Laplacian spectral characterization of roses

A rose graph is a graph consisting of cycles that all meet in one vertex. We show that except for two specific examples, these rose graphs are determined by the Laplacian spectrum, thus proving a conjecture posed by Lui and Huang [F.J. Liu and Q.X. Huang, Laplacian spectral characterization of 3-rose graphs, Linear Algebra Appl. 439 (2013), 2914--2920]. We also show that if two rose graphs have a so-called universal Laplacian matrix with the same spectrum, then they must be isomorphic. In memory of Horst Sachs (1927-2016), we show the specific case of the latter result for the adjacency matrix by using Sachs' theorem and a new result on the number of matchings in the disjoint union of paths

Nonexistence of Certain Skew-symmetric Amorphous Association Schemes

An association scheme is amorphous if it has as many fusion schemes as possible. Symmetric amorphous schemes were classified by A. V. Ivanov [A. V. Ivanov, Amorphous cellular rings II, in Investigations in algebraic theory of combinatorial objects, pages 39--49. VNIISI, Moscow, Institute for System Studies, 1985] and commutative amorphous schemes were classified by T. Ito, A. Munemasa and M. Yamada [T. Ito, A. Munemasa and M. Yamada, Amorphous association schemes over the Galois rings of characteristic 4, European J. Combin., 12(1991), 513--526]. A scheme is called skew-symmetric if the diagonal relation is the only symmetric relation. We prove the nonexistence of skew-symmetric amorphous schemes with at least 4 classes. We also prove that non-symmetric amorphous schemes are commutative.Comment: 10 page

Smooth at one end and rough at the other: influence of object texture on grasping behaviour

When picking up objects using a pinch grip, there are usually numerous places at which one could place the thumb and index finger. Yet, people seem to consistently place them at or close to the centre of mass (COM), presumably to minimize torque and therefore the required grip force. People also prefer to grasp objects by parallel surfaces and ones with higher friction coefficients (rough surfaces), to prevent the object from slipping when they lift it. Here, we examine the trade-off between friction and COM. Participants were asked to grasp and lift aluminium bars of which one end was polished and therefore smooth and the other was rough. Their finger positions were recorded to determine how they grasped the objects. The bars were oriented horizontally in the frontal plane, with the centre aligned with the participants’ body midline. The bars varied in the horizontal offset between the COM and the edge of the rough region. The offset could be 0, 1 or 2 cm. We expected participants to grasp closer to the rough area than the centre of the bar. Completely rough bars and completely smooth bars served as control conditions. The slipperiness of the surface that was grasped affected the height of the grasping points, indicating that participants adjusted their grasping behaviour to the slipperiness of the surface. However, the tendency to grasp closer to the rough area was minimal. This shows that the judged COM largely determines how an object is grasped. Friction has very limited influence

Smooth at one end and rough at the other: influence of object texture on grasping behaviour

© 2017, Springer-Verlag GmbH Germany. When picking up objects using a pinch grip, there are usually numerous places at which one could place the thumb and index finger. Yet, people seem to consistently place them at or close to the centre of mass (COM), presumably to minimize torque and therefore the required grip force. People also prefer to grasp objects by parallel surfaces and ones with higher friction coefficients (rough surfaces), to prevent the object from slipping when they lift it. Here, we examine the trade-off between friction and COM. Participants were asked to grasp and lift aluminium bars of which one end was polished and therefore smooth and the other was rough. Their finger positions were recorded to determine how they grasped the objects. The bars were oriented horizontally in the frontal plane, with the centre aligned with the participants’ body midline. The bars varied in the horizontal offset between the COM and the edge of the rough region. The offset could be 0, 1 or 2 cm. We expected participants to grasp closer to the rough area than the centre of the bar. Completely rough bars and completely smooth bars served as control conditions. The slipperiness of the surface that was grasped affected the height of the grasping points, indicating that participants adjusted their grasping behaviour to the slipperiness of the surface. However, the tendency to grasp closer to the rough area was minimal. This shows that the judged COM largely determines how an object is grasped. Friction has very limited influence

Dietary Patterns and Glucose Tolerance Abnormalities in Chinese Adults

OBJECTIVE To investigate the association of the dietary pattern with the presence of newly diagnosed glucose tolerance abnormalities among Chinese adults. RESEARCH DESIGN AND METHODS A total of 20,210 adults aged 45–69 years from the 2002 China National Nutrition and Health Survey were included. Information on dietary intake was collected using a validated food frequency questionnaire. Factor analysis and cluster analysis were used to identify the food factors and dietary pattern clusters. RESULTS Four dietary pattern clusters were identified (“Green Water,” “Yellow Earth,” “Western Adopter,” and “New Affluence”). The prevalence of glucose tolerance abnormalities ranged from 3.9% in the Green Water to 8.0% in the New Affluence. After adjustment for area, age, sex, current smoking, and physical activity, subjects in the Yellow Earth cluster (prevalence ratio 1.22 [95% CI 1.04–1.43]) and New Affluence cluster (2.05 [1.76–2.37]) had significantly higher prevalence rates compared with those for the Green Water cluster. After further adjustment for BMI and waist-to-height ratio, the elevated risk in the New Affluence remained statistically significant. CONCLUSIONS Dietary patterns and food factors are associated with the presence of glucose tolerance abnormalities in China, even independent of obesity. A New Affluence diet is an important modifiable risk factor, which needs attention from the prevention point of vie

A complete characterization of plateaued Boolean functions in terms of their Cayley graphs

In this paper we find a complete characterization of plateaued Boolean functions in terms of the associated Cayley graphs. Precisely, we show that a Boolean function $f$ is $s$-plateaued (of weight $=2^{(n+s-2)/2}$) if and only if the associated Cayley graph is a complete bipartite graph between the support of $f$ and its complement (hence the graph is strongly regular of parameters $e=0,d=2^{(n+s-2)/2}$). Moreover, a Boolean function $f$ is $s$-plateaued (of weight $\neq 2^{(n+s-2)/2}$) if and only if the associated Cayley graph is strongly $3$-walk-regular (and also strongly $\ell$-walk-regular, for all odd $\ell\geq 3$) with some explicitly given parameters.Comment: 7 pages, 1 figure, Proceedings of Africacrypt 201

Effector profiles distinguish <em>formae speciales</em> of <em>Fusarium oxysporum</em>

Formae speciales (ff.spp.) of the fungus Fusarium oxysporum are often polyphyletic within the species complex, making it impossible to identify them on the basis of conserved genes. However, sequences that determine host-specific pathogenicity may be expected to be similar between strains within the same forma specialis. Whole genome sequencing was performed on strains from five different ff.spp. (cucumerinum, niveum, melonis, radicis-cucumerinum and lycopersici). In each genome, genes for putative effectors were identified based on small size, secretion signal, and vicinity to a "miniature impala" transposable element. The candidate effector genes of all genomes were collected and the presence/absence patterns in each individual genome were clustered. Members of the same forma specialis turned out to group together, with cucurbit-infecting strains forming a supercluster separate from other ff.spp. Moreover, strains from different clonal lineages within the same forma specialis harbour identical effector gene sequences, supporting horizontal transfer of genetic material. These data offer new insight into the genetic basis of host specificity in the F. oxysporum species complex and show that (putative) effectors can be used to predict host specificity in F. oxysporum