Algorithms for Hidden Markov Models With Imprecisely Specified Parameters

Hidden Markov models (HMMs) are widely used models for sequential data. As with other probabilistic graphical models, they require the specification of precise probability values, which can be too restrictive for some domains, especially when data are scarce or costly to acquire. We present a generalized version of HMMs, whose quantification can be done by sets of, instead of single, probability distributions. Our models have the ability to suspend judgment when there is not enough statistical evidence, and can serve as a sensitivity analysis tool for standard non-stationary HMMs. Efficient inference algorithms are developed to address standard HMM usage such as the computation of likelihoods and most probable explanations. Experiments with real data show that the use of imprecise probabilities leads to more reliable inferences without compromising efficiency.

Decision Making by Credal Nets

Credal nets are probabilistic graphical models which extend Bayesian nets to cope with sets of distributions. This feature makes the model particularly suited for the implementation of classifiers and knowledge-based systems. When working with sets of (instead of single) probability distributions, the identification of the optimal option can be based on different criteria, some of them eventually leading to multiple choices. Yet, most of the inference algorithms for credal nets are designed to compute only the bounds of the posterior probabilities. This prevents some of the existing criteria from being used. To overcome this limitation, we present two simple transformations for credal nets which make it possible to compute decisions based on the maximality and E-admissibility criteria without any modification in the inference algorithms. We also prove that these decision problems have the same complexity of standard inference, being NP^PP-hard for general credal nets and NP-hard for polytrees.

Hidden Markov Models With Set-Valued Parameters

Hidden Markov models (HMMs) are widely used probabilistic models of sequential data. As with other probabilistic models, they require the specification of local conditional probability distributions, whose assessment can be too difficult and error-prone, especially when data are scarce or costly to acquire. The imprecise HMM (iHMM) generalizes HMMs by allowing the quantification to be done by sets of, instead of single, probability distributions. iHMMs have the ability to suspend judgment when there is not enough statistical evidence, and can serve as a sensitivity analysis tool for standard non-stationary HMMs. In this paper, we consider iHMMs under the strong independence interpretation, for which we develop efficient inference algorithms to address standard HMM usage such as the computation of likelihoods and most probable explanations, as well as performing filtering and predictive inference. Experiments with real data show that iHMMs produce more reliable inferences without compromising the computational efficiency.

Multilinear and Integer Programming for Markov Decision Processes with Imprecise Probabilities

Markov Decision Processes (MDPs) are extensively used to encode sequences of decisions with probabilistic effects. Markov Decision Processes with Imprecise Probabilities (MDPIPs) encode sequences of decisions whose effects are modeled using sets of probability distributions. In this paper we examine the computation of Γ-maximin policies for MDPIPs using multilinear and integer programming. We discuss the application of our algorithms to “factored” models and to a recent proposal, Markov Decision Processes with Set-valued Transitions (MDPSTs), that unifies the fields of probabilistic and “nondeterministic” planning in artificial intelligence research. 

Partially Ordered Preferences in Decision Trees: Computing Strategies with Imprecision in Probabilities

Partially ordered preferences generally lead to choices that do not abide by standard expected utility guidelines; often such preferences are revealed by imprecision in probability values. We investigate five criteria for strategy selection in decision trees with imprecision in probabilities: “extensive” Γ-maximin and Γ-maximax, interval dominance, maximality and E-admissibility. We present algorithms that generate strategies for all these criteria; our main contribution is an algorithm for Eadmissibility that runs over admissible strategies rather than over sets of probability distributions.

Spatially Correlated Multiple-Ananna Channel Capacity Distributions

In this paper, we investigate the capacity of multiple-input multiple-output (MIMO) wireless communication systems over spatially correlated Rayleigh distributed flat fading channels with complex Gaussian additive noise. Specifically, we derive the probability density function of the mutual information between transmitted and received complex signals of MIMO systems. Using this density we derive the closed-form ergodic capacity (mean), delay-limited capacity, capacity variance and outage capacity formulas for spatially correlated channels and then evaluate these formulas numerically. Numerical results show how the channel correlation degrades the capacity of MIMO communication systems. We also show that the density of mutual information of correlated/uncorrelated MIMO systems can be approximated by a Gaussian density with derived mean and variance, even for a finite number of inputs and outputs.

DNA double-strand break distributions in X-ray and alpha-particle irradiated V79 cells: Evidence for non-random breakage

Many studies have shown that with increasing LET of ionizing radiation the RBE (relative biological effectiveness) for dsb (double strand breaks) induction remains around 1.0 despite the increase in the RBE for cell killing. This has been attributed to an increase in the complexity of lesions, classified as dsb with current techniques, at multiply damaged sites. This study determines the molecular weight distributions of DNA from Chinese hamster V79 cells irradiated with X-rays or 110 keV/mu m alpha-particles. Two running conditions for pulsed-field gel-electrophoresis were chosen to give optimal separation of fragments either in the 225 kbp-5.7 Mbp range or the 0.3 kbp to 225 kbp range. Taking the total fraction of DNA migrating into the gel as a measure of fragmentation, the RBE for dsb induction was less than 1.0 for both molecular weight regions studied. The total yields of dsb were 8.2 x 10(-9) dsb/Gy/bp for X-rays and 7.8 x 10(-9) dsb/Gy/bp for a-particles, measured using a random breakage model. Analysis of the RBE of alpha-particles versus molecular weight gave a different response. In the 0.4 Mbp-57 Mbp region the RBE was less than 1.0; however, below 0.4 Mbp the RBE increased above 1.0. The frequency distributions of fragment sizes were found to differ from those predicted by a model assuming random breakage along the length of the DNA and the differences were greater for alpha-particles than for X-rays. An excess of fragments induced by a single-hit mechanism was found in the 8-300 kbp region and for X-rays and alpha-particles these corresponded to an extra 0.8 x 10(-9) and 3.4 x 10(-9) dsb/bp/Gy, respectively. Thus for every alpha-particle track that induces a dsb there is a 44% probability of inducing a second break within 300 kbp and for electron tracks the probability is 10%. This study shows that the distribution of damage from a high LET alpha-particle track is significantly different from that observed with low LET X-rays. In particular, it suggests that the fragmentation patterns of irradiated DNA may be related to the higher-order chromatin repealing structures found in intact cells.

Modelling local-scale determinants and the probability of microarthropod species occurrence in Antarctic soils

Soil fauna in the extreme conditions of Antarctica consists of a few microinvertebrate species patchily distributed at different spatial scales. Populations of the prostigmatic mite Stereotydeus belli and the collembolan Gressittacantha terranova from northern Victoria Land (Antarctica) were used as models to study the effect of soil properties on microarthropod distributions. In agreement with the general assumption that the development and distribution of life in these ecosystems is mainly controlled by abiotic factors, we found that the probability of occurrence of S. belli depends on soil moisture and texture and on the sampling period (which affects the general availability of water); surprisingly, none of the analysed variables were significantly related to the G. terranova distribution. Based on our results and literature data, we propose a theoretical model that introduces biotic interactions among the major factors driving the local distribution of collembolans in Antarctic terrestrial ecosystems. (c) 2007 Elsevier Ltd. All rights reserved.

Molecular Distributions in the Inner Regions of Protostellar Disks

The distributions of molecules in the inner regions of a protostellar disk are presented. These were calculated using an uncoupled chemical/dynamical model, with a numerical integration of the vertical disk structure. A comparison between models with and without the effects of X-ray ionisation is made, and molecules are identified which are good tracers of the ionisation level in this part of the disk, notably CN and C_2H. In the region considered in this paper (r

Escape times for rigid Brownian rotators in a bistable potential from the time evolution of the Green function and the characteristic time of the probability evolution

The greatest relaxation time for an assembly of three- dimensional rigid rotators in an axially symmetric bistable potential is obtained exactly in terms of continued fractions as a sum of the zero frequency decay functions (averages of the Legendre polynomials) of the system. This is accomplished by studying the entire time evolution of the Green function (transition probability) by expanding the time dependent distribution as a Fourier series and proceeding to the zero frequency limit of the Laplace transform of that distribution. The procedure is entirely analogous to the calculation of the characteristic time of the probability evolution (the integral of the configuration space probability density function with respect to the position co-ordinate) for a particle undergoing translational diffusion in a potential; a concept originally used by Malakhov and Pankratov (Physica A 229 (1996) 109). This procedure allowed them to obtain exact solutions of the Kramers one-dimensional translational escape rate problem for piecewise parabolic potentials. The solution was accomplished by posing the problem in terms of the appropriate Sturm-Liouville equation which could be solved in terms of the parabolic cylinder functions. The method (as applied to rotational problems and posed in terms of recurrence relations for the decay functions, i.e., the Brinkman approach c.f. Blomberg, Physica A 86 (1977) 49, as opposed to the Sturm-Liouville one) demonstrates clearly that the greatest relaxation time unlike the integral relaxation time which is governed by a single decay function (albeit coupled to all the others in non-linear fashion via the underlying recurrence relation) is governed by a sum of decay functions. The method is easily generalized to multidimensional state spaces by matrix continued fraction methods allowing one to treat non-axially symmetric potentials, where the distribution function is governed by two state variables. (C) 2001 Elsevier Science B.V. All rights reserved.

Angular distributions of electrons in photoionization of 3s subshell of atomic chlorine

R-matrix calculated photoelectron angular distribution asymmetry parameters, beta for Cl+ 3s3p(5) P-3(o) and 3s(2)3p(3) (D-2(o))3d P-1(o) final ionic states in photoionization of the ground state of atomic Cl are presented in the photon energy range from threshold to 80 eV. The results, characterized by prominent autoionization structures which are sensitive to multielectron correlations, are compared with those recently measured by Whitfield et al (Whitfield S B, Kehoe K, Krause M 0 and Caldwell C D 2000 Phys. Rev. Lett. 84 4818). Contrary to experiment and previous theoretical calculations, our detailed CIV3 structure calculation (Deb N C, Crothers D S F, Felfli Z and Msezane A Z 2002 J. Phys. B: At. Mol. Opt. Phys. submitted) has identified the lowest P-1(o) level of Cl+ as 3S(2)3p(3)(D-2(o))3d P-1(o) rather than 3s3p(5) P-1(o). The implications and consequences of the measured data for the 3s P-1(o) level are also discussed in the context of our calculated energies for Cl+ and beta for 3d P-1(o).

Potential improvements in the therapeutic ratio of prostate cancer irradiation: dose escalation of pathologically identified tumour nodules using intensity modulated radiotherapy.

The potential of intensity modulated radiotherapy (IMRT) to improve the therapeutic ratio in prostate cancer by dose escalation of intraprostatic tumour nodules (IPTNs) was investigated using a simultaneous integrated boost technique. The prostate and organs-at-risk were outlined on CT images from six prostate cancer patients. Positions of IPTNs were transferred onto the CT images from prostate maps derived from sequential large block sections of whole prostatectomy specimens. Inverse planned IMRT dose distributions were created to irradiate the prostate to 70 Gy and all the IPTNs to 90 Gy. A second plan was produced to escalate only the dominant IPTN (DIPTN) to 90 Gy, mimicking current imaging techniques. These plans were compared with homogeneous prostate irradiation to 70 Gy using dose–volume histograms, tumour control probability (TCP) and normal tissue complication probability (NTCP) for the rectum. The mean dose to IPTNs was increased from 69.8 Gy to 89.1 Gy if all the IPTNs were dose escalated (p=0.0003). This corresponded to a mean increase in TCP of 8.7–31.2% depending on the /ß ratio of prostate cancer (p