Computational Complexity of interacting electrons and fundamental limitations of Density Functional Theory

One of the central problems in quantum mechanics is to determine the ground state properties of a system of electrons interacting via the Coulomb potential. Since its introduction by Hohenberg, Kohn, and Sham, Density Functional Theory (DFT) has become the most widely used and successful method for simulating systems of interacting electrons, making their original work one of the most cited in physics. In this letter, we show that the field of computational complexity imposes fundamental limitations on DFT, as an efficient description of the associated universal functional would allow to solve any problem in the class QMA (the quantum version of NP) and thus particularly any problem in NP in polynomial time. This follows from the fact that finding the ground state energy of the Hubbard model in an external magnetic field is a hard problem even for a quantum computer, while given the universal functional it can be computed efficiently using DFT. This provides a clear illustration how the field of quantum computing is useful even if quantum computers would never be built.Comment: 8 pages, 3 figures. v2: Version accepted at Nature Physics; differs significantly from v1 (including new title). Includes an extra appendix (not contained in the journal version) on the NP-completeness of Hartree-Fock, which is taken from v

An Extended Model for the Evolution of Prebiotic Homochirality: A Bottom-Up Approach to the Origin of Life

A generalized autocatalytic model for chiral polymerization is investigated in detail. Apart from enantiomeric cross-inhibition, the model allows for the autogenic (non-catalytic) formation of left and right-handed monomers from a substrate with reaction rates $\epsilon_L$ and $\epsilon_R$, respectively. The spatiotemporal evolution of the net chiral asymmetry is studied for models with several values of the maximum polymer length, N. For N=2, we study the validity of the adiabatic approximation often cited in the literature. We show that the approximation obtains the correct equilibrium values of the net chirality, but fails to reproduce the short time behavior. We show also that the autogenic term in the full N=2 model behaves as a control parameter in a chiral symmetry- breaking phase transition leading to full homochirality from racemic initial conditions. We study the dynamics of the N -> infinity model with symmetric ($\epsilon_L = \epsilon_R$) autogenic formation, showing that it only achieves homochirality for $\epsilon < \epsilon_c$, where $\epsilon_c$ is an N-dependent critical value. For $\epsilon \leq \epsilon_c$ we investigate the behavior of models with several values of N, showing that the net chiral asymmetry grows as tanh(N). We show that for a given symmetric autogenic reaction rate, the net chirality and the concentrations of chirally pure polymers increase with the maximum polymer length in the model. We briefly discuss the consequences of our results for the development of homochirality in prebiotic Earth and possible experimental verification of our findings

Photoswitchable diacylglycerols enable optical control of protein kinase C.

Increased levels of the second messenger lipid diacylglycerol (DAG) induce downstream signaling events including the translocation of C1-domain-containing proteins toward the plasma membrane. Here, we introduce three light-sensitive DAGs, termed PhoDAGs, which feature a photoswitchable acyl chain. The PhoDAGs are inactive in the dark and promote the translocation of proteins that feature C1 domains toward the plasma membrane upon a flash of UV-A light. This effect is quickly reversed after the termination of photostimulation or by irradiation with blue light, permitting the generation of oscillation patterns. Both protein kinase C and Munc13 can thus be put under optical control. PhoDAGs control vesicle release in excitable cells, such as mouse pancreatic islets and hippocampal neurons, and modulate synaptic transmission in Caenorhabditis elegans. As such, the PhoDAGs afford an unprecedented degree of spatiotemporal control and are broadly applicable tools to study DAG signaling

Associations between SNPs and immune-related circulating proteins in schizophrenia

Genome-wide association studies (GWAS) and proteomic studies have provided convincing evidence implicating alterations in immune/inflammatory processes in schizophrenia. However, despite the convergence of evidence, direct links between the genetic and proteomic findings are still lacking for schizophrenia. We investigated associations between single nucleotide polymorphisms (SNPs) from the custom-made PsychArray and the expression levels of 190 multiplex immunoassay profiled serum proteins in 149 schizophrenia patients and 198 matched controls. We identified associations between 81 SNPs and 29 proteins, primarily involved in immune/inflammation responses. Significant SNPxDiagnosis interactions were identified for eight serum proteins including Factor-VII[rs555212], Alpha-1-Antitrypsin[rs11846959], Interferon-Gamma Induced Protein 10[rs4256246] and von-Willebrand-Factor[rs12829220] in the control group; Chromogranin-A[rs9658644], Cystatin-C[rs2424577] and Vitamin K-Dependent Protein S[rs6123] in the schizophrenia group; Interleukin-6 receptor[rs7553796] in both the control and schizophrenia groups. These results suggested that the effect of these SNPs on expression of the respective proteins varies with diagnosis. The combination of patient-specific genetic information with blood biomarker data opens a novel approach to investigate disease mechanisms in schizophrenia and other psychiatric disorders. Our findings not only suggest that blood protein expression is influenced by polymorphisms in the corresponding gene, but also that the effect of certain SNPs on expression of proteins can vary with diagnosis

Chiral Polymerization in Open Systems From Chiral-Selective Reaction Rates

We investigate the possibility that prebiotic homochirality can be achieved exclusively through chiral-selective reaction rate parameters without any other explicit mechanism for chiral bias. Specifically, we examine an open network of polymerization reactions, where the reaction rates can have chiral-selective values. The reactions are neither autocatalytic nor do they contain explicit enantiomeric cross-inhibition terms. We are thus investigating how rare a set of chiral-selective reaction rates needs to be in order to generate a reasonable amount of chiral bias. We quantify our results adopting a statistical approach: varying both the mean value and the rms dispersion of the relevant reaction rates, we show that moderate to high levels of chiral excess can be achieved with fairly small chiral bias, below 10%. Considering the various unknowns related to prebiotic chemical networks in early Earth and the dependence of reaction rates to environmental properties such as temperature and pressure variations, we argue that homochirality could have been achieved from moderate amounts of chiral selectivity in the reaction rates.Comment: 15 pages, 6 figures, accepted for publication in Origins of Life and Evolution of Biosphere

Damage to the prefrontal cortex increases utilitarian moral judgements

The psychological and neurobiological processes underlying moral judgement have been the focus of many recent empirical studies1–11. Of central interest is whether emotions play a causal role in moral judgement, and, in parallel, how emotion-related areas of the brain contribute to moral judgement. Here we show that six patients with focal bilateral damage to the ventromedial prefrontal cortex (VMPC), a brain region necessary for the normal generation of emotions and, in particular, social emotions12–14, produce an abnor- mally ‘utilitarian’ pattern of judgements on moral dilemmas that pit compelling considerations of aggregate welfare against highly emotionally aversive behaviours (for example, having to sacrifice one person’s life to save a number of other lives)7,8. In contrast, the VMPC patients’ judgements were normal in other classes of moral dilemmas. These findings indicate that, for a selective set of moral dilemmas, the VMPC is critical for normal judgements of right and wrong. The findings support a necessary role for emotion in the generation of those judgements

Partitioning of on-demand electron pairs

We demonstrate the high fidelity splitting of electron pairs emitted on demand from a dynamic quantum dot by an electronic beam splitter. The fidelity of pair splitting is inferred from the coincidence of arrival in two detector paths probed by a measurement of the partitioning noise. The emission characteristic of the on-demand electron source is tunable from electrons being partitioned equally and independently to electron pairs being split with a fidelity of 90%. For low beam splitter transmittance we further find evidence of pair bunching violating statistical expectations for independent fermions

Belowground DNA-based techniques: untangling the network of plant root interactions

Contains fulltext : 91591.pdf (publisher's version ) (Closed access)7 p

Sprouty2 mediated tuning of signalling is essential for somite myogenesis

Background: Negative regulators of signal transduction cascades play critical roles in controlling different aspects of normal embryonic development. Sprouty2 (Spry2) negatively regulates receptor tyrosine kinases (RTK) and FGF signalling and is important in differentiation, cell migration and proliferation. In vertebrate embryos, Spry2 is expressed in paraxial mesoderm and in forming somites. Expression is maintained in the myotome until late stages of somite differentiation. However, its role and mode of action during somite myogenesis is still unclear. Results: Here, we analysed chick Spry2 expression and showed that it overlaps with that of myogenic regulatory factors MyoD and Mgn. Targeted mis-expression of Spry2 led to inhibition of myogenesis, whilst its C-terminal domain led to an increased number of myogenic cells by stimulating cell proliferation. Conclusions: Spry2 is expressed in somite myotomes and its expression overlaps with myogenic regulatory factors. Overexpression and dominant-negative interference showed that Spry2 plays a crucial role in regulating chick myogenesis by fine tuning of FGF signaling through a negative feedback loop. We also propose that mir-23, mir-27 and mir-128 could be part of the negative feedback loop mechanism. Our analysis is the first to shed some light on in vivo Spry2 function during chick somite myogenesis