Curse of dimensionality reduction in max-plus based approximation methods: theoretical estimates and improved pruning algorithms

Max-plus based methods have been recently developed to approximate the value function of possibly high dimensional optimal control problems. A critical step of these methods consists in approximating a function by a supremum of a small number of functions (max-plus "basis functions") taken from a prescribed dictionary. We study several variants of this approximation problem, which we show to be continuous versions of the facility location and $k$-center combinatorial optimization problems, in which the connection costs arise from a Bregman distance. We give theoretical error estimates, quantifying the number of basis functions needed to reach a prescribed accuracy. We derive from our approach a refinement of the curse of dimensionality free method introduced previously by McEneaney, with a higher accuracy for a comparable computational cost.Comment: 8pages 5 figure

Interest, Instructional Strategies, and the Creation of Group Space

Research on small-group work and on whole class discussions has shown specific benefits for student learning. At the same time, research on interest stresses the generation of situational interest when particular learning conditions are met. This qualitative study explores whether the type of instructional strategy (small group vs. whole class discussion) influences triggering of situational interest about theoretical and practice-oriented pedagogical topics among preservice science teachers (N = 44). Triggering of interest was identified by participation rate, degree of comfort during interactions, and quality of arguments. Results show that whole class discussions of theoretical topics shifted towards practical teaching issues, while small groups sustained the theoretical nature of a topic. Both interaction patterns imply triggering of situational interest. But the small group interaction patterns indicate the collective construction of a “triple problem-solving space”, in which content, social/relational, and interest were balanced from the start; the whole class discussions needed first to renegotiate the content

A reduced complexity numerical method for optimal gate synthesis

Although quantum computers have the potential to efficiently solve certain problems considered difficult by known classical approaches, the design of a quantum circuit remains computationally difficult. It is known that the optimal gate design problem is equivalent to the solution of an associated optimal control problem, the solution to which is also computationally intensive. Hence, in this article, we introduce the application of a class of numerical methods (termed the max-plus curse of dimensionality free techniques) that determine the optimal control thereby synthesizing the desired unitary gate. The application of this technique to quantum systems has a growth in complexity that depends on the cardinality of the control set approximation rather than the much larger growth with respect to spatial dimensions in approaches based on gridding of the space, used in previous literature. This technique is demonstrated by obtaining an approximate solution for the gate synthesis on $SU(4)$- a problem that is computationally intractable by grid based approaches.Comment: 8 pages, 4 figure

Characterization of Exosomes and Their Role in Cellular Migration in Chemosensitive and Chemoresistant Ovarian Cancer Cells

Chemotherapy-resistant cells that remain after primary cancer treatment lead to recurrence and metastasis, resulting in a poor prognosis for patients. Chemoresistant cells were created by our collaborators using the human ovarian cancer cell line, OVCAR8, by selection of cells that survived serial culture with cisplatin, a platinum-based chemotherapeutic. The cisplatin-resistant cells (OVCAR8R) demonstrate a morphology unique from the original cisplatin-sensitive cells (OVCAR8) which could correlate with their difference in aggressiveness. My research goal is to isolate and characterize exosomes from the OVCAR8 and OVCAR8Rlines. Exosomes are small vesicles secreted from cells and contribute to the tumor microenvironment(TME). It has been found that exosomes secreted from cancerous cells hold the ability to influence neighboring cells and increase their metastatic ability. Exosomes contain a unique signature of packaged proteins and RNA that may be responsible for their role in cancer progression. The goal of these experiments is to determine the differences between the exosomal cargo derived from chemosensitive and chemoresistant ovarian cancer cells as well as the effects that exosomes isolated from each line have on promoting cellular migration. Exosome isolation and characterization could be employed as a noninvasive diagnostic tool to identify early-stage ovarian cancer

Changing Attitudes toward Irish Canadians: The Impact of the 1847 Famine Influx in the Province of Canada

Throughout the nineteenth century, Canada regularly received Irish immigrants who became a tolerated and important part of Canadian society. However, between 1845 and 1852, Ireland endured a dreadful famine which saw more than two million Irish paupers emigrate, with their destinations varying across the world. A large portion of Irish famine immigrants travelled to the comparatively empty British North American colony in Canada, passing almost entirely through Quebec. Canadians at first welcomed the idea of large numbers of immigrants to help expand the western frontier, but with a massive exodus of Irish paupers fleeing Ireland in 1847, what arrived in the ports of Quebec ended up terrifying the people of Canada. The deplorable condition of the immigrants strained the Canadian social institutions beyond their means, and shifted the view of Irish Canadians into a negative light. Although quarantined at Grosse Isle, and various other makeshift quarantine stations throughout the St. Lawrence River valley, the unexpectedly diseaseridden immigrants caused typhus, cholera, and dysentery to run rampant wherever they arrived, claiming the lives of thousands of Canadians, as well as many of their own. Societal conditions set in place by previous generations of Irish immigrants to Canada, which allowed them to be a welcomed part of Canadian communities, were broken by this new wave of Irish exiles, and caused public opinion to turn against the Irish immigrants. The betrayal of social norms caused a violent Protestant-Canadian nativist response that lasted for decades after their arrival

The Partition of Ireland: Anglo-Irish Relations as Reflected in a Political Idea

After years of postponement, and at the time of writing, Britain is set to leave the European Union on December 31, 2020, after complications mainly due to the new-age “Irish Question:\u27\u27 how to handle the border between Northern Ireland and the Republic of Ireland in the south