Case study of the uniaxial anisotropic spin-1 bilinear-biquadratic Heisenberg model on a triangular lattice

We study the spin-1 model on a triangular lattice in the presence of a uniaxial anisotropy field using a cluster mean-field (CMF) approach. The interplay among antiferromagnetic exchange, lattice geometry, and anisotropy forces Gutzwiller mean-field approaches to fail in a certain region of the phase diagram. There, the CMF method yields two supersolid phases compatible with those present in the spin-1/2 XXZ model onto which the spin-1 system maps. Between these two supersolid phases, the three-sublattice order is broken and the results of the CMF approach depend heavily on the geometry and size of the cluster. We discuss the possible presence of a spin liquid in this region.

Low-energy behavior of strongly interacting bosons on a flat-band lattice above the critical filling factor

Bosons interacting repulsively on a lattice with a flat lowest band energy dispersion may, at sufficiently small filling factors, enter into a Wigner-crystal-like phase. This phase is a consequence of the dispersionless nature of the system, which in turn implies the occurrence of single-particle localized eigenstates. We investigate one of these systems-the sawtooth lattice-filled with strongly repulsive bosons at filling factors infinitesimally above the critical point where the crystal phase is no longer the ground state. We find, in the hard-core limit, that the crystal retains its structure in all but one of its cells, where it is broken. The broken cell corresponds to an exotic kind of repulsively bound state, which becomes delocalized. We investigate the excitation spectrum of the system analytically and find that the bound state behaves as a single particle hopping on an effective lattice with reduced periodicity, and is therefore gapless. Thus, the addition of a single particle to a flat-band system at critical filling is found to be enough to make kinetic behavior manifest.

Thermometry precision in strongly correlated ultracold lattice gases

The precise knowledge of the temperature of an ultracold lattice gas simulating a strongly correlated
system is a question of both fundamental and technological importance. Here, we address such
question by combining tools from quantum metrology together with the study of the quantum
correlations embedded in the system at finite temperatures. Within this frame we examine the spin-
1 2 XY chain, first estimating, by means of the quantum Fisher information, the lowest attainable
bound on the temperature precision. We then address the estimation of the temperature of the sample
from the analysis of correlations using a quantum non demolishing Faraday spectroscopy method.
Remarkably, our results show that the collective quantum correlations can become optimal
observables to accurately estimate the temperature of our model in a given range of temperatures.

Solar phase functions of cometary nuclei

Relatively few measurements of the solar phase function of cometary nuclei exist, despite the importance of this parameter in determining accurate sizes and its use in modeling surface properties. We make use of robotic telescopes and servicemode observing to monitor cometary nuclei over months at a time, combining intensive observations at a single epoch with regular short light-curve segments to efficiently account for brightness changes due to both nucleus rotation and changing solar phase angle. We present our latest results on comets 8P/Tuttle, 14P/Wolf, 67P/Churyumov- Gerasimenko and 110P/Hartley 3.

Practical Lattice-Based Digital Signature Schemes

Digital signatures are an important primitive for building secure systems and are used in most real-world security protocols. However, almost all popular signature schemes are either based on the factoring assumption (RSA) or the hardness of the discrete logarithm problem (DSA/ECDSA). In the case of classical cryptanalytic advances or progress on the development of quantum computers, the hardness of these closely related problems might be seriously weakened. A potential alternative approach is the construction of signature schemes based on the hardness of certain lattice problems that are assumed to be intractable by quantum computers. Due to significant research advancements in recent years, lattice-based schemes have now become practical and appear to be a very viable alternative to number-theoretic cryptography. In this article, we focus on recent developments and the current state of the art in lattice-based digital signatures and provide a comprehensive survey discussing signature schemes with respect to practicality. Additionally, we discuss future research areas that are essential for the continued development of lattice-based cryptography.

A First Step Towards Cost Functions for Quantum-dot Cellular Automata Designs

Quantum-dot cellular automata (QCA) is potentially a very attractive alternative to CMOS for future digital designs. Circuit designs in QCA have been extensively studied. However, how to properly evaluate the QCA circuits has not been carefully considered. To date, metrics and area-delay cost functions directly mapped from CMOS technology have been used to compare QCA designs, which is inappropriate due to the differences between these two technologies. In this paper, several cost metrics specifically aimed at QCA circuits are studied. It is found that delay, the number of QCA logic gates, and the number and type of crossovers, are important metrics that should be considered when comparing QCA designs. A family of new cost functions for QCA circuits is proposed. As fundamental components in QCA computing arithmetic, QCA adders are reviewed and evaluated with the proposed cost functions. By taking the new cost metrics into account, previous best adders become unattractive and it has been shown that different optimization goals lead to different “best” adders.

Rational Partial Choice Functions and Their Application to Belief Revision.

Necessary and sufficient conditions for choice functions to be rational have been intensively studied in the past. However, in these attempts, a choice function is completely specified. That is, given any subset of options, called an issue, the best option over that issue is always known, whilst in real-world scenarios, it is very often that only a few choices are known instead of all. In this paper, we study partial choice functions and investigate necessary and sufficient rationality conditions for situations where only a few choices are known. We prove that our necessary and sufficient condition for partial choice functions boils down to the necessary and sufficient conditions for complete choice functions proposed in the literature. Choice functions have been instrumental in belief revision theory. That is, in most approaches to belief revision, the problem studied can simply be described as the choice of possible worlds compatible with the input information, given an agent’s prior belief state. The main effort has been to devise strategies in order to infer the agents revised belief state. Our study considers the converse problem: given a collection of input information items and their corresponding revision results (as provided by an agent), does there exist a rational revision operation used by the agent and a consistent belief state that may explain the observed results?

Nuclear translocation and functions of growth factor receptors

Cellular signal transduction in response to environmental signals involves a relay of precisely regulated signal amplifying and damping events. A prototypical signaling relay involves ligands binding to cell surface receptors and triggering the activation of downstream enzymes to ultimately affect the subcellular distribution and activity of DNA-binding proteins that regulate gene expression. These so-called signal transduction cascades have dominated our view of signaling for decades. More recently evidence has accumulated that components of these cascades can be multifunctional, in effect playing a conventional role for example as a cell surface receptor for a ligand whilst also having alternative functions for example as transcriptional regulators in the nucleus. This raises new challenges for researchers. What are the cues/triggers that determine which role such proteins play? What are the trafficking pathways which regulate the spatial distribution of such proteins so that they can perform nuclear functions and under what circumstances are these alternative functions most relevant?

Nuclear trafficking and functions of endocytic proteins implicated in oncogenesis

A subset of proteins predominantly associated with early endosomes or implicated in clathrin-mediated endocytosis can shuttle between the cytoplasm and the nucleus. Although the endocytic functions of these proteins have been extensively studied, much less effort has been expended in exploring their nuclear roles. Membrane trafficking proteins can affect signalling and proliferation and this can be achieved either at a nuclear or endocytic level. Furthermore, some proteins, such as Huntingtin interacting protein 1, are known as cancer biomarkers. This review will highlight the limits of our understanding of their nuclear functions and the relevance of this to signalling and oncogenesis.