We show that equitable partitions, which are generalizations of graph symmetries, and Fourier transforms are fundamentally related. For a partition of a graph's vertices we define a Fourier similarity transform of the graph's adjacency matrix built from the matrices used to carryout discrete Fourier transformations. We show that the matrix (graph) decomposes into a number of smaller matrices (graphs) under this transformation if and only if the partition is an equitable partition. To extend this result to directed graphs we define two new types of equitable partitions, equitable receiving and equitable transmitting partitions, and show that if a partition of a directed graph is both, then the graph's adjacency matrix will similarly decomposes under this transformation. Since the transformation we use is a similarity transform the collective eigenvalues of the resulting matrices (graphs) is the same as the eigenvalues of the original untransformed matrix (graph).

Background: RNA has been recognized as a key player in cellular regulation in recent years. In many cases, non-coding RNAs exert their function by binding to other nucleic acids, as in the case of microRNAs and snoRNAs. The specificity of these interactions derives from the stability of inter-molecular base pairing. The accurate computational treatment of RNA-RNA binding therefore lies at the heart of target prediction algorithms. Methods: The standard dynamic programming algorithms for computing secondary structures of linear single-stranded RNA molecules are extended to the co-folding of two interacting RNAs. Results: We present a program, RNAcofold, that computes the hybridization energy and base pairing pattern of a pair of interacting RNA molecules. In contrast to earlier approaches, complex internal structures in both RNAs are fully taken into account. RNAcofold supports the calculation of the minimum energy structure and of a complete set of suboptimal structures in an energy band above the ground state. Furthermore, it provides an extension of McCaskill's partition function algorithm to compute base pairing probabilities, realistic interaction energies, and equilibrium concentrations of duplex structures.

We define a faithful linear monoidal functor from the partition category, and hence from Deligne's category Rep(S_t), to the additive Karoubi envelope of the Heisenberg category. We show that the induced map on Grothendieck rings is injective and corresponds to the Kronecker coproduct on symmetric functions. We then generalize the above results to any group G, the case where G is the trivial group corresponding to the case mentioned above. Thus, to every group G we associate a linear monoidal category Par(G) that we call a group partition category. We give explicit bases for the morphism spaces and also an efficient presentation of the category in terms of generators and relations. We then define an embedding of Par(G) into the group Heisenberg category associated to G. This embedding intertwines the natural actions of both categories on modules for wreath products of G. Finally, we prove that the additive Karoubi envelope of Par(G) is equivalent to a wreath product interpolating category introduced by Knop, thereby giving a simple concrete description of that category.

<p><strong>Apstrakt je obrađen tehnologijama za optičko prepoznavanje teksta (OCR).</strong></p><p>U radu je ispitana raspodela pektinaza u vodenim dvofaznim sistemima sastavljenim od polietilen glikola 4000 i jednog od dva dekstrana, sirovog i dekstrana 40000. Koncepcija rada je podrazumevala definisanje sistema u kojima su vr&scaron;eni eksperimenti raspodele, ispitivanje parametara raspodele pektinaza komercijalnog enzimskog preparata u model sistemima i, konačno, kultivaciju Polyporus squamosus u dvofaznim sistemima.<br />Ispitivanje uticaja masenih udela polietilen glikola na raspodelu pektinaza u model sistemu, pri konstantnom udelu sirovog dekstrana od 7.5% (w/w), pokazalo je negativan uticaj na parametre raspodele, te su najveće vrednosti koeficijenta raspodele (K) dobijene pri najmanjem ispitivanom udelu polietilen glikola, 5% (w/w), i iznosili su za endo-pektinazu (endo-p) 1.76, odnosno za egzo- pektinazu (egzo-p) 1.22. Istu zavisnost je pokazalo i ispitivanje u model sistemu sa dekstranom 40000, ali je vrednost K_endo bila mnogo niža (0.22). Povećanje udela sirovog dekstrana, pri stalnom udelu, 5% (w/w), polietilen glikola, negativno je uticalo na vrednosti parametara raspodele egzo-p, te su maksimalne vrednosti dobijene pri najmanjem udelu, 3% (w/w), dekstrana (K_egzo 0.79, prinos u gornjoj fazi (Y) 62.04%, stepen preči&scaron;ćenosti u gornjoj fazi (st.preč.) 5.5).<br />Sa povećanjem dužine veznih linija u model sistemu sa sirovim dekstranom opadale su vrednosti parametara raspodele pektinaza. Najbolji rezultati (K_endo 1.66, Y_endo 60.85%, K_egzo 0.95, Y_egzo 47.07%) dobijeni su najkraćoj veznoj liniji, dužine 7.44%. Povećanje odnosa zapremina u istom sistemu smanjilo je koeficijente raspodele endo- i egzo-p, kao i njihove stepene preči&scaron;ćenosti u gornjoj fazi, a u isto vreme povećalo prinose u toj fazi.<br />Dodatak amonijum sulfata i natrijum sulfata u model sistem polietilen glikol/sirovi dekstran u koncentraciji od po 15 mmoI/l povećao je K_endo 1-25, odnosno 1.2 puta, dok je K_egzo u prisustvu 15 mmol/l amonijum sulfata ili 5 mmol/l natrijum sulfata bio za 60% veći. Povećanje rN vrednosti KH₂PO₄-Na₂HPO₄ pufera povećalo je koeficijente raspodele oba tipa pektinaza, te je K_endo, na rN 7.5, bio 0.9, a K_egzo 0.76, na rN 7.0. Najbolja raspodela endo-p u gornju fazu model sistema ostvarena je pri 0.4 mol/l fosfatnog pufera (K 4.21, Y 85.78%, st.preč. 10). Vrednosti iznad 0.1 mol/l fosfatnog pufera nisu imale značajnijeg uticaja na raspodelu egzo-p.<br />Kultivacija Polyporus squamosus je bila moguća u dvofaznom sistemu polietilen glikol/sirovi dekstran, sa pektinom. kao inducerom, pri čemu je ostvareno odvajanje biomase od pektinaza njihovom raspodelom u suprotne faze. U sistemu sastava 5% (w/w) polietilen glikol/4% (w/w) sirovi dekstran, količina produkovane biomase je bila 4.5 puta veća od one u homogenom medijumu, ukupne egzo-p aktivnosti 1.82 puta veća, a endo-p aktivnosti jednaka onoj u homogenom medijumu. Drugog dana kultivacije ostvarene su najveće vrednosti parametara raspodele (K_endo 2.45, Y_endo 80.22%, st.preč._endo 7; K_egzo 0.6, Yegzo 49.83%, st.preč._egzo 5.19). Povećanje koncentracije amonijum sulfata za 15 mmol/l u podlozi za kultivaciju u dvofaznom sistemu sastava 5% (w/w) polietilen glikol/4% (w/w) sirovi dekstran, povećalo je koeficijent raspodele endo-p za 81%, vrednost ove aktivnost u grnjoj fazi za 37%, a da nije uticalo na raspodelu biomase P. squamosus.<br />Prisustvo različitih koncentracija fosfata nije uticalo na raspodelu biomase P. squamosus u dvofaznom sistemu. Pri 0.2 mol/l KH2PO4 postignuto je idealno odvajanje biomase od endo-p, uz K_egzo 112. Najveća vrednost ukupnih produkovanih aktivnosti oba tipa ostvarena je pri 0,1 mol/l fosfata, uz koeficijente raspodele za endo-p i egzo-p 3.9 i 0.95 i visoke stepene njihove preči&scaron;ćenosti u gornjoj fazi (5.89 i 14.36, redom).<br />Kultivacija P. squamosus je ostvarena i u dvofaznom sistemu koji je sadržao suve izlužene repine rezance, sa raspodelom biomase u donju fazu. Koeficijenti raspodele su iznosili 4.70, odnosno 2.78, za endo-p, odnosno egzo-p. Prinosi oba enzima u gornjoj fazi su bili 90.71% za endo-p i 85.24% za egzo-p, uz najveće stepene njihove preči&scaron;ćenosti, 4.26 i 7.98, redom.</p> / <p><br /><strong>Abstract was processed by technology for Optical character recognition (OCR).</strong></p><p>Partition of pectinases in aqueous two-phase systems composed of polyethylene glycol 4,000 and crude dextran or dextran 40,000 was studied in this work. As the first step, phase diagrams were constructed, than partition of commercial pectinases was studied in model systems and finally, cultivation of Polyporus squamosus in aqueous two-phase systems was conducted.<br />Increasing of the concentration of polyethylene glycol in model system at fixed 7.5% (w/w) crude dextran decreased partition parameters. Maximal values for partition coefficient (К) of endo-pectinase (endo-p), 1.76, and exo-pectinase (ехо-р), 1.22, were obtained at 5% (w/w) polyethylene glycol. The same was revealed in investigations in model system with dextran 40,000, but Kendo was lower (0.22). Increasing of concentration of crude dextran at fixed 5% (w/w) polyethylene glycol decreased partition parameters of ехо-р, so their maximal values (Кexo 0.79, top phase yield (Y) 62.04% and purification factor in top phase 5.5) were obtained at 3% (w/w) crude dextran.<br />Increasing of the tie-line length caused decreasing of partition parameters and maximal results were achieved at the shortest tie-line 7.44% (Kendo 1-66, Yendo 60.85%, Кехо 0.95, Yexo 47.07%) in model system with crude dextran. With increasing of the volume ratio, partition coefficients of endo-p and ехо-р were decreased, as well as their purification factor in top phase, while top phase yield for both enzymes had higher values.<br />The addition of 15 mmol ammonium sulphate/l and 15 mmol sodium sulphate/l in model system, composed of polyethylene glycol and crude dextran, increascd Kendo 1.25 and 1.2 times, respectively, while Кехо in the presence of 15 mmol ammonium sulphate/l or 5 mmol sodium sulphate/l was 60% higher. Increasing of рН of KH2PO4- Na2HPO4 buffer favoured partition of both endo-p and ехо- p in top phase, so Kendo was 0.9 at рН 7.5 and Кехо was 0.76 at рН 7.0. The favourable partition of endo-p in top phase was achieved in the presence of 0.4 mol phosphate buffer/l (К 4.21, Y 85.78% and purification factor in top phase 10). Concentrations of phosphate buffer above 0.1 mol/l didn&rsquo;t have significant influence on partition of ехо-р.<br />Cultivation of Роlуроrus squamosus in polyethylene glycol/crude dextran aqueous two-phase system was accomplished with pectin as inducer and biomass was separated from pectinases by their partition into opposite phases. In system composed of 5% (w/w) polyethylene glycol and 4% (w/w) crude dextran, amounts of produced biomass and ехо-р activity were 4.5 and 1.82 times higher, respectively, and endo-p activity equal to those obtained in homogeneous cultivation. At the second day of cultivation the highest values of partition parameters were obtained (Kendo 2.45, Yendo 80.22%, purification factor for endo-p 7; Кeхо 0.6, Yexo 49.83%, purification factor for ехо-р 5.19). Increasing of concentration of ammonium sulphate in two-phase medium for 15 mmol/l increased Kendo for 81% and endo-p activity in top phase for 37%, but didn&rsquo;t influence partition of biomass.<br />Presence of phosphate at various concentrations didn&rsquo;t affect partition of biomass in two-phase system. At 0.2 mol KH2PO4/I tlie onesided partition of endo-p was accomplished while Кeхо was 1.12. The highest amounts of produced activities of endo-p and ехо-р were obtained at 0.1 mol phosphate/l and partition coefficients were 3.9 and 0.95, respectively, followed by high values of purification factors in top phase (5.89 and 14.36, rcspectively).<br />Cultivation of P. squamosus was accomplished in two-phase system containing dry sugar beet extraction waste and fungal growth was restrected to bottom phase. Partition coefficients were 4.70 and 2.78 for endo-p and ехо-р, respectively. Тор phase yields amounted 90.71% for endo-p and 85.24% for ехо-р followed by the highest obtained purification factors in top phase (4.26 and 7.98, respectively).</p>

京都大学 / 0048 / 新制・論文博士 / 博士(理学) / 乙第12910号 / 論理博第1546号 / 新制||理||1590(附属図書館) / 32120 / ソウル大学大学院数学科 / (主査)教授 中島 啓, 教授 小野 薫, 教授 向井 茂 / 学位規則第4条第2項該当 / Doctor of Science / Kyoto University / DFAM

The Abraham Solvation Parameter Model (ASPM) is a linear, free-energy relationship that can be used to predict various solute properties based on solute-solvent interactions. The ASPM has been used to predict log (K or Cs,organic/Cs,gas) values, as well as log (P or Cs,organic/Cs,water) values for solute transfer into the following organic solvents: 2-methoxyethanol, 2-ethoxyethanol, 2-propoxyethanol, 2-isopropoxyethanol and 2-butoxyethanol. The derived log (K or Cs,organic/Cs,gas) correlations describe the experimental data to within 0.14 log units (or less). The derived log (P or Cs,organic/Cs,water) correlations describe the experimental data to within 0.16 log units (or less). The ASPM has also been used to predict the enthalpies of solvation of organic solutes dissolved in the following solvents: acetic acid, dimethyl carbonate, diethyl carbonate, 1-butanol, 1-pentanol, 1-hexanol. The derived enthalpy of solvation correlations, using the L solute descriptor, describe the experimental data to within 2.50 log units (or less). The derived enthalpy of solvation correlations, using the V solute descriptor, describe the experimental data to within 3.10 log units (or less). Validation analyses have been performed on several of the correlations; and, as long as the solute descriptors fall within the given ranges as reported, the original correlations show good predictive ability for determining 1) solute transfer into, and 2) enthalpy of solvation for the aforementioned solvents.

We introduce the Partition Principle PP, an axiom introduced by Russell in the context of its similarities and differences with the Axiom of Choice AC. We start by proving some properties of PP, and AC, and show that AC, entails PP. To address the problem of whether the converse holds, we develop the Zermelo-Fraenkel ZF set theory and examine its consistency and build a model in which AC, fails. We follow this with a discussion of forcing, a technique introduced by Paul Cohen to build new models of set theory from existing ones, which have differing properties from the starting model. We conclude by examining candidate models called permutation models where AC, fails, which may be useful as candidate models for forcing a model in which PP, holds but AC, does not. We conjecture that such a model exists, and that PP, does not entail AC. / Thesis / Master of Science (MSc)

The thermotropic behavior of multilamellar vesicles of dipalmitoylphosphatidylcholine (DPPC), or of DPPC in admixture with cardiolipin or cholesterol, in the presence of various N-alkyl derivatives of both adriamycin-14-valerate has been investigated by high sensitivity differential scanning calorimetry. The analogues, particularly the 14-valerate derivatives, which were most lipophilic as judged by their lipid/buffer, and to a lesser extent by their octanol/buffer, partition coefficients, were the most effective in depressing the tm of the investigated lipids; correlations, however, were not absolute. Other factors, such as the distribution of the drugs between the solid and liquid-crystalline phases of the bilayer, were also important to the observed membrane perturbations. With all anthracyclines, however, no major changes in the transition enthalpy were observed. In the case of vesicles prepared from pure DPPC, curve fitting analysis based on ideal solution theory (J.M. Sturtevant (1984) Proc. Natl. Acad. Sci. USA 81, 1398-1400) applied at relatively low drug concentrations where single peak transitions were produced, adequately described the differential scanning calorimetric results. At high drug concentrations, however, the presence of multipeak transitions were indicative of non-ideality.

For a graph G=(V,E), a nonempty subset S contained in V is called a defensive alliance if for each v in S, there are at least as many vertices from the closed neighborhood of v in S as in V-S. If there are strictly more vertices from the closed neighborhood of v in S as in V-S, then S is a strong defensive alliance. A (strong) defensive alliance is called global if it is also a dominating set of G. The alliance partition number (respectively, strong alliance partition number) is the maximum cardinality of a partition of V into defensive alliances (respectively, strong defensive alliances). The global (strong) alliance partition number is defined similarly. For each parameter we give both general bounds and exact values. Our major results include exact values for the alliance partition number of grid graphs and for the global alliance partition number of caterpillars.

Because of the huge amounts of data made available by the technology boom in the late twentieth century, new methods are required to turn data into usable information. Much of this data is categorical in nature, which makes estimation difficult in highly multivariate settings. In this thesis we review various multivariate statistical methods, discuss various statistical methods of natural language processing (NLP), and discuss a general class of models described by Erosheva (2002) called generalized mixed membership models. We then propose extensions of the information partition function (IPF) derived by Engler (2002), Oliphant (2003), and Tolley (2006) that will allow modeling of discrete, highly multivariate data in linear models. We report results of the modified IPF model on the World Health Organization's Survey on Global Aging (SAGE).