Fourier’s law, or the law of heat conduction, is well-known for nearly two centuries, which states that the energy flux is proportional to the temperature gradient. However, the rigorous derivation of Fourier’s law from microscopic Hamiltonian dynamics remains a great challenge to theorists. In this talk, I will show the derivation of macroscopic thermodynamic laws, including Fourier’s law, from billiard-like deterministic dynamical system. A stochastic energy exchange model is numerically derived from a dynamical billiards heat conduction model that is not mathematically tractable. Then we take the mesoscopic limit of this energy exchange model by constructing two martingale problems. We find that Fourier’s law is satisfied by the steady state of the mesoscopic limit equation.

A classical result of Borel and Bernstein shows that the category of smooth complex representations of a p-adic reductive group G which are generated by their Iwahori-invariant vectors is equivalent to the category of modules over a certain Iwahori-Hecke algebra H.  This makes the algebra H an extremely useful tool in studying the representation theory of G, and thus in the Local Langlands Program.  When the field of complex numbers is replaced by a field of characteristic p, this equivalence no longer holds.  However, Schneider has recently shown that one can recover an equivalence by passing to derived categories and upgrading H to a certain differential graded algebra.  We will attempt to shed some light on this derived equivalence by relating several functorial constructions on both sides.  If time permits, we'll show how these methods can be used to calculate the H-module structure on all (pro-p-)Iwahori cohomology spaces with coefficients in irreducible representations, when G = GL_2(Q_p).

This is the first of two background talks for the mini course on multi-cell systems.

Inversion problems are generally cast as constrained optimizations including a forward (data fidelity) component and a regularization (prior) component. Alternating direction method of multipliers (ADMM) yields a variable splitting scheme to separate the forward and regularization components, and thus it enables a prior or regularizer to be plugged in inversion independently. In this talk, we will review three journal papers that focus on Magnetic Resonance (MR) parameter mapping using model based Compressive Sensing (CS) approaches. We will illustrate that ADMM is suited for solving such complex physical sensor model (e.g. Magnetic Resonance Imaging) with any proper regularity criteria.

I'll explain recent joint work with Lance Gurney. We prove that any family of ordinary abelian varieties parameterised by a p-adic formal scheme S lifts to a unique family over W(S) which admits a delta-structure in the sense of Joyal, Buium, and Bousfield. In the case where S is the spectrum of a perfect field of characteristic p, this specialises to the classical result of Serre-Tate and Messing that every ordinary abelian variety over a perfect field k lifts to a unique one over the ring W(k) of Witt vectors together with a lift of Frobenius.

We consider the attractive XXZ spin chain in the Ising phase. The energies of the systems are characterized by certain cluster break-up thresholds for down-spin configurations. We show that the bipartite entanglement of all states associated with a fixed number of clusters  satisfies a logarithmically corrected (or enhanced) area law. This generalizes a result by Beaud/Warzel, who considered energies in the droplet spectrum (i.e., the 1-cluster regime). (Based on a joint work with: C. Fischbacher and G. Stolz)

Neural network design has accomplished remarkable advances in complex tasks previously thought to be reserved solely for higher cognitive ability. Neural networks can now accurately classify images, play sophisticated games, translate and speak naturally, and even mimic artistic styles.  Unfortunately, neural networks have performed sub-par where human performance often excel, which is true for few-shot learning tasks where the objective is to classify a set of query samples based on only a few support examples.  Recent neural networks for few-shot learning have found that they can learn pairwise similarity metrics via stochastic gradient descent when a subset of support and query samples are repeatedly and randomly selected from the training set (known as episodic training). In this work, we propose a novel Soft Weight Network (SWN) that allows the network to generate embedded features and soft weights to cross compare every query-support pairing. The benchmarks of SWNs against the state-of-the-art few-shot learning algorithms show that the performance of SWNs on Omniglot and miniImageNet are more favorable when compared to the current/recent few-shot learning approaches.

Bio: Gregory Ditzler (IEEE S’04–M’15–SM'18) received a BSc from the Pennsylvania College of Technology (2008), an MSc degree from Rowan University (2011), and a PhD from Drexel University (2015). He is currently an Assistant Professor at the University of Arizona in the Electrical & Computer Engineering Department. He received an Outstanding Article Award from the IEEE Computational Intelligence Society Magzine (2018), the best paper at the IEEE International Conference on Cloud and Autonomic Computing (2017), best student paper at the IEEE/INNS International Joint Conference on Neural Networks (2014), a Nihat Bilgutay Fellowship (2013), Koerner Family Engineering Fellowship (2014), Drexel University’s Office of Graduate Studies Research Excellence Award (2015), and Rowan University’s Research Achievement Award (2009). In 2016 and 2018, he was selected as a summer faculty fellow at the Air Force Research Lab to work on adversarial learning algorithms. He is a senior member of the IEEE. His research has been supported by the ARFL, ARO, DOE and ONR.

This past summer I was privileged enough to work at Argonne national lab. There I worked on computational chemistry and my main project was on molecular dynamics using Qiskit.   Qiskit is a powerful computational framework developed by IBM for the purpose for quantum computing. It gives the user access to quantum simulators and Quantum computers across the globe. Using DiNT(Direct Nonadiabatic trajectories),a program designed for classical molecular dynamics, and Qiskit we develope a hybrid program to compute the trajectories of diatomic molecules. I shall share some of my results and experiences during my time at Argonne.

Gas chromatography (GC) is a technique used in analytical chemistry for separation and analysis  of compounds that can be vaporized without decomposition. In particular, separation of different components of a mixture or the relative amounts of such components may be achieved. When applied to biodiesel fuels, GC allows us to identify the fatty acid methyl esters (FAMEs) present in the sample, whose presence depends on the underlying feedstock type.  Typically, a set of replicate chromatograms is measured for each sample, and several biofuel classes are compared together. Each chromatogram quantifies molecular abundance at each of several retention times, which in turn correspond to particular carbon chains. Variation in peak height relative to retention time serves to differentiate biofuel classes. However, inherent in GC is measurement error in the form of variation in peak location (known as drift), which must be removed prior to chemometric analysis. This is usually accomplished by aligning each chromatogram to that of a reference sample.  Another important factor to consider in GC is the type of column used, which is essentially a tube coated on the inside with a polymer. A carrier gas (mobile phase) provides a mechanism for the sample to interact with the column (stationary phase) and the data to be measured. This causes each compound to elute at a different retention time and thus different FAMEs may be identified. Longer columns yield better separation of FAMEs at the cost of longer data acquisition time.  In the first part of this talk, I will discuss a method of optimizing chromatogram alignment using the Hotelling trace criterion (HTC). The HTC can be thought of as the multivariate and multi-class extension of the square of the two-sample t-statistic. Large values for the HTC correspond to better separation of groups of principal component scores for each class.  In the second part of this talk, I will discuss an approach to quantifying equivalence between  longer and shorter columns using the Mahalanobis distance. The Mahalanobis distance measures the distance between the multivariate means of two probability distributions while accounting for variation and the correlation between random variables. I will show that a shorter, faster column can produce statistically equivalent data, relative to a longer, slower column.  Finally, I will briefly discuss current/future work on identification of an optimal reference sample for chromatogram alignment.

Development of teachers’ equity literacy is crucial when attempting to create environments that are inviting to students and optimal learning. Equity literacy relies on teachers’ comprehension of equity and inequity, and the understanding that equitable teachers develop not just cultural proficiency, but also the abilities that contribute to the disruption of inequities. This presentation will introduce the concept of equity literacy and exemplify its utility by describing how teacher discursive practices may create an equitable/inequitable learning environment.

This is a series of NSF Noyce Seminars for the AZ Noyce Mathematics Teaching (MaTh) Scholars Project in Secondary Mathematics Education. (PI: Cynthia Anhalt; Co-PI: Marta Civil; Co-PI: Jennifer Wolfe; Co-PI: Rebecca McGraw).

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.

This is a series of NSF Noyce Seminars for the AZ Noyce Mathematics Teaching (MaTh) Scholars Project in Secondary Mathematics Education. (PI: Cynthia Anhalt; Co-PI: Marta Civil; Co-PI: Jennifer Eli; Co-PI: Rebecca McGraw).