Set Of Operators Research Articles

Stabilizing reinforcement learning control: A modular framework for optimizing over all stable behavior

We propose a framework for the design of feedback controllers that combines the optimization-driven and model-free advantages of deep reinforcement learning with the stability guarantees provided by using the Youla-Kučera parameterization to define the search domain. Recent advances in behavioral systems allow us to construct a data-driven internal model; this enables an alternative realization of the Youla-Kučera parameterization based entirely on input–output exploration data. Perhaps of independent interest, we formulate and analyze the stability of such data-driven models in the presence of noise. The Youla-Kučera approach requires a stable “parameter” for controller design. For the training of reinforcement learning agents, the set of all stable linear operators is given explicitly through a matrix factorization approach. Moreover, a nonlinear extension is given using a neural network to express a parameterized set of stable operators, which enables seamless integration with standard deep learning libraries. Finally, we show how these ideas can also be applied to tune fixed-structure controllers

Abstract 2341: Morph: A feature extraction toolset for spatial transcriptomics

Abstract Accurately defining spatial characteristics of tumors has been a challenge in cancer research. Specifically, there is still a lack of spatial transcriptomic (ST) bioinformatic methods that infer tumor boundaries, a necessity for tumor microenvironment (TME) analyses, that are fully automated and handle non-rectangular grids (like the one found in Visium). Here we introduce Morph, a toolset that not only addresses these limitations, but also accurately extracts tumor regions, layers surrounding them, and distances related to such regions. Morph was tested on a dataset composed of 117 ST slides across 6 different cancer types, including primary and metastatic tumors. More broadly, Morph is a computationally efficient tool based on mathematical morphology that is designed to work without any approximations on ST slides (that can be composed of spots in a hexagonal lattice) of any resolution. The toolset accepts a variety of input types, such as tumor purity and manual annotation, and can perform a diverse set of morphological operations, such as erosion, dilation, opening and closing, using a number of structuring elements with different shapes and sizes, such as a hexagon of side 1. Moreover, Morph runs quickly (seconds per sample). Its main focus is to unveil the aforementioned features of any spatially distinct tumor region (here defined as microregion) for various downstream analyses, such as spatially-varying copy number variations, cell-type distribution, and tumor-microenvironment interaction. Overall, we developed a spatial transcriptomics toolset that is not limited to any specific technology platform, and that can accurately extract ST features facilitating the discovery of spatial transcriptomic and interaction patterns. Citation Format: André Luiz N. Targino da Costa, Jingxian Liu, Chia-Kuei Mo, Erik Storrs, Austin N. Southard-Smith, Reyka G. Jayasinghe, Julia T. Wang, Michael D. Iglesia, Michael Wendl, Siqi Chen, Andrew Houston, Alla Karpova, Yize Li, Li Ding. Morph: A feature extraction toolset for spatial transcriptomics [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2024; Part 1 (Regular Abstracts); 2024 Apr 5-10; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2024;84(6_Suppl):Abstract nr 2341.

Classical shadows based on locally-entangled measurements

We study classical shadows protocols based on randomized measurements in n-qubit entangled bases, generalizing the random Pauli measurement protocol (n=1). We show that entangled measurements (n≥2) enable nontrivial and potentially advantageous trade-offs in the sample complexity of learning Pauli expectation values. This is sharply illustrated by shadows based on two-qubit Bell measurements: the scaling of sample complexity with Pauli weight k improves quadratically (from ∼3k down to ∼3k/2) for many operators, while others become impossible to learn. Tuning the amount of entanglement in the measurement bases defines a family of protocols that interpolate between Pauli and Bell shadows, retaining some of the benefits of both. For large n, we show that randomized measurements in n-qubit GHZ bases further improve the best scaling to ∼(3/2)k, albeit on an increasingly restricted set of operators. Despite their simplicity and lower hardware requirements, these protocols can match or outperform recently-introduced "shallow shadows" in some practically-relevant Pauli estimation tasks.

The use of evidence in criminal proceedings as a component of the evidetiary process

The article is devoted to elucidating the essence and content of the use of evidence, as well as to justifying the identification of such a category as a separate component of evidentiary process in criminal proceedings. It was found that despite the absence of the category "use of evidence” among the provisions of Part 2 of Art. 91 of the Criminal Procedure Code of Ukraine, the term is used by the legislator in a number of articles of the current CPC of Ukraine. The positions of domestic scientists regarding the essence of the use of evidence were analyzed. It was found that the majority of doctrinal definitions of this term boil down to the understanding of the use of evidence as the manipulation of it (evidence, their procedural sources, evidentiary information) for the performance of intermediate and final tasks (that is, the achievement of certain positive results) in criminal proceedings.
 Based on the study of the provisions of the current legislation and doctrinal sources, it was established that evidence is used by justifying, making, and implementing decisions in criminal proceedings. The following forms of evidence use are singled out: procedural decisions, decisions on submitting evidence to the court and substantiating legal positions with them, on submitting motions and complaints during the pre-trial investigation, tactical decisions of the prosecution and other subjects of evidence. The general mechanism of making the listed decisions and the place of use of evidence in the system of components of evidentiary activity are considered.
 The use of evidence is defined as a component of the evidentiary process, a set of logical and instrumental operations consisting in justifying with evidence (evidential information), making and implementing decisions by the subject of proof in order to fulfill their own tasks in criminal proceedings.
 Further research prospects in the analyzed field are related to the scientific and theoretical study of the essence, types and mechanism of decision­making in criminal proceedings as a form of evidence use.

Precise certification of a qubit space

We demonstrate an implementation of the precise test of dimension on the qubit, using the public IBM quantum computer, using the determinant dimension witness. The accuracy is below 10−3 comparing to maximal possible value of the witness in higher dimension. The test involving minimal independent sets of preparation and measurement operations (gates) is applied both for specific configurations and parametric ones. The test is robust against nonidealities such as incoherent leakage and erroneous gate execution. Two of the IBM devices failed the test by more than 5 standard deviations, which has no simple explanation.

Molybdenum carbide nanoclusters with ultrafast electron transfer ability promotes molecular oxygen selective electrocatalytic reduction to hydroxyl radicals for pollutant control

A treatment strategy of in situ generation and activation of hydrogen peroxide to degrade pollutants by the heterogeneous Fenton-like technology is promising for water pollution. However, the selective activation of oxygen to hydroxyl radicals (OH) by cathode materials is still challenging. Here, molybdenum carbide (MoC) supported on a heteroatoms-doped (N, P, S) carbon carrier catalyst was successfully prepared, which rapidly produced OH and degraded paracetamol (APAP) pollutants. A high APAP degradation efficiency with a specific energy consumption of 0.24 kWh g−1 TOC was achieved. After 10 sets of continuous operations, the APAP degradation rate remains unchanged. Combined with density functional theory calculations, molecular oxygen adsorption obtains one electron with proton hydrogen transfer to hydroperoxyl (OOH) on the MoC surface, and the adsorbed OOH directly activate into OH due to the ultrafast electron transfer ability of MoC. Differential charge density analysis also shows that Mo transfers electrons to O. This strategy provides a new idea for optimizing catalysts to improve the heterogeneous Fenton-like performance.

Coordinating scheduling and rejection decisions in a two-machine flow shop scheduling problem

We study a two-machine flow shop scheduling problem where any operation can be rejected at a certain cost. A solution for such a problem requires two sets of decisions. The first involves the partition of the set of operations into two subsets: the set of operations that are accepted for scheduling in the shop, and the set of rejected operations. The second decision involves scheduling the set of accepted operations in the shop. The objective is to find a solution that minimizes the sum of the makespan and the total rejection cost. We prove that the problem is NP-hard even if all processing operations have identical processing times and identical rejection costs on either one of the two machines. We show, however, that the problem is fixed parameterized tractable with respect to a parameter that combine the number of different processing times on both machines with the number of different rejection costs on one out of the two machines. We also provide a pseudo-polynomial time algorithm for the problem, which we then convert into a fully polynomial time approximation scheme. This is achieved by dividing the problem into a set of subproblems and deriving a fully polynomial time approximation scheme for each one of them, separately. Finally, we present an integer linear programming formulation of the problem and two simple 2-approximation algorithms.

A compositional simulation framework for Abstract State Machine models of Discrete Event Systems

Modeling complex system requirements often requires specifying system components in separate models, which can be validated and verified in isolation from each other, and then integrating all components’ behavior in order to validate the operation of the whole system. If models are executable, as for state-based formal specifications, engines to orchestrate the simulation of separate component operational models are extremely useful. This paper presents an approach for the co-simulation, according to predefined orchestration schemas, of state-based models of separate components of a Discrete Event System. More precisely, we exploit the Abstract State Machine (ASM) formal method as state-based formalism, and we ( i ) define a set of operators to compose ASMs that communicate with each other through I/O events, and ( ii ) present an engine to execute the compositional simulation of the ASMs as a whole assembly. As proof of concepts, we use a set of model examples of Discrete Event Systems of increasing complexity to show the application of our approach and to evaluate its effectiveness in co-simulating models of real systems.

New physics in the third generation. A comprehensive SMEFT analysis and future prospects

We present a comprehensive analysis of electroweak, flavor, and collider bounds on the complete set of dimension-six SMEFT operators in the U(2)5-symmetric limit. This operator basis provides a consistent framework to describe a wide class of new physics models and, in particular, the motivated class of models where the new degrees of freedom couple mostly to the third generation. By analyzing observables from all three sectors, and consistently including renormalization group evolution, we provide bounds on the effective scale of all 124 U(2)5-invariant operators. The relation between flavor-conserving and flavor-violating observables is analyzed taking into account the leading U(2)5 breaking in the Yukawa sector, which is responsible for heavy-light quark mixing. We show that under simple, motivated, and non-tuned hypotheses for the parametric size of the Wilson coefficients at the high scale, all present bounds are consistent with an effective scale as low as 1.5 TeV. We also show that a future circular e+e− collider program such as FCC-ee would push most of these bounds by an order of magnitude. This would rule out or provide clear evidence for a wide class of compelling new physics models that are fully compatible with present data.

On Recursion Operators for Full-Fledged Nonlocal Symmetries of the Reduced Quasi-classical Self-dual Yang–Mills Equation

We introduce the idea of constructing recursion operators for full-fledged nonlocal symmetries and apply it to the reduced quasi-classical self-dual Yang–Mills equation. It turns out that the discovered recursion operators can be interpreted as infinite-dimensional matrices of differential functions which act on the generating vector functions of the nonlocal symmetries simply by matrix multiplication. To the best of our knowledge, there are no other examples of such recursion operators in the literature so far, so our approach is completely innovative. Further, we investigate the algebraic properties of the discovered operators and discuss the R\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {R}}$$\\end{document}-algebra structure on the set of all recursion operators for full-fledged nonlocal symmetries of the equation in question. Finally, we illustrate the action of the obtained recursion operators on particularly chosen full-fledged symmetries and emphasize their advantages compared to the action of traditionally used recursion operators for shadows.

Generating operators of symmetry breaking—From discrete to continuous

Based on the “generating operator” of the Rankin–Cohen brackets introduced in Kobayashi–Pevzner [arXiv:2306.16800], we present a method to construct various fundamental operators with continuous parameters such as invariant trilinear forms on infinite-dimensional representations, the Fourier and the Poisson transforms on the anti-de Sitter space, and integral symmetry breaking operators for the fusion rules, among others, out of a countable set of differential symmetry breaking operators.

Источниковедческий потенциал военной публицистики Н.С. Гумилева и С.М. Городецкого: между литературой и историческим документом

The article examines N.S. Gumilev’s and S.M. Gorodetsky’s military essays, published during the First World War in the newspapers “Birzhevye Vedomosti” and “Russkoe Slovo”, respectively. It is noted that these texts are autobiographical and relate to artistic journalism, a borderline field of writing that has common features with both literature and journalism. It is proposed a methodology for determining the documentary nature of these texts and their source potential, including a set of operations that can be divided into external criticism (establishing historical conditions for the writing and publication of texts, including the nature of the relationship between the writer and the periodical, as well as promptness of publishing materials in the newspaper and the relevance of the information reported in them) and internal criticism (consideration the immanent characteristics of the text as a whole, its connections with works and biography of the author, as well as the literary tradition). The application of this methodology based on the material of military essays by two poets revealed the dominance of the artistic component in Gumilev’s publications and the journalistic component in Gorodetsky’s texts. Based on this, it is concluded about the nature of the documentality of the considered texts and the specifics of the methodology of their analysis, which differs from the traditional literary approach.

Assessment of routine operation and maintenance work of a small community water treatment plant in North Guwahati, Assam, India

A water treatment plant's efficiency is reliant on its regular maintenance and operation. Many water treatment plants across the world are outsourced to private enterprises for day to day operation and maintenance. However, the impact of outsourcing may not always be profitable as design of faulty treatment units or carrying out improper routine operation and maintenance works by the private enterprise may ultimately affect the quality of potable water produced. The current study aims to evaluate the routine operation and maintenance tasks performed by an outsourced private enterprise at a small community water treatment facility in Assam. The performance monitoring of the treatment plant indicates that the plant is unable to produce potable water meeting national water quality standards. The turbidity of treated water is not able to meet the BIS acceptable limit of 1 NTU but it complies with the BIS permissible limit of 5 NTU. In general, the plant operators lack the skills required to operate the treatment plant effectively. Coagulant dosing is completely based on personal experience of plant operators instead of using jar test results. The backwashing of filter beds is carried out arbitrarily without considering the turbidity of filtered water. These factors have resulted in malfunctioning of the treatment units ultimately affecting the quality of potable water produced from the plant. The skill set of plant operators and chemist has been enhanced with bilingual stepwise instruction charts and on-hand training at the site. This aids in raising the standard of produced potable water. The turbidity of treated water is observed to be close to the BIS acceptable limit of 1 NTU.

Qubit gate operations in elliptically trapped polariton condensates

We consider bosonic condensates of exciton-polaritons optically confined in elliptical traps. A superposition of two non-degenerated p-type states of the condensate oriented along the two main axes of the trap is represented by a point on a Bloch sphere, being considered as an optically tunable qubit. We describe a set of universal single-qubit gates resulting in a controllable shift of the Bloch vector by means of an auxiliary laser beam. Moreover, we consider interaction mechanisms between two neighboring traps that enable designing two-qubit operations such as CPHASE and CNOT gates. Both the single- and two-qubit gates are analyzed in the presence of error sources in the context of polariton traps, such as pure dephasing and spontaneous relaxation mechanisms, leading to a fidelity reduction of the final qubit states and quantum concurrence, as well as the increase of Von Neumann entropy. We also discuss the applicability of our qubit proposal in the context of DiVincenzo’s criteria for the realization of local quantum computing processes. Altogether, the developed set of quantum operations would pave the way to the realization of a variety of quantum algorithms in a planar microcavity with a set of optically induced elliptical traps.

Interacting topological quantum chemistry in 2D with many-body real space invariants

The topological phases of non-interacting fermions have been classified by their symmetries, culminating in a modern electronic band theory where wavefunction topology can be obtained from momentum space. Recently, Real Space Invariants (RSIs) have provided a spatially local description of the global momentum space indices. The present work generalizes this real space classification to interacting 2D states. We construct many-body local RSIs as the quantum numbers of a set of symmetry operators on open boundaries, but which are independent of the choice of boundary. Using the U(1) particle number, they yield many-body fragile topological indices, which we use to identify which single-particle fragile states are many-body topological or trivial at weak coupling. To this end, we construct an exactly solvable Hamiltonian with single-particle fragile topology that is adiabatically connected to a trivial state through strong coupling. We then define global many-body RSIs on periodic boundary conditions. They reduce to Chern numbers in the band theory limit, but also identify strongly correlated stable topological phases with no single-particle counterpart. Finally, we show that the many-body local RSIs appear as quantized coefficients of Wen-Zee terms in the topological quantum field theory describing the phase.

Development of Tools for Creating Parallel Data Mining Algorithms

The purpose of this work is to develop tools for building parallel data mining algorithms for execution in a distributed environment. A formal model of a data mining algorithm is proposed, characterized by a representation of the algorithm in the form of a set of independent operations that change the state of the knowledge model and structural blocks that allow modifying the structure of the algorithm, including for parallel execution. A method is proposed for creating parallel algorithms for data mining, in contrast to existing ones, using a decomposition of the algorithm into thread-safe functional blocks and allowing parallelization, both by changing the structure of the parallel algorithm and by configuring its execution. A methodology is proposed for parallelizing data mining algorithms, which differs from those known in that the proposed method of creating parallel data mining algorithms taking into account the characteristics of a distributed environment is applied to sequential analysis algorithms. To create parallel data mining algorithms, software templates built on the basis of a formal model and separating the implementation of the algorithm from distributed execution tools are proposed. A library of parallel data mining algorithms has been developed for execution in a distributed environment, including the proposed templates.

MetaStore: Analyzing Deep Learning Meta-Data at Scale

The process of training deep learning models produces a huge amount of meta-data, including but not limited to losses, hidden feature embeddings, and gradients. Model diagnosis tools have been developed to analyze losses and feature embeddings with the aim to improve the performance of these models. However, gradients, despite carrying rich information that is potentially relevant for model interpretation and data debugging, have yet to be fully explored due to their size and complexity. Each single gradient has a size as large as the number of parameters of the neural net - often measured in the tens of millions. This makes it extremely challenging to efficiently collect, store, and analyze large numbers of gradients in these models. In this work, we develop MetaStore to fill this gap. MetaStore leverages our observation that storing certain compact intermediate results produced in the back propagation process, namely, the prefix and suffix gradients, is sufficient for the exact restoration of the original gradient. These prefix and suffix gradients are much more compact than the original gradients, thus allowing us to address the gradient collection and storage challenges. Furthermore, MetaStore features a rich set of analytics operators that allow the users to analyze the gradients for data debugging or model interpretation. Rather than first having to restore the original gradients and then run analytics on top of this decompressed view, MetaStore directly executes these operators on the compact prefix and suffix structures, making gradient-based analytics efficient and scalable. Our experiments on popular deep learning models such as VGG, BERT, and ResNet and benchmark image and text datasets demonstrate that MetaStore outperforms strong baseline methods from 4 to 678x in storage costs and from 2 to 1000x in running time.

SMEFT at NNLO+PS: Vh production

In the context of the Standard Model effective field theory (SMEFT) the next-to-next-to-leading (NNLO) QCD corrections to the Higgsstrahlungs (Vh) processes in hadronic collisions are calculated and matched to a parton shower (PS). NNLO+PS precision is achieved for the complete sets of SMEFT operators that describe the interactions between the Higgs and two vector bosons and the couplings of the Higgs, a W or a Z boson, and light fermions. A POWHEG-BOX implementation of the computed NNLO SMEFT corrections is provided that allows for a realistic exclusive description of Vh production at the level of hadronic events. This feature makes it an essential tool for future Higgs characterisation studies by the ATLAS and CMS collaborations. Utilising our new Monte Carlo code the numerical impact of NNLO+PS corrections on the kinematic distributions in pp → Zh → ℓ+ℓ−h production is explored, employing well-motivated SMEFT benchmark scenarios.

Effective field theories of axion, ALP and dark photon

With the help of Young tensor technique, we enumerate the complete and independent set of effective operators up to dim-8 for the extension of the standard model with a Goldstone boson by further imposing the Adler’s zero condition in the soft momentum limit. Such basis can be reduced to describe the axion or majoron effective Lagrangian if further (symmetry) constraints are imposed. Then reformulating dark photon as combination of Goldstone boson and transverse gauge boson, the effective operators of the Goldstone boson can be extended to effective chiral Lagrangian description of the dark photon. For the first time we obtain 0 (0), 6 (44), 1 (1), 44 (356), 32 (520) operators in Goldstone effective field theory, and 9 (49), 0 (0), 108 (676), 10 (426), 1904 (40783) operators in dark photon effective field theory at the dimension 4, 5, 6, 7, 8 for one (three) generation of fermions.

Development of high-gain switched-capacitor based bi-directional converter for electric vehicle applications

High efficiency, high voltage transfer ratio (VTR), and low input ripple current is required in any bidirectional DC-DC converter (BDC) that plays a major role in interfacing batteries in applications like dc microgrids and electric vehicles (EVs). For meeting these requirements, a switched capacitor-based BDC is proposed to interface the battery with a propulsion system via DC Link. It has a simple circuit with only a set of switching operations, High VTR, and lesser ripple current on the low voltage (LV) side are advantages of the proposed High Gain Switched-Capacitor Bi-directional DC-DC Converter (SC-BDC) making it appropriate for use in EVs. The steady-state analysis, design consideration of passive components, loss and efficiency analysis are presented. Finally, the proposed High Gain SC-BDC is compared with few of the existing BDC in the literature. The feasibility of the converter was demonstrated by simulating a 200 W converter and validating results produced in a MATLAB environment.