Complexity Theory, Game Theory, and Economics: The Barbados Lectures

This document collects the lecture notes from my mini-course "Complexity Theory, Game Theory, and Economics," taught at the Bellairs Research Institute of McGill University, Holetown, Barbados, February 19--23, 2017, as the 29th McGill Invitational Workshop on Computational Complexity. The goal of this mini-course is twofold: (i) to explain how complexity theory has helped illuminate several barriers in economics and game theory; and (ii) to illustrate how game-theoretic questions have led to new and interesting complexity theory, including recent several breakthroughs. It consists of two five-lecture sequences: the Solar Lectures, focusing on the communication and computational complexity of computing equilibria; and the Lunar Lectures, focusing on applications of complexity theory in game theory and economics. No background in game theory is assumed.Comment: Revised v2 from December 2019 corrects some errors in and adds some recent citations to v1 Revised v3 corrects a few typos in v

Protein docking refinement by convex underestimation in the low-dimensional subspace of encounter complexes

We propose a novel stochastic global optimization algorithm with applications to the refinement stage of protein docking prediction methods. Our approach can process conformations sampled from multiple clusters, each roughly corresponding to a different binding energy funnel. These clusters are obtained using a density-based clustering method. In each cluster, we identify a smooth “permissive” subspace which avoids high-energy barriers and then underestimate the binding energy function using general convex polynomials in this subspace. We use the underestimator to bias sampling towards its global minimum. Sampling and subspace underestimation are repeated several times and the conformations sampled at the last iteration form a refined ensemble. We report computational results on a comprehensive benchmark of 224 protein complexes, establishing that our refined ensemble significantly improves the quality of the conformations of the original set given to the algorithm. We also devise a method to enhance the ensemble from which near-native models are selected.Published versio

Improving Local Search for Structured SAT Formulas via Unit Propagation Based Construct and Cut Initialization (Short Paper)

This work is dedicated to improving local search solvers for the Boolean satisfiability (SAT) problem on structured instances. We propose a construct-and-cut (CnC) algorithm based on unit propagation, which is used to produce initial assignments for local search. We integrate our CnC initialization procedure within several state-of-the-art local search SAT solvers, and obtain the improved solvers. Experiments are carried out with a benchmark encoded from a spectrum repacking project as well as benchmarks encoded from two important mathematical problems namely Boolean Pythagorean Triple and Schur Number Five. The experiments show that the CnC initialization improves the local search solvers, leading to better performance than state-of-the-art SAT solvers based on Conflict Driven Clause Learning (CDCL) solvers

Effective Auxiliary Variables via Structured Reencoding

Extended resolution shows that auxiliary variables are very powerful in theory. However, attempts to exploit this potential in practice have had limited success. One reasonably effective method in this regard is bounded variable addition (BVA), which automatically reencodes formulas by introducing new variables and eliminating clauses, often significantly reducing formula size. We find motivating examples suggesting that the performance improvement caused by BVA stems not only from this size reduction but also from the introduction of effective auxiliary variables. Analyzing specific packing-coloring instances, we discover that BVA is fragile with respect to formula randomization, relying on variable order to break ties. With this understanding, we augment BVA with a heuristic for breaking ties in a structured way. We evaluate our new preprocessing technique, Structured BVA (SBVA), on more than 29 000 formulas from previous SAT competitions and show that it is robust to randomization. In a simulated competition setting, our implementation outperforms BVA on both randomized and original formulas, and appears to be well-suited for certain families of formulas

A Load-Based Multihop Routing Using Whitebox Routers in Backbone Network

White box routers are multi-hop networks. Clients and routers form this kind of network, with the routers serving as its backbone and including many radio interfaces. It is critical to distribute the load uniformly and prevent interference for Wireless Mesh Network (WMNs) to be able to provide backbone support. As a routing system for multi-radio backbone networks, we introduce Load-based Multihop-White Box Routing (L-MWBR). This protocol accounts for variations in transmit rates, packet loss ratios, intra- and interflow interference, and traffic volumes. In multi-radio networks, the L-MWBR measure is useful for locating pathways that are superior in terms of load balancing and lowering the amount of interference that occurs between multiple flows and within individual flows. There are various current routing measures in multi-radio backbone networks, and the results of the simulation reveal that the L-MWBR method works substantially better than other metrics

De novo backbone and sequence design of an idealized α/β-barrel protein: evidence of stable tertiary structure

We have designed, synthesized, and characterized a 216 amino acid residue sequence encoding a putative idealized α/β-barrel protein. The design was elaborated in two steps. First, the idealized backbone was defined with geometric parameters representing our target fold: a central eight parallel-stranded β-sheet surrounded by eight parallel α-helices, connected together with short structural turns on both sides of the barrel. An automated sequence selection algorithm, based on the dead-end elimination theorem, was used to find the optimal amino acid sequence fitting the target structure. A synthetic gene coding for the designed sequence was constructed and the recombinant artificial protein was expressed in bacteria, purified and characterized. Far-UV CD spectra with prominent bands at 222 nm and 208 nm revealed the presence of α-helix secondary structures (50%) in fairly good agreement with the model. A pronounced absorption band in the near-UV CD region, arising from immobilized aromatic side-chains, showed that the artificial protein is folded in solution. Chemical unfolding monitored by tryptophan fluorescence revealed a conformational stability (ΔGH_2O) of 35 kJ/mol. Thermal unfolding monitored by near-UV CD revealed a cooperative transition with an apparent T_m of 65 °C. Moreover, the artificial protein did not exhibit any affinity for the hydrophobic fluorescent probe 1-anilinonaphthalene-8-sulfonic acid (ANS), providing additional evidence that the artificial barrel is not in the molten globule state, contrary to previously designed artificial a/ b-barrels. Finally, ^1H NMR spectra of the folded and unfolded proteins provided evidence for specific interactions in the folded protein. Taken together, the results indicate that the de novo designed α/β-barrel protein adopts a stable three-dimensional structure in solution. These encouraging results show that de novo design of an idealized protein structure of more than 200 amino acid residues is now possible, from construction of a particular backbone conformation to determination of an amino acid sequence with an automated sequence selection algorithm

A Simple Python Testbed for Federated Learning Algorithms

Nowadays many researchers are developing various distributed and decentralized frameworks for federated learning algorithms. However, development of such a framework targeting smart Internet of Things in edge systems is still an open challenge. In this paper, we present our solution to that challenge called Python Testbed for Federated Learning Algorithms. The solution is written in pure Python, and it supports both centralized and decentralized algorithms. The usage of the presented solution is both validated and illustrated by three simple algorithm examples.Comment: 6 pages, 7 figures, 3 algorithms, as accepted at ZINC 2023, Published by IEEE Xplor