Making Three out of Two: Three-Way Online Correlated Selection

Two-way online correlated selection (two-way OCS) is an online algorithm that, at each timestep, takes a pair of elements from the ground set and irrevocably chooses one of the two elements, while ensuring negative correlation in the algorithm\u27s choices. Whilst OCS was initially invented by Fahrbach, Huang, Tao, and Zadimoghaddam to break a natural long-standing barrier in the edge-weighted online bipartite matching problem, it is an interesting technique on its own due to its capability of introducing a powerful algorithmic tool, namely negative correlation, to online algorithms. As such, Fahrbach et al. posed two tantalizing open questions in their paper, one of which was the following: Can we obtain n-way OCS for n > 2, in which the algorithm can be given n > 2 elements to choose from at each timestep? In this paper, we affirmatively answer this open question by presenting a three-way OCS. Our algorithm uses two-way OCS as its building block and is simple to describe; however, as it internally runs two instances of two-way OCS, one of which is fed with the output of the other, the final output probability distribution becomes highly elusive. We tackle this difficulty by approximating the output distribution of OCS by a flat, less correlated function and using it as a safe "surrogate" of the real distribution. Our three-way OCS also yields a 0.5093-competitive algorithm for edge-weighted online matching, demonstrating its usefulness

Constant-Factor Approximation Algorithms for the Parity-Constrained Facility Location Problem

Facility location is a prominent optimization problem that has inspired a large quantity of both theoretical and practical studies in combinatorial optimization. Although the problem has been investigated under various settings reflecting typical structures within the optimization problems of practical interest, little is known on how the problem behaves in conjunction with parity constraints. This shortfall of understanding was rather discouraging when we consider the central role of parity in the field of combinatorics. In this paper, we present the first constant-factor approximation algorithm for the facility location problem with parity constraints. We are given as the input a metric on a set of facilities and clients, the opening cost of each facility, and the parity requirement - odd, even, or unconstrained - of every facility in this problem. The objective is to open a subset of facilities and assign every client to an open facility so as to minimize the sum of the total opening costs and the assignment distances, but subject to the condition that the number of clients assigned to each open facility must have the same parity as its requirement. Although the unconstrained facility location problem as a relaxation for this parity-constrained generalization has unbounded gap, we demonstrate that it yields a structured solution whose parity violation can be corrected at small cost. This correction is prescribed by a T-join on an auxiliary graph constructed by the algorithm. This auxiliary graph does not satisfy the triangle inequality, but we show that a carefully chosen set of shortcutting operations leads to a cheap and sparse T-join. Finally, we bound the correction cost by exhibiting a combinatorial multi-step construction of an upper bound

Improved Learning-Augmented Algorithms for the Multi-Option Ski Rental Problem via Best-Possible Competitive Analysis

In this paper, we present improved learning-augmented algorithms for the multi-option ski rental problem. Learning-augmented algorithms take ML predictions as an added part of the input and incorporates these predictions in solving the given problem. Due to their unique strength that combines the power of ML predictions with rigorous performance guarantees, they have been extensively studied in the context of online optimization problems. Even though ski rental problems are one of the canonical problems in the field of online optimization, only deterministic algorithms were previously known for multi-option ski rental, with or without learning augmentation. We present the first randomized learning-augmented algorithm for this problem, surpassing previous performance guarantees given by deterministic algorithms. Our learning-augmented algorithm is based on a new, provably best-possible randomized competitive algorithm for the problem. Our results are further complemented by lower bounds for deterministic and randomized algorithms, and computational experiments evaluating our algorithms' performance improvements.Comment: 23 pages, 1 figur

Effects of high fat diet-induced obesity on vitamin D metabolism and tissue distribution in vitamin D deficient or supplemented mice

Background Vitamin D deficiency has been often observed in obese persons. One of the mechanisms suggested for low vitamin D status in obesity was decreased bioavailability of vitamin D (VD) due to sequestration in adipose tissue. However, only few studies have investigated this mechanism via quantifying vitamin D levels from tissues from the obese. Methods Six-wk-old C57BL/6 mice were fed 10 or 45% kcal fat (CON or HFD) diets containing 50, 1000 or 25,000 IU vitamin D3/kg diet (LVd, CVd or HVd) for 13 wks. Serum 25-hydroxyvitamin D (25(OH)D) levels were determined by radioimmunoassay and liver and adipose tissue cholecalciferol (VD3) and 25-hydrocholecalciferol (25(OH)D3) levels were measured by LC-MS/MS. mRNA levels of jejunal Mttp, Cd36, Sr-b1, Npc1l1, and Abca1 and liver and adipose tissue 25-hydroxylases (Cyp2r1 and Cyp27a1) were determined by real-time PCR. Results Serum 25(OH)D levels were affected by dietary vitamin D content but differential effects were observed between HFD and CON groups. When vitamin D intake was at a supplementary level, the HFD-HVd group had lower serum 25(OH)D levels than the CON-HVd group, while there was no significant difference between the HFD and CON groups fed LVd or CVd. Total amount of VD3 in liver and adipose tissue were significantly higher in HFD-HVd group compared with the CON-HVd group. However, no difference in total amount of tissue VD3 was observed between the CON and HFD groups fed CVd. In jejunum, mRNA levels of Mttp and Abca1 were significantly higher in HFD groups than CON groups. There was no difference in mRNA levels of liver 25-hydroxylases by both dietary fat amount and vitamin D content. Conclusion A significant amount of VD3 seemed to be stored in the liver and adipose tissue when dietary vitamin D is at a supplementation level; thus excess body adiposity could contribute to relatively low serum 25(OH)D level when vitamin D was supplemented.This research was funded by the grant from National Research Foundation (NRF) of Korea (NRF-2018R1D1A1B070491) and Seoul National University Research Grant by Research Affairs at Seoul National University (350–20160050)

Translocation of residual ethoprophos and tricyclazole from soil to spinach

The dissipation of ethoprophos and tricyclazole in soil and their translocation tendency to spinach were investigated. Prior to field trials, the analytical method for the determination of these pesticide residues was optimized and validated on soil and spinach. The field trial was conducted under greenhouse conditions for two different pretreatment periods with the pesticides. After treating with pesticides 30 (PBI-30) and 60 days (PBI-60) before seeding, soil samples were collected on different days for the dissipation study of soil. Spinach samples were harvested from the soil, and 50% and 100% mature spinach samples were collected. The initial amounts of ethoprophos residue in the PBI-60 and PBI-30 soils were 0.21 and 2.74 mg/kg, respectively, and these both decreased to less than 0.01 mg/kg on the day of spinach harvest. Similar initial residues of tricyclazole were observed in the PBI-60 (0.87 mg/kg) and PBI-30 soils (0.84 mg/kg), and these decreased to 0.44 and 0.34 mg/kg, respectively. The half-lives of ethoprophos in the soils were calculated as 7.6 and 4.8 days, respectively, while relatively long half-lives of 36.5 and 77.0 days were calculated for tricyclazole. According to the pesticide residue amounts in the spinach, the translocation rate from the soil to the spinach was determined. In the case of ethoprophos, the residual amount was already rapidly degraded in the soil, and the translocation rate could not be confirmed. On the other hand, for tricyclazole, it was confirmed that 1.19 to 1.61% of the residual amount in soil was transferred to spinach. According to these results, safe management guidelines for tricyclazole in soil were suggested considering the maximum residue limit on spinach.This work was supported by the Rural Development Administration (PJ0152772020)

Measurement of the top quark forward-backward production asymmetry and the anomalous chromoelectric and chromomagnetic moments in pp collisions at √s = 13 TeV

Abstract The parton-level top quark (t) forward-backward asymmetry and the anomalous chromoelectric (d̂ t) and chromomagnetic (μ̂ t) moments have been measured using LHC pp collisions at a center-of-mass energy of 13 TeV, collected in the CMS detector in a data sample corresponding to an integrated luminosity of 35.9 fb−1. The linearized variable AFB(1) is used to approximate the asymmetry. Candidate t t ¯ events decaying to a muon or electron and jets in final states with low and high Lorentz boosts are selected and reconstructed using a fit of the kinematic distributions of the decay products to those expected for t t ¯ final states. The values found for the parameters are AFB(1)=0.048−0.087+0.095(stat)−0.029+0.020(syst),μ̂t=−0.024−0.009+0.013(stat)−0.011+0.016(syst), and a limit is placed on the magnitude of | d̂ t| < 0.03 at 95% confidence level. [Figure not available: see fulltext.

Search for Physics beyond the Standard Model in Events with Overlapping Photons and Jets

Results are reported from a search for new particles that decay into a photon and two gluons, in events with jets. Novel jet substructure techniques are developed that allow photons to be identified in an environment densely populated with hadrons. The analyzed proton-proton collision data were collected by the CMS experiment at the LHC, in 2016 at root s = 13 TeV, and correspond to an integrated luminosity of 35.9 fb(-1). The spectra of total transverse hadronic energy of candidate events are examined for deviations from the standard model predictions. No statistically significant excess is observed over the expected background. The first cross section limits on new physics processes resulting in such events are set. The results are interpreted as upper limits on the rate of gluino pair production, utilizing a simplified stealth supersymmetry model. The excluded gluino masses extend up to 1.7 TeV, for a neutralino mass of 200 GeV and exceed previous mass constraints set by analyses targeting events with isolated photons.Peer reviewe

Calibration of the CMS hadron calorimeters using proton-proton collision data at root s=13 TeV

Methods are presented for calibrating the hadron calorimeter system of theCMSetector at the LHC. The hadron calorimeters of the CMS experiment are sampling calorimeters of brass and scintillator, and are in the form of one central detector and two endcaps. These calorimeters cover pseudorapidities vertical bar eta vertical bar ee data. The energy scale of the outer calorimeters has been determined with test beam data and is confirmed through data with high transverse momentum jets. In this paper, we present the details of the calibration methods and accuracy.Peer reviewe