Shiva diagrams for composite-boson many-body effects: how they work

The purpose of this paper is to show how the diagrammatic expansion in fermion exchanges of scalar products of N-composite-boson (“coboson”) states can be obtained in a practical way. The hard algebra on which this expansion is based, will be given in an independent publication. Due to the composite nature of the particles, the scalar products of N-coboson states do not reduce to a set of Kronecker symbols, as for elementary bosons, but contain subtle exchange terms between two or more cobosons. These terms originate from Pauli exclusion between the fermionic components of the particles. While our many-body theory for composite bosons leads to write these scalar products as complicated sums of products of “Pauli scatterings” between two cobosons, they in fact correspond to fermion exchanges between any number P of quantum particles, with 2 ≤P≤N. These P-body exchanges are nicely represented by the so-called “Shiva diagrams”, which are topologically different from Feynman diagrams, due to the intrinsic many-body nature of the Pauli exclusion from which they originate. These Shiva diagrams in fact constitute the novel part of our composite-exciton many-body theory which was up to now missing to get its full diagrammatic representation. Using them, we can now “see” through diagrams the physics of any quantity in which enters N interacting excitons — or more generally N composite bosons —, with fermion exchanges included in an exact — and transparent — way.     

正则黑洞熵

应用隧道效应所得到的能量谱计算配分函数,进而计算黑洞熵.当本结论取一级近似时,熵修正的对数项与考虑广义不确定关系对黑洞熵修正的对数项一致,然而在计算中没有不确定因子.虽然对数修正项前的因子与考虑热波动对黑洞熵修正中对数项前的因子相同,但所给结论中当黑洞的热容量为负时也不存在发散项.所以本结论具有普遍性. 关键词： 广义不确定关系 热波动 正则系综 量子修正     

正则黑洞熵与相变

应用隧道效应对黑洞Hawking辐射研究得到的辐射谱,对非旋转黑洞的正则熵进行讨论.所得熵遵守Bekenstein-Hawking 面积定律,并带有修正项,主要修正项与面积的对数成正比,另有与黑洞热容量有关的修正项.利用所给出的正则熵,对黑洞的相变进行讨论,得到当黑洞的热容量出现发散时,正则熵在该处并不出现复数,由此认为此相变为二级相变. 关键词： 正则系综 量子修正 黑洞相变     

On the Distribution of Eigenvalues of Grand Canonical Density Matrices

Using physical arguments and partition theoretic methods, we demonstrate under general conditions, that the eigenvalues w(m) of the grand canonical density matrix decay rapidly with their index m, like w(m)exp[–B ^–1(ln m)^1+1/ ], where B and are positive constants, O(1), which may be computed from the spectrum of the Hamiltonian. We compute values of B and for several physical models, and confirm our theoretical predictions with numerical experiments. Our results have implications in a variety of questions, including the behaviour of fluctuations in ensembles, and the convergence of numerical density matrix renormalization group techniques.     

Canonical versus grand canonical occupation numbers for simple systems

An ideal gas ofN indistinguishable particles is described by a canonical ensemble (c.e.) and also by a grand canonical ensemble (g.c.e.) which hasN as themean total number of particles, the temperature and volume being the same in both cases. Exact mean occupation numbersn _j(N) are found if the system has only two states 1 and 2 of energiesE ₂E ₁. This should apply to quantum wells and similar simple systems. For systems which have captured one particle, the theory gives the simplest answers, and one find a maximum discrepancy of 17% between the two ensembles for the fermion case. It occurs whenE ₂–E ₁53 meV at room temperature. ForN=1 the mean occupation number for the c.e. is identical for fermions and for bosons, being in both cases given byn ₂(1)={exp[(E ₂-E ₁)/kT]+1}^-1,n ₁(1)=1-n ₂(1) For largeN one reverts to the usual situation and the discrepancy between the ensembles becomes small.     

Ergodic Properties of Microcanonical Observables

The problem of the existence of a strong stochasticity threshold in the FPU- model is reconsidered, using suitable microcanonical observables of thermodynamic nature, like the temperature and the specific heat. Explicit expressions for these observables are obtained by exploiting rigorous methods of differential geometry. Measurements of the corresponding temporal autocorrelation functions locate the threshold at a finite value of the energy density, which is independent of the number of degrees of freedom.     

In silico models for the prediction of dose-dependent human hepatotoxicity

The liver is extremely vulnerable to the effects of xenobiotics due to its critical role in metabolism. Drug-induced hepatotoxicity may involve any number of different liver injuries, some of which lead to organ failure and, ultimately, patient death. Understandably, liver toxicity is one of the most important dose-limiting considerations in the drug development cycle, yet there remains a serious shortage of methods to predict hepatotoxicity from chemical structure. We discuss our latest findings in this area and present a new, fully general in silico model which is able to predict the occurrence of dose-dependent human hepatotoxicity with greater than 80% accuracy. Utilizing an ensemble recursive partitioning approach, the model classifies compounds as toxic or non-toxic and provides a confidence level to indicate which predictions are most likely to be correct. Only 2D structural information is required and predictions can be made quite rapidly, so this approach is entirely appropriate for data mining applications and for profiling large synthetic and/or virtual libraries.     

Field-Template,QSAR, Ensemble Molecular Docking,and 3D-RISM Solvation Studies Expose Potential of FDA-Approved Marine Drugs as SARS-CoVID-2 Main Protease Inhibitors

Currently, SARS-CoV-2 (severe acute respiratory syndrome coronavirus 2) has infected people among all countries and is a pandemic as declared by the World Health Organization (WHO). SARS-CoVID-2 main protease is one of the therapeutic drug targets that has been shown to reduce virus replication, and its high-resolution 3D structures in complex with inhibitors have been solved. Previously, we had demonstrated the potential of natural compounds such as serine protease inhibitors eventually leading us to hypothesize that FDA-approved marine drugs have the potential to inhibit the biological activity of SARS-CoV-2 main protease. Initially, field-template and structure–activity atlas models were constructed to understand and explain the molecular features responsible for SARS-CoVID-2 main protease inhibitors, which revealed that Eribulin Mesylate, Plitidepsin, and Trabectedin possess similar characteristics related to SARS-CoVID-2 main protease inhibitors. Later, protein–ligand interactions are studied using ensemble molecular-docking simulations that revealed that marine drugs bind at the active site of the main protease. The three-dimensional reference interaction site model (3D-RISM) studies show that marine drugs displace water molecules at the active site, and interactions observed are favorable. These computational studies eventually paved an interest in further in vitro studies. Finally, these findings are new and indeed provide insights into the role of FDA-approved marine drugs, which are already in clinical use for cancer treatment as a potential alternative to prevent and treat infected people with SARS-CoV-2.     

Synergizing Off-Target Predictions for In Silico Insights of CENH3 Knockout in Cannabis through CRISPR/Cas

The clustered regularly interspaced short palindromic repeats (CRISPR)/Cas-mediated genome editing system has recently been used for haploid production in plants. Haploid induction using the CRISPR/Cas system represents an attractive approach in cannabis, an economically important industrial, recreational, and medicinal plant. However, the CRISPR system requires the design of precise (on-target) single-guide RNA (sgRNA). Therefore, it is essential to predict off-target activity of the designed sgRNAs to avoid unexpected outcomes. The current study is aimed to assess the predictive ability of three machine learning (ML) algorithms (radial basis function (RBF), support vector machine (SVM), and random forest (RF)) alongside the ensemble-bagging (E-B) strategy by synergizing MIT and cutting frequency determination (CFD) scores to predict sgRNA off-target activity through in silico targeting a histone H3-like centromeric protein, HTR12, in cannabis. The RF algorithm exhibited the highest precision, recall, and F-measure compared to all the tested individual algorithms with values of 0.61, 0.64, and 0.62, respectively. We then used the RF algorithm as a meta-classifier for the E-B method, which led to an increased precision with an F-measure of 0.62 and 0.66, respectively. The E-B algorithm had the highest area under the precision recall curves (AUC-PRC; 0.74) and area under the receiver operating characteristic (ROC) curves (AUC-ROC; 0.71), displaying the success of using E-B as one of the common ensemble strategies. This study constitutes a foundational resource of utilizing ML models to predict gRNA off-target activities in cannabis.     

Prediction of adsorption of small molecules in porous materials based on ab initio force field method

Computational prediction of adsorption of small molecules in porous materials has great impact on the basic and applied research in chemical engineering and material sciences. In this work,we report an approach based on grand canonical ensemble Monte Carlo(GCMC) simulations and ab initio force fields. We calculated the adsorption curves of ammonia in ZSM-5 zeolite and hydrogen in MOF-5(a metal-organic-framework material). The predictions agree well with experimental data. Because the predictions are based on the first principle force fields,this approach can be used for the adsorption prediction of new molecules or materials without experimental data as guidance.