Optimization guide for programs compiled under IBM FORTRAN H (OPT=2)

Guidelines are given to provide the programmer with various techniques for optimizing programs when the FORTRAN IV H compiler is used with OPT=2. Subroutines and programs are described in the appendices along with a timing summary of all the examples given in the manual

Holistic ICT environments for effective mathematics teaching and learning

To understand the numbers world, each child must face a path that includes propaedeutic phases and only overcoming these phases will allow the child to consolidate processes before tackling new ones. If this does not happen, the child becomes self-convinced of \u201dnot being able to understand math\u201d and becomes increasingly aware of it throughout primary school. The transition to middle school may have a significant impact on a child, with specific difficulties or disabilities in learning mathematics, especially if his/her difficulties have not yet been identified. The present thesis studies the contributions of Information and Communication Technology (ICT) in supporting various aspects of mathematical teaching and learning. A multidimensional approach was used. In the first part, empirical studies assessed the effectiveness of digital tools to identify individual differences based on cognitive profiles and emotional responses associated with math performance in children from Northern Italy. In the second part a meta-analysis and systematic review analysis were carried out to evaluate the effectiveness of interventions supporting math learning by means of ICT in the school and home environments respectively. Altogether the thesis indicates that designing holistic ICT environments proves successful for effective mathematics teaching and learning not only for typically developing children but also for students in disadvantaged situations, including those suffering from dyscalculia

Towards Synthetic Life: Establishing a Minimal Segrosome for the Rational Design of Biomimetic Systems

DNA segregation is a fundamental life process, crucial for renewal, reproduction and propagation of all forms of life. Hence, a dedicated segregation machinery, a segrosome, must function reliably also in the context of a minimal cell. Conceptionally, the development of such a minimal cell follows a minimalistic approach, aiming at engineering a synthetic entity only consisting of the essential key elements necessary for a cell to survive. In this thesis, various prokaryotic segregation systems were explored as possible candidates for a minimal segrosome. Such a minimal segrosome could be applied for the rational design of biomimetic systems including, but not limited to, a minimal cell. DNA segregation systems of type I (ParABS) and type II (ParMRC) were compared for ensuring genetic stabilities in vivo using vectors derived from the natural secondary chromosome of Vibrio cholerae. The type II segregation system R1-ParMRC was chosen as the most promising candidate for a minimal segrosome, and it was characterized and reconstituted in vitro. This segregation system was encapsulated into biomimetic micro-compartments and its lifetime prolonged by coupling to ATP-regenerating as well as oxygen-scavenging systems. The segregation process was coupled to in vitro DNA replication using DNA nanoparticles as a mimic of the condensed state of chromosomes. Furthermore, another type II segregation system originating from the pLS20 plasmid from Bacillus subtilis (Alp7ARC) was reconstituted in vitro as a secondary orthogonal segrosome. Finally, a chimeric RNA segregation system was engineered that could be applied for an RNA-based protocell. Overall, this work demonstrates successful bottom-up assemblies of functional molecular machines that could find applications in biomimetic systems and lead to a deeper understanding of living systems

Liquid phase exfoliation and size dependent properties of van der Waals crystals

Van der Waals crystals exhibit comparatively strong, typically covalent bonds in two dimensions and comparatively weak, typically non-covalent bonds between the two-dimensional lattice. This enables to separate individual two-dimensional layers of a van der Waals crystal which can be thinned down to atomic thickness in a process called exfoliation. The resulting nanosheets typically exhibit completely different properties compared to their corresponding bulk counterparts which can be exploited for various applications in advanced devices. Different methods have been presented for preparation of two-dimensional nanomaterials each with their respective up- and downsides. While some techniques can provide materials of highest quality, suitable for fundamental studies of inherent material properties, they typically lack scalability. Other methods focus on a high production rate of the nanomaterial, but introduce imperfections to the material due to the harsh conditions required. In recent years, exfoliation in the liquid phase has emerged to a widely used production technique due to the scalability and its wide applicability. While the industrial relevance of two-dimensional nanomaterials is somewhat linked to the quality of the material that can be prepared by high throughput methods, a deeper understanding of underlying fundamentals for the nanosheet preparation is required to improve state-of-the-art techniques. In the case of liquid-exfoliated nanosheets, this can be achieved by statistical studies of the nanomaterial dimensions that can be prepared and isolated by size selection techniques. In this work, sonication-assisted liquid phase exfoliation using different conditions and solvents and subsequent size selection was applied to a total of 17 different van der Waals crystals. The material dimensions of all fractions were quantified through statistical atomic force microscopy. The findings presented in this work demonstrate a fundamental correlation between the nanomaterial lateral size and thickness which is ascribed to equipartition of energy between processes of nanosheet delamination and tearing. This provides an experimental proxy to determine the ratio between the in-plane binding strength and the out-of-plane interlayer attraction. Isolation of different size-fractions of the same material and the knowledge over the nanomaterial dimensions in these fractions enables to study size-dependent changes of material properties in a quantitative manner. Measurements of optical properties on different sizes of dispersed nanosheets reveal systematic changes of the spectra with nanosheet size and enable to de-rive spectroscopic metrics for the size, thickness and concentration for different van der Waals nanomaterials, typically using extinction and absorbance spectroscopy. Structurally and compositionally different materials show similar changes in their optical response with changing material size which can be ascribed to a combination of confinement and dielectric screening effects, as well as changing contributions form scattering and electronically different material edges. Unifying principles across various materials were identified for the changes of the optical spectra with material dimensions. The knowledge of material dimensions and the understanding of the optical spectra enables to study the stability of different nanomaterial systems as function of time using optical spectroscopy such as extinction, absorbance or photoluminescence. A dependence of the speed and degree of the material decomposition on the storage temperature and the water content of the solvent is conveniently accessible for different material dimensions. The results presented within this work provide an advanced understanding of the exfoliation of layered crystals, unifying principles of optical properties as function of nanomaterial dimensions and proof-of-concept experiments for quantification of the material decomposition

A statistical mechanical model of economics

Statistical mechanics pursues low-dimensional descriptions of systems with a very large number of degrees of freedom. I explore this theme in two contexts. The main body of this dissertation explores and extends the Yard Sale Model (YSM) of economic transactions using a combination of simulations and theory. The YSM is a simple interacting model for wealth distributions which has the potential to explain the empirical observation of Pareto distributions of wealth. I develop the link between wealth condensation and the breakdown of ergodicity due to nonlinear diffusion effects which are analogous to the geometric random walk. Using this, I develop a deterministic effective theory of wealth transfer in the YSM that is useful for explaining many quantitative results. I introduce various forms of growth to the model, paying attention to the effect of growth on wealth condensation, inequality, and ergodicity. Arithmetic growth is found to partially break condensation, and geometric growth is found to completely break condensation. Further generalizations of geometric growth with growth in- equality show that the system is divided into two phases by a tipping point in the inequality parameter. The tipping point marks the line between systems which are ergodic and systems which exhibit wealth condensation. I explore generalizations of the YSM transaction scheme to arbitrary betting functions to develop notions of universality in YSM-like models. I find that wealth condensation is universal to a large class of models which can be divided into two phases. The first exhibits slow, power-law condensation dynamics, and the second exhibits fast, finite-time condensation dynamics. I find that the YSM, which exhibits exponential dynamics, is the critical, self-similar model which marks the dividing line between the two phases. The final chapter develops a low-dimensional approach to materials microstructure quantification. Modern materials design harnesses complex microstructure effects to develop high-performance materials, but general microstructure quantification is an unsolved problem. Motivated by statistical physics, I envision microstructure as a low-dimensional manifold, and construct this manifold by leveraging multiple machine learning approaches including transfer learning, dimensionality reduction, and computer vision breakthroughs with convolutional neural networks