Holographic Algorithm with Matchgates Is Universal for Planar #\#CSP Over Boolean Domain

We prove a complexity classification theorem that classifies all counting constraint satisfaction problems ($\#$CSP) over Boolean variables into exactly three categories: (1) Polynomial-time tractable; (2) $\#$P-hard for general instances, but solvable in polynomial-time over planar graphs; and (3) $\#$P-hard over planar graphs. The classification applies to all sets of local, not necessarily symmetric, constraint functions on Boolean variables that take complex values. It is shown that Valiant's holographic algorithm with matchgates is a universal strategy for all problems in category (2).Comment: 94 page

Scaling in the vicinity of the four-state Potts fixed point

We study a self-dual generalization of the Baxter-Wu model, employing results obtained by transfer matrix calculations of the magnetic scaling dimension and the free energy. While the pure critical Baxter-Wu model displays the critical behavior of the four-state Potts fixed point in two dimensions, in the sense that logarithmic corrections are absent, the introduction of different couplings in the up- and down triangles moves the model away from this fixed point, so that logarithmic corrections appear. Real couplings move the model into the first-order range, away from the behavior displayed by the nearest-neighbor, four-state Potts model. We also use complex couplings, which bring the model in the opposite direction characterized by the same type of logarithmic corrections as present in the four-state Potts model. Our finite-size analysis confirms in detail the existing renormalization theory describing the immediate vicinity of the four-state Potts fixed point.Comment: 19 pages, 7 figure

Two novel nonlinear companding schemes with iterative receiver to reduce PAPR in multi-carrier modulation systems

Companding transform is an efficient and simple method to reduce the Peak-to-Average Power Ratio (PAPR) for Multi-Carrier Modulation (MCM) systems. But if the MCM signal is only simply operated by inverse companding transform at the receiver, the resultant spectrum may exhibit severe in-band and out-of-band radiation of the distortion components, and considerable peak regrowth by excessive channel noises etc. In order to prevent these problems from occurring, in this paper, two novel nonlinear companding schemes with a iterative receiver are proposed to reduce the PAPR. By transforming the amplitude or power of the original MCM signals into uniform distributed signals, the novel schemes can effectively reduce PAPR for different modulation formats and sub-carrier sizes. Despite moderate complexity increasing at the receiver, but it is especially suitable to be combined with iterative channel estimation. Computer simulation results show that the proposed schemes can offer good system performances without any bandwidth expansion

Olig2/Plp-positive progenitor cells give rise to Bergmann glia in the cerebellum.

NG2 (nerve/glial antigen2)-expressing cells represent the largest population of postnatal progenitors in the central nervous system and have been classified as oligodendroglial progenitor cells, but the fate and function of these cells remain incompletely characterized. Previous studies have focused on characterizing these progenitors in the postnatal and adult subventricular zone and on analyzing the cellular and physiological properties of these cells in white and gray matter regions in the forebrain. In the present study, we examine the types of neural progeny generated by NG2 progenitors in the cerebellum by employing genetic fate mapping techniques using inducible Cre-Lox systems in vivo with two different mouse lines, the Plp-Cre-ER(T2)/Rosa26-EYFP and Olig2-Cre-ER(T2)/Rosa26-EYFP double-transgenic mice. Our data indicate that Olig2/Plp-positive NG2 cells display multipotential properties, primarily give rise to oligodendroglia but, surprisingly, also generate Bergmann glia, which are specialized glial cells in the cerebellum. The NG2+ cells also give rise to astrocytes, but not neurons. In addition, we show that glutamate signaling is involved in distinct NG2+ cell-fate/differentiation pathways and plays a role in the normal development of Bergmann glia. We also show an increase of cerebellar oligodendroglial lineage cells in response to hypoxic-ischemic injury, but the ability of NG2+ cells to give rise to Bergmann glia and astrocytes remains unchanged. Overall, our study reveals a novel Bergmann glia fate of Olig2/Plp-positive NG2 progenitors, demonstrates the differentiation of these progenitors into various functional glial cell types, and provides significant insights into the fate and function of Olig2/Plp-positive progenitor cells in health and disease

Perturbative analysis of generally nonlocal spatial optical solitons

In analogy to a perturbed harmonic oscillator, we calculate the fundamental and some other higher order soliton solutions of the nonlocal nonlinear Schroedinger equation (NNLSE) in the second approximation in the generally nonlocal case. Comparing with numerical simulations we show that soliton solutions in the 2nd approximation can describe the generally nonlocal soliton states of the NNLSE more exactly than that in the zeroth approximation. We show that for the nonlocal case of an exponential-decay type nonlocal response the Gaussian-function-like soliton solutions can't describe the nonlocal soliton states exactly even in the strongly nonlocal case. The properties of such nonlocal solitons are investigated. In the strongly nonlocal limit, the soliton's power and phase constant are both in inverse proportion to the 4th power of its beam width for the nonlocal case of a Gaussian function type nonlocal response, and are both in inverse proportion to the 3th power of its beam width for the nonlocal case of an exponential-decay type nonlocal response.Comment: 13 pages, 16 figures, accepted by Phys. Rev.

Interplay between single particle coherence and kinetic energy driven superconductivity in doped cuprates

Within the kinetic energy driven superconducting mechanism, the interplay between the single particle coherence and superconducting instability in doped cuprates is studied. The superconducting transition temperature increases with increasing doping in the underdoped regime, and reaches a maximum in the optimal doping, then decreases in the overdoped regime, however, the values of this superconducting transition temperature in the whole superconducting range are suppressed to low temperature due to the single particle coherence. Within this superconducting mechanism, we calculate the dynamical spin structure factor of cuprate superconductors, and reproduce all main features of inelastic neutron scattering experiments in the superconducting-state.Comment: 7 pages, 3 figures, typo correcte

Recent progress in random metric theory and its applications to conditional risk measures

The purpose of this paper is to give a selective survey on recent progress in random metric theory and its applications to conditional risk measures. This paper includes eight sections. Section 1 is a longer introduction, which gives a brief introduction to random metric theory, risk measures and conditional risk measures. Section 2 gives the central framework in random metric theory, topological structures, important examples, the notions of a random conjugate space and the Hahn-Banach theorems for random linear functionals. Section 3 gives several important representation theorems for random conjugate spaces. Section 4 gives characterizations for a complete random normed module to be random reflexive. Section 5 gives hyperplane separation theorems currently available in random locally convex modules. Section 6 gives the theory of random duality with respect to the locally $L^{0}-$convex topology and in particular a characterization for a locally $L^{0}-$convex module to be $L^{0}-$pre$-$barreled. Section 7 gives some basic results on $L^{0}-$convex analysis together with some applications to conditional risk measures. Finally, Section 8 is devoted to extensions of conditional convex risk measures, which shows that every representable $L^{\infty}-$type of conditional convex risk measure and every continuous $L^{p}-$type of convex conditional risk measure ($1\leq p<+\infty$) can be extended to an $L^{\infty}_{\cal F}({\cal E})-$type of $\sigma_{\epsilon,\lambda}(L^{\infty}_{\cal F}({\cal E}), L^{1}_{\cal F}({\cal E}))-$lower semicontinuous conditional convex risk measure and an $L^{p}_{\cal F}({\cal E})-$type of ${\cal T}_{\epsilon,\lambda}-$continuous conditional convex risk measure ($1\leq p<+\infty$), respectively.Comment: 37 page

Observation of an in-plane magnetic-field-driven phase transition in a quantum Hall system with SU(4) symmetry

In condensed matter physics, the study of electronic states with SU(N) symmetry has attracted considerable and growing attention in recent years, as systems with such a symmetry can often have a spontaneous symmetry-breaking effect giving rise to a novel ground state. For example, pseudospin quantum Hall ferromagnet of broken SU(2) symmetry has been realized by bringing two Landau levels close to degeneracy in a bilayer quantum Hall system. In the past several years, the exploration of collective states in other multi-component quantum Hall systems has emerged. Here we show the conventional pseudospin quantum Hall ferromagnetic states with broken SU(2) symmetry collapsed rapidly into an unexpected state with broken SU(4) symmetry, by in-plane magnetic field in a two-subband GaAs/AlGaAs two-dimensional electron system at filling factor around $\nu=4$. Within a narrow tilting range angle of 0.5 degrees, the activation energy increases as much as 12 K. While the origin of this puzzling observation remains to be exploited, we discuss the possibility of a long-sought pairing state of electrons with a four-fold degeneracy.Comment: 13 pages, 4 figure

Triaxial nuclear models and the outer crust of nonaccreting cold neutron stars

The properties and composition of the outer crust of nonaccreting cold neutron stars are studied by applying the model of Baym, Pethick, and Sutherland (BPS) and taking into account for the first time triaxial deformations of nuclei. Two theoretical nuclear models, Hartree-Fock plus pairing in the BCS approximation (HF-BCS) with Skyrme SLy6 parametrization and Hartree-Fock-Bogolyubov (HFB) with Gogny D1S force, are used to calculate the nuclear masses. The two theoretical calculations are compared concerning their neutron drip line, binding energies, magic neutron numbers, and the sequence of nuclei in the outer crust of nonaccreting cold neutron stars, with special emphasis on the effect of triaxial deformations. The BPS model is extended by the higher-order corrections for the atomic binding, screening, exchange and zero-point energies. The influence of the higher-order corrections on the sequence of the outer crust is investigated.Comment: 7 page