Low-energy excitations of the one-dimensional half-filled SU(4) Hubbard model with an attractive on-site interaction: Density-matrix renormalization-group calculations and perturbation theory

We investigate low-energy excitations of the one-dimensional half-filled SU(4) Hubbard model with an attractive on-site interaction U < 0 using the density matrix renormalization group method as well as a perturbation theory. We find that the ground state is a charge density wave state with a long range order. The ground state is completely incompressible since all the excitations are gapful. The charge gap which is the same as the four-particle excitation gap is a non-monotonic function of U, while the spin gap and others increase with increasing |U| and have linear asymptotic behaviors.Comment: 4 pages, 3 figures, submitte

An improved perturbation approach to the 2D Edwards polymer -- corrections to scaling

We present the results of a new perturbation calculation in polymer statistics which starts from a ground state that already correctly predicts the long chain length behaviour of the mean square end--to--end distance $\langle R_N^2 \rangle\$, namely the solution to the 2~dimensional~(2D) Edwards model. The $\langle R_N^2 \rangle$ thus calculated is shown to be convergent in $N$, the number of steps in the chain, in contrast to previous methods which start from the free random walk solution. This allows us to calculate a new value for the leading correction--to--scaling exponent~$\Delta$. Writing $\langle R_N^2 \rangle = AN^{2\nu}(1+BN^{-\Delta} + CN^{-1}+...)$, where $\nu = 3/4$ in 2D, our result shows that $\Delta = 1/2$. This value is also supported by an analysis of 2D self--avoiding walks on the {\em continuum}.Comment: 17 Pages of Revtex. No figures. Submitted to J. Phys.

Gaucher disease and the synucleinopathies: refining the relationship

Gaucher disease (OMIM 230800, 230900, 231000), the most common lysosomal storage disorder, is due to a deficiency in the enzyme glucocerebrosidase. Gaucher patients display a wide spectrum of clinical presentation, with hepatosplenomegaly, haematological changes, and orthopaedic complications being the predominant symptoms. Gaucher disease is classified into three broad phenotypes based upon the presence or absence of neurological involvement: Type 1 (non-neuronopathic), Type 2 (acute neuronopathic), and Type 3 (subacute neuronopathic). Nearly 300 mutations have been identified in Gaucher patients, with the majority being missense mutations. Though studies of genotype-to-phenotype correlations have revealed significant heterogeneity, some consistent patterns have emerged to inform prognostic and therapeutic decisions. Recent research has highlighted a potential role for Gaucher disease in other comorbidities such as cancer and Parkinson's Disease. In this review, we will examine the potential relationship between Gaucher disease and the synucleinopathies, a group of neurodegenerative disorders characterized by the development of intracellular aggregates of α-synuclein. Possible mechanisms of interaction will be discussed

Gaucher Disease and Cancer: Concept and Controversy

Gaucher disease is an inherited disorder caused by a deficiency in the lysosomal hydrolase glucocerebrosidase. There is a wide spectrum of clinical presentations, with the most common features being hepatosplenomegaly, skeletal disease, and cytopenia. Gaucher disease has been classified into three broad phenotypes based upon the presence or absence of neurological involvement: Type 1 (nonneuronopathic), Type 2 (acute neuronopathic), and Type 3 (subacute neuronopathic). The two main treatment options include enzyme replacement therapy and substrate reduction therapy. Recently, discussion has escalated around the association of Gaucher disease and cancer, with conflicting reports as to whether Gaucher patients have an increased risk of malignancy. In this review, we present both the concept and controversy surrounding the association of Gaucher disease with cancer

Electrical and pyroelectric properties of in-plane polarized lead lanthanum titanate thin film

Author name used in this publication: N. Chong2001-2002 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Critical exponents of the degenerate Hubbard model

We study the critical behaviour of the \SUN{} generalization of the one-dimensional Hubbard model with arbitrary degeneracy $N$. Using the integrability of this model by Bethe Ansatz we are able to compute the spectrum of the low-lying excitations in a large but finite box for arbitrary values of the electron density and of the Coulomb interaction. This information is used to determine the asymptotic behaviour of correlation functions at zero temperature in the presence of external fields lifting the degeneracy. The critical exponents depend on the system parameters through a $N\times N$ dressed charge matrix implying the relevance of the interaction of charge- and spin-density waves.Comment: 18 page

Few-Shot Single-View 3-D Object Reconstruction with Compositional Priors

The impressive performance of deep convolutional neural networks in single-view 3D reconstruction suggests that these models perform non-trivial reasoning about the 3D structure of the output space. However, recent work has challenged this belief, showing that complex encoder-decoder architectures perform similarly to nearest-neighbor baselines or simple linear decoder models that exploit large amounts of per category data in standard benchmarks. On the other hand settings where 3D shape must be inferred for new categories with few examples are more natural and require models that generalize about shapes. In this work we demonstrate experimentally that naive baselines do not apply when the goal is to learn to reconstruct novel objects using very few examples, and that in a \emph{few-shot} learning setting, the network must learn concepts that can be applied to new categories, avoiding rote memorization. To address deficiencies in existing approaches to this problem, we propose three approaches that efficiently integrate a class prior into a 3D reconstruction model, allowing to account for intra-class variability and imposing an implicit compositional structure that the model should learn. Experiments on the popular ShapeNet database demonstrate that our method significantly outperform existing baselines on this task in the few-shot setting

A robust computational algorithm for inverse photomask synthesis in optical projection lithography

Inverse lithography technology formulates the photomask synthesis as an inverse mathematical problem. To solve this, we propose a variational functional and develop a robust computational algorithm, where the proposed functional takes into account the process variations and incorporates several regularization terms that can control the mask complexity. We establish the existence of the minimizer of the functional, and in order to optimize it effectively, we adopt an alternating minimization procedure with Chambolle's fast duality projection algorithm. Experimental results show that our proposed algorithm is effective in synthesizing high quality photomasks as compared with existing methods.published_or_final_versio

Microstructure and electric properties of lead lanthanum titanate thin film under transverse electric fields

Author name used in this publication: N. Chong2001-2002 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Epitaxial growth and planar dielectric properties of compositionally graded (Ba[sub 1-x]Sr[sub x])TiO₃ thin films prepared by pulsed-laser deposition

2001-2002 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe