Constrained Optimal Querying: Huffman Coding and Beyond

Huffman coding is well known to be useful in certain decision problems involving minimizing the average number of (freely chosen) queries to determine an unknown random variable. However, in problems where the queries are more constrained, the original Huffman coding no longer works. In this paper, we proposed a general model to describe such problems and two code schemes: one is Huffman-based, and the other called GBSC (Greedy Binary Separation Coding). We proved the optimality of GBSC by induction on a binary decision tree, telling us that GBSC is at least as good as Shannon coding. We then compared the two algorithms based on these two codes, by testing them with two problems: DNA detection and 1-player Battleship, and found both to be decent approximating algorithms, with Huffman-based algorithm giving an expected length 1.1 times the true optimal in DNA detection problem, and GBSC yielding an average number of queries 1.4 times the theoretical optimal in 1-player Battleship

A Stochastic Programming Model for a Day-Ahead Electricity Market: a Heuristic Methodology and Pricing

This thesis presents a multi-stage linear stochastic mixed integer programming (SMIP) model for planning power generation in a pool-type day-ahead electricity market. The model integrates a reserve demand curve and shares most of the features of a stochastic unit commitment (UC) problem, which is known to be NP-hard. We capture the stochastic nature of the problem through scenarios, resulting in a large-scale mixed integer programming (MIP) problem that is computationally challenging to solve. Given that an independent system operator (ISO) has to solve such a problem within a time requirement of an hour or so, in order to release operating schedules for the next day real-time market, the problem has to be solved efficiently. For that purpose, we use some approximations to maintain the linearity of the model, parsimoniously select a subset of scenarios, and invoke realistic assumptions to keep the size of the problem reasonable. Even with these measures, realistic-size SMIP models with binary variables in each stage are still hard to solve with exact methods. We, therefore, propose a scenario-rolling heuristic to solve the SMIP problem. In each iteration, the heuristic solves a subset of the scenarios, and uses part of the obtained solution to solve another group in the subsequent iterations until all scenarios are solved. Two numerical examples are provided to test the performance of the scenario-rolling heuristic, and to highlight the difference between the operative schedules of a deterministic model and the SMIP model. Motivated by previous studies on pricing MIP problems and their applications to pricing electric power, we investigate pricing issues and compensation schemes using MIP formulations in the second part of the thesis. We show that some ideas from the literature can be applied to pricing energy/reserves for a relatively realistic model with binary variables, but some are found to be impractical in the real world. We propose two compensation schemes based on the SMIP that can be easily implemented in practice. We show that the compensation schemes with make-whole payments ensure that generators can have non-negative profits. We also prove that under some assumptions, one of the compensation schemes has the interesting theoretical property of minimizing the variance of the profit of generators to zero. Theoretical and numerical results of these compensation schemes are presented and discussed

Bi-level Mixed-Integer Nonlinear Optimization for Pelagic Island Microgrid Group Energy Management Considering Uncertainty

To realize the safe, economical and low-carbon operation of the pelagic island microgrid group, this paper develops a bi-level energy management framework in a joint energy-reserve market where the microgrid group (MG) operator and renewable and storage aggregators (RSA) are independent stakeholders with their own interests. In the upper level, MG operator determines the optimal transaction prices with aggregators to minimize MG operation cost while ensuring all safety constraints are satisfied under uncertainty. In the lower level, aggregators utilize vessels for batteries swapping and transmission among islands in addition to energy arbitrage by participating in energy and reserve market to maximize their own revenue. An upper bound tightening iterative algorithm is proposed for the formulated problem with nonlinear terms and integer variables in the lower level to improve the efficiency and reduce the gap between upper bound and lower bound compared with existing reformulation and decomposition algorithm. Case studies validate the effectiveness of the proposed approach and demonstrate its advantage of the proposed approach in terms of optimality and computation efficiency, compared with other methods.Comment: Accepted by CSEE Journal of Power and Energy System

The formation and stability of junctions in single-wall carbon nanotubes

The structure and stability of molecular junctions, which connect two single-wall carbon nanotubes (SWCNTs) of different diameters and chiral angles, (n(1), m(1))-(n(2), m(2)), are systematically investigated by density functional tight binding calculations. More than 100 junctions, which connect well-aligned SWCNTs, were constructed and calculated. For a highly stable junction between two chiral (n(1), m(1)) and (n(2), m(2)) SWCNTs with opposite handedness, the number of pentagon-heptagon (5/7) pairs required to build the junction can be denoted as vertical bar vertical bar n(2) - n(1)vertical bar - vertical bar m(2) - m(1)vertical bar vertical bar + min{vertical bar n(2) - n(1)vertical bar, vertical bar m(2) - m(1)vertical bar} with (n(2), m(2)) rotating pi/3 angle or not. While for a junction connected by two zigzag, armchair or two chiral SWCNTs with the same handedness, the number of 5/7 pairs is equal to vertical bar n(1) - n(2)vertical bar + vertical bar m(1) - m(2)vertical bar. Similar to the formation energies of grain boundaries in graphene, the curve of the formation energies vs. chiral angle difference present an 'M' shape indicating the preference of similar to 30 degree junctions. Moreover, the formation energies of the zigzag-type and armchair-type junctions with zero misorientation angles are largely sensitive to the diameter difference of two sub-SWCNTs

Photoproduction of C-even quarkonia at EIC and EicC

The $\eta_c$ photoproduction in $ep$ collision has long been proposed as an ideal process to probe the existence of odderon. In the current work, we systematically investigate the photoproduction of various $C$-even heavy quarkonia (exemplified by $\eta_{c(b)}$, and $\chi_{c(b)J}$ with $J=0,1,2$) via one-photon exchange channel, at the lowest order in $\alpha_s$ and heavy quark velocity in the context of NRQCD factorization. We find that the photoproduction rates of the $C$-even quarkonia through this mechanism are comparable in magnitude with that through the odderon-initiated mechanism, even in the Regge limit ($s\gg -t$), though the latter types of predictions suffers from considerable theoretical uncertainties. The future measurements of these types of quarkonium photoproduction processes in \texttt{EIC} and \texttt{EicC} are crucial to ascertain which mechanism plays the dominant role.Comment: 16 pages, 9 figure

MEV Makes Everyone Happy under Greedy Sequencing Rule

Trading through decentralized exchanges (DEXs) has become crucial in today's blockchain ecosystem, enabling users to swap tokens efficiently and automatically. However, the capacity of miners to strategically order transactions has led to exploitative practices (e.g., front-running attacks, sandwich attacks) and gain substantial Maximal Extractable Value (MEV) for their own advantage. To mitigate such manipulation, Ferreira and Parkes recently proposed a greedy sequencing rule such that the execution price of transactions in a block moves back and forth around the starting price. Utilizing this sequencing rule makes it impossible for miners to conduct sandwich attacks, consequently mitigating the MEV problem. However, no sequencing rule can prevent miners from obtaining risk-free profits. This paper systemically studies the computation of a miner's optimal strategy for maximizing MEV under the greedy sequencing rule, where the utility of miners is measured by the overall value of their token holdings. Our results unveil a dichotomy between the no trading fee scenario, which can be optimally strategized in polynomial time, and the scenario with a constant fraction of trading fee, where finding the optimal strategy is proven NP-hard. The latter represents a significant challenge for miners seeking optimal MEV. Following the computation results, we further show a remarkable phenomenon: Miner's optimal MEV also benefits users. Precisely, in the scenarios without trading fees, when miners adopt the optimal strategy given by our algorithm, all users' transactions will be executed, and each user will receive equivalent or surpass profits compared to their expectations. This outcome provides further support for the study and design of sequencing rules in decentralized exchanges.Comment: 14 Pages, ACM CCS Workshop on Decentralized Finance and Security (DeFi'23

Decentralized Funding of Public Goods in Blockchain System:Leveraging Expert Advice

Public goods projects, such as open-source technology, are essential for the blockchain ecosystem's growth. However, funding these projects effectively remains a critical issue within the ecosystem. Currently, the funding protocols for blockchain public goods lack professionalism and fail to learn from past experiences. To address this challenge, our research introduces a human oracle protocol involving public goods projects, experts, and funders. In our approach, funders contribute investments to a funding pool, while experts offer investment advice based on their expertise in public goods projects. The oracle's decisions on funding support are influenced by the reputations of the experts. Experts earn or lose reputation based on how well their project implementations align with their advice, with successful investments leading to higher reputations. Our oracle is designed to adapt to changing circumstances, such as experts exiting or entering the decision-making process. We also introduce a regret bound to gauge the oracle's effectiveness. Theoretically, we establish an upper regret bound for both static and dynamic models and demonstrate its closeness to an asymptotically equal lower bound. Empirically, we implement our protocol on a test chain and show that our oracle's investment decisions closely mirror optimal investments in hindsight

Decentralized Funding of Public Goods in Blockchain System:Leveraging Expert Advice

Public goods projects, such as open-source technology, are essential for the blockchain ecosystem's growth. However, funding these projects effectively remains a critical issue within the ecosystem. Currently, the funding protocols for blockchain public goods lack professionalism and fail to learn from past experiences. To address this challenge, our research introduces a human oracle protocol involving public goods projects, experts, and funders. In our approach, funders contribute investments to a funding pool, while experts offer investment advice based on their expertise in public goods projects. The oracle's decisions on funding support are influenced by the reputations of the experts. Experts earn or lose reputation based on how well their project implementations align with their advice, with successful investments leading to higher reputations. Our oracle is designed to adapt to changing circumstances, such as experts exiting or entering the decision-making process. We also introduce a regret bound to gauge the oracle's effectiveness. Theoretically, we establish an upper regret bound for both static and dynamic models and demonstrate its closeness to an asymptotically equal lower bound. Empirically, we implement our protocol on a test chain and show that our oracle's investment decisions closely mirror optimal investments in hindsight