Talks

Globalization has created complex problems that can no longer be adequately understood and mitigated using traditional data analysis techniques and data sources. As such, there is a need for the integration of nontraditional data streams and approaches such as social media and machine learning to address these new challenges. In this talk, I will discuss how our team is applying approaches from the weather forecasting community including data collection, assimilating heterogeneous data streams into models, and quantifying uncertainty to forecast influenza and other infectious diseases. In addition, I will demonstrate that although epidemic forecasting is still in its infancy, it’s a growing field with great potential and mathematical modeling will play a key role in making this happen. 

In my presentation I will comment on the preliminary advances and results that we have in the Centro de Estudios de Variabilidad y Cambio Climático (CEVARCAM, FICH-UNL), where since last year a group of researchers is being formed in the line of assessing the impact of climate change on the health of the population. Particularly we study the incidence of infectious diseases and their relationship with different hydroclimatic and environmental indicators in Northeast Argentina. I work in deterministic modelling of infectious diseases while another partner works in stochastic modeling.

Artificial Neural Networks (ANNs) have been demonstrated to be an excellent method for dealing with various kind of tasks, such as image classification and natural language processing. These ANNs can also be used for regression since they are considered to be an universal function approximator, thanks to it's great capacity of dealing with non linear tasks. On the other hand, Floris Takens have shown to be possible to access and reconstruct the underlying dynamics of a system in the space state, starting from a single measured time series. In other words, Takens' theorem says it is possible to get information of a higher dimensional system from vectors build from a one-dimensional time series. This enables better time-series representations that can be fed into the ANNs. In this work, I will apply Echo State Networks (ESNs), one among the types of ANNs, to make forecasts of the dynamics of physical systems, such as Lorenz, Fokker-Planck and Vlasov Equations. I also pretend to apply these ESNs, together with Takens Vectors, into real time series, such as epidemics spread and financial series.

Brazilian Spotted Fever is an infectious, acute febrile disease, of varying severity, whose clinical presentation in humans can vary from mild and atypical forms to severe forms, with a high lethality rate. It is caused by a bacterium of the genus Rickettsia (Rickettsia rickettsii) and transmitted by ticks of the genus Amblyomma. In some locations in the state of São Paulo, the capybara (Hydrochoerus hydrochaeris) participates in the disease cycle as an amplifier of the etiologic agent after contact with infected ticks. As a result of this possible participation of the capybara in the cycle and the eventual need to carry out population management of the species, the State of São Paulo, through the Secretariat of Infraestructure and Environment and the Secretariat of Health, published Resolution SMA-SES No. 01/2016, which provides the -œTechnical guidelines for the surveillance and control of Brazilian Spotted Fever in the State of São Paulo - classification of areas and recommended measures -, which establishes criteria for the management of capybaras in situations where this species is associated with the risk of transmitting Brazilian Spotted Fever to humans.

The prediction of dengue outbreaks based on disease surveillance is  a very hard problem and a lot of work  had been done in this direction. In this talk, we present two studies with different techniques to partially address the problem. First, with the data for the state of São Paulo, we propose a time-scale separation to adjust the parameters and explore some cell phone data. In the second, using the incidence data for the state of Rio de Janeiro, inspired by the work of Saba, Vale, Moret and Miranda, we propose a way to identify a correlation network that would capture the space connections between the outbreaks.

In this work we analyse results obtained when considering individuals as mobile agents, which can interact for a period of time that depends on the agent dinamics. In this way, as the probability of disease transmission depends on this contact time, the spatial dynamics will strongly influence the disease spreading. Surprisingly, the size of the endemic population will have three different regimes depending on the speed: elimination of the disease if it is very low, inversely proportional to the speed for intermediate values, and a final case that depends on the contact. Moreover, we recently found that these last two regimes also depend heavily on the type of the dynamics (ballistic or diffusive). The same goes for the critical speed at which the disease disappears.

In this work we study the quantum learnability of constant-depth classical circuits under the uniform distribution and in the distribution-independent framework of PAC learning. In order to attain our results, we establish connections between quantum learning and quantum-secure cryptosystems. We then achieve the following results. 1) Hardness of learning AC0 and TC0 under the uniform distribution. Our first result concerns the concept class TC0 (resp. AC0), the class of constant-depth and polynomial-sized circuits with unbounded fan-in majority gates (resp. AND, OR, NOT gates). We show that if there exists no quantum polynomial-time (resp. strong sub-exponential time) algorithm to solve the Ring Learning with Errors (RLWE) problem, then there exists no polynomial-time quantum learning algorithm for TC0 (resp. AC0) under the uniform distribution (even with access to quantum membership queries). The main technique in this result uses explicit pseudo-random functions that are believed to be quantum-secure to construct concept classes that are hard to learn quantumly under the uniform distribution. 2) Hardness of learning TC02 in the PAC setting. Our second result shows that if there exists no quantum polynomial time algorithm for the LWE problem, then there exists no polynomial time quantum PAC learning algorithm for the class TC02, i.e., depth-2 TC0 circuits. The main technique in this result is to establish a connection between the quantum security of public-key cryptosystems and the learnability of a concept class that consists of decryption functions of the cryptosystem. This gives a strong (conditional) negative answer to one of the "Ten Semi-Grand Challenges for Quantum Computing Theory" raised by Aaronson [Aar05], who asked if AC0 and TC0 can be PAC-learned in quantum polynomial time.

Recently, Bravyi, Gosset, and König (Science, 2018) exhibited a search problem called the 2D Hidden Linear Function (2D HLF) problem that can be solved exactly by a constant-depth quantum circuit using bounded fan-in gates (or QNC^0 circuits), but cannot be solved by any constant-depth classical circuit using bounded fan-in AND, OR, and NOT gates (or NC^0 circuits). In other words, they exhibited a search problem in QNC^0 that is not in NC^0. We strengthen their result by proving that the 2D HLF problem is not contained in AC^0, the class of classical, polynomial-size, constant-depth circuits over the gate set of unbounded fan-in AND and OR gates, and NOT gates. We also supplement this worst-case lower bound with an average-case result: There exists a simple distribution under which any AC^0 circuit (even of nearly exponential size) has exponentially small correlation with the 2D HLF problem. Our results are shown by constructing a new problem in QNC^0, which we call the Relaxed Parity Halving Problem, which is easier to work with. We prove our AC^0 lower bounds for this problem, and then show that it reduces to the 2D HLF problem.  https://arxiv.org/abs/1906.08890

A scientific understanding of modern deep learning is still in its early stages. As a first step towards understanding the learning dynamics of neural networks, one can simplify the problem by studying limits that might have theoretical tractability and practical relevance. I’ll begin with a brief survey of our earlier body of work that has investigated the infinite width limit of deep networks, a topic of active study recently. With these results in hand, it nonetheless appears there is still a gap towards theoretically describing neural networks at finite width. I’ll argue that the choice of learning rate is one crucial factor in dynamics away from the infinite width limit and naturally classifies deep networks into two classes separated by a sharp transition. This is elucidated in a class of solvable simple models we present, which give quantitative predictions for the two classes. Quite remarkably, we test these predictions empirically in practical settings and find excellent agreement. 

Yasaman Bahri is a research scientist on the Google Brain team. Her current research program is to build a scientific understanding of deep learning using a combination of theoretical analysis and empirical investigation. Prior to Google, she was at the University of California, Berkeley, where she received her Ph.D. in physics in 2017, specializing in theoretical quantum condensed matter.