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.

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.

Direction dependence in supernova data: constraining isotropy

We revise and extend the extreme value statistic, introduced in Gupta et al., to study direction dependence in the high-redshift supernova data, arising either from departures, from the cosmological principle or due to direction-dependent statistical systematics in the data. We introduce a likelihood function that analytically marginalizes over the,Hubble constant and use it to extend our previous statistic. We also introduce a new statistic that is sensitive to direction dependence arising from living off-centre inside a large void as well as from previously mentioned reasons for anisotropy. We show that for large data sets, this statistic has a limiting form that can be computed analytically. We apply our statistics to the gold data sets from Riess et al., as in our previous work. Our revision and extension of the previous statistic show that the effect of marginalizing over the Hubble constant instead of using its best-fitting value on our results is only marginal. However, correction of errors in our previous work reduces the level of non-Gaussianity in the 2004 gold data that were found in our earlier work. The revised results for the 2007 gold data show that the data are consistent with isotropy and Gaussianity. Our second statistic confirms these results.

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.

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.

Lacunary Fourier series and a qualitative uncertainty principle for compact Lie groups

We define lacunary Fourier series on a compact connected semisimple Lie group G. If f is an element of L-1 (G) has lacunary Fourier series and f vanishes on a non empty open subset of G, then we prove that f vanishes identically. This result can be viewed as a qualitative uncertainty principle.

The principle of microscopic reversibility in organic chemistry - a critique

The principle of microscopic reversibility is one of the few generalising principles used in organic chemistry which have their roots in the fundamental laws of thermodynamics. It has, therefore, been highly popular. However, although the principle has some important uses, its general application is not without pitfalls. The principle is easy to misunderstand and to misapply: indeed, some of its formulations are semantically dubious. The principle is most dangerous when used as a charm, for it is more subtle than some of its formulations suggest. But above all, the principle may not be used for deducing or disproving the mechanism of a reaction, except when the mechanism in the reverse direction is known independently. For, such use is, perhaps, the deadliest misapplication.

First-principle description of magnonic PdnFem multilayers

Ab-initio calculations are used to determine the parameters that determine magnonic band structure of PdnFem multilayers (n = 2, m <= 8). We obtain the layer-resolved magnetization, the exchange coupling, and the magnetic anisotropy of the Pd-Fe structures. The Fe moment is 3.0 mu(B) close to the Pd layers and 2.2 mu(B) in the middle of the Fe layers. An intriguing but not usually considered aspect is that the elemental Pd is nonmagnetic, similar to Cu spacer layers in other multilayer systems. This leads to a pre-asymptotic ferromagnetic coupling through the Pd (about 40 mJ/m(2)). Furthermore, the Pd acquires a small moment due to spin polarization by neighboring Fe atoms, which translates into magnetic anisotropy. The anisotropies are large, in the range typical for L1(0) structures, which is beneficial for high-frequency applications. (C) 2011 American Institute of Physics. doi:10.1063/1.3556763]

Performance analysis of single-symbol maximum likelihood decodable linear STBCs

Performance of space-time block codes can be improved using the coordinate interleaving of the input symbols from rotated M-ary phase shift keying (MPSK) and M-ary quadrature amplitude modulation (MQAM) constellations. This paper is on the performance analysis of coordinate-interleaved space-time codes, which are a subset of single-symbol maximum likelihood decodable linear space-time block codes, for wireless multiple antenna terminals. The analytical and simulation results show that full diversity is achievable. Using the equivalent single-input single-output model, simple expressions for the average bit error rates are derived over flat uncorrelated Rayleigh fading channels. Optimum rotation angles are found by finding the minimum of the average bit error rate curves.

Ultrafast Raman loss spectroscopy (URLS): instrumentation and principle

In this paper, we report on the concept and the design principle of ultrafast Raman loss spectroscopy (URLS) as a structure-elucidating tool. URLS is an analogue of stimulated Raman scattering (SRS) but more sensitive than SRS with better signal-to-noise ratio. It involves the interaction of two laser sources, namely, a picosecond (ps) Raman pump pulse and a white-light (WL) continuum, with a sample, leading to the generation of loss signals on the higher energy (blue) side with respect to the wavelength of the Raman pump unlike the gain signal observed on the lower energy (red) side in SRS. These loss signals are at least 1.5 times more intense than the SRS signals. An experimental study providing an insight into the origin of this extra intensity in URLS as compared to SRS is reported. Furthermore, the very requirement of the experimental protocol for the signal detection to be on the higher energy side by design eliminates the interference from fluorescence, which appears on the red side. Unlike CARS, URLS signals are not precluded by the non-resonant background and, being a self-phase-matched process, URLS is experimentally easier. Copyright (C) 2011 John Wiley & Sons, Ltd.

Continuum theory of edge states of topological insulators: variational principle and boundary conditions

We develop a continuum theory to model low energy excitations of a generic four-band time reversal invariant electronic system with boundaries. We propose a variational energy functional for the wavefunctions which allows us to derive natural boundary conditions valid for such systems. Our formulation is particularly suited for developing a continuum theory of the protected edge/surface excitations of topological insulators both in two and three dimensions. By a detailed comparison of our analytical formulation with tight binding calculations of ribbons of topological insulators modelled by the Bernevig-Hughes-Zhang (BHZ) Hamiltonian, we show that the continuum theory with a natural boundary condition provides an appropriate description of the low energy physics.

Fast Likelihood Computation in Speech Recognition using Matrices

Acoustic modeling using mixtures of multivariate Gaussians is the prevalent approach for many speech processing problems. Computing likelihoods against a large set of Gaussians is required as a part of many speech processing systems and it is the computationally dominant phase for Large Vocabulary Continuous Speech Recognition (LVCSR) systems. We express the likelihood computation as a multiplication of matrices representing augmented feature vectors and Gaussian parameters. The computational gain of this approach over traditional methods is by exploiting the structure of these matrices and efficient implementation of their multiplication. In particular, we explore direct low-rank approximation of the Gaussian parameter matrix and indirect derivation of low-rank factors of the Gaussian parameter matrix by optimum approximation of the likelihood matrix. We show that both the methods lead to similar speedups but the latter leads to far lesser impact on the recognition accuracy. Experiments on 1,138 work vocabulary RM1 task and 6,224 word vocabulary TIMIT task using Sphinx 3.7 system show that, for a typical case the matrix multiplication based approach leads to overall speedup of 46 % on RM1 task and 115 % for TIMIT task. Our low-rank approximation methods provide a way for trading off recognition accuracy for a further increase in computational performance extending overall speedups up to 61 % for RM1 and 119 % for TIMIT for an increase of word error rate (WER) from 3.2 to 3.5 % for RM1 and for no increase in WER for TIMIT. We also express pairwise Euclidean distance computation phase in Dynamic Time Warping (DTW) in terms of matrix multiplication leading to saving of approximately of computational operations. In our experiments using efficient implementation of matrix multiplication, this leads to a speedup of 5.6 in computing the pairwise Euclidean distances and overall speedup up to 3.25 for DTW.