Abstract:
Wnts are secreted glycoproteins that regulate cell morphologies and behaviors by stimulating complicate intracellular signaling cascades. Previous work has established that Wnt signaling controls many oncogenic and developmental processes [1,2]. More recent studies have revealed that Wnt signaling is critically involved in key processes of the formation and plasticity of the nervous system, including neurogenesis [3], axon guidance [4], dendritic development [5], synaptic differentiation [6] and plasticity [7,8]. Abnormalities of Wnt signaling are implicated in major brain disorders such as Alzheimer's disease [9-11], Parkinson's disease [12,13], schizophrenia [14,15], and drug abuse [16]. Wnt5a is member of the Wnt protein family and plays important roles in outgrowth, guidance and branching of axons [17,18]; genesis of dopaminergic neurons [19]; and formation and plasticity of both excitatory and inhibitory synapses [20-22]. Wnt5a administration was reported to improve specific pathological processes of Alzheimer's [11] and Parkinson's diseases in animal models [12].Wnt proteins bind to receptors to activate the Wnt/β-catenin canonical pathway and β-catenin-independent non-canonical pathways, which include the planar cell polarity (PCP) pathway and the Wnt/calcium (Ca2+) pathway [2,23-26]. In the canonical pathway, Wnts (such as Wnt3a) inhibit glycogen synthase kinase 3β (GSK-3β) and consequently stabilize β-catenin to regulate transcription [1]. Wnt5a is a prototypic Wnt ligand that activates the non-canonical pathways [27,28]. The activation of the PCP pathway stimulates Rho GTPases and c-Jun N-terminal kinase (JNK) to regulate cell morphogenesis and movement [29], whereas the activation of the Wnt/Ca2+ pathway causes Ca2+ to activate protein kinase C (PKC) and calcium/calmodulin dependent protein kinase II (CaMKII) [30]. In neurons, Wnt secretion is intimately governed by synaptic activity, especially the activation of NMDA receptors (NMDAR) [7].In contrast to

Abstract:
CD4+CD25+Foxp3+ regulatory T cells (Tregs) can inhibit cytotoxic responses. Though several studies have analyzed Treg frequency in the peripheral blood mononuclear cells (PBMCs) of pancreatic ductal adenocarcinoma (PDA) patients using flow cytometry (FCM), few studies have examined how intratumoral Tregs might contribute to immunosuppression in the tumor microenvironment. Thus, the potential role of intratumoral Tregs in PDA patients remains to be elucidated. In this study, we found that the percentages of Tregs, CD4+ T cells and CD8+ T cells were all increased significantly in tumor tissue compared to control pancreatic tissue, as assessed via FCM, whereas the percentages of these cell types in PBMCs did not differ between PDA patients and healthy volunteers. The percentages of CD8+ T cells in tumors were significantly lower than in PDA patient PBMCs. In addition, the relative numbers of CD4+CD25+Foxp3+ Tregs and CD8+ T cells were negatively correlated in the tissue of PDA patients, and the abundance of Tregs was significantly correlated with tumor differentiation. Additionally, Foxp3+ T cells were observed more frequently in juxtatumoral stroma (immediately adjacent to the tumor epithelial cells). Patients showing an increased prevalence of Foxp3+ T cells had a poorer prognosis, which was an independent factor for patient survival. These results suggest that Tregs may promote PDA progression by inhibiting the antitumor immunity of CD8+ T cells at local intratumoral sites. Moreover, a high proportion of Tregs in tumor tissues may reflect suppressed antitumor immunity.

Abstract:
An area law is proved for the Renyi entanglement entropy of possibly degenerate ground states in one-dimensional gapped quantum systems. Suppose in a chain of $n$ spins the ground states of a local Hamiltonian with energy gap $\epsilon$ are constant-fold degenerate. Then, the Renyi entanglement entropy $R_\alpha(0<\alpha<1)$ of any ground state across any cut is upper bounded by $\tilde O(\alpha^{-3}/\epsilon)$, and any ground state can be well approximated by a matrix product state of subpolynomial bond dimension $2^{\tilde O(\epsilon^{-1/4}\log^{3/4}n)}$.

Abstract:
We show that the 2D local Hamiltonian problem with the restriction that the ground state satisfies area laws is QMA-complete. We also prove similar results in 2D translationally invariant systems and for the 3D Heisenberg and Hubbard models. Consequently, in general the ground states of local Hamiltonians satisfying area laws do not have efficient classical representations that support efficient computation of local expectation values unless QMA=NP. Conceptually, even if in the future area laws are proved for the ground state in 2D gapped systems, there is still a long way to go towards understanding the computational complexity of 2D gapped systems.

Abstract:
We study the problem of computing energy density in one-dimensional quantum systems. We show that the ground-state energy per site or per bond can be computed in time (i) independent of the system size and subexponential in the desired precision if the ground state satisfies area laws for the Renyi entanglement entropy (this is the first rigorous formulation of the folklore that area laws imply efficient matrix-product-state algorithms); (ii) independent of the system size and polynomial in the desired precision if the system is gapped. As a by-product, we prove that in the presence of area laws (or even an energy gap) the ground state can be approximated by a positive semidefinite matrix product operator of bond dimension independent of the system size and subpolynomial in the desired precision of local properties.

Abstract:
We propose an efficient algorithm for the ground state of frustration-free one-dimensional gapped Hamiltonians. This algorithm is much simpler than the original one by Landau et al., and thus may be easily accessible to a general audience in the community. We present all the details in two pages.

Abstract:
We study the scaling of quantum discord (a measure of quantum correlation beyond entanglement) in spin models analytically and systematically. We find that at finite temperature the block scaling of quantum discord satisfies an area law for any two-local Hamiltonian. We show that generically and heuristically the two-site scaling of quantum discord is similar to that of correlation functions. In particular, at zero temperature it decays exponentially and polynomially in gapped and gapless (critical) systems, respectively; at finite temperature it decays exponentially in both gapped and gapless systems. We compute the two-site scaling of quantum discord in the XXZ chain, the XY chain (in a magnetic field), and the transverse field Ising chain at zero temperature.

Abstract:
An efficient numerical method is developed using the matrix product formalism for computing the properties at finite energy densities in one-dimensional (1D) many-body localized (MBL) systems. Arguing that any efficient (possibly quantum) algorithm can only have a polynomially small energy resolution, we propose a (rigorous) polynomial-time (classical) algorithm that outputs a diagonal density operator supported on a microcanonical ensemble of an inverse polynomial bandwidth. The proof uses no other conditions for MBL but assumes that the effect of any local perturbation (e.g., injecting conserved charges) is restricted to a region whose radius grows logarithmically with time. A non-optimal version of this algorithm efficiently simulates the quantum phase estimation algorithm in 1D MBL systems; a heuristic version of the algorithm can be easily coded and used to, e.g., detect energy-tuned dynamical quantum phase transitions between MBL phases. We extend the algorithm to two and higher spatial dimensions using the projected entangled pair formalism.

Abstract:
We construct a solvable spin chain model of many-body localization (MBL) with a tunable mobility edge. This simple model not only demonstrates analytically the existence of mobility edges in interacting one-dimensional (1D) disordered systems, but also allows us to study their physics. By establishing a connection between MBL and a quantum central limit theorem (QCLT), we show that many-body localization-delocalization transitions can be visualized as tuning a mobility edge in the energy spectrum. Since the effective disorder strength for individual eigenstates depends on energy density, we identify "energy-resolved disorder strength" as a physical mechanism for the appearance of mobility edges, and support the universality of this mechanism by arguing its presence in a large class of models including the random-field Heisenberg chain. We also construct models with multiple mobility edges. All our constructions can be made translationally invariant.

Abstract:
We study the computational complexity of quantum discord (a measure of quantum correlation beyond entanglement), and prove that computing quantum discord is NP-complete. Therefore, quantum discord is computationally intractable: the running time of any algorithm for computing quantum discord is believed to grow exponentially with the dimension of the Hilbert space so that computing quantum discord in a quantum system of moderate size is not possible in practice. As by-products, some entanglement measures (namely entanglement cost, entanglement of formation, relative entropy of entanglement, squashed entanglement, classical squashed entanglement, conditional entanglement of mutual information, and broadcast regularization of mutual information) and constrained Holevo capacity are NP-hard/NP-complete to compute. These complexity-theoretic results are directly applicable in common randomness distillation, quantum state merging, entanglement distillation, superdense coding, and quantum teleportation; they may offer significant insights into quantum information processing. Moreover, we prove the NP-completeness of two typical problems: linear optimization over classical states and detecting classical states in a convex set, providing evidence that working with classical states is generically computationally intractable.