Ductal carcinoma in situ (DCIS)--a type of breast cancer whose growth is confined to the duct lumen--is a significant precursor to invasive breast carcinoma. DCIS is commonly detected as a subtle pattern of calcifications in mammograms. Radiologic imaging (including mammography) is used to plan surgical resection of the tumor (lumpectomy), but multiple surgeries are often required to fully eliminate DCIS. On the other hand, pathologists use pre-surgical biopsies to stage the DCIS, assess its metastatic potential, and choose adjuvant therapies. There is currently no technique to combine these data to improve surgical and therapeutic planning. Mechanistic, patient-tailored computational models may provide such a link between multiple data types. In this talk, we focus on developing and calibrating biologically-grounded mathematical models to individual patients, encouraging (and validated!) results in quantitatively predicting clinical progression, the implications for making and quantitatively testing biological hypotheses, and the role of mathematical modeling in facilitating a deeper understanding of pathology and mammography.

Everywhere we turn, we find that networks have become increasing appropriate descriptions of relevant interactions. In the high tech world, we see mobile networks, the Internet, the World Wide Web, and a variety of online social networks. In economics, we are increasingly experiencing both the positive and negative effects of a global networked economy. In epidemiology, we find disease spreading over our ever growing social networks, complicated by mutation of the disease agents. In problems of world health, distribution of limited resources, such as water resources, quickly becomes a problem of finding the optimal network for resource allocation. In biomedical research, we are beginning to understand the structure of gene regulatory networks, with the prospect of using this understanding to manage the many diseases caused by gene misregulation. In this talk, I look quite generally at some of the models we are using to describe these networks, and at some of the methods we are developing to indirectly infer network structure from measured data. In particular, I will discuss models and techniques which cut across many disciplinary boundaries.

The celebrated work of Leray (eighty years ago) settled the basic questions concerning the well-posedness of the Navier-Stokes equations in the plane (two dimensions). However, the basic premise of this work was the assumption that the initial velocity field is (at least) locally square integrable (namely, locally finite kinetic energy).
Thus, some primary fluid dynamical objects (notably point vortices) have been excluded (as they generate non square integrable velocities).
The topic of well posedness of such flows has been taken up only some twenty five years ago, and the final uniqueness result was obtained by Gallagher and Gallay five years ago.
In this talk we review the story of such flows, including basic open problems concerning the behavior of steady state solutions in bounded domains.

The goal of Computer Vision is the automatic labeling of images containing multiple objects as well as noise and clutter. Recent work has focused on two main tasks. The first is the classification among object classes in segmented images containing only one object and the second is the detection of a particular object class in a large image. Both tasks have been primarily addressed using discriminative learning.
It is not clear however how these methods can extend to deal with the recognition of multiple object classes in images containing a number of objects in a wide range of configurations.
I will present an approach which starts from simple statistical models for individual objects. With these models the important notion of invariance can be clearly formulated.
Furthermore the individual object models can be composed to define models for object configurations. Decisions are likelihood based and do not depend on pretrained decision boundaries.
The model formulation also leads to a coarse to fine strategy for efficient computation of the optimal scene annotation.
These ideas will be illustrated in several applications reading handwritten zipcodes, detecting faces, and tracking vesicles in video microscopy.

We will review some recent results related to wave propagation in random media and applications to imaging. We'll explain how some relevant physical scales influence the nature of the inverse problem and present different adapted techniques. In particular, we will focus on a regime in which the wave strongly interacts with the medium and present some related results of asymptotics of random PDEs, possibly non-linear.
Various numerical simulations confirming the theory will be shown.

Non-local maximum principles have recently been found to be very useful for proving the global regularity of smooth solutions to critical advection-diffusion equations, such as the critically diffusive SQG equation. In this talk I will discuss some recent results in which non-local maximum principles are successfully applied to equations that are "slightly super-critical", and even to equations without diffusion. This is joint work with M. Dabkowski and A. Kiselev.

Security at major locations of economic or political importance or transportation or other infrastructure is a key concern around the world, particularly given the threat of terrorism. Limited security resources prevent full security coverage at all times; instead, these limited resources must be deployed intelligently taking into account differences in priorities of targets requiring security coverage, the responses of the adversaries to the security posture and potential uncertainty over the types of adversaries faced. Game theory is well-suited to adversarial reasoning for security resource allocation and scheduling problems. Casting the problem as a Bayesian Stackelberg game, we have developed new algorithms for efficiently solving such games to provide randomized patrolling or inspection strategies: we can thus avoid predictability and address scale-up in these security scheduling problems, addressing key weaknesses of human scheduling. Our algorithms are now deployed in multiple applications. ARMOR, our first game theoretic application, has been deployed at the Los Angeles International Airport (LAX) since 2007 to randomizes checkpoints on the roadways entering the airport and canine patrol routes within the airport terminals. IRIS, our second application, is a game-theoretic scheduler for randomized deployment of the Federal Air Marshals (FAMS) requiring significant scale-up in underlying algorithms; IRIS has been in use since 2009. Similarly, a new set of algorithms are deployed in the port of Boston for a system called PROTECT for randomizing US coast guard patrolling; PROTECT is now headed to New York; and GUARDS is under evaluation for national deployment by the Transporation Security Administration (TSA). These applications are leading to real-world use-inspired research in computational game theory in scaling up to large-scale problems, handling significant adversarial uncertainty, dealing with bounded rationality of human adversaries, and other fundamental challenges. This talk will outline our algorithms, key research results and lessons learned from these applications.

In 1998, a seminal study by Mann, Bradley and Hughes took advantage of climate signals embedded in an array of high-resolution paleoclimate proxy data to conclude that “Northern Hemisphere mean annual temperatures for three of the past eight years are warmer than any other year since (at least) AD 1400.” The so-called “hockey stick” reconstruction showed relatively stable temperatures for most of the millennium, until the start of the Industrial Revolution, when reconstructed temperatures began a steep rise to a level not seen in the last millennium.
Since 2001, when the third assessment report by the Intergovernmental Panel on Climate Change featured the “hockey stick” prominently, this graph has become the emblem of the debate on anthropogenic global warming. No other picture conveys how anomalous recent climate change is in the context of natural variations in temperature over the past millennium. Defended as definitive proof of global warming by many climate scientists and sympathetic members of the public, hailed as a "misguided and illegitimate investigation" by some politicians, it remains one of the most hotly debated climate studies ever published. After a questionable a congressional inquiry was conducted under the aegis of Edward Wegman (then president of the American Statistical Association), most statisticians are now convinced that the "hockey stick" is a fluke due to the overfitting of noisy data.
In this talk, I will describe the most recent statistical methods developed to reconstruct climate fields ; explain how their performance can be assessed in a realistic geophysical context ; and show that, contrary to popular belief, climate scientists are, in fact, working hand-in-hand with professional statisticians, with some promising results.

The evolution of the velocity field of incompressible fluids is governed by the Navier-Stokes equations. The pressure term in these equations is a Lagrange multiplier used to enforce the incompressibility constraint. Unfortunately, the non-local (and non-linear) nature of the pressure causes numerous problems, both from a numerical and analytical perspective.
In order to produce efficient (and unconditionally stable) numerical schemes, Liu, Liu and Pego replaced the incompressibility constraint with an explicit formula for the pressure. While this helped the numerics, some analytical questions become much harder. I will briefly address a few resolved, and unresolved analytical issues related to these equations.

We compare several growth models on the two dimensional lattice.
In some models, like internal DLA and rotor-router aggregation, the scaling limits are universal; in particular, starting from a point source yields a disk. In the abelian sandpile, particles are added at the origin and whenever a site has four particles or more, the top four particles topple, with one going to each neighbor. Despite similarities to other models, for the sandpile, the intriguing pattern that arises is not circular and depends on the particular lattice. A scaling limit exists for the sandpile, as was recently shown by Pegden and Smart, but it is not universal and still mysterious. This research has been greatly influenced by pictures of the relevant sets, which I will show in the talk. They suggest a connection to conformal mapping which has not been established yet. Talk based on joint works with Lionel Levine.

Rhythms of the nervous system are produced in all cognitive states, and have been shown to be highly associated with a myriad of cognitive tasks. Thus, changes in these rhythms, however they come about, are likely to change the ability to do such tasks. This talk focuses on the beta (12-30 Hz) and alpha (9-11) rhythms, and pathological states due to anesthesia and PD; it is about three related studies, the latter two emerging from the first one. The first concerns an early stage of anesthesia, in which, paradoxically, the subject gets more excited and disoriented. With low propofol, the brain rhythms show an increase in beta oscillations, which in normal awake state is associated with brain functions including motor preparation and higher-order processing.
The second concerns the beta oscillations associated with abnormal motor control in Parkinson’s disease. The relationship between the two phenomena can be seen from the underlying physiology using modeling as well as experiments. Finally, the first story led to looking at higher doses of propofol at which consciousness is lost, and uses experimental data to get new ideas about the physiological basis for the loss of consciousness. Again, the focus on relevant physiology of the rhythms is what led, though modeling, to the new insights. Applications to other states of consciousness, such as coma, may be discussed.