Playing Stackelberg Opinion Optimization with Randomized Algorithms for Combinatorial Strategies

From a perspective of designing or engineering for opinion formation games in social networks, the "opinion maximization (or minimization)" problem has been studied mainly for designing subset selecting algorithms. We furthermore define a two-player zero-sum Stackelberg game of competitive opinion optimization by letting the player under study as the first-mover minimize the sum of expressed opinions by doing so-called "internal opinion design", knowing that the other adversarial player as the follower is to maximize the same objective by also conducting her own internal opinion design. We propose for the min player to play the "follow-the-perturbed-leader" algorithm in such Stackelberg game, obtaining losses depending on the other adversarial player's play. Since our strategy of subset selection is combinatorial in nature, the probabilities in a distribution over all the strategies would be too many to be enumerated one by one. Thus, we design a randomized algorithm to produce a (randomized) pure strategy. We show that the strategy output by the randomized algorithm for the min player is essentially an approximate equilibrium strategy against the other adversarial player

Path deviations outperform approximate stability in heterogeneous congestion games

We consider non-atomic network congestion games with heterogeneous players where the latencies of the paths are subject to some bounded deviations. This model encompasses several well-studied extensions of the classical Wardrop model which incorporate, for example, risk-aversion, altruism or travel time delays. Our main goal is to analyze the worst-case deterioration in social cost of a perturbed Nash flow (i.e., for the perturbed latencies) with respect to an original Nash flow. We show that for homogeneous players perturbed Nash flows coincide with approximate Nash flows and derive tight bounds on their inefficiency. In contrast, we show that for heterogeneous populations this equivalence does not hold. We derive tight bounds on the inefficiency of both perturbed and approximate Nash flows for arbitrary player sensitivity distributions. Intuitively, our results suggest that the negative impact of path deviations (e.g., caused by risk-averse behavior or latency perturbations) is less severe than approximate stability (e.g., caused by limited responsiveness or bounded rationality). We also obtain a tight bound on the inefficiency of perturbed Nash flows for matroid congestion games and homogeneous populations if the path deviations can be decomposed into edge deviations. In particular, this provides a tight bound on the Price of Risk-Aversion for matroid congestion games

Exactly Solvable Lattice Hamiltonians and Gravitational Anomalies

We construct infinitely many new exactly solvable local commuting projector lattice Hamiltonian models for general bosonic beyond group cohomology invertible topological phases of order two and four in any spacetime dimensions, whose boundaries are characterized by gravitational anomalies. Examples include the beyond group cohomology invertible phase without symmetry in (4+1)D that has an anomalous boundary $\mathbb{Z}_2$ topological order with fermionic particle and fermionic loop excitations that have mutual $\pi$ statistics. We argue that this construction gives a new non-trivial quantum cellular automaton (QCA) in (4+1)D of order two. We also present an explicit construction of gapped symmetric boundary state for the bosonic beyond group cohomology invertible phase with unitary $\mathbb{Z}_2$ symmetry in (4+1)D. We discuss new quantum phase transitions protected by different invertible phases across the transitions.Comment: 60 pages, 14 figures, 3 tables; v2: typos corrected, references adde

TAO Conceptual Design Report: A Precision Measurement of the Reactor Antineutrino Spectrum with Sub-percent Energy Resolution

The Taishan Antineutrino Observatory (TAO, also known as JUNO-TAO) is a satellite experiment of the Jiangmen Underground Neutrino Observatory (JUNO). A ton-level liquid scintillator detector will be placed at about 30 m from a core of the Taishan Nuclear Power Plant. The reactor antineutrino spectrum will be measured with sub-percent energy resolution, to provide a reference spectrum for future reactor neutrino experiments, and to provide a benchmark measurement to test nuclear databases. A spherical acrylic vessel containing 2.8 ton gadolinium-doped liquid scintillator will be viewed by 10 m^2 Silicon Photomultipliers (SiPMs) of >50% photon detection efficiency with almost full coverage. The photoelectron yield is about 4500 per MeV, an order higher than any existing large-scale liquid scintillator detectors. The detector operates at -50 degree C to lower the dark noise of SiPMs to an acceptable level. The detector will measure about 2000 reactor antineutrinos per day, and is designed to be well shielded from cosmogenic backgrounds and ambient radioactivities to have about 10% background-to-signal ratio. The experiment is expected to start operation in 2022

Investigation of protein-protein interactions involving retinoblastoma binding protein 6 using immunoprecipitation and nuclear magnetic resonance spectroscopy

>Magister Scientiae - MScRetinoblastoma Binding Protein 6 (RBBP6) is a 200 KDa multi-domain protein that has been shown to play a role in mRNA processing, cell cycle arrest and apoptosis. RBBP6 interacts with tumour suppressor proteins such as p53 and pRb and has been shown cooperate with Murine Double Minute 2 (MDM2) protein in catalyzing ubiquitination and suppression of p53. Unpublished data from our laboratory has suggested that RBBP6 and MDM2 interact with each other through their RING finger domains. RBBP6 has also been shown to have its own E3 ubiquitin ligase activity, catalyzing ubiquitination of Y-Box Binding Protein 1 (YB-1) in vitro and in vivo. YB- 1 is a multifunctional oncogenic protein that is generally associated with poor prognosis in cancer, tumourigenesis, metastasis and chemotherapeutic resistance. Unpublished data from our laboratory shows that RBBP6 catalyzes poly-ubiquitination of YB-1, using Ubiquitin-conjugating enzyme H1 (UbcH1) as E2 ubiquitin conjugating enzyme

Competitive Demand Learning: A Non-cooperative Pricing Algorithm with Coordinated Price Experimentation

We consider a periodical equilibrium pricing problem for multiple firms over a planning horizon of T periods. At each period, firms set their selling prices and receive stochastic demand from consumers. Firms do not know their underlying demand curve, but they wish to determine the selling prices to maximize total revenue under competition. Hence, they have to do some price experiments such that the observed demand data are informative to make price decisions. However, uncoordinated price updating can render the demand information gathered by price experimentation less informative or inaccurate. We design a nonparametric learning algorithm to facilitate coordinated dynamic pricing, in which competitive firms estimate their demand functions based on observations and adjust their pricing strategies in a prescribed manner. We show that the pricing decisions, determined by estimated demand functions, converge to underlying equilibrium as time progresses. We obtain a bound of the revenue difference that has an order of O(F^2 T^3/4) and a regret bound that has an order of O(F T^1/2) with respect to the number of the competitive firms F and T . We also develop a modified algorithm to handle the situation where some firms may have the knowledge of the demand curve

On the Efficiency of An Election Game of Two or More Parties: How Bad Can It Be?

We extend our previous work on two-party election competition [Lin, Lu & Chen 2021] to the setting of three or more parties. An election campaign among two or more parties is viewed as a game of two or more players. Each of them has its own candidates as the pure strategies to play. People, as voters, comprise supporters for each party, and a candidate brings utility for the the supporters of each party. Each player nominates exactly one of its candidates to compete against the other party's. A candidate is assumed to win the election with higher odds if it brings more utility for all the people. The payoff of each player is the expected utility its supporters get. The game is egoistic if every candidate benefits her party's supporters more than any candidate from the competing party does. In this work, we first argue that the election game always has a pure Nash equilibrium when the winner is chosen by the hardmax function, while there exist game instances in the three-party election game such that no pure Nash equilibrium exists even the game is egoistic. Next, we propose two sufficient conditions for the egoistic election game to have a pure Nash equilibrium. Based on these conditions, we propose a fixed-parameter tractable algorithm to compute a pure Nash equilibrium of the egoistic election game. Finally, perhaps surprisingly, we show that the price of anarchy of the egoistic election game is upper bounded by the number of parties. Our findings suggest that the election becomes unpredictable when more than two parties are involved and, moreover, the social welfare deteriorates with the number of participating parties in terms of possibly increasing price of anarchy. This work alternatively explains why the two-party system is prevalent in democratic countries