RNA and DNA strands produce ionic current signatures when driven through an alpha-hemolysin channel by an applied voltage. Here we combine this nanopore detector with a support vector machine (SVM) to analyze DNA hairpin molecules on the millisecond time scale. Measurable properties include duplex stem length, base pair mismatches, and loop length. This nanopore instrument can discriminate between individual DNA hairpins that differ by one base pair or by one nucleotide.

We introduce a computational method for classification of individual DNA molecules measured by an alpha-hemolysin channel detector. We show classification with better than 99% accuracy for DNA hairpin molecules that differ only in their terminal Watson-Crick basepairs. Signal classification was done in silico to establish performance metrics (i.e., where train and test data were of known type, via single-species data files). It was then performed in solution to assay real mixtures of DNA hairpins. Hidden Markov Models (HMMs) were used with Expectation/Maximization for denoising and for associating a feature vector with the ionic current blockade of the DNA molecule. Support Vector Machines (SVMs) were used as discriminators, and were the focus of off-line training. A multiclass SVM architecture was designed to place less discriminatory load on weaker discriminators, and novel SVM kernels were used to boost discrimination strength. The tuning on HMMs and SVMs enabled biophysical analysis of the captured molecule states and state transitions; structure revealed in the biophysical analysis was used for better feature selection.

We consider the Hamiltonian dynamics and thermodynamics of spherically symmetric Einstein-Maxwell spacetimes with a negative cosmological constant. We impose boundary conditions that enforce every classical solution to be an exterior region of a Reissner-Nordström-anti-de Sitter black hole with a nondegenerate Killing horizon, with the spacelike hypersurfaces extending from the horizon bifurcation two-sphere to the asymptotically anti-de Sitter infinity. The constraints are simplified by a canonical transformation, which generalizes that given by Kuchař in the spherically symmetric vacuum Einstein theory, and the theory is reduced to its true dynamical degrees of freedom. After quantization, the grand partition function of a thermodynamical grand canonical ensemble is obtained by analytically continuing the * Dedicated to Karel Kuchař on the occasion of his sixtieth birthday. (Physical Review D did not, alas, permit a dedication in the published version of this paper.) † On leave

Figure 4. Comparison of single-mismatch detection with gold-quenched beacons versus DABCYL-quenched beacons. Titration of 5 µM of random target mixed with 4.2 nM of gold-DNA-rhodamine 6G conjugate and 0.6 µM of gold (A), and 5 µM of random target mixed with 10 nM of molecular beacon (B), with the perfect target (target 2) and the mismatch one (target 3). Target concentrations vary from 67 pM to 13 µM. For both probes, the perfect target (solid line) produces a faster and sharper increase of fluorescence than the target containing the mismatch (dashed line). Fluorescence intensities due to the buffer and the gold have been subtracted. The inset graphs in (A) and (B) show the evolution of the fluorescence as a function of time when the probe is mixed with 5 µM of random targets. In both cases, the random targets do not induce any change of fluorescence of the probe during the time of the titration. The hybridization is thus very specific to the matched or the mismatched targets. (C) Ratio between the titration curve with the perfect target (target 2) and the titration curve with the mismatched one (target 3). (D) Resolution of a matched and a mismatched target, competing for hybridization. Molecular beacon (dashed line), gold-DNA-dye conjugate (solid line). α is the population ratio of match to mismatch targets. The concentration of perfect target is fixed at 0.2 µM. D

We perform a Hamiltonian reduction of spherically symmetric Einstein gravity with a thin dust shell of positive rest mass. Three spatial topologies are considered: Euclidean (R 3 ), Kruskal (S 2 × R), and the spatial topology of a diametrically identified Kruskal (RP 3 \{a point at infinity}). For the Kruskal and RP 3 topologies the reduced phase space is four-dimensional, with one canonical pair associated with the shell and the other with the geometry; the latter pair disappears if one prescribes the value of the Schwarzschild mass at an asymptopia or at a throat. For the Euclidean topology the reduced phase space is necessarily two-dimensional, with only the canonical pair associated with the shell surviving. A time-reparametrization on a twodimensional phase space is introduced and used to bring the shell Hamilto- * Electronic address: friedman@thales.phys.uwm.edu † On leave of absence from Department of Physics, University of Helsinki. Present address: MaxPlanck-Institut für Gravitationsphysik, Schlaatzweg 1, D-14473 Potsdam, Germany. Electronic address: louko@aei-potsdam.mpg.de ‡ Electronic address: winters@csd.uwm.edu 1 nians to a simpler (and known) form associated with the proper time of the shell. An alternative reparametrization yields a square-root Hamiltonian that generalizes the Hamiltonian of a test shell in Minkowski space with respect to Minkowski time. Quantization is briefly discussed. The discrete mass spectrum that characterizes natural minisuperspace quantizations of vacuum wormholes and RP 3 -geons appears to persist as the geometrical part of the mass spectrum when the additional matter degree of freedom is added.

Background: We describe Support Vector Machine (SVM) applications to classification and clustering of channel current data. SVMs are variational-calculus based methods that are constrained to have structural risk minimization (SRM), i.e., they provide noise tolerant solutions for pattern recognition. The SVM approach encapsulates a significant amount of model-fitting information in the choice of its kernel. In work thus far, novel, information-theoretic, kernels have been successfully employed for notably better performance over standard kernels. Currently there are two approaches for implementing multiclass SVMs. One is called external multi-class that arranges several binary classifiers as a decision tree such that they perform a single-class decision making function, with each leaf corresponding to a unique class. The second approach, namely internal-multiclass, involves solving a single optimization problem corresponding to the entire data set (with multiple hyperplanes).

We consider the Hamiltonian dynamics and thermodynamics of spherically symmetric spacetimes within a one-parameter family of five-dimensional Lovelock theories. We adopt boundary conditions that make every classical solution part of a black hole exterior, with the spacelike hypersurfaces extending from the horizon bifurcation three-sphere to a timelike boundary with fixed intrinsic metric. The constraints are simplified by a Kucha\v{r}-type canonical transformation, and the theory is reduced to its true dynamical degrees of freedom. After quantization, the trace of the analytically continued Lorentzian time evolution operator is interpreted as the partition function of a thermodynamical canonical ensemble. Whenever the partition function is dominated by a Euclidean black hole solution, the entropy is given by the Lovelock analogue of the Bekenstein-Hawking entropy; in particular, in the low temperature limit the system exhibits a dominant classical solution that has no counterpart in Einstein's theory. The asymptotically flat space limit of the partition function does not exist. The results indicate qualitative robustness of the thermodynamics of five-dimensional Einstein theory upon the addition of a nontrivial Lovelock term.Comment: 22 pages, REVTeX v3.

Markov statistical methods may make it possible to develop an unsupervised learning process that can automatically identify genomic structure in prokaryotes in a comprehensive way. This approach is based on mutual information, probabilistic measures, hidden Markov models, and other purely statistical inputs. This approach also provides a uniquely common ground for comparative prokaryotic genomics. The approach is an on-going effort by its nature, as a multi-pass learning process, where each round is more informed than the last, and thereby allows a shift to the more powerful methods available for supervised learning at each iteration. It is envisaged that this "bootstrap" learning process will also be useful as a knowledge discovery tool. For such an ab initio prokaryotic gene-finder to work, however, it needs a mechanism to identify critical motif structure, such as those around the start of coding or start of transcription (and then, hopefully more).For eukaryotes, even with better start-of-coding identification, parsing of eukaryotic coding regions by the HMM is still limited by the HMM's single gene assumption, as evidenced by the poor performance in alternatively spliced regions. To address these complications an approach is described to expand the states in a eukaryotic gene-predictor HMM, to operate with two layers of DNA parsing. This extension from the single layer gene prediction parse is indicated after preliminary analysis of the C. elegans alt-splice statistics. State profiles have made use of a novel hash-interpolating MM (hIMM) method. A new implementation for an HMM-with-Duration is also described, with far-reaching application to gene-structure identification and analysis of channel current blockade data.