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# Crime Victimisation, Australia methodology

Reference period
2018 - 2019
Released
1/06/2020
Next release Unknown
First release

## Explanatory notes

### Introduction

This publication presents results from the Crime Victimisation Survey, a topic on the Multipurpose Household Survey (MPHS) conducted throughout Australia from July 2018 to June 2019. The MPHS, undertaken each financial year by the Australian Bureau of Statistics (ABS), is a supplement to the monthly Labour Force Survey (LFS) and is designed to collect statistics for a number of small, self-contained topics.

This publication covers the Crime Victimisation topic and presents details about the prevalence of a selected range of personal and household crimes, including the socio-demographic characteristics of persons experiencing the selected crimes, experiences of repeat victimisation, and the characteristics of the most recent incident of each crime type experienced. Some estimates from previous iterations of the Crime Victimisation Survey are also included in this publication.

The Crime Victimisation Survey is being conducted again as part of the MPHS for the reference period 2019-20, with results expected to be released in early 2021.

### Scope and coverage

The scope of the Crime Victimisation Survey was restricted to people aged 15 years and over who were usual residents of private dwellings and excludes:

• members of the Australian permanent defence forces;
• certain diplomatic personnel of overseas governments, customarily excluded from Census and estimated resident population counts;
• overseas residents in Australia; and
• members of non-Australian defence forces (and their dependants).

Additionally, the 2018-19 MPHS scope excluded:

• persons living in non-private dwellings such as hotels, university residences, boarding schools, hospitals, nursing homes, homes for people living with disabilities, and prisons; and
• persons resident in the Indigenous Community Strata (ICS).

The scope for MPHS included households residing in urban, rural, remote and very remote parts of Australia, except the ICS. In the LFS, rules are applied which aim to ensure that each person in coverage is associated with only one dwelling, and hence has only one chance of selection in the survey. See Labour Force, Australia (cat. no. 6202.0) for more detail.

### Data collection

The Crime Victimisation Survey is one of a number of small, self-contained topics on the Multipurpose Household Survey (MPHS), conducted throughout Australia from July 2018 to June 2019. The MPHS is a supplement to the monthly LFS. In 2018–19, the MPHS topics were:

• Crime Victimisation;
• Patient Experiences in Australia;
• Barriers and Incentives to Labour Force Participation;
• Retirement and Retirement Intentions;
• Qualifications and Work; and
• Income (Personal, Partner's, Household).

For all topics, general demographic information such as age, sex, labour force characteristics, education and income are also available.

ABS interviewers conducted personal interviews during the 2018-19 financial year for the monthly LFS. Each month, one eighth of the dwellings in the LFS sample were rotated out of the survey and selected for the MPHS. After the LFS had been fully completed for each person in scope and coverage, a usual resident aged 15 years or over was selected at random (based on a computer algorithm) and asked the additional MPHS questions.

In the MPHS, if the randomly selected person was aged 15 to 17 years, permission was sought from a parent or guardian before conducting the interview. If permission was not given, the parent or guardian was asked the questions on behalf of the 15 to 17 year old (proxy interview). Questions relating to sexual assault and the involvement of alcohol or substances in the most recent incident of physical assault and face-to-face threatened assault were not asked of proxy respondents. Only persons aged 18 years and over were asked questions on sexual assault and the involvement of alcohol or substances in the most recent incident of physical assault and face-to-face threatened assault.

Data were collected using Computer Assisted Interviewing (CAI), whereby responses were recorded directly onto an electronic questionnaire in a notebook computer, with interviews conducted either face-to-face or over the telephone. The majority of interviews were conducted over the telephone.

### Sample size

After taking into account sample loss, the response rate for the Crime Victimisation Survey was 71.8%. In total, information was collected from 28,719 fully responding persons. This includes 477 proxy interviews for people aged 15 to 17 years, where permission was not given by a parent or guardian for a personal interview.

### Weighting

Weighting is the process of adjusting results from a sample survey to infer results for the total in-scope population. To do this, a 'weight' is allocated to each enumerated person. The weight is a value which indicates the number of persons in the population represented by the sample person.

The first step in calculating weights for each unit is to assign an initial weight, which is the inverse of the probability of being selected in the survey. For example, if the probability of a person being selected in the survey was 1 in 600, then the person would have an initial weight of 600 (that is, they represent 600 people).

### Benchmarks

The initial weights were calibrated to align with independent estimates of the population of interest, referred to as 'benchmarks'. Weights calibrated against population benchmarks ensure that the survey estimates conform to the independently estimated distribution of the population rather than the distribution within the sample itself. Calibration to population benchmarks helps to compensate for over-or-under-enumeration of particular categories of persons/households which may occur due to either the random nature of sampling or non-response.

For household estimates, the MPHS was benchmarked to independently calculated estimates of the total number of households in Australia. The MPHS estimates do not (and are not intended to) match estimates for the total Australian person/household populations obtained from other sources.

The survey was benchmarked to the Estimated Resident Population (ERP) living in private dwellings in each state and territory at December 2018, based on the 2016 Census. People living in Indigenous communities were excluded.

While the LFS benchmarks are revised every five years to take into account the outcome of the five-yearly rebasing of the ERP following the latest Census, the supplementary surveys and MPHS (from which the statistics in this publication are taken) are not. Small differences will therefore exist between the civilian population aged 15 years and over reflected in the LFS and other labour household survey estimates, as well as over time.

### Estimation

Survey estimates of counts of persons are obtained by summing the weights of persons with the characteristic of interest.

### Confidentiality

To minimise the risk of identifying individuals in aggregate statistics, a technique called perturbation is used to randomly adjust cell values. Perturbation involves a small random adjustment of the statistics and is considered the most satisfactory technique for avoiding the release of identifiable statistics while maximising the range of information that can be released. These adjustments have a negligible impact on the underlying pattern of the statistics.

After perturbation, a given published cell value will be consistent across all tables. However, adding up cell values to derive a total will not necessarily give the same result as published totals.

Perturbation has been applied to Crime Victimisation Survey datasets since 2013–14. Data from previous cycles (2008-09 to 2012–13) have not been perturbed, but underwent a different confidentialisation method to protect the confidentiality of respondents.

### Reliability of estimates

All sample surveys are subject to error which can be broadly categorised as either sampling error or non-sampling error.

Sampling error is the difference between the published estimates, derived from a sample of persons, and the value that would have been produced if the total population (as defined by the scope of the survey) had been included in the survey.

Non-sampling error may occur in any statistical collection, whether it is based on a sample or a full count such as a census. Sources of non-sampling error include non-response, errors in reporting by respondents or recording of answers by interviewers, and errors in coding and processing data. Every effort is made to reduce non-sampling error by careful design and testing of questionnaires, training and supervision of interviewers, and extensive editing and quality control procedures at all stages of data processing.

Only data with a relative standard error (RSE) of less than 25% are included in the publication commentary (unless otherwise noted), and any differences between populations and changes over time that are referred to are statistically significant. All data contained in the commentary are available for download as data cubes from the Data downloads section. For more information about relative standard error and statistical significance refer to the Technical Note.

### Interpretation of results

Crime victimisation surveys are best suited to measuring crimes against specific individuals or households. Respondents need to be aware of and recall what happened to them and how it happened, as well as be willing to relate what they know to interviewers.

Not all types of crime are suitable for measurement by household surveys. No reliable information can be obtained about crimes without specific victims, such as trafficking in narcotics. Crimes of which a person may not be aware cannot be measured effectively through a household survey, for example crimes involving deception. It may also be difficult to obtain information about some crimes, such as sexual offences and assault committed by other household or family members, due to the sensitivity of the crime and an increased reluctance to disclose. Some of these crimes may not be fully represented in the data collected. Household survey data exclude crimes against commercial establishments or government agencies.

This survey covered only selected types of personal and household crimes and does not represent all crime in Australia. Personal crimes covered in the survey were physical assault, threatened assault (face-to-face and non-face-to-face), robbery and sexual assault. Household crimes covered were break-in, attempted break-in, motor vehicle theft, theft from a motor vehicle, malicious property damage and other theft.

Information collected in this survey is essentially 'as reported' by respondents and hence may differ from that which might be obtained from other surveys or administrative data sources. This factor should be considered when interpreting the estimates and when making comparisons with other data sources.

### Experiences of family and domestic violence

There is limited information available in this publication about family and domestic violence. The Crime Victimisation Survey collects information about experiences of personal violence and the relationship between the victim and perpetrator, however this information alone is not sufficient to reliably measure the number of people who have experienced family and domestic violence.

The Crime Victimisation Survey collects incident characteristics information, including relationship to the offender, only for the most recent incident of each type of personal crime experienced in the 12 months prior to interview. This means that not all experiences of personal violence by each relationship type - including current and previous partners - are captured in the survey. In addition, as interviews are conducted by telephone in the respondent’s home, there is no requirement for a private interview setting for the Crime Victimisation Survey (as is the case for the ABS’s Personal Safety Survey). This non-private setting means respondents may be less likely to disclose any experiences of violence by their partner if their partner is present in the home at the time of interview. As a result, the statistics on relationship type available in this publication cannot be used to draw conclusions about the prevalence of family and domestic violence in Australia.

Due to the ongoing relationship between victim and perpetrator, family and domestic violence is often a recurring event, and the protracted nature of this violence cannot be reliably measured within the framework of the Crime Victimisation Survey. Further information about defining and measuring family and domestic violence is available in Defining the Data Challenge for Family Domestic and Sexual Violence (cat. no. 4529.0) and statistics are available in Personal Safety, Australia (cat. no. 4906.0), Directory of Family, Domestic, and Sexual Violence Statistics, 2018 (cat. no. 4533.0), and Recorded Crime - Victims, Australia (cat. no. 4510.0).

### Statistical measures of crime victimisation

The level of victimisation can be measured and expressed in more than one way. The most common measure derived from crime victimisation surveys is prevalence, that is, the number of the relevant population that have experienced a given crime at least once in the reference period. Victimisation rates used in this publication represent the prevalence of selected crimes in Australia, and are expressed as a percentage of the total relevant population. Reporting rates used in this publication are expressed as the percentage of persons/households whose most recent incident of each type of crime had been reported to the police.

### Comparability of time series

The 2018-19 Crime Victimisation Survey is the eleventh in a series of annual Crime Victimisation Surveys conducted by the ABS. The ten previous surveys in this series included the majority of the questions asked in 2018-19. As a similar methodology has been adopted for the surveys, data on the prevalence of personal and household crimes is comparable across the survey periods. This has enabled some time series comparisons to be made in this publication.

The Crime Victimisation Survey series replaced the previous Crime and Safety Surveys and was introduced because of a change to the collection methodology. The new method of collection mainly uses personal telephone interviews of selected respondents. Data collections between 1990 and 2005 required respondents to complete questionnaires by themselves and mail these back to the ABS. This difference in mode of collection and changes to survey content means that Crime Victimisation Survey data collected using the MPHS are generally not directly comparable with data from Crime and Safety Surveys prior to 2008–09.

### Comparability with previous crime victimisation surveys

In 2010-11 significant changes to the 'Area of Usual Residence', 'Capital City' and 'Balance of State/Territory' geographical items were made. From 2008-09 to 2012-13 the Australian Standard Geographical Classification (ASGC) (cat. no. 1216.0) was used to characterise Geographical Classifications. From 2013-14 onwards the Australian Statistical Geography Standard (ASGS) (cat. no. 1270.0.55.001) was used. The ASGS is updated on a five yearly basis in accordance with the Census of Population and Housing. Consequently, the 2018-19 Crime Victimisation Survey saw the introduction of the updated ASGS. More information on this can be found in Australian Statistical Geography Standard (ASGS): Volume 1 - Main Structure and Greater Capital City Statistical Areas, July 2016.

For the 2018-19 reference period, the following data have not been published at the state/territory level:

• Robbery;
• Sexual assault;
• Police reporting data for non face-to-face threatened assault;
• Police reporting data for motor vehicle theft; and
• Contribution of alcohol or another substance data for physical assault and face-to-face threatened assault.

A review of data quality found that due to low prevalence and/or high error or volatility, estimates for the above data items are too statistically unreliable for general use. National estimates for these data items are still available in the data cubes, and users are advised to exercise caution when using state and territory level data for these data items from previous iterations of the survey.

### Comparability with police statistics

Data for selected crimes reported to and recorded by police agencies in a calendar year are available in Recorded Crime - Victims, Australia(cat. no. 4510.0). The Crime Victimisation Survey provides an additional source of data on crime victimisation for the selected crimes, including crime not reported to or detected by police. This survey identifies the nature of this unreported crime, as well as giving information about experiences of repeat victimisation. The information from the survey should be viewed as complementary to police recorded crime statistics.

The terms used for the crimes (such as robbery and physical assault) may not necessarily correspond with the legal or police definitions used. This is because responses obtained in this survey are based on the respondent's perception of the behaviours they experienced. The definitions of terms used in the publication are based on the wording of the questions asked of the respondent and specifications provided to interviewers. Definitions of crime types included in this survey can be found in the Glossary.

The Crime Victimisation Survey collects information on crimes that were reported to police, as well as crimes that went unreported. In this publication, reporting rates are based on whether or not the most recent incident of each crime type experienced in the 12 months prior to interview was reported to police. Interviews were conducted over a 12 month period from 1 July 2018 to 30 June 2019. The actual reference period for a particular respondent was determined by the date of their interview. There is no way of verifying that a crime was reported to police, where the respondent indicated that police were informed.

Another source of variation between the survey results and crimes recorded by police relates to differences in scope. This survey collects information on the personal crimes of physical assault, threatened assault (face-to-face and non-face-to-face), and robbery for all persons aged 15 years and over, and sexual assault for persons aged 18 years and over. In contrast, police statistics include victims of all ages, and any comparisons should take this into consideration. Furthermore, police statistics for a given reference period may include criminal incidents that came to the attention of police during the reference period, but did not occur during it.

Due to differences between collections, caution should be exercised when comparing data from surveys and administrative by-product collections that relate to crime and justice topics. For more information on comparisons between sources, please refer to Measuring Victims of Crime: A Guide to Using Administrative and Survey data, June 2011 (cat. no. 4500.0.55.001).

### Comparability with other ABS surveys

Caution should be exercised when comparing across ABS surveys and with administrative by-product data that address the access and use of health services. Estimates from the Crime Victimisation Survey may differ from those obtained in other surveys (such as the Personal Safety Survey, National Aboriginal and Torres Strait Islander Health Survey, National Aboriginal and Torres Strait Islander Social Survey, and General Social Survey) due to differences in survey mode, methodology and questionnaire design.

### Comparability with monthly LFS statistics

Since the Crime Victimisation Survey is conducted as a supplement to the Labour Force Survey (LFS), data items collected in the LFS are also available in this publication. However, there are some important differences between the two surveys. The LFS had a response rate of over 90% compared to the MPHS response rate of 71.8%. The scope of the Crime Victimisation Survey and the LFS also differ, as outlined in the preceding sections. Due to the differences between the samples, data from the Crime Victimisation Survey and the LFS are weighted separately. Variances may therefore be found in the estimates for those data items collected in the LFS and published as part of the Crime Victimisation Survey.

### Other methodological issues

When interpreting data from the 2018-19 MPHS, consideration should be given to the representativeness of the survey sample in relation to the entire in-scope population. This is affected by the response rate and scope and coverage rules. For example, people living in boarding houses, refuges or on the streets are excluded from this survey and may experience different levels of victimisation than those surveyed who live in private dwellings.

### Equivalised weekly household income

Equivalised weekly household income is household income adjusted by the application of an equivalence scale to facilitate comparison of income levels between households of differing size and composition, reflecting that a larger household would normally need more income than a smaller household to achieve the same standard of living. Using an equivalising factor for household income enables the direct comparison of the relative economic well-being of households of different size and composition (for example, lone person households, families and group households of unrelated individuals).

For more information about equivalised weekly household income see Household Income and Wealth, Australia (cat. no. 6523.0) and Survey of Income and Housing, User Guide, Australia (cat. no. 6553.0).

### Socio-Economic Indexes for Areas (SEIFA)

Socio-Economic Indexes for Areas (SEIFA) is a classification developed by the ABS that ranks areas in Australia according to relative socio-economic advantage and disadvantage. SEIFA uses a broad definition of relative socio-economic advantage and disadvantage in terms of people's access to material and social resources, and their ability to participate in society.

The indexes are based on information from the five-yearly Census, and each index summarises a different aspect of the socio-economic conditions of people living in an area. Every geographic area in Australia is given a SEIFA number which shows how disadvantaged or advantaged that area is compared with other areas in Australia.

The Crime Victimisation Survey uses two indexes from the 2016 Socio-Economic Indexes for Areas (SEIFA) – the Index of Relative Socio-Economic Advantage and Disadvantage; and the Index of Relative Socio-Economic Disadvantage. These measures are derived from Census variables related to income, educational attainment, unemployment, occupational skill level and whether a dwelling has a motor vehicle.

For more detail, see the following:

### Country of birth

Country of birth data are classified according to the Standard Australian Classification of Countries (SACC), 2016 (cat. no. 1269.0).

### Education

Education data are classified according to the Australian Standard Classification of Education ASCED, 2001 (cat. no 1272.0). The ASCED is a national standard classification which can be applied to all sectors of the Australian education system including schools, vocational education and training and higher education. The ASCED comprises two classifications: Level of Education and Field of Education.

### Products and services

Data cubes containing all tables for this publication in Excel spreadsheet format are available from the Data downloads section. The spreadsheets present tables of estimates and proportions, and their corresponding relative standard errors (RSEs).

As well as the statistics included in this and related publications, the ABS may have other relevant data available on request. Subject to confidentiality and sampling variability constraints, tables can be tailored to individual requirements. A list of data items from this survey is available from the Data downloads section. All enquiries should be directed to the National Information and Referral Service on 1300 135 070, or email client.services@abs.gov.au.

### Acknowledgements

ABS surveys draw extensively on information provided by individuals, businesses, governments and other organisations. Their continued cooperation is very much appreciated and without it, the wide range of statistics published by the ABS would not be available. Information received by the ABS is treated in strict confidence as required by the Census and Statistics Act 1905.

### Privacy

The ABS Privacy Policy outlines how the ABS will handle any personal information that you provide to the ABS.

## Technical note - data quality

### Reliability of the estimates

The estimates in this publication are based on information obtained from a sample survey. Errors in data collection or processing, known as non-sampling error, can impact on the reliability of the resulting statistics. In addition, the reliability of estimates based on sample surveys are also subject to sampling variability. That is, the estimates may differ from those that would have been produced had all persons in the population been included in the survey. This is known as sampling error.

### Non-sampling error

Non-sampling error may occur in any statistical collection, whether it is based on a sample or a full count such as a census. Sources of non-sampling error include non-response, errors in reporting by respondents or recording of answers by interviewers, and errors in coding and processing data.

It is not possible to quantify non-sampling error, however, every effort is made to reduce non-sampling error by careful design and testing of questionnaires, training and supervision of interviewers, and extensive editing and rigorous quality control procedures at all stages of data processing.

### Sampling error

Sampling error refers to the difference between an estimate obtained from surveying a sample of persons, and the result that would have been obtained if all persons had been surveyed.

One measure of sampling error is given by the standard error (SE), which indicates the extent to which an estimate might have varied by chance because only a sample of persons was surveyed. There are about two chances in three (67%) that a sample estimate will differ by less than one SE from the number that would have been obtained if all persons had been surveyed, and about 19 chances in 20 (95%) that the difference will be less than two SEs.

### Relative standard error

In this publication, the standard error of the estimate is expressed as a percentage of the estimate, known as the relative standard error (RSE), which is a useful measure as it indicates the size of the error relative to the estimate.

$$\large{\text{RSE%} = (\frac{SE}{estimate}) \times 100}$$

Only estimates (counts or percentages) with an RSE of less than 25% are considered sufficiently reliable for most analytical purposes. However, estimates with an RSE over 25% are also published. Estimates with an RSE in the range 25% to 50% are less reliable and should be used with caution, while estimates with an RSE greater than 50% are considered too unreliable for general use.

The Excel files available from the Data downloads section contain all the data tables produced for this release, including all estimates and their corresponding RSEs. All cells in the Excel spreadsheets containing an estimate with an RSE of 25% or greater are annotated with asterisks, indicating whether the RSE of the estimate is in the range 25% to 50% (single asterisk *) or is greater than 50% (double asterisk **).

### Calculation of standard error

Standard error (SE) can be calculated using the estimate (count or percentage) and the corresponding RSE. For example, if the estimated number of persons who experienced physical assault in the last 12 months was 462,200, with a corresponding RSE of 5.0%, the SE (rounded to the nearest 100) is calculated by:

$$\large{\begin{array}{l}\text{SE of estimate} \\{=(\frac{RSE\%}{100}) \times estimate}\\{=0.05 \times 462,200}\\{=23, 100}\end{array}}$$

Therefore, there is about a two in three chance that the result that would have been obtained had all persons been included in the survey falls within the range of one standard error below to one standard error above the estimate (439,100 to 485,300), and about a 19 in 20 chance that the result would have fallen within the range of two standard errors below to two standard errors above the estimate (416,000 to 508,400). This example is illustrated in the diagram below:

### Relative standard error of proportions

Proportions formed from the ratio of two estimates are also subject to sampling error. The size of the error depends on the accuracy of both the numerator and the denominator. A formula to approximate the RSE of a proportion is given below. This formula is only valid when x is a subset of y:

$$\large{\text{RSE }(\frac{x}{y})\approx \sqrt{[RSE(x)]^{2}-[RSE(y)]^{2}}}$$

As an example, if 86,600 persons experienced physical assault by an intimate partner, representing 29.5% of all persons who experienced physical assault by a known person (293,600); and if the RSE for the number of persons experiencing physical assault by an intimate partner is 7.7% and the RSE for the number of persons experiencing physical assault by a known person is 6.7%; then, applying the above formula, the RSE of the proportion is:

$$\large{\text{RSE } = \sqrt{[(7.7)]^{2}-[(6.7)]^{2}} = 3.8\text%}$$

Using the formula given above, the standard error (SE) for the proportion of persons who experienced physical assault by an intimate partner (as a proportion of those who experienced physical assault by a known person) is 1.1% (0.038 x 29.5). There are about two chances in three that the true proportion of persons who experienced physical assault by an intimate partner (as a proportion of those who experienced physical assault by a known person) is between 28.4% and 30.6%, and 19 chances in 20 that the true proportion is between 27.3% and 31.7%.

### Standard error of the difference between estimates

The difference between two survey estimates (counts or percentages) is also subject to sampling error, and can therefore be measured using standard error. The standard error of the difference between two estimates is determined by the individual standard errors of the two estimates and the relationship (correlation) between them. An approximate standard error of the difference between two estimates (x,y) can be calculated using the following formula:

$$\large{SE (x-y) \approx \sqrt{[S E(x)]^{2}+[S E(y)]^{2}}}$$

While this formula will only be exact for differences between separate and uncorrelated characteristics or sub populations, it provides a good approximation for the differences likely to be of interest in this publication.

### Significance testing

The difference between two survey estimates can be tested for statistical significance, in order to determine the likelihood of there being a real difference between the populations with respect to the characteristic being measured. The standard error of the difference between two survey estimates (x and y) can be calculated using the formula in the preceding section. This standard error is then used in the following formula to calculate the test statistic:

$$\large{\left(\frac{x-y}{S E(x-y)}\right)}$$

If the value of the test statistic is greater than 1.96, then this supports, with a 95% level of confidence, a real (i.e. statistically significant) difference between the two populations with respect to the characteristic being measured. If the test statistic is not greater than 1.96, it cannot be stated with a 95% level of confidence that there is a real difference between the populations with respect to that characteristic.

The following survey estimates have been significance tested to determine whether any differences are statistically significant:

• Annual changes between 2017–18 and 2018–19 in personal and household crime victimisation rates (Tables 4c and 6c);
• Annual changes between 2017–18 and 2018–19 in personal and household crime reporting rates (Tables 5c and 7c);
• Annual changes between 2017-18 and 2018-19 in the proportion of persons who believed alcohol or any other substance contributed to their most recent incident of physical assault and face-to-face threatened assault (Table 8c);
• Differences between state and territory personal and household crime victimisation rates and equivalent national victimisation rates for 2018–19 (Tables 2, 3, 4c, and 6c); and
• Differences between state and territory personal and household crime reporting rates and equivalent national reporting rates for 2018–19 (Tables 2, 3, 5c, and 7c).

Significant differences have been annotated with a footnote in the above tables. In all other tables which do not show the results of significance testing, users should take RSEs into account when comparing estimates for different populations, or undertake significance testing using the formula provided to determine whether there is a statistically significant difference between any two estimates.

Only data with a relative standard error (RSE) of less than 25% are included in the publication commentary, unless otherwise indicated, and any differences between populations and changes over time that are referred to are statistically significant. All data contained in the commentary are available for download as data cubes from the Data downloads section.

## Glossary

### Show all

#### Alcohol and/or any other substance

Includes any illegal or legal drugs or mood altering substances that the person believed contributed to the most recent incident of physical assault or face-to-face threatened assault. Other substances include marijuana, cocaine, ice, heroin, ecstasy, steroids, pharmaceuticals, inhalants, kava etc. Either the victim or perpetrator may have been under the influence of alcohol and/or any other substance at the time of the incident. This also includes:

• incidents that occurred when the victim or perpetrator were ‘hungover’; and
• incidents where the victim believed that their drink had been spiked.

#### Attempted break-in

An incident where an attempt was made to forcibly enter a home or other private residence. Includes attempts to break into a caravan (if the caravan was the person's permanent residence), garage, shed or any detached secure building such as games/hobby rooms or granny flats. Attempted break-in also includes incidents where a person saw someone acting suspiciously around the property, if it was suspected that their intent was to break in and steal property. Excludes any attempted break-in that resulted in an actual break-in (e.g. where someone attempted to break in through a door but then gained entry through a window) and attempted break-in to a motor vehicle.

#### Assault

Includes both physical assault and threatened assault (both face-to-face threatened assault and non-face-to-face threatened assault).

#### Balance of state/territory

Comprises statistical areas outside the Greater Capital City Statistical Areas of states and territories as defined in the Australian Statistical Geography Standard (ASGS): Volume 1 - Main Structure and Greater Capital City Statistical Areas, July 2016 (cat. no. 1270.0.55.001).

#### Break-in

An act of unauthorised forced entry into a home or other private residence. Includes forced entry to a caravan (if the caravan was the person's permanent residence), garage, shed or any detached secure building such as games/hobby rooms or granny flats. Excludes forced entry into motor vehicles or front or rear yards and incidents where attempts to gain unlawful entry were not successful (see attempted break-in above).

#### Employed

All people aged 15 years and over who, during the week prior to interview:

• worked for one hour or more for pay, profit, commission or payment in kind in a job or business, or on a farm (comprising employees, employers and own account workers)
• worked for one hour or more without pay in a family business or on a farm (i.e. contributing family workers)
• were employees who had a job but were not at work and were:
• away from work for less than four weeks up to the end of the reference week
• away from work for more than four weeks up to the end of the reference week and received pay for some or all of the four week period to the end of the reference week
• away from work as a standard work or shift arrangement
• on a strike or locked out
• employers or own account workers, who had a job, business or farm, but were not at work.

#### Face-to-face threatened assault

Any verbal and/or physical threat to inflict physical harm, made face-to-face, where the person being threatened believed the threat was likely and able to be carried out. Excludes any incident where the person being threatened did not encounter the perpetrator in person (e.g. threats made via telephone, text message, e-mail, in writing or through social media) – these incidents are counted under non face-to-face threatened assault.

#### Family member

Includes parent, child, sibling or other family member.

#### Full-time (employed)

Employed people who usually worked 35 hours or more a week (in all jobs) and those who, although usually working less than 35 hours a week, worked 35 hours or more during the reference week (i.e. the week before the interview).

#### Greater Capital City Statistical Areas (GCCSA)

Greater Capital City Statistical Areas (GCCSA) are geographical areas built from Statistical Areas Level 4 (SA4), as defined in the Australian Statistical Geography Standard (ASGS): Volume 1 - Main Structure and Greater Capital City Statistical Areas, July 2016 (cat. no. 1270.0.55.001). They are designed to represent the functional extent of each of the eight State and Territory capital cities. This includes the population within the urban area of the city, as well as people who regularly socialise, shop or work within the city, and live in small towns and rural areas surrounding the city. Within each State and Territory, the area not defined as being part of the Greater Capital City is represented by a Balance of State/Territory region.

#### Household

A group of two or more related or unrelated people who usually reside in the same dwelling, who regard themselves as a household, and who make common provision for food or other essentials for living; or a person living in a dwelling who makes provision for their own food and other essentials for living, without combining with any other person.

#### Household crime

Crimes that were committed with the intent to deprive another person of, or deliberately damage, their personal property. The selected household crimes included in the survey are break-in, attempted break-in, motor vehicle theft, theft from a motor vehicle, malicious property damage and other theft. Includes incidents occurring in all Australian households that the person lived in during the 12 months prior to interview. For the purposes of the survey, the household is considered the victim where anyone living in the household (not only the respondent) may have experienced an incident of household crime during the 12 months prior to interview. Excludes incidents where personal property was stolen by force or threat from a person in the household (these incidents are counted under robbery).

#### Incident

A single occurrence of a crime event, which may involve one or more crime types.

#### Intimate partner

Includes current partner, previous partner, boyfriend/girlfriend/ex-boyfriend/ex-girlfriend or date.

#### Known by sight only

Where the person recognised the perpetrator(s) by sight only but did not have a personal relationship with them.

#### Labour force status

A classification of the civilian population aged 15 years and over, including employed, unemployed or not in the labour force, as defined in Labour Force, Australia (cat. no. 6202.0). These definitions conform closely to the international standard definitions adopted by the International Conference of Labour Statisticians.

#### Level of highest non-school qualification

Non-school qualifications are awarded for education attainments other than those of pre-primary, primary or secondary education. They include qualification at the following levels: Postgraduate degree, Master degree, Graduate Diploma and Graduate Certificate, Bachelor degree, Advanced Diploma and Diploma and Certificates I, II, III and IV. Non-school qualifications may be attained concurrently with school qualifications.

#### Malicious property damage

Intentional or wilful (not accidental) damage, defacement or destruction of any part of the person's home or anything usually kept at home. Property is something tangible in nature, including land, conveyances, animals or other objects capable of being privately owned. Destruction can mean any alteration that may render something imperfect or inoperative, including destruction of property, graffiti or vandalism, partial destruction, killing or harming an owned animal and removing or destroying a plant or other part of an owned landscape. Excludes any rental, investment or holiday properties owned by a member of the household. Excludes acts such as turning off water meters and flicking safety switches if no damage to the item occurred.

#### Medical attention

Includes incidents where a person was admitted to hospital and incidents where a person was seen by a doctor or another medical practitioner but not admitted to hospital.

#### Motor vehicle parts

Examples include license plates, tyres, wheels/rims, car audio and DVD equipment.

#### Motor vehicle theft

An incident where a motor vehicle was stolen from any member of the household. This includes cars, SUVs, motorcycles (including motorised scooters), buses, trucks and motor homes. Includes privately owned vehicles and business/employer/company owned vehicles only if the vehicle was used exclusively by members of the household. Excludes vehicles used mainly for business purposes, boats, trailers and company vehicles not used exclusively by household members. For the purpose of this survey, motor vehicle theft incidents are considered to be household crimes.

#### Non-face-to-face threatened assault

Any threat to inflict physical harm where the person being threatened believed the threat was likely and able to be carried out, and where they did not encounter the perpetrator face-to-face (e.g. via telephone, text message, e-mail, in writing or through social media).

#### Not in the labour force

Persons who were neither employed nor unemployed as defined by Labour Force Status.

#### Other known person

Used to describe the relationship of the perpetrator to the victim where the perpetrator was known to the victim, but the relationship did not match any of the known person categories specified in the survey.

#### Other theft

Any unlawful taking of money or goods owned by a household member (other than from motor vehicles owned by a household member) with the intent to permanently deprive the owner of the money or goods, without the use or threat of force or violence, coercion or deception. Includes:

• property belonging to a member of the household not covered by the other types of crime included in the survey;
• property belonging to a household member stolen from a vehicle not owned by a household member; and
• property stolen from a yard or garden (e.g. statues or plants).

Excludes any incidents involving theft covered in other crime types in the survey (e.g. property stolen during a break-in or robbery). Other theft is considered to be a household crime for the purposes of the survey.

#### Part-time (employed)

Employed people who usually worked less than 35 hours a week (in all jobs) and either did so during the reference week (i.e. the week before the interview), or were not at work in the reference week.

#### Perpetrator

A person who commits a crime, as identified by the person who experienced the crime. There may be one or more perpetrators involved in any single crime incident.

#### Personal crime

Crimes that were committed against a person which threatened or caused physical harm to the person. The types of personal crime included in the survey are physical assault, threatened assault (including face-to-face threatened assault and non face-to-face threatened assault), robbery (including attempts), and sexual assault (including attempts).

#### Physical assault

An act of physical force or violence committed by an perpetrator(s) against another person. Examples of physical force or violence include being beaten, pushed, grabbed, shoved, slapped, hit with an open hand or fist, kicked, bitten, choked, stabbed, shot, burnt, being hit with something such as a bat or being dragged or hit deliberately by a vehicle. Includes assault that occurred while the person was at work. Excludes incidents that occurred during the course of play on a sporting field or organised sport, and incidents of sexual assault which also involved physical assault (these are counted under sexual assault).

#### Police

State and territory police agencies. Excludes federal police, except in the Australian Capital Territory.

#### Private vehicle

Any motor vehicle used mainly for private purposes (i.e. non-business purposes).

#### Professional relationship

A relationship where the perpetrator was known to the person primarily through the course of the person's and/or perpetrator’s occupation. Includes where the person was working in a business for which the perpetrator was a client at the time of the incident; relationships between medical professionals and patients; and relationships between police/security officers and perpetrators.

#### Public transport or public vehicle

Includes buses, trains, trams, ferries and taxis.

#### Qualification

Refers to a formal certification, issued by a relevant approved body, in recognition that a person has achieved an appropriate level of learning outcomes or competencies relevant to identified individual, professional, industry or community needs. Excludes statements of attainment awarded for partial completion of a course of study at a particular level.

#### Relationship to perpetrator

Refers to the relationship of the perpetrator to the victim at the time of the incident, as perceived by the victim. More than one response could be provided if there were multiple perpetrators involved in the incident.

#### Relative standard error

A measure of the extent to which an estimate might have varied by chance because only a sample of dwellings was surveyed, and not the entire in-scope population. Relative standard error (RSE) is obtained by expressing the standard error as a percentage of the estimate. For more details refer to the Technical Note.

#### Reporting rate

The total number of persons/households that reported the most recent incident of a crime type to police, expressed as a percentage of the total number of persons/households that experienced the crime type. Includes incidents where the person who experienced the crime did not report the incident themselves, but were aware of another person who did.

#### Robbery

An act of stealing (or attempting to steal) property from a person by physically attacking them or threatening them with force or violence. Includes incidents that occurred at the person's place of work. Excludes pickpocketing or other types of theft from a person that did not involve physical or threatened violence (these are counted under other theft).

#### Sexual assault

An act of a sexual nature carried out against a person's will or without their consent, through the use of physical force, intimidation or coercion and/or involving physical contact. Includes any actual or attempted forced sexual activity such as rape, attempted rape or indecent assault (e.g. being touched inside clothing or intentional rubbing of genitals against the person) and assault with the intent to sexually assault. Includes incidents that occurred at the person's place of work. Excludes sexual harassment that did not involve or lead to an actual or attempted sexual assault. For this survey, only persons aged 18 years and over were asked questions about sexual assault, and respondents had the option of refusal to answer.

#### Social marital status

The relationship status of an individual in terms of whether they form a couple relationship with another person living in the same usual residence, and the nature of that relationship. A marriage exists when two people live together as husband and wife, or partners, regardless of whether the marriage is formalised through registration. Individuals are, therefore, regarded as married if they are in a de facto marriage, or if they are living with the person to whom they are registered as married.

#### Theft from a motor vehicle

An incident where property owned by any member of the household was stolen from a motor vehicle owned (for private use) by any member of that household. Excludes property stolen that belonged to someone not living in the household (e.g. a friend or other relative) and property owned by a business or employer (e.g. a work computer, mobile phone or work tools). Also excludes property stolen from commercial vehicles (e.g. a self-employed business operator whose vehicle is mainly used for work purposes) and any break-in to a motor vehicle where nothing was stolen. For the purposes of this survey, incidents of theft from a motor vehicle are considered to be household crimes.

#### Threatened assault

A verbal, written and/or physical threat to inflict physical harm where the person being threatened believed the threat was likely and able to be carried out. Threatened assault may occur face-to-face or via non-face-to-face methods (such as SMS, email or over the phone). Includes any threat or attempt to strike the person which could cause pain; situations where a gun or other weapon was left in an obvious place (including fake or toy guns/weapons where the threatened person thought it was real) or if the person knew the perpetrator had access to a gun (including toy guns, starter pistol, etc.) or weapon. Also includes incidents where the person was threatened in their line of work. Excludes verbal abuse and any incident of name calling or swearing which did not involve a physical threat, and threats that resulted in an actual assault (these are counted under physical assault).

#### Unemployed

People aged 15 years and over who were not employed during the reference week (i.e. the week before the interview), and:

• had actively looked for full-time or part-time work at any time in the four weeks up to the end of the reference week and were available for work in the reference week; or
• were waiting to start a new job within four weeks from the end of the reference week and could have started in the reference week if the job had been available then.

#### Victim

A person or household who has experienced at least one incident of a selected type of crime in the 12 months prior to interview. A person/household may have experienced more than one incident of the same crime type, but is only counted as a victim once.

#### Victimisation rate

The total number of persons/households that experienced a crime type, expressed as a percentage of all persons/households. This is a measure of how prevalent a crime type is in a given population and is used to measure changes in crime rates over time.

#### Weapon used

Where the person believed a weapon was present during the crime incident (even if they did not see a weapon), or where a weapon was not used during the incident but the person was threatened that a weapon might be used. Examples include knife, gun, bat/bar, bottle/glass and syringe/hypodermic needle.

## Quality declaration

### Institutional environment

For information on the institutional environment of the Australian Bureau of Statistics (ABS), including the legislative obligations of the ABS, financing and governance arrangements, and mechanisms for scrutiny of ABS operations, please see the ABS Institutional Environment.

### Relevance

This publication presents information from the 2018–19 Crime Victimisation Survey, which is the eleventh in the series. In the Crime Victimisation Survey, respondents aged 15 years and over (or 18 years and over for questions regarding sexual assault) were asked questions about their experiences of selected personal crimes (physical assault, threatened assault, robbery and sexual assault) and selected household crimes (break-in, attempted break-in, motor vehicle theft, theft from a motor vehicle, malicious property damage and other theft). Information was collected from one person selected at random in each selected household.

The Crime Victimisation topic is collected as part of the Multipurpose Household Survey (MPHS). The MPHS is a supplement to the monthly Labour Force Survey (LFS) and is designed to produce annual statistics on a small number of self-contained topics. The scope of the LFS is restricted to persons aged 15 years and over and excludes members of the permanent defence forces; certain diplomatic personnel of overseas governments usually excluded from Census and estimated resident populations; overseas residents in Australia; and members of non-Australian defence forces (and their dependants). Refer to Labour Force, Australia (cat. no. 6202.0) for further information regarding the LFS. In addition, the 2018–19 MPHS excluded persons living in the Indigenous Community Strata (ICS), persons living in non-private dwellings such as hotels, university residences, students at boarding schools, patients in hospitals, inmates of prisons and residents of other institutions (e.g. retirement homes, homes for persons with disabilities).

### Timeliness

The MPHS is conducted annually with enumeration undertaken over the financial year. As the survey reference period was the 12 months prior to the survey interview during 2018–19, the data relate to experiences occurring at some time between July 2017 and June 2019.

Generally, data from the Crime Victimisation Survey are released approximately 7 to 8 months after final enumeration, with data from MPHS topics progressively released from approximately 6 months after the end of enumeration.

The Crime Victimisation topic has been collected each year as part of the MPHS since 2008-09. The Crime Victimisation Survey is being conducted again as part of the MPHS for the reference period 2019-20, with results expected to be released in early 2021.

### Accuracy

The LFS, and consequently the MPHS, is primarily designed to provide estimates for the whole of Australia and, secondly, for each state and territory.

The 2018-19 Crime Victimisation Survey comprised a sample of 28,719 fully responding households, which represented a national response rate of 71.9%.

Two types of error can impact on the accuracy of an estimate based on a sample survey: non-sampling error and sampling error. Non-sampling error arises from inaccuracies in collecting, recording and processing the data. Every effort is made to minimise non-sampling error through carefully designed questionnaires, intensive training and supervision of interviewers, and rigorous data processing procedures. Non-sampling error also arises because information cannot be obtained from all persons selected in the survey (non-response).

Sampling error occurs because a sample, rather than the entire in scope population, is surveyed. One measure of the likely difference resulting from not including all in scope dwellings in the survey is given by the standard error (SE). There are about two chances in three that a sample estimate will differ by less than one SE from the figure that would have been obtained if all dwellings had been included in the survey, and about 19 chances in 20 the difference will be less than two SEs.

Another measure of the likely difference is the relative standard error (RSE), which is obtained by expressing the SE as a percentage of the estimate. The RSE is a useful measure in that it provides an immediate indication of the percentage error likely to have occurred due to sampling and therefore avoids the need to also refer to the size of the estimate.

Only estimates with RSEs less than 25% are considered sufficiently reliable for most analytical purposes. Estimates with RSEs between 25% and 50% have been included in the data tables and are annotated to indicate they are subject to high sample variability and should be used with caution. In addition, estimates with RSEs greater than 50% have also been included and annotated to indicate they are considered too unreliable for general use.

### Coherence

The ABS conducted National Crime and Safety Surveys in 1975, 1983, 1993, 1998, 2002 and 2005. In 2006–07, a review of these crime surveys found the need for more timely and regular crime victimisation headline indicators (on an annual basis), and the need for flexibility to cater for new and emerging areas of crime.

In 2008–09, a redesigned ABS Crime Victimisation Survey was introduced (via the MPHS) which collected information about people's experiences of selected personal and household crimes, and has been conducted annually since. Differences in survey methodology and enumeration periods, as well as changes to the survey content, means that data from the Crime Victimisation Survey series (which commenced in 2008–09) are not comparable with earlier ABS Crime and Safety surveys. Comparisons across reference periods are only possible for the period 2008–09 and beyond.

In addition to the core crime victimisation topics, some editions of the survey have included an additional rotating module. These modules have covered a range of topics, including feelings of safety (2008–09), perceptions of social disorder (2009–10 and 2010–11), personal fraud, (2010–11 and 2014–15), perceptions of the justice system (2011–12) and home security measures (2017–18).

From the 2010–11 Crime Victimisation Survey onwards, respondents 18 years and over who were personally interviewed and who had experienced physical assault or face-to-face threatened assault were asked whether they believed alcohol or any other substance contributed to their most recent experience of these offences (see the Data Collection section of the Explanatory Notes for more information).

The terms used to describe the various types of offences in this publication are based on behavioural definitions used in the survey, and may not necessarily correspond with legal or police definitions.

### Interpretability

To aid in the interpretation of the crime victimisation data, detailed information on concepts, definitions, terminology and other technical aspects of the survey can be found in the relevant web pages included with this release. This includes the Explanatory Notes, Glossary, Abbreviations, and Technical Note.

### Accessibility

All tables containing estimates and associated RSEs are available in Excel spreadsheets and can be accessed from the Data downloads section. For the 2018–19 release, any RSEs greater than 50% have been suppressed, while the corresponding estimate has been published with an annotation indicating that it is too unreliable for general use.

Additional tables may also be available on request through a customised data consultancy. The Data downloads section includes an Excel spreadsheet containing a complete list of the data items available. Users should note that detailed data can be subject to high RSEs, which may be subject to confidentiality and sampling variability constraints.

For further information about these and related statistics, contact the National Information and Referral Service on 1300 135 070, or email client.services@abs.gov.au.

The ABS Privacy Policy outlines how the ABS will handle any personal information that you provide to the ABS.

## Abbreviations

### Show all

 ABS Australian Bureau of Statistics ASGS Australian Statistical Geography Standard CAI Computer Assisted Interviewing ERP Estimated Resident Population GCCSA Greater Capital City Statistical Area ICS Indigenous Community Strata LFS Labour Force Survey MPHS Multipurpose Household Survey NSW New South Wales NT Northern Territory Qld Queensland RSE Relative Standard Error SA South Australia SE Standard Error SEIFA Socio-Economic Indexes for Areas Tas. Tasmania Vic. Victoria WA Western Australia


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# Quantum Computing Lecture 22 Michele Mosca. Correcting Phase Errors l Suppose the environment effects error on our quantum computer, where This is a description.

## Presentation on theme: "Quantum Computing Lecture 22 Michele Mosca. Correcting Phase Errors l Suppose the environment effects error on our quantum computer, where This is a description."— Presentation transcript:

Quantum Computing Lecture 22 Michele Mosca

Correcting Phase Errors l Suppose the environment effects error on our quantum computer, where This is a description of errors in phase because we use powers of operator Z

Quantum Error Correction l We can encode l Consider error termacting on the logical 0 gives Z error in upper bit Such error arriving in decoder is shown next slide

Quantum Error Correction error Please observe repetitions of these patterns

Equivalently, cancelling pairs of H inside the diagram we get Final circuit for correcting phase errors

Quantum Error Correction l If the error effected on the system in state is of the form

Quantum Error Correction l and if the state only consists of mixtures of superpositions of codewords and then the correction procedure (call it ) will map

Correcting both phase errors and bit flip errors l Consider the codewords of Shor’s code l We can easily correct any single X- error in one of the 3 three-bit parts l We can then also correct a single Z- error on one of the 9 qubits. l This means we can also correct Y-errors on one of the 9 qubits

Quantum Error Correction l Theorem 10.2: Suppose C is a quantum code and is the error-correction operation constructed in the proof of Theorem 10.1 to recover from a noise process with operation elements. Suppose is a quantum operation with elements which are linear combinations of the. Then the error correction operation also corrects the effects of the noise process on the code C.

Correcting any error l Since any error operator E k can be written as a linear combination of I,X,Z and Y, then the same procedure will correct ANY error acting on just 1 of the 9 qubits. l If where is a quantum operator whose operator terms are correctable with correction operator, then

Correcting any error l Theorem 10.1 (Quantum Error Correction Conditions) Let C be a quantum code, and let P be the projector onto C. Suppose is a quantum operation with operation elements A necessary and sufficient condition for the existence of an error-correction operation correcting on C is that for some Hermitian matrix of complex numbers. l (no mention of efficiency)

Degenerate Codes l Consider the 9-qubit code. l A single Z-error on the first qubit of a codeword produces the same outcome as a single Z-error on either the 2 nd or 3 rd qubit. l The correction procedure will correct these errors regardless l A degenerate code is one where two correctable errors produce the same effect on the codewords (this is impossible with classical codes).

Quantum Hamming Bound l Any non-degenerate quantum error correcting code that encodes k logical qubits into n qubits and can correct errors on up to t qubits must have l If t=k=1, we get (there exists a 5- qubit code that accomplishes this)

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Intelligent UAV-Assisted Localisation to Conserve Battery Energy in Military sensor Networks

Wireless sensor networks (WSNs) are extensively used in military applications for border area monitoring, battle-field surveillance, tracking enemy troops, where the sensor nodes run on battery power. Localisation of sensor nodes is extremely important to identify the location of event in military applications for further actions. Existing localisation algorithms consume more energy by heavy computation and communication overheads. The objective of the proposed research is to increase the lifetime of the military sensor networks by reducing the power consumption in each sensor node during localisation. For the state-of-the-art, we propose a novel intelligent unmanned aerial vehicle anchor node (IUAN) with an intelligent arc selection (IAS)-based centralised localisation algorithm, which removes computation cost and reduces communication cost at every sensor node. The IUAN collects the signal strength, distance data from sensor nodes and the central control station (CCS) computes the position of sensor nodes using IAS algorithm. Our approach significantly removes computation cost and reduces communication cost at each sensor node during localisation, thereby radically extends the lifetime and localisation coverage of the military sensor networks.

Wireless sensor networks (WSNs) are useful in different areas such as natural disaster management systems, forest fire detection, ocean navigation, industrial automation and control, etc. WSN provides many services to military and Air Force like border area monitoring, information collection, battlefield surveillance, detection of intrusions and attacks. Akyildiz1, et al. explained the applications of sensor networks and factors influencing the WSN design. Yick2, et al. explained the types of WSNs, their operating systems and platforms, standards, data storage methods, power management, task distribution, data aggregation, security mechanisms. WSN is a collection of sensor nodes and energy lack of a single sensor node causes severe impacts. Sensor node’s battery energy is consumed in active mode, idle mode and sleep modes. Anastasi3, et al. explained mobility-based energy conservation schemes using mobile sink-based and mobile relay-based approaches. Aguiar4, et al. proposed an integer programming model for optimizing energy consumption.

The process of estimating the physical location of sensor nodes is localisation and it is important as the sensed data becomes meaningless without the location of the event. The detailed classification of the localisation algorithms is explained by Han5, et al. Pal6 explained the centralised and distributed localisation schemes. Existing localisation algorithms consume more energy by heavy computation and communication overheads, thereby deplete the sensor node’s battery quickly. Ou and Ssu7 proposed a localisation scheme with high communication and computation overhead. Ou8 proposed a localisation scheme with beacon scheduling where each sensor node executes heavy computations to determine their locations. Mobile anchor node-based localisation proposed by Liao9, et al. insists communication between sensor nodes during localisation, which causes delay, data loss and high energy consumption. High beacon overhead localisation scheme is given by Ssu10, et al. Sheu11, et al. proposed a localisation scheme which involves inter-sensor communications. Xiao12, et al. proposed a localisation scheme which involves anchor classification phase, distance estimation phase and location estimation phase. Satyamurti13, et al. proposed artificial neural network assisted node localisation to estimate the location errors using artificial neural models. Pescaru14 and Curiac proposed anchor node-based localisation for WSN using video and compass information fusion. Han15, et al. proposed a mobile anchor-assisted localisation algorithm. High communication and computational overhead reduces the overall lifetime of WSN. Any approach in WSN must conserve the battery energy of sensor nodes. The authers have proposed an IUAN approach with IAS algorithm to conserve energy in each sensor node to extend the life time of military sensor networks.

The UAV can fly and broadcast beacons on their own energy. Guerrero16, et al. proposed an approach that uses UAVs to carry positioning device and transmitter to localise the sensor nodes. Yadav17, et al. explained the localisation using global positioning system (GPS)-enabled flying anchor nodes. Vincent18, et al. employ the UAVs to distribute the energy burden across the WSN. Our main idea was to collect the location and distance data from the sensor nodes and compute their locations at (CCS). In our approach, UAV was empowered with intelligence and utilised as flying anchor node. This is referred as IUAN and its novel design is shown in Fig.1.

The IUAN contains IUAN control unit (ICU), sensor ID database (DBSID), visitor queue (VQ), signal strength-distance database (DBSSD), IUAN location database (DBILOC) and location-distance database (DBLD). The ICU controls the overall operation of the IUAN like receiving sensor identity (SID) from sensor nodes, activating GPS receivers, communication with CCS, guiding the IUAN in an optimistic trajectory. When an IUAN enters into the transmission range of a sensor node, the sensor node transmits its SID to that IUAN and the ICU executes the sequence of processes to construct the location- distance message (LDM). IUAN may receive the SIDs from multiple sensor nodes and the VQ stores the SIDs along with their signal strength (SSs) and corresponding time of reception SIDTOR. SIDTOR is the time at which the IUAN receives the SID. Whenever the IUAN receives the SID (at TORSID), it stores the SID, its own location (LOCIUAN) along with TORIUAN to the DBILOC where TORIUAN = TORSID. The Table 1 gives the structure of the DBILOC.

The IUAN authenticates the SIDs in the VQ using the DBSID as DBSID contains valid sensor id numbers. The invalid SIDs are ignored and LD messages are constructed for only the valid sensor nodes. The DBSSD is used to withstand with radio irregularity. The signal strength at the locations around the transmission range of a sensor node varies with the distance and environmental effects. The path loss effect causes the radio signal to attenuate variously in different directions. The proposed work assumes the radio irregularity model (RIM) explained by Zhou19, et al. The Table 2 shows the structure of DBSSD with sample values of the Signal Strengths (SSs) at 3.048 m away from the mica2 mote in four directions. The SS is calculated based on signal strength-distance relation using received signal strength indication (RSSI) measurements with the knowledge of degree of irregularity (DOI).

For a valid SID, an IUAN fetches the distance (D) between itself and the sensor node using the corresponding SSSID. In our approach, the computation cost for the signal strength and distance measurements were shifted from the sensor nodes to the powerful IUAN to conserve the energy at each sensor node. During the validation of SID and distance-fetching process, the IUAN moves to different locations. Hence after fetching the distance, the IUAN fetches the corresponding location information (LOCIUAN) at which it received the SID, using the TORIUAN and TORSID. This mechanism ensures the collection of valid location and distance information. The IUAN constructs the LDM and stores it in the DBLD database, where eachLDM contains the location (L), distance (D) and the corresponding SID.

The Table 3 shows the list of symbols used in the LDM construction algorithm (Algorithm 1) and corresponding flow diagram is shown in Fig. 2. After constructing the LDM, the ICU removes the corresponding entries from the VQ and DBILOC to manage the storage efficiency. The IUANs constructs the LDMs and reaches the CCS, where CCS aggregates DBLD database of all IUANs and selects the sufficient LDMs to calculate the locations of the sensor nodes. If an IUAN (say IUAN-100) is shot down by enemies, it immediately transmits its crashed code to the nearby sensor node (say SN-51). When another IUAN (say IUAN-200) reaches SN-51 later, it transmits the crashed code of IUAN-100 to IUAN-200. When IUAN- 200 reaches CCS, it identifies that the IUAN-100 is crashed by the enemies.

Algorithm 1: LDM Construction

Input: SID from Sensor Node

Output: LD Message (LDM)

1. Begin
2. Interrupt Process 1: Whenever SIDi is received from sensor node
3. measure SSSIDi
4. VQ ← enqueue (SIDi, SSSIDi, TORSIDi)
5. DBGLOC ← insert(LOCIUAN, SIDi, TORIUAN=TORSIDi)
6. end Interrupt Process 1
7. while(VQ != NULL)
8. if SIDi ∉ DBSID then
9. VQ ←dequeue (SIDi, SSSIDi, TORSIDi)
10. else
11. D←select D from DBSSD where SS=SSSIDi
12. L←select LOCIUAN from DBILOC where TORIUAN = TORSIDi
13. LDM.x ←LOCIUAN.x
14. LDM.y←LOCIUAN.y
15. LDM.d←D
16. LDM.id←SIDi
17. LDM←ConstructLDMPacket (LDM.x, LDM.y, LDM.d, LDM.id)
18. insert LDM into DBLD
19. VQ←dequeue (SIDi, SSSIDi, TORSIDi)
20. delete LOCIUAN, SIDi, TORIUAN from DBILOC where TORIUAN=TORSIDi and SID = SIDi
21. end if
22. end while
23. End

For the state-of-the-art, the authers have proposed a novel approach to remove the computation cost at each sensor node during localisation process. Our approach computes the location of sensor nodes at CCS where the computing and communication resources are not constraint. The proposed algorithm aggregates the LDMs from different IUANs and computes the location of a sensor node with three relevant LDMs. Each LDM has the LOCIUAN and distance between the LOCIUAN and corresponding sensor node location (LOCS). The proposed algorithm is an optimum version of the trilateration method. Our algorithm selects the boundary points and arc angles to construct the intelligent arc segments, where the intersection of these arcs gives the location of the sensor node. The algorithm starts with three LDMs, where these messages are collected within the range of a sensor node, as shown in Fig. 3. The proposed algorithm has 6 phases.

In phase 1, the LD messages are processed to extract the IUANcentres {C1,C2,C3} and the corresponding IUANDistances {r1,r2,r3}, where ri is the distance between IUANcentre C1 and the sensor node. In phase 2, the boundary points (BPoints) around each IUANCentre are calculated using the 2D translation, as shown in Fig. 4. All Bpoints and IUANCentres contain the associated ‘x’ and ‘y’ coordinate values and based on these both the IUANcentres and BPoints are classified as the ‘x’ axis centre points (XCPoints), ‘x’ axis boundary points (XBPoints), ‘y’ axis centre points (YCPoints), ‘y’ axis boundary points (YBPoints). Each IUANCentre has four associated bounday points. Eg:{P1,P2,P3,P4}is the set of boundary points around the IUAN centre (C1). A complete circle around this centre can be constructed using these 4 boundary points and corresponding distance/radius r1. Similarly, three circles can be constructed around three centres. The intersection of these three circles gives the location of sensor node. Our approach optimises the trilateration method by constructing the intelligent arcs using intelligent boundary points instead of considering the complete circles, which reduces the computation cost significantly.

Phase 3 selects the intelligent boundary points on ‘x’ axis and ‘y’ axis, which contribute to the construction of the intelligent arcs and these are referred as IXB Points, and IYB Points respectively. Among 6 boundary points {P2,P4,Q2,Q4,R2,R4} on ‘x’ axis, only 3 points contribute to the intelligent arcs. Similarly among 6 boundary points {P1,P3,Q1,Q3,R1,R3} on ‘y’ axis, only three points contribute to the intelligent arcs. The XCPoints and XBPoints are grouped (Points1) and sorted (Points 2). The intelligent points IXBPoints are selected from (Points 2), where IXBPoints lies between the range of first and last XCPoints in Points 2. This selection decision is taken based on the fact that, the boundary points lie out of this range are not contributing to the intelligent arcs. Similarly IYBPoints are selected. The Fig. 5 shows the intelligent boundary points IXBPoints and IYBPoints selected in phase 3.

Definition of an arc: An arc can be constructed with a centre point C(x,y) and radius (r). The points on the arc are defined as the set of points P(h,k) using the parametric Eqns (1) and (2), ∀⊖, ⊖1 ≤ ⊖ ≤ ⊖2 where 0 ≤ ⊖1 ≤ 2π and ⊖1 < ⊖2 < (⊖1+2π). The point P1(x1,y1) with ⊖ = ⊖1 is called the start point of the arc, and the point P2(x2,y2) with ⊖ = ⊖2 is called the end point of the arc.

$h=x+r\mathrm{cos}\left(\text{θ}\right)$ (1)

$k=y+r\mathrm{sin}\left(\text{θ}\right)$ (2)

After selecting the intelligent boundary points, phase 4 identifies the starting and ending angles of each intelligent arc. The sensor node is positioned, where the three intelligent arcs intersect. So any 2 arbitrary arcs can be constructed, as the intersection of any two intelligent arcs gives the sensor node location. Phase 5 constructs any two arbitrary intelligent arcs using the parametric Eqns (1) and (2). Phase 6 compares the points on the arbitrarily selected intelligent arcs and identifies the intersection point, which is the location of the sensor node S(LOCS.x, LOCS.y) as shown in the Figs. 6(a) and 6(b). The Algorithm 2 explains the mathematical logic behind the proposed IAS algorithm.

Algorithm 2: Intelligent Arc Selection-based Centralised Localisation Algotithm

• Input: LDM1, LDM2, LDM3, where LDM1 id= LDM2.id= LDM3.id
• Output: Sensor Node’s Location S (LOCS.x, LOCS.y)
• Begin
• (IUANCentres, IUANDistances) ←ExtractLDMessage (LDM1, LDM2, LDM3)
• (XCPoints, XBPoints, YCPoints, YBPoints) ←Bpoints
• (IUANCentres,IUANDistances)
• IXBPoints←IXBPoints (XCPoints, XBPoints)
• IYBPoints←IYBPoints (YCPoints, YBPoints)
• St_End_Angles←Start_End_ArcAngles (IXBPoints, IYBPoints)
• (A1, A2) ←Arc_Segments (XCPoints, YCPoints, St_End_Angles, IUANDistances)
• (LOCS.x, LOCS.y) ←Sensor_Location (A1, A2)
• End

Phase 1: Extracting Location Distance (LD) Messages

1. Procedure ExtractLDMessage
2. C(1).x←LDM1.x
3. C(1).y←LDM1.y
4. C(2).x←LDM2.x
5. C(2).y←LDM2.y
6. C(3).x←LDM3.x
7. C(3).y←LDM3.y
8. r1←LDM1.d
9. r2←LDM2.d
10. r3←LDM3.d
11. IUANCentres ←{C(1).x , C(1).y, C(2).x , C(2).y, C(3).x, C(3).y}
12. IUANDistances ←{r1, r2, r3}
13. return (IUANCentres, IUANDistances)
14. End

Phase 2: Computation of Boundary Points

1. Procudre BPoints(IUANCentres, IUANDistances)
2. P(1).x←C(1).x
3. P(1).y←C(1).y+r1
4. P(2).x←C(1).x-r1
5. P(2).y←C(1).y
6. P(3).x←C(1).x
7. P(3).y←C(1).y-r1
8. P(4).x←C(1).x+r1
9. P(4).y←C(1).y
10. Q(1).x←C(2).x
11. Q(1).y←C(2).y+r2
12. Q(2).x←C(2).x-r2
13. Q(2).y←C(2).y
14. Q(3).x←C(2).x
15. Q(3).y←C(2).y-r2
16. Q(4).x←C(2).x+r2
17. Q(4).y←C(2).y
18. R(1).x←C(3).x
19. R(1).y←C(3).y+r3
20. R(2).x←C(3).x-r3
21. R(2).y←C(3).y
22. R(3).x←C(3).x
23. R(3).y←C(3).y-r3
24. R(4).x←C(3).x+r3
25. R(4).y←C(3).y
26. XCPoints←{C(1).x , C(2).x , C(3).x}
27. YCPoints←{C(1).y , C(2).y , C(3).y}
28. XBPoints←{P(2).x , P(4).x , Q(2).x, Q(4).x , R(2).x, R(4).x}
29. YBPoints←{P(1).y , P(3).y , Q(1).y, Q(3).y , R(1).y, R(3).y}
30. return (XCPoints, XBPoints, YCPoints, YBPoints)
31. End

Phase 3: Selecting Intelligent Boundary Points on ‘X’ and ‘Y’ axis

1. Procedure IXBPoints (XCPoints, XBPoints)
2. Points1←{C(1).x , C(2).x , C(3).x, P(2).x , P(4).x , Q(2).x, Q(4).x , R(2).x, R(4).x}
3. Points2←Sort (Points1), where C(i).x < C(j).x < C(k).x; ∀ i,j,k = 1,2,3; i≠j≠k
4. IXBPoints ⊂ Points2, where C(i).x < {IXBPoints} < C(k).x
5. IXBPoints←{P(m).x , Q(n).x , R(o).x}, wher m,n,o are either 2 or 4
6. return (IXBPoints)
7. End
8. Procedure IYBPoints (YCPoints, YBPoints)
9. Points1←{C(1).y , C(2).y , C(3).y, P(1).y , P(3).y , Q(1).y, Q(3).y , R(1).y, R(3).y}
10. Points2←Sort (Points1), where C(i).y < C(j).y < C(k).y; ∀ i,j,k = 1,2,3; i≠j≠k
11. IYBPoints ⊂ Points2, where C(i).y < {IYBPoints} < C(k).y
12. IYBPoints←{P(m).y , Q(n).y , R(o).y}, wher m,n,o are either 1 or 3
13. return (IYBPoints)
14. End

Phase 4:

1. Procedure Start_End_ArcAngles (IXBPoints, IYBPoints)
2. if P(m).y = P(1).y then ⊖1 ←π/2
3. else ⊖1 ←3π/2
4. end if
5. if P(m).x = P(4).x then ⊖2 ←0π
6. else ⊖2 ←π
7. end if
8. if Q(m).y = Q(1).y then ⊖3 ←π/2
9. else ⊖3 ←3π/2
10. end if
11. if Q(m).x = Q(4).x then ⊖4 ←0π
12. else ⊖4 ←π
13. end if
14. return (Ɵ1, Ɵ2, Ɵ34)
15. End

Phase 5:

1. Procedure Arc_Segments (XCPoints, YCPoints, St_End_Angles, IUANDistances)
2. A1(i).x ←C(1).x+r1.cos (⊖), where ⊖1 ≤ ⊖i ≤⊖2 ∀i=1,2,…n
3. A1(i).y ←C(1).y+r1.sin (⊖), where ⊖1 ≤ ⊖i ≤⊖2 ∀i=1,2,…n
4. A2(j).x ←C(2).x+r2.cos (⊖), where ⊖3 ≤ ⊖j ≤⊖4 ∀j=1,2,…n
5. A2(j).y ←C(2).y+r2.sin (⊖), where ⊖3 ≤ ⊖j ≤⊖4 ∀j=1,2,…n
6. A1 ←{(A1(i).x, A1(i).y) ∀ i=1,2,…n }: set of points on arc A1
7. A2 ←{(A2(j).x, A2(j).y) ∀ j=1,2,…n }: set of points on arc A2
8. return (A1, A2)
9. End

Phase 6:

1. Procedure Sensor_Location (A1, A2)
2. Compare {(A1(1).x, A1(1).y), ... (A1(n).x, A1(n).y)} and {{(A2(1).x, A2(1).y), ... (A2(n).x, A2(n).y)}
3. if ((A1(i).x, A1(i).y) = (A2(j).x, A2(j).y)) then
4. LOCs.x←A1(i).x
5. LOCs.y←A1(i).y
6. end if
7. return S(LOCS.x, LOCS.y)
8. End

The central control station stores the location of sensor nodes in the sensor position database (DBSP) along with the SID. This database is used to identify the location of event as each sensor node sends the sensed information along with its identification.

The authers analysis assumes the stationary sensor nodes in two dimensions, where the latitude and longitude of the sensor nodes are considered. The power consumed by the IUAN is not taken into account for this analysis. The RIM model is assumed to withstand the radio irregularity. The performance of the proposed IUAN-assisted intelligent arc selection-based localisation algorithm is compared with the existing schemes in terms of its communication and computation cost to prove its efficiency. For numerical analysis of the communication cost, the first-order radio model explained by Heinzelman20, et al. is considered. The proposed approach calculates the sensor node position by three LD messages. The analysis assumes 60nJ energy consumption for transmission/reception of one byte of data. Each message is assumed to be of 34 byte size. From the survey, it was observed that the localisation schemes Ou7 , et al., Sheu11, et al. cause each sensor node to use 14 and 16 messages, respectively to calculate their position. Figure 7 shows the comparison of localisation-communication cost of sensor nodes.

Our approach removes the computation overhead involved in localisation at individual sensor nodes. After transmitting three SIDs, a sensor node will not bother about the localisation process as the IUAN and CCS computes the sensor node location. But existing algorithms insist each sensor node to execute heavy calculations to find their locations. This consumes huge energy from sensor node’s battery. Our intelligent arc selection approach further reduces the energy consumption and localisation time in the CCS by minimising the computation cost. Our approach executes less computations to find the location of sensor nodes than Ou7, et al. and Sheu11, et al. Figure 8 shows the localisation-computation cost at sensor nodes.

Our approach increases the localisation coverage. In existing schemes, the sensor nodes are constrained to receive the radio beacons from same flying anchor, which is not at all possible as the trajectory of the flying anchors are not very efficient. With the basic anchor-guiding mechanisms, our method provides better localisation coverage. If an IUAN is not able to receive three SIDs from a same sensor node, the next IUAN can collect the balance as the CCS aggregates the LD messages of all IUAN. This ensures the better location coverage. Figure 9 shows the comparision of the localisation coverage effieciency of IUAN approach, Ou7, et al. and Sheu11, et al.

For the state-of-the-art, a novel IUAN-based localisation approach is proposed to conserve the energy in military sensor networks. The proposed localisation approach reduces the communication overhead and removes the computation cost at each sensor node, thereby reduces the overall energy consumption. Our approach used RIM model to withstand the radio irregularity problem, thereby the location accuracy is guaranteed. The IUAN approach shifts the localisation overheads from sensor nodes to the powerful CCS, where the CCS calculates the location of sensor nodes using IAS algorithm with low computation costs. The authors approach significantly reduces overall energy consumption at each sensor node, and thereby increases the overall lifetime of military sensor networks with high localisation coverage.

1. Akyildiz, IF, Su, W, Sankarasubramaniam, Y & Cayirci, E. Wireless sensor networks: A survey. Comput. Networks, 2002, 38, 393-422. [Full text via CrossRef]

2. Yick, J, Mukherjee, B & Ghosal, D. Wireless sensor network survey. Comput. Networks, 2008, 52, 2292-2330. [Full text via CrossRef]

3. Anastasi, G, Conti, M, Francesco, MD & Passarella, A. Energy conservation in wireless sensor networks: A survey. Ad Hoc Networks, 2009, 7, 537-568. [Full text via CrossRef]

4. Aguiar, ABD, Neto, ADMS, Pinheiro, PR & Coelho, ALV. Applicability of a novel integer programming model for wireless sensor networks. Int. J. Comput. Sci. Info. Security, 2009, 3(1),1-7.

5. Han, G, Xu, H, Duong, TQ, Jiang, J & Hara, T. Localization algorithms of Wireless Sensor Networks: A survey. Telecommun. Sys., 2013, 52(4), 2419-2436. [Full text via CrossRef]

6. Pal, A. Localization Algorithms in Wireless Sensor Networks: Current Approaches and Future Challenges. J. Network Protoc. Algorithms, 2010, 2(1), 45-74.

7. Ou, CH & Ssu, KF. Sensor position determination with flying anchor in three dimensional wireless sensor networks. IEEE Trans. Mobile Comput., 2008, 7(9), 1084-1097. [Full text via CrossRef]

8. Ou, CH. A localization scheme for wireless sensor networks using mobile anchors with directional antennas. IEEE Sensors J., 2011, 11 (7), 1607-1616. [Full text via CrossRef]

9. Liao, WH, Lee, YC & Kedia, SP. Mobile anchor positioning for wireless sensor networks. IET Commun., 2011, 5(7), 914- 921. [Full text via CrossRef]

10. Kuo-Feng Ssu, Chia-Ho Ou & Hewijin Christine Jiau. Localization with mobile anchor points in wireless sensor networks. IEEE Trans. Vehicular Techno., 2005, 54(3), 1187-1197. [Full text via CrossRef]

11. Sheu, JP, Hu, WK & Lin, JC. Distributed localization scheme for mobile sensor networks. IEEE Trans. Mobile Comput., 2010, 9(4), 516-526. [Full text via CrossRef]

12. Xiao, Q.; Xiao, B.; Cao, J. & Wang, J. Multihop rangefree localization in anisotropic wireless sensor networks: A pattern-driven scheme. IEEE Trans.Mobile Comput., 2010, 9(11), 1592-1607. [Full text via CrossRef]

13. Satyamurti, S & Joshi, R. ANN assisted node localization in WSN using TDOA. Int. J. Innovative Research in Comput. Comm. Eng., 2014, 2(4), 3871-3877.

14. Pescaru, D. & Curiac, D.I. Anchor node localization for wireless sensor networks using video and compass information fusion. Sensors, 2014, 14, 4211-4224. [Full text via CrossRef]

15. Han, G.; Zhang, C.; Lloret, J.; Shu, L. & Rodrigues, J.J.P.C. A mobile anchor assisted localization algorithm based on regular hexagon in wireless sensor networks. The Sci. World J., 2014, (2014), 1-13. [Full text via CrossRef]

16. Guerrero, E.; Gao, Q. & Xiong, H.G. Employing Unmanned Aerial Vehicles for localization of sensor nodes in wireless sensor networks. J. Networking Techno., 2010, 1(1), 44-57.

17. Yadav, V.; Mishra, M.K.; Singh, A.K. & Gore, M.M. Localization Scheme for three dimensional wireless sensor networks using GPS enabled mobile sensor nodes. Int. J. Next Generation Networks, 2009, 1(1), 60-72

18. Vincent, P.; Tummala, M. & McEachen, J. A new method for distributing power usage across a sensor network. Ad Hoc Networks, 2008, 6, 1258-1280. [Full text via CrossRef]

19. Zhou, G, Tian, HE, Krishnamurthy, S & Stankovic, J.A. Models and solutions for radio irregularity in wireless sensor networks. ACM Trans. Sensor Networks, 2005, 2(2), 221–262. [Full text via CrossRef]

20. Heinzelman, W.R.; Chandrakasan, A. & Balakrishnan, H. Energy-efficient communication protocol for wireless microsensor networks. In Proceedings of the 33rd Hawaii International Conference on System Sciences, 2000. [Full text via CrossRef]

 Mr P. Shunmuga Perumal received ME in VLSI Design from Anna University, India. He is received his PhD from Anna University, Chennai, India. He is currently working as a Teaching Fellow in the Department of Information Science and Technology, College of Engineering, Anna University, India. His research interests include : Wireless sensor networks, power generation, wireless networks and location based services. Dr V. Rhymend Uthariaraj received his PhD from Anna University, Chennai, India. He is currently a Professor and Director at the Ramanujan Computing Centre, College of Engineering, Anna University, Chennai, India. His research interests include wireless sensor networks, power generation, network security, pervasive computing, distributed computing and computer algorithms. Mr V.R. Elgin Christo received BTech in Information Technology from Anna University, Chennai, India. He is pursuing his MTech in Information Technology in Anna University, Chennai, India. His area of interests include : Wireless sensor networks, embedded systems, power generation, wireless networks, Algorithm designs and location based services.


text:
# How to integrate$\int_0^1 \frac{\ln x}{x-1}dx$ without power series expansion

Discussion in 'Mathematics' started by student, Aug 2, 2020 at 2:25 AM.

1. ### studentGuest

I happen to watch the video here, which gives a solution to the definite integral below using the power series approach. Then answer is $\frac{\pi^2}{6}$, given by:

$$\int_0^1 \frac{\ln x}{x-1}dx=\int_{-1}^0 \frac{\ln(1+u)}{u}du=\sum_{n=0}^{\infty}\frac{1}{(n+1)^2}=\frac{\pi^2}{6},$$

where the power seires expansion of the function $\ln(1+u)$ is used.

I tried for some time, but could not find another approach. Does anyone know any alternative methods to evaluate above definite integral without using the infinite series expansion?

Any comments or ideas are really appreciated.


text:
### Karen Unicode Tutorials - XeLaTex

XeLaTeX is a TeX typesetting engine like Latex, except it fully supports Unicode and modern font technologies such as OpenType, Graphite and Apple Advanced Typography (AAT). It natively supports Unicode and the input file is assumed to be in UTF-8 encoding by default. XeLaTeX can use any fonts installed in the operating system without configuring TeX font metrics, and can make direct use of advanced typographic features of OpenType, AAT and Graphite technologies such as alternative glyphs and swashes, optional or historic ligatures, and variable font weights.

Here is a simple example document.

test.tex
\documentclass{article} % save as utf-8, run with xelatex
\usepackage{fontspec}
\XeTeXlinebreaklocale "my"
\XeTeXlinebreakskip = 0pt plus 0.1pt

\begin{document}
\fontspec[Script=Myanmar]{Karen Text}

လၢထံးလၢသီန့ၣ်ယွၤတ့လီၤမူခိၣ်ဒီးဟီၣ်ခိၣ်လီၤ ...

\end{document}

## Discussion

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text:
Volume 375 - 14th International Symposium on Radiative Corrections (RADCOR2019) - B Decay
Completing the four-body contributions to $\bar{B}\rightarrow X_s \gamma$ at NLO
L.T. Moos,* T. Huber
*corresponding author
Full text: pdf
Pre-published on: 2019 December 19
Published on: 2020 February 18
Abstract
We report on the status of the ongoing calculation of multiparticle contributions to the inclusive radiative $\bar{B} \rightarrow X_s \gamma$ decay at next-to leading order. This effort amounts to the evaluation of the four-particle process $b\rightarrow s \bar{q} q \gamma$ at the one-loop level, supplemented by the corresponding five-particle tree-level cuts $b\rightarrow s \bar{q} q \gamma + g$ of the gluon bremsstrahlung. Knowledge of these pieces will formally complete the $\bar{B} \rightarrow X_s \gamma$ decay at the next-to-leading order. The different steps such as the generation of the amplitude, its
renormalization, and the treatment of occuring IR-divergences are discussed. Moreover, we elaborate on the subtleties that arise when treating $\gamma_5$ in $D$ dimensions.
DOI: https://doi.org/10.22323/1.375.0031
Open Access


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## $2^{\aleph_0}$ pairwise non-isomorphic maximal-closed subgroups of Sym$(\mathbb{N})$ via the classification of the reducts of the Henson digraphs

25 Sep 2015  ·  Agarwal Lovkush, Kompatscher Michael ·

Given two structures $\mathcal{M}$ and $\mathcal{N}$ on the same domain, we say that $\mathcal{N}$ is a reduct of $\mathcal{M}$ if all $\emptyset$-definable relations of $\mathcal{N}$ are $\emptyset$-definable in $\mathcal{M}$. In this article the reducts of the Henson digraphs are classified... Henson digraphs are homogeneous countable digraphs that omit some set of finite tournaments. As the Henson digraphs are $\aleph_0$-categorical, determining their reducts is equivalent to determining all closed supergroups $G<$ Sym$(\mathbb{N})$ of their automorphism groups. A consequence of the classification is that there are $2^{\aleph_0}$ pairwise non-isomorphic Henson digraphs which have no proper non-trivial reducts. Taking their automorphisms groups gives a positive answer to a question of Macpherson that asked if there are $2^{\aleph_0}$ pairwise non-conjugate maximal-closed subgroups of Sym$(\mathbb{N})$. By the reconstruction results of Rubin, these groups are also non-isomorphic as abstract groups. read more

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MathSciNet bibliographic data MR369279 10H05 Levinson, Norman Zeros of derivative of Riemann's $\xi$$\xi$-function. Bull. Amer. Math. Soc. 80 (1974), 951–954; corrigendum, ibid. 81 (1975), 506. Article

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