Reflexive insensitive modal logics

We analyze a class of modal logics rendered insensitive to reflexivity by way of a modification to the semantic definition of the modal operator. We explore the extent to which these logics can be characterized, and prove a general completeness theorem on the basis of a translation between normal modal logics and their reflexive-insensitive counterparts. Lastly, we provide a sufficient semantic condition describing when a similarly general soundness result is also available

Tailed radio galaxies as tracers of galaxy clusters. Serendipitous discoveries with the GMRT

We report on the discovery of four new radio galaxies with tailed morphology. Tailed radio galaxies are generally found in rich environments, therefore their presence can be used as tracer of a cluster. The radio galaxies were found in the fields of Giant Metrewave Radio Telescope (GMRT) observations carried out at 610 MHz and 327 MHz devoted to other studies. We inspected the literature and archives in the optical and X-ray bands to search for galaxy clusters or groups hosting them. All the tailed radio galaxies serendipitously found in the GMRT fields are located in rich environments. Two of them belong to the candidate cluster NCS J090232+204358, located at z(phot)=0.0746; one belongs to the cluster MaxBCGJ223.97317+22.15620 at z(phot)=0.2619; finally we suggest that the fourth one is probing a galaxy cluster at z=0.1177, located behind A262, and so far undetected in any band. Our results strenghten the relevance of high sensitivity and high resolution radio data in the detection of galaxy clusters at intermediate redshift.Comment: 8 pages, accepted for publication on Astronomy & Astrophysic

Fiat-Shamir for highly sound protocols is instantiable

The Fiat–Shamir (FS) transformation (Fiat and Shamir, Crypto '86) is a popular paradigm for constructing very efficient non-interactive zero-knowledge (NIZK) arguments and signature schemes from a hash function and any three-move interactive protocol satisfying certain properties. Despite its wide-spread applicability both in theory and in practice, the known positive results for proving security of the FS paradigm are in the random oracle model only, i.e., they assume that the hash function is modeled as an external random function accessible to all parties. On the other hand, a sequence of negative results shows that for certain classes of interactive protocols, the FS transform cannot be instantiated in the standard model. We initiate the study of complementary positive results, namely, studying classes of interactive protocols where the FS transform does have standard-model instantiations. In particular, we show that for a class of “highly sound” protocols that we define, instantiating the FS transform via a q-wise independent hash function yields NIZK arguments and secure signature schemes. In the case of NIZK, we obtain a weaker “q-bounded” zero-knowledge flavor where the simulator works for all adversaries asking an a-priori bounded number of queries q; in the case of signatures, we obtain the weaker notion of random-message unforgeability against q-bounded random message attacks. Our main idea is that when the protocol is highly sound, then instead of using random-oracle programming, one can use complexity leveraging. The question is whether such highly sound protocols exist and if so, which protocols lie in this class. We answer this question in the affirmative in the common reference string (CRS) model and under strong assumptions. Namely, assuming indistinguishability obfuscation and puncturable pseudorandom functions we construct a compiler that transforms any 3-move interactive protocol with instance-independent commitments and simulators (a property satisfied by the Lapidot–Shamir protocol, Crypto '90) into a compiled protocol in the CRS model that is highly sound. We also present a second compiler, in order to be able to start from a larger class of protocols, which only requires instance-independent commitments (a property for example satisfied by the classical protocol for quadratic residuosity due to Blum, Crypto '81). For the second compiler we require dual-mode commitments. We hope that our work inspires more research on classes of (efficient) 3-move protocols where Fiat–Shamir is (efficiently) instantiable

An elusive radio halo in the merging cluster Abell 781?

Deep radio observations of the galaxy cluster Abell 781 have been carried out using the Giant Metrewave Radio Telescope at 325 MHz and have been compared to previous 610 MHz observations and to archival VLA 1.4 GHz data. The radio emission from the cluster is dominated by a diffuse source located at the outskirts of the X-ray emission, which we tentatively classify as a radio relic. We detected residual diffuse emission at the cluster centre at the level of S(325 MHz)~15-20 mJy. Our analysis disagrees with Govoni et al. (2011), and on the basis of simple spectral considerations we do not support their claim of a radio halo with flux density of 20-30 mJy at 1.4 GHz. Abell 781, a massive and merging cluster, is an intriguing case. Assuming that the residual emission is indicative of the presence of a radio halo barely detectable at our sensitivity level, it could be a very steep spectrum source.Comment: 5 pages, 4 figures, 1 table - Accepted for publication on Monthly Notices of the Royal Astronomical Society Letter

Bounding regions to plane steepest descent curves of quasi convex families

Two dimensional steepest descent curves (SDC) for a quasi convex family are considered; the problem of their extensions (with constraints) outside of a convex body $K$ is studied. It is shown that possible extensions are constrained to lie inside of suitable bounding regions depending on $K$. These regions are bounded by arcs of involutes of the boundary of $K$ and satisfy many inclusions properties. The involutes of the boundary of an arbitrary plane convex body are defined and written by their support function. Extensions SDC of minimal length are constructed. Self contracting sets (with opposite orientation) are considered, necessary and/or sufficients conditions for them to be subsets of a SDC are proved.Comment: 34 pages, 4 figure

On variational problems related to steepest descent curves and self dual convex sets on the sphere

Let $\mathcal{C}$ be the family of compact convex subsets $S$ of the hemisphere in \rn with the property that $S$ contains its dual $S^*;$ let $u\in S^*$, and let $\Phi(S,u)=\frac{2}{\omega_n}\int_{S}\ \,\, d\sigma(\theta).$ The problem to study $\inf \big\{\Phi(S,u), S \in \mathcal{C}, \, u\in S^* \big\}$ is considered. It is proved that the minima of $\Phi$ are sets of constant width $\pi/2$ with $u$ on their boundary. More can be said for $n=3$: the minimum set is a Reuleaux triangle on the sphere. The previous problem is related to the one to find the maximal length of steepest descent curves for quasi convex functions, satisfying suitable constraints. For $n=2$ let us refer to \cite{Manselli-Pucci}. Here quite different results are obtained for $n\geq 3$.Comment: 13 pages, 1 figur