The asymmetric skew divergence smooths one of the distributions by mixing it, to a degree determined by the parameter $\lambda$, with the other distribution. Such divergence is an approximation of the KL divergence that does not require the target distribution to be absolutely continuous with respect to the source distribution. In this paper, an information geometric generalization of the skew divergence called the $\alpha$-geodesical skew divergence is proposed, and its properties are studied.

In Escherichia coli, DNA replication termination is orchestrated by two clusters of Ter sites forming a DNA replication fork trap when bound by Tus proteins. The formation of a ‘locked’ Tus-Ter complex is essential for halting incoming DNA replication forks. However, the absence of replication fork arrest at some Ter sites raised questions about their significance. In this study, we examined the genome-wide distribution of Tus and found that only the six innermost Ter sites (TerA-E and G) were significantly bound by Tus. We also found that a single ectopic insertion of TerB in its non-permissive orientation could not be achieved, advocating against a need for ‘back-up’ Ter sites. Finally, examination of the genomes of a variety of Enterobacterales revealed a new replication fork trap architecture mostly found outside the Enterobacteriaceae family. Taken together, our data enabled the delineation of a narrow ancestral Tus-dependent DNA replication fork trap consisting of only two Ter sites.

Clock Network Design (CDN) is a critical step while designing any Integrated-Circuits (ICs). It holds vital importance in the performance of entire circuit. Due to continuous scaling, 3D ICs stacked with TSV are gaining importance, with an objective to continue with the Moore's law. Through-Silicon-Via (TSV) provides the vertical interconnection between two die, which allows the electrical signal to flow through it. 3D ICs has many advantages over conventional 2D planar ICs like reduced power, area, cost, wire-length etc. The proposed work is mainly focused on power reduction and obstacle avoidance for 3D ICs. Various techniques have already been introduced for minimizing clock power within specified clock constraints of the 3D CND network. Proposed 3D Clock Tree Synthesis (CTS) is a combination of various algorithms with an objective to meet reduction in power as well as avoidance of obstacle or blockages while routing the clock signal from one sink to other sink. These blockages like RAM, ROM, PLL etc. are fixed during the placement process. The work is carried out mainly in three steps- first is Generation of 3D Clock tree avoiding the blockages, then Buffering and Embedding and finally validating the results by SPICE simulation. The experimental result shows that our CTS approach results in significant 9% reduction in power as compare to the existing work.

Since general relativity (GR) has already established that matter can simultaneously have two different values of mass depending on its context, we argue that the missing mass attributed to non-baryonic dark matter (DM) actually obtains because there are two different values of mass for the baryonic matter involved. The globally obtained "dynamical mass'' of baryonic matter can be understood as a small perturbation to a background spacetime metric even though it's much larger than the locally obtained "proper mass". Having successfully fit the SCP Union2.1 SN Ia data without accelerating expansion or a cosmological constant, we employ the same ansatz to compute dynamical mass from proper mass and explain galactic rotation curves (THINGS data), the mass profiles of X-ray clusters (ROSAT and ASCA data) and the angular power spectrum of the cosmic microwave background (Planck 2015 data) without DM. We compare our fits to modified Newtonian dynamics (MOND), metric skew-tensor gravity (MSTG) and scalar-tensor-vector gravity (STVG) for each data set, respectively, since these modified gravity programs are known to generate good fits to these data. Overall, we find our fits to be comparable to those of MOND, MSTG and STVG. While this favorable comparison does not establish the validity of our proposition, it does provide confidence in using the fits to pursue an underlying action. Indeed, the functional form of our ansatz reveals an interesting structure in these fits.

A transform approach based on a variable initial time (VIT) formulation is developed for discrete-time signals and linear time-varying discrete-time systems or digital filters. The VIT transform is a formal power series in z^(-1) which converts functions given by linear time-varying difference equations into left polynomial fractions with variable coefficients, and with initial conditions incorporated into the framework. It is shown that the transform satisfies a number of properties that are analogous to those of the ordinary z-transform, and that it is possible to do scaling of z^(- i) by time functions which results in left-fraction forms for the transform of a large class of functions including sinusoids with general time-varying amplitudes and frequencies. Using the extended right Euclidean algorithm in a skew polynomial ring with time-varying coefficients, it is shown that a sum of left polynomial fractions can be written as a single fraction, which results in linear time-varying recursions for the inverse transform of the combined fraction. The extraction of a first-order term from a given polynomial fraction is carried out in terms of the evaluation of z^(i) at time functions. In the application to linear time-varying systems, it is proved that the VIT transform of the system output is equal to the product of the VIT transform of the input and the VIT transform of the unit-pulse response function. For systems given by a time-varying moving average or an autoregressive model, the transform framework is used to determine the steady-state output response resulting from various signal inputs such as the step and cosine functions.

Motivated by a common Mathematical Finance topic, this paper surveys several results concerning windings of 2-dimensional processes, including planar Brownian motion, complex-valued Ornstein-Uhlenbeck processes and planar stable processes. In particular, we present Spitzer's asymptotic Theorem for each case. We also relate this study to the pricing of Asian options.

This paper presents an approach to the two-dimensional analysis of elastic isotropic deep beams using the finite difference method (FDM). Deep beams are subjected to in-plane loading and present a shear span to height ratio of less than 2.50; consequently, Euler-Bernoulli beam theory and Timoshenko beam theory do not apply. Deep beams analysis is generally conducted using numerical methods such as the finite element method and to a lesser extent the FDM; the strut-and-tie model and the stress field method are also widely utilized. Analytical approaches usually make use of the Airy stress function, where stresses are formulated in terms of the stress function; however, the exact solution of this function satisfying all of the boundary conditions can hardly be found, even for simple cases. In this paper, deep beams were analyzed using the FDM. The FDM is an approximate method for solving problems described with differential equations. The FDM does not involve solving differential equations; equations are formulated with values at selected nodes of the structure. Therefore, the deep beam was discretized with a two-dimensional grid, and additional nodes were introduced at the boundaries and at positions of discontinuity (openings, brutal change of material properties, non-uniform grid spacing), the number of additional nodes corresponding to the number of boundary conditions at the node of interest. The introduction of additional nodes allowed us to apply the governing equations at boundary nodes and satisfy the boundary and continuity conditions. An Airy stress function approach and a displacement potential function approach were considered in this study whereby strong formulations of equations (equilibrium, kinematic, and constitutive) were set. Stress and stability analyses were carried out with this model; furthermore, deep beams of varying stiffness, layered beams, and beams having openings were analyzed. For slender beams, the results obtained with the Airy stress function approach showed good agreement with those of the Euler-Bernoulli beam theory, and for deep beams, the shapes of stress distributions were in good agreement with a proper understanding of the behavior of structures. On the other hand, the displacement potential function approach delivered unsatisfactory results, probably due to the use of an inefficient equation solver; a more powerful tool will be needed in future research for this purpose.

This paper presents an approach to the Kirchhoff-Love plate theory (KLPT) using the finite difference method (FDM). The KLPT covers the case of small deflections, and shear deformations are not considered. The FDM is an approximate method for solving problems described with differential equations. The FDM does not involve solving differential equations; equations are formulated with values at selected points of the structure. Generally in the case of KLPT, the finite difference approximations are derived based on the fourth-order polynomial hypothesis (FOPH) and second-order polynomial hypothesis (SOPH) for the deflection surface. The FOPH is made for the fourth and third derivative of the deflection surface while the SOPH is made for its second and first derivative; this leads to a 13-point stencil for the governing equation. In addition, the boundary conditions and not the governing equations are applied at the plate edges. In this paper, the FOPH was made for all of the derivatives of the deflection surface; this led to a 25-point stencil for the governing equation. Furthermore, additional nodes were introduced at plate edges and at positions of discontinuity (continuous supports/hinges, incorporated beams, stiffeners, brutal change of stiffness, etc.), the number of additional nodes corresponding to the number of boundary conditions at the node of interest. The introduction of additional nodes allowed us to apply the governing equations at the plate edges and to satisfy the boundary and continuity conditions. First-order analysis, second-order analysis, buckling analysis, and vibration analysis of plates were conducted with this model. Moreover, plates of varying thickness and plates with stiffeners were analyzed. Finally, a direct time integration method (DTIM) was presented. The FDM-based DTIM enabled the analysis of forced vibration of structures, with damping taken into account. In first-order, second-order, buckling, and vibration analyses of rectangular plates, the results obtained in this paper were in good agreement with those of well-established methods, and the accuracy was increased through a grid refinement.