Ergodic control of partially observed Markov chains

The ergodic or long-run average cost control problem for a partially observed finite-state Markov chain is studied via the associated fully observed separated control problem for the nonlinear filter. Dynamic programming equations for the latter are derived, leading to existence and characterization of optimal stationary policies.

Structural and Sequence Characteristics of Long alpha Helices in Globular Proteins

Elucidation of the detailed structural features and sequence requirements for iv helices of various lengths could be very important in understanding secondary structure formation in proteins and, hence. in the protein folding mechanism. An algorithm to characterize the geometry of an alpha helix from its C-alpha coordinates has been developed and used to analyze the structures of long cu helices (number of residues greater than or equal to 25) found in globular proteins, the crystal structure coordinates of which are available from the Brookhaven Protein Data Bank, Ail long a helices can be unambiguously characterized as belonging to one of three classes: linear, curved, or kinked, with a majority being curved. Analysis of the sequences of these helices reveals that the long alpha helices have unique sequence characteristics that distinguish them from the short alpha helices in globular proteins, The distribution and statistical propensities of individual amino acids to occur in long alpha heices are different from those found in short alpha helices, with amino acids having longer side chains and/or having a greater number of functional groups occurring more frequently in these helices, The sequences of the long alpha helices can be correlated with their gross structural features, i.e., whether they are curved, linear, or kinked, and in case of the curved helices, with their curvature.

Self-Organization of n-Alkane Chains in Water: Length Dependent Crossover from Helix and Toroid to Molten Globule

We demonstrate a chain length dependent crossover in the structural properties of linear hydrocarbon (n-alkane) chains using detailed atomistic simulations in explicit water. We identify a number of exotic structures of the polymer chain through energy minimization of representative snapshots collected from molecular dynamics trajectory. While the collapsed state is ring-like (circular) for small chains (CnH2n+2; n <= 20) and spherical for very long ones (n = 100), we find the emergence of ordered helical structures at intermediate lengths (n similar to 40). We find different types of disordered helices and toroid-like structures at n = 60. We also report a sharp transition in the stability of the collapsed state as a function of the chain length through relevant free energy calculations. While the collapsed state is only marginally metastable for C20H42, a clear bistable free energy surface emerges only when the chain is about 30 monomers long. For n = 30, the polymer exhibits an intermittent oscillation between the collapsed and the coil structures, characteristic of two stable states separated by a small barrier.

Monte Carlo simulation of Ising chains showing several phase transitions

A Monte Carlo simulation of Ising chains with competing short-range and infiniterange interactions has been carried out. Results show that whenever the system does not enter a metastable state, variation of temperature brings about phase transitions in the Ising chain. These phase transitions, except for two sets of interaction strengths, are generally of higher order and involve changes in the long-range order while the short-range order remains unaffected.

Mixed saturated-unsaturated alkyl-chain assemblies: Solid solutions of zinc stearate and zinc oleate

The linear saturated stearic acid and the bent mono-unsaturated oleic acid do not mix and form solid solutions. However, the zinc salts of these acids can. From X-ray diffraction and DSC measurements we show that the layered zinc stearate and zinc oleate salts form a homogeneous solid solution at all composition ratios. The solid solutions exhibit a single melting endotherm, with the melting temperature varying linearly with composition but with the enthalpy change showing a minimum. By monitoring features in the infrared spectra that are characteristic of the global conformation of the hydrocarbon chain, and hence can distinguish between stearate and oleate chains, it is shown that solid solution formation is realized by the introduction of gauche defects in a fraction of the stearate chains that are then no longer linear. This fraction increases with oleate concentration. It has also been possible from the spectroscopic measurements to establish a quantitative relation between molecular conformational order and the thermodynamic enthalpy of melting of the solid solutions.

Key Factors Influencing Economic Relationships and Communication in Finnish Food Chains

The aim of this report is to discuss the role of the relationship type and communication in two Finnish food chains, namely the pig meat-to-sausage (pig meat chain) and the cereal-to-rye bread (rye chain) chains. Furthermore, the objective is to examine those factors influencing the choice of a relationship type and the sustainability of a business relationship. Altogether 1808 questionnaires were sent to producers, processors and retailers operating in these two chains of which 224 usable questionnaires were returned (the response rate being 12.4%). The great majority of the respondents (98.7%) were small businesses employing less than 50 people. Almost 70 per cent of the respondents were farmers. In both chains, formal contracts were stated to be the most important relationship type used with business partners. Although for many businesses written contracts are a common business practice, the essential role of the contracts was the security they provide regarding the demand/supply and quality issues. Relative to the choice of the relationship types, the main difference between the two chains emerged especially with the prevalence of spot markets and financial participation arrangements. The usage of spot markets was significantly more common in the rye chain when compared to the pig meat chain, while, on the other hand, financial participation arrangements were much more common among the businesses in the pig meat chain than in the rye chain. Furthermore, the analysis showed that most of the businesses in the pig meat chain claimed not to be free to choose the relationship type they use. Especially membership in a co-operative and practices of a business partner were mentioned as the reasons limiting this freedom of choice. The main business relations in both chains were described as having a long-term orientation and being based on formal written contracts. Typical for the main business relationships was also that they are not based on the existence of the key persons only; the relationship would remain even if the key people left the business. The quality of these relationships was satisfactory in both chains and across all the stakeholder groups, though the downstream processors and the retailers had a slightly more positive view on their main business partners than the farmers and the upstream processors. The businesses operating in the pig meat chain seemed also to be more dependent on their main business relations when compared to the businesses in the rye chain. Although the communication means were rather similar in both chains (the phone being the most important), there was some variation between the chains concerning the communication frequency necessary to maintain the relationship with the main business partner. In short, the businesses in the pig meat chain seemed to appreciate more frequent communication with their main business partners when compared to the businesses in the rye chain. Personal meetings with the main business partners were quite rare in both chains. All the respondent groups were, however, fairly satisfied with the communication frequency and information quality between them and the main business partner. The business cultures could be argued to be rather hegemonic among the businesses both in the pig meat and rye chains. Avoidance of uncertainty, appreciation of long-term orientation and independence were considered important factors in the business cultures. Furthermore, trust, commitment and satisfaction in business partners were thought to be essential elements of business operations in all the respondent groups. In order to investigate which factors have an effect on the choice of a relationship type, several hypotheses were tested by using binary and multinomial logit analyses. According to these analyses it could be argued that avoidance of uncertainty and risk has a certain effect on the relationship type chosen, i.e. the willingness to avoid uncertainty increases the probability to choose stable relationships, like repeated market transactions and formal written contracts, but not necessary those, which require high financial commitment (like financial participation arrangements). The probability of engaging in financial participation arrangements seemed to increase with long-term orientation. The hypotheses concerning the sustainability of the economic relations were tested by using structural equation model (SEM). In the model, five variables were found to have a positive and statistically significant impact on the sustainable economic relationship construct. Ordered relative to their importance, those factors are: (i) communication quality, (ii) personal bonds, (iii) equal power distribution, (iv) local embeddedness and (v) competition.

Exact entanglement studies of strongly correlated systems: role of long-range interactions and symmetries of the system

We study the bipartite entanglement of strongly correlated systems using exact diagonalization techniques. In particular, we examine how the entanglement changes in the presence of long-range interactions by studying the Pariser-Parr-Pople model with long-range interactions. We compare the results for this model with those obtained for the Hubbard and Heisenberg models with short-range interactions. This study helps us to understand why the density matrix renormalization group (DMRG) technique is so successful even in the presence of long-range interactions. To better understand the behavior of long-range interactions and why the DMRG works well with it, we study the entanglement spectrum of the ground state and a few excited states of finite chains. We also investigate if the symmetry properties of a state vector have any significance in relation to its entanglement. Finally, we make an interesting observation on the entanglement profiles of different states (across the energy spectrum) in comparison with the corresponding profile of the density of states. We use isotropic chains and a molecule with non-Abelian symmetry for these numerical investigations.

Periodically Clickable Polyesters: Study of Intrachain Self-Segregation Induced Folding, Crystallization, and Mesophase Formation

A series of polyesters based on 2-propargyl-1,3-propanediol or 2,2-dipropargyl-1,3-propanediol or 2-allyl-2-propargyl-1,3-propanediol and 1,20-eicosanedioic acid were prepared by solution polycondensation using the corresponding diacid chloride; these polyesters were quantitatively ``clicked'' with a fluoroalkyl, azide, namely CF3(CF2)(7)CH2CH2N3, to yield polyesters carrying long-chain alkylene segments in the backbone and either one or two perfluoroalkyl segments located at periodic intervals along the polymer chain. The immiscibility of the alkylene and fluoroalkyl segments causes the polymer chains to fold in a zigzag fashion to facilitate the segregation of these segments; the folded chains further organize in the solid state to form a lamellar structure with alternating domains of alkyl (HC) and fluoroalkyl (FC) segments. Evidence for the self-segregation is provided by DSC, SAXS, WAXS, and TEM studies; in two of the samples, the DSC thermograms showed two distinct endotherms associated with the melting of the individual domains, while the WAXS patterns confirm the existence of two separate peaks corresponding to the interchain distances within the crystalline lattices of the HC and FC domains. SAXS data, on the other hand, reveal the formation of an extended lamellar morphology with an interlamellar spacing that matches reasonably well with those estimated from TEM studies. Interestingly, a smectic-type liquid crystalline phase is observed at temperatures between the two melting transitions. These systems present a unique opportunity to develop interesting nanostructured polymeric materials with precise control over both the domain size and morphology; importantly, the domain sizes are far smaller than those typically observed in traditional block copolymers.

Novel NIR-absorbing conjugated polymers for efficient polymer solar cells: effect of alkyl chain length on device performance

Three low bandgap conjugated polymers, i.e., PDTPBT-C8, PDTPBT-C6 and PDTPBT-C5, which consist of alternating N-alkyl dithieno[3,2-b: 2',3'-d] pyrrole and 2,1,3-benzothiadiazole units and carry 1-octylnonyl, 1-hexylheptyl and 1-pentylhexyl as side chains, respectively, were synthesized. These polymers show strong absorption in the wavelength range of 600-900 nm with enhanced absorption coefficient as the length of alkyl chain decreases. The film morphology of the polymers and 1-(3-methoxycarbonyl) propyl-1-phenyl-[6,6]-C-61 (PCBM) blends is also dependent on the alkyl chain length. As the length decreases, the film becomes more uniform and the domian size decreases from 400-900 nm for PDTPBT-C8 to similar to 50 nm for PDTPBT-C5.

The synthesis and properties of meso-tetra(4-alkylamidophenyl)porphyrin liquid crystals and their Zn complexes

A series of novel, long-chain-substituted, porphyrin derivatives, meso-tetra (4-alkylamidophenyl) porphyrin ligands and their Zn complexes (alkyl = 8,10,12,14,16,18) were prepared by acylation of the amino groups of 5,10,15,20-tetra(4-aminophenyl)porphyrin by alkyl chloride. Mesomorphism was investigated by DSC, polarized optical microscopy (POM) and X-ray diffraction (XRD). Only ligands containing chains > 12 carbon atoms displayed liquid crystalline behaviour, which exhibited a high phase transition temperature and a broad mesophase temperature span, Zn complexes showed no liquid crystalline behaviour. Cyclic voltammetry, luminescence spectra and surface photovoltage spectroscopy revealed that covalent linking of an alkylamido group to the tetraphenylporphyrin molecule influences, significantly, the properties of the porphyrin macrocycle.

Phase transition and conformational variation of N-alkylated branched poly(ethyleneimine) comblike polymer

A series of branched poly(ethyleneimine) (PEI) derived polymers with different lengths of n-alkyl side chains, denoted as PEI(n)Cs (n = 12, 14, 16, 18, 20, number of carbon atoms in alkyl side group), have been prepared by a N-alkylation method, and systematically characterized by differential scanning calorimertry (DSC) and wide-angle X-ray diffraction (WARD) as well as Fourier transform infrared spectroscopy (FTIR). The side chains grafted on these comblike polymers are long enough to form crystalline phase composed of paraffin-like crystallites. The crystallization of the side chains forces the branched poly(ethyleneimine) molecules to pack into layered structure, between which the crystallites are located. The melting temperatures of the side chain crystallites increase from -12.36 to +51.49 degreesC with increasing the length of the side chains from n. = 12 to n = 20, which are a little bit lower than the corresponding pristine n-alkanes. PEI18C was taken as an example in this work for the investigation of phase transition and conformational variation of the side chains with temperature changing.

The effects of different alkyl substitution on the structures and properties of poly(3-alkylthiophenes)

In order to investigate the influence of different alkyl side chain substitution on the structures and properties of P3ATs, X-ray diffraction, differential scanning calorimetry (DSC), thermal gravity analysis (TGA), Fourier transform infrared spectra (FTIR) and ultraviolet-visible spectra (W-VIS) were applied to characterizing the samples of ploy(3-octylthiophene) (P3OT), poly(3-dodecylthiophene) (P3DDT) and poly(3-octadecylthiophene) (P3ODT). It is found that the different length of alkyl group substitution leads to great difference in molecular chain packings, according to the room temperature X-ray diffraction results. The temperature dependence of X-ray diffraction experiments were also performed to study the melting processes of P3ATs. With the increase in the number of carbon atoms in alkyl side chains, the melting point decreases, and the thermal stability decreases too. The results of both FTIR and W-VIS spectra indicate that the conjugation length of P3DDT is the longest. among the three P3ATs. (C) 2001 Elsevier Science B.V. All rights reserved.

Entanglement generation in harmonic chains: Tagging by squeezing

We address the problem of springlike coupling between bosons in an open-chain configuration where the counter-rotating terms are explicitly included. We show that fruitful insight can be gained by decomposing the time-evolution operator of this problem into a pattern of linear-optics elements. This allows us to provide a clear picture of the effects of the counter-rotating terms in the important problem of long-haul entanglement distribution. The analytic control over the variance matrix of the state of the bosonic register allows us to track the dynamics of the entanglement. This helps in designing a global addressing scheme, complemented by a proper initialization of the register, which quantitatively improves the entanglement between the extremal oscillators in the chain, thus providing a strategy for feasible long-distance entanglement distribution.

Raman and ab initio studies of simple and binary 1-Alkyl-3-methylimidazolium ionic liquids

Raman spectra of the ionic liquids, 1-butyl-3-methylimidazolium hexafluorophosphate ([C(4)mim][PF(6)]), 1-hexyl-3-methylimidazolium chloride ([C(6)mim]Cl), and 1-hexyl-3-methylimidazolium hexafluorophosphate ([C(6)mim][PF(6)]), and binary mixtures thereof, have been assigned using ab initio MP2 calculations. The previously reported anti and gauche forms of the [C(4)mim](+) cation have been observed, and this study reveals this to be a general feature of the long-chain I-alkyl derivatives. Analysis of mixtures Of [C(6)mim]Cl and [C(6)mim][PF(6)] has provided information on the nature of the hydrogen bonding between the imidazolium headgroup and the anions, and the invariance of the essentially 50:50 mixture of the predominant conformers informs on the nature of glass formation in these systems.

Study of the transamidative ring expansion of N--halogenoalkyl--lactams of alkyl chain lengths 2–12 in liquid ammonia and other liquid amines: syntheses of 7-, 8- and 9-membered 1,5-diaza cyclic ketones, including routes to (±)-dihydroperiphylline and (±)-celabenzine

N-(3-Halogenopropyl)-4-phenylazetidin-2-ones undergo amination in liquid ammonia followed by transamidative ring expansion to give the eight-membered 4-phenyl -1,5-diazacyclooctan-2-one in excellent yield. Ring expansion of the amines in liquid ammonia is found to be much more effective than in hydrocarbon solvents. Formation of 7-, 8-, and 9-membered azalactams from the requisite -halogenoalkyl--lactams is an excellent synthetic process, though it is not applicable to 10membered rings. In the cases of rings of 13-, 15- and 17-members, although amination and apparent expansion takes place, the large rings appear not to be stable to ammonia and the final products are acyclic amides. N-[4-Halogenobut-2(Z)-enyl]-4-phenylazetidin-2-one satisfactorily forms a 9-membered (Z)-olefinic azalactam, but the (E)-isomer gives an acyclic amino amide. By using alkyl-substituted -lactam side-chains, C-substituted medium rings can be obtained; the relative instability of N-acyl -lactams to ammonia, however, leads to acylamino amides rather than expanded rings.Employing ethylamine in place of ammonia, it is shown that N-ethylated azalactams are formed satisfactorily, and using allylamine, N-allyl medium rings capable of further elaboration are obtained. The chemistry of these systems is discussed. Using transamidation in liquid ammonia, a short synthesis of the 9-membered spermidine alkaloid (±)-dihydroperiphylline is reported. Synthesis of key intermediates, whose transformation into the 13-membered alkaloids of the celabenzine group has already been effected, has been carried out.X-Ray single-crystal structure determinations for 4-phenyl-1,5-diazacyclononan-2-one, trans-4-phenyl-8-methyl-1,5-diazacyclooctan-2-one and (Z)-4-phenyl-1,5-diazacyclonon-7-en-2-one are reported, and comment is made on certain conformational features.