Serendipity and Tensor Product Affine Pyramid Finite Elements

Using the language of finite element exterior calculus, we define two families of $H^1$-conforming finite element spaces over pyramids with a parallelogram base. The first family has matching polynomial traces with tensor product elements on the base while the second has matching polynomial traces with serendipity elements on the base. The second family is new to the literature and provides a robust approach for linking between Lagrange elements on tetrahedra and serendipity elements on affinely-mapped cubes while preserving continuity and approximation properties. We define shape functions and degrees of freedom for each family and prove unisolvence and polynomial reproduction results.Comment: Accepted to SMAI Journal of Computational Mathematic

On Floating Breakwaters Efficiency - a 2DV Parametric Based Analysis

In long term evolution numerical models, the interactions of a floating barrier with the wave field is then deputed to some parametrized transfer functions, which mimic wave energy transmission and dissipation in the frequency domain. This thesis provide, as final result, two transfer functions (one for incident waves, one for reflected ones) for a particular class of compact shaped floating breakwaters. These functions are based on three main parameters, which have been derived on physical model results. The first one (x) is the ratio between the incoming wave frequency and an approximation of FB heave natural frequency, based on principal FB cross section dimensions. Wave steepness has been considered to be the second variable which helps in describing the amount of dissipated energy. An FB draft to water depth ratio has been identified. Available algorithms for the decomposition into incident and reflected waves of flume records are mostly Stokes-FFT based. Therefore they suffer some limitations for relatively high wave steepness (Ch. 4). Since the latter is considered as a crucial parameter, a lot of effort has been drawn in solving some conundrums of actual methods. Two algorithms are proposed. The first one (Ch. 5), based on empirical mode decomposition, did not give satisfactory results. The second one (Ch. 6) is based on linear waves superposition, but, getting rid of linear dispersion relation, detects automatically each phase celerity. The proposed algorithm appears to be effective for relatively shallow water waves, for which the phase modulation approach is more consistent than Stokes formulations. A Stokes 2nd order algorithm has also been implemented. In Ch. 7 the experimental set up is presented. A second order analysis of transmission and reflection processes is also introduced.Results are given (and discussed) in Ch. 8. Linear transmission and reflection transfer functions are derived, based on experimental data fitting. These are finally validated with irregular wave test measurements.It is found that the transmission process mainly depends on frequency (x) and on FB relative draft. The last parameter does not enter the reflection process, which basically described by x and wave steepness. In particular, steeper waves loose more energy, and are less reflected. For transmitted waves only, a significant amount of energy transfer from primary to secondary harmonics is observed

Kin and culture: clan, household and family formation in late antique Armenia

The importance of Armenia’s hereditary naxarar elite in the late antique and medieval eras has long been acknowledged by scholars, and the region’s peripheral position has made these landed aristocrats a focus of academics of the Byzantine and Sasanian Empires also. However, study of naxarar families has not been accompanied by dedicated scholarship concerning the nature of family itself as an institution within Armenia. The following thesis acts as a first step, examining how Armenian families formed, operated and what expectations were placed upon their members from the fifth century until the mid-seventh century CE. The thesis argues the family was perhaps the most significant political entity in late antique Armenian life. Membership within a naxarar clan was more significant than official service in the Aršakuni royal court or Byzantine or Sasanian imperial administration. Indeed, monarchical and imperial courts, as well as the native Christian clerical administration, even drew on these clans to support their authority. Clan power was safeguarded from imperial interference by Armenia’s geography, strategic location and probably the institution’s deep integration at less prestigious (and less visible) levels of society, with clerics, lesser nobles and perhaps non-nobles all being arranged in clans. This was reinforced by the interlacing nature of the household, which incorporated individuals of various clans and social classes through marriage, service, slavery and dayeakut‘iwn and, in doing so, better embedded the family within the social framework. Armenia is not unique in emphasising the family’s place as a critical institution, and Kin and Culture finds substantial parallels between Armenian and Iranian practice, most notably that of the Sasanians’ Parthian predecessors. However, Armenia is a particularly visible example of clan power. Analysis explicitly through the lens of family and family practices has implications for our understandings of late antique Armenian culture, society and law

An extensive English language bibliography on graph theory and its applications

Bibliography on graph theory and its application

Tensor Computation: A New Framework for High-Dimensional Problems in EDA

Many critical EDA problems suffer from the curse of dimensionality, i.e. the very fast-scaling computational burden produced by large number of parameters and/or unknown variables. This phenomenon may be caused by multiple spatial or temporal factors (e.g. 3-D field solvers discretizations and multi-rate circuit simulation), nonlinearity of devices and circuits, large number of design or optimization parameters (e.g. full-chip routing/placement and circuit sizing), or extensive process variations (e.g. variability/reliability analysis and design for manufacturability). The computational challenges generated by such high dimensional problems are generally hard to handle efficiently with traditional EDA core algorithms that are based on matrix and vector computation. This paper presents "tensor computation" as an alternative general framework for the development of efficient EDA algorithms and tools. A tensor is a high-dimensional generalization of a matrix and a vector, and is a natural choice for both storing and solving efficiently high-dimensional EDA problems. This paper gives a basic tutorial on tensors, demonstrates some recent examples of EDA applications (e.g., nonlinear circuit modeling and high-dimensional uncertainty quantification), and suggests further open EDA problems where the use of tensor computation could be of advantage.Comment: 14 figures. Accepted by IEEE Trans. CAD of Integrated Circuits and System

Autonomous Volterra algorithm for steady-state analysis of nonlinear circuits

published_or_final_versio

Multiple-Access Techniques for Communication Satellites - Analog Modulation, Frequency- Division Multiplexing, and Related Signal Processing Methods

Analog modulation, frequency-division multiplexing and signal processing for multiple-access satellite communicatio

Criminal Discovery, Scientific Evidence, and DNA

At bottom the case against Claus von Bilow was a scientific case. It would have to be refuted by scientific evidence, \u27 wrote Alan Dershowitz. The von Bilow case is not alone. Many recent notorious criminal trials involved scientific proof. For example, the prosecution offered hypnotically refreshed testimony and bite mark evidence in the Ted Bundy case. Fiber evidence proved critical in the trial of Wayne Williams for the murder of two of the thirty young black males killed in Atlanta in the late 1970s.\u27 Other illustrations include the pathology and serology testimony in the Jean Harris trial, the forensic analysis of physical evidence in the Jeffrey MacDonald Green Beret Doctor case, and the ballistics, shoeprint, and fingerprint evidence in the Night Stalker serial murder prosecution. Indeed, reliance on scientific proof has become so common that its absence in a particular case is noteworthy. A news account of the Central Park Jogger case commented that [a]mong the defense\u27s strongest points in attacking the prosecution\u27s case was the surprising absence of physical evidence-no weapons, no blood stains, no strands of hair, no pieces of skin, no foot- prints link any of the teenagers to the crimes. Even the popular press has written on the subject. The New York Times relates that the importance of expert testimony is growing as technological advances enable courts to dispose of cases by using scientific tools. Time reports that forensic science is growing so fast that even the most sophisticated researchers cannot keep up. This development raises a number of issues for the legal system. The standard for admitting novel scientific evidence, such as Deoxyribonucleic Acid (DNA), continues to vex the courts. The admissibility of laboratory reports in criminal prosecutions is unresolved. The contours of an indigent accused\u27s right to defense experts still is being explored. The expansion of the bases of expert testimony in Federal Rule of Evidence 703 (Rule 703) remains controversial. One issue that appears to be settled is the need for pretrial discovery of scientific evidence. Virtually all jurisdictions track Federal Criminal Rule 16 (Rule 16) and make reports of scientific tests discoverable. The leading texts on criminal procedure give the subject scant attention, apparently assuming that the current discovery rules are adequate. Indeed, one commentator noted that the limited litigation over Rule no doubt reflects the general recognition of the necessity to afford the defense discovery of the results and reports of medical examinations and scientific tests and of the longstanding and widespread practice of many prosecutors of making such information available on request. \u2