Consistent Group and Coset Reductions of the Bosonic String

Dimensional reductions of pure Einstein gravity on cosets other than tori are inconsistent. The inclusion of specific additional scalar and p-form matter can change the situation. For example, a D-dimensional Einstein-Maxwell-dilaton system, with a specific dilaton coupling, is known to admit a consistent reduction on S^2= SU(2)/U(1), of a sort first envisaged by Pauli. We provide a new understanding, by showing how an S^3=SU(2) group-manifold reduction of (D+1)-dimensional Einstein gravity, of a type first indicated by DeWitt, can be broken into in two steps; a Kaluza-type reduction on U(1) followed by a Pauli-type coset reduction on S^2. More generally, we show that any D-dimensional theory that itself arises as a Kaluza U(1) reduction from (D+1) dimensions admits a consistent Pauli reduction on any coset of the form G/U(1). Extensions to the case G/H are given. Pauli coset reductions of the bosonic string on G= (G\times G)/G are believed to be consistent, and a consistency proof exists for S^3=SO(4)/SO(3). We examine these reductions, and arguments for consistency, in detail. The structures of the theories obtained instead by DeWitt-type group-manifold reductions of the bosonic string are also studied, allowing us to make contact with previous such work in which only singlet scalars are retained. Consistent truncations with two singlet scalars are possible. Intriguingly, despite the fact that these are not supersymmetric models, if the group manifold has dimension 3 or 25 they admit a superpotential formulation, and hence first-order equations yielding domain-wall solutions.Comment: Latex, 5 figures, 45 pages, minor correction

Spectrum of Higher Derivative 6D Chiral Supergravity

Gauged off-shell Maxwell-Einstein supergravity in six dimensions with N=(1,0) supersymmetry has a higher derivative extension afforded by a supersymmetrized Riemann squared term. This theory admits a supersymmetric Minkowski x S^2 compactification with a U(1) monopole of unit charge on S^2. We determine the full spectrum of the theory on this background. We also determine the spectrum on a non-supersymmetric version of this compactification in which the monopole charge is different from unity, and we find the peculiar feature that there are massless gravitini in a representation of the S^2 isometry group determined by the monopole charge.Comment: typos correcte

Splitting of Folded Strings in AdS_4*CP^3

We study classically splitting of two kinds of folded string solutions in AdS_4*CP^3. Conserved charges of the produced fragments are computed for each case. We find interesting patterns among these conserved charges.Comment: minor changes, 14 pages, no figure

More about Birkhoff's Invariant and Thorne's Hoop Conjecture for Horizons

A recent precise formulation of the hoop conjecture in four spacetime dimensions is that the Birkhoff invariant $\beta$ (the least maximal length of any sweepout or foliation by circles) of an apparent horizon of energy $E$ and area $A$ should satisfy $\beta \le 4 \pi E$. This conjecture together with the Cosmic Censorship or Isoperimetric inequality implies that the length $\ell$ of the shortest non-trivial closed geodesic satisfies $\ell^2 \le \pi A$. We have tested these conjectures on the horizons of all four-charged rotating black hole solutions of ungauged supergravity theories and find that they always hold. They continue to hold in the the presence of a negative cosmological constant, and for multi-charged rotating solutions in gauged supergravity. Surprisingly, they also hold for the Ernst-Wild static black holes immersed in a magnetic field, which are asymptotic to the Melvin solution. In five spacetime dimensions we define $\beta$ as the least maximal area of all sweepouts of the horizon by two-dimensional tori, and find in all cases examined that $\beta(g) \le \frac{16 \pi}{3} E$, which we conjecture holds quiet generally for apparent horizons. In even spacetime dimensions $D=2N+2$, we find that for sweepouts by the product $S^1 \times S^{D-4}$, $\beta$ is bounded from above by a certain dimension-dependent multiple of the energy $E$. We also find that $\ell^{D-2}$ is bounded from above by a certain dimension-dependent multiple of the horizon area $A$. Finally, we show that $\ell^{D-3}$ is bounded from above by a certain dimension-dependent multiple of the energy, for all Kerr-AdS black holes.Comment: 25 page

A robust genetic algorithm for learning temporal specifications from data

We consider the problem of mining signal temporal logical requirements from a dataset of regular (good) and anomalous (bad) trajectories of a dynamical system. We assume the training set to be labeled by human experts and that we have access only to a limited amount of data, typically noisy. We provide a systematic approach to synthesize both the syntactical structure and the parameters of the temporal logic formula using a two-steps procedure: first, we leverage a novel evolutionary algorithm for learning the structure of the formula; second, we perform the parameter synthesis operating on the statistical emulation of the average robustness for a candidate formula w.r.t. its parameters. We compare our results with our previous work [9] and with a recently proposed decision-tree [8] based method. We present experimental results on two case studies: an anomalous trajectory detection problem of a naval surveillance system and the characterization of an Ineffective Respiratory effort, showing the usefulness of our work

Generalized cusp in AdS_4 x CP^3 and more one-loop results from semiclassical strings

We evaluate the exact one-loop partition function for fundamental strings whose world-surface ends on a cusp at the boundary of AdS_4 and has a "jump" in CP^3. This allows us to extract the stringy prediction for the ABJM generalized cusp anomalous dimension Gamma_{cusp}^{ABJM} (phi,theta) up to NLO in sigma-model perturbation theory. With a similar analysis, we present the exact partition functions for folded closed string solutions moving in the AdS_3 parts of AdS_4 x CP^3 and AdS_3 x S^3 x S^3 x S^1 backgrounds. Results are obtained applying to the string solutions relevant for the AdS_4/CFT_3 and AdS_3/CFT_2 correspondence the tools previously developed for their AdS_5 x S^5 counterparts.Comment: 48 pages, 2 figures, version 3, corrected misprints in formulas 2.12, B.86, C.33, added comment on verification of the light-like limi

Spinning strings at one-loop in AdS_4 x P^3

We analyze the folded spinning string in AdS_4 x P^3 with spin S in AdS_4 and angular momentum J in P^3. We calculate the one-loop correction to its energy in the scaling limit of both ln S and J large with their ratio kept fixed. This result should correspond to the first subleading strong coupling correction to the anomalous dimension of operators of the type Tr(D^S(Y^\dagger Y)^J) in the dual N=6 Chern-Simons-matter theory. Our result appears to depart from the predictions for the generalized scaling function found from the all-loop Bethe equations conjectured for this AdS_4/CFT_3 duality. We comment on the possible origin of this difference.Comment: 24 pages; v2: References added and typos correcte

Prevalence of apical periodontitis and endodontic treatment in a Kosovar adult population

<p>Abstract</p> <p>Background</p> <p>Despite numerous studies on the prevalence of apical periodontitis (AP) and endodontic treatment in diverse geographical populations, there are currently no data on the prevalence of these conditions in populations of adults native to Kosovo. Therefore, little is known about how widespread these conditions are, and whether there is any correlation between root canal treatment and AP. The purpose of our research was to address this anomaly by investigating AP and endodontic treatment in an adult Kosovar population based on radiographic examination.</p> <p>Methods</p> <p>The sample used for this study consisted of randomly selected individuals referred to the University Dentistry Clinical Center of Kosovo in the years 2006-2007. Orthopantomographs of 193 patients were evaluated. The periapical status of all teeth (with the exception of third molars) was examined according to Ørstavik's Periapical Index. The quality of the root canal filling was rated as 'adequate' or 'inadequate' based on whether all canals were filled, the depth of fill relative to the radiographic apex and the quality of compaction (absence/presence of voids). Data were analyzed statistically using the Chi-square test and calculation of odds ratios.</p> <p>Results</p> <p>Out of 4131 examined teeth, the prevalence of apical periodontitis (AP) and endodontic treatment was 12.3% and 2.3%, respectively. Of 95 endodontically-treated teeth, 46.3% were associated with AP. The prevalence of AP increased with age. The prevalence in subjects aged over 60 years old (20.2%) was higher than in other age groups. A statistically significant difference was found for the frequency of endodontically-treated teeth associated with AP in the 40-49 year age group (P < 0.001). Of some concern was the discovery that only 30.5% of the endodontically-treated teeth examined met the criteria of an acceptable root canal filling. Inadequately root-filled teeth were associated with an increased AP risk.</p> <p>Conclusions</p> <p>The prevalence of AP and the frequency of endodontically-treated teeth with AP in this Kosovar population are higher than those found in other countries. Inadequate root canal fillings were associated with an increased prevalence of AP.</p