Sequence Of Operators Research Articles

Tangent Space Generators of Matrix Product States and Exact Floquet Quantum Scars

The advancement of quantum simulators motivates the development of a theoretical framework to assist with efficient state preparation in quantum many-body systems. Generally, preparing a target entangled state via unitary evolution with time-dependent couplings is a challenging task and very little is known about the existence of solutions and their properties. In this work we develop a constructive approach for preparing matrix product states (MPS) via continuous unitary evolution. We provide an explicit construction of the operator that exactly implements the evolution of a given MPS along a specified direction in its tangent space. This operator can be written as a sum of local terms of finite range, yet it is in general non-Hermitian. Relying on the explicit construction of the non-Hermitian generator of the dynamics, we demonstrate the existence of a Hermitian sequence of operators that implements the desired MPS evolution with an error that decreases exponentially with the operator range. The construction is benchmarked on an explicit periodic trajectory in a translationally invariant MPS manifold. We demonstrate that the Floquet unitary generating the dynamics over one period of the trajectory features an approximate MPS-like eigenstate embedded among a sea of thermalizing eigenstates. These results show that our construction is not only useful for state preparation and control of many-body systems, but also provides a generic route towards Floquet scars—periodically driven models with quasilocal generators of dynamics that have exact MPS eigenstates in their spectrum. Published by the American Physical Society 2024

Molecular basis for the transcriptional regulation of an epoxide-based virulence circuit in Pseudomonas aeruginosa.

The opportunistic pathogen Pseudomonas aeruginosa infects the airways of people with cystic fibrosis (CF) and produces a virulence factor Cif that is associated with worse outcomes. Cif is an epoxide hydrolase that reduces cell-surface abundance of the cystic fibrosis transmembrane conductance regulator (CFTR) and sabotages pro-resolving signals. Its expression is regulated by a divergently transcribed TetR family transcriptional repressor. CifR represents the first reported epoxide-sensing bacterial transcriptional regulator, but neither its interaction with cognate operator sequences nor the mechanism of activation has been investigated. Using biochemical and structural approaches, we uncovered the molecular mechanisms controlling this complex virulence operon. We present here the first molecular structures of CifR alone and in complex with operator DNA, resolved in a single crystal lattice. Significant conformational changes between these two structures suggest how CifR regulates the expression of the virulence gene cif. Interactions between the N-terminal extension of CifR with the DNA minor groove of the operator play a significant role in the operator recognition of CifR. We also determined that cysteine residue Cys107 is critical for epoxide sensing and DNA release. These results offer new insights into the stereochemical regulation of an epoxide-based virulence circuit in a critically important clinical pathogen.

Characterizing and Engineering Rhamnose-Inducible Regulatory Systems for Dynamic Control of Metabolic Pathways in Streptomyces.

Fine-tuning gene expression is of great interest for synthetic biotechnological applications. This is particularly true for the genus Streptomyces, which is well-known as a prolific producer of diverse natural products. Currently, there is an increasing demand to develop effective gene induction systems. In this study, bioinformatic analysis revealed a putative rhamnose catabolic pathway in multiple Streptomyces species, and the removal of the pathway in the model organism Streptomyces coelicolor impaired its growth on minimal media with rhamnose as the sole carbon source. To unravel the regulatory mechanism of RhaR, a LacI family transcriptional regulator of the catabolic pathway, electrophoretic mobility shift assays (EMSAs) were performed to identify potential target promoters. Multiple sequence alignments retrieved a consensus sequence of the RhaR operator (rhaO). A synthetic biology-based strategy was then deployed to build rhamnose-inducible regulatory systems, referred to as rhaRS1 and rhaRS2, by assembling the repressor/operator pair RhaR/rhaO with the well-defined constitutive kasO* promoter. Both rhaRS1 and rhaRS2 exhibited a high level of induced reporter activity, with no leaky expression. rhaRS2 has been proven successful for the programmable production of actinorhodin and violacein in Streptomyces. Our study expanded the toolkit of inducible regulatory systems that will be broadly applicable to many other Streptomyces species.

Composition of some positive linear integral operators

Abstract This article is devoted to constructing sequences of integral operators with the same Voronovskaja formula as the generalized Baskakov operators, but having different behavior in other respects. For them, we investigate the eigenstructure, the inverses, and the corresponding Voronovskaja type formulas. A general result of Voronovskaja type for composition of operators is given and applied to the new operators. The asymptotic behavior of differences between the operators is investigated, and as an application, we obtain a formula involving Euler’s gamma function.

Interpolating Between Rényi Entanglement Entropies for Arbitrary Bipartitions via Operator Geometric Means

AbstractThe asymptotic restriction problem for tensors can be reduced to finding all parameters that are normalized, monotone under restrictions, additive under direct sums and multiplicative under tensor products, the simplest of which are the flattening ranks. Over the complex numbers, a refinement of this problem, originating in the theory of quantum entanglement, is to find the optimal rate of entanglement transformations as a function of the error exponent. This trade-off can also be characterized in terms of the set of normalized, additive, multiplicative functionals that are monotone in a suitable sense, which includes the restriction-monotones as well. For example, the flattening ranks generalize to the (exponentiated) Rényi entanglement entropies of order $$\alpha \in [0,1]$$ α ∈ [ 0 , 1 ] . More complicated parameters of this type are known, which interpolate between the flattening ranks or Rényi entropies for special bipartitions, with one of the parts being a single tensor factor. We introduce a new construction of subadditive and submultiplicative monotones in terms of a regularized Rényi divergence between many copies of the pure state represented by the tensor and a suitable sequence of positive operators. We give explicit families of operators that correspond to the flattening-based functionals, and show that they can be combined in a nontrivial way using weighted operator geometric means. This leads to a new characterization of the previously known additive and multiplicative monotones, and gives new submultiplicative and subadditive monotones that interpolate between the Rényi entropies for all bipartitions. We show that for each such monotone there exist pointwise smaller multiplicative and additive ones as well. In addition, we find lower bounds on the new functionals that are superadditive and supermultiplicative.

Convergence of power sequences of operators via their stability

This paper is concerned with the convergence of power sequences and stability of Hilbert space operators, where “convergence” and “stability” are considered with respect to weak, strong and norm topologies. It is proved that an operator has a convergent power sequence if and only if it is a (not necessarily orthogonal) direct sum of an identity operator and a stable operator. This reduces the issue of convergence of the power sequence of an operator T to the study of stability of T. The question of when the limit of the power sequence is an orthogonal projection is investigated. Among operators sharing this property are hyponormal and contractive ones. In particular, a hyponormal or a contractive operator with no identity part is stable if and only if its power sequence is convergent. In turn, a unitary operator has a weakly convergent power sequence if and only if its singular-continuous part is weakly stable and its singular-discrete part is the identity. Characterizations of the convergence of power sequences and stability of subnormal operators are given in terms of semispectral measures.

Genome-wide transcription response of Staphylococcus epidermidis to heat shock and medically relevant glucose levels.

Skin serves as both barrier and interface between body and environment. Skin microbes are intermediaries evolved to respond, transduce, or act in response to changing environmental or physiological conditions. We quantified genome-wide changes in gene expression levels for one abundant skin commensal, Staphylococcus epidermidis, in response to an internal physiological signal, glucose levels, and an external environmental signal, temperature. We found 85 of 2,354 genes change up to ~34-fold in response to medically relevant changes in glucose concentration (0-17 mM; adj p ≤0.05). We observed carbon catabolite repression in response to a range of glucose spikes, as well as upregulation of genes involved in glucose utilization in response to persistent glucose. We observed 366 differentially expressed genes in response to a physiologically relevant change in temperature (37-45°C; adj p ≤ 0.05) and an S. epidermidis heat-shock response that mostly resembles the heat-shock response of related staphylococcal species. DNA motif analysis revealed CtsR and CIRCE operator sequences arranged in tandem upstream of dnaK and groESL operons. We identified and curated 38 glucose-responsive genes as candidate ON or OFF switches for use in controlling synthetic genetic systems. Such systems might be used to instrument the in-situ skin microbiome or help control microbes bioengineered to serve as embedded diagnostics, monitoring, or treatment platforms.

A simulation-based investigation of the robustness of sequences of operation to zone-level faults in single-duct multi-zone variable air volume air handling unit systems

A simulation-based investigation of the robustness of sequences of operation to zone-level faults in single-duct multi-zone variable air volume air handling unit systems

Applications of a variable anchoring iterative method to equation and inclusion problems on Hadamard manifolds

In this paper, we introduce a new iterative technique with a variable anchoring operator for reckoning the solution of a variational inequality problem over the set of the common fixed points of a nearly nonexpansive sequence of operators in the framework of Hadamard manifolds. We also establish a convergence result on the proposed algorithm for approximating a solution of the problem, under suitable assumptions. We apply our results for finding the solutions of a system of nonlinear equations, and of inclusion problems to support their utility. Our work improves results in the recent literature. Numerical simulations are given for a better understanding of the effectiveness of our outcomes.

The Convergence of Some Positive Linear Operators on the Space of Multivariate Continuous Periodic Functions

As a consequence of a general result, we prove that in the case of singular integrals the set of convergence consists only of the two functions 1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extbf{1}$$\\end{document} and cos\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\cos $$\\end{document}. We prove also a multivariate version of this result and apply it to find the necessary and sufficient conditions for the convergence of the sequences of positive linear operators associated to the rectangular and triangular summation.

Does the Sequence of Bimaxillary Orthognathic Surgery Affect Accuracy in Skeletal Class III Patients?

BackgroundIt is necessary to determine whether the sequence of maxillary and mandibular surgeries in bimaxillary orthognathic surgery affects the accuracy of surgical outcomes. PurposeThe study aimed to measure and compare the accuracy among patients who underwent maxilla-first versus mandible-first bimaxillary surgery to correct a class III skeletal pattern. Study designThis retrospective cohort study included consecutive patients treated by a single surgeon at one center using Le Fort I and bilateral sagittal split osteotomy surgery. Exclusions included patients scheduled for one-jaw or maxilla-segmental surgery and those with craniofacial syndromes, such as clefts. Predictor variableThe predictor variable was operative sequence for bimaxillary operations, divided into maxilla- or mandible-first groups. Outcome variableThe outcome variable was accuracy, measured using linear discrepancies between landmarks in the virtual plan and actual operative outcomes. The measurement of linear discrepancy that was closer to 0 was considered the more accurate result. CovariatesSex, age, maxilla sagittal rotation degree, amount of posterior maxilla impaction, mandibular autorotation (°), and intermediate splint thickness (mm) were the covariates. AnalysesStatistical analysis was performed using Student’s t-test and Pearson’s correlation, with statistical significance set at P < 0.05. ResultsThe sample comprised 60 patients with a mean age of 22.8 ± 3.7 years, of whom 36 (60%) were male. In the maxilla-first group, there were 30 subjects (60% male; mean age: 23.1 ± 4.2 years), with a mean mandibular autorotation of 0.41° (range: 0°–2.5°). The mandible-first group comprised 30 patients (60% male; mean age: 22.6 ± 3.3 years), with a mean mandibular autorotation of 5.46° (range: 1.9°–9.2°). The linear discrepancies for all landmarks did not significantly differ between mandible- and maxilla-first groups (P > 0.18). The mean 3D discrepancies for all landmarks in maxilla-first group was 1.23 ± 0.5 mm and 1.23 ± 0.33 mm in mandible-first group, with no significant difference observed between the groups (P > 0.98). The amount of mandibular autorotation for intermediate splint application showed no significant correlation with the linear discrepancies (P > 0.58). ConclusionsIn patients with skeletal class III malocclusion, mandible-first surgery in bimaxillary orthognathic surgery demonstrates accurate outcomes comparable to maxilla-first surgery.

An Improvement of the Order of Approximation by the Sequence of Bernstein-Kantorovich Operators

An Improvement of the Order of Approximation by the Sequence of Bernstein-Kantorovich Operators

Approximation behaviour of generalized Baskakov-Durrmeyer-Schurer operators

The goal of this manuscript is to introduce a new sequence of generalized-Baskakov Durrmeyer-Schurer Operators. Further, basic estimates are calculated. In the subsection sequence, rapidity of convergence and order of approximation are studied in terms of first and second-order modulus of continuity. We prove a Korovkin-type approximation theorem and obtain the rate of convergence of these operators. Moreover, local and global approximation properties are discussed in different functional spaces. Lastly, A-statistical approximation results are presented.

On the convergence of sequences of positive linear operators towards composition operators

On the convergence of sequences of positive linear operators towards composition operators

Approximation theorems via Pp -statistical convergence on weighted spaces

Abstract In this paper, we obtain some Korovkin type approximation theorems for double sequences of positive linear operators on two-dimensional weighted spaces via statistical type convergence method with respect to power series method. Additionally, we calculate the rate of convergence. As an application, we provide an approximation using the generalization of Gadjiev-Ibragimov operators for Pp -statistical convergence. Our results are meaningful and stronger than those previously given for two-dimensional weighted spaces.

Approximation properties of the univariate and bivariate Bernstein-Stancu operators of max-product kind

This paper presents the nonlinear maximum product type of univariate and bivariate Bernstein–Stancu operators and uses new definitions to investigate the approximation properties. The order of approximation obtained with the nonlinear maximum product type of operator sequences would be better than the degree of approximation of the known linear operator sequences.

Parametric Bernstein operators based on contagion distribution

This paper proposes the extended form of the ‐Bernstein operators with the Pólya–Eggenberger distribution, also known as contagion distribution, using the integral operators for . We will refer to these sequence of operators as the “Parametric‐Bernstein operators based on contagion distribution” or simply the modified form of ‐Bernstein operators. These operators are defined with the help of two parameters, namely, and . We observe the significance of both these parameters. Subsequently, we calculate their moments and on the basis of Korovkin's approximation theorem we assert that our defined operators converge for a real valued continuous function . We give some basic properties, study the Voronovskaya type asymptotic result and discuss the ‐statistical approximation of our operators. We also use the modulus of continuity to study the rate of convergence. Alongside our primary work, we have also defined the King‐type modification that preserves the operators at and . Further, using modulus of continuity, we compare the properties and behavior of both the operators.

Convergence results in Orlicz spaces for sequences of max-product sampling Kantorovich operators

In this paper, we provide a unifying theory concerning the convergence properties of the so-called max-product sampling Kantorovich operators based upon generalized kernels in the setting of Orlicz spaces. The approximation of functions defined on both bounded intervals and on the whole real axis has been considered. Here, under suitable assumptions on the kernels, considered in order to define the operators, we are able to establish a modular convergence theorem for these sampling-type operators. As a direct consequence of the main theorem of this paper, we obtain that the involved operators can be successfully used for approximation processes in a wide variety of functional spaces, including the well-known interpolation and exponential spaces. This makes the Kantorovich variant of max-product sampling operators suitable for reconstructing not necessarily continuous functions (signals) belonging to a wide range of functional spaces. Finally, several examples of Orlicz spaces and of kernels for which the above theory can be applied, are presented.

Investigating levels of remote operation in high-level on-road autonomous vehicles using operator sequence diagrams

The continuing development of autonomous vehicle technology is making the presence of fully autonomous vehicles (SAE Level 5 of Driving Automation) on the road an ever more likely possibility. Similarly, regulation changes show countries are preparing for autonomous vehicles to increase their presence on public roads for both testing and use after sale. With this in mind, solutions to the problem of disengagement from the autonomous driving system by Level 5 vehicles, due to damage, operation outside of expected parameters or software failure among other reasons are being investigated including remote operation. This research aims to give evidence for the inclusion of remote operation into the autonomous driving and define the types of remote operation that may occur from existing literature. The four types of remote operation are Remote Monitoring, Remote Assistance, Remote Management and Remote Driving. Operator sequence diagrams are used to evaluate these types of remote operation in likely scenarios they may occur and draw conclusions about the role and the tasks the operator will be required to complete.

Vibrational ADAPT-VQE: Critical points lead to problematic convergence.

Quantum chemistry is one of the most promising applications for which quantum computing is expected to have a significant impact. Despite considerable research in the field of electronic structure, calculating the vibrational properties of molecules on quantum computers remains a relatively unexplored field. In this work, we develop a vibrational Adaptive Derivative-Assembled Pseudo-Trotter Variational Quantum Eigensolver (vADAPT-VQE) formalism based on an infinite product representation (IPR) of anti-Hermitian excitation operators of the Full Vibrational Configuration Interaction (FVCI) wavefunction, which allows for preparing eigenstates of vibrational Hamiltonians on quantum computers. In order to establish the vADAPT-VQE algorithm using the IPR, we study the exactness of disentangled Unitary Vibrational Coupled Cluster (dUVCC) theory and show that dUVCC can formally represent the FVCI wavefunction in an infinite expansion. To investigate the performance of the vADAPT-VQE algorithm, we numerically study whether the vADAPT-VQE algorithm generates a sequence of operators that may represent the FVCI wavefunction. Our numerical results indicate frequent appearance of critical points in the wavefunction preparation using vADAPT-VQE. These results imply that one may encounter diminishing usefulness when preparing vibrational wavefunctions on quantum computers using vADAPT-VQE and that additional studies are required to find methods that can circumvent this behavior.