Computing Different Realizations of Linear Dynamical Systems with Embedding Eigenvalue Assignment

In this paper we investigate realizability of discrete time linear dynamical systems (LDSs) in fixed state space dimension. We examine whether there exist different Θ = (A,B,C,D) state space realizations of a given Markov parameter sequence Y with fixed B, C and D state space realization matrices. Full observation is assumed in terms of the invertibility of output mapping matrix C. We prove that the set of feasible state transition matrices associated to a Markov parameter sequence Y is convex, provided that the state space realization matrices B, C and D are known and fixed. Under the same conditions we also show that the set of feasible Metzler-type state transition matrices forms a convex subset. Regarding the set of Metzler-type state transition matrices we prove the existence of a structurally unique realization having maximal number of non-zero off-diagonal entries. Using an eigenvalue assignment procedure we propose linear programming based algorithms capable of computing different state space realizations. By using the convexity of the feasible set of Metzler-type state transition matrices and results from the theory of non-negative polynomial systems, we provide algorithms to determine structurally different realization. Computational examples are provided to illustrate structural non-uniqueness of network-based LDSs.

A Manufacturing SCOS Model (MSCOS) Based on the Similarity of Parameter Sequences Between Tasks and Service Composition

Service composition and optimal selection (SCOS) is a core issue in cloud manufacturing (CMfg) when integrating distributed manufacturing services for complex manufacturing tasks. Generally, a set of recommended task parameter sequences (Tps) will be given when publishing manufacturing tasks. The similarity between the service composition parameter sequence (SCps) and Tps also reflects the rationality of the service composition. However, various evaluation models based on QoS have been proposed, ignoring the rationality between the Tps and SCps. Considering the similarity of the Tps and SCps in an evaluation model, we propose a manufacturing SCOS framework called MSCOS. The framework includes two parts: an evaluation model and an algorithm for both optimization and selection. In the evaluation model, based on the numerical proximity and geometric similarity between the Tps and SCps, improving the technique for order preference by similarity to an ideal solution (TOPSIS) with the grey correlation degree (GC), we propose the GC&TOPSIS (GTOPSIS). In the optimization and selection algorithm, an improved flower pollination algorithm (IFPA) is proposed to achieve optimization and selection based on polyline characteristics between the fitness values in the population. Experiments show that the MSCOS evaluation effect and optimal selection offer better performance than commonly used algorithms.

Constructing Keyed Hash Algorithm Using Enhanced Chaotic Map with Varying Parameter

A keyed hash algorithm is proposed based on 1-D enhanced quadratic map (EQM) with varying parameter. Three measures, including assigning unique one-time keys, key expansion, and hash length extension, are taken to enhance its security. First, the message is transformed into a parameter sequence for the EQM to be absorbed, and then the extended keys are generated as the initial values of the EQM. Finally, the EQM is iterated with redundant loops to transform the variable values into a hash value. The algorithm is so flexible that it can generate hash value with different lengths of 256, 512, 1024, or more bits through a parameter switcher, and redundant loops can eliminate the transient effect of chaos and mitigate the increasing threat of the side-channel attack. Security evaluations and comparison demonstrated its practicability and reliability.

Hydropathy patterning complements charge patterning to describe conformational preferences of disordered proteins

Understanding the conformational ensemble of an intrinsically disordered protein (IDP) is of great interest due to its relevance to critical intracellular functions and diseases. It is now well established that the polymer scaling behavior can provide a great deal of information about the conformational properties as well as liquid-liquid phase separation of an IDP. It is, therefore, extremely desirable to be able to predict an IDP’s scaling behavior from the protein sequence itself. The work in this direction so far has focused on highly charged proteins and how charge patterning can perturb their structural properties. As naturally occurring IDPs are composed of a significant fraction of uncharged amino acids, the rules based on charge content and patterning are only partially helpful in solving the problem. Here, we propose a new order parameter, sequence hydropathy decoration (SHD), which can provide a near quantitative understanding of scaling and structural properties of IDPs devoid of charged residues. We combine this with a charge patterning parameter, sequence charge decoration (SCD), to obtain a general equation, parameterized from extensive coarse-grained simulation data, for predicting protein dimensions from the sequence. We finally test this equation against available experimental data and find a semi-quantitative match in predicting the scaling behavior. We also provide guidance on how to extend this approach to experimental data, which should be feasible in the near future. Graphical TOC Entry

Convergence of Markovian stochastic approximation for Markov random fields with hidden variables

This paper studies the convergence of the stochastic algorithm of the modified Robbins–Monro form for a Markov random field (MRF), in which some of the nodes are clamped to be observed variables while the others are hidden ones. Based on the theory of stochastic approximation, we propose proper assumptions to guarantee the Hölder regularity of both the update function and the solution of the Poisson equation. Under these assumptions, it is proved that the control parameter sequence is almost surely bounded and accordingly the algorithm converges to the stable point of the log-likelihood function with probability [Formula: see text].

On the S-instability and degeneracy of discrete deep learning models

A probability model exhibits instability if small changes in a data outcome result in large and, often unanticipated, changes in probability. This instability is a property of the probability model, given by a distributional form and a given configuration of parameters. For correlated data structures found in several application areas, there is increasing interest in identifying such sensitivity in model probability structure. We consider the problem of quantifying instability for general probability models defined on sequences of observations, where each sequence of length $N$ has a finite number of possible values that can be taken at each point. A sequence of probability models, indexed by $N$, and an associated parameter sequence result to accommodate data of expanding dimension. Model instability is formally shown to occur when a certain log probability ratio under such models grows faster than $N$. In this case, a one component change in the data sequence can shift probability by orders of magnitude. Also, as instability becomes more extreme, the resulting probability models are shown to tend to degeneracy, placing all their probability on potentially small portions of the sample space. These results on instability apply to large classes of models commonly used in random graphs, network analysis and machine learning contexts.

Optimization in the Stripping Process of CO2 Gas Using Mixed Amines

The aim of this work was to explore the effects of variables on the heat of regeneration, the stripping efficiency, the stripping rate, the steam generation rate, and the stripping factor. The Taguchi method was used for the experimental design. The process variables were the CO2 loading (A), the reboiler temperature (B), the solvent flow rate (C), and the concentration of the solvent (monoethanolamine (MEA) + 2-amino-2-methyl-1-propanol (AMP)) (D), which each had three levels. The stripping efficiency (E), stripping rate ( m ˙ CO 2 ), stripping factor (β), and heat of regeneration (Q) were determined by the mass and energy balances under a steady-state condition. Using signal/noise (S/N) analysis, the sequence of importance of the parameters and the optimum conditions were obtained, and the optimum operating conditions were further validated. The results showed that E was in the range of 20.98–55.69%; m ˙ CO 2 was in the range of 5.57 × 10−5–4.03 × 10−4 kg/s, and Q was in the range of 5.52–18.94 GJ/t. In addition, the S/N ratio analysis showed that the parameter sequence of importance as a whole was A > B > D > C, while the optimum conditions were A3B3C1D1, A3B3C3D2, and A3B2C2D2, for E, m ˙ CO 2 , and Q, respectively. Verifications were also performed and were found to satisfy the optimum conditions. Finally, the correlation equations that were obtained were discussed and an operating policy was discovered.

Deciphering an evolutionary sequence of merger stages in infrared-luminous starburst galaxies atz∼ 0.7

Based on optical and near-IRMagellanFIRE spectra of 25 starburst galaxies at 0.5 < z < 0.9, a recent publication showed that their attenuation properties can be explained by a single-parameter sequence of total obscurations ranging fromAV = 2 toAV = 30 toward the starburst core centers in a mixed stars and dust configuration. We investigate here the origin of this sequence for the same sample. We show that total attenuations anticorrelate with the starburst sizes in radio (3 GHz) with a significance larger than 5σand a scatter of 0.26 dex. More obscured and compact starbursts also show enhanced N2 (=[NII]/Hα) ratios and larger line velocity widths that we attribute to an increasing shock contribution toward later merger phases, driven by deeper gravitational potential wells at the coalescence. Additionally, the attenuation is also linked to the equivalent width (EW) of hydrogen recombination lines, which is sensitive to the luminosity weighted age of the relatively unobscured stellar populations. Overall, the correlations amongAV, tot, radio size, line width, N2 and EW of Balmer and Paschen lines converge toward suggesting an evolutionary sequence of merger stages: all of these quantities are likely to be good time-tracers of the merger phenomenon, and their large spanned range appears to be characteristic of the different merger phases. Half of our sample at higher obscurations have radio sizes approximately 3 times smaller than early type galaxies at the same redshift, suggesting that, in analogy with local ultraluminous infrared galaxies (ULIRGs), these cores cannot be directly forming elliptical galaxies. Finally, we detect mid-IR AGN torus for half of our sample and additional X-ray emission for 6 starbursts; intriguingly, the latter have systematically more compact sizes, suggestive of emerging AGNs toward later merger stages, possibly precursors of a later QSO phase.