k.a. Chambéry University) is a public university in the region of Savoy, with one campus in Annecy and two around Chambéry.
We investigate the out-of-equilibrium dynamics after a quantum quench of the reduced fidelities between the states of a subregion A at different times. Precisely, we consider the fidelity between the time-dependent state of A and its initial value, as well as with the state at infinite time. We denote these fidelities as the reduced Loschmidt echo (RLE) and the final-state fidelity (FSF), respectively. If region A is the full system, the RLE coincides with the standard Loschmidt echo. We focus on quenches from Gaussian states in several instances of the XY spin chain. In the hydrodynamic limit of long times and large sizes of A, with their ratio fixed, the reduced fidelities admit a quasiparticle picture interpretation. Interestingly, for some quenches in the hydrodynamic regime the RLE features a complicated structure with an infinite sequence of nested lightcones, corresponding to quasiparticles with arbitrary large group velocities. This leads to a 'staircase' of cusp-like singularities in the time-derivative of the fidelity. At the sub-hydrodynamic regime for some quenches the RLE exhibits cusp-like singularities, similar to the so-called dynamical quantum phase transitions (DQPT). We conjecture a criterion for the occurrence of the DQPT and for the 'critical' times at which the singularities occur. Finally, we discuss the hydrodynamic limit of the FSF. In particular, we show that it provides a valuable tool to detect the so-called quantum Mpemba effect.
Accurate forecasting of photovoltaic (PV) and wind power generation is vital for reliable renewable energy operations. However, their differing temporal characteristics, especially in periodicity, pose challenges for unified prediction models. This paper proposes a periodicity-aware hybrid deep learning framework designed to enhance forecasting accuracy for both PV and wind power generation. The framework incorporates Time2Vec (T2V) to extract periodic and non-periodic temporal features and combines Bidirectional Temporal Convolutional Networks (BiTCN) with Bidirectional Gated Recurrent Units (BiGRU) through a flexible serial-parallel architecture. Based on the autocorrelation of the input data, the model selects a parallel structure for strongly periodic PV and a serial structure for weakly periodic wind data. The T2V layer enhances feature representation, while the serial–parallel design provides architecture-level flexibility that improves forecasting accuracy. The proposed T2V–BiTCN–BiGRU model was evaluated on real-world PV and wind datasets from China and Belgium. Experimental results demonstrate that the model consistently outperforms IEDN-RNET, VAM-MTL, and CEEMDAN-EWT-BiTCN-BiLSTM-AT, achieving high R2 and low MAE, RMSE, and MAPE across datasets. Moreover, the model maintains robust accuracy and stability, confirming its generalizability. This work highlights the effectiveness of combining periodicity-aware encoding with architecture-level hybrid models, providing a novel and flexible approach for high-precision hybrid wind and solar power forecasting.
We introduce a smoothed variant of the Smoothly Clipped Absolute Deviation (SCAD) thresholding rule for wavelet denoising by replacing its piecewise linear transition with a raised cosine. The resulting shrinkage function is odd, continuous on R, and continuously differentiable away from the main threshold, yet retains the hallmark SCAD properties of sparsity for small coefficients and near unbiasedness for large ones. This smoothness places the rule within the continuous thresholding class for which Stein’s unbiased risk estimate (SURE) is valid. As a result, unbiased risk computation, stable data-driven threshold selection, and the asymptotic theory of Kudryavtsev and Shestakov apply. A corresponding nonconvex prior is obtained whose posterior mode coincides with the estimator, yielding a transparent Bayesian interpretation. We give an explicit SURE risk expression, discuss the oracle scale of the optimal threshold, and describe both global and level-dependent adaptive versions. The smooth SCAD rule therefore offers a tractable refinement of SCAD, combining low bias, exact sparsity, and analytical convenience in a single wavelet shrinkage procedure.
Classical results of Brent, Kuck, and Maruyama (IEEE Trans. Computers 1973) and Brent (JACM 1974) show that any algebraic formula of size s can be converted to one of depth O(log s) with only a polynomial blow-up in size. In this paper, we consider a fine-grained version of this result depending on the degree of the polynomial computed by the algebraic formula. Given a homogeneous algebraic formula of size s computing a polynomial P of degree d, we show that P can also be computed by an (unbounded fan-in) algebraic formula of depth O(log d) and size poly(s). Our proof shows that this result also holds in the highly restricted setting of monotone, non-commutative algebraic formulas. This improves on previous results in the regime when d is small (i.e. d = s^o(1) ). In particular, for the setting of d = O(log s), along with a result of Raz (STOC 2010, JACM 2013), our result implies the same depth reduction even for inhomogeneous formulas. This is particularly interesting in light of recent algebraic formula lower bounds, which work precisely in this “low-degree” and “low-depth” setting. We also show that these results cannot be improved in the monotone setting, even for commutative formulas.
Faced with political opposition to efficient carbon pricing, climate policy resorts to alternative instruments, which come with welfare and fiscal costs of acceptability. To assess these costs, this study examines second-best policies combining a constant carbon tax with subsidies to carbon-free electricity generation and storage. Using a stylized dynamic model of the energy transition featuring fossil and clean energy sources and a carbon budget, we show that the lower the carbon tax, the greater the carbon pricing gap, and the larger the subsidies required to meet the carbon budget. Overaccumulation of clean capital may be needed to crowd out fossil fuels. Calibration to the European energy market reveals costs of acceptability up to 2.6% of welfare and a budget shortfall equivalent to 56% of the present value of electricity consumption. This suggests that relying on green subsidies for the energy transition may be unwise.
