27 research outputs found
Mathematical Knowledge for Teaching as Decision-Making for the University Mathematician Developing Coherence in Review of Discrete Mathematics
Mathematicians teaching at the university level have a deep understanding and appreciation for the mathematics that they teach. However, they rarely receive much formal training in teaching. Thus, university mathematicians must rely on their mathematical understandings and personally developed ideas of teaching to guide their decision-making. Relatively little research exists on mathematicians’ teaching practices. The purpose of this study was to examine the mathematical knowledge for teaching (MKT) of a university mathematician teaching discrete mathematics and how he leveraged his knowledge to make decisions and develop coherence among mathematical ideas during a semester review. An enactivist perspective examining a mathematician’s decision-making in planning, enacting, and reflecting upon their lessons in this study shed light on how this mathematician practically approached his teaching duties. By enacting four distinct coherence strategies, the mathematician in this case study revealed a personal standard for mathematical storytelling which guided his decision enactment. These strategies fostered rich connections among mathematical ideas and among topics from earlier in the semester meaningfully with a single culminating topic: the chromatic polynomial. Implications of this study for research include recognized advantages of graph theoretic visualizations for the analysis of teacher decisions and coherence, benefits of dual coding for the Knowledge Quartet MKT framework, and a stance on inactivism\u27s consideration of cognitive actions. For teaching, this research supports the benefits of mathematical storytelling and review units which feature a new context to reframe previously seen topics
XV Міжнародна конференція з математичної, природничо-наукової та технологічної освіти (ICon-MaSTEd 2022) 18-20 травня 2022 року, м. Кривий Ріг, Україна
Матеріали XV Міжнародної конференції з математичної, природничо-наукової та технологічної освіти (ICon-MaSTEd 2022) 18-20 травня 2022 року, м. Кривий Ріг, Україна.Proceedings of the XV International Conference on Mathematics, Science and Technology Education (ICon-MaSTEd 2022) 18-20 May 2022, Kryvyi Rih, Ukraine
An aptamer-based sensing platform for luteinising hormone pulsatility measurement
Normal fertility in human involves highly orchestrated communication across the hypothalamic-pituitary-gonadal (HPG) axis. The pulsatile release of Luteinising Hormone (LH) is a critical element for downstream regulation of sex steroid hormone synthesis and the production of mature eggs. Changes in LH pulsatile pattern have been linked to hypothalamic dysfunction, resulting in multiple reproductive and growth disorders including Polycystic Ovary Syndrome (PCOS), Hypothalamic Amenorrhea (HA), and delayed/precocious puberty. Therefore, assessing the pulsatility of LH is important not only for academic investigation of infertility, but also for clinical decisions and monitoring of treatment. However, there is currently no clinically available tool for measuring human LH pulsatility. The immunoassay system is expensive and requires large volumes of patient blood, limiting its application for LH pulsatility monitoring.
In this thesis, I propose a novel method using aptamer-enabled sensing technology to develop a device platform to measure LH pulsatility. I first generated a novel aptamer binding molecule against LH by a nitrocellulose membrane-based in vitro selection then characterised its high affinity and specific binding properties by multiple biophysical/chemical methods. I then developed a sensitive electrochemical-based detection method using this aptamer. The principal mechanism is that structure switching upon binding is associated with the electron transfer rate changes of the MB redox label. I then customised this assay to numerous device platforms under our rapid prototyping strategy including 96 well automated platform, continuous sensing platform and chip-based multiple electrode platform. The best-performing device was found to be the AELECAP (Automated ELEctroChemical Aptamer Platform) – a 96-well plate based automatic micro-wire sensing platform capable of measuring a series of low volume luteinising hormone within a short time.
Clinical samples were evaluated using AELECAP. A series of clinical samples were measured including LH pulsatility profile of menopause female (high LH amplitude), normal female/male (normal LH amplitude) and female with hypothalamic amenorrhea (no LH pulsatility). Total patient numbers were 12 of each type, with 50 blood samples collected every 10 mins in 8 hours. Results showed that the system can distinguish LH pulsatile pattern among the cohorts and pulsatility profiles were consistent with the result measured by clinical assays.
AELECAP shows high potential as a novel approach for clinical aptamer-based sensing. AELECAP competes with current automated immunometric assays system with lower costs, lower reagent use, and a simpler setup. There is potential for this approach to be further developed as a tool for infertility research and to assist clinicians in personalised treatment with hormonal therapy.Open Acces
List, Sample, and Count
Counting plays a fundamental role in many scientific fields including chemistry, physics, mathematics, and computer science. There are two approaches for counting, the first relies on analytical tools to drive closed form expression, while the second takes advantage of the combinatorial nature of the problem to construct an algorithm whose output is the number of structures. There are many algorithmic techniques for counting, they cover the explicit approach of counting by listing to the approximate approach of counting by sampling.
This thesis looks at counting three sets of objects. First, we consider a subclass of boolean functions that are monotone. They appear naturally in great variety of contexts including combinatorics, cryptography, voting theory, and game theory. Next, we consider permutations of n pairs of numbers, called Skolem sequences. These sequences are employed in several areas including construction of Steiner triple systems, binary sequences with controllable complexity, interference resistant codes, and graph labeling. Finally, we consider a variation of the n-queens problem, called the queens of the night. This constraint satisfaction problem is not just a recreational puzzle, but rather it is useful in designing conflict free access in parallel systems. In each case we verify previously known values and provide the next unknown exact value(s) in the counting sequence. Furthermore, we approximate the count for the next unknown values in the sequence by employing a sampling procedure
2016-2017 Boise State University Undergraduate Catalog
This catalog is primarily for students, but can serve many audiences. In this catalog you will find an overview of Boise State University and information on admission, registration, grades, tuition and fees, financial aid, housing, student services, and other important policies and procedures. However, most of this catalog is devoted to describing the various programs and courses offered at Boise State
Real topological string theory
The Thesis comprises work done at SISSA (Trieste) and UAM (Madrid) under supervision of A. Uranga during academic years 2013-2016 and published in the following works.
In the first one we describe the type IIA physical realization of the unoriented topological string introduced by Walcher, describe its M-theory lift, and show that it allows to compute the open and unoriented topological amplitude in terms of one-loop diagram of BPS M2-brane states. This confirms and allows to generalize the conjectured BPS integer expansion of the topological amplitude. The M-theory lift of the orientifold is freely acting on the M-theory circle, so that integer multiplicities are a weighted version
of the (equivariant subsector of the) original closed oriented Gopakumar-Vafa invariants.
The M-theory lift also provides new perspective on the topological tadpole cancellation conditions.
We finally comment on the M-theory version of other unoriented topological strings,
and clarify certain misidentifications in earlier discussions in the literature.
In the second
we consider the real topological string on certain non-compact toric Calabi-Yau three-folds X, in its physical realization describing an orientifold of type IIA on X with an O4-plane and a single D4-brane stuck on top. The orientifold can be regarded as a new kind of surface operator on the gauge theory with 8 supercharges arising from the singular geometry. We use the M-theory lift of this system to compute the real Gopakumar-Vafa invariants (describing wrapped M2-brane BPS states) for diverse geometries. We show that the real topological string amplitudes pick up certain signs across flop transitions, in a well-defined pattern consistent with continuity of the real BPS invariants. We further give some preliminary proposals of an intrinsically gauge theoretical description of the effect of the surface operator in the gauge theory partition function.
In the third, which is in preparation, we focus
on target space physics related to real topological strings, namely
we discuss the physical superstring correlation functions in type I theory (or equivalently type II with orientifold)
that compute real topological string amplitudes.
As it turns out that direct computation presents a problem,
which also affects the standard case,
we consider the correlator corresponding to holomorphic derivative
of the real topological amplitude , at fixed worldsheet Euler character .
This corresponds in the low-energy effective action to N=2 Weyl tensor,
appropriately reduced to the orientifold invariant part, and raised to power .
In this case, we are able to perform computation, and show that appropriate insertions in the physical string correlator
give precisely the holomorphic derivative of topological amplitude.
Finally, we apply this method to the standard closed oriented case as well,
and prove a similar statement for the topological amplitude ,
which solves a small issue affecting that computation