General Constraints Research Articles

Bootstrapping Coulomb and Higgs branch operators

We apply the numerical conformal bootstrap to correlators of Coulomb and Higgs branch operators in 4d mathcal{N} = 2 superconformal theories. We start by revisiting previous results on single correlators of Coulomb branch operators. In particular, we present improved bounds on OPE coefficients for some selected Argyres-Douglas models, and compare them to recent work where the same cofficients were obtained in the limit of large r charge. There is solid agreement between all the approaches. The improved bounds can be used to extract an approximate spectrum of the Argyres-Douglas models, which can then be used as a guide in order to corner these theories to numerical islands in the space of conformal dimensions. When there is a flavor symmetry present, we complement the analysis by including mixed correlators of Coulomb branch operators and the moment map, a Higgs branch operator which sits in the same multiplet as the flavor current. After calculating the relevant superconformal blocks we apply the numerical machinery to the mixed system. We put general constraints on CFT data appearing in the new channels, with particular emphasis on the simplest Argyres-Douglas model with non-trivial flavor symmetry.

Comparison of data-driven and general temporal constraints on compressed sensing for breast DCE MRI.

Current breast DCE-MRI strategies provide high sensitivity for cancer detection but are known to be insufficient in fully capturing rapidly changing contrast kinetics at high spatial resolution across both breasts. Advanced acquisition and reconstruction strategies aim to improve spatial and temporal resolution and increase specificity for disease characterization. In this work, we evaluate the spatial and temporal fidelity of a modified data-driven low-rank-based model (known as MOCCO, model consistency condition) compressed-sensing (CS) reconstruction compared to CS with temporal total variation with radial acquisition for high spatial-temporal breast DCE MRI. Reconstruction performance was characterized using numerical simulations of a golden-angle stack-of-stars breast DCE-MRI acquisition at 5-second temporal resolution. Specifically, MOCCO was compared with CS total variation and conventional SENSE reconstructions. The temporal model for MOCCO was prelearned over the source data, whereas CS total variation was performed using a first-order temporal gradient sparsity transform. The MOCCO reconstruction was able to capture rapid lesion kinetics while providing high image quality across a range of optimal regularization values. It also recovered kinetics in small lesions (1.5 mm) in line-profile analysis and error images, whereas g-factor maps showed relatively low and constant values with no significant artifacts. The CS-TV method demonstrated either recovery of high spatial resolution with reduced temporal accuracy using large regularization values, or recovery of rapid lesion kinetics with reduced image quality using low regularization values. Simulations demonstrated that MOCCO with radial acquisition provides a robust imaging technique for improving temporal fidelity, while maintaining high spatial resolution and image quality in the setting of bilateral breast DCE MRI.

On the theory and applications of mechanism design and coalitional games in electricity markets

Although the specific structures of electricity markets are diverse around the world, they were all conceived on the premise of predictable, controllable generation with nonnegligible marginal costs. Recent changes, specifically, the increasing renewable integration, have challenged such assumptions. In light of this shift, this thesis intends to devise new frameworks and advance our understanding of the future markets. The first part focuses on mechanism design when the model fully reflects the physics of the grid and the participants. We consider a market that involves continuous goods, general nonconvex constraints, and second stage costs. We then design the payments and conditions under which coalitions cannot influence the outcome. Under the incentive-compatible VCG mechanism, we prove that coalition-proof outcomes are achieved if bids are convex and constraints are polymatroids. By relaxing incentive-compatibility, we investigate core-selecting mechanisms that are coalition-proof without conditions. We show that they generalize the economic rationale of the LMP mechanism, and can approximate truthfulness without the price-taking assumption. Finally, they are budget-balanced. The second part coordinates regional markets to exploit the geographic diversification of renewables. In Europe, reserves remain an exclusive responsibility of regional operators. This limited coordination and the sequential structure hinder the utilization of generation and transmission. To promote reserve exchange, a preemptive model can optimally withdraw inter-area transmission capacity from day-ahead energy for reserves. This bilevel program however does not suggest costs that guarantee coordination. We formulate a new preemptive model that allows us to obtain stable benefits immune to deviations. Our proposal, least-core benefits, achieves minimal stability violation with a tractable computation.

The well-tempered cosmological constant: the Horndeski variations

Well tempering is one of the few classical field theory methods for solving the original cosmological constant problem, dynamically canceling a large (possibly Planck scale) vacuum energy and leaving the matter component intact, while providing a viable cosmology with late time cosmic acceleration and an end de Sitter state. We present the general constraints that variations of Horndeski gravity models with different combinations of terms must satisfy to admit an exact de Sitter spacetime that does not respond to an arbitrarily large cosmological constant. We explicitly derive several specific scalar-tensor models that well temper and can deliver a standard cosmic history including current cosmic acceleration. Stability criteria, attractor behavior of the de Sitter state, and the response of the models to pressureless matter are considered. The well tempered conditions can be used to focus on particular models of modified gravity that have special interest— not only removing the original cosmological constant problem but providing relations between the free Horndeski functions and reducing them to a couple of parameters, suitable for testing gravity and cosmological data analysis.

2차원 구조물에 대한 일반적인 제한조건을 고려하는 선형 정적 응답 위상최적설계 방법론

변위와 응력, 변형률, 고유진동수 등의 일반적인 제한조건을 고려하는 새로운 위상최적설계 방법을 제안한다. 기존의 밀도법 기반 위상최적설계는 인공밀도를 사용하기 때문에 중간밀도를 갖는 요소가 발생하여 일반적인 제한조건을 고려하기 어렵다. 제안한 방법론은 제한조건을 고려한 위상최적설계 수행후 일정한 수의 요소들을 제거하고 나머지 요소들의 상대밀도는 1로 설정한다. 이 과정을 하나의 사이클이라고 하며 부피와 일반적인 제한조건이 충족될 때까지 계속 진행한다. 상대밀도가 1인 요소의 응답을 사용하여 위상최적설계를 수행하기 때문에 일반적인 제한조건에 정확한 응답을 적용할 수 있다. 예제에 적용하고 기존의 방법과 비교하여 제안된 방법을 검증하였다.

Convex Primal Formulations for Convex Hull Pricing With Reserve Commitments

Convex hull pricing has been introduced recently to increase transparency and reduce uplift payments for the U.S. wholesale markets. A convex primal formulation approach is one of the most efficient methods to obtain a high-quality convex hull price. Even though significant progress has been made, the co-optimization of energy and ancillary services is much more challenging due to the discrete nature in formulating ancillary services, for example, the regulating reserve commitment variables, which are binary introduced by some Independent System Operators (ISOs), such as Midcontinent ISO (MISO), to capture the special characteristics of certain generators, such as combined-cycle units. In this paper, we propose convex primal formulations for convex hull pricing considering regulating, spinning, and online/offline-supplemental reserves, in which the regulating reserve commitment variables are considered. Accordingly, we can solve a linear program, instead of a mixed-integer program, which is much harder to solve, to derive the minimum uplift payments and exact convex hull price for the case without general ramping constraints. For the case with general ramping constraints, an upper bound of the minimum uplift payment can also be derived. The final computational experiments on MISO cases verify the effectiveness of our approach in solution quality and computational time.

Two-dimensional graded metamaterials with auxetic rectangular perforations

This work describes the in-plane uniaxial tensile mechanical properties of two-dimensional graded rectangular perforations metamaterials using numerical homogenization finite element approaches benchmarked by experimental results. The metamaterial configuration is based on graded patterns of centre-symmetric perforated cells that can exhibit an auxetic (negative Poisson’s ratio) behavior. Global and local equivalent mechanical properties of the metamaterial are measured using digital image correlation techniques mapped over Finite Element models to identify strain patterns and related stress distributions at different scales. The samples and their numerical counterpart are parametrized against the spacing and aspect ratios of the cells. The overall stiffness behavior of the graded perforated metamaterial plates features a higher degree of compliance that depends both on the geometries of the cells of the graded areas, but also on the graded pattern used. Local Poisson’s ratio effects show a general constraint of the auxetic behavior compared to the case of uniform plates, but also interesting and controllable shape changes due to the uniaxial tensile loading applied.

First- and second-order optimality conditions in optimistic bilevel set-valued programming

ABSTRACT In this work we adapt the main results from Khanh and Tung [First and second-order optimality conditions without differentiability in multivalued vector optimization. Positivity. 2015;19:817–841] for a general set-valued optimization problem to an optimistic bilevel set-valued programming problem as an optimization problem with implicitly given set-valued constraints. Using the optimal value function, we convert our problem into a one level set-valued optimization problem with general inequality constraints and derive both necessary conditions and sufficient conditions of order one and two. The main tools we exploit are approximations of set-valued mappings. To illustrate the obtained results, some examples are given.

Kinetic gravity braiding wormhole geometries

An interesting class of scalar-tensor models, denoted by kinetic gravity braiding (KGB), has recently been proposed. These models contain interactions of the second derivatives of the scalar field that do not lead to additional degrees of freedom and exhibit peculiar features, such as an essential mixing of the scalar $\phi$ and tensor kinetic $X$ terms. In this work, we consider the possibility that wormhole geometries are sustained by the KGB theory. More specifically, we present the full gravitational field equations in a static and spherically symmetric traversable wormhole background, and outline the general constraints at the wormhole throat, imposed by the flaring-out conditions. Furthermore, we present a plethora of analytical and numerical wormhole solutions by considering particular choices of the KGB factors. The analysis explicitly demonstrates that the KGB theory exhibits a rich structure of wormhole geometries, ranging from asymptotically flat solutions to asymptotically anti-de Sitter spacetimes.

Black Holes and the Supermassive Compact Object at the Galactic Center: Multi-arts of Thought and Nature

Black Holes and the Supermassive Compact Object at the Galactic Center: Multi-arts of Thought and Nature

Convex Parameter Recovery for Interacting Marked Processes

We introduce a new general modeling approach for multivariate discrete event data with categorical interacting marks, which we refer to as marked Bernoulli processes. In the proposed model, the probability of an event of a specific category to occur in a location may be influenced by past events at this and other locations. We do not restrict interactions to be positive or decaying over time as it is commonly adopted, allowing us to capture an arbitrary shape of influence from historical events, locations, and events of different categories. In our modeling, prior knowledge is incorporated by allowing general convex constraints on model parameters. We develop two parameter estimation procedures utilizing the constrained Least Squares (LS) and Maximum Likelihood (ML) estimation, which are solved using variational inequalities with monotone operators. We discuss different applications of our approach and illustrate the performance of proposed recovery routines on synthetic examples and a real-world police dataset.

A generalized Nachtmann theorem in CFT

Correlators of unitary quantum field theories in Lorentzian signature obey certain analyticity and positivity properties. For interacting unitary CFTs in more than two dimensions, we show that these properties impose general constraints on families of minimal twist operators that appear in the OPEs of primary operators. In particular, we rederive and extend the convexity theorem which states that for the family of minimal twist operators with even spins appearing in the reflection-symmetric OPE of any scalar primary, twist must be a monotonically increasing convex function of the spin. Our argument is completely non-perturbative and it also applies to the OPE of nonidentical scalar primaries in unitary CFTs, constraining the twist of spinning operators appearing in the OPE. Finally, we argue that the same methods also impose constraints on the Regge behavior of certain CFT correlators.

Event‐triggered distributed algorithm for searching general Nash equilibrium with general step‐size

SummaryIn this article, searching the general Nash equilibrium in the noncooperation game is discussed under the general constraints of containing bounded constraint, coupled equality constraint, and private inequality constraint. Meanwhile, the continuous‐time event‐triggered distributed subgradient projective algorithm (C‐ETDSP algorithm), to greatly cut down the number of communication flows, is designed. In the C‐ETDSP algorithm, the demand for step‐size is weakened to a general step‐size of square nonsummable. Then it is proved that the Zeno behavior did not exist in the continuous‐time event‐triggered mechanism. In addition, the convergence of different types of step‐sizes is further compared. Finally, the effectiveness of the design algorithm and the correctness of the theoretical results are verified by a simulation example.

Constraining photohadronic scenarios for the unified origin of IceCube neutrinos and ultrahigh-energy cosmic rays

The diffuse neutrino flux measured in IceCube is comparable with the ultrahigh-energy cosmic ray (UHECR) flux, which has led to the concept of a unified origin of high-energy neutrino and UHECR backgrounds. We construct a generic unification model of sources to explain UHECR data at $\gtrsim 10^{19}$ eV, and high-energy neutrinos with energies that exceed $\sim100$ TeV in the framework of photo-meson production processes, and provide general constraints on the source properties. A source environment with moderately efficient in-situ production of $\gtrsim 100$ TeV neutrinos with an optical depth of $0.1 \lesssim \tau_{p\gamma}\lesssim 0.6$ must be realized to accelerate cosmic rays to ultrahigh energies. The measured fluxes of cosmic rays and neutrinos set a bound on the source luminosity and its rate density. Although the results are rather general and applicable to unknown source population, among the proposed source candidates, low-luminosity gamma-ray bursts (GRBs) and tidal disruption events (TDEs) could satisfy the requirements if the Lorentz bulk factor of plasma outflow and the equipartition parameters for cosmic rays and magnetic field are appropriately selected.

Generalized f−sum rules and Kohn formulas on nonlinear conductivities

The $f$-sum rule and the Kohn formula are well-established general constraints on the electric conductivity in quantum many-body systems. We present their generalization to non-linear conductivities at all orders of the response in a unified manner, by considering two limiting quantum time-evolution processes: a quench process and an adiabatic process. Our generalized formulas are valid in any stationary state, including the ground state and finite temperature Gibbs states, regardless of the details of the system such as the specific form of the kinetic term, the strength of the many-body interactions, or the presence of disorders.

Distributed Discrete-Time Algorithms for Convex Optimization With General Local Constraints on Weight-Unbalanced Digraph

This article investigates the convex optimization problem with general local constraints including $N$ equality constraints, $N$ inequality constraints, and $N$ closed convex set constraints. Especially, the objective function of the considered problem is the sum of $N$ convex functions, which are seen as local objective functions. First, for the distributed setting, a weight-unbalanced digraph with $N$ nodes is introduced to describe the communication topology. Clearly, in the distributed setting, each node is responsible for a local objective function accompanied with an equality constraint, an inequality constraint, and a closed convex set constraint, which are viewed as local constraints. The aim of this article is to solve the considered convex optimization problem in a distributed manner, i.e., to lead the states of all nodes to a common optimal solution of the considered problem under the condition that each node only knows its own local objective function, and local constraints, and the information of its neighbors’ states. Towards this end, by resorting to the exact penalty function method and the gradient descent-like method, two distinct distributed discrete-time algorithms are developed for two different cases, respectively. Furthermore, the convergence properties of the designed algorithms are rigorously analyzed under some common and standard assumptions, and the convergence rates are described in detail. Finally, simulation results are provided to verify the theoretical results.

The KK principle and rotational symmetry

The KK principle and rotational symmetry

On linearised vacuum constraint equations on Einstein manifolds* *Preprint UWThPh-2020-02.

We show how to parameterise solutions of the general relativistic vector constraint equation on Einstein manifolds by unconstrained potentials. We provide a similar construction for the trace-free part of tensors satisfying the linearised scalar constraint. Previous work of ours has provided similar different constructions for solutions of the linearized constraints in the case where the cosmological constant Λ is zero. We use our new potentials to show that one can shield linearised gravitational fields using linearised gravitational fields without imposing the TT gauge (as done in previous work), for any value of .

Convergence Analysis of the Approximation Problems for Solving Stochastic Vector Variational Inequality Problems

In this paper, we consider stochastic vector variational inequality problems (SVVIPs). Because of the existence of stochastic variable, the SVVIP may have no solutions generally. For solving this problem, we employ the regularized gap function of SVVIP to the loss function and then give a low-risk conditional value-at-risk (CVaR) model. However, this low-risk CVaR model is difficult to solve by the general constraint optimization algorithm. This is because the objective function is nonsmoothing function, and the objective function contains expectation, which is not easy to be computed. By using the sample average approximation technique and smoothing function, we present the corresponding approximation problems of the low-risk CVaR model to deal with these two difficulties related to the low-risk CVaR model. In addition, for the given approximation problems, we prove the convergence results of global optimal solutions and the convergence results of stationary points, respectively. Finally, a numerical experiment is given.

Trochaic bias overrides stress typicality in English lexical development.

This paper investigates whether typical stress patterns in English nouns and verbs are available as a prosodic cue for categorisation and accelerated word learning during first language acquisition. The stress typicality hypothesis states that left-stressed nouns and right-stressed verbs should be acquired earlier than the reverse configurations if stress effectively signals lexical class membership. In this view, class-typical stress patterns are expected to facilitate learning of novel items. A series of generalized additive models (GAMs) based on a comprehensive set of lexical data (CELEX) as well as a large set of age-of-acquisition (AoA) and concreteness ratings reveals that stress typicality plays a minor role in early acquisition, as it is generally superseded by a preference for left-hand (or 'trochaic') patterns in both nouns and verbs. This may be explained by general cognitive constraints (perceptual salience and recency) or exposure to the dominant pattern in the ambient language.