IA Scholar Query: Integer Programming with 2-Variable Equations and 1-Variable Inequalities.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgWed, 07 Dec 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440Scaling of the quantum approximate optimization algorithm on superconducting qubit based hardware
https://scholar.archive.org/work/obi5ik2hwnhbto3clzmzfvv2pu
Quantum computers may provide good solutions to combinatorial optimization problems by leveraging the Quantum Approximate Optimization Algorithm (QAOA). The QAOA is often presented as an algorithm for noisy hardware. However, hardware constraints limit its applicability to problem instances that closely match the connectivity of the qubits. Furthermore, the QAOA must outpace classical solvers. Here, we investigate swap strategies to map dense problems into linear, grid and heavy-hex coupling maps. A line-based swap strategy works best for linear and two-dimensional grid coupling maps. Heavy-hex coupling maps require an adaptation of the line swap strategy. By contrast, three-dimensional grid coupling maps benefit from a different swap strategy. Using known entropic arguments we find that the required gate fidelity for dense problems lies deep below the fault-tolerant threshold. We also provide a methodology to reason about the execution-time of QAOA. Finally, we present a QAOA Qiskit Runtime program and execute the closed-loop optimization on cloud-based quantum computers with transpiler settings optimized for QAOA. This work highlights some obstacles to improve to make QAOA competitive, such as gate fidelity, gate speed, and the large number of shots needed. The Qiskit Runtime program gives us a tool to investigate such issues at scale on noisy superconducting qubit hardware.Johannes Weidenfeller, Lucia C. Valor, Julien Gacon, Caroline Tornow, Luciano Bello, Stefan Woerner, Daniel J. Eggerwork_obi5ik2hwnhbto3clzmzfvv2puWed, 07 Dec 2022 00:00:00 GMTResearch on Maintenance Strategies for Different Transmission Sections to Improve the Consumption Rate Based on a Renewable Energy Production Simulation
https://scholar.archive.org/work/f5wk4a6z25cdlbypluor45ctaa
Renewable energy consumption is one of the most important factors in meeting the goal of "30 and 60" in China. However, the maintenance of the transmission section affects the amount of generation transfer, further affecting the consumption of renewable energy. Hence, in this study, a time-series renewable energy production simulation (REPS) is proposed in order to accurately predict the power generation in a simulated situation. According to the results of the REPS, the sensitivity of the different sections' maintenance can be calculated and determined. The appropriate maintenance strategies can be selected for different situations by comparing the consumption rate; as an example, we conducted a case study. The results show that the quota in the transmission section has higher sensitivity; a larger quota indicates a greater sensitivity to the consumption rate. The results also show that a larger quota is more suitable for maintenance in February or November, since the consumption rate is higher regardless of if it is in a single-transmission-section maintenance strategy or in a two-section simultaneous maintenance strategy.Xiaojing Hu, Haoling Min, Sai Dai, Zhi Cai, Xiaonan Yang, Qiang Ding, Zhanyong Yang, Feng Xiaowork_f5wk4a6z25cdlbypluor45ctaaWed, 07 Dec 2022 00:00:00 GMTOn Cutting Planes for Extended Formulation of Signomial Programming
https://scholar.archive.org/work/w3avoigvyncj3kk5sbgdyefvdu
The generation of cutting planes is crucial in solving non-convex Mixed-Integer Non-linear Programming problems to ϵ-global optimality. In this paper, we study the signomial-term set, i.e., the graph of a signomial-term function, which arises in the extended formulation of Signomial Programming, and we show that it suffices to consider the signomial-term set as the epigraph/hypograph of the associated signomial-term function. We present a useful reformulation of the signomial-term set, written as the zero-sublevel set of the difference of two concave power functions. We propose three types of valid linear inequalities: intersection cuts and two types of outer approximation cuts. We construct signomial-term-free sets which do not contain any point of the signomial-term set in their interiors, and show that these signomial-term-free sets are maximal in the nonnegative orthant, so they yield strong intersection cuts. The two types of outer approximation cuts are linearizations of two different convex relaxations, that differ in underestimators for the concave power function over a hyper-rectangle. On the one hand, we show that the concave power function is supermodular, and construct the first convex relaxation based on the supermodular inequalities. On the other hand, we factorize the concave power function into bivariate concave power functions, and give their closed-form convex envelopes over rectangles. Then the second convex relaxation is constructed by a lift-and-project method. We implement the proposed cuts within the solver and show that they have good performance on MINLPLib instances.Liding Xu, Claudia D'Ambrosio, Leo Liberti, Sonia Haddad Vanierwork_w3avoigvyncj3kk5sbgdyefvduTue, 06 Dec 2022 00:00:00 GMTManaging Sets of Flying Base Stations Using Energy Efficient 3D Trajectory Planning in Cellular Networks
https://scholar.archive.org/work/ytrd3pyvyjgsxo6dqnyuxtdty4
Unmanned aerial vehicles (UAVs) in cellular networks have garnered considerable interest. One of their applications is as flying base stations (FBSs), which can increase coverage and quality of service (QoS). Because FBSs are battery-powered, regulating their energy usage is a vital aspect of their use; and therefore the appropriate placement and trajectories of FBSs throughout their operation are critical to overcoming this challenge. In this paper, we propose a method of solving a multi-FBS 3D trajectory problem that considers FBS energy consumption, operation time, flight distance limits, and inter-cell interference constraints. Our method is divided into two phases: FBS placement and FBS trajectory. In taking this approach, we break the problem into several snapshots. First, we find the minimum number of FBSs required and their proper 3D positions in each snapshot. Then, between every two snapshots, the trajectory phase is executed. The optimal path between the origin and destination of each FBS is determined during the trajectory phase by utilizing a proposed binary linear problem (BLP) model that considers FBS energy consumption and flight distance constraints. Then, the shortest path for each FBS is determined while taking obstacles and collision avoidance into consideration. The number of FBSs needed may vary between snapshots, so we present an FBS set management (FSM) technique to manage the set of FBSs and their power. The results demonstrate that the proposed approach is applicable to real-world situations and that the outcomes are consistent with expectations.Mohammad Javad Sobouti, Amir Hossein Mohajerzadeh, Seyed Amin Hosseini Seno, Halim Yanikomerogluwork_ytrd3pyvyjgsxo6dqnyuxtdty4Tue, 06 Dec 2022 00:00:00 GMTBounded arbitrage and nearly rational behavior
https://scholar.archive.org/work/a3lhgiuq2bcyvpouowstblu5xq
We establish the equivalence between a principle of almost absence of arbitrage opportunities and nearly rational decision-making. The implications of such principle are considered in the context of the aggregation of probabilistic opinions and of stochastic choice functions. In the former a bounded arbitrage principle and its equivalent form as an approximately Pareto condition are shown to bound the difference between the collective probabilistic assessment of a set of states and a linear aggregation rule on the individual assessments. In the latter we show that our general principle of limited arbitrage opportunities translates into a weakening of the McFadden-Richter axiom of stochastic rationality, and gives an upper bound for the minimum distance of a stochastic choice function to another in the class of random utility maximization models.Leandro Nascimentowork_a3lhgiuq2bcyvpouowstblu5xqTue, 06 Dec 2022 00:00:00 GMTHolographic duals of the 𝒩=1* gauge theory
https://scholar.archive.org/work/7s25tigeunhljixdk43vzcooou
We use the long-wavelength effective theory of black branes (blackfold approach) to perturbatively construct holographic duals of the vacua of the 𝒩=1* supersymmetric gauge theory. Employing the mechanism of Polchinski and Strassler, we consider wrapped black five-brane probes with D3-brane charge moving in the perturbative supergravity backgrounds corresponding to the high and low temperature phases of the gauge theory. Our approach recovers the results for the brane potentials and equilibrium configurations known in the literature in the extremal limit, while away from extremality we find metastable black D3-NS5 configurations with horizon topology ℝ^3×𝕊^2×𝕊^3 in certain regimes of parameter space, which cloak potential brane singularities. We uncover novel features of the phase diagram of the 𝒩=1* gauge theory in different ensembles and provide further evidence for the appearance of metastable states in holographic backgrounds dual to confining gauge theories.Jay Armas, Giorgos Batzios, Jan Pieter van der Schaarwork_7s25tigeunhljixdk43vzcooouTue, 06 Dec 2022 00:00:00 GMTHilbert-Poincaré series of matroid Chow rings and intersection cohomology
https://scholar.archive.org/work/lawngmuvovftvllwafkbtlt3ei
We study the Hilbert series of four objects arising in the Chow-theoretic and Kazhdan-Lusztig framework of matroids. These are, respectively, the Hilbert series of the Chow ring, the augmented Chow ring, the intersection cohomology module, and its stalk at the empty flat. We develop a parallelism between the Kazhdan-Lusztig polynomial of a matroid and the Hilbert series of its Chow ring. This extends to a parallelism between the Z-polynomial of a matroid and the Hilbert series of its augmented Chow ring. This suggests to bring ideas from one framework to the other. Our two main motivations are the real-rootedness conjecture for all of these polynomials, and the problem of computing them. We provide several intrinsic definitions of these invariants; also, by leveraging that they are valuations under matroid polytope subdivisions, we deduce a fast way for computing them for a large class of matroids. Uniform matroids are a case of combinatorial interest; we link the resulting polynomials with certain real-rooted families such as the (binomial) Eulerian polynomials, and we settle a conjecture of Hameister, Rao, and Simpson. Furthermore, we prove the real-rootedness of the Hilbert series of the augmented Chow rings of uniform matroids via a result of Haglund and Zhang; and in addition, we prove a version of a conjecture of Gedeon in the Chow setting: uniform matroids maximize coefficient-wisely these polynomials for matroids with fixed rank and size. By relying on the nonnegativity of the Kazhdan-Lusztig polynomials and the semi-small decompositions of Braden, Huh, Matherne, Proudfoot, and Wang, we strengthen the unimodality of the Hilbert series of Chow rings, augmented Chow rings, and intersection cohomologies to γ-positivity, a property for palindromic polynomials that lies between unimodality and real-rootedness; this settles a conjecture of Ferroni, Nasr, and Vecchi.Luis Ferroni, Jacob P. Matherne, Matthew Stevens, Lorenzo Vecchiwork_lawngmuvovftvllwafkbtlt3eiTue, 06 Dec 2022 00:00:00 GMTUniform-in-Time Propagation of Chaos for Mean Field Langevin Dynamics
https://scholar.archive.org/work/7cqkgrnzmzbj5nvwvnzsttjpci
We study the uniform-in-time propagation of chaos for mean field Langevin dynamics with convex mean field potenital. Convergences in both Wasserstein-2 distance and relative entropy are established. We do not require the mean field potenital functional to bear either small mean field interaction or displacement convexity, which are common constraints in the literature. In particular, it allows us to study the efficiency of the noisy gradient descent algorithm for training two-layer neural networks.Fan Chen and Zhenjie Ren and Songbo Wangwork_7cqkgrnzmzbj5nvwvnzsttjpciTue, 06 Dec 2022 00:00:00 GMT7. Framing the Problem and Identifying Potential Solutions
https://scholar.archive.org/work/tnkxzditffdobb77q7y5hrtspa
The creation of effective policy and practice starts by framing the problem to be solved. This requires deciding what is important, identifying the current and potential future threats, diagnosing the actual cause of the problems, and identifying solutions, including innovating to create new ones when required. In this chapter we describe various techniques that can be used to frame the problem including horizon scanning, situation models and theory of change diagrams. These can be used to identify the analytical questions and specific assumptions that underpin the assessment of evidence and decision making.Nafeesa Esmail, Rhys Green, Silviu O. Petrovan, Nick Salafsky, Nigel G. Taylor, Jeremy D. Wilsonwork_tnkxzditffdobb77q7y5hrtspaTue, 06 Dec 2022 00:00:00 GMTOnline Resource Allocation for Reusable Resources
https://scholar.archive.org/work/xojbyba4wjgddjvzrc2qvjspwm
We study a general model on reusable resource allocation under model uncertainty. A heterogeneous population of customers arrive at the decision maker's (DM's) platform sequentially. Upon observing a customer's type, the DM selects an allocation decision, which leads to rewards earned and resources occupied. Each resource unit is occupied for a random duration, and the unit is available for another allocation after the usage duration. Our model captures numerous applications involving admission control and assortment planning. The DM aims to simultaneously maximize multiple types of rewards, while satisfying the resource constraints and being uncertain about the customers' arrival process. We develop a near-optimal algorithm that achieves (1-ϵ) fraction of the optimal expected rewards, where the error parameter ϵ decays to zero as the resource capacity units and the length of the horizon grow. The algorithm iteratively applies the Multiplicative Weight Update algorithm in a novel manner, which balances the trade-off among the amounts of rewards earned, resources occupied and usage durations.Xilin Zhang, Wang Chi Cheungwork_xojbyba4wjgddjvzrc2qvjspwmTue, 06 Dec 2022 00:00:00 GMTA Strongly Polynomial Algorithm for Approximate Forster Transforms and its Application to Halfspace Learning
https://scholar.archive.org/work/a64hkzezjfcvvl3zlmv76dz3j4
The Forster transform is a method of regularizing a dataset by placing it in radial isotropic position while maintaining some of its essential properties. Forster transforms have played a key role in a diverse range of settings spanning computer science and functional analysis. Prior work had given weakly polynomial time algorithms for computing Forster transforms, when they exist. Our main result is the first strongly polynomial time algorithm to compute an approximate Forster transform of a given dataset or certify that no such transformation exists. By leveraging our strongly polynomial Forster algorithm, we obtain the first strongly polynomial time algorithm for distribution-free PAC learning of halfspaces. This learning result is surprising because proper PAC learning of halfspaces is equivalent to linear programming. Our learning approach extends to give a strongly polynomial halfspace learner in the presence of random classification noise and, more generally, Massart noise.Ilias Diakonikolas and Christos Tzamos and Daniel M. Kanework_a64hkzezjfcvvl3zlmv76dz3j4Tue, 06 Dec 2022 00:00:00 GMTA Monthly Hydropower Scheduling Model of Cascaded Reservoirs with the Zoutendijk Method
https://scholar.archive.org/work/zle5jufvdbfphgs4uoxh4cyjza
A monthly hydropower scheduling determines the monthly flows, storage, and power generation of each reservoir/hydropower plant over a planning horizon to maximize the total revenue or minimize the total operational cost. The problem is typically a complex and nonlinear optimization that involves equality and inequality constraints including the water balance, hydraulic coupling between cascaded hydropower plants, bounds on the reservoir storage, etc. This work applied the Zoutendijk algorithm for the first time to a medium/long-term hydropower scheduling of cascaded reservoirs, where the generating discharge capacity is handled with an iterative procedure, while the other head-related nonlinear constraints are represented with exponential functions fitting to discrete points. The procedure starts at an initial feasible solution, from which it finds a feasible improving direction, along which a better feasible solution is sought with a one-dimensional search. The results demonstrate that the Zoutendijk algorithm, when applied to six cascaded hydropower reservoirs on the Lancang River, worked very well in maximizing the hydropower production while ensuring the highest firm power output to be secured.Binbin Zhou, Suzhen Feng, Zifan Xu, Yan Jiang, Youxiang Wang, Kai Chen, Jinwen Wangwork_zle5jufvdbfphgs4uoxh4cyjzaTue, 06 Dec 2022 00:00:00 GMTFluctuation theorems for a mechanical work observable
https://scholar.archive.org/work/ow4j5cwsv5hcfdpq43rnr24lim
Of indisputable relevance for non-equilibrium thermodynamics, fluctuations theorems have been generalized to the framework of quantum thermodynamics, with the notion of work playing a key role in such contexts. The typical approach consists of treating work as a stochastic variable and the acting system as an eminently classical device with a deterministic dynamics. Inspired by technological advances in the field of quantum machines, here we look for eventual corrections to work fluctuations theorems when the acting system is allowed to enter the quantum domain. This entails including the acting system in the dynamics and letting it share a nonclassical state with the system acted upon. Moreover, favoring a mechanical perspective to this program, we employ a concept of work observable. For simplicity, we choose as theoretical platform the autonomous dynamics of a two-particle system with an elastic coupling. For some specific processes, we derive several fluctuation theorems within both the quantum and classical statistical arenas. In the quantum results, we find that, along with entanglement and quantum coherence, aspects of inertia also play a significant role since they regulate the route to mechanical equilibrium.Thales Augusto Barbosa Pinto Silva, Renato Moreira Angelowork_ow4j5cwsv5hcfdpq43rnr24limTue, 06 Dec 2022 00:00:00 GMTAn Index Policy for Minimizing the Uncertainty-of-Information of Markov Sources
https://scholar.archive.org/work/ynsjfmgt4vaszdi2xh77ddlcf4
This paper focuses on the information freshness of finite-state Markov sources, using the uncertainty of information (UoI) as the performance metric. Measured by Shannon's entropy, UoI can capture not only the transition dynamics of the Markov source but also the different evolutions of information quality caused by the different values of the last observation. We consider an information update system with M finite-state Markov sources transmitting information to a remote monitor via m communication channels. Our goal is to explore the optimal scheduling policy to minimize the sum-UoI of the Markov sources. The problem is formulated as a restless multi-armed bandit (RMAB). We relax the RMAB and then decouple the relaxed problem into M single bandit problems. Analyzing the single bandit problem provides useful properties with which the relaxed problem reduces to maximizing a concave and piecewise linear function, allowing us to develop a gradient method to solve the relaxed problem and obtain its optimal policy. By rounding up the optimal policy for the relaxed problem, we obtain an index policy for the original RMAB problem. Notably, the proposed index policy is universal in the sense that it applies to general RMABs with bounded cost functions.Gongpu Chen, Soung Chang Liewwork_ynsjfmgt4vaszdi2xh77ddlcf4Tue, 06 Dec 2022 00:00:00 GMTThe Curious Case of Integrator Reach Sets, Part I: Basic Theory
https://scholar.archive.org/work/ebtkx2xtvva3fmrwyrossbnziq
This is the first of a two part paper investigating the geometry of the integrator reach sets, and the applications thereof. In this Part I, assuming box-valued input uncertainties, we establish that this compact convex reach set is semialgebraic, translated zonoid, and not a spectrahedron. We derive the parametric as well as the implicit representation of the boundary of this reach set. We also deduce the closed form formula for the volume and diameter of this set, and discuss their scaling with state dimension and time. We point out that these results may be utilized in benchmarking the performance of the reach set over-approximation algorithms.Shadi Haddad, Abhishek Halderwork_ebtkx2xtvva3fmrwyrossbnziqTue, 06 Dec 2022 00:00:00 GMTComplementary Romanovski-Routh polynomials and their zeros
https://scholar.archive.org/work/npw5fqnsyfejrf6lclvavtjlqe
The efficacy of numerical methods like integral estimates via Gaussian quadrature formulas depends on the localization of the zeros of the associated family of orthogonal polynomials. In this regard, following the renewed interest in quadrature formulas on the unit circle, and R_II-type polynomials, which include the complementary Romanovski-Routh polynomials, in this work we present a collection of properties of their zeros. Our results include extreme bounds, convexity, and density, alongside the connection of such polynomials to classical orthogonal polynomials via asymptotic formulas.Luana L. Silva Ribeiro and Alagacone Sri Ranga and Yen Chi Lunwork_npw5fqnsyfejrf6lclvavtjlqeTue, 06 Dec 2022 00:00:00 GMTSailing League Problems
https://scholar.archive.org/work/p4eqahl65zg7farsa4s54bw2ii
We describe a class of combinatorial optimization problems which typically occur in professional sailing league competitions. We discuss connections to mathematical design theory. Moreover, we give suitable boolean quadratic and integer linear optimization problem formulations, as well as further heuristics and restrictions, that can be used to solve sailing league problems in practice. We apply those techniques to three case studies obtained from real sailing leagues and compare the results with used tournament plans.Robert Schüler, Achill Schürmannwork_p4eqahl65zg7farsa4s54bw2iiTue, 06 Dec 2022 00:00:00 GMTOn the foundations and extremal structure of the holographic entropy cone
https://scholar.archive.org/work/snsjcvl5snfzvmhkfgzmj7urje
The holographic entropy cone (HEC) is a polyhedral cone first introduced in the study of a class of quantum entropy inequalities. It admits a graph-theoretic description in terms of minimum cuts in weighted graphs, a characterization which naturally generalizes the cut function for complete graphs. Unfortunately, no complete facet or extreme-ray representation of the HEC is known. In this work, starting from a purely graph-theoretic perspective, we develop a theoretical and computational foundation for the HEC. The paper is self-contained, giving new proofs of known results and proving several new results as well. These are also used to develop two systematic approaches for finding the facets and extreme rays of the HEC, which we illustrate by recomputing the HEC on 5 terminals and improving its graph description. We also report on some partial results for 6 terminals. Some interesting open problems are stated throughout.David Avis, Sergio Hernández-Cuencawork_snsjcvl5snfzvmhkfgzmj7urjeTue, 06 Dec 2022 00:00:00 GMTOnline Min-Max Paging
https://scholar.archive.org/work/wx6l7bwgyzgyxgxwvaahieukea
Motivated by fairness requirements in communication networks, we introduce a natural variant of the online paging problem, called min-max paging, where the objective is to minimize the maximum number of faults on any page. While the classical paging problem, whose objective is to minimize the total number of faults, admits k-competitive deterministic and O(log k)-competitive randomized algorithms, we show that min-max paging does not admit a c(k)-competitive algorithm for any function c. Specifically, we prove that the randomized competitive ratio of min-max paging is Ω(log(n)) and its deterministic competitive ratio is Ω(klog(n)/log(k)), where n is the total number of pages ever requested. We design a fractional algorithm for paging with a more general objective – minimize the value of an n-variate differentiable convex function applied to the vector of the number of faults on each page. This gives an O(log(n)log(k))-competitive fractional algorithm for min-max paging. We show how to round such a fractional algorithm with at most a k factor loss in the competitive ratio, resulting in a deterministic O(klog(n)log(k))-competitive algorithm for min-max paging. This matches our lower bound modulo a poly(log(k)) factor. We also give a randomized rounding algorithm that results in a O(log^2 n log k)-competitive algorithm.Ashish Chiplunkar, Monika Henzinger, Sagar Sudhir Kale, Maximilian Vötschwork_wx6l7bwgyzgyxgxwvaahieukeaTue, 06 Dec 2022 00:00:00 GMTThe Apogee to Apogee Path Sampler
https://scholar.archive.org/work/my2d5xabxvbfhma2ul2x65ayou
Amongst Markov chain Monte Carlo algorithms, Hamiltonian Monte Carlo (HMC) is often the algorithm of choice for complex, high-dimensional target distributions; however, its efficiency is notoriously sensitive to the choice of the integration-time tuning parameter, T. When integrating both forward and backward in time using the same leapfrog integration step as HMC, the set of local maxima in the potential along a path, or apogees, is the same whatever point (position and momentum) along the path is chosen to initialise the integration. We present the Apogee to Apogee Path Sampler (AAPS), which utilises this invariance to create a simple yet generic methodology for constructing a path, proposing a point from it and accepting or rejecting that proposal so as to target the intended distribution. We demonstrate empirically that AAPS has a similar efficiency to HMC but is much more robust to the setting of its equivalent tuning parameter, the number of apogees that the path crosses.Chris Sherlock, Szymon Urbas, Matthew Ludkinwork_my2d5xabxvbfhma2ul2x65ayouTue, 06 Dec 2022 00:00:00 GMT