Discretization of Planar Geometric Cover Problems

We consider discretization of the 'geometric cover problem' in the plane: Given a set $P$ of $n$ points in the plane and a compact planar object $T_0$, find a minimum cardinality collection of planar translates of $T_0$ such that the union of the translates in the collection contains all the points in $P$. We show that the geometric cover problem can be converted to a form of the geometric set cover, which has a given finite-size collection of translates rather than the infinite continuous solution space of the former. We propose a reduced finite solution space that consists of distinct canonical translates and present polynomial algorithms to find the reduce solution space for disks, convex/non-convex polygons (including holes), and planar objects consisting of finite Jordan curves.Comment: 16 pages, 5 figure

Identifying a new particle with jet substructures

We investigate a potential of measuring properties of a heavy resonance X, exploiting jet substructure techniques. Motivated by heavy higgs boson searches, we focus on the decays of X into a pair of (massive) electroweak gauge bosons. More specifically, we consider a hadronic Z boson, which makes it possible to determine properties of X at an earlier stage. For $m_X$ of O(1) TeV, two quarks from a Z boson would be captured as a "merged jet" in a significant fraction of events. The use of the merged jet enables us to consider a Z-induced jet as a reconstructed object without any combinatorial ambiguity. We apply a conventional jet substructure method to extract four-momenta of subjets from a merged jet. We find that jet substructure procedures may enhance features in some kinematic observables formed with subjets. Subjet momenta are fed into the matrix element associated with a given hypothesis on the nature of X, which is further processed to construct a matrix element method (MEM)-based observable. For both moderately and highly boosted Z bosons, we demonstrate that the MEM with current jet substructure techniques can be a very powerful discriminator in identifying the physics nature of X. We also discuss effects from choosing different jet sizes for merged jets and jet-grooming parameters upon the MEM analyses.Comment: 36 pages, 11 figures, published in JHE

Deterministic Relay Networks with State Information

Motivated by fading channels and erasure channels, the problem of reliable communication over deterministic relay networks is studied, in which relay nodes receive a function of the incoming signals and a random network state. An achievable rate is characterized for the case in which destination nodes have full knowledge of the state information. If the relay nodes receive a linear function of the incoming signals and the state in a finite field, then the achievable rate is shown to be optimal, meeting the cut-set upper bound on the capacity. This result generalizes on a unified framework the work of Avestimehr, Diggavi, and Tse on the deterministic networks with state dependency, the work of Dana, Gowaikar, Palanki, Hassibi, and Effros on linear erasure networks with interference, and the work of Smith and Vishwanath on linear erasure networks with broadcast.Comment: 5 pages, to appear in proc. IEEE ISIT, June 200

Uterine Artery Doppler Velocimetry During Mid-second Trimester to Predict Complications of Pregnancy Based on Unilateral or Bilateral Abnormalities

We performed this study to evaluate uterine artery Doppler velocimetry (UADV) measurement of unilateral or bilateral abnormalities as a predictor of complications in pregnancy during the mid-second trimester (20-24 weeks). We enrolled 1,090 pregnant women who had undergone UADV twice: once between the 20th and 24th week (1st stage) and again between the 28th and 32nd week (2nd stage) of pregnancy, and then delivered at Yonsei Medical Center. UADV was performed bilaterally. Follow-up UADV was performed between the 28th and 32nd week, and the frequencies of pregnancy-induced hypertension (PIH), fetal growth restriction (FGR), and preterm delivery (before 34 weeks of gestation) were determined. Chi-squared and t-tests were used where appropriate, with p < .05 considered significant. According to the results of UADV performed between 20-24 weeks of gestation, 825 women (75.7%) were included in the normal group, 196 (18.0%) in the unilateral abnormality group, and 69 (6.3%) in the bilateral abnormality group. The incidences of FGR were 8.0%, 10.2%, and 26.1%, and the incidences of PIH were 0.1%, 3.6%, and 14.5%, respectively. The incidence of PIH was significantly lower in the normal group. The incidences of preterm delivery were 2.2%, 5.6%, and 8.7%, respectively. PIH developed in 46.7% of patients with bilateral abnormal findings in both the 1st and 2nd stage tests, and developed in none of the patients with normal findings in both tests. Abnormal results found by UADV performed between the 20-24th weeks of pregnancy, such as high S/D ratios regardless of placental location and the presence of an early diastolic notch, were associated with significant increases in the incidences of intrauterine growth restriction (IUGR) and PIH. This was true for both bilateral and unilateral abnormalities. Abnormal findings in bilateral UADV during the second trimester especially warrant close follow up for the detection of subsequent development of pregnancy complications