On the axiomatic approach to the maximum entropy principle of inference

Recent axiomatic derivations of the maximum entropy principle from consistency conditions are critically examined. We show that proper application of consistency conditions alone allows a wider class of functionals, essentially of the form ∝ dx p(x)[p(x)/g(x)] s , for some real numbers, to be used for inductive inference and the commonly used form − ∝ dx p(x)ln[p(x)/g(x)] is only a particular case. The role of the prior densityg(x) is clarified. It is possible to regard it as a geometric factor, describing the coordinate system used and it does not represent information of the same kind as obtained by measurements on the system in the form of expectation values.

A comment on the consistency of truncated nonlinear integral equation based theories of freezing

We report the results of two studies of aspects of the consistency of truncated nonlinear integral equation based theories of freezing: (i) We show that the self-consistent solutions to these nonlinear equations are unfortunately sensitive to the level of truncation. For the hard sphere system, if the Wertheim–Thiele representation of the pair direct correlation function is used, the inclusion of part but not all of the triplet direct correlation function contribution, as has been common, worsens the predictions considerably. We also show that the convergence of the solutions found, with respect to number of reciprocal lattice vectors kept in the Fourier expansion of the crystal singlet density, is slow. These conclusions imply great sensitivity to the quality of the pair direct correlation function employed in the theory. (ii) We show the direct correlation function based and the pair correlation function based theories of freezing can be cast into a form which requires solution of isomorphous nonlinear integral equations. However, in the pair correlation function theory the usual neglect of the influence of inhomogeneity of the density distribution on the pair correlation function is shown to be inconsistent to the lowest order in the change of density on freezing, and to lead to erroneous predictions. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.

A comment on the consistency of truncated nonlinear integral equation based theories of freezing

We report the results of two studies of aspects of the consistency of truncated nonlinear integral equation based theories of freezing: (i) We show that the self-consistent solutions to these nonlinear equations are unfortunately sensitive to the level of truncation. For the hard sphere system, if the Wertheim–Thiele representation of the pair direct correlation function is used, the inclusion of part but not all of the triplet direct correlation function contribution, as has been common, worsens the predictions considerably. We also show that the convergence of the solutions found, with respect to number of reciprocal lattice vectors kept in the Fourier expansion of the crystal singlet density, is slow. These conclusions imply great sensitivity to the quality of the pair direct correlation function employed in the theory. (ii) We show the direct correlation function based and the pair correlation function based theories of freezing can be cast into a form which requires solution of isomorphous nonlinear integral equations. However, in the pair correlation function theory the usual neglect of the influence of inhomogeneity of the density distribution on the pair correlation function is shown to be inconsistent to the lowest order in the change of density on freezing, and to lead to erroneous predictions. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.

The averaging principle and the diagram technique

Rae and Davidson have found a striking connection between the averaging method generalised by Kruskal and the diagram technique used by the Brussels school in statistical mechanics. They have considered conservative systems whose evolution is governed by the Liouville equation. In this paper we have considered a class of dissipative systems whose evolution is governed not by the Liouville equation but by the last-multiplier equation of Jacobi whose Fourier transform has been shown to be the Hopf equation. The application of the diagram technique to the interaction representation of the Jacobi equation reveals the presence of two kinds of interactions, namely the transition from one mode to another and the persistence of a mode. The first kind occurs in the treatment of conservative systems while the latter type is unique to dissipative fields and is precisely the one that determines the asymptotic Jacobi equation. The dynamical equations of motion equivalent to this limiting Jacobi equation have been shown to be the same as averaged equations.

Fourier transform of the collagen triple-helical structure and its significance

The Fourier transforms of the collagen molecular structure have been calculated taking into consideration various side chain atoms, as well as the presence of bound water molecules. There is no significant change in the calculated intensity distribution on including the side chain atoms of non-imino-acid residues. Taking into account the presence of about two bound water molecules per tripeptide unit, the agreement with the observed x-ray pattern is slightly improved. Fourier transforms have also been calculated for the detailed molecular geometries proposed from other laboratories. It is found that there are no major differences between them, as compared to our structure, either in the positions of peak intensity or in the intensity distribution. Hence it is not possible to judge the relative merits of the various molecular geometries for the collagen triple helix from a comparison of the calculated transforms with the meagre data available from its x-ray fibre pattern. It is also concluded that the collagen molecular structure should be regarded as a somewhat flexible chain structure, capable of adapting itself to the requirements of the different side groups which occur in each local region.

Boxicity and cubicity of asteroidal triple free graphs

The boxicity of a graph G, denoted box(G), is the least integer d such that G is the intersection graph of a family of d-dimensional (axis-parallel) boxes. The cubicity, denoted cub(G), is the least dsuch that G is the intersection graph of a family of d-dimensional unit cubes. An independent set of three vertices is an asteroidal triple if any two are joined by a path avoiding the neighbourhood of the third. A graph is asteroidal triple free (AT-free) if it has no asteroidal triple. The claw number psi(G) is the number of edges in the largest star that is an induced subgraph of G. For an AT-free graph G with chromatic number chi(G) and claw number psi(G), we show that box(G) <= chi(C) and that this bound is sharp. We also show that cub(G) <= box(G)([log(2) psi(G)] + 2) <= chi(G)([log(2) psi(G)] + 2). If G is an AT-free graph having girth at least 5, then box(G) <= 2, and therefore cub(G) <= 2 [log(2) psi(G)] + 4. (c) 2010 Elsevier B.V. All rights reserved.

Thermodynamic consistency of the ternary functions

A ternary thermodynamic function has been developed based on statistico-thermodynamic considerations, with a particular emphasis on the higher-order terms indicating the effects of truncation at the various stages of the treatment. Although the truncation of a series involved in the equation introduces inconsistency, the latter may be removed by imposing various thermodynamic boundary conditions. These conditions are discussed in the paper. The present equation with higher-order terms shows that the α function of a component reduces to a quadratic function of composition at constant compositional paths involving the other two components in the system. The form of the function has been found to be representative of various experimental observations.

Thermodynamic consistency of the interaction parameter formalism

The apparent contradiction between the exact nature of the interaction parameter formalism as presented by Lupis and Elliott and the inconsistencies discussed recently by Pelton and Bale arise from the truncation of the Maclaurin series in the latter treatment. The truncation removes the exactness of the expression for the logarithm of the activity coefficient of a solute in a multi-component system. The integrals are therefore path dependent. Formulae for integration along paths of constant Xi,or X i/Xj are presented. The expression for In γsolvent given by Pelton and Bale is valid only in the limit that the mole fraction of solvent tends to one. The truncation also destroys the general relations between interaction parameters derived by Lupis and Elliott. For each specific choice of parameters special relationships are obtained between interaction parameters.

Weak consistency of read-only transactions: A tool to improve concurrency in heterogeneous locking protocols

Three different types of consistencies, viz., semiweak, weak, and strong, of a read-only transaction in a schedule s of a set T of transactions are defined and these are compared with the existing notions of consistencies of a read-only transaction in a schedule. We present a technique that enables a user to control the consistency of a read-only transaction in heterogeneous locking protocols. Since the weak consistency of a read-only transaction improves concurrency in heterogeneous locking protocols, the users can help to improve concurrency in heterogeneous locking protocols by supplying the consistency requirements of read-only transactions. A heterogeneous locking protocol P' derived from a locking protocol P that uses exclusive mode locks only and ensures serializability need not be deadlock-free. We present a sufficient condition that ensures the deadlock-freeness of Pprime, when P is deadlock-free and all the read-only transactions in Pprime are two phase.

Principle of a Dual Current Source Converter for AC Motor Drives

The principle of operation of a dual current source converter is briefly explained. The combination of two single current source converters (SCSC) to form a ``dual (duplex) current source converter'' (DCSC) is proposed. The DCSC is shown to have the following merits: 1) it retains all the advantages of the SCSC; 2) it reduces the harmonic content of the current waveform considerably; and 3) since the load current is shared equally between two current source converters, ratings of the individual components employed in the circuit are considerably lowered. A DCSC can be an attractive choice for sophisticated large horsepower drives where a good performance of the drive rather than cost is a prime factor. An open-loop control scheme employing the DCSC for an ac motor drive has been successfully implemented in the laboratory. Oscillograms of the improved load current waveforms are shown.

Analytical modeling of quantum threshold voltage for triple gate MOSFET

In this work a physically based analytical quantum threshold voltage model for the triple gate long channel metal oxide semiconductor field effect transistor is developed The proposed model is based on the analytical solution of two-dimensional Poisson and two-dimensional Schrodinger equation Proposed model is extended for short channel devices by including semi-empirical correction The impact of effective mass variation with film thicknesses is also discussed using the proposed model All models are fully validated against the professional numerical device simulator for a wide range of device geometries (C) 2010 Elsevier Ltd All rights reserved

A structural principle for a class of adaptive systems

A feature common to many adaptive systems for identification and control is the adjustment.of gain parameters in a manner ensuring the stability of the overall system. This paper puts forward a principle which assures such a result for arbitrary systems which are linear and time invariant except for the adjustable parameters. The principle only demands that a transfer function be positive real. This transfer function dependent on the structure of the system with respect to the parameters. Several examples from adaptive identification, control and observer schemes are given as illustrations of the conceptual simplification provided by the structural principle.

Sequence Independent Recombination Triple Helices: A Molecular Dynamics Study

Recent experimental studies have shown that the Rec-A mediated homologous recombination reaction involves a triple helical intermediate, in which the third strand base forms hydrogen bonds with both the bases in the major groove of the Watson-Crick duplex. Such 'mixed' hydrogen bonds allow formation of sequence independent triplexes. DNA triple helices involving 'mixed' hydrogen bonds have been studied, using model building, molecular mechanics (MM) and molecular dynamics (MD). Models were built for a tripler comprising all four possible triplets viz., G.C*C, C.G*G, A.T*T and T.A*A. To check the stability of all the 'mixed' hydrogen bonds in such triplexes and the conformational preferences of such tripler structures, MD studies were carried out starting from two structures with 30 degrees and 36 degrees twist between the basepairs. It was observed that though the two triplexes converged towards a similar structure, the various hydrogen bonds between the WC duplex and the third strand showed differential stabilities. An MD simulation with restrained hydrogen bonds showed that the resulting structure was stable and remained close to the starting structure. These studies help us in defining stable hydrogen bond geometries involving the third strand and the WC duplex. It was observed that in the C.G*G triplets the N7 atom of the second strand is always involved in hydrogen bonding. In the G.C*C triplets, either N3 or O2 in the third strand cytosine can interchangeably act as a hydrogen bond acceptor.

Molecular Mechanics Studies of Homopolymeric and Mixed Sequence Py.Pu*Pu Triple Helices,

DNA triple helices containing two purine strands and one pyrimidine strand (C.G*G and T.A*A) have been studied, using model building followed by energy minimisation, for different orientations of the third strand resulting from variation in the hydrogen bonding between the Watson-Crick duplex and the third strand and the glycosidic torsion angle in the third strand. Our results show that in the C.G*G case the structure with a parallel orientation of the third strand, resulting from Hoogsteen hydrogen bonds between the third strand and the Watson-Crick duplex, is energetically the most favourable while in the T.A*A case the antiparallel orientation of the third strand, resulting from reverse Hoogsteen hydrogen bonds, is energetically the most favourable. These studies when extended to the mixed sequence triplexes, in which the second strand is a mixture of G and A, correspondingly the third strand is a mixture of G and APT, show that though the parallel orientation is still energetically more favourable, the antiparallel orientation becomes energetically comparable with an increasing number of thymines in the third strand. Structurally, for the mixed triplexes containing G and T in the third strand, it is seen that the basepair non-isomorphism between the C.G*G and the T.A*T triplets can be overcome with some changes in the base pair parameters without much distortion of either the backbone or the hydrogen bonds.

Structural Polymorphism in d(T).d(A)*d(T) Triple Helices

DNA triple helices containing two thymine strands and one adenine strand have been studied, using model building followed by energy minimisation, for different orientations of the third strand resulting from variation in the hydrogen bonding between the Watson-Crick duplex and the third strand and the glycosidic torsion angle in the third strand. Our results show that the structure with a parallel orientation of the third strand, in which the third strand base forms Hoogsteen hydrogen bonds with the adenine base in the Watson-Crick duplex, is energetically the most favourable. An antiparallel orientation of the third strand is also possible, in which the third strand base hydrogen bonds to both the bases in the Watson-Crick duplex. This structure is energetically comparable to the parallel structure. For the parallel triplex a 200ps molecular dynamics simulation starting from two different starting structures indicates that at 300K significant structural heterogeneity exists in this tripler structure. The results are compared with existing structural data on this class of triplexes derived from theoretical and NMR techniques.