A Linear Frequency Principle Model to Understand the Absence of Overfitting in Neural Networks

Why heavily parameterized neural networks(NNs) do not overfit the data is an important long standing open question. We propose a phenomenological model of the NN training to explain this non-overfitting puzzle. Our linear frequency principle(LFP) model accounts for a key dynamical feature of NNs: they learn low frequencies first, irrespective of microscopic details. Theory based on our LFP model shows that low frequency dominance of target functions is the key condition for the non-overfitting of NNs and is verified by experiments. Furthermore,through an ideal two-layer NN, we unravel how detailed microscopic NN training dynamics statistically gives rise to an LFP model with quantitative prediction power.     

Unusual Normal and Superconducting State Properties Observed in Hydrothermal Fe_(1-δ)Se Flakes

The electronic and superconducting properties of Fe_(1-δ)Se single-crystal flakes grown hydrothermally are studied by the transport measurements under zero and high magnetic fields up to 38.5 T. The results contrast sharply with those previously reported for nematically ordered Fe Se by chemical-vapor-transport(CVT) growth. No signature of the electronic nematicity, but an evident metal-to-nonmetal crossover with increasing temperature,is detected in the normal state of the present hydrothermal samples. Interestingly, a higher superconducting critical temperature T_c of 13.2 K is observed compared to a suppressed T_c of 9 K in the presence of the nematicity in the CVT Fe Se. Moreover, the upper critical field in the zero-temperature limit is found to be isotropic with respect to the field direction and to reach a higher value of ~42 T, which breaks the Pauli limit by a factor of 1.8.     

Nonlocal Effects of Low-Energy Excitations in Quantum-Spin-Liquid Candidate Cu_3Zn(OH)_6FBr

We systematically study the low-temperature specific heats for the two-dimensional kagome antiferromagnet,Cu_3Zn(OH)_6FBr.The specific heat exhibits a T~(1.7) dependence at low temperatures and a shoulder-like feature above it.We construct a microscopic lattice model of Z_2 quantum spin liquid and perform large-scale quantum Monte Carlo simulations to show that the above behaviors come from the contributions from gapped anyons and magnetic impurities.Surprisingly,we find the entropy associated with the shoulder decreases quickly with grain size d,although the system is paramagnetic to the lowest temperature.While this can be simply explained by a core-shell picture in that the contribution from the interior state disappears near the surface,the 5.9-nm shell width precludes any trivial explanations.Such a large length scale signifies the coherence length of the nonlocality of the quantum entangled excitations in quantum spin liquid candidate,similar to Pippard's coherence length in superconductors.Our approach therefore offers a new experimental probe of the intangible quantum state of matter with topological order.     

Equilibrium threshold strategies in observable queueing systems under single vacation policy

This paper studies the equilibrium behavior of customers in continuous/discrete time queueing systems under single vacation policy. In the single vacation queueing system, the server can only take exactly one vacation when no customers exist in the system. This scheme is more practical under many specific circumstances. Based on the reward–cost structure, equilibrium behavior is considered in the fully observable and almost observable cases. The threshold strategies in equilibrium are obtained and the stationary system behavior is analyzed under the corresponding strategies. Finally, we illustrate the effect of the information level as well as several parameters on the equilibrium thresholds and social benefits via numerical experiments. The research results could instruct the customers to take optimal strategies and provide the managers with reference information on the pricing problem in the queueing system.     

Multi-Scale Permutation Entropy: A Potential Measure for the Impact of Sleep Medication on Brain Dynamics of Patients with Insomnia

Insomnia is a common sleep disorder that is closely associated with the occurrence and deterioration of cardiovascular disease, depression and other diseases. The evaluation of pharmacological treatments for insomnia brings significant clinical implications. In this study, a total of 20 patients with mild insomnia and 75 healthy subjects as controls (HC) were included to explore alterations of electroencephalogram (EEG) complexity associated with insomnia and its pharmacological treatment by using multi-scale permutation entropy (MPE). All participants were recorded for two nights of polysomnography (PSG). The patients with mild insomnia received a placebo on the first night (Placebo) and temazepam on the second night (Temazepam), while the HCs had no sleep-related medication intake for either night. EEG recordings from each night were extracted and analyzed using MPE. The results showed that MPE decreased significantly from pre-lights-off to the period during sleep transition and then to the period after sleep onset, and also during the deepening of sleep stage in the HC group. Furthermore, results from the insomnia subjects showed that MPE values were significantly lower for the Temazepam night compared to MPE values for the Placebo night. Moreover, MPE values for the Temazepam night showed no correlation with age or gender. Our results indicated that EEG complexity, measured by MPE, may be utilized as an alternative approach to measure the impact of sleep medication on brain dynamics.     

Optimal time decay of the quantum Landau equation in the whole space

We are concerned with the Cauchy problem of the quantum Landau equation in the whole space. The existence of local in time nearby quantum Maxwellian solutions is proved by the iteration method and generalized maximum principle. Based on Kawashima?s compensating function and nonlinear energy estimates, the global existence and the optimal time decay rate of those solutions are obtained under some conditions on initial data.     

The development of nonradiative dielectric waveguide transmitting front-end in Ka-band

The operating theory,design method and experimental results of the nonradiative dielectric waveguide (NRD-guide) transmitting front-end in millimeter wave band are related in details in this paper. As a kind of dielectric waveguide,the NRD-guide possesses fine transmission performances, and it can be used to fabricate the millimeter wave hyterodyne integrated circuits. The two kinds NRD-guide transmitting front-ends substantiated in the paper, the voltage controlling oscillator(VCO) and twin-Gunn-diode power-combiner,have very similar structures to each other and possess compact sizes, fine machinery and electric performances.For the VCO front-end in Ka-band, the frequency modulation band is greater than 150MHz, the output power is larger than 20mW.For the power-combiner, the output power is larger than 40mW,the combination efficiency is better than 90%,the frequency stabilization reaches 1.68×10^–5. Combined with the receiving front-end reported before,the transmitter and receiver can be composed to a dielectric waveguide R/T module to be applied in some millimeter wave sub-systems.     

Symmetry results for decay solutions of semilinear elliptic systems on half spaces

In this paper, we prove that the decaying positive solutions of semi-linear elliptic systems on the half space with Neumann type condition is symmetric with respect to a line orthogonal to the boundary hyperplane. The monotonicity result is also obtained. Our methods employ the Alexandrov-Serrin method of moving planes combined with Hopf’s lemma at a corner. Our result can be applied to the Lane-Emden system and the stationary Schrödinger system.     

A Distributed Architecture for Secure Delegated Quantum Computation

In this paper, we propose a distributed secure delegated quantum computation protocol, by which an almost classical client can delegate a (dk)-qubit quantum circuit to d quantum servers, where each server is equipped with a 2k-qubit register that is used to process only k qubits of the delegated quantum circuit. None of servers can learn any information about the input and output of the computation. The only requirement for the client is that he or she has ability to prepare four possible qubits in the state of (|0〉+eiθ|1〉)/2, where θ∈{0,π/2,π,3π/2}. The only requirement for servers is that each pair of them share some entangled states (|0〉|+〉+|1〉|−〉)/2 as ancillary qubits. Instead of assuming that all servers are interconnected directly by quantum channels, we introduce a third party in our protocol that is designed to distribute the entangled states between those servers. This would simplify the quantum network because the servers do not need to share a quantum channel. In the end, we show that our protocol can guarantee unconditional security of the computation under the situation where all servers, including the third party, are honest-but-curious and allowed to cooperate with each other.     

On the fractional integral of Weyl inL p

This work has been partially supported by D.G.C.Y.T., grant PS88-0115, Spain