Two-batch liar games on a general bounded channel

We consider an extension of the 2-person R\'enyi-Ulam liar game in which lies are governed by a channel $C$, a set of allowable lie strings of maximum length $k$. Carole selects $x\in[n]$, and Paul makes $t$-ary queries to uniquely determine $x$. In each of $q$ rounds, Paul weakly partitions $[n]=A_0\cup >... \cup A_{t-1}$ and asks for $a$ such that $x\in A_a$. Carole responds with some $b$, and if $a\neq b$, then $x$ accumulates a lie $(a,b)$. Carole's string of lies for $x$ must be in the channel $C$. Paul wins if he determines $x$ within $q$ rounds. We further restrict Paul to ask his questions in two off-line batches. We show that for a range of sizes of the second batch, the maximum size of the search space $[n]$ for which Paul can guarantee finding the distinguished element is $\sim t^{q+k}/(E_k(C)\binom{q}{k})$ as $q\to\infty$, where $E_k(C)$ is the number of lie strings in $C$ of maximum length $k$. This generalizes previous work of Dumitriu and Spencer, and of Ahlswede, Cicalese, and Deppe. We extend Paul's strategy to solve also the pathological liar variant, in a unified manner which gives the existence of asymptotically perfect two-batch adaptive codes for the channel $C$.Comment: 26 page

Two-player envy-free multi-cake division

We introduce a generalized cake-cutting problem in which we seek to divide multiple cakes so that two players may get their most-preferred piece selections: a choice of one piece from each cake, allowing for the possibility of linked preferences over the cakes. For two players, we show that disjoint envy-free piece selections may not exist for two cakes cut into two pieces each, and they may not exist for three cakes cut into three pieces each. However, there do exist such divisions for two cakes cut into three pieces each, and for three cakes cut into four pieces each. The resulting allocations of pieces to players are Pareto-optimal with respect to the division. We use a generalization of Sperner's lemma on the polytope of divisions to locate solutions to our generalized cake-cutting problem.Comment: 15 pages, 7 figures, see related work at http://www.math.hmc.edu/~su/papers.htm

The Coldest Place in the Universe: Probing the Ultra-Cold Outflow and Dusty Disk in the Boomerang Nebula

Our Cycle 0 ALMA observations confirmed that the Boomerang Nebula is the coldest known object in the Universe, with a massive high-speed outflow that has cooled significantly below the cosmic background temperature. Our new CO 1-0 data reveal heretofore unseen distant regions of this ultra-cold outflow, out to $\gtrsim120,000$ AU. We find that in the ultra-cold outflow, the mass-loss rate (dM/dt) increases with radius, similar to its expansion velocity ($V$) - taking $V\propto r$, we find $dM/dt \propto r^{0.9-2.2}$. The mass in the ultra-cold outflow is $\gtrsim3.3$ Msun, and the Boomerang's main-sequence progenitor mass is $\gtrsim4$ Msun. Our high angular resolution ($\sim$0".3) CO J=3-2 map shows the inner bipolar nebula's precise, highly-collimated shape, and a dense central waist of size (FWHM) $\sim$1740 AU$\times275$ AU. The molecular gas and the dust as seen in scattered light via optical HST imaging show a detailed correspondence. The waist shows a compact core in thermal dust emission at 0.87-3.3 mm, which harbors $(4-7)\times10^{-4}$ Msun~of very large ($\sim$mm-to-cm sized), cold ($\sim20-30$ K) grains. The central waist (assuming its outer regions to be expanding) and fast bipolar outflow have expansion ages of $\lesssim1925$ yr and $\le1050$ yr: the "jet-lag" (i.e., torus age minus the fast-outflow age) in the Boomerang supports models in which the primary star interacts directly with a binary companion. We argue that this interaction resulted in a common-envelope configuration while the Boomerang's primary was an RGB or early-AGB star, with the companion finally merging into the primary's core, and ejecting the primary's envelope that now forms the ultra-cold outflow.Comment: accepted ApJ, 12 Apr, 201

A New Component in the Radio Continua of PNe

A byproduct of experiments designed to map the CMB is the recent detection of a new component of foreground galactic emission. The anomalous foreground at 10–30 GHz, unexplained by traditional emission mechanisms, correlates with 100 mum dust emission, and is thus presumably due to dust.Is the anomalous foreground ubiquitous in the Galaxy? I will present evidence obtained with the CBI and SIMBA+SEST supporting the existence of the new component in the ISM at large, and in specific objects, in the form of a 31 GHz excess over free-free emission in PNe

Variants of the human PPARG locus and the susceptibility to chronic periodontitis

Apart from its regulatory function in lipid and glucose metabolism, peroxisome proliferator-activated receptor (PPAR)γ has impact on the regulation of inflammation and bone metabolism. The aim of the study was to investigate the association of five polymorphisms (rs10865710, rs2067819, rs3892175, rs1801282, rs3856806) within the PPARG gene with chronic periodontitis. The study population comprised 402 periodontitis patients and 793 healthy individuals. Genotyping of the PPARG gene polymorphisms was performed by PCR and melting curve analysis. Comparison of frequency distribution of genotypes between individuals with periodontal disease and healthy controls for the polymorphism rs3856806 showed a P-value of 0.04 but failed to reach significance after correction for multiple testing (P  0.90). A 3-site analysis (rs2067819-rs1801282-rs3856860) revealed five haplotypes with a frequency of ≥1% among cases and controls. Following adjustment for age, gender and smoking, none of the haplotypes was significantly different between periodontitis and healthy controls after Bonferroni correction. This study could not show a significant association between PPARG gene variants and chronic periodontitis

A Borsuk-Ulam Equivalent that Directly Implies Sperner\u27s Lemma

We show that Fan’s 1952 lemma on labelled triangulations of the n-sphere with n + 1 labels is equivalent to the Borsuk–Ulam theorem. Moreover, unlike other Borsuk–Ulam equivalents, we show that this lemma directly implies Sperner’s Lemma, so this proof may be regarded as a combinatorial version of the fact that the Borsuk–Ulam theorem implies the Brouwer fixed-point theorem, or that the Lusternik–Schnirelmann–Borsuk theorem implies the KKM lemma

ALMA view of the circumstellar environment of the post-common-envelope-evolution binary system HD101584

We study the circumstellar evolution of the binary HD101584, consisting of a post-AGB star and a low-mass companion, which is most likely a post-common-envelope-evolution system. We used ALMA observations of the 12CO, 13CO, and C18O J=2-1 lines and the 1.3mm continuum to determine the morphology, kinematics, masses, and energetics of the circumstellar environment. The circumstellar medium has a bipolar hour-glass structure, seen almost pole-on, formed by an energetic jet, about 150 km/s. We conjecture that the circumstellar morphology is related to an event that took place about 500 year ago, possibly a capture event where the companion spiraled in towards the AGB star. However, the kinetic energy of the accelerated gas exceeds the released orbital energy, and, taking into account the expected energy transfer efficiency of the process, the observed phenomenon does not match current common-envelope scenarios. This suggests that another process must augment, or even dominate, the ejection process. A significant amount of material resides in an unresolved region, presumably in the equatorial plane of the binary system.Comment: A&A Letter, accepte