Union bounds on the symbol error probability of LoRa modulation for flat Rician block fading channels

In this paper the symbol error performance of LoRa modulation is addressed for flat Rician block fading channels. First the exact symbol error probability of the LoRa modulation on Rician fading is derived. Then the upper and lower union bounds are employed on the derived symbol error probability. The proposed bounds are compared against the exact symbol error probability, the numerical evaluation of the symbol error probability and the state-of-art approximation of the LoRa symbol error probability. Numerical results show that while the proposed upper bound is very tight to the exact symbol error probability, there is approximately a 2.5 dB gap for the lower bound.     

类锂体系激发态的精确判据

利用Gálvez Porras关于原子体系电子在核处密度和径向期待值的精确不等式，分别建立了波函数的两套精确判据，它们是独立于能量判据之外的检验波函数精确度的判据. 以类锂体系激发态为研究对象，首先对1s2 3s态的电子在核处密度和径向期待值的上界进行了检查，然后对锂原子1s2 3s态在不同计算方法下由电子在核处密度上界定义的R6值和的上界定义的R4值分别进行了测试，同时还对锂原子双激发态的电子在核处密度和径向期待值的上界进行了检验. 研究表明这两套不等式都可作为原子体系各种能态波函数的精确判据. 关键词： 电子在核处密度 径向期待值 全实加关联 精确判据     

Variational principles of magnetostatics

Variational principles of magnetostatics are formulated, which permit evaluation of the upper and lover bounds on the energy of a magnetic field produced by a known spatial current density distribution with the help of rather broad classes of trial functions. The potentialities for the use of these variational principles as applied to practical problems is demonstrated with an example of the well-known problem of the calculation of the inductance of a straight solenoid of finite length. In particular, it is shown that the formula appearing in all the textbooks for this inductance, in fact, defines the upper bound for the true value of the inductance.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 70–75, July, 1987.     

On Estimation of Fully Entangled Fraction

We study the fully entangled fraction （FEF） of arbitrary mixed states. New upper bounds of FEF are derived. These upper bounds make complements on the estimation of the value of FEF. For weakly mixed quantum states, an upper bound is shown to be very tight to the exact value of FEF.     

Bottleneck Problems: An Information and Estimation-Theoretic View

Information bottleneck (IB) and privacy funnel (PF) are two closely related optimization problems which have found applications in machine learning, design of privacy algorithms, capacity problems (e.g., Mrs. Gerber’s Lemma), and strong data processing inequalities, among others. In this work, we first investigate the functional properties of IB and PF through a unified theoretical framework. We then connect them to three information-theoretic coding problems, namely hypothesis testing against independence, noisy source coding, and dependence dilution. Leveraging these connections, we prove a new cardinality bound on the auxiliary variable in IB, making its computation more tractable for discrete random variables. In the second part, we introduce a general family of optimization problems, termed “bottleneck problems”, by replacing mutual information in IB and PF with other notions of mutual information, namely f-information and Arimoto’s mutual information. We then argue that, unlike IB and PF, these problems lead to easily interpretable guarantees in a variety of inference tasks with statistical constraints on accuracy and privacy. While the underlying optimization problems are non-convex, we develop a technique to evaluate bottleneck problems in closed form by equivalently expressing them in terms of lower convex or upper concave envelope of certain functions. By applying this technique to a binary case, we derive closed form expressions for several bottleneck problems.     

Self-Adaptive Learning of Task Offloading in Mobile Edge Computing Systems

Mobile edge computing (MEC) focuses on transferring computing resources close to the user’s device, and it provides high-performance and low-delay services for mobile devices. It is an effective method to deal with computationally intensive and delay-sensitive tasks. Given the large number of underutilized computing resources for mobile devices in urban areas, leveraging these underutilized resources offers tremendous opportunities and value. Considering the spatiotemporal dynamics of user devices, the uncertainty of rich computing resources and the state of network channels in the MEC system, computing resource allocation in mobile devices with idle computing resources will affect the response time of task requesting. To solve these problems, this paper considers the case in which a mobile device can learn from a neighboring IoT device when offloading a computing request. On this basis, a novel self-adaptive learning of task offloading algorithm (SAda) is designed to minimize the average offloading delay in the MEC system. SAda adopts a distributed working mode and has a perception function to adapt to the dynamic environment in reality; it does not require frequent access to equipment information. Extensive simulations demonstrate that SAda achieves preferable latency performance and low learning error compared to the existing upper bound algorithms.     

Non-uniform Specification and Large Deviations for Weak Gibbs Measures

We establish bounds for the measure of deviation sets associated to continuous observables with respect to not necessarily invariant weak Gibbs measures. Under some mild assumptions, we obtain upper and lower bounds for the measure of deviation sets of some non-uniformly expanding maps, including quadratic maps and robust multidimensional non-uniformly expanding local diffeomorphisms. For that purpose, a measure theoretical weak form of specification is introduced and proved to hold for the robust classes of multidimensional non-uniformly expanding local diffeomorphisms and Viana maps.     

KnowRU: Knowledge Reuse via Knowledge Distillation in Multi-Agent Reinforcement Learning

Recently, deep reinforcement learning (RL) algorithms have achieved significant progress in the multi-agent domain. However, training for increasingly complex tasks would be time-consuming and resource intensive. To alleviate this problem, efficient leveraging of historical experience is essential, which is under-explored in previous studies because most existing methods fail to achieve this goal in a continuously dynamic system owing to their complicated design. In this paper, we propose a method for knowledge reuse called “KnowRU”, which can be easily deployed in the majority of multi-agent reinforcement learning (MARL) algorithms without requiring complicated hand-coded design. We employ the knowledge distillation paradigm to transfer knowledge among agents to shorten the training phase for new tasks while improving the asymptotic performance of agents. To empirically demonstrate the robustness and effectiveness of KnowRU, we perform extensive experiments on state-of-the-art MARL algorithms in collaborative and competitive scenarios. The results show that KnowRU outperforms recently reported methods and not only successfully accelerates the training phase, but also improves the training performance, emphasizing the importance of the proposed knowledge reuse for MARL.     

Robustness quantification method for network intrusion detection models

Deep learning techniques have been successfully applied to network intrusion detection tasks, but as in the case of autonomous driving and face recognition, the reliability of the system itself has become a pressing issue. Robustness is a key attribute to determine whether a deep learning system is secure and reliable, and we also choose to explore the security of intrusion detection models from a new perspective of robustness quantification. In this paper, we focus on the intrusion detection model based on long and short-term memory, and use a fine-grained linear approximation method to derive a more accurate robustness bound on the nonlinear activation function with tighter linear constraints. We can use this bound to quantitatively measure the robustness of the detection model and determine whether the model is susceptible to the influence of adversarial samples. In our experiments, we test networks with various structures on the MNIST dataset, and the results show that our proposed method can effectively deduce the robustness bounds of output elements, and has good scalability and applicability.     

Distillation protocols: output entanglement and local mutual information

A complementary behavior between local mutual information and average output entanglement is derived for arbitrary bipartite ensembles. This leads to bounds on the yield of entanglement in distillation protocols that involve disinguishing. This bound is saturated in the hashing protocol for distillation, for Bell-diagonal states.     

Bounds on size-dependent behaviour of composites

Computational homogenisation is a powerful strategy to predict the effective behaviour of heterogeneous materials. While computational homogenisation cannot exactly compute the effective parameters, it can provide bounds on the overall material response. Thus, central to computational homogenisation is the existence of bounds. Classical first-order computational homogenisation cannot capture size effects. Recently, it has been shown that size effects can be retrieved via accounting for elastic coherent interfaces in the microstructure. The primary objective of this contribution is to present a systematic study to attain computational bounds on the size-dependent response of composites. We show rigorously that interface-enhanced computational homogenisation introduces two relative length scales into the problem and investigate the interplay between them. To enforce the equivalence of the virtual power between the scales, a generalised version of the Hill–Mandel condition is employed, and accordingly, suitable boundary conditions are derived. Macroscopic quantities are related to their microscopic counterparts via extended average theorems. Periodic boundary conditions provide an effective behaviour bounded by traction and displacement boundary conditions. Apart from the bounds due to boundary conditions for a given size, the size-dependent response of a composite is bounded, too. The lower bound coincides with that of a composite with no interface. Surprisingly, there also exists an upper bound on the size-dependent response beyond which the expected ‘smaller is stronger’ trend is no longer observed. Finally, we show an excellent agreement between our numerical results and the corresponding analytical solution for linear isotropic materials which highlights the accuracy and broad applicability of the presented scheme.     

Upper bounds on superpartner masses from upper bounds on the Higgs boson mass

The LHC is putting bounds on the Higgs boson mass. In this Letter we use those bounds to constrain the minimal supersymmetric standard model (MSSM) parameter space using the fact that, in supersymmetry, the Higgs mass is a function of the masses of sparticles, and therefore an upper bound on the Higgs mass translates into an upper bound for the masses for superpartners. We show that, although current bounds do not constrain the MSSM parameter space from above, once the Higgs mass bound improves big regions of this parameter space will be excluded, putting upper bounds on supersymmetry (SUSY) masses. On the other hand, for the case of split-SUSY we show that, for moderate or large tanβ, the present bounds on the Higgs mass imply that the common mass for scalars cannot be greater than 10(11) GeV. We show how these bounds will evolve as LHC continues to improve the limits on the Higgs mass.     

Bounds to the wave-vector dependent susceptibility of the ising model

It is shown that rigorous upper and lower bounds to the wave-vector dependent susceptibility of the Ising Model are obtained either when an upper bound to the spin pair correlation function and a lower bound to the susceptibility at zero wave-vector are given, or when a lower bound to the former and an upper bound to the latter are given. An example of the numerical computation of the bounds is presented for the Ising model on the sc lattice.     

Estimations of the Free Energy for the Hubbard Model

A series of upper bounds and two lower bounds for the partition function of the Hubbard model have been derived. These bounds are expressible by certain properties of the Falicov-Kimball model. The upper bounds have been derived mainly by the use of the Golden-Thompson inequality and its generalizations, and the Hölder inequality. The lower bounds are based on the Bogoliubov-Peierls inequality. The numerical values of bounds have also been calculated for small systems.     

Upper and lower bounds for the speed of pulled fronts with a cut-off

We establish rigorous upper and lower bounds for the speed of pulled fronts with a cut-off. For all reaction terms of KPP type a simple analytic upper bound is given. The lower bounds however depend on details of the reaction term. For a small cut-off parameter the two leading order terms in the asymptotic expansion of the upper and lower bounds coincide and correspond to the Brunet-Derrida formula. For large cut-off parameters the bounds do not coincide and permit a simple estimation of the speed of the front.     

Upper bounds on the convective heat transport in a rotating fluid layer of infinite Prandtl number: case of large Taylor numbers

By means of the Howard-Busse method of the optimum theory of turbulence we obtain upper bounds on the convective heat transport in a horizontal fluid layer heated from below and rotating about a vertical axis. We consider the interval of large Taylor numbers where the intermediate layers of the optimum fields expand in the direction of the corresponding internal layers. We consider the 1 - α-solution of the arising variational problem for the cases of rigid-stress-free, stress-free, and rigid boundary conditions. For each kind of boundary condition we discuss four cases: two cases where the boundary layers are thinner than the Ekman layers of the optimum field and two cases where the boundary layers are thicker than the Ekman layers. In most cases we use an improved solution of the Euler-Lagrange equations of the variational problem for the intermediate layers of the optimum fields. This solution leads to corrections of the thicknesses of the boundary layers of the optimum fields and to lower upper bounds on the convective heat transport in comparison to the bounds obtained by Chan [J. Fluid Mech. 64, 477 (1974)] and Hunter and Riahi [J. Fluid Mech. 72, 433 (1975)]. Compared to the existing experimental data for the case of a fluid layer with rigid boundaries the corresponding upper bounds on the convective heat transport is less than two times larger than the experimental results, the corresponding upper bound on the convective heat transport, obtained by Hunter and Riahi is about 10% higher than the bound obtained in this article. When Rayleigh number and Taylor number are high enough the upper bound on the convective heat transport ceases to depend on the boundary conditions. Received 30 January 2001 and Received in final form 28 May 2001     

Surface electronic structure of SnO2(110)

We report theoretical investigations on the surface electronic structure of the (110)-face of SnO₂, a semiconductor of rutile bulk structure. Starting with a tight binding Hamiltonian for the bulk, we determine the surface electronic structure using the scattering theoretic method. As results we obtain the surface bound states, the surface resonances and the wave-vector resolved surface layer densities of states. The dominant features are two backbond states in the stomach gap of the main valence band and two Sn-s derived states in the lower conduction band region. In the upper valence band region, only weak resonances occur, like in other materials with relatively strong ionicity.     

A terahertz time-domain study on the estimation of opto-mechanical properties of pharmaceutical tablets using the Hashin–Shtrikman bounds for refractive index: a case study of microcrystalline cellulose and starch acetate compacts

This work highlights the use of Hashin–Shtrikman (H–S) bounds in the prediction and verification of the effective refractive index, the height and the Young’s modulus of given training sets of pharmaceutical compacts using the measured time delay of a THz pulse traversing the compacts. Set A consisted of 13 microcrystalline cellulose (MCC) compacts whereas set B was made up of 5 starch acetate (SA) compacts. MCC is a typical ingredient of many pharmaceutical tablets. In the case of the MCC compacts, tight and closely matched bounds were obtained between the experimental, the calculated upper, lower bound values for the effective refractive index, and the height values. This promising outcome has shown the high possibility of utilizing H–S bounds in the verification and prediction of the decision level of useful parameters, which can serve as a quality check for pharmaceutical tablets. For the SA compacts, although less tight bounds were observed, the experimental values for the effective refractive index and the Young’s modulus were closely matched with the upper and the lower bounds, respectively. We therefore speculate based on the above observations that the MCC tablets contain an almost evenly distributed spherically shaped air voids whereas in the SA compacts, this assumption might not necessary be true.     

Solution bounds for varying geometry beams

The theory of differential and integral inequalities is applied to obtain upper and lower bounds to the transfer matrix for beams with varying geometry. Various techniques of generating and refining these bounds are investigated. Numerical results indicate that these bounds can be refined to produce numerical agreement of the upper and the lower bound to a given number of significant digits.Proceeding from bounds on the transfer matrix elements a theory is developed for determining upper and lower bounds on the natural frequencies and mode shapes and on the solution state vector for static loading of such beams. This procedure is then extended to the analysis of multispan beams with varying geometry. Numerical results are presented for various configurations.