Counting proofs in propositional logic

We give a procedure for counting the number of different proofs of a formula in various sorts of propositional logic. This number is either an integer (that may be 0 if the formula is not provable) or infinite

Absence of Ground States for a Class of Translation Invariant Models of Non-relativistic QED

We consider a class of translation invariant models of non-relativistic QED with net charge. Under certain natural assumptions we prove that ground states do not exist in the Fock space

Elongation and fluctuations of semi-flexible polymers in a nematic solvent

We directly visualize single polymers with persistence lengths ranging from $\ell_p=0.05$ to 16 $\mu$m, dissolved in the nematic phase of rod-like {\it fd} virus. Polymers with sufficiently large persistence length undergo a coil-rod transition at the isotropic-nematic transition of the background solvent. We quantitatively analyze the transverse fluctuations of semi-flexible polymers and show that at long wavelengths they are driven by the fluctuating nematic background. We extract both the Odijk deflection length and the elastic constant of the background nematic phase from the data.Comment: 4 pages, 4 figures, submitted to PR

Formation and Interaction of Membrane Tubes

We show that the formation of membrane tubes (or membrane tethers), which is a crucial step in many biological processes, is highly non-trivial and involves first order shape transitions. The force exerted by an emerging tube is a non-monotonic function of its length. We point out that tubes attract each other, which eventually leads to their coalescence. We also show that detached tubes behave like semiflexible filaments with a rather short persistence length. We suggest that these properties play an important role in the formation and structure of tubular organelles.Comment: 4 pages, 3 figure

Complexity Bounds for Ordinal-Based Termination

`What more than its truth do we know if we have a proof of a theorem in a given formal system?' We examine Kreisel's question in the particular context of program termination proofs, with an eye to deriving complexity bounds on program running times. Our main tool for this are length function theorems, which provide complexity bounds on the use of well quasi orders. We illustrate how to prove such theorems in the simple yet until now untreated case of ordinals. We show how to apply this new theorem to derive complexity bounds on programs when they are proven to terminate thanks to a ranking function into some ordinal.Comment: Invited talk at the 8th International Workshop on Reachability Problems (RP 2014, 22-24 September 2014, Oxford

Amici Curiae Brief of the International Municipal Lawyers Association and Legal Scholars in Support of Defendants-Appellees in Portland Pipe Line Corporation, et al. v. City of South Portland, et al.

This brief to the Maine Supreme Judicial Court was filed in support of the City of South Portland by the Amici Curiae, including the International Municipal Lawyers Association and legal scholars, to provide the Court with a background on the role of local governments in land use planning, and to explain why the City of South Portland’s Clear Skies Ordinance falls easily within the City’s authority and was not preempted by state legislation.After studying the potential for bulk loading of crude oil within its boundaries, the City of South Portland concluded that the infrastructure requirements and environmental impacts of the activity posed a threat to public health and welfare and were incompatible with the community’s vision of itself for the future. The City therefore decided to enact the Clear Skies Ordinance, which prohibits the storing and handling of petroleum or petroleum products for the bulk loading of crude oil onto any marine tank vessel in specified zoning districts. Litigation followed, with plaintiffs arguing that the City lacked authority to enact the Ordinance and that, even if it had such authority in the first instance, that authority had been preempted by other state law. Defendants prevailed on summary judgment in the U.S. District Court for the District of Maine, and during the course of an appeal to the United States Court of Appeals for the First Circuit, the Circuit certified several questions to the Maine Supreme Judicial Court. This brief was filed in support of the City with regard to those certified questions.The brief begins by discussing how central the role of local governments is in making land use decisions, emphasizing the highly localized impacts of land use decisions for public health and welfare. It then describes the zoning mechanisms by which local governments exercise their land use power, and discusses why the zoning power is so important for protecting public health and environmental quality, and responding to the changing needs of communities.Next, the brief explains the legal underpinnings of the City of South Portland’s home rule authority. The Constitution of the State of Maine contains a broad grant of home rule authority that is further strengthened by a statutorily imposed rebuttable presumption of validity for exercises of that authority. Local exercises of zoning authority are consistent within this home rule grant, and the brief discusses why the Clear Skies Ordinance falls squarely within the local zoning power. Finally, the brief explains why the Ordinance has not been expressly or impliedly preempted by state law. For all of those reasons, the brief concludes that the City’s enactment of the Ordinance was valid in the first instance and should not be overturned

Measuring surface-area-to-volume ratios in soft porous materials using laser-polarized xenon interphase exchange NMR

We demonstrate a minimally invasive nuclear magnetic resonance (NMR) technique that enables determination of the surface-area-to-volume ratio (S/V) of soft porous materials from measurements of the diffusive exchange of laser-polarized 129Xe between gas in the pore space and 129Xe dissolved in the solid phase. We apply this NMR technique to porous polymer samples and find approximate agreement with destructive stereological measurements of S/V obtained with optical confocal microscopy. Potential applications of laser-polarized xenon interphase exchange NMR include measurements of in vivo lung function in humans and characterization of gas chromatography columns.Comment: 14 pages of text, 4 figure

Identification of novel clostridium perfringens type E strains that carry an iota toxin plasmid with a functional enterotoxin gene

Clostridium perfringens enterotoxin (CPE) is a major virulence factor for human gastrointestinal diseases, such as food poisoning and antibiotic associated diarrhea. The CPE-encoding gene (cpe) can be chromosomal or plasmid-borne. Recent development of conventional PCR cpe-genotyping assays makes it possible to identify cpe location (chromosomal or plasmid) in type A isolates. Initial studies for developing cpe genotyping assays indicated that all cpe-positive strains isolated from sickened patients were typable by cpe-genotypes, but surveys of C. perfringens environmental strains or strains from feces of healthy people suggested that this assay might not be useful for some cpe-carrying type A isolates. In the current study, a pulsed-field gel electrophoresis Southern blot assay showed that four cpe-genotype untypable isolates carried their cpe gene on a plasmid of ~65 kb. Complete sequence analysis of the ~65 kb variant cpe-carrying plasmid revealed no intact IS elements and a disrupted cytosine methyltransferase (dcm) gene. More importantly, this plasmid contains a conjugative transfer region, a variant cpe gene and variant iota toxin genes. The toxin genes encoded by this plasmid are expressed based upon the results of RT-PCR assays. The ~65 kb plasmid is closely related to the pCPF4969 cpe plasmid of type A isolates. MLST analyses indicated these isolates belong to a unique cluster of C. perfringens. Overall, these isolates carrying a variant functional cpe gene and iota toxin genes represent unique type E strains. © 2011 Miyamoto et al

Ground State and Resonances in the Standard Model of Non-relativistic QED

We prove existence of a ground state and resonances in the standard model of the non-relativistic quantum electro-dynamics (QED). To this end we introduce a new canonical transformation of QED Hamiltonians and use the spectral renormalization group technique with a new choice of Banach spaces.Comment: 50 pages change

Generic flow profiles induced by a beating cilium

We describe a multipole expansion for the low Reynolds number fluid flows generated by a localized source embedded in a plane with a no-slip boundary condition. It contains 3 independent terms that fall quadratically with the distance and 6 terms that fall with the third power. Within this framework we discuss the flows induced by a beating cilium described in different ways: a small particle circling on an elliptical trajectory, a thin rod and a general ciliary beating pattern. We identify the flow modes present based on the symmetry properties of the ciliary beat.Comment: 12 pages, 6 figures, to appear in EPJ