticles are nowadays some of the most promising materials for catalytic, electrocatalytic and electroanalytical applications thanks to their novel optical, catalytic, magnetic, and sensing properties. Such novel features, often different and enhanced with respect to the monometallic counterparts, make these systems good candidates to be conveniently applied in a wide range of fields. The possibility to obtain different kinds of bimetallic composites (in terms of composition, structure, metal loading, morphology, etc.) goes in parallel with the need of powerful and accurate characterization tools. Among the commonly involved techniques like Optical Spectroscopy and Dynamic Light Scattering (DLS), also the more powerful Transmission Electron Microscopy (HR-TEM) and Extended X-Ray Absorption Fine Structure (EXAFS) are widely used. However, these analytical tools present some drawbacks in terms of high costs and low accessibility. In this context, electrochemistry and particularly Cyclic Voltammetry, is here proposed as an alternative, low cost, easy to use and simple characterization technique. The possibility to use electrochemical methods to study the final structure of bimetallic nanocomposites was already demonstrated in the Literature [1-2], but there is still lack of information on how such systems change and evolve in time and after aging periods. Therefore, Cyclic Voltammetry is here used, as a complementary technique to HR-TEM and EXAFS not only to investigate the structure of alloyed or core-shell gold-based (Au-Pt; Au-Pd; Au-Ag) systems (by studying the quantity and type of metals present in the materials), but also to elucidate the evolution and growth in time of such bimetallic samples. Time evolution characterization allows to control the morphology and to fix it at the desired point. Finally, the characterized gold-based nanocomposites are used in electrochemical sensing and electrocatalytic applications. A strong improvement in the response, in terms of higher peak currents and electrocatalytic effects, of the bimetallic systems with respect to the monometallic counterparts is evidenced, due to the intimate contact between the two metals, which is responsible of synergistic effects. Also, the effects of an eventual carbonaceous support on the properties of the metal nanoparticles and the possible synergistic effects between composites and supports are investigated [3]. [1] K. Tschulik, K. Ngamchuea, C. Ziegler, M.G. Beier, C. Damm, A. Eychmueller, R.G. Compton, Adv. Funct. Mater., 2015, 25, 5149\u20135158. [2] V. Pifferi, C. Chan-Thaw, S. Campisi, A. Testolin, A. Villa, L. Falciola, L. Prati, Molecules, 2016, 21, 261. [3] A. Testolin, S.Cattaneo, W. Wang, D. Wang, V. Pifferi, L. Prati, L. Falciola, A. Villa, Surfaces, 2019, 2, 205-215

Pyramiding resistance genes and widening the genetic base of the apple (Malus 7 domestica Borkh.) crop

Apple breeding is active worldwide and yet the apple crop is in a precarious state as it relies on few dominant cultivars and only the Rvi6 (formerly Vf) gene, that confers resistance to scab, has been extensively exploited in the cultivars entered the market in recent years. However, there are some 20 disease resistance genes described in apple and the apple germplasm includes thousands of accessions in the repositories. In this paper, a breeding programme is described, whereby 36 genotypes, including ancient and contemporary apple cultivars, were crossed to produce a new set of selections that combine extensive genetic resources with pyramided resistance genes to several apple diseases, such as scab and powdery mildew. The 110 cross combinations carried out successfully, of the 260 initially planned, produced 7,876 offsprings, reduced to 2,969 after screening with molecular markers associated with five resistance genes. Selections with three or two resistance genes and good agronomic characteristics were kept for further field observations with the aims of creating new cultivars for the market and new parents for future breeding projects

Au Nanoparticles Decorated Graphene-Based Hybrid Nanocomposite for As(III) Electroanalytical Detection

Electrochemical sensors integrating hybrid nanostructured platforms are a promising alternative to conventional detection techniques for addressing highly relevant challenges of heavy metal determination in the environment. Hybrid nanocomposites based on graphene derivatives and inorganic nanoparticles (NPs) are ideal candidates as active materials for detecting heavy metals, as they merge the relevant physico-chemical properties of both the components, finally leading to a rapid and sensitive current response. In this work, a hybrid nanocomposite formed of reduced graphene oxide (RGO) sheets, surface functionalized by π-π interactions with 1-pyrene carboxylic acid (PCA), and decorated in situ by Au NPs, was synthesized by using a colloidal route. The hybrid nanocomposite was characterized by cyclic voltammetry and electrochemical impedance spectroscopy with respect to the corresponding single components, both bare and deposited as a layer-by-layer junction onto the electrode. The results demonstrated the high electrochemical activity of the hybrid nanocomposite with respect to the single components, highlighting the crucial role of the nanostructured surface morphology of the electrode and the PCA coupling agent at the NPs-RGO interphase in enhancing the nanocomposite electroactivity. Finally, the Au NP-decorated PCA-RGO sheets were tested by anodic stripping voltammetry of As(III) ion—a particularly relevant analyte among heavy metal ions—in order to assess the sensing ability of the nanocomposite material with respect to its single components. The nanocomposite has been found to present a sensitivity higher than that characterizing the bare components, with LODs complying with the directives established by the U.S. EPA and in line with those reported for state-of-the-art electrochemical sensors based on other Au-graphene nanocomposites

Biogeography of orchids and their pollination syndromes in small Mediterranean islands

Aims Despite the research on orchid in insular conditions, few studies are focused on the spatial distribution of their reproductive syndromes across complex insular systems. By using island species-area relationships (ISAR), we explore orchid biogeography in the Central Western-Mediterranean islands. In this study, we aim to investigate variation in ISARs using orchid pollination mechanisms as proxies to establish permanent populations explaining how the c and z parameters of ISARs vary among island types and pollination strategies and defining the most influential factors in shaping orchids' distribution.LocationMediterranean Basin.TaxonOrchidaceae. MethodsChecklist of native orchids was obtained for 112 islands of Central-Western Mediterranean Basin. The Arrhenius power function (S=c center dot Az$$S=c\cdotp {A}z$$) was used to fit ISARs for the total number of orchids as well as for functional groups defined by the pollination strategies, across different island types. We used GLM to investigate the relation between pollination syndromes with area and isolation as well as elevation, island origin, taxa richness of the source area and habitat diversity.ResultsWe found that ISARs differ between continental and volcanic islands depending on isolation. The z-value was found to be higher for more specialized strategies while the c-value increases from autogamy to allogamy, supporting the role of these two parameters in understanding distributional dynamics. Distance from the mainland is a negative predictor for all the strategies except when deception is decoupled; island area is a positive predictor only for allogamic, deceptive and food deceptive strategies, while habitat diversity is a positive predictor for allogamic, rewarding and deceptive strategies. Main Conclusions Pollination syndromes contribute in explaining the distribution of orchids in insular conditions. Furthermore, we identified differences in ISARs across pollination syndromes in which the intercept increases when the pollination shifts from a generalist to a more specialized one