For many years, big companies have been collecting and storing your personal data. These data include your location traces, online browsing histories, purchasing histories, daily activities/social relationship, health status, or even voice recordings. They are collected via a variety of platforms, including computers, smart phones, and Internet-of-Things (IoT) devices, and are being used for multiple data analytics purposes, such as targeted advertisement, location-based services, or to obtain statistical information. While these data help to enhance user experience and improve companies’ products and services, they also bring severe privacy concerns. Thus it is critical to adopt technical measures to protect users’ private data without hampering the data utility. One of the most promising approaches is to obfuscate or perturb users’ data before uploading to a server, and formal privacy metrics such as local differential privacy (LDP) has been used to measure the privacy leakage. However the main challenge is how to guarantee a small amount of leakage while still enabling data query/analytics with reasonable accuracy. In this talk, I will present our recent research advances in privacy-preserving data analytics in the local setting. We first focus on enhancing the utility of complex query types with LDP guarantees, where we design efficient data perturbation mechanisms for correlated multi-dimensional data such as key-value data, and supporting hybrid queries on location data (both individual and statistical). Another effort is on exploiting context-aware privacy definitions, where incorporating prior knowledge about the data allows us to design adaptive data perturbation mechanisms that enhance the utility/privacy tradeoff. Finally, I will discuss some future research challenges and open problems in this area.

Over the last few decades, the autonomous discrete Painleve 1 equation has been studied from several different perspectives. One can view the dP1 equation as a Quispel-Roberts-Thompson mapping, where each point in an orbit is gotten from the previous by intersecting and reflecting. Another perspective is that of Okamoto and Sakai, where the dynamics are understood through the geometry of a special surface called the space of initial values. Using these perspectives, one can gain insight into several related combinatorial problems, such as counting 4-valent planar maps, and blossom trees.

In this talk we will discuss an integrable deautonomization of the discrete Painleve 1 equation. This specific equation arises from a recurrence relation for orthogonal polynomials with respect to an exponential weight, and has connections to counting 4-valent maps of any genus. From the Q.R.T. and Okamoto/Sakai perspectives we can understand the non-autonomous dynamics and address questions from the 4-valent map counting problem.

The basic question of interest for this talk is the following. Does the Galois group of a field (with respect to its algebraic closure or separable closure) determine the field? Looking at the example of the field of real and complex numbers, this question might seem uninteresting. On the other hand it is a surprising theorem that the Galois group of the field of rational numbers (with respect to an algebraic closure) does determine the field of rational numbers uniquely (up to isomorphism). In the past two decades S. Mochizuki has provided a fresh insight into this question, notably that Galois groups do sometimes see the addition law and multiplication law of a field separately and that this provides us with a way of changing the addition law without changing the Galois group. I hope to provide a low brow view of this topic (with plenty of concrete examples) and then, if time permits, discuss some recent work in which I was able to provide an algebraic approach to this idea of Mochizuki by showing that in fact there is still a universal addition law in the theory of p-adic fields from which all relevant addition laws arise. A large part of this talk is intended for a wide audience (with some basic knowledge of Galois theory).

Mark your calendars for the next Tools You Can Use session to be held on Tuesday, November 19 at 3:30pm. We will reveal "The Things- Mysteries of the University." We will present helpful and lesser known resources for teaching, computing, HR/personnel, research/grants, and more!

We want to know what mysteries you would pull over for. Please tell us what you want to learn more about here.

Motivated by a possible approach to uniqueness problems for global mild solutions to  3d-incompressible Navier-Stokes equations,  we consider a relaxed version of the  LeJan-Sznitman stochastic cascade associated with Navier-Stokes equations that permits stochastic explosion to  occur in the genealogy of the cascade. In this talk we will describe this relaxation as well as an approach to criteria for non-explosion and explosion. This is based on joint work with Radu Dascaliuc, Enrique Thomann, and Tuan Pham at Oregon State University.

Advisor: Anatoli Tumin
               Aerospace and Mechanical Engineering
               University of Arizona

Recent advances in materials and fabrication concepts coupled with miniaturization of wireless energy transfer schemes enable the construction of soft high-performance electronic and optoelectronic systems with sizes, shapes and physical properties matched to biological systems. Applications range from continuous monitors for health diagnosis to minimally invasive exploratory tools for neuroscience. This seminar explores basic science and engineering aspects for the creation of such systems and outlines modeling and related computational challenges and opportunities. Applications of such systems are discussed in the context of imperceptible body-worn devices for the assessment of hemodynamics, sweat and thermal properties of the skin.  Highly miniaturized embodiments featuring advanced capabilities in energy harvesting and photonics allow for deployment as multifunctional subdermal neuroscience tools for wireless recording of genetically targeted indicators and optogenetic stimulation of the brain, peripheral nervous system and the heart. The seminar will highlight areas of opportunity for advanced modeling tools as well as computational challenges in the context of these applications.

Bio:  Dr. Philipp Gutruf is an Assistant Professor in the Biomedical Engineering Department at the University of Arizona. He received his postdoctoral training in the Rogers Research Group at Northwestern University and the University of Illinois Urbana-Champaign (UIUC) where he developed a broad set of soft, highly miniaturized wireless battery free tools for the characterization and stimulation of biological systems. Dr. Gutruf received his PhD in 2016 at RMIT University where he worked on oxide based stretchable electronics, sensors and photonics, with emphasis on device fabrication and material concepts for intrinsically stretchable devices. He has authored over 36 journal articles and received 4 patents and his work has been highlighted on 8 journal covers. He has also been the recipient of prestigious scholarships and fellowships such as the International Postgraduate Research Scholarship (IPRS) and the Australian Nano Technology Network Travel Fellowship.

It is well known that relocation strategies in ecology and in economics can make the difference between extinction and persistence. In this talk I present a unifying model for the dynamics of ecological populations and street vendors, an important part of many informal economies. I discuss the effects of chemotactic movement of populations subject to the Allee Effect by discussing the existence of equilibrium solutions subject to various boundary conditions and the evolution problem when the chemotaxis effect is small.  On an interesting note, I present numerical simulations, which show that in fact chemotaxis can help overcome the Allee effect as well as some partial analytical results in this direction. I will conclude by making a connection to the Ideal Free Distribution and analyze what happens under competition, showing that the Ideal Free Distribution is locally evolutionarily stable.

University of Arizona Mathematics Professor Sergey Cherkis will speak at the "Everything is Math" Public Lecture on November 21st.

The annual Duncan Buell Everything is Mathematics Lecture Series gives the Tucson community a window into the mathematical research our UA faculty do here in Tucson.

The lecture series is made possible in part by a generous endowment by UA mathematics alumnus Duncan Buell, now professor of Computer Science and Engineering at the University of South Carolina.

RSVP recommended to save your seat.

Data assimilation is a powerful technique that is widely used for Earth system applications (atmosphere, ocean, sea ice, land, waves) to combine observations with a numerical model to produce a forecast that is better than the observations or model alone.  It is a multi-disciplinary science, combining elements of earth system science, remote sensing and instrumentation, applied mathematics, computer science, and electrical engineering.

 Data assimilation for NWP is a sequential process that mathematically combines current observations with a model forecast (or background), along with their respective error estimates, to obtain the best estimate of the current model state (e.g. atmosphere). These analyses (initial conditions) have numerous applications, but are most often used to initialize the NWP model, including the short-range forecast for the next data assimilation cycle. Many of the advancements in the skill of weather forecasting over the past two decades can be attributed to improvements in data assimilation, to the global observing system (especially satellites), and to the effective assimilation remotely sensed observations. 

In this presentation, I highlight the challenges of developing and implementing operational data assimilation systems for NWP.  I first summarize the underlying theory and science of modern data assimilation systems.  I next describe the “art” of data assimilation, much of which involves estimating the observation and background error covariances (as truth is not known), selecting a “good mix” of observations, and balancing system complexity against computational timing constraints.  The background error covariances are especially important, as they govern the spread the observation information to the surrounding model grid points and variables, and partially control the relative weights given to the observations and the background. These background error covariances are estimated through various techniques, including static parameterizations that include multivariate balances found in nature, and ensemble estimates that include the situation- or flow-dependent “errors of the day”.   Deciding on the optimal or “hybrid” combination of these background error statistics requires extensive tuning, and ultimately a final judgment call.

Finally, I will highlight the challenges for the next decade. In particular, data assimilation for high resolution global cloud-resolving or convective-permitting models requires development of computationally efficient methods to include non-Gaussian error distributions, allow for more nonlinearity and include additional probabilistic information from ensembles.

Meetings vary week to week, but are always geared toward undergraduates with interest in mathematics (of any major). Email madisondelmoe@email.arizona.edu to be added to the email list if you would like to be notified about weekly events and other activities.

Abstract:  The internet is composed of communication protocols such as the Transmission Control Protocol (TCP). These protocols should be robust against adversarial attacks (e.g. message replay) and benign malfunction (e.g. packet loss). Given a formal model of a communication protocol that is provably robust against benign malfunction, we automatically synthesize an adversarial program that causes the protocol to malfunction (e.g. deadlock). We apply this technique to TCP, and analyze the synthesized attacks. Finally, we use block-diagrams to formalize threat models, and employ this formalization to define a generalized version of the Attacker Synthesis Problem.

Bio:  Max von Hippel graduated from the University of Arizona Honors College with a BS in Math (Comprehensive Option) and Minor in Computer Science.  His favorite classes were Math 415B and Math 401B - algebra and logic - and now he studies Formal Methods - the algebra of logic.  He previously completed an Honors Senior Thesis on IoT Security with Dr. Ming Li and Dr. Bryden Cais. You can read more about Max's research interests on his homepage, here: https://www.khoury.northeastern.edu/people/max-von-hippel/

Abstract: The simultaneous inference of many parameters, based on a corresponding set of observations, is a key research problem that has received much attention in the high-dimensional setting. Many practical situations involve heterogeneous data where the most common setting involves unknown effect sizes observed with heteroscedastic errors. Effectively pooling information across samples while correctly accounting for heterogeneity presents a significant challenge in large-scale inference. The first part of my talk addresses the selection bias issue in large-scale estimation problem by introducing the “Nonparametric Empirical Bayes Smoothing Tweedie” (NEST) estimator, which efficiently estimates the unknown effect sizes and properly adjusts for heterogeneity via a generalized version of Tweedie’s formula. The second part of my talk focuses on a parallel issue in multiple testing. We show that there can be a significant loss in information from basing hypothesis tests on standardized statistics rather than the full data. We develop a new class of heteroscedasticity–adjusted ranking and thresholding (HART) rules that aim to improve existing methods by simultaneously exploiting commonalities and adjusting heterogeneities among the study units. The common message in both NEST and HART is that the variance structure, which is subsumed under standardized statistics, is highly informative and can be exploited to achieve higher power in both shrinkage estimation and multiple testing problems.

Stochastic epidemic models describe how infectious diseases spread through populations. These models are constructed by first assigning individuals to compartments (e.g., susceptible, infectious, and removed) and then defining a stochastic process that governs the evolution of sizes of these compartments through time. Stochastic epidemic models and their deterministic counterparts are useful for evaluating strategies for controlling the infectious disease spread and for predicting the future course of a given epidemic. However, fitting these models to data turns out to be a challenging task, because even the most vigilant infectious disease surveillance programs offer only noisy snapshots of the number of infected individuals in the population. Such indirect observations of the infectious disease spread result in high dimensional missing data (e.g., number and times of infections) that needs to be accounted for during statistical inference. I will demonstrate that combining stochastic process approximation techniques with high dimensional Markov chain Monte Carlo algorithms makes Bayesian data augmentation for stochastic epidemic models computationally tractable. I will present examples of fitting stochastic epidemic models to  incidence time series data collected during outbreaks of Influenza and Ebola viruses.

Meetings vary week to week, but are always geared toward undergraduates with interest in mathematics (of any major). Email madisondelmoe@email.arizona.edu to be added to the email list if you would like to be notified about weekly events and other activities.