Information Visualization

(1)

Information Visualization

(2)

outline

• Visual Perception

• High-dimensional Data Visualization

• Hierarchical(tree) Data Visualization

• Graphs and Networks Visualization

• Time Series Data Visualization

• Text and Document Visualization

• Geographical Data Visualization

(3)

outline

(4)

Visual Perception

• Seek to better understand visual perception and visual information processing

– Multiple theories or models exist

– Need to understand physiology and cognitive psychology

(5)

One (simple) Model

• Two stage process

– Parallel extraction of low-level properties of scene

– Sequential goal-directed processing

(6)

Stage 1 - Low-level, Parallel

• Neurons in eye & brain responsible for different kinds of information

– Orientation, color, texture, movement, etc.

• Arrays of neurons work in parallel

• Occurs “automatically”

• Rapid

• Information is transitory, briefly held in iconic store

• Bottom-up data-driven model of processing

• Often called “pre-attentive” processing

(7)

Stage 2 - Sequential, Goal-Directed

• Splits into subsystems for object

recognition and for interacting with environment

• Increasing evidence supports

independence of systems for symbolic

object manipulation and for locomotion &

action

• First subsystem then interfaces to verbal linguistic portion of brain, second

interfaces to motor systems that control muscle movements

(8)

Stage 2 Attributes

• Slow serial processing

• Involves working and long-term memory

• More emphasis on arbitrary aspects of symbols

• Top-down processing

(9)

Preattentive Processing

• How does human visual system analyze images?

– Some things seem to be done preattentively, without the need for focused attention

– Generally less than 200-250 ms (eye movements take 200 ms)

– Seems to be done in parallel by low-level vision system

(10)

How Many 3’s?

1281768756138976546984506985604982826762 9809858458224509856458945098450980943585 9091030209905959595772564675050678904567 8845789809821677654876364908560912949686

(11)

How Many 3’s?

1281768756138976546984506985604982826762 9809858458224509856458945098450980943585 9091030209905959595772564675050678904567 8845789809821677654876364908560912949686

(12)

What Kinds of Tasks?

• Target detection

– Is something there?

• Boundary detection

– Can the elements be grouped?

• Counting

– How many elements of a certain type are present?

(13)

Example

• Determine if a blue circle is present

(14)

Hue

• Can be done rapidly (preattentively) by people

• Surrounding objects called “distractors”

(15)

Shape

• Can be done preattentively by people

(16)

Hue and Shape

• Cannot be done preattentively

• Must perform a sequential search

• Conjuction of features (shape and hue) causes it

(17)

Example

• Is there a boundary in the display?

(18)

Hue versus Shape

• Left: Boundary detected preattentively based on hue regardless of shape

• Right: Cannot do mixed color shapes preattentively

(19)

Gestalt Laws

• Background

– German psychologists, early 1900’s

– Attempt to understand pattern perception – Founded Gestalt school of psychology

– Provided clear descriptions of many basic perceptual phenomena

• Gestalt Laws of Pattern Perception

(20)

Gestalt Laws

• Proximity

– Things close together are

perceptually grouped together

• Similarity

– Similar elements get grouped together

(21)

Gestalt Laws

• Figure & Ground

– Figure is foreground, ground is behind

• Continuity

– More likely to construct visual entities out of

smooth, continuous visual elements

(22)

Gestalt Laws

• Symmetry

– Symmetrical patterns are perceived more as a whole

• Closure

– A closed contour is seen as an object

(23)

Visual Encoding

• Marks: geometric primitives

– Points – Lines – Areas

• Visual channels: control appearance of marks

– Position – Color – Size – …

(24)

Variables of the Image

(25)

Visual Channel

• Visual Channel Types and Rankings

(26)

Visual Channel Types and Rankings

containment

similarity proximity connection relational

grouping

position hue pattern shape categorical

what/where

position length angle area

lightness/saturation Stipple density

ordered how much

(27)

more accurate

Visual Channel Types and Rankings

(28)

outline

(29)

How Many Variables?

• Data sets of dimensions 1, 2, 3 are common

• Number of variables per class

– 1 - Univariate data – 2 - Bivariate data – 3 - Trivariate data

– >3 - Hypervariate data

(30)

Representations

• Some standard ways for low-dimensional data

(31)

More Dimensions

• Fundamentally, we have 2 geometric (position) display dimensions

• For data sets with >2 variables, we must project data down to 2D

• Come up with visual mapping that locates each dimension into 2D plane

• Computer graphics: 3D->2D projections

(32)

Scatterplot Matrix

• Represent each possible pair of variables in their own 2-D

scatterplot

(33)

• Generalized Sensitivity Scatterplot

Scatterplot

(34)

Parallel Coordinates

• Encode variables along a horizontal row

• Vertical line specifies different values that variable can take

• Data point represented as a polyline

(35)

Parallel Coords Example

(36)

Issue

• Different variables can have values taking on quite different ranges

• Must normalize all down (e.g., 0->1)

(37)

Challenges

• Too much data

(38)

Dimensional Reordering

• Which dimensions are most like each other?

Same dimensions ordered according to similarity

(39)

Reducing Density

(40)

Star Plots

• Space out the n variables at equal angles around a circle

• Each “spoke” encodes a variable’s value

• Data point is now a

“shape”

(41)

Star Plots

(42)

Star Coordinates

(43)

Dust & Magnet

• Altogether different metaphor

• Data cases represented as small bits of iron dust

• Different attributes given physical manifestation as magnets

• Interact with objects to explore data

(44)

Interface

(45)

Interaction

• Iron bits (data) are drawn toward magnets (attributes) proportional to that data

element’s value in that attribute

– Higher values attracted more strongly

• All magnets present on display affect position of all dust

• Individual power of magnets can be changed

• Dust’s color and size can connected to attributes as well

(46)

Interaction

• Moving a magnet makes all the dust move

– Also command for shaking dust

• Different strategies for how to position magnets in order to explore the data

(47)

Dust & Magnet

(48)

Dense Pixel Display

• Represent data case or a variable as a pixel

• Million or more per display

• Rely on use of color

• Value ranges are mapped to a fixed color sequence of full color (hue)scale but

monotonically decreasing brightness

• Data values belonging to one attribute are displayed in a separate view ‐ only one

pixel per data value without need for a border

(49)

One Representation

• Grouping arrangement

• One pixel per variable

• Each data case has its own small rectangular icon

• Plot out variables for data point in that icon using a grid or spiral layout

(50)

Illustration

(51)

Pixel Bar Chart

• Make each pixel within a bar correspond to a data point in that group represented by the bar

• Can do millions that way

• Color the pixel to represent the value of one of the data point’s variables

(52)

Pixel Bar Chart

Product type is x-axis divider Customers ordered by

y-axis: dollar amount x-axis: number of visits

Color is (a) dollar amount spent, (b) number of visits, (c) sales quantity

(53)

Stacked Graph

(54)

Small Multiples

(55)

Summary

• We’ve seen many general techniques for multivariate

– Scatterplot matrix – Parallel coordinates – Dense Pixel Display – Stacked Graph

– …

• Know strengths and limitations of each

• Know which ones are good for which circumstances

(56)

outline

(57)

Hierarchies

• Definition

– Data repository in which cases are related to subcases

– Can be thought of as imposing an ordering in which cases are parents or ancestors of other cases

• Pervasive in the world

– Family histories, ancestries

– File/directory systems on computers – Organization charts

– Object-oriented software classes

(58)

Trees

• Hierarchies often represented as trees

– Directed, acyclic graph

• Two main representation schemes

– Node-link – Space-filling

(59)

Spatial Layout

• Primary concern of graph drawing is the spatial layout of nodes and edges

• Often (but not always) the goal is to effectively depict the graph structure

– connectivity, path-following – network distance

– clustering

– ordering (e.g., hierarchy level)

(60)

Indentation

• place all items along vertically spaced rows

• indentation used to show parent/child relationships

• commonly used as a component in an

interface

• breadth and depth contend for space

• often requires a great deal of scrolling

(61)

Node-Link Diagrams

• nodes are distributed in space, connected by straight or curved lines

• typical approach is to use 2D space to break apart breadth and depth

• often space is used to communicate hierarchical orientation

(62)

Node-Link Diagrams

• Root at top, leaves at bottom is very common

(63)

Node-Link Diagrams

• Root can be at center with levels growing outward too

(64)

Basic Algorithm

– Recursive algorithm

– Height on separate levels – Width in unique columns

– Make room for subtrees upwards

(65)

Reingold-Tilford Algorithm

• goal

– make smarter use of space

– maximize density and symmetry

• design concerns

– clearly encode depth level – no edge crossings

– isomorphic subtrees drawn identically – compact

• approach

– bottom up recursive approach

– for each parent make sure every subtree is drawn – pack subtrees as closely as possible

– center parent over subtrees

(66)

Radial Layout

• node-link diagram in polar coordinates

• radius encodes depth with root in center

• angular sectors

assigned to subtrees

• Reingold-Tilford can be applied

(67)

Potential Problems

• For top-down, width of fan-out uses up horizontal real estate very quickly

– At level n, there are 2ⁿ nodes

• Tree might grow a lot along one particular branch

– Hard to draw it well in view without knowing how it will branch

(68)

InfoVis Solutions

• Techniques developed in Information Visualization largely try to assist the problems

• Alternatively, Information Visualization techniques attempt to show more

attributes of data cases in hierarchy or focus on particular applications of trees

(69)

SpaceTree

• Uses conventional 2D layout techniques with some clever additions

Grosjean, Plaisant, Bederson InfoVis ‘02

(70)

Characteristics

• Vertical or horizontal

• Subtrees are triangles

– Size indicates depth

– Shading indicates number of nodes inside

• Navigate by clicking on nodes

– Strongly restrict zooming

(71)

SpaceTree

(72)

3D Approaches

• Add a third dimension into which layout can go

• Compromise of top-down and centered techniques mentioned earlier

• Children of a node are laid out in a cylinder

“below” the parent

– Siblings live in one of the 2D planes

(73)

Cone Trees

• Pros

– More effective area to lay out tree

– Use of smooth animation to help person track updates – Aesthetically pleasing

• Cons

– As in all 3D, occlusion obscures some nodes – Non-trivial to

implement and requires some

graphics horsepower

(74)

Alternative Solutions

• Change the geometry

• Apply a hyperbolic transformation to the space

• Root is at center, subordinates around

• Apply idea recursively, distance decreases

between parent and child as you move farther from center, children go in wedge rather than circle

(75)

Hyperbolic Browser

• Focus + Context Technique

– Detailed view blended with a global view

• First lay out the hierarchy on the hyperbolic plane

• Then map this plane to a disk

• Start with the tree’s root at the center

• Use animation to navigate along this representation of the plane

(76)

2D Hyperbolic Browser

• Approach: Lay out the hierarchy on the

hyperbolic plane and map this plane onto a display region.

• Comparison

– A standard 2D browser: 100 nodes (w/3 character text strings)

– Hyperbolic browser: 1000 nodes, about 50 nearest the focus can show from 3 to dozens of characters

(77)

Hyperbolic Browser

(78)

Key Attributes

• Natural magnification (fisheye) in center

• Layout depends only on 2-3 generations from current node

• Smooth animation for change in focus

• Don’t draw objects when far enough from root (simplify rendering)

(79)

Problems

• Orientation

– Watching the view can be disorienting

– When a node is moved, its children don’t keep their relative orientation to it as in Euclidean plane, they rotate

– Not as symmetric and regular as Euclidean techniques, two important attributes in

aesthetics

(80)

Space-Filling

• Each item occupies an area

• Children are “contained” under parent

(81)

Treemap

• Space-filling representation developed by Shneiderman and Johnson, Vis ‘91

• Children are drawn inside their parent

• Alternate horizontal and vertical slicing at each successive level

• Use area to encode other variable of data items

(82)

Treemap

• Example

(83)

Applications

• Can use Treemap idea for a variety of domains

– File/directory structures – Basketball statistics

– Software diagrams – …

(84)

Treemap Affordances

• Good representation of two attributes beyond node-link: color and area

• Not as good at representing structure

– What happens if it’s a perfectly balanced tree of items all the same size?

– Also can get long-thin aspect ratios

– Borders help on smaller trees, but take up too much area on large, deep ones

(85)

Treemap Variations

• Cluster Treemap

– Compromises treemap algorithm to avoid bad aspect ratios

– Basic algorithm (divide and conquer) with some hand tweaking

– Takes advantage of shallow hierarchy

• Squarified treemap

– Bruls, Huizing, van Wijk, EuroGraphics ‘00 – Alternate approach, similar results

– Small changes in data values can cause dramatic changes in layout

(86)

Treemap Variations

• Strip treemap

– Use strips to place items

– Put new rectangle into strip if it makes average

aspect ratio of all rectangles in strip go down, keep it there. Or if it makes aspect ratio go up, put it

back and move to next strip

(87)

Compare results

(88)

Showing Structure

• Regular borderless treemap makes it

challenging to discern structure of hierarchy, particularly large ones

– Supplement Treemap view

– Change rectangles to other forms

(89)

Enclosure diagrams

(90)

Cushion Treemap

• Add shading and texture to help convey structure of hierarchy

(91)

Voronoi Treemaps

• Use polygons instead of rectangles

(92)

Voronoi Treemaps

(93)

Radial Space-Filling

• What if we used a radial rather than a rectangular space-filling technique?

– We saw node-link trees with root in center and growing outward already...

• Make pie-tree with root in center and children growing outward

– Radial angle now corresponds to a variables rather than area

(94)

SunBurst

• Root directory at center, each successive level drawn farther out from center

• Sweep angle of item corresponds to size

• Color maps to file type or age

• Interactive controls for moving deeper in hierarchy, changing the root, etc.

• Double-click on directory makes it new root

(95)

SunBurst

(96)

• Node-link diagrams or space-filling techniques?

• It depends on the properties of the data

– Node-link typically better at exposing structure of information structure

– Space-filling good for focusing on one or two additional variables of cases

More Alternatives

(97)

Circle Packing

(98)

Icicle Tree

• Similar to the node-link diagram

• The nodes are space-filling

(99)

Summary

• Node-link diagrams or space-filling techniques?

• It depends on the properties of the data

– Node-link typically better at exposing structure of information structure

– Space-filling good for focusing on one or two additional variables of cases

(100)

outline

(101)

What is a Graph

• Vertices (nodes) connected by Edges (links)

• Graph edges can be directed or undirected

• Graph edges can have values (weights)

(102)

Graph Uses

• In information visualization, any number of data sets can be modeled as a graph

– Telephone system – World Wide Web

– Distribution network for on-line retailer – Call graph of a large software system – Semantic map in an AI algorithm

– Set of connected friends

• Graph/network visualization is one of the oldest and most studied areas of InfoVis

(103)

Graph Visualization

www.nytimes.com/interactive/2008/05/05/science/20080506_DISEASE.html

(104)

Graph Visualization Challenges

• Graph layout and positioning

– Make a concrete rendering of abstract graph

• Navigation/Interaction

– How to support user changing focus and moving around the graph

• Scale

– Above two issues not too bad for small graphs, but large ones are much tougher

(105)

Aesthetic Considerations

• Crossings -- minimize towards planar

• Total Edge Length -- minimize towards proper scale

• Area -- minimize towards efficiency

• Maximum Edge Length -- minimize longest edge

• Uniform Edge Lengths -- minimize variances

• Total Bends -- minimize orthogonal towards straight-line

(106)

Layout Algorithms

• Entire research community’s focus

• Common Layout Techniques

– Hierarchical – Force-directed – Circular

– Geographic-based – Clustered

– Attribute-based – Matrix

(107)

Circular Layout

• Ultra-simple

• May not look so great

• Space vertices out around circle

• Draw lines to connect vertices

(108)

Circular Layout

(109)

Arc Diagram Layout

(110)

Force-directed Layout

• Example of constraint-based layout technique

• Impose constraints (objectives) on layout

– Shorten edges

– Minimize crossings – …

• Define through equations

• Create optimization algorithm that

attempts to best satisfy those equations

(111)

Force-directed Layout

• Spring model (common)

– Edges : Springs (gravity attraction)

– Vertices : Charged particles (repulsion)

• Equations for forces

• Iteratively recalculate to update positions of vertices

• Seeking local minimum of energy

– Sum of forces on each node is zero

(112)

Force-directed Layout

(113)

Variants

• Spring layout

– Simple force-directed spring embedder

• Fruchterman-Reingold Algorithm

– Add global temperature

– If hot, nodes move farther each step – If cool, smaller movements

– Generally cools over time

• Kamada-Kawai algorithm

– Examines derivatives of force equations

– Brought to zero for minimum energy

(114)

Force-directed Layout

• very flexible, aesthetic layouts on many types of graphs

• can add custom forces

• relatively easy to implement

• repulsion loop is O(n²) per iteration

– can speed up to O(NlogN) using quadtree or k-d tree

• prone to local minima

– can use simulated annealing

(115)

Node-link Layout

• understandable visual mapping

• can show overall structure, clusters, paths

• flexible, many variations

• all but the most trivial algorithms are > O(N²)

• not good for dense graphs

– hairball problem!

(116)

Matrix Representations

• There has been renewed interest in matrix representations of graphs recently

• The regularity, symmetry, and structure of a matrix are a win – people understand

them well

• But they don’t scale up really well

(117)

Adjacency Matrix

• Great for

dense graphs

• Can spot clusters

(118)

Hybrid Layout

• NodeTrix

– Hybrid of matrix and node-link

(119)

Really Big Graphs

• May be difficult to keep all in memory

• Often visualized as “hairballs”

• Smart visualizations do structural clustering, so you see a high-level overview of topology

(120)

Hierarchical Edge Bundles

• Bundle edges that go from/to similar nodes together

– Like wires in a house

• Uses B-spline curves for edges

• Reduces the clutter from many edges

(121)

Hierarchical Edge Bundles

(122)

Summary

• Graph Visualization need to consider

– layout

– simplification – interaction – Scale

• Facilitate understanding of complex socioeconomic patterns

(123)

outline

(124)

Time Series Data

• Fundamental chronological component to the data set

• Each data case is likely an event of some kind

• One of the variables can be the date and time of the event

• Examples:

– sunspot activity – medicines taken – cities visited

– stock prices

(125)

Time Series User Tasks

• Examples

– When was something greatest/least?

– Is there a pattern?

– Are two series similar?

– Do any of the series match a pattern?

– Provide simpler, faster access to the series

(126)

Classification

• Discrete points vs. interval points

• Linear time vs. cyclic time

• Ordinal time vs. continuous time

• Ordered time vs. branching time vs. time with multiple perspectives

(127)

Fundamental Tradeoff

• Is the visualization time-dependent, ie, changing over time (beyond just being interactive)?

– Static

• Shows history, multiple perspectives, allows comparison

– Dynamic (animation)

• Gives feel for process & changes over time, has more space to work with

(128)

Standard Presentation

• Present time data as a 2D line graph with time on x-axis and some other variable on y-axis

(129)

Periodic Visualization

• Visualizations can be very good at helping us spot patterns in data

• Often, these patterns are periodic, most often repeating in time

(130)

Calendars

Dow Jones Industrial Average 2006 - 2009

(131)

Heat Maps

• each dot shows the time of each of the third of a million emails Stephen Wolfram have sent since 1989

(132)

Spirals

• Standard x-y timeline or tabular display is problematic for periodic data

– It has endpoints

• Use spiral to help display data

– One loop corresponds to one period

• Scale to large data sets

• Support identification of periodic structures in the data

• Compare multiple datasets

(133)

Spirals

• One year per loop

• Same month on radial bars

• Quantity represented by size of blob

(134)

ThemeRiver

• Background: a user is less interested in document themselves than in theme

changes within the whole collection over time

• River height (thickness) encodes relative frequency of themes

• ThemeRiver provides users a macro-view of thematic changes

• Helps users identify time-related patterns, trends, and relationships across a large

collection of documents

(135)

ThemeRiver

(136)

ThemeRiver

(137)

Summary

• Think about the data

– What characteristics?

– Can InfoVis help?

• Think about the visualization techniques

(138)

outline

(139)

Text is Everywhere

• We use documents as primary information artifact in our lives

• Our access to documents has grown tremendously in recent years due to networking infrastructure

– WWW

– Digital libraries

(140)

Big Question

• What can information visualization provide to help users in understanding and

gathering information from text and document collections?

• Related Topic - Information Retrieval

• InfoVis, seems to be most useful when

– Perhaps not sure precisely what you’re looking for

– More of a browsing task than a search one

(141)

Challenge

• Text is nominal data

– Does not seem to map to geometric/graphical presentation as easily as ordinal and

quantitative data

• The “Raw data --> Data Table” mapping now becomes more important

(142)

One Text Visualization

Uses:

Layout Font Style Color

(143)

Word Counts

(144)

Tag/Word Clouds

• Currently very “hot” in research community

• Have proven to be very popular on web

• Idea is to show word/concept importance through visual means

– Tags: User-specified metadata (descriptors) about something

– Sometimes generalized to just reflect word frequencies

(145)

Tag/Word Clouds

(146)

Tag/Word Clouds

(147)

Problems

• Actually not a great visualization

– Hard to find a particular word

– Long words get increased visual emphasis – Font sizes are hard to compare

– Alphabetical ordering not ideal for many tasks

• Why So Popular?

– Serve as social signifiers that provide a

friendly atmosphere that provide a point of entry into a complex site

– Act as individual and group mirrors – Fun, not business-like

(148)

Wordle

www.wordle.net

(149)

Wordle

• Tightly packed words, sometimes vertical or diagonal

• Word size is linearly correlated with

frequency (typically square root in cloud)

• Multiple color palettes

• User gets some control

(150)

Layout Algorithm

• Idea:

– sort words by weight, decreasing order for each word w

w.position := makeInitialPosition(w);

while w intersects other words:

updatePosition(w);

– Init position randomly chosen according to distribution for target shape

– Update position moves out radically

(151)

Beyond Individual Words

• Can we show combinations of words, phrases, and sentences?

(152)

Word Tree

(153)

Word Tree

• Shows context of a word or words

– Follow word with all the phrases that follow it

• Font size shows frequency of appearance

• Continue branch until hitting unique phrase

• Clicking on phrase makes it the focus

• Ordered alphabetically, by frequency, or by first appearance

(154)

Interaction

(155)

Phrase Nets

• Examine unstructured text documents

• Presents pairs of terms from phrases such as

– X and Y – X’s Y – X at Y

– X (is | are | was | were) Y

• Uses special graph layout algorithm with compression and simplification

(156)

Examples

(157)

Overviews of Documents

• Can we provide a quick browsing,

overview UI, maybe especially useful for small screens?

(158)

Document Cards

• Compact visual representation of a document

• Show key terms and important images

(159)

Document Cards

• Layout algorithm searches for empty spacerectangles to put things

(160)

Interaction

• Hover over non-image space shows abstract in tooltip

• Hover over image and see caption as tooltip

• Click on page number to get full page

• Click on image goes to page containing it

• Clicking on a term highlights it in overview and all tooltips

(161)

Text Themes

• Look for sets of regions in a document (or sets of documents) that all have common theme

– Closely related to each other, but different from rest

• Need to run clustering process

(162)

Themescapes

• Self-organizing maps didn’t reflect density of regions all that well -- Can we improve?

• Use 3D representation, and have height represent density or number of

documents in region

(163)

Themescapes

(164)

WebTheme

(165)

Topic Modeling

• Hot topic in text analysis and visualization

• Latent Dirichlet Allocation

• Unsupervised learning

• Produces “topics” evident throughout doc collection, each modeled by sets of

words/terms

• Describes how each document contributes to each topic

(166)

TIARA

• Keeps basic ThemeRiver metaphor

• Embed word clouds into bands to tell more about what is in each

• Magnifier lens for getting more details

• Uses Latent Dirichlet Allocation to do text analysis and summarization

(167)

Representation

(168)

Features

(169)

TextFlow

• Showing how topics merge and split

(170)

ParallelTopics

(171)

outline

(172)

Geographical Data

• Fundamentally different from other kinds of data since they are inherently spatially structured in two or three dimensions

(173)

Dot Map

• Visualizing specific points

• Nominal data

• Arranged by Latitude/Longitude

(174)

Dot Map

sanfrancisco.crimespotting.org

(175)

Dot Map

• Clustering, e.g. k-means algorithm

(176)

Choropleth Map

• Areas are shaded or patterned in

proportion to the measurement of the statistical variable being displayed on the map

(177)

Choropleth

(178)

Problems

• Easy to slant data to suit the

cartographer’s purpose (by adjusting the slicing values)

• Create the illusion of rapid breaks whereas data varies continuously and gradually in the real world

• Allow small areas (like major cities) to

overwhelm the data of large regions (like states)

(179)

Cartogram

• A cartogram is a diagram which uses the form of a map to present numeric

information while maintaining some degree of geographic accuracy.

(180)

Cartogram

(181)

Flow map

• a mix of maps and flow charts, that show the movement of objects from one

location to another

(182)