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We study an online inventory trading problem where a user seeks to maximize the aggregate revenue of trading multiple inventories over a time horizon. The trading constraints and concave revenue functions are revealed sequentially in time, and the user needs to make irrevocable decisions. The problem has wide applications in various engineering domains. Existing works employ the primal-dual framework to design online algorithms with sub-optimal, albeit near-optimal, competitive ratios (CR). We exploit the problem structure to develop a new divide-and-conquer approach to solve the online multi-inventory problem by solving multiple calibrated single-inventory ones separately and combining their solutions. The approach achieves the optimal CR of łn θ + 1 if Nłeq łn θ + 1, where N is the number of inventories and θ represents the revenue function uncertainty; it attains a CR of 1/[1-e^-1/(łnθ+1) ] in [łn θ +1, łn θ +2) otherwise. The divide-and-conquer approach reveals novel structural insights for the problem, (partially) closes a gap in existing studies, and generalizes to broader settings. For example, it gives an algorithm with a CR within a constant factor to the lower bound for a generalized one-way trading problem with price elasticity with no previous results. When developing the above results, we also extend a recent CR-Pursuit algorithmic framework and introduce an online allocation problem with allowance augmentation, both of which can be of independent interest.

Lymphatic metastasis influences clinical treatment and prognosis of patients with non-small-cell lung cancer (NSCLC). There is an urgency to understand the molecular features and mechanisms of lymph node metastasis. We analyzed the molecular features on pairs of the primary tumor and lymphatic metastasis tissue samples from 15 NSCLC patients using targeted next-generation sequencing. The potential metastasis-related genes were screened from our cohort based on cancer cell fraction. After filtering with gene functions, candidate metastasis-related events were validated in the MSK cohort with Fisher’s exact test. The molecular signature and tumor mutational burden were similar in paired samples, and the average mutational concordance was 42.0% ± 28.9%. Its metastatic mechanism is potentially a linear progression based on the metastatic seeding theory. Furthermore, mutated ataxia telangiectasia mutated and Rad3-related (ATR) and tet methylcytosine dioxygenase 2 (TET2) genes were significantly enriched in lymphatic metastases (p ≤ 0.05). Alterations in these two genes could be considered metastasis-related driving events. Mutated ATR and TET2 might play an active role in the metastasis of lymph nodes with NSCLC. More case enrollment and long-term follow-up will further verify the clinical significance of these two genes.

We carry out a comparative study of energy consumption of the conventional internal combustion truck and modern electric truck, traveling from origin to destination over the national highway subject to a hard deadline. We focus on understanding energy saving of the latter over the former and key contributing factors. Our study is unique in that (i) it is based on extensive simulations using real-world data over the U.S. highway system, and (ii) we factor in the power system energy-conversion efficiency when calculating the energy consumption of electric trucks for fair comparison. The results show that on average the electric truck save 10% energy as compared to the internal combustion truck, and this saving will improve as power systems incorporate more renewable generation. Furthermore, the energy saving mainly comes from the energy efficiency of electric motors, and other electric-truck features, e.g., regenerative breaking, only have minor contributions.

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