Beauty and Distance in the Stable Marriage Problem

The stable marriage problem has been introduced in order to describe a complex system where individuals attempt to optimise their own satisfaction, subject to mutually conflicting constraints. Due to the potential large applicability of such model to describe all the situation where different objects has to be matched pairwise, the statistical properties of this model have been extensively studied. In this paper we present a generalization of this model, introduced in order to take into account the presence of correlations in the lists and the effects of distance when the player are supposed to be represented by a position in space.Comment: 8 pages, 3 figures, submitted to ep

The Constructional Approach to “hand” and “leg” in English

The human body is one of the few domains of everyday life perceived and coded by all languages of the world. According to the embodiment hypothesis, the universal physical experience is one of the bases for the way cognition and language are structured. The latter is reflected, among other things, in the fact that body part terms are universally polysemic and involved in various idioms. Such linguistic properties of lexemes denoting parts of the body are both the consequence and the proof of the metaphorical and metonymical nature of language. In this paper, I shall analyse the polysemy and idioms of hand and leg in English on the examples from the Corpus of Contemporary American English and compare them to the ways the same body part terms are coded in some unrelated languages. My presupposition, which I aim to prove, is that metaphor, metonymy and body-part polysemy and idiomaticity are linguistically universal

Scaling Behavior in the Stable Marriage Problem

We study the optimization of the stable marriage problem. All individuals attempt to optimize their own satisfaction, subject to mutually conflicting constraints. We find that the stable solutions are generally not the globally best solution, but reasonably close to it. All the stable solutions form a special sub-set of the meta-stable states, obeying interesting scaling laws. Both numerical and analytical tools are used to derive our results.Comment: 6 pages, revtex, 3 figures. To appear in J. de Physique I, vol 7, No 12 (December

The marriage problem: from the bar of appointments to the agency

We study the stable marriage problem from different points of view. We proposed a microscopic dynamic that lead the system to a stationary state that we are able to characterize analytically. Then, we derive a thermodynamical description of the Nash equilibrium states of the system that agree very well with the results of Monte Carlo simulations. Finally, through large scale numerical simulations we compare the Global Optimum of the society with the stable marriage of lower energy. We showed that both states are strongly correlated and that the selffish attitude results in a benefit for most of the practitioners belonging to blocking pairs in the Global Optimum of the society.Comment: 15 pages, 9 figures. To be published in Physica A (2005

Acceptability and Marketability of CUSQCA Ice Cream Cone

This study focused on the acceptability and marketability of CUSQCA (Cucumber, Squash, and Carrot) Ice Cream Cone with 30 grams, 60 grams, and 90 grams proportion to the group of consumers, ice cream cone sellers and ice cream cone makers of Barangay Sta. Cruz, Antipolo City, and Marikina Polytechnic College, Marikina City during the school year 2022-2023. The study utilized the experimental method which involves a total of 90 respondents from the group of consumers, ice cream cone sellers, and ice cream cone makers who were determined through purposive sampling. Based on the findings, he consumers, ice cream cone sellers, and ice cream cone makers evaluated the acceptability level of the CUSQCA Ice Cream Cone with 30 and 60 grams proportion in terms of appearance, aroma, taste, and texture as Very Acceptable (VA), while they evaluated the 90 grams proportion as Extremely Acceptable. In addition, the three groups of respondents evaluated the level of marketability of CUSQCA Ice Cream cone with 30 grams proportion as Very High Potential (VHP). Comments and suggestions were provided by the respondents to further improve the product

Persistence of American Indian students at a comprehensive state university.

The nature of the conclusions suggest that further research on cultural problems and lack of integration into the university community would be fruitful in expanding and understanding of persistence among American Indian students.The principal research question of this study is: In what ways do American Indian students at the University of Oklahoma who are successful in completing coursework differ from those who are less successful (and eventually dropout)?The statistical analysis consists of two steps. In the first step, bivariate correlations were computed. In the second step, components of the model were examined in an integrated series of regression solutions. The analysis of the bivariate correlation matrix can be summarized by stating that: (a) American Indian students arriving at the University of Oklahoma campus in 1975 who developed higher feelings of integration into the University community were those having fathers of higher educational attainment and having lower attachment to Indian culture; (b) American Indian students arriving in 1975 who persisted were those having higher A.C.T. scores, higher G.P.A.'s in high school, higher family incomes, parents of higher educational attainment, lower attachment to Indian culture, and high feelings of integration into the University community.The research model for this study focuses on the effects of a group of five antecedent variables on the dependent variable, persistence, and has provisions for influence by an intervening variable. The five antecedent variables are: (1) scholastic aptitude; (2) family income; (3) familial educational level; (4) physical Indianness; (5) attachment to Indian culture. In addition to these five variables there is an intervening variable, integration into the University community, and a dependent variable, persistence in completing coursework.The findings of the study suggest that those American Indian students who persisted for eight semesters had high grade point averages in high school, had high A.C.T. composite scores, had fathers with high educational attainment, had less attachment to Indian culture and most of all were well integrated into the university community.This is an ex-post facto descriptive study which examines the entire cohort of American Indian students enrolled in the University of Oklahoma as freshmen in the Fall of 1975. Data are collected on these students for each semester of their collegiate careers, from matriculation to graduation or termination of the university experience.The findings in the multiple regression table identify three variables that contribute to persistence at the University of Oklahoma; high school grade point average, A.C.T. composite score, and integration into the University community. Each of these have independent significant effects upon persistence. They are the key variables in the model of persistence. Father's educational level and attachment to Indian culture are the two key variables in accounting for who becomes integrated into the University community

Consistency analysis of Kaluza-Klein geometric sigma models

Geometric sigma models are purely geometric theories of scalar fields coupled to gravity. Geometrically, these scalars represent the very coordinates of space-time, and, as such, can be gauged away. A particular theory is built over a given metric field configuration which becomes the vacuum of the theory. Kaluza-Klein theories of the kind have been shown to be free of the classical cosmological constant problem, and to give massless gauge fields after dimensional reduction. In this paper, the consistency of dimensional reduction, as well as the stability of the internal excitations, are analyzed. Choosing the internal space in the form of a group manifold, one meets no inconsistencies in the dimensional reduction procedure. As an example, the SO(n) groups are analyzed, with the result that the mass matrix of the internal excitations necessarily possesses negative modes. In the case of coset spaces, the consistency of dimensional reduction rules out all but the stable mode, although the full vacuum stability remains an open problem.Comment: 13 pages, RevTe

The Cora Lake Shear Zone: a Natural Laboratory in the Continental Lower Crust

Preserved lower-crustal terranes provide a view into deep earth processes unparalleled in spatial and temporal resolution. We use this rich data set of field observations and microstructural samples to document long-term strain localization in the dry lower crustal root of a continental strike-slip fault system, model the passive seismic properties its deformation, and create a novel method of interpolating missing orientation data using neural networks. The Cora Lake shear zone is a 4-6 kilometer wide and >90 km long zone of mylonite and ultramylonite which hosts frictional melt (pseudotachylyte) veins with various intensities of ductile fabric overprint. High-resolution electron microprobe analyses constrain rupture to deep crustal conditions contemporaneous with all stages of ductile deformation in the shear zone. The cyclic rupture and ductile overprint of pseudotachylyte in the Cora Lake shear zone suggests a strong lower crust with a complex connection between ductile root and overlying brittle fault system. Experimental flow laws combined with microstructural observations predict a major viscosity contrast across the shear zone, resulting in stress amplification and the formation of the ~1km wide zone of ultramylonite intermixed with pseudotachylyte. These high stresses likely set the stage for deep aftershocks triggered by slip on the shear zone’s upper crustal extension.In order to determine whether an analogous active or relict structure would be visible to geophysical techniques in the subsurface setting today, we model the passive effect of deformation-induced crystallographic preferred orientations and mylonitic layering in the Cora Lake shear zone. Although the mylonites in the Cora Lake shear zone produce low Vp and Vs anisotropy due to destructive interference between deforming minerals, mylonitic and gneissic layering contributes significantly to the magnitude and geometry of anisotropy.Lastly, we use ~400,000 crystallographic orientations collected from the Cora Lake shear zone to test the effectiveness of a machine learning technique in predicting missing values against the common neighbor-averaging approach. Our neural networks outperform neighbor-averaging, and do so by apparently exploiting previously unknown predictive relationships within technique-specific orientation pattern metadata. This illustrates the potential value of machine learning approaches in the ever more data-driven earth sciences