Optimal approach to rotational state reconstruction of linear molecules

We present a simulation for the reconstruction of the rotational quantum state of linear molecules to retrieve the density matrix. An optimal approach in the sense of minimal error limit is proposed, in which a variable set of angular frequency is properly chosen and the least square inversion is then applied. This approach of reconstruction from time-dependent molecular-axis angular distribution is proved adaptable for various object states, which has a good numerical stability independent of the selected rotational space.

State reconstruction of molecular spatial rotation

We establish a reconstruction approach for the rotational quantum state of linear molecules possessing a magnetic manifold. Our approximate method contains an iteration with generalized matrix inverses, processing the tomographic integral of the time-dependent molecular-axis distribution in a polar angle. As shown in a simulated example for an alignment state, the density matrix is determined in a high fidelity. An analytic tomographic formula is also derived for the symmetric top rotation. The state coherent in the quantum space of both the angular momentum and its magnetic projection can be approximately retrieved from the observable time-resolved solid-angle distribution of the molecular axis.

Challenges in estimating ancestral state reconstructions:the evolution of migration in Sylvia warblers as a study case

Our current understanding of how species have evolved is mainly based on comparative phylogenetic methods,which use phylogenies to infer the evolution of traits.The development of ancestral state reconstruction(ASR)methods has provided the tools to reconstruct trait evolution,which are widely used in fields like evolutionary biology,macroecology and paleontology.As there are different elements involved in those analyses,with different levels of uncertainty(i.e.relating to branch length estimation,trait coding,statistical framework,taxon sampling or software),the various combinations of these elements likely have a strong impact on the reconstruction of the evolution of traits,potentially leading to opposite conclusions.To assess the impact of these different elements in ASR,we performed a set of analyses,including all possible combinations of such elements and using the evolution of migratory behavior in Sylvia warblers as a case study,which was coded as a continuous or as a discrete character.Our results show that taxon sampling,character coding,tree shape,statistical framework and software all significantly affect ASR,both individually and in combination.Not all reconstructed tree nodes show discrepancies,but in the critical ones most pairwise comparisons between analyses lead to conflicting and unexpectedly antagonistic results(zero migration vs fully migratory),thus challenging interpretations of trait evolution.We propose some possible solutions to partly inform decisions,involving the method selection and the incorporation of biological or fossil evidence regarding how traits evolve,but our results demand serious rethinking about how the research community currently uses ASR.

THE STATE SPACE RECONSTRUCTION TECHNOLOGY OF DIFFERENT KINDS OF CHAOTIC DATA OBTAINED FROM DYNAMICAL SYSTEM

Certain deterministic nonlinear systems may show chaotic behavior. We consider the motion of qualitative information and the practicalities of extracting a part from chaotic experimental data. Our approach based on a theorem of Takens draws on the ideas from the generalized theory of information known as singular system analysis. We illustrate this technique by numerical data from the chaotic region of the chaotic experimental data. The method of the singular-value decomposition is used to calculate the eigenvalues of embedding space matrix. The corresponding concrete algorithm to calculate eigenvectors and to obtain the basis of embedding vector space is proposed in this paper. The projection on the orthogonal basis generated by eigenvectors of timeseries data and concrete paradigm are also provided here. Meanwhile the state space reconstruction technology of different kinds of chaotic data obtained from dynamical system has also been discussed in detail.

AN ANALYTIC AND APPLICATION TO STATE SPACE RECONSTRUCTION ABOUT CHAOTIC TIME SERIES

The state space, reconstruction is the major important quantitative index for describing non-linear chaotic time series. Based on the work of many scholars, such as: AT. H. Packard, F. Takens, M. Casdagli, J. F. Gibson, CHEN Yu-shu et al, the state space was reconstructed using the method of Legendre coordinate. Several different scaling regimes for lag time tau were identified. The influence for state space reconstruction of lag time tau was discussed. The result tells us that is a good practical method for state space reconstruction.

RAD-seq data reveals robust phylogeny and morphological evolutionary history of Rhododendron

Rhododendron is famous for its high ornamental value.However,the genus is taxonomically difficult and the relationships within Rhododendron remain unresolved.In addition,the origin of key morphological characters with high horticulture value need to be explored.Both problems largely hinder utilization of germplasm resources.Most studies attempted to disentangle the phylogeny of Rhododendron,but only used a few genomic markers and lacked large-scale sampling,resulting in low clade support and contradictory phylogenetic signals.Here,we used restriction-site associated DNA sequencing(RAD-seq)data and morphological traits for 144 species of Rhododendron,representing all subgenera and most sections and subsections of this species-rich genus,to decipher its intricate evolutionary history and reconstruct ancestral state.Our results revealed high resolutions at subgenera and section levels of Rhododendron based on RAD-seq data.Both optimal phylogenetic tree and split tree recovered five lineages among Rhododendron.Subg.Therorhodion(cladeⅠ)formed the basal lineage.Subg.Tsutsusi and Azaleastrum formed cladeⅡand had sister relationships.CladeⅢincluded all scaly rhododendron species.Subg.Pentanthera(cladeⅣ)formed a sister group to Subg.Hymenanthes(cladeⅤ).The results of ancestral state reconstruction showed that Rhododendron ancestor was a deciduous woody plant with terminal inflorescence,ten stamens,leaf blade without scales and broadly funnelform corolla with pink or purple color.This study shows significant distinguishability to resolve the evolutionary history of Rhododendron based on high clade support of phylogenetic tree constructed by RAD-seq data.It also provides an example to resolve discordant signals in phylogenetic trees and demonstrates the application feasibility of RAD-seq with large amounts of missing data in deciphering intricate evolutionary relationships.Additionally,the reconstructed ancestral state of six important characters provides insights into the innovation of key characters in Rhododendron.

Root Endophyte Shift and Key Genera Discovery in Rice under Barnyardgrass Stress

Despite increasing knowledge of barnyardgrass(Echinochloa crus-galli) interference with rice, relatively little is known how endophytes improve the ability of rice against barnyardgrass stress. Here, we provided a detailed temporal characterization of rice root-associated microbiomes during co-cultivation with barnyardgrass and a comparison with the microbiomes of weed-free rice plants. Alpha diversity analysis indicated that barnyardgrass had the opposite effects on endophytic bacteria and fungi in rice roots, in terms of the community diversity, richness and coverage at the rice seedling stage. Principal coordinate analysis showed that barnyardgrass had only a minor effect on the community composition of endophytes in rice roots at the rice seedling stage, but showed a significant and maximum interference at the heading stage. Rice recruited many endophytes to resist biotic stress from barnyardgrass, especially for fungi. PICRUSt(phylogenetic investigation of communities by reconstruction of unobserved states) predictive analysis indicated that 23 metabolic pathways of bacteria were overrepresented in rice. In addition, the main trophic mode of fungi was pathotroph according to FUNGuild analysis. A positive correlation between bacteria and fungi in rice roots was found via network analysis. Anaeromyxobacter, Azospira and Pseudolabrys were the vital bacteria, Phaeosphaeria and Funneliformis were the dominant fungi in maintaining the stability of the ecological network. These results provided data and a theoretical basis for the in-depth understanding of what role endophytes play in rice resistance to barnyardgrass stress and will have implications on improving the resistance of rice against biotic stress using root microbiota.

Reconstructing ancestral ranges in historical biogeography:properties and prospects

Recent years have witnessed a proliferation of quantitative methods for biogeographic inference. In particular, novel parametric approaches represent exciting new opportunities for the study of range evolution. Here, we review a selection of current methods for biogeographic analysis and discuss their respective properties. These methods include generalized parsimony approaches, weighted ancestral area analysis, dispersal-vicariance analysis, the dispersal--extinction--cladogenesis model and other maximum likelihood approaches, and Bayesian stochastic mapping of ancestral ranges, including a novel approach to inferring range evolution in the context of island biogeography. Some of these methods were developed specifically for problems of ancestral range reconstruction, whereas others were designed for more general problems of character state reconstruction and subsequently applied to the study of ancestral ranges. Methods for reconstructing ancestral history on a phylogenetic tree differ not only in the types of ancestral range states that are allowed, but also in the various historical events that may change the ancestral ranges. We explore how the form of allowed ancestral ranges and allowed transitions can both affect the outcome of ancestral range estimation. Finally, we mention some promising avenues for future work in the development of model-based approaches to biogeographic analysis.

Hidden in plain sight:Morphological and phylogenetic evidence for Bouteloua arizonica,a species distinct from Bouteloua aristidoides(Poaceae,Chloridoideae)

Two varieties of Bouteloua aristidoides have been recognized,the widespread var.aristidoides and the more narrowly distributed var.arizonica.The two varieties differ in inflorescence form even more than that seen between many other closely related species of Bouteloua.We therefore asked whether these taxa might be better regarded as distinct species.A total of 93 vouchers were studied by using morphometry(principal components analysis and statistical tests),leaf micromorphology,ancestral state reconstruction,and/or molecular(ITS,trnC-rpoB and trnT-L-F)phylogenetic analyses.Except from the ITS tree,all results supported elevation of B.aristidoides var.arizonica to the rank of species,thus the new combination Bouteloua arizonica(M.E.Jones)L.F.Cuellar&Columbus comb.nov.et stat.nov.,is proposed.Chloroplast and combined chloroplast-nuclear molecular trees depicted var.arizonica as monophyletic(even in sympatric populations with var.aristidoides)and reveals phylogenetic structure within var.aristidoides for which the presence of new undescribed varieties of B.aristidoides(different from B.arizonica)is addressed.B.arizonica differs from B.aristidoides in having fewer branches per inflorescence,a bigger branch with more spikelets,and a shorter branch extension.Scanning electron microscopy revealed the presence of papillae on leaves of B.arizonica as a clear synapomorphy.Growing mature plants of B.arizonica from seeds in a greenhouse revealed a strong cleistogamous nature for this species for which gene flow in sympatric populations with B.aristidoides seems unlikely.A taxonomic treatment and distribution map for identification of B.arizonica is provided.

The phylogeny of francolins(Francolinus, Dendroperdix, Peliperdix and Scleroptila) and spurfowls(Pternistis) based on chick plumage(Galliformes: Phasianidae)

Background: This paper describes the chick plumage of spurfowl(Pternistis) and francolin(Francolinus, Dendroperdix Peliperdix and Scleroptila) chicks, tests its significance for phylogenetic relationships and also explores the patterns of character evolution in the francolin and spurfowl lineages.Previously regarded as monophyletic, the two evolutionar?ily distant clades are now divided into five genera.Questions considered were whether chick plumage supports the dichotomy between spurfowls and francolins and what role habitat matching plays.Methods: The study was based mainly on photographs of chick skins from the American Museum of Natural History and the Natural History Museum at Tring.Eight plumage characters were selected for comparative scoring, summa?rised in a matrix.These characters were subsequently analysed phylogenetically and their evolution was traced on the existing molecular phylogeny using a parsimony approach.Results: Based on chick plumage the phylogeny of species groups among francolins and spurfowls, was largely unresolved possibly ascribed to a high degree of symplesiomorphy inherent among the Phasianids.This possibly could have resulted in a high degree of polytomy particularly among the spurfowls and francolins.Furthermore, the ancestral state reconstructions revealed high prevalence of symplesiomorphic states and reversals which do not help in the classification of groups.Although the differences are described that separate some African francolins from spurfowls, other francolins(in Asia and Africa) share remarkably similar characteristics with spurfowls.Plain dark dorsal plumage is probably advantageous for avoiding detection by predators in forests, while facial stripes optimise the breaking of body shapes in dense grass cover(as in Scleroptila spp.) and semi?striped faces are advantageous for stationary camouflage under tree and bush cover(as in Pternistis spp.).Conclusions: Although symplesiomorphy is a hereditary explanation for downy colours and patterns, the traits rel?evant for habitat matching are combined in a manner which is determined(adaptation) by natural selection.

The improved local linear prediction of chaotic time series

Based on the Bayesian information criterion, this paper proposes the improved local linear prediction method to predict chaotic time series. This method uses spatial correlation and temporal correlation simultaneously. Simulation results show that the improved local linear prediction method can effectively make multi-step and one-step prediction of chaotic time series and the multi-step prediction performance and one-step prediction accuracy of the improved local linear prediction method are superior to those of the traditional local linear prediction method.

Searching for Strange Attractor in Sliver Irregularity Series

The chaotic nonlinear time series method is applied to analyze the sliver irregularity in textile processing.Because it unifies the system's determinacy and randomness,it seems more adaptive to describe the sliver irregularity than conventional methods.Firstly,the chaos character,i.e.fractal dimension,positive Lyapunov exponent,and state space parameters,including time delay and reconstruction dimension,are calculated respectively.As a result,a positive Lyapunov exponent and a fractal dimension are obtained,which demonstrates that the system is chaotic in fact.Secondly,both local linear forecast and global forecast models based on the reconstructed state are adopted to predict a segment part of the sliver irregularity series,which proves the validity of this analysis.Therefore,the sliver irregularity series shows the evidence of chaotic phenomena,and thus laying the theoretical foundation for analyzing and modeling the sliver irregularity series by applying the chaos theory,and providing a new way to understand the complexity of the sliver irregularity much better.

LQ Speed Control of Pump Controlled Motor System

A linear quadric (LQ) optimal speed control algorithm is proposed for the speed control of a pump controlled motor hydraulic system. The control theme consists of optimal state feedback and disturbing compensation based on observation. The optimal state feedback bases on LQ cost function. The disturbing compensation is realized through reconstructing the state of load torque. A series of simulation are performed, and the results show that the control performance is satisfactory and can be maintained under changes of load torque.

Determining the state of a three-level atom by interaction with two radiation fields

An unknown state of a quantum system S is usually determined by repeatedly measuring a set of non-commuting observables. The state can also be obtained from the repeated measurements of a single separable observable when the system S interacts with an assistant system A in a known state. In this paper, we study the quantum state tomography of a three-level atom （the system S） interacting with two radiation fields as the assistant system A. We obtain the initial state of S by repeatedly measuring a separable observable O = Sz n1 n2, in which Sz is the atom operator, and hi and h2 are the photon number operators of the two radiation fields. We achieve the one-to-one mapping M between the initial density matrix of the system S and the measured results of the single separable observable. We also give a concrete numerical example.

Quantum state and process tomography via adaptive measurements

We investigate quantum state tomography(QST) for pure states and quantum process tomography(QPT) for unitary channels via adaptive measurements. For a quantum system with a d-dimensional Hilbert space, we first propose an adaptive protocol where only 2d. 1 measurement outcomes are used to accomplish the QST for all pure states. This idea is then extended to study QPT for unitary channels, where an adaptive unitary process tomography(AUPT) protocol of d2+d.1measurement outcomes is constructed for any unitary channel. We experimentally implement the AUPT protocol in a 2-qubit nuclear magnetic resonance system. We examine the performance of the AUPT protocol when applied to Hadamard gate, T gate(/8 phase gate), and controlled-NOT gate,respectively, as these gates form the universal gate set for quantum information processing purpose. As a comparison, standard QPT is also implemented for each gate. Our experimental results show that the AUPT protocol that reconstructing unitary channels via adaptive measurements significantly reduce the number of experiments required by standard QPT without considerable loss of fidelity.

Quantum state tomography for generic pure states

We examine the problem of whether a multipartite pure quantum state can be uniquely determined by its reduced density matrices.We show that a generic pure state in three party Hilbert space HA■HB■HC, where dim(HA) = 2 and dim(HB) = dim(HC), can be uniquely determined by its reduced states on subsystems HA■HB and HA■HC. Then, we generalize the conclusion to the case that dim(H_1) > 2. As a corollary, we show that a generic N-qudit pure quantum state is uniquely determined by only two of its[(N+1)/2]-particle reduced density matrices. Furthermore,our results indicate a method to uniquely determine a generic N-qudit pure state of dimension D = d^N with only O(D) local measurements, which is an improvement compared to the previous known approach that uses O(D log^2 D) or O(D log D) local measurements.

Reconstructing unknown quantum states using variational layerwise method

In order to gain comprehensive knowledge of an arbitrary unknown quantum state,one feasible way is to reconstruct it,which can be realized by finding a series of quantum operations that can refactor the unitary evolution producing the unknown state.We design an adaptive framework that can reconstruct unknown quantum states at high fidelities,which utilizes SWAP test,parameterized quantum circuits(PQCs)and layerwise learning strategy.We conduct benchmarking on the framework using numerical simulations and reproduce states of up to six qubits at more than 96%overlaps with original states on average using PQCs trained by our framework,revealing its high applicability to quantum systems of different scales theoretically.Moreover,we perform experiments on a five-qubit IBM Quantum hardware to reconstruct random unknown single qubit states,illustrating the practical performance of our framework.For a certain reconstructing fidelity,our method can effectively construct a PQC of suitable length,avoiding barren plateaus of shadow circuits and overuse of quantum resources by deep circuits,which is of much significance when the scale of the target state is large and there is no a priori information on it.This advantage indicates that it can learn credible information of unknown states with limited quantum resources,giving a boost to quantum algorithms based on parameterized circuits on near-term quantum processors.

New considerations on the phylogeny of Sessilida(Protista:Ciliophora:Peritrichia)based on multiple-gene information,with emphasis on colonial taxa

The subclass Peritrichia,containing two orders Sessilida and Mobilida,is a major group of ciliates with worldwide distribution and high species diversity.Several studies have investigated the phylogeny of peritrichs;however,the evolutionary relationships and classification of some families and genera within the Sessilida remain unclear.In the present study,we isolated and identified 22 peritrich populations representing four families and six genera and obtained 64 rDNA sequences to perform phylogenetic analyses and assess their systematic relationships.Ancestral character reconstruction was also carried out to infer evolutionary routes within the Sessilida.The results indicate:(1)family Vaginicolidae is monophyletic and acquisition of the typical peritrich lorica represents a single evolutionary divergence;(2)core epistylidids evolved from a Zoothamnium-like ancestor and experienced spasmoneme loss during evolution;(3)Campanella clusters with species in the basal clade and shows stable morphological differences with other epistylidids,supporting its assignment to a separate family;(4)the structure of the peristomial lip may be a genus-level character rather than a diagnostic character for discriminating Epistylididae and Operculariidae,thus a redefinition of Operculariidae should be carried out when more species have been investigated;(5)some characters,such as lifestyle(solitary or colonial),spasmoneme and living habit(sessile or free-swimming),evolved repeatedly among sessilids indicating that species with non-contractile stalks or that are free-swimming have multiple evolutionary routes and might derive from any sessilid lineage without a lorica.The close phylogenetic relationships of some morphologically distinct sessilids imply that the diagnoses of some genera and families should be improved.