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.

Simulation study on reconstruction model of three-dimensional temperature distribution within visible range in furnace

This paper presents a reconstruction model of three-dimensional temperature distribution in furnace based on radiative energy images captured by charge-coupled device （CCD） cameras within the visible wavelength range. Numerical simulation case was used in this study and a zigzag eccentric temperature distribution was assumed to verify the model. Least square QR-factorization （LSQR） method was introduced to deal with reconstruction equation. It is found that the reconstructed temperature distributions in low-temperature areas had some fluctuations and high-temperature areas were reconstructed well. The whole reconstruction relative error was mainly due to errors in low-temperature areas and the relative error for highest-temperature reconstruction was quite small.

Research on Testing System for Three-dimensional Distribution of Luminous Intensity of LED

In terms of asymmetrical three-dimensional distribution(ID) of luminous intensity(LI) of light-emitting-diode(LED),a testing system was conducted in this study. Design and principle of the testing system were introduced. 31 photometers were placed on a concentric circle,and all of them were used to gather LI data of LED at the same time. The data acquisition card(DAC) was used to gather multichannel data and controlled motor. Experimental results indicated that the testing system had achieved the goal of testing three-dimensional distribution of LI. And each parameter could meet the requirements of industrial production and measurement.

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.

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.

Characteristics and distribution of microstructures in high pressure die cast alloys with X-ray microtomography:A review

Al and Mg alloy high pressure die castings(HPDC)are increasingly used in automotive industries.The microstructures in the castings have decisive effect on the casting mechanical properties,in which the microstructure characteristics are fundamental for the investigation of the microstructure-property relation.During the past decade,the microstructure characteristics of HPDC Al and Mg alloys,especially micro-pores andα-Fe,have been investigated from two-dimensional(2D)to threedimensional with X-ray micro-computed tomography(μ-CT).This paper provides an overview of the current understanding regarding the 3D characteristics and formation mechanisms of microstructures in HPDC alloys,their spatial distributions,and the impact on mechanical properties.Additionally,it outlines future research directions for the formation and control of heterogeneous microstructures in HPDC alloys.

Risk Assessment of Coal Mine Water Hazard Based on Three-Dimensional Model of Geology and Underground Space

Mine safety have top-five disasters,which including the water,gas,fire,dust and geological dynamic disaster.The coal mine water disaster is one of the important factors which restricted the development of China’s coal production.It is showed by statistics that 60%of mine accidents are affected by groundwater,which not only result in the production losses,casualties and a variety of

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.

Three-dimensionally ordered macroporous cross-linked polystyrene incorporating functional group via hydrophilic spacer arm

A versatile and effective method for incorporating functional groups on the pore wall of three-dimensionally ordered macroporous cross-linked polystyrene（3DOM CLPS） by hydrophilic spacer arm has been investigated.The 3DOM CLPS with pore size 865 nm was prepared by sacrifice template method.The hydrophilic spacer arm（polyethylene glycol,molecular weight is 600） was grafted to the 3DOM CLPS via nucleophilic substitution reaction.The other side of active hydroxyl can be further converted into a lot of other functional groups.In this report,the chelating ligand 2-mercaptobenzothiazole（MBZ） group was introduced on the end of the PGE chain to evidence the versatile functionalization approach.The functionalized ordered macroporous materials were characterized by FT-IR,element analyzer,SEM.The results reveal that the pores were successfully bonded with 2-mercaptobenzothiazole groups via hydrophilic spacer arms and the original morphology of ordered macroporous materials were remained after functionalization.The MBZ group density is 0.052 mmol/m^2.The functionalized 3DOM CLPS are expected to application as heavy metal ions adsorbent.

Continuous imaging space in three-dimensional integral imaging

We report an integral imaging method with continuous imaging space. This method simultaneously reconstructs real and virtual images in the virtual mode, with a minimum gap that separates the entire imaging space into real and virtual space. Experimental results show that the gap is reduced to 45% of that in a conventional integral imaging system with the same parameters.

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）.

Using"Three-dimensional Space Resources"for Fenlong Technology to Improve Grain Econoloy and Expand Human Living Spaces

Fenlong Technology has been applied to increase yield by 20%-50%,improve quality by 5%,and retain water by 100%in 40 kinds of crop cultivated land and saline-alkali land in 26 provinces of China.This paper clarified for the first time the scientific theory system of Fenlong Technology using three-dimensional space resources"Fenlong Agricultural Nature Theory"and the development of the relative"limits"of agricultural growth,which provides a huge power support and natural force for expanding human living spaces.Through inventing and creating a scientific and technological system of farming tools,farming machinery,farming modes,and magic weapons for cultivation,Fenlong Technology can increase grain,promote ecological development,and greatly expand the living spaces of the Chinese nation and achieve sustainable development.Using Fenlong Technology,China has expanded from the current single"cultivated land agriculture"to the"big pattern agriculture"of Fenlong"cultivated land+saline land+degraded grassland+marginal land+desertified land+river water",flexibly used 147 million ha of"three-dimensional space resources"of land,and the newly increased food,meat,and fish can feed 300 million to 400 million people,increased the water storage by 100 billion m^(3),and reduced the collection of groundwater by 20 million to 60 billion m^(3).

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.

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.

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 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.

Three-Dimensional Space Interpolation of Grey / Depth Image Sequence-A New Technique of Computer Graphics Synthesis

This paper advances a three-dimensional space interpolation method of grey / depth image sequence, which breaks free from the limit of original practical photographing route. Pictures can cruise at will in space. By using space sparse sampling, great memorial capacity can be saved and reproduced scenes can be controlled. To solve time consuming and complex computations in three-dimensional interpolation algorithm, we have studied a fast and practical algorithm of scattered space lattice and that of 'Warp' algorithm with proper depth. By several simple aspects of three dimensional space interpolation, we succeed in developing some simple and practical algorithms. Some results of simulated experiments with computers have shown that the new method is absolutely feasible.