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

Coupling a model of human thermoregulation with computational fluid dynamics for predicting human-environment interaction

This paper describes the methods developed to couple a commercial CFD program with a multi-segmented model of human thermal comfort and physiology. A CFD model is able to predict detailed temperatures and velocities of airflow around a human body, whilst a thermal comfort model is able to predict the response of a human to the environment surrounding it. By coupling the two models and exchanging information about the heat transfer at the body surface the coupled system can potentially predict the response of a human body to detailed local environmental conditions. This paper presents a method of exchanging data, using shared files, to provide a means of dynamically exchanging simulation data with the IESD-Fiala model during the CFD solution process. Additional code is used to set boundary conditions for the CFD simulation at the body surface as determined by the IESD-Fiala model and to return information about local environmental conditions adjacent to the body surface as determined by the CFD simulation. The coupled system is used to model a human subject in a naturally ventilated environment. The resulting ventilation flow pattern agrees well with other numerical and experimental work

Expanding the expressive power of Monadic Second-Order logic on restricted graph classes

We combine integer linear programming and recent advances in Monadic Second-Order model checking to obtain two new algorithmic meta-theorems for graphs of bounded vertex-cover. The first shows that cardMSO1, an extension of the well-known Monadic Second-Order logic by the addition of cardinality constraints, can be solved in FPT time parameterized by vertex cover. The second meta-theorem shows that the MSO partitioning problems introduced by Rao can also be solved in FPT time with the same parameter. The significance of our contribution stems from the fact that these formalisms can describe problems which are W[1]-hard and even NP-hard on graphs of bounded tree-width. Additionally, our algorithms have only an elementary dependence on the parameter and formula. We also show that both results are easily extended from vertex cover to neighborhood diversity.Comment: Accepted for IWOCA 201

Global Conformational Dynamics of a Y-Family DNA Polymerase during Catalysis

High-resolution analysis of protein, and DNA conformational changes during DNA polymerization, established relationships between the enzymatic function and conformational dynamics of individual domains for a DNA polymerase

Assessing heat-related health risk in Europe via the Universal Thermal Climate Index (UTCI)

In this work the potential of the Universal Thermal Climate Index (UTCI) as a heat-related health risk indicator in Europe is demonstrated. The UTCI is a bioclimate index that uses a multi-node human heat balance model to represent the heat stress induced by meteorological conditions to the human body. Using 38 years of meteorological reanalysis data, UTCI maps were computed to assess the thermal bioclimate of Europe for the summer season. Patterns of heat stress conditions and non-thermal stress regions are identified across Europe. An increase in heat stress up to 1°C is observed during recent decades. Correlation with mortality data from 17 European countries revealed that the relationship between the UTCI and death counts depends on the bioclimate of the country, and death counts increase in conditions of moderate and strong stress, i.e. when UTCI is above 26°C and 32°C. The UTCI’s ability to represent mortality patterns is demonstrated for the 2003 European heatwave. These findings confirm the importance of UTCI as a bioclimatic index that is able to both capture the thermal bioclimatic variability of Europe, and relate such variability with the effects it has on human health

A Combined Perceptual, Physico-Chemical, and Imaging Approach to ‘Odour-Distances’ Suggests a Categorizing Function of the Drosophila Antennal Lobe

How do physico-chemical stimulus features, perception, and physiology relate? Given the multi-layered and parallel architecture of brains, the question specifically is where physiological activity patterns correspond to stimulus features and/or perception. Perceived distances between six odour pairs are defined behaviourally from four independent odour recognition tasks. We find that, in register with the physico-chemical distances of these odours, perceived distances for 3-octanol and n-amylacetate are consistently smallest in all four tasks, while the other five odour pairs are about equally distinct. Optical imaging in the antennal lobe, using a calcium sensor transgenically expressed in only first-order sensory or only second-order olfactory projection neurons, reveals that 3-octanol and n-amylacetate are distinctly represented in sensory neurons, but appear merged in projection neurons. These results may suggest that within-antennal lobe processing funnels sensory signals into behaviourally meaningful categories, in register with the physico-chemical relatedness of the odours

Synthetic retinal analogues modify the spectral and kinetic characteristics of microbial rhodopsin optogenetic tools

Optogenetic tools have become indispensable in neuroscience to stimulate or inhibit excitable cells by light. Channelrhodopsin-2 (ChR2) variants have been established by mutating the opsin backbone or by mining related algal genomes. As an alternative strategy, we surveyed synthetic retinal analogues combined with microbial rhodopsins for functional and spectral properties, capitalizing on assays in C. elegans, HEK cells and larval Drosophila. Compared with all-trans retinal (ATR), Dimethylamino-retinal (DMAR) shifts the action spectra maxima of ChR2 variants H134R and H134R/T159C from 480 to 520 nm. Moreover, DMAR decelerates the photocycle of ChR2(H134R) and (H134R/T159C), thereby reducing the light intensity required for persistent channel activation. In hyperpolarizing archaerhodopsin-3 and Mac, naphthyl-retinal and thiophene-retinal support activity alike ATR, yet at altered peak wavelengths. Our experiments enable applications of retinal analogues in colour tuning and altering photocycle characteristics of optogenetic tools, thereby increasing the operational light sensitivity of existing cell lines or transgenic animals

Synthetic retinal analogues modify the spectral and kinetic characteristics of microbial rhodopsin optogenetic tools

Optogenetic tools have become indispensable in neuroscience to stimulate or inhibit excitable cells by light. Channelrhodopsin-2 (ChR2) variants have been established by mutating the opsin backbone or by mining related algal genomes. As an alternative strategy, we surveyed synthetic retinal analogues combined with microbial rhodopsins for functional and spectral properties, capitalizing on assays in C. elegans, HEK cells and larval Drosophila. Compared with all-trans retinal (ATR), Dimethylamino-retinal (DMAR) shifts the action spectra maxima of ChR2 variants H134R and H134R/T159C from 480 to 520 nm. Moreover, DMAR decelerates the photocycle of ChR2(H134R) and (H134R/T159C), thereby reducing the light intensity required for persistent channel activation. In hyperpolarizing archaerhodopsin-3 and Mac, naphthyl-retinal and thiophene-retinal support activity alike ATR, yet at altered peak wavelengths. Our experiments enable applications of retinal analogues in colour tuning and altering photocycle characteristics of optogenetic tools, thereby increasing the operational light sensitivity of existing cell lines or transgenic animals

Psychological growth in aging Vietnam veterans: redefining shame and betrayal

This study offers alternative interpretations of war-related distress embedded within the social and political context of the Vietnam War. Subjective interpretations from aging Vietnam veterans were analyzed using interpretative phenomenological analysis. A central theme—Moral authenticity: Overcoming the betrayal and shame of war—overarched five subordinate themes. Four subordinate themes encapsulated layers of war-related betrayal associated with shame. Shame was likely to be described as either (a) internal/sense of personal failure, with no acts of rage; or (b) external/reckless or threatening acts of others, engendering rage. A fifth theme, reparation with self, reflected humility, gratitude, and empathy, currently undefined domains of the growth construct

In vivo Bioluminescence Imaging of Ca(2+) Signalling in the Brain of Drosophila

Many different cells' signalling pathways are universally regulated by Ca(2+) concentration [Ca(2+)] rises that have highly variable amplitudes and kinetic properties. Optical imaging can provide the means to characterise both the temporal and spatial aspects of Ca(2+) signals involved in neurophysiological functions. New methods for in vivo imaging of Ca(2+) signalling in the brain of Drosophila are required for probing the different dynamic aspects of this system. In studies here, whole brain Ca(2+) imaging was performed on transgenic flies with targeted expression of the bioluminescent Ca(2+) reporter GFP-aequorin (GA) in different neural structures. A photon counting based technique was used to undertake continuous recordings of cytosolic [Ca(2+)] over hours. Time integrals for reconstructing images and analysis of the data were selected offline according to the signal intensity. This approach allowed a unique Ca(2+) response associated with cholinergic transmission to be identified by whole brain imaging of specific neural structures. Notably, [Ca(2+)] transients in the Mushroom Bodies (MBs) following nicotine stimulation were accompanied by a delayed secondary [Ca(2+)] rise (up to 15 min. later) in the MB lobes. The delayed response was sensitive to thapsigargin, suggesting a role for intra-cellular Ca(2+) stores. Moreover, it was reduced in dunce mutant flies, which are impaired in learning and memory. Bioluminescence imaging is therefore useful for studying Ca(2+) signalling pathways and for functional mapping of neurophysiological processes in the fly brain