Graph Kernels

We present a unified framework to study graph kernels, special cases of which include the random walk (Gärtner et al., 2003; Borgwardt et al., 2005) and marginalized (Kashima et al., 2003, 2004; Mahé et al., 2004) graph kernels. Through reduction to a Sylvester equation we improve the time complexity of kernel computation between unlabeled graphs with n vertices from O(n^6) to O(n^3). We find a spectral decomposition approach even more efficient when computing entire kernel matrices. For labeled graphs we develop conjugate gradient and fixed-point methods that take O(dn^3) time per iteration, where d is the size of the label set. By extending the necessary linear algebra to Reproducing Kernel Hilbert Spaces (RKHS) we obtain the same result for d-dimensional edge kernels, and O(n^4) in the infinite-dimensional case; on sparse graphs these algorithms only take O(n^2) time per iteration in all cases. Experiments on graphs from bioinformatics and other application domains show that these techniques can speed up computation of the kernel by an order of magnitude or more. We also show that certain rational kernels (Cortes et al., 2002, 2003, 2004) when specialized to graphs reduce to our random walk graph kernel. Finally, we relate our framework to R-convolution kernels (Haussler, 1999) and provide a kernel that is close to the optimal assignment kernel of Fröhlich et al. (2006) yet provably positive semi-definite

Massless and massive graviton spectra in anisotropic dilatonic braneworld cosmologies

We consider a braneworld model in which an anisotropic brane is embedded in a dilatonic background. We solve the background solutions and study the behavior of the perturbations when the universe evolves from an inflationary Kasner phase to a Minkowski phase. We calculate the massless mode spectrum, and find that it does not differ from what expected in standard four-dimensional cosmological models. We then evaluate the spectrum of both light (ultrarelativistic) and heavy (nonrelativistic) massive modes, and find that, at high energies, there can be a strong enhancement of the Kaluza-Klein spectral amplitude, which can become dominant in the total spectrum. The presence of the dilaton, on the contrary, decrease the relative importance of the massive modes.Comment: 18 pages, 4 figures, Typos correction

Dynamic Effects of Wind Loads on a Gravity Damper

AbstractThe gravity damper is safety device used for the air treatment that prevent overpressure inside the unit through the opening. It is a normally closed valve under the effect of the gravity force, which, under the action of the incident air flow, allows to manage any excess mass. Clearly, although the device is rather simple and therefore reliable, the operating conditions may prove burdensome, especially if the gravity dampers are applied to installations of energy transformation, such as the gas turbines; this is mainly due to the need to develop large masses of air at speeds rather incurred. This article describes an experiment carried out on a gravity damper designed to be installed in a gas turbine. The characterization has been performed in numerical (CFD-FEM), considering both the mode shapes and the natural frequencies of the device in working condition as well as any phenomenon of detachment of the fluid that can trigger vortex shedding and subsequently validated in the wind tunnel facilities of the University of Perugia. In particular, what is wanted to be highlighted is the fact that, after a preliminary analysis, it has been clearly evident that, under the operating conditions, the structure would be affected by phenomena of vortex shedding. The shedding frequency is next to some natural frequencies of the structure, with obvious repercussions on the integrity of the structure. An experimental vibration analysis performed in the wind tunnel at flow regime has in fact allowed to identify the phenomenon of lock-in

Bethe Ansatz Equations for General Orbifolds of N=4 SYM

We consider the Bethe Ansatz Equations for orbifolds of N =4 SYM w.r.t. an arbitrary discrete group. Techniques used for the Abelian orbifolds can be extended to the generic non-Abelian case with minor modifications. We show how to make a transition between the different notations in the quiver gauge theory.Comment: LaTeX, 66 pages, 9 eps figures, minor corrections, references adde

Bootstrapping Conditional GANs for Video Game Level Generation

Generative Adversarial Networks (GANs) have shown im-pressive results for image generation. However, GANs facechallenges in generating contents with certain types of con-straints, such as game levels. Specifically, it is difficult togenerate levels that have aesthetic appeal and are playable atthe same time. Additionally, because training data usually islimited, it is challenging to generate unique levels with cur-rent GANs. In this paper, we propose a new GAN architec-ture namedConditional Embedding Self-Attention Genera-tive Adversarial Network(CESAGAN) and a new bootstrap-ping training procedure. The CESAGAN is a modification ofthe self-attention GAN that incorporates an embedding fea-ture vector input to condition the training of the discriminatorand generator. This allows the network to model non-localdependency between game objects, and to count objects. Ad-ditionally, to reduce the number of levels necessary to trainthe GAN, we propose a bootstrapping mechanism in whichplayable generated levels are added to the training set. Theresults demonstrate that the new approach does not only gen-erate a larger number of levels that are playable but also gen-erates fewer duplicate levels compared to a standard GAN

Space/Time Noncommutativity in String Theories without Background Electric Field

The appearance of space/time non-commutativity in theories of open strings with a constant non-diagonal background metric is considered. We show that, even if the space-time coordinates commute, when there is a metric with a time-space component, no electric field and the boundary condition along the spatial direction is Dirichlet, a Moyal phase still arises in products of vertex operators. The theory is in fact dual to the non-commutatitive open string (NCOS) theory. The correct definition of the vertex operators for this theory is provided. We study the system also in the presence of a $B$ field. We consider the case in which the Dirichlet spatial direction is compactified and analyze the effect of these background on the closed string spectrum. We then heat up the system. We find that the Hagedorn temperature depends in a non-extensive way on the parameters of the background and it is the same for the closed and the open string sectors.Comment: 18 pages, JHEP styl

Dynamics of interacting skyrmions in magnetic nano-track

Controlling multiple skyrmions in nanowires is important for their implementation in racetrack memory or neuromorphic computing. Here, we report on the dynamical behavior of two interacting skyrmions in confined devices with a comparison to a single skyrmion case. Although the two skyrmions shrink near the edges and follow a helical path, their behavior is different. Because the leading skyrmion is between the edge and the trailing one, its size is reduced further and collapses at a lower current density compared to the single skyrmion case. For higher current density, both skyrmions are annihilated with a core-collapse mechanism for the leading one followed by a bubble-collapse mechanism for the trailing one

Quantifying molecular oxygen isotope variations during a Heinrich stadial

International audienceδ 18 O of atmospheric oxygen (δ 18 O atm) undergoes millennial-scale variations during the last glacial period, and systematically increases during Heinrich stadials (HSs). Changes in δ 18 O atm combine variations in biospheric and water cycle processes. The identification of the main driver of the millennial variability in δ 18 O atm is thus not straightforward. Here, we quantify the response of δ 18 O atm to such millennial events using a freshwater hosing simulation performed under glacial boundary conditions. Our global approach takes into account the latest estimates of isotope frac-tionation factor for respiratory and photosynthetic processes and make use of atmospheric water isotope and vegetation changes. Our modeling approach allows to reproduce the main observed features of a HS in terms of climatic conditions , vegetation distribution and δ 18 O of precipitation. We use it to decipher the relative importance of the different processes behind the observed changes in δ 18 O atm. The results highlight the dominant role of hydrology on δ 18 O atm and confirm that δ 18 O atm can be seen as a global integrator of hydrological changes over vegetated areas

New Penrose Limits and AdS/CFT

We find a new Penrose limit of AdS_5 x S^5 giving the maximally supersymmetric pp-wave background with two explicit space-like isometries. This is an important missing piece in studying the AdS/CFT correspondence in certain subsectors. In particular whereas the Penrose limit giving one space-like isometry is useful for the SU(2) sector of N=4 SYM, this new Penrose limit is instead useful for studying the SU(2|3) and SU(1,2|3) sectors. In addition to the new Penrose limit of AdS_5 x S^5 we also find a new Penrose limit of AdS_4 x CP^3.Comment: 30 page