Studies on the Spectrum and the Energy of Graphs

Department of Mathematics, Cochin University of Science and Technology

Design and study of self-assembled functional organic and hybrid systems for biological applications

The focus of self-assembly as a strategy for the synthesis has been confined largely to molecules, because of the importance of manipulating the structure of matter at the molecular scale. We have investigated the influence of temperature and pH, in addition to the concentration of the capping agent used for the formation of the nano-bio conjugates. For example, the formation of the narrower size distribution of the nanoparticles was observed with the increase in the concentration of the protein, which supports the fact that γ-globulin acts both as a controller of nucleation as well as stabiliser. As analyzed through various photophysical, biophysical and microscopic techniques such as TEM, AFM, C-AFM, SEM, DLS, OPM, CD and FTIR, we observed that the initial photoactivation of γ-globulin at pH 12 for 3 h resulted in small protein fibres of ca. Further irradiation for 24 h, led to the formation of selfassembled long fibres of the protein of ca. 5-6 nm and observation of surface plasmon resonance band at around 520 nm with the concomitant quenching of luminescence intensity at 680 nm. The observation of light triggered self-assembly of the protein and its effect on controlling the fate of the anchored nanoparticles can be compared with the naturally occurring process such as photomorphogenesis.Furthermore,our approach offers a way to understand the role played by the self-assembly of the protein in ordering and knock out of the metal nanoparticles and also in the design of nano-biohybrid materials for medicinal and optoelectronic applications. Investigation of the potential applications of NIR absorbing and water soluble squaraine dyes 1-3 for protein labeling and anti-amyloid agents forms the subject matter of the third chapter of the thesis. The study of their interactions with various proteins revealed that 1-3 showed unique interactions towards serum albumins as well as lysozyme. 69%, 71% and 49% in the absorption spectra as well as significant quenching in the fluorescence intensity of the dyes 1-3, respectively. Half-reciprocal analysis of the absorption data and isothermal titration calorimetric (ITC) analysis of the titration experiments gave a 1:1 stoichiometry for the complexes formed between the lysozyme and squaraine dyes with association constants (Kass) in the range 104-105 M-1. We have determined the changes in the free energy (ΔG) for the complex formation and the values are found to be -30.78, -32.31 and -28.58 kJmol-1, respectively for the dyes 1, 2 and 3. Furthermore, we have observed a strong induced CD (ICD) signal corresponding to the squaraine chromophore in the case of the halogenated squaraine dyes 2 and 3 at 636 and 637 nm confirming the complex formation in these cases. To understand the nature of interaction of the squaraine dyes 1-3 with lysozyme, we have investigated the interaction of dyes 1-3 with different amino acids. These results indicated that the dyes 1-3 showed significant interactions with cysteine and glutamic acid which are present in the side chains of lysozyme. In addition the temperature dependent studies have revealed that the interaction of the dye and the lysozyme are irreversible. Furthermore, we have investigated the interactions of these NIR dyes 1-3 with β- amyloid fibres derived from lysozyme to evaluate their potential as inhibitors of this biologically important protein aggregation. These β-amyloid fibrils were insoluble protein aggregates that have been associated with a range of neurodegenerative diseases, including Huntington, Alzheimer’s, Parkinson’s, and Creutzfeldt-Jakob diseases. We have synthesized amyloid fibres from lysozyme through its incubation in acidic solution below pH 4 and by allowing to form amyloid fibres at elevated temperature. To quantify the binding affinities of the squaraine dyes 1-3 with β-amyloids, we have carried out the isothermal titration calorimetric (ITC) measurements. The association constants were determined and are found to be 1.2 × 105, 3.6× 105 and 3.2 × 105 M-1 for the dyes, 1-3, respectively. To gain more insights into the amyloid inhibiting nature of the squaraine dyes under investigations, we have carried out thioflavin assay, CD, isothermal titration calorimetry and microscopic analysis. The addition of the dyes 1-3 (5μM) led to the complete quenching in the apparent thioflavin fluorescence, thereby indicating the destabilization of β-amyloid fibres in the presence of the squaraine dyes. Further, the inhibition of the amyloid fibres by the squaraine dyes 1-3, has been evidenced though the DLS, TEM AFM and SAED, wherein we observed the complete destabilization of the amyloid fibre and transformation of the fibre into spherical particles of ca. These results demonstrate the fact that the squaraine dyes 1-3 can act as protein labeling agents as well as the inhibitors of the protein amyloidogenesis. The last chapter of the thesis describes the synthesis and investigation of selfassembly as well as bio-imaging aspects of a few novel tetraphenylethene conjugates 4-6.Expectedly, these conjugates showed significant solvatochromism and exhibited a hypsochromic shift (negative solvatochromism) as the solvent polarity increased, and these observations were justified though theoretical studies employing the B3LYP/6-31g method. We have investigated the self-assembly properties of these D-A conjugates though variation in the percentage of water in acetonitrile solution due to the formation of nanoaggregates. Further the contour map of the observed fluorescence intensity as a function of the fluorescence excitation and emission wavelength confirmed the formation of J-type aggregates in these cases. To have a better understanding of the type of self-assemblies formed from the TPE conjugates 4-6, we have carried out the morphological analysis through various microscopic techniques such as DLS, SEM and TEM. 70%, we observed rod shape architectures having ~ 780 nm in diameter and ~ 12 μM in length as evidenced through TEM and SEM analysis. We have made similar observations with the dodecyl conjugate 5 at ca. 70% and 50% water/acetonitrile mixtures, the aggregates formed from 4 and 5 were found to be highly crystalline and such structures were transformed to amorphous nature as the water fraction was increased to 99%. To evaluate the potential of the conjugate as bio-imaging agents, we have carried out their in vitro cytotoxicity and cellular uptake studies though MTT assay, flow cytometric and confocal laser scanning microscopic techniques. Thus nanoparticle of these conjugates which exhibited efficient emission, large stoke shift, good stability, biocompatibility and excellent cellular imaging properties can have potential applications for tracking cells as well as in cell-based therapies. In summary we have synthesized novel functional organic chromophores and have studied systematic investigation of self-assembly of these synthetic and biological building blocks under a variety of conditions. The investigation of interaction of water soluble NIR squaraine dyes with lysozyme indicates that these dyes can act as the protein labeling agents and the efficiency of inhibition of β-amyloid indicate, thereby their potential as anti-amyloid agents.

The Parity of the Number of Irreducible Factors for Some Pentanomials

It is well known that Stickelberger-Swan theorem is very important for determining reducibility of polynomials over a binary field. Using this theorem it was determined the parity of the number of irreducible factors for some kinds of polynomials over a binary field, for instance, trinomials, tetranomials, self-reciprocal polynomials and so on. We discuss this problem for type II pentanomials namely x^m +x^{n+2} +x^{n+1} +x^n +1 \in\ IF_2 [x]. Such pentanomials can be used for efficient implementing multiplication in finite fields of characteristic two. Based on the computation of discriminant of these pentanomials with integer coefficients, it will be characterized the parity of the number of irreducible factors over IF_2 and be established the necessary conditions for the existence of this kind of irreducible pentanomials.

Divisibility of Trinomials by Irreducible Polynomials over F_2

Irreducible trinomials of given degree n over F_2 do not always exist and in the cases that there is no irreducible trinomial of degree n it may be effective to use trinomials with an irreducible factor of degree n. In this paper we consider some conditions under which irreducible polynomials divide trinomials over F_2. A condition for divisibility of self-reciprocal trinomials by irreducible polynomials over F_2 is established. And we extend Welch's criterion for testing if an irreducible polynomial divides trinomials x^m + x^s + 1 to the trinomials x^am + x^bs + 1.

Workforce Issues in the Greater Boston Health Care Industry: Implications for Work and Family

Interviews with more than 40 leaders in the Boston area health care industry have identified a range of broadly-felt critical problems. This document synthesizes these problems and places them in the context of work and family issues implicit in the organization of health care workplaces. It concludes with questions about possible ways to address such issues. The defining circumstance for the health care industry nationally as well as regionally at present is an extraordinary reorganization, not yet fully negotiated, in the provision and financing of health care. Hoped-for controls on increased costs of medical care – specifically the widespread replacement of indemnity insurance by market-based managed care and business models of operation--have fallen far short of their promise. Pressures to limit expenditures have produced dispiriting conditions for the entire healthcare workforce, from technicians and aides to nurses and physicians. Under such strains, relations between managers and workers providing care are uneasy, ranging from determined efforts to maintain respectful cooperation to adversarial negotiation. Taken together, the interviews identify five key issues affecting a broad cross-section of occupational groups, albeit in different ways: Staffing shortages of various kinds throughout the health care workforce create problems for managers and workers and also for the quality of patient care. Long work hours and inflexible schedules place pressure on virtually every part of the healthcare workforce, including physicians. Degraded and unsupportive working conditions, often the result of workplace "deskilling" and "speed up," undercut previous modes of clinical practice. Lack of opportunities for training and advancement exacerbate workforce problems in an industry where occupational categories and terms of work are in a constant state of flux. Professional and employee voices are insufficiently heard in conditions of rapid institutional reorganization and consolidation. Interviewees describe multiple impacts of these issues--on the operation of health care workplaces, on the well being of the health care workforce, and on the quality of patient care. Also apparent in the interviews, but not clearly named and defined, is the impact of these issues on the ability of workers to attend well to the needs of their families--and the reciprocal impact of workers' family tensions on workplace performance. In other words, the same things that affect patient care also affect families, and vice versa. Some workers describe feeling both guilty about raising their own family issues when their patients' needs are at stake, and resentful about the exploitation of these feelings by administrators making workplace policy. The different institutions making up the health care system have responded to their most pressing issues with a variety of specific stratagems but few that address the complexities connecting relations between work and family. The MIT Workplace Center proposes a collaborative exploration of next steps to probe these complications and to identify possible locations within the health care system for workplace experimentation with outcomes benefiting all parties.

Análisis de las relaciones bilaterales entre Estados Unidos y Colombia en el contexto de la cooperación internacional en materia de extradición periodo 1997-2008

Esta monografía busca identificar y analizar los efectos de la cooperación internacional en materia de extradición en las relaciones bilaterales de Estados Unidos y Colombia durante 1997 y 2008. Para la obtención de lo anterior, se analizaron los motivos que indujeron tanto a Estados Unidos como a Colombia para llevar a cabo este tipo de procesos; igualmente se analizó la reciprocidad en materia de extradición en las relaciones bilaterales entre dichos actores internacionales; las condiciones favorables y/o desfavorables que trae consigo la cooperación internacional en materia de extradición; y finalmente, determinar si la relación costo-beneficio es el móvil para la ejecución de los procesos de extradición o si existen otras circunstancias que motivan a los Estados objeto de investigación a mantener dicha relación bilateral. El análisis de las relaciones bilaterales entre Estados Unidos y Colombia en el contexto de la cooperación internacional en materia de extradición se realizó con base en la teoría de la interdependencia compleja de Keohane y Nye, y el análisis de la relación costo-beneficio de dicha relación bilateral se basó en la teoría del neoliberalismo.

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Las interacciones organizacionales desde la visión ecológica: el mutualismo

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