Efficient Certified RAT Verification

Clausal proofs have become a popular approach to validate the results of SAT solvers. However, validating clausal proofs in the most widely supported format (DRAT) is expensive even in highly optimized implementations. We present a new format, called LRAT, which extends the DRAT format with hints that facilitate a simple and fast validation algorithm. Checking validity of LRAT proofs can be implemented using trusted systems such as the languages supported by theorem provers. We demonstrate this by implementing two certified LRAT checkers, one in Coq and one in ACL2

Directed and Elliptic Flow in Pb+Pb collisions at 40 and 158 AGeV

Directed and elliptic flow are reported for charged pions and protons as a function of transverse momentum, rapidity, and centrality in 40 and 158 AGeV Pb + Pb collisions. The standard method of correlating particles with an event plane is used. The directed flow of protons is small and shows little variation near to midrapidity, but rises fast towards projectile rapidity in the 40 AGeV data. For most peripheral collisions the flat region becomes negative resulting in $v_1$ changing sign three times. Elliptic flow doesn't seem to change very much from 40 AGeV to 158 AGeV. The difference is smaller than anticipated from the overall energy dependence from AGS to RHIC.Comment: Presented at 16th International Conference on Ultrarelativistic Nucleus-Nucelus Collisions, Quark Matter 2002 (QM 2002), Nantes, France, 18-24 Jul 2002, 4 pages, 3 figure

Efficient Certified Resolution Proof Checking

We present a novel propositional proof tracing format that eliminates complex processing, thus enabling efficient (formal) proof checking. The benefits of this format are demonstrated by implementing a proof checker in C, which outperforms a state-of-the-art checker by two orders of magnitude. We then formalize the theory underlying propositional proof checking in Coq, and extract a correct-by-construction proof checker for our format from the formalization. An empirical evaluation using 280 unsatisfiable instances from the 2015 and 2016 SAT competitions shows that this certified checker usually performs comparably to a state-of-the-art non-certified proof checker. Using this format, we formally verify the recent 200 TB proof of the Boolean Pythagorean Triples conjecture

QRAT+: Generalizing QRAT by a More Powerful QBF Redundancy Property

The QRAT (quantified resolution asymmetric tautology) proof system simulates virtually all inference rules applied in state of the art quantified Boolean formula (QBF) reasoning tools. It consists of rules to rewrite a QBF by adding and deleting clauses and universal literals that have a certain redundancy property. To check for this redundancy property in QRAT, propositional unit propagation (UP) is applied to the quantifier free, i.e., propositional part of the QBF. We generalize the redundancy property in the QRAT system by QBF specific UP (QUP). QUP extends UP by the universal reduction operation to eliminate universal literals from clauses. We apply QUP to an abstraction of the QBF where certain universal quantifiers are converted into existential ones. This way, we obtain a generalization of QRAT we call QRAT+. The redundancy property in QRAT+ based on QUP is more powerful than the one in QRAT based on UP. We report on proof theoretical improvements and experimental results to illustrate the benefits of QRAT+ for QBF preprocessing.Comment: preprint of a paper to be published at IJCAR 2018, LNCS, Springer, including appendi

Solving and Verifying the Boolean Pythagorean Triples Problem via Cube-and-Conquer

We solved a long-outstanding open problem in Ramsey theory, using SAT solving

New Human Papilloma Virus E2 Transcription Factor Mimics: A Tripyrrole-Peptide Conjugate with Tight and Specific DNA-Recognition

BACKGROUND: Human papillomavirus (HPV) is the main causative agent of cervical cancer, particularly high risk strains such us HPV-16, -18 and -31. The viral encoded E2 protein acts as a transcriptional modulator and exerts a key role in viral DNA replication. Thus, E2 constitutes an attractive target for developing antiviral agents. E2 is a homodimeric protein that interacts with the DNA target through an α-helix of each monomer. However, a peptide corresponding to the DNA recognition helix of HPV-16 E2 binds DNA with lower affinity than its full-length DNA binding domain. Therefore, in an attempt to promote the DNA binding of the isolated peptide, we have designed a conjugate compound of the E2 α-helix peptide and a derivative of the antibiotic distamycin, which involves simultaneous minor- and major-groove interactions. METHODOLOGY/PRINCIPAL FINDINGS: An E2 α-helix peptide-distamycin conjugate was designed and synthesized. It was characterized by NMR and CD spectroscopy, and its DNA binding properties were investigated by CD, DNA melting and gel shift experiments. The coupling of E2 peptide with distamycin does not affect its structural properties. The conjugate improves significantly the affinity of the peptide for specific DNA. In addition, stoichiometric amounts of specific DNA increase meaningfully the helical population of the peptide. The conjugate enhances the DNA binding constant 50-fold, maintaining its specificity. CONCLUSIONS/SIGNIFICANCE: These results demonstrate that peptide-distamycin conjugates are a promising tool to obtain compounds that bind the E2 target DNA-sequences with remarkable affinity and suggest that a bipartite major/minor groove binding scaffold can be a useful approach for therapeutic treatment of HPV infection

A kinematic analysis of the spine during rugby scrummaging on natural and synthetic turfs

Artificial surfaces are now an established alternative to grass (natural) surfaces in rugby union. Little is known, however, about their potential to reduce injury. This study characterises the spinal kinematics of rugby union hookers during scrummaging on third-generation synthetic (3G) and natural pitches. The spine was sectioned into five segments, with inertial sensors providing three-dimensional kinematic data sampled at 40 Hz/sensor. Twenty-two adult, male community club and university-level hookers were recruited. An equal number were analysed whilst scrummaging on natural or synthetic turf. Players scrummaging on synthetic turf demonstrated less angular velocity in the lower thoracic spine for right and left lateral bending and right rotation. The general reduction in the range of motion and velocities, extrapolated over a prolonged playing career, may mean that the synthetic turf could result in fewer degenerative injuries. It should be noted, however, that this conclusion considers only the scrummaging scenario

Parton coalescence at RHIC

Using a covariant coalescence model, we study hadron production in relativistic heavy ion collisions from both soft partons in the quark-gluon plasma and hard partons in minijets. Including transverse flow of soft partons and independent fragmentation of minijet partons, the model is able to describe available experimental data on pion, kaon, and antiproton spectra. The resulting antiproton to pion ratio is seen to increase at low transverse momenta and reaches a value of about one at intermediate transverse momenta, as observed in experimental data at RHIC. A similar dependence of the antikaon to pion ratio on transverse momentum is obtained, but it reaches a smaller value at intermediate transverse momenta. At high transverse momenta, the model predicts that both the antiproton to pion and the antikaon to pion ratio decrease and approach those given by the perturbative QCD. Both collective flow effect and coalescence of minijet partons with partons in the quark-gluon plasma affect significantly the spectra of hadrons with intermediate transverse momenta. Elliptic flows of protons, Lambdas, and Omegas have also been evaluated from partons with elliptic flows extracted from fitting measured pion and kaon elliptic flows, and they are found to be consistent with available experimental data.Comment: 12 pages, 11 figure

Relativistic Nucleus-Nucleus Collisions: from the BEVALAC to RHIC

I briefly describe the initial goals of relativistic nuclear collisions research, focusing on the LBL Bevatron/Bevalac facility in the 1970's. An early concept of high hadronic density fireball formation, and subsequent isentropic decay (preserving information as to the high density stage) led to an outline of physics observables that could determine the nuclear matter equation of state at several times nuclear ground state matter density. With the advent of QCD the goal of locating, and characterizing the hadron-parton deconfinement phase transformation suggested the need for higher $\sqrt{s}$, the research thus moving to the BNL AGS and CERN SPS, finally to RHIC at BNL. A set of physics observables is discussed where present data span the entire $\sqrt{s}$ domain, from Bevalac and SIS at GSI, to top RHIC energy. Referring, selectively, to data concerning bulk hadron production, the overall $\sqrt{s}$ evolution of directed and radial flow observables, and of pion pair Bose-Einstein correlation are discussed. The hadronization process is studied in the grand canonical statistical model. The resulting hadronization points in the plane T vs. $\mu_B$ converge onto the parton-hadron phase boundary predicted by finite $\mu_B$ lattice QCD, from top SPS to RHIC energy. At lower SPS and top AGS energy a steep strangeness maximum occurs at which the Wroblewski parameter $\lambda_s \approx$ 0.6; a possible connection to the QCD critical point is discussed. Finally the unique new RHIC physics is addressed: high $p_T$ hadron suppression and jet "tomography".Comment: 19 pages, 11 figure