Critical behavior of su(1|1) supersymmetric spin chains with long-range interactions

We introduce a general class of su$(1|1)$ supersymmetric spin chains with long-range interactions which includes as particular cases the su$(1|1)$ Inozemtsev (elliptic) and Haldane-Shastry chains, as well as the XX model. We show that this class of models can be fermionized with the help of the algebraic properties of the su$(1|1)$ permutation operator, and take advantage of this fact to analyze their quantum criticality when a chemical potential term is present in the Hamiltonian. We first study the low energy excitations and the low temperature behavior of the free energy, which coincides with that of a $(1+1)$-dimensional conformal field theory (CFT) with central charge $c=1$ when the chemical potential lies in the critical interval $(0,\mathcal E(\pi))$, $\mathcal E(p)$ being the dispersion relation. We also analyze the von Neumann and R\'enyi ground state entanglement entropies, showing that they exhibit the logarithmic scaling with the size of the block of spins characteristic of a one-boson $(1+1)$-dimensional CFT. Our results thus show that the models under study are quantum critical when the chemical potential belongs to the critical interval, with central charge $c=1$. From the analysis of the fermion density at zero temperature, we also conclude that there is a quantum phase transition at both ends of the critical interval. This is further confirmed by the behavior of the fermion density at finite temperature, which is studied analytically (at low temperature), as well as numerically for the su$(1|1)$ elliptic chain.Comment: 13 pages, 6 figures, typeset in REVTe

Generalized isotropic Lipkin-Meshkov-Glick models: ground state entanglement and quantum entropies

We introduce a new class of generalized isotropic Lipkin-Meshkov-Glick models with su$(m+1)$ spin and long-range non-constant interactions, whose non-degenerate ground state is a Dicke state of su$(m+1)$ type. We evaluate in closed form the reduced density matrix of a block of $L$ spins when the whole system is in its ground state, and study the corresponding von Neumann and R\'enyi entanglement entropies in the thermodynamic limit. We show that both of these entropies scale as $a\log L$ when $L$ tends to infinity, where the coefficient $a$ is equal to $(m-k)/2$ in the ground state phase with $k$ vanishing su$(m+1)$ magnon densities. In particular, our results show that none of these generalized Lipkin-Meshkov-Glick models are critical, since when $L\to\infty$ their R\'enyi entropy $R_q$ becomes independent of the parameter $q$. We have also computed the Tsallis entanglement entropy of the ground state of these generalized su$(m+1)$ Lipkin-Meshkov-Glick models, finding that it can be made extensive by an appropriate choice of its parameter only when $m-k\ge3$. Finally, in the su$(3)$ case we construct in detail the phase diagram of the ground state in parameter space, showing that it is determined in a simple way by the weights of the fundamental representation of su$(3)$. This is also true in the su$(m+1)$ case; for instance, we prove that the region for which all the magnon densities are non-vanishing is an $(m+1)$-simplex in $\mathbf R^m$ whose vertices are the weights of the fundamental representation of su$(m+1)$.Comment: Typeset with LaTeX, 32 pages, 3 figures. Final version with corrections and additional reference

Image Tagging and Gearing Resources applied to students’ graphic materials: Learning techniques in pursuit of Inclusiveness for Urban and Landscape Design

Inclusiveness can be considered a requirement for contemporary statements in urban and landscape design referring to age, condition, gender or nature. But how is inclusiveness influenced by spatial design? Can this relation be measured or proven? And more precisely, which interactions are considered across different generations or between human and non-human agents? This paper describes student’s work evaluation procedures through a methodology consisting of selecting picture-based content from initial reference materials provided by teaching staff, as well as graphic material designed and produced by the students, to further analyze these through data visualization techniques and the production of info-graphics. In a latter step, a gearing game – which is a type of sociogram used to understand agents and matters of interest – is utilized to drive a discussion about design statements for further stages of development concerning students’ design projects. The first stages of the methodology are strongly influenced by how the students perceive elements from reference materials and represent these in their own design productions. A literature review further investigates the dichotomy between representation and perception, and the generation of subjective images. As a final consideration, this work aims to create combined methodologies by incorporating participatory observation methods (e.g. photovoice and flow charts) from the social sciences into urban and landscape design, as they are understood through an accurate design of the learning experience. Similarly, non-representational design and dataviz diagrams from urban and landscape design could potentially be implemented in the teaching of social sciences

Mixed-mode impedance and reflection coefficient of two-port devices

From the point of view of mixed-mode scattering parameters, Smm, a two-port device can be excited using different driving conditions. Each condition leads to a particular set of input reflection and input impedance coefficient definitions that should be carefully applied depending on the type of excitation and symmetry of the two-port device. Therefore, the aim of this paper is to explain the general analytic procedure for the evaluation of such reflection and impedance coefficients in terms of mixed-mode scattering parameters. Moreover, the driving of a two-port device as a one-port device is explained as a particular case of a two-port mixed-mode excitation using a given set of mixed-mode loads. The theory is applied to the evaluation of the quality factor, Q, of symmetrical and non- symmetrical inductors.Ministerio de Innovación y Ciencia TEC2010-14825/MIC, TEC2010-21484Junta de Andalucía TIC-253

Lipoteichoic acid and molecular weight of hyaluronic acid could explain the late inflammatory response trigger by hyaluronic acid fillers

Introduction: Hyaluronic acid is a safe dermal filler, but sometimes late granuloma is generated. This adverse effect is an inflammatory process, and its causes are not clear. Late granuloma generation could be due to the reaction to residual components of the bacterial wall present into hyaluronic acid, such as lipoteichoic acid (LTA). Other possibility is hyaluronic acid degraded could be trigger this inflammatory reaction. // Objective: Study possible molecular mechanism that could be implicated into the late granuloma formation. We wonder whereas inflammatory response activation is triggered by lower molecular weight hyaluronic acid or Gram-positive bacterial components as LTA. // Methods: We analyzed one adverse case generated by hyaluronic acid injections. Our study with one nodule through chemical and immunofluorescence histologic technics. // Results: In this case, observe a late granuloma without infectious process. Histological analysis shown few large Langerhans cells around fillers and multiple immunological cells infiltrated. Immunofluorescent study shown immunological cells (CD45 positives cells) with high TLR2 expression (hyaluronic acid and LTA receptor). // Limitations: The difficulty of obtaining biopsy samples of nodules implies that the number of cases analyzed is very low. // Conclusion: New model is proposed in which weight of hyaluronic acid and LTA could be able to trigger inflammation. This process could be mediated by TLR2 expressed in infiltrated immune cells

Indirect effects of bullying on school mathematics achievement in Chile

Students who experience bullying at school present different negative outcomes, including lower academic achievement. However, the process by which bullying is connected to academic achievement is not clear. Using the Trends in International Mathematics and Science Study (TIMSS) dataset from Chilean schools in 2011, we sought to estimate the indirect effects of bullying on mathematics achievement via two key socio-motivational factors, namely school belonging and students’ engagement. Results of our multilevel latent covariate analyses showed that schools’ bullying rates were predictive of school differences in mathematics achievement, but these effects were explained by broader characteristics of the school environment such as perceived levels of safety and discipline. Crucially, the hypothesized indirect pathway was evident at the within-school level, showing that individual experiences of bullying are related to a poorer sense of belonging with the school as a whole, as well as poorer classroom engagemen