Hadwiger's conjecture for graphs with forbidden holes

Given a graph $G$, the Hadwiger number of $G$, denoted by $h(G)$, is the largest integer $k$ such that $G$ contains the complete graph $K_k$ as a minor. A hole in $G$ is an induced cycle of length at least four. Hadwiger's Conjecture from 1943 states that for every graph $G$, $h(G)\ge \chi(G)$, where $\chi(G)$ denotes the chromatic number of $G$. In this paper we establish more evidence for Hadwiger's conjecture by showing that if a graph $G$ with independence number $\alpha(G)\ge3$ has no hole of length between $4$ and $2\alpha(G)-1$, then $h(G)\ge\chi(G)$. We also prove that if a graph $G$ with independence number $\alpha(G)\ge2$ has no hole of length between $4$ and $2\alpha(G)$, then $G$ contains an odd clique minor of size $\chi(G)$, that is, such a graph $G$ satisfies the odd Hadwiger's conjecture

TossingBot: Learning to Throw Arbitrary Objects with Residual Physics

We investigate whether a robot arm can learn to pick and throw arbitrary objects into selected boxes quickly and accurately. Throwing has the potential to increase the physical reachability and picking speed of a robot arm. However, precisely throwing arbitrary objects in unstructured settings presents many challenges: from acquiring reliable pre-throw conditions (e.g. initial pose of object in manipulator) to handling varying object-centric properties (e.g. mass distribution, friction, shape) and dynamics (e.g. aerodynamics). In this work, we propose an end-to-end formulation that jointly learns to infer control parameters for grasping and throwing motion primitives from visual observations (images of arbitrary objects in a bin) through trial and error. Within this formulation, we investigate the synergies between grasping and throwing (i.e., learning grasps that enable more accurate throws) and between simulation and deep learning (i.e., using deep networks to predict residuals on top of control parameters predicted by a physics simulator). The resulting system, TossingBot, is able to grasp and throw arbitrary objects into boxes located outside its maximum reach range at 500+ mean picks per hour (600+ grasps per hour with 85% throwing accuracy); and generalizes to new objects and target locations. Videos are available at https://tossingbot.cs.princeton.eduComment: Summary Video: https://youtu.be/f5Zn2Up2RjQ Project webpage: https://tossingbot.cs.princeton.ed

The Kerr/CFT Correspondence

Quantum gravity in the region very near the horizon of an extreme Kerr black hole (whose angular momentum and mass are related by J=GM^2) is considered. It is shown that consistent boundary conditions exist, for which the asymptotic symmetry generators form one copy of the Virasoro algebra with central charge c_L=12J / \hbar. This implies that the near-horizon quantum states can be identified with those of (a chiral half of) a two-dimensional conformal field theory (CFT). Moreover, in the extreme limit, the Frolov-Thorne vacuum state reduces to a thermal density matrix with dimensionless temperature T_L=1/2\pi and conjugate energy given by the zero mode generator, L_0, of the Virasoro algebra. Assuming unitarity, the Cardy formula then gives a microscopic entropy S_{micro}=2\pi J / \hbar for the CFT, which reproduces the macroscopic Bekenstein-Hawking entropy S_{macro}=Area / 4\hbar G. The results apply to any consistent unitary quantum theory of gravity with a Kerr solution. We accordingly conjecture that extreme Kerr black holes are holographically dual to a chiral two-dimensional conformal field theory with central charge c_L=12J / \hbar, and in particular that the near-extreme black hole GRS 1915+105 is approximately dual to a CFT with c_L \sim 2 \times 10^{79}.Comment: 21 pages, no figure

Extracting bull and bear markets from stock returns

Traditional methods used to partition the market index into bull and bear regimes often sort returns ex post based on a deterministic rule. We model the entire return distribution; two states govern the bull regime and two govern the bear regime, allowing for rich and heterogeneous intra-regime dynamics. Our model can capture bear market rallies and bull market corrections. A Bayesian estimation approach accounts for parameter and regime uncertainty and provides probability statements regarding future regimes and returns. Applied to 123 years of data our model provides superior identification of trends in stock prices.Markov switching, bear market rallies, bull market corrections, Gibbs sampling

Results of A Local Combination Therapy Antibiogram For \u3cem\u3ePseudomonas Aeruginosa\u3c/em\u3e Isolates: Is Double Worth The Trouble?

Purpose: To determine the frequency at which fluoroquinolones and aminoglycosides demonstrate in vitro activity against non-urinary, non-skin/skin structure Pseudomonas aeruginosa isolates exhibiting decreased susceptibilities to one or more β-lactam agents. Methods: β-lactam-non-susceptible P. aeruginosa isolates recovered from blood, bone, lower respiratory tract, pleural fluid, cerebrospinal fluid, or peritoneal fluid cultures between October 2010 and October 2014 were reviewed from four community hospitals within a single health-system. Only the first isolate per patient was included for analysis. The likelihood that each isolate was susceptible to a non-β-lactam antimicrobial was then determined and summarized within a combination antibiogram. Results: In total, 179 P. aeruginosa isolates with decreased susceptibilities to one or more β-lactam agents were assessed. Because no appreciable differences in antimicrobial susceptibility profile were observed between hospitals, the isolates were evaluated in aggregate. Susceptibility rates for β-lactam monotherapy ranged from 34% to 75%. Aminoglycosides possessed increased antibacterial activity compared to fluoroquinolones. Tobramycin was the non-β-lactam most likely to expand antimicrobial coverage against β-lactam-non-susceptible P. aeruginosa with activity against 64%, 66%, and 65% of cefepime-, piperacillin-tazobactam-, and meropenem-non-susceptible isolates, respectively (p \u3c 0.001 for all). Conclusions: The results of this study support the use of aminoglycosides over fluoroquinolones for achieving optimal, empiric antimicrobial combination therapy for P. aeruginosa when dual antimicrobial therapy is clinically necessary. Future efforts aimed at optimizing combination therapy for P. aeruginosa should focus on systemic interventions that limit the selection of fluoroquinolones in combination with β-lactams to expand coverage based on local susceptibility rates