Locally constrained homomorphisms on graphs of bounded treewidth and bounded degree.

A homomorphism from a graph G to a graph H is locally bijective, surjective, or injective if its restriction to the neighborhood of every vertex of G is bijective, surjective, or injective, respectively. We prove that the problems of testing whether a given graph G allows a homomorphism to a given graph H that is locally bijective, surjective, or injective, respectively, are NP-complete, even when G has pathwidth at most 5, 4 or 2, respectively, or when both G and H have maximum degree 3. We complement these hardness results by showing that the three problems are polynomial-time solvable if G has bounded treewidth and in addition G or H has bounded maximum degree

Performance characteristics of the 12 GHz, 200 watt transmitter experiment package for CTS

The experiment package consists of a 200 W output stage tube (OST) powered by a power processing system (PPS). Descriptions of both the PPS and OST are given. The PPS provides the necessary voltages with a measured dc/dc conversion efficiency of 89 percent. The OST, a traveling wave tube with multiple collectors, has a saturated rf output power of 224 W and operates at an overall efficiency exceeding 40 percent over an 85 MHz bandwidth at 12 GHz. OST performance given includes frequency response, saturation characteristics, group delay, AM to PM conversion, inter-modulation distortion, and two channel gain suppression. Single and dual channel FM video performance is presented. It was determined that for 12 MHz peak to peak frequency deviation on each channel, dual channel FM television signals can be transmitted through the TEP at 60 W, each channel, with 40 MHz channel spacing (center to center)

The Smell of Blue Light: A New Approach toward Understanding an Olfactory Neuronal Network

Olfaction is one of the most important senses throughout the animal kingdom. It enables animals to discriminate between a wide variety of attractive and repulsive odorants and often plays a decisive role in species specific communication. In recent years the analysis of olfactory systems both invertebrates and invertebrates has attracted much scientific interest. In this context a pivotal question is how the properties and connectivities of individual neurons contribute to a functioning neuronal network that mediates odor-guided behavior. As a novel approach to analyze the role of individual neurons within a circuitry, techniques have been established that make use of light-sensitive proteins. In this review we introduce a non-invasive, optogenetic technique which was used to manipulate the activity of individual neurons in the olfactory system of Drosophila melanogaster larvae. Both channelrhodopsin-2 and the photosensitive adenylyl cyclase PAC α in individual olfactory receptor neurons (ORNs) of the olfactory system of Drosophila larvae allows stimulating individual receptor neurons by light. Depending on which particular ORN is optogenetically activated, repulsion or attraction behavior can be induced, indicating which sensory neurons underlie which type of behavior

Asymptotics of the Farey Fraction Spin Chain Free Energy at the Critical Point

We consider the Farey fraction spin chain in an external field $h$. Using ideas from dynamical systems and functional analysis, we show that the free energy $f$ in the vicinity of the second-order phase transition is given, exactly, by $$f \sim \frac t{\log t}-\frac1{2} \frac{h^2}t \quad \text{for} \quad h^2\ll t \ll 1 .$$ Here $t=\lambda_{G}\log(2)(1-\frac{\beta}{\beta_c})$ is a reduced temperature, so that the deviation from the critical point is scaled by the Lyapunov exponent of the Gauss map, $\lambda_G$. It follows that $\lambda_G$ determines the amplitude of both the specific heat and susceptibility singularities. To our knowledge, there is only one other microscopically defined interacting model for which the free energy near a phase transition is known as a function of two variables. Our results confirm what was found previously with a cluster approximation, and show that a clustering mechanism is in fact responsible for the transition. However, the results disagree in part with a renormalisation group treatment

Lower Bounds for the Graph Homomorphism Problem

The graph homomorphism problem (HOM) asks whether the vertices of a given $n$-vertex graph $G$ can be mapped to the vertices of a given $h$-vertex graph $H$ such that each edge of $G$ is mapped to an edge of $H$. The problem generalizes the graph coloring problem and at the same time can be viewed as a special case of the $2$-CSP problem. In this paper, we prove several lower bound for HOM under the Exponential Time Hypothesis (ETH) assumption. The main result is a lower bound $2^{\Omega\left( \frac{n \log h}{\log \log h}\right)}$. This rules out the existence of a single-exponential algorithm and shows that the trivial upper bound $2^{{\mathcal O}(n\log{h})}$ is almost asymptotically tight. We also investigate what properties of graphs $G$ and $H$ make it difficult to solve HOM$(G,H)$. An easy observation is that an ${\mathcal O}(h^n)$ upper bound can be improved to ${\mathcal O}(h^{\operatorname{vc}(G)})$ where $\operatorname{vc}(G)$ is the minimum size of a vertex cover of $G$. The second lower bound $h^{\Omega(\operatorname{vc}(G))}$ shows that the upper bound is asymptotically tight. As to the properties of the "right-hand side" graph $H$, it is known that HOM$(G,H)$ can be solved in time $(f(\Delta(H)))^n$ and $(f(\operatorname{tw}(H)))^n$ where $\Delta(H)$ is the maximum degree of $H$ and $\operatorname{tw}(H)$ is the treewidth of $H$. This gives single-exponential algorithms for graphs of bounded maximum degree or bounded treewidth. Since the chromatic number $\chi(H)$ does not exceed $\operatorname{tw}(H)$ and $\Delta(H)+1$, it is natural to ask whether similar upper bounds with respect to $\chi(H)$ can be obtained. We provide a negative answer to this question by establishing a lower bound $(f(\chi(H)))^n$ for any function $f$. We also observe that similar lower bounds can be obtained for locally injective homomorphisms.Comment: 19 page

A versatile high-performance visual fiducial marker detection system with scalable identity encoding

Fiducial markers have a wide field of applications in robotics, ranging from external localisation of single robots or robotic swarms, over self-localisation in marker-augmented environments, to simplifying perception by tagging objects in a robot’s surrounding. We propose a new family of circular markers allowing for a computationally efficient detection, identification and full 3D position estimation. A key concept of our system is the separation of the detection and identification steps, where the first step is based on a computationally efficient circular marker detection, and the identification step is based on an open-ended ‘Necklace code’, which allows for a theoretically infinite number of individually identifiable markers. The experimental evaluation of the system on a real robot indicates that while the proposed algorithm achieves similar accuracy to other state-of-the-art methods, it is faster by two orders of magnitude and it can detect markers from longer distances

Solar cycle variation in solar f-mode frequencies and radius

Using data from the Global Oscillation Network Group (GONG) covering the period from 1995 to 1998, we study the change with solar activity in solar f-mode frequencies. The results are compared with similar changes detected from the Michelson Doppler Imager (MDI) data. We find variations in f-mode frequencies which are correlated with solar activity indices. If these changes are due to variation in solar radius then the implications are that the solar radius decreases by about 5 km from minimum to maximum activity.Comment: To appear in Solar Physic

Optogenetically Induced Olfactory Stimulation in Drosophila Larvae Reveals the Neuronal Basis of Odor-Aversion behavior

Olfactory stimulation induces an odor-guided crawling behavior of Drosophila melanogaster larvae characterized by either an attractive or a repellent reaction. In order to understand the underlying processes leading to these orientations we stimulated single olfactory receptor neurons (ORNs) through photo-activation within an intact neuronal network. Using the Gal4-UAS system two light inducible proteins, the light-sensitive cation channel channelrhodopsin-2 (ChR-2) or the light-sensitive adenylyl cyclase (Pacα) were expressed in all or in individual ORNs of the larval olfactory system. Blue light stimulation caused an activation of these neurons, ultimately producing the illusion of an odor stimulus. Larvae were tested in a phototaxis assay for their orientation toward or away from the light source. Here we show that activation of Pacα expressing ORNs bearing the receptors Or33b or Or45a in blind norpA mutant larvae induces a repellent behavior away from the light. Conversely, photo-activation of the majority of ORNs induces attraction towards the light. Interestingly, in wild type larvae two ligands of Or33b and Or45a, octyl acetate and propionic ethylester, respectively, have been found to cause an escape reaction. Therefore, we combined light and odor stimulation to analyze the function of Or33b and Or45a expressing ORNs. We show that the larval olfactory system contains a designated neuronal pathway for repellent odorants and that activation of a specific class of ORNs already determines olfactory avoidance behavior