3,393 research outputs found
UMSL Bulletin 2023-2024
The 2023-2024 Bulletin and Course Catalog for the University of Missouri St. Louis.https://irl.umsl.edu/bulletin/1088/thumbnail.jp
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
UMSL Bulletin 2022-2023
The 2022-2023 Bulletin and Course Catalog for the University of Missouri St. Louis.https://irl.umsl.edu/bulletin/1087/thumbnail.jp
Revisiting Block-Diagonal SDP Relaxations for the Clique Number of the Paley Graphs
This work addresses the block-diagonal semidefinite program (SDP) relaxations
for the clique number of the Paley graphs. The size of the maximal clique
(clique number) of a graph is a classic NP-complete problem; a Paley graph is a
deterministic graph where two vertices are connected if their difference is a
quadratic residue modulo certain prime powers. Improving the upper bound for
the Paley graph clique number for odd prime powers is an open problem in
combinatorics. Moreover, since quadratic residues exhibit pseudorandom
properties, Paley graphs are related to the construction of deterministic
restricted isometries, an open problem in compressed sensing and sparse
recovery. Recent work provides evidence that the current upper bounds can be
improved by the sum-of-squares (SOS) relaxations. In particular the bounds
given by the SOS relaxations of degree 4 (SOS-4) are asymptotically growing at
an order smaller than square root of the prime. However computations of SOS-4
become intractable with respect to large graphs. Gvozdenovic et al. introduced
a more computationally efficient block-diagonal hierarchy of SDPs that refines
the SOS hierarchy. They computed the values of these SDPs of degrees 2 and 3
(L2 and L3 respectively) for the Paley graph clique numbers associated with
primes p less or equal to 809. These values bound from the above the values of
the corresponding SOS-4 and SOS-6 relaxations respectively. We revisit these
computations and determine the values of the L2 relaxation for larger p's. Our
results provide additional numerical evidence that the L2 relaxations, and
therefore also the SOS-4 relaxations, are asymptotically growing at an order
smaller than the square root of p
When Deep Learning Meets Polyhedral Theory: A Survey
In the past decade, deep learning became the prevalent methodology for
predictive modeling thanks to the remarkable accuracy of deep neural networks
in tasks such as computer vision and natural language processing. Meanwhile,
the structure of neural networks converged back to simpler representations
based on piecewise constant and piecewise linear functions such as the
Rectified Linear Unit (ReLU), which became the most commonly used type of
activation function in neural networks. That made certain types of network
structure \unicode{x2014}such as the typical fully-connected feedforward
neural network\unicode{x2014} amenable to analysis through polyhedral theory
and to the application of methodologies such as Linear Programming (LP) and
Mixed-Integer Linear Programming (MILP) for a variety of purposes. In this
paper, we survey the main topics emerging from this fast-paced area of work,
which bring a fresh perspective to understanding neural networks in more detail
as well as to applying linear optimization techniques to train, verify, and
reduce the size of such networks
Finite-Size Security for Discrete-Modulated Continuous-Variable Quantum Key Distribution Protocols
Discrete-Modulated (DM) Continuous-Variable Quantum Key Distribution (CV-QKD)
protocols are promising candidates for commercial implementations of quantum
communication networks due to their experimental simplicity. While tight
security analyses in the asymptotic limit exist, proofs in the finite-size
regime are still subject to active research. We present a composable
finite-size security proof against independently and identically distributed
(i.i.d.) collective attacks for a general DM CV-QKD protocol. We introduce a
new energy testing theorem to bound the effective dimension of Bob's system and
rigorously prove security within Renner's epsilon-security framework. We
introduce and build up our security argument on so-called acceptance testing
which, as we argue, is the proper notion for the statistical analysis in the
finite-size regime and replaces the concept of parameter estimation for
asymptotic security analyses. Finally, we extend and apply a numerical security
proof technique to calculate tight lower bounds on the secure key rate. To
demonstrate our method, we apply it to a quadrature phase-shift keying
protocol, both for untrusted, ideal and trusted non-ideal detectors. The
results show that our security proof method yields secure finite-size key rates
under experimentally viable conditions up to at least 73 km transmission
distance.Comment: 28 pages, 6 Figure
Testing symmetry on quantum computers
Symmetry is a unifying concept in physics. In quantum information and beyond,
it is known that quantum states possessing symmetry are not useful for certain
information-processing tasks. For example, states that commute with a
Hamiltonian realizing a time evolution are not useful for timekeeping during
that evolution, and bipartite states that are highly extendible are not
strongly entangled and thus not useful for basic tasks like teleportation.
Motivated by this perspective, this paper details several quantum algorithms
that test the symmetry of quantum states and channels. For the case of testing
Bose symmetry of a state, we show that there is a simple and efficient quantum
algorithm, while the tests for other kinds of symmetry rely on the aid of a
quantum prover. We prove that the acceptance probability of each algorithm is
equal to the maximum symmetric fidelity of the state being tested, thus giving
a firm operational meaning to these latter resource quantifiers. Special cases
of the algorithms test for incoherence or separability of quantum states. We
evaluate the performance of these algorithms on choice examples by using the
variational approach to quantum algorithms, replacing the quantum prover with a
parameterized circuit. We demonstrate this approach for numerous examples using
the IBM quantum noiseless and noisy simulators, and we observe that the
algorithms perform well in the noiseless case and exhibit noise resilience in
the noisy case. We also show that the maximum symmetric fidelities can be
calculated by semi-definite programs, which is useful for benchmarking the
performance of these algorithms for sufficiently small examples. Finally, we
establish various generalizations of the resource theory of asymmetry, with the
upshot being that the acceptance probabilities of the algorithms are resource
monotones and thus well motivated from the resource-theoretic perspective.Comment: v3: 51 pages, 41 figures, 31 tables, final version accepted for
publication in Quantum Journa
Design and Real-World Evaluation of Dependable Wireless Cyber-Physical Systems
The ongoing effort for an efficient, sustainable, and automated interaction between humans, machines, and our environment will make cyber-physical systems (CPS) an integral part of the industry and our daily lives. At their core, CPS integrate computing elements, communication networks, and physical processes that are monitored and controlled through sensors and actuators. New and innovative applications become possible by extending or replacing static and expensive cable-based communication infrastructures with wireless technology. The flexibility of wireless CPS is a key enabler for many envisioned scenarios, such as intelligent factories, smart farming, personalized healthcare systems, autonomous search and rescue, and smart cities.
High dependability, efficiency, and adaptivity requirements complement the demand for wireless and low-cost solutions in such applications. For instance, industrial and medical systems should work reliably and predictably with performance guarantees, even if parts of the system fail. Because emerging CPS will feature mobile and battery-driven devices that can execute various tasks, the systems must also quickly adapt to frequently changing conditions. Moreover, as applications become ever more sophisticated, featuring compact embedded devices that are deployed densely and at scale, efficient designs are indispensable to achieve desired operational lifetimes and satisfy high bandwidth demands.
Meeting these partly conflicting requirements, however, is challenging due to imperfections of wireless communication and resource constraints along several dimensions, for example, computing, memory, and power constraints of the devices. More precisely, frequent and correlated message losses paired with very limited bandwidth and varying delays for the message exchange significantly complicate the control design. In addition, since communication ranges are limited, messages must be relayed over multiple hops to cover larger distances, such as an entire factory. Although the resulting mesh networks are more robust against interference, efficient communication is a major challenge as wireless imperfections get amplified, and significant coordination effort is needed, especially if the networks are dynamic.
CPS combine various research disciplines, which are often investigated in isolation, ignoring their complex interaction. However, to address this interaction and build trust in the proposed solutions, evaluating CPS using real physical systems and wireless networks paired with formal guarantees of a system’s end-to-end behavior is necessary. Existing works that take this step can only satisfy a few of the abovementioned requirements. Most notably, multi-hop communication has only been used to control slow physical processes while providing no guarantees. One of the reasons is that the current communication protocols are not suited for dynamic multi-hop networks.
This thesis closes the gap between existing works and the diverse needs of emerging wireless CPS. The contributions address different research directions and are split into two parts. In the first part, we specifically address the shortcomings of existing communication protocols and make the following contributions to provide a solid networking foundation:
• We present Mixer, a communication primitive for the reliable many-to-all message exchange in dynamic wireless multi-hop networks. Mixer runs on resource-constrained low-power embedded devices and combines synchronous transmissions and network coding for a highly scalable and topology-agnostic message exchange. As a result, it supports mobile nodes and can serve any possible traffic patterns, for example, to efficiently realize distributed control, as required by emerging CPS applications.
• We present Butler, a lightweight and distributed synchronization mechanism with formally guaranteed correctness properties to improve the dependability of synchronous transmissions-based protocols. These protocols require precise time synchronization provided by a specific node. Upon failure of this node, the entire network cannot communicate. Butler removes this single point of failure by quickly synchronizing all nodes in the network without affecting the protocols’ performance.
In the second part, we focus on the challenges of integrating communication and various control concepts using classical time-triggered and modern event-based approaches. Based on the design, implementation, and evaluation of the proposed solutions using real systems and networks, we make the following contributions, which in many ways push the boundaries of previous approaches:
• We are the first to demonstrate and evaluate fast feedback control over low-power wireless multi-hop networks. Essential for this achievement is a novel co-design and integration of communication and control. Our wireless embedded platform tames the imperfections impairing control, for example, message loss and varying delays, and considers the resulting key properties in the control design. Furthermore, the careful orchestration of control and communication tasks enables real-time operation and makes our system amenable to an end-to-end analysis. Due to this, we can provably guarantee closed-loop stability for physical processes with linear time-invariant dynamics.
• We propose control-guided communication, a novel co-design for distributed self-triggered control over wireless multi-hop networks. Self-triggered control can save energy by transmitting data only when needed. However, there are no solutions that bring those savings to multi-hop networks and that can reallocate freed-up resources, for example, to other agents. Our control system informs the communication system of its transmission demands ahead of time so that communication resources can be allocated accordingly. Thus, we can transfer the energy savings from the control to the communication side and achieve an end-to-end benefit.
• We present a novel co-design of distributed control and wireless communication that resolves overload situations in which the communication demand exceeds the available bandwidth. As systems scale up, featuring more agents and higher bandwidth demands, the available bandwidth will be quickly exceeded, resulting in overload. While event-triggered control and self-triggered control approaches reduce the communication demand on average, they cannot prevent that potentially all agents want to communicate simultaneously. We address this limitation by dynamically allocating the available bandwidth to the agents with the highest need. Thus, we can formally prove that our co-design guarantees closed-loop stability for physical systems with stochastic linear time-invariant dynamics.:Abstract
Acknowledgements
List of Abbreviations
List of Figures
List of Tables
1 Introduction
1.1 Motivation
1.2 Application Requirements
1.3 Challenges
1.4 State of the Art
1.5 Contributions and Road Map
2 Mixer: Efficient Many-to-All Broadcast in Dynamic Wireless Mesh Networks
2.1 Introduction
2.2 Overview
2.3 Design
2.4 Implementation
2.5 Evaluation
2.6 Discussion
2.7 Related Work
3 Butler: Increasing the Availability of Low-Power Wireless Communication Protocols
3.1 Introduction
3.2 Motivation and Background
3.3 Design
3.4 Analysis
3.5 Implementation
3.6 Evaluation
3.7 Related Work
4 Feedback Control Goes Wireless: Guaranteed Stability over Low-Power Multi-Hop Networks
4.1 Introduction
4.2 Related Work
4.3 Problem Setting and Approach
4.4 Wireless Embedded System Design
4.5 Control Design and Analysis
4.6 Experimental Evaluation
4.A Control Details
5 Control-Guided Communication: Efficient Resource Arbitration and Allocation in Multi-Hop Wireless Control Systems
5.1 Introduction
5.2 Problem Setting
5.3 Co-Design Approach
5.4 Wireless Communication System Design
5.5 Self-Triggered Control Design
5.6 Experimental Evaluation
6 Scaling Beyond Bandwidth Limitations: Wireless Control With Stability Guarantees Under Overload
6.1 Introduction
6.2 Problem and Related Work
6.3 Overview of Co-Design Approach
6.4 Predictive Triggering and Control System
6.5 Adaptive Communication System
6.6 Integration and Stability Analysis
6.7 Testbed Experiments
6.A Proof of Theorem 4
6.B Usage of the Network Bandwidth for Control
7 Conclusion and Outlook
7.1 Contributions
7.2 Future Directions
Bibliography
List of Publication
Sample-efficient model-based reinforcement learning for quantum control
We propose a model-based reinforcement learning (RL) approach for noisy time-dependent gate optimization with reduced sample complexity over model-free RL. Sample complexity is defined as the number of controller interactions with the physical system. Leveraging an inductive bias, inspired by recent advances in neural ordinary differential equations (ODEs), we use an autodifferentiable ODE, parametrized by a learnable Hamiltonian ansatz, to represent the model approximating the environment, whose time-dependent part, including the control, is fully known. Control alongside Hamiltonian learning of continuous time-independent parameters is addressed through interactions with the system. We demonstrate an order of magnitude advantage in sample complexity of our method over standard model-free RL in preparing some standard unitary gates with closed and open system dynamics, in realistic computational experiments incorporating single-shot measurements, arbitrary Hilbert space truncations, and uncertainty in Hamiltonian parameters. Also, the learned Hamiltonian can be leveraged by existing control methods like GRAPE (gradient ascent pulse engineering) for further gradient-based optimization with the controllers found by RL as initializations. Our algorithm, which we apply to nitrogen vacancy (NV) centers and transmons, is well suited for controlling partially characterized one- and two-qubit systems
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