We train a neural network as the universal exchange–correlation functional of density-functional theory that simultaneously reproduces both the exact exchange–correlation energy and the potential. ...This functional is extremely nonlocal but retains the computational scaling of traditional local or semilocal approximations. It therefore holds the promise of solving some of the delocalization problems that plague density-functional theory, while maintaining the computational efficiency that characterizes the Kohn–Sham equations. Furthermore, by using automatic differentiation, a capability present in modern machine-learning frameworks, we impose the exact mathematical relation between the exchange–correlation energy and the potential, leading to a fully consistent method. We demonstrate the feasibility of our approach by looking at one-dimensional systems with two strongly correlated electrons, where density-functional methods are known to fail, and investigate the behavior and performance of our functional by varying the degree of nonlocality.
Alzheimer's disease (AD) is the most common form of dementia in older adults that damages the brain and results in impaired memory, thinking and behaviour. The identification of differentially ...expressed genes and related pathways among affected brain regions can provide more information on the mechanisms of AD. In the past decade, several studies have reported many genes that are associated with AD. This wealth of information has become difficult to follow and interpret as most of the results are conflicting. In that case, it is worth doing an integrated study of multiple datasets that helps to increase the total number of samples and the statistical power in detecting biomarkers. In this study, we present an integrated analysis of five different brain region datasets and introduce new genes that warrant further investigation.
The aim of our study is to apply a novel combinatorial optimisation based meta-analysis approach to identify differentially expressed genes that are associated to AD across brain regions. In this study, microarray gene expression data from 161 samples (74 non-demented controls, 87 AD) from the Entorhinal Cortex (EC), Hippocampus (HIP), Middle temporal gyrus (MTG), Posterior cingulate cortex (PC), Superior frontal gyrus (SFG) and visual cortex (VCX) brain regions were integrated and analysed using our method. The results are then compared to two popular meta-analysis methods, RankProd and GeneMeta, and to what can be obtained by analysing the individual datasets.
We find genes related with AD that are consistent with existing studies, and new candidate genes not previously related with AD. Our study confirms the up-regualtion of INFAR2 and PTMA along with the down regulation of GPHN, RAB2A, PSMD14 and FGF. Novel genes PSMB2, WNK1, RPL15, SEMA4C, RWDD2A and LARGE are found to be differentially expressed across all brain regions. Further investigation on these genes may provide new insights into the development of AD. In addition, we identified the presence of 23 non-coding features, including four miRNA precursors (miR-7, miR570, miR-1229 and miR-6821), dysregulated across the brain regions. Furthermore, we compared our results with two popular meta-analysis methods RankProd and GeneMeta to validate our findings and performed a sensitivity analysis by removing one dataset at a time to assess the robustness of our results. These new findings may provide new insights into the disease mechanisms and thus make a significant contribution in the near future towards understanding, prevention and cure of AD.
The accurate (or even approximate) solution of the equations that govern the dynamics of dissipative quantum systems remains a challenging task in quantum science. While several algorithms have been ...designed to solve those equations with different degrees of flexibility, they rely mainly on highly expensive iterative schemes. Most recently, deep neural networks have been used for quantum dynamics, but current architectures are highly dependent on the physics of the particular system and usually limited to population dynamics. Here we introduce an artificial-intelligence-based surrogate model that solves dissipative quantum dynamics by parametrizing quantum propagators as Fourier neural operators, which we train using both data set and physics-informed loss functions. Compared with conventional algorithms, our quantum neural propagator avoids time-consuming iterations and provides a universal superoperator that can be used to evolve any initial quantum state for arbitrarily long times. To illustrate the wide applicability of the approach, we employ our quantum neural propagator to compute the population dynamics and time-correlation functions of the Fenna–Matthews–Olson complex.
Based on a generalization of Hohenberg-Kohn's theorem, we propose a ground state theory for bosonic quantum systems. Since it involves the one-particle reduced density matrix γ as a variable but ...still recovers quantum correlations in an exact way it is particularly well suited for the accurate description of Bose-Einstein condensates. As a proof of principle we study the building block of optical lattices. The solution of the underlying v-representability problem is found and its peculiar form identifies the constrained search formalism as the ideal starting point for constructing accurate functional approximations: The exact functionals Fγ for this N-boson Hubbard dimer and general Bogoliubov-approximated systems are determined. For Bose-Einstein condensates with N_{BEC}≈N condensed bosons, the respective gradient forces are found to diverge, ∇_{γ}F∝1/sqrt1-N_{BEC}/N, providing a comprehensive explanation for the absence of complete condensation in nature.
Misconceptions, lack of knowledge, and negative attitudes towards sharks act as barriers preventing actions required to tackle threats to shark populations, limiting the success of global shark ...conservation initiatives. Peru, a major player for the international trade of shark products, recently approved the 'National Action Plan for the Conservation and Management of Sharks, Rays and Chimaeras' (PAN-Tib); a guiding document for conservation initiatives aimed at these fishes. Within PAN-Tib, the assessment of Peruvians' current knowledge and attitudes towards sharks is listed as a research priority. Between June and October 2016, 2004 Peruvians were surveyed along the coast to characterize their (i) shark meat consumption patterns, and (ii) knowledge and attitudes towards sharks. Results suggest that shark meat consumption is extended, but not necessarily frequent, and higher in the northern regions of the country. However, 77.5% of shark meat consumers were unaware that they had eaten sharks. Although 57.6% of the participants recognized that sharks are present in Peruvian waters, only 19.4% of the surveyed population was capable of naming at least one local shark species. Moreover, Peruvians have very negative attitudes towards sharks. They fear them and view them as man-eaters, despite this, no shark attacks have ever been reported in the country. These results highlight the need to: (i) encourage sustainable shark meat consumption, and (ii) promote communication campaigns aimed at increasing knowledge about sharks, and their importance as a source of employment and food for coastal communities, as for the national economy.
Abstract Computing excited-state properties of molecules and solids is considered one of the most important near-term applications of quantum computers. While many of the current excited-state ...quantum algorithms differ in circuit architecture, specific exploitation of quantum advantage, or result quality, one common feature is their rooting in the Schrödinger equation. However, through contracting (or projecting) the eigenvalue equation, more efficient strategies can be designed for near-term quantum devices. Here we demonstrate that when combined with the Rayleigh–Ritz variational principle for mixed quantum states, the ground-state contracted quantum eigensolver (CQE) can be generalized to compute any number of quantum eigenstates simultaneously. We introduce two excited-state (anti-Hermitian) CQEs that perform the excited-state calculation while inheriting many of the remarkable features of the original ground-state version of the algorithm, such as its scalability. To showcase our approach, we study several model and chemical Hamiltonians and investigate the performance of different implementations.
Some of the most spectacular failures of density-functional and Hartree-Fock theories are related to an incorrect description of the so-called static electron correlation. Motivated by recent ...progress in the
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-representability problem of the one-body density matrix for pure states, we propose a method to quantify the static contribution to the electronic correlation. By studying several molecular systems we show that our proposal correlates well with our intuition of static and dynamic electron correlation. Our results bring out the paramount importance of the occupancy of the highest occupied natural spin-orbital in such quantification.
Some of the most spectacular failures of density-functional and Hartree-Fock theories are related to an incorrect description of the so-called static electron correlation. Motivated by recent progress in the
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-representability problem of the one-body density matrix for pure states, we propose a way to quantify the static contribution to the electronic correlation.
The concept of active spaces simplifies the description of interacting quantum many-body systems by restricting to a neighborhood of active orbitals around the Fermi level. The respective ...wavefunction ansatzes which involve all possible electron configurations of active orbitals can be characterized by the saturation of a certain number of Pauli constraints 0 ≤ n i ≤ 1 , identifying the occupied core orbitals (ni = 1) and the inactive virtual orbitals (nj = 0). In Part I, we generalize this crucial concept of active spaces by referring to the generalized Pauli constraints. To be more specific, we explain and illustrate that the saturation of any such constraint on fermionic occupation numbers characterizes a distinctive set of active electron configurations. A converse form of this selection rule establishes the basis for corresponding multiconfigurational wavefunction ansatzes. In Part II, we provide rigorous derivations of those findings. Moroever, we extend our results to non-fermionic multipartite quantum systems, revealing that extremal single-body information has always strong implications for the multipartite quantum state. In that sense, our work also confirms that pinned quantum systems define new physical entities and the presence of pinnings reflect the existence of (possibly hidden) ground state symmetries.
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