scholarly journals A relation between porosity convergence and pretangent spaces

2021 ◽  
Vol 110 (124) ◽  
pp. 41-46
Author(s):  
Maya Altınok ◽  
Mehmet Küçükaslan
Keyword(s):  
Mathematical Analysis ◽  
The Other

The convergence of porosity is one of the relatively new concept in Mathematical analysis. It is completely structurally different from the other convergence concepts. Here we give a relation between porosity convergence and pretangent spaces.

scholarly journals Adversity magnifies the importance of social information in decision-making

2016 ◽  
Author(s):  
Alfonso Perez-Escudero ◽  
Gonzalo G de Polavieja
Keyword(s):  
Decision Making ◽  
Mathematical Analysis ◽  
Social Information ◽  
The Other ◽  
Adverse Conditions ◽  
Social Species ◽  
Life Threatening ◽  
Low Levels ◽  
The Impact ◽  
Different Levels

In adverse conditions, individuals follow the majority more strongly. This phenomenon is very general across social species, but explanations have been particular to the species and context, including antipredatory responses, deflection of responsibility, or increase in uncertainty. Here we show that the impact of social information in realistic decision-making typically increases with adversity, giving more weight to the choices of the majority. The conditions for this social magnification are very natural, but were absent in previous decision-making models due to extra assumptionsthat simplified mathematical analysis, like very low levels of stochasticity or the assumption that when one option is good the other one must be bad. We show that decision-making in collectives can quantitatively explain the different impact of social influence with different levels of adversity for different species and contexts, including life-threatening situations in fish and simple experiments in humans.

MODELING DISPROPORTIONAL EFFECTS OF EDUCATING INFECTED KENYAN YOUTH ON HIV/AIDS

2020 ◽  
Vol 28 (02) ◽  
pp. 311-349
Author(s):  
MARILYN RONOH ◽  
FARAIMUNASHE CHIROVE ◽  
JOSEPHINE WAIRIMU ◽  
WANDERA OGANA
Keyword(s):  
Network Analysis ◽  
Adolescent Girls ◽  
Young Women ◽  
Mathematical Analysis ◽  
Deterministic Model ◽  
The Other ◽  
Adolescent Boys ◽  
Comprehensive Knowledge ◽  
Age And Sex ◽  
Hiv Aids

We formulate an age and sex-structured deterministic model to assess the effect of increasing comprehensive knowledge of HIV/AIDS disease in the infected Adolescent Girls and Young Women (AGYW) and, Adolescent Boys and Young Men (ABYM) populations in Kenya. Mathematical analysis of infection through sub-network analysis was carried out to trace various infection routes and the veracity of various transmission routes as well as the associated probabilities. Using HIV data in Kenya on our model, disproportional effects were observed when dispensation of comprehensive knowledge of HIV/AIDS was preferred in one population over the other. Effective dispensation of comprehensive knowledge of HIV/AIDS in both the infected AGYW and ABYM populations significantly slows down the infection spread but may not eradicate it.

Coupon Bond Duration and Convexity Analysis

2021 ◽  
pp. 316-345
Author(s):  
Vedran Kojić ◽  
Margareta Gardijan Kedžo ◽  
Zrinka Lukač
Keyword(s):  
Mathematical Analysis ◽  
Empirical Data ◽  
Differential Calculus ◽  
Risk Measures ◽  
The Other ◽  
Complete Analysis ◽  
Elementary Algebra ◽  
Convexity Properties ◽  
Convexity Analysis ◽  
Coupon Bond

Coupon bond duration and convexity are the primary risk measures for bonds. Given their importance, there is abundant literature covering their analysis, with calculus being used as the dominant approach. On the other hand, some authors have treated coupon bond duration and convexity without the use of differential calculus. However, none of them provided a complete analysis of bond duration and convexity properties. Therefore, this chapter fills in the gap. Since the application of calculus may be complicated or even inappropriate if the functions in question are not differentiable (as indeed is the case with the bond duration and convexity functions), in this chapter the properties of bond duration and convexity functions by using elementary algebra only are proved. This provides an easier way of approaching this problem, thus making it accessible to a wider audience not necessarily familiar with tools of mathematical analysis. Finally, the properties of these functions are illustrated by using empirical data on coupon bonds.

scholarly journals Two conceptions of fraction equivalence

2021 ◽  
Author(s):  
Pernille Ladegaard Pedersen ◽  
Mette Bjerre
Keyword(s):  
Conceptual Understanding ◽  
Mathematical Analysis ◽  
Past Research ◽  
Rational Numbers ◽  
The Other ◽  
Unified Framework ◽  
Future Directions ◽  
Equivalent Fractions

AbstractIn this study, we present a mathematical analysis distinguishing two conceptions of equivalence: proportional equivalence and unit equivalence. These two conceptions have distinct meanings in relation to equivalent fractions: one is grounded in proportionality, while the other is grounded in equal wholes. We argue that (a) the distinction of equivalence gives a unified framework of equal fractions that has not previously been described in the literature; (b) a conceptual understanding of both fraction equivalences is integral to understanding rational numbers; and (c) knowledge of both conceptions of equivalence is important for developing a conceptual understanding of fraction arithmetic. Past research has largely overlooked the distinction between the two types of equivalence. However, this may provide an important foundation for central topics that build on equivalence, and a better understanding of these two types of equivalence may support a more flexible understanding of fractions. Last, we propose future directions for teaching equivalence in mathematics.

scholarly journals Failure to learn during roving, analysing the unsupervised bias hypothesis

2018 ◽  
Author(s):  
David Higgins ◽  
Michael Herzog
Keyword(s):  
Synaptic Plasticity ◽  
Mathematical Analysis ◽  
Recent Literature ◽  
The Other ◽  
Original Form ◽  
Task Representation ◽  
Task Sequencing ◽  
Multiple Tasks ◽  
Task Representations ◽  
And Task

AbstractWe examine the unsupervised bias hypothesis [11] as an explanation for failure to learn two bisection tasks, when task sequencing is randomly alternating (roving). This hypothesis is based on the idea that a covariance based synaptic plasticity rule, which is modulated by a reward signal, can be biased when reward is averaged across multiple tasks of differing difficulties. We find that, in our hands, the hypothesis in its original form can never explain roving. This drives us to develop an extended mathematical analysis, which demonstrates not one but two forms of unsupervised bias. One form interacts with overlapping task representations and the other does not. We find that overlapping task representations are much more susceptible to unsupervised biases than non-overlapping representations. Biases from non-overlapping representations are more likely to stabilise learning. But this in turn is incompatible with the experimental understanding of perceptual learning and task representation, in bisection tasks. Finally, we turn to alternative network encodings and find that they also are unlikely to explain failure to learn during task roving as a result of unsupervised biases. As a solution, we present a single critic hypothesis, which is consistent with recent literature and could explain roving by a, much simpler, certainty normalised reward signalling mechanism.

scholarly journals On the influence of vibrations upon the form of certain sponge-spicules

1917 ◽  
Vol 89 (622) ◽  
pp. 573-587 ◽  
Keyword(s):  
Mathematical Analysis ◽  
Nodal Point ◽  
The Other ◽  
Water Currents ◽  
Spicule Formation ◽  
Basal Thickening ◽  
Complicated Process ◽  
Sponge Spicules ◽  
The Moment ◽  
Straight Rod

It has been pointed out recently* by one of us that the development of the remarkable chessman-spicule or discorhabd in the genus Latrunculia is a somewhat complicated process depending upon several factors. The protorhabd or axial thread appears first as a slender rod capable of independent growth. With these protorhabds two kinds of silica-secreting cells appear to be associated, viz., formative cells which are responsible for the actual deposition of the silica upon the protorhabd, and accessory silicoblasts which are supposed to collect supplies of silica and bring them to the formative cells to be used in the process of spicule-formation. The spicule in this case consists of an elongated axis with whorls of flattened lobes arranged at more or less definite intervals along its length, and it was suggested that the position of these whorls is determined by the fact that the spicule, at the time of their commencement, is in a state of vibration, due to the water currents flowing through the sponge, the whorls corresponding to the nodes or positions of comparative rest. The special accumulation of silica on the nodes appears to be due, not directly to the vibrations of the spicule, but to the fact that the formative cells exhibit a kind of tropism which induces them to settle down and perform their work in the positions where they are least disturbed by the vibrations. The whorls in this case are not sharply defined at the moment of their first appearance, so that it is impossible to obtain accurate measurements for mathematical analysis ; nevertheless, there are certain facts connected with their arrangement which, in our opinion, afford a fairly conclusive demonstration of the view that they are deposited approximately upon the nodes of a vibrating rod. Two species were investigated, Latrunculia apicalis and L. bocagei . In both species the spicule, at a certain stage of its development, consists of a straight rod with four thickenings, representing a basal manubrium and three incipient whorls. There is a basal thickening at one end, an apical thickening at the other, a median thickening at or near the centre, and a subsidiary thickening, usually between the median and apical thickenings, but occasionally between the median and basal thickenings. If these thickenings correspond to nodes, we have to account for the fact that a subsidiary thickening is developed only on one side of the median thickening. The solution of this difficulty is to be found in the arrangement of the formative cells (observed in Latrunculia bocagei only, though doubtless occurring in the other species also), for while there is a ring of formative cells round the median thickening and a similar ring round the subsidiary thickening, there is none around the part of the spicule where a second subsidiary thickening might be looked for, and hence no whorl is developed in this situation, in spite of its being a nodal point. No formative cells have yet been observed in relation to the basal and apical thickenings.

A MATHEMATICAL ANALYSIS OF THE DISTRIBUTION IN MAIZE OF HELIOTHIS ARMIGERA Hb. (OBSOLETA F.)

1942 ◽  
Vol 20d (8) ◽  
pp. 235-261 ◽  
Author(s):  
Marjory G. Walker
Keyword(s):  
Mathematical Analysis ◽  
Mathematical Theory ◽  
Random Distribution ◽  
Heliothis Armigera ◽  
The Other ◽  
Good Representation ◽  
Poisson Series ◽  
Egg Distribution ◽  
Rough Approximation ◽  
Maize Plants

The distribution among maize plants of the eggs of the American boll-worm, Heliothis armigera Hb., is discussed and analysed.The problem is considered in relation lo what is known of the connection between the state of development of maize plants and their attractiveness to ovipositing boll-worm moths. The actual frequency distribution of the eggs suggests a random as opposed to a uniform distribution, but it is shown that the conditions required for a pure mathematical random distribution cannot be satisfied. Because the maize plants differ from one another in absolute degree of attractiveness at any one time, and in relative degree of attractiveness with the passing of time, it is not true that every plant has the same chance of receiving any given egg.It is demonstrated that a mathematical theory, which is eventually one of random distribution, but which incorporates a modification to allow for the varying degrees of attractiveness of the plants, gives a fairly good representation of the egg distribution found in the field.Theoretical distributions to fit the data are calculated by two methods. One is a discontinuous process which is presented as only a rough approximation of what it is intended lo express. The other uses the compound Poisson series of Greenwood and Yule. The continuous variation in nature both in space and time, which is the essential difficulty of the problem, is discussed.

LA GÉOMÉTRIE DE L'ASTROLABE AU Xe SIÈCLE Geometry of the Astrolabe in the Tenth Century

2000 ◽  
Vol 10 (1) ◽  
pp. 7-77 ◽  
Author(s):  
Abgrall Philippe
Keyword(s):  
Present Article ◽  
Mathematical Analysis ◽  
Critical Edition ◽  
Eleventh Century ◽  
Stereographic Projection ◽  
Tenth Century ◽  
The Other ◽  
Conical Projection ◽  
Geometrical Transformation ◽  
History Of

Many studies on the astrolabe were written during the period from the ninth to the eleventh century, but very few of them related to projection, i.e., to the geometrical transformation underlying the design of the instrument. Among those that did, the treatise entitled The Art of the Astrolabe, written in the tenth century by Abū Sahl al-Qūhī, represents a particulary important phase in the history of geometry. This work recently appeared in a critical edition with translation and commentary by Roshdi Rashed. It contains the earliest known theory of the projection of the sphere, a theory developed in a commentary written by a contemporary mathematician, Ibn Sahl. Following R. Rashed, the present article offers here a thorough mathematical analysis of al-Qūhī's treatise and of the commentary by Ibn Sahl. It also presents, with commentary, an account of a contemporary treatise on the projection of the sphere, written by al-[Sdotu]āġānī. The latter work is concerned with the conical projection of a sphere on a plane, from a point on an axis of the sphere, other than its pole. The author consciously avoids the case of stereographic projection, but he studies all the other cases of conical projection which, if we employ the terms of al-Qūhī's theory, are compatible with the movement of the instrument (i.e. the rotation of the sphere around its axis). These three texts provide clear evidence of the emergence, during the second half of the tenth century, of a new field of study, that of projective geometry.

Dual-pivot and beyond: The potential of multiway partitioning in quicksort

2018 ◽  
Vol 60 (3) ◽  
pp. 173-177 ◽  
Author(s):  
Sebastian Wild
Keyword(s):  
Mathematical Analysis ◽  
Memory Hierarchy ◽  
Main Memory ◽  
The Other ◽  
Theoretical Investigations

Abstract Since 2011 the Java runtime library uses a Quicksort variant with two pivot elements. For reasons that remained unclear for years it is faster than the previous Quicksort implementation by more than 10 %; this is not only surprising because the previous code was highly-tuned and is used in many programming libraries, but also since earlier theoretical investigations suggested that using several pivots in Quicksort is not helpful. In my dissertation I proved by a comprehensive mathematical analysis of all sensible Quicksort partitioning variants that (a) indeed there is hardly any advantage to be gained from multiway partitioning in terms of the number of comparisons (and more generally in terms of CPU costs), but (b) multiway partitioning does significantly reduce the amount of data to be moved between CPU and main memory. Moreover, this more efficient use of the memory hierarchy is not achieved by any of the other well-known optimizations of Quicksort, but only through the use of several pivots.

scholarly journals A Graphical-Based Mathematical Model for Simulating Excitability in a Single Cardiac Cell

2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
S. H. Sabzpoushan ◽  
A. Ghajarjazy
Keyword(s):  
Mathematical Analysis ◽  
Phase Plane ◽  
Biological Systems ◽  
Biological Properties ◽  
Cardiac Cells ◽  
The Other ◽  
Phase Plane Analysis ◽  
Cardiac Cell ◽  
Plane Analysis ◽  
Phase Plane Method

Excitability is a phenomenon seen in different kinds of systems, e.g., biological systems. Cardiac cells and neurons are well-known examples of excitable biological systems. Excitability as a crucial property should be involved in mathematical models of cardiac cells, along with the other biological properties. Excitability of mathematical cardiac-cell models is usually investigated in the phase plane (or the phase space) which is not applicable with simple mathematical analysis. Besides, the possible roles of each model parameter in the excitability property cannot be investigated explicitly and independently using phase plane analysis. In this paper, we present a new graphical-based method for designing excitability of a single cardiac cell. Each parameter in the presented approach not only has electrophysiological interpretation but also its role in regulating excitability is evident and can be analysed explicitly. Our approach is simpler and more tractable by mathematical analysis than the phase plane method. Another advantage of our approach is that the other important feature of the cardiac cell action potential, i.e., plateau morphology, can be designed and regulated separately from the excitability property. To evaluate our presented approach, we applied it for simulating excitability in well-known complex electrophysiological models of ventricular and atrial cells. Results show that our model can simulate excitability and time evolution of the plateau phase simultaneously.

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