Graded IR Filters: Distinguishing Between Single and Multipoint NO2 center dot center dot center dot I Halogen Bonded Supramolecular Synthons (P, Q, and R Synthons)

The NO2 center dot center dot center dot I supramolecular synthon is a halogen bonded recognition pattern that is present in the crystal structures of many compounds that contain these functional groups. These synthons have been previously distinguished as P, Q, and R types using topological and geometrical criteria. A five step IR spectroscopic sequence is proposed here to distinguish between these synthon types in solid samples. Sets of known compounds that contain the P, Q, and R synthons are first taken to develop IR spectroscopic identifiers for them. The identifiers are then used to create graded IR filters that sieve the synthons. These filters contain signatures of the individual NO2 center dot center dot center dot I synthons and may be applied to distinguish between P, Q, and R synthon varieties. They are also useful to identify synthons that are of a borderline character, synthons in disordered structures wherein the crystal structure in itself is not sufficient to distinguish synthon types, and in the identification of the NO2 center dot center dot center dot I synthons in compounds with unknown crystal structures. This study establishes clear differences for the three different geometries P, Q, and Rand in the chemical differences in the intermolecular interactions contained in the synthons. Our IR method can be conveniently employed when single crystals are not readily available also in high throughput analysis. It is possible that such identification may also be adopted as an input for crystal structure prediction analysis of compounds with unknown crystal structures.

A Gaussian network model study suggests that structural fluctuations are higher for inactive states than active states of protein kinases

We performed Gaussian network model based normal mode analysis of 3-dimensional structures of multiple active and inactive forms of protein kinases. In 14 different kinases, a more number of residues (1095) show higher structural fluctuations in inactive states than those in active states (525), suggesting that, in general, mobility of inactive states is higher than active states. This statistically significant difference is consistent with higher crystallographic B-factors and conformational energies for inactive than active states, suggesting lower stability of inactive forms. Only a small number of inactive conformations with the DFG motif in the ``in'' state were found to have fluctuation magnitudes comparable to the active conformation. Therefore our study reports for the first time, intrinsic higher structural fluctuation for almost all inactive conformations compared to the active forms. Regions with higher fluctuations in the inactive states are often localized to the aC-helix, aG-helix and activation loop which are involved in the regulation and/or in structural transitions between active and inactive states. Further analysis of 476 kinase structures involved in interactions with another domain/protein showed that many of the regions with higher inactive-state fluctuation correspond to contact interfaces. We also performed extensive GNM analysis of (i) insulin receptor kinase bound to another protein and (ii) holo and apo forms of active and inactive conformations followed by multi-factor analysis of variance. We conclude that binding of small molecules or other domains/proteins reduce the extent of fluctuation irrespective of active or inactive forms. Finally, we show that the perceived fluctuations serve as a useful input to predict the functional state of a kinase.

Inner Bound on the GDOF of the K-User MIMO Gaussian Symmetric Interference Channel

The K-user multiple input multiple output (MIMO) Gaussian symmetric interference channel where each transmitter has M antennas and each receiver has N antennas is studied from a generalized degrees of freedom (GDOF) perspective. An inner bound on the GDOF is derived using a combination of techniques such as treating interference as noise, zero forcing (ZF) at the receivers, interference alignment (IA), and extending the Han-Kobayashi (HK) scheme to K users, as a function of the number of antennas and the log INR/log SNR level. Several interesting conclusions are drawn from the derived bounds. It is shown that when K > N/M + 1, a combination of the HK and IA schemes performs the best among the schemes considered. When N/M < K <= N/M + 1, the HK-scheme outperforms other schemes and is found to be GDOF optimal in many cases. In addition, when the SNR and INR are at the same level, ZF-receiving and the HK-scheme have the same GDOF performance.

Outer Bounds on the Sum Rate of the K-User MIMO Gaussian Interference Channel

This paper derives outer bounds on the sum rate of the K-user MIMO Gaussian interference channel (GIC). Three outer bounds are derived, under different assumptions of cooperation and providing side information to receivers. The novelty in the derivation lies in the careful selection of side information, which results in the cancellation of the negative differential entropy terms containing signal components, leading to a tractable outer bound. The overall outer bound is obtained by taking the minimum of the three outer bounds. The derived bounds are simplified for the MIMO Gaussian symmetric IC to obtain outer bounds on the generalized degrees of freedom (GDOF). The relative performance of the bounds yields insight into the performance limits of multiuser MIMO GICs and the relative merits of different schemes for interference management. These insights are confirmed by establishing the optimality of the bounds in specific cases using an inner bound on the GDOF derived by the authors in a previous work. It is also shown that many of the existing results on the GDOF of the GIC can be obtained as special cases of the bounds, e. g., by setting K = 2 or the number of antennas at each user to 1.

Study of Wrist Pulse Signals Using a Bi-Modal Gaussian Model

Wrist pulse signals contain important information about the health of a person and hence diagnosis based on pulse signals has assumed great importance. In this paper we demonstrate the efficacy of a two term Gaussian model to extract information from pulse signals. Results have been obtained by conducting experiments on several subjects to record wrist pulse signals for the cases of before exercise and after exercise. Parameters have been extracted from the recorded signals using the model and a paired t-test is performed, which shows that the parameters are significantly different between the two groups. Further, a recursive cluster elimination based support vector machine is used to perform classification between the groups. An average classification accuracy of 99.46% is obtained, along with top classifiers. It is thus shown that the parameters of the Gaussian model show changes across groups and hence the model is effective in distinguishing the changes taking place due to the two different recording conditions. The study has potential applications in healthcare.

Fluctuation theory of Rashba Fermi gases: Gaussian and beyond

Fermi gases with generalized Rashba spin-orbit coupling induced by a synthetic gauge field have the potential of realizing many interesting states, such as rashbon condensates and topological phases. Here, we address the key open problem of the fluctuation theory of such systems and demonstrate that beyond-Gaussian effects are essential to capture the finite temperature physics of such systems. We obtain their phase diagram by constructing an approximate non-Gaussian theory. We conclusively establish that spin-orbit coupling can enhance the exponentially small transition temperature (T-c) of a weakly attracting superfluid to the order of the Fermi temperature, paving a pathway towards high T-c superfluids.

MULTI-INSTRUMENT DETECTION IN POLYPHONIC MUSIC USING GAUSSIAN MIXTURE BASED FACTORIAL HMM

We formulate the problem of detecting the constituent instruments in a polyphonic music piece as a joint decoding problem. From monophonic data, parametric Gaussian Mixture Hidden Markov Models (GM-HMM) are obtained for each instrument. We propose a method to use the above models in a factorial framework, termed as Factorial GM-HMM (F-GM-HMM). The states are jointly inferred to explain the evolution of each instrument in the mixture observation sequence. The dependencies are decoupled using variational inference technique. We show that the joint time evolution of all instruments' states can be captured using F-GM-HMM. We compare performance of proposed method with that of Student's-t mixture model (tMM) and GM-HMM in an existing latent variable framework. Experiments on two to five polyphony with 8 instrument models trained on the RWC dataset, tested on RWC and TRIOS datasets show that F-GM-HMM gives an advantage over the other considered models in segments containing co-occurring instruments.

On the Gaussian Many-to-One X Channel

In this paper, the Gaussian many-to-one X channel (XC), which is a special case of general multiuser XC, is studied. In the Gaussian many-to-one XC, communication links exist between all transmitters and one of the receivers, along with a communication link between each transmitter and its corresponding receiver. As per the XC assumption, transmission of messages is allowed on all the links of the channel. This communication model is different from the corresponding manyto- one interference channel (IC). Transmission strategies, which involve using Gaussian codebooks and treating interference from a subset of transmitters as noise, are formulated for the above channel. Sum-rate is used as the criterion of optimality for evaluating the strategies. Initially, a 3 x 3 many-to-one XC is considered and three transmission strategies are analyzed. The first two strategies are shown to achieve sum-rate capacity under certain channel conditions. For the third strategy, a sum-rate outer bound is derived and the gap between the outer bound and the achieved rate is characterized. These results are later extended to the K x K case. Next, a region in which the many-to-one XC can be operated as a many-to-one IC without the loss of sum-rate is identified. Furthermore, in the above region, it is shown that using Gaussian codebooks and treating interference as noise achieve a rate point that is within K/2 -1 bits from the sum-rate capacity. Subsequently, some implications of the above results to the Gaussian many-to-one IC are discussed. Transmission strategies for the many-to-one IC are formulated, and channel conditions under which the strategies achieve sum-rate capacity are obtained. A region where the sum-rate capacity can be characterized to within K/2 -1 bits is also identified. Finally, the regions where the derived channel conditions are satisfied for each strategy are illustrated for a 3 x 3 many-to-one XC and the corresponding many-to-one IC.

Nonparametric Bayesian Density Modeling with Gaussian Processes

We present the Gaussian process density sampler (GPDS), an exchangeable generative model for use in nonparametric Bayesian density estimation. Samples drawn from the GPDS are consistent with exact, independent samples from a distribution defined by a density that is a transformation of a function drawn from a Gaussian process prior. Our formulation allows us to infer an unknown density from data using Markov chain Monte Carlo, which gives samples from the posterior distribution over density functions and from the predictive distribution on data space. We describe two such MCMC methods. Both methods also allow inference of the hyperparameters of the Gaussian process.

Image deconvolution using a Gaussian scale mixtures model to approximate the wavelet sparseness constraint

This paper proposes to use an extended Gaussian Scale Mixtures (GSM) model instead of the conventional ℓ1 norm to approximate the sparseness constraint in the wavelet domain. We combine this new constraint with subband-dependent minimization to formulate an iterative algorithm on two shift-invariant wavelet transforms, the Shannon wavelet transform and dual-tree complex wavelet transform (DTCWT). This extented GSM model introduces spatially varying information into the deconvolution process and thus enables the algorithm to achieve better results with fewer iterations in our experiments. ©2009 IEEE.

Models and algorithms for tracking of maneuvering objects using variable rate particle filters

Standard algorithms in tracking and other state-space models assume identical and synchronous sampling rates for the state and measurement processes. However, real trajectories of objects are typically characterized by prolonged smooth sections, with sharp, but infrequent, changes. Thus, a more parsimonious representation of a target trajectory may be obtained by direct modeling of maneuver times in the state process, independently from the observation times. This is achieved by assuming the state arrival times to follow a random process, typically specified as Markovian, so that state points may be allocated along the trajectory according to the degree of variation observed. The resulting variable dimension state inference problem is solved by developing an efficient variable rate particle filtering algorithm to recursively update the posterior distribution of the state sequence as new data becomes available. The methodology is quite general and can be applied across many models where dynamic model uncertainty occurs on-line. Specific models are proposed for the dynamics of a moving object under internal forcing, expressed in terms of the intrinsic dynamics of the object. The performance of the algorithms with these dynamical models is demonstrated on several challenging maneuvering target tracking problems in clutter. © 2006 IEEE.

Efficient line launch for bandwidth improvement of 10 Gbit/s multimode fibre links using elliptical Gaussian beam

A novel elliptical Gaussian beam line launch is shown to allow improved system capacity for high speed multimode fibre links. This launch maintains higher bandwidth than dual launch even with misalignment of ±6 μm despite not requiring testing at installation. ©2010 IEEE.

Tractable nonparametric bayesian inference in poisson processes with Gaussian process intensities

The inhomogeneous Poisson process is a point process that has varying intensity across its domain (usually time or space). For nonparametric Bayesian modeling, the Gaussian process is a useful way to place a prior distribution on this intensity. The combination of a Poisson process and GP is known as a Gaussian Cox process, or doubly-stochastic Poisson process. Likelihood-based inference in these models requires an intractable integral over an infinite-dimensional random function. In this paper we present the first approach to Gaussian Cox processes in which it is possible to perform inference without introducing approximations or finitedimensional proxy distributions. We call our method the Sigmoidal Gaussian Cox Process, which uses a generative model for Poisson data to enable tractable inference via Markov chain Monte Carlo. We compare our methods to competing methods on synthetic data and apply it to several real-world data sets. Copyright 2009.