Renormalization group-like proof of the universality of the Tutte polynomial for matroids

In this paper we give a new proof of the universality of the Tutte polynomial for matroids. This proof uses appropriate characters of Hopf algebra of matroids, algebra introduced by Schmitt (1994). We show that these Hopf algebra characters are solutions of some differential equations which are of the same type as the differential equations used to describe the renormalization group flow in quantum field theory. This approach allows us to also prove, in a different way, a matroid Tutte polynomial convolution formula published by Kook, Reiner and Stanton (1999). This FPSAC contribution is an extended abstract.Comment: 12 pages, 3 figures, conference proceedings, 25th International Conference on Formal Power Series and Algebraic Combinatorics, Paris, France, June 201

Role of thyroid hormones in early postnatal development of skeletal muscle and its implications for undernutrition

Published online by Cambridge University Press 09 Mar 2007Energy intake profoundly influences many endocrine axes which in turn play a central role in development. The specific influence of a short period of mild hypothyroidism, similar to that induced by undernutrition, in regulating muscle development has been assessed in a large mammal during early postnatal life. Hypothyroidism was induced by providing methimazole and iopanoic acid in the feed of piglets between 4 and 14 d of age, and controls were pair-fed to the energy intake of their hypothyroid littermates. Thyroid status was evaluated, and myofibre differentiation and cation pump concentrations were then assessed in the following functionally distinct muscles: longissimus dorsi (l. dorsi), soleus and rhomboideus. Reductions in plasma concentrations of thyroxine (T4; 32%, P < O·Ol), triiodothyronine (T3;48%, P < 0·001), free T3, (58%, P < 0·001)and hepatic 5'-monodeiodinase (EC 1.11.1.8) activity (74%, P < 0·001) occurred with treatment. Small, although significant, increases in the proportion of type I slow-twitch oxidative fibres occurred with mild hypothyroidism, in l. dorsi (2%, P < 0·01) and soleus(7%, P < 0·01). Nuclear T3-receptor concentration in l. dorsi of hypothyroid animals compared with controls increased by 46% (P < 0·001), a response that may represent a homeostatic mechanism making muscle more sensitive to low levels of circulating thyroid hormones. Nevertheless, Na+, K+-ATPase (EC 3.6.1.37) concentration was reduced by 15–16% in all muscles (l.dorsi P< 0·05,soleus P < 0·001, rhomboideus P < 0·05), and Ca2+-ATPase (EC 3.6.1.38) concentration was significantly reduced in the two slow-twitch muscles: by 22% in rhomboideus (P < 0·001) and 23% in soleus (P < 0·05). It is concluded that during early postnatal development of large mammals a period of mild hypothyroidism, comparable with that found during undernutrition, induces changes in myofibre differentiation and a down-regulation of cation pumps in skeletal muscle. Such changes would result in slowness of movement and muscle weakness, and also reduce ATP hydrolysis with a concomitant improvement in energetic efficiency.A. P. Harrison, D. R. Tivey, T. Clausen, C. Duchamp and M. J. Daunce

Dobinski-type relations: Some properties and physical applications

We introduce a generalization of the Dobinski relation through which we define a family of Bell-type numbers and polynomials. For all these sequences we find the weight function of the moment problem and give their generating functions. We provide a physical motivation of this extension in the context of the boson normal ordering problem and its relation to an extension of the Kerr Hamiltonian.Comment: 7 pages, 1 figur

Hierarchical Dobinski-type relations via substitution and the moment problem

We consider the transformation properties of integer sequences arising from the normal ordering of exponentiated boson ([a,a*]=1) monomials of the form exp(x (a*)^r a), r=1,2,..., under the composition of their exponential generating functions (egf). They turn out to be of Sheffer-type. We demonstrate that two key properties of these sequences remain preserved under substitutional composition: (a)the property of being the solution of the Stieltjes moment problem; and (b) the representation of these sequences through infinite series (Dobinski-type relations). We present a number of examples of such composition satisfying properties (a) and (b). We obtain new Dobinski-type formulas and solve the associated moment problem for several hierarchically defined combinatorial families of sequences.Comment: 14 pages, 31 reference

Response of electrically coupled spiking neurons: a cellular automaton approach

Experimental data suggest that some classes of spiking neurons in the first layers of sensory systems are electrically coupled via gap junctions or ephaptic interactions. When the electrical coupling is removed, the response function (firing rate {\it vs.} stimulus intensity) of the uncoupled neurons typically shows a decrease in dynamic range and sensitivity. In order to assess the effect of electrical coupling in the sensory periphery, we calculate the response to a Poisson stimulus of a chain of excitable neurons modeled by $n$-state Greenberg-Hastings cellular automata in two approximation levels. The single-site mean field approximation is shown to give poor results, failing to predict the absorbing state of the lattice, while the results for the pair approximation are in good agreement with computer simulations in the whole stimulus range. In particular, the dynamic range is substantially enlarged due to the propagation of excitable waves, which suggests a functional role for lateral electrical coupling. For probabilistic spike propagation the Hill exponent of the response function is $\alpha=1$, while for deterministic spike propagation we obtain $\alpha=1/2$, which is close to the experimental values of the psychophysical Stevens exponents for odor and light intensities. Our calculations are in qualitative agreement with experimental response functions of ganglion cells in the mammalian retina.Comment: 11 pages, 8 figures, to appear in the Phys. Rev.

The use of the Kalman filter in the automated segmentation of EIT lung images

In this paper, we present a new pipeline for the fast and accurate segmentation of impedance images of the lungs using electrical impedance tomography (EIT). EIT is an emerging, promising, non-invasive imaging modality that produces real-time, low spatial but high temporal resolution images of impedance inside a body. Recovering impedance itself constitutes a nonlinear ill-posed inverse problem, therefore the problem is usually linearized, which produces impedance-change images, rather than static impedance ones. Such images are highly blurry and fuzzy along object boundaries. We provide a mathematical reasoning behind the high suitability of the Kalman filter when it comes to segmenting and tracking conductivity changes in EIT lung images. Next, we use a two-fold approach to tackle the segmentation problem. First, we construct a global lung shape to restrict the search region of the Kalman filter. Next, we proceed with augmenting the Kalman filter by incorporating an adaptive foreground detection system to provide the boundary contours for the Kalman filter to carry out the tracking of the conductivity changes as the lungs undergo deformation in a respiratory cycle. The proposed method has been validated by using performance statistics such as misclassified area, and false positive rate, and compared to previous approaches. The results show that the proposed automated method can be a fast and reliable segmentation tool for EIT imaging

Quantitative TEM imaging of the magnetostructural and phase transitions in FeRh thin film systems

Equi-atomic FeRh is a very interesting material as it undergoes a magnetostructural transition from an antiferromagnetic (AF) to a ferromagnetic (FM) phase between 75-105 °C. Its ability to present phase co-existence separated by domain walls (DWs) above room temperature provides immense potential for exploitation of their DW motion in spintronic devices. To be able to effectively control the DWs associated with AF/FM coexistence in FeRh thin films we must fully understand the magnetostructural transition and thermomagnetic behaviour of DWs at a localised scale. Here we present a transmission electron microscopy investigation of the transition in planar FeRh thin-film samples by combining differential phase contrast (DPC) magnetic imaging with in situ heating. We perform quantitative measurements from individual DWs as a function of temperature, showing that FeRh on NiAl exhibits thermomagnetic behaviour consistent with the transition from AF to FM. DPC imaging of an FeRh sample with HF-etched substrate reveals a state of AF/FM co-existence and shows the transition from AF to FM regions proceeds via nucleation of small vortex structures, which then grow by combining with newly nucleated vortex states into larger complex magnetic domains, until it is in a fully-FM state

Reshaping of Bulbar Odor Response by Nasal Flow Rate in the Rat

The impact of respiratory dynamics on odor response has been poorly studied at the olfactory bulb level. However, it has been shown that sniffing in the behaving rodent is highly dynamic and varies both in frequency and flow rate. Bulbar odor response could vary with these sniffing parameter variations. Consequently, it is necessary to understand how nasal airflow can modify and shape odor response at the olfactory bulb level.To assess this question, we used a double cannulation and simulated nasal airflow protocol on anesthetized rats to uncouple nasal airflow from animal respiration. Both mitral/tufted cell extracellular unit activity and local field potentials (LFPs) were recorded. We found that airflow changes in the normal range were sufficient to substantially reorganize the response of the olfactory bulb. In particular, cellular odor-evoked activities, LFP oscillations and spike phase-locking to LFPs were strongly modified by nasal flow rate.Our results indicate the importance of reconsidering the notion of odor coding as odor response at the bulbar level is ceaselessly modified by respiratory dynamics

Gap junctions in olfactory neurons modulate olfactory sensitivity

<p>Abstract</p> <p>Background</p> <p>One of the fundamental questions in olfaction is whether olfactory receptor neurons (ORNs) behave as independent entities within the olfactory epithelium. On the basis that mature ORNs express multiple connexins, I postulated that gap junctional communication modulates olfactory responses in the periphery and that disruption of gap junctions in ORNs reduces olfactory sensitivity. The data collected from characterizing connexin 43 (Cx43) dominant negative transgenic mice OlfDNCX, and from calcium imaging of wild type mice (WT) support my hypothesis.</p> <p>Results</p> <p>I generated OlfDNCX mice that express a dominant negative Cx43 protein, Cx43/β-gal, in mature ORNs to inactivate gap junctions and hemichannels composed of Cx43 or other structurally related connexins. Characterization of OlfDNCX revealed that Cx43/β-gal was exclusively expressed in areas where mature ORNs resided. Real time quantitative PCR indicated that cellular machineries of OlfDNCX were normal in comparison to WT. Electroolfactogram recordings showed decreased olfactory responses to octaldehyde, heptaldehyde and acetyl acetate in OlfDNCX compared to WT. Octaldehyde-elicited glomerular activity in the olfactory bulb, measured according to odor-elicited <it>c-fos </it>mRNA upregulation in juxtaglomerular cells, was confined to smaller areas of the glomerular layer in OlfDNCX compared to WT. In WT mice, octaldehyde sensitive neurons exhibited reduced response magnitudes after application of gap junction uncoupling reagents and the effects were specific to subsets of neurons.</p> <p>Conclusions</p> <p>My study has demonstrated that altered assembly of Cx43 or structurally related connexins in ORNs modulates olfactory responses and changes olfactory activation maps in the olfactory bulb. Furthermore, pharmacologically uncoupling of gap junctions reduces olfactory activity in subsets of ORNs. These data suggest that gap junctional communication or hemichannel activity plays a critical role in maintaining olfactory sensitivity and odor perception.</p