Optimization in Machine Learning:a Distribution-Space Approach

We present the viewpoint that optimization problems encountered in machine learning can often be interpreted as minimizing a convex functional over a function space,but with a non-convex constraint set introduced by model parameterization.This observation allows us to repose such problems via a suitable relaxation as convex optimization problems in the space of distributions over the training parameters.We derive some simple relationships between the distribution-space problem and the original problem,e.g.,a distribution-space solution is at least as good as a solution in the original space.Moreover,we develop a numerical algorithm based on mixture distributions to perform approximate optimization directly in the distribution space.Consistency of this approximation is established and the numerical efficacy of the proposed algorithm is illustrated in simple examples.In both theory and practice,this formulation provides an alternative approach to large-scale optimization in machine learning.

Boosting Adversarial Training with Learnable Distribution

In recent years,various adversarial defense methods have been proposed to improve the robustness of deep neural networks.Adversarial training is one of the most potent methods to defend against adversarial attacks.However,the difference in the feature space between natural and adversarial examples hinders the accuracy and robustness of the model in adversarial training.This paper proposes a learnable distribution adversarial training method,aiming to construct the same distribution for training data utilizing the Gaussian mixture model.The distribution centroid is built to classify samples and constrain the distribution of the sample features.The natural and adversarial examples are pushed to the same distribution centroid to improve the accuracy and robustness of the model.The proposed method generates adversarial examples to close the distribution gap between the natural and adversarial examples through an attack algorithm explicitly designed for adversarial training.This algorithm gradually increases the accuracy and robustness of the model by scaling perturbation.Finally,the proposed method outputs the predicted labels and the distance between the sample and the distribution centroid.The distribution characteristics of the samples can be utilized to detect adversarial cases that can potentially evade the model defense.The effectiveness of the proposed method is demonstrated through comprehensive experiments.

On analyzing space-time distribution of evaporation duct height over the global ocean

The statistical features of the evaporation duct over the global ocean were comprehensively investigated with reanalysis data sets from the National Centers for Environmental Prediction. These data sets have time and spatial resolutions of 1 h and 0.313°x0.312°, respectively. The efficiency of the analysis was evaluated by processing weather buoy data from the Pacific Ocean and measuring propagation loss in the Yellow Sea of China. The distribution features of evaporation duct height （EDH） and the related meteorological factors for different seas were analyzed. The global EDH is generally high and demonstrates a latitudinal distribution for oceans at low latitudes. The average EDH is approximately 11 m over oceans beside the equator with a latitude of less than 20°. The reasons for the formation of the global EDH features were also analyzed for different sea areas.

Simulation and Prediction on Space-Time Distribution of Water Quality in Dianchi Lake

It is very important in pollution treatment to clarify the space-time distribution of water quality in Dianchi Lake. Based on the sample data obtained from 10 observation stations every month from 2008 to 2009, it uses space-time semi-variogram and ordinary kriging method to simulate the space-time variance and distribution of water quality indictors (TN, TP, BOD, CODMn, DO, Chlorophyl-α, etc.). Because the space-time semivariogram also has a certain of ex-trapolation function. From the simulation results, the pollution is mainly concentrated at the North (Caohai) and the Southwest area (Haikou), and water pollution has a increase trend.

Space-time Dynamics of Dendroctonus valens Population in China and Spatial Sampling Technique based on Its Spatial Distribution Pattern

Red turpentine beetle （RTB）, Dendroctongs valens LeConte, is a destructive forest invasive species in China, it mainly attacks Pings tabuliformis and P. bungeana. So far it has spread rapidly to the provinces of Shanxi, Hebei, Henan, Shanxi and Beijing since its first outbreak in Shanxi Province in 1998, and has caused extensive tree mortality. Space-time dynamics of D. valens population and spatial sampling technique based on its spatial distribution pattern were ana- lyzed using geostatistical methods in the pure P. tabuliforis forests and mixedwood stands which were at different damage levels. According to the spatial distribu- tion of D. valeas population, the specific spatial sampling technique was also studied, and then was compared with traditional sampling technique. The spatial sam- piing technique combined with sampling theory and the biological characteristics of D. valens population, which not only could calcnlate the error of the sampling, but also could discuss the optimal sampling number and the optimum size of plot according to different damage levels and different stand types. This helps to explain population expansion and colonization mechanism of D. valens, and to provide a good reference for adopting snitable control measures.

Was Polchinski Wrong? Colombeau Distributional Rindler Space-Time with Distributional Levi-CivitàConnection Induced Vacuum Dominance. Unruh Effect Revisited

The vacuum energy density of free scalar quantum field in a Rindler distributional space-time with distributional Levi-Cività connection is considered. It has been widely believed that, except in very extreme situations, the influence of acceleration on quantum fields should amount to just small, sub-dominant contributions. Here we argue that this belief is wrong by showing that in a Rindler distributional background space-time with distributional Levi-Cività connection the vacuum energy of free quantum fields is forced, by the very same background distributional space-time such a Rindler distributional background space-time, to become dominant over any classical energy density component. This semiclassical gravity effect finds its roots in the singular behavior of quantum fields on a Rindler distributional space-times with distributional Levi-Cività connection. In particular we obtain that the vacuum fluctuations have a singular behavior at a Rindler horizon . Therefore sufficiently strongly accelerated observer burns up near the Rindler horizon. Thus Polchinski’s account doesn’t violate the Einstein equivalence principle.

Debris cloud structure and hazardous fragments distribution under hypervelocity yaw impact

This study investigates how the debris cloud structure and hazardous fragment distribution vary with attack angle by simulating a circular cylinder projectile hypervelocity impinging on a thin plate using the finite element-smoothed particle hydrodynamics(FE-SPH)adaptive method.Based on the comparison and analysis of the experimental and simulation results,the FE-SPH adaptive method was applied to address the hypervelocity yaw impact problem,and the variation law of the debris cloud structure with the attack angle was obtained.The screening criterion of the hazardous fragment at yaw impact is given by analyzing the debris formation obtained by the FE-SPH adaptive method,and the distribution characteristics of hazardous fragments and their relationship with the attack angle are given.Moreover,the velocity space was used to evaluate the distribution range and damage capability of asymmetric hazardous fragments.The maximum velocity angle was extended from fully symmetrical working conditions to asymmetrical cases to describe the asymmetrical debris cloud distribution range.In this range,the energy density was calculated to quantitatively analyze how much damage hazardous fragments inflict on the rear plate.The results showed that the number of hazardous fragments generated by the case near the 35°attack angle was the largest,the distribution range was the smallest,and the energy density was the largest.These results suggest that in this case,debris cloud generated by the impact had the strongest damage to the rear plate.

Analysis of temporal and spatial distribution characteristics of ammonium chloride smoke particles in confined spaces

In response to the demand for short-range detection of anti-smoke environment interference by laser fuzes,this study proposes a smoke environment simulation of non-uniform continuous point source diffusion and investigates an experimental laboratory smoke environment using an ammonium chloride smoke agent.The particle size distribution,composition,and mass flow distribution of the smoke were studied.Based on a discrete phase model and a kεturbulence model,a numerical simulation was developed to model the smoke generation and diffusion processes of the smoke agent in a confined space.The temporal and spatial distribution characteristics of the smoke mass concentration,velocity,and temperature in the space after smoke generation were analyzed,and the motion law governing the smoke diffusion throughout the entire space was summarized.Combined with the experimental verification of the smoke environment laboratory,the results showed that the smoke plume changed from fan-shaped to umbrella-shaped during smoke generation,and then continued to spread around.Meanwhile,the mass concentration of smoke in the space decreased from the middle outward;the changes in temperature and velocity were small and stable.In the diffusion stage(after 900 s),the mass concentration of smoke above 0.8 m was relatively uniform across an area of smoke that was 12 m thick.The concentration decreased over time,following a consistent decreasing trend,and the attenuation was negligible in a very short time.Therefore,this system was suitable for conducting experimental research on laser fuzes in a smoke environment.Owing to the stability of the equipment and facilities,the setup could reproduce the same experimental smoke environment by artificially controlling the smoke emission of the smoke agent.Overall,this work provides a theoretical reference for subsequent research efforts regarding the construction of uniform smoke environments and evaluating laser transmission characteristics in smoky environments.

A Method for Improving Power Distribution Characteristics of Space Time Block Codes

Improving power distribution characteristics of space time block codes(STBCs),namely peak to average power ratio(PAPR),average to minimum power ratio(Ave/min),and probability of transmitting"zero"by antenna,makes easier their practical implementation.To this end,this study proposes to multiply full diversity STB C with a non-singular matrix in multiple input multiple output(MIMO)or multiple input single output(MISO)systems with linear or maximum likelihood(ML)receivers.It is proved that the obtained code achieves full diversity and the order of detection complexity does not change.The proposed method is applied to different types of STBCs.The bit error rate(BER)and power distribution characteristics of the new codes demonstrate the superiority of the introduced method.Further,lower and upper bounds on the BER of the obtained STBCs are derived for all receivers.The proposed method provides trade-off among PAPR,spectral efficiency,energy efficiency,and BER.

STATIONARY DISTRIBUTIONS OF INFINITE PARTICLE SYSTEMS WITH NONCOMPACT STATE SPACE.

This paper deals with the preblem of existence and uniqueness of the stationary distributions (abbr., s. d.'s) for the processes constructed in [4] .The main results are stated in § 1. For the reader's convenience we first restate the existence theorems (Theorem 1 and 2) of the processes given in [4]. Then two existence theorems (Theorem 3 and 4) and a uniqueness theorem (Theorem 5) for the s. d.'s of the processes are presented. The last result (Theorem 6), as an application of the previous ones, is about the Schlgl model which comes from nonequilibrium statisticali physics. The details of the proofs of Theorem 3—6 are given in § 2—4.

Electron beam modeling and analyses of the electric field distribution and space charge effect

In electron beam technology, one of the critical focuses of research and development efforts is on improving the measurement of electron beam parameters. The parameters are closely related to the generation, emission, operation environment, and role of the electron beam and the corresponding medium. In this study, a field calculation method is proposed, and the electric field intensity distribution on the electron beam’s cross-section is analyzed. The characteristics of beam diffusion caused by the space charge effect are investigated in simulation, and the obtained data are compared with the experiment. The simulation demonstrated that the cross-sectional electric field distribution is primarily affected by the electron beam current, current density distribution, and electron beam propagation speed.

Combination and distribution of reservoir space in complex carbonate rocks

This paper discusses the reservoir space in carbonate rocks in terms of types,combination features,distribution regularity,and controlling factors,based on core observations and tests of the North Truva Oilfield,Caspian Basin.According to the reservoir space combinations,carbonate reservoirs can be divided into four types,i.e.,pore,fracture-pore,pore-cavity-fracture,and pore-cavity.Formation and distribution of these reservoirs is strongly controlled by deposition,diagenesis,and tectonism.In evaporated platform and restricted platform facies,the reservoirs are predominately affected by meteoric fresh water leaching in the supergene-para-syngenetic period and by uplifting and erosion in the late stage,making both platform facies contain all the above-mentioned four types of reservoirs,with various pores,such as dissolved cavities and dissolved fractures,or structural fractures occasionally in favorable structural locations.In open platform facies,the reservoirs deposited continuously in deeper water,in an environment of alternative high-energy shoals（where pore-fracture-type reservoirs are dominant） and low-energy shoals（where pore reservoirs are dominant）.

Distributed Multicircular Circumnavigation Control for UAVs with Desired Angular Spacing

This paper addresses a multicircular circumnavigation control for UAVs with desired angular spacing around a nonstationary target.By defining a coordinated error relative to neighboring angular spacing,under the premise that target information is perfectly accessible by all nodes,a centralized circular enclosing control strategy is derived for multiple UAVs connected by an undirected graph to allow for formation behaviors concerning the moving target.Besides,to avoid the requirement of target’s states being accessible for each UAV,fixed-time distributed observers are introduced to acquire the state estimates in a fixed-time sense,and the upper boundary of settling time can be determined offline irrespective of initial properties,greatly releasing the burdensome communication traffic.Then,with the aid of fixed-time distributed observers,a distributed circular circumnavigation controller is derived to force all UAVs to collaboratively evolve along the preset circles while keeping a desired angular spacing.It is inferred from Lyapunov stability that all errors are demonstrated to be convergent.Simulations are offered to verify the utility of proposed protocol.

Preliminary Study on the Distribution of Meridional Wind in Near Space

Based on high-altitude wind data in about one year, the seasonal changes and vertical profiles of meridional wind in near space were studied, and the reasons for the increase of meridional wind in spring and winter were analyzed. Meanwhile, the seasonal distribution of atmospher- ic circulation in the stratosphere was studied, and the seasonal changes and mechanism of wind conversion from the east to the west were re- vealed. The results show that the speed of meridional wind in near space was the highest in spring, followed by autumn and winter, while it was the lowest in summer; the increase of meridional wind in spring and winter was related to weather systems in the troposphere, such as the development of strong warm ridge over Xinjianq and cold trouclh system, and the svstem resulted in the increase of meridional wind.

Distribution of Stresses in Particulate Half Space under Surface Pressure

Reducing the linear system of two first order equilibrium equations involving normal stress σ(ρ,θ) and shearing stress v(ρ,θ), by elimination, to two decoupled second order equations in σ and v, we find that, for pressure only case, v(ρ,θ) vanishes in the half space. Consequently, the second order equation in σ can be simplified. In the language of linear system analysis, the medium(system) function, characterizing the mechanical behavior of a particulate medium in pressure only case, is obtained from the simplified second order equation ( 2 ρ+ 2 θ)σ(ρ,θ)=0 and can be inverted to give impulse reponse explicitly. Thus, response σ α(ρ,θ) may be computed directly from input, i.e., the surface pressure φ α(ρ) , by integration. Some explicit formulas for transmission problems, including response to input of strip linearly increasing pressure, are given in the paper.

Joint DOA and time delay estimation method for space-time coherent distributed signals based on search

Under dense urban fading environment, performance of joint multi-path parameter estimation method based on traditional point signal model degrades seriously. In this paper, a new space and time signal model based on multipath distribution function is given after new space and time manifold is reconstructed. Then joint spacetime signal subspace is obtained by converting acquired channel from time domain to frequency domain .Then space and time spectrum is formulated by the space sub-matrix and time sub-matrix taken out of joint space-time signal subspace, and parameters are estimated by searching the minimum eigenvalues of the space matrix and the time matrix. Lastly, A space and time parameters matching process is performed by using the orthogonal property between joint noise subspace and the space-time manifold. In contrast with tradition MUSIC, the algorithm we present here only need two 1- dimension searching and was not sensitive to different distribution function.

Space Group Distribution in Substituted Phenols

Analysis on the space group distribution in 78 substituted phenols re-vealed its unusual high frequencies in groups with non-centrosymmetry or polar axis orhigher symmetry or Z' > 1. Based on the characteristics of intermolecular H-bondsformed by two OH groups,the space group distribution could be rationalized well.

Space Topologies and Their Dual Space Topologies for Conventional Functional Space Topologies

In this paper, we have studied the topology of some classical functional spaces. Among these spaces, there are standard spaces, spaces that can be metrizable and others that cannot be metrizable. But they are all topological vector spaces and it is in this context that we have chosen to present this work. We are interested in the topology of its spaces and in the topologies of their dual spaces. The first part, we presented the fundamental topological properties of topological vector spaces. The second part, we studied Frechet spaces and particularly the space S(Rn) of functions of class C∞ on Rn which are as well as all their rapidly decreasing partial derivatives. We have also studied its dual S'(Rn) the space of tempered distributions. The last part aims to define a topological structure on an increasing union of Frechet spaces called inductive limit of Frechet spaces. We study in particular the space D(Ω) of functions of class C∞ with compact supports on Ω as well as its dual D' (Ω) the space distributions over the open set Ω.

An Analytical Study on Distribution of Statically Determinate Stresses in Particulate Half Space

General solution of stresses solved from the two dimensiona l system of equilibrium equations in Cartesian coordinates is characterized by the presence of two families of characteristic lines along which initial stresses and discontinuities in them are transmitted intact far down to infinity.This is against our intuition and not verifiable by experimental findings. For the fundamental case of infinite uniform pressure on the upper surface,a comparison between solutions from equilibrium equations in Cartesian coordinates and from those in polar coordinates is carried out in details.The semi infinite characteristic lines in the former are bent up to exponential spirals with both ends on the upper surface in the latter.Thus,the transmission pattern from solution in polar coordinates comes closer to actual situation.However,in polar reference frame,the solution for distribution of stresses in particulate half space under surface strip pressure or so can then only be obtained from boundary value problem of second order partial differential equation.

Emittance Growth Caused by the Transverse Nonuniform Space Charge Distributions of Bunched Beam in Linac

The nonlinear space charge effect of bunched beam in linac is one of the im-portant factors that induces the emittance growth due to the conversion of the field en-ergy to kinetic energy.In this paper,the internal field energies associated with sometransverse nonuniform space charge distributions of a bunched beam,such as Gaussiandistribution,waterbag distribution and parabolic distribution,are worked out.And theemittance growth caused by these nonuniformities are obtained.