A non-partitionable Cohen-Macaulay simplicial complex

A long-standing conjecture of Stanley states that every Cohen-Macaulay simplicial complex is partitionable. We disprove the conjecture by constructing an explicit counterexample. Due to a result of Herzog, Jahan and Yassemi, our construction also disproves the conjecture that the Stanley depth of a monomial ideal is always at least its depth.Comment: Final version. 13 pages, 2 figure

Entanglement of electrons in interacting molecules

Quantum entanglement is a concept commonly used with reference to the existence of certain correlations in quantum systems that have no classical interpretation. It is a useful resource to enhance the mutual information of memory channels or to accelerate some quantum processes as, for example, the factorization in Shor's Algorithm. Moreover, entanglement is a physical observable directly measured by the von Neumann entropy of the system. We have used this concept in order to give a physical meaning to the electron correlation energy in systems of interacting electrons. The electronic correlation is not directly observable, since it is defined as the difference between the exact ground state energy of the many--electrons Schroedinger equation and the Hartree--Fock energy. We have calculated the correlation energy and compared with the entanglement, as functions of the nucleus--nucleus separation using, for the hydrogen molecule, the Configuration Interaction method. Then, in the same spirit, we have analyzed a dimer of ethylene, which represents the simplest organic conjugate system, changing the relative orientation and distance of the molecules, in order to obtain the configuration corresponding to maximum entanglement.Comment: 15 pages, 7 figures, standard late

Quantum Cryptography Based on the Time--Energy Uncertainty Relation

A new cryptosystem based on the fundamental time--energy uncertainty relation is proposed. Such a cryptosystem can be implemented with both correlated photon pairs and single photon states.Comment: 5 pages, LaTex, no figure

Effects on the maternofetal unit of the rabbit model after substitution of the amniotic fluid with perfluorocarbons

Objectives: Exchanging amniotic fluid (AF) with perfluorocarbon (PFC) may serve as a medium for fetoscopic surgery. This study evaluates the distribution and physiologic effects of intraamniotic PFC as a medium for fetoscopy. Methods: Fetuses of 17 pregnant rabbits underwent either exchange of the AF with PFC, electrolyte solution (ES), or control. The quality of vision during fetoscopy was assessed in AF and PFC. After 6 h, we determined the distribution of PFC in the maternofetal unit. Results: Quality of vision during fetoscopy was better in PFC than with AF. There was no difference in fetal survival between the study groups. PFC was demonstrated on X-ray in the pharynx of 4 fetuses, and the esophagus in 1. Conclusions: PFC provided an ideal medium for fetoscopy without fetal compromise. Copyright (c) 2005 S. Karger AG, Basel

A Comprehensive Archival Search for Counterparts to Ultra-Compact High Velocity Clouds: Five Local Volume Dwarf Galaxies

We report five Local Volume dwarf galaxies (two of which are presented here for the first time) uncovered during a comprehensive archival search for optical counterparts to ultra-compact high velocity clouds (UCHVCs). The UCHVC population of HI clouds are thought to be candidate gas-rich, low mass halos at the edge of the Local Group and beyond, but no comprehensive search for stellar counterparts to these systems has been presented. Careful visual inspection of all publicly available optical and ultraviolet imaging at the position of the UCHVCs revealed six blue, diffuse counterparts with a morphology consistent with a faint dwarf galaxy beyond the Local Group. Optical spectroscopy of all six candidate dwarf counterparts show that five have an H$\alpha$-derived velocity consistent with the coincident HI cloud, confirming their association, the sixth diffuse counterpart is likely a background object. The size and luminosity of the UCHVC dwarfs is consistent with other known Local Volume dwarf irregular galaxies. The gas fraction ($M_{HI}/M_{star}$) of the five dwarfs are generally consistent with that of dwarf irregular galaxies in the Local Volume, although ALFALFA-Dw1 (associated with ALFALFA UCHVC HVC274.68+74.70$-$123) has a very high $M_{HI}/M_{star}$$\sim$40. Despite the heterogenous nature of our search, we demonstrate that the current dwarf companions to UCHVCs are at the edge of detectability due to their low surface brightness, and that deeper searches are likely to find more stellar systems. If more sensitive searches do not reveal further stellar counterparts to UCHVCs, then the dearth of such systems around the Local Group may be in conflict with $\Lambda$CDM simulations.Comment: 18 pages, 4 tables, 4 figures, ApJ Accepte

Evolution of a global string network in a matter dominated universe

We evolve the network of global strings in the matter-dominated universe by means of numerical simulations. The existence of the scaling solution is confirmed as in the radiation-dominated universe but the scaling parameter $\xi$ takes a slightly smaller value, $\xi \simeq 0.6 \pm 0.1$, which is defined as $\xi = \rho_{s} t^{2} / \mu$ with $\rho_{s}$ the energy density of global strings and $\mu$ the string tension per unit length. The change of $\xi$ from the radiation to the matter-dominated universe is consistent with that obtained by Albrecht and Turok by use of the one-scale model. We also study the loop distribution function and find that it can be well fitted with that predicted by the one-scale model, where the number density $n_{l}(t)$ of the loop with the length $l$ is given by $n_{l}(t) = \nu/[t^2 (l + \kappa t)^2]$ with $\nu \sim 0.040$ and $\kappa \sim 0.48$. Thus, the evolution of the global string network in the matter-dominated universe can be well described by the one-scale model as in the radiation-dominated universe.Comment: 10 pages, 5 figure

Jumping without Using Legs: The Jump of the Click-Beetles (Elateridae) Is Morphologically Constrained

To return to their feet, inverted click-beetles (Elateridae) jump without using their legs. When a beetle is resting on its dorsal side, a hinge mechanism is locked to store elastic energy in the body and releases it abruptly to launch the beetle into the air. While the functional morphology of the jumping mechanism is well known, the level of control that the beetle has over this jumping technique and the mechanical constraints governing the jumps are not entirely clear. Here we show that while body rotations in air are highly variable, the jumps are morphologically constrained to a constant “takeoff” angle (79.9°±1.56°, n = 9 beetles) that directs 98% of the jumping force vertically against gravity. A physical-mathematical model of the jumping action, combined with measurements from live beetle, imply that the beetle may control the speed at takeoff but not the jumping angle. In addition, the model shows that very subtle changes in the exact point of contact with the ground can explain the vigorous rotations of the body seen while the beetle is airborne. These findings suggest that the evolution of this unique non-legged jumping mechanism resulted in a jumping technique that is capable of launching the body high into the air but it is too constrained and unstable to allow control of body orientation at landing

The rhizoferrin biosynthetic gene in the fungal pathogen Rhizopus delemar is a novel member of the NIS gene family

This work was supported by the Natural Sciences and Engineering Research Council of Canada award to MM (grant number 611181). C. Carroll thanks Simon Fraser University for a travel and research award.Iron is essential for growth and in low iron environments such as serum many bacteria and fungi secrete ferric iron-chelating molecules called siderophores. All fungi produce hydroxamate siderophores with the exception of Mucorales fungi, which secrete rhizoferrin, a polycarboxylate siderophore. Here we investigated the biosynthesis of rhizoferrin by the opportunistic human pathogen, Rhizopus delemar. We searched the genome of R. delemar 99–880 for a homologue of the bacterial NRPS-independent siderophore (NIS) protein, SfnaD that is involved in biosynthesis of staphyloferrin A in Staphylococcus aureus. A protein was identified in R. delemar with 22% identity and 37% similarity with SfnaD, containing an N-terminal IucA/IucC family domain, and a C-terminal conserved ferric iron reductase FhuF-like transporter domain. Expression of the putative fungal rhizoferrin synthetase (rfs) gene was repressed by iron. The rfs gene was cloned and expressed in E.coli and siderophore biosynthesis from citrate and diaminobutane was confirmed using high resolution LC–MS. Substrate specificity was investigated showing that Rfs produced AMP when oxaloacetic acid, tricarballylic acid, ornithine, hydroxylamine, diaminopentane and diaminopropane were employed as substrates. Based on the production of AMP and the presence of a mono-substituted rhizoferrin, we suggest that Rfs is a member of the superfamily of adenylating enzymes. We used site-directed mutagenesis to mutate selected conserved residues predicted to be in the Rfs active site. These studies revealed that H484 is essential for Rfs activity and L544 may play a role in amine recognition by the enzyme. This study on Rfs is the first characterization of a fungal NIS enzyme. Future work will determine if rhizoferrin biosynthesis is required for virulence in Mucorales fungi.PostprintPeer reviewe

Affine Constellations Without Mutually Unbiased Counterparts

It has been conjectured that a complete set of mutually unbiased bases in a space of dimension d exists if and only if there is an affine plane of order d. We introduce affine constellations and compare their existence properties with those of mutually unbiased constellations, mostly in dimension six. The observed discrepancies make a deeper relation between the two existence problems unlikely.Comment: 8 page