Graph Wavelets for Spatial Traffic Analysis
Graph Wavelets for Spatial Traf?c Analysis
BUCS-TR-2002-020
Mark Crovella Eric Kolaczyk
Department of Computer Science Department of Math and Statistics Boston University Boston University
Boston MA02215Boston MA02215
July15,2002
Abstract
A number of problems in network operations and engineering call for new methods of traf-
?c analysis.While most existing traf?c analysis methods are fundamentally temporal,there is
a clear need for the analysis of traf?c across multiple network links—that is,for spatial traf?c
analysis.In this paper we give examples of problems that can be addressed via spatial traf?c
analysis.We then propose a formal approach to spatial traf?c analysis based on the wavelet
transform.Our approach(graph wavelets)generalizes the traditional wavelet transform so that
it can be applied to data elements connected via an arbitrary graph topology.We explore the
necessary and desirable properties of this approach and consider some of its possible realiza-
tions.We then apply graph wavelets to measurements from an operating network.Our results
show that graph wavelets are very useful for our motivating problems;for example,they can
be used to form highly summarized views of an entire network’s traf?c load,to gain insight
into a network’s global traf?c response to a link failure,and to localize the extent of a failure
event within the network.
This work was supported in part by NSF awards ANI-9986397and ANI-0095988,and by ONR award N00014-99-1-0219.
1Introduction
To date,the traf?c analysis tools developed in the research community and the traf?c analysis needs of network engineers and operators have been somewhat disconnected.Most research on traf?c analysis has focused on the properties of traf?c?owing over individual links,treated as a timeseries[1].However,network engineers and operators are very often more concerned with the properties of traf?c over multiple links,or whole networks.
In fact,there are many network engineering challenges that could be aided by better tools for traf?c analysis.For example,traf?c properties play a central role in1)provisioning and capacity planning;2)network con?guration and traf?c engineering;3)failure detection and diagnosis;and 4)attack detection and prevention.However,traf?c analysis tools and methods focused on these kinds of problems are generally not well developed.As a result,many network operators and engineers are forced to address these problems manually or via ad-hoc tools.
A common thread running through these problems is the importance of comparison and anal-ysis of traf?c patterns across multiple,or all,network links simultaneously.We call this spatial traf?c analysis.1Spatial traf?c analysis seeks to answer questions about traf?c patterns in and between“regions”—topologically localized sets of links—of a network.For example,traf?c engineering can be aided by summarizations of average traf?c in different network regions;and failure and attack detection can be aided by comparisons of traf?c across different network regions.
Providing useful,practical tools for spatial traf?c analysis is dif?cult.Two problems arise:?rst,the large quantity and high dimensionality of the data involved is unmanageable without methods for ef?cient and?exible data summarization.Second,algorithms must be developed that correctly and intelligently make use of such summaries for the solution of network engineering problems.Given the many degrees of freedom introduced by the wealth of data,such algorithms are not immediately obvious.Good solutions for these two problems are interrelated,because each in?uences the other.
In this paper we present new techniques for spatial traf?c analysis.These techniques are based on explicit consideration of network topology;we believe that effective network engineering must consider both the traf?c properties on the network’s links and the manner in which the links are connected.Thus our approach is intended to support a whole-network view of data traf?c.
To enable this view,we develop a new set of formal tools based on wavelet analysis.Our principal insight in this thrust is that traditional wavelet analysis can be generalized for use on data elements connected via an arbitrary graph topology,leading to discrete-space analogues of the well-known wavelet transform.That is,in contrast to the traditional use of wavelets in traf?c analysis,we apply wavelets to the spatial domain rather than the temporal domain.In this paper we show one way to accomplish this,and we develop a formal framework for what we call graph wavelets.Graph wavelets are quite general and?exible,and we explore some of the variations that are possible.
Using measurements taken from an operating network(Abilene[2])we show that graph wavelets can provide considerable leverage on whole-network traf?c analysis.We show how graph wavelets can be used to form highly summarized views of an entire network’s traf?c load;how they can be 1More accurately,we might instead write topological to distinguish between this context and that in which the actual spatial geography of the network is incorporated into the analysis.However we use spatial to emphasize the similarity in spirit of our methods to those in the spatial analysis domain.
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used to gain insight into a network’s global traf?c response to a link failure;and how they can help localize the extent of a failure event.
The examples in this paper use link counts available from routers via SNMP.However the methods are general enough to apply to other kinds of measurements associated with the network graph:for example,to study spatial correlation patterns in packet loss.Furthermore,the methods apply equally well to measurements associated with a graph’s edges(links)or vertices(routers).
The remainder of the paper is organized as follows.In Section2we review related work.Then in Section3we describe example motivating problems,and we present an informal introduction to graph wavelets as tools for addressing those problems.Section4lays out the formal aspects of graph wavelets:their de?nition and certain basic properties.Section5then presents detailed examples of how graph wavelets shed light on the nature of measurements taken from the Abilene network.Finally,in Section6we conclude.
2Background and Related Work
The vast majority of research into network traf?c analysis has focused on the behavior of traf?c on individual links over time.This approach has yielded a number of insights.Most salient among these are observations about the time scaling behavior of traf?c:self-similarity and long-range dependence,[3,4];and multifractality and local scaling[5,6].Many of the key results in traf?c time scaling analysis have been facilitated by the use of powerful tools,in particular the techniques of wavelet analysis(e.g.,[7]).
These temporal traf?c analyses have been quite successful in illustrating the presence of sur-prising patterns in the traf?c?owing over individual links.However remarkably little research has sought to investigate whether traf?c patterns are discernable across multiple links.
A similar trend has taken place in the development of network anomaly detection systems.The authors in[8]propose that an anomaly detection system should:
1.summarize the nature of typical network conditions in some compact set of metrics,
2.continually compare current conditions to the typical metrics,and
3.draw operator attention to deviations from typical conditions in as precise and informative
manner as possible.
In a style similar to time scaling analysis,work in anomaly detection has generally approached the summarization task in step1from a single-link,temporal analysis standpoint–for example,[9].
These timeseries-based approaches to anomaly detection have also made use of wavelet anal-ysis.An example is[10],which explores the diagnostic utility of the traf?c energy function;this function is easily obtained using multiresolution analysis.Another approach applying wavelet analysis to anomaly detection is[11],which focuses on analysis of traf?c?ow measurements.
In contrast,the approach we take to anomaly detection—and traf?c analysis generally—focuses on the spatial domain:that is,the relationship between traf?c on topologically related links.In that sense our work bears a relation to[11],which shows that comparing traf?c?ows in the incoming and outgoing directions of an access link is useful for identifying anomalies such as denial of service attacks and?ash crowd behavior.
2
Generally speaking,in?elds ranging from image processing to geography,experience has found that scale is a concept of fundamental importance to the analysis of spatially indexed data. We will argue in Section III(and throughout this paper)that many of the spatial challenges faced by network engineers similarly involve scale in some essential fashion.And therefore our emphasis here is on methods for the multiscale analysis2of spatial network data.
The image processing literature arguably has to date the most well known and technically de-veloped body of multiscale analysis techniques for spatial data.Modern representatives from this body perhaps can be said to begin with early work on Laplacian pyramid?ltering[13](which itself formalized still earlier ideas in image processing and computer vision),which was soon fol-lowed and replaced by the current paradigm based on two-dimensional wavelets and their exten-sions.Wavelet-based tools have had a fundamental impact on a variety of standard tasks in image processing,including compression(witness their key role in the JPEG2000standard),denoising, segmentation,and classi?cation.
However,wavelet-based methods for images are not immediately applicable to the analysis of spatial network data,for the simple reason that the former are designed for standard topologies and not arbitrary network topologies.On the other hand,there has been recent success in extending the basic wavelet framework to non-standard topologies(e.g.,[14,15,16]),although none of this work so far is relevant to network analysis.What is needed is a notion of wavelets on graphs, which we develop in detail in this paper.
3Motivation and Approach
In this section we provide a more detailed motivation for the notion of spatial traf?c analysis,and complement that with an informal illustration of our approach to the problem.
3.1Spatial Traf?c Analysis:Motivation
A number of example problems in network engineering and operations will serve to highlight the need for a whole-network approach to traf?c analysis.
1.Identifying Spatial Aspects of Typical Operating Conditions
An important problem facing network operators and engineers is the identi?cation and inter-pretation of typical operating conditions.This is fundamentally a whole-network problem.
As an example,spatial analysis plays a role in traf?c engineering.The goal of traf?c engi-neering is to assign traf?c?ows to network paths in a way that meets some design criterion.
One commonly sought criterion can be load balancing across the network.Engineers may seek to balance load so as to minimize the effects of any single link failure,or to minimize the utilization of the busiest links.
2Multiscale analysis,as used in the various literatures,refers simply to the analysis of a given object(s)at multiple scales.While the term“multiresolution analysis”sometimes is used interchangeably with“multiscale analysis,”the former has a speci?c technical meaning in the mathematics and engineering communities(referring to a sequence of successive approximation spaces,as developed originally by Mallat and Meyer–e.g.,see[12]).The latter more accurately describes the perspective and contributions in this paper and will be used throughout.
3
A valuable precursor to load balancing is an understanding of which network regions are
carrying the most load,and which regions are relatively less utilized.Armed with this knowledge,network engineers can make high-level,qualitative decisions about the intended outcome of route changes when performing load balancing.Summary information about traf?c loads over varying network locations and region sizes provides help in making these kinds of traf?c engineering decisions.
2.Understanding Shifts in Traf?c Patterns
A related goal involves understanding the shifts in traf?c patterns as a result of traf?c engi-
neering decisions or network equipment failures.
Some networks are engineered with suf?cient bandwidth for“protection,”i.e.,so that traf?c shifts due to equipment failures can be absorbed without manual intervention in the routing system.In contrast,some networks are provisioned with the expectation that equipment fail-ures will be addressed through explicit traf?c engineering actions.In each case,it is essential to have a whole-network view of how traf?c patterns shift when equipment fails or traf?c is manually re-routed.This whole-network view must provide quantitative information about which regions of the network experienced increased load and which experienced decreased load as a result of the network event.
3.Identifying Regions Exhibiting Traf?c Anomalies
When traf?c exhibits unusual characteristics,an immediate and fundamental question con-cerns the size and extent of the region over which the anomaly occurs.
For example,if observed traf?c load increases to an unusual level,this may be due to a num-ber of factors.Traf?c throughout the network may have risen,due to some external driver of increased demand such as a breaking news story.Alternatively,traf?c in a localized network region may be increased due to a?ash crowd effect(publication of a popular video or report that drives traf?c to a single location).Finally,traf?c load may be due to a particular pair of hosts engaging in abnormally high traf?c.These three scenarios are primarily distinguished by the size of the“neighborhood”over which the anomalously high traf?c is observed,and they each demand a different response from network operators.
As another example,rapidly detecting denial of service(DoS)attacks is crucial for respon-sive network management.Unfortunately,increased traf?c on a single link is not a good indicator of the presence or nature of a DoS attack.Most DoS attacks are distributed,with ?ooding packets arriving from multiple sources along multiple paths.Accurate identi?ca-tion of a distributed DoS attack using traf?c counts requires the simultaneous assessment of traf?c on multiple links of the network.
3.2Spatial Traf?c Analysis:Approach
The problems just described all concern questions about one or more“regions”or“neighborhoods”within a given network.To place our discussion of network neighborhoods in a formal setting we consider the graph that is isomorphic to the network as follows:routers or switches in the network correspond to vertices in the graph;and communication links in the network correspond to edges in the graph.We will call the collection of routers and links the network and the corresponding
4
Figure1:Example Network:Abilene
graph the network graph.Furthermore,we will reserve the terms“links”and“routers”for the network elements and the terms“edges”and“vertices”for the graph elements.3 Furthermore,another graph will be important:the network line graph.For any given graph
its corresponding line graph is de?ned such that and there is an edge in for each pair of edges in that share a common endpoint;i.e.,
The network line graph is the line graph of the network graph.
The two kinds of graphs are both useful because in a network,certain measurements are as-sociated with the routers,and certain measurements are associated with the links.When we are concerned with comparing measurements associated with routers,then we will be concerned with the adjacency relationships of routers,and so with the network graph.However when we are con-cerned with measurements associated with links(as will be the case in all of the examples in this paper)we will be concerned with the adjacency relationships of links,and so our analyses will involve the network line graph.All of the numerical results that follow in this paper will be based on network line graphs.However,our graph wavelets are de?ned for arbitrary connected graphs.
Our examples in this paper use the network shown in Figure1.This is a map of the Abilene network,which is the network supporting Internet2(this image is from[2]).4This network has11 routers and14links.The corresponding line graph(not shown)has14vertices and23edges.
Armed with these tools,we can begin to explore methods for analyzing measurements with respect to network neighborhoods.In the remainder of this section we present an intuitive view of our proposed approach.A formal,rigorous development is deferred to the next section.
For purposes of discussion here,let us de?ne the zero-hop neighborhood of a link as the link itself.The one-hop neighborhood is the link,and the set of all links that can be reached in one hop;that is,by traversing a single edge in the network line graph.The two-hop neighborhood of a link is its one-hop neighborhood and all the links that can be reached from any link in that neighborhood in one additional hop,and so on.
3We will consider edges in the graph to be undirected.This is a simpli?cation,and we discuss some implications of this simpli?cation below.
4We have omitted one link from this?gure for which we have no data.Internet2is a project developing new network applications and technologies;it has built and uses the Abilene network for testing and deploying these experimental systems.All of the links shown are OC-48,running at2.48Gbps.
5
Consider the NYC-Cleveland link.Its one-hop neighborhood consists of the three links from
Indianapolis to Washington DC,and its two-hop neighborhood consists of those three links plus
the Indianapolis-Kansas City,Indianapolis-Atlanta,and Washington DC-Atlanta links.
The central idea in our approach to spatial network data analysis is the comparison of metrics
between neighborhoods.For example,for any given link and metric,we might de?ne a comparison
at level(where,for convenience,is an even number)as the average of that metric over all links
in the-hop neighborhood,minus the average over all links that are in the-hop but not the -hop neighborhood.That is,we compare the average measurement in a“disk”around the link to the average measurement in the corresponding“ring”around the disk;if the metric is larger
on average closer to the link,the comparison will be positive.So the level2comparison for the
NYC-Cleveland link might consist of the average measurements on the Indianapolis-Cleveland
and NYC-Washington links,minus the measurements on the NYC-Cleveland link.5
A number of considerations motivate this general style of data analysis.First,data traf?c on
nearby links may often be highly correlated;this will occur for a number of reasons,including
the fact that each link carries data?ows which themselves likely pass over multiple links.Thus it
may often be reasonable to summarize the traf?c on many links in a neighborhood with a single
value.Second,differences between neighborhoods are important,as can be seen from the example
problems in this section;we wish to draw attention to such differences in our analysis.Third,
different effects will be expected to occur at different spatial scales in the network;hence,we
de?ne comparisons at varying levels so as to?exibly detect a wide range of phenomena.
The general notion of summarization and comparison over varying locations and scales is the
underlying principle of wavelet analysis.Indeed,the example problems and approach described in
this section bear strong similarity to problems in signal and image processing,domains in which
wavelet analysis has provided considerable leverage.However,traditional wavelet analysis has
restricted itself primarily to regular spaces,e.g.,[12].Therefore,in pursuit of a formal basis
for attacking the problems described here,it is necessary and appropriate to extend the notion of
wavelets to certain graph topologies,which we do in the next section.
4Graph Wavelets
In this section we approach the topic of whole-network wavelet analysis in a more formal fashion.
After reviewing some basic concepts and principles from traditional wavelet analysis we develop
a framework for a class of graph-based wavelets.
4.1Traditional Wavelets and Multiscale Analysis
At the most basic level,a multiscale analysis(based on wavelets or otherwise)is simply a coor-
dinated way of examining local differences in a set of measurements,across a range of scales.
Multiscale analyses based on wavelets,of course,are now the most common and well-known
example of this approach.Although there are currently a host of wavelet functions available,pos-
sessed of a variety of different properties and characteristics,at their most basic these functions
share the two fundamental properties that they(i)are localized(having either?nite or essentially 5This description in terms of simple averages over neighborhoods of different levels is a simpli?cation for purposes of illustration.
6
?6?4?20246
?0.50
0.5
1
x Ψ(x )
Figure 2:Haar (dot-dashed)and Mexican Hat (solid)Wavelet Functions on the Real Line.
?505
?5
5Figure 3:Mexican Hat Wavelet Function on the Plane.The central disk is strongly positive,and the surrounding ring is strongly negative.
?nite support)and (ii)have zero integral (and hence,excluding the trivial case,they must oscillate positive and negative).By virtue of this locally oscillating behavior,the inner product of a wavelet,say ,with another function,say ,yields coef?cients that are essentially the weighted difference of information in on the regions of positive and negative support of .Any other properties or characterisics of ,such as compact support or smoothness,are the result of using additional “degrees of freedom”in the overall design process.
Figure 2shows two examples of wavelet functions on the real line I R.The ?rst is a symmetric variant of the well-known Haar wavelet,piecewise constant and of ?nite support.The second is the
one-dimensional analogue of the so-called “mexican hat”wavelet,
,which is in?nitely differentiable and of in?nite support.Both have zero integral and unit norm.When these two functions are rotated about their point of symmetry,the results are radially sym-metric analogues in the plane I R .The analogue of the latter is the mexican hat wavelet,whose relative shape and magnitude are shown in Figure 3in the form of an image.
Traditionally,a wavelet analysis of ,for functions de?ned on some subset of a Euclidean
space (e.g.,I R or I R )is based on the collection of coef?cients
,where is a shifted and dilated version of by and ,respectively.For I R,
7
the mapping is known as a continuous wavelet transform.If on the other hand and,for Z,this mapping is known as a discrete wavelet transform.And in the latter case,when the function is chosen appropriately,it is possible to create a system of wavelet functions that are orthonormal.Within each of these classes of wavelet transforms(con-tinuous,discrete-redundant,and discrete-orthogonal)there are numerous examples to be found, customized to have various additional properties felt to be useful for a particular application(s). See[12],for example.
Regardless of the speci?cs,the end result of a wavelet transform is an alternative representation of the information in with respect to an indexing in scale and location.Which particular class of wavelet transform is preferable(as well as the choice of wavelet function within class),if any,typically depends on the uses to which one intends to put such a representation.For example, the continuous wavelet transform has been quite popular in astronomy,particularly for the detec-tion of point sources and anomolies in satellite image data(e.g.,[17]).Alternatively,the discrete wavelet transform and its extensions have proven especially useful for the tasks of denoising and compression(e.g.,[18]).Our own contribution in this paper can be said to more closely resemble the traditional continuous wavelet transform in spirit.
More recently,there has been much work on so-called“second generation”wavelets(e.g., [19]).Systems of such wavelets are not necessarily composed of either shifts or dilations of some single function.Nevertheless,the members are localized and indexed across a range of scales and locations within scales,have zero integral,and share some common characteristic(s)in their de?nition.Examples include piecewise constant wavelets de?ned on general measure spaces[14], wavelets on triangular meshes of arbitrary topology[15],and wavelets on the sphere[20,16].The wavelets we develop in this paper,in extending the traditional framework described above to the context of network graphs,are a new contribution to this second generation of wavelets.
4.2A Class of Wavelets for Graphs
Let be a connected graph,of degree,corresponding to a network of interest. Without loss of generality,we assume that measurements correspond to vertices,. That is,is either the network graph itself or the network line graph(as de?ned in Section3.2) depending on whether the actual measurements are taken at routers or on links of the underlying network.
The vertex set is a(?nite)metric space when equipped with the shortest path distance metric (in units of“hops”)de?ned with respect to.In fact,it is a measure space when equipped with simple counting measure as well,say.In extending the notion of wavelets to graphs,we seek a collection of functions I R,localized with respect to a range of scale/location indices
,such that at a minimum we have.Additional properties are built in by choice.
As foreshadowed by our discussion in Section3.2,the construction of our graph wavelets centers on the notion of comparing network measurements within a given region(s)(e.g.,a simple “disk”)to those in a surrounding region(s)(e.g.,a simple“ring”),with both sets of regions centered on a particular vertex and calibrated to a scale.The notion of regions will be made explicit through the concept of hop-neighborhoods.Speci?cally,we de?ne the-hop neighborhood about,,to be the set of vertices that are less than or equal to hops from. The zero-hop neighborhood of will simply be itself i.e.,.Similarly,we let
8
Figure4:Schematic Illustration of Graph Wavelet Weighting Scheme:Weights obtained from analogue of mexican hat wavelet.
be the set of vertices exactly hops away from.We call
the-hop ring about.
In addition to the condition of having zero integral,we will require that each function be constant within hop rings and zero on hop rings outside.These constraints have the effect of imposing a type of symmetry on and a scaling of the underlying support.Figure4 shows an illustration of this effect,based on the construction given below,which may be compared to Figure3for example.
Let denote the largest for which the hop ring is non-empty.Given the nature of the graph topology,in contrast to that of Euclidean space,this is a necessary and well-de?ned parameter in our construction.Within this framework there is still a good deal of freedom in choosing the form of our wavelet functions.Speci?cally,we note that our symmetry condition implies that de?nition of can be reduced to that of a set of constants on rings,for .Note then that
(1)
With the choice of,we reduce the problem further to that of?nding an appropriate set of constants that depend only on scale and hop distances.But it can be seen from(1)that,for each location and scale,if and only if.
We therefore have the following result regarding wavelets on graphs.
Theorem1Let be as above.For each and,de?ne I R as
(2)
9
where(excluding the trivial case),
if
otherwise
and is a normalizing constant.
Then the system of functions satis?es
and
and for functions I R
Ave(3)
It can be seen that our system of graph wavelets most closely resembles the traditional con-tinuous wavelet transform in spirit,as opposed to the discrete wavelet transform,in that the set of wavelet coef?cients produced under our transform are indexed at all scales and all locations within scale allowed by the graph topology.Note,however,that these wavelets are not de?ned as trans-lations of some single simple function.Nor,while there is an explicit scaling in their support, does the actual“shape”of the wavelets have to necessarily scale with in any obvious manner.The lack of translation-invariance is unavoidable,due to the underlying network topology.However, a sense of scaling of shape is often desireable for the purpose of comparing wavelet coef?cients across scales or between two different types of wavelets,and may be accomplished by linking the choice of’s to some common mechanism.
For example,a straightforward approach is to begin with a function supported(perhaps after appropriate re-scaling)on the unit interval,for which,and the shape of which is appealing for analysis on the real line.Then,letting the be averages of on equal-length subintervals i.e.,,it follows automatically that the sum to zero and that their“shape”scales with.
We illustrate this approach with two choices of,taken from the functions shown in Figure2. Each function is restricted to the positive real line,truncated at,re-scaled so as to live on,and re-normalized so as to maintain the properties of zero integral and unit norm.In the case of the Haar wavelet function,for odd,this results in the?rst of the being equal and positive,the second being equal and negative,and all being equal in absolute value.The wavelet coef?cient of is then essentially the difference of averages of measurements on the disc and the ring.However,when is even,we will have for.The wavelet coef?cients are then still proportional to the difference of averages on a disc and surrounding ring of equal‘radius’,but now the disc and ring are separated by a thin ring whose measurements are ignored(due to their ring corresponding to this zero coef?cient).If one instead derives the from the other function shown in Figure2 (i.e.,the analogue of the mexican hat wavelet),there is no such phenomenon for either even or odd,though the coef?cients now yield a more general weighted average of measurements on the rings in.
Figure5shows the coef?cients resulting in the case of,for both of these choices of. The two wavelet functions have been modi?ed to sit on the unit interval,as described above.The
10
00.20.40.60.81
?1?0.5
0.5
1
1.5
2
Figure 5:Average Sampling of Haar (dot-dashed)and Mexican Hat (solid)Wavelets,:Wavelet functions in Figure 2are adjusted to the unit interval.Weights obtained by average sam-pling are shown using piecewise constant segments of appropriate height and length (:Haar;:Mexican Hat).
values of the weights
,for and ,obtained by average sampling of the functions,are shown on the same plot through the use of piecewise constant segments of appropriate height
and length.For this particular choice of the values of the
weights are almost identical,thus indicating a common treatment of the values of at the central vertex for each wavelet
coef?cient
under either choice of wavelet.However,the treatment of values at vertices of or hops from receive almost opposite treatment by the two wavelet functions,although whereas exactly for the Haar wavelet is only close to zero for the mexican hat
wavelet.Of course,for larger choice of the overall pattern (“shape”)in the
becomes more rich for the mexican hat wavelet,while that for the Haar wavelet remains unchanged (other than the ?uctuations with odd and even ,as described above).
Figure 4provides a schematic illustration of how the relate to a hypothetical network graph
local to a vertex ,for
.Weights from Figure 5for the mexican hat wavelet have been used.The result may be compared to the image representation of the actual two-dimensional mexican hat wavelet in Figure 3.
On a ?nal note,we mention that numerical computation of our graph wavelet coef?cients is straightforward.A direct implementation of the formulas underlying Theorem 1,using the
adjacency matrix of the graph ,yields an algorithm that produces all coef?cients at a single scale in time .We have used this direct algorithm to develop the results shown next in Section V .
5Graph Wavelets in Practice
To illustrate the utility and features of traf?c analysis based on graph wavelets we apply it to the most fundamental measure of network performance:bytes carried per unit time.We use measure-ments from the Abilene network,taken by polling RMON2MIBs on core routers,which includes counts of bytes and packets ?owing over each of the links shown in Figure 1.We aggregate the bytes ?owing over each link,placing the measurements into 30second intervals on a common
11
-6e+09-4e+09
-2e+09
2e+09
4e+09
6e+09
8e+09350400450500550600
Time (30 sec. increments)
Traffic j = 3j = 1Figure 6:Isolating Periodicity on the NYC-Cleveland Link
-4e+09
-2e+09
2e+09
4e+09
150200250300
350
Time (30 sec. increments)Traffic j = 1j = 3j = 5Figure 7:Haar coef?cents for the Denver-Kansas City Link during Failure Event
timebase.For simplicity in this example,we sum the bytes ?owing in both directions over any link;however our analysis can be extended to the case in which traf?c in different directions is considered separately.The measurement period we focus on is Wednesday,April 24,2002starting at approximately 11:00pm UTC.
For simplicity,and to integrate the material of Section IV with the motivation in Section III-B in a more immediate fashion,our ?rst few examples will use the Haar-style wavelet for our analysis;later we contrast the features of the Haar and the mexican hat wavelets as applied to our data.Also,as described in Section 4.2,the Haar-style wavelet involves zero weightings for certain rings when is even;therefore,to simplify interpretation of the analysis results further,we will restrict our attention initially to analyses where is odd,and address the case where is even later.
Our ?rst example is shown in Figure 6.This is a plot of traf?c on the NYC-Cleveland link during a typical portion of the measurement period (upper line),along with the values for coef-?cients when (lower line)and (middle line).Note the periodic traf?c pattern on the link.Understanding the nature of this anomalous behavior effect falls under the category of “identifying regions exhibiting traf?c anomalies”as discussed in Section 3.1.This periodicity may be introduced by a dominant application,by interactions between applications or ?ows,or by an
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Figure8:Network-Wide View of Wavelet Coef?cients
incipient fault in a network element such as a router.An important question therefore is where else on the network this perodicity is visible;that is,over what spatial neighborhood is the periodicity occurring?
In this case we can immediately infer the extent of the periodicity by inspecting the and coef?cients.The comparison shows little evidence of periodicity,indicating that the link itself is behaving very similarly to its one-hop neighbors(NYC-Washington and Cleveland-Indianapolis).On the other hand,the comparison does show evidence of periodicity,indicat-ing that the periodic traf?c pattern on these three links(Washington-NYC-Cleveland-Indianapolis) is different from the behavior of the wider neighborhood–that is,the effect is localized to the one-hop neighborhood.
Our next example is shown in Figure7.This is a plot of traf?c on the Denver-Kansas City link spanning the period of a service outage on this link.This event falls under our discussion of “identifying regions exhibiting traf?c anomalies”in Section3.1,i.e.,given that there is a change in the traf?c on a link,how widespread through the network is this change?We can look at wavelet coef?cients before and after the event to answer this question.As shown in the Figure,traf?c drops to approximately half its previous level as a result of the failure;coef?cients at and3show drops as well,but the drop is greater at than3;and shows virtually no change.This tells us that this traf?c change is a local one,but not a network-wide event(since the largest-scale coef?cient is unchanged).
In fact,we can also learn about network-wide behavior during this service outage event.Fig-ure8shows two sets of wavelet coef?cients for each link in the network(data for the Indianapolis-Atlanta link is not shown to lessen clutter).In each inset chart,traf?c is shown in the top bar,and coef?cients for and5are shown in successive bars underneath.The left hand bars show
13
coef?cients before the service outage event,and the right hand bars show coef?cients during the service outage event.
-8e+09-6e+09
-4e+09
-2e+09
2e+09
4e+09450455460465470475480485490495500
Time (30 sec. increments)Traffic j = 1j = 2j = 3-8e+09-6e+09-4e+09-2e+0902e+094e+09450455460465470475480485490495500Time (30 sec. increments)Traffic j = 1j = 2j = 3
(a)Haar Wavelet (b)Mexican Hat Wavelet
Figure 9:Comparison of Haar and Mexican Hat Wavelets;Atlanta-Houston Link
Looking at the and 5coef?cients (lowest set of bars)before the event versus during the event,it is clear that the network’s response to the service outage was to shift traf?c from its northern path to its southern path.That is,links along the path NYC-Cleveland-Indiapolis-Denver-Sunnyvale had generally negative (or small)coef?cients during the event,while links along the path NYC-WashDC-Atlanta-Houston-Los Angeles-Sunnyvale had generally positive coef?cients.This suggests that the two intercoastal paths are principle paths through the network,shedding light on typical traf?c source-destination paths.These comparisons highlight the utility of wavelet-based analysis to capture system-wide effects.
In contrast to this north-south effect,wavelet analysis can inform us about traf?c levels on a
east-west axis as well.Looking at the
coef?cients across the network before the outage (left hand set of bars),it is clear that they are largest (most positive)in the east,and smallest (most negative)in the west.This tells us that in the period before the failure,the network was generally more heavily loaded in its eastern region as compared to its western region.
Finally,we consider how the choice of wavelet function affects the properties of the trans-form.To do so,we examine the regions around the Atlanta-Houston link.Analyzing using the Haar wavelet yields the results shown in Figure 9(a).This plot shows that the coef?cients
are close to zero,while the
coef?cients are strongly negative.To interpret this recall that even numbered Haar coef?cients include a ring with zero weight,which in the
case is the one-hop ring (as shown in Figure 5).So these coef?cients show that the traf?c on this link is simi-lar to its immediate neighbors,but on average is much less than traf?c in the ring that is two hops
away.The
coef?cients are not as strongly negative,which shows that the average of the link and its one-hop neighbors is comparatively more similar to the two-and three-hop rings.
This abrupt change in values from to to is an indirect effect of the lack of smoothness of the underlying function used in the Haar case (see Figure 2).This lack of smoothness places a sharp emphasis on the difference between the inner disk and outer ring.
Replacing the Haar with the mexican hat yields more gradually changing coef?cients.For
and 3,the mexican hat has positive weight only at ,that is,on the central link.
14
Furthermore,the most negative values move out more slowly than in the Haar case;for example, when the Haar emphasizes the two-hop ring while the mexican hat emphasizes the one-hop ring(see Figure5).This effect can be seen in Figure9(b).The?gure shows that,as the traf?c comparison moves outward by rings,the difference between the traf?c on the Atlanta-Houston link and its weighted neighbors changes gradually and smoothly.
The difference gives insight into the relative utility of the different functions.The Haar wavelet is useful for precise distinctions between rings(as in Figure6);however,it is quite aggres-sive,with each new level averaging in another ring in full measure.The mexican hat wavelet is more gradual and better suited for?ner study of the successive neighborhoods of a particular node. 6Conclusion
As discussed in Section1,in contrast to the traditional use of wavelets in traf?c analysis,we apply wavelets in the spatial domain rather than the temporal domain.However an even higher goal is to build tools that can fuse these two views(spatial and temporal analysis)into a single framework that allows network operators and engineers to ask questions such as:“Is this region of the network experiencing unusual conditions?How long has this been going on?”Achieving this combined spatio-temporal view is a considerable challenge;what we present here is one step toward that goal.
More generally,we hope to move toward study of system-wide effects in large scale networks. The interaction of network topology and traf?c characteristics is a potentially important but largely unexplored area,in part due to lack of good tools.We believe that it will be easier to understand how whole networks behave as spatial traf?c analysis tools like those we describe here mature.
Lastly,we note that for some network analysis problems,graph wavelets analogous to the con-tinuous wavelet transform(as described in this paper)might be less appropriate than an approach analogous to the discrete-orthogonal wavelet transform.The discrete transform differs most funda-mentally from the continuous transform in the sense that the discrete transform involves wavelets constructed to sit on a nested series of coarsenings of the underlying data space.While the concept of coarsening is straightforward in Euclidean space,it is much less so on arbitrary graph topologies (e.g.,see[21]).However,just as the development of the continuous wavelet transform was a pre-cursor to that of the discrete-orthogonal wavelet transform in the context of traditional wavelets, the approach we describe here may serve as a precursor for an analogue of the discrete wavelet transform for graphs.
Acknowledgments
We gratefully acknowledge the help of Paul Barford and Joel Sommers at U.Wisconsin,and Guy Almes,Matt Zekauskas and Steve Corbato at Internet2for providing us with access to Abilene traf?c measurements.
15
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17
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Windows系统自带画图工具教程87586
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高中英语泛读教学初探
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变得更为重要了。 3.适应时代新要求 现在的学生，大部分都要走出去的，开展泛读课程能够让学生开阔眼界，增强英语的理解和表达能力。因为我们阅读的材料涉及到国外的文化，风俗习惯等各个方面，这样对学生将来的学习、工作有很大的作用！ 二、两者的区分度 精读，顾名思义在于一个“精”字，在我看来，就是要把文章中的每个词，每个句子都弄清楚，真正的吃透文章，所花的时间较长！而泛读则要求广泛的阅读，要求没有精读高，只要读懂文章的大意，不必追究文章的深刻内涵，这和高考中的阅读理解较为相似，通过广泛阅读文章，提高我们的阅读能力。 三、课堂的实施情况 1.材料的选择 现在的泛读课还是在摸索阶段，阅读材料大多来自于网上的一些美文或是一些名著中的节选。这些材料基本上是学生比较容易读懂的，有时候还会把相同主题的几篇文章放在一起让学生对比阅读，这样学生可以了解更多的信息，实现我们的阅读目标。 2.环节的设计 首先，词汇的处理。不管是精读还是泛读，词汇是首要的，所以在泛读教学过程对于词汇的处理是至关重要的。因为泛读不像精读那样要求对文章逐字逐句地掌握，所以在处理生词时，我们教师会忽略一些不影响理解的词。对于一些影响阅读理解但是可以通过上下文猜测出来词就设计成猜词理解。 其次，问题的设计。给足学生时间，从文章的整体把握入手，回答一些问题，让
高考英语主谓一致用法全汇总
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02 某些集体名词，如people，police，cattle等，只当复数看待，谓语动词必须用复数。 The police are searching for the thief.警察正在搜捕那个贼。03 单、复数同形的名词作主语时，谓语动词应根据意义决定单、复数。 如： A sheep is over there.那边有只羊。 Some sheep are over there.那边有些羊。 04 名词所有格之后的名词被省略，这种情况一般只指商店、工厂、住宅等，作主语时，动词一般用单数。 如： The doctor’s is across the street.诊所在街道的对面。 My uncle’s is not far from here.我叔叔家离这儿不远。常见的省略名词有the baker’s，the barber’s，the carpenter’s，the Zhang’s等。 表示店铺的名词，一般作集体名词看待，但用作主语时，谓语动词往往用复数。 如：
细节决定成败——认识“画图”软件教学案例
细节决定成败 ——认识“画图”软件教学案例 【事件背景】 2014年9月29日按照学校教学安排，把精心准备的《认识“画图”软件》一课在学科组内做了认真的课堂展示。这节课是小学三年级的课，前节课学生初步认识了纸牌游戏软件，对在Windows中打开软件、认识窗口有了初步的了解。但是学生初学画图，鼠标拖动操作还不熟练，在技巧上还有待于逐步尝试掌握。根据学生原有的水平我提出了一个设计思路，即“作品欣赏，激发兴趣，互相讨论，任务驱动，指导点评”。 课堂中重难点的处理我主要是采用任务驱动教学法，设置了三个学习任务，分别以不同形式完成。对于第一个任务：启动“画图”软件，让学生自学教材P31，完成“画图”软件的启动。是为培养学生的自主学习能力，多数学生都能顺利启动后，找两个同学示范启动，锻炼了学生的动手操作和语言表达能力。第二个任务：认识“画图”软件的窗口组成我主要是用事先录制好的微课展示让学生记住。学生对这种形式感到很新奇，自然很快就记住了。第三个任务是这节课的重点也是难点：尝试用画图工具简单作画。 【事件描述】 根据教学设计，我全身心的投入到本节课的教学实践之中，课堂伊始效果良好，学生不仅对学习内容表现出了极大的兴趣，而且行为表现也很规范，学习状态认真。所以很顺畅的完成了第一个学习任务，紧接着便进入第二个环节的学习，即认识画图软件的窗口。为了很好的完成这一重要的学习任务，我对教学设计几经修改，最后决定采用‘微课’的形式，我便精心制作课件，录音合成，以图示加拟人风格的自述形式进行软件的自我介绍。当初我想这样做一定会收到事半功倍的效果，期待着在课堂上那称心一幕的出现。事实又是怎样的呢？
高中英语主谓一致讲解
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泛 读——高中英语教学的有效途径
泛读——高中英语教学的有效途径 发表时间：2011-10-11T11:23:04.337Z 来源：《科学教育前沿》2011年第7期供稿作者：李黎 [导读] 很多老师认为，泛读即广泛的阅读，所以读得越多就越好，而实际上，泛读既是指广泛的阅读，同时也指泛泛而读。 李黎（广汉市第四中学校四川德阳 618300） 中图分类号：Ｇ63 文献标识码：Ａ文章编号：ISSN1004-1621（2011）07-029-02 《英语新课程标准》要求学生具备综合阅读的能力，着重提高学生用英语获取信息、处理信息、分析和解决问题的能力；逐步培养学生用英语进行思维和表达的能力。再想想高考中运用到阅读技能的，不仅仅有阅读的40分，还包括了完形填空的30分和短文改错的10分。"读书破万卷，下笔如有神"，广泛阅读，并且注重好词好句的积累，也是写作得高分的关键。阅读被提高到了如此高的地位，可谓"得阅读者得天下"。 阅读分为精读和泛读两种。精读是要逐字逐句的读，逐字逐句的理解意思、结构；而泛读是广泛的阅读，泛泛而读，追求的是阅读的速度和量。大纲中所强调的培养学生阅读能力，最终是要培养学生用英语进行思维和表达的能力，泛读将起着非常重要的作用。著名学者柯鲁克先生主张："中国英语教学应采用大量阅读为主要教学手段，进而取代字斟句酌讲解的精读这种传统的教学模式。"那么在英语教学中如何搞好泛读的教学呢？ 一、泛读材料的选择 泛读的材料需精心选择，搭配合理，才能培养学生的阅读兴趣，同时拓宽学生的知识面，提高学生应对各种文体的泛读材料的能力，根据目前课程标准以及考试大纲要求，泛读内容要注意：在体裁的选择上，要有记叙文、议论文、说明文、应用文等各种文体的泛读。在题材的选择上，要涉及到科普、政治经济、历史地理、人物传记、社会文化、故事传说等题材。可供高中生泛读的材料有很多，而高中生的时间却并不多，所以教师要帮助学生选择合适的泛读材料，优化学生的学习时间，提高他们的学习效率。以下几种较好的泛读材料，可供参考： 重视高考的真题。高考题是命题小组成员精心编制的，经过严格的校对审核，是很好的泛读材料。2004年到2011年全国高考真题约有140套，每份试卷中的第一篇阅读比较简单，可以供高一的学生阅读，第二篇可以给高二的学生阅读，第三篇和第四篇可供高三的学生阅读。 英文报纸类的泛读材料。报纸的最大优势在于新，时代性强，更能激发学生的兴趣。英语报纸目前有很多可供选择，比如：English Weekly、China Daily、21st Century、Learning English、Student English Times等等。可指导学生根据自身的英语程度作出适当的选择。 二、泛读的教学方法 1.泛读技能的培养 在近几年高考中，阅读理解题更加强调对学生的知识面、理解能力以及阅读速度的考察，试题形式更多样化，内容涉及面更宽。《普通高等学校招生全国统一考试考试大纲的说明（英语）》对阅读理解部分进行了解释和说明：阅读文章是我国考生接触外语的最主要的途径，因此，阅读理解在试卷中占权重较大。该部分要求考生读懂公告，说明，广告以及书，报，杂志中关于一般性话题的简短文章。考生应能： ( 1 ) 理解主旨和要义（2）理解文中具体信息 ( 3 ) 根据上下文推断生词的词义。 ( 4 ) 作出简单判断和推理 ( 5 ) 理解文章的基本结构 ( 6 ) 理解作者的意图，观点和态度。要想在很短的时间内完成这些任务，就必须要保证阅读的速度，而阅读的速度需要有阅读的技能来保证。进行泛读教学时应参照《英语课程标准》中有关阅读技能目标的要求，要教会学生在泛读中注意： 1）重视主题句（topic sentence）。主题句一般都位于一段话的段首，或者一篇文章的文首。找出文章的主题句，可以给我们启发和想象，帮助我们确定文章的和内容走向，加快泛读的速度。 2）猜测词义的技巧。即对生词进行猜测。根据出题人的意思，可能有以下几种不同的情况： 第一、根据上下文对生词意思进行猜测。比如，2011年英语高考真题（全国卷）中的68题，68. What does the word "residents" in Paragraph 1 probably refer to? A. chickens B. tomatoes C. gardens D. people 看该词在阅读材料中所在的位置：The family's old farm house has become a chicken bourse ,its residents arriving next month.这道题的答案就显然是跟上文中出现的chicken有关的。 第二、根据构词法。阅读的基础在于词汇，因此掌握基本构词法，例如，前后缀、合成和转化等等，是非常有必要的，由已知的单词，即可猜测出生词的含义。 第三、根据日常经验猜词。有些生词根据上下文的意思，再借助常识和生活经验就可以猜测出它的词义。 第四、利用从句猜词。有的生词后面有定语从句或者同位语从句，这两种从句都有解释的功能，根据这个从句，就可以猜出该词的含义。 3）推理判断的技巧。教师要教会学生根据已知的内容与常识相结合，顺着作者的思路去分析、判断和推理，猜出作者的弦外之意。例如，2011年普通高等学校招生全国统一考试（四川卷）英语中，阅读题49.The underline part "its idea" in Paragraph 3 refers to the idea of____ A. the equipment B. the project C. the digital media D. the physical library 该题便是考查推理判断的技巧。根据阅读材料中的"…the project is already providing chances for some of the many small new local companies working at the new technologies."推理可知its即是the project。 4）跳读、略读等忽略生词的技巧。在阅读中，出题人会有意不解释某些单词的含义，从文中其它部分或者用构词法也无法猜出这个生词的意思，这种单词往往不影响整篇文章的理解，用不着管它。这时候就可以忽略不看，继续浏览下文，节约阅读时间，提高泛读的效率。 2.课堂泛读与课外泛读相结合 1）课堂上的泛读。在传统的教学方式中，精读长期占据课堂，而泛读往往认为应该留在课后，实际泛读不仅仅应在课后进行，还要坚持每天上课都会有一篇文章的泛读，不管是听力课，还是精读课，先给出几分钟的时间，读一篇短文，然后再进行其它课。课堂上可用自己设计的几个简单的T--F question 、Yes-No question和wh-question，来考查学生泛读的效果。 2）课外的泛读。课外的泛读更是必不可少，每天花15分钟时间，高一读三篇小短文，这样，一学期下来就积累了几百上千篇的泛读
最新pymol作图的一个实例
Pymol作图的实例 这是一个只是用鼠标操作的初步教程 Pdb文件3ODU.pdb 打开文件 pymol右侧 All指所有的对象，2ODU指刚才打开的文件，(sele)是选择的对象 按钮A:代表对这个对象的各种action， S：显示这个对象的某种样式， H：隐藏某种样式， L：显示某种label， C：显示的颜色 下面是操作过程： 点击all中的H，选择everything，隐藏所有 点击3ODU中的S，选择cartoon，以cartoon形式显示蛋白质 点击3ODU中的C，选择by ss，以二级结构分配颜色，选择 点击右下角的S，窗口上面出现蛋白质氨基酸序列，找到1164位ITD，是配体 点击选择ITD ，此时sele中就包含ITD这个残基，点击（sele）行的A，选 择rename selection，窗口中出现，更改sele 为IDT，点击（IDT）行的S选择sticks，点击C，选择by element，选择，，调 整窗口使此分子清楚显示。 寻找IDT与蛋白质相互作用的氢键： IDT行点击A 选择find，选择polar contacts，再根据需要选择，这里选择to other atoms in object ,分子显示窗口中出现几个黄色的虚线，IDT行下面出现了新的一行，这就是氢键的对象，点击这一行的C，选择 red red，把氢键显示为红色。 接着再显示跟IDT形成氢键的残基 点击3ODU行的S，选择lines，显示出所有残基的侧链，使用鼠标转动蛋白质寻找与IDT 以红色虚线相连的残基，分别点击选择这些残基。注意此时selecting要是
residures。选择的时候要细心。取消选择可以再次点击已选择的残基。使用上述的方法把选择的残基（sele）改名为s1。点击S1行的S选择sticks，C选择by elements,点击L选择residures显示出残基名称.在这个例子中发现其中有一个N含有3个氢键有两个可以找到与其连接的氨基酸残基，另一个找不到，这是因为这个氢键可能是与水分子形成的，水分子在pdb文件中只用一个O表示，sticks显示方式没有显示出来水分子，点击all行S选择nonbonded，此时就看到一个水与N形成氢键 ，点击分子空白处，然后点击选择这个水分子，更改它的名字为w。在all 行点击H，选择lines，在选择nonbonded，把这些显示方式去掉只留下cartoon。点击w行s 选择nb-spheres. 到目前为止已经差不多了 下面是一些细节的调整 残基名称位置的调整：点击右下角是3-button viewing 转变为3-button viewing editing，这样就可以编辑修改 pdb文件了，咱们修改的是label的位置。按住ctrl键点击窗口中的残基名称label，鼠标拖拽到适合的部位，是显示更清晰。 然后调整视角方向直到显示满意为止，这时就可以保存图片了，file>>save image as>>png
如何上好高中英语阅读泛读课
如何上好高中英语阅读泛读课 河北省霸州市第一中学李丽丽摘要：在高中英语教学中, 培养学生阅读理解能力一直是教学的重点。在信息发达的当今世界，很大程度上取决于通过阅读进行交流的能力，新课程要求教师创造性地使用教材,开设泛读课，培养学生的阅读兴趣，使学生掌握阅读技巧，提高阅读能力，让学生掌握获取信息，处理信息和综合运用信息的能力，实现语言交际的目的，泛读课就是提高这种交际表达能力的有效途径。 关键字：高中英语、英语阅读、泛读课 高中英语阅读分为泛读( Extensive Reading ) 和精读( Intensive Reading )，前者侧重于信息的获取，后者则侧重于语言知识的掌握。而且泛读课与精读课也不同，前者属于单项技能训练课，其特征体现在“泛”与“读”两个方面。就“泛”而言，教材选用语言材料的内容呈百科知识性，包括社会生活各个方面。同时，语言材料的文体呈多样性，既有文学作品，又有记叙文、说明文、议论文、新闻、广告等语言风格不同的文章。就“读”而言，泛读课的阅读量大。泛读课的重要任务是指导学生掌握各种阅读方法，从而提高阅读理解的准确性，加快阅读速度，并且通过学生的大量阅读，逐渐扩大其词汇量。泛读课应帮助生活在信息爆炸时代的学生能通过阅读可以快速、准确地获取并处理信息。 一、开展高中英语阅读泛读课的必要性 新《课标》要求学生具备的综合阅读能力包括语篇领悟能力和语言解码能力，强调多学科知识的贯通，注重培养学生的语篇分析能力、判断能力以及根据语义进行逻辑推理的能力，提高阅读速度，增加其阅读量和扩大词汇量。 英语高考成绩的高低主要取决于学生的阅读水平。每年高考中的完形填空和阅读理解两大题占的分值很大，学生英语高考成绩的好坏主要就是看这两道题的答题情况，而且这两道题主要是考察学生的阅读能力。所以，学生要想高考取得高分，就必须具备较高的阅读水平。只有依靠大量的阅读，不断扩大词汇量，广泛了解英语国家的文化背景、风俗习惯、历史地理等各方面的知识，才能提高英语的综合水平。 二、高中英语阅读泛读课实施的具体方法 （一）教师应更新观念，正确引导学生。 由于长期以来受“应试教育”观念的影响，某些教师指导的失误，学生成为解题的机器，为做题而阅读，为考试而阅读，而不是为获取知识、信息而阅读。因此，在大力推进素质教育的今天，英语教师应更新观念，还英语学习本来面目，在英语阅读能力培养上正确引导学生，让学生进行自主阅读，使其以积极主动的、探究式的态度参与阅读，享受阅读的乐趣。所以，新形式下的高中英语教师应做到以下几点： 1.高中英语阅读课泛读材料的选取 泛读材料的选择应尽量做到：第一，泛读材料的长度适中，生词量不宜过多，对新的或较难的语言现象要把握好，明显超出学生理解能力范围的句子结构可以进行必要的改写。材料整体安排上应做到从易到难，这样做学生在阅读过程中凭借已有的语言文化背景知识和生活经验，通过联想、重建等创造性思维，可以领会文章表达的意思，从而吸收信息。第二，体裁要多样，题材要丰富。这样有利于拓宽学生的知识结构和激发学生的阅读兴趣，并能增强学生适应各种阅读材料的能力。第三，阅读材料应具有可行性。即选择材料应避免过于平淡，要选择那些趣味性和知识性较强的文章，也要选择有一定深度、内容具有教育意义和富有哲理性的文章。第四，练习应具有可用性。泛读材料的检测练习的形式力求多变，可以包括问答、填空、排列顺序、列表、选择等，以拓展学生解题思维。 2.鼓励学生多进行课外阅读 目前，多数高中英语教师反映在教学中存在课时紧、课程重的教学现象。所以，在课堂上抽出很多时间来进行泛读是不切合实际的，这就要求教师积极开发学生的非智力因素，利用课余时间阅读，激发他们大量进行阅读的兴趣。课内的文章数量与时间都非常有限，课外则有很大的空间和很多的时间，学生可以自由支配时间进行泛读。课内外互相促进，互为补充。因为，新《课标》在课程中还强调要“激发和培养学生的学习兴趣，帮助学生树立学英语的自信心，养成良好的学习习惯，和形成有效的学习策略，发展学生自立学习的能力和合作能力。”待兴趣激活后，再让学生进行知识型阅读，这便是水到渠成之事了。近些年来的阅读理解试题增加了阅读量，提高了对阅读速度的要求，并加大了阅读材料的文字难度，对词汇理解的要求有所提高。一词多义、熟词生义、多种时态的混用、结构复杂的长句、省略句及插入语言现象也随处可见。结合高中学生已有一定词汇量的前提，进行大量阅读，培养阅读技巧，进行侧重于获取信息的泛读将是提高阅读理解的有效途径。而报刊提供了丰富鲜活的泛读材料。报刊的内容故事性强，知识面广，既有利于学生开阔眼界，验证、巩固、充实课文所学内容，自然地吸收活的语言也有利于增加语感，提高英语欣赏水平和文化素养，还有助于培养观察力和判断力。 3.指导学生掌握阅读技巧 泛读材料不同于精读课本上的课文。课本上的课文要求学生逐词、逐句地阅读宜细嚼慢咽，其目的在于透彻理解。而泛读的目的则是扩大知识范围，进一步提高捕捉信息的能力，我们不能照搬精读的阅读方法。常见的阅读泛读方法有以下几种： （1）略读( Skimming ) 又称为掠读或扫读 要求学生在限定的时间内快速浏览全文，即阅读时不要从头到尾、一字不漏地读下去，而是采用跳跃式的阅读方法。在阅读过程中善于抓住文章的关键词、句和主题句，对全文进行结构分段、找出其中的联系，从而理清文章的脉络，了解
最全的几何画板实例教程
上篇用几何画板做数理实验 图1-0.1 我们主要认识一下工具箱和状态栏，其它的功能在今后的学习过程中将学会使用。 案例一四人分饼 有一块厚度均匀的三角形薄饼，现在要把它平 均分给四个人，应该如何分？ 图1-1.1 思路：这个问题在数学上就是如何把一个三角形分成面积相等的四部分。 方案一：画三角形的三条中位线，分三角形所成的四部 分面积相等，（其实四个三角形全等）。如图1-1.2。 图1-1.2
方案二：四等分三角形的任意一边，由等底等高的三角 形面积相等，可以得出四部分面积相等，如图1-1.3。 图1-1.3 用几何画板验证： 第一步：打开几何画板程序，这时出现一个新绘图文件。 说明：如果几何画板程序已经打开，只要由菜单“文件” “新绘图”，也可以新建一个绘图文件。第二步：(1)在工具箱中选取“画线段”工具； (2)在工作区中按住鼠标左键拖动，画出一条线段。如图 1-1.4。 注意：在几何画板中，点用一个空心的圈表示。 图1-1.4 第三步：(1)选取“文本”工具；(2)在画好的点上单击左 键，可以标出两点的标签，如图1-1.5： 注意：如果再点一次，又可以隐藏标签，如果想改标签 为其它字母，可以这样做： 用“文本”工具双击显示的标签，在弹出的对话框中进 行修改，(本例中我们不做修改)。如图1-1.6 图1-1.6 在后面的操作中，请观察图形，根据需要标出点或线的 标签，不再一一说明 B 图1-1.5 第四步：(1)再次选取“画线段”工具，移动鼠标与点A 重合，按左键拖动画出线段AC；(2)画线段BC，标出标 签C，如图1-1.7。 注意：在熟悉后，可以先画好首尾相接的三条线段后再 标上标签更方便。 B 图1-1.7
(完整版)高中英语主谓一致专项练习题及答案
高中英语主谓一致专项练习题 1. One-third of the area _____ covered with green trees. About seventy percent of the trees _____ been planted. A. are; have B. is; has C. is; have D. are; has 2. The number of teachers in our college _____ greatly increased last term.A number of teachers in this school _____ from the countryside. A. was; is B. was; are C. were; are D. were; is 3. What _____ the population of China? One-third of the population _____ workers here. A. is; are B. are; are C. is; is D. are; is 4. Not only he but also we _____ right. He as well as we _____ right. A. are; are B. are; is C. is; is D. is; are 5. What he’d like _____ a digital watch. What hed like _____ textbooks. A. are; are B. is; is C. is; are D. are; is 6. He is one of the boys who _____ here on time. He is the only one of the boys who _____ here on time. A. has come; have come B. have come; has come C. has come; has come D. have come; have come 7. Either you or he _____ interested in playing chess. _____ you or he fond of music at present? A. are; Are B. is; Are C. are; Is D. is; Is 8. Many a professor _____ looking forward to visiting Germany now. Many scientists _____ studied animals and plants in the last two years. A. is; have B. is; has C. are; have D. is; are 9. A knife and a fork _____ on the table. A knife and fork _____ on the table. A. is; is B. are; are C. are; is D. is; are 10. Her family _____ much larger than mine four years ago. Her family _____ dancing and singing when I came in last night. A. were; was B. was; were C. was; was D. were; were 11. How and why Jack came to China _____ not known. When and where to build the new library _____ not been decided. A. is; has B. are; has C. is; have D. are; have 12. Now Tom together with his classmates _____ football on the playground. A. play B. are playing C. plays D. is playing 13. Two hundred and fifty pounds _____ too unreasonable a price for a second-hand car. A. is B. are C. were D. be 14. All but Dick _____ in Class Three this term. A. are B. is C. were D. was
画图工具教程
画图工具阶段教学指引如何使用画图工具 画图工具妙用文字工具 画图工具妙用圆形工具 画图工具妙用曲线工具 如何让画图工具存JPG格式 Win98 画图工具持JPG图片一法 Win98 画图工具持JPG图片二法 画图工具应用之屏幕拷贝 画图工具应用之双色汉字 画图工具应用之放大修改 画图工具应用之工具与颜色配置 画图工具应用之灵活编辑 画图工具操作技巧 画图工具应用技巧 画图工具另类技巧检测LCD的暗点
如何使用画图工具 想在电脑上画画吗？很简单，Windows 已经给你设计了一个简洁好用的画图工具，它在开始菜单的程序项里的附件中，名字就叫做“画图”。 启动它后，屏幕右边的这一大块白色就是你的画布了。左边是工具箱，下面是颜色板。 现在的画布已经超过了屏幕的可显示范围，如果你觉得它太大了，那么可以用鼠标拖曳角落的小方块，就可以改变大小了。 首先在工具箱中选中铅笔，然后在画布上拖曳鼠标，就可以画出线条了，还可以在颜色板上选择其它颜色画图，鼠标左键选择的是前景色，右键选择的是背景色，在画图的时候，左键拖曳画出的就是前景色，右键画的是背景色。
选择刷子工具，它不像铅笔只有一种粗细，而是可以选择笔尖的大小和形状，在这里单击任意一种笔尖，画出的线条就和原来不一样了。 图画错了就需要修改，这时可以使用橡皮工具。橡皮工具选定后，可以用左键或右键进行擦除，这两种擦除方法适用于不同的情况。左键擦除是把画面上的图像擦除，并用背景色填充经过的区域。试验一下就知道了，我们先用蓝色画上一些线条，再用红色画一些，然后选择橡皮，让前景色是黑色，背景色是白色，然后在线条上用左键拖曳，可以看见经过的区域变成了白色。现在把背景色变成绿色，再用左键擦除，可以看到擦过的区域变成绿色了。 现在我们看看右键擦除：将前景色变成蓝色，背景色还是绿色，在画面的蓝色线条和红色线条上用鼠标右键拖曳，可以看见蓝色的线条被替换成了绿色，而红色线条没有变化。这表示，右键擦除可以只擦除指定的颜色－－就是所选定的前景色，而对其它的颜色没有影响。这就是橡皮的分色擦除功能。 再来看看其它画图工具。 是“用颜料填充”，就是把一个封闭区域内都填上颜色。 是喷枪，它画出的是一些烟雾状的细点，可以用来画云或烟等。 是文字工具，在画面上拖曳出写字的范围，就可以输入文字了，而且还可以选择字体和字号。 是直线工具，用鼠标拖曳可以画出直线。 是曲线工具，它的用法是先拖曳画出一条线段，然后再在线段上拖曳，可以把线段上从拖曳的起点向一个方向弯曲，然后再拖曳另一处，可以反向弯曲，两次弯曲后曲线就确定了。 是矩形工具，是多边形工具，是椭圆工具，是圆角矩形，多边形工具的用法是先拖曳一条线段，然后就可以在画面任意处单击，画笔会自动将单击点连接