High-quality-factor dual-band Fano resonances induced by dual bound states in the continuum using a planar nanohole slab

In photonics, it is essential to achieve high-quality (Q)-factor resonances to improve optical devices’ performances. Herein, we demonstrate that high-Q-factor dual-band Fano resonances can be achieved by using a planar nanohole slab (PNS) based on the excitation of dual bound states in the continuum (BICs). By shrinking or expanding the tetramerized holes of the superlattice of the PNS, two symmetry-protected BICs can be induced to dual-band Fano resonances and their locations as well as their Q-factors can be flexibly tuned. Physical mechanisms for the dual-band Fano resonances can be interpreted as the resonant couplings between the electric toroidal dipoles or the magnetic toroidal dipoles based on the far-field multiple decompositions and the near-field distributions of the superlattice. The dual-band Fano resonances of the PNS possess polarization-independent feature, and they can be survived even when the geometric parameters of the PNS are significantly altered, making them more suitable for potential applications.

Mathematical Modeling Reveals Quantitative Properties of KEAP1-NRF2 Signaling

In response to oxidative and electrophilic stresses, cells launch an NRF2-mediated transcriptional antioxidant program. The activation of NRF2 depends on a redox sensor, KEAP1, which acts as an E3-ligase adaptor to promote the ubiquitination and degradation of NRF2. While a great deal has been learned about the molecular details of KEAP1, NRF2, and their interactions, the quantitative aspects of signal transfer conveyed by this redox duo are still largely unexplored. In the present study, we examined the signaling properties including response time, half-life, maximal activation, and response steepness (ultrasensitivity) of NRF2, through a suite of mathematical models. The models describe, with increasing complexity, the reversible binding of KEAP1 dimer and NRF2 via the ETGE and DLG motifs, NRF2 production, KEAP1-dependent and independent NRF2 degradation, and perturbations by different classes of NRF2 activators. Our simulations revealed that at the basal condition, NRF2 molecules are largely sequestered by KEAP1, with the KEAP1-NRF2 complex comparably distributed in either an ETGE-bound only (open) state or an ETGE and DLG dual-bound (closed) state, corresponding to the unlatched and latched configurations of the conceptual hinge-latch model. With two-step ETGE binding, the open and closed states operate in cycle mode at the basal condition and transition to equilibrium mode at stressed conditions. Class I-V, electrophilic NRF2 activators, which modify redox-sensing cysteine residues of KEAP1, shift the balance to a closed state that is unable to degrade NRF2 effectively. Total NRF2 has to accumulate to a level that nearly saturates existing KEAP1 to make sufficient free NRF2, therefore introducing a signaling delay. At the juncture of KEAP1 saturation, ultrasensitive NRF2 activation, i.e., a steep rise in the free NRF2 level, can occur through two simultaneous mechanisms, zero-order degradation mediated by DLG binding and protein sequestration (molecular titration) mediated by ETGE binding. These response characteristics of class I-V activators do not require disruption of DLG binding to unlatch the KEAP1-NRF2 complex. In comparison, class VI NRF2 activators, which directly compete with NRF2 for KEAP1 binding, can unlatch or even unhinge the KEAP1-NRF2 complex. This causes a shift to the open state of KEAP1-NRF2 complex and ultimately its complete dissociation, resulting in a fast release of free NRF2 followed by stabilization. Although class VI activators may induce free NRF2 to higher levels, ultrasensitivity is lost due to lower free KEAP1 and thus its NRF2-sequestering effect. Stress-induced NRF2 nuclear accumulation is enhanced when basal nuclear NRF2 turnover constitutes a small load to NRF2 production. Our simulation further demonstrated that optimal abundances of cytosolic and nuclear KEAP1 exist to maximize ultrasensitivity. In summary, by simulating the dual role of KEAP1 in repressing NRF2, i.e., sequestration and promoting degradation, our mathematical modeling provides key novel quantitative insights into the signaling properties of the crucial KEAP1-NRF2 module of the cellular antioxidant response pathway.

The sufficient condition to find an exact dual bound in a separable quadratic optimization problem

The paper considers nonconvex separable quadratic optimization problems subject to inequality constraints. A sufficient condition is given for finding the value and the point of the global extremum of a problem of this type by calculating the Lagrange dual bound. The peculiarity of this condition is that it is easily verified and requires from the Hessian matrix of the Lagrange function only that its region of positive definiteness is not empty. The result obtained for the dual bound also holds for the bound obtained using SDP relaxation.

Electric Vehicle Routing with Public Charging Stations

We introduce the electric vehicle routing problem with public-private recharging strategy in which vehicles may recharge en route at public charging infrastructure as well as at a privately-owned depot. To hedge against uncertain demand at public charging stations, we design routing policies that anticipate station queue dynamics. We leverage a decomposition to identify good routing policies, including the optimal static policy and fixed-route-based rollout policies that dynamically respond to observed queues. The decomposition also enables us to establish dual bounds, providing a measure of goodness for our routing policies. In computational experiments using real instances from industry, we show the value of our policies to be within 10% of a dual bound. Furthermore, we demonstrate that our policies significantly outperform the industry-standard routing strategy in which vehicle recharging generally occurs at a central depot. Our methods stand to reduce the operating costs associated with electric vehicles, facilitating the transition from internal-combustion engine vehicles.

A Stochastic Programming Approach for Scheduling Extra Metro Trains to Serve Passengers from Uncertain Delayed High-Speed Railway Trains

The metro system is an important component of the urban transportation system due to the large volume of transported passengers. Hub stations connecting metro and high-speed railway (HSR) networks are particularly critical in this system. When HSR trains are delayed due to a disruption on the HSR network, passengers of these trains arriving at the hub station at night may fail to get their last metro connection. The metro operator can thus decide to schedule extra metro trains at night to serve passengers from delayed HSR trains. In this paper, we consider the extra metro train scheduling problem in which the metro operator decides how many extra metro trains to dispatch and their schedules. The problem is complex because (i) the arrival of delayed HSR trains is usually uncertain, and (ii) the operator has to minimize operating costs (i.e., number of additional trains and operation-ending time) but maximize the number of served passengers, which are two conflicting objectives. In other words, the problem we consider is stochastic and biobjective. We formulate this problem as a two-stage stochastic program with recourse and use an epsilon-constrained method to find a set of nondominated solutions. We perform extensive numerical experiments using realistic instances based on the Beijing metro network and two HSR lines connected to this network. We find that our stochastic model outperforms out-of-sample a deterministic model that relies on forecasts of the delay by a range of 3–5%. Moreover, we show that our solutions are nearly optimal by computing a perfect information dual bound and obtaining average optimality gaps below 1%.

Integrated Planning for Multimodal Networks with Disruptions and Customer Service Requirements

Multimodal carriers are third-party logistics providers who utilize multiple modes of transportation to deliver timely door-to-door services to their customers. Notwithstanding frequent service disruptions, customers have ever-increasing expectations for on-time deliveries, posing significant challenges to tactical planning. Inspired by the operations of actual carriers, we study the tactical decision planning of multimodal freight networks, considering operational disruptions, timetabling restrictions, and explicit customer service requirements. Despite our focus on tactical planning, our models integrate long-term commitments by penalizing deviations from strategic goals with last-minute operational planning decisions, which are recourse actions aiming to accommodate service disruptions. After improving the dual bound of our initial formulation, we provide reduced-sized models for the special cases of nonpropagating delays and nonreactive last-minute decisions. This latter formulation is utilized to construct scenario-based and trip-based heuristics, which we combine in a hybrid search loop. Our computational study illustrates that our approach attains high-quality solutions for real-sized instances that are otherwise unsolvable by off-the-shelf optimization software, and a significant improvement over a nontrivial rolling horizon benchmark.

Improving Lagrange Dual Bounds for Quadratic Extremal Problems

Introduction. Due to the fact that quadratic extremal problems are generally NP-hard, various convex relaxations to find bounds for their global extrema are used, namely, Lagrangian relaxation, SDP-relaxation, SOCP-relaxation, LP-relaxation, and others. This article investigates a dual bound that results from the Lagrangian relaxation of all constraints of quadratic extremal problem. The main issue when using this approach for solving quadratic extremal problems is the quality of the obtained bounds (the magnitude of the duality gap) and the possibility to improve them. While for quadratic convex optimization problems such bounds are exact, in other cases this issue is rather complicated. In non-convex cases, to improve the dual bounds (to reduce the duality gap) the techniques, based on ambiguity of the problem formulation, can be used. The most common of these techniques is an extension of the original quadratic formulation of the problem by introducing the so-called functionally superfluous constraints (additional constraints that result from available constraints). The ways to construct such constraints can be general in nature or they can use specific features of the concrete problems. The purpose of the article is to propose methods for improving the Lagrange dual bounds for quadratic extremal problems by using technique of functionally superfluous constraints; to present examples of constructing such constraints. Results. The general concept of using functionally superfluous constraints for improving the Lagrange dual bounds for quadratic extremal problems is considered. Methods of constructing such constraints are presented. In particular, the method proposed by N.Z. Shor for constructing functionally superfluous constraints for quadratic problems of general form is presented in generalized and schematized forms. Also it is pointed out that other special techniques, which employ the features of specific problems for constructing functionally superfluous constraints, can be used. Conclusions. In order to improve dual bounds for quadratic extremal problems, one can use various families of functionally superfluous constraints, both of general and specific type. In some cases, their application can improve bounds or even provide an opportunity to obtain exact values of global extrema.