On homogeneous warped product Einstein metrics

In this article we study homogeneous warped product Einstein metrics and its connections with homogeneous Ricci solitons. We show that homogeneous $(\lambda,n+m)$-Einstein manifolds (which are the bases of homogeneous warped product Einstein metrics) are one-dimensional extensions of algebraic solitons. This answers a question from a paper of C. He, P. Petersen and W. Wylie, where they prove the converse statement. Our proof is strongly based on their results, but it also makes use of sharp tools from the theory of homogeneous Ricci solitons. As an application, we obtain that any homogeneous warped product Einstein metric with homogeneous base is diffeomorphic to a product of homogeneous Einstein manifolds.Comment: 9 page

Symmetry reduction and heuristic search for error detection in model checking

The state explosion problem is the main limitation of model checking. Symmetries in the system being verified can be exploited in order to avoid this problem by defining an equivalence (symmetry) relation on the states of the system, which induces a semantically equivalent quotient system of smaller size. On the other hand, heuristic search algorithms can be applied to improve the bug finding capabilities of model checking. Such algorithms use heuristic functions to guide the exploration. Bestfirst is used for accelerating the search, while A* guarantees optimal error trails if combined with admissible estimates. We analyze some aspects of combining both approaches, concentrating on the problem of finding the optimal path to the equivalence class of a given error state. Experimental results evaluate our approach

The present state of the water exchange through the Strait of Gibraltar

The present two-way exchange through the Strait of Gibraltar stems from the fresh water deficit of the Mediterranean basin. The size of the exchanged flows is the outcome of the climatology over the basin and the morphology and internal hydraulics of the Strait. Its highly constraining topography imposes an upper bound to the flows that cannot be exceeded, a limit known as maximal exchange, which is associated with the minimum salinity difference (density, in fact) between the inflowing (Atlantic) and outflowing (Mediterranean) waters. A relevant question is whether or not the present exchange has achieved this limit. A simple steady-state model of the Mediterranean Sea and Strait of Gibraltar system in which the deep water formation rate is balanced by the Mediterranean outflow, strongly suggests that the exchange is quite close to (or, indeed, it is) maximal. The Strait topography requires two hydraulic control sections for this limit to be achieved, which could be thought as if one of them controls the outflow (the section of the main sill of Camarinal) and the second one the inflow (the narrowest section or Tarifa Narrows, to the east of the main sill). Oceanwards of Camarinal, the outflow accelerates and settles as one of the fastest and brisk bottom currents of the world ocean. East of Tarifa Narrows the inflow becomes a swift jet, the Atlantic Jet, which enters the Mediterranean Sea and sets up the basic features of the Alboran Sea surface circulation. The steady exchange so far depicted is not realistic. The flows undergo large fluctuations at different time scales, which modify the former description drastically. Of special importance are the tides and associated tidal flows, which can be up to 5 times greater than the long-term averaged flows. Under such huge fluctuations, the hydraulic control in Camarinal sill is periodically lost about two hours before high water, during the rising tide, when the tidal currents still head toward the Atlantic Ocean. The flooding of the control is revealed by the release of a vast internal hydraulic jump that progresses towards the Mediterranean Sea while evolving into a regularly shaped train of great amplitude internal waves that carry away part of the tidal energy accumulated nearby the sill during the rising tide. Whenever the hydraulic control at Camarinal is lost, a second sill located to the west (Espartel sill, the westernmost gateway of the Strait) takes over the control of the Mediterranean outflow. The hydraulic control at Espartel is very seldom flooded, which is a fundamental fact for understanding the internal dynamics of the exchange under large barotropic fluctuations. Without this sill, the Strait dynamics would be very different. It is behind the powerful, but periodically inverting, bottom currents nearby Camarinal sill and the also strong, but already unidirectional, bottom currents in Espartel sill and beyond, a reason for which this sill might well be considered as the proper source of the Mediterranean plume in the Atlantic Ocean.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Is the Western Mediterranean Transition showing up in the Strait of Gibraltar?

Physical and chemical properties (temperature, salinity, pH) of the Mediterranean outflow near the seafloor at Espartel sill, at the westernmost section of the Strait of Gibraltar, have been measured by a monitoring station aimed at following the changes that are taking place in the Mediterranean Sea. Presently, temperature and salinity series are longer than 13 years and they show a slight positive trend (warmer and saltier) that has increased after year 2013. The possibility of this increase being the result of the arrival of the so-called Western Mediterranean Transition (WMT), which started in year 2005 after the huge production of new and denser-than-usual Western Mediterranean Deep Water (WMDW), has been considered. The hypothesis that the water of the WMT is now showing up in the Strait has been put forward by some authors and gets strong support from the pH time series recorded at the station, which shows a sudden and sustained decrease (acidification) starting in early 2016. This decrease is consistent with the fact that the water now being observed flowing out is younger, i.e. has been in contact with the atmosphere more recently, than the WMDWit used to flow out previously to this year. It was only after the large new WMDW production of the harsh winters of 2012 and 2013 and the expected uplift of older layers of WMDW they caused that WMT waters were made available to flow out the Mediterranean Sea.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Abstraction in directed model checking

Abstraction is one of the most important issues to cope with large and infinite state spaces in model checking and to reduce the verification efforts. The abstract system is smaller than the original one and if the abstract system satisfies a correctness specification, so does the concrete one. However, abstractions may introduce a behavior violating the specification that is not present in the original system. This paper bypasses this problem by proposing the combination of abstraction with heuristic search to improve error detection. The abstract system is explored in order to create a database that stores the exact distances from abstract states to the set of abstract error states. To check, whether or not the abstract behavior is present in the original system, effcient exploration algorithms exploit the database as a guidance

Immortal homogeneous Ricci flows

We show that for an immortal homogeneous Ricci flow solution any sequence of parabolic blow-downs subconverges to a homogeneous expanding Ricci soliton. This is established by constructing a new Lyapunov function based on curvature estimates which come from real geometric invariant theory.Comment: Final version, to appear in Invent. Mat

Graphical Verification of a Spatial Logic for the Graphical Verification of a Spatial Logic for the pi-calculus

The paper introduces a novel approach to the verification of spatial properties for finite [pi]-calculus specifications. The mechanism is based on a recently proposed graphical encoding for mobile calculi: Each process is mapped into a (ranked) graph, such that the denotation is fully abstract with respect to the usual structural congruence (i.e., two processes are equivalent exactly when the corresponding encodings yield the same graph). Spatial properties for reasoning about the behavior and the structure of pi-calculus processes are then expressed in a logic introduced by Caires, and they are verified on the graphical encoding of a process, rather than on its textual representation. More precisely, the graphical presentation allows for providing a simple and easy to implement verification algorithm based on the graphical encoding (returning true if and only if a given process verifies a given spatial formula)