Epidemic spreading induced by diversity of agents' mobility

In this paper, we study into the impact of the preference of an individual for public transport on the spread of infectious disease, through a quantity known as the public mobility. Our theoretical and numerical results based on a constructed model reveal that if the average public mobility of the agents is fixed, an increase in the diversity of the agents' public mobility reduces the epidemic threshold, beyond which an enhancement in the rate of infection is observed. Our findings provide an approach to improve the resistance of a society against infectious disease, while preserving the utilization rate of the public transportation system.Comment: 8 pages, 5 figure

Signs of criticality in social explosions

The success of an on-line movement could be defined in terms of the shift to large-scale and the later off-line massive street actions of protests. The role of social media in this process is to facilitate the transformation from small or local feelings of disagreement into large-scale social actions. The way how social media achieves that effect is by growing clusters of people and groups with similar effervescent feelings, which in another case would never be in communication. It is natural to think that these kinds of macro social actions, as a consequence of the spontaneous and massive interactions, will attain the growth and divergence of the correlation length, giving rise to important simplifications on several statistics. In this work, we report the presence of signs of criticality in social demonstrations. Namely, the same power-law exponents are found whenever the distributions are calculated, either considering the same windows-time or the same number of hashtags. The exponents for the distributions during the event were found to be smaller than before (and after) the event. The latter also happens whenever the hashtags are counted only once per user or if all their usages are considered. By means of network representations, we show that the systems present two kinds of high correlations, characterised by either high or low values of modularity. The temporal points of high modularity are characterised by a sustained correlation while the ones of low modularity are characterised by a punctual correlation. The importance of analysing systems near a critical point is that any small disturbance can escalate and induce large-scale -- nationwide -- chain reactions.Comment: 11 pages, 6 figure

Fourier sparsity, spectral norm, and the Log-rank conjecture

We study Boolean functions with sparse Fourier coefficients or small spectral norm, and show their applications to the Log-rank Conjecture for XOR functions f(x\oplus y) --- a fairly large class of functions including well studied ones such as Equality and Hamming Distance. The rank of the communication matrix M_f for such functions is exactly the Fourier sparsity of f. Let d be the F2-degree of f and D^CC(f) stand for the deterministic communication complexity for f(x\oplus y). We show that 1. D^CC(f) = O(2^{d^2/2} log^{d-2} ||\hat f||_1). In particular, the Log-rank conjecture holds for XOR functions with constant F2-degree. 2. D^CC(f) = O(d ||\hat f||_1) = O(\sqrt{rank(M_f)}\logrank(M_f)). We obtain our results through a degree-reduction protocol based on a variant of polynomial rank, and actually conjecture that its communication cost is already \log^{O(1)}rank(M_f). The above bounds also hold for the parity decision tree complexity of f, a measure that is no less than the communication complexity (up to a factor of 2). Along the way we also show several structural results about Boolean functions with small F2-degree or small spectral norm, which could be of independent interest. For functions f with constant F2-degree: 1) f can be written as the summation of quasi-polynomially many indicator functions of subspaces with \pm-signs, improving the previous doubly exponential upper bound by Green and Sanders; 2) being sparse in Fourier domain is polynomially equivalent to having a small parity decision tree complexity; 3) f depends only on polylog||\hat f||_1 linear functions of input variables. For functions f with small spectral norm: 1) there is an affine subspace with co-dimension O(||\hat f||_1) on which f is a constant; 2) there is a parity decision tree with depth O(||\hat f||_1 log ||\hat f||_0).Comment: v2: Corollary 31 of v1 removed because of a bug in the proof. (Other results not affected.

An Unsupervised Autoregressive Model for Speech Representation Learning

This paper proposes a novel unsupervised autoregressive neural model for learning generic speech representations. In contrast to other speech representation learning methods that aim to remove noise or speaker variabilities, ours is designed to preserve information for a wide range of downstream tasks. In addition, the proposed model does not require any phonetic or word boundary labels, allowing the model to benefit from large quantities of unlabeled data. Speech representations learned by our model significantly improve performance on both phone classification and speaker verification over the surface features and other supervised and unsupervised approaches. Further analysis shows that different levels of speech information are captured by our model at different layers. In particular, the lower layers tend to be more discriminative for speakers, while the upper layers provide more phonetic content.Comment: Accepted to Interspeech 2019. Code available at: https://github.com/iamyuanchung/Autoregressive-Predictive-Codin

Lower Bounds for Function Inversion with Quantum Advice

Function inversion is the problem that given a random function $f: [M] \to [N]$, we want to find pre-image of any image $f^{-1}(y)$ in time $T$. In this work, we revisit this problem under the preprocessing model where we can compute some auxiliary information or advice of size $S$ that only depends on $f$ but not on $y$. It is a well-studied problem in the classical settings, however, it is not clear how quantum algorithms can solve this task any better besides invoking Grover's algorithm, which does not leverage the power of preprocessing. Nayebi et al. proved a lower bound $ST^2 \ge \tilde\Omega(N)$ for quantum algorithms inverting permutations, however, they only consider algorithms with classical advice. Hhan et al. subsequently extended this lower bound to fully quantum algorithms for inverting permutations. In this work, we give the same asymptotic lower bound to fully quantum algorithms for inverting functions for fully quantum algorithms under the regime where $M = O(N)$. In order to prove these bounds, we generalize the notion of quantum random access code, originally introduced by Ambainis et al., to the setting where we are given a list of (not necessarily independent) random variables, and we wish to compress them into a variable-length encoding such that we can retrieve a random element just using the encoding with high probability. As our main technical contribution, we give a nearly tight lower bound (for a wide parameter range) for this generalized notion of quantum random access codes, which may be of independent interest.Comment: ITC full versio

On the Algorithmic Power of Spiking Neural Networks

Spiking Neural Networks (SNN) are mathematical models in neuroscience to describe the dynamics among a set of neurons that interact with each other by firing instantaneous signals, a.k.a., spikes. Interestingly, a recent advance in neuroscience [Barrett-Den\`eve-Machens, NIPS 2013] showed that the neurons' firing rate, i.e., the average number of spikes fired per unit of time, can be characterized by the optimal solution of a quadratic program defined by the parameters of the dynamics. This indicated that SNN potentially has the computational power to solve non-trivial quadratic programs. However, the results were justified empirically without rigorous analysis. We put this into the context of natural algorithms and aim to investigate the algorithmic power of SNN. Especially, we emphasize on giving rigorous asymptotic analysis on the performance of SNN in solving optimization problems. To enforce a theoretical study, we first identify a simplified SNN model that is tractable for analysis. Next, we confirm the empirical observation in the work of Barrett et al. by giving an upper bound on the convergence rate of SNN in solving the quadratic program. Further, we observe that in the case where there are infinitely many optimal solutions, SNN tends to converge to the one with smaller l1 norm. We give an affirmative answer to our finding by showing that SNN can solve the l1 minimization problem under some regular conditions. Our main technical insight is a dual view of the SNN dynamics, under which SNN can be viewed as a new natural primal-dual algorithm for the l1 minimization problem. We believe that the dual view is of independent interest and may potentially find interesting interpretation in neuroscience.Comment: To appear in ITCS 201

An effective SDRAM power mode management scheme for performance and energy sensitive embedded systems

Abstract- We present an effective power mode management scheme used in SDRAM memory controllers. The scheme employs a bus utilization monitoring mechanism to initiate proper operations of SDRAM chips. Our approach reduces energy consumption by actively switching memories to low-power mode at low bus utilization. At higher bus utilization, the scheme switches memories to open page mode to reduce precharge energy as well as program execution time. This bus utilization predictor reduces memory energy consumption without the expense of increasing program execution time. It achieved the performance level of open page policy by consuming 20 % less of memory energy. I