Separation Logic for Small-step Cminor

Cminor is a mid-level imperative programming language; there are proved-correct optimizing compilers from C to Cminor and from Cminor to machine language. We have redesigned Cminor so that it is suitable for Hoare Logic reasoning and we have designed a Separation Logic for Cminor. In this paper, we give a small-step semantics (instead of the big-step of the proved-correct compiler) that is motivated by the need to support future concurrent extensions. We detail a machine-checked proof of soundness of our Separation Logic. This is the first large-scale machine-checked proof of a Separation Logic w.r.t. a small-step semantics. The work presented in this paper has been carried out in the Coq proof assistant. It is a first step towards an environment in which concurrent Cminor programs can be verified using Separation Logic and also compiled by a proved-correct compiler with formal end-to-end correctness guarantees.Comment: Version courte du rapport de recherche RR-613

Proof-Carrying Code with Correct Compilers

In the late 1990s, proof-carrying code was able to produce machine-checkable safety proofs for machine-language programs even though (1) it was impractical to prove correctness properties of source programs and (2) it was impractical to prove correctness of compilers. But now it is practical to prove some correctness properties of source programs, and it is practical to prove correctness of optimizing compilers. We can produce more expressive proof-carrying code, that can guarantee correctness properties for machine code and not just safety. We will construct program logics for source languages, prove them sound w.r.t. the operational semantics of the input language for a proved-correct compiler, and then use these logics as a basis for proving the soundness of static analyses

Reformulation of the Stochastic Potential Switching Algorithm and a Generalized Fourtuin-Kasteleyn Representation

A new formulation of the stochastic potential switching algorithm is presented. This reformulation naturally leads us to a generalized Fourtuin-Kasteleyn representation of the partition function Z. A formula for internal energy E and that of heat capacity C are derived from derivatives of the partition function. We also derive a formula for the exchange probability in the replica exchange Monte Carlo method. By combining the formulae with the Stochastic Cutoff method, we can greatly reduce the computational time to perform internal energy and heat capacity measurements and the replica exchange Monte Carlo method in long-range interacting systems. Numerical simulations in three dimensional magnetic dipolar systems show the validity and efficiency of the method.Comment: 11 pages, 6 figures, to appear in PR

Continuous loading of 1^{1}S0_{0} calcium atoms into an optical dipole trap

We demonstrate an efficient scheme for continuous trap loading based upon spatially selective optical pumping. We discuss the case of $^{1}$S$_{0}$ calcium atoms in an optical dipole trap (ODT), however, similar strategies should be applicable to a wide range of atomic species. Our starting point is a reservoir of moderately cold ($\approx 300 \mu$K) metastable $^{3}$P$_{2}$-atoms prepared by means of a magneto-optic trap (triplet-MOT). A focused 532 nm laser beam produces a strongly elongated optical potential for $^{1}$S$_{0}$-atoms with up to 350 $\mu$K well depth. A weak focused laser beam at 430 nm, carefully superimposed upon the ODT beam, selectively pumps the $^{3}$P$_{2}$-atoms inside the capture volume to the singlet state, where they are confined by the ODT. The triplet-MOT perpetually refills the capture volume with $^{3}$P$_{2}$-atoms thus providing a continuous stream of cold atoms into the ODT at a rate of $10^7$s$^{-1}$. Limited by evaporation loss, in 200 ms we typically load $5 \times 10^5$ atoms with an initial radial temperature of 85 $\mu$K. After terminating the loading we observe evaporation during 50 ms leaving us with $10^5$ atoms at radial temperatures close to 40 $\mu$K and a peak phase space density of $6.8 \times 10^{-5}$. We point out that a comparable scheme could be employed to load a dipole trap with $^{3}$P$_{0}$-atoms.Comment: 4 pages, 4 figure

Bose-Einstein condensation of alkaline earth atoms: 40^{40}{Ca}

We have achieved Bose-Einstein condensation of $^{40}$Ca, the first for an alkaline earth element. The influence of elastic and inelastic collisions associated with the large ground state s-wave scattering length of $^{40}$Ca was measured. From these findings, an optimized loading and cooling scheme was developed that allowed us to condense about $2 \cdot 10^4$ atoms after laser cooling in a two-stage magneto-optical trap and subsequent forced evaporation in a crossed dipole trap within less than 3 s. The condensation of an alkaline earth element opens novel opportunities for precision measurements on the narrow intercombination lines as well as investigations of molecular states at the $^1$S--$^3$P asymptotes

Effect of buffer on heparin binding and sensing in competitive aqueous media

Although buffer-specific effects on molecular recognition are known in biological science, they remain rare in supramolecular chemistry. The binding between a cationic dye, Mallard Blue (MalB), and polyanionic heparin in aqueous NaCl (150 mM) is studied in three commonly-used buffers (Tris-HCl, HEPES, Phosphate, each 10 mM). Although MalB has a very similar UV-Vis spectrum in each buffer, the sensory response towards heparin was different in each case. This can be ascribed to differences in the complex formed. In Tris-HCl which has the least competitive chloride counter-anions, MalB exhibits a hypsochromic shift of 25 nm, assigned to strong binding and aggregation of the dye on heparin. In more competitive HEPES, containing a sulfonate anion, there is weaker binding and less aggregation of MalB along the heparin; the hypsochromic shift is only 15 nm. In phosphate buffer, MalB can interact quite strongly with buffer phosphate anions; although heparin binding is still observed, the hypsochromic shift associated with dye aggregation is only 5 nm. As such, specific buffer interactions with the MalB-heparin complex mediate host-guest binding and sensing. Buffer choice must be made carefully in studies of molecular recognition – we would caution against using phosphate and sulfonate containing buffers when studying electrostatic binding

Liveness-Based Garbage Collection for Lazy Languages

We consider the problem of reducing the memory required to run lazy first-order functional programs. Our approach is to analyze programs for liveness of heap-allocated data. The result of the analysis is used to preserve only live data---a subset of reachable data---during garbage collection. The result is an increase in the garbage reclaimed and a reduction in the peak memory requirement of programs. While this technique has already been shown to yield benefits for eager first-order languages, the lack of a statically determinable execution order and the presence of closures pose new challenges for lazy languages. These require changes both in the liveness analysis itself and in the design of the garbage collector. To show the effectiveness of our method, we implemented a copying collector that uses the results of the liveness analysis to preserve live objects, both evaluated (i.e., in WHNF) and closures. Our experiments confirm that for programs running with a liveness-based garbage collector, there is a significant decrease in peak memory requirements. In addition, a sizable reduction in the number of collections ensures that in spite of using a more complex garbage collector, the execution times of programs running with liveness and reachability-based collectors remain comparable