A Reciprocity Theorem for Monomer-Dimer Coverings

The problem of counting monomer-dimer coverings of a lattice is a longstanding problem in statistical mechanics. It has only been exactly solved for the special case of dimer coverings in two dimensions. In earlier work, Stanley proved a reciprocity principle governing the number $N(m,n)$ of dimer coverings of an $m$ by $n$ rectangular grid (also known as perfect matchings), where $m$ is fixed and $n$ is allowed to vary. As reinterpreted by Propp, Stanley's result concerns the unique way of extending $N(m,n)$ to $n < 0$ so that the resulting bi-infinite sequence, $N(m,n)$ for $n \in {Z}$, satisfies a linear recurrence relation with constant coefficients. In particular, Stanley shows that $N(m,n)$ is always an integer satisfying the relation $N(m,-2-n) = \epsilon_{m,n}N(m,n)$ where $\epsilon_{m,n} = 1$ unless $m\equiv$ 2(mod 4) and $n$ is odd, in which case $\epsilon_{m,n} = -1$. Furthermore, Propp's method is applicable to higher-dimensional cases. This paper discusses similar investigations of the numbers $M(m,n)$, of monomer-dimer coverings, or equivalently (not necessarily perfect) matchings of an $m$ by $n$ rectangular grid. We show that for each fixed $m$ there is a unique way of extending $M(m,n)$ to $n < 0$ so that the resulting bi-infinite sequence, $M(m,n)$ for $n \in {Z}$, satisfies a linear recurrence relation with constant coefficients. We show that $M(m,n)$, a priori a rational number, is always an integer, using a generalization of the combinatorial model offered by Propp. Lastly, we give a new statement of reciprocity in terms of multivariate generating functions from which Stanley's result follows.Comment: 13 pages, 12 figures, to appear in the proceedings of the Discrete Models for Complex Systems (DMCS) 2003 conference. (v2 - some minor changes

Wireless Communication in Process Control Loop: Requirements Analysis, Industry Practices and Experimental Evaluation

Wireless communication is already used in process automation for process monitoring. The next stage of implementation of wireless technology in industrial applications is for process control. The need for wireless networked control systems has evolved because of the necessity for extensibility, mobility, modularity, fast deployment, and reduced installation and maintenance cost. These benefits are only applicable given that the wireless network of choice can meet the strict requirements of process control applications, such as latency. In this regard, this paper is an effort towards identifying current industry practices related to implementing process control over a wireless link and evaluates the suitability of ISA100.11a network for use in process control through experiments

Clonal dynamics underlying the skewed CD4/CD8 ratio of mouse thymocytes revealed by TCR-independent barcoding

T cell differentiation in the thymus generates CD4+ helper and cytotoxic CD8+ cells as the two principal T cell lineages. Curiously, at the end of this complex selection process, CD4+ cells invariably outnumber CD8+ cells. Here, we examine the dynamics of repertoire formation and the emergence of the skewed CD4/CD8 ratio using high-resolution endogenous CRISPR/Cas9 barcoding that indelibly marks immature T cells at the DN2/DN3 pre-TCR stage. In wild-type mice, greater clone size of CD4+ cells and an intrinsically greater probability of Tcr β clonotypes for pMHCII interactions are major contributors to the skewed CD4/CD8 ratio. Clonal perturbations of thymocyte differentiation following the precocious expression of a rearranged iNKT invariant TCR α chain are due to loss of Tcr β clonotypes from the CD4 lineage-committed pre-selection repertoire. The present barcoding scheme offers a novel means to examine the clonal dynamics of lymphocyte differentiation orthogonal to that using TCR clonotypes

Directed flow as effect of transient matter rotation in hadron and nucleus collisions

We discuss directed flow introduced for description of nucleus collisions and consider its possible behavior in hadronic and nuclei reactions due to rotation of the transient matter.Comment: 18 pages, 6 figure

Chalcogenide-glass polarization-maintaining photonic crystal fiber for mid-infrared supercontinuum generation

In this paper, we report the design and fabrication of a highly birefringent polarization-maintaining photonic crystal fiber (PM-PCF) made from chalcogenide glass, and its application to linearly-polarized supercontinuum (SC) generation in the mid-infrared region. The PM fiber was drawn using the casting method from As38Se62 glass which features a transmission window from 2 to 10 $\mu m$ and a high nonlinear index of 1.13.10$^{-17}$m$^{2}$W$^{-1}$. It has a zero-dispersion wavelength around 4.5 $\mu m$ and, at this wavelength, a large birefringence of 6.10$^{-4}$ and consequently strong polarization maintaining properties are expected. Using this fiber, we experimentally demonstrate supercontinuum generation spanning from 3.1-6.02 $\mu m$ and 3.33-5.78 $\mu m$ using femtosecond pumping at 4 $\mu m$ and 4.53 $\mu m$, respectively. We further investigate the supercontinuum bandwidth versus the input pump polarization angle and we show very good agreement with numerical simulations of the two-polarization model based on two coupled generalized nonlinear Schr\"odinger equations.Comment: 13 pages, 8 figure

A new neurosurgical tool incorporating differential geometry and cellular automata techniques

Using optical coherence imaging, it is possible to visualize seizure progression intraoperatively. However, it is difficult to pinpoint an exact epileptic focus. This is crucial in attempts to minimize the amount of resection necessary during surgical therapeutic interventions for epilepsy and is typically done approximately from visual inspection of optical coherence imaging stills. In this paper, we create an algorithm with the potential to pinpoint the source of a seizure from an optical coherence imaging still. To accomplish this, a grid is overlaid on optical coherence imaging stills. This then serves as a grid for a two-dimensional cellular automation. Each cell is associated with a Riemannian curvature tensor representing the curvature of the brain's surface in all directions for a cell. Cells which overlay portions of the image which show neurons that are firing are considered "depolarized"

Body composition estimated by bioelectrical impedance analyses is diminished by prenatal stress in neonatal lambs and by heat stress in feedlot wethers

Body composition correlates to carcass value in livestock, which makes the ability to accurately estimate body composition in the live animal beneficial (Berg and Marchello, 1994). Bioelectrical impedance analysis (BIA) is a clinical tool used to assess body composition in humans (Lukaski et al., 1985), but its use in livestock has been minimal. Lean and fat content contribute to profitability for livestock producers, and poor body composition can be caused by stress that occurs either during in utero development (De Blasio et al., 2007) or during postnatal growth (Boyd et al., 2015). Maternal hyperthermia-induced placental insufficiency (Brown et al., 2015) and sustained maternal inflammation (Cadaret et al., 2018) are two established causes of intrauterine growth restriction (IUGR). IUGR-born animals are characterized by asymmetrical growth restriction that alters lifelong body composition due to impaired muscle growth capacity (Yates et al., 2018). In addition, acute heat stress during periods of peak postnatal growth can alter body composition in livestock (Boyd et al., 2015). We postulate that BIA can detect these changes in the live animal. Thus, the objective of this study was to determine whether BIA measurements can predict changes to body composition in live neonatal lambs exposed to intrauterine stress and in heat-stressed feedlot lambs

Maternal inflammation at 0.7 gestation in ewes leads to intrauterine growth restriction and impaired glucose metabolism in offspring at 30 d of age

Fetal programming associated with intrauterine growth restriction (IUGR) leads to lifelong deficits in growth and metabolic function (Hales and Barker, 2013). IUGR arises when fetuses respond to poor in utero conditions by developing adaptations that repartition nutrients to critical tissues and away from skeletal muscle (Yates et al., 2012, 2018). This fetal programming is beneficial in utero but leads to persistent reductions in muscle mass and glucose homeostasis in offspring (DeFronzo et al., 1981). Recent studies by our laboratory in sheep and rats demonstrate that maternal inflammation during gestation induces fetal inflammatory adaptations that impair growth and disrupt muscle glucose metabolism (Cadaret et al., 2017, 2018). IUGR fetal skeletal muscle exhibits indicators of enhanced inflammatory sensitivity, which could disrupt glucose uptake and oxidation (Yates et al., 2016; Cadaret et al., 2018). Enhanced inflammatory responsiveness would help explain growth and metabolic deficits observed in IUGR offspring. We hypothesize that fetal programming induced by maternal inflammation persists in offspring and contributes to impaired growth and glucose metabolism at 30 d. Therefore, the objective of this study was to determine whether sustained maternal inflammation induced by bacterial endotoxin at 0.7 gestation leads to fetal programming that contributes to deficits in growth and glucose metabolism in offspring

Using caribou knowledge in expanding the Wabakimi protected area

When Wabakimi Wilderness Park was created in 1983, conservation of woodland caribou (Rangifer tarandus caribou) was one of the primary considerations. Twelve years later, in April 1995, the Government of Ontario announced that the Park, measuring some 155 000 ha, was to be expanded into a ca. 890 000 ha protected area. This was done following 2.5 yr of deliberations of the Wabakimi Park Boundary Committee. The Committee tried to reach consensus on an expanded protected area by examining a variety of options in terms of criteria related to a range of key values, one of which was woodland caribou. The analysis procedure involved dividing the 1.25-million-ha study area into more than sixty "assessment units". These were defined primarily on the basis of approximate sub-watershed boundaries. Each assessment unit was ranked on a five-level scale with respect to goodness for each value, including seasonal caribou habitat. High-value habitats for wintering, calving, and migration dominated the assessment of habitat importance for caribou.The initial assessment phase included six park expansion concepts ranging in size from just over 200 000 ha to about 1 million ha. One of the concepts (about 750 000 ha), was based specifically on the caribou value. In the second phase, four refined options were examined, ranging from just under 600 000 to roughly a million ha. Two additional options were added to the four and submitted to the Ontario Ministry of Natural Resources for consideration. The Committee was, in the end, unable to reach full consensus on which of the final options to recommend. However, upon consideration of the Committee's final report and other input, the Ontario Government announced in April 1995 the more than five-fold expansion. The new protected area contains about 475 000 ha of high-value caribou habitat. Caribou were a key value in determining both the ultimate size and configuration of the expansion