ICGE: an R package for detecting relevant clusters and atypical units in gene expression

Background: Gene expression technologies have opened up new ways to diagnose and treat cancer and other diseases. Clustering algorithms are a useful approach with which to analyze genome expression data. They attempt to partition the genes into groups exhibiting similar patterns of variation in expression level. An important problem associated with gene classification is to discern whether the clustering process can find a relevant partition as well as the identification of new genes classes. There are two key aspects to classification: the estimation of the number of clusters, and the decision as to whether a new unit (gene, tumor sample ... ) belongs to one of these previously identified clusters or to a new group. Results: ICGE is a user-friendly R package which provides many functions related to this problem: identify the number of clusters using mixed variables, usually found by applied biomedical researchers; detect whether the data have a cluster structure; identify whether a new unit belongs to one of the pre-identified clusters or to a novel group, and classify new units into the corresponding cluster. The functions in the ICGE package are accompanied by help files and easy examples to facilitate its use. Conclusions: We demonstrate the utility of ICGE by analyzing simulated and real data sets. The results show that ICGE could be very useful to a broad research community.

A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations.

The effects of complex boundary conditions on flows are represented by a volume force in the immersed boundary methods. The problem with this representation is that the volume force exhibits non-physical oscillations in moving boundary simulations. A smoothing technique for discrete delta functions has been developed in this paper to suppress the non-physical oscillations in the volume forces. We have found that the non-physical oscillations are mainly due to the fact that the derivatives of the regular discrete delta functions do not satisfy certain moment conditions. It has been shown that the smoothed discrete delta functions constructed in this paper have one-order higher derivative than the regular ones. Moreover, not only the smoothed discrete delta functions satisfy the first two discrete moment conditions, but also their derivatives satisfy one-order higher moment condition than the regular ones. The smoothed discrete delta functions are tested by three test cases: a one-dimensional heat equation with a moving singular force, a two-dimensional flow past an oscillating cylinder, and the vortex-induced vibration of a cylinder. The numerical examples in these cases demonstrate that the smoothed discrete delta functions can effectively suppress the non-physical oscillations in the volume forces and improve the accuracy of the immersed boundary method with direct forcing in moving boundary simulations.

Attenuation tomography. Modelling regional love waves: Imperial Valley to Pasadena

Abstract to Part I

The inverse problem of seismic wave attenuation is solved by an iterative back-projection method. The seismic wave quality factor, Q, can be estimated approximately by inverting the S-to-P amplitude ratios. Effects of various uncertain ties in the method are tested and the attenuation tomography is shown to be useful in solving for the spatial variations in attenuation structure and in estimating the effective seismic quality factor of attenuating anomalies.

Back-projection attenuation tomography is applied to two cases in southern California: Imperial Valley and the Coso-Indian Wells region. In the Coso-Indian Wells region, a highly attenuating body (S-wave quality factor (Q_β ≈ 30) coincides with a slow P-wave anomaly mapped by Walck and Clayton (1987). This coincidence suggests the presence of a magmatic or hydrothermal body 3 to 5 km deep in the Indian Wells region. In the Imperial Valley, slow P-wave travel-time anomalies and highly attenuating S-wave anomalies were found in the Brawley seismic zone at a depth of 8 to 12 km. The effective S-wave quality factor is very low (Q_β ≈ 20) and the P-wave velocity is 10% slower than the surrounding areas. These results suggest either magmatic or hydrothermal intrusions, or fractures at depth, possibly related to active shear in the Brawley seismic zone.

No-block inversion is a generalized tomographic method utilizing the continuous form of an inverse problem. The inverse problem of attenuation can be posed in a continuous form , and the no-block inversion technique is applied to the same data set used in the back-projection tomography. A relatively small data set with little redundancy enables us to apply both techniques to a similar degree of resolution. The results obtained by the two methods are very similar. By applying the two methods to the same data set, formal errors and resolution can be directly computed for the final model, and the objectivity of the final result can be enhanced.

Both methods of attenuation tomography are applied to a data set of local earthquakes in Kilauea, Hawaii, to solve for the attenuation structure under Kilauea and the East Rift Zone. The shallow Kilauea magma chamber, East Rift Zone and the Mauna Loa magma chamber are delineated as attenuating anomalies. Detailed inversion reveals shallow secondary magma reservoirs at Mauna Ulu and Puu Oo, the present sites of volcanic eruptions. The Hilina Fault zone is highly attenuating, dominating the attenuating anomalies at shallow depths. The magma conduit system along the summit and the East Rift Zone of Kilauea shows up as a continuous supply channel extending down to a depth of approximately 6 km. The Southwest Rift Zone, on the other hand, is not delineated by attenuating anomalies, except at a depth of 8-12 km, where an attenuating anomaly is imaged west of Puu Kou. The Ylauna Loa chamber is seated at a deeper level (about 6-10 km) than the Kilauea magma chamber. Resolution in the Mauna Loa area is not as good as in the Kilauea area, and there is a trade-off between the depth extent of the magma chamber imaged under Mauna Loa and the error that is due to poor ray coverage. Kilauea magma chamber, on the other hand, is well resolved, according to a resolution test done at the location of the magma chamber.

Abstract to Part II

Long period seismograms recorded at Pasadena of earthquakes occurring along a profile to Imperial Valley are studied in terms of source phenomena (e.g., source mechanisms and depths) versus path effects. Some of the events have known source parameters, determined by teleseismic or near-field studies, and are used as master events in a forward modeling exercise to derive the Green's functions (SH displacements at Pasadena that are due to a pure strike-slip or dip-slip mechanism) that describe the propagation effects along the profile. Both timing and waveforms of records are matched by synthetics calculated from 2-dimensional velocity models. The best 2-dimensional section begins at Imperial Valley with a thin crust containing the basin structure and thickens towards Pasadena. The detailed nature of the transition zone at the base of the crust controls the early arriving shorter periods (strong motions), while the edge of the basin controls the scattered longer period surface waves. From the waveform characteristics alone, shallow events in the basin are easily distinguished from deep events, and the amount of strike-slip versus dip-slip motion is also easily determined. Those events rupturing the sediments, such as the 1979 Imperial Valley earthquake, can be recognized easily by a late-arriving scattered Love wave that has been delayed by the very slow path across the shallow valley structure.

Determination of source finiteness and depth of large earthquakes

In this thesis, a method to retrieve the source finiteness, depth of faulting, and the mechanisms of large earthquakes from long-period surface waves is developed and applied to several recent large events.

In Chapter 1, source finiteness parameters of eleven large earthquakes were determined from long-period Rayleigh waves recorded at IDA and GDSN stations. The basic data set is the seismic spectra of periods from 150 to 300 sec. Two simple models of source finiteness are studied. The first model is a point source with finite duration. In the determination of the duration or source-process times, we used Furumoto's phase method and a linear inversion method, in which we simultaneously inverted the spectra and determined the source-process time that minimizes the error in the inversion. These two methods yielded consistent results. The second model is the finite fault model. Source finiteness of large shallow earthquakes with rupture on a fault plane with a large aspect ratio was modeled with the source-finiteness function introduced by Ben-Menahem. The spectra were inverted to find the extent and direction of the rupture of the earthquake that minimize the error in the inversion. This method is applied to the 1977 Sumbawa, Indonesia, 1979 Colombia-Ecuador, 1983 Akita-Oki, Japan, 1985 Valparaiso, Chile, and 1985 Michoacan, Mexico earthquakes. The method yielded results consistent with the rupture extent inferred from the aftershock area of these earthquakes.

In Chapter 2, the depths and source mechanisms of nine large shallow earthquakes were determined. We inverted the data set of complex source spectra for a moment tensor (linear) or a double couple (nonlinear). By solving a least-squares problem, we obtained the centroid depth or the extent of the distributed source for each earthquake. The depths and source mechanisms of large shallow earthquakes determined from long-period Rayleigh waves depend on the models of source finiteness, wave propagation, and the excitation. We tested various models of the source finiteness, Q, the group velocity, and the excitation in the determination of earthquake depths.

The depth estimates obtained using the Q model of Dziewonski and Steim (1982) and the excitation functions computed for the average ocean model of Regan and Anderson (1984) are considered most reasonable. Dziewonski and Steim's Q model represents a good global average of Q determined over a period range of the Rayleigh waves used in this study. Since most of the earthquakes studied here occurred in subduction zones Regan and Anderson's average ocean model is considered most appropriate.

Our depth estimates are in general consistent with the Harvard CMT solutions. The centroid depths and their 90 % confidence intervals (numbers in the parentheses) determined by the Student's t test are: Colombia-Ecuador earthquake (12 December 1979), d = 11 km, (9, 24) km; Santa Cruz Is. earthquake (17 July 1980), d = 36 km, (18, 46) km; Samoa earthquake (1 September 1981), d = 15 km, (9, 26) km; Playa Azul, Mexico earthquake (25 October 1981), d = 41 km, (28, 49) km; El Salvador earthquake (19 June 1982), d = 49 km, (41, 55) km; New Ireland earthquake (18 March 1983), d = 75 km, (72, 79) km; Chagos Bank earthquake (30 November 1983), d = 31 km, (16, 41) km; Valparaiso, Chile earthquake (3 March 1985), d = 44 km, (15, 54) km; Michoacan, Mexico earthquake (19 September 1985), d = 24 km, (12, 34) km.

In Chapter 3, the vertical extent of faulting of the 1983 Akita-Oki, and 1977 Sumbawa, Indonesia earthquakes are determined from fundamental and overtone Rayleigh waves. Using fundamental Rayleigh waves, the depths are determined from the moment tensor inversion and fault inversion. The observed overtone Rayleigh waves are compared to the synthetic overtone seismograms to estimate the depth of faulting of these earthquakes. The depths obtained from overtone Rayleigh waves are consistent with the depths determined from fundamental Rayleigh waves for the two earthquakes. Appendix B gives the observed seismograms of fundamental and overtone Rayleigh waves for eleven large earthquakes.

Nucleon structure functions from ν_µ-Fe interactions and a study of the valence quark distribution

Data were taken in 1979-80 by the CCFRR high energy neutrino experiment at Fermilab. A total of 150,000 neutrino and 23,000 antineutrino charged current events in the approximate energy range 25 < E_v < 250GeV are measured and analyzed. The structure functions F2 and xF_3 are extracted for three assumptions about σ_L/σ_T:R=0., R=0.1 and R= a QCD based expression. Systematic errors are estimated and their significance is discussed. Comparisons or the X and Q^2 behaviour or the structure functions with results from other experiments are made.

We find that statistical errors currently dominate our knowledge of the valence quark distribution, which is studied in this thesis. xF_3 from different experiments has, within errors and apart from level differences, the same dependence on x and Q^2, except for the HPWF results. The CDHS F_2 shows a clear fall-off at low-x from the CCFRR and EMC results, again apart from level differences which are calculable from cross-sections.

The result for the the GLS rule is found to be 2.83±.15±.09±.10 where the first error is statistical, the second is an overall level error and the third covers the rest of the systematic errors. QCD studies of xF_3 to leading and second order have been done. The QCD evolution of xF_3, which is independent of R and the strange sea, does not depend on the gluon distribution and fits yield

ʌ_(LO) = 88^(+163)_(-78) ^(+113)_(-70) MeV

The systematic errors are smaller than the statistical errors. Second order fits give somewhat different values of ʌ, although α_s (at Q^2_0 = 12.6 GeV^2) is not so different.

A fit using the better determined F_2 in place of xF_3 for x > 0.4 i.e., assuming q = 0 in that region, gives

ʌ_(LO) = 266^(+114)_(-104) ^(+85)_(-79) MeV

Again, the statistical errors are larger than the systematic errors. An attempt to measure R was made and the measurements are described. Utilizing the inequality q(x)≥0 we find that in the region x > .4 R is less than 0.55 at the 90% confidence level.

Dense, efficient chip-to-chip communication at the extremes of computing

The scalability of CMOS technology has driven computation into a diverse range of applications across the power consumption, performance and size spectra. Communication is a necessary adjunct to computation, and whether this is to push data from node-to-node in a high-performance computing cluster or from the receiver of wireless link to a neural stimulator in a biomedical implant, interconnect can take up a significant portion of the overall system power budget. Although a single interconnect methodology cannot address such a broad range of systems efficiently, there are a number of key design concepts that enable good interconnect design in the age of highly-scaled CMOS: an emphasis on highly-digital approaches to solving ‘analog’ problems, hardware sharing between links as well as between different functions (such as equalization and synchronization) in the same link, and adaptive hardware that changes its operating parameters to mitigate not only variation in the fabrication of the link, but also link conditions that change over time. These concepts are demonstrated through the use of two design examples, at the extremes of the power and performance spectra.

A novel all-digital clock and data recovery technique for high-performance, high density interconnect has been developed. Two independently adjustable clock phases are generated from a delay line calibrated to 2 UI. One clock phase is placed in the middle of the eye to recover the data, while the other is swept across the delay line. The samples produced by the two clocks are compared to generate eye information, which is used to determine the best phase for data recovery. The functions of the two clocks are swapped after the data phase is updated; this ping-pong action allows an infinite delay range without the use of a PLL or DLL. The scheme's generalized sampling and retiming architecture is used in a sharing technique that saves power and area in high-density interconnect. The eye information generated is also useful for tuning an adaptive equalizer, circumventing the need for dedicated adaptation hardware.

On the other side of the performance/power spectra, a capacitive proximity interconnect has been developed to support 3D integration of biomedical implants. In order to integrate more functionality while staying within size limits, implant electronics can be embedded onto a foldable parylene (‘origami’) substrate. Many of the ICs in an origami implant will be placed face-to-face with each other, so wireless proximity interconnect can be used to increase communication density while decreasing implant size, as well as facilitate a modular approach to implant design, where pre-fabricated parylene-and-IC modules are assembled together on-demand to make custom implants. Such an interconnect needs to be able to sense and adapt to changes in alignment. The proposed array uses a TDC-like structure to realize both communication and alignment sensing within the same set of plates, increasing communication density and eliminating the need to infer link quality from a separate alignment block. In order to distinguish the communication plates from the nearby ground plane, a stimulus is applied to the transmitter plate, which is rectified at the receiver to bias a delay generation block. This delay is in turn converted into a digital word using a TDC, providing alignment information.

Negative regulators of a growth factor-mediated signaling pathway in the nematode Caenorhabditis elegans

Vulval differentiation in C. elegans is mediated by an Epidermal growth factor (EGF)- EGF receptor (EGFR) signaling pathway. I have cloned unc-101, a negative regulator of vulval differentiation of the nematode C. elegans. unc-101 encodes a homolog of AP47, the medium chain of the trans-Golgi clathrin-associated protein complex. This identity was confirmed by cloning and comparing sequence of a C. elegans homolog of AP50, the medium chain of the plasma membrane clathrin-associated protein complex. I provided the first genetic evidence that the trans-Golgi clathrin-coated vesicles are involved in regulation of an EGF signaling pathway. Most of the unc-101 alleles are deletions or nonsense mutations, suggesting that these alleles severely reduce the unc-101 activity. A hybrid gene that contains parts of unc-101 and mouse AP4 7 rescued at least two phenotypes of unc-101 mutations, the Unc and the suppression of vulvaless phenotype of let-23(sy1) mutation. Therefore, the functions of AP47 are conserved between nematodes and mammals.

unc-101 mutations can cause a greater than wild-type vulval differentiation in combination with certain mutations in sli-1, another negative regulator of the vulval induction pathway. A mutation in a new gene, rok-1, causes no defect by itself, but causes a greater than wild-type vulval differentiation in the presence of a sli-1 mutation. The unc-101; rok-1; sli-1 triple mutants display a greater extent of vulval differentiation than any double mutant combinations of unc-101, rok-1 and sli-1. Therefore, rok-1 locus defines another negative regulator of the vulval induction pathway.

I analyzed a second gene encoding an AP47 homolog in C. elegans. This gene, CEAP47, encodes a protein 72% identical to both unc-101 and mammalian AP47. A hybrid gene containing parts of unc-101 and CEAP47 sequences can rescue phenotypes of unc-101 mutants, indicating that UNC- 101 and CEAP47 proteins can be redundant if expressed in the same set of cells.

Descriptive set theory and the ergodic theory of countable groups

The primary focus of this thesis is on the interplay of descriptive set theory and the ergodic theory of group actions. This incorporates the study of turbulence and Borel reducibility on the one hand, and the theory of orbit equivalence and weak equivalence on the other. Chapter 2 is joint work with Clinton Conley and Alexander Kechris; we study measurable graph combinatorial invariants of group actions and employ the ultraproduct construction as a way of constructing various measure preserving actions with desirable properties. Chapter 3 is joint work with Lewis Bowen; we study the property MD of residually finite groups, and we prove a conjecture of Kechris by showing that under general hypotheses property MD is inherited by a group from one of its co-amenable subgroups. Chapter 4 is a study of weak equivalence. One of the main results answers a question of Abért and Elek by showing that within any free weak equivalence class the isomorphism relation does not admit classification by countable structures. The proof relies on affirming a conjecture of Ioana by showing that the product of a free action with a Bernoulli shift is weakly equivalent to the original action. Chapter 5 studies the relationship between mixing and freeness properties of measure preserving actions. Chapter 6 studies how approximation properties of ergodic actions and unitary representations are reflected group theoretically and also operator algebraically via a group's reduced C^*-algebra. Chapter 7 is an appendix which includes various results on mixing via filters and on Gaussian actions.