Kinetic Scalar Curvature Extended f(R)f(R) Gravity

In this work we study a modified version of vacuum $f(R)$ gravity with a kinetic term which consists of the first derivatives of the Ricci scalar. We develop the general formalism of this kinetic Ricci modified $f(R)$ gravity and we emphasize on cosmological applications for a spatially flat cosmological background. By using the formalism of this theory, we investigate how it is possible to realize various cosmological scenarios. Also we demonstrate that this theoretical framework can be treated as a reconstruction method, in the context of which it is possible to realize various exotic cosmologies for ordinary Einstein-Hilbert action. Finally, we derive the scalar-tensor counterpart theory of this kinetic Ricci modified $f(R)$ gravity, and we show the mathematical equivalence of the two theories.Comment: NPB Accepte

On Casimir Pistons

In this paper we study the Casimir force for a piston configuration in $R^3$ with one dimension being slightly curved and the other two infinite. We work for two different cases with this setup. In the first, the piston is "free to move" along a transverse dimension to the curved one and in the other case the piston "moves" along the curved one. We find that the Casimir force has opposite signs in the two cases. We also use a semi-analytic method to study the Casimir energy and force. In addition we discuss some topics for the aforementioned piston configuration in $R^3$ and for possible modifications from extra dimensional manifolds.Comment: 20 pages, To be published in MPL

Experiences from porting the Contiki operating system to a popular hardware platform

In contrast to original belief, recent work has demonstrated the viability of IPv6-based Wireless Sensor Networks (WSNs). This has led to significant research and standardization efforts with outcomes such as the "IPv6 over Low-Power Wireless Personal Area Networks " (6LoWPAN) specification. The Contiki embedded operating system is an important open source, multi-platform effort to implement 6LoWPAN functionality for constrained devices. Alongside its RFC-compliant TCP/IP stack (uIP), it provides support for 6LoWPAN and many related standards. As part of our work, we have made considerable fixes and enhancements to one of Contiki's ports. In the process, we made significant optimizations and a thorough evaluation of Contiki's memory and code footprint characteristics, focusing on network-related functionality. In this paper we present our experiences from the porting process, we disclose our optimizations and demonstrate their significance. Lastly, we discuss a method of using Contiki to deploy an embedded Internet-to-6LoWPAN router. Our porting work has been made available to the community under the terms of the Contiki license

Classical multivariate Hermite coordinate interpolation on n-dimensional grids

In this work, we study the Hermite interpolation on n-dimensional non-equally spaced, rectilinear grids over a field k of characteristic zero, given the values of the function at each point of the grid and the partial derivatives up to a maximum degree. First, we prove the uniqueness of the interpolating polynomial, and we further obtain a compact closed form that uses a single summation, irrespective of the dimensionality, which is algebraically simpler than the only alternative closed form for the n-dimensional classical Hermite interpolation [1]. We provide the remainder of the interpolation in integral form; moreover, we derive the ideal of the interpolation and express the interpolation remainder using only polynomial divisions, in the case of interpolating a polynomial function. Finally, we perform illustrative numerical examples to showcase the applicability and high accuracy of the proposed interpolant, in the simple case of few points, as well as hundreds of points on 3D-grids using a spline-like interpolation, which compares favorably to state-of-the-art spline interpolation methods

Curvature-Independent Last-Iterate Convergence for Games on Riemannian Manifolds

Numerous applications in machine learning and data analytics can be formulated as equilibrium computation over Riemannian manifolds. Despite the extensive investigation of their Euclidean counterparts, the performance of Riemannian gradient-based algorithms remain opaque and poorly understood. We revisit the original scheme of Riemannian gradient descent (RGD) and analyze it under a geodesic monotonicity assumption, which includes the well-studied geodesically convex-concave min-max optimization problem as a special case. Our main contribution is to show that, despite the phenomenon of distance distortion, the RGD scheme, with a step size that is agnostic to the manifold's curvature, achieves a curvature-independent and linear last-iterate convergence rate in the geodesically strongly monotone setting. To the best of our knowledge, the possibility of curvature-independent rates and/or last-iterate convergence in the Riemannian setting has not been considered before

Using building simulation to model the drying of flooded building archetypes

With a changing climate, London is expected to experience more frequent periods of intense rainfall and tidal surges, leading to an increase in the risk of flooding. This paper describes the simulation of the drying of flooded building archetypes representative of the London building stock using the EnergyPlus-based hygrothermal tool ‘University College London-Heat and Moisture Transfer (UCL-HAMT)’ in order to determine the relative drying rates of different built forms and envelope designs. Three different internal drying scenarios, representative of conditions where no professional remediation equipment is used, are simulated. A mould model is used to predict the duration of mould growth risk following a flood on the internal surfaces of the different building types. Heating properties while keeping windows open dried dwellings fastest, while purpose built flats and buildings with insulated cavity walls were found to dry slowest