We design and analyze deterministic truthful approximation mechanisms for multi-unit Combinatorial Auctions involving only a constant number of distinct goods, each in arbitrary limited supply. Prospective buyers (bidders) have preferences over multisets of items, i.e., for more than one unit per distinct good. Our objective is to determine allocations of multisets that maximize the Social Welfare. Our main results are for multi-minded and submodular bidders. In the first setting each bidder has a positive value for being allocated one multiset from a prespecified demand set of alternatives. In the second setting each bidder is associated to a submodular valuation function that defines his value for the multiset he is allocated. For multi-minded bidders, we design a truthful FPTAS that fully optimizes the Social Welfare, while violating the supply constraints on goods within factor (1+e), for any fixed e>0 (i.e., the approximation applies to the constraints and not to the Social Welfare). This result is best possible, in that full optimization is impossible without violating the supply constraints. For submodular bidders, we obtain a PTAS that approximates the optimum Social Welfare within factor (1+e), for any fixed e>0, without violating the supply constraints. This result is best possible as well. Our allocation algorithms are Maximal-in-Range and yield truthful mechanisms, when paired with Vickrey-Clarke-Groves payments.

Financial time series often exhibit low signal-to-noise ratio, posing significant challenges for accurate data interpretation and prediction and ultimately decision making. Generative models have gained attention as powerful tools for simulating and predicting intricate data patterns, with diffusion models emerging as particularly effective methods. This paper introduces a novel approach utilizing a diffusion model as a denoiser for financial time series in order to improve data predictability and trading performance. By leveraging the forward and reverse processes of a conditional diffusion model to add and remove noise progressively, we reconstruct original data from noisy inputs. Our extensive experiments demonstrate that diffusion model-based denoised time series significantly enhance the performance on downstream future return classification tasks. Moreover, trading signals derived from the denoised data yield more profitable trades with fewer transactions, thereby minimizing transaction costs and increasing overall trading efficiency. Finally, we show that by using classifiers trained on denoised time series, we can recognize how noisy the market is and obtain excess returns.