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Graduate

ISL Colloquium presents "On the Convergence of Langevin Monte Carlo: The Interplay between Tail Growth and Smoothness"

Topic: 
On the Convergence of Langevin Monte Carlo: The Interplay between Tail Growth and Smoothness
Abstract / Description: 

We study sampling from a target distribution $e^{-f}$ using the unadjusted Langevin Monte Carlo (LMC) algorithm. For any potential function $f$ whose tails behave like $|x|^\alpha$ for $\alpha \in [1,2]$, and has $\beta$-H\"older continuous gradient, we derive the sufficient number of steps to reach the $\eps$-neighborhood of a $d$-dimensional target distribution as a function of $\alpha$ and $\beta$. Our rate estimate, in terms of $\eps$ dependency, is not directly influenced by the tail growth rate $\alpha$ of the potential function as long as its growth is at least linear, and it only relies on the order of smoothness $\beta$.

Our rate recovers the best known rate which was established for strongly convex potentials with Lipschitz gradient in terms of $\eps$ dependency, but we show that the same rate is achievable for a wider class of potentials that are degenerately convex at infinity.


This talk is hosted by the ISL Colloquium. To receive talk announcements, subscribe to the mailing list isl-colloq@lists.stanford.edu.

Date and Time: 
Thursday, October 28, 2021 - 4:00pm

Q-FARM Seminar presents a double feature

Topic: 
An optical lattice with sound; Programmable Interactions and Emergent Geometry in an Array of Atomic Ensembles
Abstract / Description: 

ABSTRACT #1: Quantized sound waves – phonons – govern the elastic response of crystalline materials, and play an integral part in determining their thermodynamic properties and electrical response. The physics of lattice phonons and elasticity is absent in simulators of quantum solids constructed of neutral atoms in periodic light potentials: unlike real solids, traditional optical lattices are silent because they are infinitely stiff. Here we present the realization of optical lattices with sound, using a Bose-Einstein condensate coupled to a confocal optical resonator. Optical photons in this multimode cavity both image the phonons and mediate short-range atom-atom interactions causing a crystallization transition that supports these phonons. Dynamical susceptibility measurements reveal the phonon dispersion relation, showing that these collective excitations exhibit a sound speed dependent on the BEC-photon coupling strength. These results pave the way for exploring the rich physics of elasticity in quantum solids.

ABSTRACT #2: Tunable interactions are an essential component of flexible platforms for quantum simulation and computation. While most physical systems rely on local interactions dictated by the physical proximity of constituents, we now realize programmable nonlocal interactions by using an array of atomic ensembles within an optical cavity. Here photons carry information between atomic spins and the spectrum of a drive field sets the distance dependence of interactions. By programming the interactions, we access effective geometries where the dimensionality, topology, and metric are entirely distinct from the physical geometry of the array. As examples, we engineer an antiferromagnetic triangular ladder, a Moebius strip with sign-changing interactions, and a treelike geometry inspired by concepts of quantum gravity. Our work opens broader prospects for simulating frustrated magnets and topological phases, investigating quantum optimization paradigms, and engineering entangled resource states for sensing and computation.

Date and Time: 
Wednesday, October 27, 2021 - 12:00pm
Venue: 
Physics & Astrophysics Building, Room 102/103 + Zoom

SystemX Seminar: Robots that Work Together, Robots that Play Together

Topic: 
Robots that Work Together, Robots that Play Together
Abstract / Description: 

For robots to effectively operate in our world, they must master the skills of dynamic interaction. Autonomous cars must safely negotiate their trajectories with other vehicles and pedestrians as they drive to their destinations. UAVs must avoid collisions with other aircraft, as well as dynamic obstacles on the ground. Disaster response robots must coordinate to explore and map new disaster sites. In this talk I will describe recent work in my lab using distributed optimization to obtain algorithms for robots to cooperate, and game theoretic methods to obtain algorithms for robots to compete. I will present an algorithm for fleets of autonomous cars to cooperatively track a large number of vehicles and pedestrians in a city, an algorithm for multiple robots to manipulate an object to a goal while avoiding collisions, and a distributed multi-robot SLAM algorithm, all derived using the same underlying distributed optimization framework. I will also discuss algorithms based on the theory of dynamic games, in which each actor has its own objective and constraints. I will describe examples in autonomous drone racing, car racing, and autonomous driving that use game theoretic principles to solve for Nash equilibrium trajectories in real-time, in a receding horizon fashion. Throughout the talk, I will show results from hardware experiments with ground robots, autonomous cars, and quadrotor UAVs collaborating and competing in the scenarios above.

Date and Time: 
Thursday, October 28, 2021 - 5:30pm
Venue: 
Huang 18

SystemX BONUS Seminar: New consumer use cases are shaping the display architectures of tomorrow’s mixed reality headsets and smart glasses

Topic: 
New consumer use cases are shaping the display architectures of tomorrow’s mixed reality headsets and smart glasses
Abstract / Description: 

For the past decade, display and sensor hardware developments for mixed reality and smart glasses were merely a shot in the dark, providing enough display immersion and visual comfort for developers to build up apps, especially for the enterprise field. On the sensor side, emphasis was put on 6DOF head tracking and spatial mapping, gesture sensing and later eye tracking. Today, as universal use cases for consumer emerge such as co-presence, digital twin and remote conferencing, new requirements are expressed in the product requirement documents (PRD) to enable such experiences, both on the display and sensing side. It is not only a race to smaller form factor and light weight devices for large field of view (FOV) and lower power, but the requirements are also on additional display and sensing features specifically tuned to implement such new universal use cases. Broad acceptance of wearable displays especially in the consumer field is contingent on enabling these new display and sensing requirements in small form factors and low power.

Date and Time: 
Tuesday, October 26, 2021 - 2:30pm
Venue: 
Packard 202

SystemX Seminar: Flexible Electronics with Two-Dimensional and Layered Chalcogenide Compounds

Topic: 
Flexible Electronics with Two-Dimensional and Layered Chalcogenide Compounds
Abstract / Description: 

 

As of today, more than 20 billion devices, almost three times the number of people on earth, are connected to the internet. More than half of that are Internet-of-Things (IoT) devices and it is expected that flexible electronics will play a big role in developing new types of IoT sensor systems. Applications include environmental monitoring, food packaging, and biomedical applications like vital sign and disease detection on skin or inside of the human body. However, there are several material, device and integration challenges to solve before flexible IoT systems can become a reality. Most flexible substrates require low process temperature (typically <250 °C), which hinders the direct growth of high-quality semiconductors making the choice of materials limited. At the same time, typical device dimensions are on the micron-scale which leads to low performance and high power consumption. Here, I will show how layered and two-dimensional (2D) chalcogenide compounds can offer attractive solutions for the components needed in flexible electronics overcoming the previously mentioned limitations. I will present our recent work on flexible devices including transistors, sensors, solar cells and memory. In future, combining these devices, we can imagine self-powered flexible IoT systems enabled by low energy consumption and integrated energy harvesters.

Date and Time: 
Thursday, October 21, 2021 - 5:30pm
Venue: 
Huang 018 + Zoom

The Decade of Digital Inclusion An Event Series in Connecting the Next Billion

Topic: 
The Decade of Digital Inclusion An Event Series in Connecting the Next Billion
Abstract / Description: 

Join leaders from around the globe for a field-defining conversation about the challenges and opportunities of connecting the next billion. Your ticket includes access to all virtual sessions during the October 22 symposium in addition to all pre- and post-symposium virtual sessions.

If you'd like to join us for our virtual evening gala to celebrate the groundbreaking work of Andrea Goldsmith, 2020 Marconi Fellow, tickets are available separately.


OVERVIEW OF THE MARCONI SOCIETY EVENT

Defining the next decade of equitable connectivity

We believe Internet access is a basic human right. Join leaders in policy, technology, and digital inclusion advocacy to learn about the critical challenges of connecting the next billion and to develop innovative, practical solutions.

The Decade of Digital Inclusion is your opportunity to join a community of innovators working toward a digitally inclusive future. This timely conversation can only be hosted by the Marconi Society, a nonprofit that bridges the communities of advanced technology and digital inclusion.

In addition to the symposium series, we will make history by recognizing and honoring one of the industry's leading stars, Andrea Goldsmith, as our 2020 Marconi Fellow.

Date and Time: 
Friday, October 22, 2021 - 8:00am

EST Seminar: Merging spintronics and quantum thermodynamics to harvest ambient thermal energy

Topic: 
Merging spintronics and quantum thermodynamics to harvest ambient thermal energy
Abstract / Description: 

Student organizer contact: Kirstin Schauble (kschaub@stanford.edu)


I will present a novel concept that blends spintronics and quantum thermodynamics to generate electricity. This concept is invoked to explain experimental observations of electrical generation across oxide1 and molecular spintronic devices that comprise paramagnetic centers sandwiched between electrodes with full transport spin polarization. The presence of so-called quantum resources2,3, leading to a source of work of quantum origin called ergotropy, appears to be manifest in sub-kBT spectral features, as well in an apparent signature of a phase transition of the spin fluctuations on the paramagnetic centers. I will discuss our present research tracks to better understand this spintronic quantum engine. General info may also be found at www.spinengine.tech.

References:

1. Katcko, K. et al. Spin-driven electrical power generation at room temperature. Communications Physics 2, 116 (2019).

2. Bresque, L. et al. Two-Qubit Engine Fueled by Entanglement and Local Measurements. Phys. Rev. Lett. 126, 120605 (2021).

3. Klatzow, J. et al. Experimental Demonstration of Quantum Effects in the Operation of Microscopic Heat Engines. Phys. Rev. Lett. 122, 110601 (2019).

Date and Time: 
Tuesday, October 19, 2021 - 10:30am

Probability Seminar: Probabilistic Littlewood–Offord anti-concentration results via model theory

Topic: 
Probabilistic Littlewood–Offord anti-concentration results via model theory
Abstract / Description: 

The classical Erdos–Littlewood–Offord theorem says that for any n nonzero vectors in R^d, a random signed sum concentrates on any point with probability at most O(n^{1/2}). Combining tools from probability theory, additive combinatorics, and model theory, we obtain an anti-concentration probability of n^{-1/2+o(1)} for any o-minimal set S in R^d — such as a hypersurface defined by a polynomial in x1,...,xn,exp(x1),...,exp(xn), or a restricted analytic function — not containing a line segment. We do this by showing such o-minimal sets have no higher-order additive structure, complementing work by Pila on lower-order additive structures developed to count rational and algebraic points of bounded height.

This is joint work with Jacob Fox and Matthew Kwan.

 

Date and Time: 
Monday, October 25, 2021 - 4:00pm
Venue: 
Sequoia 200

Probability Seminar: Cutoff for the asymmetric riffle shuffle

Topic: 
Cutoff for the asymmetric riffle shuffle
Abstract / Description: 

In the Gilbert–Shannon–Reeds shuffle, a deck of N cards is cut into two approximately equal parts which are riffled together uniformly at random. This Markov chain famously undergoes total variation cutoff after (3/2)*log_2(N) shuffles. We prove cutoff for asymmetric riffle shuffles in which the deck is cut into differently sized parts before riffling, confirming a conjecture of Lalley from 2000.

Date and Time: 
Monday, October 18, 2021 - 4:00pm
Venue: 
Sequoia 200

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