Cohen-Macaulay admissible clutters

There is a one-to-one correspondence between square-free monomial ideals and clutters, which are also known as simple hypergraphs. It was conjectured that unmixed admissible clutters are Cohen-Macaulay. We prove the conjecture for uniform admissible clutters of heights 2 and 3. For admissible clutters of greater heights, we give a family of examples to show that the conjecture may fail. When the height is 4, we give an additional condition under which unmixed admissible clutters are Cohen-Macaulay.Comment: 13 pages, final version to appear in J. Comm. Al

Efficient and accurate calculation of exact exchange and RPA correlation energies in the Adiabatic-Connection Fluctuation-Dissipation theory

Recently there has been a renewed interest in the calculation of exact-exchange and RPA correlation energies for realistic systems. These quantities are main ingredients of the so-called EXX/RPA+ scheme which has been shown to be a promising alternative approach to the standard LDA/GGA DFT for weakly bound systems where LDA and GGA perform poorly. In this paper, we present an efficient approach to compute the RPA correlation energy in the framework of the Adiabatic-Connection Fluctuation-Dissipation formalism. The method is based on the calculation of a relatively small number of eigenmodes of RPA dielectric matrix, efficiently computed by iterative density response calculations in the framework of Density Functional Perturbation Theory. We will also discuss a careful treatment of the integrable divergence in the exact-exchange energy calculation which alleviates the problem of its slow convergence with respect to Brillouin zone sampling. As an illustration of the method, we show the results of applications to bulk Si, Be dimer and atomic systems.Comment: 12 pages, 6 figures. To appear in Phys. Rev.

Instrumentation and robotic image processing using top-down model control

A top-down image processing scheme is described. A three-dimensional model of a robotic working environment, with robot manipulators, workpieces, cameras, and on-the-scene visual enhancements is employed to control and direct the image processing, so that rapid, robust algorithms act in an efficient manner to continually update the model. Only the model parameters are communicated, so that savings in bandwidth are achieved. This image compression by modeling is especially important for control of space telerobotics. The background for this scheme lies in an hypothesis of human vision put forward by the senior author and colleagues almost 20 years ago - the Scanpath Theory. Evidence was obtained that repetitive sequences of saccadic eye movements, the scanpath, acted as the checking phase of visual pattern recognition. Further evidence was obtained that the scanpaths were apparently generated by a cognitive model and not directly by the visual image. This top-down theory of human vision was generalized in some sense to the frame in artificial intelligence. Another source of the concept arose from bioengineering instrumentation for measuring the pupil and eye movements with infrared video cameras and special-purpose hardware

Symbolic Powers of Monomial Ideals

We investigate symbolic and regular powers of monomial ideals. For a square-free monomial ideal $I$ in $k[x_0, \ldots, x_n]$ we show $I^{t(m+e-1)-e+r)}$ is a subset of $M^{(t-1)(e-1)+r-1}(I^{(m)})^t$ for all positive integers $m$, $t$ and $r$, where $e$ is the big-height of $I$ and $M = (x_0, \ldots, x_n)$. This captures two conjectures ($r=1$ and $r=e$): one of Harbourne-Huneke and one of Bocci-Cooper-Harbourne. We also introduce the symbolic polyhedron of a monomial ideal and use this to explore symbolic powers of non-square-free monomial ideals.Comment: 15 pages. Fixed typ

Positive Psychology: The Use of the Framework of Achievement Bests to Facilitate Personal Flourishing

The Framework of Achievement Bests, which was recently published in Educational Psychology Review, makes a theoretical contribution to the study of positive psychology. The Framework of Achievement Bests provides an explanatory account of a person’s optimal best practice from his/her actual best. Another aspect emphasizes on the saliency of the psychological process of optimization, which is central to our understanding of person’s optimal functioning in a subject matter. Achieving an exceptional level of best practice (e.g. achieving excellent grades in mathematics) does not exist in isolation, but rather depends on the potent impact of optimization. This chapter, theoretical in nature, focuses on an in‐depth examination of the expansion of the Framework of Achievement Bests. Our discussion of the Framework of Achievement Bests, reflecting a methodical conceptualization, is benchmarked against another notable theory for understanding, namely: Martin Seligman’s PERMA theory. For example, for consideration, one aspect that we examine entails the extent to which the Framework of Achievement Bests could explain the optimization of each of the five components of PERMA (e.g. how does the Framework of Achievement Bests explain the optimization of engagement?)

Achievement Bests Framework, Cognitive Load Theory, and Equation Solving

The Framework of Achievement Bests provides an explanatory account into the process of optimization, which details how a person reaches from one level of best practice to that of a more optimal level. This framework, we contend, is significant in its explanatory account of personal growth, an internal state of flourishing, and the achievement of exceptionality. This chapter conceptualizes the applicability of the Framework of Achievement Bests to the context of instructional designs. We highlight the tenet of element interactivity, which is integral to the design of a particular mathematics instruction and its potential effectiveness. Element interactivity entails the interaction between elements within a learning material. Owing to the limited working memory capacity, an instruction that incurs high level of element interactivity would impose high cognitive load leading to reduced learning. Our conceptualization postulates the possible alignment between suboptimal and optimal instructional designs with realistic and optimal levels of best practice, respectively. This postulation (e.g., suboptimal instructional design → realistic level of best practice), which recognizes the importance of cognitive load imposition, is significant from a practical point of view. By focusing on instructional designs, it is possible to assist individuals to achieve optimal best practice in learning

Spacecraft Reed-Solomon downlink module

Apparatus and method for providing downlink frames to be transmitted from a spacecraft to a ground station. Each downlink frame includes a synchronization pattern and a transfer frame. The apparatus may comprise a monolithic Reed-Solomon downlink (RSDL) encoding chip coupled to data buffers for storing transfer frames. The RSKL chip includes a timing device, a bus interface, a timing and control unit, a synchronization pattern unit, and a Reed-Solomon encoding unit, and a bus arbiter

Rapid Organocatalytic Formation of Carbon Monoxide: Application towards Carbonylative Cross Couplings

Herein, the first organocatalytic method for the transformation of non‐derivatized formic acid into carbon monoxide (CO) is introduced. Formylpyrrolidine (FPyr) and trichlorotriazine (TCT), which is a cost‐efficient commodity chemical, enable this decarbonylation. Utilization of dimethylformamide (DMF) as solvent and catalyst even allows for a rapid CO generation at room temperature. Application towards four different carbonylative cross coupling protocols demonstrates the high synthetic utility and versatility of the new approach. Remarkably, this also comprehends a carbonylative Sonogashira reaction at room temperature employing intrinsically difficult electron‐deficient aryl iodides. Commercial 13C‐enriched formic acid facilitates the production of radiolabeled compounds as exemplified by the pharmaceutical Moclobemide. Finally, comparative experiments verified that the present method is highly superior to other protocols for the activation of carboxylic acids