Understanding how the brain processes musical pitch errors is key to advancing music perception and auditory rehabilitation. This pilot study (N=1) examined neural responses to pitch deviations in a trained musician using a portable dry-electrode electroencephalography (EEG) system. The participant listened passively to seven 10-second violin excerpts with systematically varied pitch errors: none, medium, or high. EEG data were recorded, preprocessed, and analyzed for oscillatory patterns in the beta band across temporal and central brain regions. Findings revealed a graded increase in right-temporal beta power with error magnitude, alongside distinct temporal dynamics suggesting a sequential process: initial detection of deviations, evaluation of error severity, and adjustment of predictive models. These results highlight a potential cascade in passive pitch-error processing, extending prior work on active performance to naturalistic listening contexts. This work offers preliminary insights into the neural basis of pitch perception and suggests applications in music education and auditory training, though further research with larger cohorts is needed to confirm these findings.

Motivated by online advertising applications, we study incentive properties of stationary mechanisms that satisfy budget constraints in expectation at a stationary equilibrium. We consider a general repeated auction setting where a seller sells identical items to buyers with budget constraints and the buyers' value distributions can be arbitrarily correlated. We introduce the novel notion of budget-constrained incentive compatibility (BCIC) under which each buyer chooses an optimal bidding strategy among stationary budget-feasible bidding strategies. Armed with the notion of BCIC, we characterize Bayesian optimal mechanisms that satisfy the budget constraints in expectation with respect to the profit, utility and welfare objectives in the restricted setting where the buyers' value distributions are independent. Furthermore, in the general setting where the buyers' value distributions are correlated, we provide the first systematic study on the incentive properties of different budget management mechanisms, including those studied in the literature and, to the best of our knowledge, used in the industry. We explore the following mechanisms and show some popular mechanisms are not incentive compatible even when restricting attention to stationary budget-feasible deviations: throttling, thresholding, bid shading, reserve pricing and two versions of multiplicative boosting.

Motivated by the popularity of online ride and delivery services, we study natural variants of classical multi-vehicle minimum latency problems where the objective is to route a set of vehicles located at depots to serve requests located on a metric space so as to minimize the total latency. In this paper, we consider point-to-point requests that come with source-destination pairs and release-time constraints that restrict when each request can be served. The point-to-point requests and release-time constraints model taxi rides and deliveries. For all the variants considered, we show constant-factor approximation algorithms based on a linear programming framework. To the best of our knowledge, these are the first set of results for the aforementioned variants of the minimum latency problems. Furthermore, we provide an empirical study of heuristics based on our theoretical algorithms on a real data set of taxi rides.

In online advertising, advertisers purchase ad placements by participating in a long sequence of repeated auctions. One of the most important features advertising platforms often provide, and advertisers often use, is budget management, which allows advertisers to control their cumulative expenditures. Advertisers typically declare the maximum daily amount they are willing to pay, and the platform adjusts allocations and payments to guarantee that cumulative expenditures do not exceed budgets. There are multiple ways to achieve this goal, and each one, when applied to all budget-constrained advertisers simultaneously, steers the system toward a different equilibrium. While previous research focused on online stochastic optimization techniques or game-theoretic equilibria of such settings, our goal in this paper is to compare the ``system equilibria'' of a range of budget management strategies in terms of the seller's profit and buyers' utility. In particular, we consider six different budget management strategies including probabilistic throttling, thresholding, bid shading, reserve pricing, and multiplicative boosting. We show these methods admit a system equilibrium in a rather general setting, and prove dominance relations between them in a simplified setting. Our study sheds light on the impact of budget management strategies on the tradeoff between the seller's profit and buyers' utility. Finally, we also empirically compare the system equilibria of these strategies using real ad auction data in sponsored search and randomly generated bids. The empirical study confirms our theoretical findings about the relative performances of budget management strategies.

Motivated by the importance of energy storage networks in smart grids, we provide an algorithmic study of the online energy storage management problem in a network setting, the first to the best of our knowledge. Given online power supplies, either entirely renewable supplies or those in combination with traditional supplies, we want to route power from the supplies to demands using storage units subject to a decay factor. Our goal is to maximize the total utility of satisfied demands less the total production cost of routed power. We model renewable supplies with the zero production cost function and traditional supplies with convex production cost functions. For two natural storage unit settings, private and public, we design poly-logarithmic competitive algorithms in the network flow model using the dual fitting and online primal dual methods for convex problems. Furthermore, we show strong hardness results for more general settings of the problem. Our techniques may be of independent interest in other routing and storage management problems.

We study online combinatorial auctions with production costs proposed by Blum et al. [4] using the online primal dual framework. In this model, buyers arrive online, and the seller can produce multiple copies of each item subject to a non-decreasing marginal cost per copy. The goal is to allocate items to maximize social welfare less total production cost. For arbitrary (strictly convex and differentiable) production cost functions, we characterize the optimal competitive ratio achievable by online mechanisms/algorithms. We show that online posted pricing mechanisms, which are incentive compatible, can achieve competitive ratios arbitrarily close to the optimal, and construct lower bound instances on which no online algorithms, not necessarily incentive compatible, can do better. Our positive results improve or match the results in several previous work, e.g., Bartal et al. [a], Blum et al. [4], and Buchbinder and Conen [6]. Our lower bounds apply to randomized algorithms and resolve an open problem by Buchbinder and Gonen [6].

We define a notion of network capacity region of networks that generalizes the notion of network capacity defined by Cannons et al. and prove its notable properties such as closedness, boundedness and convexity when the finite field is fixed. We show that the network routing capacity region is a computable rational polytope and provide exact algorithms and approximation heuristics for computing the region. We define the semi-network linear coding capacity region, with respect to a fixed finite field, that inner bounds the corresponding network linear coding capacity region, show that it is a computable rational polytope, and provide exact algorithms and approximation heuristics. We show connections between computing these regions and a polytope reconstruction problem and some combinatorial optimization problems, such as the minimum cost directed Steiner tree problem. We provide an example to illustrate our results. The algorithms are not necessarily polynomial-time.

We propose a new no-regret learning algorithm. When used against an adversary, our algorithm achieves average regret that scales as with the number T of rounds. This regret bound is optimal but not rare, as there are a multitude of learning algorithms with this regret guarantee. However, when our algorithm is used by both players of a zero-sum game, their average regret scales as , guaranteeing a near-linear rate of convergence to the value of the game. This represents an almost-quadratic improvement on the rate of convergence to the value of a game known to be achieved by any no-regret learning algorithm, and is essentially optimal as we show a lower bound of . Moreover, the dynamics produced by our algorithm in the game setting are strongly-uncoupled in that each player is oblivious to the payoff matrix of the game and the number of strategies of the other player, has limited private storage, and is not allowed funny bit arithmetic that can trivialize the problem; instead he only observes the performance of his strategies against the actions of the other player and can use private storage to remember past played strategies and observed payoffs, or cumulative information thereof. Here, too, our rate of convergence is nearly-optimal and represents an almost-quadratic improvement over the best previously known strongly-uncoupled dynamics.