Isoperimetric Problem and Meta-fibonacci Sequences

Let G = (V,E) be a simple, finite, undirected graph. For S ⊆ V, let $\delta(S,G) = \{ (u,v) \in E : u \in S \mbox { and } v \in V-S \}$ and $\phi(S,G) = \{ v \in V -S: \exists u \in S$ , such that (u,v) ∈ E} be the edge and vertex boundary of S, respectively. Given an integer i, 1 ≤ i ≤ ∣ V ∣, the edge and vertex isoperimetric value at i is defined as b e (i,G) =  min S ⊆ V; |S| = i |δ(S,G)| and b v (i,G) =  min S ⊆ V; |S| = i |φ(S,G)|, respectively. The edge (vertex) isoperimetric problem is to determine the value of b e (i, G) (b v (i, G)) for each i, 1 ≤ i ≤ |V|. If we have the further restriction that the set S should induce a connected subgraph of G, then the corresponding variation of the isoperimetric problem is known as the connected isoperimetric problem. The connected edge (vertex) isoperimetric values are defined in a corresponding way. It turns out that the connected edge isoperimetric and the connected vertex isoperimetric values are equal at each i, 1 ≤ i ≤ |V|, if G is a tree. Therefore we use the notation b c (i, T) to denote the connected edge (vertex) isoperimetric value of T at i. Hofstadter had introduced the interesting concept of meta-fibonacci sequences in his famous book “Gödel, Escher, Bach. An Eternal Golden Braid”. The sequence he introduced is known as the Hofstadter sequences and most of the problems he raised regarding this sequence is still open. Since then mathematicians studied many other closely related meta-fibonacci sequences such as Tanny sequences, Conway sequences, Conolly sequences etc. Let T 2 be an infinite complete binary tree. In this paper we related the connected isoperimetric problem on T 2 with the Tanny sequences which is defined by the recurrence relation a(i) = a(i − 1 − a(i − 1)) + a(i − 2 − a(i − 2)), a(0) = a(1) = a(2) = 1. In particular, we show that b c (i, T 2) = i + 2 − 2a(i), for each i ≥ 1. We also propose efficient polynomial time algorithms to find vertex isoperimetric values at i of bounded pathwidth and bounded treewidth graphs.

A simple and rapid method for quantification of hapten specific antibodies

A sensitive and simple method for quantification of antibodies against small molecules is described using DNP-lysozyme as the enzyme conjugate. The anti-DNP antiserum was raised against DNP-bovin serum albumin conjugate. Anti-DNP antibody or its monovalent fragment (Fab) reduced the enzyme activity of DNP-lysozyme conjugate in a concentration-dependent manner. The inhibition of enzyme activity is a specific measure of the antibody and Fab content of the sample. The specificity of the reaction was assessed by reduction of antibody-induced inhibition by DNP-lysine. The ability of DNP-lysine to reduce the antibody-induced inhibition of DNP-lysozyme activity also makes possible a sensitive assay for DNP-lysine.

Preparation of lower oxide of sulphur

RECENT work on the lower oxide of sulphur1,2 has established that disulphur monoxide (S2O) or its polymeric form is produced when sulphur is burnt in oxygen under reduced pressure. It has now been shown that it is possible to make use of an oxide of a heavy metal as a source of limited supply of oxygen to prepare the disulphur monoxide. For example, when a mixture of finely powdered cupric oxide and sulphur (1 : 5 by weight) is heated under vacuum in a glass tube gaseous products are evolved. which, on cooling in a trap surrounded by liquid air, will give an orange-red condensate (S2O)x. This condensate also gives off sulphur dioxide in stages as the temperature is raised, finally leaving a residue of elemental sulphur. Copper sulphide and excess of sulphur are left behind in the reaction tube.

Fatty acid component of vitamin A ester in sheep liver

Vitamin A, when extracted along with other lipids from sheep liver, had an E1cm.1% value of 14.4, which was raised to 45.57 on removal of the phospholipids by cold acetone. Selective hydrolysis of triglycerides by an extract of acetone-dried sheep pancreas in the presence of HgCl2 as inhibitor of vitamin A esterase, followed by chromatography through alumina gave a product with E1cm.1% value of 276. This on chromatography through magnesium oxide raised the E1cm.1, value to 601.5, representing 64% pure vitamin A ester calculated as palmitate, and the total recovery was 23% of the starting oil. The purified ester preparation, when subjected to reverse-phase chromatography on silicone-impregnated paper, gave a single ultraviolet fluorescent band. The fluorescent band on hydrolysis gave only one fatty acid. This was conclusively identified to be palmitic acid.

Characterization of viral proteins ofOryctes baculovirus and comparison between two geographical isolates

BacilliformOryctes baculovirus particles have been visualized in electron micrographs of midgut sections from virus infectedOryctes rhinoceros beetles. Morphologically the Indian isolate (Oryctes baculovirus, KI) resembled the previously reportedOryctes baculovirus, isolate PV505. The constituent proteins of baculovirus KI have been analysed by sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE) and by Western blots using polyclonal antibodies raised against the complete viral particles, as probes. A total of forty eight viral proteins have been identified. Fourteen viral proteins were located on the viral envelope. Among the proteins constituting the nucleocapsid, three were located internally within the capsid. A 23.5 kDa protein was tightly associated with viral DNA in the nucleocapsid core. Two envelope and seven capsid proteins stained positive for glycosylation. Comparison between the viral proteins of KI and PV505 revealed differences in SDS-PAGE profiles and glycosylation patterns. Immunoblotting of KI and PV505 proteins with anti KI antiserum demonstrated antigenic differences between the two viral isolates.

IPCC:accomplishments,controversies and challenges

The Intergovernmental Panel on Climate Change (IPCC) has successfully produced four assessment reports since 1990 along with a number of special reports and greenhouse gas inventory guidelines. It has very rigorous and robust procedures and guidelines for preparing the assessment reports largely based on synthesis of peer-reviewed and published scientific literature. IPCC has attracted controversy since the Second Assessment Report of 1995. The recent controversies surrounding the IPCC reports surfaced nearly two years after the release of the report in 2007, especially in the wake of the crucial Copenhagen Climate Convention. Many of the controversies can be traced to the use of information sourced from reports published outside the scientific journals such as reports of the World Wildlife Fund. It is true that there are a few errors in the IPCC reports, which may have escaped the multilayered rigorous review process. Many of the errors found in the main reports, which are over a thousand page each, have not been quoted in the crucial and most referred Summary for Policy Makers. IPCC may have to develop a more robust policy for sourcing literature published outside the scientific journals. The United Nations Secretary General has requested the prestigious Inter-Academy Council to review the IPCC principles, procedures and guidelines. The controversies raised in the recent past do not in any way change the main conclusions of the IPCC Assessment Report.

Induction of allergen-specific IgE and IgG responses by anti-idiotypic antibodies

In order to explore idiotypic, anti-idiotypic, and anti-anti-idiotypic responses to allergens, BALB/c mice were immunized with affinity- purified human idiotypic antibodies directed against a highly purified shrimp allergen. This resulted in the production of anti-idiotypic antibodies which were quantitated by using rabbit idiotypic antibodies raised against the same purified allergen. The mouse anti-idiotypic antibodies recognized shrimp-specific human idiotypic antibodies of the IgE isotype from 18 of 20 individuals, and IgG antibodies from 14 of 20 shrimp-sensitive patients. Immunization of BALB/c mice with affinity- purified, allergen-specific anti-idiotypic antibodies induced anti- allergen IgE and IgG responses in the absence of the allergen. This paper thus presents evidence that anti-idiotypic antibodies raised against allergen-specific idiotypic antibodies may substitute for the original allergen in the induction of allergen-specific idiotypic antibodies. The demonstration of shared idiotopes on IgG and IgE antibodies in the sera of shrimp-sensitive patients supports the use of allergen-specific anti-idiotypic antibodies as surrogate allergens.

Binding of deoxyadenylate and deoxycytidylate antibodies to double-stranded DNA

Antibodies raised against deoxyadenylate and deoxycytidylate were found to react with double stranded DNA as assessed by highly sensitive avidin-biotin microELISA. The binding was specific as it was completely inhibited by the homologous hapten. The antibodies did not react with tRNA and rRNA. These antibodies were also shown to react with supercoiled and relaxed forms of pBR322 DNA as demonstrated by gel retardation assay. ssDNA, single-stranded DNA; dsDNA, double-stranded DNA; CT DNA, calf thymus DNA; AB microELISA, avidin-biotin microELISA; dpA, deoxyadenylate; dpC, deoxycytidylate; avidin-HRP, avidin-horseradish peroxidase

Cytotoxic activity of daunomycin and adriamycin encapsulated in immunoliposomes against avian myeloblastosis virus-infected cells

Immunoliposomes were prepared using the antibody raised against the avian myeloblastosis virus envelope glycoprotein, gp80. Adriamycin was encapsulated into immunoliposomes. More drug was delivered into target cells when the drug encapsulated in immunoliposomes was incubated with the cells. The drug encapsulated in immunoliposomes was able to inhibit the RNA synthesis twice more than free drug in the virus-transformed myeloblasts. Pre-treatment of cells with ammonium chloride, reversed the effect of drug encapsulated in immunoliposomes. The drugs encapsulated in immunoliposomes had marginal effect on the RNA synthesis of non-target cells, the yolk sac cells. Colony formation by virus-transformed cells and focus formation by virus-infected yolk sac cells was inhibited significantly by the drug encapsulated in immunoliposomes.

Passive immunization with an antibody to the beta-subunit of ovine luteinizing hormone as a method of early abortion--a feasibility study in monkeys (Macaca radiata)

Antiserum to the beta-subunit of ovine luteinizing hormone (oLH-beta) raised in monkeys (Macaca radiata) has been tested by a variety of criteria both in vivo and in vitro to establish its ability to neutralize oLH, hLH, and human chorionic gonadotropin (hCG). Passive administration of this antiserum caused inhibition of ovulation and termination of pregnancy in recipient monkeys as indicated by premature vaginal bleeding and a significant reduction in serum progesterone and estrogen levels. The results suggest that antiserum raised in monkeys against oLH-beta can neutralize monkey LH as well as monkey CG.

A monoclonal antibody recognizing the C-terminal region of chicken egg white riboflavin carrier protein terminates early pregnancy in mice

In order to identify the functionally relevant epitopes on chicken riboflavin carrier protein, we have raised monoclonal antibodies to the vitamin carrier. One of these, 6B2C12, was found to interact specifically with a synthetic oligopeptide corresponding to the C-terminal 17 amino acid residues of the chicken egg white riboflavin carrier protein, which is missing in part in the egg yolk riboflavin carrier protein. This epitope is conserved through evolution in mammals including humans. Administration of the ascites fluid of 6B2C12 to pregnant mice intraperitoneally, resulted in the termination of pregnancy indicating that this epitope is involved in or closely associated with the transplacental transport of the vitamin from the maternal circulation to the growing fetus.

Characterization of hot deformation behavior of brasses using processing maps: Part II. β Brass and α-β brass

The hot deformation behaviors of β brass in the temperature range of 550°C to 800°C and α-β brass in the temperature range of 450°C to 800°C have been characterized in the strain rate range of 0.001 to 100 s−1 using processing maps developed on the basis of the Dynamic Materials Model. The map for β brass revealed a domain of superplasticity in the entire temperature range and at strain rates lower than 1 s−1, with a maximum efficiency of power dissipation of about 68 pct. The temperature variation of the efficiency of power dissipation in the domain is similar to that of the diffusion coefficient for zinc in β brass, confirming that the diffusion-accommodated flow controls the superplasticity. The material undergoes microstructural instability in the form of adiabatic shear bands and strain markings at temperatures lower than 700°C and at strain rates higher than 10 s−1. The map for α-β brass revealed a wide domain for processing in the temperature range of 550°C to 800°C and at strain rates lower than 1 s−1, with a maximum efficiency of 54 pct occurring at about 750°C and 0.001 s−1. In the domain, the α phase undergoes dynamic recrystallization and controls the hot deformation of the alloy, while the β phase deforms superplastically. At strain rates greater than 1 s−1, α-β brass exhibits microstructural instabilities manifested as flow rotations at lower temperatures and localized shear bands at higher temperatures.

Preparation and characterization of immunoliposomes for targeting of antiviral agents

Antibodies specific to avian myeloblastosis virus envelope glycoprotein gp80 were raised. Immunoliposomes were prepared using anti-avian myeloblastosis virus envelope glycoprotein gp80 antibody. The antibody was palmitoylated to facilitate its incorporation into lipid bilayers of liposomes. The fluorescence emission spectra of palmitoylated IgG have exhibited a shift in emission maximum from 330 to 370 nm when it was incorporated into the liposomes. At least 50% of the incorporated antibody molecules were found to be oriented towards the outside in the liposomes. The average size of the liposome was found to be 300 A, and on an average, 15 antibody molecules were shown to be present in a liposome. When adriamycin encapsulated in immunoliposomes was incubated in a medium containing serum for 72 h, about 75% of the drug was retained in liposomes. In vivo localization studies, revealed an enhanced delivery of drug encapsulated in immunoliposomes to the target tissue, as compared to free drug or drug encapsulated in free liposomes. These data suggest a possible use of the drugs encapsulated in immunoliposomes to deliver the drugs in target areas, thereby reducing side effects caused by antiviral agents.

A Bilinear Constitutive Model for Isotropic Bimodulus Materials

Proper formulation of stress-strain relations, particularly in tension-compression situations for isotropic biomodulus materials, is an unresolved problem. Ambartsumyan's model [8] and Jones' weighted compliance matrix model [9] do not satisfy the principle of coordinate invariance. Shapiro's first stress invariant model [10] is too simple a model to describe the behavior of real materials. In fact, Rigbi [13] has raised a question about the compatibility of bimodularity with isotropy in a solid. Medri [2] has opined that linear principal strain-principal stress relations are fictitious, and warned that the bilinear approximation of uniaxial stress-strain behavior leads to ill-working bimodulus material model under combined loading. In the present work, a general bilinear constitutive model has been presented and described in biaxial principal stress plane with zonewise linear principal strain-principal stress relations. Elastic coefficients in the model are characterized based on the signs of (i) principal stresses, (ii) principal strains, and (iii) on the value of strain energy component ratio ER greater than or less than unity. The last criterion is used in tension-compression and compression-tension situations to account for different shear moduli in pure shear stress and pure shear strain states as well as unequal cross compliances.

Antigenic determinants on chicken riboflavin carrier protein. A study with monoclonal antibodies

Monoclonal antibodies raised against chicken egg white riboflavin carrier protein were classified into seven categories each recognizing a distinct epitope. Of these, six were directed against conformation dependent epitopes and one to a sequential epitope. The roles of lysine residues and the post-translationally attached phosphate and oligosaccharide moieties in the antigenicity of riboflavin carrier protein recognized by the monoclonal antibodies were investigated. The binding region of three monoclonal antibodies could be located within the 87–219 amino acid sequence of the protein and one antibody among these recognized a sequence of 182–204 amino acid residues. All the monoclonal antibodies were able to recognize riboflavin carrier proteins present in the sera of pregnant rats, cows and humans indicating that the epitopes to which they are directed are conserved through evolution from chicken to the human.