Rectangular Table Research Articles

The conformal geometry of billiards

In the absence of friction and other external forces, a billiard ball on a rectangular billiard table follows a predictable path. As it reflects off the sides of the table, the ball will either (1) return to its original position and direction, or (2) travel all over the table, spending equal time in regions with equal area. Because of this dichotomy, we say the rectangular table is optimal: billiard trajectories define an easily understood dynamical system on the phase space of positions and directions. In this article, we ask:

Combining discrete SVM and fixed cardinality warping distances for multivariate time series classification

Time series classification is a supervised learning problem aimed at labeling temporally structured multivariate sequences of variable length. The most common approach reduces time series classification to a static problem by suitably transforming the set of multivariate input sequences into a rectangular table composed by a fixed number of columns. Then, one of the alternative efficient methods for classification is applied for predicting the class of new temporal sequences. In this paper, we propose a new classification method, based on a temporal extension of discrete support vector machines, that benefits from the notions of warping distance and softened variable margin. Furthermore, in order to transform a temporal dataset into a rectangular shape, we also develop a new method based on fixed cardinality warping distances. Computational tests performed on both benchmark and real marketing temporal datasets indicate the effectiveness of the proposed method in comparison to other techniques.

ANALYZING OR EXPLAINING BETA DIVERSITY? COMMENT.

In 2005, we published a paper (Legendre et al. 2005; hereafter referred to as LBP) explaining the ecological and statistical basis for the analysis of the variation in species composition among sites (this is one operational definition of beta diversity), a subject of great impor tance for the understanding of the generation and maintenance of beta diversity and the establishment of ecologically sound ecosystem conservation policies. Tuomisto and Ruokolainen (2006) (hereafter referred to as TR) pointed out several issues in our 2005 paper. As a response, this note seeks to clarify the issues behind this contention. Our major point of disagreement concerns the links between (1) the ecological predictions derived from neutral theories of beta diversity, (2) the statistical hypotheses derived from these predictions, and (3) the statistical methods used to test these hypotheses. In LBP, TR, and the present Comment, distance-based methods refer to statistical methods where the geo graphic relationships among sites are represented by a distance matrix. These methods include the Mantel test and the derived method of regression on distance matrices. The raw-data approach refers to multiple regression and canonical analysis, where the spatial relationships among sites are represented by a rectan gular table containing geographic coordinates, a poly nomial of the geographic coordinates, principal coordinates of a neighbor matrix (PCNM) (Borcard and Legendre 2002), or derived forms. The purpose of this Comment is to show that (1) some predictions of Hubbell's neutral theory, especially the presence of positive autocorrelation, can be stated and tested using the raw-data approach, (2) the distance approach as proposed by TR (partitioning on distance matrices) is statistically flawed, and (3) when a raw-data hypothesis is translated into distances, the correspond ing statistical test lacks power; therefore, whenever a hypothesis can be formulated in terms of raw data

Reference directions and reference objects in spatial memory of a briefly viewed layout

Two experiments investigated participants’ spatial memory of a briefly viewed layout. Participants saw an array of five objects on a table and, after a short delay, indicated whether the target object indicated by the experimenter had been moved. Experiment 1 showed that change detection was more accurate when non-target objects were stationary than when non-target objects were moved. This context effect was observed when participants were tested both at the original learning perspective and at a novel perspective. In Experiment 2, the arrays of five objects were presented on a rectangular table and two of the non-target objects were aligned with the longer axis of the table. Change detection was more accurate when the target object was presented with the two objects that were aligned with the longer axis of the table during learning than when the target object was presented with the two objects that were not aligned with the longer axis of the table during learning. These results indicated that the spatial memory of a briefly viewed layout has interobject spatial relations represented and utilizes an allocentric reference direction.

From there to Rehearsing Sex: A space of freedom among theory and the dead meandering to assist with resistance

On a rectangular table, four heads recollect their personal experiences of existence. In the absence of physical body no gender or sex differations exist. However, in depicting images of their existence the four heads recall relationships and emotions characterized by all the stereotypes of engendered relations. Submisal, obedience, resistance, are evident. The limits and power play of family and sex bondages are revealed. Through a constant state of sleep and/or death the heads speak with their eyes closed the truths of their selves. Pursuance of pleasure (achieved through sex) and desire of fulfillment motivates their every action and thought and allows to endure the pain that emerges from the lack of completeness. Language is the medium that gives meaning to an existential life, sets the space of one's freedom, constructs or deconstructs reason. "Rehearsing Sex" can be seen/heard as a paradigm of queer theory, where sexual identities and relations are being revised and reconstructed.

Effects of Sex and Seating Arrangement on Selection of Leader

Effects of a person's sex and seating arrangement were tested with 310 participants (151 men and 159 women; M age=20.0, SD=3.3) from a large southwestern U.S. university who were asked to select a leader from among five persons depicted around a rectangular table. Participants chose a person shown seated at the head of the table as the leader of a group, regardless of that person's sex. This conflicts with prior research indicating gender bias against women as leaders.

Classroom notes: A look at billiards

This note will demonstrate the surprising fact that any shot from a corner of a rectangular billiards table will always reach a pocket if the ball rolls long enough and the slope of the shot and the dimensions of the table are rational numbers. Under these conditions it will be shown how to find the pocket into which the ball falls, the length of the path and the number of times the ball banks off a cushion. Uniqueness of the starting and mid-point of ball-reaching paths and the case for real table dimensions and shot slope are examined.

Stabilization of one degree-of-freedom control type levitation table with permanent magnet repulsive forces

It is impossible to levitate an object by using only permanent magnets (PMs). Many researches have been reported to reduce the number of control degree-of-freedom (DOF) in magnetic levitation systems. This paper presents a one-DOF control type magnetic levitation table supported by repulsive forces of four sets of PMs. Each set of PMs is composed of two PMs on a fixed frame and one PM on the levitated table. The PMs are located at the four corners of the rectangular table and the corresponding positions of the frame. The magnetic poles of the PMs on the table are opposed to those of the fixed PMs, so that repulsive forces act on the table and the frame. This paper, first, discusses theoretically the relative position range of the sets of PMs to the center of gravity of the table from the viewpoint of the stability condition of the motion of equation. In the discussion, the repulsive force and stiffness produced by a set of the PMs are assumed to be known parameters because they can be numerically calculated. Then an experimental table is constructed, in which the unstable motion is actively stabilized by a linear motor. Dynamic responses are measured, and results prove that the proposed magnetic levitation table is successfully held in stable equilibrium by only one-DOF active control.

Simulation of fabric drape using a thin plate element with finite rotation

The draping behavior of fabric is simulated by using four node quadrilateral thin plate elements with finite rotation. The finite element formulation is based on the total Lagrangian approach. An exact representation of finite rotation is introduced. The strain energy function accounting for the material symmetry is obtained by the tensor representation theory. To avoid shear locking, the assumed strain technique for transverse shear is adopted. The conjugate gradient method with a proposed line search algorithm is employed to minimize energy and reach the final shape of fabric. The draping behavior of a rectangular piece of fabric over a rectangular table is simulated.

The Delights of Memory, II: Doss

(The lights rise on the freight yards in Mesa City. On one side, we see a field heaped with fine-grained coal, and, beyond that, on the same side, a small adobe bungalow used as a resthouse and office for railroad men. In the accessible interior of this bungalow, there are: an old woodstove; wall lockers; a plain rectangular table; some straightbacked, wooden chairs; a few railroad lanterns hung on the wall behind a square, heavy oak desk; a water pitcher with a glass draped over its spout; an old axe, and a poster with the rules of the resthouse. Upstage, toward the center, a well-appointed private car sits, on a track, in state. Beyond this, there is the vague outline of a large adobe building, the city train station.

演習クラスにおける着席行動の研究 女子大学における３事例の分析

The purpose of this study was to examine the conditions under which human territoriality (self/other boundary-regulation mechanism) appears in seat-taking behavior. Seat-taking in a social psychology seminar class of twelve students at a women's university was observed during the 1983, 1984 and 1985 academic years by female part-time lecturer (the author herself). At the beginning of each class, the lecturer drew the figure of the students' seating arrangement at a rectangular table, while calling each student's name. Questionnaires were also administered to the students at the end of the observation in the period 1983 and 1985 academic years. The results obtained were: 1) each student was more attached to one seating area and seating side than the others, 2) this fact reflected her seating preference to some extent, 3) no student monopolize the special seats to which she was most attached, 4) extra spaces were left between the lecturer's and the student's seat. The third finding was considered to be due to homogeneity of the student with respect to major, grade and sex and their temporal relationships within the seminar group. Also the fourth result was due to the status difference between the lecturer and the students, which led to the recognition that the seating places were mutually exclusive for both sides of them.

Mathematical billiards

A ball is shot at an angle of 45 degrees from the corner of a rectangular billiard table of size m × n (where m and n are integers). It always bounces off from a side at 45 degrees until it lands in a corner pocket. Will it always land in a corner or will it keep bouncing for ever? And how many times will it bounce? And which corner pocket will it land in?Try it for yourself. For example in the 7 × 4 table shown the ball will bounce 9 times and then fall into the top left-hand corner pocket.This is a well-known problem but we now present a simpler proof than we've seen elsewhere of the fact that the ball always ends up in a corner pocket, and we derive a formula for the number of bounces and we determine the finishing pocket.

A note on piecewise linear and multilinear table interpolation in many dimensions

This note is concerned with N-dimensional rectangular table interpolation, where N is relatively large (4 to 10). Two interpolants are considered: a piecewise multilinear generalization of piecewise bilinear interpolation on rectangles, and a piecewise linear generalization of piecewise linear interpolation on triangles. We show that the two interpolants have similar approximation properties, but the piecewise linear interpolant is much cheaper to evaluate.

Simulation of a Policy Aimed at the Reduction of Wood Use in the Sudan

A rectangular economic input-output table for the Sudan is presented, based on nine sectors, thirty-seven commodities, six primary inputs, and seven final demand categories. Four possible models of intermediate consumption are derived by using linear programming and entropy maximizing. The table is then linked to a coefficient representing wood use per unit of output in the Sudanese economy. A policy aimed at a reduction in wood use is tested by simulating the introduction of more efficient charcoal stoves into urban households. Implementation of the policy would lead to a significant reduction in total wood used, from 88 km2 to 194 km2 per year, depending on which of the four models for intermediate consumption is utilized. Reallocation of the resulting savings by households into energyintensive commodities, however, reduces the effectiveness of the policy by as much as 48%.

Whitman and the Crowd

Sciences of the American Council of Learned Societies and the Academy of Sciences of the USSR met in Moscow to arrange continued cooperation between scholars of the two countries. The protocol then signed includes the field of literature and language and identifies the following areasfor attention: of the history of American and Russian literatures and their mutual relations; the work of William Faulkner, Walt Whitman; literature and national consciousness; semiotics in literature and linguistics; exchange of scholarly materials regarding Eskimo languages. Accordingly, two Soviet scholars participated in the Faulkner and Yoknapatawpha Conference at the Center for the Study of Southern Culture of the University of Mississippi in the summer of 1982. And, as the second step in this infant endeavor, four Americans participated in the Walt Whitman Conference held at the A. M. Gorky Institute of World Literature in Moscow in October 1982. I was one of the four. The building occupied by the Gorky Institute was formerly a nobleman's palace and figures in War and Peace. It retains a sense of its former days, although one who comes into the foyer and faces the shallow slope of the broad stairs for the first time is primarily aware of having entered an institution. The stately details are there, but the initial glance reveals a concierge's desk, metal coatracks, and the familiar, tired wood of nineteenth-century educational edifices the world round. The conference took place in a large, second-floor room, once, I guessed, a ballroom. A long rectangular table extended across one end of the room, and during the conference the Americans and Soviets satfacing one another over it. The rest of the room was filled with chairs arranged in rows, but if the

Social Organization and Spatial Organization

In afirst experiment groups offivesubjects solved problems while seated at either a circular or a rectangular table. The leader's position at the end of the rectangular table enhanced his ability to direct the group. Leaders of the circular table did not benefit from a privileged position and were forced to ease group tension arising from competing solutions put forth by group members. In the second study, the experimenter either actively intervened in afour-member discussion or refrained. The groups all discussed at a circular table before moving to a rectangular table in a different room. Before-after comparisons of the seats chosen were made. Choice of seats at the rectangular table reflected the social relations that developed in the first part of the experiment.

Factors in social perception: seating position.

Ss made 8-point scale ratings of 5 target individuals photographed while seated at a rectangular table. Occupancy of the head position (rather than side locations) was consistent with higher ratings on all of the following scales: (1) Talkativeness, (2) Persuasiveness, (3) Leadership, (4) Self-confidence, (5) Friendliness, and (6) Intelligence. The occupant of the head position was also considered to “contribute most” to the group's performance. Sommer's (1967) hypothesis that status and/or dominance ascribes to an individual automatically as a function of the location he occupies was supported. Results were interpreted to demonstrate a “halo effect” reflecting cultural standards and traditions regarding the organization of social space. Some suggestions for future studies were presented.

Some Effects of Seating Position on Social Perception

Summer's (1967) hypothesis that status and/or dominance may be ascribed to an individual automatically as a function of the location he occupies was supported. Ss made semantic-differential scale ratings of target individuals photographed while seated at a rectangular table. As predicted, occupancy of the head position (as opposed to side locations) was associated with higher ratings on all six of the following scales: (1) Talkativeness, (2) Persuasiveness, (3) Dominance, (4) Leadership, (5) Self-confidence, and (6) Intelligence. The occupant of the head position was also chosen significantly more often as the one who “probably contributed the most” to the group's task performance. The results are interpreted to indicate a general “halo effect” reflecting cultural standards and traditions regarding the organization of social space.

Group opinion change as a function of circular vs rectangular seating arrangement

Group opinion change was investigated as a function of an organized minority under circular and rectangular table arrangements. It was hypothesized that there would be less opinion change in a circular setting because of the equivalent spatial distance between all group members. The results did not indicate any differences between the two spatial arrangements, but a statistically significant opinion shift occurred under each condition.