Nonnegative Discrete Symbols and Their Probabilistic Interpretation

We review the quantizer–dequantizer formalism of constructing symbols of the density operators and quantum observables, such as Wigner functions and tomographic-probability distributions. We present a tutorial consideration of the technique of obtaining minimal sets of dequantizers (quorum) related to the observable eigenvalues for one-qubit states. We discuss a generalization of the quantizer–dequantizer scheme on the example of spin-1/2 states. We consider the possibilities of extending the results to two-qubit systems using spin tomograms of the state density matrix.     

Electrons in a Nonideal Partially Degenerated Plasma with Multiple Ionization

We consider peculiarities in the behavior of free electrons in an extremely-dense hot plasma with multiple ionization and partial degeneration. In different ways, we exhibit the strong Coulomb coupling of electrons and ions in the behavior of low- and high-kinetic-energy electrons. As a result, a necessity arises to consider, along with classical fast Debye electrons, their complementary cellular group of electrons constantly interacting with central ions of cells. We discuss the distribution of free electrons between the two groups, along with the role of two-group effects, of a not point character of ions in electron-transfer processes, and the consequences of the X-ray emitting X-pinch hot spot for the plasma. The existence of the physical limits for X-pinch plasma compression is among those consequences.     

Mean Field Analysis of Large-Scale Interacting Populations of Stochastic Conductance-Based Spiking Neurons Using the Klimontovich Method

We investigate the dynamics of large-scale interacting neural populations, composed of conductance based, spiking model neurons with modifiable synaptic connection strengths, which are possibly also subjected to external noisy currents. The network dynamics is controlled by a set of neural population probability distributions (PPD) which are constructed along the same lines as in the Klimontovich approach to the kinetic theory of plasmas. An exact non-closed, nonlinear, system of integro-partial differential equations is derived for the PPDs. As is customary, a closing procedure leads to a mean field limit. The equations we have obtained are of the same type as those which have been recently derived using rigorous techniques of probability theory. The numerical solutions of these so called McKean–Vlasov–Fokker–Planck equations, which are only valid in the limit of infinite size networks, actually shows that the statistical measures as obtained from PPDs are in good agreement with those obtained through direct integration of the stochastic dynamical system for large but finite size networks. Although numerical solutions have been obtained for networks of Fitzhugh–Nagumo model neurons, which are often used to approximate Hodgkin–Huxley model neurons, the theory can be readily applied to networks of general conductance-based model neurons of arbitrary dimension.     

Power Spectrum of a Noisy System Close to a Heteroclinic Orbit

We consider a two-dimensional dynamical system that possesses a heteroclinic orbit connecting four saddle points. This system is not able to show self-sustained oscillations on its own. If endowed with white Gaussian noise it displays stochastic oscillations, the frequency and quality factor of which are controlled by the noise intensity. This stochastic oscillation of a nonlinear system with noise is conveniently characterized by the power spectrum of suitable observables. In this paper we explore different analytical and semianalytical ways to compute such power spectra. Besides a number of explicit expressions for the power spectrum, we find scaling relations for the frequency, spectral width, and quality factor of the stochastic heteroclinic oscillator in the limit of weak noise. In particular, the quality factor shows a slow logarithmic increase with decreasing noise of the form \(Q\sim [\ln (1/D)]^2\). Our results are compared to numerical simulations of the respective Langevin equations.     

Measuring and Modeling the U.S. Regulatory Ecosystem

Over the last 23 years, the U.S. Securities and Exchange Commission has required over 34,000 companies to file over 165,000 annual reports. These reports, the so-called “Form 10-Ks,” contain a characterization of a company’s financial performance and its risks, including the regulatory environment in which a company operates. In this paper, we analyze over 4.5 million references to U.S. Federal Acts and Agencies contained within these reports to measure the regulatory ecosystem, in which companies are organisms inhabiting a regulatory environment. While individuals across the political, economic, and academic world frequently refer to trends in this regulatory ecosystem, far less attention has been paid to supporting such claims with large-scale, longitudinal data. In this paper, in addition to positing a model of regulatory ecosystems, we document an increase in the regulatory energy per filing, i.e., a warming “temperature.” We also find that the diversity of the regulatory ecosystem has been increasing over the past two decades. These findings support the claim that regulatory activity and complexity are increasing, and this framework contributes an important step towards improving academic and policy discussions around legal complexity and regulation.     

A Theory of Hydrodynamic Turbulence Based on Non-equilibrium Statistical Mechanics

In earlier papers, we have studied the turbulent flow exponents \(\zeta _p\), where \(\langle |\Delta \mathbf{v}|^p\rangle \sim \ell ^{\zeta _p}\) and \(\Delta \mathbf{v}\) is the contribution to the fluid velocity at small scale \(\ell \). Using ideas of non-equilibrium statistical mechanics we have found

$$\begin{aligned} \zeta _p={p\over 3}-{1\over \ln \kappa }\ln \Gamma \left( {p\over 3}+1\right) \end{aligned}$$

where \(1/\ln \kappa \) is experimentally \(\approx \,0.32\,\pm \,0.01\). The purpose of the present note is to propose a somewhat more physical derivation of the formula for \(\zeta _p\). We also present an estimate \(\approx \,100\) for the Reynolds number at the onset of turbulence.

     

Theoretical analysis of somatostatin receptor 5 with antagonists and agonists for the treatment of neuroendocrine tumors

We report on SSTR5 receptor modeling and its interaction with reported antagonist and agonist molecules. Modeling of the SSTR5 receptor was carried out using multiple templates with the aim of improving the precision of the generated models. The selective SSTR5 antagonists, agonists and native somatostatin SRIF-14 were employed to propose the binding site of SSTR5 and to identify the critical residues involved in the interaction of the receptor with other molecules. Residues Q2.63, D3.32, Q3.36, C186, Y7.34 and Y7.42 were found to be highly significant for their strong interaction with the receptor. SSTR5 antagonists were utilized to perform a 3D quantitative structure–activity relationship study. A comparative molecular field analysis (CoMFA) was conducted using two different alignment schemes, namely the ligand-based and receptor-based alignment methods. The best statistical results were obtained for ligand-based (\({q}^{2} = 0.454\), \({r}^{2}\) = 0.988, noc = 4) and receptor-guided methods (docked mode 1:\({q}^{2} = 0.530\), \({r}^{2} = 0.916\), noc = 5), (docked mode 2:\({q}^{2}\) = 0.555, \({r}^{2 }= 0.957\), noc = 5). Based on CoMFA contour maps, an electropositive substitution at \(\hbox {R}^{1}\), \(\hbox {R}^{2}\) and \(\hbox {R}^{4}\) position and bulky group at \(\hbox {R}^{4}\) position are important in enhancing molecular activity.     

A study of the Immune Epitope Database for some fungi species using network topological indices

In the last years, the encryption of system structure information with different network topological indices has been a very active field of research. In the present study, we assembled for the first time a complex network using data obtained from the Immune Epitope Database for fungi species, and we then considered the general topology, the node degree distribution, and the local structure of this network. We also calculated eight node centrality measures for the observed network and compared it with three theoretical models. In view of the results obtained, we may expect that the present approach can become a valuable tool to explore the complexity of this database, as well as for the storage, manipulation, comparison, and retrieval of information contained therein.     

Modelling of hundreds of wavelength long,highly resonant, 3D subwavelength patterned scattering structures

In this paper, we study the performances of the Dipole Discrete Approximation method for modelling the reflectivity of a highly resonant, 3D subwavelength patterned structure extending over tens of thousands wavelength square. The computation time of the whole reflectivity spectrum (80 wavelengths) was about 3 h on a computer and requires about 1.5 GB in memory. These performances make the DDA an unique numerical tool for modelling the scattering by large 3D structures supporting long-range interactions.     

A 3D-CMOS compatible silicon photo-sensor with a large vertical photosensitive area

This paper introduces design and simulation of a three-dimensional complementary metal–oxide–semiconductor CMOS compatible photo-sensor based on a silicon substrate. In the structure of photo-sensor, a vertical n+/p junction as a photosensitive area is formed on one side of a U-groove, and perpendicular to a lateral n-i-p structure on top-side of the silicon surface. This configuration enables a direct butt-coupling of a fiber-optic to the photosensitive area, which is a privilege for many remote monitoring applications. The device analysis is carried out by a two-dimensional simulation using SILVACO TCAD simulator. The thickness of the photo-sensitive area is investigated by considering the figures of merit for the two different thicknesses of 30 and 50 µm. The simulated results (according to the parameters defined for the Si substrate) show a very low dark current of 70 and 100 (fA/μm) for the 30 and 50 µm thicknesses, respectively. In addition, a high photo-current to dark current ratio of ~3000 is achieved under an intensity of 2 mW/cm² at 633 nm wavelength, according to the wavelength of red He–Ne laser. The sensor demonstrates a responsivity of 0.33 A/W corresponding to 65% external quantum efficiency and a ?3 dB frequency response of 0.2 GHz under a small signal of 2 mW/cm² at 633 nm wavelength for 10 V reverse bias.