Lower Bound Research Articles

A new target accessibility control method based on SMC

ABSTRACT In this paper, a sliding mode control method based on improved intelligent decision (IID-SMC) algorithm is proposed to improve the accuracy of the puncture needle to reach the target and reduce the time required in the puncture process. First of all, around the straight line of the puncture needle and the direction of the rotation of the needle, the independent control law is designed to realise the mutual decoupling and reduce the mutual interference. Secondly, the error range of this method in the process of puncture is analysed, and the upper bound of the error in the process of puncture is given. Finally, the method is verified by simulation and experiment platform.

Efficacy and Safety of the Melphalan/Hepatic Delivery System in Patients with Unresectable Metastatic Uveal Melanoma: Results from an Open-Label, Single-Arm, Multicenter Phase 3 Study.

Uveal melanoma (UM) has a poor prognosis once liver metastases occur. The melphalan/Hepatic Delivery System (melphalan/HDS) is a drug/device combination used for liver-directed treatment of metastatic UM (mUM) patients. The purpose of the FOCUS study was to assess the efficacy and safety of melphalan/HDS in patients with unresectable mUM. Eligible patients with mUM received treatment with melphalan (3.0 mg/kg ideal body weight) once every 6 to 8 weeks for a maximum of six cycles. The primary end point was the objective response rate (ORR). The secondary end points included duration of response (DOR), overall survival (OS), and progression-free survival (PFS). The study enrolled 102 patients with mUM. Treatment was attempted in 95 patients, and 91 patients received treatment. In the treated population (n = 91), the ORR was 36.3 % (95 % confidence interval [CI], 26.44-47.01), including 7.7 % of patients with a complete response. Thus, the study met its primary end point because the lower bound of the 95 % CI for ORR exceeded the upper bound (8.3 %) from the benchmark meta-analysis. The median DOR was 14 months, and the median OS was 20.5 months, with an OS of 80 % at 1 year. The median PFS was 9 months, with a PFS of 65 % at 6 months. The most common serious treatment-emergent adverse events were thrombocytopenia (15.8 %) and neutropenia (10.5 %), treatedmostly on an outpatient basis with observation. No treatment-related deaths were observed. Treatment with melphalan/HDS provides a clinically meaningful response rate and demonstrates a favorable benefit-risk profile in patients with unresectable mUM (study funded by Delcath; ClinicalTrials.gov identifier: NCT02678572; EudraCT no. 2015-000417-44).

A certified wavelet-based physics-informed neural network for the solution of parameterized partial differential equations

Abstract Physics Informed Neural Networks (PINNs) have frequently been used for the numerical approximation of Partial Differential Equations (PDEs). The goal of this paper is to construct PINNs along with a computable upper bound of the error, which is particularly relevant for model reduction of Parameterized PDEs (PPDEs). To this end, we suggest to use a weighted sum of expansion coefficients of the residual in terms of an adaptive wavelet expansion both for the loss function and an error bound. This approach is shown here for elliptic PPDEs using both the standard variational and an optimally stable ultra-weak formulation. Numerical examples show a very good quantitative effectivity of the wavelet-based error bound.

Feasibility Verification and Upper Bound Computation in Global Minimization Using Approximate Active Index Sets

We propose a new upper bounding procedure for global minimization problems with continuous variables and possibly nonconvex inequality and equality constraints. Upper bounds are crucial for standard termination criteria of spatial branch-and-bound (SBB) algorithms to ensure that they can enclose globally minimal values sufficiently well. However, whereas for most lower bounding procedures from the literature, convergence on smaller boxes is established, this does not hold for several methods to compute upper bounds even though they often perform well in practice. In contrast, our emphasis is on the convergence. We present a new approach to verify the existence of feasible points on boxes, on which upper bounds can then be determined. To this end, we resort to existing convergent feasibility verification approaches for purely equality and box constrained problems. By considering carefully designed modifications of subproblems based on the approximation of active index sets, we enhance such methods to problems with additional inequality constraints. We prove that our new upper bounding procedure finds sufficiently good upper bounds so that termination of SBB algorithms is guaranteed after a finite number of iterations. Our theoretical findings are illustrated by computational results on a large number of standard test problems. These results show that compared with interval Newton methods from the literature, our proposed method is more successful in feasibility verification for both, a full SBB implementation (42 instead of 26 test problems) and exhaustive sequences of boxes around known feasible points (120 instead of 29 test problems). History: Accepted by Antonio Frangioni, Area Editor for Design & Analysis of Algorithms–Continuous. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0162 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0162 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Complex-Valued Noisy Sinewaves Frequency Estimator Based on DTFT Linearization and Interpolation

AbstractThis paper proposes an Interpolated Discrete-Time Fourier Transform (LIpDTFT) estimator for complex-valued noisy sinewave frequency based on the Linearization of the DTFT module behavior around the spectrum peak. It belongs to a class of LIpDTFT estimators that compensate the poor Discrete Fourier Transform (DFT) frequency resolution by interpolating two DTFT samples located very close to an initial frequency estimate. As compared with other DTFT-based frequency estimators recently proposed in the literature, the proposed LIpDTFT estimator ensures a smaller interpolation error and a lower processing effort. Moreover, if the rectangular window is adopted, it almost attains the unbiased Cramér-Rao Lower Bound (CRLB) even if a very small number of samples is analyzed. The accuracies ensured in different operating conditions by the proposed frequency estimator and other state-of-the-art DTFT-based algorithms are compared to each other through computer simulations.

Non-Gaussian Multivariate Process Capability Based on the Copulas Method: An Application to Aircraft Engine Fan Blades

Abstract Process Capability Indices (PCIs) are major tools in Geometric Dimensioning & Tolerancing (GD&T) for quantifying the production quality, monitoring production or prioritizing projects. Initially, PCIs were constructed for studying each characteristic of the process independently. Then, they have been extended to analyze several dependent characteristics simultaneously. Nowadays, with the increasing complexity of the production parts, for example in aircraft engines, the conformity of one part may rely on the conformity of hundreds of characteristics. Moreover, those characteristics being dependent, it may be misleading to make decisions only based on univariate PCIs. However, classical multivariate PCIs in the literature do not allow treating such amount of data efficiently, unless assuming Gaussian distribution, which is not always true. Regarding those issues, we advocate for PCIs based on some transformation of the conformity rates. This presents the advantage of being free from distributional assumptions, such as the Gaussian distribution. In addition, it has direct interpretation, allowing it to compare different processes. To estimate the PCIs of parts with hundreds of characteristics, we propose to use Vine Copulas. This is a very flexible class of models, which gives precise estimation even in high dimension. From an industrial perspective, the computation of the estimator can be costly. To answer this point, we explain how to compute a lower bound of the proposed PCI, which is faster to calculate. We illustrate our method adaptability with simulations under Gaussian and non-Gaussian distributions. We apply it to compare the production of Fan Blades of two different factories.

Enhanced Moving Source Localization with Time and Frequency Difference of Arrival: Motion-Assisted Method for Sub-Dimensional Sensor Networks

Localizing a moving source by Time Difference of Arrival (TDOA) and Frequency Difference of Arrival (FDOA) commonly requires at least N+1 sensors in N-dimensional space to obtain more than N pairs of TDOAs and FDOAs, thereby establishing more than 2N equations to solve for 2N unknowns. However, if there are insufficient sensors, the localization problem will become underdetermined, leading to non-unique solutions or inaccuracies in the minimum norm solution. This paper proposes a localization method using TDOAs and FDOAs while incorporating the motion model. The motion between the source and sensors increases the equivalent length of the baseline, thereby improving observability even when using the minimum number of sensors. The problem is formulated as a Maximum Likelihood Estimation (MLE) and solved through Gauss–Newton (GN) iteration. Since GN requires an initialization close to the true value, the MLE is transformed into a semidefinite programming problem using Semidefinite Relaxation (SDR) technology, while SDR results in a suboptimal estimate, it is sufficient as an initialization to guarantee the convergence of GN iteration. The proposed method is analytically shown to reach the Cramér–Rao Lower Bound (CRLB) accuracy under mild noise conditions. Simulation results confirm that it achieves CRLB-level performance when the number of sensors is lower than N+1, thereby corroborating the theoretical analysis.

Reinforcement Learning Approaches for Exploring Discrepancy Variations: Implications for Supply Chain Optimization

Combinatorics discrepancy theory studies the ways in which a given state deviates from the ideal. A set system's disparity in its classical form has been shown to be bound in certain situations. Though they may not hold for other types of discrepancy, no mathematician has been able to produce an example that defies these limits as of yet. Due to the large number of set systems (kmn for m sets and n elements, each choosing one of k possible values), it is not viable to use traditional techniques, such as human reasoning or computer brute forcing, to identify the few set systems with a significant discrepancy. However, in a 2021 preprint, Adam Zsolt Wagner shows how the deep cross-entropy method—a popular Neural Network (NNs)-based Reinforcement-Learning (RL) technique—could effectively find examples that disprove open conjectures in two other combinatorial subfields: pattern avoidance and graph theory. Therefore, in light of these encouraging findings, we wondered if Wagner's method could help us find examples that defy the upper bound of discrepancy variations. To start answering this question, we examined whether Wagner's approach might be extended to find set systems that exhibit significant inconsistencies, either as classical or variant (prefix and fractional in our instance) systems. Our findings could help approximation algorithms, which employ discrepancy theory to tackle certain problems, as well as discrepancy theory itself.

Quantised adaptive consensus control of heterogeneous nonlinear multi-agent systems under external disturbance

This paper is primarily devoted to the distributed consensus tracking control for heterogeneous nonlinear multi-agent systems (MASs) with a directed communication topology. Taking the considered heterogeneous nonlinear MASs own unknown nonlinear term and quantised input signals, the adaptive radial basis function neural networks (RBFNNs)-based approximator is utilised to tackle these interesting challenges. Next, considering the boundness of disturbances, the upper bound of time-varying disturbance is utilised in the controller design. Then, a distributed dynamic compensator is developed to complete coordination task, which only requires to exchange output information via the communication network. In addition, the compensator transforms the adaptive output consensus problem into asymptotic tracking problem, without needing extra stability conditions. Finally, by means of the Lyapunov stability theory, the satisfying result of the consensus error converging to zero asymptotically can be obtained. Through simulations, the effectiveness of the developed protocol is illustrated.

Abstract PO5-14-08: External Reproducibility of PD-L1 IHC 22C3 pharmDx on Breast Cancer Specimens at CPS ≥ 1 and CPS ≥ 10 Cutoffs

Abstract Background: PD-L1 IHC 22C3 pharmDx is an approved companion diagnostic for pembrolizumab treatment in triple-negative breast cancer (TNBC). Clinical evidence for pembrolizumab approval in TNBC was demonstrated by KEYNOTE-355 (NCT02819518), which investigated the clinical validity of PD-L1 IHC 22C3 pharmDx in identifying patients with PD-L1 expressing Combined Positive Score (CPS) ≥ 10 in previously untreated locally recurrent unresectable or metastatic TNBC.1 The role of immune checkpoint inhibitors for breast cancer as a whole is not as well defined as it is for TNBC. In this study, we show evidence of the reproducibility of PD-L1 IHC 22C3 pharmDx in PD-L1 expression determination in breast cancer specimens at the CPS ≥ 1 and CPS ≥ 10 cutoffs documenting robust assay performance in breast cancer. Methods: A blinded, randomized study was conducted at three external sites using formalin-fixed, paraffin-embedded breast cancer specimens. Reproducibility of PD-L1 IHC 22C3 pharmDx was assessed at the inter-site, intra-site/inter-day, inter-observer, and intra-observer endpoints at the CPS ≥ 1 and CPS ≥ 10 cutoffs. To assess inter-site and intra-site reproducibility, five replicate sets of pre-qualified unstained specimens were stained and evaluated at each of the three external sites. To assess inter-observer and intra-observer reproducibility, one set of pre-stained specimens was evaluated three times by each of three external pathologists. Negative percent agreement (NPA), positive percent agreement (PPA), and overall percent agreement (OA), based on comparisons to consensus diagnostic outcome, were computed with corresponding two-sided 95% percentile bootstrap confidence intervals. Acceptance criteria required at least 85.0% for the lower-bound (LB) of the two-sided 95% confidence interval (CI) on NPA, PPA, and OA for all endpoints. Results: All but one endpoint in the external reproducibility study met pre-determined acceptance criteria. Both the inter- and intra-site reproducibility endpoints had 95% CI LB values of 98.8% for NPA, 95.9% for PPA, and 97.9% OA at the CPS ≥ 1 cutoff. At the CPS ≥ 10 cutoff, the inter-site reproducibility endpoint had 95% CI LB values of 88.0% for NPA, 87.1% for PPA, and 89.5% OA, and the intra-site reproducibility endpoint had 95% CI LB values of 96.7% for NPA, 92.2% for PPA, and 95.6% OA. The inter-observer reproducibility endpoint had 95% CI LB values of 95.3% for NPA, 92.3% for PPA, and 94.7% OA at the CPS ≥ 1 cutoff. At the CPS ≥ 10 cutoff, the inter-observer reproducibility endpoint had 95% CI LB values of 84.9% for NPA, 86.8% for PPA, and 87.3% OA. The intra-observer reproducibility endpoint had 95% CI LB values of 97.0% for NPA, 95.0% for PPA, and 96.6% OA at the CPS ≥ 1 cutoff. At the CPS ≥ 10 cutoff, the intra-observer reproducibility endpoint had 95% CI LB values of 92.2% for NPA, 89.2% for PPA, and 91.7% OA. Conclusions: Acceptance criteria were met for all endpoints in the breast cancer external reproducibility study of PD-L1 IHC 22C3 pharmDx at the CPS ≥ 1 and CPS ≥ 10 cutoffs, except for inter-observer at the CPS ≥ 10 cutoff, which had a 95% CI LB value of 84.9% for NPA.

The maximum genus of the generalized Petersen Graph, GP (<em>n, k</em>) for the cases <em>k</em> = 1, 2

In Topological graph theory, the maximum genus of graphs has been a fascinating subject. For a simple connected graph G, the maximum genus γM(G) is the largest genus of an orientable surface on which G has a 2-cell embedding. γM(G) has the upper bound, γM(G)≤[β/2], where β(G) denotes the Betti number and G is said to be upper embeddable if the equality holds. In this study, the maximum genus of GP(n, k) is established as γM(GP(n,k))=[(n+1)/2] for k = 1 and k = 2 by proving the upper embeddability of generalized Petersen graph, GP(n, k) for the cases k = 1 and k = 2. The proof is done by obtaining spanning trees T and examining the components in the edge complements GP(n, k)\T for the cases k = 1 and k = 2 of GP(n, k).

Probabilistic unitary synthesis with optimal accuracy

The purpose of unitary synthesis is to find a gate sequence that optimally approximates a target unitary transformation. A new synthesis approach, called probabilistic synthesis, has been introduced, and its superiority has been demonstrated over traditional deterministic approaches with respect to approximation error and gate length. However, the optimality of current probabilistic synthesis algorithms is unknown. We obtain the tight lower bound on the approximation error obtained by the optimal probabilistic synthesis, which guarantees the sub-optimality of current algorithms. We also show its tight upper bound, which improves and unifies current upper bounds depending on the class of target unitaries. These two bounds reveal the fundamental relationship of approximation error between probabilistic approximation and deterministic approximation of unitary transformations. From a computational point of view, we show that the optimal probability distribution can be computed by the semidefinite program (SDP) we construct. We also construct an efficient probabilistic synthesis algorithm for single-qubit unitaries, rigorously estimate its time complexity, and show that it reduces the approximation error quadratically compared with deterministic algorithms.

Measurement-free mediated semi-quantum key distribution protocol based on single-particle states

A novel measurement-free mediated semi-quantum key distribution (MSQKD) protocol is proposed based on single-particle states. It enables two classical users to establish a secret key with the assistance of a third party. This protocol simplifies the third party’s role to solely generating qubits in X-basis and conducting Bell measurements. A distinctive feature of this protocol is the efficient grouping and reordering of qubits by the classical users with a minimum of three delay lines. Security analyses demonstrate that the protocol can withstand various attack strategies, including collective attack, measurement attack, fake state attack, and modification attack. The noise tolerance is given by deriving a lower bound of the protocol’s key rate in the asymptotic scenario. Simulations on the IBM Quantum Experience platform are conducted to illustrate the feasibility of this protocol. Compared with existing MSQKD protocols, the proposed protocol consumes fewer quantum resources and achieves a qubit efficiency of 1/8.

Binary Graph Convolutional Network With Capacity Exploration.

The current success of Graph Neural Networks (GNNs) usually relies on loading the entire attributed graph for processing, which may not be satisfied with limited memory resources, especially when the attributed graph is large. This paper pioneers to propose a Binary Graph Convolutional Network (Bi-GCN), which binarizes both the network parameters and input node attributes and exploits binary operations instead of floating-point matrix multiplications for network compression and acceleration. Meanwhile, we also propose a new gradient approximation based back-propagation method to properly train our Bi-GCN. According to the theoretical analysis, our Bi-GCN can reduce the memory consumption by an average of ∼31x for both the network parameters and input data, and accelerate the inference speed by an average of ∼51x, on three citation networks, i.e., Cora, PubMed, and CiteSeer. Besides, we introduce a general approach to generalize our binarization method to other variants of GNNs, and achieve similar efficiencies. Although the proposed Bi-GCN and Bi-GNNs are simple yet efficient, these compressed networks may also possess a potential capacity problem, i.e., they may not have enough storage capacity to learn adequate representations for specific tasks. To tackle this capacity problem, an Entropy Cover Hypothesis is proposed to predict the lower bound of the width of Bi-GNN hidden layers. Extensive experiments have demonstrated that our Bi-GCN and Bi-GNNs can give comparable performances to the corresponding full-precision baselines on seven node classification datasets and verified the effectiveness of our Entropy Cover Hypothesis for solving the capacity problem.

A randomized trial of retropubic versus single-incision sling amongst patients undergoing vaginal prolapse repair.

Choice of midurethral sling type may impact efficacy and complications in women undergoing transvaginal native tissue repair of pelvic organ prolapse (POP). The primary aim was to determine if single-incision (SI) sling is noninferior to retropubic (RP) sling for management of stress urinary incontinence (SUI) amongst patients undergoing reconstructive or obliterative native tissue vaginal repair. The secondary aims were to compare adverse events and surgeon ease of use with sling assignment. A multicenter, noninferiority, randomized trial of women with ≥ Stage II POP and objectively confirmed SUI undergoing reconstructive or obliterative vaginal repair was performed. Women were randomized to concomitant SI (Altis sling, Coloplast Minneapolis, MN) with suprapubic sham incisions or RP sling. The primary, dichotomous outcome was abnormal lower urinary tract function within 12 months post-surgery, defined as: bothersome SUI symptoms (>1 PFDI question #17); retreatment for SUI; or treatment for urinary retention. Secondary outcomes were adverse events, patient global impression of improvement of bladder function (PGI-I) and surgeon ease of use (1 worst, 10 best). All subjects completed validated questionnaires and underwent a POP-Q, cough stress test and post void residual (PVR) pre-operatively, at 6 weeks and 12 months post operatively. Assuming a subjective cure rate for RP of 82%, 80% power and one-sided 5% significance level, we estimated that 127 patients in each arm were needed to declare noninferiority of the SI sling if the upper bound of the 95% confidence interval for the between group difference per protocol in abnormal bladder function was less than 12%. Assuming a 10% loss to follow-up, the total enrollment goal was 280. Between 12/2018 and 1/2023, 280 subjects were enrolled across 7 sites and 255 were randomized: 126 to SI and 129 to RP sling. There were no pre-operative or operative characteristic differences between groups. Overall, 81% had reconstructive and 19% had obliterative native tissue repairs. The primary outcome, abnormal lower urinary tract function at 12 months, occurred in 29 (25%) of SI vs. 24 (20%) of RP sling group (Risk difference 0.04472, 95% CI (-0.03-0.1133), p = 0.001 for noninferiority). Bothersome SUI occurred in 20% vs. 17% (p=0.27) and was re-treated in 4% vs. 2% (p=0.44) of SI vs. RP groups, respectively. Adverse events were reported in 24 (16%) of SI vs. 14 (9%) of RP group (95% CI, 0.95-3.29; p=0.7) and included de novo or worsening urgency incontinence symptoms, urinary tract infection, mesh exposure, need for prolonged catheter drainage, and de novo pain, without differences between groups. PGI-I (very satisfied & satisfied) was 71% vs. 67% (p=0.43) and median surgeon ease of sling use was 8 [7-10] vs. 9 [8-10], p=0.03 in SI vs. RP, respectively. For women undergoing vaginal repair, SI was noninferior to RP sling for SUI symptoms and complications, including treatment for urinary retention, did not differ.

Bounding toric singularities with normalized volume

AbstractWe study the normalized volume of toric singularities. As it turns out, there is a close relation to the notion of (nonsymmetric) Mahler volume from convex geometry. This observation allows us to use standard tools from convex geometry, such as the Blaschke–Santaló inequality and Radon's theorem to prove nontrivial facts about the normalized volume in the toric setting. For example, we prove that for every there are only finitely many ‐Gorenstein toric singularities with normalized volume at least . From this result it directly follows that there are also only finitely many toric Sasaki–Einstein manifolds of volume at least in each dimension. Additionally, we show that the normalized volume of every toric singularity is bounded from above by that of the rational double point of the same dimension. Finally, we discuss certain bounds of the normalized volume in terms of topological invariants of resolutions of the singularity. We establish two upper bounds in terms of the Euler characteristic and of the first Chern class, respectively. We show that a lower bound, which was conjectured earlier by He, Seong, and Yau, is closely related to the nonsymmetric Mahler conjecture in convex geometry.

Toripalimab Plus Bevacizumab as First-line Treatment for Advanced Hepatocellular Carcinoma: A Prospective, Multicenter, Single-Arm, Phase II Trial.

This phase II, multicenter, prospective, single-arm study aimed to evaluate the efficacy and safety of toripalimab plus bevacizumab in treating advanced hepatocellular carcinoma (HCC). Treatment-naïve patients with advanced HCC received toripalimab 240 mg plus bevacizumab 15 mg/kg every 3 weeks. Primary endpoints included safety and tolerability, and objective response rate (ORR) assessed by the investigator per Response Evaluation Criteria in Solid Tumors (RECIST) version 1.1. Fifty-four patients were enrolled between Apr 17, 2020 and Dec 11, 2020. As assessed by the investigator according to RECIST v1.1, the ORR was 31.5% [95% confidence interval (CI), 19.5-45.6] and the lower bound of the 95% CI was above the pre-specified boundary of 10%. The independent review committee (IRC) assessed ORR according to modified RECIST (mRECIST) was 46.3% (95% CI, 32.6-60.4). The median progression-free survival were 8.5 months (95% CI, 5.5-11.0) and 9.8 months (95% CI, 5.6-not evaluable) assessed by the investigator according to RECIST v1.1 and IRC according to mRECIST criteria, respectively. The median overall survival (OS) was not reached, and the 12- and 24-month OS rates were 77.3% and 63.5%, respectively. Grade 3 or higher treatment-emergent adverse events (TEAEs) occurred in 27 patients (50.0%). The most common TEAEs were proteinuria (59.3%), hypertension (38.9%), aspartate aminotransferase increased (33.3%), amylase increased (29.6%), platelet count decreased (27.8%), and bilirubin increased (27.8%). Toripalimab plus bevacizumab showed a favorable efficacy and safety profile, supporting further studies of this combination regimen as a first-line treatment of advanced HCC.

Uncertainty relation and the constrained quadratic programming

The uncertainty relation is a fundamental concept in quantum theory, plays a pivotal role in various quantum information processing tasks. In this study, we explore the additive uncertainty relation pertaining to two or more observables, in terms of their variance, by utilizing the generalized Gell-Mann representation in qudit systems. We find that the tight state-independent lower bound of the variance sum can be characterized as a quadratic programming problem with nonlinear constraints in optimization theory. As illustrative examples, we derive analytical solutions for these quadratic programming problems in lower-dimensional systems, which align with the state-independent lower bounds. Additionally, we introduce a numerical algorithm tailored for solving these quadratic programming instances, highlighting its efficiency and accuracy. The advantage of our approach lies in its potential ability to simultaneously achieve the optimal value of the quadratic programming problem with nonlinear constraints but also precisely identify the extremal state where this optimal value is attained. This enables us to establish a tight state-independent lower bound for the sum of variances, and further identify the extremal state at which this lower bound is realized.

Revisiting the complexity of and algorithms for the graph traversal edit distance and its variants

The graph traversal edit distance (GTED), introduced by Ebrahimpour Boroojeny et al. (2018), is an elegant distance measure defined as the minimum edit distance between strings reconstructed from Eulerian trails in two edge-labeled graphs. GTED can be used to infer evolutionary relationships between species by comparing de Bruijn graphs directly without the computationally costly and error-prone process of genome assembly. Ebrahimpour Boroojeny et al. (2018) propose two ILP formulations for GTED and claim that GTED is polynomially solvable because the linear programming relaxation of one of the ILPs always yields optimal integer solutions. The claim that GTED is polynomially solvable is contradictory to the complexity results of existing string-to-graph matching problems. We resolve this conflict in complexity results by proving that GTED is NP-complete and showing that the ILPs proposed by Ebrahimpour Boroojeny et al. do not solve GTED but instead solve for a lower bound of GTED and are not solvable in polynomial time. In addition, we provide the first two, correct ILP formulations of GTED and evaluate their empirical efficiency. These results provide solid algorithmic foundations for comparing genome graphs and point to the direction of heuristics. The source code to reproduce experimental results is available at https://github.com/Kingsford-Group/gtednewilp/.

Pricing and Positioning of Horizontally Differentiated Products with Incomplete Demand Information

How to Manage Horizontally Differentiated Products When Customer Preferences and Demand Distributions Are Unknown In the paper “Pricing and Positioning of Horizontally Differentiated Products with Incomplete Demand Information,” we consider the problem of determining the optimal prices and product configurations of horizontally differentiated products when customers purchase according to a locational choice model and where the problem parameters are initially unknown to the decision maker. We propose a data-driven algorithm that learns the optimal prices and product configurations from accumulating sales data, and we show that their regret—the expected cumulative loss caused by not using optimal decisions—after T time periods is [Formula: see text]. We accompany this result by proving an almost-matching lower bound of regret, implying that our algorithms are asymptotically near optimal. In an extension, we show how our algorithm can be adapted for the case of fixed locations.