Linear Lambda Research Articles

Universal and nonuniversal features in the crossover from linear to nonlinear interface growth

We study a restricted solid-on-solid model involving deposition and evaporation with probabilities p and 1 - p, respectively, in one-dimensional substrates. It presents a crossover from Edwards-Wilkinson (EW) to Kardar-Parisi-Zhang (KPZ) scaling for p approximately 0.5. The associated KPZ equation is analytically derived, exhibiting a coefficient lambda of the nonlinear term proportional to q identical with p - 1/2, which is confirmed numerically by calculation of tilt-dependent growth velocities for several values of p. This linear lambda - q relation contrasts to the apparently universal parabolic law obtained in competitive models mixing EW and KPZ components. The regions where the interface roughness shows pure EW and KPZ scaling are identified for 0.55< or =p< or =0.8, which provides numerical estimates of the crossover times tc. They scale as tc approximately lambda -phi with phi=4.1+/-0.1, which is in excellent agreement with the theoretically predicted universal value phi=4 and improves previous numerical estimates, which suggested phi approximately 3.

Weak typed Böhm theorem on IMLL

In the Böhm theorem workshop on Crete, Zoran Petric called Statman’s “Typical Ambiguity theorem” the typed Böhm theorem. Moreover, he gave a new proof of the theorem based on set-theoretical models of the simply typed lambda calculus. In this paper, we study the linear version of the typed Böhm theorem on a fragment of Intuitionistic Linear Logic. We show that in the multiplicative fragment of intuitionistic linear logic without the multiplicative unit 1 (for short IMLL) the weak typed Böhm theorem holds. The system IMLL exactly corresponds to the linear lambda calculus with multiplicative pairing. The system IMLL also exactly corresponds to the free symmetric monoidal closed category without the unit object. As far as we know, our separation result is the first one with regard to these systems in a purely syntactical manner.

The Linear Logical Abstract Machine

We derive an abstract machine from the Curry-Howard correspondence with a sequent calculus presentation of Intuitionistic Propositional Linear Logic. The states of the register based abstract machine comprise a low-level code block, a register bank and a dump holding suspended procedure activations. Transformation of natural deduction proofs into our sequent calculus yields a type-preserving compilation function from the Linear Lambda Calculus to the abstract machine. We prove correctness of the abstract machine with respect to the standard call-by-value evaluation semantics of the Linear Lambda Calculus.

Synthetic Domain Theory and Models of Linear Abadi & Plotkin Logic

In a recent article [L. Birkedal, R. E. Møgelberg, and R. L. Petersen. Parametric domain-theoretic models of linear Abadi & Plotkin logic. Technical Report TR-2005-57, IT University of Copenhagen, February 2005] the first two authors and R.L. Petersen have defined a notion of parametric LAPL-structure. Such structures are parametric models of the equational theory PILLY, a polymorphic intuitionistic / linear type theory with fixed points, in which one can reason using parametricity and, for example, solve a large class of domain equations [L. Birkedal, R. E. Møgelberg, and R. L. Petersen. Parametric domain-theoretic models of linear Abadi & Plotkin logic. Technical Report TR-2005-57, IT University of Copenhagen, February 2005, L Birkedal, R. E. Møgelberg, and R. L. Petersen. Parametric domain-theoretic models of polymorphic intuitionistic / linear lambda calculus. In Proceedings of the Twenty-first Conference on the Mathematical Foundations of Programming Semantics, 2005. To appear].Based on recent work by Simpson and Rosolini [G. Rosolini and A. Simpson. Using synthetic domain theory to prove operational properties of a polymorphic programming language based on strictness. Manuscript, 2004] we construct a family of parametric LAPL-structures using synthetic domain theory and use the results of loc. cit. and results about LAPL-structures to prove operational consequences of parametricity for a strict version of the Lily programming language. In particular we can show that one can solve domain equations in the strict version of Lily up to ground contextual equivalence.

Diffusion of Single Star-Branched Dendrimer-like DNA

We report a single-molecule fluorescence study on the diffusion of star-branched polymer dendrimer-like DNA (DL-DNA). The DL-DNA molecules were synthesized from ligating Y-shaped DNA to the fourth generation. It was found through single particle tracking that the diffusion coefficient of DL-DNA changes in a nonmonotonic fashion with its increased concentration possibly due to arm arrest and arm retraction. The diffusion of DL-DNA in linear lambda DNA solution displayed a monotonic concentration dependence 1 order of magnitude greater than the diffusion of DL-DNA in DL-DNA solution. This difference is attributed to the different conformation of DL-DNA and lambda DNA and the entanglement of lambda DNA with a large radius of gyration. Our diffusion study facilitates DL-DNA transportation for drug delivery.

Evaluation of on-line flue gas measurements by MISiCFET and metal-oxide sensors in boilers

Metal insulator silicon carbide field-effect transistor sensors, metal-oxide sensors, and a linear Lambda sensor in an electronic nose was used to measure on-line in hot flue gases from a boiler. Flue gas from a 100-MW pellets-fuelled boiler has been used to feed the experimental setup. Several reference instruments, which measure the flue gases in parallel to the sensor array, are connected to the electronic nose. Data was collected during six weeks and then evaluated. Using principal component analysis as the data evaluation method, different operating modes for the boiler have been identified in the data set. The different modes could be described in terms of high or low O/sub 2/ and CO concentration. Furthermore, we have shown that it seems possible to use a sensor array to determine the operating mode of the boiler and, by partial least-squares models, measure the CO concentration when the boiler operates in its optimum mode.

A Lambda Calculus for Quantum Computation

The classical lambda calculus may be regarded both as a programming language and as a formal algebraic system for reasoning about computation. It provides a computational model equivalent to the Turing machine and continues to be of enormous benefit in the classical theory of computation. We propose that quantum computation, like its classical counterpart, may benefit from a version of the lambda calculus suitable for expressing and reasoning about quantum algorithms. In this paper we develop a quantum lambda calculus as an alternative model of quantum computation, which combines some of the benefits of both the quantum Turing machine and the quantum circuit models. The calculus turns out to be closely related to the linear lambda calculi used in the study of linear logic. We set up a computational model and an equational proof system for this calculus, and we argue that it is equivalent to the quantum Turing machine.

Chromatographic behaviour and purification of linear lambda phage and plasmid DNA molecules on 2-hydroxyethyl methacrylate–ethylene dimethacrylate-based supports

The HEMA-BIO 1000 support, which is based on a copolymer of 2-hydroxyethyl methacrylate and ethylene dimethacrylate, was used for separation of lambda DNA and its fragments and plasmid pBR322 DNA. The separation of fragments greater than 6.6 kbp was demonstrated according to the slalom chromatography mechanism on column for size-exclusion chromatography in the case of linear lambda DNA fragments. The influence of particle size of column packing, mobile phase rate, and KCl concentration in mobile phase is discussed. The purification of plasmid DNA pBR322 using size-exclusion chromatography was more rapid compared to gel electrophoresis. The presence of salts in the eluate is not disadvantageous. DNA can be recovered from the eluate by ethanol precipitation. Plasmid DNA pBR322 isolated in this way was suitable for different biological applications (cleavage with restrictases, electrotransformation into bacterial cells).

Principles of solid state oxygen sensors for lean combustion gas control

This paper gives an overview about oxygen sensors for automotive applications to control the air–fuel ratio in order to reduce emissions and fuel consumption. The three-way catalyst system (TWC) using the potentiometric sensors based on zirconia represents the most effective system for the emission control at this time. New control strategies with linear lambda control at λ=1, for direct injection engines and other lean burn engines operating with excess air ( λ>1) need alternative sensor concepts. Hence, current limiting electrochemical pumping cells (amperometric sensors) based on zirconia have been developed for engine control applications. As a future option we present also new research works in resistive type oxygen sensors based on semiconducting metal oxides.

Operational Properties of Lily, a Polymorphic Linear Lambda Calculus with Recursion

Plotkin has advocated the combination of linear lambda calculus, polymorphism and fixed point recursion as an expressive semantic metalanguage. We study its expressive power from an operational point of view. We show that the naturally call-by-value operators of linear lambda calculus can be given a call-by-name semantics without affecting termination at exponential types and hence without affecting ground contextual equivalence. This result is used to prove properties of a logical relation that provides a new extensional characterisation of ground contextual equivalence and relational parametricity properties of polymorphic types.

Girard translation and logical predicates

We present a short proof of a folklore result: the Girard translation from the simply typed lambda calculus to the linear lambda calculus is fully complete. The proof makes use of a notion of logical predicates for intuitionistic linear logic. While the main result is of independent interest, this paper can be read as a tutorial on this proof technique for reasoning about relations between type theories.

Separation of Different Conformations of Plant Mitochondrial DNA Molecules by Field Inversion Gel Electrophoresis

Mitochondrial (mt) DNA structure in higher plants is still unclear as to the circularity or linearity of the genome. We have developed a system to electrophoretically separate distinct populations of mtDNA, with some populations enriched for networked linear and circular DNA molecules. Using field inversion gel electrophoresis (FIGE) and electron microscopy (EM), we have identified four distinct populations of mtDNA from two Brassica species. Using FIGE, two slow migrating mtDNA populations ran faster than a 66 kbp Escherichia coli circular plasmid marker, while these same populations comigrated in the compression zone in contour-clamped homogeneous electrophoretic field (CHEF) gels. A fast-migrating mtDNA population was also resolved by FIGE as a diffuse band between 20 to 70 kbp when compared with linear lambda (λ) markers. FIGE resolved the 66 kbp circular marker into several multimers, while CHEF resolved only open-circular monomers and linears. In agreement with FIGE results, EM analysis indicated the two slow migrating mtDNA populations contained circular (both supercoiled and relaxed circles) and free linear molecules of 10-60 kbp, and networked linear molecules of 45–140 kbp total size that may represent recombination intermediates. The fast migrating population consisted of 10–50 kbp linear molecules. Well-bound mtDNA showed only long linear molecules of 40–150 kbp with no detection of circles or complex/rosette molecules. This report shows that FIGE has clear advantages over CHEF for separating large DNA molecules with different conformations, and may be very useful for studies to characterize genome structure in complex systems such as plant mitochondria.

Call-by-name, Call-by-value, Call-by-need, and the Linear Lambda Calculus

Girard described two translations of intuitionistic logic into linear logic, one where A → B maps to (!A) –○ B, and another where it maps to !(A –○ B). We detail the action of these translations on terms, and show that the first corresponds to a call-by-name calculus, while the second corresponds to call-by-value. We further show that if the target of the translation is taken to be an affine calculus, where ! controls contraction but weakening is allowed everywhere, then the second translation corresponds to a call-by-need calculus, as recently defined by Ariola, Felleisen, Maraist, Odersky and Wadler. Thus the different calling mechanisms can be explained in terms of logical translations, bringing them into the scope of the Curry-Howard isomorphism.

Atypical sieving of open circular DNA during pulsed field agarose gel electrophoresis

Pulsed field agarose gel (PFG) electrophoresis, originally used to improve the resolution by length of linear DNA [Cantor et al. (1988) Annu. Rev. Biophys. Biophys. Chem. 17, 287-304], is found here to cause atypical sieving of 48.5-97.0-kb open circular DNA. Two procedures of PFG electrophoresis are used: rotating gel electrophoresis with rotation of 2 pi radians [2 pi RGE; Serwer, P., & Hayes, S.J. (1989) Appl. Theor. Electrophor. (in press)] and field inversion gel electrophoresis [FIGE; Carle, G.F., Frank, M., & Olson, M. V. (1986) Science 232, 65-68]. During 2 pi RGE at 6 V/cm, the electrophoretic mobility (mu) of 48.5-kb open circular DNA increases in magnitude as agarose percentage (A) increases from 0.4 to 1.5. The sieving revealed by this mu vs A relationship is highly atypical (possibly unique) for any particle. The extent of this atypical sieving increases as electrical potential gradient, DNA length, and pulse time increase. In some cases a maximum is observed in a plot of mu's magnitude vs A. The mu of open circular lambda DNA is smaller in magnitude than the mu of equally long linear lambda DNA. Atypical sieving has also been observed by use of FIGE. As pulse times used during FIGE decrease below those achievable by 2 pi RGE, the progressive loss of circular DNA's atypical sieving is accompanied by both a dramatic increase in mu's magnitude at the lower A values and a decrease in mu's magnitude at the higher A values. At the lower A values, open circular DNA sometimes migrates more rapidly than linear DNA of the same length.(ABSTRACT TRUNCATED AT 250 WORDS)

Light Chain Nephropathy

In 13 specimens of renal tissue from 11 patients, deposits of monoclonal immunoglobulin light chains and continuous granular electron-dense material within tubular basement membranes and in association with the glomerular basement membrane were identified. All but one patient were men n the fifth to seventh decades of life, and each presented with azotemia and features of glomerular rather than tubulointerstitial disease. Osteolytic bone lesions occurred in only three patients, and a bone marrow plasmacytosis greater than 30 percent consistent with plasma cell myeloma was identified in only four patients. Light chain distribution in the nephron was confirmed with immunoelectron microscopy and was not associated with deposition of other serum proteins such as immunoglobulin heavy chains, complement, transferrin, alpha 2 macroglobulin and albumin. The electron dense deposits differed in distribution and character from those associated with membranoproliferative glomerulonephritis type II (dense deposit disease), amyloidosis, cryoglobulinemia, macroglobulinemia and benign monoclonal gammopathy. Serum from six of these patients did not bind to normal human or rat renal parenchyma in vitro. Kappa light chain nephropathy was characterized by predominant linear tubular basement membrane kappa deposits, and nodular mesangial and linear glomerular basement membrane kappa immunostaining. Lambda light chain nephropathy was characterized by linear lambda glomerular basement membrane and tubular basement membrane immunostaining. Manifestations of glomerular dysfunction dominated the clinical presentation of light chain nephropathy, and most patients did not have typical features of multiple myeloma. The diagnosis was predicated upon thorough immmunohistologic assessment of renal biopsy material.

A site-specific endodeoxyribonuclease from Streptomyces albus CMI 52766 sharing site-specificity with Providencia stuartii endonuclease PstI.

A class II site-specific endodeoxyribonuclease (SalPI) was identified in cell-free extracts of Streptomyces albus CMI 52766 after high speed centrifugation and fractionation through Bio Gel AO.5M. SalPI cleaves lambda DNA into at least 18 fragments. Five cleavage sites were located in the linear lambda map by the use of double and triple restriction enzyme digests involving EcoRI, HindIII, SalGI and another new Streptomyces enzyme, SacI. The results were indistinguishable from those previously obtained for a Providencia stuartii enzyme, PstI, by Smith, Blattner & Davies (Nucleic Acids Res. 1976 3, 343). SalPI and PstI were shown by a double digest test to have the same site specificity. None of 34 phages tested was obviously restricted by S. albus CMI 52766, and correspondingly DNA from two of them was not cleaved in vitro by SalPI. DNA from Streptomyces phage that does not form plaques on S. albus CMI 52766, and plasmid SCP2 DNA from S. coelicolor A3 (2), were both cleaved.

Dependence of transfection efficiency of calcium treated Escherichia coli cells on bacterial genotype and form of Lambda DNA.

The transfecting activity of linear lambda DNA is 100 times higher in calcium treated E. coli K12 (lambda i434) than in non-lysogenic strains: the levels of transfection are 1-2.10(7) and 1-2.10(5) infective centers per 1 mug of lambda DNA respectively. The high efficiency of lysogenic cells transfection is not due to the spontaneously liberated "helper" phage. Evidently, it is called forth by transfecting DNA-prophage recombination or/and by inhibition of nuclease activity in lysogenic cells. Both ring forms lambda DNA (supercoiled and open circles) show very low infectivity, if any, in calcinated cells.

Ethidium binding affinity of circular lambda deoxyribonucleic acid determined fluorometrically.

Ethidium-binding isotherms for purified circular lambda DNA, isolated from a superinfected lysogen, and for linear lambda DNA, isolated from the purified phage, were constructed from fluorescence measurements of ethidium-DNA MIXTURES. The measurements were made in 0.01 M Tris-HC1-0.001 M EDTA,pH 7.1, buffer at 20 degrees and in the same buffer containing 0.1, 0.4, or 1.0 M NaC1. When NaC1 was present, differences in the binding affinity for supercoiled and linear DNA could be quantitated. As the ethidium concentration was increased, supercoiled lambda DNA molecules bound the intercalating dye first more and then less avidly than nonsupercoiled ones. The number of potential supercoils in a circular lambda DNA molecular in the absence of dye was calculated from the amount of dye bound when it exhibited the same affinity for dye as its linear counterpart. The point of equivalent affinity shifted from 0.053 mol of dye bound per mol of nucleotide in 0.1 M NaC1 to 0.067 mol in 1.0 M NaC1. This corresponds to the removal of 164 and 206 supercoiling turns per molecule and superhelix densities in the absence of dye equal to 0.036 and 0.045 superhelical turns per 10 base pairs. If this difference in the number of supercoils reflects a salt-dependent change in the average rotation angle between base pairs of the Watson-Crick helix the angle differs by 0.32% in the two ionic environments.

Purification of closed circular lambda deoxyribonucleic acid and its sedimentation properties as a function of Sodium chloride concentration and ethidium binding.

The sedimentation of circular lambda DNA suggests that the molecular undergoes significant changes in shape and super-coiling as the NaC1 concentration increases. Closed circular lambda DNA, species I, isolated and purified from superinfected immune bacteria, sediments in sucrose gradients of low ionic strength at a rate 2.0 times faster than linear lambda DNA, species III. The addition of ethidium causes the sedimentation rate of species I DNA to decrease until enough dye is bound to remove 121 supercoils per molecule. At this point, species I co-sediments with nicked and nonsupercoiled species II. Futher additions of ethidium cause the sedimentation rate to increase until the relative rate of species I is again at least twice that of species III. This classical behavior is altered when NaC1 is present in the buffer. In 1.0 M NaC1 the changes in S are complex. Initially, species I sediments 1.55 times faster than species III. Titration with ethidium caused a decrease in S to an early minimum value, than an increase to a first maximum, followed by a decrease to the S of species II. At this point enough dye has intercalated to remove 208 superhelical turns. Further additions of dye introduce supercoils and cause S to increase again. In 0.1 to 0.4 M NaC1 the relative S of species I is 1.69 and 1.59, respectively. If titrated with ethidium, S first increases to a maximum value then decreases to the minimum rate when enough dye is bound to remove 158 and 183 supercoils, respectively. The results indicate an increase in the superhelix density from 0.026 turns per 10 base pairs in buffer alone to 0.045 in the same buffer with 1.0 M NaC1. If this change in superhelix density results from a concomitant change in the average rotation angle between base pairs in the Watson-Crick helix, the addition of 1.0 M NaC1 alters the rotation angle by 0.68 degrees per base pair.