Observation of Log-Periodic Oscillations in the Quantum Dynamics of Electrons on the One-Dimensional Fibonacci Quasicrystal

We revisit the question of quantum dynamics of electrons on the off-diagonal Fibonacci tight-binding model. We find that typical dynamical quantities, such as the probability of an electron to remain in its original position as a function of time, display log-periodic oscillations on top of the leading-order power-law decay. These periodic oscillations with the logarithm of time are similar to the oscillations that are known to exist with the logarithm of temperature in the specific heat of Fibonacci electrons, yet they offer new possibilities for the experimental observation of this unique phenomenon

Optimal Lower Bounds for Anonymous Scheduling Mechanisms

We consider the problem of designing truthful mechanisms on m unrelated machines, to minimize some optimization goal. Nisan and Ronen [Nisan, N., A. Ronen. 2001. Algorithmic mechanism design. Games Econom. Behav. 35 166–196] consider the specific goal of makespan minimization, and show a lower bound of 2, and an upper bound of m. This large gap inspired many attempts that yielded positive results for several special cases, but very partial success for the general case: the lower bound was slightly increased to 2.61 by Christodoulou et al. [Christodoulou, G., E. Koutsoupias, A. Kovács. 2010. Mechanism design for fractional scheduling on unrelated machines. ACM Trans. Algorithms (TALG) 6(2) 1–18] and Koutsoupias and Vidali [Koutsoupias, E., A. Vidali. 2007. A lower bound of 1+phi for truthful scheduling mechanisms. Proc. 32nd Internat. Sympos. Math. Foundations Comput. Sci. (MFCS)], while the best upper bound remains unchanged. In this paper we show the optimal lower bound on truthful anonymous mechanisms: no such mechanism can guarantee an approximation ratio better than m. Moreover, our proof yields similar optimal bounds for two other optimization goals: the sum of completion times and the lp norm of the schedule.United States-Israel Binational Science FoundationIsrael. Ministry of ScienceGoogle Inter-University Center for Electronic Markets and Auction

Sequence-to-Sequence Contrastive Learning for Text Recognition

We propose a framework for sequence-to-sequence contrastive learning (SeqCLR) of visual representations, which we apply to text recognition. To account for the sequence-to-sequence structure, each feature map is divided into different instances over which the contrastive loss is computed. This operation enables us to contrast in a sub-word level, where from each image we extract several positive pairs and multiple negative examples. To yield effective visual representations for text recognition, we further suggest novel augmentation heuristics, different encoder architectures and custom projection heads. Experiments on handwritten text and on scene text show that when a text decoder is trained on the learned representations, our method outperforms non-sequential contrastive methods. In addition, when the amount of supervision is reduced, SeqCLR significantly improves performance compared with supervised training, and when fine-tuned with 100% of the labels, our method achieves state-of-the-art results on standard handwritten text recognition benchmarks

Cognitive Sub-Nyquist Hardware Prototype of a Collocated MIMO Radar

We present the design and hardware implementation of a radar prototype that demonstrates the principle of a sub-Nyquist collocated multiple-input multiple-output (MIMO) radar. The setup allows sampling in both spatial and spectral domains at rates much lower than dictated by the Nyquist sampling theorem. Our prototype realizes an X-band MIMO radar that can be configured to have a maximum of 8 transmit and 10 receive antenna elements. We use frequency division multiplexing (FDM) to achieve the orthogonality of MIMO waveforms and apply the Xampling framework for signal recovery. The prototype also implements a cognitive transmission scheme where each transmit waveform is restricted to those pre-determined subbands of the full signal bandwidth that the receiver samples and processes. Real-time experiments show reasonable recovery performance while operating as a 4x5 thinned random array wherein the combined spatial and spectral sampling factor reduction is 87.5% of that of a filled 8x10 array.Comment: 5 pages, Compressed Sensing Theory and its Applications to Radar, Sonar and Remote Sensing (CoSeRa) 201