Perturbation Theory For Operators Research Articles

A local and hierarchical Koopman spectral analysis of fluid dynamics

AbstractA local and hierarchical Koopman spectral analysis is proposed to extend Koopman spectral analysis typically used in a linear system or an ergodic process to its application in general nonlinear dynamics. The continuous and analytic Koopman eigenfunctions and eigenvalues, derived from operator perturbation theory, are capable of dealing with a nonlinear transition process with mathematical rigorousness. A proliferation rule is identified to derive high‐order eigenvalues and eigenfunctions from lower‐order ones, thus various spectral patterns may be generated through recursive proliferations. The locally linear map around each state constructs base local Koopman eigenvalues and eigenfunctions from an algebraic eigenvalue problem, and high‐order ones are generated via the proliferation rule to express the systematic nonlinearity. The aforementioned hierarchy simplifies the Koopman spectral analysis and is verified by studying the development of Kármán vortex streets. The triangular chain and the lattice distribution of Koopman eigenvalues confirm the critical role of the proliferation rule and the hierarchy structure of Koopman eigenvalues. The local spectral analysis on the transition process shows that the periodic flow forms as the growth rates of the critical Koopman modes reduce to zero, and meanwhile, the Koopman modes at the same frequency superpose on each other to form the well‐known Fourier or Floquet modes, where the latter are the enhanced nonlinear motions due to the alignment of Koopman eigenvalues with the critical ones.

Kadanoff-Baym Equations for Interacting Systems with Dissipative Lindbladian Dynamics.

The extraordinary quantum properties of nonequilibrium systems governed by dissipative dynamics have become a focal point in contemporary scientific inquiry. The nonequilibrium Green's functions (NEGF) theory provides a versatile method for addressing driven nondissipative systems, utilizing the powerful diagrammatic technique to incorporate correlation effects. We here present a second-quantization approach to the dissipative NEGF theory, reformulating Keldysh ideas to accommodate Lindbladian dynamics and extending the Kadanoff-Baym equations accordingly. Generalizing diagrammatic perturbation theory for many-body Lindblad operators, the formalism enables correlated and dissipative real-time simulations for the exploration of transient and steady-state changes in the electronic, transport, and optical properties of materials.

Structure Factors for Hot Neutron Matter from AbInitio Lattice Simulations with High-Fidelity Chiral Interactions.

We present the first abinitio lattice calculations of spin and density correlations in hot neutron matter using high-fidelity interactions at next-to-next-to-next-to-leading order in chiral effective field theory. These correlations have a large impact on neutrino heating and shock revival in core-collapse supernovae and are encapsulated in functions called structure factors. Unfortunately, calculations of structure factors using high-fidelity chiral interactions were well out of reach using existing computational methods. In this Letter, we solve the problem using a computational approach called the rank-one operator (RO) method. The RO method is a general technique with broad applications to simulations of fermionic many-body systems. It solves the problem of exponential scaling of computational effort when using perturbation theory for higher-body operators and higher-order corrections. Using the RO method, we compute the vector and axial static structure factors for hot neutron matter as a function of temperature and density. The abinitio lattice results are in good agreement with virial expansion calculations at low densities but are more reliable at higher densities. Random phase approximation codes used to estimate neutrino opacity in core-collapse supernovae simulations can now be calibrated with abinitio lattice calculations.

Instability of periodic waves for the Korteweg–de Vries–Burgers equation with monostable source

In this paper, it is proved that the KdV–Burgers equation with a monostable source term of Fisher–KPP type has small-amplitude periodic traveling wave solutions with finite fundamental period. These solutions emerge from a subcritical local Hopf bifurcation around a critical value of the wave speed. Moreover, it is shown that these periodic waves are spectrally unstable as solutions to the PDE, that is, the Floquet (continuous) spectrum of the linearization around each periodic wave intersects the unstable half plane of complex values with positive real part. To that end, classical perturbation theory for linear operators is applied in order to prove that the spectrum of the linearized operator around the wave can be approximated by that of a constant coefficient operator around the zero solution, which intersects the unstable complex half plane.

Non-Empirical Calculations of Reduced Quartic, Sextic, and Octic Constants of Effective Vibrational–Rotational Hamiltonians, Based on the Operator Perturbation Theory

Non-Empirical Calculations of Reduced Quartic, Sextic, and Octic Constants of Effective Vibrational–Rotational Hamiltonians, Based on the Operator Perturbation Theory

Correction: Perturbation Theory for Second Order Elliptic Operators with BMO Antisymmetric Part

Correction: Perturbation Theory for Second Order Elliptic Operators with BMO Antisymmetric Part

Tonkaya struktura mul'tipletov Fe2+, magnitnaya anizotropiya i vzaimosvyaz' magnitnykh i elektricheskikh struktur v Fe2Mo3O8

The effective Hamiltonians of the fine structure of Fe2+ (5D) terms are derived using the methods of operator perturbation theory taking into account covalent bonds between iron and oxygen ions. The energy operators of coupling of magnetic and electric dipole moments with the electric field are obtained for states of multiplets Fe2+ (5E) and Fe2+ (5T2) with minimal sets of parameters. The energy spectra of low-lying states, the magnetic anisotropy parameters, and the distribution of quadrupole and induced electric dipole moments over all positions in the unit cell are calculated. The results of calculations are compared with available experimental data.

Perturbation Theory for Second Order Elliptic Operators with BMO Antisymmetric Part

In the present paper we study perturbation theory for the Lp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^p$$\\end{document} Dirichlet problem on bounded chord arc domains for elliptic operators in divergence form with potentially unbounded antisymmetric part in BMO. Specifically, given elliptic operators L0=div(A0∇)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_0 = \ ext {div}(A_0\ abla )$$\\end{document} and L1=div(A1∇)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_1 = \ ext {div}(A_1\ abla )$$\\end{document} such that the Lp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^p$$\\end{document} Dirichlet problem for L0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_0$$\\end{document} is solvable for some p>1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p>1$$\\end{document}; we show that if A0-A1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A_0 - A_1$$\\end{document} satisfies certain Carleson condition, then the Lq\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^q$$\\end{document} Dirichlet problem for L1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_1$$\\end{document} is solvable for some q≥p\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$q \\ge p$$\\end{document}. Moreover if the Carleson norm is small then we may take q=p\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$q=p$$\\end{document}. We use the approach first introduced in Fefferman–Kenig–Pipher ’91 on the unit ball, and build on Milakis–Pipher–Toro ’11 where the large norm case was shown for symmetric matrices on bounded chord arc domains. We then apply this to solve the Lp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^p$$\\end{document} Dirichlet problem on a bounded Lipschitz domain for an operator L=div(A∇)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L = \ ext {div}(A\ abla )$$\\end{document}, where A satisfies a Carleson condition similar to the one assumed in Kenig–Pipher ’01 and Dindoš–Petermichl–Pipher ’07 but with unbounded antisymmetric part.

Distributed Banach–Picard Iteration for Locally Contractive Maps

The Banach–Picard iteration is widely used to find fixed points of locally contractive (LC) maps. This article extends the Banach–Picard iteration to distributed settings; specifically, we assume the map of which the fixed point is sought to be the average of individual (not necessarily LC) maps held by a set of agents linked by a communication network. An additional difficulty is that the LC map is not assumed to come from an underlying optimization problem, which prevents exploiting strong global properties, such as convexity or Lipschitzianity. Yet, we propose a distributed algorithm and prove its convergence, in fact showing that it maintains the linear rate of the standard Banach–Picard iteration for the average LC map. As another contribution, our proof imports tools from perturbation theory of linear operators, which, to the best of our knowledge, are scarcely exploited in the theory of distributed computation.

Generalized Carleson perturbations of elliptic operators and applications

We extend in two directions the notion of perturbations of Carleson type for the Dirichlet problem associated to an elliptic real second-order divergence-form (possibly degenerate, not necessarily symmetric) elliptic operator. First, in addition to the classical perturbations of Carleson type, that we call additive Carleson perturbations, we introduce scalar-multiplicative and antisymmetric Carleson perturbations, which both allow non-trivial differences at the boundary. Second, we consider domains which admit an elliptic PDE in a broad sense: we count as examples the 1-sided NTA (a.k.a. uniform) domains satisfying the capacity density condition, the 1-sided chord-arc domains, the domains with low-dimensional Ahlfors-David regular boundaries, and certain domains with mixed-dimensional boundaries; thus our methods provide a unified perspective on the Carleson perturbation theory of elliptic operators. Our proofs do not introduce sawtooth domains or the extrapolation method. We also present several applications to some Dahlberg-Kenig-Pipher operators, free-boundary problems, and we provide a new characterization of A ∞ A_{\infty } among elliptic measures.

Randomized Benchmarking beyond Groups

Randomized benchmarking (RB) is the gold standard for experimentally evaluating the quality of quantum operations. The current framework for RB is centered on groups and their representations, but this can be problematic. For example, Clifford circuits need up to $O(n^2)$ gates, and thus Clifford RB cannot scale to larger devices. Attempts to remedy this include new schemes such as linear cross-entropy benchmarking (XEB), cycle benchmarking, and non-uniform RB, but they do not fall within the group-based RB framework. In this work, we formulate the \emph{universal randomized benchmarking (URB) framework} which does away with the group structure and also replaces the recovery gate plus measurement component with a general ``post-processing'' POVM. Not only does this framework cover most of the existing benchmarking schemes, but it also gives the language for and helps inspire the formulation of new schemes. We specifically consider a class of URB schemes called \emph{twirling schemes}. For twirling schemes, the post-processing POVM approximately factorizes into an intermediate channel, inverting maps, and a final measurement. This leads us to study the twirling map corresponding to the gate ensemble specified by the scheme. We prove that if this twirling map is strictly within unit distance of the Haar twirling map in induced diamond norm, the probability of measurement as a function of gate length is a single exponential decay up to small error terms. The core technical tool we use is the matrix perturbation theory of linear operators on quantum channels.

DETERMINATION OF THE TRANSMISSION LINE RESISTANCE MATRIX WITH DEVIATIONS OF DESIGN PARAMETERS FROM NOMINAL

Context. UHF transmission systems make extensive use of transmission line segments, the characteristics of which have a significant impact on the performance of various information technologies. One of the problems of production of transmission lines is to obtain a given wave impedance, which significantly affects the electrical and information characteristics of the entire set of equipment. Currently, there is a burning issue of estimating the influence of disturbing factors on various electrical characteristics of long line segments. To date, the most fully developed methods for assessing the effect of disturbing factors on the wave impedance of a homogeneous line (the wave impedance is constant) under regular perturbations. In this case, the influence of perturbations on the reflection coefficient of matched lines was mainly considered. The effect of perturbations on the other characteristics of homogeneous and, especially, inhomogeneous lines has not been sufficiently studie
 Objective. The purpose of this paper is to determine the effect of wave impedance perturbations on the transmission line impedance matrix. Knowing the perturbed impedance matrix, it is possible to determine the distortion of the characteristics of any device built on transmission line segments. 
 Method. The paper uses the method of perturbation theory of linear differential operators applied to equations describing processes in inhomogeneous long lines.
 Results. The obtained results make it possible to estimate the influence of regular and irregular perturbations of the wave resistance (wave conductance) on the transmission line matrix considered as a quadrupole. Such matrix can be any quadrupole matrix: resistance matrix, conductance matrix, circuit matrix. This makes it possible, according to the desired function of the circuit (gain, input impedance, reflection coefficient), to determine the allowable deviation of the wave impedance from the nominal value in order to select a tolerance for reproducing the wave impedance. 
 Conclusions. The proposed criterion for estimating line parameter deviations using the norm of the four-pole matrix is inherently an integral criterion and can be used to preliminarily estimate the frequency domain of the strongest distortions, regardless of the functional purpose of the transmission line segment. The developed approach is applicable to both homogeneous and heterogeneous transmission lines and covers both regular and irregular wave impedance perturbations.

Essential m-dissipativity and hypocoercivity of Langevin dynamics with multiplicative noise

We provide a complete elaboration of the L^2-Hilbert space hypocoercivity theorem for the degenerate Langevin dynamics with multiplicative noise, studying the longtime behavior of the strongly continuous contraction semigroup solving the abstract Cauchy problem for the associated backward Kolmogorov operator. Hypocoercivity for the Langevin dynamics with constant diffusion matrix was proven previously by Dolbeault, Mouhot and Schmeiser in the corresponding Fokker–Planck framework and made rigorous in the Kolmogorov backwards setting by Grothaus and Stilgenbauer. We extend these results to weakly differentiable diffusion coefficient matrices, introducing multiplicative noise for the corresponding stochastic differential equation. The rate of convergence is explicitly computed depending on the choice of these coefficients and the potential giving the outer force. In order to obtain a solution to the abstract Cauchy problem, we first prove essential self-adjointness of non-degenerate elliptic Dirichlet operators on Hilbert spaces, using prior elliptic regularity results and techniques from Bogachev, Krylov and Röckner. We apply operator perturbation theory to obtain essential m-dissipativity of the Kolmogorov operator, extending the m-dissipativity results from Conrad and Grothaus. We emphasize that the chosen Kolmogorov approach is natural, as the theory of generalized Dirichlet forms implies a stochastic representation of the Langevin semigroup as the transition kernel of a diffusion process which provides a martingale solution to the Langevin equation with multiplicative noise. Moreover, we show that even a weak solution is obtained this way.

Prescribed Webster Scalar Curvatures on Compact Pseudo-Hermitian Manifolds

In this paper, we investigate the problem of prescribing Webster scalar curvatures on compact pseudo-Hermitian manifolds. In terms of the method of upper and lower solutions and the perturbation theory of self-adjoint operators, we can describe some sets of Webster scalar curvature functions which can be realized through pointwise CR conformal deformations and CR conformally equivalent deformations respectively from a given pseudo-Hermitian structure.

P-I Boundary Control of Countercurrent Heat Exchanger

Heat exchangers are generally described by two coupled partial differential equations (PDEs), and belong to the class of systems of conservation laws. In this paper we propose a result on the regulation of heat exchangers, in which we are choosing a proportional-integral (PI)-controller implemented on an output feedback from a boundary condition. First, a study on the existence and uniqueness of solutions of uncontrolled system is carried out, and we give a condition on the parameters of the system that ensures that the control-observation problem is well-posedness. Secondly we successively study the stability of the system controlled by a proportional and integral action, when the gains are adjusted following respectively a classic Lyapunov approach, and using a recent result that combines Lyapunov's approach and operator perturbation theory.

Periodic Solution for some Class of Linear Partial Differential Equation with infinite Delay using Semi-Fredholm perturbations

Abstract In this work, we study the existence of periodic solutions for a class of linear partial functional differential equations with infinite delay. Inspiring by an existing study, by applying the perturbation theory of semi-Fredholm operators, we introduce a suitable a priori estimate on the norm of the operator L to establish the periodicity of solutions in the case where the linear part is nondensely defined and satisfies the Hille-Yosida condition and without considering the exponential stability condition on the semigroup generated by the part of this operator on the closure of it’s domain. Moreover, in the special case where the linear part generates a strongly continuous semigroup and perturbed by a compact linear operator, we give some sufficient conditions to derive periodic solution from bounded ones. Finally, our theoretical results are illustrated by applications in both densely and nondensely cases.

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The IR transmittance spectrum of an isotopic mixture of chlorodifluoromethane (CHF2Cl, Freon-22) with a 33% fraction of 13C and a natural ratio of chlorine isotopes was measured in the frequency range 1400-740 cm–1 with a resolution of 0.001 cm–1 at a temperature of 20C. An ab initio calculation of the structure and sextic potential energy surface and surfaces of the components of the dipole moment has been carried out by the the electronic quantum-mechanical method of Möller-Plesset, MP2/cc-pVTZ. Then the potential was optimized by replacing the harmonic frequencies with the frequencies calculated by the electronic method of coupled clusters, CCSD(T)/aug-cc-pVQZ. The fundamental and combination frequencies were calculated using the operator perturbation theory of Van Vleck (CVPTn) of the second and fourth order (n=2,4). Resonance effects were modeled using an additional variational calculation in the basis up to fourfold VCI excitation (4). The average prediction error for the fundamental frequencies of the 12C isotopologues was ~1.5 cm–1. The achieved accuracy made it possible to reliably predict the isotopic frequency shifts of the 13C isotopologues. It is shown that the strong Fermi resonance ν4/2ν6 dominates in the 12C isotopologues and is practically absent in 13C. The literature assumption [Spectrochim. Acta A, 44: 553] about the splitting of ν1 (CH) due to the resonance ν1/ν2+ν7+ν9 is confirmed. The coefficients of the polyadic quantum number are determined. The analysis made it possible to carry out a preliminary identification of the centers of the vibrational-rotational bands of isotopologues 13CHF235Cl и 13CHF237Cl in the spectrum of the mixture in preparation for individual analyzes of the vibrational-rotational structures of individual vibrational transitions.

Неэмпирический анализ изотопических сдвигов и резонансных эффектов в инфракрасном спектре высокого разрешения фреона-22 (CHF-=SUB=-2-=/SUB=-Cl), обогащенного -=SUP=-13-=/SUP=-C

The IR transmittance spectrum of an isotopic mixture of chlorodifluoromethane (CHF2Cl, Freon-22) with a 33% fraction of 13C and a natural ratio of chlorine isotopes was measured in the frequency range 1400-740 cm–1 with a resolution of 0.001 cm–1 at a temperature of 20C. An ab initio calculation of the structure and sextic potential energy surface and surfaces of the components of the dipole moment has been carried out by the the electronic quantum-mechanical method of Möller-Plesset, MP2/cc-pVTZ. Then the potential was optimized by replacing the harmonic frequencies with the frequencies calculated by the electronic method of coupled clusters, CCSD(T)/aug-cc-pVQZ. The fundamental and combination frequencies were calculated using the operator perturbation theory of Van Vleck (CVPTn) of the second and fourth order (n=2,4). Resonance effects were modeled using an additional variational calculation in the basis up to fourfold VCI excitation (4). The average prediction error for the fundamental frequencies of the 12C isotopologues was ~1.5 cm–1. The achieved accuracy made it possible to reliably predict the isotopic frequency shifts of the 13C isotopologues. It is shown that the strong Fermi resonance ν4/2ν6 dominates in the 12C isotopologues and is practically absent in 13C. The literature assumption [Spectrochim. Acta A, 44: 553] about the splitting of ν1 (CH) due to the resonance ν1/ν2+ν7+ν9 is confirmed. The coefficients of the polyadic quantum number are determined. The analysis made it possible to carry out a preliminary identification of the centers of the vibrational-rotational bands of isotopologues 13CHF235Cl и 13CHF237Cl in the spectrum of the mixture in preparation for individual analyzes of the vibrational-rotational structures of individual vibrational transitions.

NUMERICAL STUDYING ENERGY PARAMETERS OF MULTIELECTRON ATOM IN A MAGNETIC FIELD: HELIUM

There are presented the results of calculating the energies of the helium atom energy in a homogeneous magnetic field on the basis of the new numerical quantum-mechanical approach. The approach is based on the numerical difference solution of the Schrödinger equation, the model potential method and the operator perturbation theory formalism. The obtained results on energy of the helium atom in dependence upon the magnetic field strength are compared with available theoretical results, obtained on the basis of alternative numerical Hartree-Fock and diagonalization methods.

IFPTML Mapping of Drug Graphs with Protein and Chromosome Structural Networks vs. Pre-Clinical Assay Information for Discovery of Antimalarial Compounds.

The parasite species of genus Plasmodium causes Malaria, which remains a major global health problem due to parasite resistance to available Antimalarial drugs and increasing treatment costs. Consequently, computational prediction of new Antimalarial compounds with novel targets in the proteome of Plasmodium sp. is a very important goal for the pharmaceutical industry. We can expect that the success of the pre-clinical assay depends on the conditions of assay per se, the chemical structure of the drug, the structure of the target protein to be targeted, as well as on factors governing the expression of this protein in the proteome such as genes (Deoxyribonucleic acid, DNA) sequence and/or chromosomes structure. However, there are no reports of computational models that consider all these factors simultaneously. Some of the difficulties for this kind of analysis are the dispersion of data in different datasets, the high heterogeneity of data, etc. In this work, we analyzed three databases ChEMBL (Chemical database of the European Molecular Biology Laboratory), UniProt (Universal Protein Resource), and NCBI-GDV (National Center for Biotechnology Information—Genome Data Viewer) to achieve this goal. The ChEMBL dataset contains outcomes for 17,758 unique assays of potential Antimalarial compounds including numeric descriptors (variables) for the structure of compounds as well as a huge amount of information about the conditions of assays. The NCBI-GDV and UniProt datasets include the sequence of genes, proteins, and their functions. In addition, we also created two partitions (cassayj = caj and cdataj = cdj) of categorical variables from theChEMBL dataset. These partitions contain variables that encode information about experimental conditions of preclinical assays (caj) or about the nature and quality of data (cdj). These categorical variables include information about 22 parameters of biological activity (ca0), 28 target proteins (ca1), and 9 organisms of assay (ca2), etc. We also created another partition of (cprotj = cpj) including categorical variables with biological information about the target proteins, genes, and chromosomes. These variables cover32 genes (cp0), 10 chromosomes (cp1), gene orientation (cp2), and 31 protein functions (cp3). We used a Perturbation-Theory Machine Learning Information Fusion (IFPTML) algorithm to map all this information (from three databases) into and train a predictive model. Shannon’s entropy measure Shk (numerical variables) was used to quantify the information about the structure of drugs, protein sequences, gene sequences, and chromosomes in the same information scale. Perturbation Theory Operators (PTOs) with the form of Moving Average (MA) operators have been used to quantify perturbations (deviations) in the structural variables with respect to their expected values for different subsets (partitions) of categorical variables. We obtained three IFPTML models using General Discriminant Analysis (GDA), Classification Tree with Univariate Splits (CTUS), and Classification Tree with Linear Combinations (CTLC). The IFPTML-CTLC presented the better performance with Sensitivity Sn(%) = 83.6/85.1, and Specificity Sp(%) = 89.8/89.7 for training/validation sets, respectively. This model could become a useful tool for the optimization of preclinical assays of new Antimalarial compounds vs. different proteins in the proteome of Plasmodium.