Covariance Estimation in High Dimensions via Kronecker Product Expansions

This paper presents a new method for estimating high dimensional covariance matrices. The method, permuted rank-penalized least-squares (PRLS), is based on a Kronecker product series expansion of the true covariance matrix. Assuming an i.i.d. Gaussian random sample, we establish high dimensional rates of convergence to the true covariance as both the number of samples and the number of variables go to infinity. For covariance matrices of low separation rank, our results establish that PRLS has significantly faster convergence than the standard sample covariance matrix (SCM) estimator. The convergence rate captures a fundamental tradeoff between estimation error and approximation error, thus providing a scalable covariance estimation framework in terms of separation rank, similar to low rank approximation of covariance matrices. The MSE convergence rates generalize the high dimensional rates recently obtained for the ML Flip-flop algorithm for Kronecker product covariance estimation. We show that a class of block Toeplitz covariance matrices is approximatable by low separation rank and give bounds on the minimal separation rank $r$ that ensures a given level of bias. Simulations are presented to validate the theoretical bounds. As a real world application, we illustrate the utility of the proposed Kronecker covariance estimator for spatio-temporal linear least squares prediction of multivariate wind speed measurements.Comment: 47 pages, accepted to IEEE Transactions on Signal Processin

Low-Complexity LP Decoding of Nonbinary Linear Codes

Linear Programming (LP) decoding of Low-Density Parity-Check (LDPC) codes has attracted much attention in the research community in the past few years. LP decoding has been derived for binary and nonbinary linear codes. However, the most important problem with LP decoding for both binary and nonbinary linear codes is that the complexity of standard LP solvers such as the simplex algorithm remains prohibitively large for codes of moderate to large block length. To address this problem, two low-complexity LP (LCLP) decoding algorithms for binary linear codes have been proposed by Vontobel and Koetter, henceforth called the basic LCLP decoding algorithm and the subgradient LCLP decoding algorithm. In this paper, we generalize these LCLP decoding algorithms to nonbinary linear codes. The computational complexity per iteration of the proposed nonbinary LCLP decoding algorithms scales linearly with the block length of the code. A modified BCJR algorithm for efficient check-node calculations in the nonbinary basic LCLP decoding algorithm is also proposed, which has complexity linear in the check node degree. Several simulation results are presented for nonbinary LDPC codes defined over Z_4, GF(4), and GF(8) using quaternary phase-shift keying and 8-phase-shift keying, respectively, over the AWGN channel. It is shown that for some group-structured LDPC codes, the error-correcting performance of the nonbinary LCLP decoding algorithms is similar to or better than that of the min-sum decoding algorithm.Comment: To appear in IEEE Transactions on Communications, 201

Information Preserving Component Analysis: Data Projections for Flow Cytometry Analysis

Flow cytometry is often used to characterize the malignant cells in leukemia and lymphoma patients, traced to the level of the individual cell. Typically, flow cytometric data analysis is performed through a series of 2-dimensional projections onto the axes of the data set. Through the years, clinicians have determined combinations of different fluorescent markers which generate relatively known expression patterns for specific subtypes of leukemia and lymphoma -- cancers of the hematopoietic system. By only viewing a series of 2-dimensional projections, the high-dimensional nature of the data is rarely exploited. In this paper we present a means of determining a low-dimensional projection which maintains the high-dimensional relationships (i.e. information) between differing oncological data sets. By using machine learning techniques, we allow clinicians to visualize data in a low dimension defined by a linear combination of all of the available markers, rather than just 2 at a time. This provides an aid in diagnosing similar forms of cancer, as well as a means for variable selection in exploratory flow cytometric research. We refer to our method as Information Preserving Component Analysis (IPCA).Comment: 26 page

Room temperature photonic crystal defect lasers at near-infrared wavelengths in InGaAsP

Room temperature lasing from optically pumped single defects in a two-dimensional (2-D) photonic bandgap (PBG) crystal is demonstrated. The high-Q optical microcavities are formed by etching a triangular array of air holes into a half-wavelength thick multiquantum-well waveguide. Defects in the 2-D photonic crystal are used to support highly localized optical modes with volumes ranging from 2 to 3 (lambda/2n)(3). Lithographic tuning of the air hole radius and the lattice spacing are used to match the cavity wavelength to the quantum-well gain peak, as well as to increase the cavity Q. The defect lasers were pumped with 10-30 ns pulses of 0.4-1% duty cycle. The threshold pump power was 1.5 mW (approximate to 500 μW absorbed)

Shutdowns effect during operation of steam pipeline of tpp on the fracture toughness of 15Kh1M1F steel

Показано, що локальний параметр механіки руйнування – статична тріщиностійкість (JIC), чутлива до зміни стану металу внаслідок деградації в експлуатаційних умовах. Виявлено, що кількість зупинок технологічного процесу під час експлуатації сталі, орієнтація зразків (осьова й тангенціальна) та місце їх розташування в перерізі стінки труб (біля зовнішньої та внутрішньої поверхонь труб) впливають на рівень статичної тріщиностійкості. За однакової тривалості експлуатації на головних парогонах ТЕС, але різної кількості зупинок блоків, які супроводжуються значними перепадами температури в стінці труб, найбільше зниження рівня JIC сталі 15Х1М1Ф зафіксували для металу, що переніс більшу кількість зупинок. Цим доказано, що показник JIC високочутливий до зміни стану експлуатованого металу під впливом теплозмін. Проаналізовано механізми руйнування металу у вихідному стані та після експлуатації, виділено вплив кількості пусків-зупинок технологічного процесу на інформативні фрактографічні ознаки.The main steam pipelines of TPP are subjected to a combined effect of number of technological factors causing the degradation of steel. Lot of operational factors affect the workability of energy equipment. Among these factors are hard temperature-force operating conditions (temperature of the steam pipelines is up to 570oC and the steam pressure – 24 MPa) and hydrogenated environment. One more reason of the loss workability of equipment was revealed recently. This is a frequent shutdown of the process caused by exploitation of the blocks in a maneuvering mode. It is known that fracture toughness (JIC) is a local parameter of fracture mechanics sensitive to changes in the state of the metal as a result of its degradation in service conditions. It was shown that JR-curves significantly differ for the steel 15Kh1M1F in virgin state and used for a same time (~2⋅105 h), but at different numbers of process shutdowns on the steam pipeline. It was revealed that number of shutdowns during longtime operation of steel and orientation of the specimens (axial and tangential) and its location in the cross section of tube wall (near the outer or inner surface of the tube) affect the value of fracture toughness. At the same operation time of steel on the main steam pipeline of TPP, but at different numbers of shutdowns the maximum reduction of the JIC level was revealed for the 15Kh1M1F steel after more shutdowns. Consequently, JIC level is the sensitive indicator of changes in the state of the metal under the influence of thermal cycles caused by shutdowns. The fractographic features of the steel in virgin state and after operation during the same time on the main steam pipeline of TPP, but at different numbers of shutdowns were analyzed. The wide stretch zone with following ductile fracture by forming of dimple structure was revealed on the fracture surface of steel in virgin state. A few fractographic features were revealed on the fracture surfaces of long-time operated steel. That is, the stretch zone on the fracture surface of the metal operated at smaller number of shutdowns is significantly less than in the non-operated metal, but in the steel operated at larger number shutdowns - it disappears. Ductile increment of cracks during static active loading of specimens of operated steel are essentially decreased and the continuity of the crack fronts disappeared. At the stage of spontaneous fracture the steel operated at smaller number shutdowns was destroyed by the mixed inter- and transgranular fracture, but the steel after more shutdowns – practically only by intergranular fracture. Intergranular fracture was considered as an indicator of the weakening the boundaries between the neighbouring grains

Influence of Metal-Graphene Contact on the Operation and Scalability of Graphene Field-Effect-Transistors

We explore the effects of metal contacts on the operation and scalability of 2D Graphene Field-Effect-Transistors (GFETs) using detailed numerical device simulations based on the non-equilibrium Green's function formalism self-consistently solved with the Poisson equation at the ballistic limit. Our treatment of metal-graphene (M-G) contacts captures: (1) the doping effect due to the shift of the Fermi level in graphene contacts, (2) the density-of-states (DOS) broadening effect inside graphene contacts due to Metal-Induced-States (MIS). Our results confirm the asymmetric transfer characteristics in GFETs due to the doping effect by metal contacts. Furthermore, at higher M-G coupling strengths the contact DOS broadening effect increases the on-current, while the impact on the minimum current (Imin) in the off-state depends on the source to drain bias voltage and the work-function difference between graphene and the contact metal. Interestingly, with scaling of the channel length, the MIS inside the channel has a weak influence on Imin even at large M-G coupling strengths, while direct source-to-drain (S -> D) tunneling has a stronger influence. Therefore, channel length scalability of GFETs with sufficient gate control will be mainly limited by direct S -> D tunneling, and not by the MIS.Comment: 7 figures, accepted by TE

Regularities of changing the mechanical characteristics of the 12KH1MF steel from different zones of steam pipeline bend from TPP

Гини парогонів ТЕС характеризуються неоднаковою деформацією металу різних зон: розтягненої, нейтральної, стисненої. Як результат – різні механічні властивості цих зон унаслідок деградації. Досліджено міру деградації сталі 12Х1МФ з різних зон гину після 2,5·105 год її експлуатації у системі парогонів ТЕС. Стан металу оцінювали за результатами візуального обстеження та за механічними характеристиками за одновісного розтягу та удару на повітрі. Виявили, що максимальних змін внаслідок експлуатації зазнають механічні характеристики сталі розтягненої та нейтральної зон гину.Hard temperature-power operating mode of the steam pipeline (vapor pressure up to 14 MPa, temperature – up to 565 oC and a large number of shutdowns of the process), and long-term influence of an aggressive hydrogenating environment on stressed metal promote degradation of its structure and reduce the mechanical properties, which were ensured by their workability at the beginning of operation. Therefore, the diagnostics of the technical state of metal of the steam pipeline ensures the reliability of their operation and does not lose relevance to the power system of Ukraine with critically worn-out equipment. Features of degradation of thermal power plant steam pipeline bending were caused by non-identical conditions of deformation of the metal in different zones (tensile, compressed and neutral) of bend as on the stage of production and the follow long-term operation. Due to the technological features of production and peculiarities of the cross-sectional shape of bends the maximum tensile stresses occur in the tensile zone of bending, where the wall thickness of tube is minimal. Mechanical properties of metal from different bend zones were differed after long-term impact of stress. The level of degradation of 12Kh1MF steel from different zones of bend after 2,5·105 hours of operation in the steam pipeline system of TPP was evaluated in this paper. Technical state of metal was estimated by visual inspection of bend and using mechanical characteristics determined at uniaxial tension and impact test on the air. During visual inspection of outer surface of the pipe an axial cracks in the tensile zone of bend, caused by high temperature creep, were detected. It was established that mechanical properties of operated steel from tensile and neutral zones of bend is maximally changed. That is, the characteristics of plasticity, determined on the tangential specimens were sensitive to changes in the technical state of steel. Reduction of area of metal from tensile zone of bend is in 2 times lower than the minimum allowable value (27% and 55% respectively). Impact toughness level of the metal from tensile zone of bend determined on specimens of both orientations was lower than the regulated value for heat-resistant steels too. This confirmed that the brittle fracture resistance characteristic is also highly sensitive to changes in the technical state of the pipeline bend metal. Taking into account the fact that degradation of damaged bending has reached the maximum degree (since the bend has been damaged during operation), the level of the impact toughness of the metal can be proved expediency of stopping the exploitation the actual structural elements of steam pipeline

Convergent Incremental Optimization Transfer Algorithms: Application to Tomography

No convergent ordered subsets (OS) type image reconstruction algorithms for transmission tomography have been proposed to date. In contrast, in emission tomography, there are two known families of convergent OS algorithms: methods that use relaxation parameters , and methods based on the incremental expectation-maximization (EM) approach . This paper generalizes the incremental EM approach by introducing a general framework, "incremental optimization transfer". The proposed algorithms accelerate convergence speeds and ensure global convergence without requiring relaxation parameters. The general optimization transfer framework allows the use of a very broad family of surrogate functions, enabling the development of new algorithms . This paper provides the first convergent OS-type algorithm for (nonconcave) penalized-likelihood (PL) transmission image reconstruction by using separable paraboloidal surrogates (SPS) which yield closed-form maximization steps. We found it is very effective to achieve fast convergence rates by starting with an OS algorithm with a large number of subsets and switching to the new "transmission incremental optimization transfer (TRIOT)" algorithm. Results show that TRIOT is faster in increasing the PL objective than nonincremental ordinary SPS and even OS-SPS yet is convergent.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85980/1/Fessler46.pd