Recent observations of rapid changes within the Greenland and West Antarctic Ice Sheets indicate that ice sheets are far more dynamic than many glaciologists would have predicted only a decade ago. At present ice-sheet models used in climate-change assessments, such as the IPCC reports, lack the physics required to capture these rapid changes. Given the impact that variations in ice-sheet volume have on sea level, it is critical that improved ice-sheet models be developed soon. I will touch on some of the mechanisms of rapid change in ice sheets, focusing on the buttressing role of ice shelves. In addition, I will discuss the near-term future of computational glaciology, and why some have labeled the present as the "golden age of glaciology".

The Earth's magnetic field is continually regenerated by dynamo action in the liquid iron core. Numerical models for this process first achieved self-sustaining magnetic fields about ten years ago, and the results have been spectacular. Models have successfully reproduced important features of the Earth's magnetic field, including the dipole dominance and the episodic reversal of polarity. However, it is generally acknowledged that these models are unrealistic in many respects. All of the models currently use physical properties that are very far from Earth-like values. As a consequence, the nature of the dynamics is altered and the potential to address important geophysical questions is limited. The challenge for making improvements lies in dealing with the effects of unresolved flow. Simple models based on eddy diffusion are probably inadequate because the influences of rotation and a strong magnetic field make the small-scale flow highly anisotropic. Alternative strategies that reproduce the expected anisotropy and evolve with the large-scale fields are described. Encouraging results are presented for both plane-layer and spherical-shell dynamo models and a summary of the outstanding challenges is given.

Cell migration is an essential process involved in many key functions of normal physiology and disease including cellular development in embryogenesis, neuronal growth, cancer metastasis or tumor invasion, and tissue repair in wound healing or immune response. Fluorescent Speckle Microscopy (FSM) is a new live cell imaging technique for probing the molecular regulation mechanisms of this process. Time-lapse FSM images of fluorescently labeled proteins in live cells contain a rich set of information about the dynamics of the target protein structure. In this talk, I will first give you an introduction to cell migration and this new imaging technique. I will then show you how multi-dimensional data can be extracted from raw FSM movies focusing on the reconstruction of intracellular forces. In the end, examples will be given to demonstrate how advanced analysis of these data and mathematical modeling make it possible to do quantitative study of the regulation mechanisms of cellular functions at the molecular level.

Both the `reverse engineering' of biological networks (for example, by integrating sequence data and expression data) and the analysis of their underlying design (by revealing the evolutionary mechanisms responsible for the resulting topologies) can be re-cast as problems in classification: predicting a categorical label in high-dimensional feature spaces. In the case of inferring biological networks, predicting up- or down- regulation of genes allows us to learn ab intio the transcription factor binding sites (or `motifs') and to generate a predictive model of transcriptional regulation. In the case of revealing evolutionary designs, quantitative, unambiguous model validation can be performed, clarifying which of several possible theoretical models of how biological networks evolve might best (or worst) describe real-world networks. In either case, by taking a machine learning approach, we statistically validate the models both on held-out data and via randomizations of the original dataset to assess statistical significance. By allowing the data to decide which features are the most important (based on predictive power rather than overabundance relative to an assumed null model) we learn models which are both statically validated and biologically interpretable. 'References':

1) Manuel Middendorf, Anshul Kundaje, Chris Wiggins, Yoav Freund, and Christina Leslie. Predicting genetic regulatory response using classification. ISMB 2004; q-bio/0411028

2) Manuel Middendorf, Anshul Kundaje, Mihir Shah, Yoav Freund, Chris H. Wiggins, and Christina Leslie. Motif discovery through predictive modeling of gene regulation. RECOMB 2005.

3) M. Middendorf, E. Ziv, and C. H. Wiggins. Inferring network mechanisms: the drosophila melanogaster protein interaction network. PNAS 2005; q-bio/0408010.

4) Manuel Middendorf, et al. Discriminative topological features reveal biological network mechanisms. BMC Bioinformatics 2004; q-bio/0402017.

Discrete droplets offer significant advantages over single-phase flows in the design of some microfluidics-based biochemical assays. To realize these advantages, fundamental operations must be controlled and optimized, including manipulation of reactor volume, encapsulation, merging, mixing, and detection. In this presentation we address some current limitations in these processes, particularly that in which the minimum droplet size is restricted by the device geometry. We show that the presence of surfactants at the liquid-liquid interface leads to the formation of micron-scale and smaller threads at a flow-focusing junction. Threads stretch and break into picoliter droplets. The process is sustained in a specific range of flow rates and surfactant concentrations. Analysis of the mechano-chemical coupling between flow and surfactant transport at these length scales suggests ways to tailor the process for future devices.

The transformation of a narrow beam into a hollow cone when incident along the optic axis of a biaxial crystal, predicted by Hamilton in 1832, created a sensation when observed by Lloyd soon afterwards. It was possibly the earliest prediction of a qualitiatively new phenmenon using mathematics, and the prototype of the conical intersections reflecting the degeneracy structure of families of matrices, now popular in quantum chemistry. But the fine structure of the light cone contains many subtle features, slowly revealed by experiment, whose definitive explanation, involving new mathematical asymptotics, has been achieved only recently, along with definitive experimental test of the theory. Radically different phenomena arise when chirality and absorption are incorporated in addition to biaxiality.

Flagellated bacteria, such as E. Coli, propel themselves using multiple flagella - long, thin helical filaments - that are rotated using nanoscale motors. We will discuss several aspects of the fluid mechanics associated with bacterial motility, studied using scale modeling, numerical simulations and microscale experiments. The phenomena explored include the mechanics of flagellar bundling, in which several distinct filaments combine into a single helical bundle via viscous hydrodynamic interactions, the flow fields associated with viscous helical motions, and mechanisms for hydrodynamic synchronization of adjacent flagella motion. We will also show how the flagella motion can be harnessed in engineered systems to enhance low Reynolds number mixing, to pump fluids, and to transport objects through microfluidic systems.

In the popular imagination, quantum computers would be almost magical devices, able to "solve impossible problems in an instant" by trying exponentially many solutions in parallel. In this talk, I'll describe four results in quantum computing theory that directly challenge this view.

First, I'll show that any quantum algorithm to decide whether a function f:[n]->[n] is one-to-one or two-to-one needs to query the function at least n^{1/5} times. This provides strong evidence that collision-resistant hash functions, and hence secure electronic commerce, would still be possible in a world with quantum computers.

Second, I'll show that in the "black-box" or "oracle" model that we know how to analyze, quantum computers could not solve NP-complete problems in polynomial time, even with the help of nonuniform "quantum advice states.",

Third, I'll show that quantum computers need exponential time to find local optima -- and surprisingly, that the ideas used to prove this result also yield new classical lower bounds for the same problem.

Finally, I'll show how to do "pretty-good quantum state tomography",

using a number of measurements that increases only linearly, not exponentially, with the number of qubits. This illustrates how one can sometimes turn the limitations of computational devices on their head, and use them to develop new techniques for experimentalists.

No quantum computing background is assumed.

Several of the deepest principles in physics can be seen as limits on 'technology': for example, the Second Law of Thermodynamics and the impossibility of superluminal communication. In this talk, I'll ask whether the hardness of NP-complete computational problems would likewise be useful to assume as a physical principle. To investigate this question, I'll study the computational effects of living in a universe with closed timelike curves, a universe where the Schroedinger equation was nonlinear, a universe with particular many-particle entangled states left over from the Big Bang, or a universe where you could kill yourself with some probability and then 'postselect' on remaining alive. I'll show that one can make definite, nontrivial statements about what problems could be efficiently solved in each of these universes -- and also about what problems still couldn't be.

Colloidal suspensions consist of micron sized solid particles suspended in a solvent. The particles are Brownian so that the suspension as a whole behaves as a thermal system governed by the laws of statistical mechanics. For example at high volume fractions, mono-dispersed suspensions will crystallize. If the number density of particles is reduced, such crystals will undergo a thermodynamic melting transition. The thermodynamic nature of these systems has allowed scientists to use colloidal suspensions as models for investigating numerous processes that typically take place on the atomic scale but are often very difficult to investigate. In this talk I will describe the experimental techniques we use to investigate the 3D structure and dynamics of these systems as well as review experiments we have conducted aimed at understanding defect nucleation, translation, and entanglement in colloidal crystals. I will then describe ongoing experiments aimed at elucidating various non-equilibrium processes such as the epitaxial growth of thin films and various lubrication phenomena.

The activity of neurons in an area of the brain referred to as primary motor cortex provides the signals that control the ability to execute movements. One of the crucial questions, still unresolved, is that of identifying the code used by this neural ensemble. We address this question through the analysis of data obtained for an awake behaving monkey. An implanted multielectrode array records the activity of about one hundred neurons in primary motor cortex during the execution of a sequence of straight reaches to nearby targets. A natural representation for the ensemble activity is provided by a high-dimensional space in which each axis represents the activity of a single neuron as an independent degree of freedom. However, the observed correlations among neurons whose activity is detectably modulated by the task suggest that the population defines a low-dimensional space within the high-dimensional space of independent firing activities. We have used linear and nonlinear methods for dimensionality reduction to find the low-dimensional structure that captures the underlying relationship between population neural activity and behavioral task. The use of multidimensional scaling in conjunction with an empirical measure of geodesic distances yields a low-dimensional manifold whose intrinsic coordinates capture the geometry of the task in the external physical space.

Cosmological observations of the distant universe are usually interpreted to imply either the existence of "dark energy" or indications of a breakdown in general relativity. In the talk I will discuss a third approach: nonlinear dynamics of the expansion history of the universe are more complicated than usually assumed.

Over the last ten years more than a dozen mammalian whole genomes have been fully sequenced, providing a digital library of unprecedented scope and detail and posing new challenges in decoding the information contained therein. At the same time, experimental biology has been revolutionized by the discovery of non-coding RNA, termed "biological dark matter" in the popular media. I describe how these developments are unified in what may well be the first time that scale invariance, long a cornerstone of modern physics, establishes for itself a central and essential role in molecular biology, evolution, and medicine [1]. Application of these ideas to the discovery of new microRNAs in mouse embryonic stem cells is discussed, and if time, the first massively parallel sequencing of the short RNome of mouse stem cells will be reported.

[1] W Salerno, P Havlak, and J Miller (2006). Scale-invariant structure of whole-genome intersections and alignments. Proc Natl Acad Sci USA, 103(35): p. 13121-5.

The collision of two black holes is thought to be one of the most energetic events in the universe, emitting in gravitational waves as much as 5-10% of the rest mass energy of the system. An international effort is currently underway to detect gravitational waves from black hole collisions and other cataclysmic events in the universe. The early success of the detectors will rely on the matched filtering technique to extract what are, by the time the waves reach earth, very weak distortions in the local geometry of space and time. In the case of black hole mergers numerical simulations are needed to obtain predictions of waveforms during the final stages of coalescence. 2005 was a watershed year for numerical simulations of black holes, and we are now beginning to explore the fascinating landscape of black hole collisions in the fully non-linear regime of Einstein's theory. In this talk I will describe the computational challenges and techniques required to simulate black holes within the framework of Einstein's theory of general relativity, and present results form recent successful simulations of black hole coalescence.

For its molecular simplicity, ice is an exceedingly complex system and is one of the most fascinating material in the world of condensed matter physics. For example, it is known to possess non-trivial proton dynamics and residual disorder and entropy well below the freezing point of water. Theoretically, such entropy, originally estimated by Linus Pauling in 1935, arises from the extremely large number of ways of arranging for the two short and two long proton bond lengths surrounding each oxygen ion. It has recently been found that there exist a remarkable analogy between the statistical physics of certain geometrically frustrated magnetic materials and the problem of proton ordering in ice, hence the name "spin ice". In this talk I will briefly review the broad problem of frustration in condensed matter physics. I will then discuss the discovery of spin ice materials and highlight some of the interesting experimental and theoretical developments surrounding the "spin ice" problem over the past ten years or so and discuss some of the current open questions.

The Euler equations, describing a potential flow of infinitely deep 2-D ideal incompressible fluid with free surface, takes a compact closed form after the conformal mapping of the domain filled with fluid up to the lower half-plane. The "conformal" evolution equations of surface dynamics are suitable both for analytic study and numerical simulation. The main tool of analytic investigation is the consideration of singularity dynamics in the upper half-plane. In a typical situation the singularities are the moving and broadening cuts. As far as the cuts are narrow, the problem can be solved analytically. It describes the formation of drops and shapes of surface, similar to the "Saffman fingers". A certain class of initial data can be described approximately by the famous Laplace Growth Equation (LGE). In this and even more general cases the conformal evolutionary equations have "extra" constants of motion, which are not connected with natural symmetries of the system. It leads to conjecture that the system in completely integrable but this question is still open.

The conformal equations could be efficiently solved numerically by the use of the spectral code. We elaborated a comfortable and stable numeric algorithm making possible to model the nonlinear wave propagation during a very long time (up to 100 000 periods). We performed long-time modeling of nonlinear stage of the Stokes wave modulational instability and found that the instability leads to formation of solitonic turbulence and finally, to the appearance of freak waves.

In granular materials, or other spatially disordered systems such as colloidal glasses, gels, and foams, in which thermal fluctuations are believed to be negligible, a jamming transition has been proposed: upon increasing the volume density (or "packing fraction") of particles above a critical value, the sudden appearance of a finite shear stiffness signals a transition between flowing liquid and rigid (but disordered) solid states. We carry out numerical simulations of a soft sphere model of a granular material in two dimensions at zero temperature, computing the shear viscosity of the flowing state as a function of both particle volume density and applied shear stress. About the jamming transition we find an excellent scaling collapse of our data to a function of a single scaling variable. By considering velocity correlations we extract a correlation length and show that it too obeys a scaling collapse, diverging at the jamming transition. Our results confirm that jamming is a true second order critical phenomenon that, as originally proposed by Liu and Nagel, extends to driven steady states along the non-equilibrium axis of applied shear stress.

Most of the interesting things that happen in living organisms require interactions among many components, and it is convenient to think of these as a "network" of interactions. We use this language at the level of single molecules (the network of interactions among amino acids that determine protein structure), single cells (the network of protein-DNA interactions responsible for the regulation of gene expression), and complex multicellular organisms (the networks of neurons in our brain). In this talk I'll try to look at two very different kinds of theoretical physics problems that arise in thinking about such networks. The first problems are phenomenological: Given what our experimentalist friends can measure, can we generate a global view of network function and dynamics? I'll argue that maximum entropy methods can be useful here, and show how such methods have been used in very recent work on networks of neurons, enzymes, genes, and (in disguise) amino acids. In this line of reasoning there are of course interesting connections to statistical mechanics, and we'll see that natural statistical mechanics questions about the underlying models actually teach us something about how the real biological system works, in ways that will be tested through new experiments. In the second half of the talk I'll ask if there are principles from which we might actually be able to predict the structure and dynamics of biological networks. I'll focus on optimization principles, in particular the optimization of information flow in transcriptional regulation. Even setting up these arguments forces us to think critically about our understanding of the signals, specificity and noise in these systems, all current topics of research. Although we don't know if we have the right principles, trying to work out the consequences of such optimization again suggests new experiments.

Two-dimensional conformally invariant systems are scale-invariant systems with local interactions, such as, for example, critical statistical systems. Domain walls in them are fluctuating fractal curves. The study of the shape of these curves is a recent development in critical phenomena. I will show how these curves are related to quantum Gaussian field theory and how their fractal spectrum is found using this field theory.

Two different physical realizations of turbulent flows will be reviewed: shear turbulence and natural convection. We will discuss how the statistical properties of turbulence fluctuations are affected by the presence of important underlying velocity or thermal gradients; implications range from the quest to the "ultimate state of thermal convection," as predicted by Kraichnan in 1962, to the improvement of eddy viscosity models close to wall boundaries.

Molecular dynamics simulations are used to investigate driven nano-scale flows of liquids along open "chemical channels": patterns of completely-wetting solid embedded in a planar substrate, and sandwiched between less wetting solid regions. Liquid placed atop a long straight wetting stripe evolves into connected "pearls," due to a Rayleigh-like surface tension instability, which propagate and merge when a pressure gradient is applied. In more complicated wetting patterns involving dividing and combining junctions, propagating pearls again appear, and exhibit intriguing stability and bifurcation behavior when the liquid flows. The numerical results in the straight-channel case are compared to a simple long-wavelength approximation and a full stability analysis based on the Stokes equations. The different approaches are qualitatively but not quantitatively consistent, which we attribute to the presence of a broad interfacial region and substantial thermal fluctuations.

Nanomaterials, such as block copolymeric membranes and nanodiamonds, can be engineered for controlled and localized drug delivery via implantable devices. Inflammatory responses against these implants, however, can result in degradation and rejection of these devices.

Our laboratory has developed a 'nano-cloaking' technology via copolymer/nanodiamond functionalization with anti-inflammatory and chemotherapeutic molecules. This technique has allowed the platform materials to serve as broadly applicable therapeutic delivery systems. These NanoCloak's dramatically inhibited inflammatory responses in vitro. Furthermore, in vivo studies using copolymeric interfaces showed that NanoCloak enables implant cloaking in an animal model which is envisioned to significantly impact the chronicity of implant functionality.

We also interrogated the cyto-regulatory networks via cytokine expression levels (IL-6, TNF?, iNOS) via quantitative PCR and found that the copolymers/nanodiamonds interface well with their surrounding biological environment at a genetic level. Monitoring of internal cellular processes as well as cytokine release at the tissue-nanomaterial interface revealed the absence of basal cellular inflammatory responses.

Dr. Dean Ho is currently an Assistant Professor in the Departments of Biomedical Engineering and Mechanical Engineering in the Robert R. McCormick School of Engineering and Applied Science and Member of the Robert H. Lurie Comprehensive Cancer Center at the Feinberg School of Medicine at Northwestern University where he directs the Laboratory for Nanoscale Biotic-Abiotic Systems Engineering (N-BASE). He completed his Ph.D. in Biomedical Engineering at UCLA, and was a Research Associate in the Departments of Electrical Engineering and Bioengineering at the California Institute of Technology as well as in the UCLA Mechanical and Aerospace Engineering Department from 2005-2006.

Close-packed nanoparticles separated by short spacer molecules form a new class of solids with unique behavior that arises from the interplay of nanoscale confinement and tunable coupling. I will discuss experiments performed by our group on the ultrathin limit of such solids, a single layer of close-packed metal nanoparticles. It turns out that such layers can be self-assembled with very high degree of structural order by a simple drying mechanism. With inter-particle spacings of 1-2nm, electrons can tunnel across these layers and the resulting nonlinear current-voltage characteristics reflect strong Coulomb blockade effects. Surprisingly, the short molecular spacers also provide for tensile strength and the layers can be draped over holes, forming flexible membranes of remarkable resilience.

The fabrication and properties of semiconductor quantum dots has received significant attention in recent years due to their potential application in a wide range of nanoscale integrated systems (diodes, filters, etc). One feature of quantum dots is that they can form spontaneously, or self-assemble, as the result of an instability when a thin solid film is deposited onto a solid substrate. We first investigate the self-assembly of quantum dots in a thin solid film caused by epitaxial stress and wetting interactions between the film and the substrate. We derive an evolution equation that governs the shape of the film surface and show that the presence of wetting interactions can lead to the formation of spatially regular arrays of quantum dots. We then consider the growth of a thin solid film by molecular beam epitaxy which precedes the formation of quantum dots. For the case of Levy flights, we develop the analog theory of step-flow growth and determine the step-flow velocity as a function of the terrace length.

When a bubble (or drop) is placed in a strong viscous flow (e.g. a shear flow), it develops very sharp tips at its ends. Similarly sharp structures occur when a viscous fluid is sucked away from its interface with the ambient air (selective withdrawal). We have constructed a code to solve for stationary solutions of the flow equations for arbitrary viscosity ratios, both for the drop and the selective withdrawal geometry. The code resolves tip curvatures of more than $10^8$ times the bubble radius. We compare the shape and stability of drops to an earlier theory by Taylor (1964). We then focus on the highly curved tip region, not considered by Taylor. We find that the shape near the tip is universal, i.e. independent of the driving flow and of the geometry of the interface. A similar statement applies to the stability of solutions, which is controlled by the viscosity ratio. This leaves open major questions as to the proper interpretation of recent experiments in the selective withdrawal geometry.

A granular material is a large conglomeration of discrete macroscopic particles. It has unique properties different from other familiar forms of matter. One of the most interesting properties of a granular material is the absence of the cohesive force between its component particles, and a flow of such a material can be seen as a special "fluid",

with zero surface-tension. We explored this aspect of granular flow in two specific experiments. First, we performed the granular analog to "water bell" experiments. When a wide jet of granular material impacts on a fixed cylindrical target, it deforms into a sharply-defined sheet or cone with a shape that mimics a liquid with zero surface tension. The jets' particulate nature appears when the number of particles in the beam cross-section is decreased: the emerging structures broaden, gradually disintegrating into diffuse sprays. The experiment has a counterpart in the behavior of quark-gluon plasmas generated by colliding heavy ions in RHIC, where a high collision density gives rise to collective behavior also described as a liquid. Second, we performed granular analog of viscous fingering experiments in the Hele-Shaw geometry. In the absence of surface tension, the ordinary viscous fingering is expected to be singular. However, it is hard, if not impossible, to realize this with normal fluids. We showed that near the yield stress of a granular flow, the grain/gas interface exhibits a fractal structure and local cusps, both suggestive of a finite time singularity. Furthermore, we find a novel scaling law for fingering width as compared with normal fluid fingering.

Adult songbirds transmit specific songs to juveniles who then train their own song production systems to mimic the adult song. The neural and auditory bases for this cultural behavior are known in broad, qualitative outline to be associated with identified collections of neurons in the male songbird brain and the bird's auditory apparatus. The overall song learning, training, and production system is straightforward enough that one can expect to develop a quantitative set of models with increasing complexity and resolution. These would allow the prediction of new phenomena in the song system as well as provide an integrated view of existing observations.

We will outline some of the established aspects of the songbird nervous/auditory system and describe our efforts to develop a "coarse grained" computational description of its function. We will also describe ingredients missing at present with an optimistic eye toward how we need to proceed to their incorporation. To proceed from a coarse grained account we will need both additional anatomical and electrophysiological information as well as computational development of models.

A suggestion for developing and verifying the needed models will be outlined. The method is applicable to networks in many arenas of physics and biological physics. It is computationally demanding.

A role for physicists in providing quantitative computational models of this functional nervous system and others, perhaps more complex, will be discussed.

We poorly understand the microscopic properties of amorphous solids, such as transport, force propagation, or even the nature of their mechanical stability. These questions are related to the presence of soft modes in their vibrational spectrum. We explain the nature of these modes in repulsive, short-range systems. This enables to derive a microscopic criterion of rigidity which extends a previous result of Maxwell. This implies that rigidity is not a local property, but is characterized by a length which depends on the packing geometry, and which can be large and even diverge, e.g. near the random close packing. We argue that this description applies to granular media, silica and colloidal glasses. We propose a description of the glass transition in hard sphere systems in terms of these soft modes. This leads to several predictions, in particular a non-trivial power law scaling characterizing the packing geometry in the glass phase, that we check numerically.

Granular and continuous materials fail in fundamentally different ways, yet inherently discontinuous natural fault materials have often been modeled as continuum processes. I will present the results of laboratory experiments which complement existing numerical simulations, rock mechanics experiments, seismological observations, and geologic studies to highlight the granular conrols on fault behavior. We perform experiments in a quasi-two-dimensional shear zone containing several thousand 5 mm circular and elliptical photoelastic plastic disks, allowing us to monitor the spatiotemporal evolution of both internal stress and strain. While the time, length, and strength scales are vastly different from the natural case, the frictional behvior is found to be in agreement. Therefore, the experiments allow us to isolate the effects of granular interactions and choice of boundary conditions on the fault behavior, through the observation of large populations of stick-slip and creep events.

The Method of Maximum Likelihood is a standard of modern statistical analysis: it is generally the first and often the last choice of analysts when choosing among models with imperfect data. The theory of maximum likelihood is very beautiful: a conceptually simple approach to an amazingly broad collection of problems. This theory provides a simple recipe that purports to lead to the optimum solution for all parametric problems and beyond, and not only promises an optimum estimate, but also a simple all-purpose assessment of its accuracy. And all this comes with no need for the specification of a priori probabilities, and no complicated derivation of distributions. Furthermore, it is capable of being automated in modern computers and extended to any number of dimensions.

At a superficial level, the idea of maximum likelihood must be prehistoric: early hunters and gatherers may not have used the words "method of maximum likelihood" to describe their choice of where and how to hunt and gather, but it is hard to believe they would have been surprised if their method had been described in those terms. It seems a simple, even unassailable idea: Who would rise to argue in favor of a method of minimum likelihood, or even mediocre likelihood? And yet the mathematical history of the topic shows this "simple idea" is really anything but simple, and it reveals unsuspected pitfalls that are still of relevance. Joseph Louis Lagrange, Johann Heinrich Lambert, Daniel Bernoulli, Leonard Euler, Pierre Simon Laplace, and Carl Friedrich Gauss are only some of those who explored the topic, not always in ways we would sanction today. In the 20th century Ronald A. Fisher played a particularly important role leading to the modern theory, but such rigor as that theory enjoys today is due to primarily to Abraham Wald. I will review some parts of that history from Lagrange to the 1950s, drawing attention to ancient difficulties that remain of concern.

Our laboratory has worked on pinch-off and coalescence in several unusual experimental fluid systems, including superfluid helium-4. The singularities produced during these events can usually be described by a self-similar form, where quantities such as pressure and velocity diverge and length scales shrink to zero with characteristic power-law exponents. These solutions are often universal in the sense that they do not depend on the initial conditions, but this is not always the case. In most of our experiments, conventional high-speed video is used to examine the pinch-off and coalescence of classical and superfluid liquid drops and gaseous bubbles. However, investigating the asymptotic regime can be difficult due to the finite resolution of the camera and the diffraction of light. To avoid this problem, we developed an electrical technique using drops of liquid mercury to monitor the diameter of the singular region to just a few nanometers. In addition, we have explored the effects of dimensionality on pinch-off and coalescence using thin, quasi-2D liquid lenses floating on water (like drops of oil in vegetable soup). These results have motivated us to investigate idealized 2D pinch-off using boundary-integral simulations. Our analysis shows that unlike axisymmetric drops, non-viscous 2D pinch-off is described by a self-similar solution of the second-kind, where the power-law exponent is a non-rational number. We calculate this number independently solving a nonlinear eigenvalue problem. Another type of singularity in classical fluid flow is the motion of a liquid/solid/gas contact-line (e.g. droplet sliding on a plate). We are currently exploring this problem using superfluid droplets on cesium surfaces. Results and future work will be discussed.

Topological quantum computation is a new, emerging paradigm for a fault-tolerant quantum computation. The proposed topological quantum computer relies on the existence of non-Abelian anyons, which are quasiparticle excitations that display non-Abelian braiding statistics. Among various prospective candidates, certain fractional quantum Hall states are thought to possess the non-Abelian anyons suitable for topological quantum computation. In this talk, I will talk about (a) the intellectual motivation for topological quantum computation, (b) how Fibonacci anyons may be used for topological quantum computation, and (c) our recent experimental effort toward detection of the non-Abelian braiding statistics.

In our recent experiments, a light pulse is stopped and extinguished in one part of space and then revived and sent back on its way at a different location. In the process, the light pulse is slowed to 15 miles per hour and is also spatially compressed from 1 kilometer to only 20 microns. The light pulse is converted to matter, and a matter imitation of the light pulse travels between the two locations. At the revival position, the matter copy is converted back to light. Matter, as opposed to light, is easily manipulated, and changes induced in the matter copy are reflected in the revived optical pulse. The work demonstrates a powerful new method for coherent processing of optical information and has applications in optical computing and quantum information processing.

Molecular targeting is central to drug-based cancer therapy, but remains challenging because drugs often lack specificity, which may cause toxic side effects. I shall survey a translational bottom-up strategy to curb side effects by reassessing the bearing of physico-chemical laws on the molecular phenotype.

Modulating side effects is difficult because targets within superfamilies are evolutionarily and hence structurally related. I shall focus primarily on kinases, the quintessential signal transducers and also important cancer targets. The lack of specificity of the anticancer drug imatinib enables it to be used to treat chronic myeloid leukemia, where its target is the Bcr-Abl kinase, as well as a portion of gastrointestinal stromal tumors (GISTs), where its target is the C-Kit kinase. However, imatinib also has cardiotoxic effects traceable to its impact on the C-Abl kinase. Motivated by this finding, we created a modified version of imatinib that hampers Bcr-Abl inhibition, re-focuses the impact on the C-Kit kinase and promotes inhibition of an additional target, JNK, required to reinforce prevention of cardiotoxicity. We established the molecular blueprint for target discrimination in vitro using spectrophotometric and colorimetric assays and through a phage displayed kinase screening library. We demonstrated controlled inhibitory impact on C-Kit kinase in human cell lines, and established the therapeutic impact of the engineered compound in a novel GIST mouse model, revealing a marked reduction of cardiotoxicity. These findings identify the re-engineered imatinib as an agent to treat GISTs with curbed side effects. The result probably reflects the first bottom-up translational approach to redesign a drug to curb its side effects.

Prior to the mid-1970s, optimization research centered on effective search within irregular, sometimes nonlinear attractor basins with a single minimum. Conjugate gradient methods, for example, were developed in that framework. The study of spin glasses and Monte Carlo simulation brought a realization that most interesting problems have multiple minima, and most engineering applications are satisfied with any minimum that satisfies certain objectives. A second contribution was the realization that phase transitions in disordered systems have consequences for the cost of search in typical (but not worst-case) conditions. Recent methods, such as message-passing solutions to cavity mean-field descriptions of combinatoric problems have brought at least a thousand-fold increase in the size of typically hard problems which are now numerically tractable. But now such methods are being used as Shannon-optimal decoders, in a situation in which only one solution, the correct decoding, is of interest. Provably correct methods such as linear and semidefinite programming may also apply. We have been studying combinatoric problems lying right at the boundary between convex and harder optimization, such as Sudoku.

How do we make hard decisions? A decision is a deliberation process that involves accumulation of evidence for possible alternatives, ultimately leading to the commitment to a categorical choice. Recent physiological studies with behaving nonhuman primates have begun to uncover neural signals at the single-cell level that are correlated with specific aspects of subject's decision computations. In this talk, I will present a biophysically-based recurrent network model of spiking neurons for decision making. I will show that this model accounts for a range of observations from two sets of monkey 'experiments': one on perceptual decision making in a visual motion direction discrimination task, the other on internal valuation of competing alternatives and action selection in a foraging task. This model suggests a unified circuit mechanism for decision making, namely NMDA-receptor dependent slow neuronal reverberation that can be described theoretically in terms of stochastic attractor dynamical systems.

Models suggest that the earth and magnets crackle alike! Recent studies show that slowly increasing magnetic fields in magnets can trigger so-called "magnetizing avalanches". It turns out that we can model statistics of earthquakes, especially in irregularly shaped fault zones, very similarly, and this similarity motivates a new way of analyzing seismic data. I will show how we can understand the universal, i.e. detail independent, effects of disorder in both systems in terms of the theory of phase transitions.